Pairwise Model Research Articles

Co-Occurrence Patterns Do Not Predict Mutualistic Interactions Between Plant and Butterfly Species.

Biotic interactions are crucial for determining the structure and dynamics of communities; however, direct measurement of these interactions can be challenging in terms of time and resources, especially when numerous species are involved. Inferring species interactions from species co-occurrence patterns is increasingly being used; however, recent studies have highlighted some limitations. To our knowledge, no attempt has been made to test the accuracy of the existing methods for detecting mutualistic interactions in terrestrial ecosystems. In this study, we compiled two literature-based, long-term datasets of interactions between butterflies and herbaceous plant species in two regions of Germany and compared them with observational abundance and presence/absence data collected within a year in the same regions. We tested how well the species associations generated by three different co-occurrence analysis methods matched those of empirically measured mutualistic associations using sensitivity and specificity analyses and compared the strength of associations. We also checked whether flower abundance data (instead of plant abundance data) increased the accuracy of the co-occurrence models and validated our results using empirical flower visitation data. The results revealed that, although all methods exhibited low sensitivity, our implementation of the Relative Interaction Intensity index with pairwise null models performed the best, followed by the probabilistic method and Spearman's rank correlation method. However, empirical data showed a significant number of interactions that were not detected using co-occurrence methods. Incorporating flower abundance data did not improve sensitivity but enhanced specificity in one region. Further analysis demonstrated incongruence between the predicted co-occurrence associations and actual interaction strengths, with many pairs exhibiting high interaction strength but low co-occurrence or vice versa. These findings underscore the complexity of ecological dynamics and highlight the limitations of current co-occurrence methods for accurately capturing species interactions.

The alterations of repetitive transcranial magnetic stimulation on the energy landscape of resting-state networks differ across the human cortex.

Repetitive transcranial magnetic stimulation (rTMS) is a promising intervention tool for the noninvasive modulation of brain activity and behavior in neuroscience research and clinical settings. However, the resting-state dynamic evolution of large-scale functional brain networks following rTMS has rarely been investigated. Here, using resting-state fMRI images collected from 23 healthy individuals before (baseline) and after 1 Hz rTMS of the left frontal (FRO) and occipital (OCC) lobes, we examined the different effects of rTMS on brain dynamics across the human cortex. By fitting a pairwise maximum entropy model (pMEM), we constructed an energy landscape for the baseline and poststimulus conditions by fitting a pMEM. We defined dominant brain states (local minima) in the energy landscape with synergistic activation and deactivation patterns of large-scale functional networks. We calculated state dynamics including appearance probability, transitions and duration. The results showed that 1 Hz rTMS induced increased and decreased state probability, transitions and duration when delivered to the FRO and OCC targets, respectively. Most importantly, the shortest path and minimum cost between dominant brain states were altered after stimulation. The absolute sum of the costs from the source states to the destinations was lower after OCC stimulation than after FRO stimulation. In conclusion, our study characterized the dynamic trajectory of state transitions in the energy landscape and suggested that local rTMS can induce significant dynamic perturbation involving stimulated and distant functional networks, which aligns with the modern view of the dynamic and complex brain. Our results suggest low-dimensional mapping of rTMS-induced brain adaption, which will contribute to a broader and more effective application of rTMS in clinical settings.

Energy of functional brain states correlates with cognition in adolescent-onset schizophrenia and healthy persons.

Adolescent-onset schizophrenia (AOS) is rare, under-studied, and associated with more severe cognitive impairments and poorer outcomes than adult-onset schizophrenia. Neuroimaging has shown altered regional activations (first-order effects) and functional connectivity (second-order effects) in AOS compared to controls. The pairwise maximum entropy model (MEM) integrates first- and second-order factors into a single quantity called energy, which is inversely related to probability of occurrence of brain activity patterns. We take a combinatorial approach to study multiple brain-wide MEMs of task-associated components; hundreds of independent MEMs for various sub-systems are fit to 7 Tesla functional MRI scans. Acquisitions were collected from 23 AOS individuals and 53 healthy controls while performing the Penn Conditional Exclusion Test (PCET) for executive function, which is known to be impaired in AOS. Accuracy of PCET performance was significantly reduced among AOS compared to controls. A majority of the models showed significant negative correlation between PCET scores and the total energy attained over the fMRI. Across all instantiations, the AOS group was associated with significantly more frequent occurrence of states of higher energy, assessed with a mixed effects model. An example MEM instance was investigated further using energy landscapes, which visualize high and low energy states on a low-dimensional plane, and trajectory analysis, which quantify the evolution of brain states throughout this landscape. Both supported patient-control differences in the energy profiles. Severity of psychopathology was correlated positively with energy. The MEM integrated representation of energy in task-associated systems can help characterize pathophysiology of AOS, cognitive impairments, and psychopathology.

