Cardiac implantable electronic device (CIED) infections are a serious complication of both initial device implants and generator change procedures, and they are associated with a wide range of presentations. Reported rates of CIED infections vary widely from 0.1% to 19.9%, but it is estimated that they occur in 0.5% of initial device implants and 1-7% of subsequent implants. It is widely accepted that the administration of local antibiotics within the pocket as well as extracellular matrices (ECMs) can be utilized to reduce the incidence of CIED infections. We describe a case where the use of an additional biological ECM scaffold sutured directly into the incision site was utilized in addition to a biological ECM pouch in order to reduce the risk of infection. We propose that biological ECM could be utilized to reinforce the incision site directly as well as ECM within the pocket to reduce the instances of CIED infections. Further investigation of the use of biological ECM to prevent infection is warranted and paramount to further decrease the number of complications associated with device implantation. Cardiac implantable electronic device (CIED) infections are a serious complication of both initial device implants and generator change procedures. They are associated with a wide range of presentations from cellulitis to pocket infections with subsequent sepsis . ReporteTreatment for CIED infections ranges from the administration of oral antibiotics to pocket revision procedures to laser lead extraction, depending on the location and severity of the infection. Although there has been some debate regarding the administration of long term antibiotics in lieu of pocket revision or device extraction, current guidelines recommend an aggressive approach of combined antimicrobial treatment and complete device removal . The aveThe patient was a 75-year-old male with a history of coronary atherosclerosis, hypertension, and hyperlipidemia. He reported a prior history of sequential knee replacements with infections in each knee as well as a family history of immunoglobin deficiencies, which made him a very high risk for post-implantation infection. Initial implantation of a dual-chamber pacemaker was performed due to sick sinus syndrome. The device was placed in the left pectoral region without the utilization of a biological ECM pouch. At the initial two-week post-procedure wound check, erythema was observed at the incision with tenderness. Three weeks of oral antibiotics were administered, and the infection cleared without the removal of the device. A few years later, the patient developed congestive heart failure along with chronic right ventricular pacing, and the patient needed an upgrade of his dual-chamber pacemaker to a cardiac resynchronization therapy (CRT) system. This device was implanted using a biological ECM pouch due to the patient's history of prior infection.Six weeks after the implantation of the CRT pacemaker, the patient was admitted to the hospital for a moderately sized hematoma and suspected infection of the device pocket and incision. Laser lead extraction of the complete device system was performed, and cultures obtained from the leads were determined to be acid-fast bacilli along with gram-negative rods. After a six-week regimen of broad-spectrum intravenous antibiotics, the patient underwent device reimplantation on the contralateral side. Due to concern regarding the patient's high risk of CIED infection within the pocket as well as at the incision site, a 10 cm by 1 cm strip of biological ECM, commonly used for vascular reconstruction, was utilized in addition to a biological ECM pouch enclosing the device. Both the strip and the pouch were hydrated in a gentamicin solution to further enhance the antimicrobial effects of the ECM, as described in the literature [Initial techniques for reducing CIED infections involved the administration of antibiotic prophylaxis and placement of antibiotics inside the device pocket . These mIt is widely accepted that administration of local antibiotics within the pocket as well as ECMs can be utilized to reduce the incidence of CIED infections ,19. ThisThis report describes a case where the utilization of biological ECM at the incision site in combination with a biological ECM pouch played a significant role in preventing infection in a patient with a high risk of infection. This case contributes to the current efforts to reduce CIED infections through the novel application of biological ECM scaffolding sutured directly into the incision site where prior infections had been observed. Further investigation of the use of biological ECM to prevent infection is warranted and paramount to further decrease the number of complications associated with device implantation.


A key quality attribute for solid oral dosage forms is their hardness and ability to withstand breaking or grinding. If the product is to be manufactured continuously, it can be of interest to monitor the hardness of the material at different stages of manufacturing. Using the controlled process parameters of roll compaction/dry granulation specific compaction force, roll speed and gap width, hardness of the resulting ribbons and granules can be predicted. For the first time, in this study two yield variables  are used to predict the granules failure load. The increase in granule hardness was monitored in-line when the specific compaction force was increased during the compaction process. This opens the way for in-line control of material hardness, and its use for feedback and feedforward control loops for future continuous manufacturing processes.  DetaileWhen looking at tablets as the final dosage form, mechanical strength is an essential CQA as it prohibits breaking and grinding. On the other hand, early studies showed that if the mechanical strength is increased dissolution can be impeded . In 1985By definition, hardness is the surface property which quantifies a materials resistance to a permanent shape modification . Its relStudies on correlating the torque of the granulation unit of a roll compactor to ribbon hardness were first published in 2012 . A roll The same group later focused on the development of using vibration- and acoustic pressure in-line measurements to determine ribbon hardness in-line, which is promising but also bears limitations as the system reacts sensitively to the attachment of the sensors and the surrounding vibration/acoustic environment .For continuous manufacturing efforts it is of interest to re-evaluate the impact of controlled process parameters  on microhardness of ribbons and failure load of granules with regards to the torque of the granulation unit  for different types of materials. For the first time, the quality parameter of granule failure load was evaluated in conjunction to the torque of the granulation unit and correlations were established for materials with different behavior upon compaction. A correlation was established to predict hardness parameters based on the yield parameters torque of the granulation unit and the throughput of material and the novel principle was tested using real-time granulation data. The study was performed to establish these correlations in order to progress in advanced process control for RCDG.22.1Dibasic calcium phosphate anhydrate  was used as brittle model material. Microcrystalline Cellulose  was used as plastic model material.A formulation was also investigated. It consisted of 25% Diclofenac‑sodium , 10% crosposvidone  and 65% MCC .2.22.2.1All materials were processed on a development to small scale manufacturing roll compactor  that was equipped with a hybrid sealing system and a 360° rotating conical sieve . A 1.5 mm rasp sieve was used for all experiments. Depending on the planned analytics, smooth or knurled rolls were used. The gap width was varied between 1.5 and 2.5, the roll speed between 1 and 6 rpm and the SCF between 2 and 18 kN/cm. The specific process parameters are listed for each experiment in the results section. The throughput of the process was determined using a lab scale balance  that was placed underneath the outlet of the compactor. A collection vessel was placed on the balance and a software  was used to track the mass every 10 s.2.2.2The torque of the granulation unit was tracked together with the process parameters of the roll compactor in the compactor's software. The parameter is tracked every 10 s in the unit of Nm. It is not the average over 10 s but the as-is value at the tracking time-point. The torque of the granulation unit without material was tracked to determine the idle torque for each impeller speed. Idle torque values are listed in The idle torque values were deducted from the observed torque values to obtain the corrected torque (corr. torque). For results shown in 2.2.3max) was held for 5 s. Afterwards, for 5 s, the system was unloaded. The maximum penetration depth (hmax) at maximum indentation load is used to calculate the Martens Hardness (HM) according to Eq. Ribbon microhardness was determined using a microhardness system . The system was equipped with a vickers pyramid indenter which penetrated into ribbons. Penetration depth and indentation load were recorded. A total of 150 data points were recorded in 15 s (10 Hz) for every measurement. The initial 5 s were the loading phase, in which the force increased until 2000 mN were reached. This maximum load of 2000 mN  in a round die of 100 mmϵ can be obtained using the current and the initial difference in height of the punches. For large values of ϵ, the relationship described in Eq. α) and the cohesive strength (τ).Analysis was performed according to Arndt et al.  and is ba) was used for the calculation of each sieve class lnP=lAfterwards, the weighted average failure load for a granule type was calculated by cumulating all size classes' failure loads after multiplying them with their respective relative mass fraction.2.2.53 full factorial experimental design was conducted to determine the effect of the process parameters SCF, gap width and impeller speed on ribbon microhardness and granule failure load as well as the torque of the granulation unit. Factors and their levels are shown in Using MCC as excipient, a 233.13 full factorial experiment while Increasing the SCF lead to a significant increase in failure load of the granules, the ribbon microhardness as well as the additional power consumption of the granulation unit. For all output parameters the SCF showed the largest impact. As it is the dominant process parameter in RCDG this is not surprising and in-line with published research . The incRibbon microhardness significantly increases at increasing SCF  c and 3 By nature, adjusting the impeller speed affects the additional power consumption of the granulation unit  a, Eq. . At an iAs expected, the results of the experiments show that hardness of the ribbons and failure load of the granules react similarly to changes of SCF. The torque of the granulation unit reacts to the changes in process parameters as well but not in the same way as the hardness does. Supposedly, this is based on the effect of the throughput and it has to be analyzed in detail, whether a change in hardness itself has an impact on the torque of the granulation unit. As an increase in SCF will increase the failure load of the granules  and simi3.22 of 0.808 for MCC. Obtaining reproducible failure load values for high SCF for MCC was challenging, as reproducible volumetric filling of the die is more difficult, if the granule sizes are large. At 5 and 6 kN/cm, a large quantity of material was in size classes of 850–1200 μm and 1200–1500 μm. The impact of these difficulties was larger, if more material was produced at these sizes as the weighted average was calculated (see 2.2.4. Determination of granule failure load). Based on these difficulties, linear correlation results for MCC are acceptable.Correlation of SCF and failure load  b and d)It is therefore possible to predict the failure load of the granules based on linear correlation when looking at the SCF at constant gap width and roll speed. The linear increase of the torque of the granulation unit has to be further investigated, as the increase based on increased hardness and increased throughput have to be differentiated.3.33.4As mentioned in At three SCFs, the speed of the compaction rolls was varied  to vary the throughput of material  a and c)Increasing roll speed reduces the dwell time in the compaction zone. Therefore, it had to be tested, whether increasing the roll speed might decrease the hardness of the resulting granules. For both materials, the failure load of granules produced at two SCFs Secondly, a prediction of granule failure load based on current throughput and corrected torque can be made. The correlations shown in These values can then be compared to the failure load measured  b and d)2 (0.991 for DCPA and 0.808 for MCC). The value for DCPA (0.56 N), lies almost perfectly on the linear correlation plot whereas, in an overall less convincing correlation for MCC based on strong fluctuations, the calculated failure load for 5 kN/cm deviates stronger from the measured value . TherThe predicted failure load values deviate from the measured and calculated ones. For DCPA, the predicted failure load is slightly below the measured failure load (0.55 N to 0.56 N), however this difference cannot be regarded as relevant. In conclusion, both methods to determine the granule failure load in-line (based on SCF only and based on corrected torque and throughput) can be regarded as equally suitable. For MCC, the prediction of granule hardness based on the corrected torque and the throughput outshine the prediction based on SCF alone. With only a slight deviation to the measured value (0.39 N to 0.38 N), there is no relevant discrepancy in granule failure load using the real-time prediction based on resulting process parameters. Therefore, the method has proven usable for real-time hardness prediction.3.6To test whether the dependencies of torque, throughput and SCF are also valid for a mixture of API and excipients, a formulation was prepared and granulated. Raw data is listed in Table S3 in the supplementary material.Analogous to It can be concluded that the behavior of the torque of the granulation unit while processing a formulation is similar to pure excipients.4Linear correlations of SCF and failure load were established for two materials. It was proven that failure load is independent from the chosen roll speed. Based on the torque of the granulation unit that were measured for different SCF at varying throughputs, a correlation was established that allows to evaluate the impact of the material hardness on the torque of the granulation unit for a specific throughput at constant impeller speed. This correlation was used to predict the granule hardness completely based on process parameters. Therefore, the expected failure load of granules produced with controlled process parameters e.g. SCF and gap width can be compared to the in-line predicted failure load based on resulting process parameters (throughput and the corrected torque of the granulation unit). This opens the possibility of a feedback control loop based on granule failure load controlling the SCF.Furthermore, if the current granule failure load can be predicted, the optimal compression pressure to obtain tablets of a certain tensile strength could be calculated. This could lead to an in-line determination of compression pressure that can be incorporated into a feedforward control loop. This would allow varying the process parameter of compression pressure in real-time in order to obtain in-specification tablets during the whole production run. More work and validation of the shown correlations is required in order to implement these control loops.Drug Delivery Innovation Center (DDIC), INVITE GmbH, Leverkusen.This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. This work was supported by the The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.


Borel map of atp as the map which assigns to the germ of a smooth solution of p its formal Taylor power series at p. In this work we continue the study initiated in Barostichi et al. (Math. Nachr. 286(14–15):1439–1451, p.Given a locally integrable structure  Borel map and the Borel property for locally integrable structures. If one thinks about an integrable structure as a system of  PDEs with the right number of basic solutions, it becomes an intriguing question to study the relationship between formal solutions  and solutions. The relationship between the two comes, of course, from associating to a smooth solution its formal Taylor series at a distinguished point (e.g. the origin) in the structure. The Taylor series of a solution can be written as a series in the elements of a set of basic first integrals u, as the Borel map (at the origin).The purpose of this paper is to discuss our recent results on the Borel property), in a series of papers of the second author with Barostichi and Petronilho [We have started the study of this map, in particular the natural question of when it is surjective , as it partial Borel maps in Sect. There are also structural aspects of the Borel map which make its study very appealing: We encounter one such aspect when we study Z(K), where Our main new necessary condition Theorem  for the Hence one of the remaining objectives of the paper is a discussion of the possible gap between the necessity of the condition and the stronger conditions known to be sufficient. A particular case in question is an application of the result on partial Borel maps to structures whose characteristic set is of maximal dimension; in that case, we see that the Borel map is surjective if none of the solutions of the structure is open Theorem .This result highlights yet another interesting problem to which the Borel property has a curious connection, namely the question whether there is a solution  which is actually open; it also, therefore connects with the question of whether a maximum principle is valid for solutions of the given structure. We shall, however, in this paper not follow these lines of inquiry further.Instead, we have decided to focus on the study of what we think is the main geometric question left over in our approach here in a special model case of tube structures. We obtain a rather complete picture in that case, which is discussed in Sect. Theorems  and 8.3.In the last two sections of the paper, Sects.  