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Aggregation Profiling of C9orf72 Dipeptide Repeat Proteins Transgenically Expressed in Drosophila melanogaster Using an Analytical Ultracentrifuge Equipped with Fluorescence Detection. The recent development of a fluorescence detection system for the analytical ultracentrifuge has allowed for the characterization of protein size and aggregation in complex mixtures. Protocols are described here to analyze protein aggregation seen in various human neurodegenerative diseases as they are presented in transgenic animal model systems. Proper preparation of crude extracts in appropriate sample buffers is critical for success in analyzing protein aggregation using sedimentation velocity methods. Furthermore, recent advances in sedimentation velocity analysis have led to data collection using single multispeed experiments, which may be analyzed using a wide distribution analysis approach. In this chapter, we describe the use of these new sedimentation velocity methods for faster determination of a wider range of sizes. In Chapter 7 of this book, we describe how agarose gel electrophoresis can be used to complement the analytical ultracentrifugation work, often as a prelude to careful biophysical analysis to help screen conditions in order to improve the success of sedimentation velocity experiments.

Everything Old Is New Again, and a Compiler Bug - AndreyKarpov https://randomascii.wordpress.com/2016/09/16/everything-old-is-new-again-and-a-compiler-bug/ ====== Annatar The author of the article is obviously very experienced and extremely talented. Personally, I find it a tragedy that he is wasting his time on Windows, on a platform, which in his own words, _in the crazy world of Windows there are a lot of programs that think that injecting their DLLs into all processes is a good idea. Whether malware or anti-malware or something else these injected DLLs end up causing a good portion of all of Chrome’s crashes. And in this case one of these injected DLLs decided that changing the FPU exception flags in somebody else’s process was a good idea._ _The fld instruction is part of the x87 FPU and it loads a floating-point value onto the x87’s peculiar eight-register stack, so it seems initially plausible that it could have caused a FLT_STACK check._ _Who designs a stack with just eight entries? Intel. It must have seemed like a good idea at the time._ Not to mention something those of us who grew up on Motorola MOS 6502, MC68000, SPARC, UltraSPARC and MIPS families always knew: intel might be really fast now, but under the hood, the architecture was and still is really, really shoddy. It's covered up by raw speed, but woe to one if they have to work with things "under the hood". I chuckled, half in amusement and half in grotesque disgust, when I read the bit about the stack with only eight entries, because the first thing I thought of when I read that was of UltraSPARC and register windows, effectively giving one 256 stacks by means of i0-i7 and o0-o7 registers (which in reality are part of the r0-r31 physical registers). I'm kind of comparing apples to oranges, but the difference in design approaches is striking. What a contrast! intel designers were always bad, even from the very first 4004, through 8008 to 8086. Their two shots at making things right, the i960 and Itanium RISC processors were both epic failures. They are so bad at designing _clean, elegant architectures_ , that a competitor, Advanced Micro Devices, had to implement 64-bit extensions on _their_ processors, and then intel had to license that from them. How much longer is intel going to be _the_ mainstream, I wonder? Is there any will for change of the status quo?

Q: Multiple SQL or Case statements in Scalar function I am struggling with a SQL function for a report I am writing. The function polls an audit table for the original value of a particular field (SecondarySchoolCode). If it finds a value in the audit table for the current row it should return the value, if there is no value for the current row then the original parameter I supplied to the function should be returned instead. I have tried using a Case statement but it is not returning the parameter back if there is no match in the audit table. Any suggestions on how to accomplish this? ALTER FUNCTION [dbo].[fn_AuditOriginalHSAttendingCode] ( @StudentID VARCHAR(255), @SecondarySchoolCode VARCHAR(255), @ColumnName VARCHAR(255) ) RETURNS VARCHAR(255) AS BEGIN DECLARE @Result AS VARCHAR(255); RETURN (SELECT TOP (1) CASE WHEN @ColumnName <> 'SecondarySchoolCode' THEN @SecondarySchoolCode ELSE dbo.GDSAuditDetail.ValueBeforeChange END FROM dbo.GDSAuditDetail INNER JOIN dbo.StudentSchool INNER JOIN dbo.Student ON dbo.StudentSchool.StudentId = dbo.Student.ID INNER JOIN dbo.SecondarySchool ON dbo.StudentSchool.SecondarySchoolId = dbo.SecondarySchool.ID INNER JOIN dbo.GDSAudit ON dbo.Student.ID = dbo.GDSAudit.EntityId ON dbo.GDSAuditDetail.GDSAuditId = dbo.GDSAudit.ID WHERE (dbo.Student.ID = @studentID) and dbo.GDSAuditDetail.GDSColumn='SecondarySchoolCode' ORDER BY dbo.GDSAudit.InsertedDate ASC) The call to the function looks like this: dbo.fn_AuditOriginalHSAttendingCode(dbo.Student.ID , dbo.SecondarySchool.SecondarySchoolCode , dbo.GDSAuditDetail.GDSColumn) A: I'm not sure what all of your relationships are, but based on your stated requirements and your current query, you are joining to some tables you don't need. The reason you don't get anything back when the audit doesn't exist is because there are no rows from which to select a TOP 1. This should always return at least one row for an existing Student. SELECT TOP (1) ISNULL(dbo.GDSAuditDetail.ValueBeforeChange, @SecondarySchoolCode) FROM dbo.Student LEFT JOIN dbo.GDSAudit ON dbo.Student.ID = dbo.GDSAudit.EntityId LEFT JOIN dbo.GDSAuditDetail ON dbo.GDSAuditDetail.GDSAuditId = dbo.GDSAudit.ID AND dbo.GDSAuditDetail.GDSColumn='SecondarySchoolCode' WHERE (dbo.Student.ID = @studentID) ORDER BY dbo.GDSAudit.InsertedDate ASC

Please help with verifying or updating older sections of this article. At least some were last verified for version 1.24. The religion that a nation follows and how tolerant it is of other faiths is an important aspect of gameplay in EUIV. The religion of a nation will confer specific benefits, enable different mechanics, and affect diplomatic actions as nations of mutually accepted religions have a better chance of reaching agreements with one another. Religion is also connected to unrest and provinces of non-tolerated religions are more rebellious. The player has some control over religion by having the option to change the state religion, send missionaries to convert heathen or heretic provinces to the state religion, and carry out religious decisions. Religions and denominations [ edit ] Religion by province in 1444. For more details use the navigation box (legend) above. Since EU4 first came out many of its featured religions have been further developed and fleshed out with unique mechanics. The following table details which religions are expanded by which DLC (in order of appearance). DLC Expanded mechanics Wealth of Nations Reformed Reformed Hindu Hindu Norse El Dorado Inti Inti Mayan Mayan Nahuatl Common Sense Protestant Protestant Mahayana Mahayana Theravada Theravada Vajrayana The Cossacks Tengri Rights of Man Coptic Coptic Fetishist Mandate of Heaven Confucian Confucian Shinto Third Rome Orthodox Cradle of Civilization Sunni Sunni Shia Shia Ibadi Rule Britannia Anglican Emperor Hussite Hussite Catholic Religious unity [ edit ] Religious unity is the percentage of a country's development provided by provinces that follow the state religion or a positively tolerated heretic or heathen religion, excluding any assigned to trade companies. Provinces of the state religion always contribute 100% unity regardless of tolerance. Provinces of a heretic or heathen religion contribute a percentage determined by how tolerated they are. The effects of tolerance on religious unity per province are as follows: Tolerance Contribution < 0 +0% 0 +25% 1 +50% 2 +75% 3 +100% For example, suppose a Catholic country has a 10 development Catholic province, a 4 development Protestant province, and a 16 development Sunni province. If heretic tolerance is +1 and heathen tolerance is -2, the country's religious unity will be (100% * 10 + 50% * 4 + 0% * 16) / (10 + 4 + 16) = 40% Ideas and policies which increase religious unity: Traditions Ideas Bonuses Policies +50% — Bengali idea 1: Bengali Hindu-Sufi Syncretism Gujarat Sultanate idea 1: Garba! Indian Sultanate idea 1: Tolerate the Idol Worshipers Jaunpuri idea 3: Sants and Sufis — — +33% South Indian traditions — — — +30% Sami traditions — — — +25% Bosnian traditions Granadan traditions Papal traditions Punjabi traditions Humanist idea 1: Tolerance Bahmani idea 2: Legacy of Gisu Daraz Ferraran idea 1: Papal Recognition Hessian idea 3: Welcome the Reformers Kazani idea 1: Steppe Tolerance Malvi idea 2: Malvi Art & Architecture Permian idea 6: Komi Tolerance Urbinate idea 4: A Humanist Court Zaporozhian idea 6: Steppe Tolerance — — +20% Ayutthayan traditions Bamberger idea 1: Bishop of Bamberg East Frisian idea 3: Center of Religious Thought Javan idea 1: Candi Shrines Karamanid idea 6: Home of the Whirling Dervishes Burmese idea 3: Nat Worship West African idea 4: Ancestors and Crescent — Humanist-Aristocratic: Enlightened Aristocracy Religious-Diplomatic: Policy of Calculated Delay Religious-Offensive: The Anti-Heresy Act +15% — Luccan idea 1: Mending the Papal Schisms Smolenskian idea 1: Smolenskian Resolve — — +10% — Ansbach idea 3: Franconian Reformers Bayreuther idea 4: Franconian Reformers Gond idea 2: Tribal Religion Highlander idea 4: Episcopalianism Pueblo idea 6: Clown Societies — — Religious unity directly affects the following: for each percentage point of religious unity:[1] +0.01 Monthly fervor +0.05 Maximum absolutism +5% Clergy loyalty equilibrium +5% Brahmins loyalty equilibrium for each percentage point of religious unity below 100%:[2] +1.0% Stability cost modifier +0.03 National unrest −1.0% Church power −0.01 Yearly devotion +0.001 Yearly corruption Tolerance [ edit ] Countries have three tolerance values. These tolerance values are national, but have provincial effects depending on the province's religion, relative to the state religion. Each point of positive tolerance gives:[3] −1 Local unrest Each point of negative tolerance gives:[4] +1.25 Local unrest −10% Local tax modifier −10% Local goods produced modifier Additionally, positive tolerance of heretics and heathens allows those provinces to contribute to religious unity (see above). Note that there are some national ideas which remove all penalties for having negative tolerance. Traditions Ideas Bonuses Policies yes Colonial traditions Texan traditions Vermont traditions Hungarian idea 7: Create the Estates General Kiwi idea 1: Maori Seats Piratical idea 1: Religious Apathy Rothenburg idea 1: Zarfat Registry — — Tolerance of the true faith [ edit ] This refers to the state religion. For example, if the state religion is Catholic, Catholic provinces will use this tolerance value. The base value of tolerance of the true faith is +3, and there is no maximum value. Ideas and policies that affect tolerance of the true faith: Traditions Ideas Bonuses Policies +3 Byzantine traditions — — — +2 Ladakh traditions Lan Xang traditions Laotian traditions Leonese traditions Lusatian traditions Québécois traditions Romanian traditions Sukhothai traditions Tapuian traditions Tirhuti traditions Trierian traditions Religious idea 4: Devoutness *Ainu idea 6: Yukar Al-Haasa idea 2: Lord of the Bedouin of the East Anhalt idea 3: Incorporation of the Bishopric Amago idea 6: Kizuki Antemoro idea 5: Religious Control Ardabili idea 3: Leader of all Shiites Asakura idea 6: Control of Buddhist Sects Asturian idea 2: Camino de Santiago Bamberger idea 6: Vierzehnheiligen Berg idea 7: Respecting the Autonomy of the Clergy Bharathi idea 5: Ganga Bremish idea 2: Memories of Verden Cham idea 1: Memory of the My Son Temples Chernihiv idea 6: Renovate the Transfiguration Cathedral Chosokabe idea 7: Support of the Temples Cornish idea 3: Prayer Book Traditionalism Dithmarscher idea 2: Kirchspiele Farsi idea 1: Land of the Persians French ducal idea 4: Religious Conviction Fulani Jihad idea 5: Islamic Scholarship Garhwali idea 6: Protecting the Land of the Gods Garjati idea 6: Jagannath Cult Georgian idea 3: Legacy of Saint Nino Greek idea 1: Greek Orthodox Faith Hejazi idea 1: Custodian of the Two Holy Cities Herzegovinian idea 1: Eparchy Interlacustrine idea 4: Holy Lineages Khorasani idea 6: Great Sheiks of Khorasan Kitabatake idea 2: Blessing of Amaterasu Lan Na idea 4: The White Elephant Lorraine idea 6: Trois-Évêchés Manipur idea 4: Mayek Medri Bahri idea 2: Christian Legacy Miao idea 1: Sacrificing to the Spirits Moravian idea 2: Religious Sanctuary Mossi idea 6: Honoring the Masks Münster idea 1: Great Procession Najdi idea 7: Enforce Tawhid Northumbrian idea 3: Cradle of British Christianity Offaly idea 4: The Fear of God Ogasawara idea 7: Zenko-ji Orleanaise idea 3: Faith and Devotion Papal idea 1: Ecclesiastical Primacy Pegu idea 3: Dhammazedi Perugian idea 3: Meeting of the Five Conclaves Pueblo idea 6: Clown Societies Rajputana idea 5: Protectors of the Dharma Rostov idea 3: Ecclesiastical Center Sami idea 5: Defend the Noaidi Traditions Samtskhe idea 7: A Sacred Land Songhai idea 6: Sharia Tokugawa idea 6: Toshogu Transylvanian idea 6: Unitarian Zeal Trent idea 1: Prince-Bishop Tumbuka idea 4: Office of the Mulwa Tyrconnell idea 3: Religious Patrons Ulmer idea 7: Finish the Ulm Minster Württemberger idea 5: Grosse Kirchenordnung Yarkandi idea 4: Empower the Khojas Yi idea 5: Promote the Bimoism Mushasha ambition — +1 Clanricarde traditions Thomondian traditions Croatian idea 4: Antemurale Christianitatis Dhundhari idea 3: Restore Hindu Ceremonies Genevan idea 4: Spiritual Leader of Geneva Gujarati Princedom idea 5: Protect the Dwarkadhish Temple Hatakeyama idea 3: Mount Koya Kanem Bornuan idea 4: House of Kanem Khmer idea 2: Theravada Buddhism Kievan idea 5: Center Of Orthodox Church Montenegrin idea 2: Metropolitanate of Montenegro Muscovite idea 3: Seat of Metropolitan Bishop Nepalese Princedom idea 3: Institute New Festivals Prussian idea 1: Legacy of the Teutonic Knight Ruthenian idea 7: Birth of Russian Orthodoxy Saluzzo idea 6: Chiesa San Giovanni Sardinian idea 2: Papal Restoration Sindhi idea 4: Expand the Makli Necropolis Swahili idea 3: Great Mosque of Kilwa Teutonic idea 7: One State, One Religion Theodorian idea 7: Cave Monasteries Three Leagues idea 2: The League of God's House Tunisian idea 7: Tunisian Caliphate Utrecht idea 1: Devotio Moderna Vindhyan idea 3: A Sacred Land Welsh idea 7: Welsh Church — — Additional modifiers: +0.5 for ‘Trading in’ incense for ‘Trading in’ incense –2 for ruler with ‘Sinner’ personality Tolerance of heretics [ edit ] This refers to different religions within the same religious group. For example, if the state religion is Catholic, the religion group is Christian, and provinces that are Protestant, Reformed, Coptic, Orthodox, or Anglican will use this tolerance value. The base value of tolerance of heretics is −2. The possible maximum value is +3. Ideas and policies that affect tolerance of heretics: Traditions Ideas Bonuses Policies +5 — American idea 1: Freedom of Religion — — +4 Athenian traditions Bosnian traditions Cypriot traditions Epirote traditions Naxian traditions — — — +3 Dali traditions Lithuanian traditions Ajami idea 2: In Honor of Ali Bohemian idea 1: Compacta of Prague Dutch idea 5: Embrace Humanism Lusatian idea 6: Rights for all Religions Qara Qoyunlu 3: In Honor of Ali Saxon idea 4: Wittenberg University Transylvanian idea 5: Patent of Toleration Polish ambition — +2 Al-Haasa traditions Humanist idea 3: Ecumenism Alaskan idea 5: Alaskan Religious Diversity Baden idea 4: Cuius Regio, Eius Religio Burgundian idea 6: Allow Freedom of Worship Canadian idea 5: The Quebec Act Dortmund idea 7: Reinoldikirche East Frisian idea 5: Refuge of the Mennonites French idea 7: Liberté, Égalité, Fraternité Ilkhanid idea 2: Favor Sufism Kurdish idea 2: Li Gora Gawirî Kurd Misilman e Luccan idea 1: Mending the Papal Schisms Lur idea 4: Popular Religion Pomeranian idea 4: Religious Freedom Ruthenian idea 2: Foreign Influences Swiss idea 2: Swiss Tolerance Thüringian idea 3: Protector of Reformers Utsunomiya idea 7: Mount Nikko Gelre ambition Religious-Plutocratic: The Tolerance Act +1 — Albanian idea 6: Albanian Tolerance Arawak idea 4: Tribal Tolerance Circassian idea 7: Religious Flexibility Frisian idea 6: Difference of Opinion Garhwali idea 7: Crossroads of Faith Kikuchi idea 5: Religious Coexistence Ouchi idea 6: Welcome the Westerners Prussian idea 7: Religious Toleration Sligonian idea 7: Pragmatism Over All Tibetan idea 4: The Way of Virtue Urbinate idea 4: A Humanist Court Vijayanagar idea 4: Tolerance Westphalian idea 6: Religious Toleration — — Additional modifiers: +1 for ruler with ‘Tolerant’ personality Heretic conversion events [ edit ] Tolerance of heretics of ≥ 2 will allow provinces to randomly convert to those heretic religions. The mean time to happen is 5000 months, lowered by Innovative Ideas and having a neighboring province with the new religion while increased by having the theocracy government type. Provinces with the "Religious Zeal" modifier will not receive these events at all. A province is more likely to convert via event to a particular religion if a neighboring province has that religion. Adjacency is not required for most conversions. However, the following conversions only occur if a neighboring province has the new religion: Orthodox ↔ other Christian Buddhist, Shinto → Confucian In addition, only Japanese-culture provinces can convert to Shinto as the result of an event. Tolerance of heathens [ edit ] This refers to religions of other religious groups. For example, if the state religion group is Christian, provinces that are of Muslim, Eastern, or Pagan religious groups will use this tolerance value. The base value of tolerance of heathens is −3. The possible maximum value is +3. Ideas and policies that affect Tolerance of heathens: Traditions Ideas Bonuses Policies +3 Ottoman traditions Semien traditions Andalusian idea 3: Alh Ulh Dhimma Granada idea 1: People of the Book Rûmi idea 4: Sultan of Rûm Siddi idea 1: Goma — — +2 Javan traditions Kaffan traditions Kazani traditions Malian traditions Pagarruyung traditions Permian traditions Humanist idea 7: Humanist Tolerance Arakanese idea 2: Rohingya Immigrants Carib idea 6: Religious Syncretism French idea 7: Liberté, Égalité, Fraternité Golden Horde idea 7: Religious Pragmatism Guarani idea 4: Jesuit Conversions Ito idea 6: Sympathy for New Faiths Kutai idea 2: Muslim Trading Communities Laotian idea 3: Satsana Phi Luzon idea 4: Tagalog Syncretism Malayan sultanate idea 2: Sufi Legacy Mindanao idea 1: An Islamicized Barangay Mysorean idea 3: Religious Tolerance Omani idea 3: Association With Unbelievers Sadiyan idea 2: Crossroad of Religions Tripuran idea 3: Religious Syncretism Samtskhe ambition — +1 — Albanian idea 6: Albanian Tolerance Circassian idea 7: Religious Flexibility Frisian idea 6: Difference of Opinion Garhwali idea 7: Crossroads of Faith Kikuchi idea 5: Religious Coexistence Ouchi idea 6: Welcome the Westerners Sligonian idea 7: Pragmatism Over All Tibetan idea 4: The Way of Virtue Vijayanagar idea 4: Tolerance Westphalian idea 6: Religious Toleration — — Additional modifiers: +1 for ruler with ‘Tolerant’ personality Defender of the Faith [ edit ] Each Christian or Muslim denomination can have one Defender of the Faith. It costs 500 ducats for a country to claim the title. Countries with female rulers, regencies or which are subject nations cannot claim the title. Being Defender of the Faith gives the following modifiers (without ): +1 Missionary +5% Morale of armies +5% Morale of navies −0.03 Monthly war exhaustion +1 Yearly prestige +5% Technology cost +1 Yearly papal influence +0.5 Yearly devotion Additionally, all other countries of the same religion get a +10 “Defender of Faith” relations boost with the title holder. Countries automatically call the Defender of the Faith of their religion to arms if attacked by a nation of another religion. Since patch 1.8, it seems the Defender of the Faith gets a call to arms only for countries on the same continent or sharing their border. The Defender of the Faith doesn't get a call to arms if the country attacked is a co-belligerent (e.g., if France is the Catholic Defender of the Faith and Venice (Catholic) is allied with Serbia (Orthodox), then if Ottomans (Sunni) attack Serbia and make Venice co-belligerent, France doesn't get a call to arms). Catholic countries that hold the Defender of the Faith title cannot be excommunicated by the Papacy, regardless of relations. The Defender of the Faith loses the title, but no prestige, if they refuse or lose the war. If Defender of the Faith refuses a call to war, it gets a 5-years truce with the country that was calling. Therefore, if your ally is Defender of the Faith and you have a common enemy of the "defended" religion, this ally will not be able to join you in an offensive war against this enemy, as AI wouldn't break a truce. Note: If the title holder ends any war with a result other than a white peace or victory, the title will be lost. Depending on the strength of the Faith (based on number of countries), multiple tiers of Defender of the Faith are available:[5] Amount of countries Effects – Defender of the Faith Effects – All countries with the true faith 1–5 +1 Missionary Missionary −10% Missionary maintenance cost 5–10 +1 Missionary Missionary −10% Missionary maintenance cost Missionary maintenance cost +0.5 Yearly prestige Yearly prestige −0.03 Monthly war exhaustion 10–20 +1 Missionary Missionary −20% Missionary maintenance cost Missionary maintenance cost +5% Morale of armies Morale of armies +5% Morale of navies Morale of navies +1.0 Yearly prestige 20–50 +1 Missionary Missionary −20% Missionary maintenance cost Missionary maintenance cost +5% Morale of armies Morale of armies +5% Morale of navies Morale of navies +1.0 Yearly prestige Yearly prestige −0.03 Monthly war exhaustion Monthly war exhaustion +20% Manpower in true faith provinces 50+ +1 Missionary Missionary −20% Missionary maintenance cost Missionary maintenance cost +5% Morale of armies Morale of armies +5% Morale of navies Morale of navies +1.0 Yearly prestige Yearly prestige −0.03 Monthly war exhaustion Monthly war exhaustion +20% Manpower in true faith provinces −20% Missionary maintenance cost[6] Achievements [ edit ] God Tier Become a Tier 5 Defender of the Faith as a nation that is neither Catholic nor Sunni. Conversion [ edit ] Province conversion [ edit ] The most common way to convert provinces is the use of missionaries, but there are also several other methods. If you have the Cradle of Civilization DLC , you have the ability to directly convert your subjects' provinces to your subjects' State religion.[7] Missionaries are envoys that can convert a province to a nation's official religion. Missionaries slowly convert provinces over time: each month, the effective missionary strength in that province is added as ongoing progress, and when it reaches 100% the province is converted. If strength is insufficient (less than 0%), the province will never convert (although the missionary will not lose progress). An active missionary in a province will increase the unrest there by +6%. [8] Each country has 1 missionary by default. More can be obtained through the following: Ideas and policies: Traditions Ideas Bonuses Policies +1 Asturian traditions Bamberger traditions Colognian traditions Divine traditions Sindhi traditions Religious idea 1: Missionary Schools Ajuuraan idea 3: Gareen Imams Castilian idea 2: Spanish Inquisition Circassian idea 4: Franciscan Missionaries Ethiopian idea 5: The Ark of the Covenant Fulani Jihad idea 1: Wandering Scholars Herzegovinian idea 2: Saint Sava Jerusalem idea 4: Land of the Heathen Lotharingian idea 6: Land of Bishops Münster idea 3: Founding of Monasteries Mushasha idea 2: Messianic Legacy of Muhammad bin Falah Najdi idea 2: Hanbali School Otomo idea 5: Christian Converts Perugian idea 5: Heartbeat of Christianity Teutonic idea 6: Promote Prussian Bishops Tyrconnell idea 4: St Patrick's Purgatory Utrecht idea 5: City of Churches Bremish ambition Leinster ambition Munster ambition Najdi ambition Northumbrian ambition — Decisions and events: Event modifier Trigger Duration +2 Counter-Reformation Decision: “Embrace the Counter-Reformation” until one of the four “The Counter-Reformation Ends” events. +1 Melchior Klesl Austrian event: “Melchior Klesl” Option: ‘Such devotion! We have need of this man on the privy council.’ until ruler changes. Missionary maintenance [ edit ] The player can adjust the missionary maintenance cost by a slider on the economy interface between zero and full funding. Reducing the funding reduces missionary strength linearly, up to −5% missionary strength without funding. At full funding the costs of an active missionary per month is calculated based on the development and local autonomy of the province as follows[9]: The following ideas reduce missionary maintenance cost: Traditions Ideas Bonuses Policies −50% — Religious idea 6: Inquisition — — −25% Jerusalem traditions — — — Base missionary strength is 2%. Modifiers that increase strength include: Advisors: +2% from an Inquisitor advisor from an Inquisitor advisor Stability: +0.5% for each point of positive stability for each point of positive stability Piety: Up to +3% for Muslim states that are inclined towards Mysticism Up to for Muslim states that are inclined towards Mysticism Patriarch Authority: Up to +2% for Orthodox states that have Patriarch Authority. Up to for Orthodox states that have Patriarch Authority. Coptic Blessing: +1.5% for Coptic states that have the Send Monks to Establish Monasteries blessing. ( Rights of Man only) for Coptic states that have the Send Monks to Establish Monasteries blessing. ( Rights of Man only) Building: +3% for a Cathedral for a Cathedral Decisions: A number of national decisions increase (or decrease) missionary strength. A number of national decisions increase (or decrease) missionary strength. Events: Many events give a temporary bonus (or penalty) to missionary strength. Many events give a temporary bonus (or penalty) to missionary strength. Province's current religion: +2% in pagan provinces. in pagan provinces. Holy Roman Empire: +1% for being the dominant religion in the Holy Roman Empire for being the dominant religion in the Holy Roman Empire State Edict: +1% enacting Enforce Religious Unity (provinces within the stated area) enacting Enforce Religious Unity (provinces within the stated area) Converting religions through the Religion tab gives a +10% "Religious Zeal" bonus for ten years, but only to converting heretics, not heathens. "Religious Zeal" bonus for ten years, but only to converting heretics, not heathens. Several ideas also affect missionary strength: Traditions Ideas Bonuses Policies +3.0% — Religious idea 3: Divine Supremacy Byzantine idea 7: Restore the Ecumenical Patriarch — — +2.0% Bremish traditions Jerusalem traditions Najdi traditions Armenian idea 1: Apostolic Church Austrian idea 5: Edict of Restitution Asturian idea 5: Millenarian Revival Castilian idea 2: Spanish Inquisition Divine idea 4: Let No Man Tolerate the Witch Hindustani idea 6: Patronize Sufi Missionaries Javan idea 3: Dharmasastra Kanem Bornuan idea 4: House of Kanem Moldavian idea 5: Metropolis of Moldavia Nubian idea 5: Nubian Religious Unity Nuremberger idea 5: Franconian Centre of Reformation Pagarruyung idea 1: Tantric Legacy Palatinate idea 5: Heidelberg Catechism Rigan idea 4: Denounce Witchcraft Savoyard idea 4: Crush the Vaudois Sindhi idea 2: Bab ul Islam Sumatran idea 2: Porch of Mecca Teutonic idea 4: Assume Religious Authority Trent idea 7: Trent Religious Unity Utrecht idea 5: City of Churches Tsutsui ambition — +1.0% Ajuuraan traditions Lan Xang traditions Tibetan traditions Air idea 7: Ineslemen Teachings Arabian idea 4: Spreading the Prophet's Word Athenian idea 6: Preserve Archbishop of Athens Breton idea 4: Breton Catholicism Fulani Jihad idea 3: Fulani Jihads Genevan idea 5: Calvin's Laws German idea 5: Cuius Regio, Eius Religio Hejazi idea 6: Hajj Icelandic idea 3: Christian Identity Khivan idea 4: Djuma Mosque Kievan idea 5: Center Of Orthodox Church Leinster idea 1: Legacy of Palladius Muscovite idea 3: Seat of Metropolitan Bishop Novgorod idea 2: City of Churches Québécois idea 7: Jesuit Missions Saluzzo idea 6: Chiesa San Giovanni Sukhothai idea 4: Wat Si Sawai Sami ambition Religious-Aristocratic: The Witchcraft Act Religious-Diplomatic: Policy of Calculated Delay Religious-Espionage: Enforce Religious Law Religious-Trade: Religiously Sponsored Guilds In addition, a few ideas specifically affect missionary strength when converting heretics, but have no effect when converting heathens. Traditions Ideas Bonuses Policies +3% — Bavarian idea 4: Establish the Geistlicher Rat Colognian idea 5: Pivotal Ecclesiastic Territory Rûmi idea 7: Protector of Dar al-Islam — Religious-Offensive: The Anti-Heresy Act +2% — Aachen idea 5: Expel Heretical Officials Anhalt idea 7: The Confessor Ardabili idea 4: Conversion of the Masses Bamberger idea 5: Witch Burner Bulgarian idea 2: Root Out the Heresies Flemish idea 3: Beeldenstorm Irish idea 4: Loyal Catholics Manx idea 6: Burn the Heretic Mushasha idea 7: Sufis and Shias of the Middle East Ulster idea 5: Catholic Ascendency Finnish ambition Münster ambition — +1% Kievan traditions Clevian idea 3: Avid Reformers Herzegovinian idea 2: Saint Sava Welsh idea 7: Welsh Church — — Things that decrease this speed include: Province's current religion: −2% in Coptic, Muslim and Shinto provinces. in Coptic, Muslim and Shinto provinces. Province's current religion: −1% in Orthodox and Sikh provinces. in Orthodox and Sikh provinces. Culture: −2% for non-accepted cultures. for non-accepted cultures. Territories : provinces in territories get −2% . The penalty is only removed when the province is fully cored. : provinces in territories get . The penalty is removed when the province is fully cored. Trade company provinces get −100% provinces get Provincial development: −0.1% for each point of a province development level. for each point of a province development level. Religious Centers: Rome, Mecca, the initial Sikh province and all Protestant and Reformed Centers of Reformation get −5% . Rome, Mecca, the initial Sikh province and all Protestant and Reformed Centers of Reformation get . Recently converted provinces get −100% , called Religious Zeal for 30 years. Centers of reformation [ edit ] The first three European nations to convert to Protestant, the first three to convert to Reformed, and a British nation if it takes one of the appropriate choices to convert to Anglicanism, have a random European province designated as a Center of Reformation. These centers of reformation will automatically convert nearby provinces to their religion. Provinces converted by a center of reformation get the −100% religious zeal modifier to missionary strength in that province for 30 years. Missionaries can't work in the same province that is being converted by a center of reformation. Each center of reformation can only convert one province at a time. Players will receive a notification if all provinces within the center's range have been converted to its religion. A center of reformation is destroyed if its province is converted to another religion. The primary method for a Catholic nation to slow or stop the spread of the reformation is to conquer and convert a province with a center of reformation, thereby eliminating its missionary effect on neighboring provinces. A center of reformation will cease to convert provinces after start of the Age of Absolutism. Conversion using trade policy [ edit ] Muslim nations can enable "Propagate religion" policy in trade nodes inside a trade company region, provided that they control at least 50% of trade power in this node. While this policy is active, it will work the same way as a center of reformation. National conversion [ edit ] There are several different ways a country may change religion. By direct action [ edit ] Some religions may convert among certain heresies/sects via the Religion panel, at a cost of 100 prestige. This is true for Catholic, Protestant and Reformed Christians, Hindus and Sikhs once Sikhism is unlocked, as well as all Buddhists. Conversion by this method will give a whopping 10% missionary strength against Heretics for ten years, making conversion of provinces of the old faith quite rapid, unless it is entirely blocked due to local Religious Zeal modifiers. Sikhs can also convert to Sunni or Shia Islam this way. Conversion is also possible through decisions in some cases, which causes a -4 stability hit (except for Sikh or Sunni/Shia conversion, which only reduces it by 2). With the Sword and Crescent DLC, Sunni and Shiite (but not Ibadi) Muslims may convert to the other denomination if both their capital and the majority of their province development follows the other denomination. Without Mandate of Heaven, Japanese daimyos, but not the Shogun or Japan itself, may convert to Catholicism by decision if the majority of their territories are Catholic, which can happen following certain events in the 16th century. With Mandate of Heaven, the Open outcome for the Ikko - Ikki, Neo-Confucianism, and Spread of Christianity Incidents will unlock a decision to convert to Mahayana, Confucianism, and Catholic respectively. Pagan nations that are not Tengri may convert to any non-Pagan faith if they control a province of that faith; Tengri nations are limited to Vajrayana Buddhism. Muslims owning a Sikh province may decide to convert to Sikhism - this decision probably mostly exists to allow Punjab to easily follow its historical religion. By event [ edit ] Totemist and Animist pagans get events to convert to Catholic, Protestant, or Reformed Christianity if they have neighbors of the appropriate denomination and a sufficient positive opinion with that neighbor. Tengri pagans with a dominant secondary faith may be prompted to change to it or face a -3 stability hit; they also have event chains that end in conversion to their secondary religion. Kongo and Ming have special event chains to convert to Catholicism. A nation in the British region, typically England, can get an event, based on the wives of Henry VIII, to convert to Anglicanism with the Rule Britannia DLC. Some nations, for example Sweden, have unique events enabling them to change religion. Countries that have the Indian Sultanate government by default, but are neither Muslim nor were forcefully converted to another religion, will quickly be forced to choose by event between conversion to the appropriate branch of Islam, or facing a large amount of rebels and a stability hit. This generally only is the case if they have been released as a vassal or in a peace deal, which will likely make them Hindu initially, because Indian sultanates rarely convert the local religion, and indeed have no need to due to their large bonus to heathen tolerance. AI will always choose to convert. Forced conversion by other nations [ edit ] A nation can force a heretic country to change their state religion as part of a peace deal. The revolutionary target may also do this to heathens. Without an appropriate casus belli such as "Cleansing of Heresy" or "Religious Conformance" (unique to the Holy Roman Emperor against HRE members), this will have the same war score cost as annexing the nation. When a country is converted this way, only the state religion and the capital province's religion change. Note that at 100 war score, you can make the defeated opponent force convert you this way even if he wouldn't want that as part of a peace deal. Once the religion of the Holy Roman Empire has been locked, the emperor can also request a prince to change their state religion depending on their opinion of the Emperor. Similarly to when forcing a religion of an enemy country, the prince has its capital converted while the rest of the provinces remained unaffected. With the Common Sense DLC, suzerains may force their subject nations to change religions if they follow a different faith. If heretic, this gives +50 liberty desire, and if heathen +100 liberty desire, both gradually ticking down. Forced conversion by rebels [ edit ] Nations can support religious zealots in other countries. These rebels convert a province's religion to the one they represent when occupation is achieved. Supporting religious zealots is only possible if the desired religion is present in the target nation and is the likely rebel type in a province with unrest above 0. If there are no such provinces in the target nation, one way to achieve it is to sell the target a province of the correct religion. Generally the nation will be able to overpower the rebels if left to its own devices, so it is critical to support them militarily. This can be done by declaring war against the target nation using the "Support Rebels" casus belli. A nation that is broken by religious rebels, or that accepts their demands, will convert to the rebels' religion provided that the rebels' religion is the plurality religion in terms of development. For most countries, giving in to religious rebels is the only way to change between religious groups. However, only Animist rebels, not other types, can convert a non-Pagan nation to a Pagan faith. Thus Animism must serve as a springboard to conversion to other pagan faiths. Strategy [ edit ]

IN THE SUPREME COURT OF PENNSYLVANIA EASTERN DISTRICT COMMONWEALTH OF PENNSYLVANIA, : No. 495 EAL 2018 : Respondent : : Petition for Allowance of Appeal from : the Order of the Superior Court v. : : : QUINCEY ROSSER, : : Petitioner : ORDER PER CURIAM AND NOW, this 12th day of March, 2019, the Petition for Allowance of Appeal is DENIED. 

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A local Teamsters union and two of its members sought to intervene in a class action lawsuit brought by United Parcel Service employees against the trustees of the New England Teamsters and Trucking Industry Pension Fund ("the Fund"). The district court left open the possibility of intervention at the remedial stage of the case--if one is required--but denied intervention for the liability proceedings on two grounds: appellants' motion was untimely and their interests were adequately represented by the existing parties. We find no abuse of discretion in the decision to deny intervention, and therefore affirm. I. 2 Five UPS employees filed this lawsuit in December 1986, claiming that the Fund's trustees had breached their fiduciary duty by assigning the UPS workers an unreasonably low benefit level and by prohibiting transfer of assets contributed on the workers' behalf to a separate pension plan. Plaintiffs claim entitlement to a higher benefit than other employees whose employers contribute to the Fund at the same rate as UPS because of their uniquely favorable actuarial characteristics. See Affidavit of Steven H. Klubock at p 7, Appendix at 138. Plaintiffs argue that these actuarial attributes mean that contributions made on their behalf end up heavily subsidizing the pensions of non-UPS workers; plaintiffs argue that UPS dollars instead should be used to support an increased benefit for UPS pensioners.1 3 The prospective intervenors--two non-UPS employees and the local union that represents them, Teamsters Local 122--claim entitlement to the same benefit as the UPS class members because their employer pays into the Fund at the same rate as UPS. In light of their assertedly equal standing, the intervenors contend that any resolution of the present parties' claims without their participation presents a strong possibility of unfairness to them. 4 Appellants first sought to intervene as defendants in March 1990, more than three years after the action began. Discovery had closed in mid-1989, and in October of that year the court had scheduled trial for June 25, 1990. In addition, substantial other pretrial activity had occurred. In July 1987, the district court denied the defendants' motion to dismiss. In October 1988, the district court denied cross-motions for summary judgment. On March 29, 1989, the court granted plaintiffs' motion to certify the plaintiff class. 5 The district court denied the motion to intervene on May 8, 1990, with a brief notation written at the bottom of the first page of applicants' motion. The court's ruling was as follows: 6 Motion to Intervene is denied. The Court will entertain a renewed Motion to Intervene at the remedy stage of the case, if such a stage is required. 7 The proposed intervenors then appealed to this court. After oral argument, we remanded the case because, without a statement of reasons from the district court, we were unable to perform a meaningful review of that court's action. See Fed.R.Civ.P. 24(a) and (b) (enumerating requirements for intervention). We therefore directed the court to submit an explanation "specify[ing] which intervention requirement, or combination of requirements, it found that appellants have failed to meet" and "its reasons for so finding," Order of the Court, Sept. 24, 1990. 8 The district court responded by listing two requirements. First, it held that "[a]ppellants failed to establish that their interests would not be adequately represented at the liability stage by the [D]efendants." Memorandum, Sept. 27, 1990 (emphasis in original). Second, the court held that the intervention motion was not timely filed: "To have granted said Motion at that late date would have caused a delay in the trial of a 1986 case which had been scheduled since October 6, 1989 for trial on June 25, 1990. Fed.R.Civ.P. 24(b)(2)." Id. 9 We now resume consideration of the appeal. II. 10 Appellants moved to intervene as defendants in this action either as of right under Rule 24(a) or permissively under Rule 24(b). We concentrate our discussion on Rule 24(a) because our conclusion that the court acted within its discretion in denying intervention as of right effectively disposes of the permissive intervention question as well. See International Paper Co. v. Town of Jay, 887 F.2d 338, 344 (1st Cir.1989) (A " 'district court has less discretion to limit the participation of an intervenor of right than that of a permissive intervenor.' ") (quoting Stringfellow v. Concerned Neighbors in Action, 480 U.S. 370, 382, 107 S.Ct. 1177, 1185, 94 L.Ed.2d 389 (1987) (Brennan, J., concurring)) (emphasis in International Paper). 11 Rule 24(a) provides that an applicant seeking intervention as of right must meet four requirements. First, the application must be timely. Second, the applicant must have a direct and substantial interest in the subject matter of the litigation. Third, the applicant must be so situated that the disposition of the action may as a practical matter impair or impede its ability to protect that interest. Finally, the applicant's interest must be inadequately represented by existing parties. Travelers Indemnity Co. v. Dingwell, 884 F.2d 629, 637 (1st Cir.1989); International Paper, 887 F.2d at 342. 12 An applicant's failure to meet any one of these requirements is a sufficient basis for denying intervention as of right, Travelers, 884 F.2d at 637, and our review is strictly limited to deciding whether the district court abused its discretion. International Paper, 887 F.2d at 344. In this case, although the district court gave two bases for its decision--adequacy of representation and untimeliness--we need go no further than the court's conclusion that intervention in the liability phase of the case should be denied as untimely sought. 13 The timeliness requirement "is of first importance," United Nuclear Corp. v. Cannon, 696 F.2d 141, 143 (1st Cir.1982), and the trial court's determination on that factor is entitled to substantial deference. See NAACP v. New York, 413 U.S. 345, 366, 93 S.Ct. 2591, 2603, 37 L.Ed.2d 648 (1973) (establishing abuse of discretion standard for timeliness factor); United States v. Metropolitan Dist. Comm'n, 865 F.2d 2, 5 (1st Cir.1989). Despite limited analysis by the district court, we are unable to say that its decision to reject the application as untimely fell outside the wide boundaries of its discretion. 14 In Culbreath v. Dukakis, 630 F.2d 15, 17, 20-24 (1st Cir.1980), we specified four factors to be considered in evaluating the timeliness of an intervention motion. These factors, as recently reiterated in Metropolitan Dist. Comm'n, 865 F.2d at 5, are: 15 (i) the length of time the prospective intervenors knew or reasonably should have known of their interest before they petitioned to intervene; (ii) the prejudice to existing parties due to the intervenor's failure to petition for intervention promptly; (iii) the prejudice the prospective intervenors would suffer if not allowed to intervene; and (iv) the existence of unusual circumstances militating for or against intervention. 16 We regret that the district court, in its response after remand, failed to address each of these factors. The court instead referred only to an anticipated delay in the trial if intervention were granted, a circumstance relevant to the prejudice factor. We nevertheless have chosen not to remand the case again and instead have examined whether the decision to deny intervention is supportable upon full application of the four-part Culbreath test to the facts contained in the record. See Fiandaca v. Cunningham, 827 F.2d 825, 833-35 (1st Cir.1987) (applying Culbreath test, "a step not taken by the district court," to determine whether that court could have found application to be untimely). We thus turn to the four Culbreath factors. 17 (i) The promptness of applicants' motion. The individual applicants claim not to have known anything about this case until the first week of March 1990. The union's chief executive officer, however, acknowledged in an affidavit dated March 15, 1990, that he had read about the litigation in a Boston newspaper "[s]ome time ago." The officer, John F. Murphy, recalled that the news story "indicated that several UPS employees were suing the Pension Fund to get a better pension." Murphy stated that he learned in November 1989 for the first time "that this lawsuit involved more than a few employees and could have an impact on the Union and its participants." 18 The applicants argue that their motion was prompt for purposes of the Culbreath test, despite the passage of more than three years since filing of the case, because they acted quickly after learning of the lawsuit's potential impact on themselves. At least with respect to the union, this argument is without merit. 19 Murphy admitted that he saw a newspaper report on the case long before March 1990. Even if the report Murphy saw referred only to the original five UPS plaintiffs, subsequent publicity and minimal investigation should have alerted him to the fact that this could become a substantial class action lawsuit. The plaintiffs' 1986 complaint requested class certification. Two articles in Boston newspapers in 1988 also reported the large numbers of UPS employees potentially involved. See The Boston Globe, Oct. 7, 1988, at 90 ("Teamsters pension fund attacked; Move is made to split 12,000 UPS workers from the program"); The Boston Herald, Aug. 12, 1988, at 58 ("UPS drivers consider breakaway from Teamsters"). Moreover, it seems that a lawsuit in which only a few UPS employees challenged the benefit procedure would have had the same impact on the union at the liability stage as a lawsuit involving thousands of UPS employees; in either case, the issue would be the propriety of the benefit levels set for UPS employees. 20 In addition, Murphy does not, and cannot, argue that the union's interest only recently developed because of a change in the nature of plaintiffs' claims. From the outset, the UPS employees asserted entitlement to higher pension benefits, the same claim that the applicants now say implicates their rights. Cf. Fiandaca, 827 F.2d at 834 (applicants had no inherent interest in the merits of the litigation until after defendant proposed to settle dispute by implicating plaintiffs' residence). 21 It was incumbent upon Murphy, as the union's top executive, to probe behind the headlines that he admitted seeing about this case. Cf. Culbreath, 630 F.2d at 21 ("We see no excuse for the failure of large, sophisticated labor unions to learn of a suit and reported decisions so related to the promotion prospects of their members."). See also Narragansett Indian Tribe v. Ribo, Inc., 868 F.2d 5, 7 (1st Cir.1989) ("Parties having knowledge of the pendency of litigation which may affect their interest sit idle at their peril.") (emphasis added). Local 122's delay in seeking intervention is therefore not excusable. 22 The circumstances differ somewhat with respect to the individual applicants, who did not become aware of the lawsuit at all until March 1990. They, too, however, had access to information about the litigation through the news coverage. In addition, the individuals' lack of knowledge is directly attributable to the union's failing to pursue the information it possessed. We think it is within the trial court's discretion to refuse to allow the individual applicants to evade, through personal ignorance, the repercussions of dilatory action on the part of their group representative--at least when the individuals, as in this case, had the opportunity to learn of the lawsuit through the press or other public means. 23 The district court, therefore, properly could have found that the applicants unduly delayed in filing their intervention motion. 24 (ii) Prejudice to existing parties. This factor apparently weighed heavily in the district court's mind. Avoiding such prejudice has, in fact, been "described as 'the purpose of the basic requirement that the application to intervene be timely,' " United Nuclear Corp., 696 F.2d at 143 (quoting Culbreath, 630 F.2d at 22). The court believed that allowing intervention just over three months before the scheduled trial date, and months after the close of discovery, inevitably would delay the start of the trial--unquestionably a detriment to the plaintiffs.2 Appellants sought to defuse the potency of this factor by stating in their motion that, if permitted to intervene, they would not seek to reopen discovery. The fact remains, however, that plaintiffs almost certainly would need to conduct discovery of appellants to adequately prepare for a trial that included the appellants as defendants. We previously have noted that intervention is less likely to cause prejudice when it relates to an ancillary issue than when it relates to the merits, see Public Citizen v. Liggett Group, Inc., 858 F.2d 775, 786 (1st Cir.1988). In this case, the applicants seek to oppose plaintiffs' primary argument that UPS employees are entitled to higher benefits than other employees, such as themselves. The district court evidently recognized that plaintiffs would want to understand the nature of the applicants' argument in order to meet it, and would need time to prepare. As a result, a delay in the trial reasonably could be expected. 25 Thus, the second factor supports the district court's conclusion of untimeliness. 26 (iii) Prejudice to the prospective intervenors. Appellants argue that this factor weighs in their favor because they will be required to abide by the results of a litigation that directly impacts them without having had a voice in the decision. In our view, however, the potential harm to appellants from exclusion on liability issues is minimal. Indeed, appellants' brief fails to explain how their absence from the liability phase would be likely to affect the outcome on liability, and it instead concentrates on the ways in which exclusion from the remedial phase of the case would be prejudicial. The nature of the case reveals that this was not an accidental imbalance of attention. 27 The question on liability is whether the defendant trustees breached their fiduciary duty to the UPS employees by setting pension benefits without regard to those employees' uniquely favorable actuarial characteristics. We think it unlikely that the applicants' position on this particular question would differ from that of the Fund. Both presumably would seek to show that the UPS plaintiffs are not entitled to singularly high benefits, and that the Fund properly may refuse to allow the UPS plaintiffs to set up a separate pension plan. It is not until there is a finding of liability against the trustees that the interests of the applicants would be likely to diverge markedly from that of the trustees. Once the focus turns toward developing a remedy, the trustees' responsibility would be to balance the interests of the UPS employees against the other employees served by the Fund, including the applicants. At that point, it would be important for the applicants to have a voice in the process equivalent to that of the plaintiffs.3 28 This, at least, must have been the view of the district court judge, who explicitly acknowledged that the intervention factors might play out differently when, and if, remedial issues are reached. We find no abuse of discretion in this view, and thus conclude that the third timeliness factor also supports the court's decision.4 29 (iv) Unusual circumstances. Although no special circumstance appears to militate for intervention, it is significant that the district court's decision against intervention did not deny all participation by the applicants in this litigation. The district court obviously anticipates two discrete parts of the case, and has indicated its willingness to consider intervention again if it is necessary to conduct proceedings on a remedy. We are confident that the court would give serious consideration to a renewed motion to intervene and, indeed, think it unlikely based on our review of the case that the court would deny such a motion. Thus, it appears that the applicants will have the opportunity to participate in the case at the stage they acknowledge is the most critical for them. In our view, this later opportunity to participate supports the district court's decision not to delay the start of the liability phase of the case. Any possible prejudice resulting from plaintiffs' exclusion from the first part of the case would likely be offset by their later participation. 30 In summary, then, our review of the Culbreath factors fails to turn up any indication that the district court acted outside its discretion in denying the motion to intervene at this juncture of the case. Because our task is to determine only whether the court properly balanced the timeliness factors, it is clear that in this case, where the factors uniformly support the court's decision, there was no abuse of discretion. Our scrutiny suggests that the court articulated only the delay factor because that loomed large in its mind and none of the other factors counseled in favor of intervention at the liability stage. 31 Accordingly, the judgment of the district court is affirmed. This court having issued a decision on the merits, plaintiffs' motion regarding jurisdiction is dismissed as moot. Costs to plaintiffs. This description of plaintiffs' argument is based primarily on oral argument, the affidavit of actuary Steven Klubock and the Joint Stipulation dated June 4, 1990 that was signed by counsel for both plaintiffs and defendants. Plaintiffs' argument apparently has been refined during the pendency of the litigation. In their complaint, plaintiffs seem to have raised a more general claim, that the benefit for employees whose employers historically contributed to the Fund at the maximum rate was lower relative to the contributions made on their behalf than the benefits of employees whose employers contributed to the Fund at a lower rate. See Complaint at pp 36-38. See also District Court Memorandum of Decision, July 31, 1987 (denying defendants' motion to dismiss). This more general argument would seem applicable to all employees, whether or not working for UPS, whose employers made contributions on their behalf at the maximum rate for an extended period of time. The present argument, however, distinguishes UPS employees from all other Fund participants We recognize that plaintiffs' argument originally was formulated more broadly in that it challenged generally the benefit level set for employees whose employers had contributed to the Fund at the maximum rate for a substantial period of time. See supra at note 1. Under that formulation, the applicants, who claim to fall in that category and thus be similarly situated to the plaintiffs, would have more of a direct interest in the liability issue. We question whether the prejudice from a denial of intervention would be any greater, however, even if we analyzed the issue in the context of the broader argument. It seems that the applicants' interest then would be aligned with one or the other of the parties, depending upon applicants' outlook. They could join the plaintiffs in claiming entitlement to a higher benefit for their class of employees or join the trustees in claiming that the health of the Fund requires the benefit system to continue in its present form This factor--the prejudice suffered by the prospective intervenors from a denial of intervention--sometimes turns solely on whether the applicant demonstrates inadequate representation by an existing party, which is also a general intervention requirement. See, e.g., Narragansett Indian Tribe, 868 F.2d at 8; United Nuclear Corp., 696 F.2d at 143. We do not believe, however, that a finding of no prejudice as part of the timeliness inquiry, based on adequate representation, necessarily leads to a finding of adequate representation on the general requirement, and, as earlier stated, we explicitly refrain from deciding the issue of adequate representation in this case. But it is worth noting that "the adequacy of existing representation is sometimes regarded as only a minimal barrier to intervention," Moosehead San. Dist. v. S.G. Phillips Corp., 610 F.2d 49, 54 (1st Cir.1979), and that "[i]f the applicant shows that the representation may be inadequate ..., then the court is precluded from finding that the interest is adequately represented," Flynn v. Hubbard, 782 F.2d 1084, 1090 (1st Cir.1986) (Coffin, J., concurring) (emphasis in original). See also Trbovich v. United Mine Workers, 404 U.S. 528, 538 n. 10, 92 S.Ct. 630, n. 10, 30 L.Ed.2d 686 (1972). Moreover, the burden of persuasion that representation is adequate appears to rest on the party opposing intervention. See Flynn, 782 F.2d at 1090 n. 4; C. Wright, A. Miller & M. Kane, 7C Federal Practice and Procedure Sec. 1909 at 314 (1986). Thus, it may be that the inadequate representation requirement would be met in circumstances that do not establish prejudice under the Culbreath test. We raise this point only to clarify that our opinion does not address the question of adequate representation; we express no view at this time on whether the two factors should lead to similar results

A 5-kilobase pair promoter fragment of the murine epididymal retinoic acid-binding protein gene drives the tissue-specific, cell-specific, and androgen-regulated expression of a foreign gene in the epididymis of transgenic mice. The murine epididymis synthesizes and secretes a retinoic acid-binding protein (mE-RABP) that belongs to the lipocalin superfamily. The gene encoding mE-RABP is specifically expressed in the mouse mid/distal caput epididymidis under androgen control. In transgenic mice, a 5-kilobase pair (kb) promoter fragment, but not a 0.6-kb fragment, of the mE-RABP gene driving the chloramphenicol acetyltransferase (CAT) reporter gene restricted high level of transgene expression to the caput epididymidis. No transgene expression was detected in any other male or female tissues. Immunolocalization of the CAT protein and in situ hybridization of the corresponding CAT mRNA indicated that transgene expression occurred in the principal cells of the mid/distal caput epididymidis, thereby mimicking the spatial endogenous mE-RABP gene expression. Transgene and mE-RABP gene expression was detected from 30 days and progressively increased until 60 days of age. Castration, efferent duct ligation, and hormone replacement studies demonstrated that transgene expression was specifically regulated by androgen but not by any other testicular factors. Altogether, our results demonstrate that the 5-kb promoter fragment of the mE-RABP gene contains all of the information required for the hormonal regulation and the spatial and temporal expression of the mE-RABP gene in the epididymis.

«Nous refusons la passivité face à l’abstention, au vote Front national et à la droitisation de la société. Nous refusons les renoncements face aux inégalités sociales, à la dégradation environnementale, aux discriminations et à l’affaissement démocratique. Nous refusons la paralysie de nos institutions. «Nous n’acceptons pas que la menace du FN, le risque terroriste et l’état d’urgence permanent servent de prétexte pour refuser de débattre des défis extraordinaires auxquels notre société est confrontée. Il n’y a pas de fatalité à l’impuissance politique. La France est riche de son énergie vitale et de ses talents qui aspirent à forger un avenir bienveillant. Nous voulons faire de la prochaine élection présidentielle la conclusion d’un débat approfondi qui est passionnément désiré et attendu dans le pays. «Nous voulons du contenu, des idées, des échanges exigeants. Nous appelons à une grande primaire des gauches et des écologistes. Notre primaire est la condition sine qua non pour qu’un candidat représente ces forces à l’élection présidentielle en incarnant le projet positif dont la France a besoin pour sortir de l’impasse. Elle est l’opportunité de refonder notre démocratie. En signant cet appel, je m’engage à voter lors de la primaire des gauches et des écologistes. Je participerai dans la mesure du possible aux débats qui seront organisés pour la nourrir. Signez et faites signer, pour réanimer le débat politique, pour se réapproprier l’élection présidentielle, pour choisir notre candidat-e !» Pour signer et faire signer l'appel, rendez-vous sur le site notreprimaire.fr Les premiers signataires A lire la version longue de l'appel

Red cell associated IgG in patients suffering from Plasmodium falciparum malaria. Quantitation of red cell associated IgG in 62 Gambian patients with P. falciparum malaria and 23 normal adult controls was carried out, using a purified 125I-labelled anti IgG. The number of IgG molecules per red cell was found to be between 90-897 molecules for patients with malaria and 100-233 for controls. 12 patients with malaria had raised levels of RBC associated IgG. There was no correlation between severity of anaemia and RBC associated IgG levels in patients with malaria nor was there a correlation between reticulocytosis and RBC associated IgG levels. It is concluded that although immune haemolysis may occur in some patients with malaria who have high levels of IgG or activated complement components on their red cells, other factors such as marrow suppression or ineffective erythropoiesis play an important role in the pathogenesis of the post-malaria anaemia.

1. Field of the Invention The present invention relates to the treatment of allergic or inflammatory diseases or other Syk-mediated diseases or conditions. More particularly, the present invention relates to the topical or systemic administration of certain 3,6-substituted imidazol[1,2-b]pyridazine analogs for the treatment of such diseases or conditions. 2. Description of the Related Art Syk is a tyrosine kinase that plays a critical role in mast cell degranulation, eosiniphil activation, lipid mediator synthesis and cytokine production. Accordingly, Syk kinase is implicated in various inflammatory and allergic disorders in particular asthma. It has been shown that Syk binds to the phosphorylated gamma chain of the high affinity IgE receptor (Fcε RI) signaling via N-terminal SH2 domains and is essential for downstream signaling [Taylor et al, Molecular and Cellular Biology 1995; 15:4149-4157]. Syk kinase is important in the intracellular propagation of signaling following the crosslinking of the high affinity IgG receptor (FcγRI) by IgG. Since the mediators released as the results of Fcε RI and FcγRI are responsible at least in part for adverse effects associated with allergic responses or inflammation, compounds that inhibit Syk kinase may be effective in inhibiting those adverse effects [Sirganian et. al. Molecular Immunology 2002, 38:1229-1233]. The term “Syk-mediated disease” or “Syk-mediated condition”, as used herein, means any disease or other deleterious condition in which Syk protein kinase is known to play a role. Such conditions include, without limitation, inflammation and allergic disorders, especially asthma. As taught in WO 2004/014382 (Rigel Pharmaceuticals) certain 2,4-pyridinediamine compounds have Syk kinase inhibitory activity. Lai et. al. describe a series of oxindoles having Syk kinase activity [Biorganic and Medicinal Chemistry Letters 2003, 13:3111-3114. Cywin et. al. describe the activity of a series of [1,6]naphthyridine compounds that inhibit Syk kinase [Biorganic and Medicinal Chemistry Letters 2003, 13:1415-1418]. Yamamoto et. al. describe an orally available imidazo[1,2,c]pyrimidine Syk kinase inhibitor [Journal of Pharmacology and Experimental Theapeutics 2003, 306:1174-1181]. WO2004/085409 discloses 5-substituted 2,3-diaminopyrazines.

import unittest class TestKnittingJob(unittest.TestCase): def test___init__(self): # knitting_job = KnittingJob(plugin_class, port, knitpat_file) assert True # TODO: implement your test here def test_configure_job(self): # knitting_job = KnittingJob(plugin_class, port, knitpat_file) # self.assertEqual(expected, knitting_job.configure_job()) assert True # TODO: implement your test here def test_get_plugin_name(self): # knitting_job = KnittingJob(plugin_class, port, knitpat_file) # self.assertEqual(expected, knitting_job.get_plugin_name()) assert True # TODO: implement your test here def test_knit_job(self): # knitting_job = KnittingJob(plugin_class, port, knitpat_file) # self.assertEqual(expected, knitting_job.knit_job()) assert True # TODO: implement your test here def test_start_job(self): # knitting_job = KnittingJob(plugin_class, port, knitpat_file) # self.assertEqual(expected, knitting_job.start_job()) assert True # TODO: implement your test here if __name__ == '__main__': unittest.main()

Respecification of ectoderm and altered Nodal expression in sea urchin embryos after cobalt and nickel treatment. In the sea urchin embryo, Nodal is the earliest known signal to play a role in the specification of the oral ectodermal territory. Nodal, a TGF-beta ligand, is first expressed in the presumptive oral ectoderm at approximately 7 H of development. Nodal overexpression produces a distinctive bell-shaped phenotype with expanded oral ectoderm, which resembles the oralized phenotype obtained as a result of nickel (Ni) treatment. To date, a detailed analysis of gene expression in Ni-treated embryos has not been undertaken. Because treatment with cobalt (Co) produces similar results to those seen with Ni treatment in other systems, we were interested in determining how Co influences sea urchin embryonic development. Here we report that Co also induces oralization of the ectoderm, and the effects of Ni and Co depend on functional Nodal signaling. Although both metals upregulate nodal gene expression, they do not initiate nodal transcription precociously. Analysis of the perturbation of Nodal receptor function suggests that Ni and Co contribute to nodal upregulation in the absence of nodal autoregulation, but cannot fully oralize the ectoderm in the absence of Nodal signaling.

