The state-of-the-art genome annotation tools output GFF3 format files, while this format is not accepted as submission format by the International Nucleotide Sequence Database Collaboration (INSDC) databases. Converting the GFF3 format to a format accepted by one of the three INSDC databases is a key step in the achievement of genome annotation projects. However, the flexibility existing in the GFF3 format makes this conversion task difficult to perform. Until now, no converter is able to handle any GFF3 flavour regardless of source.Here we present EMBLmyGFF3, a robust universal converter from GFF3 format to EMBL format compatible with genome annotation submission to the European Nucleotide Archive. The tool uses json parameter files, which can be easily tuned by the user, allowing the mapping of corresponding vocabulary between the GFF3 format and the EMBL format. We demonstrate the conversion of GFF3 annotation files from four different commonly used annotation tools: Maker, Prokka, Augustus and Eugene.https://github.com/NBISweden/EMBLmyGFF3.EMBLmyGFF3 is freely available at  They deogy.org; . GAG proWhile the NCBI doesn’t accept their GenBank Flat File format but rather an.sqn intermediate file for submission, EBI accepts submission in their EMBL flat file format. Here the difficulty is to generate an EMBL flat file from a GFF3 file. Several tools have been developed to perform this step i.e. Artemis , seqret The information contained and the vocabulary used in a GFF3 file can differ a lot depending of the annotation tool used. On top of that the vocabulary used by the GFF3 format and by the EMBL format can differ in many points. Those differences make it difficult to create a universal GFF3 to EMBL converter that would avoid pre-processing of the GFF3 annotation file. The challenge undoubtedly lies in the implementation of a correct mapping between the feature types described in the 3rd column, as well as the different attribute’s tags of the 9th column of the GFF3 file and the corresponding EMBL features and qualifiers.In collaboration with the European Nucleotide Archive we have developed a tool addressing these difficulties called EMBLmyGFF3, which is a universal GFF3 to EMBL converter allowing the submission to the ENA database. To our knowledge, this is the only tool able to deal with any flavour of GFF3 file without any pre-processing of the file. Indeed, the originality lies in json mapping files allowing the mapping of vocabulary between GFF3 and EMBL formats.The EMBLmyGFF3 tool is an implementation in the python programming language of the verbose documentation provided by the European Bioinformatics Institute . The impfeature module contains the description of all the EMBL features and their associated qualifiers. The feature module handles a parameter file in json format, called translation_gff_feature_to_embl_feature.json, allowing the proper mapping of the feature types described in the 3rd column of the GFF3 file to the chosen EMBL features.(i) The Below is an example how to map the GFF3 feature type “three_prime_UTR” to the EMBL feature type “3′UTR”:We also provide the possibility to decide which features will be printed in the output using the “remove” parameter. In the following example the feature type “three_prime_UTR” will be ignored:qualifier module defines all the EMBL qualifiers  and has methods to access and print them. Within the GFF3 file, the qualifiers are the attribute’s tags of the 9th column. It is common that an attribute’s tag doesn’t correspond to a EMBL qualifier name. To address this difficulty, the module handles a parameter file in json format, called translation_gff_attribute_to_embl_qualifier.json, allowing proper mapping of the attribute’s tag described in the 9th column of the GFF3 file to the chosen EMBL qualifier. Below is an example how to map the “Dbxref” attribute’s tags from the GFF3 file to the “db_xref” qualifier expected by the EMBL format.(ii) The In the same way, the converter also allows the possibility to map the “source” (2nd column) as well as the “score” (6th column) from the GFF3 to an EMBL qualifier using the translation_gff_other_to_embl_qualifier.json mapping file.note=“source:Prokka” instead of of note=“Prokka”.Using the qualifier’s json files, we provide the possibility to add a prefix or a suffix to the attribute’s value. In the following example, if the “source” value within the GFF3 file is e.g. “Prokka”, the EMBL output will look like The key elements of our converter that make it universal are the parameter files in json format that describe how to map the feature types of the 3rd column, as well as the different attribute’s tags of the 9th column of the GFF3 file to the correct EMBL features and qualifiers. The json files are accessible using the –expose_translations parameter. By default, when the json parameter file doesn’t contain mapping information for a feature or qualifier, the tool checks if the name of the feature type or the tag from the GFF3 file exists within the EMBL features or qualifiers accordingly. Where relevant, the feature type or tag will be skipped, and the user will be informed, giving the possibility to add the correct mapping information in cases where this information is needed.As requirements, the tool takes as input a GFF3 annotation file and the FASTA file that has been used to produce the annotation, as well as metadata required by ENA. There are metadata that are not contained in GFF3 format, but that are mandatory or recommended for producing a valid EMBL flat file. When all the mandatory metadata are filled, the tool will proceed to the conversion; otherwise it will help the user to fill the needed information.Candida intermedia strains performed with the genome annotation pipeline MAKER [Ectocarpus subulatus performed with Eugene [The software has been used to convert the GFF3 annotation file produced by different annotation tools . Three test cases are included into the source code distribution. The EMBL files produced have been successfully checked using the ENA flat file validator version 1.1.178 distributed by EMBL-EBI . EMBLmyGne MAKER , as wellh Eugene . The resTo assess the performance of our tool we have converted 5 different genomes and annotations Table Going from an annotation in one of the many existing GFF3 flavours to a correctly formatted EMBL file ready for submission is a bridge that is in most cases cumbersome and difficult to cross. We have filled this gap by developing the software EMBLmyGFF3, which has been designed to be able to easily adapt to the different GFF3 files that could be met. It successfully converts annotation files from different annotation tools and checks the integrity of the results using the official flat file validator provided by EMBL-EBI. EMBLmyGFF3 facilitates the submission of GFF3 annotations derived from any source. We hope it will help to increase the amount of data that are actually deposited to public databases. We think EMBLmyGFF3 may play a role in the FAIRification of the annotation data management by helping in the interoperability of the GFF3 format.As any kind of format the structure sanity of the GFF3 file used is primordial. EMBLmyGFF3 relies on the bcbio-gff library to parse the Generic Feature Format , which is not dedicated to review or fix potential structure problems of the format. The EMBLmyGFF3 performs the data conversion using the current state of the mapping information present in the json files. Prior knowledge from the user about the data types contained in the GFF file and what he/she would like to be represented into the EMBL file is important in order to tune the EMBLmyGFF3 behaviour. When necessary, the users have to adjust the conversion by modifying the corresponding json files.As the tool review each feature one by one, the computational time is tightly related to the number of features contained in the annotation file. We have seen that it could take several hours for huge genome annotation. The low speed could be inconvenient and we will work on the optimization of the computational time in a new release.