Theorem . There a Theorem .We would like to note that the current paper leaves open a number of fascinating problems concerning the behaviour of the Borel map and the relation between the algebra of formal solutions and the algebra of solutions; we discuss a number of them in section A. Let N over which we assume given a locally integrable structure n. Thus n whose orthogonal bundle p. It is clear that If q in a neighborhood of p. ring ofk- jets of solutions atp. We have well defined homomorphisms  formal solutions for atp. Recall that For each mentclass2pt{minimp. We shall also say that p if We shall refer to the ring homomorphism B. Let p is the center of a smooth coordinate system B  dense in F. The following properties are equivalent:Let The equivalence of (1) and (2) follows from , p. 22. P after dividing its coefficient We apply Proposition k such that j and the sequences of the corrresponding coefficients are bounded in Now a sequence tisfying  then \doA. We keep the notation established in the previous section and start with a digression regarding the theory of tensor products in the category of Fréchet spaces.Let mentclasspt{minimamentclasspt{minimamentclasspt{minimamentclasspt{minimaBy a property of the topology , TheoremB. Denote by  partial Borel maps for The Borel map If V is an open neighborhood of the origin and if we denote by u at the origin belongs the We show the converse. Firstly we remark that if V of the origin such that both induced mapsBy a Baire category argument  solution u for u for ented in . Denote U. If we recall that for a compact set  every algebraic hypersurface through z intersects P, we can state Theorem III.5.1 in [The following theorem gives a complete characterization of hypocomplexity in terms of the compact neighborhoods of the origin in mentclasspt{minimaFor every compact neighborhood For every compact neighborhood The following properties are equivalent:As a consequence we obtain:If For a proof see  at the origin. Write the coordinates in In the preceding section we have seen that when Z(K) in Suppose that for every u be a solution for K of the origin in u over K in the Z(K). Now by hypothesis there is a non constant complex curve k. On the other hand, the Faà di Bruno formula givesLet By hypothesis there is j and thus Case 1: j we necessarily must have jCase 2.: Summing up when We assume Now since0,0)from  we obtaik there exists a polynomial Our argument in the proof of Theorem For the CR structure defined in Remark M also does not contain any regular curve. For such a compact neighborhood of the origin holomorphic hull of K has an affirmative answer, that is, the holomorphic hull of K does not contain any germ of a  regular curve curve through the origin.Write the coordinates in own (see ) that thIn this section we recall two conditions which imply the surjectivity of the Borel map.A. Here we assume that p and let  peak function at p if  finite type if C and The following theorem is the main result in  :p is surjective.If V.We shall present a sketch of a proof of this result based on the characterization given in Proposition For any j let A depends on By  Lemma 5.k, it follows that On the other hand, let us consider B. Next we introduce a very similar condition stated in [W for p such that the following conditions holds:p;p, C such that p.There are smooth solutions The main result in [tated in  which noesult in  is the fp implies the surjectivity of the Borel map for p.Property mentclasspt{minimaentclass1pt{minimaB. Assume that We first study the case In what follows we then assume that Our discussion of the surjectivity of the Borel map for this particular CR structure will be given in terms of the (germ of the) variety V be as before.If If Let We have already seen that if q) such thatFor (2) we can assume without loss of generality that t-space over which We have now to face the situation when V be as before. Assume that V contains the (germ of) a non trivial real analytic curve Let x, s)-space defined by the first integrals if u  is a smooth solution for  near the origin then  is a smooth solution for  near the origin, that is,Write u is any smooth solution for v is defined as above then we obtain the boundsNow if each entclass1pt{minimaC. In the rest of this section we shall focus on the case when We shall now study some of the cases when p is odd then the Borel map is surjective;if p is even then the Borel map is not surjective.if Let In each one of the cases where the Borel map is not surjective, the necessary condition established in Theorem We will first concentrate on the second statement.C1. Given B. up to a complex linear change of coordinates:To this aim, we define Choose then Let now R we have that d. On the other hand R. The open set V. Putting U is simply connected, With this choice of We can thus consider C2. We are now going to treat the first claim in Theorem In order to do so we are going to study the properties of some particular domains of The restriction map To achieve the proof of the Proposition, we modify the construction in , and somFixed j large enough we have j. The conclusion follows from these inequalities and again from the fact that j.Put Fix an increasing sequence For all Suppose first that The next statement is an immediate consequence of the chain rule.k (where the variable j).Fix j if Thus, to obtain an estimate for Let j for all j). Taking in account the definition of j, so that for some In the following we always consider Let The estimate above, together with Lemma j, and thusConsider now together  and  be a germ of smooth real hypersurface of Define g is defined on a neighborhood of 0 in Define the Cayley transformation Consider now for Using the notation of section 3 with In view of Theorem U of 0 in g at 0 is given by the Taylor expansion of Let Define the domainsUsing a suitable change of coordinates we can map By using the methods above, we can deduce directly the following  consequence:f does not vanish at 0 and the domain With the notation of Theorem Let us consider the tube manifold A. In most of this section we shall assume that the locally integrable structure p is the center of a smooth coordinate system B  and Let igin. By  there arZ(K).Notice in particular that if we consider the continuous functions on p there is z near the origin in u we further obtainBy the Whitney extension theorem  the germ variety of I.We continue to work under the notation established in the last section. Let I is a manifold ideal then V(I) is the germ of a regular submanifold of real codimension If The first claim is an immediate consequence of  whereas  principal maximal ideals, that is the ones generated by a single element V of ideal of V, i.e. the ideal of V. It is clear that We shall now restrict our attention Let We remark that in the previous statement no assumption is made about the minimality of Let Clearly I is a principal maximal ideal we can even assume that We can assume that we are in the situation described in Section 1B in such a way Let V(I) the same is true for V(I) if V(I) and recall that We start by settingLet is as in  then \doWe take advantage of . By TaylI is a manifold ideal is not satisfied, the conclusion of Theorem x, y, s), whose orthogonal I is not a manifold ideal, and we have that I, since there is no Nullstellensatz does not hold for a  ideal of If the assumption that V(I) then On the other hand, consider the structure mentclass2pt{minimA certain number of questions arise, in our opinion, naturally from the results presented in the previous sections. Despite the quite elementary nature of some of them (the topic of the algebraic properties of the ring Is the necessary condition found in Theorem We conjecture that this should be the case, at least when the structure Does the conclusion of Theorem The method used in the proof of Theorem not generated by the basic solutions Is there an example in which the maximal ideal The results in Sect. p and q does the structure in Theorem For what values of p and q have different parity.We expect that the Borel property should hold precisely when Is the image of In other words, in the cases settled so far the image of Suppose that two integrable structures n variables: if, however, there are enough solutions, one might hope that the ring It is clear that the answer to the previous question is negative if


Concrete structures expand and contract in response to temperature changes which can result in structural strain and cracking. However, there is a limited amount of robust field data on hybrid concrete floor structures. Shortage of such data impacts on our understanding of how concrete structures respond to thermal effects and ultimately the overall design of concrete structures. Thus, a comprehensive structural and environmental monitoring strategy was implemented by the authors during the construction of an educational building. Sensors were embedded in the precast and in situ components of a hybrid concrete lattice girder flat slab so that the thermal response of the floor during the manufacture, construction and operational stages could be investigated. Many aspects of the thermal behaviour of the floor during the construction phase were monitored using the embedded sensors. The early-age thermal effects during curing and the impact of the variation of ambient temperature  and solar radiation on the behaviour of concrete floor is explored in the paper. Values for restraint factors and the in situ restrained coefficient of thermal expansion of concrete are calculated using the data from the embedded sensors. Numerical modelling of the thermal behaviour of the hybrid concrete floor was undertaken and validated using the real-time field measurements. The data presented and analysed in this paper can be used to improve the understanding and modelling of the thermal behaviour of a hybrid