Related papers: A Case Study on the Parametric Occurrence of Multi…
The study of the interplay between the structure and dynamics of complex multilevel systems is a pressing challenge nowadays. In this paper, we use a semi-annealed approximation to study the stability properties of Random Boolean Networks…
We develop a data-driven machine learning approach to identifying parameters with steady-state solutions, locating such solutions, and determining their linear stability for systems of ordinary differential equations and dynamical systems…
Well-mixed chemical reaction networks (CRNs) contain many distinct chemical species with copy numbers that fluctuate in correlated ways. While those correlations are typically monitored via Monte Carlo sampling of stochastic trajectories,…
Mathematical modelling has become an established tool for studying the dynamics of biological systems. Current applications range from building models that reproduce quantitative data to identifying systems with predefined qualitative…
We propose a numerical technique for parameter inference in Markov models of biological processes. Based on time-series data of a process we estimate the kinetic rate constants by maximizing the likelihood of the data. The computation of…
Despite significant progress on stability analysis of conventional multiagent networked systems with weakly coupled state-network dynamics, most of the existing results have shortcomings in addressing multiagent systems with highly coupled…
Key features of biological activity can often be captured by transitions between a finite number of semi-stable states that correspond to behaviors or decisions. We present here a broad class of dynamical systems that are ideal for modeling…
The standard two-step model of homogeneous-catalyzed reactions had been theoretically analyzed at various levels of approximations from time to time. The primary aim was to check the validity of the quasi-steady-state approximation, and…
The paper discusses a simple method of using the parametric continuation method to designate complex diagrams of steady states. The main advantage of the discussed approach is the fact that it does not require the installation of huge…
It has been recently observed that the dynamical properties of mass action systems arising from many models of biochemical reaction networks can be derived by considering the corresponding properties of a related generalized mass action…
The neural dynamics of the nematode C. elegans are experimentally low-dimensional and correspond to discrete behavioral states, where previous modeling work has found neural proxies for some of these states. Experimental results further…
We characterize completely the capacity for (nondegenerate) multistationarity of mass action reaction networks with one-dimensional stoichiometric subspace in terms of reaction structure. Specifically, we show that networks with two or more…
Multistationary chemical reaction networks are of interest to scientists and mathematicians alike. While some criteria for multistationarity exist, obtaining explicit reaction rates and steady states that exhibit multistationarity for a…
Gene regulatory networks with dynamics characterized by multiple stable states underlie cell fate-decisions. Quantitative models that can link molecular-level knowledge of gene regulation to a global understanding of network dynamics have…
Random Boolean Network has been used to find out regulation patterns of genes in organism. his approach is very interesting to use in a game such as N Person PD. Here we assume that action is influenced by input in the form of choices of…
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…
A generic scheme for the parametrization of mixed state systems is introduced, which is then adapted to bipartite systems, especially to a 2-qubit system. Various features of 2-qubit entanglement are analyzed based on the scheme. Our…
Stochastic modelling provides an indispensable tool for understanding how random events at the molecular level influence cellular functions. In practice, the common challenge is to calibrate a large number of model parameters against the…
Considering stationary states of continuous-variable systems undergoing an open dynamics, we unveil the connection between properties and symmetries of the latter and the dynamical parameters. In particular, we explore the relation between…
Stochastic reaction networks are mathematical models frequently used in, but not limited to, biochemistry. These models are continuous-time Markov chains whose transition rates depend on certain parameters called rate constants, which…