The Internet on the router level, is a complex network embedded in a geographical space. We provide experimental evidences suggesting that the average travel time for a message, with fixed length, increases roughly as the square root of the geographical distance. To understand this scaling law and other measurable topological properties of the Internet as a graph, we introduce and study a simple network model. The model is based on a few realistic socio-economic facts/assumptions and qualitatively reproduces the experimentally observed stylized facts. In contrast with similar large communication networks, like the wired telephone network for example, which grew according to a designed topology governed by a central administration, the Internet grows in a less controlled manner. This rapid and seemingly uncontrolled growth raises a lot of problems with routing, resource reservation and administration. In order to keep track of the potential problems and offer rapid solutions to these, one has to understand the topological structure of the Internet as a graph embedded in a geographical space. Right from the early days of the Internet it was clear that beside gathering useful experimental facts on the properties of the Internet, modelling is also necessary. In the absence of large-scale topological data initial studies focused on simple heuristic models. As a first attempt simple random growth was considered as the main driving process4. Later, when experimental data suggested that we deal with a small-world type network that exhibits a “fat tail” degree distribution, models that used random but preferential growth were considered1.The Internet’s topological structure is in the continuous focus of network and computer scientists6 in order to explain more subtle topological features as well. Models based on first principles, starting from the main question “what really matters when it comes to topology construction?” were also considered more than a decade ago, and these approaches explained also the relative robustness of the Internet against targeted attacks on the hubs8.As more accurate measurements on the topology of the Internet became possible, the preferential attachment driven models were improved10, and location based growth12. Considering the Internet as a spatial network 13, was also helpful in understanding it’s evolution and making connections with important socio-economic parameters14. Topological features of the Internet are correlated with the data transmission speed, and as a result many useful statistical information concerning the topology can be extracted from Round Trip Time (RTT) measurements with “ping” or “traceroute” commands16.More research went in the direction of k-shell decomposition models17, i.e. power law type dependence among relevant variables. In many case scaling is just a first, simpler approach for a more complicated functional dependence, however scaling can have also a deeper meaning suggesting universalities and self-organisation. Proving that a functional dependence that resembles a power-law is indeed a rigorous scaling with deeper consequences is not a trivial task and needs a more elaborated statistical and modelling study. In our approach we will look for scaling laws only as a first, simpler approach to the relevant functional dependences in the observed trends.In studying large complex system like the Internet, a first task is to reveal universally valid statistical features and laws. Statistical physics taught us, that complexity is always accompanied by scaling laws18. The coarse-grained result is that the estimated average travel time scales roughly proportionally with the square root of the travel distance. We argued that this interesting scaling law appears partly due to the topology of the complex network on which mobilities are made and partly due to some socio-economic effects . Our aim here is to prove the existence of a similar dynamical scaling for the RTT on the Internet and understand it in the framework of a simple and realistic network model embedded in the geographical space. The Internet model we are attempting to construct here will be motivated by simple first-principle socio-economic assumptions. The model is able to reproduce statistically the known topological properties that can be measured by large scale “traceroute” experiments15. The present work offers thus contribution in this research field from two direction. First, as an experimental result we present an interesting and universally valid statistical law for the data transmission speed on the Internet. Second, we consider a simple modelling approach to the Internet as a graph, trying to understand in a unified context all stylised facts (including the one reported here) known for the Internet.Recently our group revealed an interesting dynamical scaling between travel time and travel distance , holding on ten orders of spatial magnitudes for human traveling modesThe present study does not aim at ending the debates on the Internet’s topological properties nor at giving solutions related to its’ rapid growth. We only intend to emphasise another stylised fact and a simple explanation for it, that might have had less attention recently and could be of importance in future engineering and optimisation problems for the Internet.15 obtained with “traceroute”. These experiments prove that the average response time (RTT) is increasing with the square root of the distance (measured on geodesic lines) between the considered routers. The Caida dataset offers also information on the topology of the Internet as a graph. The “ping” experiments were conducted around the globe starting the command from two fixed locations in Europe  were considered: one in Budapest (Hungary) and one in Cluj-Napoca (Romania). By using the GPS coordinates we calculated the geodesic distance (d) between the source and target routers.The experiment is based on the Internet Control Message Protocol (ICMP) echo request packet sending and receivingsee Fig. . Their gd, for all pinged router pairs. Using a logarithmic binning method  one gets the averaged trend plotted with black dots on Fig. The destination routers’ ability to respond was tested for weeks on a 24 hour basis. Response times were averaged on the number of times the target was reached. Experiments were conducted between September 2013 and March 2015. On Fig. “Traceroute” operates in a somehow similar manner as “ping” does. In this case the ICMP echo request maps the RTT round trip time, but with the difference that it repeats itself with increasing life time (or TTL - time to live) settings, revealing the intermediate hops as well. This process roughly follows the steps: (1) the sender sends out a sequence of three datagrams to an invalid port address with a TTL set to 1; (2) the first router to receive the packets will send it back with TTL set to 0; (3) the sender now will send the message again with TTL set to 2; (4) the packet will be received back now after two hops; (5…) the process is repeated incrementing TTL with unity until the message reaches its final destination; (n) since the packages were sent to an inexistent port the final destination replies with an ICMP Port Unreachable message.15, which contains summaries of “traceroute” probing with the Paris Traceroute protocol since the year 200715. Our aim was to use recent data, so we limited our study to files only from 2017. The traceroute dataset allows to reveal also the network topology on router level, since we can map all first-order neighbours of the nodes (routers in our case). The most active monitors at that time were from Netherlands and Switzerland. As a consequence, for an easier handling of the large dataset and to reduce the computational challenges with the big amount of data, we selected a restricted geographic area sketched in Fig. For this experiment we used the already available data from the IPv4 Routed/24 Topology Datasetd) scaling, as it is revealed by these experiments. In this case the source for the traceroute experiment were located inside the region shown in Fig. 18 for the “ping” and “traceroute” experiments. Apart of the fact that the data for the traceroute experiments scatter in a larger manner due to a poorer statistics, both data is consistent with a power law trend having the scaling exponent of 1/2.Before focusing on the unveiled graph topology and compare the observed features with the ones given by models, we present here our results for the RTT versus distance . In the simplest approximation 23. An equivalent formulation of this is that the probability for a person in the given city to be “wired” depends on the GDP per capita. In the studied region however, the city’s GDP is roughly proportional with the total population, since we considered a territory where the economic development is rather homogeneous. In Fig. 24, while the data for France is obtained form a discussion forum on the Internet. The linear fit for the cities in Germany has a coefficient of determination Recent results indicate that the “connectivity” of a city usually depends on it’s Gross Domestic Product (GDP)Wi) will determine the weight  and is confirmed in many geographical areas26. For smaller settlements a better statistics is given by the log-normal distribution26, taking into account however that the wired Internet network interconnects mainly the larger cities, we consider that the Tsallis-Pareto distribution is justified in our model. For generating the Tsallis-Pareto distribution of the Wi values we used the implemented generator from the scipy package of Python27. In order to simplify the scaling properties of our model the generated Wi values were renormalized, so that the maximal value to be always one.In such a view the population of the cities  for the giant component. For each parameter set the computer simulation results were averaged over 100 independent realizations of the graph with fixed N and β parameters.Simulations for a relatively large system  31 one can determine the shortest topological path between the nodes. Since the ICMP echo request protocol is programmed to go on routes with the minimal number of hops, we can assume that any message will follow the shortest topological path. In such manner one can study again the scaling for the number hops (H) as a function of the distance between the nodes. Results averaged on several realizations with For the elaborated model one can study the hops number versus geodesic distance. By using the Breadth-first search algorithm implemented in Igraph’s Python package18 when the nontrivial scaling of the human travel time as a function of the geodesic distance was investigated.From comparison between the model and experimental data we conclude that our simple one parameter wiring model implemented in a geometric space is capable of qualitatively reproducing the observed statistical features of the Internet network at router level. In this view the nontrivial scaling for the average travel time of a message as a function of the geodesic distance is the result of the specific network topology. However, the difference between the scaling exponent for the number of hops as a function of distance (≈2/3), and for the scaling exponent of RTT as a function of distance (≈1/2) suggests that a constant average delay on routers cannot account totally for this scaling. Apart of network topology presumably other elements has to be taken into account for building a more realistic model. This is somehow similar with what we have learned in


