This simulation study investigated to what extent departures from construct similarity as well as differences in the difficulty and targeting of scales impact the score transformation when scales are equated by means of concurrent calibration using the partial credit model with a common person design. Practical implications of the simulation results are discussed with a focus on scale equating in health-related research settings. The study simulated data for two scales, varying the number of items and the sample sizes. The factor correlation between scales was used to operationalize construct similarity. Targeting of the scales was operationalized through increasing departure from equal difficulty and by varying the dispersion of the item and person parameters in each scale. The results show that low similarity between scales goes along with lower transformation precision. In cases with equal levels of similarity, precision improves in settings where the range of the item parameters is encompassing the person parameters range. With decreasing similarity, score transformation precision benefits more from good targeting. Difficulty shifts up to two logits somewhat increased the estimation bias but without affecting the transformation precision. The observed robustness against difficulty shifts supports the advantage of applying a true-score equating methods over identity equating, which was used as a naive baseline method for comparison. Finally, larger sample size did not improve the transformation precision in this study, longer scales improved only marginally the quality of the equating. The insights from the simulation study are used in a real-data example. The process of equating aims to make scores issued by different multi-item scales comparable . Smith aObserved-score equating procedures apply a transformation to approximate the observed-score distributions from different scales. Typically, these procedures first use methods to reduce random variation in the raw scores through, for example, pre-smoothing, estimation of score probabilities, or item response theory (IRT) modeling  and thenTrue-score equating also aligns scores from different scales. The so-called “true score” is established through a latent variable model . True-scequating . Howeverequating .Several assessment designs are available to achieve score comparability through true-score equating. A concurrent calibration of scales can be applied in a common person design  or using a non-equivalent anchor test (NEAT) design. NEAT designs are used when test-takers have answered different scales with some common items, so-called anchor items. NEAT designs are considered more economical and practical than common person designs but also pose challenges, mainly in selecting the best anchor items . The conEquating with a common person design, also called form-to-form equating, is highly relevant in different fields of questionnaire-based measurement. In educational settings where test-takers can prepare for an examination with a “drill-and-practice” session before undergoing the actual exam, the different scales should be equivalent in terms of their difficulty . For heaThe multi-item assessment context mimicked in this simulation study is motivated by health-related settings. Individual information about functioning, physical and mental health, as well as living conditions are getting more and more routinely assessed by health systems . AssessmIn theory, equating is described as ideal when the requirements of equal construct, equal reliability, symmetry, equity, and population invariance are met . By and equation-type and story-type exercises would typically lead to a multidimensional measure of algebra , a Rasch-type model for polytomous response options , 1985. IAppendix is available as Online Supplemental Material for interested readers that describes the measurement assumptions of the PCM and the criteria applied in this study to determine whether the assumptions are met.Many true-score equating simulation studies focus on IRT, that is, two-parameter logistic (2PL) or higher-order models for dichotomous item ratings. Rasch-based simulation studies interested in equating are rarer. The effect of lack of similarity of scales in a common person design is very little investigated. This study aims to shed light on the accuracy of score transformations across scales equated through concurrent calibration with a Rasch model. Especially, we want to come up with some concrete insights about the effect of departures from scale similarity, equity, and targeting when equating with the PCM and using a common person design. Before diving into Rasch-based true-score equating, an The true-score equating approach in a common person design uses a process with distinct analysis steps to arrive at a score transformation rule that links the scores from the equated scales. The steps required to equate two scales, called Scale X and Scale Y, throughout the study are described in what follows and shown in Appendix A in the Supplemental Online Materials). However, separate calibrations of the two scales produce independent estimates of Preliminary to the equating of scales, it is essential to consider the degree to which items exhibit proper fit within the respective scales . An analfor form X, andfor form Y. The The e scales .In this study design, where all test-takers have filled all different scales to be equated, the equating strategy can consist of a joint calibration of all the The The concurrent calibration in Step B equates Scale X and Scale Y and puts the two metrics on a common measurement continuum. for the anchored form X, andfor the anchored form Y.The process of preliminary fixing the ontinuum .When considering a latent trait being measured, each test-taker is expected to have only one ability level. Still, their test scores can vary because of the characteristics of the test versions used for the assessment. The concurrent calibration and analysis with anchored item estimates puts different scales on a common metric. A three-step score transformation is necessary to find the score on Scale Y that is the most equivalent to a score on Scale X. First, for a person  Scale Y . Table 1After equating, the concordance table directly links observed scores in one scale to the expected score on an equated scale. Applied psychometric equating studies using the Rasch model routinely report the respective fit of the scales to be equated to the Rasch model, often also the fit of the equated test versions to the Rasch model, and typically provide a user-friendly score concordance table that should facilitate score transformations in the applied work field .This simulation study hopes to contribute to the methodological literature in the field of true-score equating with the Rasch model and to provide some insights into the impact of characteristics of the scales on score transformations. The general objective of the study is to use simulated data to investigate the precision of score transformations based on Rasch-based equating in a common person design when varying the degree of similarity, the degree of equity, and the targeting of scales.Concordance tables allow converting individual raw scores from one scale to the other. Data from a common person design, where all test-takers answered all equated scales, permit checking the transformation quality directly. For example, it is possible to directly determine for each simulated test-taker whether a transformation of a raw score on Scale X  is reported, that normalizes the RMSE by the score range of the scales:The bigger the NRMSE, the higher the discrepancy between the score obtained through true-score equating  in Afghanistan in 2019 . In thissimdata from R package mirt for the simulation of uni- and multidimensional data for IRT models , item difficulty thresholds (via argument d) as well as their mean difficulty (via argument mu), the sample size (via argument N), and the type of items simulated, e.g., dichotomous or polytomous (via argument itemtype). This study used the itemtype = “gpcm,” that is, a generalized PCM parameterization, but by constraining slope parameters to equal 1, as the generating of multidimensional data is not directly available for Rasch models in mirt.When simulating data with simdata arguments theta or sigma. The argument theta permits the direct input of a vector of logit-scaled sigma also permits simulating simdata option sigma represents the dispersion or variance of the The different degrees of similarity between scales were operationalized by varying the degree of multidimensionality . Unidimensionality across scales indicates perfect similarity. Simulation of the similarity of the scales is closely related to the simulation of the person parameter. The person parameters . Across all settings, a higher similarity of the scales goes along with lower NRMSE, that is, higher equating precision. The precision improves almost linearly with increasing similarity  show the generated mean factor correlations. In any case, a higher similarity across scales increases the precision of the score equating. However, the advantage in the precision of the small The NRMSE values are generally indicating better transformation precision with ability dispersions Appendix C in the Supplemental Online Materials, Table C.8 to Table C.11). What matters most to the quality of the equating is that scales, measuring a similar construct, encompass the ability spectrum of the test-taker. Based on  Scale Y  and reve Scale Y . IdeallyThis example briefly illustrates how insights gained from the simulation study can be helpful for empirical studies where true-score equating with a common person design is conducted. This example will show how the statistical characteristics, especially the psychometric properties, of two test forms can enable researchers to appropriately anticipate the equating precision prior to the equating.The data were kindly made available by the Asia Foundation, who conducted the World Health Organization’s and World Bank’s MDS in Afghanistan in 2019 in about 14,000 households . The MDSTwo scales of the same length were created for the purpose of this example . The PerN = 1,000 MDS participants. The first group was intentionally selected from the middle score range of the Capacity Scale and with scores covering the entire measurement continuum. In this first group, there was only a slight difference between the mean Capacity and the mean Performance scores for all participants . With 20 items, the NRMSE dropped to 0.16 to 0.17 . For the empirical data of group 1, the observed NRMSE was 0.13, from the Capacity to the Performance Scale score and reversely. This observed transformation precision for the empirical data is somewhat better than what we would expect based on the simulation outcomes. However, the empirical data may have benefited from the lack of extreme values, which would have impacted the NRMSE more negatively. Cases with very high performance problems or very high difficulties in terms of their capacity were underrepresented . With 20 items, the NRMSE dropped to 0.09 to 0.1 . For the empirical data of group 2, the observed NRMSE was 0.1 from the Capacity to the Performance Scale score and 0.11 for the reverse transformation. For identity equating, the NRMSE was 0.21. The empirical example also supports the robustness of true-score equating, but not identity equating, in the presence of shifts in difficulty between the scales to be equated found in the simulation study. Thus, the transformation precision that can be expected based on the psychometric characteristics found in the