Combining Biomarkers to Improve Diagnostic Accuracy in Detecting Diseases With Group-Tested Data.

We consider the problem of combining multiple biomarkers to improve the diagnostic accuracy of detecting a disease when only group-tested data on the disease status are available. There are several challenges in addressing this problem, including unavailable individual disease statuses, differential misclassification depending on group size and number of diseased individuals in the group, and extensive computation due to a large number of possible combinations of multiple biomarkers. To tackle these issues, we propose a pairwise model fitting approach to estimating the distribution of the optimal linear combination of biomarkers and its diagnostic accuracy under the assumption of a multivariate normal distribution. The approach is evaluated in simulation studies and applied to data on chlamydia detection and COVID-19 diagnosis.

Sleep patterns in adolescents and associations with substance use

ObjectivesGood sleep during adolescence is crucial for maintaining physical and psychological health; however, sleep disturbance during this period may contribute to health risks, such as substance use. This study aimed to identify the latent sleep patterns across male and female adolescents, and their association with drug use. MethodA cross-sectional study was conducted involving 1391 high school students (aged 15-17; 56.4% female). Participants completed the brief Pittsburgh Sleep Quality Index alongside other sleep measures, and the Timeline Follow-Back and Drug Use History Questionnaire to measure substance use. A multiple-group latent class analysis was used to identify sleep patterns across sexes, and pairwise Logistic Regression models to compare their association with substance use. ResultsFour sleep patterns were identified with varying degrees of sleep difficulties: "Good Sleep" (43.3%), "Night Awakenings" (31.8%), "Poor Efficiency and Sleep Onset" (9.4%), and "Poor Sleep" (15.5%). Female adolescents were more likely to belong to Poor Sleep and Poor Efficiency and Sleep Onset patterns, and male adolescents to Good Sleep. Likewise, binge drinking and using alcohol for a longer period were associated with experiencing Poor Efficiency and Sleep Onset (OR=1.03 and 2.3, respectively); smoking tobacco within the past month was linked to Night Awakenings (OR=2.2); and using cannabis or illegal drugs to the Poor Sleep pattern (OR=2.4 and 2.6, respectively). ConclusionsVaried sleep difficulties exist among adolescents that significantly correlate with different aspects of drug use. Targeted interventions that address both sleep and drug prevention are recommended.

Spontaneous Brain Activity Emerges from Pairwise Interactions in the Larval Zebrafish Brain

Brain activity is characterized by brainwide spatiotemporal patterns that emerge from synapse-mediated interactions between individual neurons. Calcium imaging provides access to recordings of whole-brain activity at single-neuron resolution and, therefore, allows the study of how large-scale brain dynamics emerge from local activity. In this study, we use a statistical mechanics approach—the pairwise maximum entropy model—to infer microscopic network features from collective patterns of activity in the larval zebrafish brain and relate these features to the emergence of observed whole-brain dynamics. Our findings indicate that the pairwise interactions between neural populations and their intrinsic activity states are sufficient to explain observed whole-brain dynamics. In fact, the pairwise relationships between neuronal populations estimated with the maximum entropy model strongly correspond to observed structural connectivity patterns. Model simulations also demonstrated how tuning pairwise neuronal interactions drives transitions between observed physiological regimes and pathologically hyperexcitable whole-brain regimes. Finally, we use virtual resection to identify the brain structures that are important for maintaining the brain in a physiological dynamic regime. Together, our results indicate that whole-brain activity emerges from a complex dynamical system that transitions between basins of attraction whose strength and topology depend on the connectivity between brain areas. Published by the American Physical Society 2024