To estimate of the number of children younger than 5 years who were household contacts of people with tuberculosis and were eligible for tuberculosis preventive treatment in 2017.To estimate the number of eligible children, we obtained national values for the number of notified cases of bacteriologically confirmed pulmonary tuberculosis in 2017, the proportion of the population younger than 5 years in 2017 and average household size from published sources. We obtained global values for the number of active tuberculosis cases per household with an index case and for the prevalence of latent tuberculosis infection among children younger than 5 years who were household contacts of a tuberculosis case through systematic reviews, meta-analysis and Poisson regression models.The estimated number of children younger than 5 years eligible for tuberculosis preventive treatment in 2017 globally was 1.27 million , which corresponded to an estimated global coverage of preventive treatment in children of 23% at best. By country, the estimated number ranged from less than one in the Bahamas, Iceland, Luxembourg and Malta to 350 000 (95% UI: 320 000–380 000) in India. Regionally, the highest estimates were for the World Health Organization (WHO) South-East Asia Region  and the WHO African Region .Tuberculosis preventive treatment in children was underutilized globally in 2017. Treatment should be scaled up to help eliminate the pool of tuberculosis infection and achieve the End TB Strategy targets. Mycobacteria tuberculosis, –The management of latent tuberculosis infection is a critical component of the World Health Organization’s (WHO’s) End TB Strategy. Given that between a quarter and a third of the global population is estimated to be infected with ,A recent survey of policy and practice on latent tuberculosis infection in countries with a low tuberculosis burden and in African countries found that many lacked recording and reporting systems for infection.Consequently, the aim of this study was to use tuberculosis notification data from 2017 to estimate of the number of children younger than 5 years in individual countries who were household contacts of people with pulmonary tuberculosis and who were eligible for tuberculosis preventive treatment. This information should help countries implement and monitor preventive treatment.,Countries with a low tuberculosis burden comprised the 113 high-income or upper-middle-income countries in which the estimated annual incidence of tuberculosis disease in 2015 was fewer than 100 cases per 100 000 population, WHO’s 2015 guidelines on the management of latent tuberculosis infection are intended primarily for these countries.N, was calculated using:n was the number of notified cases of bacteriologically confirmed, pulmonary tuberculosis in the country, C was the average number of active tuberculosis cases per household with an index case, h was the average household size, p was the proportion of the national population that was younger than 5 years, T was the proportion of child household contacts who had active tuberculosis, and L was the prevalence of a confirmed latent tuberculosis infection among child household contacts. For countries with a high tuberculosis burden, L was not included in the calculation because eligibility for tuberculosis preventive treatment did not depend on confirmation of infection. We did not estimate numbers for countries or territories with a population under 300 000.In countries with a high tuberculosis burden, the number of children eligible for tuberculosis preventive treatment was defined as the number younger than 5 years who are household contacts (hereafter referred to as child household contacts) of people with bacteriologically confirmed pulmonary tuberculosis and who do not themselves have active tuberculosis, regardless of whether they have a confirmed tuberculosis infection (in accordance with WHO guidelines on the management of tuberculosis in children).n and p for 2017, country-specific values of h for different years and a global estimate of T. To obtain a global value for L, we updated a recent systematic review and meta-analysis, and to obtain a global value for C, we carried out a new systematic review of the literature from 1 January 2005 to 11 November 2017.For the updated and new systematic reviews: (i) household contacts were defined as people living in the same household or people who satisfied the definition of a household contact in the original publication; (ii) an index case was defined as the first identified case of new or recurrent tuberculosis disease in a person of any age in a specific household or as defined in the original publication; (iii) a person was defined as having a tuberculosis infection if the induration 48 to 72 hours after a tuberculin skin test was 10 mm or greater or, if this information was not available, the person satisfied the definition of a tuberculosis infection in the original publication; and (iv) a prevalent tuberculosis case was defined as a case of active disease that was diagnosed at the baseline visit during the study or within 3 months of diagnosis of the index case.L, we included studies in the updated systematic review that reported the prevalence of tuberculosis infection among child contacts in countries with an annual incidence of tuberculosis under 100 cases per 100 000 population at the time of the study, according to WHO estimates.To obtain a global value for C, we included studies in the new systematic review that reported the number of index tuberculosis cases, the number of household contacts and the number of prevalent active tuberculosis cases among household contacts. We excluded studies if: (i) data on contacts other than household contacts were included; (ii) the number of cases or household contacts was less than 10; (iii) only child contacts were included (this would have led to an underestimate of the number of active tuberculosis cases in the household); or (iv) the study was not published in English  vaccination status and the age of index cases. For the new systematic review, we extracted information on the age and number of index cases and the number of active tuberculosis cases among household contacts. In evaluating the quality of individual studies, we used a checklist modified from an existing tool to assess issues related to contact investigations and tuberculosis infection.L) was conducted using a logistic-normal random-effects model.The meta-analysis of the prevalence of a confirmed latent tuberculosis infection among child household contacts (C) was estimated as follows. For each study, the average number of active tuberculosis cases among contacts in each household was calculated by dividing the number of prevalent active tuberculosis cases among household contacts by the number of index cases, which was assumed to be equal to the number of households. Data were pooled using mixed-effects, Poisson regression models. Subsequently, the average number of tuberculosis cases per household was calculated as the pooled average number of tuberculosis cases among contacts in each household plus one to account for the index case. The heterogeneity of study findings was assessed by visual inspection of forest plots and the effect of the national tuberculosis burden on estimates was assessed in a subgroup analysis. We also conducted a sensitivity analysis by excluding an outlier value for the number of tuberculosis cases per household to assess its influence on the pooled estimate.The average number of active tuberculosis cases per household with an index case  or funnel plots because their utility has not been established in the meta-analyses of proportions obtained from observational studies.L) in countries with a low tuberculosis burden included 17 studies  included 58 studies . Furthermore, excluding the one outlier reduced the average number of cases per household by only 0.002.Our systematic review of the number of active tuberculosis cases per household with an index case . Globally, the estimated number of child contacts eligible for preventive treatment was 1.27 million (95% UI: 1.24 to 1.31). Viewed regionally, the highest estimate was for the WHO South-East Asia Region: 510 000  that was derived from a modelling study in 22 countries with a high tuberculosis burden,Fifth, we assumed that children were judged eligible for tuberculosis preventive treatment according to WHO guidelines.In conclusion, using our estimate of the number of children younger than 5 years eligible for tuberculosis preventive treatment, we calculated that the coverage of preventive treatment in children in 2017 was only 23%. Despite its proven efficacy, tuberculosis preventive treatment is still being underutilized. As the End TB Strategy targets can only be achieved by addressing the pool of tuberculosis infection, urgent action is needed to scale up the implementation of preventive treatment.


In the original article, there was an error. In all mentions of hydroxybutyrate should be gamma (γ), not beta (β): γ-hydroxybutyrate.This correction refers to the main text, to the legend of Figure The authors apologize for this error and state that this does not change the scientific conclusions of the article in any way.The original article has been updated.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


Manufacturer-recommended exposure mA was typically resulting in 3–5 times greater patient doses for calcium score scans compared with other dedicated CT scanners at Nottingham University Hospitals. Image noise was used as a measure of image quality in phantom and patient data. The noise was quantified from the standard deviation in Hounsfield units within regions of interest in the myocardium. Noise in phantom data was found to vary linearly with the inverse square root of the applied mAs. It was assumed that a linear relationship would also apply to patient data but it was predicted that the linear gradient would vary between patients owing to differing patient size and composition. This noise model was used to calculate the exposure mA required to achieve a target noise level of 25 Hounsfield units in the myocardium for each patient. To maintain the image quality for patients of different sizes, three measures of size, weight, body mass index (BMI) and lateral dimension, were all tested for goodness of fit to the noise model. It was found that BMI correlated best with the noise model for small patients, and therefore, BMI was chosen as a measure of patient size for the revised mA table. Using this methodology, doses to small patients were reduced by a factor of four compared with manufacturer-recommended settings. A threshold of 130 Hounsfield units (HU) is used for defining calcified regions.3 The Agatston score is a method of quantifying the degree of calcification whereby the area of the lesion is multiplied by a weighting factor (determined by the CT number) and the scores of all the affected slices are summed.4 The NICE guidelines require classification of patients into three groups; those with a score of 0, who do not need any further tests; those with a score between 1 and 400, who will need to have a CT coronary angiography; and those with a score > 400, who will go on to have conventional angiography. The upper threshold of 400 has been shown to correspond to patients with advanced plaque disease, with 90% specificity for at least one obstructive coronary lesion.5 A score of zero has a high negative-predictive value (95%) for excluding significant coronary artery disease.3The National Institute for Health and Care Excellence (NICE) guidelines for patients with chest pain of recent onset was published in 2010. Its aim was to set a pathway for diagnosing patients who have angina-like symptoms but no history of cardiac disease.6 The first four patients scanned on the Discovery