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Part I of this work [2] developed the exact diffusion algorithm to remove the bias that is characteristic of distributed solutions for deterministic optimization problems. The algorithm was shown to be applicable to a larger set of…
Motivation: Stochastic reaction networks are a widespread model to describe biological systems where the presence of noise is relevant, such as in cell regulatory processes. Unfortu-nately, in all but simplest models the resulting discrete…
Very often, models in biology, chemistry, physics, and engineering are systems of polynomial or power-law ordinary differential equations, arising from a reaction network. Such dynamical systems can be generated by many different reaction…
The activation of matrix metalloproteinase 2 (MMP2) is a crucial event during tumor metastasis and invasion, and this pathway network consists of 3 monomers. The pathway network of the activation obeys to a set of specified reaction rules.…
In this paper, we study a new iterative method for finding the fixed point of a weak Bregman relatively nonexpansive mapping and the set of solutions of generalized mixed equilibrium problems in Banach spaces.
In this paper, we deal with a notion of Banach space-valued mappings defined on a set consisting of finite graphs with uniformly bounded vertex degree. These functions will be endowed with certain boundedness and additivity criteria. We…
We review in a unified way results for two types of stochastic chemical reaction systems for which moments can be effectively computed: feedforward networks and complex-balanced networks.
The convergence to equilibrium of renormalized solutions to reaction-cross-diffusion systems in a bounded domain under no-flux boundary conditions is studied. The reactions model complex balanced chemical reaction networks coming from…
In living cells, chemical reactions are connected by sharing their products and substrates, and form complex networks, e.g. metabolic pathways. Here we developed a theory to predict the sensitivity, i.e. the responses of concentrations and…
Stochastic reaction networks are mathematical models with a wide range of applications in biochemistry, ecology, and epidemiology, and are often complex to analyze. Except for some special cases, it is generally difficult to predict how the…
In this paper, using the Bregman distance, we introduce a new projection-type algorithm for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points. Then the strong convergence of the sequence…
We study stationary distributions in the context of stochastic reaction networks. In particular, we are interested in complex balanced reaction networks and reduction of such networks by assuming a set of species (called non-interacting…
Zero-one reaction networks are pivotal to cellular signaling, and establishing the equivalence of such networks represents a foundational computational challenge in the realm of chemical reaction network research. Herein, we propose a…
Understanding and predicting the behavior of large-scale multi-agents in games remains a fundamental challenge in multi-agent systems. This paper examines the role of heterogeneity in equilibrium formation by analyzing how smooth…
For dynamical systems arising from chemical reaction networks, persistence is the property that each species concentration remains positively bounded away from zero, as long as species concentrations were all positive in the beginning. We…
Reaction networks are systems in which the populations of a finite number of species evolve through predefined interactions. Such networks are found as modeling tools in many biological disciplines such as biochemistry, ecology,…
This paper presents new results about the optimization based generation of chemical reaction networks (CRNs) of higher deficiency. Firstly, it is shown that the graph structure of the realization containing the maximal number of reactions…
The close-to-equilibrium regularity of solutions to a class of reaction-diffusion systems is investigated. The considered systems typically arise from chemical reaction networks and satisfy a complex balanced condition. Under some…
Discovery of atomistic systems with desirable properties is a major challenge in chemistry and material science. Here we introduce a novel, autoregressive, convolutional deep neural network architecture that generates molecular equilibrium…
Multi agent consensus algorithms with update steps based on so-called balanced asymmetric chains, are analyzed. For such algorithms it is shown that (i) the set of accumulation points of states is finite, (ii) the asymptotic unconditional…