second group agrees with the findings in the simulation study.In the second group, the factor correlation was This simulation study supports that, when equating scales, construct similarity is essential for a good score transformation precision. The factor correlation between scales, in other words, their construct similarity, explained to a large extent the score transformation quality. Higher correlation goes along with better transformation precision. The importance of the scale similarity in equating is not surprising, but this study also shows the relevance of the targeting, something few other studies have investigated so far. The precision of the score transformations improves with good targeting, when the scales have a broad measurement scope that embraces the ability spectrum of the test-taker. With highest similarity, the quality of the targeting did not have any notable impact on the transformation quality. With lower similarity of the scales, however, the impact of insufficient targeting was reinforced and further deteriorated the transformation precision. For a given With diminishing correlation between dimensions, the equated scales become more dissimilar, negatively affecting the score transformation precision. When observing equating in practice, similarity of the scales is often an implicit assumption that transfers into practice as a subjective evaluation of what the scales to equate are aiming to assess. Unidimensionality, or sufficient unidimensionality for a robust score transformation is not sufficiently supported by only assuming that scales measure a common latent trait. As mentioned in the introduction, also characteristics of the assessment, such as for example the response options or the general phrasing of the scale items, can strongly affect the degree of similarity of scales.In practice, the validity of a transformation rule between equated scales is often assumed if the single and equated scales fit the Rasch model but is rarely discussed in terms of transformation precision. We recommend always testing the between-scale dimensionality, for example by means of multidimensional Rasch analysis, which provides a tangible value of the degree of association between two scales. Good psychometric properties of the scales to be equated are not a sufficient guarantee for good score transformation precision. The separate analyses of the scales in this simulation presented generally acceptable to good psychometric properties. But, despite otherwise good psychometric properties, already with factor correlations of 0.75, the quality of a score transformation is negatively impacted, with average score departures up to possible .Studies reporting the degree of associations are rare, and critical cut-off values for judging the degree of association are missing with no consensus on what is sufficient unidimensionality . The empWhen the unidimensionality between the equated scales does not hold, alternative strategies that could be applied in practice are only marginally discussed in the literature. For example, multidimensional equating procedures exist . Also, iIn the research literature, the effects of targeting are more widely studied in terms of differences in difficulty across equated scales than in terms of differences in the degree of dispersion of the  the 2PL  or under the 2PL , or acro the 2PL  that repDrawing strong conclusions based on this simulation with a limited number of settings should be considered with caution, as for any simulation study. Only some assessment characteristics have been varied and observed systematically within a limited range. The sample sizes used in this study are representative for the health research field where equating studies are the most commonly undertaken. However, health assessment can also take place as part of national or international surveys in the general or more specific populations providing larger health data pools. The number of response options and the discrimination of items were kept constant to avoid disordering of thresholds and item misfit, as these were out of the research scope. More than three response options could have been considered. Measurement scales with more than five response options are not uncommon and are known to result in a more refined assessment . To be fThis simulation study has also several strengths. Many methodological equating studies use existing data or simulate data that are conditioned on parameters derived from analyses with the existing data instead of generating data following a simulation design. Real data or simulations conditioned on actual parameters describe realistic data collection settings. However, the generalizability of findings of such studies may be diminished and confined to settings with similar characteristics. Artificial data generate and target effects precisely through a standardized setting. Through the R environment , this stThis study showed that when observing similarity, equity and targeting of scales, the similarity was the most important determinant of equating precision. Similarity indicates that scales measure a common construct. The targeting of the scales also affected the precision of the equating, with a moderating effect and increasing impact when the similarity of the scales decreased. Differences in difficulty across scales had no notable effect on the precision of score transformations across equated scales for true-score equating. In that sense, the requirement for equity in true-score equating may not be a strong requirement when difficulty shifts are below two logits. This simulation study highlights the effects of scale characteristics and departures from similarity and suggests ways to improve the quality and transparency of the equating procedure, such as the assessment of the factor correlation by means of the multidimensional PCM and an analysis of the transformation precision. According to Click here for additional data file.Supplemental material, sj-pdf-1-epm-10.1177_00131644221143051 for What Affects the Quality of Score Transformations? by Carolina Fellinghauer, Rudolf Debelak and Carolin Strobl in Educational and Psychological Measurement


Serapias show a strategy defined as shelter imitation. The floral elements form a tubular structure that insects use during their resting phases. The purpose of this article was to clarify the mechanisms that guarantee pollination with particular attention to the morphological interactions between orchids and pollinators and whether pollinaria reconfiguration is necessary in the promotion of cross-pollination in Serapias. Breeding system experiments and hand-pollination treatments indicated that Serapias was highly self-compatible, shows low value of natural fruit set and is pollinator limited. Time-lapse photos showed that the pollinarium had no refolding of the stipe or caudicle after its removal from the flower. The morphology of the flower determined the attack of the pollinarium on the occiput/vertex of insect. When the insect left the flower, the pollinarium was unable to encounter the stigma. When the insect made a second visit to another flower, the pollen masses of the first pollinarium ended up on the stigma and at the same time, the insect picked up a second pollinarium. Our observations and analyses suggested that morphological interactions between flower and pollinator are crucial to the success of pollination and to prevent self-pollination and thus that pollinarium reconfiguration is unnecessary in shelter deceptive orchids, such as Serapias species, for the promotion of cross-pollination. Serapias represent a case of interactions between plant and pollinator; the formation of the tubular shape of the flower is an essential preadaptation for the development of resting site mimicry originating exclusively in Serapias among Mediterranean orchids.Orchidaceae, one of the most numerous families in the world’s flora, have evolved various pollination strategies to favour cross-pollination, such as deceptive pollination and pollinarium reconfiguration. Among the terrestrial orchids of the Mediterranean, only species belonging to the genus  Serapias show a strategy defined as shelter imitation. The floral elements form a tubular structure that insects use during their resting phases. Breeding system experiments and hand-pollination treatments indicated that Serapias was highly self-compatible, shows low value of natural fruit set and is pollinator limited. Time-lapse photos showed that the pollinarium had no refolding of the stipe or caudicle after its removal from the flower. Results suggested that morphological interactions between flower and pollinator are crucial to the success of pollination and to prevent self-pollination and thus that pollinarium reconfiguration is unnecessary in shelter deceptive orchids for the promotion of cross-pollination.Orchidaceae, one of the most numerous families in the world’s flora, have evolved various pollination strategies to favour cross-pollination.  Orchidaceae is the second-largest family in the plant kingdom with about 20 000 species , outnumbApart from some orchids showing spontaneous autogamy ability  and a unique callus (S. lingua). Serapias lingua and S. vomeracea are widespread species, growing in arid meadows, abandoned agricultural lands and garigues. The main pollinators of both species are hymenopteran insects of four genera  of the superfamily Apoidae : Piano Lago , S. Donato di Ninea  and Arcavacata . To minimize the effects of soil and vegetation types on our measurements, we chose sites with matched vegetation types. All populations were characterized by calcareous dry grassland ; Spartium junceum, Cytisus sessilifolius and Cistus incanus were the most common shrubs and Festuca circummediterranea, Bromus erectus and Dactylis glomerata were the dominant herbs. Two sites (Piano Lago and Arcavacata) occurred in a highly anthropized landscape context enclosed by high-traffic roads and their crosses and were built in the late 1960s, while the third site (S. Donato di Ninea) was moderately anthropized.Field experiments were conducted in April–June 2022 in three sympatric populations of S. vomeracea and S. lingua were performed in 2022 in P1 population. Approximately 150 unopened flowers from 30–40 plants (3–5 flowers per plant) for both species were bagged with a fine mesh cloth to exclude pollinators and then hand-pollinated. Treatments included artificial self-pollination (pollinia were taken from the same flower) (induced autogamy) or from a different flower on the same plant (induced geitonogamy), spontaneous autogamy (flower covered with a fine-meshed cloth but no manipulation) and cross-pollination (pollinia from a flower to the stigma of another flower located over 20 m away). In June, the number of capsules was counted and the ratio between the number of flowers treated/fruit produced for each hand-pollination treatment was determined.Pollination treatments designed to investigate the breeding systems of To test the natural reproductive success, in five square grids for each populations the number of flowers that produced fruit was counted and the fruit set was determined as the mean of the ratios (number of fruits produced/numbers of flowers available) on the plants examined. To ascertain the presence of viable embryos, at least 1000 seeds from each fruit were removed from the centre of the capsule and observed under an optical microscope (×100). Seeds were assigned to two categories (viable and unviable seeds) due to the presence or absence of viable embryos. Seed set [(the number of filled seeds in sampled fruits/the number of observed seeds) × 