scanner showed good image quality but high radiation doses compared with other dedicated CT scanners in the hospital; dose–length product range 150–250 mGy cm compared with 30–50 mGy cm. Therefore, a calcium scoring service using the Discovery scanner could only be justifiable if the radiation doses could be brought down to a similar level. The purpose of this report is to describe the methodology that was used to achieve this.Owing to an increase in demand for CT coronary angiography and other services in the main CT department of the Nottingham University Hospitals, the possibility of performing calcium scoring on the Discovery NM/CT 670 scanner  in the nuclear medicine department was explored. This is a gamma camera with an 8-slice CT that has the functionality to acquire gated CT. This scanner does not have the capability to perform dose modulation when acquiring gated CT; therefore, manual exposure parameters must be used. The initial acquisition parameters were set to those recommended by the manufacturer, which are documented in their Smartscore user manual.Image quality can be assessed in many ways, both qualitatively and quantitatively. The aim of this study was to look at image noise in the first instance and try and quantify this. Later on in the report, other factors affecting image quality, including temporal resolution and patient motion, are also described.7 The applicability of this methodology to patient data was then tested. Exposure settings must be varied with patient size to maintain image quality; therefore, different measures of patient size  were tested for correlation with the noise model. This builds on the study by McCollough et al8 who used the thorax phantom with additional attenuation rings to model small, medium and large patients. The purpose of their study design was to optimize the exposure parameters for each size of phantom to maintain image noise and then use these settings for patient exposures.The primary method of dose optimization was to use a CT thorax phantom to explore the noise characteristics of the scanner and derive a methodology for adjusting the mA to achieve a target noise level.The calcium-scoring phantom  models the CT attenuation properties of organs in the thorax . This ph3 The X-ray tube rotation time for calcium score acquisitions is scanner specific and unalterable; therefore, the mA was the only parameter that was varied between repeat acquisitions.For valid comparison between the scanners, the acquisition and reconstruction protocols must be similar. Images were acquired in the axial mode using a tube voltage of 120 kVp. Because image noise differs across the field of view (FOV), it was ensured that the phantom was positioned centrally within the bore of the scanner.The thickness and number of slices that each scanner can acquire per rotation is different; the Discovery is an 8-slice scanner with a slice thickness of 2.5 mm and the Definition AS is a 32-slice scanner with a slice thickness of 1.2 mm. It was ensured for the comparison that both datasets were reconstructed as 5 mm slices, as this was the smallest slice thickness common to both scanners. Images were reconstructed using filtered back projection (FBP), as this was the only reconstruction method available on the Discovery scanner.The datasets were loaded into the Hybrid viewer program on a Hermes workstation . Three circular regions of interest (ROIs) of 2 cm diameter were created in the central “heart” region in one of the datasets on one slice. These ROIs were copied to the same slice and the same locations for all the other datasets from that scanner . An aver9 The number of photons is proportional to the tube current, therefore the noise should vary inversely with the square root of the tube current time product. The standard deviation of pixel values in HU is a measure of the noise in the image.8 A plot of the noise characteristics for the two scanners is shown in For a filtered back projection (FBP) reconstruction of the CT data, it is known that the image noise will vary with the inverse square root of the number of photons per pixel.It can be seen in To translate what has been observed with the phantom data to patient data, it was assumed that a linear relationship would also result if a patient were imaged repeatedly at different values of mAs. It would be expected that the gradient of the characteristic noise plot would vary between patients of different size and composition, but that the noise would tend to zero as the mAs increased. To determine the linear equation for each patient, a minimum of two points on the line are needed. It is possible to derive this because the fit can be forced to pass through the intercept. The second point on the line was the measured noise at the known exposure mAs. The gradient of this linear fit was then used to calculate the mA required to achieve the target noise level, given that the tube exposure time per rotation is fixed at 0.52 s.8 Therefore, it was decided that 25 HU would be a reasonable starting point in the optimization process.Looking at a number of clinical calcium score studies obtained on the Definition AS scanner, the noise levels ranged between 25 and 28 HU. For the initial four patients scanned on the GE Discovery scanner, the noise levels ranged from 10 to 21 HU . The typCalcium scoring assessment was made on 25 patients who had been referred from the rapid access chest pain clinic at Nottingham City Hospital over an 8-month period. The referral population consisted of 19 females and 6 males who had a NICE risk score between 10% and 30%. Patients with arrhythmias were excluded from the test. No patients were specifically prescribed rate controlling medication prior to their appointment, although some patients were already on beta blocker medication.It was very important to minimize patient motion during imaging; therefore, a hyperventilation technique was used and the images were acquired during the end-inspiratory breath-hold period. For optimal image quality, the patients were centred in the scanner using laser lights. Depending on the scanner hardware specifications, a patient’s heart rate can also be an issue. It was recommended for the Discovery scanner that the heart rate should be < 75 beats per minute (bpm); therefore, not all patients who were referred could be scanned. On both scanners, images were acquired using prospective gating to minimize patient dose.The image analysis was performed in much the same way as for the phantom data. A 2 cm circular ROI was drawn on four different CT slices within the myocardium for each patient and the standard deviation in HU were recorded. The mean of these measurements was used to determine the average noise. Using the linear fit model, the gradient of the fit was computed for each patient and used to calculate the mA required to produce image noise of 25 HU in the myocardium. The calculated mA to achieve a noise index of 25 HU in the first four patients who were scanned is given in Results in 9 There is discussion in the literature as to how best to categorize patients; the commonly suggested criteria include weight, BMI or lateral dimension. In a study by McCollough et al,8 they found that the lateral patient dimension correlated best with noise. The aim of this study, therefore, was to test which of these measures of patient size best fitted the noise model for our patient population. The “computed mA” was plotted against weight, lateral width  and BMI (As patients have different attenuating properties owing to size and composition, the mA will need to be varied for patients of different sizes to obtain the same target noise level of 25 HU. and BMI –6. An exA total of 24 patients were scanned on the Discovery scanner using the revised mA table. The resulting image noise distributions are displayed as box and whisker plots for each mA setting in Although only a small number of patients were scanned in each category, 10 patients at 45 mA, 6 at 110mA and 8 at 160 mA, overall there was good agreement with the target of 25 HU. For the “small” patient category, 7 of 10 patients achieved image noise ≤ 25 HU. The maximum noise measured in the small category was 40 HU for one patient. If the exponential fit equation in The aim of this study has been to lower the patient doses for performing calcium scoring on the GE Discovery D670 scanner. This study has made an assumption that the linear noise relationship seen with phantom data when noise is plotted against the inverse square root of the mAs would also be applicable to the patient data. It has been shown in 10The work described in this study has focused on quantification of image noise as the measure of image quality. The quantification of image noise was simplified by the use of FBP reconstruction, which allowed the standard deviation of HU in ROIs drawn within the myocardium to be used as a measure of noise. These results cannot be used for direct comparison with iterative reconstructions of the same data because noise levels for iterative reconstructions follow a non-linear relationship.11 Fortunately, in the case of calcium scoring studies, the heart should usually be positioned close to the centre of the FOV; which minimizes additional noise variations due to flux field inhomogeneity.Unlike most assessments of image quality, where features in the whole cross-section of a patient need to be assessed, the specific nature of the application of CT for calcium scoring also helped simplify the optimization process. It is known that the radiation flux homogeneity, and hence noise, in the central region of the CT FOV differs from that at the edges, reportedly by as much as 50%.Image noise is not the only factor determining image quality for calcium scoring scans, motion due to patient breathing, arrhythmias and heart rate also have a significant impact. Scanner hardware specifications and reconstruction software will limit what can be reasonably achieved clinically and differ significantly between the two scanners described in this work.The time resolution of the CT scanner limits the maximum heart rates that can be imaged without suffering from significant motion artefacts due to cardiac movement. 13 The time resolution of the GE scanner is therefore approximately one-half that of the Definition AS scanner. The effect of the differing time resolutions is shown in Time resolution is primarily determined by the X-ray tube rotation time. The minimum amount of data required to reconstruct a CT image for calcium scoring is 180º + the angle of the X-ray beam; this takes 0.238 s for the Definition AS scanner and 0.522 s for the Discovery scanner.Motion due to breathing can also be a problem. This is more likely for patients scanned on the Discovery scanner, as the scan typically takes 20 s compared with 5 s on the Definition AS scanner. The different durations are due to the X-ray tube rotation time and slice coverage per bed position. Caution must therefore be applied when interpreting images that have been compromised by motion.15 Patients in this study were not prescribed rate controlling medications before their appointment, but this may be considered in the future to help reduce issues with the heart rate.As well as image artefacts, vessel motion can also affect the quantification of calcium scores owing to the partial volume effect.It should not be assumend that manufacturer-recommended exposure settings are optimal.A phantom can be used to investigate characteristic noise variations between scanners.Motion due to patient breathing, arrhythmias and heart rate significantly impact on image quality. Scanner hardware limitations will affect the likelihood of these.None required.