--- abstract: 'The detection of a gravitational capture of a stellar-mass compact object by a massive black hole (MBH) will allow us to test gravity in the strong regime. The repeated, accumulated bursts of gravitational radiation from these sources can be envisaged as a geodesic mapping of space-time around the MBH. These sources form via two-body relaxation, by exchanging energy and angular momentum, and inspiral in a slow, progressive way down to the final merger. The range of frequencies is localised in the range of millihertz in the case of MBH of masses $\sim 10^6\,M_{\odot}$, i.e. that of space-borne gravitational-wave observatories such as LISA. In this article I show that, depending on their orbital parameters, intermediate-mass ratios (IMRIs) of MBH of masses between a hundred and a few thousand have frequencies that make them detectable (i) with ground-based observatories, or (ii) with both LISA and ground-based ones such as advanced LIGO/Virgo and third generation ones, with ET as an example. The binaries have a signal-to-noise ratio large enough to ensure detection. More extreme values in their orbital parameters correspond to systems detectable only with ground-based detectors and enter the LIGO/Virgo band in particular in many different harmonics for masses up to some $2000,\,M_{\odot}$. I show that environmental effects are negligible, so that the source should not have this kind of complication. The accumulated phase-shift is measurable with LISA and ET, and for some cases also with LIGO, so that it is possible to recover information about the eccentricity and formation scenario. For IMRIs with a total mass $\lessapprox 2000\,M_{\odot}$ and initial eccentricities up to $0.999$, LISA can give a warning to ground-based detectors with enough time in advance and seconds of precision. The possibility of detecting IMRIs from the ground alone or combined with space-borne observatories opens new possibilities for gravitational wave astronomy.' author: - 'Pau Amaro-Seoane' title: 'Detecting Intermediate-Mass Ratio Inspirals From The Ground And Space' --- Introduction {#sec:intro} ============ The typical size of a massive black hole (MBH), i.e. its Schwarzschild radius, is from the point of view of the host galaxy extremely tiny. For a $10^6\,M_{\odot}$ MBH, this difference spans over ten orders of magnitude. However, we have discovered a deep link between the properties of the galaxy and those of the MBH, in particular between the mass of the MBH and the velocity dispersion $\sigma$ of the spheroidal component of the galaxy [@KormendyHo2013]. Because the region of interest is difficult to resolve, the lower end of this correlation is uncertain. However, if we extend these correlations to smaller systems, globular clusters, or ultra-compact dwarf galaxies should harbour black holes with masses ranging between $10^2$ and $10^4,\,M_{\odot}$, i.e. intermediate-mass black holes, IMBHs [for a review, see the work of @Mezcua2017; @LuetzgendorfEtAl2013], although such black holes have never been robustly detected. The best way to probe the nature of the MBH is with gravitational waves, which allow us to extract information that is unavailable electromagnetically. The gravitational capture and plunge of a compact object through the event horizon is one of the main goals of the Laser Interferometer Space Antenna (LISA) mission [@Amaro-SeoaneEtAl2017]. A compact object of stellar mass, so dense that it defeats the tidal forces of the MBH, is able to approach very closely the central MBH, emitting a large amount of gravitational radiation as orbital energy is radiated away. This causes the semi-major axis to shrink. This “doomed” object spends many orbits around the MBH before it is swallowed. The radiated energy which can be thought of as a snapshot containing detailed information about the system will allow us to probe strong-field gravitational physics. Depending on the mass ratio $q$, we talk about either extreme-mass ratio inspirals, $q \gtrsim 10^4:1$ (EMRI, see [@Amaro-SeoaneLRR2012; @Amaro-SeoaneGairPoundHughesSopuerta2015]) or intermediate-mass ratio inspirals, $q \sim 10^2-10^4:1$ (IMRI, see e.g. [@Amaro-SeoaneEtAl07; @BrownEtAl2007; @RodriguezEtAl2012]). In galactic nuclei the predominant way of producing EMRIs is via two-body relaxation [@Amaro-SeoaneLRR2012]. At formation, these sources have extremely large eccentricities, particularly if the MBH is Kerr [@Amaro-SeoaneSopuertaFreitag2013], which is what we should expect from nature. However, in globular clusters, which harbour MBH in the range of IMBHs, the loss-cone theory, which is our tool to understand how EMRIs form, [see e.g. @BinneyTremaine08; @HeggieHut03; @Spitzer87] becomes very complex, mostly due to the fact that the IMBH is not fixed at the centre of the system. It becomes even more difficult when we add the emission of GWs—another layer of complication to the Newtonian problem. As of now, we must rely on computer simulations to address this problem. The joint detection of a GW source with different observatories has been already discussed in the literature but not in the mass ratio range that is addressed in this work. The series of works [@ASF06; @Amaro-SeoaneEtAl09a; @AS10a; @Amaro-SeoaneSantamaria10] investigated the formation, evolution, inspiraling and merger of IMBH binaries with a mass ratio not larger than 10 and the prospects of multiband detection with LISA and LIGO/Virgo. The work of [@KocsisLevin2012] explored a joint detection by different GW detectors in more detail than the previous references in the context of bursting sources emitted by binaries in galactic nuclei, also with a mass ratio not larger than 10. After the first detections of LIGO, the prospect for the detection of similar-mass ratio stellar-mass black holes with masses of about $30\,M_{\odot}$ with LIGO/Virgo and LISA was discussed in [@Sesana2016], and [@ChenAmaro-Seoane2017] clarified that this is only possible for eccentric binaries in that mass rage. In this paper I show that IMRIs, typically forming in globular clusters, but without excluding larger systems such as galactic nuclei and dense nuclear clusters, can be jointly detected with ground-based observatories and space-borne ones. In particular, the advanced Laser Interferometer Gravitational-Wave Observatory (LIGO) and Virgo, and the proposed third generation Einstein Telescope [@SathyaprakashEtAl2012; @HildEtAl2011], will be able to detect IMRIs from very eccentric and hard binaries, which form via two-body relaxation or the parabolic capture of a compact object and abrupt loss of energy. This idea was first presented in the work of [@QuinlanShapiro1989], while the energy and angular momentum changes in the case of a hyperbolic orbit were presented previously in [@Hansen1972], and see [@KocsisEtAl2006; @MandelEtAl2008; @OlearyEtAl09; @LeeEtAl2010; @HongLee2015] for more recent works. LISA however is deaf to these kind of sources. For milder eccentricities and semi-major axis, however, the combined detection with LISA and LIGO/Virgo or the ET of IMRIs is a real possibility. Due to the range of frequencies that these sources have, a decihertz observatory such as the DECi-hertz Interferometer Gravitational Wave Observatory [@KawamuraEtAl2011], the Superconducting Omni-directional Gravitational Radiation Observatory [SOGRO, see @PaikEtAl2016; @HarmsPaik2015] or the proposed geocentric Tian Qin [@LuoEtAl2016] would enhance the prospects of detection. For some systems, LISA can give advance warning to ground-based detectors weeks before the source appears in their bandwidth and with an accuracy of seconds (and possibly below) before the merger. Formation of Intermediate-mass ratio inspirals in globular clusters =================================================================== In this work the sources of interest are inspirals of compact objects on to an IMBH with a mass ratio of about $\sim 10^2-10^4:1$. The most accurate simulations of a globular cluster are the so-called direct-summation $N-$body algorithms. In this scheme, one directly integrates Newton’s equations of motion between all stars in a cluster at every timestep, with a regularisation algorithm for binaries, so that any phenomenon associated with gravity naturally arises [see e.g. @Aarseth99; @Aarseth03; @AarsethZare74 and the latter for the concept of regularisation]. Following the first implementation of [@KupiEtAl06], many modern direct-summation codes can mimic the effects of general relativity via a post-Newtonian expansion of the forces to be integrated [see section 9 of @Amaro-SeoaneLRR for a review of stellar-dynamical relativistic integrators]. The first dynamical simulation that presented the formation and evolution of an IMRI down to a few Schwarzschild radii from coalescence using this scheme is the work of [@KonstantinidisEtAl2013]. In one of the simulations we presented, we observed and tracked the spontaneous production of an IMRI between an IMBH of mass $M_{\rm BH}=500\,M_{\odot}$ and a stellar-mass black hole of mass $m_{\rm CO}=26\,M_{\odot}$. After a few Myrs, the IMRI merges and the IMBH receives a relativistic recoil [@CampanelliEtAl2006; @BakerEtAl2006; @GonzalezEtAl2007] and escapes the whole cluster. It must be noted that the IMBH was in a binary for almost all of the simulation time with another compact object, a stellar-mass black hole. The IMBH exchanged companions a few times and was ionised for a last time very abruptly to form the last binary. This binary started at a very small semi-major axis, of about $a \sim 10^{-5}$ pc, and a very large eccentricity, of $e=0.999$, which fits in the parabolic capture mechanism of [@QuinlanShapiro1989]. A few years later, [@LeighEtAl2014] find similar results for a close range of masses but with a different approach. The work of [@HasterEtAl2016] follows very closely the initial setup of [@KonstantinidisEtAl2013] and reproduces our results with a different integrator, which corroborates our findings. Last, the numerical experiments of [@MacLeodEtAl2016] explore IMBHs in a lighter range, of masses around $M_{\rm BH}=150\,M_{\odot}$. They however also report that the IMBH forms a binary for about 90% of the time. The probability distribution of semi-major axis peaks at about $\lesssim 10^{-5}$ pc. Light and Medium-size IMRIs {#sec.light} =========================== The characteristic amplitude and the GW harmonics in the quadrupolar radiation approximation can be calculated following the scheme of [@PM63], in which the orbital parameters change slowly due to the emission of radiation. This is emitted at every integer multiple of the orbital frequency, $\omega_n=n\,\sqrt{G\,M_{\rm BH}/a^3}$, with $a$ the semi-major axis. The strain amplitude in the n-th harmonic at a given distance $D$, normalized to the typical values of this work is $$\begin{aligned} h_n &= g(n,e) \frac{G^2\,M_{\rm BH} m_{\rm CO}}{D\,a\,c^4} \\ \nonumber &\simeq 8\times 10^{-23} g(n,e) \left(\frac{D}{500\,\mathrm{Mpc}}\right)^{-1} \left(\frac{a}{10^{-5}\,\mathrm{pc}}\right)^{-1} \nonumber \\ & \left(\frac{M_{\rm BH}}{10^3\,M_{\odot}}\right) \left(\frac{m_{\rm CO}}{10\,M_{\odot}}\right).\end{aligned}$$ In this expression $M_{\rm BH}$ is the mass of the IMBH, $m_{\rm CO}$ is the mass of the compact object (CO), and $g(n,\,e)$ is a function of the harmonic number $n$ and the eccentricity $e$ [see @PM63]. We consider the RMS amplitude averaged over the two GW polarizations and all directions. Other alternatives to this approach, such as the works of [@PPSLR01; @GlampedakisEtAl2002; @BarackCutler2004; @GG06] give a more accurate description of the very few last orbits, but remain substantially equivalent to [@PM63] at previous stages of the evolution. This approach gives a correct estimation of the frequency cutoff at the innermost stable circular orbit (ISCO) frequency and is enough for the main goal of this work [and see the work of @VeitchEtAl2015 for a discussion about the detection of binaries with mass ratios of 0.1 with advanced ground-based detectors using aligned-spin effective-one-body waveforms]. With this approximation, I show in Fig. (\[fig.100\]) $h_{\rm c}$ as function of the frequency of two different IMRIs, and a few moments in the evolution before the final merger, which happens at a time $T_{\rm mrg}$. For the kind of eccentricities that I am considering in this work, this time can be estimated following [@Peters64] for typical values as $$\begin{aligned} T_\mathrm{mrg} &\cong \frac{24\sqrt{2}}{85} \frac{(1-e_0)^{7/2} c^5} {G^3 M_\mathrm{BH}^2 m_{\rm CO}} a_0^4 \cong 6.4\times 10^{5} \mathrm{yrs} \\ & \nonumber \times \left(\frac{M_{\rm BH}}{10^3\,M_{\odot}}\right)^{2} \left(\frac{m_{\rm CO}}{10\,M_{\odot}}\right)^{-1} \left(\frac{R_\mathrm{P}^0}{200\,R_{\rm S}}\right)^{4}\nonumber \\ & \left(\frac{1-e_0}{10^{-5}}\right)^{-1/2}, \label{eq.Tmrg}\end{aligned}$$ where $R_\mathrm{P}^0$ and $e_0$ are the initial pericenter distance and eccentricity, respectively. In this Fig. (\[fig.100\]) the IMBH has a mass of $M_{\rm BH}=100\,M_{\odot}$ and the mass of the compact object (CO) is set to $10\,M_{\odot}$. I depict the LISA sensitivity curve and those of Advanced LIGO (LIGO, henceforth) and the ET in its D configuration [@HildEtAl2011], although I have shortened the characteristic amplitude to start at lower values for clarity, since none of the sources I have considered achieves higher values. For reference, I include as well the full waveform in the LIGO sensitivity curve as estimated by the IMRPhenomD approach of [@HusaEtAl2016; @KhanEtAl2016], which has been developed to study sytems with mass ratios of up to $q=18$. This curve is close to the peak of harmonics in amplitude for this specific case but in general this is not true, and depends on the specifics of the binary such as periastron argument, inclination angle, precession of the orbital plane, to mention a few. We can see that eccentricities corresponding to those that we can expect for a dynamical capture as described in the introduction produce IMRIs which are observable with LISA and both the ET and LIGO. In particular, the left panel corresponds to an IMRI which spends half a minute in LIGO. For lighter masses of the CO, this time becomes larger. For higher eccentricities, which can be achieved via two-body relaxation or in the parabolic braking scenario, at these masses the IMRIs can be seen only by ground-based detectors, with a significant amount of time and the vast majority of the harmonics in band. It is interesting to note that the ET has been estimated to be able to detect up to several hundred events per year, see [@Miller02; @GairEtAl09]. In Fig. (\[fig.300\]) I show a more massive system, with a total mass of $310\,M_{\odot}$. The source recedes in frequency due to the larger mass. For the systems considered in the upper panels, this allows IMRIs to spend more time in LISA and accumulate more SNR, with the resulting shortened time in the ground-based detectors which, however, is still significant. For the lower panels, however, LISA is again deaf to these sources. Finally, in Fig. (\[fig.500\]) I show a system similar to what is found in the numerical simulations of [@KonstantinidisEtAl2013]. The mass of the IMBH is set to $500\,M_{\odot}$ Higher frequencies lead the source to be observable by only ground-based detectors. Large-mass IMRIs ================ In Figs. (\[fig.1000\]), (\[fig.2000\]) and (\[fig.3000\]) we can see IMBHs with masses $M_{\rm BH}=1000\,M_{\odot}$, $2000\,M_{\odot}$ and $3000\,M_{\odot}$, respectively. For more moderate eccentricities, the IMRIs in the examples can be detected with LISA and the ET, but they do not enter the LIGO detection band. More extreme eccentricities lead to a large amount of harmonics entering the ET band for significant amounts of time. In the case of a $2000\,M_{\odot}$ IMBH, it can spend as much as 10 minutes in band in different harmonics. Larger masses, i.e. $3000\,M_{\odot}$ produce short-lived sources that however spend up to one minute in band of the ET. Environmental effects ===================== In the previous sections I have shown the evolution of an IMRI under the assumption that the binary is perfectly isolated from the rest of the stellar system. I.e. the binary evolves only due to the emission of GWs. The reason for this is that the problem is cleaner and easier to understand. However, the binary is located in a dense stellar system, typically a globular cluster. While the role of gas is negligible, since the gas density in these systems is very low. Hence, so as to assess whether surrounding stars could vary or modify the evolution *after* the IMRI has formed, in this section I investigate the impact of the stellar system in a semi-analytical approach. The basic idea is to split the evolution of both the semi-major axis and the eccentricity in two contributions, one driven by the dynamical interactions with stars (subscript [D]{}) and one due to emission of GWs (subscript [GW]{}), $\dot{a} = \dot{a}_{\rm GR} + \dot{a}_{\rm D}$, and $\dot{e} = \dot{e}_{\rm GR} + \dot{e}_{\rm D}$ with dots representing the time derivative. From [@Peters64], $$\begin{aligned} \dot{a}_{\rm GW} = &-\frac{64}{5}\frac{G^3{M}_{\rm BH}\,{m}_{\rm CO}({M}_{\rm BH}+{m}_{\rm CO})}{c^5a^3(1-e^2)^{7/2}} \\ \nonumber & \Big(1+\frac{73}{24}e^2+\frac{37}{96}e^4 \Big)\nonumber\\ \dot{e}_{\rm GW} = &-\frac{304}{15}\frac{G^3{M}_{\rm BH}\,{m}_{\rm CO}({M}_{\rm BH}+{m}_{\rm CO})}{c^5a^4(1-e^2)^{5/2}} \\ \nonumber & e\Big(1+\frac{121}{304}e^2\Big)\end{aligned}$$ The [GW]{} terms are as given in [@Peters64]. Using the relationships of [@Quinlan96], we have that $$\dot{a}_{\rm D}=-H\,\frac{G\rho}{\sigma}a^2.$$ Following the usual notation, $G$ is the gravitational constant, $\rho$ is the stellar density around the binary, $\sigma$ the corresponding velocity dispersion of the cluster and $H$ the so-called hardening constant, as introduced in the work of [@Quinlan96]. For the kind of binaries I am considering in this work, i.e. hard ones, we have that $\left({de}/{d\ln(1/a)}\right)_{\rm D}=K(e)$. Since the density drops significantly during the evolution, we can regard $\sigma$ as approximately constant and hence $de=K(e)\,d\ln(1/a)=-{K(e)}/{a}\,da$, so that $H\simeq 16$, as in the original work of [@Quinlan96] and see also [@SesanaEtAl04]. Therefore, $$\dot{e}_{\rm D}=\frac{H}{\sigma}\,{G\rho\,a}\,K(e),$$ with $K(e)\sim K_0\,e(1-e^2)$, as in the work of [@MM05]. As an example, in Fig. (\[fig.100-30-Vacuum-Dynamics\]) I show an IMRI formed by an IMBH of mass $M_{\rm BH}=100\,M_{\odot}$ and a CO of mass $m_{\rm CO}=30\,M_{\odot}$. The left panel corresponds to the case in vacuum, i.e. the binary evolves only due to the emission of GWs and the right panel takes into account stellar dynamics. The reason for this choice of parameters is twofold: On the one hand, the impact of stellar dynamics on a lighter IMRI is more pronounced and, on the other hand, $K_0$ has been estimated for more equal-mass binaries than the other cases. As expected, the role of stellar dynamics on to the binary at such a hardening stage is negligible, so that the previous results hold even if we do not take into account the surrounding stellar system around the IMRI from the moment of formation. The previous dynamical story is however crucial for the initial orbital parameters of the binary. Loudness of the sources {#sec.SNR} ======================= Low-eccentricity sources: LIGO {#sec.low-ecc} ------------------------------ As it progresses in the inspiral, a compact binary becomes observable and more circular. The characteristic amplitude $h_{\rm c}$ of an IMRI emitting at a given frequency $f$ is given by $$h_{\rm c} = \sqrt{(2\dot E/\dot f)}/(\pi D),$$ with $\dot E$ the power emitted, $\dot f$ the time derivative of the frequency and $D$ the distance to the source [@FinnThorne2000]. The sky and orientation-averaged SNR of a monochromatic source with the ansatz of ideal signal processing is given by the equation $$\left(\frac{S}{N}\right)^2 = \frac{4}{\pi D^2} \int \frac{\dot{E}}{\dot{f} \, S_h^{SA}(f)} \frac{{\rm d}f}{f^2}$$ as derived in [@FinnThorne2000], where $D$ is the distance to the source, $\dot{E}$ is the rate of energy lost by the source, $\dot{f}$ is the rate of change of frequency and $S_h^{SA}(f) \approx 5 S_h(f)$ is the sky and orientation average noise spectral density of the detector. For a source with multiple frequency components, the total SNR$^2$ is obtained by summing the above expression over each mode. In Fig. (\[fig.Enigma\]) I show the Fourier-transformed waveform of both panels of Fig (\[fig.100\]), as approximated by the algorithm of [@HuertaEtAl2018]. Theirs is a time-domain waveform that describes binaries of black holes evolving on mildly eccentric orbits, not exceeding $e\lesssim 0.2$. When the binaries enter the LIGO/Virgo band, even if they start with initially high eccentricities, they reach values below the threshold of the algorithm, which therefore is a good approximant to estimate the waveform and compute the SNR. For the IMRI examples given in Figs. (\[fig.100\]), assuming a distance of $D=500\,\textrm{Mpc}$, I find a SNR in the LIGO bandwidth of 42.87 and 42.55, for the left and right panels, respectively. In Figs. (\[fig.300\]), at the same distance, I find 17.12, 17.13 for the top-left, and top-right panels, respectively and 17.15, 16.40 for the lower-left and lower-right ones. High-eccentricity sources ------------------------- When moving to lower frequencies, the eccentricity exceeds by far the limit of the approximation of [@HuertaEtAl2018] that I have used to derive the SNR. To calculate it when the IMRIs sweep the LISA bandwidth, I use the expression (derived from Eq. 20 of [@PM63], Eq. 2.1 of [@FinnThorne2000] and Eq. 56 of [@BarackCutler2004]) $$\left(\frac{S}{N} \right)^2_n = \int^{f_n(\rm t_{fin})}_{f_n(\rm t_{ini})} \left(\frac{h_{\rm c,\,n}(f_n)}{h_{\rm det}(f_n)} \right)^2 \underbrace{\frac{1}{f_n}\,d\left(\ln(f_n) \right)}_{\textrm{simply}~ df_n}.$$ In this Eq. $f_n(t)$ is the (redshifted) frequency of the n harmonic at time $t$ ($f_n=n \times f_{\rm orbital}$), $h_{\rm c,\,n}(f_n)$ is the characteristic amplitude of the $n$ harmonic when the frequency associated to that component is $f_n$, and $h_{\rm det}$ is the square root of the sensitivity curve of the detectors. A few examples of the SNRs for the IMRI systems in the LISA band of the previous sections (and ET in parentheses for the same source) , assuming a distance of 500 Mpc and taking the contribution of the first 100 harmonics are: Fig. (\[fig.100\]) 15 (1036), left panel, and virtually 0, 0.01 (1087) for the right one. For Fig. (\[fig.300\]), the upper, left panel 50 (1994) and the upper, right panel 24 (1995), while the lower, left panel has 2 (1991), and the lower, right one approximately 0, 0.01 (2231). In Fig. (\[fig.500\]), the left panel yields an SNR of 36 (1449), and the right one of about zero, 0.05 (1461). In Fig. (\[fig.1000\]), the left panel has 79 (328), and the right one approximately zero, 0.4 (305). Fig. (\[fig.2000\]) has 7 (15) in the left panel and approximately 0 in the right one, 0.1 (37). Finally, Fig. (\[fig.3000\]) has 5 (1). In Figs. (\[fig.SNR\_Fig2bottomright\_and\_Fig3right\_ET\]) and (\[fig.SNR\_Fig3Left\_LISA\]) I give three examples of the accumulated SNR as calculated in this section. In the first figure I display in the left panel the SNR in ET of the system of Fig. (\[fig.300\]), bottom, right panel and, on the right panel, of Fig. (\[fig.500\]), right panel, also for ET. In the second one I show the accumulated SNR of the system depicted in Fig. (\[fig.500\]), left panel, for LISA. However, and for the case of LISA, this is the total accumulated SNR for the total time that the source spends on band. The observational time, the time during which we retrieve data from the source, is in all cases shorter and, hence, the accumulated, observed SNR is lower. As an example, for Fig. (\[fig.500\]), left panel, if we integrate all of the time the source spends on band, we obtain the aforementioned SNR of 36. However, if we integrate the last 10 yrs before merger, the SNR goes down to 23, and to 19 for the last 5 yrs. If we observed the source earlier in the evolution, say, e.g. 10 yrs before merger to 5 yrs before it, the SNR would be 14 and 100 yrs before merger to 95 yrs, 3. I show an example for the accumulated SNR for this system in Fig. (\[fig.SNR\_500\_10-5-yrs-before-plunge\]), 10 and 5 yrs before the final plunge. This only applies to LISA, because the time spent on the ground-based detector ET is much shorter. So as to assess whether this approach is robust, I give now the SNR for the systems of Sec. (\[sec.low-ecc\]) in the LIGO band, which have been calculated with the waveform model introduced in that section. In Fig. (\[fig.100\]), as estimated with this approach, the SNR is 41 and 40, for the left and right panels, respectively. In Fig. (\[fig.300\]) I find, from left to right, top to bottom, 12, 12, 11 and 14. These results are very close to those of Sec. (\[sec.low-ecc\]). The small differences arise from the fact that eccentricity tends to enhance the amount of energy emitted during the inspiral as the system radiates in band for longer. It is reasonable to take these estimates for circular orbits as a guideline for eccentric systems of similar mass to these. If the source is eccentric, since $a=R_{\rm per}/(1-e)$, $a$ is larger at the time the source reaches a frequency of 10 Hz. The inspiral time depends on the value of $a$, and is larger for larger $a$. Another way to see this is that $dE/dt$ is smaller when $e$ is larger at fixed periapsis (or frequency in our approximation). This is because at fixed periapsis, increasing the eccentricity puts more of the orbit further from the MBH and hence the energy flux is on average reduced. As $dE/dt$ is smaller, it takes longer to inspiral. This also explains why the SNR is slightly lower – $dE/dt$ is lower at fixed periapsis and thus at fixed frequency in this approximate model (physically, energy is being radiated out of band so we do not detect it all). Accumulated phase shift ======================= Understanding how IMRIs form and what are their orbital parameters can help us to reverse-engineer the environmental properties of the host cluster. Although the IMRIs considered in this work have very large initial eccentricities, when they reach the LIGO/Virgo band the eccentricity is virtually zero. It is however important to measure a non-zero eccentricity, because it can be a constraint on the formation mechanism as well as the stellar enviroment of the IMRI. If a residual eccentricity is present, it will induce a difference in the phase evolution of the signal as compared to a circular inspiral. Thanks to the derivation of [@KrolakEtAl1995] of the phase correction due to non-zero eccentricities, we can estimate the accumulated phase shift to lowest post-Newtonian order and to first order in $e^2$ with $$\begin{aligned} \Delta \Psi_{e}(f) & = \Psi_{\rm last} - \Psi_{\rm i} \cong - \Psi_{\rm i} =\nonumber \\ & \frac{7065}{187136}\,e_i^2\left(\pi\,f\,M_{\rm z} \right)^{-5/3}. \label{eq.Psi}\end{aligned}$$ In the last equation $e_i$ is the eccentricity at the frequency of the dominant harmonic at which it enters the detector bandwidth, $f$ is the frequency for the $n=2$ harmonic, and I have introduced the quantity $M_{\rm z}:= (1+z) G\left( M_{\rm BH} \times m_{\rm CO}\right)^{3/5} (M_{\rm BH}+m_{\rm CO})^{-1/5}/c^3$. Also, I make the approximation that $\Delta \Psi_{e}(f) = \Psi_{\rm last} - \Psi_{\rm i} \simeq -\Psi_{\rm i}$, with $\Psi_{\rm last}$ and $\Psi_{\rm i}$ the final and initial phase. This is so because of the pronounced fall-off of $\Psi_{e}(f)$ with increasing frequency, see discussion in section B.2 of [@CutlerHarms2006]. So as to derive the accumulated phase shift in terms of $f$ and the remaining time to merger, we now recall from [@Kepler1619] that the semi-major axis of the binary is $$a^3 = \frac{G\left(M_{\rm BH}+m_{\rm CO} \right)}{\left(\pi\,f\right)^2}. \label{eq.K}$$ The time for merger for $e \ll 1$ can be derived from [@Peters64] as follows, $$\begin{aligned} T_{\rm mrg} & \cong \frac{5}{256} \frac{c^5}{G^3M_{\rm BH} \times m_{\rm CO} \left(M_{\rm BH}+m_{\rm CO} \right)} \nonumber \\ & \left[\frac{G(M_{\rm BH}+m_{\rm CO})}{(\pi\,f)^2} \right]^{4/3}. \label{eq.TmrgLowEcc}\end{aligned}$$ Last, let us recall that $$e^2\,f^{19/9} \cong \textrm{constant}, \label{eq.efconst}$$ which can be derived from relation 5.12 of [@Peters64] with $1/(1-e^2) \simeq 1$ combined with Eq. (\[eq.K\])[^1] , i.e. $a \propto f^{-2/3}$. Therefore, if we use Eq. (\[eq.K\]) in Eq. (\[eq.TmrgLowEcc\]), we obtain $$\pi f \cong \left( \frac{5}{256} \right)^{3/8} M_{\rm z}^{-5/8} T_{\rm mrg}^{-3/8}. \label{eq.pif}$$ Hence, using Eqs. (\[eq.Psi\], \[eq.efconst\], \[eq.pif\]), we have that the accumulated phase shift in terms of $f$, $e_i(f)$, $M_{\rm z}$ and $T_{\rm mrg}$ is $$\begin{aligned} \Delta \Psi_{e}(f) & = \left(\frac{5}{256}\right)^{-17/12}\frac{7065}{187136} \nonumber \\ & \left(\pi f_i \right)^{19/9}e_i^2 M_{\rm z}^{25/36} T_{\rm mrg}^{17/12} \nonumber \\ & \cong 10 \left(\pi f_i \right)^{19/9}e_i^2 M_{\rm z}^{25/36} T_{\rm mrg}^{17/12}\end{aligned}$$ The accumulated phase shift is detectable if $\gtrsim \pi$. With this approximation, I find the following phase shifts in radians, for the IMRI systems presented in the previous sections, imposing a minimum threshold SNR of 5 (the numbers correspond to the panels of the figures from the top to the bottom, left to right): \(i) For LISA, and taking into account only the last five years before merger, Fig. (\[fig.100\]) has a negligible phase shift. Fig. (\[fig.300\]) 180, $3.4\times 10^6$, while the other two panels have a a negligible phase shift. Fig. (\[fig.500\]) $1.5\times 10^6$ and the right panel is negligible. Fig. (\[fig.1000\]) 8200 and the right panel is negligible. Fig. (\[fig.2000\]) $9.7\times 10^5$ and the right panel is negligible. Least, Fig. (\[fig.3000\]) has also a negligible phase shift. \(ii) For the ET, Fig. (\[fig.100\]) $\sim 5.1\times 10^{-3}$, 19000 for the left and right panels. Fig. (\[fig.300\]) $\sim 2.6\times 10^{-7}$, $\sim 3.4\times 10^{-3}$, 0.66 and 4600. Fig. (\[fig.500\]) $1.3\times 10^-3$ and 3900. Fig. (\[fig.1000\]) $3.5\times 10^{-6}$ and 450. Fig. (\[fig.2000\]) $1.3\times 10^{-2}$ and 2600. Fig. (\[fig.3000\]) has a negligible phase shift. \(iii) For LIGO, Fig. (\[fig.100\]) $4\times 10^{-6}$ and 1.2. Fig. (\[fig.300\]) $1.1 \times 10^{-10}$, $1.4 \times 10^{-6}$, $2.3 \times 10^{-4}$ and 10. The rest of the cases have negligible phase shifts. Conclusions =========== Intermediate-mass ratio inspirals are typically formed in dense stellar systems such as galactic nuclei and globular clusters, with typically very large eccentricities (from $e=0.999$) and small semi-major axis (below $a \sim 10^{-5}$pc), as found in a number of stellar-dynamics simulations of globular clusters [@KonstantinidisEtAl2013; @LeighEtAl2014; @HongLee2015; @MacLeodEtAl2016; @HasterEtAl2016]. Besides classical two-body relaxation, an interesting way of explaining the formation of these sources is the parabolic capture mechanism described by [@QuinlanShapiro1989; @KocsisEtAl2006]. In this work I show that IMRIs in clusters are detectable not only by space-borne observatories such as LISA. Depending on the properties of the IMRI, it can be detected in conjunction with LIGO/Virgo or the ET, so that ground-based and space-borne observatories should be envisaged as one instrument if they are simulataneously operative. I have considered IMBHs with masses ranging between $M_{\rm BH}=100\,M_{\odot}$ up to $3000\,M_{\odot}$ and COs with different masses. I have separated them in light and medium-size IMRIs, for IMBHs with masses up to $500\,M_{\odot}$ (which is a particular case based on the findings of [@KonstantinidisEtAl2013]) and large-mass IMRIs, for masses between $1000\,M_{\odot}$ and $3000\,M_{\odot}$. I find that light and medium-size IMRIs can be observed by LISA and ground-based detectors for eccentricities starting at $0.99$ and up to $0.9995$. In the range of frequencies of LIGO/Virgo they spend a maximum of about one minute on band. Higher eccentricity sources, however, can only be detected by ground-based detectors (see [@ChenAmaro-Seoane2017] for a discussion on the role of eccentricity for low mass ratio binaries). This is due to the fact that, as the eccentricity increases, the pericenter distance decreases, so that the characteristic frequency of the GWs emitted at the pericenter increases (see [@Wen2003], Eq. 37 for a derivation of the peak frequency in the same approximation used in this work). In some cases, the full cascade of harmonics falls entirely in the bandwidth of the ground-based detectors. The peak of large-mass IMRIs recedes in frequency as compared to light and medium-size ones, so that the cascade of harmonics is shifted towards the LISA domain. However, for eccentricities below $0.9995$, IMRIs with IMBHs covering the full range of masses considered in this work ($100\,M_{\odot}$ up to $3000\,M_{\odot}$) should be detectable with LISA with modest to large SNRs, from a few to tens, depending on the eccentricity and duration of the observation. For ground-based detectors, I compute the SNR for LIGO using the waveforms from a Fourier-transformation of the time domain Taylor T4 algorithm of [@HuertaEtAl2018] (limited to eccentricities $\lesssim 0.2$) and derive large enough SNRs, always of a few tens. Lower-frequency sources require larger eccentricities, and we cannot use these waveforms. For these detectors I use an approximate scheme to calculate the SNR, and I have compared it with the previous results for LIGO and I find that the approach is robust. The values for ET can reach as much as $\sim 2000$, and are of typically a few hundred and of tens for masses up to $2000\,M_{\odot}$. LISA has SNRs of a few tens to then significantly drop when the IMRI system has the peak of harmonics closer to the ground-based regime. By combining ground-based and space-borne observations we can impose better constraints on the system’s parameters. On the one hand, LISA can observe the inspiral and hence provide us with measurements of parameters such as the chirp mass. On the other hand, ground-base detectors detect the merger and ringdown, and therefore measure other parameters such as the final mass and spin. Thanks to this joint detection, one can split various degeneracies and get better measurements of the parameters, as compared to individual detections[^2]. I have estimated with a semi-analytical approach the possible influence of the environment [*after*]{} their formation and I find no impact, which will make it easier to detect and interpret these sources. By looking at the accumulated phase shift, one could investigate the origin of light IMRIs thanks to a residual eccentricity. I find that LISA binaries accumulate typically hundred of thousands and up to millions of radians, while ET binaries can accumulate up to 19000 radians, and typically of a few thousands. While IMRI binaries in LIGO live much shorter time, there is a case which does accumulate enough radians. LISA can warn ground-based detectors with at least one year in advance and seconds of precision, so that this observatory and LIGO/Virgo and the ET should be thought of as a single detector, if they are operating at the same time. Until LISA is launched, the perspective of detecting IMRIs from the ground opens new possibilities. Acknowledgments {#acknowledgments .unnumbered} =============== I acknowledge support from the Ram[ó]{}n y Cajal Programme of the Ministry of Economy, Industry and Competitiveness of Spain, as well as the COST Action GWverse CA16104. I thank Marc Freitag for his help in the implementation of the SNR equations in the plotting subroutines, and for extended discussions about the phase shift. I am indebted with Leor Barack, Chen Xian, Bernard Schutz, Thomas Dent, and Matthew Benacquista for general comments, with Frank Ohme for his help with the waveforms, and with Jon Gair for discussions about SNR. This work started during a visit to La Sapienza university in May 2018. I thank Roberto Capuzzo Dolcetta, Raffaella Schneider, Piero Rapagnani, Luigi Stella, Valeria Ferrari, Paolo Pani and Leonardo Gualtieri for their extraordinary hospitality. In particular I thank the students who took part in my course, because the many discussions and homework preparation led me to think about this problem. 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Glycogen determination using periodic acid-schiff: artifact of muscle preparation. It is common practice for the staining of muscle glycogen with periodic acid-Schiff (PAS) to thaw and dry muscle sections before staining. The goal is to investigate whether this thawing step results in a systematic error that is independent of muscle fiber type and muscle physiological state. Muscle samples from six fasted male subjects were obtained before or after 3 min of high-intensity cycling. Each sample was sectioned; some sections were assessed for muscle fiber composition, and others were either thawed for 20 min or kept frozen before being PAS-stained for glycogen. The response to a 20-min freeze-thaw cycle was also assessed using rested and exercised rats as our experimental model, and the changes in glycogen were measured enzymatically. The inclusion of a 20-min thawing step resulted in a significant reduction (P < 0.05) in the weighted average of the optical density of PAS (ODPAS) staining in both the nonexercised (15 +/- 1.4%) and exercised human muscles (15 +/- 1.3%), with the absolute extent being greater in the nonexercised muscle samples (P < 0.05). Moreover, the observed decrease in ODPAS was greatest in Type IIa fibers for both the nonexercised (P < 0.05) and exercised (P < 0.05) muscle samples. The findings in rats suggest that the muscle damage associated with freeze-thawing is responsible for this stimulation of glycogenolysis. For the quantitative histochemical measurement of glycogen content in skeletal muscle, the common practice of thawing unfixed muscle sections before PAS staining should be abandoned because this causes glycogen breakdown, the extent of which varies across muscle fiber types and prior exercise history.

Former Philadelphia Phillies closer Ryan Madson has agreed to a minor league contract with the Kansas City Royals that includes an invitation to major league spring training camp, the team announced Sunday. Madson, 34, is 47-30 with a 3.59 ERA and 52 saves in eight career seasons with Philadelphia. He hasn't pitched in the major leagues since 2011 because of elbow problems. Ryan Madson went 47-30 with a 3.59 ERA and 52 saves in eight career seasons with Philadelphia. Howard Smith/USA TODAY Sports Madson assumed the closer's job in Philadelphia from Brad Lidge in 2011 and saved 32 games, but a reported four-year, $44 million deal fell through and sparked a disagreement between Phillies general manager Ruben Amaro Jr. and Madson's former agent, Scott Boras. The Phillies quickly changed course in November 2011 and signed Jonathan Papelbon to a four-year, $50 million deal. Madson signed a one-year, $8.5 million contract with the Cincinnati Reds, but he underwent Tommy John surgery in spring training and missed the 2012 season. He made a failed comeback attempt with the Los Angeles Angels in 2013 and sat out the entire 2014 season. Madson has two connections in the Kansas City front office. Jim Fregosi Jr., now a special assistant to Royals general manager Dayton Moore, was the scout who signed Madson out of the 1998 first-year player draft with the Phillies. Mike Arbuckle, currently a senior advisor in Kansas City, was Philadelphia's scouting director in 1998 when the Phillies selected Madson in the ninth round of the draft.

Expert Commercial Roofing Solutions for Businesses in the Dallas/Fort Worth, TX, Area The harsh sun experienced during summers in the Dallas/Fort Worth area is hard on roofs. The UV rays break down the chemicals in the roofing system, causing them to deteriorate more rapidly than they would in more temperate climates. Luckily, the professionals at Beldon® are experts when it comes to commercial roofing systems that are specifically designed to withstand the Texas climate. We use high-performance materials and know how to apply them correctly so that you will have protection for your business well into the future. Beldon® is the Commercial Roofing Company to Trust for All Types of Systems The experts at Beldon® will analyze your commercial structure to determine the best type of roofing system based on local building codes, the shape of your roof, how much foot traffic and equipment your roof holds, and numerous other factors. 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[The effects of heat shock protein 90 and glucocorticoid receptor on apoptosis in T lymphocytes from asthmatic patients]. Using GA (geldanamycine), which specifically binding to HSP90, to induce the imbalance of HSP90/GR in function (low ratio) and analyzing the effect of low HSP90/GR ratio on T lymphocytes apoptosis induced by Dex from asthmatic patients. The expression of HSP90 and GR mRNA of T lymphocytes influenced by Dex and GA was also studied. Peripheral blood T lymphocytes were enriched from 10 asthmatic subjects and 7 healthy volunteers by nylon column. T lymphocytes were cultured in vitro with Dex and / or GA for 72 hours. Apoptosis of T lymphocytes were measured by propidium iodide staining and flowcytometry. With reverse transcription-polymerase chain reaction (RT-PCR), the expression of HSP90 and GR mRNA was detected. Dex could obviously induce the apoptosis of T lymphocytes from asthmatic patients (33.8% +/- 3.2% vs 23.2% +/- 1.5% , P < 0.01). GA had no effect on the apoptosis of T lymphocytes but could inhibit the effect of Dex (24.5% +/- 6.0% vs 33.8% +/- 3.2% , P < 0.01). Dex also had the effect of inducing apoptosis of T lymphocytes from health volunteers but the effect was less potent than that from asthmatic patients (25.9% +/- 3.5% vs 23.1% +/- 1.5 %, P < 0.05). Dex inhibited the expression of HSP90 and GR mRNA of T lymphocytes from asthmatic patients (1.23 +/- 0.16 vs 1.68 +/- 0.38 and 0.42 +/- 0.06 vs 0.54 +/- 0.07, respectively, P all < 0.05). GA could interrupt the inhibiting effect of Dex on the expression of HSP90 and GR mRNA but had no effect on it. The low ratio of HSP90/GR could reduce the inducing apoptosis effect of Dex. Dex could down-regulate the mRNA expression of HSP90 and GR and GA could interrupt the inhibiting effect of Dex.

Selective increases in regional brain glucocorticoid: a novel effect of chronic alcohol. The hypothalamo-pituitary-adrenal axis shows functional changes in alcoholics, with raised glucocorticoid release during alcohol intake and during the initial phase of alcohol withdrawal. Raised glucocorticoid concentrations are known to cause neuronal damage after withdrawal from chronic alcohol consumption and in other conditions. The hypothesis for these studies was that chronic alcohol treatment would have differential effects on corticosterone concentrations in plasma and in brain regions. Effects of chronic alcohol and withdrawal on regional brain corticosterone concentrations were examined using a range of standard chronic alcohol treatments in two strains of mice and in rats. Corticosterone was measured by radioimmunoassay and the identity of the corticosterone extracted from brain was verified by high performance liquid chromatography and mass spectrometry. Withdrawal from long term (3 weeks to 8 months) alcohol consumption induced prolonged increases in glucocorticoid concentrations in specific regions of rodent brain, while plasma concentrations remained unchanged. This effect was seen after alcohol administration via drinking fluid or by liquid diet, in both mice and rats and in both genders. Shorter alcohol treatments did not show the selective effect on brain glucocorticoid levels. During the alcohol consumption the regional brain corticosterone concentrations paralleled the plasma concentrations. Type II glucocorticoid receptor availability in prefrontal cortex was decreased after withdrawal from chronic alcohol consumption and nuclear localization of glucocorticoid receptors was increased, a pattern that would be predicted from enhanced glucocorticoid type II receptor activation. This novel observation of prolonged selective increases in brain glucocorticoid activity could explain important consequences of long term alcohol consumption, including memory loss, dependence and lack of hypothalamo-pituitary responsiveness. Local changes in brain glucocorticoid levels may also need to be considered in the genesis of other mental disorders and could form a potential new therapeutic target.

Sunday 30th April 1993, Edwards shot dead Mrs. Turvey as she walked along Milton Road in the Farley hill area of Luton. He then snatched their daughter Charlene, who he had been denied access to. He drove to a nearby wooded area, sat cuddled with the seven month old who would not stop crying. He lay her on the ground and shot her. Wednesday 15th December 1993, At St. Albans crown court he pleased guilty to manslaughter on the grounds of diminished responsibility. But denied murder. Thursday 16trh December 1993, Edwards changed his plea to guilty to murdering Marina Turvey having previously admitted manslaughter. His not guilty plea to murdering baby Charlene was accepted by the prosecution. He had already pleaded guilty to her manslaughter on the grounds of diminished responsibility, for which he was jailed for eight years. Friday 17th December 1993, Edwards found guilty, and sentenced to life.

Despite the warmth of the green color itself, I get a very cooling feeling from this work. It is lush, well-detailed, and interesting to look at; it is obviously deserving of the Daily Deviation. Congratulations! Is it me, or does the rock to the very left of the dark, auburn berry-bearing bush look a little like a human?

Q: Best/Fastest Way To Change/Access Elements of a Matrix I'm quite new to C# and I'm having difficult with our arrays, arrays of arrays, jagged arrays, matrixes and stuff. It's quite different from the C++ , since I can't get a reference (unless I use unsafe code) to a row of a matrix, using pointers and stuff. Anyway, here's the problem: I have a struct/class called "Image" that cointains 1024 columns and 768 lines. For each line/column theres a 'pixel' struct/class that contains 3 bytes. I'd like to get/set pixels in random places of the matrix as fast as possible. Let's pretend I have a matrix with 25 pixels. That is 5 rows and 5 columns, something like this: A B C D E F G H I J K L M N O P Q R S T U V X W Y And I need to compare M to H and R. Then M to L and N. Then I need to 'sum' G+H+I+L+M+N+Q+R+S. How can I do that? Possibilities: 1) Create something like pixel[5][5] (that's a jagged array, right?), which will be slow whenever I try to compare elements on different columns, right? 2) Create something like pixel[25] , which won't be as easy to code/ready because I'll need to do some (simple) math each and everything I want to access a element 3) Create something like pixe[5,5] (that's a multi-dimensional array, right?)... But I don't know how that will be translated to actual memory... If it's going to be a single block of memory, like the pixe[25], or what... Since I intend to do this operations ('random' sums/comparison of elements that are in different rows/columns) tens of thousands of times per image. And I have 1000+ imagens. Code optimization is a must... Sadly I'm not sure which structure / classe I should use. TL;DR: Whats the FASTEST and whats the EASIEST (coding wise) way of getting/setting elements in random positions of a (fixed size) matrix? edit: I do not want to compare C++ to C#. I'm just saying I AM NEW TO C# and I'd like to find the best way to accomplish this, using C#. Please don't tell me to go back to C++. A: I just finished testing, heres the result: SD Array Test1: 00:00:00.9388379 SD Array Test2: 00:00:00.4117926 MD Array Test1: 00:00:01.4977765 MD Array Test2: 00:00:00.8950093 Jagged Array Test1: 00:00:03.6850013 Jagged Array Test2: 00:00:00.5036041 Conclusion: Single dimensional array is the way to go... Sadly we lose in readability. And heres the code: int[] myArray = new int[10000 * 10000]; for (int i = 0; i < 10000; i++) { for (int j = 0; j < 10000; j++) { myArray[(i*10000)+j] = i+j; } } Stopwatch sw = new Stopwatch(); int sum = 0; sw.Start(); for (int i = 0; i < 10000; i++) { for (int j = 0; j < 10000; j++) { sum += myArray[(j * 10000) + i]; } } sw.Stop(); Console.WriteLine("SD Array Test1: " + sw.Elapsed.ToString()); sum=0; sw.Restart(); for (int i = 0; i < 10000; i++) { for (int j = 0; j < 10000; j++) { sum += myArray[(i * 10000) + j]; } } sw.Stop(); Console.WriteLine("SD Array Test2: " + sw.Elapsed.ToString()); myArray = null; int[,] MDA = new int[10000, 10000]; for (int i = 0; i < 10000; i++) { for (int j = 0; j < 10000; j++) { MDA[i, j] = i + j; } } sum = 0; sw.Restart(); for (int i = 0; i < 10000; i++) { for (int j = 0; j < 10000; j++) { sum += MDA[j, i]; } } sw.Stop(); Console.WriteLine("MD Array Test1: " + sw.Elapsed.ToString()); sw.Restart(); for (int i = 0; i < 10000; i++) { for (int j = 0; j < 10000; j++) { sum += MDA[i, j]; } } sw.Stop(); Console.WriteLine("MD Array Test2: " + sw.Elapsed.ToString()); MDA = null; int[][] JA = new int[10000][]; for (int i = 0; i < 10000; i++) { JA[i] = new int[10000]; } for (int i = 0; i < 10000; i++) { for (int j = 0; j < 10000; j++) { JA[i][j] = i + j; } } sum = 0; sw.Restart(); for (int i = 0; i < 10000; i++) { for (int j = 0; j < 10000; j++) { sum += JA[j][i]; } } sw.Stop(); Console.WriteLine("Jagged Array Test1: " + sw.Elapsed.ToString()); sw.Restart(); for (int i = 0; i < 10000; i++) { for (int j = 0; j < 10000; j++) { sum += JA[i][j]; } } sw.Stop(); Console.WriteLine("Jagged Array Test2: " + sw.Elapsed.ToString()); MDA = null; Console.ReadKey();

Schamberg disease Schamberg's disease, (also known as "progressive pigmentary dermatosis of Schamberg", "purpura pigmentosa progressiva" (PPP), and "Schamberg's purpura") is a chronic discoloration of the skin found in people of all ages, usually only affecting the feet, legs or thighs or a combination. It may occur as a single event or subsequent bouts may cause further spread. It is most common in males. It is named after Jay Frank Schamberg, who described it in 1901. There is no known cure for this disease but it is not a life-threatening condition and is mainly of cosmetic concern, although, because it can appear so suddenly, so extensively and because it usually leaves permanent discoloration of the skin, it can cause understandable psychological concern. The skin lesions sometimes cause itching, which can be treated by applying cortisone cream. The cortisone cream will only help with the itching and does not improve the discoloration of the skin. Schamberg's disease causes no other symptoms beside skin discoloration and itching. The condition is caused by inflammation of capillaries near the surface of skin and subsequent leaking of red blood cells into surrounding tissues. As the red blood cells break down and get mostly resorbed, some of the iron released by the red blood cells remains in the skin and causes the characteristic rust-colored appearance. The cause of the capillary inflammation is usually unknown. Symptoms The lesions are most frequent on the lower limbs, but may occur anywhere on the body, including the hands, arms, torso and even the neck. They may vary in number and erupt in mass numbers. They consist of irregular patches of orange or brown pigmentation with characteristic "cayenne pepper" spots appearing within and at the edge of old lesions. There are usually no symptoms, although there may be some slight itching, but there is no pain. The eruption may persist for many years. The pattern of the eruption changes, with slow extension and often some clearing of the original lesions. Schamberg's disease, or progressive pigmented purpuric dermatosis, is a chronic discoloration of the skin which usually affects the legs and often spreads slowly. This disease is more common in males and may occur at any age from childhood onward. This condition is observed worldwide and has nothing to do with race or ethnic background. Causes Schamberg's disease is caused by leaky blood vessels near the surface of the skin, capillaries, which allow red blood cells to slip through into the skin. The red blood cells in the skin then fall apart and release their iron, which is released from hemoglobin. The iron causes a rust color and this accounts for the orange tint of the rash. Although the underlying cause for the leaky blood vessels is almost always unknown, researchers suggest some potential triggers. These include the body's inflammatory reaction to some agent, such as a viral infection or a prescription or over the counter medication or supplement, such as thiamine and aspirin. Even though there is no correlation with genetics, there have been a few cases where few people in a family had this condition. Although a definite cause for capillary inflammation is almost always unknown, certain preventive measures can be taken. Doctors may prescribe medications that enhance the circulation of blood, which can keep blood vessels strong and healthy. Mechanism Schamberg's disease is a skin disorder that causes a discoloration of the lower extremities. It usually occurs in the lower extremities and rarely elsewhere. This condition is caused by leaky blood vessels near the surface of the skin. The cause of the leaky capillaries is usually not known. When the red blood cells escape the blood vessels, they end up close under the skin surface, where they break apart, releasing hemoglobin, which in turn breaks apart, releasing Iron. (Iron is the part of hemoglobin that enables it to transfer oxygen from the lungs to the cells and carbon dioxide from the cells to the lungs.) The iron released into the skin gets bound up into a complex called hemosiderin, which causes the discoloration of the skin. Diagnosis With a complete history, the results from visual examination, and the aid of appropriate laboratory testing, a dermatologist can usually determine whether the skin lesions are in fact due Schamberg's disease. Schamberg's disease can only be properly diagnosed by a healthcare provider. For a trained skin specialist such as a dermatologist, the condition is often readily diagnosed, because the visual appearance of the lesions on the skin itself usually suggests the possibility that the cause may be Schamberg's disease. While reviewing medical history is important to diagnose this condition, it is essential that the skin be physically examined. To ensure that the skin lesions are not caused by other skin conditions or infections, a doctor will often order a complete blood count (CBC) and other blood tests. Blood test results are usually normal. They are performed primarily to rule out other bleeding disorders that cause purpura. Since Schamberg's disease is usually asymptomatic beyond the visible lesions themselves, few other tests are usually indicated. Additional testing may aid diagnosis. A skin biopsy may be taken to determine capillaritis of dermal vessels. Capillaritis or pigmented purpura is skin condition that has brown-reddish patches on the skin, which is caused by leaky capillaries. Such skin biopsies are sent to a laboratory for a pathological examination, where each biopsy is observed under a microscope. A dermatologists may also perform a dermatoscopy. Treatment There is no cure for Schamberg's disease, however, this condition is not life-threatening or a major health concern. The most usual problems that patients will encounter is discoloration of the skin and, occasionally, itching. Itching may be improved by applying a cortisone cream. Rarely, in very severe or concerning cases, Colchicine treatment has been used to prevent recurrence. Some recommend that patients take a vitamin C supplement to promote collagen production, but this is not proven to be helpful. In cases where there is a known trigger, people should avoid re-exposure to that trigger, e.g., people suspected to be sensitive to food with artificial colors or preservatives should avoid foods containing those items. This is because some people have been observed to be sensitive to these agents, and the body initiates an inflammatory reaction if exposed to them again, which causes further capillary inflammation and red blood cell leakage. Several research studies have indicated that Schamberg's disease can be controlled and the number of lesions can be reduced with use a drug called aminaphtone. This drug helps reduce capillary fragility and red blood cell leakage. A study published in 2014 on the Journal of the German Society of Dermatology (Deutsche Dermatologische Gesellschaft) concludes that oral rutoside and ascorbic acid may be an efficient and well tolerated treatment for PPPD, with a recommendation for early treatment for best clinical outcome. Prognosis A patient with Schamberg's disease can live a normal and healthy life. Since there is no proven cure for this condition, the patient will have to endure the lesions on his or her skin. With appropriate treatments, the condition may get better. Although the skin lesions are not life-threatening, it may cause a cosmetic concern for some individuals. Skin lesions may cause psychological discomfort, where patients may require reassurance to help with stress and anxiety. There are a few rare cases of T-cell lymphoma that have developed from Schamberg's disease. This is not a cause for concern, since the risk factors associated with Schamberg's disease are relatively low. Recent research A few very small non-blinded studies of treatment with narrow-band ultraviolet light have been reported as promising. References External links Category:Disturbances of human pigmentation Category:Vascular-related cutaneous conditions

Taking a scenic stroll to the Pope’s Summer residence, viewing Rome from the Colosseum’s upper rings, visiting Vatican Museum’s many secret rooms, preparing seasonal dishes from a Roman farm house…Even in Rome, one of the world’s oldest touristic cities, there are still genuine experiences known to only a few. Many foreign tourists ask me the question, “are there any Italian living in Rome?” My answer is, “Of course there are, but unfortunately they never go to the places normal tourists go.” After giving travelers advices on where to go in Rome for a few years, I think it’s time to reveal the secrets. You probably already get the idea – Locals in Rome hide their secrets well. Rome is multi-layered, on the outside it seems unbearably touristic, yet on the inside there is still a strong culture core. If you are a culture-savvy traveler that looks beyond the mass-produced touristic things, keep reading. You’re about to uncover a Rome that is still quaint, old-fashioned, and unmistakably Italian. 1. Visit Castel Gandolfo – the Pope’s Summer residence Just 12 miles out of the Eternal City, the Pope’s country retreat recalls the grandeur of times gone by. Popes have come to this picturesque, lake-side town for generations, and so did his pilgrims. Perfectly curated gardens, ancient stoned roads, and carefully paired flower pots everywhere make Castel Gandolfo the best place for a scenic stroll. Not to mention the turquoise lake surrounded the town – a real gem to treasure in Rome’s hot summer days. 2. See the Grottos (Pope’s Tombs) under the ground Lots of Rome’s best secrets are under the ground. The Grottos, Rome’s vast underground graveyards house tombs of Popes. This underground world is extremely sophisticated, consisting of tombs, rooms, chapels, and encompassing structures that make meaningful connections in the past. You’ll want to go with an experienced guide that read Latin to help you decode the inscriptions on the tombs. It is truly a hidden Rome experience, and emotional. 3. View Rome from Colosseum’s upper level Nobody would miss Colosseum, but only a few know that the best views stay on top. Going to the Colosseum’s upper ring not only excludes you from the hectic tourist crowd, but also offers you a bird’s-eye view of the ancient Forum. You’ll admire the arch of Constantine and surrounding monuments from above and get a panoramic city view. I call this a true “Instagram-worthy” moment. 4. Private visit to Vatican and Sistine Chapel’s secret rooms Not many rooms of the Vatican museums and Sistine Chapel are open to the public, and the best rooms are always the hidden ones. I always strongly recommend travelers with higher budget to take the private tour, mainly because the private visit best keeps the sensory experience. Based on private connections, guards will open certain rooms just for private viewings, and you’ll admire Michelangelo and Raffaele in absolute silence. You’ll even smell the aromas from the ancient paints, and have the private space to meditate under Rome’s best masterpieces. It’s hard to imagine getting that sensory experience in a room packed with massive tour groups. 5. Meet an Italian tailor for your wardrobe classic Why do you need a tailor-made clothing when you can simply buy a designer dress in stores? Well, not only does a tailored clothing fits better, accentuates your figure, it also makes the occasion all the more special. What gets better than having a suit or dress artfully made for you in Rome? And I have to be honest, Italians simply dress better. The secret? They still do it the old-fashioned way – custom-made tailoring. Some of the best tailors in Rome have their own artisan workshops, and you’ll need to come over to have every details measured. In fact, simply visiting the pattern-filled studio is quite an experience in itself. It starts from getting to know you personally, the tailor then creates the patterns, selects the fabric, cuts and fits the finished piece on you. The ultimate Italian experience from the bygone era. Comments (0) Leave a Reply Your actual name, not your online persona, website name, company name or keywords, otherwise your comment won't be published Email (required) (will not be published) Website Comment (required) Please do not advertise and make sure your comment adds value, otherwise we regret that it won't be published. Links are not allowed here - if you would like to advertise, please contact us for details.

/* * Copyright 2003-2013 JetBrains s.r.o. * * Licensed under the Apache License, Version 2.0 (the "License"); * you may not use this file except in compliance with the License. * You may obtain a copy of the License at * * http://www.apache.org/licenses/LICENSE-2.0 * * Unless required by applicable law or agreed to in writing, software * distributed under the License is distributed on an "AS IS" BASIS, * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. * See the License for the specific language governing permissions and * limitations under the License. */ package jetbrains.mps.workbench.dialogs.project.newproject; import com.intellij.openapi.extensions.ExtensionPointName; import org.jetbrains.annotations.NotNull; import java.util.Collection; /** * Implementation of this interface extends list of groups in 'New project dialog' */ public interface ProjectTemplatesGroup { ExtensionPointName<ProjectTemplatesGroup> EP_NAME = ExtensionPointName.create("com.intellij.mps.projectGroupTemplateEP"); @NotNull String getName(); @NotNull Collection<MPSProjectTemplate> getTemplates(); }

Go Haim or Go Home Tee + Album Go Haim or Go Home + Album

Pump devices are commonly used to deliver one or more fluids to a targeted individual. For example, a medical infusion pump device may be used to deliver a medicine to a patient as part of a medical treatment. The medicine that is delivered by the infusion pump device can depend on the condition of the patient and the desired treatment plan. For example, infusion pump devices have been used to deliver insulin to the vasculature of diabetes patients so as to regulate blood-glucose levels. In some circumstances, the dosage of medicine delivered by the infusion pump acts within the patient's body over a long period of time. Such conditions, for example, may cause a patient to have an amount of non-activated insulin in his or her system even thought the infusion pump is programmed to deliver the next dosage in a series of insulin dosages.

Inga bijuga Inga bijuga is a species of legume in the family Fabaceae. It is found only in Venezuela. References bijuga Category:Endemic flora of Venezuela Category:Vulnerable flora of South America Category:Taxonomy articles created by Polbot

Q: Code separation in symfony 2 - Controller vs Service vs entity I am using symfony 2 and I have question about code separation. I would like to make sure that I correctly understand what elements should be in a controller, what in a service and what in a entity. Let's imagine that I have list of documents that I need to display. On each document before displaying I have to also perform some logic operation (e.g. add two variables). As in understand entity class takes care only on data retrieval and operation on single entity. I should not input there any custom code. As I understand this should be done by a service. But should I: use a service to pass to controller list of documents based on some criteria after performing the required logic, or use a controller to download list of documents, and than pass document to service to perform some logic? I would rather think that the first approach is appropriate to keep controller thin (thin controllers, big models) but is this approach right? What code should be in entity, what in controller and what in a service? In particular where should I relate to entity manager - in a controller or rather in service? Let's also pretend that in many place in my app I need to check if document is finalized before allowing user to perform any action (e.g. edit it). This definitely should be either in a service, as another service would be required to check this. Should I however load the document entity object in controller, send it to service to verify whether it may be finalized or rather load document in service and there perform a check? A: My Symfony 2 architecture is (with Doctrine ORM): Thin controllers with just the routing logic A service (a.k.a. "Manager") for each entity (all the business logic is here) Custom services for my other needs (ie, for using external tools like Amazon S3 or Mandrill mailing system) A repository for each entity (just methods to read entities from the DB) Each action inside a controller calls one or more methods from the entity's manager; I always try to avoid using directly the respository's "magic methods" in favor of custom made methods: inside the action, instead of calling $this->getDoctrine()->getRepository(<entity>)->findBy(array('parent' => null)); I create this method inside the repository: public function findParents() { return $this->findBy(array('parent' => null)); } And inside the action I use: $this->getDoctrine()->getRepository(<entity>)->findParents(); Of course this is a simple example, but it works quite well with more complex findBy or findOneBy queries. A: In Symfony2 is super easy decouple logic using repositories and services. For example: A entity repository with aditional custom finder use Doctrine\ORM\EntityRepository; class MyEntityRepository extends EntityRepository { public function findAllWithX($parameter) { // your DQL. manipule own data. filters. } } A fat service to handle the main business logic // could be a listener class MyFatService { public function __construct(MyEntityRepository $mer, AnotherRepository $aor, MisteriousService $mis) { $this->mer = $mer; $this->aor = $aor; $this->mis = $mis; } public function someBigAction($paramX, $paramY) { $foo = $this->mer->findAllWithX($paramX); $bar = $this->aor->findBy(....); // manipule data. complex operations. // call related services. // manipule data related to many repositories } } To define services: services: my_entity_repository: class: AppBundle\Repository\MyEntityRepository factory: [@doctrine, getRepository] arguments: - %entity.my_entity% my_another_repository: class: AppBundle\Repository\AnotherRepository factory: [@doctrine, getRepository] arguments: - %entity.my_another_entity% my_fat_service: class: AppBundle\MyFatService arguments: - @my_entity_repository - @my_another_repository - @misterious_service In your controller: public function blaAction($x, $y) { // leave the heavy work to services. // just handle request and send the response $data = $this->get('my_fat_service') ->someBigAction($x, $y); return $this->render('template.twig', ['data' => $data]); } ps: sorry for my english

The effect of the pressure-volume curve for positive end-expiratory pressure titration on clinical outcomes in acute respiratory distress syndrome: a systematic review. Methods to optimize positive end-expiratory pressure (PEEP) in acute respiratory distress syndrome (ARDS) remain controversial despite decades of research. The pressure-volume curve (PVC), a graphical ventilator relationship, has been proposed for prescription of PEEP in ARDS. Whether the use of PVC's improves survival remains unclear. In this systematic review, we assessed randomized controlled trials (RCTs) comparing PVC-guided treatment with conventional PEEP management on survival in ARDS based on the search of the National Library of Medicine from January 1, 1960, to January 1, 2010, and the Cochrane Central Register of Controlled Trials. Three RCTs were identified with a total of 185 patients, 97 with PVC-guided treatment and 88 with conventional PEEP management. The PVC-guided PEEP was associated with an increased probability of 28-day or hospital survival (odds ratio [OR] 2.7, 95% confidence interval [CI] 1.5, 4.9) using a random-effects model without significant heterogeneity (I (2) test: P = .75). The PVC-guided ventilator support was associated with reduced cumulative risk of mortality (-0.24 (95% CI -0.38, -0.11). The PVC-managed patients received greater PEEP (standardized mean difference [SMD] 5.7 cm H2O, 95% CI 2.4, 9.0) and lower plateau pressures (SMD -1.2 cm H2O, 95% CI -2.2, -0.2), albeit with greater hypercapnia with increased arterial pCO2 (SMD 8 mm Hg, 95% CI 2, 14). Weight-adjusted tidal volumes were significantly lower in PVC-guided than conventional ventilator management (SMD 2.6 mL/kg, 95% CI -3.3, -2.0). This analysis supports an association that ventilator management guided by the PVC for PEEP management may augment survival in ARDS. Nonetheless, only 3 randomized trials have addressed the question, and the total number of patients remains low. Further outcomes studies appear required for the validation of this methodology.

Effects of hip and head position on ankle range of motion, ankle passive torque, and passive gastrocnemius tension. Ankle joint range of motion (ROM) is notably influenced by the position of the hip joint. However, this result remains unexplained. Thus, the aim of this study was to test if the ankle passive torque and gastrocnemius muscle tension are affected by the hip and the head positions. The torque and the muscle shear elastic modulus (measured by elastography to estimate muscle tension) were collected in nine participants during passive ankle dorsiflexions performed in four conditions (by combining hip flexion at 90 or 150°, and head flexed or neutral). Ankle maximum dorsiflexion angle significantly decreased by flexing the hip from 150 to 90° (P < 0.001; mean difference 17.7 ± 2.5°), but no effect of the head position was observed (P > 0.05). Maximal passive torque and shear elastic modulus were higher with the hip flexed at 90° (P < 0.001). During submaximal ROM, no effects of the head and hip positioning (P > 0.05) were found for both torque and shear elastic modulus at a given common ankle angle among conditions. Shifts in maximal ankle angle due to hip angle manipulation are not related neither to changes in passive torque nor tension of the gastrocnemius. Further studies should be addressed to better understand the functional role of peripheral nerves and fasciae in the ankle ROM limits.

UNITED STATES of America, Plaintiff-Appellee, v. Angelo Eugene WILLIAMS, Defendant-Appellant. No. 98-8986. United States Court of Appeals, Eleventh Circuit. Dec. 8, 1999. Appeal from the United States District Court for the Southern District of Georgia.(No. CR498-43), B. Avant Edenfield, Judge. Before EDMONDSON and BIRCH, Circuit Judges, and OWENS*, Senior District Judge. EDMONDSON, Circuit Judge: Defendant Angelo Eugene Williams, under 18 U.S.C. § 2244(a)(1), was convicted of abusive sexual contact in the territorial jurisdiction of the United States. We vacate the conviction and sentence and remand. BACKGROUND This case arises from an incident at the Hunter Army Airfield Youth Center ("Youth Center") in October 1997. At that time, Defendant was employed as a computer specialist at the Youth Center, a recreational facility for children living on the base. Defendant's duties included maintaining the Youth Center computer room and supervising children's use of the computers. According to the Government's evidence at trial, Defendant engaged in abusive sexual contact with K.T., a ten year-old female, in the Youth Center computer room on October 14, 1997. The Government's evidence established that K.T. arrived at the Youth Center and that she went to the computer room. In the computer room, K.T., with Defendant's permission, seated herself at Defendant's computer terminal. K.T. testified that, while sitting at Defendant's terminal, Defendant touched her leg and chest and asked her for a kiss. An Army investigator testified that K.T. told him that Defendant touched her chest, * Honorable Wilbur D. Owens, Jr., Senior U.S. District Judge for the Middle District of Georgia, sitting by designation. buttocks, and vaginal area. The Government also introduced a statement in which Defendant admitted that he rubbed the inside of K.T.'s leg, that he hugged her, that he touched her chest and buttocks, and that he asked her to kiss him. At trial, Defendant testified that K.T. had indeed come to the computer room and that he had permitted her to use his computer. He testified, however, that after K.T. had used his computer for some time, he asked her to get up because he needed to use the computer. He stated that, as he instructed K.T. to leave his terminal, he rolled toward her in a roll-away chair, hitting her leg with his hand. K.T., according to Defendant, then moved away from the terminal, but later returned and attempted to use Defendant's computer again. Defendant said that he, at that point, grabbed K.T.'s shoulder and instructed her to leave his computer alone. Defendant testified that K.T. used another computer for some time and then left the computer room. Defendant admitted giving an incriminating statement to investigators, but he denied the statement was true, explaining that he caved in to the investigator's promise that he could "put this thing behind [him]" if he made a statement. Defendant requested at trial that the district court give a lesser included offense jury instruction on simple assault (18 U.S.C. § 113(a)(5)). The court refused to give the instruction, explaining that "[t]he evidence does not fit." Defendant was then convicted of violating § 2244. DISCUSSION Defendant asserts five grounds for his appeal.1 We find it necessary to address two of Defendant's contentions here. First, we address Defendant's claim that the Speedy Trial Act was violated in his case and, concluding that this claim has merit, vacate the conviction. Second, because the Government may seek to 1 Defendant claims that the district court erred by refusing to: (1) dismiss the indictment under the Speedy Trial Act; (2) charge the jury on assault as a lesser included offense; (3) appoint an expert to testify on whether Defendant fit the profile of a child molester; (4) admit favorable evidence of a Georgia Department of Family and Children's Services (DFACS) report regarding Defendant; and (5) allow Defendant to ask K.T.'s sister whether she would believe K.T. under oath with regard to the crime charged. 2 retry Defendant for this offense, we also address Defendant's claim that the district court erred in refusing to give an instruction on assault as a lesser included offense of abusive sexual contact. 1. THE SPEEDY TRIAL ACT Defendant contends that the district court erred by denying his motion to dismiss the indictment under the Speedy Trial Act, 18 U.S.C. § 3161 et seq.2 In particular, Defendant argues that the district court, in finding that the seventy-day limitation had not been violated in Defendant's case, improperly excluded from its Speedy Trial Act calculation twenty days allowed for the filing of pretrial motions. We agree that these days were improperly excluded.3 The Speedy Trial Act provides that a defendant must be brought to trial within seventy days of the filing of his indictment, or his first appearance before a judicial officer, whichever is later. United States v. Davenport, 935 F.2d 1223, 1227 (11th Cir.1991). Certain periods, however, are excluded from the seventy-day limit. United States v. Schlei, 122 F.3d 944, 985 (11th Cir.1997). "Any period of delay resulting from other proceedings concerning the defendant" must be excluded from the seventy-day calculation. 18 U.S.C. § 3161(h)(1). In this case, the Magistrate Judge voluntarily ordered that all pretrial motions be filed no later than twenty days after the Defendant's arraignment.4 The district court excluded this twenty-day period from its Speedy Trial Act calculations. The Government urges that this exclusion was proper under § 3161(h)(1) and our decision in United States v. Mejia, 82 F.3d 1032 (11th Cir.1996). We disagree. 2 The remedy for violation of the Speedy Trial Act's seventy-day limitation period is dismissal of the indictment. 18 U.S.C. § 3162(a)(2). 3 We review the district court's construction and interpretation of the Speedy Trial Act de novo. We review the district court's factual determinations on excludable time for clear error. United States v. Schlei, 122 F.3d 944, 984 (11th Cir.1997). 4 Defendant took full advantage of the twenty-day deadline, filing several discovery motions on the twentieth day. This fact, however, has no bearing upon our analysis. See United States v. Mejia, 82 F.3d 1032, 1036 (11th Cir.1996) ("Whether motions are actually filed during the extension is unimportant."). 3  In Mejia, we decided that, where a defendant moved for, and the court granted, an extension of time for filing additional pretrial motions, the district court properly excluded the extension period from Speedy Trial Act calculations. Id. at 1035-36. We reasoned that such an extension falls within § 3161(h)(1)'s language about "[a]ny period of delay resulting from other proceedings concerning the defendant." Id. It does not follow from Mejia, however, that the twenty-day period in the instant case is excludable.5 Instead, we think that Mejia presented a case different from the present case. In Mejia, the defendant sought and obtained an extension of time in which to file his motions. Id. at 1035. Implicit in the term "extension" is the notion that the defendant sought additional time not normally permitted for the filing of motions. In other words, he sought to delay the forward progression of the proceedings. That an extension of time in which to file motions will work a delay in bringing the defendant to trial seems likely. Here, on the other hand, there was no extension of time; twenty days after arraignment was the original deadline set by the court for filing pretrial motions. Moreover, twenty days after arraignment is, by local rule, the ordinary time allowed for the filing of motions in the Southern District of Georgia. See S.D. Ga. Local Criminal Rule 12.1. Therefore, even if the Magistrate by order had entered no deadline in this case, the parties would have had twenty days after the arraignment to prepare and to file their pretrial motions. In our view, such a routine time prescription is no "delay" in bringing the defendant to trial. To qualify as an excluded period under § 3161(h)(1), the period must constitute a "delay." 18 U.S.C. § 3161(h)(1). Moreover, the twenty-day period in this case was hardly extraordinary or specifically-tailored to the needs of this case. It was not the result of a motion to enlarge the time to file motions. Instead, it was "based merely upon the entry of a standard scheduling order." See United States v. Hoslett, 998 F.2d 648, 656 (9th Cir.1993). An exclusion based on a case-specific determination that additional time is needed for the 5 The court in Mejia expressly declined to comment on a case more like the instant one, where the district court sua sponte sets a deadline for the filing of pretrial motions. See Mejia, 82 F.3d at 1036 n. 3 ("[W]e decide nothing today about whether extensions for the preparation and filing of pretrial motions granted by the court upon motion of the government or by the court sua sponte result in excludable days under § 3161(h)(1)"). 4 disposition of pretrial motions is one matter; an across-the board exclusion of twenty days in every case arising in a judicial district is quite another. See id. Therefore, Mejia does not control the outcome of this case. Because our duty is to carry out the intent of Congress, we must look to the language of the statute itself. As noted previously, § 3161(h)(1) requires a "delay" as a prerequisite to exclusion. On this record, we see no indication that the judge's setting of a deadline for the filing of motions worked a "delay" within the meaning of the statute. We also look to the structure of the statute as a whole. The Speedy Trial Act makes allowance for the delay occasioned by the exigencies of particular cases. The automatic exclusions of § 3161(h)(1)(A)-(J) take account of the delay that may result from an array of particular pretrial circumstances. In addition, § 3161(h)(8)(A) excludes delay resulting from a continuance where the court specifically finds that the interests of justice furthered by the continuance outweigh the interests of the public and the defendant in a speedy trial. But, none of the exclusion provisions of the Act specifically address the situation in this case; and, they do not indicate, in our view, an intention on the part of Congress to allow for broad, across-the-board exclusions created by a district court's standard scheduling practices or local rule.6 See generally 18 U.S.C. § 3161(h)(8)(C) (providing that no continuance "because of general congestion of the court's calendar" is excludable). 6 If the customary time allowances for the filing of motions resulted in excludable time, each judicial district, in effect, would be free to amend the Speedy Trial Act by local rule. For example, considering its local rule, it appears that in the Southern District of Georgia the seventy-day limit always (or almost always) would be transformed into a ninety-day limit. We are unable to believe that Congress intended that result. 5  The twenty days allowed for the filing of pretrial motions were not properly excludable in this case.7 Therefore, more than seventy—at least eighty-one—non-excludable days elapsed between the Defendant's first appearance and the commencement of his trial. The trial court thus erred in denying Defendant's motion to dismiss the indictment under the Speedy Trial Act. 2. LESSER INCLUDED OFFENSE Defendant also asserts, on appeal, that the district court erred in declining to instruct the jury on assault as a lesser included offense of abusive sexual contact. We agree. And, because the Government may re-indict and retry Defendant for abusive sexual contact, and because the pertinent evidence in a new trial may be like the evidence in this trial, we address the issue. To establish that the district court erred in refusing to give the lesser included offense instruction, Defendant must satisfy a two-part test. First, he must show that the charged offense encompasses all of the elements of the lesser offense ( the "elements" test). Schmuck v. United States, 489 U.S. 705, 716, 109 S.Ct. 1443, 1450, 103 L.Ed.2d 734 (1989). Second, he must establish that the district court abused its discretion in failing to give the instruction. An abuse of discretion may occur where the evidence would permit the jury rationally to acquit the defendant of the greater, charged offense and convict him of the lesser. United States v. Cornillie, 92 F.3d 1108, 1109 (11th Cir.1996). Applying this two-part test, we believe that the district court erred in this case when it refused to instruct the jury on assault as a lesser included offense. 7 We follow the Sixth and Ninth Circuits. See United States v. Moran, 998 F.2d 1368, 1370-71 (6th Cir.1993); United States v. Hoslett, 998 F.2d 648, 656 (9th Cir.1993). We recognize that the Seventh Circuit has said that a sua sponte scheduling order, however routine, setting a deadline for filing motions results in excludable time. United States v. Montoya, 827 F.2d 143, 153 (7th Cir.1987). The Seventh Circuit's decision in Montoya is grounded in the premise that "[i]f the defendant believes no time or less time is needed he can so advise the court and the case may proceed without regard to possible pretrial motions." Id. We disagree, for we believe that "the burden should not be on the defendant to take affirmative steps to keep the speedy-trial clock running." Moran, 998 F.2d at 1371. The duty to comply with the Speedy Trial Act lies with the courts, not with defense counsel. By the way, the Government does not contend, nor does the record suggest, that defense counsel in this case should have known, when the twenty-day deadline was announced, that a violation of the seventy-day limit would necessarily occur. 6  First, abusive sexual contact with a child, under 18 U.S.C. § 2244(a)(1), encompasses all of the elements of simple assault under 18 U.S.C. § 113(a)(5). The elements of abusive sexual contact with a child under § 2244(a)(1) are: (1) in the special maritime and territorial jurisdiction of the United States, (2) the defendant intentionally (3) touched the genitalia, anus, groin, breast, inner thigh, or buttocks (4) of a child less than twelve years of age (5) "with an intent to abuse, humiliate, harass, degrade, or arouse or gratify the sexual desire of any person." 18 U.S.C. § 2244(a)(1); 18 U.S.C. § 2246(3). A person commits assault under § 113 when, (1) in the special maritime and territorial jurisdiction of the United States, (2) he "assaults" another person. 18 U.S.C. § 113(a). Section 113 does not define "assault", so we give that term its meaning at common law. United States v. Guilbert, 692 F.2d 1340, 1343 (11th Cir.1982). At common law, an assault was either a battery, an attempted battery, or an act that puts another in reasonable apprehension of receiving immediate bodily harm. See id. Given the arguments of the parties in this case, we focus on assault committed by a battery. The Government contends that abusive sexual contact with a child does not encompass all of the elements of common law battery; the Government says that battery requires an intent to do bodily harm. We disagree. In his Commentaries, Blackstone observed: The least touching of another's person wilfully, or in anger, is a battery; for the law cannot draw the line between different degrees of violence, and therefore totally prohibits the first and lowest stage of it: every man's person being sacred, and no other having a right to meddle with it, in any the slightest manner. United States v. Stewart, 568 F.2d 501, 505 (6th Cir.1978) (quoting 3 Blackstone, Commentaries on the Law of England 120 (E. Christian ed., 1822)). Case law is in accord with Blackstone: the intention to do bodily harm is not a necessary element of battery. State v. Duckett, 306 Md. 503, 510 A.2d 253, 257 (1986). The slightest willful offensive touching of another constitutes a battery at common law, regardless of whether the defendant harbors an intent to do physical harm. See Gates v. State, 110 Ga.App. 303, 138 S.E.2d 473, 473- 74 (1964) (affirming battery conviction on evidence that defendant intentionally "tapped" woman on buttocks 7 in public store); Wood v. Commonwealth, 149 Va. 401, 140 S.E. 114, 116 (1927) (affirming conviction for assault and battery where defendant fondled fourteen year-old girl). Furthermore, the view that common law battery (and, thus, § 113(a)(5) assault) does not contain an intent to harm element is borne out by § 113 itself. Section 113 identifies seven kinds of assault. See 18 U.S.C. § 113(a). For some of these offenses, the statute specifically sets forth a specific intent requirement. See 18 U.S.C. § 113(a)(1) (assault with intent to commit murder); 18 U.S.C. § 113(a)(3) (assault with a dangerous weapon and intent to do bodily harm). The subsections identifying assault by striking, beating or wounding, assault resulting in serious bodily injury, and simple assault (the subsection at issue in this case), however, contain no language setting out a specific intent requirement. The courts have recognized this omission, concluding that no specific intent element exists for assault by striking, beating, or wounding, United States v. Martin, 536 F.2d 535, 535-36 (2d Cir.1976), and assault resulting in serious bodily injury. United States v. Juvenile Male, 930 F.2d 727, 728-29 (9th Cir.1991). Our view of assault is also consistent with authorities recognizing that sex offenses frequently encompass simple assault as a lesser included offense. See United States v. Eades, 633 F.2d 1075, 1077 (4th Cir.1980) ("[T]he great majority of the offenses proscribed by Maryland's sexual offense statutes may be said to encompass simple assault as a lesser included offense."); see also Sills v. State, 36 Ga.App. 103, 135 S.E. 758, 758 (1926) ("An assault or assault and battery is necessarily involved in every case of rape."). Thus, we conclude that simple assault under § 113(a)(5) is a lesser included offense of abusive sexual contact under § 2244(a)(1). Next, we must decide whether an evidentiary basis exists for a rational jury to have found Defendant guilty of simple assault but not guilty of abusive sexual contact.8 We believe such a basis does exist. Defendant testified that he hit the victim, K.T., on the leg with his hand. Defendant further testified that he grabbed K.T.'s shoulders. Defendant testified that K.T. responded to being struck on the leg by stating: "Oh, 8 Excerpts from Defendant's testimony at trial are reprinted in the Appendix to this opinion to show more fully the evidentiary basis for a jury instruction on assault. 8 Mr. Williams, you didn't have to push me. Mr. Angelo, you didn't have to push me." We conclude that such testimony, if accepted by a jury, could give a rational factfinder a sufficient basis upon which to find that Defendant did touch K.T., and that the touching was offensive and not consented to by her, but that the touching was not of a sexual nature. Thus, the jury could decide that Defendant committed simple assault, rather than abusive sexual contact. 18 U.S.C. § 113(a)(5); 18 U.S.C. § 2244(a)(1). CONCLUSION Because we conclude that the district court erred in denying Defendant's motion to dismiss the indictment for violation of the Speedy Trial Act, we VACATE the conviction and sentence and REMAND to the district court with directions to dismiss the indictment without prejudice.9 VACATED AND REMANDED. APPENDIX SELECTED TESTIMONY OF DEFENDANT Q: What happened, if anything ... as far as [K.T.]? Do you remember anything about the 14th? A: Yes, she was on, she was on my system playing the games. And Ms. McMillan, the director, had come and told me about a roster, because we were planning some trips. She had sent it to Fort Stewart, but she didn't type it. I had to type it for her. So, I asked [K.T.] to get up. Now, I don't allow anybody to sit in my chair. It is like one of those big roll away chairs. And as I sit in my chair, I rolled towards [K.T.]. And with the back of my hand, I hit the chair and part of her leg. And the chair flew away, just, you know, because it had, it had rollers on it. Okay. So, I mean, my chair had rollers on it. So, when I rolled over there, I hit her chair. And that chair moved some distance, because they are regularly like homeroom chairs, you know, that they use. Right? So, the chair slid and her reaction, you know how kids are, "Oh, Mr. Williams, you didn't have to push me. Mr. Angelo, you didn't have to push me." I said, "No, I didn't push you. You just need to put meat on your bones." That's all, which I tease all the kids all the time, you know, in various ways, the different ways. 9 The preexisting case law of this Circuit was not certain on whether or not the twenty days in this case would be excludable. The charged offense is a serious one. The delay in going to trial was not great. Therefore, the indictment should be dismissed without prejudice. See 18 U.S.C. § 3162(a)(2). 9  So, I got down at the system and started typing. And I had a phone call. Q: Who? A: Yes, as a matter of fact, I had a phone call from the director asking me about the roster. So, as I was walking away, I saw [K.T.] getting ready to sit back down to finish her game. And that's when I turned and said, "No, honey, you can't mess with it now, because I have opened up some of my admin stuff, and I don't want you to mess with any of it." (R2:144-46). Q: Okay. When you said you touched her, when you grabbed her, where did you grab her? A: On her shoulders. (R2:146). Q: Did you in fact touch [K.T.] in a sexual manner? A: No, sir, I didn't. Q: Did you touch her on her breast? A: No, sir, I didn't. Q: Did you touch her on the vaginal area, on the crotch? A: No, sir, I didn't. Q: Did you touch her on her inner thigh? A: No, sir, I didn't. Q: Okay. Did you touch her on the buttocks? A: No, sir, I didn't. Q: Did you have any bent to touch her in a sexual manner? A: No, I didn't. No, I didn't. (R2:153-54). 10 

A spectacular and likely unforgettable show will take place in the sky Aug. 21. “Have you ever seen a total solar eclipse?” asks Cynthia Peterson, professor emerita of physics. “It’s a really, really exciting event!” The reason she and so many others are excited for this event has a lot to do with its rarity. The last time a total solar eclipse was visible from the mainland United States was 38 years ago, in February 1979. Very specific conditions have to be met to create an eclipse that can be viewed from Earth. The Earth and the moon must align perfectly with the sun as they speed through space, an amazing coincidence. To fully understand how this happens, Peterson says, it’s helpful to know some basic astronomy. Conditions for a Total Solar Eclipse The Earth moves in space around the sun, completing a full orbit once every 365.25 days, she explains. As the Earth and other members of our solar system travel around the sun, they continue in essentially the same plane, on a path called the ecliptic. Some celestial bodies, such as our moon, deviate from the ecliptic slightly. The orbit of the moon is inclined on the ecliptic plane at an inclination of 5 degrees. As the moon deviates 5 degrees above or below the ecliptic plane, it will cross the plane at points called nodes. “That is the first essential piece of the eclipse puzzle,” says Peterson. “The moon must be at a node for an eclipse to occur. Otherwise, the moon will not align and no eclipse will be seen from Earth.” The moon’s position in the lunar cycle is another vital eclipse component. As the Earth travels in its orbit, the moon tags along, keeping its gaze locked on Earth, always facing from the same side as it completes its own orbit around Earth once every 29.5 days. Over the course of a month, the moon’s appearance changes, from crescent to full to crescent again and finally to what appears to be its absence, when it’s called a new moon. A new moon is the other requirement for a solar eclipse. “The basic rule for a solar eclipse is to have a new moon at a node,” Peterson points out. But during an eclipse, how can our moon, which is relatively small, appear almost as big as the sun, which is pretty gigantic? Peterson explains, “The sun is 400 times bigger than the moon and the sun is also 400 times farther away from the moon, so the moon appears to fit exactly during an eclipse, when they are both the same angular size.” Holding up her fist, she demonstrates: “Find a large object ahead of you and pretend it is the sun and your fist is the moon. If you hold up your fist and look with one eye, you can’t see the object/sun.” These are the conditions for a total solar eclipse like the one coming up. “Solar eclipses happen when the new moon obstructs the sun and the moon’s shadow falls on the earth, creating a total solar eclipse.” Peterson moves her fist slightly away from herself until the edges of the object can be seen around it. “Or, when the moon covers the Sun’s center and creates a ‘ring of fire’ around the moon, it’s what’s called an annular eclipse.” It’s those bits of the sun peeking out from behind the moon – in both partial and total eclipses – that everyone needs to be careful of. It’s extremely important to view the eclipse safely, Peterson stresses. “The problem with the eclipse is that every time it happens, some people are blinded [from looking at it unprotected]. The shadow goes whipping by at 1,000 miles per hour, and you never want to stare at the sun, even a sliver of it.” So be prepared, and ensure you wear proper solar eclipse eye protection. Regular sunglasses will not help. Solar eclipse glasses can be used, welder’s goggles, or telescopes with proper lenses. Be sure the eye protection you choose is certified by the International Organization for Standardization (ISO). Other popular viewing methods are DIY viewing boxes like these. Peterson, like many others who wish to get the full eclipse experience, will be traveling to an area directly in the path of the eclipse’s shadow. These areas are called totality. The Aug. 21 eclipse will cover an expansive area of totality that will include 14 states and 14 major U.S. cities, stretching from Lincoln Beach, Oregon to Charleston, South Carolina. For a map of the path of totality, go to the NASA website. Connecticut is unfortunately hours of travel from the nearest totality. Peterson will go as far as Nebraska for the experience. “You’ll only see a partial eclipse here in Connecticut,” she says. “It will get a little darker, like a cloud covering part of the sun, and then brighten up again.” She encourages those who can to try to travel to a viewing point for the total eclipse, where they may see “amazing phenomena” like the diamond ring, shadowbands, crescent-shaped solar images under trees (instead of the usual ‘coins’ which are pinhole images of the sun), and extremely sharp shadows in the final minute before totality, due to the very narrow sun at that time. “These phenomena can only be seen in totality,” she says. The next chance to see a total solar eclipse will be in 2024, when its shadow will be cast closer to Connecticut. It will start in the U.S. in Texas, then make its way north, through northern Vermont and New Hampshire. “That’s less than seven years from now,” Peterson points out, “but that’s the end of eclipses crossing the U.S. until the 2050s.” For those on campus next week, you aren’t out of luck. For this eclipse there will be a viewing party on Horsebarn Hill behind the Dairy Bar, from 1 to 4 p.m., hosted by the Department of Physics. “We’ll have solar telescopes, a pinhole camera activity, and will do some short mini-lectures on astronomy at UConn and about how eclipses work,” says assistant professor of physics Jonathan Trump, one of the faculty members who will lead the viewing party. Peterson, longtime astronomer and scientist, says witnessing an eclipse – especially a total eclipse – can be extremely emotional. She suggests reading Annie Dillard’s essay about solar eclipses, where the author compares the contrast between viewing a partial eclipse and viewing a total eclipse to the difference between flying in an airplane versus falling out of the airplane. “Those are very different experiences.” But wherever you are on the afternoon of Aug. 21, Peterson says, stop and enjoy the show: “Good luck and clear skies!” The eclipse will be live-streamed by NASA, and can also be viewed on PBS’ NOVA at 9 p.m. on Aug. 21.