100] was calculated for each fruit.An ANOVA was used to partition the variation in reproductive success among populations and among plants within populations. All analyses were conducted using SPSS 16.0 for Windows. The data were analysed using descriptive statistics.To test for spontaneous pollinaria reconfiguration, the pollinaria from 10 flowers from populations of each of the orchid species tested were carefully removed with toothpicks, and photographs were taken every 5–10 s until further folding movements were observed.Serapias flowers, we built a small artificial carpenter bee (Ceratina cucurbitina), the main pollinator of Serapias, respecting the average size of the insect, 10 mm long and 3 mm wide  to 86.40 (±3.85) in S. vomeracea and from 82.25 (±2.25) to 84.85 (±2.95) in S. lingua . In detail, they showed a low value of natural fruit set and no population showed a percentage of reproductive success above 25 %. These data agree with those reported in other articles on the genus Serapias  due to the behaviour of the insect on a single flower; there could be cases of geitonogamy if the insect, once leaving the first flower, made the next visit to a flower of the same inflorescence. Personal observations have brought to light that, after the insect has remained in the flower throughout the night or in a moment of need for rest during the day, it moves away from the inflorescence. It is likely that insects with only one visit have already received the shelter reward and do not need to visit a second flower immediately afterwards, as happens in other deceptive or rewarding orchids. Furthermore, in deceptive food orchids, for example, insects that visit one flower and receive no reward, given the absence of floral nectar, are driven to visit a second flower, a third and so on in the same inflorescence or of another plant in a fairly rapid time. In the case of nectariferous orchids, insect that receives a reward is driven to visit another flower similar to the previous one to collect more nectar to satisfy its energy needs. This is why these species, thanks to pollinarium reconfiguration and the correlation between reconfiguration time and pollinator visiting time, limit self-pollination. Insects visiting a Serapias flower are not driven to visit a second flower as soon as they leave the first one but will do so after many hours, in most cases after 24 h. After a long time, it is highly unlikely that the insect will choose the same flower or flower of the previously visited inflorescence with thousands of similar usable flowers. It is obvious that it cannot be excluded that the insect may return randomly to the same inflorescence, thus allowing self-pollination. Therefore, it can be concluded that the pollination biology of Serapias, the perfect morphological interaction between the reproductive structures of the flower and the pollinating insect, ensures cross-pollination at the expense of self-pollination without the need for pollinarium reconfiguration.This phenomenon and the absence of bending in the populations studied cannot completely rule out the possibility of geitonogamy in Serapias may represent a case of macroevolution enforced by pollinators. Food deception has been highlighted as the ancestral trait in the mostly Mediterranean orchids, and Ophrys and Serapias diversified more recently (~4.6–6.7 Mya) than other Orchidinae (~12.8–16.5 Mya) (Ophrys the production of high levels of n-alkenes represents the key innovation of the pollination strategy, the formation of the tubular shape of the Serapias flower is considered an essential preadaptation for the development of resting site mimicry originating almost exclusively in Serapias. The evolution of floral characteristics, especially traits involved in pollinator attraction, is under pollinator-mediated selection in many plant species; thus, flower colour and shape have been shown to have an impact on pollinator attraction (Serapias perianth (Pollinator adaptation is generally considered the main reason for floral diversification in plants.


Interaction-driven modeling of diseases over real-world contact data has been shown to promote the understanding of the spread of diseases in communities. This temporal modeling follows the path-preserving order and timing of the contacts, which are essential for accurate modeling. Yet, other important aspects were overlooked. Various airborne pathogens differ in the duration of exposure needed for infection. Also, from the individual perspective, Covid-19 progression differs between individuals, and its severity is statistically correlated with age. Here, we enrich an interaction-driven model of Covid-19 and similar airborne viral diseases with (a) meetings duration and (b) personal disease progression. The enriched model enables predicting outcomes at both the population and the individual levels. It further allows predicting individual risk of engaging in social interactions as a function of the virus characteristics and its prevalence in the population. We further showed that the enigmatic nature of asymptomatic transmission stems from the latent effect of the network density on this transmission and that asymptomatic transmission has a substantial impact only in sparse communities. Disease progression results from the interplay between the population’s complex interaction dynamics, which are associated with the population’s physical contacts’ network, and the disease dynamics3, as well as characteristics such as the population age5.The SARS-CoV-2 pandemic, like other diseases, spread differently in different countries and communitiesinteractions-based contagion model (ICM) of airborne diseases for COVID-197 over real-world interaction data that is enriched with personal disease progression details that depend on the individual susceptibility to the disease. The model is termed Interactions-based Contagion Model with Individual outcomes (ICMI). The individual susceptibility determines the severity of the disease for an infected individual. For COVID-19, the probability of an individual contracting a severe form of the disease, referred to as their susceptibility to the disease, is a function of a person’s age4.Here, we present in detail an SEIR-like 10. Contacts’ temporal ordering and dynamics are crucial for understanding the transmission of infectious diseases. The interactions’ temporal path ordering was shown to affect the spreading dynamics17. Further, considering the accurate structure of human interactions is pivotal for correctly predicting the spread of epidemics, such as the Covid-19 disease18. To model the disease progression in a real-life community, we use the real-world encounters data from the Copenhagen Networks Study (CNS) dataset21. The use of real-world interaction data as the dataset for our analysis allows for a person-to-person spread of disease at the level at which it occurs in its actual temporal and local contexts23.Accurately modeling disease progression requires considering the time-respecting paths, which are the sequence and order of these interactions between the members24. Thus, the duration of the interaction is crucial for correctly simulating the airborne transmission of various pathogens. A key feature of ICM is that the interaction’s duration is correlated positively with the latent transmitted viral load if the encounter is with an infected person. Duration of interaction as a proxy for the transmitted viral load was used for estimating viral infection between animals25 and humans30. Smieszek26 noted that the time people spend interacting with each contact person decreases as the number of contact persons increases. The suggested model takes the length of the exposure into account while following real-world interactions of various scales that exist in the CNS dataset, as the proximity information enables the detection of gatherings32.An investigation of the transmission of a severe acute respiratory syndrome (SARS) in a 2003 Toronto-area community outbreak found that “longer and closer proximity exposures incurred the highest rate of disease”Combining the above with individual susceptibility, the ICMI model presents three significant contributions.7 by taking individual outcomes into account, enabling it to predict outcomes at the community and individual levels. With ICMI, the daily and average expected percentage of needed hospital beds could be predicted for communities that leverage digital proximity tracing applications34. In addition, the model considers the probability of symptomatic or severe infection in correlation with the individual’s age. It models age using a personal susceptibility parameter, First, it extends the capabilities of ICMSecond, ICMI enables us to model and predict individual risk of infection given personal daily exposure. Individual risk prediction projections are provided as a function of different variants’ virality and individual vulnerability probability due to personal immune levels. This prediction of individual risk not only enables individuals to plan their schedules to reduce their risk of infection but also presents a complementary paradigm to the current government-imposed non-pharmaceutical interventions (NPIs), providing an additional layer of personal control.36 since asymptomatic individuals continue their normal social and travel activities while being hard to trace37. The exact extent and impact of asymptomatic transmission are debatable38, and differences in asymptomatic cases’ generation time may affect the transmission and spreading factor estimations39. Here, we find that asymptomatic transmission is significant and influential only in relatively sparse networks, and its effect is mitigated in dense networks. Asymptomatic transmission influences the progression of the disease only in sparse communities.Third, the ICMI model contributes to the study of the spread of diseases caused by asymptomatic transmission. Asymptomatic transmission of diseases such as COVID-19 is considered to be the Achilles’ heel of the pandemic controlThus, taking into account the macroscopic daily outcomes of the microscopic interactions while considering individual susceptibility to severe disease enables us to predict outcomes at both the population and the personal level. The model further allows predicting individual risk of conducting meetings as a function of the virus characteristics and its prevalence in the population. We further showed that the enigmatic nature of asymptomatic transmission stems from the latent effect of the network density on this transmission and that asymptomatic transmission has a substantial effect only in sparse communities.We ran numeric simulations over the CNS real-world interaction dataset, combining two processes. The first is the interaction model (ICM). The model considers the duration of the interactions, as is described in Eq. . Figure 6. The ICMI model, however, assigns heterogeneous personal vulnerability values as described in each experiment. Personal vulnerability correlates with age, as The second process incorporated is the personal disease progression modeling according to the individual susceptibility, as described in the infection model presented in Fig. https://github.com/ScanLab-ossi/covid-simulation.The two processes are combined in each of the simulations, and each experiment is the result of 200 iterations. The simulation code is written in Python and is freely available: We start with a simulation of the disease progression over the real-world CNS temporal network. Given a variant with a minimum exposure latency i, interactions with Infectious nodes, either presymptomatic or