concrete floor. This will assist with improved design of sustainable buildings as it allows the environmental performance of the floor to be optimised with respect to controlling the internal environment, thermal mass and energy efficiency. Most concrete structures are subjected to frequent temperature changes during their design life. In fact, the internal temperature of a reinforced concrete element and relative humidity can be considered as two of the key indicators to monitor and evaluate the condition of the material and detect structure deterioration  that monitors and controls the environmental conditions and energy consumption during the operational phase of the building life cycle. The use of embedded sensors to monitor the actual behaviour of components within the building complements the data from the BMS and allows a more holistic evaluation of the performance of the building. Linking data from embedded temperature sensors in the concrete floor slabs with the room air temperature and external weather conditions in the BMS could assist with making the most effective use of thermal mass within a building in controlling internal comfort conditions and minimising energy consumption. The additional advantage of the embedded sensors is that they can be used to study the behaviour of components at all stages of its life cycle .Ge et al.  conducteObservations and findings from embedded instrumentation in a hybrid precast concrete flat slab floor in a recently constructed educational building are presented in this paper. The embedded sensors permitted real-time monitoring of the floor during the manufacture, construction and operational phases of the building. The embedded sensors in this project are part of a structural health monitoring (SHM) strategy which has been developed in the National University of Ireland Galway  to monitor the structural and environmental performance of a number of educational buildings  on the NUI Galway campus is the new home to three existing schools: Anatomy, Physiology & Pharmacology and Therapeutics Fig. . The buiThe basement was constructed using in situ concrete and above ground the majority of the structure was constructed using precast concrete components such as twinwall system, hybrid concrete lattice girder slabs and hollowcore slabs. All precast components were designed, manufactured and installed by Oran Pre-Cast Ltd., who is located 10 km from the site.The majority of the floor structure in the HBB was constructed using two-way spanning hybrid concrete lattice girder flat slab floor system (either 400 or 250 mm thick). This floor system was selected by the contractor to reduce construction time, reduce steel fixing on site, minimise formwork, improved safety and because of its high quality finish. The lattice girder plank Fig.  consistsVibrating Wire (VW) gauges (Gage Technique model TES/5.5/T) embedded in concrete that measure strain and temperature. The range of the measured strains is greater than 3000 microstrains and the resolution is better than 1 microstrain. The measured temperature range is − 20 to + 80 °C with an accuracy of ± 1 °C.Electrical resistance (ER) strain gauges (Tokyo Sokki Kenkyujo model FLA-6-11) bonded to steel reinforcement in concrete, which measure uniaxial strain. The ER gauges have a strain limit of 5% and the gauge resistance is 120 Ω (± 0.3 Ω).IP68 rated thermistor sensors (ATC Semitec model IP 68) which are capable of measuring concrete temperature. The thermistors have a temperature range of − 50 to + 110 °C with a 1% tolerance.This project used a number of sensors Fig.  which weThe embedded sensors are located within two zones of the second floor of the HBB along a number of orthogonal grids. The location of the embedded sensors in one zone of the second floor slab is shown in Fig. To collect data from the sensors, a data acquisition system consisting of CR1000 data loggers, AM16/32B multiplexers and AVW200 vibrating wire interface from Campbell Scientific were used to collect and store real-time data from the embedded instrumentation. This system has automatically recorded data from the precast planks since manufacture and the in situ concrete topping since the concrete pour on site. During the construction phase, data was manually downloaded onto a laptop, but after commissioning of the building, data is downloaded over a local network using Campbell Scientific’s NL116 Ethernet interface and compact flash module. This allows long term monitoring of the behaviour of the floor during the operational phase of building. This data is being stored on a dedicated server and is available for students for both teaching and research applications.A comprehensive material testing programme was undertaken to measure the properties of the concrete (precast and in situ) in the floor over time. Concrete specimens  were made and cured in water (in accordance with EN 12390-2 BSI ) and in Changes in the environmental conditions surrounding any concrete element will have a significant effect on its behaviour with respect to deformation, strength, durability and service life  measure both change in strain and temperature (via thermistors) in the concrete slab. Changes in the internal temperature of the concrete slab will cause expansion and contraction of both the concrete and vibrating wire gauge that is used to measure change in strain in the concrete. Failure to correct for the thermal effects in the VW strain gauges would lead to erroneous strain readings. The difference between the coefficient of thermal expansion of the concrete and VW strain gauge will give rise to an apparent change in strain in the concrete. The coefficient of thermal expansion of the VW strain gauges is 11με/°C and for this project it was assumed that the coefficient of thermal expansion of the concrete was 9με/°C. The measured strain readings (apparent strain) from the VW gauges are corrected for thermal effects using the following equation so that only strain due to shrinkage, flexure and creep is determined:The effect of the thermal correction can be seen in Fig. In the literature, there is no agreement on the time at which the concrete stiffness has exceeded that stiffness of the strain gauge so that measured strains are consistent with the strains in the concrete (Time Zero). Prior to this time, the concrete is not sufficiently stiff to transfer strains to the embedded strain gauge or to restrain the gauge under applied thermal loads. Boulay and Paties  conducteIn this study, the zero point for strain readings is assumed to be time at which the maximum concrete temperature is reached. Prior to the concrete reaching its maximum temperature, the concrete can be assumed to be in, or near to, a zero stress state due to creep ACI . The in A one-dimensional finite difference model was developed to model the temperature profile in the hybrid concrete slab. It was assumed that a one-dimensional model through the slab thickness was applicable for the internal sections of the slab and the model is validated against embedded sensors located internally in the slab. The model is based on the numerical method developed by Ross and Bray  and uses(i)0 and T1 are the surface and internal temperature at the first internal node, and Δx is the space increment in the model (through the depth of the concrete).Conduction: (ii)0 is the concrete surface temperature, and Ta is the ambient temperature.Convection: (iii)abs is the solar absorptivity of the concrete and Qinc is the incident solar radiation .Solar radiation: (iv)0k is the concrete surface temperature (in Kelvin), and Tsky is the sky temperature.Thermal irradiation: The following equations are used in the model to describe heat transfer through the concrete slab:The difference-calculation remains numerically stable, if the following is valid for the time increment:At the commencement of the pour, the precast plank is assumed to be the same temperature as the ambient temperature (15.1 °C) and the placing temperature of the concrete is assumed to be 20 °C . The degree of external restraint will depend on the member being cast  and the construction process .The maximum temperature differential and thermal gradient within the section. This is the condition of internal restraint and occurs where one part of a concrete pour expands or contracts at a different rate to another part of the same section. It typically occurs in thick sections in which there can be a large temperature differential across the section and can lead to both surface cracking and internal cracking (which may not be observable from the surface). An internal restraint can also occur when there is a large percentage of reinforcement restraining the concrete.Predicting early-age thermal cracking is very complex as there are numerous factors which affect the potential for cracking and properties of the concrete  are rapidly changing during the early stages of curing. The use of in situ instrumentation in this project allowed the thermal behaviour of the second floor slab to be recorded and this data can be used during the design process for checking early-age thermal cracking. Two important temperature considerations for control of early-age thermal cracking are Bamforth :The tempUsually either external or internal restraint dominates; however, there are some situations in which both types of restraint need to be considered.3. It is common to blend GGBS  with CEM I cements to reduce the heat