INTRODUCTION ============ B cells are important for antibody (Ab) production and for antigen presentation and cytokine production ([@R1]). In particular, cytokine-producing B cells play critical roles in multiple aspects of immunity. There are two opposing B cell subsets: regulatory B cells (Bregs) and effector B cells (Beffs) ([@R2]). Interleukin-10 (IL-10)--producing Bregs are now recognized as negative regulators of the immune system, inflammation, and autoimmunity based on studies with human subjects and mouse models of autoimmune diseases such as rheumatoid arthritis, systemic lupus erythematosus (SLE), and multiple sclerosis (MS) ([@R3]--[@R6]). The phenotype of mouse splenic Bregs is derived from two different B cell subsets: marginal zone (MZ) and B1 B cells ([@R7]). Furthermore, it was reported that the CD9^+^ B cell subset is enriched in IL-10--producing Bregs ([@R7], [@R8]), since this subset includes both the MZ and B1 B cell subsets ([@R9]). By contrast, cytokine-producing Beffs can positively modulate the immune response through the production of various cytokines ([@R2]). For example, lymphotoxin-producing Beffs are essential for the ontogenesis, homeostasis, and activation of secondary lymphoid organs, as well as for the development of tertiary lymphoid tissues at ectopic sites ([@R10]). Other Beffs have been shown to modulate the development of effector and memory CD4^+^ T cell responses via the production of cytokines such as IL-6, interferon-γ, and tumor necrosis factor ([@R11]). Therefore, a protocol that selectively depletes Beffs while sparing Bregs would represent a potent therapy for autoimmune diseases. Systemic sclerosis (SSc; also known as scleroderma) is a connective tissue disorder characterized by excessive fibrosis in the skin and various internal organs with an autoimmune etiology. More than 90% of SSc patients are positive for autoantibodies such as anti--DNA topoisomerase I, anticentromere, and anti--RNA polymerase Abs. One study demonstrated that SSc patients displayed distinct abnormalities of blood B cell compartments characterized by expanded naïve B cells and activated memory B cells ([@R12]). B cell activating factor (BAFF) has been shown to be present at elevated levels in patients with SSc and is correlated with disease severity ([@R13]). B cells of patients with SSc that were stimulated by BAFF exhibited an enhanced ability to produce IL-6 ([@R13]). In addition, B cells and BAFF were shown to promote collagen production by dermal fibroblasts in SSc ([@R14]). IL-6 plays an important role in tissue fibrosis and autoimmunity in the SSc pathogenesis ([@R15], [@R16]) and is thus considered a candidate therapeutic target. The skin fibrosis of two patients with diffuse SSc was markedly improved after treatment with the anti--IL-6 receptor Ab tocilizumab ([@R17]). A phase 2 trial of tocilizumab demonstrated clinically significant improvement of skin fibrosis in patients with SSc ([@R18]). Thus, IL-6--producing Beffs may play a critical role in the development of scleroderma; however, there is no reliable detection method for IL-6--producing Beffs, and the resulting phenotype remains unclear. By contrast, IL-10--producing Bregs were shown to suppress the skin fibrosis of the Scl-cGVHD model, an animal model for human SSc ([@R19]). IL-10--producing Bregs have been reported to be decreased in patients with SSc and were associated with disease activity ([@R20]). Here, we investigated the intracellular staining and phenotype of IL-6--producing Beffs. Furthermore, we evaluated the role of IL-6--producing Beffs and IL-10--producing Bregs in the pathogenesis of scleroderma using B cell--specific cytokine-deficient mice. On the basis of these results, we propose a new potential therapeutic strategy for SSc via alteration of the Beff and Breg balance. RESULTS ======= CD40 and lipopolysaccharide synergistically induce IL-6 production from B cells ------------------------------------------------------------------------------- To identify the stimulation condition of IL-6 production from B cells, we cultured B cells with various Toll-like receptor (TLR) agonists with or without agonistic CD40 monoclonal Ab (mAb). The TLR4 agonist \[lipopolysaccharide (LPS)\] and TLR9 agonist induced IL-6 production from B cells. Addition of the agonistic CD40 mAb in combination with LPS or TLR9 agonist signals significantly enhanced IL-6 production from B cells ([Fig. 1A](#F1){ref-type="fig"}). Similar to the results for IL-6, IL-10 production was induced by LPS and the TLR9 agonist. By contrast, addition of agonistic CD40 mAb in combination with LPS signals significantly reduced IL-10 production from B cells ([Fig. 1A](#F1){ref-type="fig"}). Thus, agonistic CD40 mAb accelerates IL-6 production from B cells stimulated with LPS, while agonistic CD40 mAb attenuates IL-10 production from B cells stimulated with LPS. ![CD40 and LPS synergistically induce IL-6 production from B cells.\ (**A**) B cells were isolated from spleens of naïve mice by magnetic sorting based on CD19 expression. Sorted B cells were cultured for 72 hours with media alone or media containing anti-CD40 mAb, along with the indicated TLR agonists. After in vitro stimulation for 72 hours, IL-6 (left) and IL-10 (right) levels in supernatants were quantified by enzyme-linked immunosorbent assay (ELISA). Bars represent the means ± SD from three independent experiments (*n* = 3 mice). Significant differences between means of media alone and individual stimuli are indicated: \**P* \< 0.001, \*\**P* \< 0.0001, analysis of variance (ANOVA) followed by Tukey's multiple comparison test. Significant differences between cultures with or without anti-CD40 mAb are indicated: ^\#^*P* \< 0.05, ^\#\#^*P* \< 0.01, ^\#\#\#^*P* \< 0.001, ^\#\#\#\#^*P* \< 0.0001, Student's *t* test. (**B**) IL-6--producing B cells were determined after in vitro stimulation by LPS, anti-CD40 mAb, and LPS + anti-CD40 mAb, with PIB \[phorbol 12-myristate 13-acetate (PMA), ionomycin, and brefeldin A\] added during the final 5 hours of cultures (5 to 48 hours). Isotype control Ab was used as negative controls for IL-6 staining. Percentages indicate the frequencies of cytoplasmic IL-6^+^ B cells within the indicated gates among total CD19^+^ B cells. Bars represent the means ± SD from three independent experiments (*n* = 3 mice). \**P* \< 0.0001, ANOVA followed by Tukey's multiple comparison test. (**C**) Representative cell surface phenotype of spleen IL-6--producing B cells after stimulation with LPS + anti-CD40 mAb for 24 hours with PIB added during the final 5 hours of culture. Cultured cells were stained for viability and cell surface molecule expression (using LEGENDScreen Mouse PE Kit from BioLegend), permeabilized, stained with anti--IL-6 mAb, and analyzed by flow cytometry. Representative cell surface molecule expression by IL-6^+^ (red line) and IL-6^−^ (black line) CD19^+^ B cells from three individuals is shown. Shaded histograms represent isotype-matched control mAb staining.](aas9944-F1){#F1} To visualize IL-6--producing B cells, we established a detection method of intracellular IL-6 staining by fluorescence-activated cell sorting (FACS). We cultured splenocytes with LPS, agonistic CD40 mAb, or LPS + agonistic CD40 mAb for various time courses (5, 12, 24, or 48 hours). We added PIB during the final 5 hours of cultures. In line with the results described above, LPS and agonistic CD40 mAb signals cooperatively induced the IL-6 production of B cells ([Fig. 1B](#F1){ref-type="fig"}). In addition, the 24-hour culture was found to be the best condition for the detection of IL-6--producing B cells, and approximately 40% of the B cells produced IL-6 ([Fig. 1B](#F1){ref-type="fig"}). Therefore, the culture with LPS and agonistic CD40 mAb for 24 hours appears to be the best condition for visualizing IL-6--producing B cells. MZ B cell-related cell surface markers are highly expressed in IL-6--producing B cells -------------------------------------------------------------------------------------- To identify whether IL-6--producing B cells represent a unique or known B cell subset, we analyzed the cell surface phenotype. We assessed the phenotype of IL-6--producing B cells following 24 hours of culture with LPS and agonistic CD40 mAb, along with 5 hours of PIB stimulation. On average, IL-6^+^ B cells expressed higher densities of CD1d, CD9, CD21, CD23, CD25, CD80, CD86, CD150 \[SLAM (Signaling lymphocyte activation molecule)\], CD155 \[PVR (Poliovirus receptor)\], CD200 (OX2), and CD267 \[TACI (transmembrane activator and calcium-modulator and cyclophilin ligand interactor)\], which is one of the BAFF receptors, when compared with IL-6^−^ B cells ([Fig. 1C](#F1){ref-type="fig"} and fig. S1). Although naïve B cells do not express CD25, we induced most of the B cells to express CD25 after 24 hours of culture with LPS and agonistic CD40 mAb, followed by 5 hours of PIB stimulation (fig. S2). By contrast, on average, IL-6^+^ B cells expressed lower densities of CD43, immunoglobulin M (IgM), and Ly-6D when compared with IL-6^−^ B cells (fig. S1). The higher expression of CD1d, CD9, and CD21 on IL-6^+^ B cells suggests that IL-6^+^ B cells might be predominantly found within the MZ B cell subset. Furthermore, IL-6^+^ B cells show higher expression of TACI, a receptor of BAFF. The MZ B cell subset is a major source of IL-6--producing B cells ----------------------------------------------------------------- We previously reported that IL-10--producing Bregs were predominantly found within the splenic CD1d^hi^ MZ and CD5^+^ B1 B cell subsets ([@R7]). To determine which B cell subsets secreted IL-6, we stained and sorted splenic B cells into three fractions \[follicular B cells (CD1d^int^CD5^−^), MZ B cells (CD1d^hi^CD5^−^), and B1 B cells (CD1d^int^CD5^+^)\] before in vitro 24-hour stimulation with LPS and agonistic CD40 mAb, followed by 5 hours of PIB stimulation ([Fig. 2A](#F2){ref-type="fig"}). The frequency of IL-6--producing B cells among sorted follicular B cells was comparable with that detected in pan-B cells. The frequency of IL-6--producing B cells among sorted B1 B cells was decreased compared with that of pan-B cells. By contrast, the frequency of IL-6--producing B cells in sorted MZ B cells was significantly increased compared with that in other B cell subsets ([Fig. 2](#F2){ref-type="fig"}, B and C). As previously reported, MZ and B1 B cell subsets produced IL-10, while the follicular B cell subset did not produce IL-10 ([Fig. 2](#F2){ref-type="fig"}, B and C). In addition, the frequency of IL-10--producing B cells in B1 B cells was significantly increased compared with that in MZ B cell subsets ([Fig. 2](#F2){ref-type="fig"}, B and C). Next, to examine whether B cells simultaneously produce IL-6 and IL-10, we stained B cells with both IL-6 and IL-10 and analyzed them by FACS. We found that IL-6-- and IL-10--producing B cells exist mutually exclusively (fig. S3). Thus, MZ B cells represent a major subset of IL-6--producing B cells in the spleen. {#F2} IL-6 is increased in bleomycin-induced scleroderma -------------------------------------------------- To determine whether and when the levels of IL-6 and IL-10 are increased in the bleomycin-induced scleroderma model, we measured the serum cytokine levels and the frequency of splenic cytokine-producing B cells. Serum IL-6 levels were gradually increased along with bleomycin treatment, while there was no change in serum IL-10 levels with bleomycin treatment ([Fig. 3A](#F3){ref-type="fig"}). In addition, the frequency of splenic IL-6--producing B cells at 3 weeks after bleomycin treatment was significantly increased compared with that detected at 3 weeks after phosphate-buffered saline (PBS) treatment ([Fig. 3B](#F3){ref-type="fig"}). {#F3} Next, to determine whether IL-6--producing Beffs infiltrate the inflamed skin, we analyzed the cytokine-producing B cells by FACS and immunohistochemistry. For FACS analysis, we collected B cells infiltrating the inflamed skin and stimulated them in vitro. The number of IL-6--producing Beffs in inflamed skin with bleomycin treatment was significantly increased compared with that in the skin of mice that received PBS treatment ([Fig. 3C](#F3){ref-type="fig"}). The numbers of IL-10--producing Bregs in inflamed skin with bleomycin treatment were also significantly increased compared with those in the skin of PBS-treated mice ([Fig. 3C](#F3){ref-type="fig"}). In addition, immunohistochemical analysis revealed the presence of IL-6--producing Beffs (IL-6^+^B220^+^) in the inflamed skin in the bleomycin-induced scleroderma model ([Fig. 3](#F3){ref-type="fig"}, D and E). Unlike in the spleen, most IL-6--producing Beffs were found in the CD1d^int^CD5^−^, not in the CD1d^hi^ B cell subset (fig. S4). Thus, IL-6--producing Beffs are increased and infiltrated the inflamed skin in the bleomycin-induced scleroderma model. Skin and lung fibrosis are attenuated in mice with B cell--specific IL-6 deficiency ----------------------------------------------------------------------------------- We next evaluated whether cytokine-producing B cells regulate the skin fibrosis of the bleomycin-induced scleroderma model. To this end, we generated mixed bone marrow chimeric mice with a B cell--specific deficiency in IL-6 production (B-IL-6^−/−^) or IL-10 production (B-IL-10^−/−^), together with control chimeras (control). The schema and validation of these mixed bone marrow chimeric mice are outlined in fig. S5. Although B cells showed complete lack of IL-6 or IL-10 production in B-IL-6^−/−^ or B-IL-10^−/−^ mice, B-IL-6^−/−^ or B-IL-10^−/−^ mice demonstrated 20% IL-6 or IL-10 deficiency in all hematopoietic cells. To compensate for the effect of this deficiency outside the B cell compartment, we generated control mice against B-IL-6^−/−^ or B-IL-10^−/−^ mice as IL-6^20%^ or IL-10^20%^ chimeras, respectively, which showed 20% IL-6 or IL-10 deficiency in all hematopoietic compartments. We left the hematopoietic compartment for 8 to 10 weeks to repopulate, and then, we injected the chimeric mice with bleomycin to induce scleroderma. IL-6 deficiency of B cells caused significant reduction in dermal thickness, type 1 collagen mRNA expression, and lung fibrosis ([Fig. 4](#F4){ref-type="fig"}, A and B, and fig. S6, A to C). In contrast, B cell IL-10 deficiency significantly augmented the dermal thickness, type 1 collagen mRNA expression, and lung fibrosis ([Fig. 4](#F4){ref-type="fig"}, C and D, and fig. S6, D to F). ![Skin fibrosis is attenuated in mice with B cell--specific IL-6 deficiency.\ (**A** to **D**) Bleomycin-induced scleroderma was induced in mice with B cell--specific IL-6 deficiency (B-IL-6^−/−^; wild-type mice lethally irradiated and reconstituted with 80% μMT plus 20% *Il6*^−/−^ bone marrow) or B cell--specific IL-10 deficiency (B-IL-10^−/−^; wild-type mice lethally irradiated and reconstituted with 80% μMT plus 20% *Il10*^−/−^ bone marrow) and control chimera groups \[wild-type mice lethally irradiated and reconstituted with 80% wild-type plus 20% *Il6*^−/−^ or *Il10*^−/−^bone marrow (IL-6^20%^ or IL-10^20%^, respectively)\]. (A and C) Skin samples were harvested 4 weeks after PBS or bleomycin treatment. Masson's trichrome stain. Representative images. Arrows indicate dermis. Scale bars, 100 μm. Right: Dermal thickness (distance from the dermal-epidermal junction to the adipose layer), shown as the means ± SD of triplicate determinations per hpf from 10 mice per group. (B and D) Expression of *col1a2* mRNA in the skin was measured by real-time polymerase chain reaction (PCR), shown as the means ± SD of triplicate determinations per hpf (high power field) from 10 mice per group. Open circles, PBS; closed circles, bleomycin. \**P* \< 0.05, \*\*\**P* \< 0.001, \*\*\*\**P* \< 0.0001, one-way ANOVA followed by Tukey's multiple comparison test. (**E** and **F**) B cells and fibroblasts were cocultured. Collagen release by fibroblasts was determined by the Sirius red assay in 72-hour culture supernatants of fibroblast cultured alone, cocultured with B cells, or recombinant TGF-β1 (5 ng/ml). IL-6 was determined by ELISA in 72-hour culture supernatants. B cells from wild-type, *Il6*^−/−^, or *Il10*^−/−^ mice were isolated by Miltenyi MACS enrichment. B cells were either in cell-cell contact with fibroblast (contact) or seeded in the upper chamber of a Transwell culture insert (Transwell). Bars represent the means ± SD from two independent experiments (*n* = 4 mice). Significant differences between fibroblast only versus other groups are indicated: \**P* \< 0.05, \*\**P* \< 0.01, \*\*\**P* \< 0.001, \*\*\*\**P* \< 0.0001, ^\#^*P* \< 0.05, ^\#\#^*P* \< 0.01, ^\#\#\#^*P* \< 0.001, ^\#\#\#\#^*P* \< 0.0001, ANOVA followed by Tukey's multiple comparison test.](aas9944-F4){#F4} IL-6--producing Beffs promote collagen secretion by fibroblasts --------------------------------------------------------------- To further determine the role of cytokine-producing B cells in the regulation and development of skin fibrosis, we cocultured and analyzed B cells and fibroblasts ([Fig. 4E](#F4){ref-type="fig"}). B cells from wild-type mice strongly induced collagen secretion by fibroblasts (white bars in "Fibro-contact B cell" versus "Fibro only"), with a magnitude comparable to that observed under stimulation with recombinant transforming growth factor--β (TGF-β; black bar in "Fibro + TGF-β"). In addition, B cells from IL-6^−/−^ mice showed significantly decreased levels of collagen secretion by fibroblasts compared with B cells from wild-type mice (*P* \< 0.001; white versus blue bars in "Fibro-contact B cell"; [Fig. 4E](#F4){ref-type="fig"}). By contrast, B cells from IL-10^−/−^ mice showed significantly increased collagen secretion by fibroblasts compared with those from wild-type mice (*P* \< 0.05; white versus red bars in "Fibro-contact B cell"). Similarly, IL-6 secretion into the supernatant was significantly induced in coculture of fibroblasts and B cells from wild-type mice (*P* \< 0.0001; white bars in "Fibro-contact B cell" versus "Fibro only"; [Fig. 4F](#F4){ref-type="fig"}). IL-6 production was significantly lower in the coculture with B cells from IL-6^−/−^ mice than with those of wild-type mice (*P* \< 0.05; white versus blue bars in "Fibro-contact B cell"; [Fig. 4F](#F4){ref-type="fig"}), while IL-6 production was stronger with B cells from IL-10^−/−^ mice than with those from wild-type mice (*P* \< 0.01; white versus red bars in "Fibro-contact B cell"; [Fig. 4F](#F4){ref-type="fig"}). However, we could not detect IL-10 production in the supernatant of these coculture systems. We then evaluated whether the increased collagen secretion induced by B cells is dependent on cell-cell contact through interactions between B cells and fibroblasts. B cell--induced collagen production by fibroblasts was significantly inhibited when we used Transwells (*P* \< 0.0001, B cells from wild-type mice; *P* \< 0.0001, B cells from IL-10^−/−^ mice; [Fig. 4E](#F4){ref-type="fig"}). Similarly, IL-6 production was significantly inhibited when we used Transwells (*P* \< 0.0001, B cells from wild-type mice; *P* \< 0.0001, B cells from IL-10^−/−^ mice; [Fig. 4F](#F4){ref-type="fig"}). Thus, IL-6--producing Beffs promote collagen secretion by fibroblasts through the interaction with B cells and fibroblasts. BAFF increases IL-6--producing Beffs but attenuates IL-10--producing Bregs -------------------------------------------------------------------------- BAFF exhibits a strong costimulatory function for B cell activation in vitro ([@R21]). We found that the IL-6^+^ B cells showed high expression levels of the BAFF receptor ([Fig. 1C](#F1){ref-type="fig"}). To determine whether BAFF modulates the cytokine production of B cells, we cultured splenic B cells with BAFF along with LPS and/or CD40. BAFF significantly enhanced IL-6 production from B cells stimulated with LPS alone and LPS + CD40 (*P* \< 0.01; [Fig. 5A](#F5){ref-type="fig"}), although only BAFF stimulation failed to induce IL-6 from B cells. By contrast, BAFF significantly inhibited IL-10 production from B cells stimulated with LPS (*P* \< 0.0001; [Fig. 5A](#F5){ref-type="fig"}). {#F5} We next evaluated whether BAFF inhibition would modulate cytokine production from B cells in vivo. To this end, we administered BAFFR (BAFF-receptor)--Fc, which neutralizes BAFF, or Fc control protein (control) to naïve mice. The frequency and number of IL-6--producing Beffs in the BAFFR-Fc--treated mice were significantly decreased compared with those of control mice ([Fig. 5B](#F5){ref-type="fig"}). By contrast, the frequency of IL-10--producing Bregs in the BAFFR-Fc--treated mice was significantly increased compared with that in control mice, although the number of IL-10--producing Bregs did not differ between the BAFFR-Fc--treated mice and control mice ([Fig. 5B](#F5){ref-type="fig"}). In addition, BAFFR-Fc significantly decreased the number of MZ B cells, the major subset of IL-6--producing Beffs ([Fig. 5B](#F5){ref-type="fig"}), but did not influence the number of B1 B cells, the major subset of IL-10--producing Bregs ([Fig. 5B](#F5){ref-type="fig"}). These results suggest that BAFF increases IL-6--producing Beffs but attenuates IL-10--producing Bregs. BAFF inhibition attenuates the skin and lung fibrosis of bleomycin-induced scleroderma -------------------------------------------------------------------------------------- Dysregulation of serum BAFF levels in Tsk/+ mice, a genetic mouse model for scleroderma, has been demonstrated ([@R15]). Thus, we explored the timing of changes in serum BAFF in bleomycin-induced scleroderma using ELISA. Serum BAFF levels in the bleomycin-induced scleroderma model gradually increased after bleomycin treatment ([Fig. 6A](#F6){ref-type="fig"}). To determine whether BAFF inhibition affects the skin fibrosis in the bleomycin-induced scleroderma model, we treated the mice with BAFFR-Fc, which neutralizes BAFF, or Fc control protein (control) three times a week for 4 weeks. The skin and lung fibrosis in the mice that received BAFFR-Fc treatment was significantly attenuated compared to that of the control group ([Fig. 6](#F6){ref-type="fig"}, B to E). In addition, BAFFR-Fc significantly decreased the number of IL-6--producing Beffs but did not influence the number of IL-10--producing Bregs ([Fig. 6F](#F6){ref-type="fig"}). These results suggest that BAFF inhibition is a potential therapeutic strategy for SSc via alteration of the Beff and Breg balance ([Fig. 6G](#F6){ref-type="fig"}). {#F6} DISCUSSION ========== Despite their recognized importance, the phenotype and function of IL-6--producing Beffs have thus far remained poorly understood, although B cells are known to produce large amounts of IL-6. Here, we demonstrated that CD40 and LPS synergistically induce IL-6 production from B cells and that the MZ B cell subset is a major source of IL-6--producing B cells. Furthermore, IL-6--producing Beffs play a pathogenic role in the bleomycin-induced scleroderma model, whereas IL-10--producing Bregs play a protective role. Moreover, we found that BAFF inhibition attenuates skin and lung fibrosis in the bleomycin-induced scleroderma model with reduction of IL-6--producing Beffs. Collectively, these findings suggest that B cells have reciprocal roles in the pathogenesis of SSc, exhibiting both pathogenic and protective functions ([Fig. 6G](#F6){ref-type="fig"}). CD40 is expressed on the surface of B cells, as well as dendritic cells and monocytes/macrophages, while the CD40 ligand (CD40L) is expressed on activated T cells. The CD40-CD40L interaction induces B cell survival, Ig class switching, and cytokine production and has been shown to play an important role in the pathogenesis of SSc ([@R22]). The CD40-CD40L interaction and antigen-specific signals were reported to be essential for IL-10 production from B cells ([@R3]), while TLR signals strongly augment the production of IL-10 in mice ([@R23]) and humans ([@R24]). The current study and previous ones have shown that CD40 and a TLR signal (LPS) synergistically promote IL-6 production from B cells, whereas the CD40 signal inhibited IL-10 production ([@R11], [@R23]). Although the fact that we found the MZ B cell subset to be a major source of IL-6--producing B cells is consistent with the literature ([@R11], [@R25]), this subset is also known to be a major component of IL-10--producing Bregs ([@R5], [@R7], [@R26]). Thus, the CD1d^high^ MZ B cell subset has the ability to become either IL-10--producing Bregs or IL-6--producing Beffs, and its fate depends on the stimulation by CD40 and TLR signals. Thus, it is difficult to evaluate the adaptive transfer of the CD1d^high^ MZ B cell effect in the bleomycin-induced scleroderma model. Together, these results suggest that TLR stimulation induces B cells into Bregs, while the T cell--B cell interaction upon TLR stimulation induces B cells into IL-6--producing Beffs. IL-6 is a multifunctional cytokine produced by various cell types such as B cells, T cells, monocytes, natural killer cells, and fibroblasts, although B cells are the major source of IL-6 ([@R11], [@R25]). Serum IL-6 levels are elevated in patients with diffuse SSc and are associated with the extent of skin thickness ([@R27]), and IL-6 plays a critical role in tissue fibrosis and autoimmunity in mouse models of SSc ([@R15], [@R16]). Inhibition of IL-6 suppresses skin fibrosis in a mouse model of SSc ([@R28]), and a phase 2 trial of tocilizumab showed clinically significant improvement of skin fibrosis in patients with SSc ([@R18]). Notably, the current study revealed that IL-6 deficiency in B cells alone attenuates the skin fibrosis in the bleomycin-induced scleroderma model, while IL-10 deficiency in B cells augments the skin fibrosis. B cells were shown to promote collagen production by dermal fibroblasts of SSc patients ([@R14]). IL-6--producing Beffs could infiltrate the inflamed skin tissue and promote collagen secretion by fibroblasts, although the phenotype of IL-6--producing Beffs in the skin was not consistent with that in the spleen. In contrast, the current study showed that IL-10--producing Bregs were increased in inflamed skin. Therefore, Bregs may infiltrate into the inflamed skin to attenuate the inflammation. The current study also revealed that IL-6--producing Beffs promote collagen secretion by fibroblasts through interaction with B cells and fibroblasts. B cells without stimulation did not produce IL-6; however, B cells cocultured with fibroblasts did produce IL-6. Thus, cell-cell contact with fibroblasts induces IL-6 production from B cells and augments collagen secretion by fibroblasts. Since these effects were inhibited when we used Transwells, additional factors, such as adhesion molecules, may play a role in these effects. In addition, IL-6 production was increased in coculture with B cells from IL-10^−/−^ mice, resulting in increased collagen secretion by fibroblasts. Collectively, these results suggest that IL-6 and IL-10 secretion from B cells promotes and inhibits the fibrosis in SSc, respectively. BAFF plays a critical role in the survival, maturation, and activation of B cells ([@R21]), and the serum BAFF levels are elevated in patients with various diseases, including SSc ([@R13]). B cells from SSc patients stimulated by BAFF exhibited enhanced ability to produce IL-6 ([@R13]). Consistent with these previous findings, in the present study, BAFF increased the numbers of IL-6--producing Beffs but attenuated IL-10--producing Bregs. However, Yang *et al.* ([@R29]) reported that BAFF enhanced IL-10 production of B cells from DBA/1J mice. This discrepancy may be due to the different mouse genetic backgrounds. By contrast, BAFF inhibition decreased IL-6--producing Beffs, but not IL-10--producing Bregs. Similarly, BAFF receptor--deficient mice showed depletion of B2 but not B1a B cells, a major subset of IL-10--producing Bregs ([@R30]). BAFF inhibition attenuated the skin fibrosis of the present SSc mouse model, which confirms the results of a previous study ([@R15]). There has been some success with respect to targeting B cells for SSc therapy. B cell depletion therapy with rituximab, a CD20 mAb that depletes human pan-B cells, has shown beneficial effects on skin and lung fibrosis in patients with SSc ([@R31], [@R32]); however, a phase 3 randomized controlled study is required to confirm the efficacy and safety of rituximab for the treatment of SSc. Two large randomized controlled trials of rituximab have been conducted in patients with SLE, with the expectation that it would be effective; however, these trials failed to achieve the primary end points ([@R33], [@R34]). Our present findings suggest that this ineffectiveness may have been due to depletion of not only Beffs but also Bregs. Thus, the outcome of pan-B cell depletion depends on the balance between Beffs and Bregs in a given patient. Moreover, the effect of B cell depletion was shown to be dependent on the timing and balance of the two opposing B cell functions in mouse models of SLE and MS ([@R6], [@R35]). By contrast, phase 3 clinical trials demonstrated the efficacy of belimumab, an anti-BAFF Ab, in patients with SLE ([@R36], [@R37]); belimumab has been approved by the U.S. Food and Drug Administration. Our results further shed light on the most likely reason for the superior effects of partial B cell depletion with BAFF inhibition compared to pan-B cell depletion with a CD20 mAb, given that BAFF inhibition therapy selectively depletes Beffs while sparing Bregs. However, a phase 2 study of atacicept, an inhibitor of BAFF and a proliferation-inducing ligand, did not reveal efficacy in the patients with MS ([@R38]). The effect of selective B cell depletion is not always beneficial, and it may depend on the contribution of B cells to the particular disease. BAFF inhibition therapy, rather than pan-B cell depletion, could be a potent therapeutic strategy for SSc ([Fig. 6G](#F6){ref-type="fig"}). Here, we have investigated the intracellular staining and phenotype of IL-6--producing Beffs. IL-6--producing Beffs play a pathogenic role in scleroderma, whereas IL-10--producing Bregs play a protective role. Furthermore, BAFF contributes to SSc pathogenesis by modulating cytokine-producing B cells. Thus, our study reveals that BAFF inhibition is a potential therapeutic strategy for SSc via alteration of the Beff and Breg balance. MATERIALS AND METHODS ===================== Study design ------------ We performed this study to determine whether cytokine-producing B cells control the development of scleroderma in a mouse model. To establish the model, we treated B cell--specific cytokine-deficient mice with bleomycin. The skin and lung fibrosis of the bleomycin-induced scleroderma model was attenuated in B cell--specific IL-6--deficient mice, while B cell--specific IL-10--deficient mice showed more severe skin and lung fibrosis. Subsequent histological analysis confirmed these findings. Sample sizes and end points were selected on the basis of our extensive experience with these systems. In selected experiments, the mice were randomly assigned to treatment groups, and the researchers were blinded to the treatment group during experimental procedures and raw data analysis. All animal experiments were performed according to institutionally approved protocols and in compliance with the guidelines of the Committee on Animal Experimentation of the Kanazawa University Graduate School of Medical Sciences. No animals or potential outliers were excluded from the data sets analyzed and presented herein. All in vitro studies were performed in replicates (*n* = 3, unless otherwise specified). Mice ---- Wild-type C57BL/6 mice, *Il10*^−/−^ mice, and μMT mice were obtained from the Jackson Laboratory. *Il6*^−/−^ mice were generated as previously reported ([@R39]). All mice were on the C57BL/6 background. For experiments, all mice used were 8 to 10 weeks of age and housed in a specific pathogen--free barrier facility. Generation of mixed bone marrow chimeras ---------------------------------------- Mice with B cell--specific IL-6 deficiency or B cell--specific IL-10 deficiency were generated using the mixed bone marrow chimera system, as described previously ([@R3], [@R10]). Briefly, recipient wild-type mice received 1000 cGy of x-ray irradiation. One day later, the recipients were reconstituted with a mixed inoculum of 80% μMT bone marrow cells supplemented with 20% bone marrow cells from *Il6*^−/−^ or *Il10*^−/−^ mice (a total of 2 × 10^6^ cells). Control groups received 80% wild-type and 20% bone marrow cells from *Il6*^−/−^ or *Il10*^−/−^ mice (a total of 2 × 10^6^ cells). Chimeric mice were left to fully reconstitute their lymphoid system for at least 8 to 10 weeks before bleomycin treatment. Chimerism was confirmed by B cell cytokine production using ELISA. Characterization of chimeras is outlined in fig. S5. Bleomycin-induced scleroderma model ----------------------------------- Bleomycin (Nippon Kayaku) was dissolved in sterile saline at a concentration of 1 mg/ml. The mice were treated with intradermal injections of either bleomycin or saline (300 μl; administered using a 27-gauge needle) into their shaved backs (the para-midline, lower back region) every other day for 4 weeks. BAFFR-Fc treatment ------------------ In vivo treatment murine BAFFR-Fc Chimera (BioLegend), which were made by fusing their extracellular domains to the Fc portion of human IgG1 and neutralize murine BAFF, and Fc control protein (BioLegend) were used in this study. To neutralize BAFF in vivo, mice received either murine BAFFR-Fc (2.5 mg/g, intraperitoneally, three times per week) or the same dose of Fc control protein. Determination of collagen content --------------------------------- The collagen content of the culture supernatant was determined using QuickZyme Soluble Collagen Assay (QuickZyme Biosciences), according to the manufacturer's instructions. The collagen content of the mouse and lung tissues was determined using QuickZyme Total Collagen Assay (QuickZyme Biosciences), according to the manufacturer's instructions. Total right lungs were used. Histological examination of skin and lung fibrosis -------------------------------------------------- All skin sections were obtained from the bleomycin-injected region of the lower back, as full-thickness sections extending down to the body wall musculature. Lung sections were obtained from the bleomycin-induced scleroderma model. The skin and lung samples were fixed in formalin, dehydrated, embedded in paraffin, and used for immunostaining. Sections (6 μm thick) were stained with H&E and Masson's trichrome to identify collagen deposition in the skin and lung. Dermal thickness, which was defined as the thickness of skin from the top of the granular layer to the junction between the dermis and intradermal fat, was evaluated. The severity of lung inflammation was determined by a semiquantitative scoring system, as previously described ([@R40]). Briefly, lung fibrosis in randomly chosen fields of sections from the left middle lobe examined at 100× magnification was graded on a scale of 0 (normal lung) to 8 (total fibrous obliteration of fields). All sections were evaluated independently by two investigators (Kie Mizumaki and Miyu Kano), in a blinded manner. Flow cytometry and intracellular cytokine staining analysis ----------------------------------------------------------- Single-cell leukocyte suspensions from spleens were generated by gentle dissection. The following mAbs were used: fluorescein isothiocyanate--, PE (phycoerythrin)--, PE-Cy5--, PE-Cy7--, PerCP-Cy5.5--, APC (allophycocyanin)--, APC-PECy7--, and BV421-conjugated mAbs to mouse CD4 (RM4-5), CD8 (53-6.7), CD11b (M1-70), CD19 (1D3), CD25 (MF-14), CD44 (IM7), IL-10 (MP5-20F3), and IL-10 (JES5-16E3), using LEGENDScreen Mouse PE Kit from BioLegend; CD1d (1B1), CD5 (53-7.3), CD21/CD35 (7G6), CD23 (B3B4), CD24 (M1/69), and CD45R/B220 (RA3-6B2) from BD Biosciences; and BAFF (121808) from R&D Systems. For two- to six-color immunofluorescence analysis, single-cell suspensions (10^6^ cells) were stained at 4°C using predetermined optimal concentrations of mAb for 20 min. Blood erythrocytes were lysed after staining using FACS Lysing Solution (Becton Dickinson). For intracellular staining, cells were fixed and permeabilized with a Cytofix/Cytoperm kit (BD Biosciences). Dead cells were detected by using LIVE/DEAD Fixable Aqua Dead Cell Stain Kit (Invitrogen Molecular Probes) before cell surface staining. Cells with the forward and side light scatter properties of lymphocytes were analyzed using a BD FACSCanto II (BD Biosciences). Data were analyzed with FlowJo software (version 10.2; Tree Star). B cell stimulation ------------------ Splenic B cells were purified with anti-CD19 mAb--coated microbeads or the Pan B cell isolation kit (Miltenyi Biotec) or by means of cell sorting with the FACSAria Fusion (BD Bioscience). B cells (2 × 10^6^ cells/ml) were resuspended in complete medium \[RPMI 1640 media containing 10% fetal bovine serum, penicillin (200 μg/ml), streptomycin (200 U/ml), 4 mM [l]{.smallcaps}-glutamine, and 5 × 10^−5^ M 2-mercaptoethanol (all from Gibco)\]. B cells were stimulated with an agonistic anti-CD40 mAb (10 μg/ml; FGK45, Enzo Life Sciences), BAFF (100 ng/ml; R&D Systems), LPS (10 μg/ml; *Escherichia coli* serotype 0111: B4, Sigma-Aldrich), or other TLR agonists (TLR1, Pam3CSK4, 300 ng/ml; TLR2, heat-killed *Listeria monocytogenes*, 10^8^ cells/ml; TLR3, polyriboinosinic acid/polyribocytidylic acid, 10 μg/ml; TLR5, Salmonella Typhimurium flagellin, 1 μg/ml; TLR6, Pam2CGDPKHPKSF, 100 ng/ml; TLR7, ssRNA40/LyoVec, 5 μg/ml; and TLR9, ODN1826, 5 μM; Invivogen). Enzyme-linked immunosorbent assay --------------------------------- IL-6, IL-10, or BAFF levels were determined by specific ELISA kits (R&D Systems) Intracellular cytokine staining ------------------------------- Intracellular cytokine expression was visualized by immunofluorescence staining and analyzed by flow cytometry as previously described. For IL-6 detection, cells (2 × 10^6^ cells/ml) were cultured with LPS (10 μg/ml) and anti-CD40 mAb (10 μg/ml; FGK45) for 24 hours with PIB \[PMA (50 ng/ml; Sigma-Aldrich), ionomycin (1 μg/ml; Sigma-Aldrich), and brefeldin A (supplied as 1000× solution; c)\] added during the final 5 hours of culture. PIB \[PMA (50 ng/ml; Sigma-Aldrich), ionomycin (1 μg/ml; Sigma-Aldrich), and brefeldin A (supplied as 1000× solution; BioLegend)\] was added for 5 hours. For IL-10 detection, cells (2 × 10^6^ cells/ml) were cultured with LPS (10 μg/ml) and PIB for 5 hours. Fc receptors were blocked with mouse Fc receptor mAb (2.4G2, BD Pharmingen) with dead cells detected using a LIVE/DEAD Fixable Aqua Dead Cell Stain Kit (Invitrogen) before cell surface staining. Stained cells were fixed and permeabilized using a Cytofix/Cytoperm kit (BD Pharmingen) according to the manufacturer's instructions and stained with APC-conjugated mouse anti--IL-6 or anti--IL-10 mAb. Preparation of skin cell suspensions for flow cytometry ------------------------------------------------------- A 1 cm × 1 cm piece of the bleomycin-injected skin region was minced and then digested in 7 ml of RPMI 1640 and 10% fetal bovine serum containing collagenase (2 mg/ml; Sigma-Aldrich), hyaluronidase (1.5 mg/ml; Sigma-Aldrich), and deoxyribonuclease (DNase) I (0.03 mg/ml; Sigma-Aldrich) at 37°C for 90 min. Digested cells were then passed through a 70-μm cell Falcon Cell Strainer (BD Biosciences) to generate single-cell suspensions. The cell suspension was centrifuged at 300*g* for 10 min. The pellet was resuspended in 70% Percoll solution (GE Healthcare) and then overlaid by 37% Percoll solution followed by centrifugation at 500*g* for 20 min at room temperature. Cells were aspirated from the Percoll interface and passed through a 70-μm cell strainer. Subsequently, the cells were harvested by centrifugation and washed. Immunohistochemical staining of mouse skin ------------------------------------------ Mice were treated with bleomycin for 2 weeks, and brefeldin A (250 μg per mouse; Sigma-Aldrich) was intravenouslly injected 6 hours before sample prepararion. The skin samples from bleomycin-injected mice were removed and frozen in liquid nitrogen using embedding medium for frozen tissue specimens \[Tissue-Tek OCT (optimum cutting temperature) Compound, Sakura Finetek\] and stored at −70°C until use. Frozen sections (5 μm thick) were immediately fixed in cold acetone and were incubated with rat anti-mouse B220 mAb (RA3-6B2 clone, BD Biosciences) and polyclonal goat anti-mouse IL-6 Ab (R&D Systems). Donkey anti-rat IgG with Alexa Fluor 488 or donkey anti-goat IgG with Alexa Fluor 594 (Thermo Fisher Scientific) were used as secondary Abs of rat anti-mouse B220 mAb or goat anti-mouse IL-6 mAb, respectively. Coverslips were mounted by using ProLong Diamond Antifade Mountant with DAPI (Thermo Fisher Scientific). Fluorescence microscopy was performed using a KEYENCE BZ-X710 fluorescence microscope (KEYENCE). Fibroblast culture ------------------ Skin samples were taken from E14.5 embryos of naïve wild-type mice. To obtain fibroblasts, the skin tissue was cut into 1-mm^3^ pieces, placed in sterile plastic dishes, and cultured in Dulbecco's modified Eagle's medium (Invitrogen) containing 10% heat-inactivated fetal bovine serum, penicillin (100 U/ml), and streptomycin (100 μg/ml; Invitrogen) at 37°C in a humidified 5% CO~2~ atmosphere. After 2 to 3 weeks of incubation, outgrowing fibroblasts were detached by brief trypsin treatment and recultured in the medium. Fibroblasts (10^5^ cells) were cultured without or with B cells (5 × 10^5^ cells) in 24-well plates for 3 days. For Transwell experiments, B cells (5 × 10^5^ cells) and fibroblasts (10^5^ cells) were seeded in the upper and lower chambers, respectively, of a 0.4-μm polycarbonate membrane Transwell (Nunc Dominique Dutscher). For fibroblast stimulation, cells were cultured with recombinant TGF-β1 (5 ng/ml; R&D Systems). The supernatant was harvested after culture. All experiments used fibroblasts between passages 2 and 5, depending on the number of cells obtained initially from the tissue samples. Cultured fibroblasts were adherent to the dish and maintained the typical spindle-shaped aspect. The purity of fibroblasts, as confirmed by flow cytometry, was \>99%, with no leukocytes found in the harvested cells. In each experiment, all the cell lines were examined at the same time and under the same conditions of culture (for example, cell density, passage, and days after plating). Reverse transcription polymerase chain reaction ----------------------------------------------- Total RNA was isolated from inflamed skin using RNeasy spin columns (Qiagen) and digested with DNase I (Qiagen) to remove chromosomal DNA. Total RNA was reverse-transcribed to a cDNA using a reverse transcription system with random hexamers (Promega). Cytokine mRNA was analyzed using real-time reverse transcription PCR (RT-PCR) quantification (Applied Biosystems). Real-time RT-PCR was performed on an ABI Prism 7000 sequence detector (Applied Biosystems). TaqMan probes and primers for *collagen alpha-2(I)* (*col1a2*) and *glyceraldehyde-3-phosphate dehydrogenase* (*gapdh)* were purchased from Applied Biosystems. *GAPDH* was used to normalize the mRNA. The relative expression of real-time RT-PCR products was determined according to the ΔΔ*C*~t~ method to compare target gene and GAPDH mRNA expression. Statistical analysis -------------------- Data are presented as means ± SD. Two-tailed Student's *t* test was used for comparisons between two groups, and *P* \< 0.05 was considered significant. Comparisons among three or more groups were performed with ANOVA followed by Tukey's multiple comparison test. Data were analyzed with GraphPad Prism (version 7; GraphPad Software). Study approval -------------- Animal studies were approved by the Committee on Animal Experimentation of the Kanazawa University Graduate School of Medical Sciences. Supplementary Material ====================== ###### http://advances.sciencemag.org/cgi/content/full/4/7/eaas9944/DC1 We thank M. Matsubara, Y. Yamada, and Y. Iwauchi for technical assistance. **Funding:** This work was supported by Japan Society for the Promotion of Science KAKENHI (grant no. JP16K10147). **Author contributions:** T.M., T.K., K.M., M.K., T.S., M.T., and A.O. contributed to data collection, analysis, and interpretation. Y.I. generated IL-6--deficient mice. T.M., Y.H., M.H., M.F., and K.T. designed the study and wrote the manuscript. All authors discussed the results and commented on the manuscript. **Competing interests:** The authors declare that they have no competing interests. **Data and materials availability:** All data needed to evaluate the conclusions in the paper are present in the paper and/or the Supplementary Materials. Additional data related to this paper may be requested from the authors. Supplementary material for this article is available at <http://advances.sciencemag.org/cgi/content/full/4/7/eaas9944/DC1> Fig. S1. Phenotypes of IL-6--producing B cells after in vitro culture. Fig. S2. CD25 expression on B cell is enhanced after stimulation. Fig. S3. IL-6-- and/or IL-10--producing B cells. Fig. S4. Phenotype of IL-6--producing B cells in the skin. Fig. S5. Scheme for the generation of B-IL-6^−/−^ or B-IL-10^−/−^ and corresponding control mice. Fig. S6. Lung fibrosis is attenuated in mice with B cell--specific IL-6 deficiency.

1. Field of the Invention The present invention relates to a production method of silver halide photographic emulsion in which reaction, mixing or the like in a production process of silver halide photographic emulsion is carried out by a chemical unit operation, and a production apparatus thereof. 2. Description of the Related Art In general, a silver halide photographic emulsion used for a photosensitive material is produced through a pre-ripening process in which a nucleus forming process (formation of a microcrystal dispersion of silver halide in protective colloid), a physical ripening process (crystal growth for obtaining a desired grain shape and size), and a crystal growth process are performed to form silver halide photographic emulsion grains having an objective size, shape and structure, a desalting process (removal of soluble salts from the dispersion), a sensitizing process (heat treatment performed in the presence of a sensitizing agent, for increasing sensitivity to light) for increasing the sensitivity of the emulsion after desalting, and a after-ripening process for adding various agents (sensitizing dye, stabilizing agent, and etc.) for giving various properties to the emulsion required as the need arises. Incidentally, in the foregoing production process of the silver halide photographic emulsion, two or more processes among these processes, may be combined and carried out in one operation. Further, in the foregoing production process, one or more production stages may be omitted from the production process. Furthermore, there is also a case where plural operations are repeated in each stage in order to obtain a desired emulsion. In addition, in a production system for industrially mass-producing silver halide emulsion, a so-called batch type production system using a large capacity reaction container is usually used. As a conventional batch-type production system for producing silver halide emulsion, there is proposed one using a tank 10 as a reaction container as exemplified in FIG. 37 (for example, see JP-A No. 5-173267). This tank 10 is constituted as a batch type reaction container apparatus having an agitator capable of producing of silver halide photographic emulsion at a time in a predetermined large amount, for example, 1000 l (1 t) In this tank 10, in order to agitate a solution with which the tank is filled, a magnetic agitation means 16 is provided such that an agitation vane 12 is rotatively driven through a transmission means 14 for transmitting a rotation driving force of a motor 15 in a non-contact manner by using a magnetic force. In addition, in order to perform a temperature control of the solution with which the tank is filled, a temperature control means 18 for heating or cooling the reaction solution is disposed at the outer peripheral part of the tank 10. The temperature control means 18 is constituted by use of means for heating or cooling by allowing a heat exchange medium (water, water vapor, liquid organic material, flame gas, etc.) to flow to a temperature control part, or a means for performing a temperature control by installing an element for electrically heating or cooling at the temperature control part. The tank 10 is constituted to be capable of being hermetically closed by mounting a sealing lid 20 to the tank 10. Further, an emulsion introduction pipe 22 with an opening and closing cock is disposed in the sealing lid 20 of the tank 10. Furthermore, a liquid transfer pipe 24 with an opening and closing cock is disposed at the bottom of the tank 10. In the butch type production system using this tank 10, at the nucleus forming process in the pre-ripening process at the time of producing a silver halide emulsion, a predetermined quantity of an aqueous dispersion medium solution containing at least a dispersion medium and water is injected through the emulsion introduction pipe 22 into the tank 10, and further, a silver salt solution or a silver salt solution and a halide solution are added under the conditions of pBr 2.5 or less and are agitated by the magnetic agitation means 16 for a predetermined time (several minutes), and temperature is controlled by means of a temperature control means 18 so as to keep the reaction solution in the tank 10 within a predetermined temperature range (for example, 5° C. to 45° C.), so that nuclei of minute tabular grains including, for example, a parallel twinning plane are formed. In this nucleus forming process, since solute ions are randomly walking in the solution when the nuclei are formed, minute tabular grain nuclei and a large number of other minute grains (especially, non-twin, single twin, or non-parallel double twin grains) are simultaneously formed in the tank 10. Next, in the butch-type production system using this tank 10, at the ripening process in the pre-ripening process at the time when the silver halide photographic emulsion is produced, grains other than the tabular grain nucleus are made to disappeared by the Ostwald ripening process, and the tabular grain nucleus is made to grow. In this ripening process, three ripening methods that have conventionally been used described below can be used. The first type of the ripening method is a method in which after nucleus formation, a pBr value of the reaction solution in the tank 10 is adjusted to 2.5 to 1.0, preferably 2.3 to 1.4, a solvent for AgX is added through the emulsion introduction pipe 22 (AgNO3 may be added during the ripening), agitation is performed by the magnetic agitation means 16, and the temperature of the reaction solution in the tank 10 is raised by the temperature control means 18 by preferably 10° C. or higher, more preferably 20° C. or higher with respect to the nucleus formation temperature, sob that ripening is performed for predetermined several minutes or more. The second type of the ripening method is a method in which after nucleus formation, a pBr value of the solution is adjusted to 2.5 or less, preferably 1.0 to 2.0, a first ripening is performed for predetermined several minutes or more in a state where there is no solvent for AgX, and next, AgNO3 is added through the emulsion introduction pipe 22 to increase the pBr value by 0.1 or more, preferably 0.3 or more, the solvent for AgX is added through the emulsion introduction pipe 22, agitation is performed by the magnetic agitation means 16, and the temperature of the reaction solution in the tank 10 is raised by the temperature control means 18 by preferably 10° C. or higher, more preferably 20° C. or higher with respect to the nucleus formation temperature, so that second type of ripening is performed for predetermined several minutes or more. The third type of ripening method is a method in which after nucleus formation, a pBr value of the solution is adjusted to 2.5 or less, preferably 1.0 to 2.0, agitation is performed by the magnetic agitation means 16 in a state where there is no solvent for AgX, the temperature of the reaction solution in the tank 10 is raised by the temperature control means 18 by preferably 10° C. or higher, more preferably 20° C. or higher with respect to the nucleus formation temperature, so that the third type of ripening is performed for predetermined several minutes or more. Incidentally, there is also a method in which AgNO3 is added during the ripening. Further, in the foregoing first to third type of ripening methods, there is also a method using a pressure ripening method in which the tank 10 is made a hermetically sealed system only at the time of ripening, and ripening is performed in a state where the pressure in the tank 10 at the time of nucleus ripening is more than several times as high as the atmospheric pressure. Further, there is also a method in which the ripening is performed by the foregoing first to third ripening methods in the presence of an anti-fogging agent. Next, in the batch type production system using this tank 10, after the ripening process in the pre-ripening process at the time of production of the silver halide emulsion has been ended, tabular grain nuclei are made to grow in the crystal growth process. In the crystal growth process, it is possible to use a method of adding a silver salt solution and a halide solution as a solute for growing a crystal of tabular grain nuclei, a flow acceleration addition method, a concentration acceleration addition method, and a combined addition method of two or more of these methods. In the batch type production system using this tank 10, also at the crystal growth stage in the pre-ripening process at the time of production of the silver halide emulsion, a predetermined quantity of silver salt solution and halide solution as solutes for growing the crystals of the tabular grain nuclei is injected from the emulsion introduction pipe 22 into the reaction solution stored in the tank 10, agitation is performed by the magnetic agitation means 16 for a predetermined time (several minutes), a temperature control is performed by the temperature control means 18 to bring the reaction solution in the tank 10 to a predetermined temperature, and a chemical reaction for suitably allowing to grow crystals is accelerated (see, for example, Japanese Patent Application Nos. 2-142635 and 2-43791). In the batch type production system using this tank 10, after the crystal growth process in the pre-ripening process at the time of production of the silver halide emulsion has been ended, the desalting process is carried out. The desalting process is a process of removing unnecessary materials (for example, K, Na) formed during the emulsion grain formation of the pre-ripening process, excessively existing ions (for example, Ag, Br, Cl) and the like. In the desalting process, various desalting methods, such as a flocculation method or a noodle washing method in which water washing is performed to effect desalting, or an ultrafiltration or an electro dialysis method in which desalting is carried out by separation (film), can be used. In the desalting process, for example, in the case where the flocculation method is used, the reaction solution which has been subjected to the pre-ripening process in the tank 10 as shown in FIG. 37 is taken out from the liquid transfer pipe 24, and is transferred to a desalting tank (not-show), and a flocculant is added to the reaction solution in the desalting tank, and a pH value of the solution is adjusted, so that emulsion grains together with gelatin, are flocculating-sedimented (natural sedimentation), a supernatant liquid containing unnecessary materials is removed, and next, after washing water is newly added into the desalting tank, the flocculation of gelatin is deflocculated by adjusting pH value of the solution. These processes are repeated two or three times. Further, in this batch type production system, after the desalting process at the time of production of the silver halide emulsion has been ended, an after-ripening process is carried out. This after-ripening process is a process in which the emulsion having a low sensitivity in the reaction solution after desalting process is sensitized to impart sensitivity suitable for practical use. In the sensitizing method at the after-ripening process in the batch type production system, there are a chemical sensitizing method and a spectral sensitizing method. The chemical sensitizing method is a method for increasing the intrinsic sensitivity of the emulsion. A typical chemical sensitizing method includes three kinds of methods, that is, a sulfur sensitizing method, a gold sensitizing method and a reduction sensitizing method. In the case where this chemical sensitizing method is performed, the reaction solution which has been subjected to the desalting process is transferred to a tank as a reaction container (not-shown) constituted similarly to the foregoing tank 10, a chemical sensitizing agent is metered and a predetermined quantity of the agent is added through an agent introduction pipe to the reaction solution stored in the tank. An agitation vane stirs the solution, and the temperature of the solution is controlled by a temperature control means so that the chemical sensitizing agent is uniformly distributed to emulsion grains to complete a desired chemical reaction equally. In addition, the spectral sensitizing method as the sensitizing method in the after-ripening process is a method in which in the case where the emulsions are used in a color photosensitive material or the like, sensitizing wavelength ranges are respectively widened into the wavelength ranges of the three primary colors of light, that is, blue (400 to 500 nm), green (500 to 600 nm), and red (600 to 700 nm) from the intrinsic sensitivities of the emulsions in the reaction solutions. The spectral sensitizing method is generally performed by adsorbing a sensitizing dye onto an emulsion. As the sensitizing dye used here, there is an orthochromatic sensitizing dye (for green) or a panchromatic dye (for red). The sensitizing dyes are dissolved in methanol to form a solution, or are made a dye solid dispersed solution in gelatin, and are added to the emulsion as the reaction solution. Incidentally, the dye solid dispersed solution in gelatin is prepared at a preparation process, and is temporarily refrigerated, and at the time of use, it is melted to add to the emulsion. When the spectral sensitizing method is used, the reaction solution which has been subjected to the desalting process is transferred to a tank as a reaction container (not-shown) constituted similarly to the foregoing tank 10, a solution in which a sensitizing dye is dissolved in methanol or a solution in which a sensitizing dye is made to a solid dispersed solution in gelatin (this solid dispersed solution in gelatin is prepared at a preparation process, is temporarily refrigerated, is melted at the time of use to be added to the emulsion) is metered and a predetermined quantity of solution is added through an agent introduction pipe to the reaction solution stored in the tank. The solution is stirred well by an agitation vane, the temperature of the solution is controlled by a temperature control means so that the chemical sensitizing agent is uniformly distributed to the emulsion grains and is uniformly adsorbed by the grains. In this batch type production system, after the after-ripening process in the production processes of the silver halide emulsion has been completed, a storage process is performed. The storage process is a process of temporarily storing the emulsion prepared in the batch operation for the purpose of supplying the emulsion to an emulsion coating process in continuous operation. Further, in addition to the function of temporal storage, this storage process also provides a function to stop the progress of ripening by cooling the emulsion to eliminate differences in characteristics among emulsion preparation batches by batch-blending a plurality of the same kind emulsions, as well as a function for quality assurance by measuring physical properties of the prepared emulsions to assure the characteristics of the emulsions. Thus, in the batch type production system, the equipment for the storage process is constituted by a cooling apparatus, a blend tank, a storage apparatus and the like. The cooling apparatus for stopping the progress of ripening may be constituted by a heat exchange system using a plate type heat exchanger or the like, or by a vacuum cooling system for effecting cooling by utilizing latent heat of vaporization. In this batch type production system, in order to perform the production process of the silver halide emulsion in one or plural stages, the tank 10 as the batch type reaction container device equipped with the agitator is used, and a plurality of chemicals in large amounts introduced into the tank 10 for producing an emulsion are forcibly mixed by a magnetic agitation means 16. The tank 10 as the batch type reaction container device equipped with the agitator is suitable for production of a large quantity of emulsion. However, when another new liquid chemical is injected through the emulsion introduction pipe 22 to the chemicals for producing the emulsion stored in the tank 10, and a plurality of chemicals in a large amount introduced into the tank 10 are agitated by the agitation vane 12 and are mixed, the liquid chemicals newly injected through the emulsion introduction pipe 22 are stagnant in the vicinity of the injection port of the emulsion introduction pipe 22 or circulates in the tank 10. Accordingly, in the initial state where a plurality of liquid chemicals in a large quantity for producing the emulsion are agitated by the agitation vane 12 to start mixing thereof, it is inevitable such a state that the liquid chemical newly injected through the injection port of the emulsion introduction pipe 22 is locally mixed at a high concentration into a part of the liquid chemicals for producing the emulsion stored in the tank 10 existing at a place where the chemicals are circulated in the tank 10, and a mixing concentration of the liquid chemicals becomes low at a portion which is remote from the injection port of the emulsion introduction pipe 22 and which the newly injected liquid chemical does not reach through the circulation by the agitation vane 12. Accordingly, when a plurality of liquid chemicals in a large amount for producing an emulsion are stirred by the agitation vane 12, a difference in history of a chemical change arises between one where mixing of the newly injected liquid chemical is started at a high concentration thereof and one where mixing of the newly injected liquid agent is started at a low concentration thereof, so that the compounds formed become non-uniform in the entire tank 10. Further, a non-uniform chemical reaction may occur due to a dead space existing in a small part in the tank 10, or due to variation in the liquid flow when the liquid chemicals for producing the emulsion is stirred by the agitation vane 12. In addition, when the liquid chemicals in a large quantity for producing an emulsion in the tank 10 are heated by the temperature control means 18, since the temperature control means 18 heats the chemicals through the wall of the tank 10, there is a case where when a heating process is started, the liquid chemicals for producing the emulsion in the tank 10 are rapidly heated only at the place close to the wall of the tank 10, and the temperature is not raised at the center in the tank 10, so that the temperature distribution of the liquid chemicals for producing the emulsion in the tank 10 becomes uneven, a history difference in the chemical change, and compounds formed becomes non-uniform in the entire tank 10. Furthermore, in the method of forming silver halide grains constituting the silver halide emulsion, which is industrially carried out today, there is a process in which a silver nitrate solution and a halide solution are added to a dispersion medium solution (protective colloid solution) typified by gelatin under vigorous agitation, and are mixed as quickly as possible to form silver halide grains. In this silver halide grain forming process, since an ionic reaction in which a silver ion and a halogen ion react with each other to form silver halide is very rapid, it is essential to quickly agitate and mix these two ionic solutions in a short time in order to perform a uniform reaction. Here, for example, in the case where nucleus formation is performed by a method in which a silver salt solution and a halide solution are added to a dispersion medium in the tank 10 from the emulsion introduction pipe 22 and are agitated by the agitation vane 12, a vortex is generated by the agitation vane 12 rotating at a high speed in the liquid chemicals for producing the emulsion in which the silver salt solution and the halide solution are added in the dispersion medium in the tank 10, and mixing by turbulent flow is carried out in the process in which the vortex is subdivided. Even in this case, once the nuclei thus formed circulate in the tank 10 to cause a so-called local recycling, and at the same time as the formation of the nuclei, crystal growth from the nuclei occurs in parallel, so that it is difficult to form mono dispersed nuclei. Further, in the field of silver halide photography, a tabular silver halide grain having a large light receiving area is widely used as a photosensitive element. In order to increase a light receiving efficiency, a thin tabular silver halide grain is preferable. However, in the batch type production system using the tank 10 and the agitation vane 12 mentioned above, when the agitation is performed by the agitation vane 12 to produce the silver halide emulsion, the tabular silver halide grains during the process of crystal growth pass through a high supersaturation region in the vicinity of the injection port of the emulsion introduction pipe 22 for adding silver ion or halide ion, and an adverse effect such that the thickness of the tabular grains increases is apt to occur. Furthermore, in the batch type production system using the tank 10 and the agitation vane 12, on the assumption that the quantity of silver halide emulsion produced at one time in the tank 10 is a predetermined constant quantity, the shape of the agitation vane 12 is determined to obtain an appropriate agitating state in the tank 10. Accordingly, when a production scale is changed to produce a desired quantity of emulsion, there is a fear that the characteristics of the emulsion are changed, and the preparation scale cannot be changed. Therefore, a predetermined quantity of silver halide emulsion larger than a desired quantity of emulsion must be produced, and as a result, there is a drawback that the silver halide emulsion produced in an excess amount is wastefully discarded. On the other hand, with respect to a newly prescribed silver halide emulsion developed by using an experimental apparatus, in the case where a small production system using the experimental apparatus is scaled up to a mass production system using a mass production apparatus, it is necessary to repeat trial production and product test many times in order to verify conditions under which the same characteristics as the emulsion characteristics obtained by the experimental apparatus for small production can be achieved in the newly prescribed silver halide emulsion produced by the production apparatus for mass production. Accordingly, there are problems that it takes a long time to develop the production system for mass production, and the loss of raw material consumed for the product test is large. Furthermore, it has been proposed that a microreactor is used for a part of a production process of silver halide photographic emulsion used for photosensitive material (see, for example, Japanese Patent Application No. 2001-76564). The microreactor used in this method is one of micro devices, in which a plurality of solutions introduce into each mixing space through microchannels having an equivalent diameter of several μm to several hundred μm having a cross-section when converted into a circle, to cause a chemical reaction. In such a microreactor, two kinds of solutions are made to flow through fine liquid supply passages called microchannels and are supplied as very thin lamella-like laminar flows into the mixing space, so that the two kinds of solutions are mixed and are allowed to react with each other in the mixing space (see, for example, JP-W No. 9-512742, WIPO International Publication WO 00/62913). In a fluid circuit used in such a microreactor, there is a case where it is required that three or more kinds of fluids are allowed to rapidly react with one another by the microreactor. However, the conventional microreactor is constituted such that two kinds of fluids are allowed to react with each other. Thus, in the case where three or more kinds of fluids are made to react with each other by the conventional microreactor, it is necessary that a fluid circuit is constituted such that two or more microreactors are connected in series by piping or the like, and three or more kinds of fluids are made to react with each other step wisely by using this fluid circuit. In such a fluid circuit, there is a limit in shortening a distance between a microreactor disposed at the upstream side and a microreactor disposed at the downstream side, a certain period of time is necessary to mix another fluid with two kinds of fluids in a reaction container to make to react with the fluids each other. Therefore, it is impossible to make to react with three kinds of fluids one another at the same time. Moreover, in the fluid circuit, as the kinds of fluids to be supplied are increased, the number of elements (microreactors) constituting the circuit is increased, so that the circuit structure becomes complicated. Incidentally, this applies in the case where three or more kinds of fluids are mixed at the same time. In addition, in the conventional microreactor, plural liquid supply passages respectively-have liquid supply ports facing a mixing space so as to open respective liquid supply openings, and solutions are introduced into the mixing space through these plural liquid supply ports. However, there exists a portion where the cross-section of the mixing space is abruptly enlarged with respect to the sum of the opening areas of these liquid supply ports, and there exists a portion in the mixing space where the direction of flow of solutions to be mixed is abruptly changed. The solutions are apt to stagnate in the vicinity of the portion where the cross-section is abruptly enlarged in this mixing space or in the vicinity of the portion where the direction of the flow of the solutions to be mixed is abruptly changed, and especially in the case where a reaction between solutions is a precipitation generation reaction accompanied by coalescence or growth, aggregation or deposition occurs in the stagnant part, and there is a fear that there occurs clogging due to this, or reduction of uniformity of a reaction product due to the mixture of aggregates or deposits. Further, in the conventional microreactor, according to the kinds of solutions supplied to plural liquid supply passages, a time when these solutions are mixed or a time when the mixing of the solutions accompanying a chemical reaction is performed, (hereinafter referred to as “mixing time”) is changed. That is, as the viscosity of the solution becomes high, the mixing time becomes longer in general, and in the case where the aggregation or deposition occurs accompanying the chemical reaction between the solutions, the aggregates or deposits become an inhibiting factor of mixing, that is, causes the lowering of diffusing power to the solution, and the mixing time is changed. In such a microreactor, since the passage length in the flow direction of the solutions in the mixing space is constant, in the case where the flow rate of the solutions is constant, a time (passing time) when the solutions pass through the mixing space becomes constant. Accordingly, in the case where the mixing time of the solutions in the mixing space is longer than the passing time, it is necessary to reduce the flow rate of the solutions in the mixing space, so that the processing rate of the solutions in the microreactor is lowered. At this time, in order to prevent the decrease in the process rate of the solution, it is conceivable to extend the passage length of the mixing space. However, in the case where such measures are taken, the microreactor is enlarged or the production cost is increased. Further, in the case where the passage length of the mixing space is extended more than needs, the aggregation, deposition or the like of the solution is promoted by contraries, the clogging occurs in the mixing space, and the maintenance of the microreactor becomes troublesome. Accordingly, in the foregoing conventional microreactor, an actuator is coupled to a block-shaped mixer element in which liquid supply passages branching from a supply part of a solution in the shape of the teeth of a comb are formed, a mechanical vibration is given to the mixer element by this actuator, and the mixing of plural solutions is accelerated by this mechanical vibration. However, in this conventional microreactor, the vibration is given to only the mixer element in which plural liquid supply passages are formed, and this vibration is transmitted to the solutions in the mixing space through the solutions in the liquid supply passages, so that the mixing of the solutions in the mixing space is accelerated. Thus, in such a microreactor, it is difficult to control the progress of the mixing of the solutions in the mixing space and the progress of the chemical reaction accompanying the mixing with high accuracy. For example, in the case where the chemical reaction between the solutions in the mixing space is desired to be performed stepwise, or in the case where the solution and reaction product are desired to be diffused and mixed over the whole length of the mixing space, it is difficult to realize such progress of the mixing or the chemical reaction.

1. Field of the Invention The present invention relates to a technology of setting a link to medical image data contained in enhanced image data composed of a plurality of medical image data recorded in one file, and extracting the medical image data contained in the enhanced image data, based on the link. 2. Description of the Related Art A medical image diagnosis apparatus captures an image of a subject and creates medical image data. A medical image diagnosis apparatus is, for example, an X-ray CT apparatus, an MRI apparatus, an ultrasound diagnosis apparatus, and a nuclear medical diagnosis apparatus. Medical image data generated by a medical image diagnosis apparatus is managed by a server for managing an image, and is readable at a terminal within a network. A report creation terminal for assisting creation of an interpretation report receives medical image data from the server, and displays on a monitor. This report creation terminal is used for interpretation of a medical image. An interpretation report is a document describing a problem presumed form interpretation of a displayed medical image by an interpreting doctor. For example, as disclosed in Japanese Unexamined Patent Application Publication JP-A 2005-301453, there is a case in which the report creation terminal links medical image data to an interpretation report. The report creation terminal generates link data indicating the storage destination of medical image data, and embeds the link data into an interpretation report. To embed into an interpretation report means a process of including the link data into data of the interpretation report. In a conventional technology, each medical image data composes one file, so that it is possible to include the name of a file into link data and thereby specify medical image data to link. In recent years, in the DICOM standard, a concept of enhanced image data (also referred to as bundle image data or multi-frame image data) composed of a plurality of medical image data recorded in one file, has appeared. In this DICOM standard, a plurality of medical image data generated by a medical image diagnosis apparatus are compiled in one file. In a case in which each medical image data composes one file, there is a need for establishment of communication every time the medical image data is sent and/or received. Therefore, numerous interactions between an apparatus sending the medical image data and an apparatus receiving the data are required, whereby an enormous load on the communication traffic is generated. On the contrary, in the case of the enhanced image data, all medical images can be sent and/or received in one communication, and therefore, numerous interactions are not required. Consequently, the load on the communication traffic is reduced. However, for reading an interpretation report, it is enough to acquire only a medical image that should be referred to. Medical image data actually cited in an interpretation report is only part of the enhanced image data. However, a conventional linking method is a method in which a file name is included in the link data, and the file name does not exist in the medical image data recorded in the enhanced image data. Therefore, in the case of employing the conventional linking method, it is necessary to receive the entire enhanced image data. As a result, a significant amount of time is required to display desired medical image data, and the efficiency of medical practices using an interpretation report as a reference is extremely decreased. In some terminals reading an interpretation report, resources cannot tolerate such large volume of enhanced image data, and the decrease of the medical efficiency in this case is significant. Moreover, in a case in which the entire enhanced image data is received, an enormous load is generated in the communication traffic within the network.

His remarks came after American and European bombs battered the coastal city of Surt — the rebels’ next objective — in Colonel Qaddafi’s tribal homeland on Sunday night, permitting the insurgents to advance to within 45 miles of the city. The rebels had pushed west on Sunday from Ajdabiya past the oil towns of Brega and Ras Lanuf, recapturing the two important refineries, and then set their sights on Surt. But on Monday there was no sign of a rebel takeover of Surt and the city seemed quiet, although a stream of civilian cars and some military vehicles was seen heading west from Surt toward Tripoli, 225 miles away. By late afternoon, however, hundreds of rebel cars and trucks came speeding down the road to a checkpoint near Bin Jawwad, a town directly east of Surt that has switched hands three times in the last month and seems to have split loyalties, rebel fighters said. The rebel advance had been too easy, and there had been no resistance, said Sherif Layas, a marketing manager from Tripoli who fought with the rebels. “This made us go forward,” he said. “And then we met the tanks.” With that, he said, they panicked and retreated en masse.

Q: Netbeans and C++ installation i have a litle problem using Netbeans 7.4 and Cygwin 4.x for compiling my C++ programms. I've done everything as in netbeans tutorial. I've installed gcc, gdb, g++ and make compilers. Everything is setup properly in Netbeans properties, every path. But i still get the same problem, i don't know what is this problem. I'm trying to compile Hello sample from Netbeans. Please help me. Here is the error log: "/usr/bin/make" -f nbproject/Makefile-Debug.mk QMAKE= SUBPROJECTS= .build-conf make[1]: Entering directory '/cygdrive/c/Users/Dragosh/Documents/NetBeansProjects/Welcome_2' "/usr/bin/make" -f nbproject/Makefile-Debug.mk dist/Debug/Cygwin_4.x-Windows/welcome_2.exe make[2]: Entering directory '/cygdrive/c/Users/Dragosh/Documents/NetBeansProjects/Welcome_2' mkdir -p build/Debug/Cygwin_4.x-Windows g++ -c -g -o build/Debug/Cygwin_4.x-Windows/welcome.o welcome.cc In file included from /usr/include/sys/reent.h:14:0, from /usr/include/wchar.h:6, from /usr/lib/gcc/x86_64-pc-cygwin/4.8.1/include/c++/cwchar:44, from /usr/lib/gcc/x86_64-pc-cygwin/4.8.1/include/c++/bits/postypes.h:40, from /usr/lib/gcc/x86_64-pc-cygwin/4.8.1/include/c++/iosfwd:40, from /usr/lib/gcc/x86_64-pc-cygwin/4.8.1/include/c++/ios:38, from /usr/lib/gcc/x86_64-pc-cygwin/4.8.1/include/c++/ostream:38, from /usr/lib/gcc/x86_64-pc-cygwin/4.8.1/include/c++/iostream:39, from welcome.cc:31: /usr/include/sys/_types.h:72:20: fatal error: stddef.h: No such file or directory #include <stddef.h> ^ compilation terminated. nbproject/Makefile-Debug.mk:66: recipe for target 'build/Debug/Cygwin_4.x-Windows/welcome.o' failed make[2]: *** [build/Debug/Cygwin_4.x-Windows/welcome.o] Error 1 make[2]: Leaving directory '/cygdrive/c/Users/Dragosh/Documents/NetBeansProjects/Welcome_2' nbproject/Makefile-Debug.mk:59: recipe for target '.build-conf' failed make[1]: *** [.build-conf] Error 2 make[1]: Leaving directory '/cygdrive/c/Users/Dragosh/Documents/NetBeansProjects/Welcome_2' nbproject/Makefile-impl.mk:39: recipe for target '.build-impl' failed make: *** [.build-impl] Error 2 BUILD FAILED (exit value 2, total time: 467ms) A: Got this issue with cygwin too, after last update to 2.830 (see setup.exe version). I am using 64 bit version. To verify that we have the same issue, try manualy compiling something supersimple with g++ usgin cygwin terminal. I checked with: $ echo -e "#include <iostream>\n int main() { return 0; }" | g++ -xc++ - And got: In file included from /usr/include/sys/reent.h:14:0, from /usr/include/wchar.h:6, from /usr/lib/gcc/x86_64-pc-cygwin/4.8.1/include/c++/cwchar:44, from /usr/lib/gcc/x86_64-pc-cygwin/4.8.1/include/c++/bits/postypes.h:40, from /usr/lib/gcc/x86_64-pc-cygwin/4.8.1/include/c++/iosfwd:40, from /usr/lib/gcc/x86_64-pc-cygwin/4.8.1/include/c++/ios:38, from /usr/lib/gcc/x86_64-pc-cygwin/4.8.1/include/c++/ostream:38, from /usr/lib/gcc/x86_64-pc-cygwin/4.8.1/include/c++/iostream:39, from <stdin>:1: /usr/include/sys/_types.h:72:20: fatal error: stddef.h: No such file or directory #include <stddef.h> ^ compilation terminated. I noticed that there are two folders of gcc here C:\cygwin\lib\gcc\x86_64-pc-cygwin\4.8.1 C:\cygwin\lib\gcc\x86_64-pc-cygwin\4.8.2 and g++ --version gives 4.8.2 Running Cygwin's latest Setup.exe and looking for installed packets showed that versions mismatch for gcc-core and gcc-g++ : gcc-core = 4.8.2-1 gcc-c++ = 4.8.1-3 I downgraded gcc-core to 4.8.1-3 and fixed the issue.

The past reporting week (October 12-18) saw very little solar activity, with a sunspot number of 12 on October 15, meaning the average daily sunspot number was only 1.7, down from the already low average of 8.4 over the previous seven days.

Cytomorphology Versus Conventional Microbiological Tests in the Diagnosis of Tuberculous Lymphadenitis. To determine the accuracy of Fine Needle Aspiration Cytology (FNAC) in the diagnosis of tuberculous lymphadenitis. Comparative cross-sectional study. Department of Pathology, Khalifa Gul Nawaz Teaching Hospital (KGNTH), Bannu, from September 2012 to March 2013. FNAC of enlarged lymph nodes was performed in the Department of Pathology, KGNTH, Bannu. Smears of the aspirates were examined under light microscope after staining with Haematoxylin and Eosin (H & E) stains. In cases of chronic lymphadenitis, the smears were stained with Ziehl-Neelsen (ZN) stain for Acid Fast Bacilli (AFB). If no AFB was visualized, the aspirate was subjected to culture on Lowenstein Jensen (LJ) medium for yield of AFB. The results were analyzed by Microsoft Excel software. Chronic granulomatous lymphadenitis was found in 110 (46.81%) out of 235 cases. AFB were seen in aspirates of 43/110 (39.09%) cases by direct microscopy. Among the remaining 67 aspirates subjected to LJ medium, only 07 (10.45%) yielded growth of AFB. Smears of 4/15 (3.6%), 13/47 (11.7%) and 33/48 (29.7%) cases with haemorrhagic, inflammatory and caseous background respectively, were confirmed by conventional microbiologic tests. Out of 125 nongranulomatous lymphadenitis cases only 05 were confirmed to be due to tuberculosis by direct microscopy while culture was not positive in any case. Thus accuracy of FNAC was 72.34%. FNAC has a good accuracy in diagnosing tuberculous lymphadenopathy.

Asymmetric halogeno-bridged complexes: new reagents in organometallic synthesis and catalysis. Several methods to synthesize bimetallic complexes in which two different metal fragments are connected by halide bridges are described. Using simple starting materials a large pool of structurally defined bimetallic complexes with unique chemical reactivities can be prepared in short time. Applications in organometallic synthesis and homogeneous catalysis are discussed.

My love of JRPGs began in childhood and remains to this day. There is something about the genre’s anime-style graphics, simplistic tunes, turn-based battles, and quests to save the world that are qualities that I cannot resist. In many ways, Fernz Gate captures the essence of the genre. However, the game is imperfect and it often feels like a shell of what a JRPG could be. Telling stories of grand adventures should be at the center of any quality JRPG. Fernz Gate makes a solid attempt at crafting an engaging tale. Players follow the main character, a typical high school boy named Alex. One day, Alex awakens to find himself in Fernland, an alternate dimension full of swords and sorcery. Disoriented by his new surroundings, Alex is fortunate enough to be found by a kind girl named Toril. She provides Alex with all the important knowledge regarding Fernland, a place to which individuals from other worlds are randomly transported. In the past, these lost souls would be guided home by a powerful Goddess. However, at the time of Alex’s arrival in Fernland, this isn’t possible. The Goddess’ magic is being subdued by the evil Overlord Clangorrah, who is attempting to gain power for himself. Consequently, the number of people from other dimensions in Fernland has been steadily increasing. As Alex’s time in Fernland progresses, he meets other displaced people. Alex joins these other lost souls in a resistance group to fight the power-hungry Clangorrah. This is Toril, a party member and the first friendly face Alex meets in Fernland. It is very likely that the plot sounds vaguely familiar here, and that’s because this game is chock-full of cliches. A perfect example of this is the Overlord, whose flimsy motivations for committing acts of evil accompany his unsettling green skin, muscular body, and not-quite-human features. To their credit, the writers did attempt to stray away from pure cliche, as the plot throws some curveballs near the end of the story. That said, even these surprises lean on tried-and-true tropes. However, Cliched or not, there is something to be said for a timeless tale of saving the world. You can tell this is an evil character just by looking at him. When I’m in the mood for a self-indulgent game, I want the mechanics to be well crafted. Fernz Gate does a decent job of implementing solid gameplay that’s admittedly uninspired. The battles are simple and turn-based, which means they sometimes get repetitive. There is also an upgrade menu to improve your weapons. It is not the most intuitive upgrade system and often felt as if I was randomly fusing weapons together, but it is acceptable. Interestingly enough, the game also includes a mini farm simulator. Players can grow fruit that increases character stats, such as speed or strength. All of these mechanics are decently executed, but they are by no means groundbreaking. In other areas, Fernz Gate utilizes fresher mechanics. The simple battle system is reinvigorated with the use of “buddies”. Players assign these buddies to members of your party and join you in battle. Specific combinations of party members and buddies unlock unique bonuses, such as increased magic damage. This kept battles entertaining because I was constantly trying out new combinations of characters. Implemented correctly, the buddy system can make battles a breeze. Fernz Gate‘s dungeon exploration is well-executed. As someone who has played a lot of JRPGs, random battles can get irritating while exploring dungeons. Fernz Gate addresses this common problem by placing Curios, in the form of purple monuments, in every dungeon. These monuments allow players to choose the rate of random encounters. I loved this feature because it let me explore dungeons quickly without running into an excessive number of enemies. As evident from the Curios mechanic, this is a game that strives to meet players’ individual needs. Upon starting a new game, players choose a difficulty setting; these range from easy to expert and can be adjusted at any time. As the difficulty increases, so do the in-game rewards. Furthermore, there is a lot of content packed into the game. This includes side quests, battle arenas, and high-level areas full of monsters. There is even an unlockable “true ending” to reward dedicated players. I may have been able to beat the main quest in 13 hours, but Fernz Gate easily contains several more hours of content. The design of the start menu makes it quite clear that this was originally a mobile game. Fernz Gate does some things right, but it also disappoints. The games most glaring issues all stem from the fact that this is clearly a mobile port. Some design and technical decisions that work on a phone do not always work on a console, including the option to buy gems to purchase in-game items. This is a mobile game standard, and it doesn’t feel right on the Switch. Likewise, the game’s mobile roots are apparent in its design. The start menu buttons look like they were intended for a touchscreen. On the Switch, they can only be selected with a controller, which is a shame because the system has touchscreen capabilities. These details hurt the overall gameplay experience. These “Get Item!” buttons would be so satisfying to physically tap using the touch screen. Beyond the port-related issues, the game also suffers from some clunky controls. Although they are solid in battle, the controls are a real issue when wandering the map. Characters move very quickly and without precision, which ends up looking very silly. This was distracting at times. One of my biggest grievances with Fernz Gate is with its stylistic choices and character design. I have always enjoyed exploring towns in JRPGs, but this was not the case in Fernz Gate. The level designs felt awkward; houses and items had strange shading and proportions. I might have been able to overlook this if the game had offered unique town designs. However, the towns all look rather similar and this eventually gets boring. The same can be said of the music. Although it never actively hindered my gameplay experience, the music was wholly forgettable. Sadly, the poor world building here makes it nearly impossible to become immersed. The disappointing level design is in stark contrast to the adorable, anime-style characters. The art is well done and charming. However, many of the characters fall back on cliches while others bear uncanny resemblances to other famous characters. This left me feeling disappointed. Some may consider this a homage to other JRPGs, but it felt like lazy and uninspired character design to me. This character with an adorable animal that lives in his ‘fro reminds me of a certain AAA JRPG. In many ways, Fernz Gate feels like the skeleton of a good JRPG. There are elements that I found quite fun. The story has a few surprising moments, the characters are lovable, and the buddy system keeps battles interesting. However, this game fails to do anything truly innovative and some features feel out of place on the Switch. If you’re gaming on a budget and absolutely need to get that JRPG fix, Fernz Gate is a decent game for $12.99. However, personally, I was rather indifferent to the whole experience it offered. Craving an RPG, but not digging this one? Personally, I enjoyed Earthlock. If sci-fi is more your thing, check out Zeno’s review of Cosmic Star Heroine. I’m always looking for JRPG recommendations, so come join our Discord and ping me @pechorin19 with some suggestions! With that, I’d like to remind our lovely readers that this site is run by passionate, Nindie-loving volunteers. Reaching out to developers, keeping a site running, writing, and editing are all time consuming. If you’d like to keep us ad-free, consider becoming a Patron or buying us a Ko-Fi.