In this paper, we compare different formulations of the multi-depot fleet size and mix vehicle routing problem (MDFSMVRP). This problem extends the multi-depot vehicle routing problem and the fleet size and mix vehicle routing problem, two logistics problems that have been extensively studied for many decades. This difficult vehicle routing problem combines complex assignment and routing decisions under the objective of minimizing fixed vehicle costs and variable routing costs. We first propose five distinct formulations to model the MDFSMVRP. We introduce a three-index formulation with an explicit vehicle index and a two-index formulation in which only vehicle types are identified. Other formulations are obtained by defining aggregated and disaggregated loading variables. The last formulation makes use of capacity-indexed variables. For each formulation, we summarize known and propose new valid inequalities, including symmetry breaking, lexicographic ordering, routing, and rounded capacity cuts. We then implement branch-and-cut and branch-and-bound algorithms for these formulations, and we fed them into a general purpose solver. We compare the bounds provided by the formulations on a commonly used set of instances in the MDFSMVRP literature, containing up to nine depots and 360 customers, and on newly generated instances. Our in-depth analysis of the five formulations shows which formulations tend to perform better on each type of instance. Moreover, our results have considerably improved available lower bounds on all instances and significantly improved quality of upper bounds that can be obtained by means of currently available methods. Distribution problems are central to the performance of many industries. The area of transportation has been widely studied, notably the vehicle routing problem (VRP) . This problem is a direct generalization of the classical VRP by considering multiple depots and different types of vehicles to serve a set of customers with known demands. It combines three decisions simultaneously: selecting the number of vehicles of each type, planning vehicle routes and assigning routes to depots. Each vehicle is characterized by a fixed and a variable cost proportional to the traveled distance. The number of available vehicles of each type is assumed to be unlimited. The simultaneous optimization of the best fleet composition, the best vehicle routes and the depot choice substantiates the challenges of this problem. The MDFSMVRP consists of designing a set of vehicle routes, each starting and ending at the same depot, visiting each customer exactly once, and respecting the capacity of the vehicles. The objective is to minimize the total fixed and variable routing costs.The literature dealing explicitly with the MDFSMVRP is not well furnished as the problem includes several prominent problems as special cases, such as the multi-depot VRP (MDVRP) and the FSMVRP. We are aware of four works focusing on the MDFSMVRP. A seminal work on this specific variant is due to Salhi and Sari . The autMany papers and book chapters have been devoted to study separately the two straightforward reductions of the MDFSMVRP. The primary decision related to the fleet consists to determine the optimal size of the fleet, which may be limited for the heterogeneous fleet vehicle routing problem (HFVRP) or unlimited for the FSMVRP. Dealing with the fleet composition goes back to the seminal papers by Gheysens et al.  and GoldThe literature for the MDVRP is also rich. This problem first appeared in the literature in the works of Kulkami and Bhave  and CarpThe MDFSMVRP is an NP-hard combinatorial problem since the VRP is NP-hard. Several authors explicitly outline the difficulty of solving to optimality either the FSMVRP instances or the MDVRP instances, or even finding tight bounds  is not allowed including loop arcs between customers n copies of each vehicle type k, with k.The MDFSMVRP is formally defined on a directed graph A solution to the problem must determine routes that minimize the total costs such that each route must start and end at the same depot, each customer is visited exactly once, and the total demand of each route does not exceed the capacity of the selected vehicle. Also, when solving this problem, the vehicle fleet composition will be found for all depots as well as for each depot. An illustration of this problem is shown in Fig. We now provide five different formulations for the MDFSMVRP. In Sect. i, j) is traversed by vehicle t housed at depot d, and equal to two for a round trip to customer j. Binary variables i is visited by vehicle t from depot d. Note that, as in Vidal et al. t housed straints  state thstraints , Coelho straints , Coelho straints , and Lahstraints .13\documt of depot d if this vehicle is used. We also note that constraints  if customer i is not visited by vehicle t of depot d. Constraints  if customer j is not visited by vehicle t housed at depot d. Constraints 23) are ln.Formulation F1 has the drawback that the number of variables and constraints increases when the number of vehicles increases. These variables are dependent on the number of customers We now propose a formulation with implicit vehicle assignment as proposed in Laporte , and Totk instead of t which refers to vehicle types instead of individual vehicles. This has the advantage of having one type of variable per vehicle type, instead of creating one variable per vehicle of each type. For the sake of briefness, we do not restate the whole definition of the variables and constraints (in this section and for the remainder of this paper), and refer to the ones already defined in Sect. t by parameter k while defining the variables and the sets. This implicit vehicle index formulation can then be defined as follows:n. F2 is much more compact than F1 since it depends on the number of vehicle types.This formulation uses the same type of variables defined in Sect. bject to  and to25straints  and 8)  k instean.Several of the valid inequalities previously defined remain valid, namely –21). Al. Al21). Vehicle symmetry breaking constraints and lexicographic ordering constraints no longer hold for this formulation because they require distinguishing between vehicle index and not vehicle types.A main disadvantage of model F2 presented in Sect. nd Trick  highlighi, j), i.e., after visiting node i and before visiting node j. Note that the loading variables could be defined only for the asymmetric version of the problem since the complete graph is considered. In this graph, a vehicle must return to the depot empty. We also use the same four-index binary variables i, j) belongs to the arc set k housed at depot d is used in the solution, and zero otherwise. In what follows, we restate all the constraints of the problem dealing with routing variables i, j), i.e., after visiting node i the load on arc  plus the demand of node i cannot exceed the capacity of the vehicle used. Constraints  must be at least equal to the demand of node i.Because of the way new variables i et al. . Constrai et al.  impose astraints  and 39)\documentstraints  have intstraints . We adapstraints –42) to  to \docustraints  represenstraints  bound thi, j). Formulation F4 has more continuous variables and constraints compared to F3.In this section, we propose a more detailed formulation based on F3 for the MDFSMVRP, referred to as F4. The motivation is to carry information related to the vehicle type on each arc by disaggregating the loading variables of Yaman  for the of Yaman  subject entclass1pt{minimaof Yaman –30),  an an\documstraints –33) of  of \docuModel F4 can also be strengthened by –44), wh, wh44), In this section, we make use of a novel formulation to model VRPs, referred to as capacity-indexed formulation. This type of formulation has only appeared a few times for basic variants of VRPs. A seminal paper proposing a capacity-indexed formulation for the time-dependent traveling salesman problem is due to Picard and Queyranne . Godinhok housed at depot d traverses arc  with a load of q units. This variable indicates the load of a given vehicle type housed at a given depot on a given arc, unlike the commodity flow formulations (F3 and F4) that require the definition of continuous variables to convey similar information. Vehicles returning to the depot must have a load q equal to zero and a vehicle k traversing arc  must not carry a load q lower that the demand of node j. This model can then be formulated as follows:k leaves a depot d with a load q then it must return to this depot with a load equal to 0. The connectivity of the solution and the vehicle capacity requirements are ensured due to constraints  with an irrelevant load, i.e., after visiting a node i, the vehicle should not carry a load between k, k traversing arc  enters node i, then the load delivered to node i must be exactly i, j) related to vehicle k and linking two customers i and j, i.e., \documentstraints . They imstraints  consistsstraints –61) are are\docuj, i.e.,  holds, td, i.e.,  holds. EA large number of formulations have been proposed for the VRP. However, a much smaller number of papers have discussed the theoretical formulations of these models, comparing their structures and dominance  constraints of type (This latter disadvantage may be overcome by using a more compact model replacing binary routing variables by binary ones indicating the flow on each arc Gouveia . By doin of type  by O(n)  of type . This is of type  have per of type  and binaIn Sect. The formulations presented in Sects. q cannot be obtained by any combination of demands. These variables can be generated and fed to the solver, which will set them to zero in any feasible solution. If one can identify these variables beforehand, it is possible to set them to zero and remove then from the model at a preprocessing phase. Thus, one can  decrease the size of the model and the memory usage by preprocessing the model and the instance a priori, identifying the subset of variables that should not be generated. We have then implemented a subset sum algorithm to identify all possible values of q from 1 to Finally, the model presented in Sect. In this section we provide details on the implementation, benchmark instances, and describe the computational experiments we have performed. Implementation and hardware information is provided in Sect. All the formulations described in Sect. We have run all instances described in the next section using all models described in Sect. In order to compare the performance of our models and algorithms, we have used a set of 14 test instances proposed by Salhi and Sari  for the These instances contain between 50 and 360 customers, and between two and nine depots. There are five vehicle types, i.e., We have also generated ten smaller instances to better evaluate the performance of the different formulations in terms of lower and upper bounds, and of running times. These instances were created by randomly selecting