of hydration and likelihood of early-age thermal cracking. CIRIA Report C660 by Bamforth . As noted previously, at most locations there were four VW strain gauges positioned through the depth of the slab . The temperature in the concrete at one location in the slab is shown in Fig. Bamforth  providesThe end of the hydration phase is difficult to determine precisely, but after the first few days it appears that the thermal response of the slab is primarily driven by the ambient air temperature and solar gain Sect. . After tLarge temperature differentials between the surface and centre of concrete elements can lead to internal restraint, which can lead to cracking and this is of critical importance for thick concrete elements. Quantifying and controlling the temperature differential within the concrete section is one of the critical design checks when considering early-age thermal cracking. The maximum recorded temperature differential within the 335 mm thick concrete topping in the second floor slab in HBB never exceeded 3 °C. Using the CIRIA Report C660 , the preThe temperature profile through the depth of the slab  at a location in the middle of the slab is shown for the first 24 h after pouring in Fig. As noted previously, in Fig. Similar to other models, the numerical model described in this paper uses adiabatic hydration models (i.e. heat transfer is not lost to/or gained from the surrounding). Previous studies  were assumed to be constant in the model and were based on typical values from the literature. However, the thermal properties of concrete change during the hardening process . During the construction phase of the HBB, both the top and bottom of the slab are exposed and, therefore, are affected by daily and seasonal environmental changes. The thermal gradients may lead to slab curvature (curling or warping of the slab) and because typically the slab is subject to some form of external restraint, additional temperature-induced stresses are developed which may create cracks in the concrete. The curvature is upward if the thermal gradient is positive (temperature decreasing from top to bottom) and downward if it is negative. Restraint to slab curvature is the cause of most early-age thermal cracking in pavements Bamforth .Distinct differences can be observed in the daily thermal gradients in the slab in response to the changes in the ambient air temperature. The thermal gradient in the slab is typically non-linear through the depth of the slab and approximately parabolic in shape at peak differentials. Temperature profiles through the slab are shown in Fig. The predicted temperature profiles on the 30 December 2015 and 19 July 2016 using the 1-D model are also shown in Fig. Although the 1-D finite-difference numerical model described in this paper is relatively simple, it can be used to predict the temperature profile during the early-age heat of hydration phase and at later stages when the environmental conditions are the dominant factor on the temperature in the concrete slab. During curing of the concrete slab, the model will tend to predict temperature rises which are conservative, but could be used to identify potential early-age thermal cracking. Accurate prediction of the concrete temperatures in slabs is critical if the thermal mass of the concrete is used as one of the passive design strategies to control comfort (heating and cooling) in a sustainable manner. Exploiting the potential of exposed concrete in buildings can lead to enhanced energy efficiency and carbon savings over the lifetime of the building.Thermal gradients were also recorded horizontally in the slab in addition to vertically through the depth of the slab as outlined above. The temperature distribution along gridline (GL) H . However, local deviations in the horizontal temperature distributions are noted in the slab perimeter along GL 22. The horizontal temperature distributions for the slab along GL 22 are shown in Fig. c) is a measure of the free strain (unrestrained concrete) produced by a unit change in temperature and its magnitude will control the expansion and contraction of the concrete in response to a given temperature change. In design of concrete structures, the value of αc can influence the control of early-age thermal cracking, provision of movement joints and construction tolerances for elements connected to concrete. A concrete with a low coefficient of thermal expansion is desirable when trying to control the risk of early-age thermal cracking; the type of aggregate used in the concrete is the dominant factor with respect to the coefficient of thermal expansion of concrete. The value of αc can vary from 8 to 13με/°C depending on the type of aggregate used in the mix. Eurocode 2 (BSI (British Standards Institution) c changes over time and with moisture content.The coefficient of thermal expansion of concrete (αr) to be measured for the in situ topping that is poured on top of the precast plank. The slope of the in situ strain–temperature relationship during the cooling phase of the temperature cycle can be used to determine αr at a number of locations in the slab and at different depths in the slab. In Fig. r is lower in the middle (4.7με/°C) of the concrete in comparison with the top (6.0με/°C) and bottom (5.9με/°C) and this finding was consistent at all locations in the slab.There is no standard method for determining the coefficient of thermal expansion of concrete in CEN, although there is a method provided in BS EN 1770 BSI  related r through the depth of the slab is shown in Fig. r determined in strain–temperature plot previously  using the embedded sensors in the 335 mm thick in situ topping was 6.6με/°C with a coefficient of variation (Cv) of 13% . The average αr for gauges located in the middle of the in situ topping was 5.7με/°C (Cv = 11%) and the average αr for gauges located in the top and bottom of the in situ topping was 6.9με/°C (Cv = 10%).The variation of αsly Fig. . The aver with depth of pour was found to be approximately represented by a parabolic curve and this correlates with the in situ data from the slab in the HBB even though the top of the in situ topping is exposed and the bottom of the in situ topping is partially insulated by the precast plank. The variation of αr with depth correlates with the variation in concrete temperature, the central core being subjected to the greater temperature rise and imposing movement on the cooler surface regions. The reduced value of the restrained coefficient of thermal expansion of concrete (αr) in the middle of the in situ topping in comparison with the top and bottom  are used in many design codes to quantify the degree of restraint when two concrete elements are cast against each other . Annex L of Eurocode 2 BSI  providesc is the coefficient of thermal expansion of unrestrained concrete (free strain) and αr is the in situ restrained coefficient of expansion strain which can be measured as outlined above. Assuming that αc was 9με/°C for the in situ topping in the HBB using limestone aggregates, values for the restraint factors can be determined using the in situ values for restrained coefficient of expansion strain (αr). The average restraint factor at the bottom of the in situ topping which is cast on top of the precast plank was 0.25 (Cv = 34%). A method for estimating the restraint factor at a joint (Rj) was proposed by ACI (American Concrete Institute)  pour; Ao is the cross-sectional area of the old (restraining) concrete; En is the modulus of elasticity of the new pour concrete; Eo is the modulus of elasticity of the old concrete.CIRIA Report C660 Bamforth  outlinesstitute) :8\documen/Ao) is in proportion to the relative thicknesses of the two slabs (hn/ho). Using the above equation, the estimated restraint at the interface of the in situ topping and the precast plank after 12 h is calculated as Rj = 0.24. This compares favourably with the restraint factor determined using the in situ data (R = 0.25) from the embedded instrumentation during the cooling phase after the heat of hydration even though there is a large variability. Thus, the equation developed by the ACI could be a useful method for determining restraint factors in hybrid concrete slabs.It is recommended that for a slab cast against an existing slab that the relative area .2) and this allowed the daily total solar irradiance (kJ/m2) to be determined and compared with the thermal behaviour of the precast plank and hybrid concrete lattice girder flat slab during construction. The total area of the second floor slab which was instrumented had limited exposure to solar radiation during construction because 11 days after the in situ topping was poured (31 July 2015), precast planks for the third floor were erected. The third floor precast planks located directly over the second floor provided shading for the majority of the slab, except at the perimeter which was still subject to partial solar radiation.The automatic weather station IRUSE  at the NThe 65 mm thick precast planks for the second floor were erected on the 6 July 2015 and data was recorded after the 10 July 2015. Nine VW strain gauges were embedded in one of the 65 mm thick precast planks  and potential of using concrete to manage thermal energy flows in a building.The concrete temperature in the in situ topping in the centre of the slab and the daily solar irradiance is shown in Fig. The magnitude and source of thermal induced loadings will