Zviad Zviad (Georgian: ზვიად) is a Georgian masculine given name. Notable people with the name include: Zviad Endeladze (born 1966), Georgian footballer Zviad Gamsakhurdia (1939–1993), dissident, scientist, writer; the first elected post-Soviet President of the Republic of Georgia Zviad Izoria (born 1984), chess grandmaster Zviad Jeladze (born 1973), Georgian footballer Zviad Kvachantiradze (born 1965), Georgian diplomat Zviad Sturua (born 1978), Georgian association footballer Category:Georgian masculine given names es:Zviad

--- abstract: 'This paper is the fourth in a series devoted to the development of a rigorous renormalisation group method for lattice field theories involving boson fields, fermion fields, or both. The third paper in the series presents a perturbative analysis of a supersymmetric field theory which represents the continuous-time weakly self-avoiding walk on $\Zd$. We now present an analysis of the relevant interaction functional of the supersymmetric field theory, which permits a nonperturbative analysis to be carried out in the critical dimension $d = 4$. The results in this paper include: proof of stability of the interaction, estimates which enable control of Gaussian expectations involving both boson and fermion fields, estimates which bound the errors in the perturbative analysis, and a crucial contraction estimate to handle irrelevant directions in the flow of the renormalisation group. These results are essential for the analysis of the general renormalisation group step in the fifth paper in the series.' author: - 'David C. Brydges[^1] and Gordon Slade$^*$' bibliography: - '../../bibdef/bib.bib' title: ' A renormalisation group method. IV. Stability analysis ' --- Introduction {#sec:ie} ============ This paper is the fourth in a series devoted to the development of a rigorous renormalisation group method. The method has been applied to analyse the critical behaviour of the continuous-time weakly self-avoiding walk [@BBS-saw4-log; @BBS-saw4], and the $n$-component $|\varphi|^4$ spin model [@BBS-phi4-log], in the critical dimension $d = 4$. In both cases, logarithmic corrections to mean-field scaling are established using our method. In part I [@BS-rg-norm] of the series, we presented elements of the theory of Gaussian integration and developed norms and norm estimates for performing analysis with Gaussian integrals involving both boson and fermion fields. In part II [@BS-rg-loc], we defined and analysed a localisation operator whose purpose is to extract relevant and marginal directions in the dynamical system defined by the renormalisation group. In part III [@BBS-rg-pt], we began to apply the formalism of parts I and II to a specific supersymmetric field theory that arises as a representation of the continuous-time weakly self-avoiding walk [@BIS09; @BBS-saw4-log], by studying the flow of coupling constants in a perturbative analysis. We now prove several nonperturbative estimates for the supersymmetric field theory studied in part III. These estimates are essential inputs for our analysis of a general renormalisation group step in part V [@BS-rg-step], and therefore for the analysis of the critical behaviour of the continuous-time weakly self-avoiding walk in dimension $d = 4$ in [@BBS-saw4-log; @BBS-saw4]. The results in this paper include: proof of stability of the interaction, estimates which enable control of Gaussian expectations involving both boson and fermion fields, estimates which bound the errors in the perturbative analysis of part III and thereby confirm that the perturbative analysis does indeed isolate leading contributions, and a crucial contraction estimate to handle irrelevant directions in the flow of the renormalisation group. All these results are needed in our analysis of a general renormalisation group step in part V. The methods and results developed in this paper are of wider applicability, but for the sake of concreteness, and for the purposes of our specific application in [@BBS-saw4-log; @BBS-saw4], we formulate the discussion in the context of the supersymmetric field theory studied in part III. Supersymmetry is helpful: it ensures that the partition function is equal to $1$, so it need never be estimated. Several mathematically rigorous approaches to renormalisation in statistical mechanics and quantum field theory have been proposed in recent decades, e.g., the books [@BG95; @Riva91; @Salm99]. Characteristic features of the approach we develop are: (i) there is no partition of unity in field space to separate large and small fields, and (ii) fluctuation fields have finite range of dependence. The avoidance of partitions of unity is important for us because it is easier to maintain supersymmetry without them. The use of finite-range fluctuation fields bears some similarity to the wavelet program reviewed in [@Fede87], but has better translation invariance properties. An attractive feature of (ii) is that independence of Gaussian fields replaces cluster expansions. The price to be paid for avoiding partitions of unity is that norms must control the size of the basic objects in all of field space, including large fields. The goal of the present paper is to acquire this control. Our analysis has antecedents in [@Abde07; @BDH95; @MS08], though our setting includes fermions as well as bosons. A systematic development of appropriate norms is given in [@BS-rg-norm]. Part of the need for these norms is to define complete spaces in order to apply the dynamical system analysis of [@BBS-rg-flow] (discussion of past errors related to completeness can be found in [@Abde07]). The norms include a notion that we call “regulators” because they control (regulate) growth when fields are large. These are always a delicate part in this approach and important ideas that guide their choice appear in [@DH00; @Falc12]. For our field theory, the choice of regulators is less delicate because the $\phi^4$ term suppresses large fields. Another feature of our analysis is the inclusion of observable fields to permit control of correlation functions; somewhat related ideas were introduced in [@DH92]. Different methods to construct the correlations in the infinite volume have been developed in [@Falc13]. The renormalisation group can be defined directly in infinite volume, but until [@Dimo09] and [@Falc13] it was not demonstrated that the infinite volume theory defined in this way coincides with the infinite volume defined by taking limits of correlation functions and pressures defined in finite volume. Our analysis also prepares the way for results about this question for the weakly self-avoiding walk. In the remainder of Section \[sec:ie\], we give the fundamental definitions and provide an informal overview of the results of this paper. The main results are then stated precisely in Section \[sec:IE\]. Proofs are given in Sections \[app:sp\]–\[sec:ipcl\]. In Appendix \[sec:Lp\], we prove a lattice Sobolev inequality that lies at the heart of our stability estimates. Finally, Appendix \[sec:further-ie\] concerns estimates of a more specialised nature that are required for the analysis of a single renormalisation group step in part V [@BS-rg-step]. Our focus throughout the paper is on the case $d=4$. Object of study {#sec:study} --------------- We begin with several definitions needed to formulate our results. Many of these definitions are recalled from parts III and I. We begin by introducing the covariance decomposition which provides the basis for a multi-scale analysis. We then introduce the space of boson and fermion fields, and define the interaction functional $I$. We also recall the definition of the renormalised polynomial $\Vpt$ from part III, and the definitions of the norms and regulators from part I. ### Covariance decomposition {#sec:cd} Let $d \ge 4$ and let $\Lambda = \Zd/L^N\Z$ denote the discrete $d$-dimensional torus of side $L^N$, with $L>1$ fixed (large). We are interested in results which remain useful in the infinite volume limit $N \to \infty$. There are several places in this paper where $L$ must be taken large, depending on unimportant parameters such as the dimension $d$, or combinatorial constants. We do not comment explicitly on each occasion where $L$ must be taken to be large, but instead *we assume throughout the paper that $L$ is large enough to satisfy each such requirement that is encountered*. For $e$ in the set $\units$ of $2d$ nearest neighbours of the origin in $\Zd$, we define the finite difference operator $\nabla^e \phi_x = \phi_{x+e}-\phi_x$, and the Laplacian $\Delta_\Zd = -\frac{1}{2}\sum_{e \in \units}\nabla^{-e} \nabla^{e}$. Let $C= (-\Delta_\Lambda + m^2)^{-1}$, where $m^2>0$ is a positive parameter and $\Delta_\Lambda$ denotes the discrete Laplacian on $\Lambda$. We fix $N$ large and $m^2$ small, and wish to perform an analysis which applies uniformly in $N,m^2$. We require decompositions of the covariances $(\Delta_\Zd + m^2)^{-1}$ and $C=(-\Delta_\Lambda +m^2)^{-1}$. For the former, the massless Green function is well-defined for $d>2$ and we may consider $m^2 \ge 0$, but for the latter we must take $m^2>0$. In [@BBS-rg-pt Section \[pt-sec:Cdecomp\]], there is a detailed discussion of decompositions we use for each of these covariances, based on [@Baue13a] (see also Section \[sec:frp\] below). In particular, in [@BBS-rg-pt Section \[pt-sec:Cdecomp\]] a sequence $(C_j)_{1 \le j < \infty}$ (depending on $m^2 \ge 0$) of positive definite covariances on $\Zd$ is defined, such that $$\lbeq{ZdCj} (\Delta_\Zd + m^2)^{-1} = \sum_{j=1}^\infty C_j \quad \quad (m^2 \ge 0).$$ The covariances $C_j$ are translation invariant and have the *finite-range* property $$\label{e:fin-range} C_{j;x,y} = 0 \quad \text{if \; $|x-y| \geq \frac{1}{2} L^j$}.$$ For $j<N$, the covariances $C_j$ can therefore be identified with covariances on $\Lambda$, and we use both interpretations. We define $$\begin{aligned} \lbeq{wjdef} w_j &= \sum_{i=1}^j C_i \quad\quad (1 \le j < \infty),\end{aligned}$$ and note that $w_j$ also obeys . There is also a covariance $C_{N,N}$ on $\Lambda$ such that $$\lbeq{NCj} C=(-\Delta_\Lambda + m^2)^{-1} = \sum_{j=1}^{N-1} C_j + C_{N,N} \quad \quad (m^2 > 0).$$ Thus the finite volume decomposition agrees with the infinite volume decomposition except for the last term in the finite volume decomposition, which is the single term that accounts for the torus. The expectation $\Ex_C$ denotes the combined bosonic-fermionic Gaussian integration on $\Ncal$, with covariance $C$, defined in [@BS-rg-norm Section \[norm-sec:Grass\]]. The integral is performed successively, using $$\lbeq{progexp} \Ex_C = \Ex_{C_N} \circ \Ex_{C_{N-1}} \theta \circ \cdots \circ \Ex_{C_1}\theta,$$ where $\theta$ defines a type of convolution and is discussed further below. ### Fields and field polynomials We study a field theory which consists of a complex boson field $\phi : \Lambda \to \C$ with its complex conjugate $\bar\phi$, a pair of conjugate fermion fields $\psi,\bar\psi$, and a *constant* complex observable boson field $\sigma \in \C$ with its complex conjugate $\bar\sigma$. The fermion field is given in terms of the 1-forms $d\phi_x$ by $\psi_x = \frac{1}{\sqrt{2\pi i}} d\phi_x$ and $\bar\psi_x = \frac{1}{\sqrt{2\pi i}} d\bar\phi_x$, where we fix some square root of $2\pi i$. This is the supersymmetric choice discussed in more detail in [@BS-rg-norm Sections \[norm-sec:df\]–\[norm-sec:supersymmetry\]] and used in [@BBS-rg-pt]. Let two points $\pp,\qq \in \Lambda$ be fixed. We work with an algebra $\Ncal$ which is defined in terms of a direct sum decomposition $$\label{e:Ncaldecomp} \Ncal = \Ncal^\varnothing \oplus \Ncal^a \oplus \Ncal^b \oplus \Ncal^{ab}.$$ Elements of $\Ncal^\varnothing$ are given by finite linear combinations of products of an even number of fermion fields with coefficients that are functions of the boson fields. This restriction to forms of even degree results in a commutative algebra. Elements of $\Ncal^a, \Ncal^b , \Ncal^{ab}$ are respectively given by elements of $\Ncal^\varnothing$ multiplied by $\sigma$, by $\bar\sigma$, and by $\sigma\bar\sigma$. For example, $\phi_x \bar\phi_y \psi_x \bar\psi_x \in \Ncal^\varnothing$, and $\sigma \bar\phi_x \in \Ncal^a$. There are canonical projections $\pi_\alpha: \Ncal \to \Ncal^\alpha$ for $\alpha \in \{\varnothing, a, b, ab\}$. We use the abbreviation $\pi_*=1-\pi_\varnothing = \pi_a+\pi_b+\pi_{ab}$. The algebra $\Ncal$ is discussed further around [@BS-rg-loc] (there $\Ncal$ is written $\Ncal/\Ical$ but to simplify the notation we write $\Ncal$ here instead). The parameter $p_\Ncal$ which appears in its definition is a measure of the smoothness of elements of $\Ncal$ (see [@BS-rg-norm Section \[norm-sec:Ncal\]]); its precise value is unimportant and can be fixed to be larger than the degree of polynomials encountered in practice in the application of the stability bounds. Constants in estimates may depend on its value, in an unimportant way. We define the forms $$\label{e:addDelta} \tau_x = \phi_x \bar\phi_x + \psi_x \bar\psi_x, \quad\quad \tau_{\nabla \nabla,x} = \frac 12 \sum_{e \in \units} \left( (\nabla^e \phi)_x (\nabla^e \bar\phi)_x + (\nabla^e \psi)_x (\nabla^e \bar\psi)_x \right) ,$$ $$\begin{aligned} \tau_{\Delta,x} &= \frac 12 \left( (-\Delta \phi)_{x} \bar{\phi}_{y} + \phi_{x} (-\Delta \bar{\phi})_{y} + (-\Delta \psi)_{x} \bar{\psi}_{y} + \psi_{x} (-\Delta \bar{\psi})_{y} \right) .\end{aligned}$$ Let $\Qcalnabla$ denote the vector space of polynomials of the form $$\begin{gathered} V = V_{\varnothing} + V_{\pp} + V_{\qq} + V_{\pp\qq},\end{gathered}$$ where $$\begin{gathered} V_{\varnothing} = g \tau^{2} + \nu \tau + z \tau_{\Delta} + y \tau_{\nabla \nabla}, \quad V_{\pp} = \lambda_{\pp} \sigma \bar{\phi}, \quad V_{\qq} = \lambda_{\qq}\bar{\sigma} \phi, \quad V_{\pp \qq} = q_{\pp\qq} \bar{\sigma}\sigma \label{e:Vx} ,\end{gathered}$$ $$\begin{aligned} \label{e:lambda-defs} & \lambda_{\pp} = -\lambdaa \,\1_{\pp}, \quad\quad \lambda_{\qq} = -\lambdab \,\1_{\qq}, \quad\quad q_{\pp\qq} = -\frac{1}{2} (\qa\1_{\pp} + \qb\1_{\qq}) ,\end{aligned}$$ $g,\nu,y,z,\lambdaa,\lambdab,\qa,\qb \in \C$, and the indicator functions are defined by the Kronecker delta $\1_{a,x}=\delta_{a,x}$. For $X \subset \Lambda$, we write $$\label{e:VXdef} V(X)=\sum_{x\in X}V_x.$$ There is an important scale, called the *coalescence scale*, defined by $$\label{e:Phi-def-jc} j_{\pp \qq} = \big\lfloor \log_{L} (2 |\pp - \qq|) \big\rfloor .$$ We assume that $\pi_{ab}V=0$ for $j<j_{ab}$; note that if the coefficient $q$ is initially equal to zero, then under the flow [@BBS-rg-pt] it remains zero below the coalescence scale due to the assumption . The goal of our analysis is to understand the Gaussian integral $\Ex_C e^{-V(\Lambda)}$. Given a positive-definite matrix $C$ whose rows and columns are indexed by $\Lambda$, we define the *Laplacian* $$\label{e:LapC} \Lcal_C = \frac 12 \Delta_{C} = \sum_{u,v \in \Lambda} C_{u,v} \left( \frac{\partial}{\partial \phi_{u}} \frac{\partial}{\partial \bar\phi_{v}} + \frac{\partial}{\partial \psi_{u}} \frac{\partial}{\partial \bar\psi_{v}} \right)$$ (see [@BS-rg-norm]). The Laplacian is intimately related to Gaussian integration. To explain this, suppose we are given an additional boson field $\xi,\bar\xi$ and an additional fermion field $\eta, \bar\eta$, with $\eta = \frac{1}{\sqrt{2\pi i}}d\xi$, $\bar\eta = \frac{1}{\sqrt{2\pi i}}d\bar\xi$, and consider the “doubled” algebra $\Ncal(\Lambdabold\sqcup \Lambdabold')$ containing the original fields and also these additional fields. We define a map $\theta : \Ncal(\Lambdabold) \to \Ncal(\Lambdabold\sqcup \Lambdabold')$ by making the replacement in an element of $\Ncal$ of $\phi$ by $\phi+\xi$, $\bar\phi$ by $\bar\phi+\bar\xi$, $\psi$ by $\psi+\eta$, and $\bar\psi$ by $\bar\psi+\bar\xi$. According to [@BS-rg-norm Proposition \[norm-prop:conv\]], for a *polynomial* $A$ in the fields, the Gaussian expectation with covariance $C$ can be evaluated using the Laplacian operator via $$\label{e:EWick} \Ex_C \theta A = e^{\Lcal_C} A,$$ where the fields $\xi,\bar\xi,\eta,\bar\eta$ are integrated out by $\Ex_C$, with $\phi, \bar\phi, \psi, \bar\psi$ kept fixed, and where $e^{\Lcal_C}$ is defined by its power series. ### Form of interaction {#sec:formint} In [@BBS-rg-pt Section \[pt-sec:WPjobs\]], we discussed reasons to define an interaction $$I_{j}(V,\Lambda)= e^{-V(\Lambda)} (1+ W_{j}(V,\Lambda)),$$ where $W_{j}$ is a certain non-local polynomial in the fields whose definition is recalled below. Our main object of study in this paper is a modified version of $I_{j}$ which is defined on subsets of $\Lambda$. We recall the relevant definitions from [@BBS-rg-pt]. For polynomials $V',V''$ in the fields, we define bilinear functions of $V'$ and $V''$ by $$\begin{aligned} \label{e:FCAB} F_{C}(V',V'') & = e^{\Lcal_C} \big(e^{-\Lcal_C}V'\big) \big(e^{-\Lcal_C}V'' \big) - V'V'', \\ \label{e:Fpi} F_{\pi ,C}(V',V'') &= F_{C}(V',\pi_\varnothing V'') + F_{C}(\pi_* V',V'').\end{aligned}$$ By definition, when $V'$ is expanded in $F_{C} (V',V'')$ as $V'=\pi_{\varnothing} V' + \pi_{*} V'$, there are cross-terms $F_C(\pi_\varnothing V', \pi_* V'') + F(\pi_* V',\pi_\varnothing V'')$, and is obtained from by replacing these cross-terms by $2 F_{C}(\pi_{*}V' , \pi_{\varnothing}V'')$. This unusual bookkeeping is appropriate (indeed necessary) in the proof of Proposition \[prop:Wbounds\]. For nonempty $X \subset \Lambda$, the space $\Ncal (X)$ is defined in [@BS-rg-norm] as consisting of elements of $\Ncal$ which depend on $\phi_x,\bar\phi_x,\psi_x,\bar\psi_x$ only with $x \in X$. Recall from [@BS-rg-loc] that we defined $F \in \Ncal_{X}$ to mean that there exists a coordinate patch $\Lambda '$ such that $F \in \Ncal (\Lambda')$ and $X \subset \Lambda'$, and we defined the condition $F \in \Ncal_X$ to guarantee that neither $X$ nor $F$ “wrap around" the torus. The operator $\LT_X : \Ncal_X \to \Vcal(X)$ is defined in [@BS-rg-loc Definition \[loc-def:LTsym\]], and the particular specification we use is that described in [@BBS-rg-pt Section \[pt-sec:loc-specs\]]. In particular, the *field dimensions* are $[\phi]=[\bar\phi]=[\psi]=[\bar\psi] =\frac{d-2}{2}$, and we set $d_+ = d$ on $\Ncal^\varnothing$. On $\Ncal^{ab}$, we take $d_+=0$. When $\LT$ acts at scale $k$ (in the sense discussed in [@BBS-rg-pt Section \[pt-sec:loc-specs\]]), on $\Ncal^a$ and $\Ncal^b$ we take $d_+=[\phi]=\frac{d-2}{2}=1$ if $k<j_{\pp\qq}$, and $d_+=0$ for $k \ge j_{\pp\qq}$. For $x\in \Lambda$, with $w_j$ given by we define $$\begin{aligned} \label{e:Wwdef} W_j(V,x) &= \frac 12 (1-\LT_{x}) F_{\pi,w_j}(V_x,V(\Lambda)) \quad\quad (j<N).\end{aligned}$$ For $j<N$, the above application of $\LT_x$ is well-defined since $F_{\pi,w_j}(V_x,V(\Lambda)) \in \Ncal_x$ due to the finite-range property of $w_j$. For $X \subset \Lambda$, we then define $$\label{e:WLTF} W_j(V,X)= \sum_{x \in X} W_j(V,x).$$ By definition, $w_0=0$ and $W_0=0$. We consider the natural paving of $\Lambda$ by disjoint blocks of side length $L^j$, for $j=0,\ldots, N$. The set of all scale-$j$ blocks is denoted $\Bcal_j$, and $\Pcal_j$ denotes the set whose elements are finite unions of blocks in $\Bcal_j$. We refer to elements of $\Pcal_j$ as scale-$j$ *polymers*. Given a polynomial $V\in \Vcal$, and $X \subset \Lambda$, let $$\label{e:Icaldef} \Ical(V,X) = e^{-V(X)}.$$ The interaction is defined, for $B \in \Bcal_j$ and $X \in \Pcal_j$, by $$\label{e:Fsoptb} I_j(V,B) = \Ical(V,B) \left( 1+W_j(V,B) \right) , \quad \quad I_j(V,X) = \prod_{B \in \Bcal_{j}(X)} I_j(V,B).$$ Due to the finite-range property , $I_j(V,B)\in \Ncal(B^+)$, where $B^+$ denotes the union of $B$ with every block $B'$ such that $B \cup B'$ is connected. We often write $I_j(V,X) = I_j^X(V)$. We also consider the interaction defined, for $b \in \Bcal_{j-1}$ and $X \in \Pcal_{j-1}$, by $$\label{e:Itildef} \tilde I_{j}(V,b) = \Ical(V,b)(1+W_j(V,b)), \quad \quad \Itilde_j(V,X) = \prod_{b \in \Bcal_{j-1} (X)} \Itilde_j(V,b).$$ Thus $\tilde I_j$ is defined on blocks and polymers of scale $j-1$, whereas $I_j$ is defined on blocks and polymers of scale $j$. An element $F \in \Ncal$ is said to be *gauge invariant* if it is invariant under the gauge flow $q \mapsto e^{-2\pi i t}q$, $\bar q \mapsto e^{+2\pi i t}\bar q$; for all $q = \phi_{x} ,\psi_{x}, \sigma$; $\bar q = \bar\phi_{x} , \psib_{x}, \bar\sigma$; and $x \in \Lambda$. The basic objects we study, including $V,F,W,I,\tilde{I}$, are all gauge invariant. Also, since we assume $V_{ab}=0$ for $j<j_{ab}$, it follows that none of these basic objects has a nonzero component in $\Ncal_{ab}$ unless $j \ge j_{ab}$. ### The renormalised field polynomial {#sec:Vpt} To simplify the notation, we write $\Lcal_{j} = \Lcal_{C_{j}}$. Given $V\in \Qcalnabla$, as in [@BBS-rg-pt] we define $$\begin{aligned} \label{e:PWdef} P_{j}(V,x) &= \LT_{x}\left( e^{\Lcal_{j+1}} W_{j}(V,x) + \frac{1}{2} F_{\pi,C_{j+1}}(e^{\Lcal_{j+1}}V_x,e^{\Lcal_{j+1}} V(\Lambda)) \right) \quad (j+1<N),\end{aligned}$$ and we write $P_j(V,X)=\sum_{x\in X}P_j(V,x)$ for $X \subset \Lambda$. The local polynomial $\Vpt$ is defined, as in [@BBS-rg-pt], by $$\label{e:Vptdef} V_{\pt,j+1}(V,x) = e^{\Lcal_{j+1}} V_x - P_j(V,x) \quad (j+1<N) .$$ By definition, $V_{\pt,j+1}(B)$ depends on fields and their derivatives at sites in $B$, in contrast to $I_j(V,B)$ which depends on fields in the larger region $B^{+}$ because of $W_j(V,B)$. By [@BBS-rg-pt Lemma \[pt-lem:EV\]] we have $e^{\Lcal_{j+1}}V =V+ 2gC_{j+1;0,0}\tau$, so $$\lbeq{VptE} V_{\pt,j+1} = V+ 2gC_{j+1;0,0}\tau -P_j(V) \quad (j+1<N) .$$ For $j<N$, an explicit formula $V_{\pt,j} = \varphi_{\pt,j-1}$ is given in [@BBS-rg-pt Proposition \[pt-prop:Vptg\]]. In particular, $P \in \Qcal$. The definition of $\Vpt$ is motivated by the fact (shown in [@BBS-rg-pt Section \[pt-sec:WPjobs\]]) that the definitions of $W$ and $\Vpt$ cooperate to arrange that, as formal power series, $$\lbeq{fps} \Ex \theta I_j(V,\Lambda) \approx I_{j+1}(\Vpt,\Lambda) +O(V^3).$$ For $B \in\Bcal_j$, we make the abbreviation $$\label{e:Ipttildef} \Ipttil(B) = \tilde{I}_{j+1}(\Vpt,B ),$$ ### The final scale {#sec:finalscale} The above definitions have been given for scales below but not including the final scale $N$. At scale $N$, the torus consists of a single block $\Lambda \in \Bcal_N$, the periodicity of the torus becomes preponderant, the definition of $\LT_x F_{\pi,w_{N,N}}(V_x,V(\Lambda))$ breaks down due to lack of a coordinate patch, and the definitions of $W$ and $P$ in and can no longer be used. Initially this may appear problematic, since we are ultimately interested in performing the last expectation and computing $I_N$. However, any apparent difficulty is only superficial. There is only one problematic scale out of an unbounded number of scales. Moveover, the covariance $C_{N,N}$ is extremely small for large $m^2L^{2N}$ (see below), and we do take the limit $N \to \infty$ before $m^2 \downarrow 0$, so the last expectation is insignificant. Nevertheless it is necessary to make appropriate definitions of $\Vpt$ and $W$ at scale $N$. We do this in such a way that the analysis at scale $N$ differs minimally from that at previous scales. For $\Vpt$, the natural choice $V_{\pt,N}=\varphi_{\pt,N-1}$ is made in [@BBS-rg-pt Definition \[pt-def:VptZd\]]; this choice defines $V_{\pt,N}$ to be equal to what it would be if the torus side length were at a higher scale than scale $N$. In terms of this choice, we define $P_{N-1}$ so that remains valid for scale $N$, namely $$\begin{aligned} \label{e:PNdef} P_{N-1}(V) & = -V_{\pt,N}(V) + \Ex_{C_{N}}\theta V .\end{aligned}$$ There is no $P_N$, the last $P_j$ is $P_{N-1}$ since the last $\Vpt$ is $V_{\pt,N}$. Thus we have arranged the definitions at the last scale in such a way that $V_{\pt,N}$ agrees with what it would be on a torus of scale greater than $N$ (the use of $\Ex_{C_N}$ rather than $\Ex_{C_{N,N}}$ is intentional and for this reason). For $W_N$, our choice is inspired by a key identity obeyed by $W_j$ for $j<N$, proved in Lemma \[lem:EW\]. The identity implies in particular that $$\begin{aligned} W_{j} (V,x) &= e^{\Lcal_j} W_{j-1} (e^{-\Lcal_j}V,x) - P_{j-1}(e^{-\Lcal_j}V,x) + \frac{1}{2} F_{\pi,C_j }( V_x,V(\Lambda)) \quad (j<N) .\end{aligned}$$ The above identity is instrumental in the proof that the perturbative analysis of [@BBS-rg-pt] is accurate beyond formal power series, and thus plays a fundamental role. We define $W_N$ to maintain this identity. Thus, with $P_{N-1}$ given by , we define $$\begin{aligned} \label{e:WNdef} W_{N}(V,x) & = e^{\Lcal_{N,N}} W_{N-1}(e^{-\Lcal_{N,N}}V,x) -P_{N-1}(e^{-\Lcal_{N,N}}V,x) + \frac 12 F_{\pi,C_{N,N}}(V_x,V(\Lambda)) .\end{aligned}$$ ### Norms and field regulators {#sec:reg} Our estimates are typically expressed in terms of the $T_\phi$ semi-norm and two important functions of $\phi$ that we refer to as *field regulators*. We now recall the relevant definitions. ### The $T_\phi$ semi-norm {#the-t_phi-semi-norm .unnumbered} We make heavy use of the $\Phi_j(\h_j)$ norm on test functions and the $T_{\phi,j}(\h_j)$ semi-norm on $\Ncal$. The definition of the $\Phi_j(\h_j)$ norm on test functions is given in [@BS-rg-norm Example \[norm-ex:h\]] in terms of a parameter $p_\Phi \ge d+1-\frac{d-2}{2}=\frac{d+4}{2}$ (consistent with the requirement above the statement of [@BS-rg-loc Proposition \[loc-prop:LTKbound\]]), and here we take $R=L^j$ in [@BS-rg-norm Example \[norm-ex:h\]] where $j$ is the scale. The value of $p_\Phi$ is fixed but unimportant, and constants in estimates may depend on it. The space $\Phi(\h)$ consists of test functions $g : \vec\Lambdabold^* \to \C$. The definition of the norm requires the specification of its “sheets” and the values of the components of $\h_j$ for each sheet (particular choices are made in Section \[sec:hex\] below). We assume that in the definition of the norm there are sheets for each of the fields $\phi,\bar\phi,\psi,\bar\psi,\sigma,\bar\sigma$. The boson and fermion fields have a common component of $\h_j$, and we sometimes abuse notation by writing $\h_j$ for this particular component value. Also, the fields $\sigma,\bar\sigma$ have a common value $\h_{\sigma,j}$. The $T_\phi(\h)$ semi-norm is defined in [@BS-rg-norm Definition \[norm-def:Tphi-norm\]], and provides a family of semi-norms indexed by the vector $\h$. We often keep $\h$ as a parameter in our results, as our applications ultimately use more than one choice. Properties of the $T_\phi$ semi-norm are derived in [@BS-rg-norm]; prominent among them is the product property of [@BS-rg-norm Proposition \[norm-prop:prod\]] which asserts that $\|FG\|_{T_\phi} \le \|F\|_{T_\phi}\|G\|_{T_\phi}$ for all $F,G \in \Ncal$. ### Fluctuation-field regulator {#sec:ffreg .unnumbered} A special case of the $\Phi(\h)$ norm is obtained by regarding the boson field as a test function: given $\h_j>0$ its $\Phi_j=\Phi_j(\h_j)$ norm is \_[\_j(\_j)]{} = \_j\^[-1]{} \_[x]{} \_[||\_1 p\_]{} L\^[j||\_1]{} |\^ \_x|. The estimates given in [@BBS-rg-pt Proposition \[pt-prop:Cdecomp\]] (see [@BBS-rg-pt]) for the covariance decomposition show, in particular, that $$\label{e:scaling-estimate} |\nabla_x^\alpha \nabla_y^\beta C_{j;x,y}| \leq cL^{-(j-1)(2[\phi]+(|\alpha|_1+|\beta|_1))}.$$ with $[\phi]$ the *field dimension* $$[\phi]=\frac{d-2}{2}$$ and where $c$ is independent of $j,L$ and $m^2\in[0,\delta]$ for $j<N$, while in the special case $C_j=C_{N,N}$, $c$ is independent of $N,L,m^2$ as long as $m^2 \in [\varepsilon L^{-2(N-1)},\delta]$ with the constant $c$ now depending on $\varepsilon>0$. This suggests that under the expectation $\Ex_{C_j}$, $|\nabla^{\alpha} \phi_x|$ is typically $O(L^{-(j-1)([\phi]+(|\alpha|_1))})$. We choose a value $\ell_j$ for $\h_j$ which makes the norm $\|\phi\|_{\Phi_j(\ell_j)}$ be small for typical $\phi$, i.e., we choose for $\h_j$ the value $$\lbeq{elldef} \ell_j = \ell_0 L^{-j[\phi]},$$ with an $L$-dependent (large) constant $\ell_0$ whose value gets fixed at below. As in [@BS-rg-norm (\[norm-e:PhiXdef\])], for $X \subset \Lambda$ we define a local norm of the boson field $\phi$ by $$\begin{aligned} \label{e:PhiXdef} \|\phi\|_{\Phi_j(X)} &= \inf \{ \|\phi -f\|_{\Phi_j} : \text{$f \in \C^\Lambda$ such that $f_{x} = 0$ $\forall x\in X$}\}.\end{aligned}$$ This definition localises the norm to $X$ by minimising over all extensions to the complement of $X$. A *small set* is defined to be a connected polymer $X \in \Pcal_j$ consisting of at most $2^d$ blocks (the specific number $2^d$ plays a role only in the combinatorial geometry of [@BS-rg-step Section \[step-sec:gl\]] and it is only important in this paper that it be a finite constant independent of $L$). The set of small sets is denoted $\Scal_j \subset \Pcal_j$. The *small set neighbourhood* of $X \subset \Lambda $ is the enlargement of $X$ defined by $$\label{e:ssn} X^{\Box} = \bigcup_{Y\in \Scal_{j}:X\cap Y \not =\varnothing } Y.$$ Given $X \subset \Lambda$ and $\phi \in \C^{\Lambda}$, we recall from [@BS-rg-norm Definition \[norm-def:ffregulator\]] that the *fluctuation-field regulator* $G_j$ is defined by $$\begin{aligned} \label{e:GPhidef} G_j(X,\phi) = \prod_{x \in X} \exp \left(|B_{x}|^{-1}\|\phi\|_{\Phi_j (B_{x}^\Box,\ell_j )}^2 \right) ,\end{aligned}$$ where $B_{x}\in \Bcal_j$ is the unique block that contains $x$, and hence $|B_x| = L^{dj}$. ### Large-field regulator {#sec:lfr .unnumbered} For $j<N$ (and $L$ large), and for $B \in \Bcal_j$, the diameter of $B^\Box$ is less than the period of the torus. We can therefore identify $B^\Box$ with a subset of $\Zd$ and use this identification to define polynomial functions from $B^\Box$ to $\C$. More generally, for $X$ with diameter less than the period of the torus, we define $$\label{e:Phipoltildef} \Phipoltil (X) = \left\{ f \in \C^{\Lambda} \mid \text{$f$ restricted to $X$ is a linear polynomial }\right\}.$$ Then, for $\phi \in \C^{\Lambda}$, we define the semi-norm $$\label{e:Phitilnorm} \| \phi \|_{\tilde{\Phi} (X)} = \inf \{ \| \phi -f\|_{\Phi} : f \in \Phipoltil (X) \}.$$ We recall from [@BS-rg-norm Definition \[norm-def:regulator\]] that the *large-field regulator* $\tilde G_j$ is defined by $$\begin{aligned} \label{e:9Gdef} \tilde G_j (X,\phi) = \prod_{x \in X} \exp \left( \frac 12 |B_{x}|^{-1}\|\phi\|_{\tilde\Phi_j (B_{x}^\Box,\ell_j)}^2 \right) .\end{aligned}$$ The definition is only used for $j<N$, since the norm on its right-hand side is not defined at the final scale $j=N$. Since $\| \phi \|_{\tilde{\Phi} (B^\Box)} \le \| \phi \|_{\Phi (B^\Box)}$ by definition, $\tilde G_j(X,\phi) \le G_j(X,\phi)^{1/2}$. The $\frac 12$ in the exponent of is a convenience that was used in [@BS-rg-norm Proposition \[norm-prop:KKK\]]. The role of $\tilde G_j$ is discussed in Section \[sec:lfp\] below. ### Regulator norms {#regulator-norms .unnumbered} The two regulators lead us to the following definition. \[def:Gnorms\] Norms on $\Ncal (X^{\Box})$ are defined, for $F \in \Ncal (X^{\Box})$ and $\Gtilp \in (0,1]$, by $$\begin{aligned} \label{e:Gnormdef1} \| F\|_{G_j} &= \sup_{\phi \in \C^\Lambda} \frac{\|F\|_{T_{\phi,j}}}{G_{j}(X,\phi)} \quad j \le N, \\ \label{e:Gnormdef2} \|F\|_{\tilde G_j^{\Gtilp}} &= \sup_{\phi \in \C^\Lambda} \frac{\|F \|_{T_{\phi,j}}}{\tilde{G}^{\Gtilp}_{j}(X,\phi)} \quad j<N.\end{aligned}$$ The norms depend on the choice of $\h_j$ used in the $T_{\phi,j}(\h_j)$ semi-norm on the right-hand sides. We write $\|F\|_j$ for the left-hand sides of – in statements that apply to both the $G$ and $\tilde G$ norms. Note that the norm $\| F\|_{G_j}$ is defined for all scales $j\le N$ whereas we $\| F\|_{\tilde G_j}$ is undefined at the last scale. At scale $N$, statements about the norm $\|F\|_j$ are to be understood as applying *only* to the $G$ norm. A fundamental property of the norms – is that each obeys the *product property* $$\label{e:norm-fac} \|F G \|_j \le \|F \|_j \|G \|_j \qquad \text{when $F\in \Ncal(X), G \in \Ncal(Y)$ for \emph{disjoint} $X,Y\in \Pcal_{j}$}.$$ This is an immediate consequence of the above mentioned product property which states that $\|FG\|_{T_\phi} \leq \|F\|_{T_\phi}\|G\|_{T_\phi}$ for *any* $F,G \in \Ncal$, together with the fact that by definition $G_j(X\cup Y,\phi)=G_j(X,\phi)G_j(Y,\phi)$ for disjoint $X,Y$, and similarly for $\tilde G_j$. Overview of results ------------------- Our goal in this paper is to obtain a thorough understanding of the interaction functional $I =I_{j}$. The main results are stated in Section \[sec:IE\], with proofs deferred to Sections \[app:sp\]–\[sec:ipcl\]. The results include proof of stability bounds for $I$, estimates on Gaussian expectations involving both boson and fermion fields, estimates verifying the accuracy of the perturbative calculations in [@BBS-rg-pt], and proof of the crucial contraction property needed to control irrelevant directions in the flow of the renormalisation group. These all play a role in the analysis of a single renormalisation group step in [@BS-rg-step]. Before making precise statements in Section \[sec:IE\], in this section we provide an informal overview of and motivation for the results. ### Stability, expectation and the large-field problem {#sec:lfp} In Section \[sec:stab\], we state a series of *stability estimates*. In particular, Proposition \[prop:Iupper\] provides the bound $$\lbeq{intro-Ibd} \|I_j(V,B)F(B)\|_{T_\phi(\ell_j)} \le 2 \|F(B)\|_{T_0(\ell_j)}G_j(B,\phi)$$ for $B \in \Bcal_j$, and for a polynomial $F(B)$ in the fields in $B$ of degree at most the parameter $p_\Ncal$ in the definition of the space $\Ncal$, under suitable hypotheses expressing a smallness condition on the coupling constants in $V$. Since $G_j(B,\phi)= \exp[\|\phi\|_{\Phi(B^\Box, \ell_j)}^2]$, provides information on the growth of the left-hand side for large fields $\phi$. This estimate does not take advantage of the quartic decay provided by $e^{-g\tau^2}$ to compensate for the quadratic part $e^{-\nu\tau}$ in $e^{-V}$ (with $\nu$ possibly negative). This is reflected by the quadratic growth in the exponent on the right-hand side of . The renormalisation group method is based on iterated expectation to progressively take into account fluctuations on increasingly larger scales. One difficulty with is that it degenerates under expectation and change of scale, as we discuss next. These ideas play a role in the proof of Proposition \[prop:ip\], which is our main estimate on Gaussian expectation. We make the abbreviation $\Ex_j = \Ex_{C_j}$ for the Gaussian expectation with covariance $C_j$. Since the expectation involves both boson and fermion fields (see [@BIS09; @BS-rg-norm]), it would more accurately be termed “super-expectation” but we use the term “expectation” for brevity. It is shown in [@BS-rg-norm Proposition \[norm-prop:EK\]], that for any $K \in \Ncal$, $$\lbeq{intro-EI00} \|\Ex_{j+1}\theta K\|_{T_\phi(\h_j)} \le \Ex_{j+1}\|K\|_{T_{\phi\sqcup \xi}(\h_j \sqcup \ell_j)}.$$ In more detail, in [@BS-rg-norm Proposition \[norm-prop:EK\]] we choose $w=\h_j$ and $w'=\ell_j$, and the hypothesis $\|C_{j+1}\|_{\Phi_{j+1}(\ell_{j+1})} \le 1$ is verified at below. The integrand on the right-hand side of is a function only of the boson field, so the super-expectation reduces to a standard Gaussian expectation with covariance $C_{j+1}$ (see [@BS-rg-norm Section \[norm-sec:cbf\]]). The fermion field ceases to play a significant role in the analysis once this inequality has been applied, and this is a beneficial aspect of our method. By – and , and by the inequality $\|\phi+\xi\|^2 \le 2(\|\phi\|^2+\|\xi\|^2)$, $$\lbeq{intro-EI0} \|\Ex_{j+1}\theta I_j(V,B)\|_{T_\phi(\ell_j)} \le \Ex_{j+1}\|I_j(V,B)\|_{T_{\phi\sqcup \xi}(\ell_j\sqcup \ell_j)} \le 2 G_j(B,\phi)^2 \Ex_{j+1} G_j(B,\xi)^2.$$ According to [@BS-rg-norm Proposition \[norm-prop:EG2\]], $ \Ex_{j+1} G_j(B,\xi)^2 \le 2$. Therefore, $$\lbeq{intro-EI1} \|\Ex_{j+1}\theta I_j(V,B)\|_{T_\phi(\ell_j)} \le 4 G_j(B,\phi)^2.$$ The left-hand side can only become smaller when the semi-norm is changed from scale $j$ to scale $j+1$ (this useful monotonicity property is proved in Lemma \[lem:Imono\] below). To see the effect of a change of scale on the right-hand side, consider the particular case $\phi_x = a$ for all $x$, where $a$ is a constant. In this case, by definition, $$\begin{aligned} L^{-dj}\|\phi\|^2_{\Phi_j(B_{x,j}^\Box, \ell_j)} &= L^{-dj} \ell_j^{-2} a^2 = L^{2} L^{-d (j+1)} \ell_{j+1}^{-2} \, a^2 = L^{2} L^{-d (j+1)} \|\phi\|^2_{\Phi_{j+1}(B_{x,j}^\Box, \ell_{j+1})} \nnb & = L^{2} L^{-d(j+1)} \|\phi\|^2_{\Phi_{j+1}(B_{x,j+1}^\Box, \ell_{j+1})} , \lbeq{martGfail}\end{aligned}$$ so for this case $G_{j}(B,a)=G_{j+1}^{L^2}(B,a)$. Thus the estimate after expectation and change of scale is substantially worse than (it is the growth in $\phi$ that is problematic, the constant $4$ in is not). It is in this way that the so-called *large-field problem* enters our analysis. We postpone the problem by setting $\phi=0$, so that the regulator plays no role in . With $\phi=0$, becomes $$\lbeq{intro-EI0a} \|\Ex_{j+1}\theta I_j(V,B)\|_{T_0(\ell_j)} \le \Ex_{j+1}\|I_j(V,B)\|_{T_{0\sqcup \xi}(\ell_j\sqcup \ell_j)} \le 4 .$$ From this, we see that control of $I_j$ is needed for *all* field values in order to estimate the expectation of the fluctuation field $\xi$, even when $\phi=0$. Thus we are able to obtain a useful estimate in the $T_0$ semi-norm at scale $j+1$, but this is not sufficient to be able to iterate these estimates as the scale advances. To deal with the large-field problem, we do not perform a separate analysis on regions of space where the field is large and where it is small, as has been done in other renormalisation group methods, e.g., [@Bala82; @Dimo13; @GK85; @GK86]. Instead, we take advantage of the factor $e^{-g\sum_{x\in B}|\phi_x|^4}$ in $I(B)$ and exploit it to capture the notion that a typical field should roughly have size $g^{-1/4}L^{-jd/4}$. For this, we need information about the size of $g$. Our ansatz is that at scale $j$, $g$ is close in size to $\gbar_j$, which is defined by the recursion $$\label{e:gbardef} \gbar_{j+1} = \gbar_j - \beta_j \gbar_j^2$$ of [@BBS-rg-pt], with a fixed initial condition $\gbar_0$, and with $\beta_j$ given in terms of the covariance $w_j$ of by $$\beta_j = 8\sum_{x \in \Lambda}(w_{j+1;0,x}^{2}-w_{j;0,x}^{2}).$$ The sequence $\beta_j$ is closely related to the *bubble diagram* $\sum_{x \in \Zd} [(-\Delta_{\Zd}^{-1})_{0x}]^2$, which diverges for $d=4$ but converges for $d>4$ since the inverse Laplacian is asymptotically a multiple of $|x|^{-(d-2)}$. By [@BBS-rg-pt Lemma \[pt-lem:betalim\]], $\beta_j \to 0$ for $d>4$ whereas $\beta_j \to \pi^{-2}\log L$ for $d=4$. Also, by choosing $\gbar_0$ to be sufficiently small, it follows that $\gbar_j$ is uniformly small. In the present paper, our focus is on the advancement of one scale to the next, rather than on all scales simultaneously. Because of this, and to provide flexibility, rather than using $\gbar_j$, we introduce a small positive $\ggen_j$ and consider $g$ at scale $j$ to be close to $\ggen_j$. We do not assume that $\ggen_j$ is given by (a different but closely related choice of $\ggen$ is used in [@BBS-saw4-log]), but we do assume that $\ggen_j$ is uniformly small for all $j$, and that we are free to choose how small it is depending on $L$. Thus we introduce $h_j \propto \ggen_j^{-1/4}L^{-jd/4}$ and seek estimates in terms of the $T_\phi(h_j)$ semi-norm. Note that for $d=4$, $h_j$ is larger than $\ell_j$ by a factor $\ggen_j^{-1/4}$. We employ the $T_\phi(h_j)$ semi-norm in conjunction with the large-field regulator $\tilde G_j$. An essential property of $\tilde G_j $ (used in the proofs of Propositions \[prop:Istab\]–\[prop:Ianalytic1:5\] and \[prop:ip\]–\[prop:cl\] below) is given in the following lemma. We apply Lemma \[lem:mart\] with specific choices of $p$, and do not thereby lose control of the size of $L$. \[lem:mart\] Let $X \subset \Lambda$. For any fixed $p >0$ (no matter how large), if $L$ is large enough depending on $p$, then for all $j+1<N$, $$\label{e:mart} \tilde{G}_{j}(X, \phi)^{p} \le \tilde{G}_{j+1}(X, \phi).$$ By definition of the regulator in , it suffices to prove that $$\lbeq{martwant} pL^{-dj}\|\phi\|^2_{\tilde\Phi_j(B_{j,x}^\Box,\ell_j)} \le L^{-(j+1)d} \|\phi\|^2_{\tilde\Phi_{j+1}(B_{j+1,x}^\Box,\ell_{j+1})}.$$ Let $d_{+} = [\phi]+1 = \frac{d-2}{2} + 1 = \frac d2$. By the definition of dimension of a polynomial given in [@BS-rg-loc Section \[loc-sec:oploc\]], a linear polynomial has dimension $ [\phi]+1 = d_+$. It is a consequence of [@BS-rg-loc Lemma \[loc-lem:phij\]], with $d_+'= d_{+}+1 = \frac{d}{2} + 1$, that $$\begin{aligned} \label{e:phij-pre} \|\phi\|_{\tilde{\Phi}_{j} (B_{j,x}^\Box,\ell_j)} & \le c L^{-d/2 - 1} \|\phi\|_{\tilde{\Phi}_{j+1} (B_{j,x}^\Box,\ell_{j+1})}.\end{aligned}$$ Therefore, since the semi-norm is non-decreasing in $X$ by definition, $$\begin{aligned} \|\phi\|^2_{\tilde\Phi_j(B_{j,x}^\Box,\ell_j)} &\le c^2 L^{-d-2} \|\phi\|^2_{\tilde\Phi_{j+1}(B_{j+1,x}^\Box,\ell_{j+1})} , \label{e:tilnormrescale}\end{aligned}$$ from which follows when $L$ is large enough that $pc^{2} L^{-2} \le 1$. The inequality does not hold for the regulator $G$: we have concluded from that for a constant field we have $G_j=G_{j+1}^{L^2}$. In contrast, the norm in $\tilde G$ scales down, because it does not examine the constant and linear parts of $\phi$. By the use of a lattice Sobolev inequality (proved in Appendix \[sec:Lp\]), we take advantage of the decay in $e^{-g\tau^2}$ to cancel the exponential quadratic $\|\phi\|_\Phi^2$ at the cost of an exponential of $\|\phi\|_{\tilde \Phi}^2$. By pursuing this strategy, we prove in Proposition \[prop:Iupper\] below that for $F(B)$ as in , $$\lbeq{intro-Ibdh} \|I_j(V,B)F(B)\|_{T_\phi(h_j)} \le 2 \|F(B)\|_{T_0(h_j)}\tilde G_j(B,\phi) ,$$ and now with this leads as above to $$\lbeq{intro-EIh} \|\Ex_{j+1}\theta I_j(V,B)F(B)\|_{T_\phi(h_j)} \le 4 \|F(B)\|_{T_0(h_j)} \tilde G_j(B,\phi)^2 \le 4 \|F(B)\|_{T_0(h_j)} \tilde G_{j+1}^{\Gtilp}(B,\phi),$$ for any fixed choice of $\Gtilp\in (0,1]$, e.g., $\Gtilp = 1/2$, with $L$ large depending on $\Gtilp$. Thus the $h$ bound reproduces itself after expectation and change of scale. In fact, our ability to choose $\Gtilp <1$ shows that the $h$ bound *improves*. On the other hand, the $\ell$ bound degrades after expectation and change of scale. However, together the scale-$(j+1)$ $\ell$ and $h$ bounds can be combined using [@BS-rg-norm Proposition \[norm-prop:KKK\]] to infer a $G_{j+1}$ bound for all $\phi$ from the $T_{0}(\ell_{j+1})$ and $\tilde G_{j+1}$ bounds. In this way it is possible to obtain bounds at scale $j+1$ of the same form as the bounds at scale $j$. We postpone the application of [@BS-rg-norm Proposition \[norm-prop:KKK\]] to the proof of [@BS-rg-step Theorem \[step-thm:mr\]]. With this motivation, throughout this paper we prove estimates in terms of the two norm pairs $$\label{e:np1} \|F\|_j = \|F\|_{G_j(\ell_j)} \quad \text{and} \quad \|F\|_{j+1} = \|F\|_{T_{0,j+1}(\ell_{j+1})},$$ and $$\label{e:np2} \|F\|_j = \|F\|_{\tilde{G}_j(h_j)} \quad \text{and} \quad \|F\|_{j+1} = \|F\|_{\tilde{G}_{j+1}^{\Gtilp}(h_{j+1})},$$ i.e., estimates on $\|F\|_{j+1}$ are expressed in terms of $\|F\|_j$ for each of the pairs and . We distinguish the cases and by writing $\h_j=\ell_j$ to indicate , and $\h_j=h_j$ to indicate . The values of $\h_\sigma$ in the $T_\phi$ norms, for sheets corresponding to the observable fields $\sigma,\bar\sigma$, are specified in below (see [@BS-rg-loc] for the $T_\phi$ norm with observables). Iteration of estimates using is possible without the accompaniment of . However, estimates in terms of the $\tilde G(h)$ norm are insufficient on their own to make estimates on remainder terms in the flow of coupling constants, and without such estimates we are unable to study critical behaviour. In the flow of coupling constants determined in [@BS-rg-step], the interaction polynomial $V_{j+1}$ at scale $j+1$ is expressed in terms of $V_{\pt,j+1}(V_j)$ plus a non-perturbative remainder $\rho_{j+1}\in \Qcal$ whose coupling constants must be shown to be third order in $\ggen_j$. Our control over these coupling constants is obtained via the $T_0$ semi-norm. To illustrate this, consider the case of $d=4$, and suppose that the $\tau^2$ term in $\rho_{j+1}$ were simply $\ggen_j^3 \tau^2$. The calculation of the $T_\phi$ semi-norm of $\tau^2$ is straightforward, and a small extension of [@BS-rg-norm Proposition \[norm-prop:taunorm\]] gives $\|\ggen_j^3\tau^2_x\|_{T_0(\h_j)} \asymp \ggen_j^3 \h_j^4$ (the symbol $\asymp$ means upper and lower bounds with different constants). Focussing only on the power of $\ggen_j$, the choice $\h_j =h_j$ gives an overall power $\ggen_j^3 ( \ggen_j^{-1/4})^4= \ggen_j^2$, which is second order rather than the desired third order. For this reason, estimates in terms of norms with $\h=h$ are insufficient. On the other hand, with the $T_0(\ell)$ semi-norm there is no loss of powers of $\ggen_j$ arising from $\|\tau^2_x\|_{T_0(\ell_j)} \asymp \ell_j^4$, and the $T_0(\ell)$ semi-norm indeed identifies $\ggen_j^3\tau^2$ as a third-order term. \[rk:h++\] In the $j+1$ members of the norm pairs –, the parameter $\h_{j+1}$ may be replaced by $\h_{++}=c\h_{j+1} >\h_{j+1}$ for any fixed $c>1$. More precisely, in Definition \[def:Gnorms\], with $j$ replaced by $j+1$, $\h_{j+1}$ becomes replaced by $\h_{++}$ in the $T_{\phi,j+1}(\h_{j+1})$ norm. Our convention is to leave $\ell_{j+1}$ in the regulator unchanged; it does not become $\ell_{++}$ in the replacement of $\h_{j+1}$ by $\h_j$. All our results remain valid with $\h_{++}$ replacing $\h_{j+1}$, with changes in constants whose precise values are without significance and indeed are not specified in our results. To avoid further elaboration of our notation, we do not make the role of $\h_{++}$ explicit in the rest of the paper, apart from one additional comment below . \[rk:scaleNnorm\] The advancement of estimates to the final scale $N$ is special, since the $\tilde G$ norm is undefined at that scale. However, the work of the $\tilde G$ norm is complete by scale $N$, as there is no further difficulty concerning degradation of estimates since the scale no longer advances. Thus, at scale $N$, we can consider the norm to be the $G$ norm with regulator $G$ replaced by a suitable large power of $G_{N-1}$, such as $G_{N-1}^{10}$ (using $G_{N-1}^2$ would be sufficient for but higher powers are required later). Then a scale-$N$ estimate $\|F\|_N \le C$ is interpreted as stating that $\|F\|_{T_\phi,N} \le C G_{N-1}(\Lambda,\phi)^{10}$. In some applications, the $T_0$ estimate obtained by setting $\phi=0$ is sufficient. More generally, the estimate states that $\|F\|_{T_\phi,N} \le C\exp[O(\|\phi\|^2)]$ (with $L$-dependent constant in the exponent), and this provides additional information concerning the growth in $\phi$. We are not always careful to distinguish the special nature of $\|\cdot\|_N$, but inspection reveals that our conclusions indeed hold with this choice. ### Accuracy of perturbative analysis One of our main results is a proof of a version of that goes beyond formal power series. The version we prove is a local one, which permits accurate estimates with errors bounded uniformly in the volume. However, the local analysis comes with a cost, which is that an explicit second-order leading term arises along with the third-order error. For simplicity, for the present discussion we set $\lambdaa=\lambdab=\qa=\qb=0$ so that observables play no role. In this setting, a particular case of what we prove is that for $b \in \Bcal_j$ and $B \in \Bcal_{j+1}$, $$\lbeq{pt-eg} \Itilde_\pt^{B\setminus b} \Ex_{j+1} \theta I(V,b) \approx \Ipttil^B \Big( 1 - \frac 12 \Ex_{j+1} \theta (V_j(b);V_j(\Lambda \setminus b) \Big) ,$$ where the *truncated expectation* (or *covariance*) is defined by $$\label{e:trun-exp-eg} \Ex_C (A; B) = \Ex_C(AB) - (\Ex_CA)(\Ex_CB).$$ We prove precise versions of with third-order error estimates, for both norm pairs –. For example, in the proof of Proposition \[prop:h\], for the norm pair we show that $$\label{e:want2-eg} \| \Itilde_\pt^{B\setminus b}\Ex_{j+1} (\theta I(V,b) - \Ipttil(b)) + \Itilde_\pt^{B} \frac 12 \Ex_{j+1} \theta (V_j(b);V_j(\Lambda \setminus b) \|_{T_{0,j+1}(\ell_{j+1})} \le O(\ggen_j^3).$$ The bound on the right-hand side is third-order as desired, but there is a second-order leading term on the left-hand side. Its origin can be seen from a small extension of the argument in [@BBS-rg-pt Section \[pt-sec:WPjobs\]], as follows. Proceeding as in [@BBS-rg-pt Section \[pt-sec:WPjobs\]], formally, to a third-order error, we obtain $$\begin{aligned} \Ex \theta I(b) & \approx e^{-\Ex \theta V(b)} \left[ 1 + \Ex \theta W(b) + \frac 12 \Ex \theta (V(b);V(b)) \right].\end{aligned}$$ The bilinear term $W(b)$ involves $V(b)$ in one argument and $V(\Lambda)$ in the other, and its partner to make the argument of [@BBS-rg-pt Section \[pt-sec:WPjobs\]] apply here has to be $\frac 12 \Ex \theta (V(b);V(\Lambda))$ rather than $ \frac 12 \Ex \theta (V(b);V(b))$. Thus we rewrite the right-hand side as $$\begin{aligned} \Ex \theta I(b) & \approx e^{-\Ex \theta V(b)} \left[ 1 + \Ex \theta W(b) + \frac 12 \Ex \theta (V(b);V(\Lambda)) - \frac 12 \Ex \theta (V(b;V(\Lambda\setminus b)) \right].\end{aligned}$$ After multiplication by $\Itilde_\pt^{B\setminus b}$, the extra term produces $-\Itilde_\pt^{B}\frac 12 \Ex \theta (V(b;V(\Lambda\setminus b))$, which is what appears in . In Proposition \[prop:hldg\], we prove that the leading term in the perturbative estimates we require is indeed second order. This is a straightforward consequence of the stability bounds. The fact that the remainder beyond the leading term is third order is proved in Proposition \[prop:h\], which is more substantial, and is our full implementation of the formal arguments of [@BBS-rg-pt Section \[pt-sec:WPjobs\]]. For the reasons discussed in Section \[sec:lfp\], we need versions of these two propositions for both norm pairs. ### Loc and the crucial contraction {#sec:cc} The renormalisation group creates an infinite-dimensional dynamical system, which has a finite number of relevant or marginal directions and infinitely many irrelevant directions. A crucial aspect of our analysis is to employ the operator $\LT$ defined and developed in [@BS-rg-loc] to extract the relevant and marginal parts of a functional of the fields, with $(1-\LT)$ projecting onto the irrelevant parts. The specific result we prove in this respect is Proposition \[prop:cl\]. A special case of Proposition \[prop:cl\] is as follows. Let $X$ be a small set as defined above . Let $U$ be the smallest collection of blocks in $\Bcal_{j+1}$ which contains $X$ ($U$ is the *closure* $U = \overline X$). Let $F(X) \in \Ncal(X^\Box)$ be such that $\LT_X F =0$; this should be interpreted as a statement that $F(X)$ is irrelevant for the renormalisation group. We prove in Proposition \[prop:cl\] that, under appropriate assumption on $V$, $$\begin{aligned} \label{e:cl-eg} \|\tilde I^{U\setminus X} \Ex \theta \left( \Itilde^{X}F (X) \right) \|_{j+1} & \le {\rm const}\, L^{-d-1} \|F(X)\|_{j} ,\end{aligned}$$ where the pair of norms is given by either choice of or . The number of distinct $X$ with closure $U$ produces an entropic factor of order $L^d$, and hence $$\begin{aligned} \label{e:cl-sum-eg} \sum_{X \in \Scal_j: \overline X =U}\|\tilde I^{U\setminus X} \Ex \theta \left( \Itilde^{X}F (X) \right) \|_{j+1} & \le {\rm const} \, L^{-1} \|F(X)\|_{j} .\end{aligned}$$ Thus a contractive factor $L^{-1}$ remains also after summation. This plays a crucial role in [@BS-rg-step] in showing that the coordinate of the dynamical system that is meant to represent the irrelevant directions is in actual fact contractive. Parameters and domains ---------------------- In this section, we reformulate estimates on the covariance decomposition that are stated in [@BBS-rg-pt], we specify the parameters that define the $T_\phi$ norms we use, we define the small parameters $\epV,\epdV$ that permeate our analysis, and we discuss the domains for $V$ which ensure stability of $I$. ### Estimate on covariance decomposition {#sec:frp} We now discuss the size of the covariances arising in the covariance decomposition, in more detail. Recall from the definition $\ell_j = \ell_0 L^{-j[\phi]}$. We may regard a covariance $C$ as a test function depending on two arguments $x,y$, and with this identification its $\Phi_j(\ell_j)$ norm is $$\begin{aligned} & \label{e:Phinorm} \|C\|_{\Phi_{j}(\ell_j)} = \ell_j^{-2} \sup_{x,y\in \Lambda} \; \sup_{|\alpha_{1}|_1 + |\alpha_{2}|_1 \le p_\Phi} L^{(|\alpha_{1}|_1+ |\alpha_{2}|_1)j} |\nabla_x^{\alpha_1} \nabla_y^{\alpha_2} C_{x,y}| ,\end{aligned}$$ where $\alpha_i$ is a multi-index. The norm of the covariance $C_j$ in the covariance decomposition can be estimated using an improved version of from [@Baue13a; @BBS-rg-pt]. For this, given $\Omega >1$ we define the $\Omega$-*scale* $\jm$ by $$\lbeq{mass-scale} \jm = \inf \{ k \geq 0: |\beta_j| \leq \Omega^{-(j-k)} \|\beta\|_\infty \text{ for all $j$} \} ,$$ and we set $$\lbeq{chidef} \chi_j = \Omega^{-(j-\jm)_+}.$$ The $\Omega$-scale indicates a scale at which the mass term in the covariance starts to play a dominant role in dramatically reducing the size of the covariance; further discussion of this point can be found in [@BBS-rg-pt Section \[pt-sec:Greekpfs\]]. It is within a constant of the value $j_m$ defined by $j_m=\lfloor \log_{L^2}m^{-2}\rfloor$, as shown in [@BBS-rg-pt Proposition \[pt-prop:rg-pt-flow\]], and $\chi_j$ could alternately be defined in terms of $j_m$. We always take the infinite volume limit before letting $m^2 \downarrow 0$, so we may assume that $m^2 \in [\varepsilon L^{-2(N-1)},\delta^2]$ for small fixed $\delta, \varepsilon$. It is shown in [@BBS-rg-pt] that there is an $L$-independent constant $c$ such that for $m^2 \in [0, \delta]$ and $j=1,\ldots,N-1$, or for $m^2 \in [\varepsilon L^{-2(N-1)},\delta]$ for $N$ large in the special case $C_j=C_{N,N}$, $$\label{e:scaling-estimate-Omega} |\nabla_x^\alpha \nabla_y^\beta C_{j;x,y}| \leq c \chi_j L^{-(j-1)(2[\phi]+(|\alpha|_1+|\beta|_1))}.$$ Let $$\lbeq{Ckstardef} C_{j*}= \begin{cases} C_j & j<N \\ C_{N,N} & j=N. \end{cases}$$ By , given $\ellconst \in (0,1]$ we can choose $\ell_0$ large depending on $L$ to obtain, for $j=1,\ldots,N$, $$\lbeq{CLbd} \|C_{j*}\|_{\Phi_j^+(\ell_j)} \le \ellconst \chicCov_j \le \min\{\ellconst, \chicCov_j\},$$ where $\Phi^+$ refers to the norm with $p_\Phi$ replaced by $p_\Phi+d$. Let $c_G=c(\alpha_G)$ be the (small) constant of [@BS-rg-norm Proposition \[norm-prop:EG2\]]. We fix the value $\ellconst = \frac{1}{10}c_G$. Then [@BS-rg-norm Proposition \[norm-prop:EG2\]] ensures that $$\begin{aligned} \max_{k=j,j+1}\Ex_{k*} ( G_{j} (X) )^{10} & \le 2^{|X|_j} \quad\quad X \in \Pcal_{j}, \label{e:EG}\end{aligned}$$ where $|X|_j$ denotes the number of scale-$j$ blocks comprising $X$ (the constants $10$ and $2$ in are convenient but somewhat arbitrary choices). The use of $\Phi^+$ in is to satisfy the hypotheses of [@BS-rg-norm Proposition \[norm-prop:EG2\]]. ### Choice of norm parameters {#sec:hex} We restrict attention here to $d=4$. For the $G$ norm, for the boson and fermion fields we choose $\ell_0$ according to and set $$\label{e:hl} \h_j = \ell_j = \ell_0 L^{-j[\phi]} .$$ For the $\tilde G$ norm, we fix a parameter $k_0$ (small, chosen as discussed under Proposition \[prop:Iupper\]), we set $$\label{e:h-def} \h_j = h_{j} = k_0 \ggen_j^{-1/4}L^{-jd/4}.$$ We assume that $\ggen_j$ can be taken to be as small as desired (uniformly in $j$, and depending on $L$), and that $$\label{e:gbarmono} \frac 12 \ggen_{j+1} \le \ggen_j \le 2 \ggen_{j+1}$$ (the above two inequalities hold for the sequence $\gbar_j$ by [@BBS-rg-pt]). For the observables, we set $$\lbeq{newhsig} \h_{\sigma,j}= \begin{cases} \ggen_j L^{(j\wedge j_{ab})[\phi]} 2^{(j-j_{ab})_+} & \h=\ell \\ \ggen_j^{1/4} L^{(j\wedge j_{ab})[\phi]} 2^{(j-j_{ab})_+} & \h=h; \end{cases}$$ see Remark \[rk:hsigmot\] for motivation of this definition. By , the above choices obey: $$\begin{aligned} \label{e:h-assumptions} \h_j \ge \ell_{j}, \quad\quad \frac{\h_{j+1}}{\h_j} L^{[\phi]} &\le 2, \quad\quad \frac{\h_{\sigma,j+1}}{\h_{\sigma,j}} \le {\rm const}\, \begin{cases} L^{[\phi]} & j < j_{ab} \\ 1 & j \ge j_{ab}. \end{cases}\end{aligned}$$ Our results for the norm pairs – require only the bounds on $\h_{j+1}$ in . However, the choice of $2$ that appears there and in is arbitrary, and, e.g., $3$ would do as well. For this reason, we can replace $\h_{j+1}$ by a larger $\h_{++}=c\h_{j+1}$, as claimed in Remark \[rk:h++\]. ### Definition of small parameter epsilonV {#sec:spdefs} The stability estimates are expressed in terms of domains defined via parameters $\epV$ and $\epVbar$, which we discuss now. Given $V \in \Qcalnabla$, we write $V_\varnothing = \sum_{M}M$ for the decomposition of its bulk part as a sum of individual field monomials such as $\nu \phi\bar\phi$, $\nu \psi\bar\psi$, $z(\Delta \phi)\bar\phi$, and so on. Then, for $0 \le j \le N$, we define $$\label{e:monobd} \epV =\epsilon_{V,j} = L^{dj} \sum_{M : \pi_*M=0} \|M_0\|_{T_{0,j}(\h_j)} + (|\lambdaa|+|\lambdab|)\h_j\h_{\sigma,j} + (|\qa|+|\qb|)\h_{\sigma,j}^2 ,$$ where $M_0$ denotes the monomial $M_x$ evaluated at $x=0$. Thus $\epV$ is a function (in fact, a norm) of the coupling constants in $V$ and of the parameters $\h_j$ and $\h_{\sigma,j}$ which define the $T_0$ semi-norm. The value of $\epV$ depends on the scale $j$, but we often leave this implicit in the notation. It measures the size of $V$ on a block $B \in \Bcal_j$ consisting of $L^{dj}$ points, and is worst case in the sense that it includes a contribution from observables whether or not the points $a$ or $b$ lie in $B$. The term $g\tau^2$ plays a special role in providing the important factor $e^{-g|\phi|^4}$ in $e^{-V}$, and we define $$\label{e:epVbar-def-old} \epVbar = \epsilon_{g\tau^2,j} = L^{dj} \|g\tau^2_0 \|_{T_{0,j}(\h_j)}.$$ By definition, $\epVbar \le \epV$. Also, there is a universal constant $C_0>0$ such that $$\label{e:epVbarasymp} C_0^{-1} |g|\h_j^4 L^{dj} \le \epVbar \le C_0 |g|\h_j^4 L^{dj} .$$ In fact, the upper bound is proved in [@BS-rg-norm Proposition \[norm-prop:taunorm\]], while the lower bound follows directly from the definition of the $T_{\phi}$ norm (see [@BS-rg-norm Definition \[norm-def:Tphi-norm\]]) since the supremum of the pairing over all unit norm test functions is larger than the pairing with a constant unit norm test function. ### Stability domains To enable the use of analyticity methods in [@BS-rg-step], we employ complex coupling constants. Given a (large) constant $C_{\DV}$, we define a domain $$\begin{aligned} \lbeq{DV1-bis} \DV_j = \{(g,\nu,z,y,\lambdaa,\lambdab,\qa,\qb)\in \C^{8} : C_\DV^{-1} \ggen_j < {\rm Re} g < C_\DV \ggen_j, & \; |{\rm Im} g| < \textstyle{\frac {1}{10}} {\rm Re} g, \nnb & |x| \le r_x \; \text{for $x\neq g$}\},\end{aligned}$$ where $r_x$ is defined (with $\lambda$ equal to $\lambdaa$ or $\lambdab$ and similarly for $q$) by $$\begin{gathered} L^{2j}r_{\nu,j} = r_{z,j}= r_{y,j}= C_{\DV} \ggen_j, \quad\quad r_{\lambda,j} = C_{\DV}, \nnb L^{2j_{ab}[\phi]}2^{2(j-j_{ab})}r_{q,j} = \begin{cases} 0 & j < j_{ab} \\ C_{\DV} & j \ge j_{ab}. \end{cases} \label{e:h-coupling-def-1-bis}\end{gathered}$$ We also use two additional domains in $\C^{8}$, which depend on the value of $\h$ (namely $\h=\ell$ or $\h=h$), as well as on parameters $\alpha,\alpha',\alpha''>0$. Given these parameters, we define $$\begin{aligned} \label{e:DVell} \bar\DV_j(\ell) &= \{V \in \Qcal : \; |{\rm Im} g| < \textstyle{\frac {1}{5}} {\rm Re} g, \; \epsilon_{V,j}(\ell_j) \le \alpha''\ggen_j \}, \\ \lbeq{DVh} \bar\DV_j(h) &= \{V \in \Qcal : \; |{\rm Im} g| < \textstyle{\frac {1}{5}} {\rm Re} g, \; \alpha \le \epsilon_{g\tau^2,j}(h_j), \; \epsilon_{V,j}(h_j) \le \alpha' \}.\end{aligned}$$ We permit the parameters $\alpha,\alpha' >0$ to depend on $C_\DV$, and $\alpha''=\alpha''_L >0$ to depend on $C_\DV, L$. Their specific values are of no importance. We sometimes need versions with larger $\alpha',\alpha''$ and smaller $\alpha$, and we denote these by $\bar\DV_j'$. This is the case in the following proposition, which is proved in Section \[app:sp\]. \[prop:monobd\] Let $d=4$. If $V \in \DV_j$ then there is a choice of parameters defining the domains – such that $$\begin{aligned} \lbeq{VDbar} V &\in \bar\DV_j(\ell) \cap \bar\DV_j(h) \quad\quad (j \le N),\end{aligned}$$ and if $V \in \bar\DV_j(\h)$ (for $\h=h$ or $\ell$) then with a new choice of parameters for $\bar\DV'$, $$\begin{aligned} \lbeq{Vptbar} V_{\pt,j+1}(V) &\in \bar\DV_{j}'(\h) \cap \bar\DV_{j+1}'(\h) \quad\quad (j < N) .\end{aligned}$$ The domain $\bar\DV_j$ is the principal domain for $V$ throughout the paper. By Proposition \[prop:monobd\], we know that $\DV_j \subset \bar\DV_j(\h_j)$ for both $\h=\ell$ and $\h=h$, so all assertions valid for $V \in \bar\DV_j$ are valid for $V\in \DV_j$. In particular, asserts that if $V \in \DV_j$, then $$\begin{aligned} \label{e:epVbarepV} \alpha &\le \epsilon_{g\tau^2,j}(h), \quad\quad \epsilon_{V,j} \le \begin{cases} \alpha''_L \ggen_j & \h = \ell \\ \alpha' & \h = h. \end{cases}\end{aligned}$$ From and , we see that $$\lbeq{epVbark0} \epVbar(h) \asymp k_0^4,$$ where $k_0$ is the small constant in the definition of $h_j$. From we see that the $g\tau^2$ term dominates $V$ in the $h$-norm, in the sense that (h) ’\^[-1]{} (h) . Together with the lower bound on $\epVbar(h)$, this is important in using the $e^{-g\tau^2}$ factor in $e^{-V}$ to obtain effective stability bounds. A bound like also holds for the case $\h=\ell$, but with an $L$-dependent constant; this follows since $\epV(\ell)$ and $\epVbar(\ell)$ are both of order $\ggen_j$ by and . However in this case, since we are interested in situations where $\ggen_j \to 0$ as $j \to \infty$, we do not have a uniform lower bound on $\epVbar(\ell)$. Our analysis throughout the paper rests on the estimates of Proposition \[prop:monobd\] but does not depend on the particular form of the observable terms in and their counterparts on the right-hand side of . If different observable terms were used instead then there is no significant change in the analysis as long as the statements of Proposition \[prop:monobd\] remain valid; this observation is useful in [@ST-phi4]. ### Definition of small parameter epsilonbar {#sec:epdVdef} An additional small parameter which is important for our analysis is $\epdV = \epdV(\h)$, which takes on different values for the two cases $\h=\ell$ and $\h=h$. Recall that the sequence $\chi_j = \Omega^{-(j-\jm)_+}$ was defined in . We define \[e:epdVdef\] = \_[j]{} = \_[j]{}\^[1/2]{} \_[j]{} & \_[j]{}=\_[j]{}\ \_[j]{}\^[1/2]{} \_[j]{}\^[1/4]{} & \_[j]{}= h\_[j]{}. In view of our assumption throughout the paper that $\ggen_j$ is small (uniformly in $j$, and small depending on $L$), we can assume that $\epdV$ is as small as desired (depending on $L$). The sequence $\chi_j$ occurring in $\epdV^2$ provides useful exponential decay beyond the $\Omega$-scale . The small parameter $\epdV$ plays a role in many aspects of the paper. For example, it arises as an upper bound for $W$ of – and for $P$ of , in the sense that there is an $L$-dependent constant $c_L$ such that for $1 \le j \le N$ and $V \in \bar\DV_j$, $$\begin{aligned} \lbeq{WBbd} \max_{B \in \Bcal_j} \|W_j(V,B)\|_{T_{0,j}(\h_j)} &\le c_L \epdV^2, \\ \lbeq{PBbd} \max_{B \in \Bcal_j} \|P_j(V,B)\|_{T_{0,j}(\h_j)} &\le c_L \epdV^2.\end{aligned}$$ The inequalities – are proved in Proposition \[prop:Wnorms\] below. Main results {#sec:IE} ============ We now state our main results. We begin in Section \[sec:stab\] with stability estimates on the interaction $I$ and a statement of the analyticity of $I$ in the polynomial $V$. In Section \[sec:pt\] we state our results concerning the accuracy of the perturbative calculations of [@BBS-rg-pt]. Finally, in Section \[sec:scale\], we state estimates on Gaussian expectation, and on the operator $(1-\LT)$ which extracts the irrelevant part of an element of $\Ncal$; both of these estimates involve advancement of the scale. Proofs are deferred to Sections \[sec:I-estimates\]–\[sec:ipcl\]. Stability estimates {#sec:stab} ------------------- In this section, we state stability estimates on $I$, and formulate the analyticity of $I$ in $V$. Proofs are given in Section \[sec:I-estimates\]. Fundamental stability bounds are given in the following proposition, which is valid for *arbitrary* choice of $\h$ in the definition of the norms, with corresponding $\epV, \epVbar$ as defined in Section \[sec:spdefs\]. According to , if $V \in \bar\DV$ then $\|W(V,B)\|_{T_0}$ (which occurs in the hypothesis) is of order $\epdV^2$ so can be made small by the requirement that $\ggen_j$ be uniformly sufficiently small. Recall that the norm $\|\phi\|_{\tilde\Phi(X)}$ was defined in ; it appears in the last exponent in . All norms in Proposition \[prop:Iupper\] are at scale $j$. The proof of makes use of the Sobolev inequality proved in Appendix \[sec:Lp\] to take advantage of the quartic decay in $e^{-g\tau^2}$. The restriction to $j<N$ in is connected with the fact that we do not define the $\tilde G$ norm at scale $N$. \[prop:Iupper\] Let $V \in \Qcal$ with $0\le |{\rm Im} g| \le \frac 12 {\rm Re}g$. Let $j \le N$ and $B \in \Bcal_j$. Let $\omega = \max_{B \in \Bcal_j}\|W(V,B)\|_{T_0}$ and fix any $u \ge 6(L^{2d}\omega)^{1/3}$. Let $F\in \Ncal(B^\Box)$ be a polynomial of degree $r \le p_\Ncal$. Let $I^*$ denote any one of the following choices:\ (a) $I_j(B)$, (b) $\tilde I_j(B)$, (c) $\Itilde_j(B \setminus X)$ with $X \in \Scal_{j-1}(B)$, (d) any of (a-c) with any number of their $1+W$ factors omitted (thus, in particular, including the case $\Ical(B)$ of ).\ (i) Then $$\begin{aligned} \label{e:Iupper-a} & \|I^* F\|_{T_{\phi}} \le \left(\frac{2r}{u} \right)^{r} \| F\|_{T_{0}} e^{O (\epV +u)(1+ \|\phi\|_{\Phi(B^{\Box})}^2)} .\end{aligned}$$ (ii) Suppose in addition that there is a constant $C$ such that $\epV \le C\epVbar$. Fix any $q \ge 0$, and let $q_1= q +2u\epVbar^{-1}$. Then for $j <N$, $$\begin{aligned} \label{e:Iupper-b} & \|I^* F\|_{T_{\phi}} \le \left(\frac{2r}{u} \right)^{r} \| F\|_{T_{0}} e^{O [(1+q_1^{2})\epVbar+u]} e^{-q \epVbar \|\phi\|_{\Phi(B^{\Box})}^2} e^{O (1+q_1) \epVbar \|\phi\|_{\tilde\Phi(B^{\Box})}^2}.\end{aligned}$$ When $r=0$, – both hold with the prefactor $\left(\frac{2r}{u} \right)^{r}$ replaced by $1$. *Notation.* We write $a \prec b$ when there is a constant $c>0$, independent of $L$ and $j$, such that $a \le c b$. If there is an $L$-dependent such constant, we write $a \prec_L b$. We write $a \asymp b$ when $a \prec b$ and $b \prec a$. We now discuss applications of Proposition \[prop:Iupper\] under the assumption that $V \in \bar\DV_j$ of –. *Application of .* Let $\h_j=\ell_j$ (defined in ) and let $V \in \bar\DV_j (\ell)$. By and , we obtain the hypotheses for when $\ggen_j$ is small uniformly in $j$. Furthermore, $u>0$ can also be chosen small enough, independently of $j$, so that $\exp [O(\epV +u)] \le 2$. With these choices, and with the fluctuation-field regulator defined by , we can restate as $$\begin{aligned} \label{e:Iupper-a-c} & \|I^* F\|_{T_{\phi}(\ell)} \le \left(\frac{2r}{u} \right)^{r} \| F\|_{T_{0}(\ell)}\, 2e^{\|\phi\|_{\Phi}^2} = \left(\frac{2r}{u} \right)^{r} \| F\|_{T_{0}(\ell)}\, 2 G(B,\phi) ,\end{aligned}$$ again with the convention that $(\frac{2r}{u} )^{r} =1$ when $r=0$. *Application of .* We apply with the choice $\h_j=h_j$ of . By and , for $V \in \bar\DV_j(h_j)$, with this choice $$\epVbar \asymp k_0^4, \quad\quad \|W(B)\|_{T_0} \prec_L\; \ggen_j^{1/2}.$$ We choose $k_{0}>0$ and take $u=\epVbar$. Then $$(1+q_1^2)\epVbar + u = \left(2+(q+2)^2 \right)\epVbar, \quad\quad (1+q_1)\epVbar = (3+q) \epVbar.$$ We conclude from that there is a constant $a$ such that, for $V \in \bar\DV(h_j)$, $$\begin{aligned} \label{e:Iupper-b-c} & \|I^* F\|_{T_{\phi}(h)} \le \left(\frac{2r}{ak_0^4} \right)^{r} \| F\|_{T_{0}(h)}\, 2 e^{-q\epVbar \|\phi\|_{\Phi(B^{\Box},h)}^2} e^{(3+q) \epVbar \|\phi\|_{\tilde\Phi(B^{\Box},h)}^2} ,\end{aligned}$$ with the usual convention when $r=0$. Since $h \ge \ell$, we have $\|\phi\|_{\Phi(\h)} \le \|\phi\|_{\Phi(\ell)}$ and hence also $\|\phi\|_{\tilde\Phi(\h)} \le \|\phi\|_{\tilde\Phi(\ell)}$. This allows us to conclude from that, for $V \in \bar\DV(h_j)$, if $q \le \bar q$ for some fixed $\bar q >0$ then we can choose $k_0$ small depending on $\bar q$ and $\Gtilp$ such that $$\begin{aligned} \label{e:Iupper-b-d} & \|I^* F\|_{T_{\phi}(h)} \le \left(\frac{2r}{ak_0^4} \right)^{r} \| F\|_{T_{0}(h)}\, 2 e^{-q ak_0^4 \|\phi\|_{\Phi(B^{\Box},h)}^2} \tilde{G}^{\Gtilp}(B,\phi).\end{aligned}$$ *Vanishing at weighted infinity.* In , a stronger bound in which $G(B,\phi)$ is replaced by a smaller power $G^{\gamma}(B,\phi)$ also holds, by the same proof. In combination with , and with $\Gcal$ denoting $G$ when $\h=\ell$ and $\tilde G$ when $\h=h$, in either case this shows that if $V \in \bar\DV$ then $$\lbeq{vai} \lim_{\|\phi\|_{\Phi(B^\Box)} \to \infty} \|I^* F\|_{T_\phi}\Gcal(X,\phi)^{-\Gtilp} =0.$$ This fact is useful in [@BS-rg-step] to establish the property used there called “vanishing at weighted infinity.” The following proposition extends and reformulates the above estimates in terms of the four norms $\|\cdot\|_j, \|\cdot\|_{j+1}$ appearing in *either* of –. However, here and throughout the paper, as discussed in Remark \[rk:scaleNnorm\], statements about the scale-$N$ norm are to be interpreted as applying *only* to the $G_{N-1}^{10}$ norm, and not also to the $\tilde G$ norm: scale-$N$ is always considered to correspond to $j+1$ and never to $j$ in –. \[prop:Istab\] Let $I_*$ denote either of $I_j,\Ipttil$, with $j_*=j$ for $I_j$, and *either* $j_*=j$ or $j_*=j+1$ for $\Ipttil$. We assume $j_* \le N$. Alternately, let $I_*$ denote any of the above with any number of their $1+W$ factors omitted. Let $B\in \Bcal_j$. Let $V \in \bar\DV_j$ and let $F\in \Ncal(B^{\Box})$ be a gauge-invariant polynomial in the fields of degree at most $p_\Ncal$ with $\pi_{ab}F=0$ if $j < j_{\pp \qq}$. Then $$\begin{aligned} \label{e:IF} \|I_*(B) F\|_{j_*} & \prec \|F\|_{T_{0,j}} , \\ \label{e:Iass} \|I_*(B)\|_{j_*} & \le 2 , \\ \label{e:I-b:5} \|I_*^{-B}\|_{T_{0,j_*} } & \le 2 .\end{aligned}$$ In addition, for $j+1 \le N$ and for a scale-$(j+1)$ block $\hat B \in \Bcal_{j+1}$, and for $X$ either a small set $X \in \Scal_j$ or the empty set $X=\varnothing$, $$\label{e:Iptass} \|\Ipttil^{\hat B\setminus X}\|_{j+1} \le 2 .$$ The following proposition states our analyticity result for the interaction, again in terms of the four norms $\|\cdot\|_j, \|\cdot\|_{j+1}$ appearing in –. We show that $I$ is analytic in $V$ by proving that there is a norm-convergent expansion of $I$ in powers of $V$. \[prop:Ianalytic1:5\] Let $I_*$ denote either of $I,\Ipttil$, with $j_*=j$ for $I$, and *either* $j_*=j$ or $j_*=j+1$ for $\Ipttil$. We assume $j_* \le N$. Alternately, let $I_*$ denote any of the above with any number of their $1+W$ factors omitted. Let $B\in \Bcal_j$. Then $I(B)$ and $\Ipttil(B)$ are analytic functions of $V \in \bar\DV_j$, taking values in $\Ncal(B^\Box), \|\cdot\|_{j_*}$. In addition, $I(B)^{-1}$ is an analytic function of $V \in \bar\DV_j$ taking values in $\Ncal(B^\Box), \|\cdot\|_{T_{0,j}}$. Recall that $\epdV$ was defined in , and that we use $\h=\ell$ for quantities related to the norm pair , and $\h=h$ for the norm pair . The following proposition measures the effect of a change in $I$ due to a change in $V$ that is appropriately bounded by $\epdV$. \[prop:JCK-app-1\] Let $j<N$, $B \in \Bcal$, $V \in \bar\DV$, $Q \in \Qcal$ with $\|Q(B)\|_{T_0} \prec \epdV$, and set $\Ihat = I(V-Q)$ and $I=I(V)$. Then $V-Q \in \bar\DV'$, $\Ihat(B)$ obeys the $I_*$ estimates of Proposition \[prop:Istab\], is an analytic function of $V\in \bar\DV$ taking values in $\Ncal(B^\Box), \|\cdot\|_j$, and obeys the estimates $$\begin{aligned} \label{e:JCK1-app} \|\Ihat(B)- I(B)\|_j &\prec \epdV , \\ \label{e:JCK2-app} \| \Ihat(B)- I(B)(1+ Q(B) ) \|_{T_{0} } &\prec_{L} \epdV^{2} .\end{aligned}$$ All quantities and norms are at scale $j$, norms are computed with either $\h=\ell$ or $\h=h$, and holds for either choice of $\|\cdot \|_j$ in –. Perturbative interaction estimates {#sec:pt} ---------------------------------- In this section, we formulate two propositions which enable a rigorous implementation of the formal perturbative calculations of [@BBS-rg-pt Section \[pt-sec:WPjobs\]]. The two propositions are applied in [@BS-rg-step Section \[step-sec:Map3estimates\]]. Their statements are in terms of the small parameter $\epdV$ defined in . Recall the map $\theta$ defined below , the polynomial $\Vpt$ defined in (and above for scale-$N$), and $\Ipttil$ defined in . For $B \in \Bcal_j$ and $X \in \Pcal_j$, we define $\delta I^X \in \Ncal (\Lambdabold \sqcup \Lambdabold')$ by $$\label{e:dIdef} \delta I (B) = \theta I_j(B) - \Ipttil(B) = \theta I_j(V,B)-\Itilde_{j+1}(\Vpt,B) , \quad\quad \delta I^X = \prod_{B \in \Bcal_j(X)}\delta I(B).$$ For small sets $U\in \Scal_{j+1}$ we define $$\hred (U) = \sum_{X \in\overline{\Pcal}_{j}(U): |X|_j \le 2} \Ipttil^{-X}\Ex_{j+1} \delta I^X, \label{e:hred-def}$$ where $|X|_j$ denotes the number of scale-$j$ blocks in $X$, and $X \in \overline\Pcal_j(U)$ indicates the restriction that $U$ is the smallest polymer in $\Pcal_{j+1}$ that contains $X$. The subscript “red” indicates that $h$ is “reduced” by the restriction $|X|_j\le 2$. (In [@BS-rg-step] we define a version without this restriction.) For [@BS-rg-step], we need to compute $\hred$ accurately to second order in $\epdV$. For this, we first recall from the definition of the truncated expectation $$\label{e:trun-exp} \Ex_C (A; B) = \Ex_C(AB) - (\Ex_CA)(\Ex_CB).$$ We also define (cf. ) $$\begin{aligned} \label{e:Epi} \Ex_{\pi ,C} (A;B) &= \Ex_C ( A;\pi_{\varnothing}B) + \Ex_C ( \pi_* A; B) .\end{aligned}$$ Then for $(U,B) \in \Scal_{j+1}\times \Bcal_{j+1}$ we define $\hldg (U,B)$ by $$\label{e:hptdefqq} \hldg (U,B) = \begin{cases} -\frac{1}{2}\Ex_{\pi ,j+1} \theta ( V_j(B); V_j(\Lambda \setminus B)) & U=B \\ \;\;\; \frac{1}{2} \Ex_{\pi ,j+1}\theta ( V_j(B); V_j(U\setminus B)) & U \supset B, |U|_{j+1}=2 \\ \;\;\; 0 &\text{otherwise} , \end{cases}$$ where we have abbreviated the subscript $C_{j+1}$ to $j+1$ on $\Ex$. For $U \in \Pcal_{j+1}$ we define $$\label{e:hldgUdef} \hldg(U) = \sum_{B \in \Bcal_{j+1} (U)} \hldg (U,B) .$$ Due to the finite-range property , $$\sum_{U \supset B : U \neq B} \hldg(U,B) = \frac{1}{2} \Ex_{\pi ,j+1}\theta (V_{j}(B) ; V_{j}(\Lambda \setminus B)) ,$$ and therefore $\hldg$ obeys the identity $$\label{e:hpt0bis} \sum_{U \supset B} \hldg (U,B) = 0.$$ The following two propositions, which are proved in Section \[sec:interaction-estimates444\], show that $\hldg$ is second order in $\epdV$, and that $\hldg(U)$ is the leading part of $\hred(U)$. The latter is a much more substantial result than the former, and is our implementation of the formal power series statement of [@BBS-rg-pt Proposition \[pt-prop:I-action\]]. \[prop:hldg\] There is a positive constant $\cldg = \cldg(L)$ such that for $j<N$, $V \in \bar\DV_j$ and $(U,B) \in \Scal_{j+1}\times \Bcal_{j+1}$, $$\begin{aligned} \label{e:want1} \|\Ipttil (U) \hldg (U,B)\|_{j+1} & \le \cldg \epdV^2 ,\end{aligned}$$ where $\|\cdot \|_{j+1}$ represents either of the two options –, with corresponding $\epdV$ of . \[prop:h\] There is a positive constant $c_{\pt}=c_{\pt}(L)$ such that for $j<N$, $V \in \bar\DV_j$ and $U \in\Scal_{j+1}$ with $|U|_{j+1}\in \{1,2\}$, $$\begin{aligned} \label{e:want2} \|\Ipttil (U) [\hred(U)-\hldg (U)]\|_{j+1} & \le c_{\pt} \epdV^{3} ,\end{aligned}$$ where $\|\cdot \|_{j+1}$ represents either of the two options –, with corresponding $\epdV$ of . Bound on expectation and crucial contraction {#sec:scale} -------------------------------------------- The next two propositions play a key role in our analysis of a single renormalisation group step in [@BS-rg-step Section \[step-sec:Map3estimates\]]. \[prop:ip\] There is an $\Econst >0$ (independent of $L$) and a $C_{\delta V}>0$ (depending on $L$) such that for $j<N$, $V \in \bar\DV_j$, disjoint $X,Y \in \Pcal_j$, and for $F(Y) \in \Ncal(Y^\Box)$, $$\label{e:integration-property} \|\Ex_{j+1} \delta I^X \theta F(Y) \|_{j+1} \le \Econst^{|X|_j+|Y|_j} (C_{\delta V}\epdV)^{|X|_j}\|F(Y)\|_j,$$ where the pair of norms is given by either of or with corresponding $\epdV$ of . The proof of Proposition \[prop:ip\] is given in Section \[sec:ippf\]. We refer to the important inequality as the *integration property*. It shows that when estimating the scale-$(j+1)$ norm of an expectation of a product involving factors of $\delta I(B)$ for scale-$j$ blocks, each factor gives rise to a small factor $\epdV$. In the next proposition, the notation $U = \overline X$ again indicates the restriction that $U$ is the smallest polymer in $\Pcal_{j+1}$ that contains $X$. As in [@BS-rg-loc Definition \[loc-def:LTXYsym\]], we use the notation $X(\varnothing)=X$, $X(a) = X \cap \{a\}$, $X(b)=X \cap \{b\}$, and $X(ab) = X \cap\{a,b\}$. Given $X \subset \Lambda$, we define $$\label{e:gamLdef} \gamma(X) = L^{-d -1} + L^{-1}\1_{X \cap \{a,b\} \not = \varnothing}.$$ \[prop:cl\] Let $j<N$ and $V\in \DV_j$. Let $X \in \Scal_j$ and $U = \overline X$. Let $F(X) \in \Ncal(X^\Box)$ be such that $\pi_\alpha F(X) =0$ when $X(\alpha)=\varnothing$, and such that $\pi_{ab}F(X)=0$ unless $j \ge j_{ab}$ (recall ). Then $$\begin{aligned} \label{e:contraction3z-new} \|\Ipttil^{U\setminus X} \Ex_{C_{j+1}} \theta F (X) \|_{j+1} & \prec \cgam(X) \kappa_F + \kappa_{\LT F} ,\end{aligned}$$ with $\kappa_F=\|F (X)\|_{j}$ and $\kappa_{\LT F} =\|\Ipttil^X \LT_X \Ipttil^{-X} F(X) \|_j$, and where the pair of norms is given by either of or . The proof of the Proposition \[prop:cl\] is given in Section \[sec:contraction3-proof\]. We refer to the inequality as the *crucial contraction*; its importance is discussed in Section \[sec:cc\] above. Estimates on small parameters {#app:sp} ============================= In this section, we provide estimates on the small parameters $\epV,\epdV$ which drive our analysis. In particular, we prove Proposition \[prop:monobd\]. Preliminaries ------------- We begin with two general lemmas. The first relates $\epsilon_{V,j}$ to $\|V(B)\|_{T_{0,j}}$ for a scale-$j$ block $B \in \Bcal_j$, and the second expresses an important monotonicity property of the $T_\phi$ semi-norm under change of scale. Recall from [@BS-rg-loc] that it follows from the definition of the $T_\phi$ semi-norm that under the direct sum decomposition of $F \in \Ncal$ due to , F\_[T\_]{} &= \_[,a,b,ab]{}\_F \_[T\_]{} = F\_\_[T\_]{} + \_F\_a\_[T\_]{} + \_F\_b\_[T\_]{} + \_\^2 F\_[ab]{}\_[T\_]{} . ### The T0 semi-norm and epsilonV \[lem:T0ep\] For $V \in \Qcal$ and $j<N$, $\epsilon_{V,j} \asymp \max_{B \in \Bcal_j} \|V(B)\|_{T_{0,j}}$. Given $V \in \Qcalnabla$, as in we write $V_\varnothing = \sum_{M} M$ for the decomposition of its bulk part as a sum of individual field monomials such as $\nu \phi\bar\phi$, $\nu \psi\bar\psi$, $z(\Delta \phi)\bar\phi$, and so on. For $0 \le j \le N$, in we defined $$\label{e:monobd-bis} \epV = L^{dj} \sum_{M : \pi_*M=0} \|M_0\|_{T_{0,j}(\h_j)} + (|\lambdaa|+|\lambdab|)\h_j\h_{\sigma,j} + (|\qa|+|\qb|)\h_{\sigma,j}^2 .$$ By direct calculation, $\|\lambda_\pp \bar\phi_{x}\|_{T_0}=\1_{x=\pp}|\lambda^a|\h$, $\|\lambda_\qq \phi_{x}\|_{T_0} = \1_{x=\qq}|\lambdab|\h$, and $|q_{\pp\qq}| = \frac{1}{2}(|\qa|\1_{x=\pp}+|\qb|\1_{x=\qq})$. Thus the last two terms on the right-hand side of are bounded above and below by multiples of $\max_{B \in \Bcal_j}\|\pi_*V(B)\|_{T_0}$, and it suffices to consider the case $V=\pi_\varnothing V$, which we assume henceforth. It follows from the triangle inequality that $\|V(B)\|_{T_0} \prec \epV$, and it suffices to prove the reverse inequality. Let $M$ be a scalar multiple of one of $g\phi\bar\phi\phi\bar\phi, g\phi\bar\phi\psi\bar\psi, \nu\phi\bar\phi, \ldots$. It suffices to prove that $$\lbeq{M0V} \|M_0\|_{T_0}|B| \prec \|V(B)\|_{T_0}.$$ For this, we employ the pairing of [@BS-rg-norm Definition \[norm-def:Tphi-norm\]], and seek dual test functions for the monomials. In more detail, given a monomial $M$ we seek a unit $\Phi$-norm test function $f_M$ such that, for all $x\in B$, $\pair{M_x,f_M}=\|M_x\|_{T_0}$ but $\pair{M'_x,f_M} = 0$ if $M' \neq M$. It then follows that $$\begin{aligned} \lbeq{T0epid} \|M_{0}\|_{T_{0}} & = |\pair{ M_{x},f_M}_{0}| = \frac{1}{|B|} |\pair{M (B),f_M}_{0}| = \frac{1}{|B|} |\pair{V (B),f_M}_{0}| \le \frac{1}{|B|} \|V (B)\|_{T_{0}},\end{aligned}$$ which is equivalent to the desired estimate for this monomial. For the existence of $f_M$, we proceed as follows (cf. [@BS-rg-loc Lemma \[loc-lem:dualbasis\]] for related ideas). Consider first the case $M=g\phi\bar\phi\phi\bar\phi$. We choose $f_M$ to be zero on all sequences except those of length four whose components are in the $\phi, \phib, \phi, \phib$ sheets, and choose it to be constant on the set of these sequences, with the constant such that $f_M$ has unit norm. This choice can be seen to have the desired properties, and it generalises in a straightforward way to all the monomials arising from $g\tau^2$ and $\nu\tau$. Next, we consider $M = \frac 12 \sum_{e \in \units}(\nabla^e\phi)(\nabla^e\bar\phi)$ (the coupling constant plays an insignificant role so we omit it for simplicity). By translation invariance, we may assume that $B$ is centred at $0\in \Lambda$, and since $j<N$ we can identify $B$ with a subset of $\Zd$. Let $v_{x_{1},x_{2}}= x_{1}\cdot x_{2} + c$ for $x_{1}$ in the $\phi$ sheet and $x_{2}$ in the $\phib$ sheet. Let $M'=\phi\bar\phi$. Then the pairing of $v$ with any monomial other than $M,M'$ vanishes. In particular, $\pair{M_x,v}_0= \frac 12 \sum_{e \in \units} \nabla_{x_1}^e \nabla_{x_2}^e v_{x,x} = d$. Also, $\pair{M_{x}',v}_{0} \asymp x\cdot x + c$, and by choosing $c\asymp L^{2j}$ such that $\sum_{x \in B}(x\cdot x + c)=0$, we can arrange that $\pair{M'(B),v}_0=0$. Let $f = v/\|v\|_{\Phi}$. Then we have $\pair{V(B),f}_0=\pair{M(B),f}_0 = |B|\pair{M_0,f}_0$ and we obtain in this case, as in . The case $M = \bar\phi \Delta\phi$ is similar, with the test function constructed from $v_{x_{1},x_{2}} = x_{1}\cdot x_{1} + c$. This completes the proof. ### Scale monotonicity We now prove a monotonicity property of the $T_\phi$ semi-norm under change of scale, which is used repeatedly throughout the paper. The property is more general than our specific application, and we formulate it under assumptions on $\h=(\h_\phi,\h_\sigma)$ obeyed by our particular choices. In our application, with $\h'=\h$ follows from the last two bounds of . \[lem:Imono\] Suppose that $F \in \Ncal$ is gauge invariant and such that $\pi_{ab}F=0$ when $j<j_{ab}$, that $\h_{\phi,j}'' \le \h_{\phi,j}' \prec L^{-[\phi]}\h_{\phi,j-1}$, that $\h_{\sigma,j}'' \prec \h_{\sigma,j}'$, and that for all $j$, $$\label{e:hprod-bis} \h_{\sigma,j}' \prec \begin{cases} L^{[\phi]}\h_{\sigma,j-1} & j < j_{ab} \\ \h_{\sigma,j-1} & j \ge j_{ab}, \end{cases} \quad\quad \h_{\sigma,j+1}'\h_{\phi,j+1}' \prec \h_{\sigma,j}\h_{\phi,j}.$$ Then, for $L$ large depending on the constant in $\prec$ in the hypothesis, $$\label{e:scale-change} \|F\|_{T_{\phi,j}(\h_{j}'')} \prec \|F\|_{T_{\phi,j}(\h_j') } \prec \|F\|_{T_{\phi,j-1}(\h_{j-1}) } .$$ By it suffices to prove that for each $\alpha$, $\|\pi_\alpha F\|_{T_\phi}$ individually obeys . Case $\alpha = \varnothing$. By definition of the norm on test functions (recall [@BS-rg-norm Example \[norm-ex:h\]]), for a test function $g$ with none of its variables corresponding to observable sheets, $$\label{e:g-norms} \|g\|_{\Phi_{j-1}(\h_{j-1})} \le \|g\|_{\Phi_{j}(\h_j')} \le \|g\|_{\Phi_{j}(\h_j'')} ,$$ provided $L$ is chosen large so that the hypothesis $\h_{\phi,j}' \prec L^{-[\phi]}\h_{\phi,j-1}$ implies that $\h_{\phi,j}' \le \h_{\phi,j-1}$. As a direct consequence of the definition $\|F\|_{T_\phi} = \sup_{\|g\|_\Phi \le 1}|\pair{F,g}_\phi|$ of the $T_\phi$ semi-norm in [@BS-rg-norm Definition \[norm-def:Tphi-norm\]], we obtain with $F$ replaced by $\pi_{\varnothing}F$ as was to be proved. In fact for this case we obtain the stronger inequality with $\prec$ replaced by $\le$. Case $\alpha = \pp\qq$. By $\|\pi_{ab} F\|_{T_\phi} = \h_\sigma^2 \|F_{ab}\|_{T_\phi}$, so the first inequality of follows immediately from the hypothesis $\h_{\sigma,j}'' \prec \h_{\sigma,j}'$ and case $\alpha =\varnothing$. Likewise the second inequality for $j \ge j_{ab}$ follows from the hypothesis $\h_{\sigma,j}' \prec \h_{\sigma,j-1}$. The second inequality for $j<j_{ab}$ is vacuous because, by hypothesis, $\pi_{ab}F=0$ for $j<j_{ab}$. Cases $\alpha=\pp$ or $\alpha=\qq$. These are similar, and we consider only $\alpha =\pp$. The fact that $\pi_\pp F = \sigma F_{\pp}$ is gauge invariant implies that its pairing with a test function $g$ is zero unless exactly one argument of $g$ has species $\sigma$ and at least one other argument has species $\phi$ or $\psi$. Therefore, for gauge invariant $F$, we can refine [@BS-rg-norm Definition \[norm-def:Tphi-norm\]] by restricting the supremum to unit norm test functions with this support property. By the second inequality of test functions with this support property satisfy with $\prec$ in place of $\le$. The constants in $\prec$ must be independent of $j$, and they are because there is only one $\sigma$ and $L$ is large. This implies for case $\alpha =\pp$ and completes the proof. The small parameter epsilonV: Proof of Proposition \[prop:monobd\] {#sec:epVW} ------------------------------------------------------------------ It suffices to prove that:\ (i) For $j \le N$ and $V \in \DV_j$, there exist $a,A >0$ (depending on $C_\DV$) and $A_L >0$ (depending on $C_\DV, L$) such that $$\begin{aligned} \label{e:epVbardefz-app} |{\rm Im} g| < \textstyle{\frac {1}{5}} {\rm Re} g, \quad\quad a k_0^4 &\le \epsilon_{g\tau^2,j}(h_j), \quad\quad \epsilon_{V,j} \le \begin{cases} A_L \ggen_j & \h = \ell \\ A k_0 & \h = h. \end{cases}\end{aligned}$$ (ii) For $j < N$ and $V \in \bar\DV_j$, the bounds hold (with different constants) when $V$ is replaced by $V_{\pt,j+1}$ (and $g$ by $\gpt$), and also when $j$ is replaced by $j+1$. We prove the above two statements in sequence.\ (i) For $j \le N$ and $V \in \DV_j$, the coupling constants obey $$C_{\DV}^{-1} \ggen_j < {\rm Re} g < C_{\DV} \ggen_j, \quad |{\rm Im} g| < \textstyle{\frac {1}{10}}{\rm Re} g < \textstyle{\frac {1}{5}} \ggen_j, \quad$$ $$\begin{gathered} \label{e:ccbds} L^{2j}|\nu|,|z| , |y| \le C_{\DV} \ggen_j, \quad |\lambda| \le C_{\DV} , \quad L^{2j_{ab}[\phi]}2^{2(j-j_{ab})}|q|\le \begin{cases} 0 & j < j_{ab} \\ C_{\DV} & j \ge j_{ab}, \end{cases}\end{gathered}$$ for $\lambda$ equal to $\lambdaa$ or $\lambdab$ and similarly for $q$. The first inequality of holds by definition. As noted in , $$\label{e:epVbardef-h-i} \epsilon_{g\tau^2,j}(\h_j) \asymp L^{dj} |g| \h_j^4 .$$ In particular, since $|g|\asymp \ggen_j $ by hypothesis, $$\label{e:epVbardef-h} \epsilon_{g\tau^2,j}(h_j) \asymp L^{dj} |g| h_j^4 \asymp k_0^4 ,$$ which proves the second bound of . The last bound of for the bulk part $V_\varnothing$ of $V$ similarly follows from direct calculation as in [@BS-rg-norm Proposition \[norm-prop:taunorm\]]; e.g., $\|\phi_x\bar\phi_x\|_{T_{0,i}} = \h_i^2$, $\|\phi_x\bar\phi_x\phi_x\bar\phi_x\|_{T_{0,i}} = \h_i^4$, $\|\phi_x\Delta \bar\phi_x\|_{T_{0,i}} = L^{-2i} \h_i^2$, while the observables contribute $$\begin{aligned} \lbeq{hsigh} |\lambda| \h_i \h_{\sigma,i} &= |\lambda| \times \begin{cases} \ggen_i \ell_0 (2/L)^{(i-j_{ab})_+ } & \h =\ell \\ k_0 (2/L)^{(i-j_{ab})_+ } & \h = h , \end{cases} \\ \lbeq{qhsig} |q|\h_{\sigma,i}^2 & \prec \begin{cases} \ggen_i^2 & \h=\ell \\ \ggen_i^{1/2} & \h=h \end{cases}\end{aligned}$$ (for we can restrict to $i \ge j_{ab}$ since otherwise $q=0$). The combination of these bounds completes the proof of , after taking into account that $\ell_0$ depends on $L$ and $k_0^4 \le k_0$. \(ii) Let $V \in \bar\DV_j$. We first consider the case $j+1<N$, $n=j$ of . By , $\Vpt =V + 2gC_{0,0}\tau - P$, with $C=C_{j+1}$ and $P=P_j$. By , $$\|2gC_{0,0}\tau_x\|_{T_{0,j}} \prec |g|L^{-2j}\h_j^2 .$$ By , Lemma \[lem:T0ep\], and , $$\begin{aligned} \lbeq{epVptbd} \epsilon_{\Vpt} & \prec \epV + |g|L^{2j} \h_j^2 + \epsilon_P \prec \epV + |g|L^{2j}\h_j^2 + \max_{B \in \Bcal_j}\|P(B)\|_{T_{0,j}} \nnb & \prec \epV + |g|L^{2j}\h_j^2 + O_L(\epdV^2).\end{aligned}$$ With the definition of $\h_j$ in –, this shows that $\epsilon_{\Vpt}$ obeys the last bound of . For the second bound of , we restrict to $\h=h$, and note that the lower bound follows from the lower bound on the $\tau^2$ term of $V$, together with the fact that the contribution to $\tau^2$ from $P$ is bounded above by $\epsilon_P \prec_L \ggen_j^{1/2}$. Finally, for the bound on the imaginary part of $\gpt$ we use the fact that it changes insignificantly from the imaginary part of $g$, since the coupling constant $g_P$ of $P$ obeys $|g_P| \prec \epsilon_{g_p\tau^2,j}(\ell_j) \le \epsilon_P(\ell_j) \prec_L \ggen_j^2$ (the first of these inequalities follows from ). For the case $j+1=N$, $n=j$ of , we simply observe that our definition of $V_{\pt,N}$ is identical to what it would be on a torus of scale larger than $N$, so the bound in this case follows from the above argument applied to the torus of scale $N+1$. For the $n=j+1$ case of , note that the computations in the proof of (i) lead to the same conclusion when $\h_j$ is replaced by $\h_{j+1}$ and $|B|=L^{dj}$ is replaced by $L^{d(j+1)}$, and since $\ggen_{j+1}\asymp \ggen_j$ by , we conclude that $V \in \bar\DV_{j+1}(\ell_{j+1}) \cap \bar\DV_{j+1}(h_j)$ (with adjusted constants). The desired result then follows exactly as in the proof of (ii), now with applied at scale-$(j+1)$. This completes the proof. \[rk:hsigmot\] The choice of $\h_\sigma$ in can be motivated as follows; we discuss this for the case $\h=\ell$. Since the norm gives a better bound on the observables when $\h_\sigma$ is chosen large, as a first attempt it would be natural to choose $\ell_\sigma$ as large as possible to make the norm of $\lambdaa\sigma\bar\phi$ agree with (or be bounded by) that of $g\tau^{2}$ on a block, namely $\ggen_j\ell_j^4 L^{dj}=\ggen_j\ell_0^4$. The coupling constant $\lambdaa$ is $O(1)$. The $T_0$ norm of $\sigma\bar\phi$ is $\ell_\sigma \ell$, and to make this no larger than the norm of $g\tau^{2}$ a block, we could choose $\ell_{\sigma,j} = \ggen_j L^{[\phi]j}$. In addition, our choice of $\ell_\sigma$ must also be appropriate for the $\sigma\bar\sigma$ term which arises in $\Vpt$. Our procedure is to take $\qa=\qb=0$ in $V$. Thus, according to the flow of $q$ given in [@BBS-rg-pt], the $\sigma\bar\sigma$ term in $\Vpt$ is given by the increment $\lambdaa\lambdab C_{j+1;a,b}\sigma\bar\sigma$ (which is only nonzero above the coalescence scale $j_{ab}$). According to , with the above choice of $\ell_\sigma$ the norm of this term is of order $L^{-2[\phi]j} \ell_\sigma^2 = \ggen_j^2$, and this is significantly smaller than the norm of the $\lambdaa \sigma \bar\phi$ term (which is good). However, a disadvantage of the choice $\ell_{\sigma,j} = \ggen_j L^{[\phi]j}$ is that it would make the monomial $\sigma\bar\sigma\phi\bar\phi$ be marginal (scale invariant), hence in the range of $\LT$ and thus in $\Vpt$. This monomial only appears after the coalescence scale, and we would prefer it to be irrelevant. To achieve this, we decrease the size of $\ell_\sigma$ to the choice $\ell_\sigma = \ggen_j 2^{(j-j_{ab})_+}L^{[\phi](j \wedge j_{ab})}$ made in . Then $\ell_\sigma$ grows as a power of $L$ below the coalescence scale, but only by a power of $2$ above the coalescence scale. This power of 2 plays a role in the proof of [@BBS-saw4 Theorem \[saw4-thm:wsaw4\]]. The small parameter epsilonbar {#sec:epdV-app} ------------------------------ For $j <N$, we define $$\lbeq{ellhatdef} \hat \ell_j^2 = \hat\ell_0^2 \ell_j^2 \|C_{(j+1)*}\|_{\Phi_{j}^+(\ell_{j})},$$ with $C_{k*}$ defined by . We choose $\hat\ell_0^2 = 100/ c_G$, where $c_G=c(\alpha_G)$ is the constant of [@BS-rg-norm Proposition \[norm-prop:EG2\]] (this choice is useful in the proof of Lemma \[lem:dIipV\] below), so that $$\lbeq{ellhatdef-1} \|C_{(j+1)*}\|_{\Phi_{j}^+(\hat\ell_{j})} = \|C_{(j+1)*}\|_{\Phi_{j}^+(\ell_{j})} \frac{\ell_j^2}{\hat\ell_j^2} = \hat\ell_0^{-2} = \frac{1}{100} c_G.