相关论文: Fundamental Decompositions and Multistationarity o…
Reaction networks are a general framework widely used in modeling diverse phenomena in different science disciplines. The dynamical process of a reaction network endowed with mass-action kinetics is a mass-action system as an ODE defined by…
Robustness of biochemical systems has become one of the central questions in Systems Biology, although it is notoriously difficult to formally capture its multifaceted nature. Maintenance of normal system function depends not only on the…
Mass-action kinetics is frequently used in systems biology to model the behaviour of interacting chemical species. Many important dynamical properties are known to hold for such systems if they are weakly reversible and have a low…
The Jacobian matrix of a dynamic system and its principal minors play a prominent role in the study of qualitative dynamics and bifurcation analysis. When interpreting the Jacobian as an adjacency matrix of an interaction graph, its…
The connection between network topology and stability remains unclear. General approaches that clarify this relationship and allow for more efficient stability analysis would be desirable. Inspired by chemical reaction networks, I…
Autocatalytic cores are minimal units in reaction networks (RNs) responsible for the emergence of autocatalysis. In the absence of explicit catalysis, i.e., when an entity appears both as reactant and product in the same reaction, they are…
While renormalization groups are fundamental in physics, renormalization of complex networks remains vague in its conceptual definition and methodology. Here, we propose a novel strategy to renormalize complex networks. Rather than…
Functional decomposition of logic circuits has profound influence on all quality aspects of the cost-effective implementation of modern digital systems. In this paper, a relational approach to the decomposition of logic circuits is…
We consider linear elimination of variables in steady state equations of a chemical reaction network. Particular subsets of variables corresponding to sets of so-called reactant-noninteracting species, are introduced. The steady state…
We apply a number of atomic decomposition schemes across the standard QM7 dataset -- a small model set of organic molecules at equilibrium geometry -- to inspect the possible emergence of trends among contributions to atomization energies…
Magombedze and Mulder (2013) studied the gene regulatory system of \textit{Mycobacterium Tuberculosis} (\textit{Mtb}) by partitioning this into three subsystems based on putative gene function and role in dormancy/latency development. Each…
A stochastic model for a chemical reaction network is embedded in a one-parameter family of models with species numbers and rate constants scaled by powers of the parameter. A systematic approach is developed for determining appropriate…
We study the reaction-diffusion process $A + B \to \emptyset$ on uncorrelated scale-free networks analytically. By a mean-field ansatz we derive analytical expressions for the particle pair-correlations and the particle density. Expressing…
Reaction networks are mainly used to model the time-evolution of molecules of interacting chemical species. Stochastic models are typically used when the counts of the molecules are low, whereas deterministic models are used when the counts…
Based on the theory of stochastic chemical kinetics, the inherent randomness and stochasticity of biochemical reaction networks can be accurately described by discrete-state continuous-time Markov chains. The analysis of such processes is,…
A classic and fundamental result about the decomposition of random sequences into a mixture of simpler ones is de Finetti's Theorem. In its original form it applies to infinite 0-1 valued exchangeable sequences. Later it was extended and…
In the modeling of complex biological systems, the use of power-law models (such as S-systems and GMA systems) often provides a remarkable accuracy over several orders of magnitude in concentrations, an unusually broad range not fully…
A crisp survey is given of chemical reaction networks from the perspective of general nonlinear network dynamics, in particular of consensus dynamics. It is shown how by starting from the complex-balanced assumption the reaction dynamics…
Networks play a prominent role in the study of complex systems of interacting entities in biology, sociology, and economics. Despite this diversity, we demonstrate here that a statistical model decomposing networks into matching and…
Bistability and multistationarity are properties of reaction networks linked to switch-like responses and connected to cell memory and cell decision making. Determining whether and when a network exhibits bistability is a hard and open…