vary during the lifetime of concrete structures. Initially, the heat generated during the heat of hydration phase can cause strains which may result in cracks which will affect the durability and performance of concrete elements. After the curing phase, interaction of the concrete with the environment (ambient temperature and solar radiation) can lead to daily and seasonal temperature changes within the structure which will cause the material to expand and contract. If movement in the structure is restrained, stresses may be induced which may contribute to cracking in the structure. In some cases, the thermal induced stresses may exceed the stresses induced by service loads (permanent and variable loading).An estimate of the thermal strains induced in the concrete slab may be determined by assuming a coefficient of thermal expansion of the 9με/°C for the concrete. As noted in Sect. Exposed concrete surfaces are subject to temperature increases due to solar radiation which can induce curvature in the slab due to the creation of temperature differentials through the concrete Sect.  and alsoA detailed account of a real-time monitoring programme is described which allows the thermal behaviour of a hybrid concrete floor during the construction phase to be investigated. The project involved embedding sensors in the precast concrete plank during manufacture and the instu topping during construction so that the response of a hybrid concrete floor to temperature variations for 1 year could be monitored. The relationship between concrete floor and external environmental conditions was investigated using data from an automatic weather station located close to the building.The data from the embedded sensors demonstrates that thermal behaviour of the concrete changes during the construction process. For the first few days after the in situ topping is poured, the heat of hydration is the dominant factor and has the potential to cause thermal cracks if the tensile strains generated in the concrete exceed the tensile strain capacity of the concrete. Although the concrete slab monitored in this project was exposed to direct solar radiation for a short period of the time, the significant effect of solar radiation on the concrete temperatures in the slab were recorded. High levels of solar radiation have the potential to cause curvature of the slab and also increase the average temperature of the concrete section. During the monitoring period described in this paper (1 year), differences in the thermal response of the slab to diurnal and seasonal temperature variations were observed and time lag between ambient temperature and concrete temperatures were noted. Variations in concrete temperatures in the concrete slab were recorded vertically through the depth of the slab and horizontally in the region of the slab which was monitored.A one-dimensional finite-difference model is described which takes account of the various heat transfer components acting on the slab and allows prediction of the temperature profile in the slab during construction and operational phase of the building. Although the model is conservative when predicting the temperature rise during the heat of hydration, it can be used to model the temperature rise and temperature differential in a hybrid concrete floor when the in situ structural topping is poured. The thermal response of the floor to the diurnal and seasonal changes in the ambient temperature is also modelled using the numerical model.The data presented in this paper can be used in conjunction with laboratory experiments to develop and validate numerical models which will allow designers to simulate the thermal behaviour of concrete components. This is particularly important in buildings in which the thermal mass of exposed concrete is used to regulate the internal environment and reduce energy consumption.Although, hybrid concrete construction is increasingly popular in concrete structures, there is little data available on the actual thermal behaviour of concrete components. The data presented in this paper can be used in conjunction with laboratory experiments to develop and validate numerical models which will allow designers to simulate the thermal behaviour of concrete components. This is particularly important in buildings in which the thermal mass of exposed concrete is used to regulate the internal environment and reduce energy consumption.The effect of solar gain on exposed concrete components can be significant in regions which have high levels of solar radiation and needs to be considered at design stage. Thermal strains induced by solar irradiance can induce additional curvature and moments in slabs. The thermal data presented in this paper is related to actual weather data and can be used for analysing the effect of solar irradiance on concrete slabs.Guidelines for designers in codes of practice in relation to restraint for suspended slabs is limited. At design stage, it is very difficult to determine the degree of restraint and the nature of restraint . The methodology described in this paper for determining the restraint factors based on the measured restrained coefficient of thermal expansion is applicable to similar hybrid precast concrete slabs.This paper demonstrates the important role which embedded sensors can play for better understanding and prediction of thermal behaviour of concrete components in real buildings. The comprehensive thermal information from the embedded sensors described in this paper have many potential applications for designers of concrete buildings:Thermal effects during the construction and operational phases of concrete, if not considered during the design process, can have a significant negative effect on the performance of concrete structures. As performance requirements of buildings continue to increase, designers must adopt a holistic approach to design and be able to demonstrate how the various components and materials work in unison to enhance the overall performance of the building. If implementing a passive design strategy, designers will require accurate numerical models validated using field data from buildings to predict the thermal behaviour of concrete floors so that it can be optimised with respect to controlling the internal environment, thermal mass and energy efficiency.


Linearizability is the de facto correctness criterion for concurrent data type implementations. Violation of linearizability is witnessed by an error trace in which the outputs of individual operations do not match those of a sequential execution of the same operations. Extensive work has been done in discovering linearizability violations, but little work has been done in trying to provide useful hints to the programmer when a violation is discovered by a tester tool. In this paper, we propose an approach that identifies the root causes of linearizability errors in the form of code blocks whose atomicity is required to restore linearizability. The key insight of this paper is that the problem can be reduced to a simpler algorithmic problem of identifying minimal root causes of conflict serializability violation in an error trace combined with a heuristic for identifying which of these are more likely to be the true root cause of non-linearizability. We propose theoretical results outlining this reduction, and an algorithm to solve the simpler problem. We have implemented our approach and carried out several experiments on realistic concurrent data types demonstrating its efficiency. The stack is linearizable when the two statements are executed atomically (see ).Our goal is to identify such root-causes. We start with a non-linearizable execution like the one in Fig. conflictingThese repairs disable the execution because each pair of statements is interleaved with mentclass2pt{minimAt the end of the first phase, our approach produces a set of all such optimal (incomparable) repairs. To isolate one as the best candidate, we use a heuristic to rank the optimal repairs. The heuristic relies on the hypothesis that repairs which disable fewer linearizable executions are more likely to represent the best candidate for the true root-cause of a linearizability bug.after the first two threads finished. This is linearizable because the pop in the third thread returns the value a written by the push in the first thread in items[1] (this is the first non-null array cell starting from the end). Focusing on the two optimal repairs mentioned above, enforcing only the atomic section in the push will disable this linearizable execution. The atomic section in the pop, which permits this execution, is ranked higher to indicate it as the more likely root-cause. This is the expected result for our example.For instance, the client in Fig. This ranking scheme can easily be extended to a set of linearizable executions. Given a set of linearizable executions, we rank optimal repairs by keeping track of how many of the linearizable executions each disables.operation), or an access (read or write) to a memory location. Then, we recall the notion of linearizability [We formalize executions of a concurrent object as sequences of events representing calling or returning from a method invocation  the library, for which we intend to identify the repair.Now, let us turn our attention to an algorithmic setup to solve this problem. The non-linearizability of a library Note that if T. Then the following iterative algorithm