Abstract C015: Selective and pairwise epistatic effects of somatic mutations in KRAS wild-type pancreatic cancer

Abstract About 8 to 10% of all pancreatic adenocarcinomas (PAAD) do not possess canonical mutations in KRAS. A sizable proportion of these KRAS wild-type (WT) pancreatic cancers harbor mutations in alternative MAPK-pathway driver genes. These alternative MAPK-pathway genes represent a set of therapeutic targets that might be exploited to treat individuals in this PAAD subset. Previous studies have prioritized the mutational- target landscape of KRAS WT PAAD by ranking genes determined by significance thresholds to be drivers by the prevalence of their somatic mutations in tumors. These prevalences usefully inform the size of the patient population that would be candidates for targeted therapeutics. However, prevalence is markedly influenced by underlying mutation rate. It is not a metric of cancer effect; it does not directly quantify the degree to which a driver mutation increases cancer cell survival and proliferation, nor do observations of co-occurrence or mutual exclusivity quantify epistasis. Therefore, to better guide the development of targeted therapeutics, we assembled a rich dataset of 6,391 PAAD tumor sequences from TCGA, UTSW, ICGC, QCMG, Yale-Gilead, and the AACR Project GENIE.We analyzed the cancer effect sizes of somatic variants in PAADs. Furthermore, we determined the selective epistatic interactions between KRAS and other PAAD driver genes. Nine of the 20 highest-effect variants were nonsynonymous substitutions in KRAS, with the prevalence of these mutations ranging from 18 to 2390 (median 93). This high frequency of highly oncogenic KRAS mutants supports the longstanding conception that KRAS mutations dominate the oncogenic landscape of PAAD. However, of the 6,391 cases analyzed, 627 (9.8%) were KRAS WT. To further investigate the oncogenic landscape of these samples, we employed a pairwise epistasis model of selection. We discovered that not only are alternative MAPK drivers (BRAF and NRAS) present in KRAS WT PAAD, but that they show antagonistic epistasis with KRAS mutation. Moreover, we found that non-MAPK drivers CTNNB1 and IDH1 also exhibit substantial antagonistic epistasis with KRAS. Also, in a KRAS-substituted background, selection for mutations in tumor suppressor genes TP53, CDKN2A, and SMAD4 was increased. Furthermore, mutations in BRAF, NRAS, CTNNB1, TP53, CDKN2A, and SMAD4, genes commonly considered to be drivers of PAAD, in addition to a previously unrecognized driver IDH1, suppressed selection for KRAS mutations. Not only MAPK drivers, but also other oncogenic drivers of PAAD at both high and low prevalence exhibit antagonistic somatic selective epistasis. Treatments targeting these variants that are antagonistically epistatic with KRAS may rescue the full strength of selection on KRAS variants, warranting continued monitoring for KRAS variants in resurgent cancer. Moreover, as resistance to KRAS inhibitors is likely caused by gained alterations in alternative MAPK drivers, exploration of treatments targeting these mutations may additionally provide an avenue to overcome therapeutic resistance in PAADs. Citation Format: Rishi M Shah, Can M Ersahin, Jeffrey D Mandell, Vincent L Cannataro, Jeffrey P Townsend. Selective and pairwise epistatic effects of somatic mutations in KRAS wild-type pancreatic cancer [abstract]. In: Proceedings of the AACR Special Conference in Cancer Research: Advances in Pancreatic Cancer Research; 2024 Sep 15-18; Boston, MA. Philadelphia (PA): AACR; Cancer Res 2024;84(17 Suppl_2):Abstract nr C015.

A comparison of factor models in China

We evaluate the performance of eleven asset pricing models in the Chinese A-share market using a variety of test portfolios and statistical methodologies. To compile the test portfolios, we construct 105 anomalies and use the 23 significant anomalies as test assets for model comparison. The results indicate that, in time-series test and anomaly explanations, the Hou et al. (2019) five-factor q model demonstrates the best overall performance. The pairwise cross-sectional R2 tests and multiple model comparison tests further affirm that the Hou et al. (2019) five-factor q model, the Fama and French (2018) six-factor (FF6) model, and the Kelly et al. (2019) five-factor Instrumented Principal Component Analysis (IPCA5) model are the top performers. Notably, the performance of the five-factor q model remains robust across various experimental designs.