asymptomatic, that are longer than Susceptible or enters state Exposed and infected. Personal progression of the disease then follows the individual state machine depicted in Fig. During each day, for each node entclass1pt{minimaentclass1pt{minimaentclass1pt{minimaentclass1pt{minimaWe further see that more contagious variants, as is the case shown in Fig. Considering the changing daily number of meetings and their lengths, we can approximate the individual probability of infection, given their daily exposure. We project here individual infection outcomes as a function of the daily number of meetings and their lengths and contextual information. Contextual information can be considered a proxy for the virality of a variant and susceptibility to the infection of an individual’s immune system.i to the virus. In this approximation, high When considering meetings’ duration, the minimum duration in the model, 40.In these two experiments, we examine the probability of becoming infected. This probability differs from the probability of being symptomatic or severely ill, which correlates with the personal susceptibility parameter, N people encountered by an average person during that time window was generated by randomly sampling from a distribution We generate random exposure data sampled from distributions fitted to the CNS real-world aggregated data. Aggregated information was taken such that an average daily outcome could be calculated. The average number of infected individuals differs on different days, depending on the spread of the virus in the community. Typically, a person would not be aware of the precise situation in their community. Hence, we consider the average of all the days in the dataset as the typical day over which we calculate individual outcomes. In a time window Figure Figure n is the total number of individuals in the simulation. The distribution of community personal susceptibility levels, Modeling asymptomatic transmission can be achieved using the individual susceptibility parameter at the community level. ICMI’s detailed individual disease progression encompasses the individual susceptibility factor per node, 41.To examine the effect of asymptomatic transmission in a population, we ran the simulation over the CNS dataset while varying the average age of the population, s.t., the percentage of asymptomatic among the infected varies between 10 and 90%. Each experiment was performed 200 times, with random placement of the initial patient zero. Figure This is also a sensitivity test for how transmission in a community differs when the population age varies.6, we demonstrated that the CNS network is very dense. Over two-thirds , infected (I), diagnosed (D), ailing (A), recognized (R), threatened (T), healed (H), and extinct (E). However, the model did not consider the temporal dynamics of human interactions nor the effect of the duration of the encounters. Our model agrees with the findings of Peirlink et al.58 that if infectiousness is the same for both symptomatic and asymptomatic patients, the size of the asymptomatic population does not largely affect the overall outbreak dynamics. Other complementary findings to ours are those of Park et al.39 and Subramanian et al.41, who have shown that a faster asymptomatic transmission rate increases the realized proportion of asymptomatic transmission. Yet these findings did not take into account how asymptomatic contagion is affected by the density of the population. In here, it was shown that asymptomatic transmission has a substantial impact only in sparse communities.The importance of considering personal differences was discussed by many. For example, age and comorbidity factors contributed to the appearance of symptoms and to early isolation after infection59. The CNS dataset was similarly used by Hambridge et al.60, who devised a temporal interaction-based SEIR model to assess the effect of various interventions on the CNS data. Unlike ICMI, the work does not consider interactions’ length, and assumes that multiple exposures on the same day increase the risk.ICMI considers the interaction’s length as a proxy for the transmitted viral load. It computes the probability of infection at the end of the day. ICMI aggregates viral load only in the case of higher-order interactions, like group meetings. Otherwise, it does not consider different interactions as having an additive effect, as there is no evidence that viral load “remains” in-between interactionsThe ICMI model is the first to consider the interaction between the daily macroscopic dynamics and the microscopic interactions to predict the spreading dynamics in a population, given the various outcomes of getting infected within the population. Given today’s abundance of digital traces, the ICMI model enables policymakers to assess the disease progression using real-world interactions typical within their communities while considering the various pathogens. We have shown that by incorporating the individual outcomes and the community age distribution, policymakers could receive an estimation of the expected number of hospital beds required as the disease progresses in the community.Devising a method for predicting individual outcomes as a function of daily exposure to a pathogen further gives a personal design tool for individuals to assess their risk in taking meetings of various lengths given the spread of the virus in the community. The method enables policymakers to decide when would be the right time to restrict large gatherings and long meetings and decide on general guidelines for the public.6. We thus showed that the effect of asymptomatic latent transmission is negligible in dense networks but not in sparser ones. An additional limitation is that the analysis of latent transmission due to asymptomatic infections does not consider that symptomatic and asymptomatic people shed different viral loads62. The option was implemented in the code and is part of our future work.The work has several limitations. The CNS dataset is the result of students’ interactions in a university. The interactions were denser than social interactions, which may result in a faster-than-reality infection processThe paper describes an SEIR-like interaction-driven contagion model of airborne disease for COVID-19 with individual outcomes (ICMI) that depend on age. It shows that ICMI, encompassing daily macroscopic dynamics with the microscopic level of interaction duration, enables outcomes prediction on both the population and the individual levels. It further allows for individual assessment of risk levels in different populations and can be used as a tool by policymakers. Using ICMI, we further showed that the effect of latent transmission due to asymptomatic infections depends highly on the structure and interaction density of the population’s social network and is higher in sparser structures.52 to explore the model further. The data would be augmented with the corresponding population age distribution to enable community-level predictions for real-life communities. Here, age was considered a proxy for personal vulnerability to the disease since we considered the recent COVID-19 pandemic a key example. However, in the case of other pathogens, other individual factors can be used.In future work, we intend to use additional datasets obtained from community digital contact tracing or community structure as provided inmacroscopic level (daily). Here, we consider the topological structure of the interactions. Who met whom, and when, during each time window. Every day, we assess the likelihood of each node being exposed and infected within a given time window. This probability is the complement of the chance that the node avoids exposure during all of its encounters with infectious nodes in that time window.Real-life temporal interactions, modeled at a duration of all interactions: how long each interaction lasted, and was it long enough to result in infection? Interaction duration is modeled at a microscopic level and correlates positively with the latent transmitted viral load, which, in turn, is positively correlated with the probability of getting infected62.The 4. Infected individuals, whether symptomatic or asymptomatic63, become infectious and can transmit the infection to others. Symptomatic individuals are removed from the network once symptoms appear. Recovered individuals cannot be reinfected with the same variant. The individual disease progression encompasses the population diversity, found to critically affect the spread of Covid-1964.Individual disease progression modeling: a personal susceptibility parameter mediates the progression and severity of the disease for infected individuals. Following the literature, for COVID-19, this parameter correlates with ageThe ICM with Individual outcomes (ICMI) model encompasses the emergent effects of the following three modeling dimensions: Susceptible, Exposed, Infectious, and either Recovered or Removed. All nodes begin in state S, but for some initial infectious patients zero nodes in state I. Nodes that interact with infectious nodes might become infected, entering state E. State E stands for exposed and infected. Infected nodes become Infectious, thus entering state I. Infectious nodes in state I transition to state R. The transition between states S and E is probabilistic and immediate. The transition between states E and I and from I to R is merely a function of time.Interacting nodes can be in one of the following states: i during that time window and thus might potentially expose it to the infection, and In the model, the probability of being exposed is calculated at the end of each time window 65. Hence, the likelihood of getting exposed and infected during each interaction with an infectious node is modeled as a Sigmoid function of the duration of the interaction.The probability of infection is inversely correlated with distance and decreases dramatically with it, and is correlated with the duration at the exposure distancei to get exposed and infected that is calculated as follows. Let i from an infected node k, where K is the set of infectious nodes that i encounters in time window i and an infectious neighbor node i becoming exposed and infected during an encounter with an infectious node k is as follows:At each encounter with an infectious node in time window 67, the virality of such pathogens is correlated in the model with the minimum exposure latency, As COVID-19 variants, such as Alpha and Delta, are associated with different exposure levels of transmitted viral loadi becoming exposed and infected (state E) is calculated as the complement of the probability of not being exposed in any of the encounters during that time window with infectious nodes, as follows:i in state Susceptible to transition from state Susceptible to state Exposed following the interactions during the time window At the end of each time window i may encounter more than one infectious node k. We consider that in gatherings in which a node interacts with several infectious others, it is exposed to a higher viral load. The duration of the interaction in a gathering is calculated as the gathering’s duration multiplied by the number of infectious nodes participating in the gathering.In the case of a gathering, it is probable that node susceptibility parameter and correlate it with age68. Hence, the higher the individual susceptibility, the more likely the probability of becoming symptomatic and severely ill. Disease progression is currently set to follow a known timeline70.Once infected, personal reactions to the infection differ based on age, comorbidity, and other latent features. To trade off accuracy with simplicity, we encompass all of the above in a personal personal susceptibility probability, referred for node i as We will now explain the individual medical progression model. Once a person is exposed and infected, the disease progression and timeline depend on their Susceptible, and following Eq. 78. For infection probability, distance is just one of the dimensions in calculating the chance of infection - the directions of standing, ventilation, and the environment are equally significant parameters81. As this information was unavailable, we chose to model proximity rather than exact distance and direction. Stronger signals correlate roughly with high proximity. Hence, we mined the CNS network for interactions for which the RSSI The CNS proximity information was registered as a function of the Received Signal Strength Indicator (RSSI). Extracting exact distance information from RSSI data is a difficult taskT consecutive undirected weighted temporal graphs 31. Each edge is a distinct interaction. Edge weight corresponds to the duration of the interaction used in the model described above. We further detect gatherings, as in31, as the effect of gatherings on contagious epidemic processes was recently researched and found significant82.We model the social network of interactions