produces Let Yes? Return NO? Produce a set of non-linearizability witnesses Check if Call Go to back to step 2.Consider a conceptual oracle, The above algorithm produces an optimal set of repairs k-th iteration of the loop. Following Remark It is easy to see that if oracle mentclass2pt{minimNote that in oracle Given a trace conflict serializable [conflict serializable, for some choice of transaction boundaries. This observation is the basis of our solution for approximating repairs for non-linearizability through an oracle that is actively seeking to repair for non-serializability violations.Observe that if every trace of lizable   trace eliminators and non-linearizability repairs are the same set of objects, and therefore the subsumption relation Any trace eliminator that removes (Sketch) For the if direction, assume by contradiction that The relationship between the set of trace eliminators for Let This is precisely why the set of trace eliminators safely overapproximates the set of linearizability repairs for a single trace. Note that Theorem Let For each Let For each For each where ith component of optimal trace eliminator for covers all atomic blocks suggested by each eliminator. Formally:If we have an implementation for an oracle If In this section, we investigate the theoretical properties of conflict serializability repairs to provide a set up for an algorithm that implements the oracle We start by introducing a few formal definitions and some theoretical connections that will give rise to an algorithm for identifying an optimal set of atomic blocks that can eliminate a trace decomposition of a trace the equivalence classes of A intervals.The equivalence classes of a decomposition Observe that the relation interval graph is defined as V is the set of intervals of E is defined as follows Given a trace Since, by definition, each edge in the interval graph is induced by an edge from either relation Figure trace graph, denoted by For the degenerate decomposition in which each event is an interval of size one by itself, the interval graph collapses into a conflict graph[Intervals are closely related to the static notion of transactions and the induced transaction boundaries on traces. For example, in the decomposition in which the intervals coincide with the boundaries of transactions (e.g. method boundaries), it is straightforward to see that the interval graph becomes precisely the ct graph widely kct graph. Since \With intervals set as single events, simple if only one vertex is repeated more than once.A cycle in a graph is Let Note that each cycle may induce several different segment sets, determined by For any In Fig. uninterrupted in a trace There is a direct connection between the notion of critical segment sets and conflict serializability repairs that the following lemma captures. A segment is called Let The immediate corollary of Lemma Lemma Let Let For each For each If For each The above algorithm produces the optimal set of trace eliminators for a buggy trace This theorem is non-trivial, because the set of cycles considered are limited to simple cycles and an argument is required for why no optimal solution is missed as the result of this limitation. An important point is that any optimal trace eliminator The first loop of the above algorithm includes in mentclass2pt{minimThe algorithm is obviously very inefficient. There are two levels of enumeration: all decompositions and all cycles of each decomposition. Assuming that there are cliqueConsider an arbitrary cycle simple cycle with at least one conflict edge in the The converse also holds, that is, every For each simple cycle M indicates the decomposition whose intervals coinciding with the library method boundaries. Since for any arbitrary decomposition Let Let Let For each If For each The above lemma can immediately be generalized. Consider the graph Note that we are slightly bending the definition of Observe that ever cycle of We can simplify the above algorithm one step further by further limiting the set of cycles The above algorithm produces the set of optimal trace eliminators for Theorem In this section, we first start by giving a detailed algorithm that produces the set of all optimal trace eliminators. These repairs suggest incomparable optimal ways of removing an erroneous trace from the library. We then present a novel heuristic that orders this set into a list such that the the ones ranked higher in the list are more likely to correspond to something that a human programmer would identify (amongst the entire set) as the ideal repair.Let Let If For each sequence In this section, we present an algorithm for enumerating all simple chordless cycles in It enumerates all non-empty As a corollary of Lemma Note that, in general, the number of simple cycles can be exponential in the number of edges. This means that enumerating only chordless cycles reduces the size asymptotically. In other words, our proposed sound optimization of Sect. k parallel conflict edges between k edges between Interestingly, this upper bound is not loose. There is a class of traces parametrized by Above enumeration algorithm generates all chordless cycles with at least one The loop enumerates all the n critical segments (illustrated in red). Consider two distinct chordless cycles Lastly, there may be as many optimal repairs as there are chordless cycles in This implies that the bound presented in Theorem We argued through the example in Sect. Let Let For each Sort Given a buggy trace Since the above algorithm is heuristic in nature, there are no theoretical guarantees for the optimality of its results. For instance, its effectiveness depends on the set of linearizable traces We demonstrate the efficacy of our approach for computing linearizability root-causes on several variations of lock-based concurrent sets/maps from the Synchrobench repository . We consIn Table C, we compute the set of optimal trace eliminators for C (the restriction to linearizable traces of the same client is only for convenience). Note that multiple trace eliminators can be ranked first since they disable exactly the same number of linearizable traces. Also, note that an optimal root-cause can disable a number of linearizable traces. This is true even for the ground truth repair .For each non-linearizable trace C, then after repairing the library according to C produces no linearizability violations.The results are presented in Table The methods in the libraries OptimisticListSortedSetWaitFreeContains and LogicalOrderingAVL use optimistic concurrency, i.e., unbounded loops that restart when certain interferences are detected. This could potentially guide our heuristic in the wrong direction of giving the ground truth a lower rank. Indeed, a ground truth that concerns statements in the loop body could disable a large number of executions which only differ in the number of loop iterations. This, however, does not happen for small-size clients  since the number of invocations are bounded, which bounds the number of interferences and therefore the number of restarts.Optimistic concurrency has the potential to mess with the heuristic, but this does not happen in small bounded clients as witnessed by our blah benchmark that does just fine.To conclude, our empirical study demonstrates that given a good client (one that exercises the problems in the library properly), our approach is very effective in identifying the method at fault and the part of its code that is the root cause of the linearizability violation.Linearizability Violations. There is a large body of work on automatic detection of specific bugs such as data races, atomicity violations, e.g. [net and Java. Emmi and Enea [s, e.g. , 41, 45.s, e.g.  proposeds, e.g.  and by Hs, e.g. ; neithernd Enea , 15 intrConcurrency Errors. There have been various techniques for fault localization, error explanation, counterexample minimization and bug summarization for sequential programs. We restrict our attention to relevant works for concurrent programs. More relevant to our work are those that try to extract simple explanations (i.e. root causes) from concurrent error traces. In [ces. In , the autces. In , the autces. In  and Tineces. In , are ortces. In , 29, 38.ces. In  use a seThere is large body of work on synchronization synthesis , 42, 43.Linearizability Repairs. Flint[s. Flint is the o