Utility-Oriented Reranking with Counterfactual Context

As a critical task for large-scale commercial recommender systems, reranking rearranges items in the initial ranking lists from the previous ranking stage to better meet users’ demands. Foundational work in reranking has shown the potential of improving recommendation results by uncovering mutual influence among items. However, rather than considering the context of initial lists as most existing methods do, an ideal reranking algorithm should consider the counterfactual context— the position and the alignment of the items in the reranked lists . In this work, we propose a novel pairwise reranking framework, Utility-oriented Reranking with Counterfactual Context (URCC), which maximizes the overall utility after reranking efficiently. Specifically, we first design a utility-oriented evaluator, which applies Bi-LSTM and graph attention mechanism to estimate the listwise utility via the counterfactual context modeling. Then, under the guidance of the evaluator, we propose a pairwise reranker model to find the most suitable position for each item by swapping misplaced item pairs. Extensive experiments on two benchmark datasets and a proprietary real-world dataset demonstrate that URCC significantly outperforms the state-of-the-art models in terms of both relevance-based metrics and utility-based metrics.

Exploring spatial segregation induced by competition avoidance as driving mechanism for emergent coexistence in microbial communities.

This study investigates the role of spatial segregation, prompted by competition avoidance, as a key mechanism for emergent coexistence within microbial communities. Recognizing these communities as complex adaptive systems, we challenge the sufficiency of mean-field pairwise interaction models, and we consider the impact of spatial dynamics. We developed an individual-based spatial simulation depicting bacterial movement through a pattern of random walks influenced by competition avoidance, leading to the formation of spatially segregated clusters. This model was integrated with a Lotka-Volterra metapopulation framework focused on competitive interactions. Our findings reveal that spatial segregation combined with low diffusion rates and high compositional heterogeneity among patches can lead to emergent coexistence in microbial communities. This reveals a novel mechanism underpinning the formation of stable, coexisting microbe clusters, which is nonetheless incapable of promoting coexistence in the case of isolated pairs of species. This study underscores the importance of considering spatial factors in understanding the dynamics of microbial ecosystems.

Study of metabolites dynamic variation during vine tea (Ampelopsis grossedentata) processing by untargeted metabolomics

Vine tea is a paramount Chinese tea with a wide variety of health benefits. The tea quality would be affected by tea processing procedures. It is essential to unravel the dynamic variation of metabolites during tea processing. To interpret the dynamic changes, the metabolic profiling was characterized by ultra-high performance liquid chromatography with quadrupole time-of-flight mass spectrometry (UPLC-Q-TOF/MS) with 1890 metabolites. Furthermore, the chemometrics methods were implemented to explore key metabolites to clarify the dynamic changes during processing. Four pair-wise models were developed with R2Y higher than 0.990. Fifteen key metabolites were explored during manufacturing process. Fixation stage was closely associated with generation of bioactive compounds of dihydromyricetin (DIH). DIH had highly significant correlation with key metabolites of 2-hydroxy lignoceric acid, lamioside, and 3-o-methylgallic acid according to mantel test. The results provide valuable information on dynamic changes of metabolites during processing in tea.

Distinct plasma metabolomic signatures differentiate autoimmune encephalitis from drug-resistant epilepsy.