In this paper, a structured illumination microscopy (SIM) image reconstruction algorithm combined with notch function (N-SIM) is proposed. This method suppresses the defocus signal in the imaging process by processing the low-frequency signal of the image. The existing super-resolution image reconstruction algorithm produces streak artifacts caused by defocus signal. The experimental results show that the algorithm proposed in our study can well suppress the streak artifacts caused by defocused signals during the imaging process without losing the effective information of the image. The image reconstruction algorithm is used to analyze the mouse hepatocytes, and the image processing tool developed by MATLAB is applied to identify, detect and count the reconstructed images of mitochondria and lipid droplets, respectively. It is found that the mitochondrial activity in oxidative stress induced growth inhibitor 1 (OSGIN1) overexpressed mouse hepatocytes is higher than that in normal cells, and the interaction with lipid droplets is more obvious. This paper provides a reliable subcellular observation platform, which is very meaningful for biomedical work. The resolution of ordinary optical microscope cannot exceed the optical diffraction limit , which lDue to the difference between theory and actual experiment, the modulation of structured light cannot ensure that its frequency and phase are exactly the same as the theoretical value. Therefore, the estimation of the modulation frequency and phase of structured light fringes have become a key step in SIM reconstruction. So far, many researchers have proposed frequency phase estimation algorithms to make the estimation of reconstruction parameters more accurate, thereby improving the quality of image reconstruction. In 2009, Shroff proposed the phase of peaks algorithm (POP) . This alWhen the high and low frequency components are separated, it is necessary to superimpose the separated frequency spectrum. Through a reasonable reconstruction algorithm to deal with the frequency spectrum of the overlapping part, the image artifacts can be reduced. In 2008, the generalized Wiener reconstruction algorithm was proposed, eight years after Gustafsson first proposed the concept of structured light super-resolution imaging . This alThe problem of artifacts in SIM super-resolution image reconstruction has always been a difficulty in this research field. In the supplementary document of the article, Huang made a comprehensive summary of the types and causes of artifacts in the current SIM super-resolution image reconstruction. When the sample moves too fast, motion artifacts will be generated. When the frequency and phase estimation of the modulated wave vector is inaccurate, ring artifacts will be generated. When the Optical Transfer Function OTF measurement of the optical system is inaccurate, snowflake artifacts will be generated. When there is a defocused background in the sample image, streak artifacts will be generated. The above artifacts can be overcome in different ways. Improving the image acquisition speed of the system can overcome the motion artifacts, accurately estimating the modulation parameters can overcome the ring artifacts and accurately measuring the OTF of the system can avoid snowflake artifacts. Streak artifacts can be removed by suppressing the defocusing background. The imaging depth by the total internal reflection imaging method is very shallow, so there is no defocusing background during data acquisition. At the same time, its imaging depth limits its observation of thick samples. Therefore, the method of using algorithms to suppress is more universal than the method of adjusting optical devices aiming to solve the problem of streak artifacts caused by defocusing background during thick sample imaging. However, many existing algorithms are not effective in suppressing such artifacts. As shown in By analyzing the mathematical model of structured light illumination imaging, a filter was designed to process the low-frequency signal in the imaging process. Under the condition of retaining the information of the image, the streak artifacts caused by defocused light in the imaging process were effectively suppressed, and the imaging quality of the image was improved. Mitochondria are organelles responsible for producing energy in organisms. They are the main place for cells to carry out aerobic respiration and are closely related to the state of cells. Long-term damage to mitochondria is shown to be associated with the occurrence of liver disease, and changes in mitochondrial function is confirmed in a variety of chronic liver diseases. Studies have shown that OSGIN1 allele imbalance is associated with the progression of liver cancer . The N-SThe optical imaging system of a wide-field microscope was actually equivalent to a low-pass filter. Due to the limitation of optical diffraction, the process of imaging the sample actually truncated the high-frequency information (the fine structure of the sample) of the sample beyond the support domain of the optical transfer function (OTF), thereby limiting the spatial resolution of the imaging. The SIM could move high-frequency information to the OTF support domain to achieve super-resolution. The imaging principle is shown in The illumination light with spatial structure excited the sample in the SIM. Based on the principle of Moiré effect, the high frequency information of the sample (the detail information of the sample) that cannot be obtained under the wide-field illumination mode was modulated into the OTF support domain of the optical microscopy imaging system. Then, through the frequency domain signal demodulation, high and low frequency signal separation, shift, reconstruction and other steps could achieve a relative wide-field microscope imaging twice the resolution. In SIM, the cosine structured light is usually applied to illuminate the sample. The Fourier transform of the spectral expression of the SIM raw image is as follows:Through the above methods, the resolution in one direction can be improved. If the super-resolution of the image in the whole plane is needed, the structural fringes need to be rotated In general, the observation sample of the optical microscope was thin after special preparation. However, the samples used in dynamic imaging of living cells were thick, this inevitably produced defocus noise. If the defocus signal was not suppressed, it would have produced streak artifacts in the process of image reconstruction , affectiFrom the Equation (1), it can be seen that the low frequency signal and defocus signal of the collected sample had the same frequency range, so the Equation (1) can be rewritten as follows:Therefore, the defocus signal only affected the low frequency spectrum of the sample spectrum and did not affect the high frequency signal. In the frequency domain, the defocus signal and the low frequency spectrum were mixed together, so the appropriate processing of the low frequency spectrum could achieve better defocus signal suppression.In this paper, based on the generalized Wiener reconstruction algorithm, the reconstruction algorithm expression was rewritten appropriately. A notch function was added to the equation to limit the defocus signal in the low frequency spectrum. The generalized Wiener reconstruction expression is as follows:The above Equation (6) is the expression of the two-dimensional Gaussian function, which can be transformed to a notch function by the following Equation (7), and the notch degree can be controlled by controlling the parameter In order to verify the N-SIM algorithm, this paper used the resolution board to analyze the algorithm. First, we added Gaussian noise with mean value of 0.1 and variance of 0.1 to the original image, then simulated the modulation of the image, and then used Wiener reconstruction algorithm, RL reconstruction algorithm, HIFI reconstruction algorithm and N-SIM algorithm to reconstruct the modulated image, respectively. The result of image reconstruction is shown in A two-dimensional structured light super-resolution imaging system was manually built in this study, as shown in After the original image was collected, the generalized Wiener-SIM, RL-SIM, HIFI-SIM and N-SIM algorithm were applied to reconstruct the original image. The reconstruction result is shown in The fluorescence intensity of the four reconstructed images was analyzed. The results are shown in In order to verify that N-SIM algorithm has more obvious suppression effect on background noise, the fluorescence intensity fluctuation on the yellow line (the yellow line only contains the fluorescence information of the background area) of the background area in Since the principle of this method was realized by suppressing the low-frequency spectrum of the sample, it might have affected the effective information (sample structure information) of the sample. In order to verify the effectiveness of this method, an adjustable parameter was given in this paper to control the suppression of the notch function on the low-frequency of the center position. When setting different values, different results would be obtained. It can be seen from The system calibration was carried out by imaging 50 nm fluorescent microbeads. The image reconstruction was performed with the N-SIM algorithm as shown in The full width at half maximum (FWHM) of the reconstruction algorithm corresponding to the imaging result was calculated by the gray value statistics of the pixels on the yellow line position in OSGIN1 gene has a strong tumor suppressor function, mainly encoding oxidative stress proteins involved in the regulation of cell death . TherefoThe sample cells in this paper were purchased from the American culture library , cultured in a basal medium supplemented with 10% fetal bovine serum and ITS-G , cultured in an incubator containing 5% carbon dioxide (37 °C), and using oleic acid and palmitic acid in 75% ethanol. The mixture was heated to 55 °C and completely dissolved for membrane formation. Lipid droplets and mitochondria in mouse hepatocytes were then stained with Bodipy493/503 and Mito-tracker Red CMXRos, respectively. Membrane formation and staining were performed in a confocal dish.Sample data acquisition through the optical system mentioned above. The CMOS