Related papers: Geometry and symmetry in biochemical reaction syst…
This essay reviews some key concepts in mathematical epidemiology and examines the intersection of this field with related scientific disciplines, such as chemical reaction network theory and Lagrange-Hamilton geometry. Through a synthesis…
Under mass-action kinetics, biochemical reaction networks give rise to polynomial autonomous dynamical systems whose parameters are often difficult to estimate. We deal in this paper with the problem of identifying the kinetic parameters of…
The catalytic reaction system (CRS) formalism by Hordijk and Steel is a versatile method to model autocatalytic biochemical reaction networks. It is particularly suited, and has been widely used, to study self-sustainment and…
Autocatalytic Sets are reaction networks theorised as networks at the basis of life. Their main feature is the ability of spontaneously emerging and self-reproducing. The Reflexively and Food-generated theory provides a formal definition of…
Graph-based reaction systems were recently introduced as a generalization of the intensely studied set-based reaction systems. They deal with simple edge-labeled directed graphs, and dynamic semantics of graph-based reaction systems is…
Many physical systems--from mechanical lattices and electrical circuits to biological tissues and architected metamaterials--can be understood as networks transmitting physical quantities. We present a unified mathematical framework for…
Recently, Hessian geometry - an extension of information geometry - has emerged as a framework to naturally connect the geometries appearing in the theory of chemical reaction networks (CRN) to their inherent thermodynamical and kinetic…
Natural physical, chemical, and biological dynamical systems are often complex, with heterogeneous components interacting in diverse ways. We show how simple graph neural networks can be designed to jointly learn the interaction rules and…
Here, the structural symmetries of a hypergraph are represented through equivalence relations on the vertex set of the hypergraph. A matrix associated with the hypergraph may not reflect a specific structural symmetry. In the context of a…
Complex systems are composed of many particles or agents that move and interact with one another. The underlying mathematical framework to model many of these systems must incorporate the spatial transport of particles and their…
Hypergraphs offer an explicit formalism to describe multibody interactions in complex systems. To connect dynamics and function in systems with these higher-order interactions, network scientists have generalised random-walk models to…
Graphs are ubiquitous data structures for representing interactions between entities. With an emphasis on the use of graphs to represent chemical molecules, we explore the task of learning to generate graphs that conform to a distribution…
Complex systems are often driven by higher-order interactions among multiple units, naturally represented as hypergraphs. Understanding dependency structures within these hypergraphs is crucial for understanding and predicting the behavior…
Representing molecular structures effectively in chemistry remains a challenging task. Language models and graph-based models are extensively utilized within this domain, consistently achieving state-of-the-art results across an array of…
Being cognizant of the abundance of multi-body interactions in various complex systems, here we investigate a possible way to incorporate multi-body interactions in dynamical networks. Adopting hypergraph as the underlying architecture aids…
Can a micron sized sack of interacting molecules autonomously learn an internal model of a complex and fluctuating environment? We draw insights from control theory, machine learning theory, chemical reaction network theory, and statistical…
Reaction networks are widely used models to describe biochemical processes. Stochastic fluctuations in the counts of biological macromolecules have amplified consequences due to their small population sizes. This makes it necessary to favor…
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…
The spatial organization of chromatin within the nucleus plays a crucial role in gene expression and genome function. However, the quantitative relationship between this organization and nuclear biochemical processes remains under debate.…
A general framework for the simulation of reaction-diffusion systems with probabilistic cellular automata is presented. The basic reaction probabilities of the chemical model translate directly into the transition rules of the automaton,…