Differentiating forms of autoimmune encephalitis (AE) from other causes of seizures helps expedite immunotherapies in AE patients and informs studies regarding their contrasting pathophysiology. We aimed to investigate whether and how Nuclear Magnetic Resonance (NMR)-based metabolomics could differentiate AE from drug-resistant epilepsy (DRE), and stratify AE subtypes. This study recruited 238 patients: 162 with DRE and 76 AE, including 27 with contactin-associated protein-like 2 (CASPR2), 29 with leucine-rich glioma inactivated 1 (LGI1) and 20 with N-methyl-d-aspartate receptor (NMDAR) antibodies. Plasma samples across the groups were analyzed using NMR spectroscopy and compared with multivariate statistical techniques, such as orthogonal partial least squares discriminant analysis (OPLS-DA). The OPLS-DA model successfully distinguished AE from DRE patients with a high predictive accuracy of 87.0 ± 3.1% (87.9 ± 3.4% sensitivity and 86.3 ± 3.6% specificity). Further, pairwise OPLS-DA models were able to stratify the three AE subtypes. Plasma metabolomic signatures of AE included decreased high-density lipoprotein (HDL, -(CH2)n-, -CH3), phosphatidylcholine and albumin (lysyl moiety). AE subtype-specific metabolomic signatures were also observed, with increased lactate in CASPR2, increased lactate, glucose, and decreased unsaturated fatty acids (UFA, -CH2CH=) in LGI1, and increased glycoprotein A (GlycA) in NMDAR-antibody patients. This study presents the first non-antibody-based biomarker for differentiating DRE, AE and AE subtypes. These metabolomics signatures underscore the potential relevance of lipid metabolism and glucose regulation in these neurological disorders, offering a promising adjunct to facilitate the diagnosis and therapeutics.

Influence of Image Compositing and Multisource Data Fusion on Multitemporal Land Cover Mapping of Two Philippine Watersheds

Cloud-based remote sensing has spurred the use of techniques to improve mapping accuracy where individual images may have lower quality, especially in areas with complex terrain or high cloud cover. This study investigates the influence of image compositing and multisource data fusion on the multitemporal land cover mapping of the Pagsanjan-Lumban and Baroro Watersheds in the Philippines. Ten random forest models for each study site were used, all using a unique combination of more than 100 different input features. These features fall under three general categories. First, optical features were derived from reflectance bands and ten spectral indices, which were further subdivided into annual percentile and seasonal median composites; second, radar features were derived from ALOS PALSAR by computing textural indices and a simple band ratio; and third, topographic features were computed from the ALOS GDSM. Then, accuracy metrics and McNemar’s test were used to assess and compare the significance of about 90 pairwise model outputs. Data fusion significantly improved the accuracy of multitemporal land cover mapping in most cases. However, image composition had varied impacts for both sites. This could imply local characteristics and feature inputs as potential determinants of the ideal composite method. Hence, the iterative screening or optimization of both input features and composites is recommended to improve multitemporal mapping accuracy.

Diagnostically distinct resting state fMRI energy distributions: A subject-specific maximum entropy modeling study.

Objective Existing neuroimaging studies of psychotic and mood disorders have reported brain activation differences (first-order properties) and altered pairwise correlation based functional connectivity (second-order properties). However, both approaches have certain limitations that can be overcome by integrating them in a pairwise maximum entropy model (MEM) that better represents a comprehensive picture of fMRI signal patterns and provides a system-wide summary measure called energy. This study examines the applicability of individual-level MEM for psychiatry and identifies image-derived model coefficients related to model parameters. Method MEMs are fit to resting state fMRI data from each individual with schizophrenia/schizoaffective disorder, bipolar disorder, and major depression (n=132) and demographically matched healthy controls (n=132) from the UK Biobank to different subsets of the default mode network (DMN) regions. Results The model satisfactorily explained observed brain energy state occurrence probabilities across all participants, and model parameters were significantly correlated with image-derived coefficients for all groups. Within clinical groups, averaged energy level distributions were higher in schizophrenia/schizoaffective disorder but lower in bipolar disorder compared to controls for both bilateral and unilateral DMN. Major depression energy distributions were higher compared to controls only in the right hemisphere DMN. Conclusions Diagnostically distinct energy states suggest that probability distributions of temporal changes in synchronously active nodes may underlie each diagnostic entity. Subject-specific MEMs allow for factoring in the individual variations compared to traditional group-level inferences, offering an improved measure of biologically meaningful correlates of brain activity that may have potential clinical utility.