camera collected 9 original images, the sampling interval was 5 ms, and a set of pictures is collected every 30 s. Then the N-SIM algorithm mentioned in the paper was used to reconstruct the image to achieve image super-resolution. After reconstruction, a dynamic image with a time resolution of 30 s could be obtained.The OSGIN1 gene overexpressed cells and normal cells were subjected to structural illumination imaging, and the collected data were super-resolution reconstructed with the N-SIM algorithm. The time interval between each frame of images was 30 s. The mitochondria in each frame of images were observed. The results are shown in It can be observed from In hepatocytes, mitochondria interact with lipid droplets, so the activity of mitochondria also has a great influence on the state of lipid droplets in cells. The samples were observed using a 100× objective lens. After image reconstruction, it was found that there were more and larger lipid droplets in normal mouse hepatocytes, and the morphology of lipid droplets in OSGIN1 gene overexpressed cells was smaller and less, as shown in In this paper, MATLAB software was applied to realize lipid droplet recognition and size detection. The size distribution of lipid droplets in normal mouse hepatocytes and OSGIN1 gene overexpressed hepatocytes was obtained as shown in Via data collection and reconstruction, it was found that OSGIN1 gene overexpressed cells had stronger mitochondrial activity. Specifically, during the same time, the number of mitochondria in OSGIN1 gene overexpressed mouse hepatocytes changed greatly, while the number of mitochondria in normal mouse hepatocytes was relatively more stable. It was also shown that there were more mitochondrial fission and fusion events in OSGIN1 gene overexpressing cells than in the normal cells.In addition, mitochondria in OSGIN1 overexpressed hepatocytes significantly promoted the decomposition of lipid droplets. This is evidenced by more and larger lipid droplets in normal hepatocytes than in OSGIN1 overexpressed hepatocytes. This observation is further confirmed by biological experiments, which verify the reliability of the system and N-SIM algorithm mentioned in this paper.In this paper, a Wiener reconstruction algorithm combined with notch function is proposed by analyzing the principle of generalized Wiener reconstruction algorithm. Through the processing of the low frequency part in the reconstruction process, the streak artifacts caused by defocused light in the image reconstruction process are successfully controlled, and the lateral resolution of 144 nm is realized, which improves the imaging quality of image reconstruction. The structured light super-resolution image reconstruction software is developed by MATLAB, which integrates the two existing reconstruction algorithms and the reconstruction algorithm proposed in this paper. In the experiment, it is found that the activity of mitochondria in OSGIN1 gene overexpressed cells is higher than that in normal cells, and the decomposition of lipid droplets is more obvious. For the two organelles of mitochondria and lipid droplets, an image recognition detection program is developed by MATLAB.The N-SIM algorithm proposed in this paper suppresses the defocused light in the imaging process. However, the imaging resolution of the system is not improved, and the reconstruction time of the algorithm is long . Camera with smaller pixels can be applied, and the algorithm process can be optimized to improve the efficiency of software operation.In summary, this paper provides a stable and reliable observation platform for biomedical researchers for mitochondria and lipid droplets in biological cells.


Dynamic magnetic resonance imaging (MRI) is a popular medical imaging technique that generates image sequences of the flow of a contrast material inside tissues and organs. However, its application to imaging bolus movement through the esophagus has only been demonstrated in few feasibility studies and is relatively unexplored. In this work, we present a computational framework called mechanics-informed MRI (MRI-MECH) that enhances that capability, thereby increasing the applicability of dynamic MRI for diagnosing esophageal disorders. Pineapple juice was used as the swallowed contrast material for the dynamic MRI, and the MRI image sequence was used as input to the MRI-MECH. The MRI-MECH modeled the esophagus as a flexible one-dimensional tube, and the elastic tube walls followed a linear tube law. Flow through the esophagus was governed by one-dimensional mass and momentum conservation equations. These equations were solved using a physics-informed neural network. The physics-informed neural network minimized the difference between the measurements from the MRI and model predictions and ensured that the physics of the fluid flow problem was always followed. MRI-MECH calculated the fluid velocity and pressure during esophageal transit and estimated the mechanical health of the esophagus by calculating wall stiffness and active relaxation. Additionally, MRI-MECH predicted missing information about the lower esophageal sphincter during the emptying process, demonstrating its applicability to scenarios with missing data or poor image resolution. In addition to potentially improving clinical decisions based on quantitative estimates of the mechanical health of the esophagus, MRI-MECH can also be adapted for application to other medical imaging modalities to enhance their functionality. The esophagus plays a crucial role in the functioning of the gastrointestinal tract, and esophageal disorders are associated with reduced quality of life. There is a high worldwide prevalence of esophageal disorders, as exemplified by studies  reportiner study  reporteder study , and funer study . An esoper study  classifiin vitro. In silico modeling of the esophagus has been performed both in the context of pure fluid mechanics  using a 3D MR angiography sequence  designed for contrast-enhanced cardiac imaging applications, which was adapted to be used for esophageal imaging using pineapple juice as an oral contrast agent. Sequence parameters included In this study, we used data from a single healthy volunteer to demonstrate this framework. The MRI output consisted of a cuboid wherein voxels in a Cartesian coordinate system had different magnitudes of intensity. The temporal resolution of the dynamic MRI (1.17 s) determined the number of images with the bolus seen within the esophagus: seven time instants in this study. The typical length of an adult esophagus is 18–25 cm . The aveMRI-MECH modeled the esophagus as a one-dimensional flexible tube. For such a one-dimensional analysis, the variation in cross-sectional areas at different points along the length of the esophagus and at different time instants had to be extracted from the three-dimensional bolus obtained from segmentation. This was performed in two steps. The first step was to generate a center line along the length of the esophagus. The bolus shapes observed at different time instants were superimposed, and then, cross-sections of the superimposed shape at different horizontal planes from the proximal to the distal end of the superimposed shape were generated. The centroids of these cross-sections were connected to form the center line. The length of the center line, in this case, was 9.65 cm. The second step, after extracting the center line, was to generate planes perpendicular to the center line, as shown in 3 and 0.003 Pa.s  at the proximal end of the esophagus opens to allow the bolus into the esophagus, closes once the fluid has passed through it, and remains closed thereafter. Hence, we specified zero velocity at The low spatial resolution of the dynamic MRI poses a problem in accurately identifying the lower esophageal sphincter (LES) cross-section. This is because the LES opening is narrower than the esophageal body and does not distend very much because of the greater wall stiffness at the EGJ. Although this could be improved by focusing the MRI only on the LES, the state of the esophagus proximal to the LES cannot be estimated in such a scenario. The LES can be identified in only 1 or 2 time instants when the LES has significantly distended due to bolus flow through it. As specified in the previous section, since pressure is specified as a Dirichlet boundary condition at the distal end of the esophagus, the intrabolus pressure prediction depends on the accurate measurement of the LES cross-sectional area. The problem of missing data for the LES cross-sectional area  was solved using a physics-informed neural network . The proIt should be noted that there is no The LES cross-sectional area  as a function of The cross-sectional areas proximal to the bolus cannot be visualized in MRI because the fluid contrast medium was completely displaced by the peristaltic contraction, and dynamic MR imaging cannot distinguish the esophagus from surrounding tissues. Hence, we assigned the inactive cross-sectional area The variation in the LES cross-sectional area is shown more clearly in The variations in bolus fluid velocity and flow rate are shown in The variation in fluid pressure is shown in oroscopy .The total intrabolus pressure, as shown in Esophageal wall stiffness  was estimated by the parameter The parameter The MRI-MECH framework assumes constant values for the inactive cross-sectional area We did not use any weight functions for the heterogeneous loss functions to calculate the total loss, as described in Eq. An important aspect of the validation of this framework was to minimize all possible errors in predictions when compared with the measurements, specifically the variation of cross-sectional areas. Thus, our framework never predicts anything different from the measurements. Furthermore, an important characteristic of bolus transport is the physical transport of fluid through the esophagus, which must follow the laws of physics, specifically the mass and momentum conservation equations. Thus, low values of the residues for the mass and momentum conservation equations imply that MRI-MECH ensures that the physical laws are accurately followed. Finally, the estimate for esophageal wall stiffness for the normal subject who underwent the MRI procedure lay in the normal range, as reported in the studies by Although MRI-MECH provides valuable insights into the nature of transport and the mechanical state of the esophagus, it has limitations. Currently, manual segmentation of the bolus geometry is more accurate and reasonable for the low temporal resolution of the dynamic MRI, but it can become tedious with improved temporal resolution. Automatic segmentation using deep learning techniques might be helpful in that aspect, but itincreases the risk of inaccurate segmentation without a large training dataset. Bolus transport, as visualized in MRI, provides no information proximal to the bolus . Hence, MRI-MECH cannot predict anything meaningful proximal to the bolus. Thus, MRI-MECH cannot be used to estimate the contraction strength, for which other diagnostic techniques such as HRM or FLIP should be used. The esophageal wall properties and neurally activated relaxation were estimated solely through the bolus shape and movement. However, the bolus shape and movement depend not only on the esophageal walls but also on the impact of the organs surrounding the esophagus. This is a limitation of the MRI-MECH framework in predicting the state and functioning of the esophagus due to a lack of information about the impact of the surrounding organs. Finally, the prediction of intrabolus pressure and esophageal wall stiffness