$$ Below the $\Omega$-scale defined by , $\hat\ell_j$ and $\ell_j$ are of the same order of magnitude, but well above the $\Omega$-scale $\hat\ell_j \ll \ell_j$. We use $\hat\ell_j$ in estimates involving integration, as a parameter which captures the size of the covariance effectively. Let $$\label{e:dVdef} \delta V = \theta V - \Vpt = \theta V - V_{\pt,j+1}(V).$$ Recall the definition of $\epdV$ from . The following lemma justifies the notation used for $\epdV$, by showing that it provides an upper bound for $\delta V$. Its restriction to $j<N$ is to keep $\delta V$ defined in . \[lem:epdV\] Let $j<N$. There is an $L$-dependent constant $C_{\delta V}$ such that for all $V \in \bar\DV_j$, and for $j_*=j$ or $j_*=j+1$, $$\label{e:dVbd} \max_{b \in \Bcal_j} \|\delta V(b)\|_{T_{0,j_*}(\h_{j_*} \sqcup \hat\ell_{j_*})} \le C_{\delta V} \epdV.$$ We fix $j<N$, concentrate first on the case $j_*=j$, and drop subscripts $j$. We show that for $V \in \Qcalnabla$ and $b \in \Bcal_j$, $$\label{e:dVbdz-old} \|\delta V(b)\|_{T_{0}(\h \sqcup \hat\ell)} \prec_L \frac{\hat\ell}{\h} \epsilon_{V} + \epdV^2 .$$ This suffices, since (using ) the first term on the right-hand side of obeys $$\frac{\hat\ell}{\h} \epsilon_{V} = \|C\|_{\Phi^+(\ell)}^{1/2} \frac{\ell}{\h} \epsilon_{V} \prec \chicCov_{j}^{1/2} \frac{\ell}{\h} \epsilon_{V} \prec_L \begin{cases} \chicCov_{j}^{1/2}\ggen = \epdV(\ell) & \h=\ell \\ \chicCov_{j}^{1/2}\ggen^{1/4} = \epdV(h) & \h=h. \end{cases}$$ This gives and reduces the proof to showing . We now prove . By and , with $C=C_{j+1}$, $$\Vpt -V= 2gC_{0,0}\tau - P.$$ Therefore, by definition of $\delta V$ in and by the triangle inequality, $$\begin{aligned} \|\delta V(b)\|_{T_{0}(\h \sqcup \hat\ell)} & \le \|\theta V(b) - V(b)\|_{T_{0}(\h\sqcup \hat\ell)} + \|V(b)-\Vpt (b)\|_{T_{0}(\h)} \nnb & \le \|\theta V(b) - V(b)\|_{T_{0}(\h \sqcup \hat\ell)} + \|C\|_{\Phi(\h)} \h^2 \|2g \tau(b)\|_{T_0(\h)} + \|P(b)\|_{T_{0}(\h)} . \label{e:dVbd1}\end{aligned}$$ For the first term on the right-hand side of , we use the triangle inequality to work term by term in the monomials in $V$. For example, the $\tau$ term makes a contribution $$\|\nu(\theta \tau(b) - \tau(b))\|_{T_{0}(\h \sqcup \hat\ell)}.$$ After expansion in the fluctuation fields $\xi,\bar\xi,\eta,\bar\eta$, the difference $\theta \tau(b) - \tau(b)$ is given by a sum of products of fluctuation fields and $\phi,\bar\phi,\psi,\bar\psi$ fields, with each term containing two fields of which at least one is a fluctuation field. Thus it is bounded by $O(\hat\ell \h)$. The end result is a bound on $\|\theta V(b) - V(b)\|_{T_{0}(\h \sqcup \hat\ell)}$ equal to $\hat\ell/\h$ times the $T_0(\h)$ semi-norm of the worst monomial in $V$ (but without the $\sigma\bar\sigma$ term which cancels). This gives $$\label{e:epsthetaV} \|\theta V(b) - V(b)\|_{T_{0}(\h \sqcup \hat\ell)} \prec \frac{\hat\ell}{\h} \gh.$$ For the second term on the right-hand side of , $$\|C\|_\Phi \h^2 \|2g \tau(b)\|_{T_0} \prec \|C\|_{\Phi(\h)} \epV = \frac{\hat\ell^2}{\h^2} \|C\|_{\Phi(\hat\ell)} \gh .$$ For the last term, we use to obtain $$\|P(b)\|_{T_0} \prec_L \epdV^2 .$$ The combination of the last three inequalities gives and the proof for the case $j_*=j$ is complete. Finally, for the case $j_*=j+1$, we start with the first line of with norms at scale $j+1$. The norm of $V-\Vpt$ is bounded by its scale-$j$ counterpart, by Lemma \[lem:Imono\]. In addition, applies also at scale $j+1$, and this give the desired conclusion and completes the proof. Estimates on field polynomials {#sec:W} ============================== In this section, we prove the following proposition, which gives our main estimates on the field polynomials $F,W,P$. As usual, $\epdV$ depends on whether $\h=\ell$ or $\h=h$, as indicated in . Recall that $P_j$ is defined for $0 \le j <N$, so there is no bound missing in . \[prop:Wnorms\] For $L$ sufficiently large and $V \in \bar\DV_j$, $$\begin{aligned} \label{e:Fepbd} \max_{B \in \Bcal_{j}} \sum_{x \in B} \sum_{B' \in \Bcal_j(\Lambda)} \|F_{\pi,C_{j*}}(V_x,V(B'))\|_{T_{0,j}(\h_{j})} &\prec_L \epdV_{j}^2 \quad (j \le N) , \\ \label{e:Wbomega} \max_{B \in \Bcal_{j}} \sum_{x\in B} \|W_j(V,x)\|_{T_{0,j}(\h_j)} &\prec_L \epdV_{j}^2 \quad (j \le N) , \\ \label{e:epP} \max_{B \in \Bcal_{j}} \sum_{x\in B} \|P_j(V,x)\|_{T_{0,j}(\h_{j})} &\prec_L \epdV_{j}^2 \quad (j < N) .\end{aligned}$$ \[rk:sm\] *Scale mismatch.* The bounds of Proposition \[prop:Wnorms\] continue to hold if $T_{0,j\pm 1}(\h_{j\pm 1})$ would be used on the left-hand sides instead of $T_{0,j}(\h_{j})$ (for indices that do not exceed the final scale). In fact, $F$ and $W$ are (non-local) polynomials of degree at most six, and $P$ is a (local) polynomial of degree at most four. A change of $\pm 1$ in $j$ in the evaluation of on of these $T_0$ semi-norms can therefore only give rise to a bounded power of $L$, and constants in – are permitted to depend on $L$. We prepare for the proof in Section \[sec:Pformula\] with useful identities for $P$ and $W$, and the proof is concluded in Section \[sec:examples4\]. The proof is based on a crucial contraction estimate from [@BS-rg-loc] for the operator $\LT$, which we recall below as Proposition \[prop:1-LTdefXY-loc\]. Preliminary identities {#sec:Pformula} ---------------------- The first lemma provides a formula for the expectation of $F$. \[lem:EthF\] For polynomials $A,B$ in the fields, and for covariances $C,w$, $$\label{e:EthF} e^{\Lcal_C} F_{\pi,w} (A,B) = F_{\pi,w+C}(e^{\Lcal_C} A, e^{\Lcal_C} B) - F_{\pi,C}(e^{\Lcal_C} A, e^{\Lcal_C} B).$$ By the definition of $F$ in , $$\begin{aligned} F_{w+C}(e^{\Lcal_C}A,e^{\Lcal_C}B) &= e^{\Lcal_C} e^{\Lcal_w} \big(e^{-\Lcal_{w}}A\big) \big(e^{-\Lcal_{w}} B\big) -(e^{\Lcal_C}A)(e^{\Lcal_C}B) \nnb &= e^{\Lcal_C} F_{w}( A, B) + e^{\Lcal_C} \left(AB \right) - (e^{\Lcal_C}A)(e^{\Lcal_C}B) \nnb &= e^{\Lcal_C} F_{w}( A, B) + F_{C}(e^{\Lcal_C}A,e^{\Lcal_C}B) . \label{e:EFAB}\end{aligned}$$ Rearrangement gives $$\label{e:EthFnopi} e^{\Lcal_C} F_{w} (A,B) = F_{w+C}(e^{\Lcal_C} A, e^{\Lcal_C} B) - F_{C}(e^{\Lcal_C} A, e^{\Lcal_C} B),$$ and, by and the fact that the projection operators commute with $e^{\Lcal_C}$, extends to the same equation with $F$ replaced by $F_\pi$. For the next lemma, we define $$\begin{aligned} \label{e:Pxydef} P_j(V'_x,V''_y) &= \frac{1}{2} \LT_{x} F_{\pi,w_{j+1}} (e^{\Lcal_{j+1}} V'_x,e^{\Lcal_{j+1}} V''_y) - \frac{1}{2} e^{\Lcal_{j+1}}\LT_{x} F_{\pi,w_{j}} ( V'_x, V''_y) \nnb & \hspace{60mm} (0 \le j < N-1) , \\ \label{e:Wpoint} W_j(V'_x,V''_y) &= \frac 12 (1-\LT_x) F_{\pi,w_j}(V'_x,V''_y) \quad (1 \le j < N) .\end{aligned}$$ Both definitions will be extended to the final scale in Section \[sec:Pbd\], but this extension is not yet needed here. By definition, for $j<N$, $$\lbeq{WVVsum} W_j(V,x) = \sum_{y \in \Lambda}W_j(V_x,V_y).$$ With the definition of $P_j(V)$ in , the next lemma shows that, for $j<N-1$, $$\lbeq{PVVsum} P_j(V,x) = \sum_{y \in \Lambda}P_j(V_x,V_y).$$ For its proof, we observe that since $e^{\Lcal_C}$ reduces the dimension of a monomial in the fields, $e^{\Lcal_C} : \Vcal \to \Vcal$, and since $\LT_X$ acts as the identity on $\Vcal$, it follows that $$\label{e:LTELT} \LT_X e^{\Lcal_C} \LT_X = e^{\Lcal_C} \LT_X.$$ \[lem:Palt\] For $x,y\in \Lambda$, $0\le j < N-1$, and for $V',V'' \in \Vcal$, $$\begin{aligned} \label{e:Palt0} P_j(V'_x,V''_y) &= \LT_{x}\left( e^{\Lcal_{j+1}} W_{j}(V_x',V_y'') + \frac{1}{2} F_{\pi,C_{j+1}}(e^{\Lcal_{j+1}}V_x',e^{\Lcal_{j+1}} V_y'') \right) .\end{aligned}$$ Consider first the case $j<N-1$. By definition of $W_j$ in , the right-hand side of can be rewritten as $$\label{e:Pxformula} \frac 12 \LT_x \big( e^{\Lcal_{j+1}} (1-\LT_x)F_{\pi,w_{j}}( V_x', V_y'') + F_{\pi,C_{j+1}} (e^{\Lcal_{j+1}} V_x',e^{\Lcal_{j+1}} V_y'') \big).$$ Application of shows that is equal to $$\begin{aligned} & \frac 12 \LT_x \big( e^{\Lcal_{j+1}} F_{\pi,w_{j}}( V_x', V_y'') + F_{\pi,C_{j+1}} (e^{\Lcal_{j+1}} V_x',e^{\Lcal_{j+1}} V_y'') \big) - \frac{1}{2} e^{\Lcal_{j+1}} \LT_x F_{\pi,w_{j}}( V_x', V_y'') . \label{e:Pxformula1}\end{aligned}$$ By , is equal to $$\begin{aligned} \frac 12 \LT_{x} F_{\pi,w_{j+1}} (e^{\Lcal_{j+1}} V_x',e^{\Lcal_{j+1}} V_y'') - \frac 12 e^{\Lcal_{j+1}}\LT_{x} F_{\pi,w_{j}} ( V_x', V_y'') ,\end{aligned}$$ which is . The following lemma computes the expectation of $W$. \[lem:EW\] For $x,y \in \Lambda$, $j < N$, and for $V',V'' \in \Vcal$, $$\begin{aligned} \label{e:Palt1b} e^{\Lcal_j} W_{j-1} (V'_x,V''_y) &= W_{j} (e^{\Lcal_j} V'_x, e^{\Lcal_j} V''_y) + P_{j-1}(V'_x,V''_y) - \frac{1}{2} F_{\pi,C_j }(e^{\Lcal_j} V_x,e^{\Lcal_j} V''_y) .\end{aligned}$$ By and the formula for $P$, $$\begin{aligned} \label{e:Palt5} e^{\Lcal_j} W_{j-1} (V'_x,V''_y) &= \frac{1}{2} e^{\Lcal_j} F_{\pi,w_{j-1}}( V'_x,V''_y) - \frac{1}{2} e^{\Lcal_j} \LT_x F_{\pi,w_{j-1} }(V'_x,V''_y) \nnb & = \frac{1}{2} e^{\Lcal_j} F_{\pi,w_{j-1}}( V'_x,V''_y) + P_{j-1}(V'_x,V''_y) \nnb & \qquad - \frac{1}{2} \LT_{x} F_{\pi,w_j} (e^{\Lcal_j} V'_x,e^{\Lcal_j} V''_y) .\end{aligned}$$ Substitution of into gives $$\begin{aligned} e^{\Lcal_j} W_{j-1} (V'_x,V''_y) & = F_{\pi,w_j}(e^{\Lcal_j}V_x',e^{\Lcal_j}V_y'') -F_{\pi,C_j}(e^{\Lcal_j}V_x',e^{\Lcal_j}V_y'') \nnb & \quad + P_{j-1}(V'_x,V''_y) - \frac{1}{2} \LT_{x} F_{\pi,w_j} (e^{\Lcal_j} V'_x,e^{\Lcal_j} V''_y) ,\end{aligned}$$ which is the same as . The next lemma applies Lemma \[lem:EW\] to obtain a formula that enables us to bound $W$ recursively, in Proposition \[prop:Wbounds\] below. \[lem:W-explicit\] For $x,y \in \Lambda$, $j<N$, and $V',V'' \in \Vcal$, $$\label{e:WWF} W_{j} (V'_x,V''_y) = (1-\LT_{x}) \Big( e^{\Lcal_j} W_{j-1} (e^{-\Lcal_j} V'_x , e^{-\Lcal_j} V''_y) + \frac{1}{2} F_{\pi ,C_j} ( V'_x,V''_y ) \Big) .$$ The equalities $$\begin{aligned} &W_{j}(e^{\Lcal_j} V'_x,e^{\Lcal_j} V''_y) = e^{\Lcal_j} W_{j-1} (V'_x,V''_y) - P_{j-1}(V'_x,V''_y) + \frac{1}{2} F_{\pi,C_j }(e^{\Lcal_j} V_x,e^{\Lcal_j} V''_y) \nnb &\quad = e^{\Lcal_j} W_{j-1} (V'_x,V''_y) -\frac{1}{2} \LT_{x} F_{\pi,w_j} (e^{\Lcal_j} V'_x,e^{\Lcal_j} V''_y) + \frac{1}{2} e^{\Lcal_j}\LT_{x} F_{\pi,w_{j-1}} ( V'_x, V''_y) \nnb & \quad + \frac{1}{2} F_{\pi,C_j }(e^{\Lcal_j} V_x,e^{\Lcal_j} V''_y) \nnb & \quad = e^{\Lcal_j} W_{j-1} (V'_x,V''_y) + \frac{1}{2} e^{\Lcal_j}\LT_{x} F_{\pi,w_{j-1}} ( V'_x, V''_y) +\frac{1}{2} F_{\pi,C_j} (e^{\Lcal_j} V'_x,e^{\Lcal_j} V''_y) \nnb & \quad - \frac{1}{2}\LT_x F_{\pi,C_j} (e^{\Lcal_j}V'_x,V''_y) - \frac{1}{2}\LT_x e^{\Lcal_j} F_{\pi,w_{j-1}}(V'_x,V''_y) \nnb & \quad = e^{\Lcal_j} W_{j-1} (V'_x,V''_y) +\frac{1}{2}(1-\LT_x) F_{\pi,C_j} (e^{\Lcal_j} V'_x,e^{\Lcal_j} V''_y) \nnb & \quad + \frac{1}{2} \LT_x e^{\Lcal_j}\LT_{x} F_{\pi,w_{j-1}} ( V'_x, V''_y) - \frac{1}{2}\LT_x e^{\Lcal_j} F_{\pi,w_{j-1}}(V'_x,V''_y) \end{aligned}$$ give the desired result. The first equality is , the second follows from the formula for $P$ in , the third uses , and for the last we used to insert an operator $\LT_x$ acting on the second term of the third right-hand side. Proof of Proposition \[prop:Wnorms\] {#sec:examples4} ------------------------------------ We now prove the estimates on $F,W,P$ stated in Proposition \[prop:Wnorms\]. We first consider $F$, then recall the crucial contraction estimate from [@BS-rg-loc] concerning the operator $\LT$, then apply the contraction estimate to obtain bounds on $W$ and $P$. ### Bound on F {#sec:Fbds} We now prove the bound on $F$. Operator bounds on the Laplacian as a map on $T_\phi$ are given in [@BS-rg-norm Proposition \[norm-prop:Etau-bound\]], which asserts that the operators $\Lcal_C$ and $e^{\pm \Lcal_C}$, restricted to the subspace of $\Ncal$ consisting of polynomials of degree $A$ with semi-norm $\|\cdot \|_{T_{\phi}}$, are bounded operators whose norms obey $$\label{e:eDC} \|\Lcal_C\| \leq A^2 \|C\|_\Phi, \quad \quad \|e^{\pm \Lcal_C }\| \le e^{A^2 \|C\|_{\Phi}}.$$ The above operator norms are for operators acting on $T_{\phi}$, with the scale fixed. Let $Y(C,x)= \{y : C_{x,y} \neq 0\}$. Recall , which implies that the diameter and volume of $Y(C_k,x)$ obey $$\label{e:YCbd} {\rm diam}\left(Y(C_k,x)\right) \le L^k, \quad\quad |Y (C_{k},x)| \le L^{dk}.$$ We recall the definition of $\Lcallr_w$ from [@BBS-rg-pt], and also recall [@BBS-rg-pt Lemma \[pt-lem:Fexpand\]], which asserts that for $V',V''$ of degree at most $A$, $$\label{e:FCsum} F_{w} (V'_{x} , V''_{y} ) = \sum_{n=1}^A \frac{1}{n!} V_x' (\Lcallr_w)^n V_y''.$$ \[lem:Fpibd-bis\] Suppose that $\|C\|_\Phi \le 1$. Then for $x,y \in \Lambda$ and $V' ,V'' \in \Vcal$, $$\label{e:FCABX} \| F_{\pi ,C} (V'_{x} , V''_{y} ) \|_{T_{0}} \prec \|C\|_{\Phi} \|V'_{x}\|_{T_{0}} \|V''_y\|_{T_{0}}\1_{y \in Y(C,x)} .$$ Also, $ F_{\pi ,C} (V'_{x} , V''_{y} ) \in \Ncal(Y(C,x))$ and $ \sum_{y \in \Lambda}W_{w} (V_x' , V_y'' ) \in \Ncal(Y(w,x))$. By , it follows from that $ F_{\pi ,C} (V'_{x} , V''_{y} ) \in \Ncal(Y(C,x))$. It then follows from that $ W_{w} (V' , V'',\{x\} ) \in \Ncal(Y(w,x))$. Now we prove . We have already shown that the left-hand side is zero for $y \not \in Y(C,x)$, so it suffices to prove without the factor $\1_{y \in Y(C,x)}$. Furthermore, by , it is enough to prove with $F_{\pi ,C}$ replaced by $F_{C}$. For $t\ge 0$, let $$\label{e:F1} F (t) = e^{\Lcal_{tC}} \left( (e^{-\Lcal_{tC}}V_x') (e^{-\Lcal_{tC}}V_y'') \right) .$$ Since $V',V''$ are polynomials in fields, by expanding each of the exponentials we find that $F (t)$ is a polynomial $\sum_{n= 0}^m F_{n}t^{n}$, for some finite $m$. According to the second inequality of , there is a $k>0$ determined by $\|tC \|_{\Phi}$ such that $$\sum_{n= 0}^m \|F_{n}\|_{T_{0}}|t|^{n} \le k \|V'_{x}\|_{T_{0}} \|V''_y\|_{T_{0}} .$$ Although $k$ depends on $\|tC \|_{\Phi}$, it is uniform for $\|tC \|_{\Phi} \le 1$. By , $$F_{C} (V'_{x} , V''_{y} ) = F (1) - F (0) = \sum_{n= 1}^m F_{n} .$$ Therefore, taking $t = \|C\|_{\Phi}^{-1} \ge 1$, we obtain $$\|F_{C} (V'_{x} , V''_{y} )\|_{T_{0}} \le \sum_{n= 1}^m \|F_{n}\|_{T_{0}} \le \frac{1}{t} \sum_{n= 1}^m \|F_{n}\|_{T_{0}}t^{n} \le k \|C\|_{\Phi} \|V'_{x}\|_{T_{0}} \|V''_y\|_{T_{0}} ,$$ which completes the proof. To estimate the covariance of $C_j$, we use to conclude that for $j \le N$, $$\begin{aligned} \lbeq{Chbd} \|C_{j*}\|_{\Phi_j(\h_k)} &\prec_L \begin{cases} \chi_j & \h_j=\ell_j \\ \chi_j \ggen_j^{1/2} & \h_j=h_j . \end{cases}\end{aligned}$$ The case $\h_j=\ell_j$ follows immediately from , and the case $\h_j=h_j$ follows from $$\label{e:ellh} \|C_{j*}\|_{\Phi_j(h_j)} = \left( \frac{\ell_{j}}{h_j}\right)^2 \|C_{j*}\|_{\Phi_j(\ell_j)} = \left( \frac{\ell_0}{k_0} \right)^2 \ggen_j^{1/2} \|C_{j*}\|_{\Phi_j(\ell_j)} \prec_L \; \ggen_j^{1/2} \chi_j.$$ Let $1 \le j \le N$. Summation of gives, for any $B \in \Bcal_{j}$, the upper bound $$\label{e:FepWbd} \sum_{x \in B} \sum_{y \in \Lambda } \|F_{\pi,C_{j*}}(V'_x,V'_y)\|_{T_{0,j}(\h_j)} \prec \|C_j \|_{\Phi_j(\h_j)} \epsilon_{V',j} \epsilon_{V'',j}.$$ We set $V'=V''=V$ in . Since $V \in \bar\DV_j$, $\epsilon_{V,j}$ is bounded by a multiple of $\ggen_j$ for $\h=\ell$, and of $1$ for $\h=h$. With , this gives $$\label{e:Fepbd-bis} \max_{B \in \Bcal_{j}} \sum_{x \in B} \sum_{y \in \Lambda } \|F_{\pi,C_{j*}}(V_x,V_y)\|_{T_{0,j}} \prec_L \epdV^2 ,$$ which is the desired estimate . ### Loc and the crucial contraction {#sec:cl} It is shown in [@BS-rg-loc Proposition \[loc-prop:opLTdefXY\]] (with $R=L^{-j}$) that $\LT_X$ is a bounded operator on $T_0$ in the sense that if $F \in \Ncal(X)$ then $$\label{e:LTXY5} \|\LT_{X}F\|_{T_0} \le \bar{C}' \|F\|_{T_0},$$ where $\bar{C}'$ depends on $L^{-j}{\rm diam}( X)$. We also recall [@BS-rg-loc Proposition \[loc-prop:1-LTdefXY\]], which is the crucial contraction estimate which we state here as follows. As in [@BS-rg-loc Definition \[loc-def:LTXYsym\]], we use the notation $X(\varnothing)=X$, $X(a) = X \cap \{a\}$, $X(b)=X \cap \{b\}$, and $X(ab) = X \cap\{a,b\}$. As discussed in Section \[sec:formint\], $d_+ = d$ on $\Ncal^\varnothing$, $d_+=0$ on $\Ncal^{ab}$, whereas when $\LT$ acts at scale $k$ on $\Ncal^a$ and $\Ncal^b$, $d_+=[\phi]=\frac{d-2}{2}=1$ if $k<j_{\pp\qq}$ and $d_+=0$ for $k \ge j_{\pp\qq}$. For $\alpha,\beta \in \{ \varnothing, a,b,ab\}$, we define $d_{\alpha}'=d_\alpha +1$, and $$\label{e:cgamobs-loc} \cgam_{\alpha,\beta} = (L^{-d_{\alpha}'} + L^{-(A+1)[\phi]}) \left( \frac{\h'_\sigma}{\h_\sigma} \right)^{|\alpha \cup \beta|} .$$ \[prop:1-LTdefXY-loc\] Let $A < p_\Ncal$ be a positive integer, and let $\varnothing \not = Y \subset X \in \Pcal_j$. Let $F_{1} \in \Ncal (X)$, and let $F_2 \in \Ncal(Y)$ with $\pi_{\alpha}F_{2}=0$ when $Y(\alpha)=\varnothing$. Let $F = F_1(1-\LT_{Y})F_2$. Let $T_\phi'$ denote the $T_{\phi,j+1}(c\h_{j+1})$ semi-norm for any fixed $c \ge 1$, and let $T_\phi$ denote the $T_{\phi,j}(\h_{j})$ semi-norm. Then $$\begin{aligned} \label{e:LTXY5a-loc} \|F\|_{T_{\phi}'} &\le \bar{C} \sum_{\alpha,\beta=\varnothing ,\pp ,\qq,\pp\qq} \cgam_{\alpha,\beta} \left(1 + \|\phi\|_{\Phi'}\right)^{A'} \nnb & \quad \quad \times \sup_{0\le t \le 1} \big( \|\pi_\beta F_{1} \pi_\alpha F_{2}\|_{T_{t\phi}} + \|\pi_\beta F_{1}\|_{T_{t\phi}}\|\pi_\alpha F_{2}\|_{T_{0}}\big) \|\sigma^{\alpha\cup\beta}\|_{T_0},\end{aligned}$$ where $A'=A+d_{\alpha}/[\phi] +1$, and $\bar C$ depends on $c$ and $L^{-j}{\rm diam}( X)$. As a corollary, we specialise to our particular setting to obtain the following proposition. We state Proposition \[prop:1-LTdefXY\] in a more general form than is needed to bound $W$, but the additional generality is used in the proof of Proposition \[prop:cl\]. \[prop:1-LTdefXY\] Let $d\ge 4$, $A=\lceil 2(d+1)/(d-2)\rceil$, and assume that $p_\Ncal >A$. Let $\varnothing \not = Y \subset X \in \Pcal_j$. Let $F_{1} \in \Ncal (X)$, let $F_2 \in \Ncal(Y)$ with $\pi_{\alpha}F_{2} =0$ when $Y(\alpha)=\varnothing$, and let $F = F_1(1-\LT_{Y})F_2$. Suppose that each of $F_1,F_2, F_1F_2$ has no component in $\Ncal_{ab}$ unless $j \ge j_{ab}$ (recall ). Let $T_\phi'$ denote the $T_{\phi,j+1}(c\h_{j+1})$ semi-norm for some fixed $c \ge 1$, and let $T_\phi$ denote the $T_{\phi,j}(\h_{j})$ semi-norm. There is a constant $\bar C$ depending on $c$ and $L^{-j}{\rm diam}( X)$ such that $$\begin{aligned} \label{e:LTXY5a} \|F\|_{T_{\phi}'} &\le \bar{C} \cgam \left(1 + \|\phi\|_{\Phi'}\right)^{A+d+1} \sup_{0\le t \le 1} \big( \|F_{1}F_{2}\|_{T_{t\phi}} + \|F_{1}\|_{T_{t\phi}}\|F_{2}\|_{T_{0}}\big) ,\end{aligned}$$ with $$\label{e:cgamobs} \gamma = \gamma(Y) = L^{-d -1} + L^{-1}\1_{Y \cap \{a,b\} \not = \varnothing}.$$ Moreover, if $\pi_*F_2=0$ then we can replace by $\gamma = L^{-d-1}$. In our setting, $d_\varnothing =d$, $d_{ab}=0$, and $d_a=d_b=1$ if $j<j_{ab}$ whereas $d_a=d_b=0$ if $j\ge j_{ab}$. Also, $[\phi]=\frac{d-2}{2}\ge 1$ for all $\alpha$. In particular, $A+d_{\alpha}/[\phi] +1 \le A+d+1$. Our choice of $A$ ensures that $(A+1) [\phi] \ge d+1 \ge d_\alpha + 1$ for all $\alpha$. By , $$\frac{\h_{\sigma,j+1}}{\h_{\sigma,j}} \le {\rm const}\, \begin{cases} L^{[\phi]} & j < j_{ab} \\ 1 & j \ge j_{ab}. \end{cases}$$ By assumption, when $|\alpha \cup \beta|=2$ we can use the $j \ge j_{ab}$ version of the above bound. Also by assumption, for $\alpha =a,b,ab$ we have $\pi_\alpha F_{2} =0$ when $Y \cap \{a,b\} = \varnothing$. Taking these points into account, from we obtain $$\gamma_{\alpha,\beta} \le 2\, \begin{cases} L^{-d-1} & |\alpha \cup \beta| =0 \\ L^{-1}\1_{Y \cap \{a,b\} \not = \varnothing} & |\alpha \cup \beta| =1,2. \end{cases}$$ This shows that $\gamma_{\alpha,\beta} \le 2 \gamma$ uniformly in $\alpha,\beta$. It follows from that $$\big( \|\pi_\beta F_{1} \pi_\alpha F_{2}\|_{T_{t\phi}} + \|\pi_\beta F_{1}\|_{T_{t\phi}}\|\pi_\alpha F_{2}\|_{T_{0}}\big) \|\sigma^{\alpha\cup\beta}\|_{T_0} \le \|F_{1}F_{2}\|_{T_{t\phi}} + \|F_{1}\|_{T_{t\phi}}\|F_{2}\|_{T_{0}}.$$ Together with Proposition \[prop:1-LTdefXY-loc\], these facts give the desired estimate and the proof is complete. ### Bound on W {#sec:Wbds} We now prove for $j<N$, beginning with the following proposition, whose proof requires our assumption that $L$ is large. We defer the case $j=N$ of (and also of ) to Sections \[sec:Pbd\]–\[sec:Waux\]. \[prop:Wbounds\] Let $j<N$. In general, $\pi_{ab}W_j =0$. Let $V',V'' \in \Vcal$. Suppose there is a sequence $v_k'$ with $v_{k-1}' \prec v_k'$ for all $k \le j$, such that $\max_{B \in \Bcal_k} \sum_{x \in B}\|V'_x\|_{T_{0,k}} \le v_k'$, and similarly for $V''$. Then there is a constant $c$ such that $$\label{e:Wbound2az} \max_{B \in \Bcal_j} \sum_{x \in B} \sum_{y \in \Lambda} \|W_{j}(V'_x,V''_y)\|_{T_{0,j}(\h_j)} \le c \chi_j \left( \frac{\ell_j}{\h_j} \right)^2 v_j' v_j'' .$$ In $W$, we can exclude the $\sigma\bar\sigma$ terms in each of $V',V''$ since these contribute zero to $F$. Thus the only possible $\sigma\bar\sigma$ contribution to $W$ can be due to the contribution to $F$ due to a contraction of $\sigma\bar\phi_a$ with $\bar\sigma \phi_b$. Such a contraction contains no boson or fermion fields, so is annihilated by $1-\LT_{\{x\}}$. This proves that $\pi_{ab}W=0$, and it remains to prove . We prove , by induction on $j$. Our induction hypothesis is that holds for $j-1$, and we use this to prove that it also holds for $j$. Initially $W_0=0$, so it is trivial to begin the induction. The starting point is Lemma \[lem:W-explicit\], which implies that $$\label{e:WWFj} W_{j} (V'_x,V''_y) = (1-\LT_{x}) \Big( e^{\Lcal_{j}} W_{j-1} (e^{-\Lcal_{j}} V'_x , e^{-\Lcal_{j}} V''_y) + \frac{1}{2} F_{\pi ,C_{j}} ( V'_x,V''_y ) \Big) .$$ We estimate using the triangle inequality on the right-hand side, retaining the cancellation in $1-\LT_{\{x\}}$ for the first term but not for the second. With , this gives $$\begin{aligned} \label{e:WWFj2} \|W_{j} (V'_x,V''_y)\|_{T_{0,j}} & \le \|(1-\LT_{x}) e^{\Lcal_{j}} W_{j-1} (e^{-\Lcal_{j}} V'_x , e^{-\Lcal_{j}} V''_y)\|_{T_{0,j}} \nnb & \quad + \frac{1}{2}(1+\bar C) \| F_{\pi ,C_{j}} ( V'_x,V''_y )\|_{T_{0,j}}.\end{aligned}$$ The constant $\bar C$ is independent of $j$, as a consequence of together with the fact that $ F_{\pi ,C_j} (V'_{x} , V''_{y} ) \in \Ncal(Y(C_j,x))$ by Lemma \[lem:Fpibd-bis\]. We begin with the second term on the right-hand side of . After application of Lemma \[lem:Fpibd-bis\] and , and summation over $x,y$, we find that there is a constant $\Fconst$ such that $$\label{e:ind2nd} \frac{1}{2}(1+\bar C) \max_{B \in \Bcal_j} \sum_{x \in B} \sum_{y \in \Lambda} \| F_{\pi ,C_{j}} ( V'_x,V''_y )\|_{T_{0,j}} \le \bar\Fconst \chi_j \left( \frac{\ell_j}{\h_j} \right)^2 v_j' v_j''.$$ For the first term on the right-hand side, we apply Proposition \[prop:1-LTdefXY\] with $F_1=1$ and $F_2 = e^{\Lcal_{j}} W_{j-1} (e^{-\Lcal_{j}} V'_x , e^{-\Lcal_{j}} V''_y)$. Note that, as required by the hypotheses of Proposition \[prop:1-LTdefXY\], $\pi_*F_2 =0$ unless $x \in \{a,b\}$; this is a consequence of the careful definition of $F_{\pi,C}$ in , which ensures that if one of $\pi_*V'$ or $\pi_*V''$ is nonzero then $\pi_*V'$ must be nonzero. The application of Proposition \[prop:1-LTdefXY\] gives the estimate $$\lbeq{ind-1Loc} \|(1-\LT_{x})F_2\|_{T_{0,j}} \le \bar{C} \gamma_x \|F_2\|_{T_{0,j-1}} ,$$ with $$\gamma_x = L^{-d-1}+L^{-1}\1_{x \in \{a,b\}},$$ and with a scale-independent constant $\bar C$ since $F_2 \in \Ncal(Y (C_{j-1},x))$ by Lemma \[lem:Fpibd-bis\]. The operators $e^{\pm \Lcal_j}$ are bounded on $T_{0,j-1}$, by and the fact that $$\lbeq{Cnormcomp} \|C_{j}\|_{\Phi_{j-1}(\h_{j-1})} \le \|C_{j}\|_{\Phi_{j}(\h_{j-1})} = (\ell_{j}/\h_{j-1})^2 \|C_{j}\|_{\Phi_{j}(\ell_{j})} \le (\ell_{j}/\h_{j-1})^2 \ellconst \le 1$$ using and . Thus, by the induction hypothesis, there is a constant $\bar A$ such that $$\label{e:W22} \max_{B \in \Bcal_j} \sum_{x \in B} \sum_{y \in \Lambda} \gamma_x \|F_2\|_{T_{0,j}} \le \bar{A} c L^{-1} \chi_j \left( \frac{\ell_j}{\h_j} \right)^2 v_j' v_j'' ,$$ where we have used the fact that $B$ contains $L^d$ blocks of scale $j-1$, our assumption on the sequences $v_k'$ and $v_k''$, and that the factors involving $\chi$ and $\ell/\h$ change only by a constant factor under a single advance of scale. The combination of , and gives $$\label{e:Wind} \max_{B \in \Bcal_j} \sum_{x \in B} \sum_{y \in \Lambda} \|W_{j}(V'_x,V''_y)\|_{T_{0,j}(\h_j)} \le (\bar C \bar A c L^{-1} + \Fconst) \chi_j \left( \frac{\ell_j}{\h_j} \right)^2 v_j' v_j'' \1_{y \in Y(C_k,x)} .$$ We require that $L > \bar C \bar A$ (which we can do in view of our general hypothesis that $L$ is large enough). Then advances the induction with the choice $c= \Fconst/(1 - \bar C \bar A L^{-1})$, since this choice gives $\bar C \bar A c L^{-1} + \Fconst =c$. This completes the proof. Let $j<N$. For $V \in \bar\DV_j$, by direct computation as in the proof of Proposition \[prop:monobd\], we find that, for any $k \le j$ and $b \in \Bcal_k$, $\sum_{x \in B}\|V_x\|_{T_{0,k}}$ is bounded above by a multiple of $\ggen_j$ for $\h=\ell$, and of $\ggen_j/\ggen_k$ for $\h=h$. We apply Proposition \[prop:Wbounds\] with these two choices for $v_k$, which do obey its hypothesis by . This gives $$\begin{aligned} \sum_{x \in B} \|W_{j}(V,x)\|_{T_{0,j}} & \prec_L\; \begin{cases} \chi_j \ggen_j^2 & \h=\ell \\ \chi_j \ggen_j^{1/2} & \h=h. \end{cases} \label{e:Wepbd-bis}\end{aligned}$$ The right-hand side is $\epdV_j^2$ and this completes the proof. ### Bound on P {#sec:Pbd} We now prove , and also prove the case $j=N$ of . We first consider $j<N-1$, and recall from Lemma \[lem:Palt\] that $$\begin{aligned} \lbeq{PVV} P_j(V_x',V_y'') & = \LT_{x}\left( e^{\Lcal_{j+1}} W_{j}(V_x',V_y'') + \frac{1}{2} F_{\pi,C_{j+1}}(e^{\Lcal_{j+1}} V_x',e^{\Lcal_{j+1}} V_y'') \right) .\end{aligned}$$ We bound the operator norms of $\LT_x$ and $e^{\Lcal_{j+1}}$ as discussed previously (using ), and apply and , to conclude that under the same hypothesis on $V',V''$ as in Proposition \[prop:Wbounds\], $$\begin{aligned} \lbeq{PVVsumbd} \max_{B \in \Bcal_j} \sum_{x\in B} \sum_{y \in \Lambda} \|P_j(V_x',V_y'')\|_{T_{0,j}(\h_{j})} & \prec \chi_j \left( \frac{\ell_j}{\h_j} \right)^2 v_j'v_j'' .\end{aligned}$$ Then we set $V'=V''=V \in \bar\DV_j$ and as in the proof of we obtain $$\max_{B \in \Bcal_{j}} \sum_{x\in B} \|P_j(V,x)\|_{T_{0,j}(\h_{j})} \prec_L\; \epdV_{j}^2$$ as desired. This completes the proof of for $j<N-1$. As discussed in Section \[sec:finalscale\], our definition of $P_{N-1}$ is designed so that $P_{N-1}$ for the torus of scale $N$ is the same local polynomial as $P_{N-1,N+1}$ on the torus of scale $N+1$. Consequently we can apply on the torus of scale $N+1$ to obtain the desired estimate on $P_{N-1}$. According to , $$\begin{aligned} \label{e:WNdef-bis} W_{N}(V,x) & = e^{\Lcal_{N,N}} W_{N-1}(e^{-\Lcal_{N,N}}V,x) -P_{N-1}(e^{-\Lcal_{N,N}}V,x) + \frac 12 F_{\pi,C_{N,N}}(V_x,V(\Lambda)) .\end{aligned}$$ This obeys by using and together with the estimates on $W_{N-1}$, $P_{N-1}$, $F_{\pi,C_{N,N}}$ obtained above. ### Auxiliary estimates on W {#sec:Waux} In , we defined $P_{N-1}(V)$ to be equal to the common value that would give on any torus of scale larger than $N$. Similarly, we extend the definition of $P_j(V'_x,V''_y)$ to $j=N-1$ by defining it to be the common value of the right-hand side of , with $j=N-1$, on any torus of scale larger than $N$. In addition, we adapt the identity to define $W_N(V_x',V''_y)$ (which has not yet been defined for distinct $V',V''$) as $$\begin{aligned} \label{e:WNVV} W_{N} ( V'_x, V''_y) &= e^{\Lcal_{N,N}} W_{N-1} (e^{-\Lcal_{N,N}}V'_x,e^{-\Lcal_{N,N}}V''_y) - P_{N-1}(e^{-\Lcal_{N,N}}V'_x,e^{-\Lcal_{N,N}}V''_y) \nnb & \quad + \frac{1}{2} F_{\pi,C_{N,N} }(V_x,V''_y) .\end{aligned}$$ Then from we see that the identity extends to scale $j=N$: $$W_N(V,x) = \sum_{y \in \Lambda} W_N(V_x,V_y).$$ Also, the estimate of Proposition \[prop:Wbounds\] now extends to scale $N$. To see this, we use the definition , the fact that $e^{\pm\Lcal_{N,N}}$ is a bounded operator, the bounds on $W_{N-1}$ and $F$ obtained previously, and finally the fact that extends to its final scale $N-1$ by application of on a larger torus. The next lemma provides a concrete upper bound on $W_j(V',V'')$ when observables are absent. \[lem:W-logwish\] Suppose that $V',V'' \in \pi_\varnothing \Vcal$, and let $|V|_j = \max \{ |g|,L^{2j}|\nu|, |z|, |y|\}$. For $j \le N$, $$\begin{aligned} \max_{B \in \Bcal_j} \sum_{x \in B}\sum_{y \in \Lambda} \|W_{j}(V'_x,V_y'')\|_{T_{0,j}(\ell_j)} & \prec_L\; \chi_j |V'|_j |V''|_j. \label{e:W-logwish}\end{aligned}$$ Let $v_k=L^{dk}\|V_x\|_{T_{0,k}(\ell_k)}$. Direct computation of the $T_{0,k}(\ell_k)$ norm shows that $v_k \prec |V|_k \le |V|_j$ for $k \le j$. Then Proposition \[prop:Wbounds\] (extended as noted above to include $j=N$) gives a bound on the left-hand side of of order $v_{j}^2$, as desired. Finally, the next lemma provides estimates for later use. \[lem:Wbil\] For $j+1\le N$, $B \in \Bcal_j$, and $V\in \bar\DV_j$, $$\begin{aligned} \label{e:Wbil} \|W_{j+1}(e^{\Lcal_{j+1}} V,B) -W_{j+1}(\Vpt,B)\|_{T_{0,j+1}} &\prec_L \epdV_j^3.\end{aligned}$$ For $j \le N$, $B \in \Bcal_j$, $V\in \bar\DV_j$, and for $Q \in \Qcal$ with $\|Q(B)\|_{T_{0,j}} \prec \epdV_{j}$, $$\begin{aligned} \lbeq{Wprimebd-app} \|W_j(Q(B),V(\Lambda))\|_{T_0,j} &\prec_L \begin{cases} \epdV_j^2 & \h=\ell \\ \epdV_j^2 \ggen_j^{1/4} & \h=h, \end{cases} \\ \lbeq{Wprimebd-app2} \|W_j(Q(B),Q(\Lambda))\|_{T_0,j} &\prec_L \begin{cases} \epdV_j^2 & \h=\ell \\ \epdV_j^2 \ggen_j^{1/2} & \h=h. \end{cases}\end{aligned}$$ By linearity and the triangle inequality, W\_[j+1]{}(e\^[\_[j+1]{}]{} V) -W\_[j+1]{}()\_[T\_[0,j+1]{}]{} & W\_[j+1]{}(P,e\^[\_[j+1]{}]{} V)\_[T\_[0,j+1]{}]{} + W\_[j+1]{}(,P)\_[T\_[0,j+1]{}]{}. We apply Proposition \[prop:monobd\], use Proposition \[prop:Wnorms\] to see that for $B_k \in \Bcal_k$ it is the case that $\sum_{x \in B_k}\|P_x\|_{T_{0,k}} \prec_L \epdV_k^2$, and then apply Proposition \[prop:Wbounds\] (including its extension to scale $N$), to see that W\_[j+1]{}(e\^[\_[j+1]{}]{} V) -W\_[j+1]{}()\_[T\_[0,j+1]{}]{} & \_L \_j ( \_j/\_j)\^2 \_j\^2 \_j & =\ 1& =h \_j\^3 , \[e:Wbilbdell-app\] as required. For –, a similar calculation, using $\epsilon_Q \prec \epdV$ (by Lemma \[lem:T0ep\] and assumption) gives the desired result. This completes the proof. Proof of Propositions \[prop:Iupper\]–\[prop:JCK-app-1\] {#sec:I-estimates} ======================================================== In this section, we prove Propositions \[prop:Iupper\]–\[prop:JCK-app-1\]. Attention is restricted here to $d=4$. We begin by proving estimates on $\Ical=e^{-V}$ of . Since norms in the global space $\Phi=\Phi(\Lambda)$ can be replaced in upper bounds by the local space $\Phi (X)$ whenever an element of $\Ncal (X)$ is being estimated (as discussed around [@BS-rg-norm]), we sometimes write simply $\Phi$ rather than $\Phi(X)$. However, decay estimates (such as below) must always be stated in localised form. Temporarily, we write $a_0,b_0$ (rather than the usual $a,b$) for the points where observables are located in $V$, and instead we use $b$ for a block in $\Bcal_{j-1}$. Also, we write $$\epV(b) = \begin{cases} L^{-d} \epsilon_{V_\varnothing} & \{a_0,b_0\} \cap b = \varnothing \\ L^{-d} \epsilon_{V_\varnothing} + (|\lambda^{a_0}|+|\lambda^{b_0}|)\h\h_\sigma + \textstyle{\frac 12}(|\q^{a_0}|+|\q^{b_0}|)\h_\sigma^2 & \{a_0,b_0\} \cap b \neq \varnothing, \end{cases}$$ as opposed to $\epV$ which always includes the contribution from the observables. \[prop:Iupperzz\] Let $j \le N$. Let $V \in \Qcal$ with $0 \le |{\rm Im}g | \le \frac 12 {\rm Re}g$.\ (i) For $b \in \Bcal_{j-1}$, $$\label{e:Iupper0zz} \|\Ical(b)\|_{T_{\phi}} \le e^{O (\epV(b)) (1+ \|\phi\|_\Phi^2)} .$$ (ii) Fix any $q \ge 0$. Suppose that $\epV \le C \epVbar$ for some $C>0$. For $B \in \Bcal_j$, and $X \in \Scal_{j-1}(B)$ or $X=\varnothing$, $$\begin{aligned} & \|\Ical(B\setminus X) \|_{T_{\phi}} \le e^{O (1+q^{2})\epV} e^{-q \epVbar \|\phi\|_{\Phi(B^{\Box})}^2} e^{O (1+q) \epV \|\phi\|_{\tilde\Phi(B^{\Box})}^2} . \label{e:IcalB}\end{aligned}$$ \(i) We write $V=g\tau^2 +Q$. By [@BS-rg-norm Proposition \[norm-prop:taunorm\]] (with $q_2 =0$) and , $$\|e^{-g\tau_x^2}\|_{T_{\phi}} \le e^{O (|g|\h^4)} = e^{O (L^{-dj}\epVbar)} .$$ By the product property, $$\begin{gathered} \label{e:egtbd} \|e^{-g\tau^2(b)}\|_{T_{\phi}} \le \prod_{x\in b} \|e^{-g\tau_{x}^2}\|_{T_{\phi}} \le e^{O (L^{-d}\epVbar)} .\end{gathered}$$ Also, since $Q$ is quadratic, from [@BS-rg-norm Proposition \[norm-prop:T0K\]] and we obtain $$\|Q (b)\|_{T_{\phi}} \le \|Q (b)\|_{T_{0}} (1+\|\phi\|_\Phi)^2 \le 2 \epV(b) (1+\|\phi\|_\Phi^2) .$$ Therefore, by the power series expansion of the exponential and the product property, $$\label{e:apos-e} \|e^{-Q (b)}\|_{T_{\phi}} \le e^{\|Q (b)\|_{T_{\phi}}} \le e^{2\epV(b) (1+\|\phi\|_\Phi^2)} .$$ With the product property, then follows from , , and the fact that $\epVbar \le \epsilon_{V_\varnothing}$. \(ii) Fix any $q'\ge 0$. Since ${\rm Re} g \le |g| \le \frac 32 {\rm Re}g$ by hypothesis, we can conclude from [@BS-rg-norm Proposition \[norm-prop:taunorm\]] that $$\|e^{-g\tau_x^2}\|_{T_{\phi}} \le e^{O (1+q'^{2})| g|\h^4} e^{-q' |g|\h^4 |\phi_x/\h|^2} .$$ By the product property and , this gives $$\begin{gathered} \label{e:egtau2} \|e^{-g\tau^2(B \setminus X)}\|_{T_{\phi}} \le e^{O (1+q'^{2}) \epVbar} e^{-q' |g|\h^4 \sum_{x\in B \setminus X}|\phi_x/\h|^2} .\end{gathered}$$ For $Y \subset \Lambda$, we define the $L^2(Y)$ norm by $$\|\phi \|^{2}_{L^2(Y)} = \frac{1}{|Y|} \sum_{x\in Y}\frac{|\phi_{x} |^{2}}{\h^{2}} .$$ Then, again writing $V=g\tau^2 +Q$, we combine with , using the product property, , and $|B\setminus X| \ge \frac 12 |B|$, to obtain $$\begin{aligned} \label{e:Ical-1} \|\Ical(B\setminus X) \|_{T_{\phi}} &\le e^{O (1+q'^{2}) \epVbar} e^{- q' |g|\h^4 |B \setminus X| \, \|\phi\|_{L^{2} (B\setminus X)}^2} e^{2\epV(1+\|\phi\|_\Phi^2)} \nnb &\le e^{O (1+q'^{2}) \epVbar} e^{- \frac 12 q' C_0^{-1}\epVbar \, \|\phi\|_{L^{2} (B\setminus X)}^2} e^{2\epV(1+\|\phi\|_\Phi^2)}\end{aligned}$$ (no $L^d$ factor is produced for the observables). By our hypothesis on $X$ and Proposition \[prop:equivalent-norms\], $$\label{e:Sob2} \|\phi\|_{L^2(B\setminus X)}^2 \geq \frac{1}{2c_2^2} \|\phi\|_{\Phi(B^{\Box})}^2 - \|\phi\|_{\tilde \Phi(B^{\Box}) }^2 .$$ We insert this into and localise the $\Phi $ norm to $\Phi (B^{\Box})$ to obtain $$\begin{aligned} \|\Ical(B\setminus X) \|_{T_{\phi}} &\le e^{O (1+q'^{2}) \epV} e^{- (\frac {1}{4}C_0^{-1} c_2^{-2} q'\epVbar -2\epV) \, \|\phi\|_{\Phi(B^\Box)}^2} e^{\frac 12 q' \epV \|\phi\|_{\tilde\Phi(B^\Box)}^2} .\end{aligned}$$ Then follows by choosing $q'=4 C_0 c_2^{2} (q+2C)$, which is $O(q)$. We prove Proposition \[prop:Iupper\] by combining Proposition \[prop:Iupperzz\] with the following elementary lemma. \[lem:exp-bounds\] For $x, u>0$ and any integer $r \ge \max\{1,u\}$, $$\begin{aligned} \label{e:exp1} (1 + x)^{2r} & \le (2r/ u)^{r} e^{u x^{2}} \\ \label{e:exp2} 1 + u^{r} (1+x)^{2r} & \le e^{2ru (1+ x^{2})} .\end{aligned}$$ For the first bound, we combine $(1+x)^{2r} \le 2^r (1+x^2)^r$ with the inequality $1+x^2 \le (r/u) e^{u x^2/r}$ (since $r \ge u$). The second bound follows from $$\begin{aligned} 1 + u^{r} (1+x)^{2r} &\le 1 + ( 2u)^{r} (1+x^{2})^{r} \le (1+2u + 2u x^{2})^{r} \le (e^{2u + 2 u x^{2}})^{r},\end{aligned}$$ where we used $r \ge 1$ in the second inequality. We first consider the choice $I^*=I(B)$. By the product property and [@BS-rg-norm Proposition \[norm-prop:T0K\]], $$\begin{aligned} \|I (B) F\|_{T_{\phi}} &\le \|\Ical (B)\|_{T_{\phi}} \|1+W(B)\|_{T_{\phi}} \| F\|_{T_{\phi}} \nnb & \le \|\Ical (B)\|_{T_{\phi}} \|1+W(B)\|_{T_{\phi}} \| F\|_{T_{0}} \left( 1 + \|\phi\|_{\Phi}\right)^r,\end{aligned}$$ where $r$ denotes the degree of $F$. By , $W$ is a degree-six polynomial in the boson and fermion fields. By and [@BS-rg-norm Proposition \[norm-prop:T0K\]], $$\begin{aligned} \label{e:1Wbd} \|1+W(B)\|_{T_{\phi}} &\le 1+\|W(B)\|_{T_{\phi}} \le 1+\|W(B)\|_{T_{0}}\left( 1 + \|\phi\|_{\Phi}\right)^6 \le e^{6\omega^{1/3} (1+\|\phi\|_{\Phi}^2)}.\end{aligned}$$ where $\omega = \max_{B \in \Bcal_j}\|W(B)\|_{T_0}$. Then, since $6(L^{2d}\omega)^{1/3} \le u$ by hypothesis, gives $$\|I(B) F\|_{T_{\phi}} \le \|\Ical (B)\|_{T_{\phi}} \| F\|_{T_{0}} \left(\frac{2r}{u} \right)^{r} e^{u + 2u \|\phi\|_{\Phi}^{2}} .$$ Then with $I^*=I(B)$ follows from . For , fix $q \ge 0$ to be the desired parameter in , and choose the variable called $q$ in to be $q_1$ defined by $q_1= q+2u\epVbar^{-1}$. This gives for the choice $I^*=I(B)$. For the case $\tilde{I}(B \setminus X)$ with $X=\varnothing$ or $X\in \Scal_{j-1}$, we replace by $$\|\prod_{b \in \Bcal_{j-1}(B\setminus X)}(1+W(b))\|_{T_{\phi}} \le e^{6L^d (L^{-d } \omega)^{1/3} (1+\|\phi\|_{\Phi}^2)} \le e^{u (1+\|\phi\|_{\Phi}^2)},$$ and proceed similarly. Omitting factors $1+W$ in the above bounds only makes it easier, so we also have the bounds if we choose $I^*$ with factors of $1+W$ missing, and the proof is complete. Let $V \in \bar\DV$. We first consider the case $I_*=I$ (possibly with some $1+W$ factors omitted) and $j_*=j$. The bound follows from and (with $q=0$), and follows similarly from the case $r=0$. Also, for $B \in \Bcal_j$, it follows from the definition of $I$, the product property, and , that $$\label{e:I-b} \|I(B)^{-1}\|_{T_0} \le e^{\|V(B)\|_{T_0}} \frac{1}{1-\|W(V,B)\|_{T_0}} \le (1 +O (\epV+\epW)) \le 2 ,$$ which gives . This completes the proof for the case $I_*=I$. Next, we consider the case $I_*=\Ipttil$. It follows from Proposition \[prop:monobd\] that $\Vpt \in \bar\DV'$, and the above result for $I_*=I$ then gives – also for $\Ipttil$ when $j_*=j$. This leaves – for the case $I_*=\Ipttil$ with $j_*=j+1$, as well as . For , we apply Lemma \[lem:Imono\] and the scale-$j$ case of (now $W_{j+1}$ occurs rather than $W_j$ but it is bounded by Remark \[rk:sm\]) to obtain $$\begin{aligned} \|\Ipttil (B)F\|_{T_{\phi,j+1} (\h_{j+1})} &\le \|\Ipttil (B)F\|_{T_{\phi,j} (\h_{j})} \prec \|F\|_{T_{0,j}} \Gcal_{j} (B,\phi) ,\end{aligned}$$ where $\Gcal_j = G_j$ for $\h_j=\ell_j$, and $\Gcal_j=\tilde G_j$ for $\h_j=h_j$. For $\h=\ell$ we set $\phi=0$ and immediately follows for $j+1$. For $\h=h$ we use the fact that $\tilde G_{j}(X,\phi) \le \tilde G_{j+1}^{\Gtilp}(X,\phi)$ by Lemma \[lem:mart\], and also follows in this case. Note that $\|F\|_{T_0,j}$ occurs in both for $j_*=j$ and $j_*=j+1$. The estimate follows similarly, and for $j+1$ follows from for $j$ by Lemma \[lem:Imono\], which implies that the $T_{\phi,j+1}$ norm is bounded above by the $T_{\phi,j}$ norm. Finally, to prove , we recall from Proposition \[prop:monobd\] that $\Vpt\in \bar\DV_{j+1}'$, and then follows exactly as the scale-$j$ case of for $\Ipttil$. This completes the proof. We first prove the analyticity of $V \mapsto \Ical = e^{-V}$ for $V$ in $\bar\DV_j$; in this case $j_*=j$. We fix $B$ and drop it from the notation. Fix $V \in \bar\DV_j$ and let $\dot{V} \in \Qcal$. We prove analyticity by showing that $I(V+\dot V)$ has a norm convergent power series expansion in $\dot V$, if $|\dot g| \le \frac{1}{8} {\rm Re}g$ and $\epsilon_{\dot{V}}$ is sufficiently small. By the integral form of the remainder in Taylor’s theorem, together with the product property of the $T_\phi$ semi-norm, $$\begin{aligned} \big\|e^{-(V+\dot V)} - \sum_{n=0}^N e^{-V} \frac{(-\dot V)^n}{n!}\big\|_{j} &= \big\| \int_0^1 \frac{1}{N!} e^{-(V+s\dot V)}\dot V^{N+1}(1-s)^{N} ds\big\|_{j} \nnb & \le \sup_\phi \Gcal(\phi)^{-1} \frac{1}{(N+1)!}\|e^{-V}\dot V^{N+1}\|_{T_\phi} e^{\|\dot V\|_{T_\phi}},\end{aligned}$$ where $\Gcal$ denotes the regulator, either $G_j$ or $\tilde G_j$. It suffices to show that the above right-hand side goes to zero as $N \to \infty$, and for this it suffices to show that insertion of summation over $N$ under the supremum leads to a convergent result. Since \_[N=0]{}\^ e\^[-V]{}V\^[N+1]{}\_[T\_]{} e\^[V\_[T\_]{}]{} e\^[-V]{} \_[T\_]{} e\^[2V\_[T\_]{}]{}, it suffices to show that $$\lbeq{eVanal} \sup_\phi \Gcal(\phi)^{-1} \|e^{-V} \|_{T_\phi} e^{2\|\dot V\|_{T_\phi}} < \infty.$$ We isolate the $\tau^2$ terms by writing $V=g\tau^2 + Q$ and $\dot V =\dot g \tau^2 + \dot Q$. By [@BS-rg-norm Proposition \[norm-prop:taunorm\]], $\|\tau_x\|_{T_\phi}=\h^2P(t)$, where $P(t)=t^2+2t+2$ and $t=|\phi_x|/\h$. Let $\epsilon = \epV + 2\epsilon_{\dot{V}}$. We use the product property of the $T_\phi$ norm, as well as [@BS-rg-norm Proposition \[norm-prop:T0K\]], to obtain $$\begin{aligned} \|e^{-V_x} \|_{T_\phi} e^{2\|\dot V_x\|_{T_\phi}} &\le \|e^{-g\tau_x^2 }\|_{T_\phi} e^{2|\dot g| \,\|\tau_x^2\|_{T_\phi}+ \|Q_x\|_{T_\phi} + 2\|\dot Q_x\|_{T_\phi}} \nnb & \le \|e^{-g\tau_x^2 }\|_{T_\phi} e^{2|\dot g |\h^4 P(t)^2 + \epsilon L^{-dj}(1+\|\phi\|_\Phi^2)}.\end{aligned}$$ By [@BS-rg-norm Proposition \[norm-prop:taunorm\]], together with the assumption in the definition of $\bar\DV$ that $|{\rm Im}g| < \frac 15 {\rm Re}g$, e\^[-g\_x\^2]{}\_[T\_]{} e\^[([Re]{}g)\^4\[-2t\^2 + 32 P(t)\^2\]]{}. Since $|\dot g| \le \frac18 {\rm Re}g$, this gives e\^[-g\_x\^2 ]{}\_[T\_]{} e\^[2|g |\^4 P(t)\^2 ]{} e\^[([Re]{}g)\^4\[-2t\^4 + 74 P(t)\^2\]]{} e\^[([Re]{}g)\^4\[q\_1-q\_2t\^2\]]{}, where $q_2 \ge 0$ can be chosen arbitrarily with a corresponding choice of $q_1$. Therefore, $$\|e^{-V_x} \|_{T_\phi} e^{2\|\dot V_x\|_{T_\phi}} \le e^{({\rm Re}g)\h^4[q_1-q_2t^2] + \epsilon L^{-dj}(1+\|\phi\|_\Phi^2)} .$$ To conclude for the $G$ norm, we take $q_2=0$ and $\epsilon_{\dot V} =\epV$, and the desired estimate follows for uniformly small $\ggen_j$. The proof of for the $\tilde G$ norm can be completed by applying the Sobolev inequality exactly as in the proof of Proposition \[prop:Iupperzz\], using the fact that we do have $\epV \le C\epVbar$ in this case by . It remains to consider the effect of $1+W$ on the above argument. Since $1+W$ is a degree-6 polynomial in the fields, it is analytic for the case of the $G$ norm, and its effect is therefore unimportant. For the case of the $\tilde G$ norm, $1+W$ is not analytic because polynomial growth in the absolute value of $\phi$ is not cancelled by the regulator in this case (since the regulator has linear functions factored out). However, it is an exercise to include the factor $1+W$ alongside the $e^{-V}$ factor in the above argument and thereby conclude analyticity also in this case. To prove the analyticity of $\Ipttil$ in $V \in \bar\DV_j$, it again suffices to consider $e^{-\Vpt}$. Let $V \in \bar\DV_j$ and consider first the case $j_*=j$. We can regard $e^{-\Vpt}$ as the composition of $V \mapsto \Vpt$ and $\Vpt \mapsto e^{-\Vpt}$. The first of these maps is polynomial in $V$. Thus, for the case of the $G$ norm, $V \mapsto \Vpt$ is analytic, while the second map is analytic by the previous argument together with the fact that $\Vpt \in \bar\DV'$ when $V \in \bar\DV$ by Proposition \[prop:monobd\]. This proves the desired analyticity when $j_*=j$ for the $G$ norm. The analyticity for the case of the $\tilde G$ norm can be established with small additional effort. Next, we consider the case $j_*=j+1$. As above, the main work lies in showing that $e^{-\Vpt}$ is an analytic function of $\Vpt \in \bar\DV$ when measured in the $\|\cdot\|_{j+1}$ norm. But it follows from Lemmas \[lem:Imono\] and \[lem:mart\] that for either of the choices – for the norm pairs, $\|F\|_{j+1} \le C\|F\|_j$ for some $C>0$ and for all $F$. Thus convergence of a power series in a neighbourhood in the $j$-norm implies convergence in a neighbourhood in the $j+1$-norm, and the analyticity for $j_*=j+1$ follows from the analyticity for $j_*=j$. Finally, it follows similarly that $I(B)^{-1}$ is analytic in $V$, as a map into the space with norm $\|\cdot\|_{T_{0,j}}$. For example, the factor $e^{g\tau^{2} (Y)}$ in $I(B)^{-1}$ is analytic in $g$ because it has an absolutely convergent power series, $$\begin{gathered} \|e^{g \tau^{2} (B)}\|_{T_{0} (\ell)} \le \sum_{n\ge 0} \frac{1}{n!} \|g\tau^{2} (B)\|_{T_{0} (\ell)}^{n} \le \sum_{n\ge 0} \frac{1}{n!} \epsilon_{g\tau^{2}}^{n} .\end{gathered}$$ A similar argument applies to the inverse of $1-W$. This completes the proof. Let $j<N$, $V \in \bar\DV$, and $Q\in\Qcal$ with $\|Q(B)\|_{T_0} \prec \epdV$. We first show that $V-Q \in \bar\DV'$. This implies that the estimates of Proposition \[prop:Istab\] apply to $\Ihat$, and that the desired analyticity follows from Proposition \[prop:Ianalytic1:5\], so then it will remain only to prove the estimates –. By Lemma \[lem:T0ep\], $\epsilon_{V-Q} \le \epV + \epsilon_{Q} \prec \epV + \max_B \|Q(B)\|_{T_0}$. The last bound of (with worse constants) then follows from the assumption on $Q$. For the middle bound of , let $g_Q$ denote the coefficient of $\tau^2$ in $Q$. By hypothesis, $L^{dj} |g_Q| \|\tau^2_0\|_{T_0(h)} \prec \ggen_j^{1/4}$, and hence $$L^{dj} |g- g_Q| \|\tau^2_0\|_{T_0(h)} \ge L^{dj} |g| \|\tau^2_0\|_{T_0(h)}-c_L\ggen_j^\eta \ge ak_0^4 - c \ggen_j^{1/4} \ge \frac 12 ak_0^4,$$ by taking $\ggen_j$ sufficiently small. Finally, for the first inequality of , we apply to see that $$|{\rm Im}g_Q| \le |g_Q| \prec \frac{\epsilon_{Q,j}(\h_j)}{L^{dj}\h_j^4} .$$ By the hypothesis on $Q$, for $\h=\ell$ the right-hand side is at most $c\ell_0^{-4} \ggen_j$, which is at most $\frac{1}{10}C_{\DV}^{-1}\ggen_j < \frac{1}{10}{\rm Re}g$ for $L$ sufficiently large (hence $\ell_0$ large). Similarly, for $\h=h$ the right-hand side is $\prec \ggen_j^{5/4}$, and hence the effect of $Q$ on the imaginary part of $g$ is negligible. This completes the proof that $V-Q\in \bar\DV'$. It remains to prove –. For $s \in [0,1]$, we write $V_s=V-sQ$, $I_s=I(V_s)$, $\Ical_s = e^{-V_{s}}$, and $W_s=W(V_{s})$, and omit the $B$ arguments. Direct calculation gives $$\begin{aligned} \label{e:Isprime} I_s' & = I_s Q + \Ical_s W_s', \\ \label{e:Isprime2} I_s'' &= I_s Q^2 + 2\Ical_s Q W_s' + \Ical_s W_s'', \\ \lbeq{Wprime} W_s' &= -W(Q,V_s) - W(V_s,Q), \\ \lbeq{Wprime2} W_s'' & = -2W(Q,Q).\end{aligned}$$ By Lemma \[lem:Wbil\], W\_s’\_[T\_0]{} \_L \_j \_j\^2 & =\ \_j \_j\^[3/4]{} & =h W\_s”\_[T\_0]{} \_L \_j \_j\^2 & =\ \_j \_j & =h. Let $\Ihat(B) = I(V-Q,B)$. By the Fundamental Theorem of Calculus, $\Ihat-I=\int_0^1 I_s' ds$, and hence by $$\lbeq{IIhatdif} \|\hat I - I\|_{j} \le \sup_{s\in [0,1]} \left( \|I_s Q\|_{j} + \|\Ical_s W_s'\|_j \right).$$ We have shown above that $V-sQ \in \bar\DV'$ (in fact this holds uniformly in $s$), and consequently holds with $V$ replaced by $V-sQ$. By , the first term on the right-hand side of is of order $\|Q\|_{T_0} \prec \epdV$. By and , the second term of is negligible compared to the first. This proves . For , we first note that $I_1 -I_0-I_0' = \hat I - I - IQ - \Ical_0 W_0'$. Using this, with a second-order Taylor remainder estimate followed by , gives $$\begin{aligned} \|\hat I - I - IQ\|_{T_0} &\le \|\Ical_0 W_0'\|_{T_0} + \sup_{s\in [0,1]} \| I_s''\|_{T_0} \nnb & \prec \|W_0'\|_{T_0} + \|Q\|_{T_0}^2 + \sup_{s\in [0,1]} \left( \| Q \|_{T_0} \| W_s'\|_{T_0} + \| W_s''\|_{T_0} \right) \prec_{L} \epdV^2 ,\end{aligned}$$ where for the last step we used together with the fact that its right-hand sides are at most $\epdV^2$. This proves . Proof of Propositions \[prop:hldg\]–\[prop:h\] {#sec:interaction-estimates444} ============================================== In this section, we prove Propositions \[prop:hldg\]–\[prop:h\]. The proof of Proposition \[prop:hldg\] is short, whereas the proof of Proposition \[prop:h\] is substantial. In the proof of Proposition \[prop:h\] it is important that $W$ and $\Vpt$ be defined as they are, and it is here that we implement the ideas in [@BBS-rg-pt Section \[pt-sec:WPjobs\]]. Proof of Proposition \[prop:hldg\] ---------------------------------- Let $j<N$ and $V \in \bar\DV_j$. Recall from that $\hldg (U,B)$ is defined for $(U,B) \in \Scal_{j+1}\times \Bcal_{j+1}$ by $$\label{e:hptdefqqz} \hldg (U,B) = \begin{cases} -\frac{1}{2} \Ex_{\pi ,j+1} \theta ( V_j(B); V_j(\Lambda \setminus B)) & U=B \\ \;\;\; \frac{1}{2} \Ex_{\pi ,j+1}\theta ( V_j(B); V_j(U\setminus B)) & U \supset B, |U|_{j+1}=2 \\ \;\;\; 0 &\text{otherwise} . \end{cases}$$ By , and , $$\label{e:EABbis} \Ex_{\pi,C} (\theta A; \theta B) = F_{\pi,C}( e^{ \Lcal_{C}} A , e^{ \Lcal_{C}} B).$$ By Proposition \[prop:Wnorms\], $$\begin{aligned} \label{e:Fepbd-xxx} \max_{B \in \Bcal_{j+1}} \sum_{x \in B} \sum_{B' \in \Bcal_{j+1}(\Lambda)} \|F_{\pi,C_{j+1}}(V_x,V(B'))\|_{T_{0,j+1}} & \prec_L\; \epdV^2 .\end{aligned}$$ As an operator on the subspace of $\Ncal$ consisting of bounded-degree polynomials in the fields, $e^{\pm \Lcal_{C_k}}$ is bounded (uniformly in $k$), due to and . With and , this gives $$\label{e:EtruncT0} \max_{B \in \Bcal_{j+1}} \sum_{x \in B} \sum_{B' \in \Bcal_{j+1}(\Lambda)} \|\Ex_{\pi,C_{j+1}}(\theta V_x;\theta V(B'))\|_{T_{0,j+1}} \prec_{L} \epdV^2,$$ from which we conclude that $$\begin{aligned} \label{e:Etruncbd} \|\hldg(U,B)\|_{T_0,j+1} &\prec_{L} \epdV^2 .\end{aligned}$$ By Proposition \[prop:Istab\], this implies that $$\begin{aligned} \label{e:2Lprimeh1} \|\Ipttil(U)\hldg(U,B) \|_{j+1} & \prec_L \epdV^2 .\end{aligned}$$ This gives and completes the proof of Proposition \[prop:hldg\]. Proof of Proposition \[prop:h\] ------------------------------- We require some preparation for the proof of Proposition \[prop:h\]. By –, $$\begin{aligned} \hldg (B) &= -\sum_{b \in \Bcal_j(B)} \frac{1}{2} \Ex_{\pi} (\theta V(b);\theta V(\Lambda \setminus B)) \nnb &= -\sum_{b \in \Bcal_j(B)} \frac{1}{2} \Ex_{\pi} ( \theta V(b);\theta V(\Lambda \setminus b)) + \sum_{b\not =b' \in \Bcal_j(B)} \frac{1}{2} \Ex_{\pi} (\theta V(b);\theta V(b')) .\end{aligned}$$ It follows from that $$\label{e:EpiE} \frac 12 \Ex_{\pi} (V';V'') + \frac 12 \Ex_{\pi}(V'';V') = \Ex (V';V''),$$ from which we conclude that $$\begin{aligned} \hldg (B) &= -\sum_{b \in \Bcal_j(B)} \frac{1}{2} \Ex_{\pi} (\theta V(b);\theta V(\Lambda \setminus b)) + \sum_{b\not =b' \in \Bcal_j(B)} \frac{1}{2} \Ex (\theta V(b);\theta V(b')). \label{e:hleadnew}\end{aligned}$$ For distinct $b,b' \in \Bcal_j$, $B \in \Bcal_{j+1}$, and for $U \in \Scal_{j+1}$ with $|U|_{j+1}\in \{1,2\}$, we define $$\begin{aligned} \label{e:R1def} R_1(b;B) & = \Ipttil^{B\setminus b} \Ex \delta I^b + \Ipttil^{B} \frac{1}{2} \Ex_{\pi} (\theta V_j(b);\theta V_j(\Lambda \setminus b)) , \\ \label{e:R2def} R_2(b,b';U) & = \frac{1}{2} \left[ \Ipttil^{U\setminus (b\cup b')}\Ex \delta I^{b\cup b'} - \Ipttil^{U} \Ex (\theta V_j(b);\theta V_j(b')) \right] ;\end{aligned}$$ note that $\Ex_{\pi}$ appears in $R_1$ but not in $R_2$. Then, by , –, and , $$\begin{aligned} \label{e:hhptB} \Ipttil^B [\hred (B) - \hldg (B)] & = \sum_{b \in \Bcal_j(B)} R_1(b;B) + \sum_{b\neq b' \in \Bcal_j} R_2(b,b';B) , \\ \label{e:hhptU} \Ipttil^U [\hred (U) - \hldg (U)] & = \sum_{b\neq b' : \overline{b\cup b'}=U} R_2(b,b';U) \quad \quad \quad\quad |U|_{j+1}= 2.\end{aligned}$$ By the triangle inequality and –, to prove Proposition \[prop:h\] it suffices to show that $$\begin{aligned} \label{e:R12suff} \| R_1(b;B) \|_{j+1} & \prec_L \, \epdV^3 , \quad\quad \| R_2(b,b';U) \|_{j+1} \prec_L \, \epdV^3 ,\end{aligned}$$ where the constants in the upper bounds depend on $L$, and $\epdV$ is given by . The appearance of $\delta I$ leads naturally to the study of $\delta V$, which was defined in as $\delta V = \theta V - \Vpt$. As a first step in the proof of , we prove the following lemma which relies heavily on results from [@BS-rg-norm]. The “5” appearing in its statement has been chosen as a convenient positive constant and is not significant. The parameter $\hat\ell_j >0$ is defined in . The constant $C_{\delta V}$ is the $L$-dependent constant of Lemma \[lem:epdV\]. \[lem:dIipV\] Let $j<N$, $b,b' \in \Bcal_j$, and $n,n' \ge 0$. Suppose that $F \in \Ncal((b\cup b')^\Box)$ obeys $\|F\|_{T_\phi(\h+\hat\ell)} \le c_F e^{\alpha \|\phi\|_{\Phi(\h)}^{2}}$ for some $c_F,\alpha >0$. If $u \in (0,2]$ obeys $\alpha + \frac{1}{20}(n+n')u \le 5$, then $$\begin{aligned} \label{e:ip-V1} \| \Ex_{j+1} \left[(\delta V(b))^n (\delta V(b'))^{n'} \theta F \right] \|_{T_{\phi}(\h)} &\prec_L c_F (C_{\delta V}\epdV)^{n+n'} e^{(2\alpha + (n+n')u) \|\phi\|_{\Phi(\h)}^2}, \end{aligned}$$ where the constant in the upper bound depends on $u,n,n'$, and where $\h$, $\hat\ell$ and all norms are at scale $j+1$. By [@BS-rg-norm Proposition \[norm-prop:EK\]] (with to provide its hypothesis on the covariance), and by the product property of the $\Ttimes_{\phi\sqcup\xi}$ semi-norm, $$\begin{aligned} &\|\Ex \left[ (\delta V(b))^{n} (\delta V(b'))^{n'} \theta F \right] \|_{T_{\phi}} \leq \Ex \| (\delta V(b))^{n} (\delta V(b'))^{n'} \theta F \|_{\Ttimes_{\phi\sqcup\xi}(\h\sqcup\hat\ell)} \nnb & \hspace{30mm} \leq \Ex \left[\| \delta V(b)\|_{\Ttimes_{\phi\sqcup\xi}(\h\sqcup\hat\ell)}^{n} \| \delta V(b')\|_{\Ttimes_{\phi\sqcup\xi}(\h\sqcup\hat\ell)}^{n'} \|\theta F \|_{\Ttimes_{\phi\sqcup\xi}(\h\sqcup\hat\ell)} \right].\end{aligned}$$ We apply [@BS-rg-norm Proposition \[norm-prop:T0K\]] to the $\Ttimes_{\phi\sqcup\xi}(\h\sqcup\hat\ell)$ semi-norm of $\delta V$, with a multi-component field with $\h=\hat\ell$ for $\xi$. With , this gives $$\| \delta V(b)\|_{\Ttimes_{\phi\sqcup\xi}(\h\sqcup\hat\ell)} \le \epdV (1+\|\phi\|_{\Phi(\h)})^4 (1 + \|\xi\|_{\Phi(\hat\ell)})^4.$$ For any $u \in (0,2]$, then gives (with a $u$-dependent constant and with $\hat{u}=u(\ell/\hat\ell)^2$) $$\label{e:dVbdpf} \| \delta V(b)\|_{\Ttimes_{\phi\sqcup\xi}(\h\sqcup\hat\ell)} \prec C_{\delta V} \epdV e^{u(\|\phi\|_{\Phi(\h)}^2 + \|\xi\|_{\Phi(\hat\ell)}^2)} = C_{\delta V} \epdV e^{u\|\phi\|_{\Phi(\h )}^2 } G(b,\xi)^{\hat{u}} .$$ Similarly, by [@BS-rg-norm Proposition \[norm-prop:derivs-of-tau-bis\]], by hypothesis, by $\|\phi+\xi\|^2 \le 2(\|\phi\|^2+\|\xi\|^2)$, and by $\h \ge \ell$, $$\begin{aligned} \|\theta F \|_{\Ttimes_{\phi\sqcup\xi}(\h\sqcup\hat\ell)} & \le \| F \|_{T_{\phi+\xi}(\h+\hat\ell)} \le c_F e^{2\alpha(\|\phi\|_{\Phi(\h)}^2 + \|\xi\|_{\Phi(\h)}^2)} \nnb & \le c_F e^{2\alpha\|\phi\|_{\Phi(\h)}^2 }G(b\cup b', \xi)^{2\alpha}.\end{aligned}$$ Therefore, with $s=n+n'$, since $G(b\cup b')=G(b)G( b')$ by [@BS-rg-norm], $$\begin{aligned} \label{e:EGpapp} \|\Ex [ (\delta V(b))^{n} (\delta V(b'))^{n'} \theta F ] \|_{T_{\phi}} & \prec (C_{\delta V}\epdV)^{s} c_F e^{(2\alpha +su)\|\phi\|_{\Phi(\h )}^2 } \Ex \left[ G(b \cup b',\xi)^{2\alpha +s\hat{u}} \right] .\end{aligned}$$ It suffices now to bound the expectation on the right-hand side by a constant. By , by our choice $\ellconst = \frac{1}{10}c_G$ above , and by and , $$\begin{aligned} (2\alpha +s\hat{u}) \|C\|_{\Phi^+(\ell)} & = 2\alpha \|C\|_{\Phi^+(\ell)} +su \|C\|_{\Phi^+(\hat\ell)} \nnb & \le 2\alpha \ellconst + su \frac{c_G}{100} \le \left( \frac{\alpha}{5} + \frac{su}{100} \right) c_G \le c_G ,\end{aligned}$$ with the last inequality true by hypothesis. Then [@BS-rg-norm Proposition \[norm-prop:EG2\]] yields the desired bound on the expectation, and the proof is complete. For $j \ge 1$, we define $A_j$ by $$\label{e:Ajdef} A_j = e^{-\delta V} - \sum_{i=0}^{j-1} \frac{(-\delta V)^i}{i!}.$$ By Taylor’s theorem with integral form of the remainder, $$\label{e:AjTaylor} A_j = \frac{1}{(j-1)!} \int_0^1 (1-t)^{j-1} (\delta V)^j e^{-t\delta V} dt.$$ It follows from the definitions that $e^{-\theta V}=e^{-\Vpt}e^{-\delta V}$, and that for $b \in \Bcal_j$, $$\begin{aligned} \delta I(b) & = e^{-\Vpt(b)}\left( A_1(b) + Z(b) \right), \label{e:dIexpansion}\end{aligned}$$ with $$\label{e:ZdefW} Z = e^{-\delta V}\theta W - W_{j+1}.$$ It is in the following proof that it is important that $W$ and $\Vpt$ be defined as they are, and our implementation of the ideas laid out in [@BBS-rg-pt Section \[pt-sec:WPjobs\]] occurs here. In particular, the identity $$\label{e:EW} \Ex_{j+1} \theta W_{j} (V, X) = W_{j+1} (\Ex_{j+1}\theta V ,X) + P (X) - \frac{1}{2} \Ex_{\pi ,j+1}\big(\theta V(X);\theta V(\Lambda)\big)$$ of Lemma \[lem:EW\] enters the proof of in a crucial manner, as does the definition $\Vpt = \Ex \theta V - P$ of (recall ). All norms in this proof are at scale $j+1$. Fix $B\in \Bcal_{j+1}$ and $b \in \Bcal_j(B)$ for $R_1$, and fix $U \in \Scal_{j+1}$ with $|U|\in \{1,2\}$ and $b\neq b' \in \Bcal_j$ with $\overline{b \cup b'}=U$ for $R_2$. To prove , it suffices to prove that $$\begin{aligned} \label{e:ExIb} \| R_1(b;B) \|_{T_\phi} &\prec_L \epdV^3 \Gcal(B,\phi) , \\ \label{e:ExIbb} \| R_2(b,b';U) \|_{T_\phi} &\prec_L \epdV^3 \Gcal(U,\phi) ,\end{aligned}$$ where $\Gcal$ represents $G$ or $\tilde G^{\Gtilp}$ according to the choice $\h=\ell$ or $\h=h$. We first prove the bound for $R_1$, and then the bound for $R_2$. *Identity for $R_1$.* We apply , , and the definition $\Vpt=\Ex\theta V -P$, to obtain $$\begin{aligned} \delta I & = e^{-\Vpt}\left( -\delta V + A_2 + Z \right) \nnb & = e^{-\Vpt}\left( -\delta V + \frac 12 (\delta V)^2 + A_3 + (1+A_1)\theta W -W_{j+1} \right) \nnb & = e^{-\Vpt}\left( \Ex\theta V -\theta V - P + \frac 12 (\theta V - \Ex\theta V)^2 + \theta W -W_{j+1}(\Ex\theta V) + \Ecal_1 \right), \label{e:dIexpansion2}\end{aligned}$$ where $$\Ecal_1 = (\theta V - \Ex\theta V)P + \frac 12 P^2 + A_3 + A_1 \theta W + W_{j+1}(\Ex\theta V) -W_{j+1}(\Vpt) .$$ Then, taking the expectation, we obtain $$\begin{aligned} \Ex \delta I(b) & = e^{-\Vpt}\left( - P + \frac 12 \Ex(\theta V(b) ; \theta V(b)) + \Ex\theta W -W_{j+1}(\Ex\theta V) + \Ex\Ecal_1 \right) ,\end{aligned}$$ with $$\label{e:ExEcal1} \Ex \Ecal_1 = \frac 12 P^2 + \Ex A_3 + \Ex (A_1 \theta W) + \big[ W_{j+1}(\Ex\theta V) -W_{j+1}(\Vpt) \big] .$$ It follows from that $\Ex(\theta V(b) ; \theta V(b)) = \Ex_\pi(\theta V(b) ; \theta V(b))$. Thus, after application of , together with use of the identity $$\Ex_\pi(\theta V(b); \theta V(b)) - \Ex_\pi(\theta V(b); \theta V(\Lambda)) = - \Ex_\pi(\theta V(b); \theta V(\Lambda \setminus b)),$$ we obtain $$\begin{aligned} \Ipttil^{B\setminus b}\Ex \delta I(b) & = \Ipttil^{B \setminus b} e^{-\Vpt(b)}\left( - \frac{1}{2} \Ex_{\pi}(\theta V (b); \theta V(\Lambda \setminus b)) + \Ex\Ecal_1 (b) \right) \nnb & = -\Ipttil^B \frac{1}{2} \Ex_{\pi}(\theta V (b); \theta V(\Lambda \setminus b)) \nnb & \quad + \Ipttil^{B \setminus b} e^{-\Vpt(b)}W_{j+1} \frac{1}{2} \Ex_{\pi}(\theta V (b); \theta V(\Lambda \setminus b)) + \Ipttil^{B \setminus b} e^{-\Vpt(b)} \Ex\Ecal_1 (b) . \label{e:EdIid}\end{aligned}$$ By definition of $R_1$, this gives $$\lbeq{R1identity} R_1(b;B) = \Ipttil^{B \setminus b} e^{-\Vpt(b)}W_{j+1} \frac{1}{2} \Ex_{\pi}(\theta V (b); \theta V(\Lambda \setminus b)) + \Ipttil^{B \setminus b} e^{-\Vpt(b)} \Ex\Ecal_1 (b) .$$ The use of has led to an important cancellation which the definitions of $W$ and $\Vpt$ were engineered to create. *Bound on $R_1$.* It suffices to obtain a bound of the form $\epdV^3 \Gcal(B,\phi)$ for the $T_\phi$ semi-norms of each of the two terms on the right-hand side of , with the last of these terms given by . The resulting five terms are of two types: one type involves $\Ipttil^{B \setminus b} e^{-\Vpt}$ multiplied by the polynomials $W_{j+1}\Ex_{\pi}(\theta V (b); \theta V(\Lambda \setminus b))$, $P^2$, $[ W_{j+1}(\Ex\theta V) -W_{j+1}(\Vpt)]$, and the second type involves two terms with expectations of the non-polynomial quantities $A_1$ and $A_3$. For the first type of term, we apply (the version with factor $(1+W(b))$ omitted) to conclude that, for a polynomial $Q$, $$\|\Ipttil^{B \setminus b} e^{-\Vpt(b)} Q(b)\|_{j+1} \prec \|Q(b)\|_{T_{0,j}}.$$ Bounds on the $T_0$ semi-norm of $W_{j+1}$, $\Ex_{\pi}(\theta V (b);\theta V(\Lambda \setminus b))$ and $P$ follow from , , and . Also, the norm of $W_{j+1}(\Ex\theta V) -W_{j+1}(\Vpt)$ is bounded in . With these bounds, we obtain an upper bound of order $\epdV^3$ for the $(j+1)$-norm of the three terms with polynomials. For the second type of term, we apply Lemma \[lem:dIipV\]. For the $A_3$ term, it follows from and the product property that $$\begin{aligned} \label{e:A3term} \|\Ipttil^{B \setminus b} e^{-\Vpt(b)}\Ex A_3(b)\|_{T_{\phi}} & \le \sup_{t\in [0,1]} \|\Ipttil^{B \setminus b} e^{-(1-t)\Vpt(b)}\|_{T_{\phi}} \| \Ex \delta V(b)^3 e^{-t\theta V(b)}\|_{T_{\phi}} .\end{aligned}$$ By and (for its hypothesis on $\omega$ we see from that $\omega \prec_L \epdV^2$), given any small $u_1>0$, $$\|e^{-t V(b)}\|_{T_{\phi}(\h+\hat\ell)} \le \|e^{-t V(b)}\|_{T_{\phi}(2\h)} \le e^{O(\epV(2\h) +u_1) \|\phi\|_{\Phi(2\h)}^2} \le e^{O(\epV(\h) +u_1) \|\phi\|_{\Phi(\h)}^2} .$$ It therefore follows from Lemma \[lem:dIipV\] that given any small $u>0$, with a constant depending on $u$ we have $$\label{e:A3term-a} \| \Ex \delta V(b)^3 e^{-t\theta V(b)}\|_{T_{\phi}} \prec_L \epdV^3 e^{O(\epV + u) \|\phi\|_\Phi^2}.$$ For the case of the regulator $G$, we bound the first factor on the right-hand side of as follows. By , the product property, and , $$\|\Ipttil^{B \setminus b} e^{-(1-t)\Vpt(b)}\|_{T_{\phi,j+1}} \le \|\Ipttil^{B \setminus b}\|_{T_{\phi,j+1}} \| e^{-(1-t)\Vpt(b)}\|_{T_{\phi,j}} \le e^{O(\epV + u) \|\phi\|_\Phi^2}.$$ Thus we obtain $$\begin{aligned} \|\Ipttil^{B \setminus b} e^{-\Vpt(b)}\Ex A_3(b)\|_{T_{\phi}} & \prec_L \epdV^3 G(B,\phi) ,\end{aligned}$$ as required. For the case of the regulator $\tilde G$, we take $u=u_1=\epVbar$ and recall from and that $\epV \prec \epVbar \asymp k_0^4$, with $k_0$ chosen small (recall the discussion above ). Then gives, for some $c_0>0$, $$\label{e:A3term-b} \| \Ex \delta V(b)^3 e^{-t\theta V(b)}\|_{T_{\phi}} \prec_L \epdV^3 e^{c_0\epVbar \|\phi\|_\Phi^2}.$$ We apply , with $q = c_0$, to see that $$\begin{aligned} \|\Ipttil^{B \setminus b} e^{-\Vpt(b)}\Ex A_3(b)\|_{T_{\phi}} & \prec_L \epdV^3 \tilde G^{\Gtilp} (B,\phi) ,\end{aligned}$$ as required. The $A_1\theta W_j$ term can be treated similarly, using Lemma \[lem:dIipV\] with $F=e^{-tV}W_j$. This completes the discussion of the bound on $R_1$. *Bound on $R_2$.* Starting from the first line of , and recalling that $Z$ is defined in , a little algebra leads to $$\Ex \delta I^{b \cup b'} = e^{-\Vpt(b\cup b')} \big( \Ex (\theta V(b) ; \theta V(b')) + \Ecal_2(b,b') \big), \label{e:EdIbb}$$ where $$\begin{aligned} \Ecal_2(b,b') & = P(b)P(b') - \Ex \big(\delta V(b) A_2(b')\big) - \Ex \big(A_2(b) \delta V(b')\big) + \Ex \big(A_2(b)A_2(b')\big) \nnb & \quad\quad + \Ex \big(A_1(b) Z(b')\big) + \Ex \big(Z(b)A_1(b')\big) + \Ex \big(Z(b)Z(b')\big).\end{aligned}$$ Therefore, $$\begin{aligned} & 2R_2(b,b';U) = \Ipttil^{U\setminus (b\cup b')}e^{-\Vpt(b \cup b')} \Ecal_2(b,b') \\ \nonumber & \quad + \Ipttil^{U\setminus (b\cup b')}e^{-\Vpt(b\cup b')}[(1+W_{j+1}(b))(1+W_{j+1}(b'))-1] \Ex (\theta V(b) ; \theta V(b')) .\end{aligned}$$ By (with two missing $1+W$ factors), the $(j+1)$-norm of the second term on the right-hand side is bounded by a multiple of the $T_0$ semi-norm of the polynomial factor, which by and is of order $\epdV^4$. The contribution due to the $PP$ term in $\Ecal_2$ can be bounded in the same way, using . The six remaining terms in $\Ecal_2$ can be handled in the same way as the $A_3$ and $A_1$ terms in $\Ecal_1$, and we omit the details. Using Lemma \[lem:dIipV\], the $\delta V A_2$ and $A_1Z$ terms are seen to be order $\epdV^3$, while the $A_2A_2$ and $ZZ$ terms are order $\epdV^4$. In particular, it is not necessary to make use of any cancellation within $Z$. Together, these estimates produce an overall bound of order $\epdV^3$, and the proof is complete. Proof of Propositions \[prop:ip\]–\[prop:cl\] {#sec:ipcl} ============================================= In this section, we prove Propositions \[prop:ip\]–\[prop:cl\]. Proof of Proposition \[prop:ip\] {#sec:ippf} -------------------------------- The main step in the proof of Proposition \[prop:ip\] is provided by the following lemma. The constant $C_{\delta L}$ is the $L$-dependent constant of Lemma \[lem:epdV\]. \[lem:dIip\] Let $X,Y \in \Pcal_j$ be disjoint. Let $F(Y) \in \Ncal (Y^{\Box})$. There is an $\Econst>0$ (independent of $L$) and a $C_{\delta V}>0$ (depending on $L$) such that $$\begin{aligned} \label{e:integration-property-a} \|\Ex \delta I^X \theta F(Y) \|_{T_{\phi}(\h/2)} &\leq \Econst^{|X|_j+|Y|_j} (C_{\delta V} \epdV)^{|X|_j} \| F(Y) \|_{\Gcal(\h)} \Gcal(X\cup Y,\phi)^5, \end{aligned}$$ where $\Gcal$ denotes $G$ or $\tilde G$ when $\h=\ell$ or $\h=h$, respectively. Norms and regulators are at scale $j$, the expectation represents $\Ex_{C_{j+1}}$, and $\delta I$ is given by . We write $\h'=\h/2$ and $\hat\ell' = \hat\ell/2$. By [@BS-rg-norm Proposition \[norm-prop:EK\]] (with to provide its hypothesis), and by the product property of the $\Ttimes_{\phi\sqcup\xi}$ semi-norm, $$\begin{aligned} \|\Ex \delta I^X \theta F(Y) \|_{T_{\phi}(\h')} & \leq \Ex \left[\| \delta I^X \|_{\Ttimes_{\phi\sqcup\xi}(\h'\sqcup \hat\ell')} \|\theta F(Y) \|_{\Ttimes_{\phi\sqcup\xi}(\h'\sqcup \hat\ell')} \right]. \label{e:ip1}\end{aligned}$$ By [@BS-rg-norm Proposition \[norm-prop:derivs-of-tau-bis\]] and (with the fact that $\h \ge \hat\ell$ for uniformly small $\ggen_j$), $$\begin{aligned} \lbeq{ip1.1} \|\theta F(Y) \|_{\Ttimes_{\phi\sqcup\xi}(\h'\sqcup\hat\ell')} & \!\! \le \| F(Y) \|_{T_{\phi+\xi}(\h'+\hat\ell')} \leq \| F(Y) \|_{T_{\phi+\xi}(\h)} \leq \| F(Y) \|_{\Gcal(\h)} \Gcal(Y,\phi+\xi).\end{aligned}$$ Since $\|\phi+\xi\|^2 \le 2\|\phi \|^2 + 2\|\xi\|^2$, and since $\Gcal \le G$ because $\tilde G \le G$, this gives $$\begin{aligned} \|\theta F(Y) \|_{\Ttimes_{\phi\sqcup\xi}(\h'\sqcup\hat\ell')} & \!\! \le \| F(Y) \|_{\Gcal(\h)} \Gcal(Y,\phi)^2 \Gcal(Y,\xi)^2 \le \| F(Y) \|_{\Gcal(\h)} \Gcal(Y,\phi)^2 G(Y,\xi)^2. \label{e:ip1.5}\end{aligned}$$ By –, for $b \in \Bcal_j$, $$\begin{aligned} \|\delta I(b)\|_{T_{\phi\sqcup\xi}(\h'\sqcup\hat\ell')} & \!\! \le \!\! \|\delta V(b)\|_{T_{\phi\sqcup\xi}(\h'\sqcup\hat\ell')} \!\! \sup_{t\in [0,1]} \|e^{-(1-t)\Vpt(b)}\|_{T_{\phi}(\h')} \|\theta e^{-t V(b)}\|_{T_{\phi\sqcup\xi}(\h'\sqcup\hat\ell')} \nnb & \quad \quad + \|\theta(e^{-V(b)}W(b)) \|_{T_{\phi\sqcup\xi}(\h'\sqcup\hat\ell')} + \|e^{-\Vpt}W_{j+1}(b)\|_{T_{\phi}(\h')}. \label{e:delItimes}\end{aligned}$$ By (now interpreted at scale $j$ rather than $j+1$; recall that the bound of Lemma \[lem:epdV\] applies to either scale), for any choice of small positive $u$, and with $\hat{u}=u(\ell/\hat\ell)^2$, $$\| \delta V(b)\|_{\Ttimes_{\phi\sqcup\xi}(\h'\sqcup\hat\ell')} \prec C_{\delta V} \epdV e^{u\|\phi\|_{\Phi(\h' )}^2 } G(b,\xi)^{\hat{u}} .$$ We now consider the supremum on the right-hand side of . Either $t \ge \frac 12$ or $1-t \ge \frac 12$. Suppose that $t \ge \frac 12$; the other case is simpler and we omit its details. By and , $\|e^{-(1-t)\Vpt(b)}\|_{T_{\phi}(\h')} \le 2\Gcal(b,\phi)$. By [@BS-rg-norm Proposition \[norm-prop:derivs-of-tau-bis\]], , the inequality $\|\phi\|^2 \le 2\|\phi+\xi\|^2 + 2\|\xi\|^2$, and the identity $\|\phi\|_{\Phi(\h')}=2\|\phi\|_{\Phi(\h)}$, $$\begin{aligned} \|\theta e^{-t V(b)}\|_{T_{\phi\sqcup\xi}(\h'\sqcup\hat\ell')} e^{u\|\phi\|_{\Phi(\h' )}^2 } &\le \|e^{-t V(b)}\|_{T_{\phi+\xi}(\h'+\hat\ell')}e^{u\|\phi\|_{\Phi(\h' )}^2 } \nnb & \le \|e^{-t V(b)}\|_{T_{\phi+\xi}(\h)} e^{8u\|\phi+\xi\|_{\Phi(\h )}^2 } e^{8u\|\xi\|_{\Phi(\h )}^2 } \nnb & \le \|e^{-t V(b)}\|_{T_{\phi+\xi}(\h)} e^{8u\|\phi+\xi\|_{\Phi(\h )}^2 } G(b,\xi)^{1/2}, \label{e:thetaeV}\end{aligned}$$ where we used $8u\|\xi\|_{\Phi(\h)}^2 \le \frac 12 \|\xi\|_{\Phi(\ell)}^2$ in the last step (we can take $u \le \frac {1}{16}$). Next, we apply when $\Gcal =G$, and with $u=\epVbar$ and $q= 8$ when $\Gcal =\tilde G$ , to obtain $$\|e^{-t V(b)}\|_{T_{\phi+\xi}(\h)} e^{8u\|\phi+\xi\|_{\Phi(\h )}^2 } \prec \Gcal(b,\phi+\xi),$$ and hence $$\begin{aligned} \|\theta e^{-t V(b)}\|_{T_{\phi\sqcup\xi}(\h'\sqcup\hat\ell')} e^{u\|\phi\|_{\Phi(\h' )}^2 } & \prec \Gcal(b,\phi+\xi)G(b,\xi)^{1/2} \nnb & \le \Gcal(b,\phi)^2 \Gcal(b, \xi)^2 G(b,\xi)^{1/2}. \label{e:thetaeV-bis}\end{aligned}$$ Since $\Gcal \le G$, we conclude from the above estimates that $$\begin{aligned} \label{e:supdV} &\|\delta V(b)\|_{T_{\phi\sqcup\xi}} \sup_{t\in [0,1]} \|e^{-(1-t)\Vpt(b)}\|_{T_{\phi}} \|\theta e^{-t V(b)}\|_{T_{\phi\sqcup\xi}} \nnb & \quad\quad \prec C_{\delta V}\epdV \Gcal (b,\phi)^3 G(b,\xi)^{\hat u + 5/2} \prec C_{\delta V}\epdV \Gcal (b,\phi)^3 G(b,\xi)^{3(\ell/\hat\ell)^2} ,\end{aligned}$$ using the fact that $u$ is small and that $\hat\ell \le \ell$ by definition. To complete the estimate on $\delta I(b)$, we now consider the two $W$ terms in . By [@BS-rg-norm Proposition \[norm-prop:derivs-of-tau-bis\]], and the fact that $\h \ge \ell$, , and , $$\begin{aligned} \|\theta(e^{-V(b)}W(b)) \|_{T_{\phi\sqcup\xi}(\h'\sqcup\hat\ell')} &\le \|e^{-V(b)}W(b) \|_{T_{\phi+\xi}(\h'+\hat\ell')} \prec \|e^{-V(b)}W(b) \|_{T_{\phi+\xi}(\h)} \nnb & \prec \|W(b)\|_{T_0} \Gcal(b,\phi+\xi) \prec_L \epdV^2 \Gcal(b,\phi)^2 \Gcal(b,\xi)^2. \label{e:eVW}\end{aligned}$$ Similarly (recall Remark \[rk:sm\]), $$\begin{aligned} \|e^{-\Vpt}W_{j+1}(b)\|_{T_{\phi}(\h')} & \!\! \prec \|e^{-\Vpt}W_{j+1}(b)\|_{T_{\phi}(\h)} \!\! \prec \|W_{j+1}(b)\|_{T_{0}(\h)}\Gcal(b,\phi) \prec_L \epdV^2 \Gcal(b,\phi). \label{e:eVW+}\end{aligned}$$ We are free to take $\epdV$ small depending on $L$, so that in the above two bounds $\prec_L \epdV^2$ can be replaced by a bound $\prec \epdV$. The combination of with – gives $$\begin{aligned} \label{e:dIass} \|\delta I (b) \|_{\Ttimes_{\phi\sqcup\xi} (\h\sqcup\ell)} &\prec C_{\delta V}\epdV \Gcal (b,\phi)^3 G(b,\xi)^{3(\ell/\hat\ell)^2}.\end{aligned}$$ As noted below Definition \[def:Gnorms\], $\Gcal(X)\Gcal(Y)=\Gcal(X\cup Y)$. Thus there is a constant $c$ (independent of $L$) such that $$\label{e:ip2} \| \delta I^X \|_{\Ttimes_{\phi\sqcup\xi}} \leq \prod_{b \in \Bcal_j(X)} \| \delta I(b) \|_{\Ttimes_{\phi\sqcup\xi}} \leq (cC_{\delta V}\epdV)^{|X|_j} \Gcal(X,\phi)^3 G(X,\xi)^{3(\ell/\hat\ell)^2}.$$ The proof is completed by inserting and into , also noting that $$\Ex G(X \cup Y,\xi)^{3(\ell/\hat\ell)^2} \le 2^{|X|_j+|Y|_j}.$$ This last inequality is a consequence of [@BS-rg-norm Proposition \[norm-prop:EG2\]], whose hypothesis is supplied by the fact that $3(\ell/\hat\ell)^2 \|C\|_{\Phi^+(\hat\ell)} = 3\|C\|_{\Phi^+(\ell)} \le 3 \ellconst \le c_G$ by our choice of $\ellconst$. We apply Lemma \[lem:dIip\] with scale-$j$ norms and $\h=\h_{j}$. Since $\h_{j+1} \le \h' = \h_j/2$, we can apply to the left-hand side of to conclude that $$\begin{aligned} \label{e:integration-property-pf} \|\Ex \delta I^X \theta F(Y) \|_{T_{\phi,j+1}(\h_{j+1})} &\leq \Econst^{|X|_j+|Y|_j} (C_{\delta V} \epdV)^{|X|_j} \| F(Y) \|_{\Gcal_j(\h_{j})} \Gcal_j(X\cup Y,\phi)^5.\end{aligned}$$ For the norm pair , it suffices to consider the case $\phi =0$, for which the regulator on the right-hand side of reduces to unity and the integration property immediately follows in this case. For the norm pair , Lemma \[lem:mart\] gives $$\label{e:Gtilmart} \tilde{G}_j(X,\cup Y,\phi)^5 \le \tilde{G}_{j+1}^{\Gtilp}(X\cup Y,\phi),$$ and with this gives in this case. This completes the proof. Proof of Proposition \[prop:cl\] {#sec:contraction3-proof} -------------------------------- For convenience, we restate Proposition \[prop:cl\] as Proposition \[prop:cl-bis\]. Its proof uses Proposition \[prop:1-LTdefXY\] in a crucial way. \[prop:cl-bis\] Let $j<N$ and $V\in \bar\DV_j$. Let $X \in \Scal_j$ and $U = \overline X$. Let $F(X) \in \Ncal(X^\Box)$ be such that $\pi_\alpha F(X) =0$ when $X(\alpha)=\varnothing$. We assume that $\pi_{ab}V=\pi_{ab}F(X)=0$ unless $j \ge j_{ab}$ (recall ). Then $$\begin{aligned} \label{e:contraction3z} \|\Ipttil^{U\setminus X} \Ex_{C_{j+1}} \theta F (X) \|_{j+1} & \prec \cgam(X) \kappa_F + \kappa_{\LT F} ,\end{aligned}$$ where $\kappa_F=\|F (X)\|_{j}$, $\kappa_{\LT F} =\|\Ipttil^X \LT_X \Ipttil^{-X} F(X) \|_j$, and where the pair of norms is given by either of or . We make the decomposition $$\label{e:KLTdeca} F(X) = D(X)+E(X),$$ with $$\begin{aligned} \label{e:EXdef} D(X) & = \Ipttil^X \LT_X \Ipttil^{-X} F(X), \quad\quad\quad E(X) = \Ipttil^X (1-\LT_X) \Ipttil^{-X} F(X).\end{aligned}$$ By the triangle inequality and the product property, $$\|\Ipttil^{U\setminus X} \Ex \theta F (X) \|_{j+1} \le \|\Ipttil^{U\setminus X} \|_{j+1} \|\Ex \theta D (X) \|_{j+1} + \|\Ipttil^{U\setminus X} \Ex \theta E (X) \|_{j+1}.$$ Since $X\in\Scal_{j}$, its closure $U$ lies in $\Scal_{j+1}$ and hence consists of at most $2^d$ blocks. Therefore, by the product property and , $\|\Ipttil^{U\setminus X} \|_{j+1}\le 2^{2^d}$. By the integration property of Proposition \[prop:ip\], $$\begin{aligned} \|\Ex \theta D (X) \|_{j+1} &\prec \|D(X)\|_j = \kappa_{\LT F}. \label{e:Lkpfii-1zbis}\end{aligned}$$ Thus the $D$ term in leads to the final term of . For the term involving $E$, we first apply the product property and [@BS-rg-norm Proposition \[norm-prop:EK\]] (with its assumption given by $h \ge \ell$ and ) to obtain $$\lbeq{cl-0} \|\Ipttil^{U\setminus X} \Ex \theta E (X) \|_{T_{\phi,j+1}(\h_{j+1})} \le \|\Ipttil^{U\setminus X} \|_{T_{\phi,j+1}(\h_{j+1})} \Ex \| E (X) \|_{T_{\phi+\xi,j+1}(2\h_{j+1})}.$$ We recall the inequality $$\begin{aligned} \label{e:FXbdKz} \|F_1(1-\LT_X) F_2\|_{T_{\phi}'} &\le \bar{C} \cgam(Y) \left(1 + \|\phi\|_{\Phi'}\right)^{A+d+1} \sup_{0\le t \le 1} \big( \|F_{1}F_{2}\|_{T_{t\phi}} + \|F_{1}\|_{T_{t\phi}}\|F_{2}\|_{T_{0}}\big)\end{aligned}$$ from Proposition \[prop:1-LTdefXY\] (where its notation is defined). To bound the semi-norm of $E(X)$, we apply (writing $a=A+d+1$ and $\cgam=\cgam(X)$), to obtain $$\begin{aligned} \lbeq{cl-1} & \| E(X) \|_{T_{\phi+\xi,j+1}(2\h_{j+1})} \prec \gamma \left(1+\|\phi+\xi\|_{\Phi_{j+1}(X^\Box,2\h_{j+1})} \right)^{a} \\ \nonumber & \quad \times \sup_{0 \le t\le 1} \left( \|F(X)\|_{T_{t(\phi+\xi),j}(\h_{j})} + \|\Ipttil^X\|_{T_{t(\phi+\xi),j}(\h_{j})} \|\Ipttil^{-X}\|_{T_{0,j}(\h_{j})} \|F(X)\|_{T_{0,j}(\h_{j})} \right) .\end{aligned}$$ Our assumption that $\pi_{ab}V=\pi_{ab}F(X)=0$ unless $j \ge j_{ab}$ provides a corresponding assumption for Proposition \[prop:1-LTdefXY\]. By the triangle inequality, the polynomial factor can be bounded as $$\begin{aligned} \left(1+\|\phi+ \xi\|_{\Phi_{j+1}(X^\Box)} \right)^{a} &\le \left(1+\|\phi\|_{\Phi_{j+1}(X^\Box )} \right)^{a} \left(1+\|\xi\|_{\Phi_{j+1}(X^\Box )} \right)^{a} \nnb & \prec \left(1+\|\phi\|_{\Phi_{j+1}(X^\Box )} \right)^{a} G_{j+1}(X,\xi),\end{aligned}$$ where in the last step we used $\h_{j+1}\ge\ell_{j+1}$ to conclude the inequality $\|\xi\|_{\Phi_{j+1}(2\h_{j+1})}\le \|\xi\|_{\Phi_{j+1}(\ell_{j+1})}$, together with the fact that the regulator dominates polynomials by . Next, we apply – (the latter in conjunction with the product property), together with the definition of $\kappa_F$, to see that the quantity under the supremum in is bounded above by a constant multiple of $\kappa_F \Gcal_j(X,\phi+\xi)$. Using $\|\phi+\xi\|^2 \le 2\|\phi\|^2 + 2\|\xi\|^2$ to estimate this last regulator, we obtain $$\begin{aligned} \| E(X) \|_{T_{\phi+\xi,j+1}(2\h_{j+1})} & \prec \gamma \kappa_F \left(1+\|\phi \|_{\Phi_{j+1}(X^\Box,2\h_{j+1})} \right)^{a} \nnb & \quad \times \Gcal_j(X,\phi)^2 \Gcal_j(X,\xi)^2 G_{j+1}(X,\xi) . \lbeq{cl-2}\end{aligned}$$ Since $\Gcal \le G$, we can then take the expectation using (with Cauchy–Schwarz to separate the regulators at the two different scales), to obtain $$\begin{aligned} \Ex \| E(X) \|_{T_{\phi+\xi,j+1}(2\h_{j+1})} & \prec \gamma \kappa_F \left(1+\|\phi \|_{\Phi_{j+1}(X^\Box,2\h_{j+1})} \right)^{a} \Gcal_j(X,\phi)^2 . \lbeq{cl-3}\end{aligned}$$ With , this gives $$\begin{aligned} \lbeq{cl-4} \|\Ipttil^{U\setminus X} \Ex \theta E (X) \|_{T_{\phi,j+1}(\h_{j+1})} & \prec \gamma \kappa_F \|\Ipttil^{U\setminus X} \|_{T_{\phi,j+1}(\h_{j+1})} \nnb & \quad \times \left(1+\|\phi \|_{\Phi_{j+1}(X^\Box,2\h_{j+1})} \right)^{a} \Gcal_j(X,\phi)^2 .\end{aligned}$$ With an application of Proposition \[prop:Iupper\], this gives $$\lbeq{cl-5} \|\Ipttil^{U\setminus X} \Ex \theta E (X) \|_{T_{\phi,j+1}(\h_{j+1})} \prec \gamma \kappa_F \Gcal_{j+1}(U,\phi)^{\Gtilp/2} \Gcal_j(X,\phi)^2 ,$$ where the exponent $\Gtilp/2$ on $\Gcal_{j+1}$ is a convenient choice. For the norm pair we set $\phi=0$, the regulators become equal to $1$, and the desired result follows from . For the norm pair , we apply Lemma \[lem:mart\] and $X \subset U$ to obtain $$\begin{aligned} \tilde G_{j+1}(U,\phi)^{\Gtilp/2} \tilde G_j(X,\phi)^2 & \prec \tilde G_{j+1}(U,\phi)^{\Gtilp/2} \tilde{G}_{j+1}(X,\phi)^{\Gtilp/2} \le \tilde G_{j+1}^{\Gtilp}(U,\phi) , \label{e:FXbdKzzz}\end{aligned}$$ and the desired result follows from . This completes the proof. Lp norm estimates {#sec:Lp} ================= Let $\phi : \Lambda \to \C$, and let $X \subset \Lambda$ be a subset of cardinality $|X|$. For $p\in [1,\infty )$, we define the $L^{p}$ norm $$\label{e:Lp-def} \|\phi\|_{L^{p} (X)} = \frac{1}{\h}\left(\frac{1}{|X|}\sum_{x\in X} |\phi (x)|^{p}\right)^{1/p}.$$ The weight $\h$ is included in the norm so that, according to and , $$\label{e:equivalent-norms4} \|\phi\|_{L^{p}(X)}^{p} \le \| \phi\|_{\Phi (X)}^{p}.$$ Proposition \[prop:equivalent-norms\] below provides a lattice Sobolev inequality which shows that can be reversed at the cost of an additional term. Our application of Proposition \[prop:equivalent-norms\] occurs in , with $p=2$. To prepare for the proposition, we first prove a lemma which shows that the reversal is possible for polynomials, even with an increase in the size of the domain of the $\Phi$ norm (recall that the small set neighbourhood $X^\Box$ of $X$ was defined in ). Throughout this appendix, we write $R=L^j$. The hypothesis below, that $R \ge R_0$, can then be achieved uniformly in $j$ by taking $L$ sufficiently large. Outside this appendix, we take the parameter $p_\Phi$ in the definition of the $\Phi$ norm to obey $p_\Phi \ge \frac{d+4}{2}$ (as mentioned in Section \[sec:reg\]), but this restriction is unnecessary in the following lemma. \[lem:PhiLp\] Let $p_\Phi, q\ge 0$ be integers. Let $Q$ denote the vector space of complex-valued polynomials defined on $\Rd$ and of degree at most $q$. Let $f$ be the restriction of any polynomial in $Q$ to $\Zd$. Let $B$ be a block of side $R$ in $\Zd$. There exists $c_0 = c_0(q,p)>0$ such that for $R\geq R_0(q,p)$ sufficiently large, $$\label{e:fequiv} \| f\|_{\Phi (B^\Box)} \le c_0 \|f\|_{L^{p} (B)} .$$ The inequality is homogeneous in $\h$ so without loss of generality we take $\h =1$. It suffices to consider the case where $p_\Phi=q$. In fact, derivatives of $f \in Q$ having order higher than $q$ vanish so the left-hand side of is constant in $q \ge p_\Phi$, and the left-hand side is an increasing function of $p_\Phi$ so the statement is strongest when $p_\Phi=q$. Thus we take $p_\Phi=q$ throughout the proof. Moreover, is trivial if $f$ is a constant, so we consider the case $q \ge 1$. Let $\Ccal^{q}$ denote the space of $q$-times differentiable functions on $\R^{d}$ with norm given by $$\|G\|_{\Ccal^{q}} = \sup_{x\in\Rd}\sup_{|\alpha| \leq q} |D^\alpha G (x)|,$$ where $\alpha$ is a multi-index and $D^\alpha$ is the derivative on $\R^d$. Without loss of generality, we assume that $B$ is centred at the origin of $\Zd$. We obtain a continuum version $\hat B^\Box\subset \Rd$ of $B^\Box$ by placing a unit $\Rd$-cube centred at each point in $B^\Box$. Let $I^\Box = R^{-1}\hat B^\Box \subset \Rd$ be its rescaled version. For $P \in Q$, let $$\|P\|_{\Ccal^{q}(I^\Box)} = \inf \{ \|P-G\|_{\Ccal^{q}} : G \in \Ccal^{q}, G|_{I^\Box}=0\} .$$ This defines a norm on $Q$. Given $F \in Q$, let $f$ be the restriction of $F$ to $\Zd$, and let $\hat F \in Q$ be defined by $\hat F(x)=F(Rx)$ for $x \in \R^d$. We prove that $$\label{e:sob1} \|f\|_{\Phi (B^\Box)} \le \|\hat F\|_{\Ccal^{q}(I^\Box)},$$ and that there is a $c_0(q,p)>0$ and an $R_0(q,p)$ such that for $R \geq R_0$, $$\label{e:sob2} \|\hat F\|_{\Ccal^{q}(I^\Box)} \le c_0 \|f\|_{L^{p} (B)}.$$ Together, these two inequalities give . We first prove . By Taylor’s theorem, $R |\nabla^{e} f (x) | \le \|D^{e} \hat F \|_{\Ccal^{0}}$. By induction on $|\alpha |$, this gives $$\label{e:finite-diff} \sup_{x \in \R^d} |\nabla_R^\alpha f(x)| \le \|\hat F\|_{\Ccal^{q}}, \quad\quad |\alpha| \le q ,$$ where $\nabla_R^\alpha = R^{|\alpha|}\nabla^\alpha$. Given $\hat G \in \Ccal^{q}$, let $g(x)= \hat G(R^{-1}x)$. By definition, $f(x)-g(x) = \hat{F}(R^{-1}x)- \hat{G}(R^{-1}x)$, so by with $\hat F$ replaced by $\hat{F}- \hat{G}$, $$\lbeq{fghats} \sup_{x \in \Z^d} |\nabla_R^\alpha[f(x)-g(x)]| \le \|\hat F - \hat G\|_{\Ccal^{q}}, \quad\quad |\alpha| \le q.$$ Therefore, $$\lbeq{fginf} \inf \left\{ \|f -g \|_\Phi : \hat G \in \Ccal^{q}, \hat G|_{I^\Box}=0 \right\} \le \|\hat F \|_{\Ccal^{q}(I^\Box)}.$$ The set of all lattice functions $g$ with $g|_{I^\Box}=0$ includes all functions $g$ arising on the left-hand side, and the infimum over this larger class is smaller that the infimum in . Thus the left-hand side of is greater than or equal to $\|f\|_{\Phi (B^\Box)}$. This proves . To prove , we define a second norm on $Q$, as follows. For $P \in Q$, let $$\|P\|_{L^p(I)} = \left( \int_I |P(x)|^p dx \right)^{1/p}.$$ Since all norms on the finite-dimensional vector space $Q$ are equivalent, there exists a constant $c_1 = c_1(q,p)$ such that, for all $P \in Q$, $$\label{e:equivalent-norm1} \|P\|_{\Ccal^{q}(I^\Box)}^p \leq c_1 \|P\|_{L^p(I)}^p.$$ The difference $$\begin{aligned} \|P\|_{L^p(I)}^p - \frac{1}{|B|} \sum_{x\in B} |P(R^{-1}x)|^p &= \int_I|P(x)|^p dx - \frac{1}{|B|} \sum_{x\in B} |P(R^{-1}x)|^p\end{aligned}$$ is a Riemann sum approximation error. It is therefore bounded in absolute value by $R^{-1}$ times the maximum over $I$ of $|DP^{p}|$, which is less than $pR^{-1} \|P\|_{\Ccal^{q}(I^\Box)}^p$ (here we use $q \ge 1$). Therefore, $$\label{e:equivalent-norm2} \left(1 - \frac{p}{R}c_{1} \right) \|P\|_{\Ccal^{q}(I^\Box)}^{p} \leq c_1\frac{1}{|B|} \sum_{x\in B} |P(R^{-1}x)|^p .$$ We take $R$ large enough that $1 - \frac{p}{R}c_{1} \ge 1/2$, and set $P= \hat F$ in , to conclude with $c_0 = (2c_1)^{1/p}$. This completes the proof of , and hence of . \[prop:equivalent-norms\] Let $B$ be a block of side $R=L^j$ in the torus $\Lambda$ of side length $L^N$, with $j \le N-1$. There are constants $c_{1}$, $c_2$ and $R_{0}$ (depending on $p_{\Phi},p$) such that for $X \subset B$ with $|X|\le c_{1} |B|$, and for $R \ge R_0$, $$\label{e:fequiv0} \|\phi\|_{\Phi (B^\Box)} \le c_2 \left( \|\phi\|_{L^{p} (B\setminus X)} + \|\phi\|_{\tilde{\Phi} (B^\Box)} \right).$$ The inequality is homogeneous in $\h$ so we may assume that $\h=1$. For any $f \in \C^\Lambda$, $$\begin{aligned} \|f\|_{L^p(B\setminus X)}^p & \geq \frac{|B\setminus X|}{|B|}\|f\|_{L^{p} (B\setminus X)}^{p} = \|f \|_{L^{p} (B)}^{p} - \frac{|X|}{|B|}\, \|f\|_{L^p(X)}^{p} .\end{aligned}$$ The restriction $j \le N-1$ is imposed to ensure that the periodicity of $\Lambda$ plays no role, and we may assume that we are working on $\Zd$ rather than on $\Lambda$. We apply Lemma \[lem:PhiLp\] with $q=1$. With $c_{0}$ the constant of Lemma \[lem:PhiLp\], let $c_{1}=(2c_0^p)^{-1}$. By hypothesis, $| X| \le (2c_0^p)^{-1}|B|$. Let $f \in Q$, with $Q$ as in Lemma \[lem:PhiLp\]. By and the fact that $X\subset B^\Box$, $\|f\|_{L^p(X)} \le \|f\|_{\Phi (X)} \le \|f\|_{\Phi (B^\Box)}$. With Lemma \[lem:PhiLp\], this gives $$\begin{aligned} \|f\|_{L^p(B\setminus X)}^p & \ge \|f \|_{L^{p} (B)}^{p} - \frac{|X|}{|B|}\, \|f\|_{\Phi (B^\Box)}^{p} \ge \left[\frac {1}{c_0^p} - \frac{1}{2 c_0^p}\right]\|f \|_{\Phi (B^\Box)}^{p}.\end{aligned}$$ Therefore, $$\label{e:fequiv2} \|f\|_{\Phi (B^\Box)} \le 2^{1/p}c_0\|f\|_{L^{p} (B\setminus X)}.$$ Given $\phi :\Zd \to \C$ and $f \in Q$, we apply the triangle inequality (twice), and to see that $$\begin{aligned} \|\phi\|_{\Phi (B^\Box)} &\le \|f\|_{\Phi (B^\Box)} + \|\phi -f\|_{\Phi (B^\Box)}\nnb &\le 2^{1/p}c_0\|f\|_{L^{p} (B\setminus X)} + \|\phi -f\|_{\Phi (B^\Box)}\nnb &\le 2^{1/p}c_0\|\phi\|_{L^{p} (B\setminus X)} + 2^{1/p}c_0\|\phi-f\|_{L^{p} (B\setminus X)} + \|\phi -f\|_{\Phi (B^\Box)}\nnb &\le 2^{1/p}c_0\|\phi\|_{L^{p} (B\setminus X)} + \big(2^{1/p}c_0+1\big)\|\phi -f\|_{\Phi (B^\Box)}.\end{aligned}$$ The desired inequality , with $c_2=2^{1/p}c_0+1$, then follows by minimising over $f \in Q$ once we note that {-f\_[(B\^)]{}: f V } = \_[(B\^)]{} by definition of the norms in and . Further interaction estimates {#sec:further-ie} ============================= This section comprises estimates of a more specialised nature, which are required in [@BS-rg-step]. The estimates are stated as three lemmas. For the first lemma, for $B \in \Bcal_{j}$ we define $$\begin{aligned} \label{e:DeltaIdef} \Delta I(B) & = \tilde{I}(V,B) - I_{}(V,B) = e^{-V(B)} \left[ \prod_{b \in \Bcal_{j-1}(B)} (1+W_{j}(V,b)) - (1+W_{j}(V,B)) \right] .\end{aligned}$$ \[lem:DelIbd\] For $j \le N$, for both choices of $\|\cdot \|_j$ in –, for $B \in \Bcal_{j}$ and $V \in \bar\DV_j$, $$\begin{aligned} \label{e:DelIbd} \|\Delta I(B)\|_{j} &\prec_{L} \epdV^{4} .\end{aligned}$$ By , together with the fact that $W_j(V,B)=\sum_{b \in \Bcal_{j-1}(B)} W_{j}(V,b)$ by , $$\begin{aligned} \Delta I(B) & = e^{-V(B)} \!\!\!\!\!\!\!\! \sumtwo{X \in \Pcal_{j-1}(B) :}{|X|_{j-1} \ge 2} \prod_{b \in \Bcal_{j-1}(X)} W_{j}(V_{j},b) .\end{aligned}$$ Then gives a bound of order $(\epdV^2)^2$ for the $T_{0}$ semi-norm of the above sum, and the desired estimate follows from this together with . \[lem:JCK-app-2\] For $V \in \bar\DV$, $X \in \Scal$ and $F \in\Ncal(X^\Box)$, $$\label{e:JCK3-app} \left\| \LT_X \left( (I^{-X}- \Itilde_{\pt}^{-X} )F\right) \right\|_{T_{0} } \prec \; C_{\delta V}\epdV \|F\|_{T_0 } .$$ All quantities and norms are at scale $j<N$, and norms are computed with either $\h=\ell$ or $\h=h$. It follows from [@BS-rg-loc Proposition \[loc-prop:opLTdefXY\]] that $$\left\| \LT_X \left( (I^{-X}- \Itilde_{\pt}^{-X} )F\right) \right\|_{T_{0} } \prec \left\| \left( (I^{-X}- \Itilde_{\pt}^{-X} )F\right) \right\|_{T_{0} }$$ To estimate the right-hand side, we use the identity $$\prod_{i}a_{i}^{-1} - \prod_{i}b_{i}^{-1} = \sum_{k}\Big(\prod_{i\le k}a_{i}^{-1}\Big) (a_{k}-b_{k}) \Big(\prod_{i\ge k}b_{i}^{-1}\Big) ,$$ the triangle inequality, the product property of the norm, and , to obtain $$\label{e:JCK3-1} \left\| \LT_X \left( (I^{-X}- \Itilde_{\pt}^{-X} )F\right) \right\|_{T_{0}} \prec \sup_{B \in \Bcal (X)} \| I (B) - \Itilde_{\pt} (B) \|_{T_{0}} \|F\|_{T_{0}} .$$ We are thus reduced to estimates on a single block, and we henceforth omit $B$ arguments. To account for the fact that $I$ involves $W_j$ whereas $\Itilde_{\pt}$ involves $W_{j+1}$, we define $\Ipt = I(\Vpt) = I_j(\Vpt)$. Then I - \_ \_[T\_[0]{}]{} I - \_[T\_[0]{}]{} + - \_ \_[T\_[0]{}]{}. By and , the second term on the right-hand side obeys $$\begin{aligned} \label{e:JCK3-2} \|\Ipt - \Itilde_{\pt}\|_{T_{0}} &= \|e^{-\Vpt} (W_{j}-W_{j+1})\|_{T_{0}} \prec_{L} \epdV^2 .\end{aligned}$$ To estimate the first term on the right-hand side of , we proceed as in the proof of and now define $V_s= V + s(\Vpt -V)$, $I_s=I(V_s)$, $\Ical_s = e^{-V_{s}}$, and $W_s=W(V_{s})$. The steps leading to give $$\|I - \Ipttil\|_{T_0} \le \sup_{s\in [0,1]} \left( \|I_s\|_{T_0} \| (\Vpt -V)\|_{T_0} + \|\Ical_s\|_{T_0} \| W_s'\|_{T_0} \right).$$ The norms of $I_s$ and $\Ical_s$ are bounded by $2$, by . Also, $ \| \Vpt -V\|_{T_0}$ was encountered in and proved to be at most $C_{\delta V}\epdV$. With , we then obtain $\| W_s'\|_{T_0} \prec_l \epdV^2$. This completes the proof. The next lemma is applied in [@BS-rg-step Lemmas \[step-lem:K4\]–\[step-lem:K7a\]]. To prepare for its statement, given $V' \in \Qcal$ we define a new element $V'' \in \Qcal$ by $$\label{e:VptVplus} V'' = V' + y (\tau_{\Delta} - \tau_{\nabla\nabla}),$$ where $y$ is the coefficient of $\tau_{\nabla\nabla}$ in $V'$. Thus the term $y\tau_{\nabla\nabla}$ in $V'$ is replaced by $y\tau_\Delta$ to produce $V''$. We also define $$\begin{aligned} \delta I^{+}(B) &= e^{-V'(B)}\big(W_{j+1}(V',B) - W_{j+1}(V'',B)\big) .\end{aligned}$$ The definition of $V''$ is motivated by the fact that, for a polymer $X$, $V''(X)$ and $V' (X)$ are equal up to a polynomial in the fields that is supported on the boundary of $X$. To see this let $\chi$, $f$ and $g$ be functions on $\Lambda$. Then $$\begin{aligned} - \sum_{x \in \Lambda,e \in \Ucal} (\nabla^{e} \chi)_{x} \big(\nabla^{e} (fg)\big)_{x} = \sum_{x \in \Lambda}\chi_{x} \Big((\Delta f)_{x}g_{x} + f_{x} (\Delta g)_{x}\Big) \nonumber \\+ \sum_{x \in \Lambda,e \in \Ucal} \chi_{x} (\nabla^{e}f)_{x}(\nabla^{e}g)_{x} .\end{aligned}$$ This is proved by using summation by parts ($\nabla^{e}$ and $\nabla^{-e}$ are adjoints) to rewrite the summand on the left as $\chi_{x} (\Delta fg)_{x}$, followed by writing $\Delta (fg)_{x}$ as the sum over $e\in\Ucal$ of $f_{x+e} g_{x+e} - f_{x}g_{x}$ and using simple algebra. Choosing $f = \phi,\psi$ and $g= \bar{\phi},\bar{\psi}$ and referring to we obtain $$- \sum_{x \in \Lambda,e \in \Ucal} (\nabla^{e} \chi)_{x} (\nabla^{e}\tau)_{x} = 2\sum_{x \in \Lambda}\chi_{x} \Big(- \tau_{\Delta ,x} + \tau_{\nabla\nabla,x}\Big) .$$ For a polymer $X$ in $\Pcal_{j+1}$ let $\chi$ be the indicator function of $X$. Then from , $$V''(X) - V'(X) = \frac{1}{2}y \sum_{x \in \Lambda,e \in \Ucal} (\nabla^{e} \chi)_{x} (\nabla^{e}\tau)_{x} .$$ Let $\partial X$ denote the points in $X$ with a neighbour in $\Lambda \setminus X$. The right hand side is a sum of $\tau_{z'}-\tau_{z}$ over nearest neighbours $z',z$ where $z$ is in $X$ and $z'$ is not in $X$. By rewriting the fields in $\tau_{z'}$ using $f_{z'} = f_{z}+ (\nabla^{e}f)_{z}$ we find that there exists a polynomial $V_\partial$ which is quadratic in the fields and their derivatives such that $$V''(X) - V'(X) = \sum_{z \in \partial X} V_{\partial,z}$$ and every term in $V_{\partial,z}$ has at least one derivative. For $X \in \Pcal_{j+1}$ and $B \in \Bcal_{j+1} (\Lambda \setminus X)$, we set $R_{X} (B)=\delta I_{X}^{(6)} (B)=0$ if $B$ does not have a neighbour in $\partial X$, and otherwise define $$\begin{aligned} R_{X} (B) & = e^{- V_{\partial} (\partial X \cap B^1)}-1 , \quad\quad \delta I_{X} (B) = R_{X} (B) I(V'',B) ,\end{aligned}$$ where $B^1 = B \cup \partial(\Lambda \setminus B)$. \[lem:sbp-bds\] Let $j<N$, and $B \in \Bcal_{j+1}$. Suppose that $V' \in \bar\DV_{j+1}$ has $y \tau_{\nabla\nabla}$ term which obeys $\|y \tau_{\nabla\nabla}(b)\|_{T_{0,j}} \prec \epdV$ when $b \in \Bcal_j$. Let $X \in \Pcal_{j+1}$. Then for both choices of $\|\cdot \|_{j+1}$ in –, $$\begin{aligned} \label{e:map6-bd0} \|\delta I^+(B)\|_{j+1} & \prec_{L} \epdV^2 , \\ \lbeq{delI6bd} \|\delta I_X (B)\|_{j+1} & \prec \; \epdV .\end{aligned}$$ By direct calculation, $\|\tau_{\nabla\nabla}(b)\|_{T_{0,j}} \asymp L^{(d-2)(j)}\h_{j}^2$, and the right-hand side is $\ell_0^2$ for $\h=\ell$ and $k_0^2 \ggen_{j}^{-1/2}$ for $\h=h$. Therefore, by hypothesis and by definition of $\epdV$, we have $$|y| \prec \begin{cases} \ell_0^{-2} \epdV & \h=\ell \\ k_0^{-2} \ggen_j^{1/2} \epdV & \h=h. \end{cases}$$ Since $V_{\partial}$ is given by a sum over $O(L^{(d-1)(j+1)})$ boundary points of terms containing at least one gradient and two fields, this gives $$\begin{aligned} \lbeq{Vpartialbd} \| V_\partial (\partial X \cap B)\|_{T_0} &\prec \begin{cases} \ell_0^{-2}\epdV L^{(d-1)(j+1)} L^{- (j+1)} \ell^{2}_{j+1} & \h=\ell \\ k_0^{-2}\ggen^{1/2} \epdV L^{(d-1)(j+1)} L^{- (j+1)} h^{2}_{j+1} & \h=h \end{cases} \nnb & = \epdV.\end{aligned}$$ To prove , we apply to obtain $$\|\delta I^+(B)\|_{j+1} \prec \|W_{j+1}(V',B) - W_{j+1}(V'',B)\|_{T_0 (\h)} ,$$ and then use – to see that the right-hand side is $\prec_l \, \epdV^2$ as required. (In fact we use a small variation of – in which we regard $V'-V''$ as supported on $\partial X \cap B$, with .) To prove , we set $I_\partial(t) = I(V'',B) e^{- tV_{\partial}}$, with $V_{\partial}=V_{\partial}(\partial X \cap B)$. By the Fundamental Theorem of Calculus, $$\delta I_{X} (B) = V_{\partial} \int_0^1 I_\partial(t) dt ,$$ and hence $$\| \delta I_{X} (B) \|_{j+1} \le \sup_{t \in [0,1]} \|I_\partial(t) V_{\partial} \|_{j+1} .$$ The polynomial $V''$ obeys our stability estimates since compared to $V'$ its $z\tau_\Delta$ term is modified by $z \mapsto z+y$ and this change is such that $\epsilon_{V''} \le \epsilon_{V'}$, and hence $V''\in\bar\DV$. By [@BS-rg-norm] and [@BS-rg-norm Proposition \[norm-prop:T0K\]], $\|e^{-tV_\partial}\|_{T_\phi} \le e^{\|V_\partial\|_{T_\phi}} \le e^{\|V_\partial\|_{T_0}(1+\|\phi\|_{\Phi}^2)}$. The bound on $\|e^{-tV_\partial}\|_{T_\phi}$ is no larger than the effect of $Q$ handled in , and thus $ e^{- tV_{\partial}}$ is a negligible perturbation of $I(V'',B)$, and $I_\partial(t)$ also obeys the stability bounds. Thus we obtain from and that $$\| \delta I_{X} (B) \|_{j+1} \prec \| V_{\partial} \|_{T_0} \prec \epdV ,$$ and the proof is complete. Acknowledgements {#acknowledgements .unnumbered} ================ The work of both authors was supported in part by NSERC of Canada. DB gratefully acknowledges the support and hospitality of the Institute for Advanced Study at Princeton and of Eurandom during part of this work. GS gratefully acknowledges the support and hospitality of the Institut Henri Poincaré, and of the Mathematical Institute of Leiden University, where part of this work was done. We thank Roland Bauerschmidt for numerous helpful discussions. [^1]: Department of Mathematics, University of British Columbia, Vancouver, BC, Canada V6T 1Z2. E-mail: [[email protected]]{}, [[email protected]]{}.