subsets of customers from the smaller instances of Salhi and Sari , namely In this section, we describe the results of computational experiments carried out in order to assess the performance of the proposed models and algorithms. Table q that can be attained, which can significantly reduce its size. For the existing instances described in Table As stated in Sect. Solving the linear programming relaxation (LR) can be quite useful as it provides a bound on the optimal value of the integer programs, and it highlights the difference between the formulations. The first experiment we conduct in this section consists of solving the LRs of the five formulations for both data sets with a time limit of 2 h. We include all the valid inequalities presented in the previous sections. Table We now present the computational results of the solutions we have obtained when applying branch-and-bound and branch-and-cut for the five proposed formulations. Table A deeper analysis of the formulations highlights a remarkable improvement over all the lower bounds and the number of solved instances compared to the LRs results. The results clearly show that formulation F1 is outperformed by all the other formulations, even on small instances. The largest instance size that can be solved by formulation F1 is 4-5-160. Model F1 could identify a feasible solution only for three (out of 14) instances, whereas formulation F2 is able to solve all the instances of the two testbeds. This implies that the compact formulation, reducing the number of generated variables, has a positive impact on the model performance. Model F2 provides tighter bounds compared to F1 but is still uncompetitive compared to the other formulations. The results of Table These results point out again that formulations F3, F4 and F5 are the most suitable among the five proposed to solve small-, medium-, and large-size instances of the MDFSMVRP. Particularly, if the aim is to provide good upper bounds to compare with an heuristic, then it would be better to use formulation F3 on large instances and formulation F5 on small instances. Similarly, if major problems of running out of memory occur, one should use formulation F5 as fewer variables will be generated, especially with a regular distribution of customers demands. Finally, if the goal is to get a good trade-off between solution quality and running time, one should choose formulation F4 as disaggregating continuous variables is likely improving the model performance.A transversal analysis over Tables Best gap (%). The results in Table As it was mentioned, the literature devoted to the MDFSMVRP is rather scarce and the published works on this specific variant are focused on heuristic methods. We are only aware of the exact bounds recently obtained by the 3-h CPLEX execution of Salhi et al. . The perWe now briefly analyze the effect of the valid inequalities proposed for each model. We study the effect of valid inequalities in each model on the gap. We have decided not to study the impact of each valid constraint proposed in each model because this would lead to a combinatorial and unmanageable comparison between valid inequalities, which is not the focus of this paper. We have compared the average gaps between two configurations of each formulation, without and with valid inequalities, on each testbed, with the maximum computing time limit of 3 h. Table We have also reported the effect of some families of valid inequalities, and the average gap yielded by models F3, F4, and F5. Specifically, we have assessed the performance of routing constraints –42) whi whi42) wIn this paper we have modeled and solved the MDFSMVP. We have presented five different formulations for this difficult distribution problem. The first one is a three-index VRP formulation with an explicit vehicle index, and the second one is more compact, in which individual vehicles are not explicitly identified. The third and the fourth models are commodity flow formulations without a vehicle index. They are based on loading variables to model capacity and connectivity requirements. The fifth and last model is a capacity-indexed formulation, which is a based more compact single commodity flow. We have also provided a survey on how these formulations relate to each other from a theoretical perspective. We have proposed several valid inequalities to strengthen the formulations and we have solved them by branch-and-cut and by branch-and-bound.We compared the bounds of these formulations on existing instances and on newly generated ones. The results show that the commodity flow formulations and the capacity-indexed formulation provide better bounds. Our results also show that compact formulations represent a very promising research avenue. On classical benchmark instances our methods could improve all previous lower bounds, and we have obtained the best upper bounds and gaps when compared to another exact method from the literature.


The experimental and computational studies of the hyperfine coupling constant of Mu suggest that it is formed in the interlayer space of talc and that its electronic structure is extremely changed due to confinement. All these results imply that the chemistry could be strongly affected by confinement in the interlayer space of clays.The purpose of the present work was to study how chemical reactions and the electronic structure of atoms are affected by confinement at the sub-nanometer scale. To reach this goal, we studied the H atom in talc, a layered clay mineral. Talc is a highly 2D-confining material with the width of its interlayer space close to angstrom. We investigated talc with a particle accelerator-based spectroscopic method that uses elementary particles. This technique generates an exotic atom, muonium (Mu), which can be considered as an isotope of the H atom. Moreover, the technique allows us to probe a single atom (H atom) at any time and explore the effects of the layered clay on a single ion (proton) or atom. The cation/electron recombination happens in two time windows: one faster than a nanosecond and the other one at longer than microseconds. This result suggests that two types of electron transfer processes take place in these clay minerals. Calculations demonstrated that the interlayer space acts as a catalytic surface and is the primary location of cation/electron recombination in talc. Moreover, the studies of the temperature dependence of Mu decay rates, due to the formation of the surrogate of H The more confined the nanostructure, the larger the expected effect of the confinement on electronic structure and chemical dynamics17. The kinetics of elementary reactions is the best probe of the effects of confinement on chemical dynamics; the most sensitive probe of confinement effects on electronic structure is the one that measures the electron density. The isotropic hyperfine coupling constant (HFCC) is very efficient in this regard20. It measures the strength of the coupling between unpaired electrons with the nuclear magnetic moment. HFCC is proportional to the electron spin density at the nuclei26.Confinement within nanostructures can affect the chemistry of atoms and moleculesIn this work, we use HFCC to characterize free radicals. After its characterization, the electron transfer and reaction dynamics, which lead to free radical formation or decay, are reported in a confined environment. We also determine how the electronic structure changes under sub-nanometer confinement, which is a particularly interesting scale. In particular, we address some unanswered questions related to confinement at its smallest level: How are chemical reactions affected by the combination of surface and confinement effects at the angstrom scale? How does the electronic structure change under angstrom-scale confinement? What is the effect of extreme confinement on the reactivity induced by ionizing radiation?32; as such, determining the behavior of H atom in various environments is crucial in the development of dimensionally constrained systems such as heterogeneous catalysts31, nanometer-scale semiconductors32, and hydrogen storage devices29.For this purpose, a good starting point is to study the effects of confinement on the H atom, which is the most fundamental entity in chemistry. Indeed, investigation of H atom and its isotopes has played a fundamental role in the evolution of modern sciencelayered nano- and sub-nano- structures33. They are able to confine molecules and have the potential to provide catalytic surfaces at the same time33. The structure of clays also leads to a large surface area, as well as swelling, and ion exchangeability properties34. Finally, the compositional and structural features of layered clay minerals enable them to be modified by a large variety of polymers, organic and biological molecules35.Clay is an excellent medium to study the effect of confinement on chemical reaction channels and on the electronic properties of the H atom. Indeed, it provides natural abundant two-dimensional 4O10Mg3(OH)2). It is a phyllosilicate with a layered structure  with magnesium atoms is sandwiched between two tetrahedral (T) sheets of silica. Each TOT layer is separated by an interlayer space around 3 Å wide . This empty space36 provides a confined environment to do chemistry. Moreover, as commercial materials, talc and clays play important roles in various applications such as catalysts in chemical industry38 and waste management in the nuclear industry39.We will focus here on talc .There are two types of surfaces in talc . Basal ones are the surfaces limiting the interlayer space and the most abundant ones, while the edges, created by the breakage of the Si–O or Mg–O bonds, are the other surfaces not in the interlayer space44. This has indeed been shown for talc36. The reaction e− + MgOH → MgO− + H is an electron transfer reaction that was reported in talc36. This reaction followed by dimerization of H atoms accounts for the H2 production in talc under irradiation36. Studying electron transfer reaction dynamics, H atom chemical dynamics and determining the electronic structures of H atom in clays, over a wide temperature range is a demanding task. It requires a technique that: i) can be used at any temperature; ii) is not limited by optical detection (as it is impossible for clays); iii) is time-resolved to be able to detect short-lived species; and iv) can provide the electronic structure of the free radicals. The only way to fulfill all above criteria is to use the hydrogen surrogate, muonium, and positive muon-based spectroscopic techniques as the positive muon (µ+)  is an exotic particle behaving as a light proton (H+)44.Electron transfer following irradiation can be used to generate H atoms or their isotopes in materials+e−), obtained after capture of an electron by a muon, has one-ninth of the mass of H with almost the same Bohr radius (0.53 Å) and ionization energy (13.539 eV for Mu and 13.598 eV for H)20. Because Mu is electronically