depends on the specification of the correct intragastric pressure. This becomes a limitation for MRI-MECH since the intragastric pressure is not known in MRI, so we used a reference value from the literature. Accurate measurement of the intragastric pressure through other diagnostic techniques, such as HRM, will increase the accuracy of the MRI-MECH predictions of intrabolus pressure and wall stiffness. The main focus of this study is to introduce a framework that can quantify the state and functioning of the esophagus through mechanics-based parameters for esophageal stiffness and active relaxation. This was accomplished with data from just one subject.All the elements in the MRI-MECH framework would remain the same even if there were multiple subjects. Moreover, the physics-informed neural network utilized in this paper does not depend on data from many subjects as typical machine learning approaches do but rather is used as an optimizer focused on individual subject data. However, the success of any framework is determined by how efficiently it can be used on many subjects for clinical practicability. A detailed study of applying this framework to many subjects is beyond the scope of this work due to the current lack of availability of volunteers, and so, it is a limitation of this work. Finally, a true validation of this framework would be through comparison with other invasive methods used on the same subject simultaneously with MR imaging. Unfortunately, that was not available for the subject and remains a limitation of this work.We presented a framework called MRI-MECH that uses dynamic MRI of swallowed fluid to quantitatively estimate the mechanical health of the esophagus. The bolus geometry, which tracks the inner cross-section of the esophagus, was extracted through manual segmentation of the MR image sequence and was used as input to the MRI-MECH framework. MRI-MECH modeled the esophagus as a one-dimensional flexible tube and used a physics-informed neural network to predict fluid velocity, intrabolus pressure, esophageal wall stiffness, and active relaxation. The PINN minimized a set of measurement losses to ensure that the predicted quantities matched the measured quantities and a set of residuals to ensure that the physics of the fluid flow problem was followed, specifically the mass and momentum conservation equation in one dimension. The LES cross-sectional area is very difficult to visualize in MRI because it is significantly smaller than the cross-sectional area at the esophageal body. In this regard, MRI-MECH enhances the capability of the dynamic MRI by calculating the LES cross-sectional area during esophageal emptying. We found that our predictions of the intrabolus pressure and the esophageal wall stiffness match those reported in other experimental studies. Additionally, we showed that the dynamic pressure variations that occur because of local acceleration/deceleration of the fluid were negligible compared to the total intrabolus pressure, whose main contribution was the elastic deformation of the esophageal walls. The mechanics-based analysis with detailed three-dimensional visualization of the bolus in MRI leads to significantly better prediction of the state of the esophagus than two-dimensional X-ray imaging techniques such as esophagram and fluoroscopy and can be easily extended to other medical imaging techniques such as computerized tomography (CT). Thus, MRI-MECH provides a new direction in mechanics-based non-invasive diagnostics that can potentially lead to improved clinical diagnosis.


Mapping network nodes and edges to communities and network functions is crucial to gaining a higher level of understanding of the network structure and functions. Such mappings are particularly challenging to design for covert social networks, which intentionally hide their structure and functions to protect important members from attacks or arrests. Here, we focus on correctly inferring the structures and functions of such networks, but our methodology can be broadly applied. Without the ground truth, knowledge about the allocation of nodes to communities and network functions, no single network based on the noisy data can represent all plausible communities and functions of the true underlying network. To address this limitation, we apply a generative model that randomly distorts the original network based on the noisy data, generating a pool of statistically equivalent networks. Each unique generated network is recorded, while each duplicate of the already recorded network just increases the repetition count of that network. We treat each such network as a variant of the ground truth with the probability of arising in the real world approximated by the ratio of the count of this network’s duplicates plus one to the total number of all generated networks. Communities of variants with frequently occurring duplicates contain persistent patterns shared by their structures. Using Shannon entropy, we can find a variant that minimizes the uncertainty for operations planned on the network. Repeatedly generating new pools of networks from the best network of the previous step for several steps lowers the entropy of the best new variant. If the entropy is too high, the network operators can identify nodes, the monitoring of which can achieve the most significant reduction in entropy. Finally, we also present a heuristic for constructing a new variant, which is not randomly generated but has the lowest expected cost of operating on the distorted mappings of network nodes to communities and functions caused by noisy data. The amount of data collected in the world has grown exponentially for at least the last decade , includiThe sources of noise in network data can be classified into several categories. The first source of noise originates from monitoring relations that are not directly observable, so collected data are only a proxy of the desired relationships. In the context of social networks, an example of this would be frequent communication between two people which may imply a trust relationship between them. To illustrate the potential shortcomings of such proxies, we can observe that some of the calls might be strictly professional or even an indication of disagreement and distrust rather than trust. Similarly, in a biological network context, we rely on proxies for protein interactions  in artificial testing systems. These proxies can produce many false positives, as bound proteins might never actually be found in the same place or at the same time within their originating cell .The second category of noisy data is caused by deliberate distortion or attempts to conceal some characteristics of the network, or even its entire existence, undertaken by the nodes of such a network. The best example of this category of noise would be covert networks, where members of the network are intentionally hiding their involvement and interactions by avoiding communicating within the network in cases when the only available means of communication can be easily tracked, such as cell phones with registered ownership ,5. To avThe presence of noise in network data distorts the detection of network edges, which is likely to modify the network’s community structure, e.g., . In the The rest of this paper is organized as follows. To address the problem of missing, mislabeled, or incorrectly included nodes or edges in a network, several approaches have been proposed. Many of them use entropy-based metrics. In , the autIn , the autIn , the proIn our earlier work , we focur networks from the given noisy network data and find their non-overlapping communities. Then, we cluster these networks into r and r approximates the probability that the corresponding structure is the ground truth. In this work, to quantify the uncertainty of a community structure and its corresponding level of predictability, we introduce three entropy-based metrics that are adopted from human mobility entropy models proposed in [Using the Bernoulli weighted random network (BWRN) algorithm, we generate a set of posed in .As discussed in  network .Given the basic noisy parameters of such a network, including the lists of nodes, weighted degrees of all nodes, communities, and hierarchy, the generator produces a set of randomly generated networks by randomly redirecting weak edges while preserving the strong ones. In the process of generating a vast number of statistically equivalent networks, the generator records the network structure for each unique network variant. Any duplicates of an already recorded network just increase the duplicate count for this network.When all networks are generated, we treat each unique network as a solution variant and assign to it the probability that this variant represents the ground truth. This probability is approximated by the ratio of the count of this network’s duplicates plus one to the total number of all generated networks. Variants with large occurrence counts correspond to networks with the most persistent patterns of network structures. Using just the Shannon entropy, we can select a variant that minimizes the uncertainty for operations planned on the network. Repeatedly generating new pools of networks from the resultant variant lowers the entropy of the result. Moreover, if the entropy or the cost of distortions is too high, the network operators can identify nodes, monitored for which can fastest reduce the entropy.s community structures derived from r networks generated by the BWRN algorithm [We apply the entropy-based metrics described in lgorithm . In our N of nodes, denoted as r times, creating a set of r networks which are statistically equivalent to each other. Then, we use the Louvain community detection algorithm [Given a network with a set enerator  to rewirlgorithm  to detecs community structures is subsequently used as a proxy for the ground-truth community structure for the given noisy network data. When This set of r, which defines the number of generated networks. The smaller r must be, because more aggressive rewiring requires generating more networks to create all feasible community structures. Because the methods presented here are heuristics, they require finding suitable values of these parameters to obtain the best results.The preprocessing steps expect that the values for the following parameters are selected: The first entropy-based metric proposed here is the classic Shannon entropy computed over an entire set of generated community structures by setting It follows from the definition that the most reliable ground-truth structure is the community structure i. The second is the temporal-uncorrelated entropy, defined asj was visited by user i. The third and final measure is the real entropy i was observed at each consecutive hourly interval. Then, the real entropy isS, we map each node onto the mobile user. Time slot t in the mobility model is mapped to community structure t. Finally, we impose the order of visitations from the most to least frequent pairings between the node s community structures.In this section, we introduce three entropy-based metrics that adopt the human mobility entropy metrics proposed in  for use k version of a candidate community structure s already established structures i. Hence, this metric penalizes unmatched members of either community with a unit cost, independent of the community size.So far, we have used the entropy measures to find the community structure fined asCT(Ckcan)The second cost function, named the fraction-based cost, is defined asy metric  between s ground-truth community structures. Then, the total penalty for the initial structure