Optical distortions as a visual disturbance are inherent in many optical devices such as spectacles or virtual reality headsets. In such devices, distortions vary spatially across the visual field. In progressive addition lenses, for example, the left and right regions of the lens skew the peripheral parts of the wearers visual field in opposing directions. The human visual system adapts to homogeneous distortions and the respective aftereffects are transferred to non-retinotopic locations. This study investigates simultaneous adaptation to two opposing distortions at different retinotopic locations. Two oppositely skewed natural image sequences were presented to 10 subjects as adaptation stimuli at two distinct locations in the visual field. To do so, subjects were instructed to keep fixation on a target. Eye tracking was used for gaze control. Change of perceived motion direction was measured in a direction identification task. The point of subjective equality (PSE), that is, the angle at which a group of coherently moving dots was perceived as moving horizontal, was determined for both retinal locations. The shift of perceived motion direction was evaluated by comparing PSE before and after adaptation. A significant shift at both retinal locations in the direction of the skew distortion of the corresponding adaptation stimulus is demonstrated. Consequently, parallel adaptation to two opposing distortions in a retinotopic reference frame was confirmed by this study. Many optical devices induce spatial distortions of the visual field as a part of their optical aberrations. An example is the progressive addition lens (PAL)  with normal or corrected-to-normal vision participated in the study. All but one were naive about the purpose of the study. The experiment was conducted in accordance with the Declaration of Helsinki and participants gave their informed written consent.Stimuli were shown on a ViewPixx monitor  with a resolution of 1, 920 × 1, 200 pixels and a refresh rate of 120 Hz viewed at a distance of 65 cm. The monitor covered a visual angle of 41° horizontally and 24° vertically. Gaze of the subjects was controlled by an EyeLink 1000 Plus eye tracker  at a sampling rate of 1 kHz. Viewing distance and head position was fixed by using a chin and forehead rest. The up and down keys on a keyboard were used by the subjects to respond in the test phase. The experiment was run with the Psychophysics Toolbox  in the undistorted frame to the new positions  given by the transformation:Adapting stimuli were generated by skew distorting natural image sequences from an open source movie Baumann, . The frawith the angle θ defining a shear mapping in vertical and horizontal direction with the same amount. To reduce boundary effects, the frames were cropped to a size of 650 × 650 pixels and masked with a Hanning window functionr is the distance to the center of the frame and N = 650 pixels is the width of the frame. Two kinds of stimuli, with opposite skew of θ = 25° and θ = −25°, were prepared. They are shown in where To test adaptation aftereffects, a random dot test was used. White dots with diameter 5 pixels on a black background were randomly positioned within a circle of diameter 14° visual angle and moved coherently at a speed of 6.6° visual angle per second. Direction of motion was diagonally upwards or downwards randomly to the left or right with an angle to the horizontal chosen randomly out of ±8, ±6.5, ±5, ±3.5, ±2, ±0.5°. Dots moving outside of the circle were randomly repositioned at the opposite side of the circle . The dot stimulus was masked with the same Hanning window function as the adaptation image sequences.Subjects were lead into the study room, seated on a chair, and introduced to the experiment procedure. The room was darkened and subjects performed a few test trials before the actual experiment started. Three different phases of the experiment are illustrated in As illustrated in In the trials of the pre-phase, the moving dot test was performed consecutively on the left and right side with the first position chosen randomly from the two stimulus locations. The dots moved for 0.3s randomly to the left or right with an angle to the horizontal chosen randomly form the given set, after which subjects answered the perceived direction of motion by clicking up or down on a keyboard. The experiment continued only after a valid key was pressed. Then, after a 0.5-s break after the key press, the test was repeated at the opposite stimulus location. Each of these trials was followed by a short top-up adaptation of 4 s. In the pre-phase, undistorted image sequences were used and presented simultaneously at both stimulus locations. After a break of 0.5 s, the next trial started with a random dot test. In 64 trials, each stimulus angle was tested 6 times (only 4 times for large angles of ±8 and ±6.5°) in a randomized order.The second phase induced adaptation by presenting the skewed images sequences for 5 min without interruption. Always oppositely distorted stimuli were used for the two stimulus locations, but location was randomly interchanged between subjects. Also in this phase the fixation point was shown in the center of the screen.The third phase, the post-adaptation phase, was similar to the first phase, but distorted stimuli consistent with the adaptation phase were used as top-up adaptation.To ensure that always the same retinal locations were stimulated, during adaptation and test the subjects' gaze was controlled and the adaptation stimuli vanished in <20 ms  as dots moving to the right but upwards. Thus, to collapse data from trials with different horizontal motion direction for analysis, answers for trials with movement to the left were inverted. The obtained curves of percentage of upwards answers depending on stimulus level were fitted for every subject with a psychometric function  using Psignifit  opposing the skew direction of the corresponding adaptation stimulus. For the right stimulus location, ΔPSE is negative if motion perception changes opposing the adaptation stimulus.t-test was used with ΔPSE for the left and right stimulus location to test the presence of a shift in perceived motion direction. A paired t-test was conducted with both ΔPSE to evaluate the significance of the difference between both stimulus locations.For statistical analysis, one-sample This change of perception indicates that the subject saw both image sequences less distorted after adaptation than in the beginning of adaptation.p < 0.01 for ΔPSEleft). On the right side, for all subjects but one the shift of PSE was negative (p < 0.01 for ΔPSEright). Thus, the shifts of perception were always in opposite directions for the left and right side (p < 0.001 for ΔPSEleft−ΔPSEright). In average, the shift for the left stimulus position was 1.13° (s = 0.8°) and for the right position −1.4° (s = 0.9°). Skew direction of the adaptation stimulus was positive for the left and negative for the right stimulus location. This means the change of motion direction perception was opposing to the skew direction of the corresponding adaptation stimulus at both stimulus locations.This study assessed the parallel presence of spatially separated aftereffects after adaptation to two spatially distinct opposing distortions in a psychophysical experiment. Subjects were exposed to two homogeneously but oppositely skew distorted natural image sequences shown at two distinct locations in the visual field at identical eccentricity. Aftereffects were measured at the identical locations by evaluating the shift of perceived motion direction measured in a direction identification task. The results show opposing shifts of PSE at the left and right side. At both stimulus locations, the direction of aftereffects opposes the skew direction of the corresponding adaptation stimulus. This shows that the human visual system is able to adapt to multiple, spatially separated distortions simultaneously. Perception is changed locally in the visual field depending on the distortions present at the test locations. So distortion adaptation does not only take place globally, but can vary across the visual field.Aftereffects result from response changes of neurons tuned to attributes changed by the adaptation stimulus Webster, . AdaptatThe motion direction aftereffect is known to be retinotopic, also with locally opposing aftereffects (Wenderoth and Wiese, Another possible explanation of our results is adaptation to curvature of a three-dimensional surface: Two distorted adaptation stimuli combined could stimulate detectors for curvature of a surface covering the area of both stimulus locations Suzuki, . OppositThe process revealed by this study is an important part of understanding of how the visual system copes with optically induced distortions. The results show that humans' visual system can reduce the amount of perceived spatially varying distortions by adaptation. Wearers of PALs or VR-glasses benefit from this process by a decrease of problems like discomfort and nausea. In the case of optically induced distortions, additional complexity arises by the fact that varying distortions are in general not spatially distinct and homogeneous but gradually change across the visual field. Also the distortions in the visual field are constantly modulated by eye movements. The distortions are not fixed relative to the retina, as it is the case in this study, but mostly relative to the head and therefore change upon gaze. To reduce the perceived distortions in VR headsets or PALs, aftereffects would thus have to occur not relative to the retinal but the spatial coordinates of an adaptation stimulus. For a single homogeneously distorted adaptation stimulus, the transsaccadic transfer of aftereffects has been shown in retinotopic as well as spatiotopic reference frames (Habtegiorgis et al., The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.The studies involving human participants were reviewed and approved by Ethics Committee of the Medical Faculty of the Eberhard Karls Universität Tübingen and the University Hospital. The patients/participants provided their written informed consent to participate in this study.All authors developed the study idea and procedure. YS performed the experiment and the analysis. All authors discussed the results and contributed to the final manuscript.SW and KR are employees of Carl Zeiss Vision International GmbH, as detailed in the affiliations. The remaining author declares that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.