equivalent to an H atom, it can be used as a surrogate of the latter when it cannot be studied directly45. Examples are H atom in ionic liquids19, in ionic solids28 and in semiconductors47. This latter case is in particular important for talc, since the band gap of talc is calculated to be 5.3 eV, proving that it is a semiconductor48. Since Mu can serve as a surrogate of H atom52, it can also be added to molecules to form free radicals25. Among many works on use of Mu as surrogate of H atom, those that measured the isotropic HFCC are most relevant to our work in this paper. For Mu in most solids, such as diamond50, C60 fullerenes (and K4C60 and K6C60)53 and sulfur52, the lowest energy site is in the center of “cages” made by surrounding nuclei in the lattice. Also in all above-mentioned studies of Mu in solids and fluids, Mu HFCC is smaller than the Mu HFCC in vacuum with smallest values in Si and Ge . When Mu is in a large enough cage, (e.g. in C60 where it has ~0.71 nm diameter) the decrease in HFCC is rather small due to weak Van der Waals interactions between Mu and the cage53. However in smaller three-dimensional cages in semiconductors (like in Si and Ge) the HFCCs are much smaller 50. Also in all above-mentioned studies of Mu in solids or fluids, HFCC mostly decreases with temperature. The calculated HFCC in sulfur is in particular interesting52. While Mu HFCC in the center of the cage  is 4013 MHz , changing the distance from the center by 50 pm strongly affected the HFCC value (4013 MHz versus +50 pm/1654 MHz and −50 pm/2339 MHz) but did not seem to significantly affect the energetics. This suggests there should be a very large negative temperature dependence of HFCC. The distance between the sulfur atoms is 400 pm in their model which is larger than interstitial distances in Si and Ge but smaller than the space in C60.Muonium (Mu ≡ μd001 (measured by X Ray Diffraction), for talc is 9.43 ± 0.02 Å  atom.The principle of the muon-based technique used in this work is described in the Methods section and illustrated in Fig. +)62 and also if it binds to a lone pair . The fraction of these muons represents the diamagnetic fraction. The oscillation of spin polarization of muons coupled to an unpaired electron leads to a faster spin precession25, depending on HFCC  with T0 = 122 ± 8 K and τ is in µs. As can be seen from the small error bars, the uncertainty on the relaxation rates is very small. Figures The decay rates of the diamagnetic fraction as a function of temperature in talc from time domain fits of the spectra over roughly 6 µs are displayed in Fig. +) at the microsecond time scale. The decay rates suggest that the diamagnetic fraction is mostly due to positive muons or to positive muons bound to oxygen lone pairs. Indeed, a molecular species like MuOH would have a slower reaction rate23. The spin relaxation of positive muons in a diamagnetic solid material is typically due to dipolar interactions between positive muons and dipoles. This could not be a potential mechanism for the observed decay rates, because such relaxation rates are usually an order of magnitude smaller than what is observed here67. Furthermore, the only spin-active nuclei with significant abundance in synthetic talc are protons, which are in MgOH sites in the layers 54.The fact that we observe this electron/cation (muon) recombination (or interaction due to polaron generation) rates at the microsecond time scale suggests the existence of electron transfer processes with much slower rate than the ultrafast electron transfer leading to Mu formation, which is more than four orders of magnitude faster .Electron transfer processes in clay minerals are important from an applied point of view, since clays can serve as host materials for photochemical reactionsThis implies that there are two types of electrons in the layered nanostructure of talc. Note that this is formed here by radiation but this can be extended more generally to all cases in chemistry or material technologies where free electrons are formed. The ultrafast electron transfer that has been observed causing Mu formation /electron recombination rate, the location of the cation (muon) must be understood. Calculations were performed in order to follow μIn our calculations, the sum of the ionic and Hartree potentials for the electrons ranges from large negative values close to the nuclei, to a maximum of 0.87 Ry. From Fig. Figure 73. The electrons that are not close enough and do not form Mu can cause the relaxation of the diamagnetic signal described above . Note that the released electrons have a greater energy than the trapped electrons, so their wavefunction will be delocalized, making the electron capture more favorable. This should however be at energies close to thermal energyk [e−], k being the rate constant and [e−] the electron concentration); (iii) the muon/electron capture rate increases when the relative kinetic energy of them is lowered as shown by recent theoretical quantum electrodynamics predictions73; (iv) the electron capture is more favorable when the lattice is closer to the equilibrium structure. At higher temperatures, many lattice degrees of freedom are excited and this could lead to an unfavorable condition for electron capture.Clearly, this capture rate has a non-Arrhenius and indeed an inverse Arrhenius behavior. This could be due to following reasons: (i) there would be more slow electrons in the interlayer at lower temperatures, due to more radiation-induced ionization at lower temperatures; (ii) two different electron transfer reactions could compete, i.e. electron capture by the muon and by other species (within the layers), such as MgOH groups  + 12.4 exp (−T2/T) with T1 = 1984 K and T2 = 33 K. 1/τ is expressed in µs−1 and the temperatures (T) is in K.Figure 19 between these electrons and the electron in Mu leads to spin relaxation. The addition reaction (of electrons to H (Mu)) could, in principle, lead to hydride ion (H−) formation as well58. (ii) The reaction of Mu with holes in talc. Studies of ionizing radiation of talc have proven that the radiation-induced holes are located on oxygen atoms (linked to magnesium or silicon atoms), as shown by ESR experiments36. (iii) The Mu + H reaction forming MuH, which is equivalent to the H2 formation under ionizing irradiation36.The temperature-dependent decay is, in principle, due to one of the following three mechanisms. (i) The Mu atom encounter electrons in the clay. The spin exchange2 that was not accounted for by stable H atom concentration36. This has been associated with an unobservable H + H reaction in talc36. Furthermore, pulse radiolysis experiments performed in nanoporous silica have attributed most of the decay of solvated electron in the ns-µs timescale range to the e− + SiOH → SiO− + H reaction74. This suggests that the reaction with Mu, which is happening in the same timescale, occurs with H atoms and not with electrons, as electrons will react preferentially with MgOH groups in the present case.This latter mechanism is the most likely one for the following reasons: i) holes are not mobile, yet they have the same concentration as electrons, and electrons and H usually outcompete holes to participate in reactions with Mu; ii) a previous work on the interaction of ionizing radiation with talc has shown a large concentration of H36. Therefore, the decay rates we report here are due to diffusion of H and Mu towards each other to form MuH. Our results show that there is a diffusional barrier around 18 kJ.mol−1, but at low temperatures, the transport takes place via quantum diffusion with an activation barrier of 0.3 kJ mol−1. It is expected that the temperature where quantum diffusion starts would be lower for H diffusion due to its larger mass as compared to Mu. This quantum tunneling occurs for a distance close to 1 to 3 Å (between Mu close to the center of interlayer space and H close to MgO). Our results therefore suggest that the relaxation mechanism of the muon in Mu is due to Mu and H diffusion . This implies that the clay material could be considered as a quantum material at low temperatures, with a much larger temperature expected for electron quantum transport and a lower temperature expected for hydrogen atom quantum transport. This is to our knowledge the first report of chemical dynamics in the interlayer space of clays, and the first report of quantum transport and quantum effects on chemical reactions in talc.It is known that H atoms are generated by radiolysis of MgOH groups in the layersD; Mu fraction, PMu and lost fraction23 which is PL = 1 − PMu − PD) is displayed in Fig. The temperature dependence of different fractions of muoniated species , it is possible that the increase in the diamagnetic fraction with temperature is linked to the fact that this population decays slower when temperature increases, and with an almost constant rate for temperatures below 50 K.The diamagnetic fraction increases in the 0–50 K temperature range and then remains constant. The lost fraction is due to the reactions of electrons and H atoms in the radiation track within clays with Mu in 0.1 to 10 ns. The lost fraction decreases with temperature. Considering that the trend depicted in Fig. This similar temperature dependence could be a coincidence, considering that the two mechanisms involved have more than three orders of magnitude difference in time scale. Considering however that one potential mechanism behind the temperature dependence shown in Fig. The measured HFCC (in this section) is used with our computational data to further understand the nature of the observed Mu (H) atom and of its precursor in talc.78, the thickness of the interlayer space may be still too large to account for this interpretation. Therefore we will compare in the following our results with those obtained assuming a confined but three-dimensional space.The following trends were observed  is to our knowledge the largest temperature dependence reported for Mu (H). Indeed, in water, the HFCC value increases with temperature by about 1% per 250 K21. The decrease we measure here is equivalent to a 30% decrease in electron density at the nucleus per 250 K. This corresponds to an electron density transfer to the atoms which are close in the clay mineral. Both the temperature dependence and the large value at 3 K are due to the highly confined environment of the Mu (H) atom in the interlayer space. This is also consistent with the observation of the kinetics data discussed above. Therefore, the highly confined environment affects both the electronic structure and the chemical dynamics, which is of crucial importance in the field of the catalytic applications of clays.The HFCC value of Mu globally decreases with temperature Fig. . It rangTo understand the nature of the Mu (H) atom site and the negative temperature dependence of its HFCC value, calculations were undertaken at the same level as the electrostatic calculations described above. The corresponding