In both cases, the heuristics for creating s feasible ground-truth community structures and denote them as Initial step 1, the initial Inductive step For the frequency-based penalty, we first compute the average frequencies of all pairs of nodes in all The heuristic for the fraction-based penalty uses the same inductive scheme of merging one pair of communities in each step, selecting a pair whose merging decreases the penalty the most, and stopping when none decreases the penalty.s community structures, and recomputing frequencies of only a pair of the candidate communities that were merged, which sped up the processing 100 times compared to the initial prototype.Both heuristics required careful implementation to be efficient, like creating a dictionary of all To present our proposed entropy-based metrics in action, we evaluate them on the real-world Caviar gang  and SiciThe Caviar network represents criminals who smuggled hashish and cocaine into Montreal, Canada. The data were collected between 1994 and 1996. During this time, the police seized shipments of drugs but delayed any arrests until the investigation was completed. The Caviar network is a weighted and directed network, where edges represent wiretapped telephone calls between members of the network.The Sicilian network was a drug-trafficking criminal organization based in Sicily, Italy. Its data was collected between 2003 and 2007. This network is also weighted and directed, with edges representing wiretapped telephone calls among members of the network. Both the Caviar and Sicilian networks were derived from data publicly released from court proceedings.The Jakarta Bombing terrorist network is an undirected weighted network composed of two snapshots showing the network before and after the 2009 Jakarta bombing in Jakarta, Indonesia. We only focus on the pre-attack snapshot because the network was denser before rather than after the attack.In the evaluation of our proposed entropy-based metrics and community prediction methods, we use the BWRN generator with The user-defined r times. In the set of rewired networks, we find the community structure r times and mark the candidate network that results in the set of rewired networks with the lowest Shannon entropy as The rewiring of the Caviar and Sicilian networks using the BWRN generator  results enerator , we rewiWe then use the set entropy-based metrics to measure the uncertainty present across the community structures of all the rewired networks. We find that over the first few rounds of rewiring, the Shannon entropy and the set entropy are constantly decreasing, until they reach a minimum value. Once this happens, further rewiring would cause the Shannon entropy and set entropy to increase. What we found to be very interesting is that further rewiring of the resulting networks with an increased entropy value brings back previously observed minimum values of the Shannon entropy and set entropy.r times, each with N nodes and L edges, takes g is the cost of generating a random number. For a larger r, rewiring all candidates may become infeasible. To continue our process of rewiring efficiently, we use a heuristic that selects a single network with the highest modularity, instead of rewiring. Because the complexity of modularity is The presence of many candidate networks to rewire among the networks rewired from the original network indicates that the original network has low uncertainty, resulting in many networks with the same community structure. Rewiring of is O(NL) , the heuIn Z, defined in To evaluate the quality of communities generated using fraction-based and frequency-based methods, we first find the rewiring step that results in the minimum Shannon entropy value. As shown for the Caviar and Sicilian networks in We use the best candidate network While we have shown that the resulting networks  that areN, the average degree k, the maximum degree C. We compute the values of these properties on the Caviar and Sicilian networks. For setting the values of The authors of  provide  Louvain  communitTo provide a baseline result, on each of the ten LFR networks, we run the Louvain algorithm 100 times, collecting the community structures obtained in each run. Then, we compute the normalized mutual information (NMI)  score beAs shown in The relative improvement in the NMI score is smaller on the Sicilian-based LFR networks than the Caviar networks. The Sicilian-based LFR network community structures also generally have higher NMI scores than those based on Caviar. This happens because the average degree of the Caviar network is 4.52 while for the Sicilian network it is 2.88. Low degrees of most nodes in the Sicilian network reduce the variance among the detected community structures.The major contribution of this paper is the introduction of entropy measures of network community structure uncertainty and their use to establish limits of such uncertainties, defined as The abstract concept of network uncertainty is important, but even more important are the downstream consequences resulting from erroneous edge assignment. They can vary widely depending on which nodes are assigned to communities or functions that are different than predicted. In the case of criminal covert networks, such uncertainty may lead to the arrest of a low-level gang member instead of the leader. To address this challenge, we introduce a novel heuristic that constructs a community structure with the minimal expected cost of uncertainty of each node community membership and function. The cost function can be predefined or provided by the users based on the application. We showed three examples of such functions and developed a methodology that starts with noisy network data and maps nodes to communities and network functions that minimize the expected cost of data uncertainty.In future work, we plan to extend the methodology to other domains in which networks are created from noisy data. We have already started to look at biomedical networks, in which data collections return massive volumes of noisy data, and the resilience of supply chains, in which diverse participants limit access to their proprietary data to preserve their competitive advantage.


Counter-propagating optical tweezers are experimental platforms for the frontier exploration of science and precision measurement. The polarization of the trapping beams significantly affects the trapping status. Using the T-matrix method, we numerically analyzed the optical force distribution and the resonant frequency of counter-propagating optical tweezers in different polarizations. We also verified the theoretical result by comparing it with the experimentally observed resonant frequency. Our analysis shows that polarization has little influence on the radial axis motion, while the axial axis force distribution and the resonant frequency are sensitive to polarization change. Our work can be used in designing harmonic oscillators which can change their stiffness conveniently, and monitoring polarization in counter-propagating optical tweezers. Optical tweezers, which take advantage of the interaction between light and matter, are a method of observing and controlling levitated mesoscopic objects. Since being proposed by Ashkin in 1970 , materiaThe trap scheme of optical tweezers includes mainly single-beam and dual-beam counter-propagating setups . Single-To investigate the dynamics of the levitated objects, it is important to calculate the interaction force between light and matter in different conditions. The numerical method of optical tweezers includes the geometric optics method , the dipIn comparison to single-beam optical tweezers, a counter-propagating setup includes interference issues. Researchers have utilized cross polarization  and paraBased on the size of the levitated object, there are three regimes: the geometrical optics regime, the Rayleigh scattering regime, and the Mie scattering regime, with the size of the levitated object larger, smaller, and close to the optical wavelength, respectively. While the geometrical optics method  and the The interaction between light and matter comes from the change in photon momentum and can be calculated by analyzing the field scattered by the levitated object. We can represent the incident field The T-matrix In a coordinate system originated on the levitated object, we can expand the ingoing field and outgoing field in ingoing and outgoing vector spherical wavefunctions (VSWFs), respectively.It is convenient to represent the incident field with ingoing and outgoing vectors, and represent the scattered field with outgoing fields. However, this makes the incident field and scattered field both carry momentum away from the levitated object. Thus, the pure ingoing and outgoing fields in their corresponding representations are more suitable for force calculation.The axial optical force can then be calculated as:2 sphere S in a vacuum chamber. The pressure in the vacuum chamber was set to 10 mBar. The NA of L1 and L2 were As Ideally, the two trapping laser beams were both linear polarized beams at the sphere’s position. According to the analysis of the scattered field , ideallyThe interaction force between light and matter is important information for designing the optical tweezers system. For counter-propagating optical tweezers, the optical force is affected by the polarization condition of two trapping beams. Researchers have utilized cross polarization  and paraIn order to describe the polarization condition of the counter-propagating beams, we introduce the Jones vector :Jn=(EnxeIf the polarization of the two trapping beams is orthogonal, for example, setting the forward trapping beam into the linear polarized laser in the x direction and the backward trapping beam into the linear polarized laser in the y direction, then it can be described by First, we analyzed the influence of the power split ratio. Considering the spatial symmetry, we only need to analyze the change in the power split ratio of one trapping beam. We assume the backward trapping laser to be ideal and change the power split ratio of the forward trapping laser in comparison with the orthogonal condition:2 sphere levitated by two The calculated optical force distribution is shown in Although the trapped particle size is larger than the interference period, the random motion of the center of mass is confined to a small range. In this work, the sphere was in a low-vacuum environment with pressure /k ≈6 nm , where kThen, we consider the polarization phase. There are four phase terms, while the absolute phase only translates the whole system in the z direction, which is not in the scope of this work. Taking spatial symmetry into consideration, there are only two independent variables. We fix one phase term, After analyzing the force distribution with different polarization conditions, we can further calculate the trap stiffness and resonant frequency, which are more convenient for experimental observations. In the linear region, the optical tweezers can be described with the harmonic oscillator model. The trap stiffness is defined as the force gradient In conclusion, we calculated the optical force distribution and resonant frequency of counter-propagating optical tweezers in different polarizations. The analysis has great potential in applications. A harmonic oscillator that can change its stiffness conveniently can be designed based on this work. For example, the traditional parametric feedback cooling is mainly based on the single-beam optical trap, such that modulate the trap stiffness by changing the power of the trapping laser is convenient . However