Q: Java Geocoding - convert latitude and longitude into an address I need for my Android App the name of the city where my car is located in the moment. I have the latitude and longitude and want to convert this with the geocoder in the address and want to get the city. I read some blocks but because I'm new to this I dont get the clue. Please can anyone help me how to do this? EDIT: I dont use this geocoding in my app. I want to use it in my Java web service and I think I have to this with HTTPRequest, is it? and with the google api url. A: What you are looking for is Reverse Geocoding. The Geocoder class should help you do what you need (taken from here): public static void getAddressFromLocation( final Location location, final Context context, final Handler handler) { Thread thread = new Thread() { @Override public void run() { Geocoder geocoder = new Geocoder(context, Locale.getDefault()); String result = null; try { List<Address> list = geocoder.getFromLocation( location.getLatitude(), location.getLongitude(), 1); if (list != null && list.size() > 0) { Address address = list.get(0); // sending back first address line and locality result = address.getAddressLine(0) + ", " + address.getLocality(); } } catch (IOException e) { Log.e(TAG, "Impossible to connect to Geocoder", e); } finally { Message msg = Message.obtain(); msg.setTarget(handler); if (result != null) { msg.what = 1; Bundle bundle = new Bundle(); bundle.putString("address", result); msg.setData(bundle); } else msg.what = 0; msg.sendToTarget(); } } }; thread.start(); } EDIT: As per your comment, then no, you can't use the Geocoder class on a normal Java web service. That being said, there are alternatives. The Google Geocoding API is usually a good place to start, that being said, they do seem to have limits. Alternatively, you could take a look at Nominatim which is an open source Reverse Geocoding service albeit it seems to be slightly limited when compared to Google's services.