Association between screen time and self-reported balance disorders in middle-aged and older adults: national health and nutrition examination survey

BackgroundBalance disorders can give rise to sensations of instability, lightheadedness, vertigo, disequilibrium, or syncope, ultimately leading to grave medical, physical, emotional, and societal ramifications. These conditions are highly prevalent among individuals aged 40 and above. Screen time encompasses activities associated with television viewing, video game playing, and non-work-related computer usage. Prolonged screen exposure may engender a spectrum of health issues and even elevate overall mortality rates. However, the available evidence on the potential link between excessive screen time and balance dysfunction remains limited.AimsThe primary aim of this study was to explore the possible association between prolonged screen exposure and impaired balance function.MethodsThis cross-sectional study utilized data from participants who completed a comprehensive questionnaire in the NHANES database between 1999 and 2002, all of whom were aged over 40 and under 85 years. Participants’ screen time was categorized into two groups (< 4 h/d and ≥4 h/d) for subsequent data analysis. Logistic regression, combined with propensity score matching (PSM), was employed to investigate the correlation between screen time and balance disorders.ResultsA total of 5176 participants were enrolled in this study, comprising 2,586 men and 2,590 women, with a prevalence rate of balance disorders at 25.7% (1331/5176). The incidence of balance disorders was found to be significantly higher among individuals who spent 4 hours or more per day on screen time compared to those with less screen time (P<0.001). Multivariate logistic analysis conducted on the unmatched cohort revealed a significant association between screen time and balance disorders, with an odds ratio (OR) 1.8 (95%CI 1.57 ∼ 2.05). These findings remained consistent even after adjusting for confounding factors, yielding an OR 1.43 (95%CI 1.24 ∼ 1.66). Moreover, the association persisted when employing various multivariate analyses such as propensity score matching adjusted model, standardized mortality ratio weighting model and pairwise algorithmic model; all resulting in ORs ranging from 1.38 to 1.43 and p-values < 0.001.ConclusionsAfter controlling for all covariates, screen time (watching TV, playing video games, and using computers outside of work) was associated with balance dysfunction among middle-aged and older adults. This finding may offer a possible idea for the prevention of dizziness and balance disorders. Nevertheless, additional research is imperative to further validate these results.

Pairwise machine learning-based automatic diagnostic platform utilizing CT images and clinical information for predicting radiotherapy locoregional recurrence in elderly esophageal cancer patients.

To investigate the feasibility and accuracy of predicting locoregional recurrence (LR) in elderly patients with esophageal squamous cell cancer (ESCC) who underwent radical radiotherapy using a pairwise machine learning algorithm. The 130 datasets enrolled were randomly divided into a training set and a testing set in a 7:3 ratio. Clinical factors were included and radiomics features were extracted from pretreatment CT scans using pyradiomics-based software, and a pairwise naive Bayes (NB) model was developed. The performance of the model was evaluated using receiver operating characteristic (ROC) curves and decision curve analysis (DCA). To facilitate practical application, we attempted to construct an automated esophageal cancer diagnosis system based on trained models. To the follow-up date, 64 patients (49.23%) had experienced LR. Ten radiomics features and two clinical factors were selected for modeling. The model demonstrated good prediction performance, with area under the ROC curve of 0.903 (0.829-0.958) for the training cohort and 0.944 (0.849-1.000) for the testing cohort. The corresponding accuracies were 0.852 and 0.914, respectively. Calibration curves showed good agreement, and DCA curve confirmed the clinical validity of the model. The model accurately predicted LR in elderly patients, with a positive predictive value of 85.71% for the testing cohort. The pairwise NB model, based on pre-treatment enhanced chest CT-based radiomics and clinical factors, can accurately predict LR in elderly patients with ESCC. The esophageal cancer automated diagnostic system embedded with the pairwise NB model holds significant potential for application in clinical practice.

