Related papers: Hypergraphic Oriented Matroid Relational Dependenc…
We address the problem of defining connected components in hypergraphs, which are models for systems with higher-order interactions. For graphs with dyadic interactions, connected components are defined in terms of paths connecting nodes…
In this paper, we propose a new method to identify biochemical reaction networks (i.e. both reactions and kinetic parameters) from heterogeneous datasets. Such datasets can contain (a) data from several replicates of an experiment performed…
The parameter region of multistationarity of a reaction network contains all the parameters for which the associated dynamical system exhibits multiple steady states. Describing this region is challenging and remains an active area of…
Hypergraphs model higher-order relations that drive real-world decisions, from drug prescriptions to recommendations. A central structural signal in such data, beyond what pairwise relations can express, is interaction compositionality:…
The analysis of the structure of chemical reaction networks is crucial for a better understanding of chemical processes. Such networks are well described as hypergraphs. However, due to the available methods, analyses regarding network…
The search for pathways that optimize the formation of a particular target molecule in a reaction network is a key problem in many settings, including reactor systems. Chemical reaction networks are mathematically well represented as…
We demonstrate that graph-based models are fully capable of representing higher-order interactions, and have a long history of being used for precisely this purpose. This stands in contrast to a common claim in the recent literature on…
We discuss the symbolic dynamics of biochemical networks with separate timescales. We show that symbolic dynamics of monomolecular reaction networks with separated rate constants can be described by deterministic, acyclic automata with a…
Directed and heterogeneous hypergraphs capture directional higher-order interactions with intrinsically asymmetric functional dependencies among nodes. As a result, damage to certain nodes can suppress entire hyperedges, whereas failure of…
In this paper, we propose an optimization-based sparse learning approach to identify the set of most influential reactions in a chemical reaction network. This reduced set of reactions is then employed to construct a reduced chemical…
Reaction rates of chemical reactions under nonequilibrium conditions can be determined through the construction of the normally hyperbolic invariant manifold (NHIM) [and moving dividing surface (DS)] associated with the transition state…
Many real-world complex systems are characterized by non-pairwise -- higher-order -- interactions among system's units, and can be effectively modeled as hypergraphs. Directed hypergraphs distinguish between source and target sets within…
Psychological network approaches propose to see symptoms or questionnaire items as interconnected nodes, with links between them reflecting pairwise statistical dependencies evaluated cross-sectional, time-series, or panel data. These…
We define an independence system associated with simple graphs. We prove that the independence system is a matroid for certain families of graphs, including trees, with bases as minimal resolving sets. Consequently, the greedy algorithm on…
The evolution of chemical reaction networks is often analyzed through kinetic models and energy landscapes, but these approaches fail to capture the deeper structural constraints governing complexity growth. In chemical reaction networks,…
Causal structure learning has long been the central task of inferring causal insights from data. Despite the abundance of real-world processes exhibiting higher-order mechanisms, however, an explicit treatment of interactions in causal…
Higher-order networks, naturally described as hypergraphs, are essential for modeling real-world systems involving interactions among three or more entities. Stochastic block models offer a principled framework for characterizing mesoscale…
Matroid theory provides a unifying framework for studying dependence across combinatorics, geometry, and applications ranging from rigidity to statistics. In this work, we study circuit varieties of matroids, defined by their minimal…
We study a family of networks of autocatalytic reactions, which we call hyperchains, that are a generalization of hypercycles. Hyperchains, and the associated dynamical system called replicator equations, are a possible mechanism for…
In a recent paper it was shown that, for chemical reaction networks possessing a subtle structural property called concordance, dynamical behavior of a very circumscribed (and largely stable) kind is enforced, so long as the kinetics lies…