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If you can see light creeping beneath exterior doors, air is also escaping. Grab a few packages of self-adhesive rubber foam weatherstripping and go to town, sealing any and all doors that lead outside. Weatherstripping already installed but you’re still suffering from a high gas bill? It might be time to replace the strips installed by the previous owners. Check out this handy tutorial on installing weatherstripping. I'm a do it all kind of guy, from Full remodels, Kitchen, Bathrooms. Granite counter tops, Installation of RO Water Filtration system, coring Granite, Marble, Mounting TV's will full cable concealment, Electrical deadbolts, Nest, Echobee thermostats, Refininsh Hardwood floors, Garbage disposal Installs, faucets, toilets, electrical toilet seats, recessed lights, Drywall, sheetrock, mudding, you name it I can do it. Im also a painter, my quality of work is exceptional, Exterior, interior, textures, crown molding, baseboards. I provide all tools and supplies necessary, sprayers, rollers, brushes, drop clothes, If there is something not on this list just message me and I'll let you know. Im genuine and I truly care about building long term business relationships. Sussex County Habitat for Humanity offers a Home Repair Program that performs repair services to help low-income homeowners impacted by age, disability and family circumstances reclaim their homes with pride and dignity. Volunteer teams work to improve the condition of homes by painting, landscaping, and performing minor repairs at minimal costs to homeowners who would otherwise be unable to complete home repairs on their own. In addition, SCHFH now offers home repair and renovation services on a larger scale that aim to alleviate critical health, life and safely issues. Able-bodied homeowners are asked to work alongside the volunteers in a cooperative effort. A variety of problems can befall your home’s doors, especially older doors that may start to sag, stick, develop drafts or experience other issues. Fixing or replacing a door is well within the capabilities of most homeowners, especially if you have a partner to help out. From installing new weather stripping to replacing the lock, you can handle it. Watch this video to see how simple it is to replace an interior door yourself. Grandma’s Handyman Service provides homeowners and businesses with superior handyman services at affordable prices. Our happy customers give us lots of repeat business and lots of nice compliments. But don’t take our word for it! Click here to read what our happy handyman customers have to say. And then call us today for minor or major repairs, small remodeling projects or just to finally get that honey-do list completed!

1. The Field of the Invention This invention relates to a liquid crystal display, and more particularly to a back light unit in the liquid crystal display that minimizes a reflection of the pattern on a wall surface of a light-guide plate and bright lines from a light input. 2. Description of the Related Arts Generally, a liquid crystal display (LCD) controls an amount of light transmitted from a back light unit. The transmission is controlled by means of a liquid crystal panel including a number of liquid crystal cells arranged in a matrix and a number of control switches for switching video signals to be applied to the liquid crystal cells, thereby displaying a desired picture on a screen. Conventional back light units will be described with reference to FIG. 1 and FIG. 2. Referring to FIG. 1, the first conventional back light unit includes a light-guide plate 4 for guiding light passing through a light input 20; a reflective plate 2 disposed under the light-guide plate 4 for reflecting light escaping from a lower and side surfaces of the light-guide 4 in an upper direction toward an upper surface of the light guide 4; a first diffusion sheet 6 for diffusing light passing through the light-guide plate 4; first and second prism sheets 8 and 10 for controlling the direction of light passing through the first diffusion sheet 6; and a second diffusion sheet 12 for diffusing light passing through the prism sheets 8 and 10. The light input 20 includes a lamp 22 for generating light, and a lamp housing 24 for housing the lamp 22. The lamp housing also reflects the tight into the light-guide plate 4. A printed pattern is provided on the lower surface of the light-guide plate 4. This printed pattern does not allow the light-guide plate 4 to exhibit total internal reflection, which would allow light to be uniformly distributed out of the upper surface of the light-guide plate 4. As mentioned above, the light escaping from the lower surface and the side surface of the light-guide plate 4 are redirected by the reflective plate 2. The light passing through the light-guide plate 4 are diffused into an entire surface area of a liquid crystal panel (not shown) by the first diffusion sheet 6. The light entering the liquid crystal panel at right angles has a large light efficiency. Thus, it is preferred that the light enter the liquid crystal panel perpendicular to the surface of the liquid crystal panel. Towards this end, two forward prism sheets are disposed to make the angle of the light exiting from the light-guide plate 4 perpendicular to the liquid crystal panel. Referring to FIG. 1, the light passing through the first and second prism sheets 8 and 10 is incident to the liquid crystal panel via the second diffusion sheet 12. The first conventional back light unit cannot obtain a desired visual angle profile until the two prism sheets are included. The extra prism and the diffusion sheets absorb more light and thus cause an increased loss of light being transmitted to the liquid crystal panel. Also, the manufacturing cost rises. A suggested structure to solve the above-mentioned problems is shown in FIG. 2. The second conventional back light unit includes a light-guide plate 4′ for guiding light passing through a light input 20; a reflective plate 2 disposed under the light-guide plate 4′ for reflecting light escaping from a lower and side surfaces of the light-guide 4′ in an upper direction toward an upper surface of the light guide 4′; a backward prism sheet 14 for controlling the direction of light passing through the light-guide plate 4′; and a diffusion sheet 12 for diffusing light passing through the prism sheet 14. The light input 20 and the reflective plate 2 have the same function and operation as those in FIG. 1. A prism-shaped pattern is provided on the lower surface of the light-guide plate 4′. This prism-shaped pattern does not allow the light-guide plate 4′ to exhibit total internal reflection, which would allow the light to be uniformly distributed out of the upper surface of the light-guide plate 4′. In this case, it is desirable that, since the angle of the light outputted from the light-guide plate 4′ is more than about 65°, vertical angles of the prism sheet 14 should be between 63° to 70°. Thus, the light passing through the prism sheet 14 make right angles with respect to the surface of the liquid crystal panel. The light passing through the prism sheets 14 are diffused into the entire surface area of the liquid crystal panel by the diffusion sheet 12. In the second conventional back light unit, the wall surface of the light-guide plate 4′ are reflected and the bright lines of the light input 20 are seen due to the backward prism sheet 14. To solve the problems of the conventional art, a new scheme is needed to reduce the manufacturing cost as well as minimize the wall surface reflection and the bright lines of the light input.

Q: How to extract text FAST 'N FREE with BeautifulSoup I'd to extract the text between the strong tags below: <div class="u-flL sh-col"> <span id="shSummary"> <div class=" vi-fnf-ship fnfvar0"> <img alt="Estimated by eBay FAST 'N FREE " src="https://ir.ebaystatic.com/rs/v/xmyxg1ubry1npie2zlpan5za3yu.png" class="vi-fnf-ship-img"> <span class="vi-fnf-ship-txt "><strong class="sh_gr_bld">FAST 'N FREE</strong></span> I took a hit-or-miss approach on the following but no luck: # shippingCost = soup.find('strong', {'class':"sh_gr_bld"}).text.strip() #shippingCost = soup.find('div', {'class': ' vi-fnf-ship fnfvar0'}).find('span', {'class': 'vi-fnf-ship-txt'})\ # .find('strong', {'class': 'sh_gr_bld'}).text # shippingCost = soup.find_all('strong[class="sh_gr_bld"]').text # shippingCost = soup.find('span', {'class': 'vi-fnf-ship-txt'}).text#.find('b', {'class': 'sh_gr_bld'}).text # shippingCost = soup.find('div') # shippingCost = soup.find_all('span', {'class': 'vi-fnf-ship-txt'}).text#.find('span').next_sibling # shippingCost = soup.select('.vi-fnf-ship-txt'):nth-of-type(1).text shippingCost = soup.select('img.vi-fnf-ship-img span.vi-fnf-ship-txt strong.sh_gr_bld').text Thanks. ==== UPDATE What I did was to prettify the soup but to no avail: soup = BeautifulSoup(response.text, 'html.parser') print(soup.prettify()) ==== NEW UPDATE I redirected the prettify output to a file.txt and saw the code. So it is in there for sure with the same tags as above. The URL of the item is: https://www.ebay.com/itm/Mens-Legacy-Air-Bubble-90-Running-Trainers-Shoes/323806767262?_trkparms=ispr%3D1&hash=item4b6463289e:m:m_fYF4CZiE5Q9q08V38EY5w&enc=AQAEAAACQBPxNw%2BVj6nta7CKEs3N0qWNuu8y9VA2HEw0wmPsL5MTRFTJmnuraG452Pk3WQNpsgmrIf6ePIv561MkEiJV0pbFv9zmD1JW8JOdsIntwNXTFqw1McvYYqbaOR4YjsvuadL81czU45zEDv4c6pnAr%2FxMKDDYWViq81G9CPiJps3CAXKI8YcKTdUooXwBzpWHe0mCqp9WtgKcdyEUl85CxBxnYT7lC9lE%2BuZeNSfmbUfYMdiOxpjW8bZGX39SM8wagpyNHh79ILbJzX49%2BBpK0I11nzUm8xxnTPF53XqIKksC20%2BA0LHzrHYhV%2FwiuVk0Pb6t%2BUbTHPnUPbe%2B2OX4Pq8o8WvpergM0K2HXjzK2YOkP0M69O%2FjtCEpv22Gd0tP5MMLmsk4fuNxzQIADa2P199CYxynr76eLUr2u63alCb3heTTvPncuJzk02EGEdi38Nm%2BPcq2PTwjY1S%2F4mZ1ZolPl4lPxmfVr4gXrCaXfMExPYokV4FOmo46FJovcncwt4oHFjpSDCufOrbH4xcqrjfTRQ%2BigsxPaH5hWpzILfWTPNXbcIcaJRceFBFZrg8Ysa3oFuHEBgaBZKHRnZmWuFqPB%2B68WmqbZ1tunmg%2BXBKzGqLLfqnBWWw3qDXYr0V2AbALr73VLCeWzQIJzm0E0D%2FdB0KTn2YTHZzfD%2FrXYEUz2i19CwLG7SA8S9no0IFA16%2BpqE4G3s%2FE%2BAKFz3aQJZVpxSTc7Imy0CTF%2FjsA92yilzyIlsIeTc2AjaKy%2BTM%2Fjg%3D%3D&checksum=323806767262b0325dcc5d12405d9773312793615829&enc=AQAEAAACQBPxNw%2BVj6nta7CKEs3N0qWNuu8y9VA2HEw0wmPsL5MTRFTJmnuraG452Pk3WQNpsgmrIf6ePIv561MkEiJV0pbFv9zmD1JW8JOdsIntwNXTFqw1McvYYqbaOR4YjsvuadL81czU45zEDv4c6pnAr%2FxMKDDYWViq81G9CPiJps3CAXKI8YcKTdUooXwBzpWHe0mCqp9WtgKcdyEUl85CxBxnYT7lC9lE%2BuZeNSfmbUfYMdiOxpjW8bZGX39SM8wagpyNHh79ILbJzX49%2BBpK0I11nzUm8xxnTPF53XqIKksC20%2BA0LHzrHYhV%2FwiuVk0Pb6t%2BUbTHPnUPbe%2B2OX4Pq8o8WvpergM0K2HXjzK2YOkP0M69O%2FjtCEpv22Gd0tP5MMLmsk4fuNxzQIADa2P199CYxynr76eLUr2u63alCb3heTTvPncuJzk02EGEdi38Nm%2BPcq2PTwjY1S%2F4mZ1ZolPl4lPxmfVr4gXrCaXfMExPYokV4FOmo46FJovcncwt4oHFjpSDCufOrbH4xcqrjfTRQ%2BigsxPaH5hWpzILfWTPNXbcIcaJRceFBFZrg8Ysa3oFuHEBgaBZKHRnZmWuFqPB%2B68WmqbZ1tunmg%2BXBKzGqLLfqnBWWw3qDXYr0V2AbALr73VLCeWzQIJzm0E0D%2FdB0KTn2YTHZzfD%2FrXYEUz2i19CwLG7SA8S9no0IFA16%2BpqE4G3s%2FE%2BAKFz3aQJZVpxSTc7Imy0CTF%2FjsA92yilzyIlsIeTc2AjaKy%2BTM%2Fjg%3D%3D&checksum=323806767262b0325dcc5d12405d9773312793615829 The FREE 'N FAST text in the shipping section. A: The "trick" is to set shipping preferences to United Kingdom before getting the main page: import requests from bs4 import BeautifulSoup url = 'https://www.ebay.com/itm/Mens-Legacy-Air-Bubble-90-Running-Trainers-Shoes/323806767262?_trkparms=ispr%3D1&hash=item4b6463289e:m:m_fYF4CZiE5Q9q08V38EY5w&enc=AQAEAAACQBPxNw%2BVj6nta7CKEs3N0qWNuu8y9VA2HEw0wmPsL5MTRFTJmnuraG452Pk3WQNpsgmrIf6ePIv561MkEiJV0pbFv9zmD1JW8JOdsIntwNXTFqw1McvYYqbaOR4YjsvuadL81czU45zEDv4c6pnAr%2FxMKDDYWViq81G9CPiJps3CAXKI8YcKTdUooXwBzpWHe0mCqp9WtgKcdyEUl85CxBxnYT7lC9lE%2BuZeNSfmbUfYMdiOxpjW8bZGX39SM8wagpyNHh79ILbJzX49%2BBpK0I11nzUm8xxnTPF53XqIKksC20%2BA0LHzrHYhV%2FwiuVk0Pb6t%2BUbTHPnUPbe%2B2OX4Pq8o8WvpergM0K2HXjzK2YOkP0M69O%2FjtCEpv22Gd0tP5MMLmsk4fuNxzQIADa2P199CYxynr76eLUr2u63alCb3heTTvPncuJzk02EGEdi38Nm%2BPcq2PTwjY1S%2F4mZ1ZolPl4lPxmfVr4gXrCaXfMExPYokV4FOmo46FJovcncwt4oHFjpSDCufOrbH4xcqrjfTRQ%2BigsxPaH5hWpzILfWTPNXbcIcaJRceFBFZrg8Ysa3oFuHEBgaBZKHRnZmWuFqPB%2B68WmqbZ1tunmg%2BXBKzGqLLfqnBWWw3qDXYr0V2AbALr73VLCeWzQIJzm0E0D%2FdB0KTn2YTHZzfD%2FrXYEUz2i19CwLG7SA8S9no0IFA16%2BpqE4G3s%2FE%2BAKFz3aQJZVpxSTc7Imy0CTF%2FjsA92yilzyIlsIeTc2AjaKy%2BTM%2Fjg%3D%3D&checksum=323806767262b0325dcc5d12405d9773312793615829&enc=AQAEAAACQBPxNw%2BVj6nta7CKEs3N0qWNuu8y9VA2HEw0wmPsL5MTRFTJmnuraG452Pk3WQNpsgmrIf6ePIv561MkEiJV0pbFv9zmD1JW8JOdsIntwNXTFqw1McvYYqbaOR4YjsvuadL81czU45zEDv4c6pnAr%2FxMKDDYWViq81G9CPiJps3CAXKI8YcKTdUooXwBzpWHe0mCqp9WtgKcdyEUl85CxBxnYT7lC9lE%2BuZeNSfmbUfYMdiOxpjW8bZGX39SM8wagpyNHh79ILbJzX49%2BBpK0I11nzUm8xxnTPF53XqIKksC20%2BA0LHzrHYhV%2FwiuVk0Pb6t%2BUbTHPnUPbe%2B2OX4Pq8o8WvpergM0K2HXjzK2YOkP0M69O%2FjtCEpv22Gd0tP5MMLmsk4fuNxzQIADa2P199CYxynr76eLUr2u63alCb3heTTvPncuJzk02EGEdi38Nm%2BPcq2PTwjY1S%2F4mZ1ZolPl4lPxmfVr4gXrCaXfMExPYokV4FOmo46FJovcncwt4oHFjpSDCufOrbH4xcqrjfTRQ%2BigsxPaH5hWpzILfWTPNXbcIcaJRceFBFZrg8Ysa3oFuHEBgaBZKHRnZmWuFqPB%2B68WmqbZ1tunmg%2BXBKzGqLLfqnBWWw3qDXYr0V2AbALr73VLCeWzQIJzm0E0D%2FdB0KTn2YTHZzfD%2FrXYEUz2i19CwLG7SA8S9no0IFA16%2BpqE4G3s%2FE%2BAKFz3aQJZVpxSTc7Imy0CTF%2FjsA92yilzyIlsIeTc2AjaKy%2BTM%2Fjg%3D%3D&checksum=323806767262b0325dcc5d12405d9773312793615829' set_ship_to_url = 'https://www.ebay.com/gh/setuserpreference' with requests.session() as s: r = s.post(set_ship_to_url, json={"userPreferedCountry":"GBR"}) # <-- set Ship To preference to United Kingdom soup = BeautifulSoup(s.get(url).content, 'html.parser') print(soup.select_one('strong.sh_gr_bld').text) Prints: FAST 'N FREE

Court of Appeals of the State of Georgia ATLANTA,____________________ December 22, 2014 The Court of Appeals hereby passes the following order: A15D0183. JOHNNY BRETT GREGORY v. J. STEPHEN SCHUSTER, JUDGE. Johnny Brett Gregory, a prison inmate, seeks to vacate an order entered in a civil action for damages. The order, which was entered on July 28, 2011, granted the defendant’s motion to have UCC documents filed by Gregory removed from the transaction registry. We lack jurisdiction.1 An application for discretionary appeal must be filed within 30 days of the entry of the order to be appealed. OCGA § 5-6-35 (d); Hill v. State, 204 Ga. App. 582 (420 SE2d 393) (1992). Gregory, however, filed his case more than three years after the entry of the trial court’s order. For this reason, this application for discretionary appeal is DISMISSED for lack of jurisdiction. Court of Appeals of the State of Georgia 12/22/2014 Clerk’s Office, Atlanta,____________________ I certify that the above is a true extract from the minutes of the Court of Appeals of Georgia. Witness my signature and the seal of said court hereto affixed the day and year last above written. , Clerk. 1 Gregory originally filed his case in the Supreme Court, which ordered that the case be re-docketed as a discretionary application and transferred to this Court. Even utilizing the date provided on the proof of service supplied by Gregory, October 2, 2014, his appeal is nonetheless untimely. 

The top of the beach house will be called "The Dock at Bradford Beach." Beach house at Bradford Beach to be used as new restaurant Members of the Milwaukee County Board got a better idea of what will happen this summer at Bradford Beach. In previous years, SURG Restaurant Group ran the tiki bars on the beach. On Monday a group from Chicago who is known for running restaurants on their lakefront, CCH Management, brought the board members up to speed on their plans."Principally we envision taking our concept which is at Montrose Beach and having a version of that at Bradford. So, we'd like to brand it The Dock at Bradford Beach. The beach house, right now you have the tiki huts that are on the beach, we envision actually using the beach house, at the top of it and making that a restaurant space where we're going to have umbrellas and tables and servers," said one of the members of CCH Management.As for a menu, the group said you can expect menu items such as "fish tacos, grass fed beef burgers, lots of salads, and some seared tuna."Also the tiki bars will still be used as remote sites, essentially to deliver drinks and food from the restaurant.To get an idea of what to expect at Bradford, click here for a look at The Dock at Montrose Beach. Members of the Milwaukee County Board got a better idea of what will happen this summer at Bradford Beach. In previous years, SURG Restaurant Group ran the tiki bars on the beach. On Monday a group from Chicago who is known for running restaurants on their lakefront, CCH Management, brought the board members up to speed on their plans. "Principally we envision taking our concept which is at Montrose Beach and having a version of that at Bradford. So, we'd like to brand it The Dock at Bradford Beach. The beach house, right now you have the tiki huts that are on the beach, we envision actually using the beach house, at the top of it and making that a restaurant space where we're going to have umbrellas and tables and servers," said one of the members of CCH Management. As for a menu, the group said you can expect menu items such as "fish tacos, grass fed beef burgers, lots of salads, and some seared tuna." Also the tiki bars will still be used as remote sites, essentially to deliver drinks and food from the restaurant. To get an idea of what to expect at Bradford, click here for a look at The Dock at Montrose Beach.

<?php /** * Zend Framework * * LICENSE * * This source file is subject to the new BSD license that is bundled * with this package in the file LICENSE.txt. * It is also available through the world-wide-web at this URL: * http://framework.zend.com/license/new-bsd * If you did not receive a copy of the license and are unable to * obtain it through the world-wide-web, please send an email * to [email protected] so we can send you a copy immediately. * * @category Zend * @package Zend_Log * @subpackage Writer * @copyright Copyright (c) 2005-2011 Zend Technologies USA Inc. (http://www.zend.com) * @license http://framework.zend.com/license/new-bsd New BSD License * @version $Id: Stream.php 23775 2011-03-01 17:25:24Z ralph $ */ /** Zend_Log_Writer_Abstract */ require_once 'Zend/Log/Writer/Abstract.php'; /** Zend_Log_Formatter_Simple */ require_once 'Zend/Log/Formatter/Simple.php'; /** * @category Zend * @package Zend_Log * @subpackage Writer * @copyright Copyright (c) 2005-2011 Zend Technologies USA Inc. (http://www.zend.com) * @license http://framework.zend.com/license/new-bsd New BSD License * @version $Id: Stream.php 23775 2011-03-01 17:25:24Z ralph $ */ class Zend_Log_Writer_Stream extends Zend_Log_Writer_Abstract { /** * Holds the PHP stream to log to. * * @var null|stream */ protected $_stream = null; /** * Class Constructor * * @param array|string|resource $streamOrUrl Stream or URL to open as a stream * @param string|null $mode Mode, only applicable if a URL is given * @return void * @throws Zend_Log_Exception */ public function __construct($streamOrUrl, $mode = null) { // Setting the default if (null === $mode) { $mode = 'a'; } if (is_resource($streamOrUrl)) { if (get_resource_type($streamOrUrl) != 'stream') { require_once 'Zend/Log/Exception.php'; throw new Zend_Log_Exception('Resource is not a stream'); } if ($mode != 'a') { require_once 'Zend/Log/Exception.php'; throw new Zend_Log_Exception('Mode cannot be changed on existing streams'); } $this->_stream = $streamOrUrl; } else { if (is_array($streamOrUrl) && isset($streamOrUrl['stream'])) { $streamOrUrl = $streamOrUrl['stream']; } if (! $this->_stream = @fopen($streamOrUrl, $mode, false)) { require_once 'Zend/Log/Exception.php'; $msg = "\"$streamOrUrl\" cannot be opened with mode \"$mode\""; throw new Zend_Log_Exception($msg); } } $this->_formatter = new Zend_Log_Formatter_Simple(); } /** * Create a new instance of Zend_Log_Writer_Stream * * @param array|Zend_Config $config * @return Zend_Log_Writer_Stream */ static public function factory($config) { $config = self::_parseConfig($config); $config = array_merge(array( 'stream' => null, 'mode' => null, ), $config); $streamOrUrl = isset($config['url']) ? $config['url'] : $config['stream']; return new self( $streamOrUrl, $config['mode'] ); } /** * Close the stream resource. * * @return void */ public function shutdown() { if (is_resource($this->_stream)) { fclose($this->_stream); } } /** * Write a message to the log. * * @param array $event event data * @return void * @throws Zend_Log_Exception */ protected function _write($event) { $line = $this->_formatter->format($event); if (false === @fwrite($this->_stream, $line)) { require_once 'Zend/Log/Exception.php'; throw new Zend_Log_Exception("Unable to write to stream"); } } }

The Women in Business Network (WIBN) is a membership organisation for women who wish to gain new business opportunities through word of mouth. Whether employed or a business owner the network has a huge diversity of businesses involved. Our members support and encourage each other through collaboration and the sharing of business contacts and opportunities. Out and about featured businesses With 55 en-suite rooms, civil ceremony licence and a wide range of party and conference facilities, Hitchin Priory is one of the leading bed and breakfasts, wedding venues, party venues and business meeting venues in the area. It’s not every day you go shopping in Hitchin for beautiful nightwear or lingerie, but when you do there’s one shop you need to put at the top of your itinerary – lingerie boutique Je Te Veux on Sun Street (just along from Strada restaurant). Featured in Lingerie in Hitchin what local people say... Tracie and the team provide, for me at least, a 40 minute experience that ranges from a great welcome, humour and a feeling that they all take pride in knowing you and wanting to make your visit memorable. The icing on the cake is Talents is a great place to get you hair cut!...

Plautus Titus Maccius Plautus (254 BC – 184 BC), born at Sassina, Umbria, was a comic playwright in the time of the Roman Republic. The years of his life are uncertain, but his plays were first produced between about 205 BC and 184 BC. Valour’s the best reward ; ‘tis valour that surpasses all things else : our liberty, our safety, life, estate, our parents, children, country, are by this preserved, protected : valour everything comprises in itself ; and every good awaits the man who is possess’d of valour. (translator Thornton) Amphitryon, Act II, scene 2, line 16. Variant translation: Courage is the very best gift of all; courage stands before everything, it does, it does! It is what maintains and preserves our liberty, safety, life, and our homes and parents, our country and children. Courage comprises all things: a man with courage has every blessing.

The basic fire policy covers loss of or damage to residential or commercial building, furniture, fixtures and fittings caused by or arising from: Damage by fire & lightning Damage by explosions of domestic boiler or domestic gas cylinder not forming part of a gas work Damage by water or other extinguishing agents used to put out the fire Damage resulting from gaining access to a fire Smoke damages caused by fire Interest Insured Items that can be insured are: Building, renovation Furniture, fixtures and fittings Office equipment, plant, machinery and utensils Stock in trade Rent Removal of debris Professionals fees Personal Effects & Household goods Premium & Extension The basic premium is calculated based on a standard fire tariff rate prescribed by Persatuan Insurans Am Malaysia (PIAM) and is affected by the class of construction of the building, trade carried out at the premise and sum insured. At an additional premium, the basic policy can be extended to cover loss of or damage to caused by and not limited to the following: Riot, strike and malicious damage; Explosion of boilers and pressure vessels; Impact damage by own vehicles and third party vehicles; Aircraft Damage; Bursting and / or overflowing of water tanks apparatus and pipes (excluding sprinkler system);

Victoria Secret is sharing sneak peeks of their lingerie photo shoot with fans, including a couple with Martha Hunt. Their newest Instagram post shows the model flashing a white bra under a black robe, as she appears to be getting ready for a shoot in the dressing room area. Martha’s hair was worn down in loose waves, as she wore natural-looking makeup. A second photo was shared earlier that was likely taken around the same time, which showed Martha laughing as stylist Emma Jade Morrison grabbed a wardrobe bag and also smiled. Meanwhile, Hunt’s been keeping her fans updated with a series of photos and videos on Instagram. Her newest post was a short video selfie, as she wore a tan turtleneck long-sleeved top and her hair down. It was geotagged in Beverly Hills, California, and a palm tree could be spotted in the reflection off the glass behind her. Although just posted two hours ago, it’s already been played over 28,400 times. And her fans were thrilled to discover that she was on Celebrity Family Feud, as she and four others battled against Bachelor Nation. Martha shared a photo of Jasmine taking a group selfie on set. Hunt wore a light yellow suit, while Jasmine wore a shimmery, pink robe dress. Prior to that, Hunt shared her support for Duke basketball in a photo where she wore an oversized Duke jersey, black leggings, and ankle boots. The dramatic black-and-white photo showed Martha holding a basketball in her right hand as she looked down to her left. The model is now a fixture at VS, but she recounted what it was like for her at the beginning to W Magazine. “My first Victoria’s Secret fashion show I was really nervous. I was just kind of figuring it out, because there’s no rule book to tell you how to do everything. It kind of takes awhile to come into your own.” “What I love about Victoria’s Secret is that they represent strong, confident and empowered women. And as a model, I’ve always seen that as the ultimate goal,” Hunt also added. Loading... Plus, Martha noted the importance of her third VS show, which was her debut as an Angel. “It was definitely different, also because I was closing the show. So that immediately just felt like more validation. Like okay, I’ve arrived, I’m here.” Since then, the model has continued to make her mark as a fan-favorite Angel.

Tag Archives: range games I have always liked puzzles. I really enjoy discovering a new puzzle. Sometimes when I have discovered a new puzzle, I enjoy it so much that I can’t seem to do enough of them. In such cases, I quickly run out of these puzzles to do and find myself looking for either a new puzzle or a way to generate them on my own. Such was the case when I discovered the “Range Puzzles”. The rules are simple: Every cell is marked either blue or gray No two gray cells can be next to one another The grid must be a connected (i.e. there is always a path from every cell to every other cell using horizontal and vertical connections. Some cells have a number inside. This indicates the number of cells that can be viewed (horizontally and vertically in both directions) by this cell, including the cell itself.

Simplemente Lo Mejor (Ricardo Arjona album) Simplemente Lo Mejor is a greatest hits album by Guatemalan singer-songwriter Ricardo Arjona that was released on December 2, 2008. The album is composed of Arjona's number-one hits, drawn from Animal Nocturno (1993) to Galería Caribe (2000). It served as his final project under the Sony Music label after signing a contract with Warner Music in 2008. A CD+DVD and a DVD edition of the album were released in several countries; these included a collection of music videos for the compilation's songs. Simplemente Lo Mejor was made available one month after the release of Arjona's eleventh studio album, 5to Piso (2008). This led to speculation that the labels were in a fight to win Arjona's fanbase and sales. Simplemente Lo Mejor reached number seven on the Mexican Albums Chart, the US Billboard Latin Pop Albums chart and number 33 on the Billboard Top Latin Albums chart. It was awarded platinum certifications in Argentina and Mexico. Background and release Background After spending the majority of his career signed to Sony and Sony BMG, Arjona signed a long-term recording deal with Warner Music Latina in September 2008. Iñigo Zabala, chairman of Warner Music Latin America commented that "he's an artist that fits perfectly with our company"; he also stated "We are a label that has a major catalog of songwriters and quality pop and rock from the likes of Maná, Alejandro Sanz, Laura Pausini, and now, Arjona." Arjona announced his eleventh studio album, 5to Piso, on 18 November 2008. In the first month of retail sales, approximately 200,000 copies were purchased; it went Platinum in Mexico, the United States and several other countries. It debuted at number one on Top Latin Albums, becoming his second chart-topper on that list, and sold more than one million copies worldwide. The album received a Grammy Award nomination for Best Latin Pop Album and a Latin Grammy Award nomination for Best Singer-Songwriter Album. Release While Warner Music released Arjona's new studio album, Sony Music released Simplemente Lo Mejor. This led to speculation that the labels were in a fight to win his fanbase and sales. 5to Piso hit shelves on 18 November 2008 in the United States, and Simplemente Lo Mejor followed on 2 December 2008. A CD+DVD edition and a DVD edition of the album were released that same day in the United States and Spain. At that time, Univisión named Simplemente Lo Mejor "a true collector's item that every fan of Arjona or just happy to his poetry should not be without." Reception Simplemente Lo Mejor entered the Top 100 Mexico at number 35 the week of its debut. The following week, the album jumped to number 17 and, on its third week of release, reached its peak of number seven. It spent three weeks inside the top ten and 27 weeks on the chart. On the US Billboard Top Latin Albums chart, the album attained a peak of number 33 and stayed on the chart for 70 weeks. It performed better on the Latin Pop Albums component chart, where it reached a peak of number seven, remaining on the chart for 88 weeks. Simplemente Lo Mejor was awarded a platinum certification in Argentina and Mexico for 40,000 copies sold and shipped, respectively. Simplemente Lo Mejor received positive critical reception; Jason Birchmeier from Allmusic awarded the compilation four-and-a-half stars out of five and stated that the compilation is "nothing short of stellar, filled with major hits and showcasing perfectly Arjona's mid-'90s rise to fame." Track listing Following, the track list of Simplemente Lo Mejor as is shown on the iTunes Store. Personnel Credits are taken from Allmusic. Ricardo Arjona – composer, direction, primary artist, producer, realization Carlos Cabral Jr. – arranger Carlos Greene – artist direction Waldo Madera – arranger Angel "Cucco" Peña – arranger, producer Chart performance Charts Sales and certifications Release history References External links Official website of Ricardo Arjona Category:2008 greatest hits albums Category:Ricardo Arjona compilation albums Category:Sony BMG Norte compilation albums Category:Spanish-language compilation albums

Neogalea The catabena moth (Neogalea sunia) is a moth of the family Noctuidae, and the only species in the genus Neogalea. It is found from the southern United States, through the Caribbean (including Guadeloupe and Martinique) to Argentina. Furthermore, it has been introduced in Australia, on Norfolk Island in 1962. Since that time it has increased its range and is now common in Queensland and northern New South Wales. It has also been introduced on Hawaii. The wingspan is about 33 mm. The larva feed on Lantana species. External links Species info References Natural History Museum Lepidoptera genus database Category:Cuculliinae

Tailored blockchain solutions About Innovaetica Innovaetica SRL is an Italian company established in December 2012, with a strong expertise in blockchain, cryptographic technologies and AI. Our core team consists in 9 international professionals in the fields of blockchain, cryptography, AI, web development and UX/UI. We help companies and organisations develop tailored blockchain solutions, in any area of application. Our main expertise is intellectual property protection through public blockchain, private customised blockchains and digital timestamping. The projects developed by Innovaetica have been awarded several national and international prizes. Prizes and achievements Winner of H2020 SME Instrument - Open Distruptive Innovation Winner of the "Inventing the future" prize Winner of the "Fund for Creativity" Prize Selected among top 100 startups by European Business and Innovation Network

Structural shifts of fecal microbial communities in rats with acute rejection after liver transplantation. Bacterial translocation and the development of sepsis after orthotopic liver transplantation (OLT) may be promoted by immunological damage to the intestinal mucosa or by quantitative and qualitative changes in intestinal microbiota. This study monitored structural shifts of gut microbiota in rats with OLT using PCR-denaturing gradient gel electrophoresis (DGGE) and real-time quantitative PCR (RT-qPCR). RT-qPCR targets six major microorganisms (Domain Bacteria, Bacteroides, Bifidobacteria, Enterobacteriaceae, Lactobacillus and Clostridium leptum subgroup). Isograft, Allograft and Sham model were studied. Bacterial translocation to host organs and plasma endotoxin were determined. Alteration in gut microbiota was associated with the elevation of plasma endotoxin and a higher rate of bacterial translocation (BT) to liver in rats with acute rejection. Dynamic analysis of DGGE fingerprints showed that the gut microbiota structure of animals in the three groups was similar before the operation. But significant alterations in the composition of fecal microbiota in Allograft group were observed at 1 and 2 weeks after the OLT. The acute rejection was accompanied by the shifts of gut microbiota towards members of Bacteroides and Ruminococcus. Results from RT-qPCR indicated that Bacteroides significantly increased at 2 weeks after the OLT, whereas numbers of Bifidobacterium spp. decreased at 1 week and recovered at 2 weeks after the OLT. In summary, our data showed that rats with acute rejection after OLT exhibited significant structure shifts in the gut microbiota which dominant by overgrowth of Bacteroides and Ruminococcus, and these were associated with elevation of plasma endotoxin and higher rate of BT.

Use of polypharmacy and self-reported mood in outpatients with bipolar disorder. Objective. As polypharmacy is routinely used for the treatment of bipolar disorder, the relation between the daily number of psychotropic medications and self-reported mood was investigated. Method. Eighty patients (35 men and 45 women) with a diagnosis of bipolar disorder I or II, recruited from academic centres, entered their mood, sleep, and psychotropic medications for 3 months into ChronoRecord software. A total of 8662 days of data was received (mean 114.7 days/per patient). Results. Seventy-nine patients took a mean of 3.8 medications daily (SD 1.7; range 1-9); one took none. Of these patients, 73 (92.4%) took mood stabilizers, 47 (58.8%) took antidepressants, 31 (38.8%) took antipsychotics, 34 (42.5%) took benzodiazepines and 17 (21.1%) took thyroid hormones. Patients reporting normal mood more frequently took fewer medications; the Pearson correlation coefficient between the number of medications and the percent of days normal was -0.481 (P < 0.001). Grouping by number of medications, ANOVA analysis showed those taking fewer medications reported normal mood more frequently (P<0.001). Conclusion. Combination treatment regimens are routinely prescribed for bipolar disorder. Patients reporting normal mood more frequently took a fewer number of daily medications. Studies are needed to better identify those patients who would benefit from polypharmacy and to optimise the combinations of medications for patients with refractory disorder.

Minted Giveaway ****giveaway is now closed*** To say I am a fan of Minted is a huge under statement. I can’t say enough wonderful things about them. I have ordered Christmas cards from Minted for the last two years and recently ordered stationary that I adore. Not only do they feature the work of such talented artists, but their customer service, timeliness, and adorable packaging makes the whole process pretty darn amazing. Today I am so excited to be offering one of my readers an art print from Minted! One lucky reader will get to choose ANY print. Even better, it can be up to 11 x 14 and framed! That’s huge. I have featured some of my favorites below, but if you hop on over to Minted you can check out their full collection. …. m i n t e d g i v e a w a y paper hearts by Amanda Bee … je t’aime by chocomocacino … love you so much by robin ott design … lovely balloons by BusyNothings … awning striped by kristie kern … ligurian houses by kelli hall … Maybe you have a spot in your home for one of these beauties. So many of their prints just make me smile. If you would like to win a framed art print for a child’s room, your kitchen, hallway, living room,bathroom or anywhere, just enter below! … m i n t e d g i v e a w a y 1. visit Minted and tell me which print you would love to win {for special Valentine Art you can browse here} for extra entries you can do the following: 2. follow a thoughtful place 3. follow a thoughtful place on instagram {@athoughtfulplace} *****just remember to leave a separate comment for each thing you do*** ****giveaway is now closed*** Related Comments I absolutely love Minted too! They are one of the few vendors of high-quality printed cards, announcements and invitations etc that are highly customisable and will ship to Australia. I made my sons birth announcement through them and will probably use them for his upcoming first birthday invites! Browsing the art prints was dangerous! So many gorgeous prints! Kelli Hall's Ligurian Houses speaks to me particularly. Not only is it a stunning image that complements our decor beautifully, but we took our honeymoon to the Cinque Terre region of Italy and this is a gorgeous representation of the wonderful memories I have of our trip. I LOVE the print with the rocking chair that says, "We will rock you!". :)But, since I don't have kids that are rocking age anymore, I think I'd choose the "Love, Love, Love You" print and hang it in the gameroom. There are so many prints that I just LOVE, but my favorite is Three Wishes by Griffinbell Studios. I really liked the graphic & the quote, but love even more that the artist name incorporates the names of my two babies! What a lucky coincidence. 🙂 Okay, I would seriously love to win this…Hahaha. I love so much of the work–and I didn't know that they hard artwork like this that could be purchased framed! Awesome. I really think I would choose…. ligurian houses by kelli hall…Love it! Fall Favorites Recent Posts Disclosure In addition to occasional sponsored posts, A Thoughtful Place uses clickable affiliate links. That means that ATP may receive a small commission from sales at no extra charge to the buyer. As always, my opinion is 100% my own and I only recommend things that I truly love or use myself. Thank you for your loyal support.

Q: Keeping a NSManagedObject up to date while retaining it I have a NSManagedObject instance that represents a user in my application. I am retaining this instance and passing it between view controllers for the interface to reference. The managed object context (MOC) the user instance belongs to is a main queue MOC that is a child of a private queue MOC that saves directly to the persistent store. My core data persistent store is updated in the background on a separate background queue. These updates are saved to a private queue MOC that is then committed to the main private queue MOC and subsequently saved to the persistent store. My question is, how can I be sure that the user NSManagedObject instance will stay up to date? I'm aware of the existence of refreshObject:mergeChanges:, however, it seems complex to set up a of NSManagedObjectContextDidSaveNotification observers to simply keep an object instance up to date. I can see this approach becoming unruly when trying to keep multiple NSManagedObject instances up to date. A: From experience, your best option is don't try to keep it up to date. You need to use implement the NSManagedObjectContextDidSaveNotification to keep your context up to date -- you can't get around that -- but to get a valid object, you'll need to re-query it after every update. The easiest approach to that will be application-dependent, but I frequently use unique, server-generated ID's to pass objects around, then fetch them out of the database using those when I need to use them. (The unique ID's are necessary because I'm generally consuming an API that uses them, so your results will vary) The only place where that technique may or may not work is where you're generating data locally, and haven't (yet) uploaded it to the database where it get's it's permanent ID. I generally special-case those and have a device ID separate from the 'real' ID, just to keep track of them until they get their real ID. Anything that doesn't have a 'real' ID is something my logic is aware of as something that needs to be persisted to server, so that works for me.

Effects of calcium-phosphate-based materials on proliferation and alkaline phosphatase activity of newborn rat periosteal cells in vitro. The effects of dental materials, intended for bone substitution, on cell growth and alkaline phosphatase activity of newborn rat periosteal cells have been studied in vitro. Confluent periosteal cells were exposed to three apatite-based materials (400 micrograms/mL) with different physico-chemical properties. The materials were a beta-tricalcium phosphate with a microporous granular structure obtained by sinterization (Synthograft, Johnson & Johnson, East Windsor, NY), a 40-60-mesh microporous durapatite ceramic (Periograf, Sterling Drug, Inc., Rensselaer, NY), and a 1-2-mm-diameter hydroxyapatite ceramic (Osprovit, Feldmuhle Aktiengeselschaft, Plochingen, Germany) with macropores larger than 100 microns. Cell proliferation and alkaline phosphatase activity were assessed by incorporation of 3H-thymidine into trichloroacetic-acid-precipitable material and by a fluorimetric method, respectively. Cell viability and compatibility with the materials were determined by morphology in phase-contrast microscopy. Periosteal cells showed increased proliferation following exposure to Synthograft, but were unaffected by Osprovit, whereas Periograf caused significantly reduced cell growth. Alkaline phosphatase activity was unaffected by Osprovit, but was decreased by both Synthograft and Periograf. The results indicated a differential response of periosteal cells to bone-substituting materials with heterogeneous physico-chemical characteristics.

[A mass in the popliteal fossa and leucocytosis caused by a paraneoplastic leukemoid reaction]. A 65-year-old woman was referred with a mass in the right popliteal fossa, fever and leucocytosis reaching 105 x 10(9)/l. Her medical history included the excision of a melanoma from the right ankle more than 20 years before. Ultrasound, CT and positron-emission tomography showed the mass in the right knee but no other lesions. The process was drained. Histological examination ofa subcutis biopsy indicated malignancy. Due to deterioration in her clinical condition amputation of the right leg was performed after which her leucocyte count normalized. The pathology specimen revealed a high-grade undifferentiated soft tissue tumour of unclear origin. Preoperatively assessed serum levels of granulocyte-stimulating factor (G-CSF), interleukin 6 and interleukin 8 were elevated to 241, 91 and 82 pg/ml respectively. After the amputation these levels returned to almost normal. This extreme leucocyte count may be explained by a paraneoplastic leukemoid reaction. It is hypothesized that the tumour cells produce G-CSF and other cytokines causing leucocytosis. Normalisation of the cytokine levels postoperatively supports this hypothesis.

Efficacy and outcomes of continuous peritoneal dialysis versus daily intermittent hemodialysis in pediatric acute kidney injury. Acute kidney injury (AKI) requiring renal replacement therapy (RRT) is associated with high patient morbidity and mortality. There is no consensus on the best RRT modality for pediatric AKI. The efficacy and safety of continuous peritoneal dialysis (cPD) and daily intermittent hemodialysis (dHD) were compared in 136 children aged 1 month to 16 years requiring RRT for AKI. Mortality, risk factors and causes of death, 1-month and 3-month renal recovery rates, and technique-related complications were assessed. Uremia control and the rate of catheter-related complications were comparable in the groups. Thirty-day survival was 60.7 % (51 out of 84) with cPD and 36.5 % (19 out of 52) with dHD (p = 0.019). Although age <1 year, extended time lag from disease onset to RRT initiation, mechanical ventilation, and extended vasopressor dependence independently predicted death, adjusted mortality was higher with dHD relative to cPD (hazard ratio [HR] 1.75, 95%CI 1.18-2.84, p = 0.022). Almost all fatalities in the dHD group (94 %) occurred during or within an hour of a HD session. Renal function normalized in 27 % of survivors after 4 weeks and in 51 % after 3 months. The risk of permanent end-stage renal disease was increased in patients with an intrinsic renal cause of AKI (HR 2.72; 95 % CI 1.37-3.83; p = 0.029) and in those with delayed RRT initiation (HR 2.17; 95 % CI 123-2.93; p = 0.015), but did not differ between patients treated with dHD and cPD. Favorable patient survival with cPD compared with dHD in children treated for AKI was evident in this study.

Llew O'Brien Llewellyn Stephen O'Brien (born 26 June 1972) is an Australian politician who has been a member of the House of Representatives since the 2016 federal election, representing the Division of Wide Bay, and deputy speaker of the House since February 2020. He is a member of the Liberal National Party of Queensland (LNP), and sat with the Nationals in federal parliament until his election as deputy speaker. Police career Prior to his election, O'Brien served as a police officer. He joined the Queensland Police in 1999. In his first speech in Parliament he spoke of his own decade long experience of living with Post Traumatic Stress Disorder brought about while serving as a traffic accident investigator. In December 2013, O'Brien was accused of having misused police resources for political purposes. He was investigated and faced managerial action, but was cleared of the allegations by Queensland Police. O'Brien has received both State and National medals for his Police service between 1999 and 2016. In 2010 he was awarded the Queensland Police Service Medal. In 2011 he was awarded the Queensland Flood and Cyclone Citation. In April 2015 he was awarded a 15-year clasp to the Queensland Police Service Medal. In 2016 he was awarded both the National Police Service Medal and the National Medal for ethical and diligent service. Political career O'Brien became a member of the National Party of Queensland in 2006, and joined the Liberal National Party of Queensland upon its formation in 2008. He has served in many roles within the parties, including Vice President, Regional Chairman, State Executive, Branch Chairman and Campaign Chairman. After the retirement announcement of long serving Member of Wide Bay and Deputy Prime Minister Warren Truss, O'Brien was preselected for the 2016 federal election and won the seat. He has served on the Joint Standing Committees for the Australian Commission for Law Enforcement Integrity; and Law Enforcement; as well as the House of Representatives Standing Committees for Indigenous Affairs; and Infrastructure, Transport and Cities. In 2016, O'Brien was also appointed as the Queensland Chair of the Federal Government's Black Spot Advisory Panel for 2016/17 by Minister for Infrastructure and Transport Darren Chester. In February 2020, O'Brien moved a spill motion for Barnaby Joyce to challenge Michael McCormack for leadership of the National Party. The challenge failed, and on 10 February O'Brien announced that he would no longer sit in the Nationals party room, but would remain a member of the LNP and continue to support the Morrison government. O'Brien was subsequently elected as Deputy Speaker of the House of Representatives, having been nominated unexpectedly by the Opposition against the Government's nominated choice, Damian Drum. References Category:1972 births Category:Living people Category:Liberal National Party of Queensland members of the Parliament of Australia Category:Members of the Australian House of Representatives for Wide Bay Category:Members of the Australian House of Representatives Category:Australian police officers Category:21st-century Australian politicians

Oct. 16 (Bloomberg) -- Prince Frog International Holdings Ltd. plunged by the most on record after short-seller Glaucus Research Group questioned the company’s sales and branded the baby-care products maker a “strong sell.” Prince Frog shares were halted in Hong Kong trading today after dropping as much as 26 percent to HK$4.66, headed for the biggest decline since its July 2011 listing. The Chinese government’s tax records indicate Prince Frog’s net income is “a fraction of reported figures,” Glaucus said while initiating coverage of the shares at “strong sell.” Queenie Hung from Wonderful Sky Financial Group, Prince Frog’s public relations firm, declined to immediately comment and said the company will issue a statement to the Hong Kong Stock Exchange later today. The allegations reflect the scrutiny that publicly traded Chinese businesses are drawing from short-sellers. Vegetable processor China Minzhong tumbled 48 percent, the most on record, in less than two hours on Aug. 26 after Glaucus questioned the company’s accounts in a report. Minzhong said it “strongly” denied the allegations. Glaucus’s statements on its performance were made with the sole objective of driving down the company’s share price and gaining from the decline, Minzhong said in a September statement. Its shares have more than doubled since its Aug. 26 close, recovering from its decline after PT Indofood Sukses Makmur, controlled by Indonesian billionaire Anthoni Salim’s investment company, offered S$488 million ($393 million) cash for the rest Minzhong, which it already had a stake in. Baby Care Besides Minzhong Food, China Metal Recycling Holdings Ltd. and China Medical Technologies Inc. have each separately been the focus of reports by Glaucus. Liquidators were appointed to China Metal in July and China Medical filed for Chapter 15 foreign-firm bankruptcy protection in New York last year. Glaucus, which has an office in Newport Beach, California, was founded by Matthew Wiechert, who has a background in investment banking, to probe companies that appear “too good to be true,” according to its website. Prince Frog, based in southern China’s Fujian province, sells skin care, bath products, oral care items, and diapers for children, according to its annual report. It reported a 31 percent rise in profit to 241.1 million yuan ($40 million) last year. Marketing investments and advertising with popular Hong Kong singer Kelly Chen boosted awareness of its brand, it said in the annual report. It also cited sales gains from selling on Chinese e-commerce sites such as T-Mall and expanding in hypermarkets such as Wal-Mart Stores Inc. and Carrefour SA. Prince Frog posted revenue of 1.6 billion yuan last year, double the 838 million yuan it reported in 2010, according to data compiled by Bloomberg. As of yesterday’s close, its stock had more than doubled from its IPO price of HK$2.60 a share. Ten of the 11 analysts covering Prince Frog recommend investors buy the stock, while one rates the stock a hold, Bloomberg data show. The stock is still up 43 percent so far this year.

Small Business Services Marino Communications’ small business and nonprofit service lines are designed to provide organizations with a vibrant, consistent, and professionally-managed online brand image. We offer several different tiers of service to support a wide range of business communication needs. If one of our standard services does not fit your current needs, please contact us. We will be happy to speak with you and develop a service solution that will meet your needs and expectations. Social media management Monthly service provides a client with a professionally-managed social media presence. The principal works with each client to develop a content strategy, assembles content provided by the client or develops original content into posts, schedules posts, monitors social media and other internet accounts, and responds to questions and comments from client customers and stakeholders. The principal reviews and updates the client’s social media strategy and regularly provides each client with analytics to demonstrate the value of Marino Communications’ services. Base price includes management of up to two social media accounts. Additional accounts extra. Price is determined on a per client basis. Social media set-up One-time service provides a client with an attractive and functional social media presence. Service includes entering all needed information into social accounts, using client-supplied photos or other image files (e.g. logos), and setting up any desired social media account linking. The client assumes all responsibility and risk for the social media account(s) after the project is completed. Social media strategy A la carte consulting service provides clients who are less well-versed in social media management with a comprehensive strategy for effectively accomplishing their digital marketing goals. Service includes time spent meeting with clients, time spent researching competitors and ideating strategic solutions, and time spent designing and preparing a written report of those strategies. Reputation management Monthly service provides clients with proactive monitoring of their social media and popular review websites (Yelp!, TripAdvisor, Google business listings). Service includes daily monitoring of social media and review website accounts, responding to customer questions and complaints, and assisting clients with coordinating solutions to customer complaints. Clients are provided a monthly report of positive/negative feedback, responses, and feedback trends. Newsletter preparation/distribution Subscription service produces a basic newsletter highlighting desired aspects of each client’s organization.

Film Review: Wrong Turn 5 (2012) A small West Virginia town is hosting the legendary Mountain Man Festival on Halloween, where throngs of costumed party goers gather for a wild night of music and mischief. But an inbred family of hillbilly cannibals kill the fun when they trick and treat themselves to a group of of visiting college students. REVIEW: I’m not entirely sure how the watchable but unremarkable WRONG TURN has managed to spawn four sequels but then again it’s small fry compared to the prolific FRIDAY THE 13TH and HALLOWEEN franchises. Like those series, and A NIGHTMARE ON ELM STREET, the set up can be summarised as ‘youngsters terrorised by unstoppable killer’ and it’s a depressing thought that such a brief sentence can describe almost 30 ostensibly different films. I suppose it’s something that WRONG TURN at least has unusual (and multiple) villains whereas Jason Voorhees and Michael Myers were / are to all intents and purposes interchangeable. But it’s an inescapable truth that all these films only show true originality when staging elaborate scenes of violence. All of which brings me to Declan O’Brien’s Wrong Turn 5: Bloodlines (2012), a film that exists solely for the purposes of depicting torture and murder in as many bizarre and sadistic ways that its makers can dream up. Fairlake, West Virginia is host to the annual Mountain Man Festival which sees hordes of youngsters – and, apparently, one TV crew – descend on the town for a few days of sex, drugs and rock n roll. Among those arriving are five college friends: druggie Billy (Simon Ginty) and his girlfriend Cruz (Amy Lennox), tough guy Gus (Paul Luebke) and his girlfriend Lita (Roxanne McKee) and floppy-haired guitar-playing singleton Julian (Oliver Hoare). However, before they even reach Fairlake they narrowly avoid running down a man in the road, total their car, get into a knife fight and are arrested by the passing sheriff. And all this within the first fifteen minutes (and I haven’t even mentioned the sex scene and the murder). With practically the entire cast now in jail, director O’Brien has to resort to ludicrous means to get his film going again. Selfless Billy – who has enough “party favours” on him to make Keith Moon think twice – tells Sheriff Angela (Camilla Arfwedson) that the drugs are all his, that his friends know nothing about it and that she should let the others go. Which, unbelievably, she does – thereby demolishing my preconceived notions about tough US policing. However, her more pressing problem is the old man she arrested with the kids: running his profile through her computer she learns he is Maynard Odets (everyone’s favourite Cenobite, Doug Bradley), a wanted fugitive. Having arranged for the US Marshals to pick him up the following morning all she has to do is make it through the night in one piece. But, as Odets informs her with relish, his three boys – grotesquely deformed inbred hillbilly cannibals – will be on their way into town to spring him from jail and slaughter everyone into the bargain. What follows is some of the most gleefully sadistic, gloating brutal and almost nihilistically bleak horror that I have witnessed for some time. In fact “horror” is not what this is, for O’Brien’s purpose here is not to frighten or scare you; what he wants to do is revolt and disgust you to the point where you will feel like taking a shower after it’s all over. The methods by which he kills off his cast are absurd in their complexity and utterly illogical in plot terms but my word they are brutal. Some may argue that their very absurdity leavens the effect of the violence but all I can say is that it didn’t work that way for me. I’ve seen some pretty extreme cinema in my time but I’ve rarely seen anything quite so relentlessly and determinedly sadistic. Moreover, Wrong Turn 5: Bloodlines (2012) denies any chance of mercy, salvation, justice, vengeance or even hope; there is no cavalry to ride to the rescue, much less a happy ending to send you home somewhat comforted. All this film has to offer is suffering and death. Call me old fashioned but I need more from my horror films than that.

Yes, I want the following logo embroidered onto the front mats. I understand that mats with custom embroidery are not returnable. I understand that if I do not select a logo my floor mats will not have a logo. These 1984 Nissan 300ZX floor mats are manufactured per order. Most orders are manufactured within two days of your floor mat order. We pride ourselves with an average 2 day turnaround time for custom car floor mats from when you place your order to shipment. These 300ZX mats are manufactured in the USA and ships direct from the factory to you. Most of our mats are in our customer's hands within 12 days or less (depending on what part of the country you are located in, see Shipping Information for more exact time frames). Because each set of car mats is custom made just for you, the picture shown is an only an example of what your car floor mats will look like. It does not represent exactly what your Nissan 300ZX mats will look like. Our mats come in two or four piece sets and use Griplock, non-skid backing, to keep the mats from moving all over your 300ZX's floor. We currently offer over 180 licensed embroidered logos. You can customize your floor mats to suit your interiors unique style by mixing and matching the material, colors, and embroidered logo. Unsure of your original interior carpet color? A selection of materials and colors that match your 1984 Nissan 300ZX original interior may be listed above. Over 180 logos may be custom embroidered on your choice fabric and color. Made from the same material as our carpet kits. Die cut or heat molded to perfectly fit each vehicles original interior. Over 300 original manufacturers colors. Includes original drivers side heel pads. Quality that meets or exceed OEM specifications. These car floor mats are dyed in a continuous range operation with additives to reduce fading, often far outlasting the 300ZX original floor mats. They have been tested for ozone humidity fading and light fastness for maximum life span. These new floor mats will add resale value to your Nissan 300ZX and you'll be amazed how fresh and clean your 300ZX's interior will feel. These floor mats are the highest quality aftermarket car mats available. We use Computer-aided, cutting-edge manufacturing processes. Our strict quality control ensures these Nissan 300ZX floor mats will fit. Really Easy Installation Floor mat installation is simple because our mats are designed and manufactured to fit your Nissan 300ZX just like the original floor mat. It's as easy as pulling them out of the box and placing them in your vehicle. Now that wasn't too tough was it? Also note The material colors shown may appear different on every computer. If you require a exact carpet color we suggest that you request a carpet sample. These car floor mats are guaranteed against manufacturing defects. In the rare occurrence of a manufacturing defect we will promptly replace or refund as per our Return Policy. These Nissan floor mats are custom made per order in the United States to extremely high standards and inspected before delivery. View By Product Quality Car Interior serves our automotive loving clients in United States and throughout the world with Quality, Speed, Security, and Confidence. We offer the best available in car interiors, floor mats, door panels, dash covers, headliners, and carpet kits for all makes and models, period! Most of products are custom made specifically for you. Our vehicle carpet kits are not made until you place your order. We do not have pallets of old automotive interior parts lying around collecting dust. Each carpet kit is custom made just for you and most of our products are manufactured here in the USA. We are proud of our interior parts and personal service and we guarantee quality. We have raised the bar in Customer Service. Your experience is our top priority, we sincerely appreciate your business and we take pride in the quality automotive interior parts we offer. Buy online for all of your auto part interior needs with confidence because your purchase is protected through our secure server ordering. Make sure you review our 100% guarantee. Enjoy our floor mats, door panels, headliners, carpet kits and many other products. We sincerely appreciate your business and wish to continue serving all of your automotive interior needs, again and again.

package; import openfl.display.Sprite; import openfl.events.Event; class NMEPreloader extends Sprite { var outline:Sprite; var progress:Sprite; public function new () { super (); var backgroundColor = getBackgroundColor (); var r = backgroundColor >> 16 & 0xFF; var g = backgroundColor >> 8 & 0xFF; var b = backgroundColor & 0xFF; var perceivedLuminosity = (0.299 * r + 0.587 * g + 0.114 * b); var color = 0x000000; if (perceivedLuminosity < 70) { color = 0xFFFFFF; } var x = 30; var height = 7; var y = getHeight () / 2 - height / 2; var width = getWidth () - x * 2; var padding = 2; outline = new Sprite (); outline.graphics.beginFill (color, 0.07); outline.graphics.drawRect (0, 0, width, height); outline.x = x; outline.y = y; addChild (outline); progress = new Sprite (); progress.graphics.beginFill (color, 0.35); progress.graphics.drawRect (0, 0, width - padding * 2, height - padding * 2); progress.x = x + padding; progress.y = y + padding; progress.scaleX = 0; addChild (progress); } public function getBackgroundColor ():Int { return 0; } public function getHeight ():Float { var height = 480; if (height > 0) { return height; } else { return flash.Lib.current.stage.stageHeight; } } public function getWidth ():Float { var width = 640; if (width > 0) { return width; } else { return flash.Lib.current.stage.stageWidth; } } public function onInit () { } public function onLoaded () { dispatchEvent (new Event (Event.COMPLETE)); } public function onUpdate (bytesLoaded:Int, bytesTotal:Int):Void { var percentLoaded = bytesLoaded / bytesTotal; if (percentLoaded > 1) { percentLoaded = 1; } progress.scaleX = percentLoaded; } }

[Late obstructions of aorto-bifemoral prostheses]. The factors underlying late thrombosis of aortobifemoral by-pass are analysed on the basis of personal experience and reported data. They are considered to be due to progressive degradation of the prosthesic tissue and, particularly, to the lack of an adequate back flow route, apart from any faults in the actual construction of the femoral anastomosis. Treatment of the thrombotic complication involves considerable technical and operating problems which have two main solutions: substitution of the thrombosed branch, or its disobstruction. Intimately linked with restoral of by-pass patency is the reconstruction of an adequate back flow route either by means of profundaplasty or by extending the branch as far as popliteal level. Of 83 patients discharged with patent prosthesis, thrombosis occurred in 7 and 10 reoperations were necessary. Reconstruction of branch patency was done in the majority of cases by thrombectomy. Profundaplasty was associated in 4 cases while in other 4 popliteal extension was necessary. Analysis of results shows that the operation of choice on the affluxion route seems to be replacement of the thrombosed branch.