Fast computation of General SimRank on heterogeneous information network

Similarity computation is a fundamental aspect of information network analysis, underpinning many research tasks including information retrieval, clustering, and recommendation systems. General SimRank (GSR), an extension of the well-known SimRank algorithm, effectively computes link-based global similarities incorporating semantic logic within heterogeneous information networks (HINs). However, GSR inherits the recursive nature of SimRank, making it computationally expensive to achieve convergence through iterative processes. While numerous rapid computation methods exist for SimRank, their direct application to GSR is impeded by differences in their underlying equations. To accelerate GSR computation, we introduce a novel approach based on linear systems. Specifically, we transform the pairwise surfer model of GSR on HINs into a new random walk model on a node-pair graph, establishing an equivalent linear system for GSR. We then develop a fast algorithm utilizing the local push technique to compute all-pair GSR scores with guaranteed accuracy. Additionally, we adapt the local push method for dynamic HINs and introduce a corresponding incremental algorithm. Experimental results on various real datasets demonstrate that our algorithms significantly outperform the traditional power method in both static and dynamic HIN contexts.

Stochastic pairwise preference convergence in Bayesian agents.

Beliefs inform the behavior of forward-thinking agents in complex environments. Recently, sequential Bayesian inference has emerged as a mechanism to study belief formation among agents adapting to dynamical conditions. However, we lack critical theory to explain how preferences evolve in cases of simple agent interactions. In this paper, we derive a Gaussian, pairwise agent interaction model to study how preferences converge when driven by observation of each other's behaviors. We show that the dynamics of convergence resemble an Ornstein-Uhlenbeck process, a common model in nonequilibrium stochastic dynamics. Using standard analytical and computational techniques, we find that the hyperprior magnitudes, representing the learning time, determine the convergence value and the asymptotic entropy of the preferences across pairs of agents. We also show that the dynamical variance in preferences is characterized by a relaxation time t^{★} and compute its asymptotic upper bound. This formulation enhances the existing toolkit for modeling stochastic, interactive agents by formalizing leading theories in learning theory, and builds towards more comprehensive models of open problems in principal-agent and market theory.

The quality and complexity of pairwise maximum entropy models for large cortical populations.

We investigate the ability of the pairwise maximum entropy (PME) model to describe the spiking activity of large populations of neurons recorded from the visual, auditory, motor, and somatosensory cortices. To quantify this performance, we use (1) Kullback-Leibler (KL) divergences, (2) the extent to which the pairwise model predicts third-order correlations, and (3) its ability to predict the probability that multiple neurons are simultaneously active. We compare these with the performance of a model with independent neurons and study the relationship between the different performance measures, while varying the population size, mean firing rate of the chosen population, and the bin size used for binarizing the data. We confirm the previously reported excellent performance of the PME model for small population sizes N < 20. But we also find that larger mean firing rates and bin sizes generally decreases performance. The performance for larger populations were generally not as good. For large populations, pairwise models may be good in terms of predicting third-order correlations and the probability of multiple neurons being active, but still significantly worse than small populations in terms of their improvement over the independent model in KL-divergence. We show that these results are independent of the cortical area and of whether approximate methods or Boltzmann learning are used for inferring the pairwise couplings. We compared the scaling of the inferred couplings with N and find it to be well explained by the Sherrington-Kirkpatrick (SK) model, whose strong coupling regime shows a complex phase with many metastable states. We find that, up to the maximum population size studied here, the fitted PME model remains outside its complex phase. However, the standard deviation of the couplings compared to their mean increases, and the model gets closer to the boundary of the complex phase as the population size grows.

Competition between phase ordering and phase segregation in the TixNbMoTaW and TixVNbMoTaW refractory high-entropy alloys

Refractory high-entropy alloys are under consideration for applications where materials are subjected to high temperatures and levels of radiation, such as in the fusion power sector. However, at present, their scope is limited because they are highly brittle at room temperature. One suggested route to mitigate this issue is by alloying with Ti. In this theoretical study, using a computationally efficient linear-response theory based on density functional theory calculations of the electronic structure of the disordered alloys, we study the nature of atomic short-range order in these multi-component materials, as well as assessing their overall phase stability. Our analysis enables direct inference of phase transitions in addition to the extraction of an atomistic, pairwise model of the internal energy of an alloy suitable for study via, e.g., Monte Carlo simulations. Once Ti is added into either the NbMoTaW or VNbMoTaW system, we find that there is competition between chemical phase ordering and segregation. These results shed light on observed chemical inhomogeneity in experimental samples, as well as providing fundamental insight into the physics of these complex systems.