results are displayed in Fig. The calculations suggest that two sites are possible for Mu (H). Position A Fig.  is in th80 while different with the cases where Mu was in a less confined space53. Concerning the larger HFCC value in site B than in vacuum, it is difficult to give a definitive answer. One probable explanation is that in this site the muon is on top of the –OH group, where there is almost no bonding with the neighboring atoms  which results in an effective decrease of the total spin density around the muon atom. A further effect that can explain the decrease of the HFCC value due to the decrease of the spin density at the muon site is the deformation of the spin density due to the electrostatic attraction of the positive Si atom below. This is similar to the observed Mu HFCC in Si and GeTo check the energies of Mu at the two sites and the temperature dependence of the HFCC, the position of Mu was shifted along the three directions. The evolution of the energy and of the HFCC values as a function of the reduced coordinates  is displayed in Fig. 8 s−1. With such a precursor and rate of Mu formation, the ratios of the amplitude of the higher frequency to the amplitude of the lower frequency (see Supplementary Information) decrease drastically when going from ~100 G to ~200 G, to the degree that the higher frequency signal would not be observed, and the amplitudes would be small in general82. Results from calculations have revealed some clues for this precursor . The transformation from C to Mu at site B occurs with a rate around 102 formation mechanism is thermally activated above 25 K, while below 25 K it is due to quantum diffusion. This suggests that clay could be considered as a quantum material at low temperatures.We have shown that a strong confinement (sub-nm), easily available in 2D-confining layered clay minerals such as talc, could have extreme effects on chemical reactions and on the electronic structure of free radicals. We have also evidenced that at least two types of electrons, with different characteristic time constants differing by at least three orders of magnitude, are generated in talc. This induces different radiation damage types in clays exposed to ionizing radiation, which is an important knowledge for the deep nuclear waste storage where clays constitute the geological barrier. Moreover, we have shown that the HWe have also evidenced that cations are preferentially located in regions with a large negative electrostatic potential, i.e. in the interlayer space. The reaction of cations with free electrons first leads to neutral chemical species located close to the middle of interlayer. This is however a local minimum on the potential energy surface. The atom (within less than 0.1 ns) then moves to the global minimum, which is close to the O atom at the border of the interlayer space (via electron transfer to the hole). This leads to the formation of a radical with a high HFCC value, in consistency with the existence of hydrogen in the interlayer space of talc. Due to extreme confinement, the HFCC value has a large temperature dependence. The interlayer space thus provides electrostatic confinement, which in turn induces large changes to the electronic structure of the atom (molecule) present.20.Comparing our data in this work with previous studies, we discovered that the effects of confinement are multifaceted. One effect is on electronic structure of an atom or molecule in confined media. The effect of the confinement on the electronic structure of the Mu at sites A and B is reflected in the iso-surfaces of the spin densities Fig.  and the Site A is in the middle of the interlayer space and the electron transfer to the neighboring O atoms decreases its HFCC value (3639 MHz) significantly with respect to the vacuum value. Site B is close to the boundary of the interlayer space and the total spin density is almost entirely localized around the muon. The six neighboring O atoms repel the electronic density localizing further the spin density and increasing the HFCC value. This can be the reason for the large HFCC observed experimentally at lowest temperatures.52. It is expected that the temperature dependence would also increase by making the potential energy surface and variation of HFCC with distance , become faster with decrease in interlayer space (increase in confinement) however with a drastic change to confinement we would also expect the changes to the atomic structures of the lattice. This means we would expect different effects that may cancel each other on the electronic structure and reaction rates. Moreover, to understand the kinetic controlled processes under confinement the barriers of different transformations should be calculated as a function of confinement. This certainly requires a long-term investigation of both theoretical and experimental effects of confinement to explore the multifaceted confinement effects.The other effect of confinement is on the richness of chemistry, such as existence of different Mu sites . Most probably, by decreasing the interlayer distance these sites would collapse into one site (one site would disappear). This will decrease the richness of chemistry inside the confined environment. Although in the first glance we also expect the reactions of electrons and protons and reactions of H and Mu , in organic synthesis and in environmental applications.2 to value-added products. In addition, we showed that muon methods provide a powerful tool for the study of confinement effects and of reactivity under confinement. Their power lies in their ability to provide efficient and relevant probes of confinement in chemistry. These probes are parameters that are proportional to the electronic structure of free radicals on different nuclei and also to reaction rates of elementary chemical reactions at a wide range of temperatures, from ultra-low temperatures where quantum effects are manifested, to temperatures relevant for industrial applications. Studies such as the present one play a fundamental role in the evolution of dimensionally constrained interfaces, modern catalysis, semiconductors, electron transfer processes, quantum materials chemistry and energy technologies.Confined layered systems such as clay minerals have then the potential to facilitate a rich chemistry, including the transformation of CO83. Characterization includes infrared spectroscopy (IR), thermogravimetric analysis (TGA), and x-ray diffraction (XRD) presented in Supplementary Information Figs Synthetic talc was synthesized by hydrothermal synthesis from gels of appropriate compositions prepared according to the conventional gelling method described previously−1 energy range with a 4 cm−1 resolution from 100 scans. A pure KBr pellet was used for the reference.In order to record infrared (IR) spectra, 1% of sample was pelletized in KBr and then analyzed by a Bruker Tensor 27 FT-IR spectrophotometer. All the spectra were collected in transmission mode in the 4000–370 cm−1 under a dinitrogen flux of 50 mL min−1 in order to reach a final temperature of 900 °C and then brought back to room temperature. Data were analyzed using the STARe software.Thermogravimetric Analysis (TGA) experiments were performed with a Mettler-Toledo TGA/DSC 1 analyzer. An alumina crucible of 70 µL containing approximately 20 mg of sample was heated at a heat flow of 10 °C.minCuKα = 1.541 Å, 40 kV/40 mA). The diffracted beam was collected by a position sensitive Vantek detector.Powder X-ray patterns were recorded on a Bruker D8 Advance diffractometer equipped with a grazing parabolic Göbel mirror and a Cu emitter  at the M20 muon channel of TRIUMF laboratory in Vancouver, Canada, and the muoniated products were studied in real time. Samples of talc were subjected to several degassing cycles to remove oxygen (pumping/flushing with nitrogen) and stored in an air-tight container for transportation to the facility. The samples were subsequently stored in an in-house made mobile glove box until the day of the measurements. They were then placed in an aluminized Mylar cell that was sealed with silver-foil tape, where it was subsequently transferred to a Horizontal Gas Flow (HGF) Cryostat (suitable for temperatures from 2.8 to 330 K) compatible with the LAMPF spectrometer. This spectrometer uses a Helmholtz coil which provides a maximum field of 4000 G and is suitable for transverse and longitudinal field studies. The muon beam arises from pion decay at rest and possesses ~100% spin-polarization. Thermalization begins as the muon interacts with the material and eventually reaches thermal equilibrium towards the end of the radiation track.The spin polarization of the positive muons  is almost 100%. This and the preferential asymmetric emission of high energy positrons (that can be detected) along the direction of the muon spin at the time of decay Fig.  allowed + is initially polarized opposite to the direction of its momentum . Before a muon interacts with the sample, it passes through a counter that sends an electronic signal to a time-digital-converter (TDC) and a counter is incremented, starting a “clock”  signals) using the following equation:−1). A fraction of muons capture electrons to form an atom considered as an isotope of the H atom, and which is called muonium (Mu ≡ μ+e−)84. Although muons in the form of Mu have four precession frequencies in transverse field, only two of these are low enough to be resolved by conventional detection apparatus:v12 and v23 are the resulting detected precession frequencies, ve and vμ are the electron (2.80247 MHz G−1) and muon (13.554 kHz G−1) Larmor frequencies respectively, and Aμ is the hyperfine coupling constant for muonium in its particular environment. Using this, we can determine the hyperfine coupling constant of muonium Mu in synthetic talc by finding the precession frequencies.Muons or muons incorporated in a diamagnetic molecule  precess at the muon Larmor frequency  functional87 with a plane-wave and charge-density cutoff of 80 Ry and 320 Ry, respectively. We used a 9 × 5 × 5 Monkhorst-Pack88 grid for the first Brillouin zone sampling of the 42-atom triclinic unit cell. The code has been used to calculate the electronic density close to the Fermi level and the electrostatic potential exerted on the muon which is the sum of the bare ionic potential and of the self-consistent Hartree potential generated by the valence electrons  has been multiplied by ge gμμμ/2πℏ to obtain the HFCC value in MHz at the muon sites reported in the manuscript. The value calculated for a free Mu atom, 4524 MHz, to be compared to be compared with the experimental hyperfine value of 4463 MHz. One can obtain a better agreement with the experimental value by correcting the spin density at the nucleus taking into account the difference in bohr radius between the H and Mu atoms. With this correction one gets 4458 MHz for the free Mu atom.For the calculations, we used Quantum Espresso (QE)supplementary information