Related papers: Stochastic reaction networks within interacting co…
The behavior of some stochastic chemical reaction networks is largely unaffected by slight inaccuracies in reaction rates. We formalize the robustness of state probabilities to reaction rate deviations, and describe a formal connection…
Mass action systems capture chemical reaction networks in homogeneous and dilute solutions. We suggest a notion of generalized mass action systems that admits arbitrary nonnegative power-law rate functions and serves as a more realistic…
Biochemical reactions can happen on different time scales and also the abundance of species in these reactions can be very different from each other. Classical approaches, such as deterministic or stochastic approach, fail to account for or…
Consider the standard stochastic reaction network model where the dynamics is given by a continuous-time Markov chain over a discrete lattice. For such models, estimation of parameter sensitivities is an important problem, but the existing…
Stochastic reaction networks (SRNs) provide models of many real-world networks. Examples include networks in epidemiology, pharmacology, genetics, ecology, chemistry, and social sciences. Here, we model stochastic reaction networks by…
Spatial reaction-diffusion models have been employed to describe many emergent phenomena in biological systems. The modelling technique most commonly adopted in the literature implements systems of partial differential equations (PDEs),…
We consider steady states of dynamics that have an underlying network structure. We study how a steady state responds to small perturbations in the network parameters and how this sensitivity is connected to the network structure. We…
We address the problem of simulation and parameter inference for chemical reaction networks described by the chemical Langevin equation, a stochastic differential equation (SDE) representation of the dynamics of the chemical species. This…
The highly variable dynamics of neocortical circuits observed in vivo have been hypothesized to represent a signature of ongoing stochastic inference but stand in apparent contrast to the deterministic response of neurons measured in vitro.…
We consider discrete-space continuous-time Markov models of reaction networks and provide sufficient conditions for the following stability condition to hold: each state in a closed, irreducible component of the state space is positive…
Stochastic reaction network models are often used to explain and predict the dynamics of gene regulation in single cells. These models usually involve several parameters, such as the kinetic rates of chemical reactions, that are not…
We develop numerical and analytical approaches to calculate mutual information between complete paths of two molecular components embedded into a larger reaction network. In particular, we focus on a continuous-time Markov chain formalism,…
Heterogeneity in gene expression across isogenic cell populations can give rise to phenotypic diversity, even when cells are in homogenous environments. This diversity arises from the discrete, stochastic nature of biochemical reactions,…
At the microscopic scale, open chemical reaction networks are described by stochastic reactions that follow mass-action kinetics and are coupled to chemostats. We show that closed chemical reaction networks -- with specific stoichiometries…
Chemical reaction networks (CRNs) are fundamental computational models used to study the behavior of chemical reactions in well-mixed solutions. They have been used extensively to model a broad range of biological systems, and are primarily…
The availability of relational data can offer new insights into the functioning of the economy. Nevertheless, modeling the dynamics in network data with multiple types of relationships is still a challenging issue. Stochastic block models…
Kinetic Monte Carlo methods such as the Gillespie algorithm model chemical reactions as random walks in particle number space. The inter-reaction times are exponentially distributed under the assumption that the system is well mixed. We…
We present a systematic mathematical analysis of the qualitative steady-state response to rate perturbations in large classes of reaction networks. This includes multimolecular reactions and allows for catalysis, enzymatic reactions,…
This article studies the estimation of latent community memberships from pairwise interactions in a network of $N$ nodes, where the observed interactions can be of arbitrary type, including binary, categorical, and vector-valued, and not…
We construct a novel class of stochastic blockmodels using Bayesian nonparametric mixtures. These model allows us to jointly estimate the structure of multiple networks and explicitly compare the community structures underlying them, while…