In this paper, we study a model of agent consensus in a social network in the presence increasing interagent influence, i.e., increasing peer pressure. Each agent in the social network has a distinct social stress function given by a weighted sum of internal and external behavioral pressures. We assume a weighted average update rule consistent with the classic DeGroot model and prove conditions under which a connected group of agents converge to a fixed opinion distribution, and under which conditions the group reaches consensus. We show that the update rule converges to gradient descent and explain its transient and asymptotic convergence properties. Through simulation, we study the rate of convergence on a scale-free network.

Human diseases involve metabolic alterations. Metabolomic profiles have served as a vital biomarker for the early identification of high-risk individuals and disease prevention. However, current approaches can only characterize individual key metabolites, without taking into account the reality that complex diseases are multifactorial, dynamic, heterogeneous, and interdependent. Here, we leverage a statistical physics model to combine all metabolites into bidirectional, signed, and weighted interaction networks and trace how the flow of information from one metabolite to the next causes changes in health state. Viewing a disease outcome as the consequence of complex interactions among its interconnected components (metabolites), we integrate concepts from ecosystem theory and evolutionary game theory to model how the health state-dependent alteration of a metabolite is shaped by its intrinsic properties and through extrinsic influences from its conspecifics. We code intrinsic contributions as nodes and extrinsic contributions as edges into quantitative networks and implement GLMY homology theory to analyze and interpret the topological change of health state from symbiosis to dysbiosis and vice versa. The application of this model to real data allows us to identify several hub metabolites and their interaction webs, which play a part in the formation of inflammatory bowel diseases. The findings by our model could provide important information on drug design to treat these diseases and beyond.

Interactions among the underlying agents of a complex system are not only limited to dyads but can also occur in larger groups. Currently, no generic model has been developed to capture high-order interactions (HOI), which, along with pairwise interactions, portray a detailed landscape of complex systems. Here, we integrate evolutionary game theory and behavioral ecology into a unified statistical mechanics framework, allowing all agents (modeled as nodes) and their bidirectional, signed, and weighted interactions at various orders (modeled as links or hyperlinks) to be coded into hypernetworks. Such hypernetworks can distinguish between how pairwise interactions modulate a third agent (active HOI) and how the altered state of each agent in turn governs interactions between other agents (passive HOI). The simultaneous occurrence of active and passive HOI can drive complex systems to evolve at multiple time and space scales. We apply the model to reconstruct a hypernetwork of hexa-species microbial communities, and by dissecting the topological architecture of the hypernetwork using GLMY homology theory, we find distinct roles of pairwise interactions and HOI in shaping community behavior and dynamics. The statistical relevance of the hypernetwork model is validated using a series of in vitro mono-, co-, and tricultural experiments based on three bacterial species.

How genes interact with the environment to shape phenotypic variation and evolution is a fundamental question intriguing to biologists from various fields. Existing linear models built on single genes are inadequate to reveal the complexity of genotype-environment (G-E) interactions. Here, we develop a conceptual model for mechanistically dissecting G-E interplay by integrating previously disconnected theories and methods. Under this integration, evolutionary game theory, developmental modularity theory, and a variable selection method allow us to reconstruct environment-induced, maximally informative, sparse, and casual multilayer genetic networks. We design and conduct two mapping experiments by using a desert-adapted tree species to validate the biological application of the model proposed. The model identifies previously uncharacterized molecular mechanisms that mediate trees' response to saline stress. Our model provides a tool to comprehend the genetic architecture of trait variation and evolution and trace the information flow of each gene toward phenotypes within omnigenic networks.

All multicellular organisms embed endogenous circadian oscillators or clocks that rhythmically regulate a wide variety of processes in response to daily environmental cycles. Previous molecular studies using rhythmic mutants for several model systems have identified a set of genes responsible for rhythmic activities and illustrated the molecular mechanisms underlying how disruptions in circadian rhythms are associated with the sort of aberrant cell cycling. However, the wide use of these forward genetic studies is impaired by a limited number of mutations that can be identified or induced only in a single genome, limiting the identification of many other conserved or non-conserved clock genes. Genetic linkage or association mapping provides an unprecedented glimpse into the genome-wide scanning and characterization of genes underlying circadian rhythms. The implementation of sophisticated statistical models into genetic mapping studies can not only identify key clock genes or clock quantitative trait loci (cQTL) but also, more importantly, reveal a complete atlas of the genetic control mechanisms constituted by gene interactomes. Here, we introduce and review an advanced statistical mechanics framework for coalescing all possible clock genes into intricate but well-organized interaction networks that regulate rhythmic cycles. The application of this framework to widely available mapping populations will reshape and further our understanding of the genetic signatures behind circadian rhythms for an enlarged range of species including microbes, plants, and humans.