Gluten sensitivity in the rectal mucosa of first-degree relatives of celiac disease patients. Rectal gluten challenge is a simple, sensitive, and specific test of mucosal gluten sensitivity. Our aims in this study were to evaluate gluten sensitivity in a group of relatives of celiac patients and to compare these findings with those obtained on small bowel histology, celiac disease-related serology, and HLA typing. A 4-h rectal gluten challenge was performed with 6 g of crude gluten in saline solution in 29 first-degree relatives, 20 well-diagnosed celiac patients, and 10 subjects in whom celiac disease had been excluded. The number of intraepithelial lymphocytes in pre- and postchallenge frozen rectal biopsies (pan T-cell immunocytochemistry) was quantified by computerized image analysis. The intraepithelial lymphocyte response after gluten instillation was significantly higher in celiac disease patients (median, 126% increase above the baseline count; 95% confidence interval: 61-213%) compared with control subjects (median, -5%; 95% confidence interval: -29-5%). Using a cut-off of 20% change in intraepithelial lymphocyte count, 14 relatives (48%) showed a celiac-like response. Two of these subjects had partial villous atrophy and increased lymphocyte counts in the small bowel mucosa. One of them also exhibited a positive celiac disease-related serology and the typical celiac human lymphocyte antibody (HLA) DQ2. The remaining 12, and all those relatives with a negative challenge, had normal small bowel mucosa and were negative for antigliadin and endomysial antibodies. The characteristic celiac HLA (DQA1 0501 DQB1 0201 heterodimer) was identified in five relatives with positive challenge (including the patient with more severe mucosal atrophy) but was also present in eight relatives with no evidence of gluten sensitivity in the rectal mucosa. Our study characterizes a subgroup of relatives of celiac patients who show mucosal evidence of sensitization after local instillation of gluten in the rectum but who have no other features of celiac disease.

#include "../../../src/xmlpatterns/iterators/qtocodepointsiterator_p.h"

Uesugi Tsunakatsu was the third head of Yonezawa Domain from the Uesugi clan. In 1645, he became the third head of Yonezawa Domain. In 1654, he married Haruhime, daughter of Hoshina Masayuki. They adopted a son of Tsunakatsu's younger sister with Kira Yoshinaka, Uesugi Tsunanori. Later his wife died because she was poisoned by her mother. After his wife died, he had a concubine who died at a young age, Ofu no Kata. References Category:1637 births Category:1664 deaths Category:Uesugi clan

what? in any raid config, you'd generally need all your disks to be the exact same size. i guess in a raid 0, you could use a bigger drive, you'd just lose the space at the end of it. bear in mind that, if you just use two disks, you'll lose half the capacity. i'd be more likely to do it across the 2 ssd's for the OS (since you don't need a ton of space on C:), then leave the 1tb for data. actually, i wouldn't just be more likely, that's what i do. 2 raid 0's for the OS (i'm not worried about data integrity, since there shouldn't really be anything important written to that disk), then 2 1tb drives in raid 1 for data (i don't care about speed, since most of it isn't being accessed frequently). ultimately, i'll probably chuck the 1tb drives into a NAS and replace them with 3tb drives. if i buy a third, i'll likely do raid5 on them. Ah thought so I'll prob just raid 0 the ssd then, I just need more sata cables now. replacing some fans; kept my stock ones on that came with the case they've been really quiet for a year now and recently they've been making a lot more noise than I'd like since I leave my computer on almost all the time it gets really annoying. forenci, make it to the mun yet? i just finished a tug that went from kerbin to duna, eve and made the return with a ton of fuel to spare. it's easily the least complex thing i've ever built. i think next, i'll sent jeb to laythe and put together a base. Damn it! Show me how! I did make it to the mun...but sadly I did not have enough fuel to get off, haha. My first Kerbin on the mun! He explored and is now stranded with three other astronauts. I've been messing around with some rocket design for a while now and think I've gotten one that could get me to the Mun and back. I think I've gotten the hang of the fuel lines and how to implement them. I'm going to try and land it on the Mun and go back to Kerbin. Then I hope to launch a rescue mission to bring them all back safely. It's quite fun. Post some screen shots of your stuff! I want to see how radically off my rocket designs are, haha. replacing some fans; kept my stock ones on that came with the case they've been really quiet for a year now and recently they've been making a lot more noise than I'd like since I leave my computer on almost all the time it gets really annoying. I'm in need of a card reader my external bugged out on me and will probably go with an internal one this time around. It's been a year with this pc I will update it with another video again since I have nothing better to do and I want to show it off lol I'm saving up for a giant upgrade in July with the 4770K (I live near a Microcenter so it'll be the same price most pay for a 4670K) and GTX 770. I pretty much have it all planned out. I was going to go straight for SLI, but decided against spending another $400 on a second GPU. Standard 8GB RAM inside an R4. Thinking I'll go with a U14S to cool the CPU, but the upgrade potential of the H220 is tempting. Probably a 256GB Samsung 840 Pro SSD. Google Fiber (which is coming around that time) basically comes with a NAS. The new rig should be silent (U14S goes up to like 33dbs with full load). Should be ~$1100 total. Man, I love Microcenter. Should be fun to see the difference. I'm going up from an E8400 & GTX 260. holy crap that rocket is too big. i used novapunch on this build, but mostly for the boosters and heavy struts. in the vab, with some dV stats post-launch, after dropping the boosters, but right before the gravity turn. Dear god that thing is huge haha. I think my rocket actually looks bigger because I was so zoomed in. The actually lander is fairly small. Interesting though. I will have to try and attempt to figure out some better configurations after seeing that. I kind of do the onion peel method where you shed tanks as things progress further. It seems to work pretty well. Hah geez. That's insane. I'm actually playing as we speak. I've got a ton of fuel to get me into the orbit of the Mun. I think my only thing is going to be after I shed my current stage if I will have enough fuel to land and then get back to Kerbin. heh, it's actually pretty small. and i have like, 2 stages i don't need on it. i have a heavy launcher that's like, 20-25 orange tanks. asparagus staging (rather than onion) makes such a huge difference. shedding weight is so hugely important in this game. I'm saving up for a giant upgrade in July with the 4770K (I live near a Microcenter so it'll be the same price most pay for a 4670K) and GTX 770. I pretty much have it all planned out. I was going to go straight for SLI, but decided against spending another $400 on a second GPU. Standard 8GB RAM inside an R4. Thinking I'll go with a U14S to cool the CPU, but the upgrade potential of the H220 is tempting. Probably a 256GB Samsung 840 Pro SSD. Google Fiber (which is coming around that time) basically comes with a NAS. The new rig should be silent (U14S goes up to like 33dbs with full load). Should be ~$1100 total. Man, I love Microcenter. Should be fun to see the difference. I'm going up from an E8400 & GTX 260. I'm sort of close to a microcenter also and 4770k you say?? Need to check that out; If I can find someone to buy my mobo/processor as a package I might do that and just upgrade my mobo and go for a 4770k too I was willing to do about a $500 upgrade and that will fall into range with the new processor. edit: eh at this point I'd rather upgrade my gfx card my current being a 7770 I want to go nvidia and get a 680 but I'd have to wait a few more months to hop on that. Already have the 3770 processor isn't much of an upgrade performance wise so I'll stick with that for another year. Yeah, there's zero point in upgrading over an Ivy or even Sandy. It makes sense for me because I'm still on a Core2 Duo. The GTX 770 is basically the GTX 680 rebranded and with a $100 price drop. I forget where the 780 lies compared to the other cards out there. 780 comes out Thursday, 770 comes out at the end of the month. WOOO! At long last I landed on the mun and returned safely to my home planet of Kerbin. I could have done it with a much smaller rocket (after watching some of Scott Manley's video's it appears clear) but nonetheless I landed on the Mun, planted a flag (new feature, woot woot), and got back safe. It was a tough go for a while but it worked out in the end. I ended up pretty much flinging my self straight into Kerbin, avoiding the need for orbiting and touching down. I was FLYING at the planet, but fortunately my parachutes held up and slowed me down and I made a nice landing. Haha, I'm so damn happy right now. I think my next goal is to work on getting some sort of orbital refueling station up in the sky. First goal is to get something in orbit, then learn how to dock properly which looks hard from all the videos I've seen, hah. a) why do you have lights pointing UP off of your command module? b) why did you blow your parachute so high? or is that a useless docking node on the top? if you want to land with more precision, look into aerobraking. it makes it really easy to conserve fuel while grabbing a stable orbit, and becomes really essential later in the game. with the rocket i posted earlier, i almost had enough fuel to visit moho, but i messed up my eve entry. Oh haha. The lights and docking node were for future missions. I plan to use the the rocket I designed for future missions where docking may be relevant. Right now I'm trying to design a solid orbiter that I can attach some fuel to. The rocket I used to land on the Mun was quite nice. I feel like I could reach some other places with it potentially but I'd like to just build a solid orbiter/lifter that can go up and drop some potential fuel stations in orbit.

The German parliament has passed legislation making it easier to deport failed asylum seekers and monitor those deemed dangerous in a move that has been slammed by opposition parties and rights groups as an assault on the rights of refugees. In legislation passed by the Bundestag late on Thursday, German authorities will be able to detain refugees due for deportation for 10 days rather than four, and monitor by ankle bracelet those deemed potentially dangerous. The legislation also restricts freedom of movement for all failed asylum seekers. It grants the federal refugee agency BAMF and other government bodies more leeway to use and share data retrieved from migrants' mobile phones. OPINION: Angela Merkel is not the great progressive messiah Refugee organisation Pro Asyl criticised the measures, saying that they robbed refugees of their right to privacy. "The agreed package of measures for tougher deportation policies is a programme that will deprive asylum-seekers of hope for protection in Germany and is aimed at discouraging them," the organisation said in a statement. Defending the move, Interior Minister Thomas de Maiziere referred to the new measures as "a conclusion of efforts to tighten asylum laws in this legislative period". The measures were decided partly as a response to a truck attack in Berlin in December in which 12 people were killed. Although attacker Anis Amri's asylum request had failed and he was under surveillance by police, the authorities failed to deport him. Amri, a 24-year-old, had been living in Germany as an asylum seeker. He was killed in Italy after he pulled a gun and shot an Italian officer in the shoulder during a routine police check. Hundreds of German investigators are investigating how Amri managed to flee Germany after the attack and whether he may have had accomplices or a support network that helped him escape.

The recent discovery that neutrinos are massive particles has considerable impact on different domains of physics: in particle physics, where the description of non-zero masses and mixing requires the extension of the Standard Model of fundamental interactions; in astrophysics, for the comprehension of various phenomena such as nucleosynthesis; in cosmology with, for instance, the search for dark matter. In the last few years positive oscillation signals have been found in a series of experiments using neutrinos produced with various sources [@sk; @lsnd]. In view of the importance of this discovery and its implications, a number of projects are running, planned in the near future, or under study in order to address many still open questions about neutrinos. Among them are those concerning their Majorana or Dirac nature, the mass hierarchy and absolute mass scale, the knowledge of the mixing angle $\theta_{13}$, the possible existence of sterile neutrinos and of $CP$ violation in the leptonic sector. In a recent paper [@zucchelli] Zucchelli has proposed an original method to produce intense, collimated and pure neutrino beams: the [*beta-beams*]{}. In contrast with the neutrino factory concept implying the production, collection and storage of muons to obtain muon and electron neutrino beams, the novel method consists in accelerating, to high energy, radioactive ions decaying through a $\beta$ process. A beta-beam facility consists of a radioactive ion production and acceleration to low energy (like at CERN ISOLDE), further acceleration to about 150 GeV/nucleon (using for example the PS/SPS accelerators at CERN) and storing of the radioactive ion bunches in a storage ring. At present $^{6}He$ and $^{18}Ne$ seem to be the best candidates [@zucchelli]. The resulting neutrino beam has three novel features, namely a single neutrino flavor (electron neutrino or anti-neutrino), a well-known energy spectrum and intensity, a strong collimation. Another important advantage: a beta-beam scheme relies on existing technology. The physics impact of such a beam has been discussed in [@zucchelli; @mauro] and includes for example oscillation searches, precision physics and $CP$ violation measurements. The feasibility of beta-beams is at present under careful study [@betabeam]. In this letter we propose to exploit the beta-beam concept to produce intense, collimated and pure neutrino beams of low energies [@cris]. Low energies means here a few tens of MeV, like those involved in nucleosynthesis and in supernova explosions, up to about a hundred MeV. We argue that the physics potential of such a facility would have an important impact on hot issues in different domains, in particular nuclear physics, particle physics and astrophysics. To illustrate this we focus on the specific example of neutrino-nucleus interaction studies and discuss some open questions that could be addressed with a low-energy beta-beam facility [@cris]. Finally, we analyze possible sites for such a facility. Nuclei are used to detect neutrinos in experiments designed to study neutrino properties, such as oscillation measurements, as well as experiments where neutrinos bring information from the interior of stars like our sun or from supernova explosions. As a consequence, a detailed understanding of neutrino induced reactions on nuclei is crucial both for the interpretation of various current experiments and for the evaluation of the feasibility and physics potential of new projects. Examples are given by the use of [@sk]: - deuteron in heavy water detectors like in SNO for solar neutrinos; - carbon in scintillator detectors such as in the LSND and KARMEN experiments using neutrinos from a beam dump [@lsnd; @karmen]; - oxygen in Cherenkov detectors like in the Super-Kamiokande detector or in next-generation large water detectors like UNO and Hyper-K [@uno]; - lead-perchlorate [@elliott] and lead in new projects for supernova neutrinos such as OMNIS and LAND [@land]. Open issues in astrophysics provide important motivations for improving our present knowledge of neutrino-nucleus interactions. In particular, the role of these reactions for nucleosynthesis is under intense investigation [@qian]. So far, experimental data on neutrino-nucleus interactions are extremely scarce. The largest ensemble of data has been obtained for carbon [@lsnd; @karmen] where discrepancies between experimental and theoretical values have been the object of intensive studies in the last years [@cris1; @c12]. There is one measurement in deuteron [@deut] and one in iron [@iron]. In the case of deuteron, where theoretical predictions are very accurate, there is still an important unknown quantity, i.e. $L_{1A}$ [@kubodera]. Theoretical calculations are therefore of absolute necessity. However, getting accurate predictions is a challenging task and necessitates as much experimental information as possible. The general expression for the cross section of the reaction ($l$ is the outgoing lepton), as a function of the incident neutrino energy $E_{\nu}$, is given by [@kuramoto] : $$\sigma(E_{\nu})={G^{2} \over {2 \pi}}cos^{2}\theta_C\sum_{f}p_lE_l \int_{-1}^{1}d(cos \, \theta)M_{\beta}, \label{e:1}$$ where $G \,cos \, \theta_C$ is the weak coupling constant, $\theta$ is the angle between the directions of the incident neutrino and the outgoing lepton, $E_l=E_{\nu}-E_{fi}$ is the outgoing lepton energy and $p_l$ its momentum, $E_{fi}$ being the energy transferred to the nucleus. The quantity $M_{\beta}$ contains the nuclear Gamow-Teller and Fermi type transition probabilities [@cris1]. The energy which can be transferred to the nucleus in a neutrino-nucleus interaction does not have any upper value since the neutrinos can have any impinging energy according to the specific neutrino source. Typical neutrino energies cover the range from the very low (up to about 10 MeV for reactor and solar neutrinos) to the low (tens of MeV for e.g. supernova neutrinos) energy regime, to the intermediate (about 100-300 MeV) and high (GeV and multi-GeV) energy range of accelerator and atmospheric neutrinos. The nuclear degrees of freedom relevant in these various energy windows are very different and the models used to describe the transition probabilities in (\[e:1\]) range from the Elementary Particle Model, Effective Field Theories, detailed microscopic approaches (Shell Model, Random-Phase Approximation and its variants) for low momentum transfer, to the Fermi Gas Model at high momentum transfer [@kuboreview]. One of the difficulties in getting accurate theoretical predictions comes from the increasing role played by the forbidden transitions when the neutrino energy increases, as pointed out in [@cris1; @cris2]. The importance of the forbidden spin-dipole transitions in nucleosynthesis has been first pointed out in [@gail1]. As an example Fig.1 shows the contribution of various states, excited in the $\nu_e$(Pb,Bi)$e^-$ reaction, to the total cross section and its evolution with increasing neutrino energy. In particular we see that already for 30-50 MeV neutrino energy the contribution of forbidden states ($J^{\pi} \neq 0^+,1^+$) becomes significant. The importance of forbidden states can also be seen directly in the flux-averaged cross sections – obtained by folding the cross sections (\[e:1\]) with the relevant neutrino flux – which are the relevant quantities for experiments. For low energy neutrino, such as supernova neutrinos, or neutrinos produced by the decay-at-rest of muons, the spin-dipole states ($J^{\pi}=0^-,1^-,2^-$) contribute by about $40 \%$ in $^{12}$C [@cris1] and $^{56}$Fe [@iron], and by about $68 \%$ in $^{208}$Pb [@cris2]. The contribution from higher forbidden states is about $5 \%$ and $25 \%$ in iron and lead respectively. Their role increases with increasing neutrino energy. Indeed, they contribute by about $30 \%$ in carbon [@cris1] and $60 \%$ in lead [@cris2] in the intermediate energy region corresponding, for example, to neutrinos produced from pion decay-in-flight. Few data exists on the spin-dipole states, mainly from charge-exchange reactions [@pn] and practically none for the higher forbidden states[^1]. More experimental information is needed to constrain theoretical calculations of the centroid, the width and the total strength of forbidden states. For example, one of the open questions concerning these states is the possible quenching of their strength. Note that understanding the quenching of the allowed Gamow-Teller ($J^{\pi}=1^+$) strength, namely the reason why the observed strength is only a fraction of the predicted one, has been a longstanding problem in nuclear physics [@gt]. This has a direct impact on the physics potential of running experiments or projects under study. Let us consider the case of lead-based projects which aim at measuring supernova neutrinos. It has been shown, for example, that the a precise measurement of the energy of the electrons emitted in the charged-current neutrino-lead reaction can provide useful information about the temperature of the initial muon/tau neutrinos produced in a supernova explosion [@cris3]. Although this result seems little sensitive to the details of the calculations, a measurement of the differential electron cross section would bring an important piece of information. Moreover, the number of charged current events in coincidence with neutrons produced in the des-excitation of $Bi$ may be used to determine whether the mixing angle $\theta_{13}$ is much larger or much smaller than $10^{-3}$. In the latter case, one would need – as far as the neutrino detection is concerned – a very precise knowledge of the reaction cross sections [@cris3]. Similar studies have been performed in various other nuclei. In [@petr] it has been shown that in Cherenkov detectors the detection of $\gamma$ rays produced in the inelastic neutrino scattering off oxygen allow to identify $\nu_{\mu,\tau}$. A low-energy beta-beam facility would provide the possibility to perform neutrino-nucleus interaction studies with various nuclei and address the many open questions [@kuboreview; @orland; @baha1]. Examples are the measurements of reaction cross sections on deuterium, carbon, oxygen, iron and lead. In the latter case, the measurement of the differential electron cross section as well as of the neutral and charged current cross sections in coincidence with one- and two-neutron emission would be of great interest. A larger set of experimental data would allow us to make reliable extrapolation from the low to the high neutrino energy regime. It would also provide important information for the extrapolation to the case of neutrino reaction on exotic nuclei, which are of astrophysical interest. Finally, one should reanalyze, in the context of a low-energy beta-beam facility, the feasibility of the experiments proposed for the ORLAND project (Oak Ridge Laboratory for Neutrino Detectors) [@orland] which has been proposed a few years ago (these include, for example, oscillation searches, measurement of the Weinberg angle at low momentum transfer). Another aspect of beta-beams should be stressed : the neutrons emitted from some beta-decay candidates also open other axes of research besides the one mentioned here. The future availability of intense radioactive ion beams at several facilities offers various possible sites for a beta-beam facility producing low-energy neutrinos. Among these are GANIL, GSI, CERN or the EURISOL project. Table 1 shows the capabilities (energy and intensities) which can be attained at these sites. Concerning GSI, lower intensities will be reached with the presently envisaged upgrade [@gsi]. We see that two configurations are possible. In sites like GANIL and for the EURISOL project (in the present shape where the ions are accelerated up to a 100 MeV/A and without a storage ring), the gamma of the parent ions is equal to one. Therefore, one can bring the ions in a $4\pi$ detector and dispose of intense neutrino sources. In sites like GSI and CERN, the ions will be accelerated and stored in a storage ring (at GSI with the future HESR). In particular, at GSI one will dispose of neutrinos spanning the tens of MeV energy range, whereas at CERN, one could span from tens to 100 MeV neutrino energy domain. In conclusion, we propose to exploit the beta-beam concept to produce intense and pure low energy neutrino beams. Such a facility would have a considerable impact in different domains of physics. Possible sites include CERN, GSI and GANIL. I am grateful to M. Lindroos for the discussions concerning the feasibility of a low-energy beta-beam facility as well as for suggesting the GANIL and GSI laboratories as possible sites. Thanks also to A. Villari and H. Weick for fruitful discussions and to R. Lombard and J. Serreau for careful reading of this manuscript. [99]{} The Super-Kamiokande Collaboration, Phys. Rev. Lett. [**81**]{}, 1562 (1998); the K2K Collaboration, Phys. Rev. Lett. [**90**]{}, 041801 (2003); the SNO Collaboration, Phys. Rev. Lett. [**87**]{}, 071301 (2001) and Phys. Rev. Lett. [**89**]{}, 011301 (2002); the KamLAND Collaboration, Phys. Rev. Lett. [**90**]{}, 021802 (2003). The LSND Collaboration, Phys. Rev. Lett. [**77**]{}, 3082 (1996) and Phys. Rev. Lett. [**81**]{}, 1774 (1998). P. Zucchelli, Phys. Lett. B [**532**]{}, 166 (2002). M. Mezzetto, J.Phys. 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Ion intensity $\gamma$ --------- -------------------------- ---------- GANIL $10^{12}~$ions/s 1 EURISOL $10^{13}~$ions/s 1 CERN $2 \times 10^{13}$ions/s 1-150 : The table shows the ion intensities and the gamma of the parent ion which could be available at possible sites for a low-energy beta-beam facility. The numbers refer to $^{6}$He as an example. Results for CERN are from [@betabeam]. [^1]: Some knowledge about the relevant states can be obtained through muon capture experiments.

Q: How to deny execution of any file on a specific apache directory? I'm using apache2 and php. I built a form that lets the user to upload files to a specific directory. I already implemented some other security things, but I would also like to deny the execution of any file on that directory. They're meant to be only downloaded and not executed by users or scripts. I've got the following code for htaccess, but it's a fake one, not sure of the syntax, nor if it's the best way of doing it: <Location "/example/mydir/"> <Files .> ForceType application/octet-stream Header set Content-Disposition attachment </Files> </Location> Could you please help me correct that code or point me to best practices? A: Providing file upload/download facilities is a huge can of worms. In addition to the possibility of attacking your server there's also questions about data smuggling. malware and intellectual property. But since you are specifically asking about the former... Disabling PHP execution in this way only provides a single layer of prevention. if that layer fails for some reason then your security is gone. Also, this only prevents execution of the content if the webserver is pointed directly at the URL of the file - it doesn't provide any protection if someone can trick the existing php code into including the content. A minimal approach would be to store the content outside of directories accessible by URLs (i.e. outside of the document root and any other mapped directories). This does not prevent the inclusion vulnerability but eliminates the direct addressing vulnerability. All access to the content must then be mediated by a PHP script. But on the upside, its a lot easier to avoid OMGWTFs like: ForceType application/octet-stream Switching off PHP execution (php_flag engine off) is a better solution to disabling execution than changing the mime type. Forcing a mime type like this is always a bad idea. An alternative/complementary approach, would be to encode the files thus preventing code inclusion vulnerabilities. It's also a good idea to allocate your own filenames to the artefacts on your host filesystem.

At least four Saskatchewan cannabis stores haven't opened yet because the province's liquor and gaming authority (SLGA) hasn't finished screening the would-be owners. "I am in the unfortunate position of holding three lottery picks but no licence yet," said Jean Paul Lim, a doctor and teacher of internal medicine at the University of British Columbia. In June 2018, Lim's numbered company — incorporated in B.C. only two months before — won the chance at running cannabis stores in Melfort, Outlook and Rosetown. That's all it remains nearly a year later — a chance — because in order to officially obtain the licence to operate the stores legally, Lim must first come out of the other end of what he calls SLGA's "due diligence" screening process. That process vets potential store operators to ensure, for example, they have a system that will properly account for all the cannabis they'll handle. "I have no idea when I can open," said Lim via email Wednesday. "Two of my three sites are already completely built out and the third is about 75-per-cent complete and on hold until I rectify the SLGA situation." Money invested, staff hired Lim said he's now invested "hundreds of thousands of dollars" into the sites and is afraid of losing them. "I am not in the driver's seat at this time," he said. Under the rules set out by the province, stores must open by October 17 of this year — the one-year anniversary of when recreational cannabis became legal in Canada. David Morris, an SLGA spokesperson, said via email Wednesday that If a store doesn't open within that timeframe, the opportunity may go to the runner-up that was drawn for that community. "If the runner-up were not interested then SLGA would need to consider other options. At this point, it's speculative to say what may or may not happen in hypothetical situations," Morris said. "The proponents that have not yet received their permit continue to move through the process. SLGA continues to work with these businesses to ensure all of the requirements necessary for obtaining a cannabis retail permit are achieved." Morris said that permit applications are considered private information, meaning SLGA won't provide details about the status of a specific permit application, but that SLGA anticipates several stores will open "in the coming weeks." Nipawin store waiting, too Licensed shops have opened in 29 of the 51 locations approved to have a cannabis store in the province. A planned shop in Nipawin has yet to open. As with Lim's locations, the store is ready to open. It has already hired two staff members. Two partnering companies won the Nipawin slot: majority partner GreenTec Holdings, a B.C.-based cannabis grower and seller, and minority partner Battlefords Agency Tribal Chiefs (BATC) Investments LP. BATC's members include Ahtahkakoop Cree Nation, Moosomin First Nation, Red Pheasant Cree Nation, Sweetgrass First Nation, Stoney Knoll First Nation, Saulteaux First Nation and Mosquito-Grizzly Bear's Head-Lean Man First Nation. "We are still waiting for the SLGA to clear us in the security screening process," Shannon Forgues, GTEC Holdings' retail manager, said via email Wednesday. "Our store is built out and staff have been hired." The companies filed their permit application shortly after the lottery winners were announced in June 2018. SLGA good to work with: company In a subsequent interview, Forgues and GTEC's chief operating officer, David Lynn, stressed that they don't fault SLGA. They said SLGA has been very good to work with compared to other groups and it's got a lot of paperwork to wade through. Between GTEC and BATC, the SLGA has to do background checks on 16 board members, Lynn said. "Let's say you were an individual entrepreneur and you were successful in this lottery — the amount of paperwork I think would be significantly less because we had to submit background checks for each board member," Lynn said. Still, Lynn wondered whether the holdup isn't getting in the way of one of the federal government's stated reasons for legalizing cannabis. "There is a real interesting irony to all this. The paperwork and the timelines are one of the reasons that the black market is still relatively strong," he said. "If you don't open up the legal stores, if you don't provide a legal alternative to people, then a lot of them are going to go back to their previous source."

Bei­jing stores cut gold prices on slump The big­gest weekly slump in the global gold price led Bei­jing’s gold stores to cut their prices for the first time this year. The price in Bei­jing de­clined by 10 yuan ($1.5) per gram on Sun­day. This was the first cut, fol­low­ing six ear­lier price in­creases this year. Gold had the big­gest weekly loss in more than three years as in­vestors de­bated prospects for higher US rates. In China, prices de­clined as trad­ing restarted after a week’s hol­i­day. Bul­lion of 99.99 per­cent pu­rity slumped 4 per­cent to 273.6 yuan per gram on the Shang­hai Gold Ex­change at 15:30 on Mon­day. Huang Liang, a gold an­a­lyst at Guo­hua Jew­elry, said the price cuts by Bei­jing’s gold stores were within ex­pec­ta­tions. “There’s a stronger ex­pec­ta­tion that the US Fed­eral Re­serve will raise rates in De­cem­ber, so the dol­lar is ris­ing and gold price is de­creas­ing,” saidHuang. Yu Guiy­ing at Bei­jing-based All Love All Life Gold Store said their jew­elry busi­ness­was not in­flu­enced by the global price slump, and the price re­duc­tions at Bei­jing’s gold stores from Sun­day would fur­ther pro­mote their sales. “But it is true that peo­ple are less in­ter­ested in pur­chas­ing gold bul­lion as an in­vest­ment prod­uct,” said Yu. Gold­man Sachs Group Inc said on Thurs­day that a drop in gold prices sig­nif­i­cantly be­low $1,250 per ounce would present in­vestors with a strate­gic buy­ing op­por­tu­nity, with the metal of­fer­ing pro­tec­tion against risks to global growth and the lim­ited ef­fec­tive­ness of cen­tral banks. China's of­fi­cial gold re­serves stood at 18.4 mil­lion met­ric tons in Septem­ber this year, up 74 per­cent from that in June 2014, ac­cord­ing to data of the Peo­ple’s Bank of China.

Robson seen as gold dust for UK women's tennis LONDON (Reuters) - With One Direction star Harry Styles and Prime Minister David Cameron among her growing army of fans, teenager Laura Robson is seen as "gold dust" for women's tennis in Britain. Robson, 19, became the most successful British woman at Wimbledon in 15 years after powering through to the second week of the prestigious tennis tournament but she lost her fourth-round match on Monday to Estonia's Kaia Kanepi. While Robson struggled to hold back tears leaving the court, campaigners for tennis and women's sport praised her performance and the inspiration the British No. 1 gave female players. The "Robson factor" has been credited for helping to double the number of young girls regularly competing in tennis in the past two years, according to the Lawn Tennis Association (LTA) which is under pressure to increase participation in the sport. "She is gold dust for women's sport," said Sue Tibbals, chief executive of the Women's Sports and Fitness Foundation which aims to boost the number of women playing sport. "She has captured the nation's attention for her tennis and also because she is such a strong, inspiring woman. At 19 she has a great career ahead of her." Robson has won praise among tennis fans for her destructive forehand but she added 20,000 people to her 280,000 following on Twitter last week when heart-throb boy band member Styles declared himself to be her fan. Cameron joined her fan bandwagon from Kazakhstan on Monday, tweeting her his best wishes ahead of her match while some of her fans lined up for two days to get tickets for Wimbledon on Monday for the chance to see her play. "That's unbelievable support .. I'm so happy that they decided to come," Robson told a news conference on Monday. ROLE MODEL Robson was bitterly disappointed by her failure to get the win which would have made her the first British woman quarter-finalist since Jo Durie 29 years ago. Durie, a former world number five, said Robson was under enormous pressure as the only British female near the top of the rankings and now guaranteed to break into the world's top 30. "Laura is out there on her own and so there is a lot of pressure on her .. but she is a great role model. She is young and with-it and people can relate to her," Durie told Reuters. Robson's appeal is undeniable with a broad smile and typical teenage interests. She loves the TV show "Hannibal" and lists her hobbies as horse-riding, cooking and shopping. "But she need to notch up some more victories to really become marketable," said Rebecca Hopkins, managing director of sports PR agency ENS Ltd. Robson has emerged on the scene as the LTA is under pressure from Sport England, the body that distributes taxpayers' money to sports, to boost participation in tennis. LTA spokesman Tom Harlow said Australian-born Robson had boosted the number of youngsters in tennis since winning silver in the doubles with Andy Murray at the 2012 Olympics. She also got through to the fourth round of last year's U.S. Open. The number of under-12s competing regularly has nearly doubled to 8,000 and 11- to 18-year-old LTA memberships are up 10 percent to about 112,000. But weekly adult tennis participation, of over-16s playing for at least 30 minutes, is still down from a peak of 530,000 in 2009 although numbers rose 19 percent last year to 445,000. "We hope that Robson's success at Wimbledon will inspire more teenage girls to pick up a racket or stay in tennis. All sports struggle to get teenage girls playing," Harlow said. A group of schoolgirls on an outing to Wimbledon for the day from Burgate School in Hampshire, said Robson was their idol. "She's the first British female player I have ever known to do well and she's great," said 15-year-old Emily Bufton-Taylor.

// // PlayerStatsComponent.swift // OctopusKit Project Template // // Created by [email protected] on 2020/07/02. // Copyright © 2020 Invading Octopus. Licensed under Apache License v2.0 (see LICENSE.txt) // import SpriteKit import GameplayKit import OctopusKit final class PlayerStatsComponent: OKComponent { private(set) var score: Int = 0 }

Q: Failing to verify crypt password What I am using to verify // username and password sent from form $myusername= filter_var($_POST['myusername'], FILTER_SANITIZE_STRING); $mypassword= filter_var($_POST['mypassword'], FILTER_SANITIZE_STRING); $sql = $dbh->prepare("SELECT * FROM $tblname WHERE UserLogin='$myusername'"); $sql->execute(); $sql = $sql->fetch(); $password_hash = $sql['UserPass']; /*** close the database connection ***/ $dbh = null; if(crypt($mypassword, $password_hash) == $password_hash){ What I am using to create the password $salt = blowfishSalt(); $mypassword = crypt($mypassword, $salt); $stmt = $dbh->prepare('INSERT INTO Users(UserLogin, UserPass, UserEmail, admin) VALUES(:UserLogin, :UserPass, :UserEmail, :admin)'); $stmt->execute(array( ':UserLogin' => $myusername, ':UserPass' => $mypassword, ':UserEmail' => $myemail, ':admin' => $admin )); blowfishSalt() function blowfishSalt($cost = 13) { if (!is_numeric($cost) || $cost < 4 || $cost > 31) { throw new Exception("cost parameter must be between 4 and 31"); } $rand = array(); for ($i = 0; $i < 8; $i += 1) { $rand[] = pack('S', mt_rand(0, 0xffff)); } $rand[] = substr(microtime(), 2, 6); $rand = sha1(implode('', $rand), true); $salt = '$2a$' . sprintf('%02d', $cost) . '$'; $salt .= strtr(substr(base64_encode($rand), 0, 22), array('+' => '.')); return $salt; } had to remove {} for function so it would format correctly in stackoverflow. I am also storing the password in the mysql database with char(128). A: You have this in verification code: crypt($mypassword, $password_hash) And this is the creation code: $mypassword = crypt($mypassword, $salt); Surely these should both use $mypassword and $salt?

Thomas I de Gadagne Thomas I de Gadagne, known as Thomas the Rich (26 or 27 August 1454, Savoy - 23 May 1533, Avignon) was a banker from a rich Florentine family who settled in Lyon in France, where he built up trading, banking and industrial business interests in Lyon and Florence. He made a huge fortune and lent large sums to the kings of France to support their military expeditions to Italy and to finance a French expedition to the Americas. Life His father brought his three sons (Thomas, François and Olivier) to Lyon in 1434. Thomas grew up in Geneva, where his family also had business interests, before following his family to Florence in 1463. He returned to Lyon in 1468 and became an apprentice in a Florentine banking family, the Pazzi. Thomas also based his own financial business in Lyon and became the richest man in the city. His two brothers then his nephews all worked for his company and he was its director until 1527. He was recognized as the most important spice merchant in the city in 1500 and sixteen years later he appeared in the 'nommées' (fiscal registers estimating the wealth of each of the city's citizens for tax purposes) as the richest inhabitant of the city, taxed on 5000 'livres tournois' - for comparison the next two richest families, the Nasi and Bonvisi, were only taxed on 2500 and 2000 livres tournois respectively.. When a 'consulat' was imposed on foreign merchants in 1523 to fund work on the city walls, he sent sixty men, compared to thirty required of Robert Albisse, twenty of Pierre Salviati and fifteen of Antoine Gondi. In 1529 the Venetian ambassador Antonio Suriano wrote estimates of each Lyon merchant's wealth - he ranked Thomas at 400,000 ducats. Florentine connections The Florentines in Lyon lived and worked by statutes officially recognized by the Republic of Florence and had to ensure internal harmony in their own community whilst also getting it protection and representation in the city of Florence and the French court. These statutes were established on 27 November 1501, putting the community under the leadership of four counselors and a consul - as the leader of the most important mercantile and banking community in Lyon, the consul more and more had the privilege of leading the payments made at the end of each of the four annual fairs. Thomas was made a counsellor in 1501 then consul in 1505.. He partly paid for the construction of the St Thomas Chapel in Notre-dame de Confort, the Florentine church in Lyon, and his heir and nephew later commissioned a painting for it of The Incredulity of Saint Thomas from Francesco Salviati. He also became a member of the wool guild back in Florence in 1497 and made major investments in Florence, mainly in the commercial and industrial sectors. - for example, he contributed 4000 florins to founding a wool textile factory in 1502 as well as owning a 60% share and sending his brother Olivier and nephew Niccolo Strozzi to manage the factory. Until his death, he remained very active in developing factories in Florence, gaining major commercial success by doing so. Thomas and the King of France Citizen of Lyon Death He died without issued in 1533 and is buried beside his wife - he left his large fortune to his nephew Thomas II de Gadagne. Bibliography M. Rocke, « The Guadagni of Florence : Family and Society », Medieval and Early Moderne Italy, 1955 Luigi Passerini, Genealogia e storia della famiglia Guadagni, Florence, Cellini, 1873, 171 p. (notice BnF no FRBNF31064839) Georges Yver, De Guadagniis, mercatoribus Florentinis Lugduni, XVI, Paris, Cerf, 1902, 115 p. (notice BnF no FRBNF31677741) Richard Gascon, Grand commerce et vie urbaine au seizième siècle : Lyon et ses marchands, Paris & La Haye, Mouton, coll. « École pratique des hautes études. Sixième section. Sciences économiques et sociales. Centre de recherches historiques. Civilisations et sociétés » (no 22), 1971, 2 vol., 1001 p. (notice BnF no FRBNF35371690) Marie-Noëlle Baudouin-Matuszek et Pavel Ouvarov, « Banque et pouvoir au XVIe siècle : la surintendance des finances d'Albisse Del Bene », Bibliothèque de l'école des chartes, t. 149-2, 1991, p. 249-291 Édouard Lejeune, La saga lyonnaise des Gadagne, Lyon, Éditions lyonnaises d'art et d'histoire, 23 mars 2004, 192 p. () Michel Francou, Armorial des Florentins à Lyon à la Renaissance, Éditions du Cosmogone, 1er mai 2009 () Patrice Béghain, Bruno Benoît, Gérard Corneloup et Bruno Thévenon (coord.), Dictionnaire historique de Lyon, Lyon, Stéphane Bachès, 2009, 1054 p. (, notice BnF no FRBNF42001687) References Category:History of Lyon Category:1454 births Category:1533 deaths Category:People from Savoy Category:Italian bankers Category:French bankers Category:French people of Italian descent Category:15th-century businesspeople Category:16th-century Italian businesspeople

Structural characterization of the full-length response regulator spr1814 in complex with a phosphate analogue reveals a novel conformational plasticity of the linker region. Spr1814 of Streptococcus pneumoniae is a response regulator (RR) that belongs to the NarL/FixJ subfamily and has a four-helix helix-turn-helix DNA-binding domain. Here, the X-ray crystal structure of the full-length spr1814 in complex with a phosphate analogue beryllium fluoride (BeF3(-)) was determined at 2.0 Å. This allows for a structural comparison with the previously reported full-length unphosphorylated spr1814. The phosphorylation of conserved aspartic acid residue of N-terminal receiver domain triggers a structural perturbation at the α4-β5-α5 interface, leading to the domain reorganization of spr1814, and this is achieved by a rotational change in the C-terminal DNA-binding domain.

Bucculatrix andalusica Bucculatrix andalusica is a moth species in the family Bucculatricidae. It is found in southern Spain. It was first described by G. Deschka in 1980. The larvae feed on Artemisia vulgaris. They mine the leaves of their host plant. Possibly creating a blotch mine. References Natural History Museum Lepidoptera generic names catalog Category:Bucculatricidae Category:Moths described in 1980 Category:Moths of Europe Category:Leaf miners

Q: How do I search a CVS repository for a particular file? Is there any way to do it? I only have client access and no access to the server. Is there a command I've missed or some software that I can install locally that can connect and find a file by filename? A: You could grep the output of cvs rlog -Nh . (note the period character at the end - this effectively means: the whole repository). That should give you info about the whole shebang including removed files and files added on branches.

Morphology of the canine pyloric sphincter in relation to function. The ultrastructure and immunocytochemistry of the canine distal pyloric muscle loop, the pyloric sphincter, were studied. Cells in this muscle were connected by gap junctions, fewer than in the antrum or corpus. The sphincter had a dense innervation and a sparse population of interstitial cells of Cajal. Most such cells were of the circular muscle type but a few were of the type in the myenteric plexus. Nerves were sometimes associated with interstitial cell profiles, but most nerves were neither close to nor associated with interstitial cells nor close to smooth muscle cells. Nerve profiles were characterized by an unusually high proportion of varicosities with a majority or a high proportion of large granular vesicles. Many of these were shown to contain material immunoreactive for vasoactive intestinal polypeptide (VIP) and some had substance P (SP) immunoreactive material. All were presumed to be peptidergic. VIP was present in a higher concentration in this muscle than in adjacent antral or duodenal circular muscle. Interstitial cells of Cajal made gap junctions to smooth muscle and to one another and might provide myogenic pacemaking activity for this muscle, but there was no evidence of a close or special relationship between nerves with VIP or SP and these cells. The absence of close relationships between nerves and either interstitial cells or smooth muscle cells leaves unanswered questions about the structural basis for previous observations of discrete excitatory responses or pyloric sphincter to single stimuli or nerves up to one per second. In conclusion, the structural observations suggest that this muscle has special neural and myogenic control systems and that interstitial cells may function to control myogenic activity of this muscle but not to mediate neural signals.

Development of a murine model of Helicobacter pylori infection. A murine model for Helicobacter pylori infection could facilitate vaccine development. This study was designed to determine the effect of various conditions of dose, frequency of administration, and fasting on H. pylori infection of mice. Balb/c and C3H/HeN mice were inoculated orogastrically with clinical isolates of H. pylori grown in liquid culture. At 2-week intervals, the stomachs were removed for secondary culture on horse blood agar and for histological analysis. H. pylori from secondary cultures or homogenized stomach tissue from infected mice was inoculated a second time in naïve animals. H. pylori was cultured with high frequency only from the stomachs of C3H/HeN mice. Fasting the mice and increasing the number of organisms inoculated did not increase the rate of infection. Histological analysis detected no inflammation, but mucus depletion and erosion were present in the stomachs of C3H/HeN mice. H. pylori organisms were not observed. Secondary cultures of H. pylori or homogenized infected stomach tissue did not cause infection when inoculated in naïve mice. Clinical isolates of H. pylori transiently infect C3H/HeN mice. This murine model is suitable for testing oral vaccines. Effective vaccination against H. pylori could prevent transient infection and reduce subsequent gastritis.

Aïn Kechra District (Oum El Bouaghi Province) Aïn Kechra District is a district of Oum El Bouaghi Province, Algeria. Category:Districts of Algeria Category:Districts of Oum El Bouaghi Province

Keanu Reeves in police corruption movie Keanu Reeves is to star with Dennis Quaid in a US police drama. The film Time For A Killing is based on the Rolling Stone magazine article The Murder of Notorious B.I.G. The article covered an investigation by Los Angeles Detective Russell Poole into gangland killings and police corruption. His probe focused on police involvement in the deaths of rappers Tupac Shakur and Notorious B.I.G, alias Biggie Smalls. Reeves will play the investigating officer in the film about the scandal which swept through the Los Angeles Police Department. Quaid is to play the Mr Fixit who organises contract killings and payments to police officers who assist The Mafia. The project, backed by FilmFour, is scheduled to go into production next summer.

Q: Where to get complete manpages In Debian 7 and in Linux Mint 16 I don't get any parameters/options when typing man insmod or insmod --help But I know there are parameters, e.g insmod --probe Where can I get complete manpages for my system or which distribution provides complete manpages? A: insmod was before provided by the module-init-tools project which has been replaced by the kmod project. The "new" insmod from kmod does not provide this options anymore. Found a hint on Arch news about the change. This will apply for Debian too: With module-init-tools being declared a dead project by its current maintainer, a new project has stepped up to take its place: kmod. This is intended to be a drop-in replacement, though deprecated functionality in module-init-tools has not been reimplemented. The options -p, -s and -f are outdated and now ignored. Long option names for that params aren't valid anymore. You can check the source code

Miami Dolphins The Miami Dolphins are a professional American football team based in the Miami metropolitan area. The Dolphins compete in the National Football League (NFL) as a member club of the league's American Football Conference (AFC) East division. The Dolphins play their home games at Hard Rock Stadium, located in the northern suburb of Miami Gardens, Florida. The Dolphins are the oldest professional sports team in Florida. Of the four AFC East teams, they are the only team in the division that was not a charter member of the American Football League (AFL). The Dolphins were founded by attorney-politician Joe Robbie and actor-comedian Danny Thomas. They began play in the AFL in 1966. The region had not had a professional football team since the days of the Miami Seahawks, who played in the All-America Football Conference in 1946, before becoming the first incarnation of the Baltimore Colts. For the first few years, the Dolphins' full-time training camp and practice facilities were at Saint Andrew's School, a private boys boarding prep school in Boca Raton. In the 1970 AFL–NFL merger, the Dolphins joined the NFL. The team made its first Super Bowl appearance in Super Bowl VI, losing to the Dallas Cowboys, 24–3. The following year, the Dolphins completed the NFL's only perfect season, culminating in a Super Bowl win, winning all 14 of their regular season games, and all three of their playoff games, including Super Bowl VII. They were the third NFL team to accomplish a perfect regular season. The next year, the Dolphins won Super Bowl VIII, becoming the first team to appear in three consecutive Super Bowls, and the second team (the first AFL/AFC team) to win back-to-back championships. Miami also appeared in Super Bowl XVII and Super Bowl XIX, losing both games. For most of their early history, the Dolphins were coached by Don Shula, the most successful head coach in professional football history in terms of total games won. Under Shula, the Dolphins posted losing records in only two of his 26 seasons as the head coach. During the period spanning 1983 to the end of 1999, quarterback Dan Marino became one of the most prolific passers in NFL history, breaking numerous league passing records. Marino led the Dolphins to five division titles, 10 playoff appearances and an appearance in Super Bowl XIX before retiring following the 1999 season. In 2008, the Dolphins became the first team in NFL history to win their division and make a playoff appearance following a league-worst 1–15 season. That same season, the Dolphins upset the 16–0 New England Patriots on the road during Week 3, handing the Patriots' their first regular season loss since December 10, 2006, in which coincidentally, they were also beaten by the Dolphins. History The Miami Dolphins joined the American Football League (AFL) when an expansion franchise was awarded to lawyer Joseph Robbie and actor Danny Thomas in 1965 for $7.5 million, although Thomas would eventually sell his stake in the team to Robbie. During the summer of 1966, the Dolphins' training camp was in St. Pete Beach with practices in August at Boca Ciega High School in Gulfport. The Dolphins had a combined 15–39–2 record in their first four seasons under head coach George Wilson, before Don Shula was hired as head coach. Shula was a Paul Brown disciple who had been lured from the Baltimore Colts, after losing Super Bowl III two seasons earlier to the AFL's New York Jets, and finishing 8–5–1 the following season. Shula got his first NFL coaching job from then-Detroit head coach George Wilson, who hired him as the defensive coordinator. The AFL merged with the NFL in 1970, and the Dolphins were assigned to the AFC East division in the NFL's new American Football Conference. For the rest of the 20th century, the Shula-led Dolphins emerged as one of the most dominant teams in the NFL with a strong running game and defense, with only two losing seasons between 1970 and 1999. They were extremely successful in the 1970s, completing the first complete perfect season in NFL history by finishing with a 14–0 regular season record in 1972 and winning the Super Bowl that year. It was the first of two consecutive Super Bowl wins and one of three appearances in a row. The 1980s and 1990s were also moderately successful. The early 80s teams made two Super Bowls despite losing both times, and saw the emergence of future Hall of Fame quarterback Dan Marino, who went on to break numerous NFL passing records, holding many of them until the late 2000s. After winning every game against the division rival Buffalo Bills in the 1970s, the two teams gradually developed a competitive rivalry in the 80s and 90s, often competing for AFC supremacy when Jim Kelly emerged as the quarterback for the Bills. The Dolphins have also maintained a strong rivalry with the New York Jets throughout much of their history. Following the retirements of Marino and Shula and the rise of Tom Brady and the New England Patriots, the Dolphins suffered a decline in the 2000s, including a 1–15 season in 2007 that was the worst in franchise history. They only made the playoffs three times in that decade and were unable to find a consistent quarterback to replace Marino, shuffling 13 quarterbacks and five head coaches. However, the Dolphins have been competitive against the Patriots despite their decline, with notable wins coming in 2004, 2008, 2014, 2018, and 2019. They also are the last team in the AFC East to win the division championship aside from the Patriots, doing so in 2008. While quarterback Ryan Tannehill provided some stability at the position throughout most of the 2010s, the team has nonetheless been mediocre, only having made the playoffs once during the decade. Super Bowls AFC Championships Rivalries The Dolphins share intense rivalries with their three AFC East opponents, but also have had historical or occasional rivalries with other teams such as their cross-state rivals Tampa Bay Buccaneers, their former divisional rivals Indianapolis Colts, the Pittsburgh Steelers, San Diego/Los Angeles Chargers, Oakland/Los Angeles/Las Vegas Raiders, and to a lesser extent, the Jacksonville Jaguars. Divisional rivalries Buffalo Bills The Dolphins and the Buffalo Bills have a long-standing rivalry, as there are stark characteristic differences between the cities of Miami and Buffalo, especially in climate and culture. The rivalry was extremely lopsided in favor of Miami during the 1970s, as the Dolphins won all 20 games against the Bills during that decade. Fortunes changed in the 1980s and 1990s when Jim Kelly became the Bills' starting quarterback. Though both teams were extremely dominant during that period, the Bills ultimately held the edge and dominated the Dolphins during their four playoff match-ups in the 1990s, with the Dolphins' only playoff win coming after Kelly's retirement. With the rise of Tom Brady and the Patriots during the 2000s and the retirements of Kelly and Dolphins great Dan Marino, the Bills-Dolphins rivalry has faded in relevance, but remains somewhat intense to this day. Some former Dolphins have gone to play for the Bills as well, most notably Dan Carpenter, Chris Hogan, and Charles Clay. New England Patriots The Dolphins dominated the New England Patriots during the 1970s and the 1990s, but there were some notable moments as well, including a game now known as the Snowplow Game. Fortunes changed when Tom Brady became the franchise quarterback for the Patriots, and since then, the Patriots have virtually dominated the AFC, especially the AFC East. Miami did pose more of a challenge to the Brady-led Patriots in the 2000s, however, winning more games against them than the Bills or Jets did during that decade. Notable wins over New England by the Dolphins include the Miracle in Miami, which involved a dramatic last-minute game-winning touchdown that paralleled "The Night that Courage Wore Orange", where in 2004, the Dolphins, at 2–11, upset the defending Super Bowl champion Patriots 28–29, and handed them the second of their 2 losses that season. The rivalry briefly intensified in 2005 when Nick Saban, Bill Belichick's former Browns defensive coordinator was hired as their new head coach and when Saban nearly signed quarterback Drew Brees, as well as in 2008, when the two teams battled for the AFC East division title. Miami and New England are also the only two franchises to have posted undefeated regular season records since the NFL-AFL merger, with Miami going 14–0 in 1972 and New England going 16–0 in 2007, but only the 1972 Dolphins were able to win the Super Bowl. New York Jets The New York Jets are perhaps Miami's most bitter rivals. Dolphins fans despise the Jets due to the sheer amount of New York City transplants who have moved to South Florida and the Jets' usual cocky demeanor. Just as the Bills-Dolphins rivalry is motivated by differences, the Dolphins-Jets series is also notable for the differences between New York and Miami. Unlike the former, this rivalry has been more consistent over the years. Some of the more memorable moments in this rivalry include Dan Marino's fake spike, Vinny Testaverde leading the Jets to a notable comeback on Monday Night Football, and former Jets quarterback Chad Pennington signing with the Dolphins and leading them to a divisional title. The two teams have also played in the 1982 AFC Championship, with Miami winning to face the Washington Redskins in Super Bowl XVII. Other Tampa Bay Buccaneers Since the founding of the Tampa Bay Buccaneers in 1976, the Dolphins and Buccaneers have shared a mellow in-state rivalry and were the only two teams in Florida until the Jacksonville Jaguars joined the NFL in 1995. Other AFC rivals The Dolphins have also had history against other AFC teams. When the Baltimore Colts were inserted into the AFC East following the AFL/NFL merger, they sparked a heated rivalry with the Dolphins, as a controversy involving the hiring of former Colts coach Don Shula forced Miami to forfeit a first-round draft pick. The Dolphins and Colts faced off several times in the AFC playoffs during the 1970s, including the AFC championship game leading up to Super Bowl VI, which the Dolphins won. The rivalry cooled down in the 1980s after the Colts struggled and moved to Indianapolis, but heated up once again in the late 90s until the Colts were reassigned into the AFC South as a result of the 2002 realignment of the NFL's divisions. The Dolphins also share historic rivalries with the Las Vegas Raiders, Los Angeles Chargers, and Pittsburgh Steelers, stemming from often competing against these teams in the playoffs during the Don Shula era. Facilities Stadiums The Dolphins originally played all home games in the Orange Bowl in Miami. They moved to the new Joe Robbie Stadium after the 1986 season. From 1993 to 2011, the Dolphins shared the stadium with Major League Baseball's Florida Marlins. The venue has had multiple naming rights deals since 1996, carrying the names Pro Player Stadium, Dolphins Stadium, Dolphin Stadium, LandShark Stadium, Sun Life Stadium, New Miami Stadium and, as of August 2016, Hard Rock Stadium. The facility is located in Miami Gardens, a suburb of Miami located approximately north of downtown Miami. The Miami Dolphins share Hard Rock Stadium with the NCAA Miami Hurricanes. The 2015–2016 season was the first season in the newly renovated Hard Rock Stadium. The Dolphins spent more than two years and over $400 million on a major overhaul to Hard Rock Stadium. Every seat was replaced and the lower level seats were moved closer to the field. There are roughly 10,000 fewer seats. Training St. Petersburg Beach hosted the Dolphins' first training camp in 1966. St. Andrew's School in Boca Raton hosted training camp in the late 1960s. The Dolphins subsequently trained in Miami Gardens at Biscayne College, later renamed St. Thomas University, from 1970 until 1993. In 1993, the Dolphins opened the Miami Dolphins Training Facility at Nova Southeastern University in Davie. In 2006, the facility added a domed field which allows the team to practice during thunderstorms which are common in the area during the summer. Franchise information Logos and uniforms Leaping dolphin (1966–2012) The Dolphins logo and uniforms remained fairly consistent from the team's founding through 2012. The team's colors were originally aqua and coral, with the coral color paying tribute to the Miami Seahawks and to the many natural coral reefs in Biscayne Bay. The team's original logo consisted of a sunburst with a leaping dolphin wearing a football helmet bearing the letter M. At their debut in 1966, a lighter & brighter orange was used instead of the deep coral color. The dolphin's head was near the center of the sunburst. In the 1967 season, the dolphin was centered on the sunburst, but it reverted to the original placement between 1968 and 1973. By 1974, the dolphin's body was centered on the sunburst in a slightly smaller logo than the 1967 version. The uniforms featured white pants with aqua and orange stripes, paired with either a white or aqua jersey. On the white jersey, aqua block numbers and names were outlined in orange, with aqua and orange sleeve stripes. These uniforms were used as the primary uniforms for road games and daytime home games, due to the extreme heat of South Florida. The team also had an aqua jersey used mainly for night home games or road games in which the opponent chose to wear white. The aqua jersey featured white block numbers and names with an orange outline, and orange and white sleeve stripes. An update was given to the logo in 1997 – the sunburst was simplified and the dolphin was darkened and given a more serious game-face expression. The uniforms remained the same, however a different block number font was used and navy drop shadows were added. On very rare occasions, an orange jersey was used for primetime games. The uniforms essentially swapped the location of orange and aqua from the aqua jersey. The orange jersey was first used on a Sunday night in 2003 against Washington, a Dolphin win. In 2004, the orange jersey was brought back for an Monday Night Football match pitting the 2–11 Dolphins against the 12–1 defending champion New England Patriots. The Dolphins scored a huge upset win after trailing by 11 points with less than 5 minutes remaining. Due to the unusual orange jerseys, the game has become known within some Dolphin circles as "The Night That Courage Wore Orange". The orange jerseys were used for a 2009 Monday night win against the New York Jets. However, the Dolphins would lose a 2010 Sunday night matchup with the Jets, their first loss in orange, and the jerseys would not be worn again until a 2016 Thursday night defeat in Cincinnati, although that set featured orange pants as part of the NFL Color Rush initiative. In 2009, the Dolphins switched to black shoes for the first time since the early 1970s glory days, following a recent trend among NFL teams. However, by 2011, they returned to wearing white shoes. The Dolphins' final game in the original style uniforms with block numbers and the iconic leaping dolphin logo was the final game of the 2012 season, a 28–0 shutout loss to the New England Patriots in Foxboro. The white jerseys were worn for the game, and as rumors of a new look had been swirling, many fans watching knew that it would likely be the last time their team would wear the leaping dolphin logo. Stylized swimming dolphin (2013–present) A radically new logo and new uniforms were unveiled shortly before the 2013 NFL Draft. The new logo features a stylized aqua dolphin swimming in front of a heavily modified version of the orange sunburst. The dolphin in the logo is more vague and artistic, and is not wearing a helmet as it is merely a silhouette of a dolphin cast in aqua and navy. Navy was incorporated as featured color for the first time, with orange becoming greatly de-emphasized. The uniforms feature both white pants and aqua pants, with a white or aqua jersey. The Dolphins continue to wear white at home, just as they had with the previous uniforms, with aqua being used for primetime home games. The white jersey features aqua numbers and names in a unique custom font, with orange and navy outlines on the numbers, however the names only use navy as an outline color. The aqua jerseys use white numbers with an orange and aqua outline, and white names with a navy outline. The helmets are white with a white facemask, just like the final years of the previous look, however navy is a prominent color on the helmet stripe, joining aqua and a de-emphasized orange. Both jerseys have large "Dolphins" text above the numbers, written in the team's new script. The pants are either aqua or white, and contain no markings other than a small team wordmark. In 2018, the team made some slight modifications to the logo and uniform set: The shades of orange and aqua were tweaked, and navy blue was removed from the color scheme, only remaining on the logo. Throwback uniforms In 2015, the Dolphins brought back their 1970s aqua uniforms for a few select games. Four years later, they brought back a white version from the same era as a second alternate uniform. The aqua throwbacks were worn during the now-famous 2018 Miracle in Miami play against the Patriots. Fight song The song was written and composed by Lee Ofman. Ofman approached the Dolphins with it before the 1972 season because he wanted music to inspire his favorite team. The fight song would soon serve as a good luck charm for the Dolphins that season. The Dolphins became the first team in NFL history to record an undefeated season, going 17–0 en route to victory over the Washington Redskins in Super Bowl VII. The following season, Miami posted an equally-impressive 15–2 record and capped the season with another title, defeating the Minnesota Vikings in Super Bowl VIII. The back-to-back championship runs, coupled with the popularity of the fight song amongst Dolphins fans, have ensured the song's longevity. The Dolphins revealed a new fight song by T-Pain and Jimmy Buffett featuring Pitbull on August 7, 2009 which was introduced for the 2009 NFL season. The fight song was played during the preseason home opener against the Jacksonville Jaguars on August 17, 2009, but was not played during the second preseason game against the Carolina Panthers on August 22, 2009, after being booed heavily in the first game. Furthermore, the team has preferred to play Buffett's song "Fins" after scores during the 2009 regular season instead of the traditional fight song. The Dolphins shorthand nickname, "The Fins," has been recognized and used by the team. Cheerleaders The team's cheerleaders are known collectively as the Miami Dolphins Cheerleaders. The company had its debut in 1978 as the Dolphins Starbrites. (The name referred to the co-sponsor, Starbrite Car Polish.) The cheerleaders' founding choreographer was June Taylor, famed colleague of Jackie Gleason, who led the squad until her retirement in 1990. Special Teams/Volunteer Program In April 2010, the Dolphins started the first Volunteer Program in the NFL. Special Teams is a unique volunteer organization created to enlist and mobilize the ongoing services of the community with the Dolphins staff, players and alumni. The mission of the Special Teams is to offer hands-on services to communities and families in need, to partner with existing organizations on worthwhile social, civic and charitable programs, to provide assistance at Miami Dolphins Foundation events, and to support community efforts in times of emergency. This program is headed by Leslie Nixon and Sergio Xiques. Since its inception, Special Teams has given over 100,000 community services hours to the South Florida and Mexico community. Mascots T.D. ("The Dolphin") On Friday, April 18, 1997, the first "official" mascot of the Miami Dolphins was introduced. The 7-foot mascot made his public debut on April 19 at Pro Player Stadium during the team's draft day party. The team then made a "Name the Mascot" contest that drew over 13,000 entries covering all 50 states and 22 countries. 529 names were suggested. The winning entry was announced at the annual Dolphins Awards Banquet on June 4, 1997. Dolfan Denny Denny Sym cheered on the Miami Dolphins for 33 years as a one-man sideline show, leading Miami crowds in cheers and chants in his glittering coral (orange) and aqua hat from the Dolphins’ first game in 1966 until 2000. Sym died on March 18, 2007. He was 72. Flipper From 1966 to 1968, and in the 1970s a live dolphin was situated in a water tank in the open (east) end of the Orange Bowl. He would jump in the tank to celebrate touchdowns and field goals. The tank that was set up in the 1970s was manufactured by Evan Bush and maintained during the games by Evan Bush and Dene Whitaker. Flipper was removed from the Orange Bowl after 1968 to save costs and the 1970s due to stress. In Ace Ventura: Pet Detective, Snowflake, a live dolphin who does special behaviors after the Dolphins score a touchdown, was the basis of the film after he is kidnapped as part of a revenge plot against Dan Marino. Radio and television In August 2010, the team launched its own regional TV "network". The Dolphins Television Network comprises 10 South Florida TV stations that agreed to carry the team-produced coverage. Preseason games are broadcast on television through WFOR in Miami-Dade and Broward counties, WTVX in West Palm Beach, WBBH in Fort Myers, and WRDQ in Orlando. Longtime TV and radio personality Dick Stockton provides play-by-play commentary, with Dolphins Hall-of-Fame QB Bob Griese and former Dolphins WR Nat Moore providing color commentary. The radio broadcast team features Jimmy Cefalo providing play-by-play commentary and Joe Rose providing color commentary during preseason games, along with Griese for regular season games. Griese replaced longtime color commentator Jim Mandich, who played for the Dolphins under Don Shula. Mandich lost his fight with cancer in 2011, opening the door for Griese as his replacement. Radio coverage is provided on WQAM-AM 560 and WKIS-FM 99.9. Additionally, games can also be heard in Spanish on WNMA-AM 1210, with Raúl Striker Jr. and Joaquin Duro providing play-by-play and color commentary, respectively. Preseason games are aired on CBS owned WFOR as does the regular season on the same station. If the team hosts an interconference opponent or plays on a Thursday night, WSVN, the local Fox affiliate will have the games being televised. When playing on Sunday night, the team's matches will be broadcast on WTVJ, the NBC O&O station. The Dolphins' radio affiliates: English Spanish Season-by-season records Players Current roster Pro Football Hall of Famers The Dolphins currently have ten players, and one coach enshrined in the Pro Football Hall of Fame, that have spent the majority (or entirety) of their careers, or made significant contributions with the Miami Dolphins. Three other players and four contributors that have spent only a "minor portion" of their careers with the Dolphins, and have been enshrined primarily with other teams, have also been enshrined in the Pro Football Hall of Fame. Retired numbers The Miami Dolphins currently have three retired jersey numbers: No. 12 for Bob Griese, which was retired on a Monday Night Football broadcast in 1985. No. 13 for Dan Marino, which was retired on September 17, 2000, during halftime of the "Ravens @ Dolphins" game on Sunday Night Football. No. 39 for Larry Csonka, which was retired on December 9, 2002 (30th anniversary of Miami's "1972 Undefeated Team"), during halftime of the "Bears @ Dolphins" game on Monday Night Football. The Dolphins have other numbers that have currently not been issued to any player, or are currently in reduced circulation. They include: No. 54 for Zach Thomas No. 99 for Jason Taylor Miami Dolphins Individual Awards Bold indicates those elected to the Pro Football Hall of Fame. Miami Dolphins NFL All-Decade Team Selections The following are Miami Dolphins (players and/or coaches) who have been selected to an "All-Decade Team" by the Pro Football Hall of Fame selection committee. Bold indicates those elected to the Pro Football Hall of Fame. Pro Bowl selections Many former and current Miami Dolphin players have represented the franchise in the Pro Bowl. Below is a list of current or former players that play or have played for the Miami Dolphins that have been selected to multiple Pro Bowls. Bold indicates those elected to the Pro Football Hall of Fame. Notable Miami Dolphins selected to one Pro Bowl: WRs Nat Moore, Chris Chambers, and Brandon Marshall RBs Ricky Williams, Ronnie Brown, Andra Franklin, Delvin Williams, and Jay Ajayi DTs Ndamukong Suh DEs Doug Betters, Trace Armstrong, Jeff Cross, and Adewale Ogunleye LBs Kim Bokamper, A. J. Duhe, and Joey Porter DBs Xavien Howard O-Linemen Tim Ruddy, Wayne Moore, Richie Incognito, and Branden Albert Ks and Ps Olindo Mare, Dan Carpenter, and Brandon Fields The Miami Dolphins 50 Greatest Players In 2015 to commemorate the Miami Dolphins 50th NFL season, the Dolphins organization announced through voting from the South Florida Media and Miami Dolphin fans the results of the 50 greatest players in Miami Dolphins franchise history. The results were announced during halftime on Monday Night Football between the Dolphins and the Giants. Here are the 50 greatest Dolphins broken down by position. Bold indicates those elected to the Pro Football Hall of Fame. Offense: QBs Bob Griese, Dan Marino, Earl Morrall HBs Jim Kiick, Mercury Morris, Tony Nathan, Ricky Williams FBs Larry Csonka WRs Mark Clayton, Mark Duper, O.J. McDuffie, Nat Moore, Paul Warfield TEs Bruce Hardy, Keith Jackson, Jim Mandich Cs Jim Langer, Mike Pouncey, Dwight Stephenson Gs Bob Kuechenberg, Larry Little, Ed Newman, Keith Sims Ts Norm Evans, Richmond Webb Defense: DTs Bob Baumhower, Tim Bowens, Manny Fernandez DEs Doug Betters, Vern Den Herder, Bill Stanfill, Jason Taylor, Cameron Wake LBs Kim Bokamper, Bob Brudzinski, Nick Buoniconti, Bryan Cox, A. J. Duhe, John Offerdahl, Zach Thomas CBs Brent Grimes, Sam Madison, Patrick Surtain Ss Dick Anderson, Glenn Blackwood, Louis Oliver, Jake Scott Special Teams: Ks Garo Yepremian Ps Reggie Roby STs Jim Jensen The Miami Dolphins Honor Roll The Miami Dolphin Honor Roll is a ring around the second tier of Hard Rock Stadium that honor former players, coaches, owners and contributors who have made significant contributions to the franchise throughout their history. Bold indicates those elected to the Pro Football Hall of Fame. Each of these players is honored with a placard on the facing of the upper level around Hard Rock Stadium including team founder-owner Joe Robbie. In place of a jersey number, Shula has the number 347, representing his record number of NFL coaching victories, 274 of them as Dolphins head coach. In 1992, at the 20 year anniversary, Miami's "1972 Undefeated Team" was enshrined into the Honor Roll. At the 40 year anniversary, which enshrined former defensive coordinator Bill Arnsparger into the Honor Roll, his name went on the Honor Roll where the "1972 Undefeated Team" inductee previously and originally was enshrined, and an updated "1972 Perfect Season Team 17–0" inductee was put into one corner of Hard Rock Stadium with special placards of Super Bowl VII and Super Bowl VIII included next to it on each side. The inductees as of 2014 include: The Joe Robbie Alumni Plaza "Walk of Fame" The Joe Robbie Alumni Plaza Walk of Fame was first established in 2011, designed to be all encompassing and recognize the best of the Miami Dolphins alumni, including those in the Pro Football Hall of Fame, the Honor Roll, and as well as the many other players who were among the unsung heroes and community leaders that the organization has produced. The "Walk of Fame" is located at the north end of Hard Rock Stadium, with a life size bronze statue of Joe Robbie, the original founder and owner of the Miami Dolphins from 1966 to 1989. Bold indicates those elected to the Pro Football Hall of Fame. The inductees as of 2018 (by yearly class) are: Class of 2011: Nick Buoniconti, Larry Csonka, Bob Griese, Jim Langer, Larry Little, Joe Robbie, Dan Marino, Don Shula, Dwight Stephenson, Paul Warfield Class of 2012: Tim Bowens, A. J. Duhe, Manny Fernandez, Nat Moore, Earl Morrall, Don Strock Class of 2013: Kim Bokamper, Mercury Morris, O. J. McDuffie, Keith Sims Class of 2014: Jeff Cross, Sam Madison, Tony Nathan, Ed Newman No classes from 2015 to 2017, due to modernization and reconstruction at Hard Rock Stadium Class of 2018: Dick Anderson, Mark Clayton, Mark Duper, Jon Giesler, John Offerdahl, Jason Taylor All-time first-round draft picks Staff Head coaches Current staff Notes References External links Category:1966 establishments in Florida Category:American Football League teams Category:American football teams in Florida Category:American football teams in Miami Category:National Football League teams Category:American football teams established in 1966

Turner Publishing Company Turner Publishing Company is an American independent book publisher based in Nashville, Tennessee. The company is in the top 101 independent publishing companies in the U.S. as compiled by Bookmarket.com and has been named four times to Publishers Weekly 's Fastest Growing Publishers List. History Turner Publishing Company was founded in 1984 in Paducah, Kentucky as a publisher of books. From 1984 to 2005 the company published specialty and commemorative titles focusing on history. During this period, Turner Publishing Company produced over five hundred titles in the categories of military history, local history, and organizational history, including: History of the FDNY (New York City Fire Department) and History of the 101st Airborne Division. In 2002 the company was sold to new management and moved to Nashville, Tennessee. Turner launched its move into trade publishing with a program of regional history titles in 2005. This series of local history photography books, called "Historic Photos," numbered over four hundred titles and sold nationwide through all major retailers of books with numerous bestsellers in local markets. After launching its first front list of national trade titles in 2007, Turner continues to produce a diverse list of an average of 25 new titles annually of fiction and non-fiction from leading authors. In 2009 Turner commenced an acquisition program, beginning with the purchase of over 400 titles from the sale of Cumberland House. Turner acquired the book division of Ancestry.com the following year, as well as the assets of Fieldstone Alliance, a publisher of business books for non-profit organizations. Turner went on to acquire selected assets of Providence House, including the rights to bestselling author Eugenia Price. Having reached capacity of its distribution facility by the year 2011, Turner outsourced distribution of its titles to Ingram Publisher Services. In 2013 Turner acquired over 1,000 crafts, pets, and general interest titles from John Wiley & Sons, including the backlist of Howell Book House. In 2014, Turner acquired Hunter House Publishers. In 2016, Turner acquired Jewish Lights Publishing and three other imprints from LongHill Partners. In 2018, Turner acquired Gurze Books. Notable Books and Authors Turner has over 2,000 titles, including 14 bestselling authors. Alan Dershowitz – The Case for Israel Keith Olbermann - Worst Person in the World Jack Cafferty – It’s Getting Ugly Out There Don Felder - Heaven and Hell Tedy Bruschi - Never Give Up Barney Hoskyns - Hotel California Barbara Wood - Domina; under the pseudonym Kathryn Harvey - Butterfly Peter D. Kiernan - Becoming China's Bitch Sheri Reynolds Alice Randall Deepak Chopra Steven Pratt Keith and Kent Zimmerman Eugenia Price Candy Spelling Scott Simon William F. Buckley William Least Heat-Moon Eleanor Clift Jack Nicklaus Hank Haney Dr. Ruth Westheimer Kirk Douglas Tony Curtis Imprints Turner: The flagship imprint Wiley: Turner publishes under the Wiley name, with permission, for over 1,000 acquired titles. Ancestry: Genealogy, acquired assets of the book division of Ancestry.com Fieldstone Alliance: Business Books for Non-profits, acquired assets of Fieldstone Alliance Iroquois Press: Fiction and Literature Ramsey and Todd: Children's books Cumberland House Press: Titles acquired from Cumberland House Press in 2009 Hunter House Jewish Lights SkyLight Paths Christian Journeys Gemstone Press Gurze Books References External links Turner Publishing Company Official website Category:Book publishing companies based in Tennessee Category:Companies based in Nashville, Tennessee Category:Publishing companies established in 1984

Effects of the dihydrolipoyl histidinate zinc complex against carbon tetrachloride-induced hepatic fibrosis in rats. This study investigated the effects of an antioxidant, dihydrolipoyl histidinate zinc complex (DHLHZn), on the hepatic fibrosis in the carbon tetrachloride (CCl4) rat model. The animals were divided into three groups: control, CCl4, and CCl4+DHLHZn. A histological assessment of the liver fibrosis was performed using stained liver samples. The oxidative stress and antioxidant levels were evaluated by measuring the malondialdehyde (MDA) and glutathione (GSH) levels in the liver. In addition, cultured human hepatic stellate cells (LI90) were exposed to antimycin-A (AMA) and divided into four groups: control, DHLHZn, AMA, and AMA+DHLHZn. The effects of DHLHZn on AMA-induced fibrosis were evaluated by measuring the expression of transforming growth factor (TGF)-β1 and collagen α1 (I). The hepatic fibrosis in the CCl4+DHLHZn group was attenuated compared to that in the CCl4 group. The MDA levels in the CCl4+DHLHZn group were significantly lower than those of the CCl4 group, whereas the GSH levels in the CCl4+DHLHZn group were significantly higher than those of the CCl4 group. Furthermore, the relative mRNA expression of TGF-β1 and collagen α1 (I) in the AMA+DHLHZn group was significantly lower than that in the AMA group. DHLHZn may attenuate the hepatic fibrosis induced by CCl4 by decreasing the degree of oxidative stress.

Geocaching Tours in Florida By Lenora Dannelke Imagine finding hidden treasures without the X-marked map or pirate ship. Try geocaching in Florida, a new way to explore while on vacation. What is Geocaching? A term that combines "geographical" and "cache," from the French word meaning "to conceal" – is the sport of searching for and finding a hidden object by means of GPS coordinates posted on a website. In other words, it’s a real life treasure hunting game. In 2000, the U.S. Department of Defense stopped scrambling signals from their Global Positioning System, and techno-nerds quickly embraced a "treasure hunting" game that employed handheld navigational receivers. Using coordinates for locations posted on web sites, they searched for creatively hidden, weather-tight "cache" containers filled with inexpensive trinkets. But the high-tech hide-and-seek soon attracted enthusiasts of all ages and descriptions, and has become a favorite form of outdoor recreation. Across the state, the sport has caught on. Gear and Preparation for Geocaching in Florida An active geocaching friend convinced me that borrowing her GPS device would add a new dimension of fun to a road trip. Programming a list of latitude and longitude coordinates into the device, she explained that caches are rated by degrees of difficulty. "They can even be hidden underwater," she warned. "But we'll start you off with something simple." Checking different web sites, the "Hidden Treasures" caches listed by Original Florida looked perfect for a novice cacher and meshed nicely with my travel route. Now it's just me and my little electronic buddy, the Garmin iQue 3600. As I impatiently cross and re-cross a road by the Maclay park admissions station, the ranger leans from the booth and says, "Slow down! It takes a few seconds for the satellites to read your location." Geocatching is simply perfect for walking tours in Florida. Obviously, he's familiar with the sport and has watched other players stalking the park's cache. I consider being blunt and asking where it's hidden, but refrain from cheating. Instead, I thank him and take his advice. Suddenly, the numbers on my screen aren't spinning like a slot machine. And I'm noticing beautiful plants and birds around me. The ranger station is surrounded with vibrant azaleas, and a cabbage palm adds a tropical touch to the stately neighborhood of water oaks and loblolly pines. A bluejay and a pair of cardinals flit through the trees, and a mockingbird perches on a nearby branch to offer tuneful encouragement. I may have found my geocaching zone. However, the cache doesn't jump out and yell, "Here I am!" The ranger, who'll probably be an old friend by the time I leave, advises, "Remember, it's smaller than a train." Unhinging the lid, I examine the contents of the cache. Lots of cool bracelets, stickers and miniature toys to choose from. I add a magnet from Wakulla Springs and remove a tiny bobble-head puppy - my first caching "treasure." After recording the exchange in the cache's log book, I flip back to peruse notations left by previous cachers, and finally feel connected to the caching community. It turns out the prize I selected was left by my friend, Geo "K," four months earlier. Synchronicity is clearly at play. During the following week, I locate caches at Steinhatchee Falls, Evinston Community Store and Post Office near Gainesville, Lafayette Blue Springs State Park along the Suwannee River and more. But the north of the state isn't the only place to look for geocaching in Florida.