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Genotype networks are a method used in systems biology to study the "innovability" of a set of genotypes having the same phenotype. In the past they have been applied to determine the genetic heterogeneity, and stability to mutations, of…

Social choice theory is the study of preference aggregation across a population, used both in mechanism design for human agents and in the democratic alignment of language models. In this study, we propose the representative social choice…

Real-world complex systems are often better modeled as hypergraphs, where edges represent group interactions involving multiple entities. Understanding and quantifying homophily (similarity-driven association) in such networks is essential…

Understanding genetic variation, e.g., through mutations, in organisms is crucial to unravel their effects on the environment and human health. A fundamental characterization can be obtained by solving the haplotype assembly problem, which…

We introduce a general modeling framework to predict the outcomes, at the population level, of individual psychology and behavior. The framework prescribes that researchers build a cost function that embodies knowledge of what trait values…

One property of networks that has received comparatively little attention is hierarchy, i.e., the property of having vertices that cluster together in groups, which then join to form groups of groups, and so forth, up through all levels of…

In the last few years we have witnessed the emergence, primarily in on-line communities, of new types of social networks that require for their representation more complex graph structures than have been employed in the past. One example is…

Compartmental models are valuable tools for investigating infectious diseases. Researchers building such models typically begin with a simple structure where compartments correspond to individuals with different epidemiological statuses,…

Graph is a universe data structure that is widely used to organize data in real-world. Various real-word networks like the transportation network, social and academic network can be represented by graphs. Recent years have witnessed the…

We describe a continuous-time modelling framework for biological population dynamics that accounts for demographic noise. In the spirit of the methodology used by statistical physicists, transitions between the states of the system are…

This paper focuses on two fundamental tasks of graph analysis: community detection and node representation learning, which capture the global and local structures of graphs, respectively. In the current literature, these two tasks are…

Temporal social networks of human interactions are preponderant in understanding the fundamental patterns of human behavior. In these networks, interactions occur locally between individuals (i.e., nodes) who connect with each other at…

Despite the remarkable success of large large-scale neural networks, we still lack unified notation for thinking about and describing their representational spaces. We lack methods to reliably describe how their representations are…

Modeling higher-order interactions (HOI) has emerged as a crucial challenge in complex systems analysis, as many phenomena cannot be fully captured by pairwise relationships alone. Hypergraphs, which generalize graphs by allowing…

The progression of a cell population where each individual is characterized by the value of an internal variable varying with time (e.g. size, weight, and protein concentration) is typically modeled by a Population Balance Equation, a first…

Over the past decade, deep neural networks have proven to be adept in image classification tasks, often surpassing humans in terms of accuracy. However, standard neural networks often fail to understand the concept of hierarchical…

Large-scale human social network structure is typically inferred from digital trace samples of online social media platforms or mobile communication data. Instead, here we investigate the social network structure of a complete population,…

Graph sparsification is a powerful tool to approximate an arbitrary graph and has been used in machine learning over homogeneous graphs. In heterogeneous graphs such as knowledge graphs, however, sparsification has not been systematically…

It is basic question in biology and other fields to identify the char- acteristic properties that on one hand are shared by structures from a particular realm, like gene regulation, protein-protein interaction or neu- ral networks or…

The increasing prevalence of relational data describing interactions among a target population has motivated a wide literature on statistical network analysis. In many applications, interactions may involve more than two members of the…