Related papers: Symbolic hunt of instabilities and bifurcations in…
We consider local bifurcations of equilibria in dynamical systems arising from chemical reaction networks with mass action kinetics. In particular, given any mass action network admitting a local bifurcation of equilibria, assuming only a…
We consider reaction networks that admit a singular perturbation reduction in a certain parameter range. The focus of this paper is on deriving "small parameters" (briefly for small perturbation parameters), to gauge the accuracy of the…
In living cells, chemical reactions form a complex network. Complicated dynamics arising from such networks are the origins of biological functions. We propose a novel mathematical method to analyze bifurcation behaviors of a reaction…
Many scientific and combinatorial problems admit multiple correct solutions, not a single label. Standard supervised learning resolves this ambiguity by choosing one solution as the target, but this hidden selector can be arbitrary,…
Biochemical networks are used in computational biology, to model the static and dynamical details of systems involved in cell signaling, metabolism, and regulation of gene expression. Parametric and structural uncertainty, as well as…
Network models are widely used as structural summaries of biochemical systems. Statistical estimation of networks is usually based on linear or discrete models. However, the dynamics of these systems are generally nonlinear, suggesting that…
Stability is a desirable property of complex ecosystems. If a community of interacting species is at a stable equilibrium point then it is able to withstand small perturbations to component species' abundances without suffering adverse…
Many decision-making algorithms draw inspiration from the inner workings of individual biological systems. However, it remains unclear whether collective behavior among biological species can also lead to solutions for computational tasks.…
We state two sufficient criteria for periodic oscillations in mass action systems. Neither criterion requires a computation of the Hurwitz determinants. Instead, both criteria exploit the linear algebra concepts of $D$-stability and…
We present herein an extension of an algebraic statistical method for inferring biochemical reaction networks from experimental data, proposed recently in [3]. This extension allows us to analyze reaction networks that are not necessarily…
External flows of energy, entropy, and matter can cause sudden transitions in the stability of biological and industrial systems, fundamentally altering their dynamical function. How might we control and design these transitions in chemical…
In the first part of this paper we give a short review of the hierarchy of stochastic models, related to physical chemistry. In the basement of this hierarchy there are two models --- stochastic chemical kinetics and the Kac model for…
Generalized mass-action systems are power-law dynamical systems arising from chemical reaction networks. Essentially, every nonnegative ODE model used in chemistry and biology (for example, in ecology and epidemiology) and even in economics…
A multistationarity region is the part of a reaction network's parameter space that gives rise to multiple steady states. Mathematically, this region consists of the positive parameters for which a parametrized family of polynomial…
A system made up of N interacting species is considered. Self-reaction terms are assumed of the logistic type. Pairwise interactions take place among species according to different modalities, thus yielding a complex asymmetric disordered…
A reaction network is a chemical system involving multiple reactions and chemical species. Stochastic models of such networks treat the system as a continuous time Markov chain on the number of molecules of each species with reactions as…
In this paper we study bifurcations in mass-action networks with two chemical species and reactant complexes of molecularity no more than two. We refer to these as planar, quadratic networks as they give rise to (at most) quadratic…
Gradient descent during the learning process of a neural network can be subject to many instabilities. The spectral density of the Jacobian is a key component for analyzing stability. Following the works of Pennington et al., such Jacobians…
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…
Biochemical reaction networks are an amalgamation of reactions where each reaction represents the interaction of different species. Generally, these networks exhibit a multi-scale behavior caused by the high variability in reaction rates…