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A detailed understanding of biochemical networks at the molecular level is essential for studying complex cellular processes. In this paper, we provide a comprehensive description of biochemical networks by considering individual atoms and…
In the study of reaction networks and the polynomial dynamical systems that they generate, special classes of networks with important properties have been identified. These include reversible, weakly reversible}, and, more recently,…
Stochastic dynamic models have been extensively used for the description of processes with uncertainties arising in the operations research, behavioral sciences, and many other application areas. A large class of the problems from these…
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…
Statistical system models provide the basis for the examination of various sorts of distributions. Classification distributions are a very common and versatile form of statistics in e.g. real economic, social, and IT systems. The…
Scale-free networks are abundant in nature and society, describing such diverse systems as the world wide web, the web of human sexual contacts, or the chemical network of a cell. All models used to generate a scale-free topology are…
In this chapter we take a look at the universal approximation question for stochastic feedforward neural networks. In contrast to deterministic networks, which represent mappings from a set of inputs to a set of outputs, stochastic networks…
Stochastic reaction networks is a powerful class of models for the representation a wide variety of population models including biochemistry. The control of such networks has been recently considered due to their important implications for…
We analyzed the stochastic behavior of systems controlled by autocatalytic reaction A+X -> X+X. Assuming the distribution of reacting particles in the system volume to be uniform, we introduced the notion of the point model of reaction…
We present a new stochastic particle system on networks which describes the flocking behavior and pattern formation. More precisely, we consider Cucker-Smale particles with decentralized formation control and multiplicative noises on…
Polymerization and formation of crosslinked polymer networks are important processes in manufacturing, materials fabrication, and in the case of hydrated polymer networks, synthesis of biomedical materials, drug delivery, and tissue…
We present our recent work on stochastic particle systems on complex networks. As a noninteracting system we first consider the diffusive motion of a random walker on heterogeneous complex networks. We find that the random walker is…
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…
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…
Many approaches to modelling reaction-diffusion systems with anomalous transport rely on deterministic equations and ignore fluctuations arising due to finite particle numbers. Starting from an individual-based model we use a…
In this paper, we consider a subclass of piecewise deterministic Markov processes with a Polish state space that involve a deterministic motion punctuated by random jumps, occurring in a Poisson-like fashion with some state-dependent rate,…
We consider a class of stochastic dynamical systems, called piecewise deterministic Markov processes, with states $(x, \s)\in \O\times \G$, $\O$ being a region in $\bbR^d$ or the $d$--dimensional torus, $\G$ being a finite set. The…
We study stochastic pairwise interaction network systems whereby a finite population of agents, identified with the nodes of a graph, update their states in response to both individual mutations and pairwise interactions with their…
Stochastic reaction-diffusion processes may be presented in terms of integrable quantum chains and can be used to describe various biological and chemical systems. Exploiting the integrability of the models one finds in some cases good…
Within systems biology there is an increasing interest in the stochastic behavior of genetic and biochemical reaction networks. An appropriate stochastic description is provided by the chemical master equation, which represents a continuous…