相关论文: Mixed volume of small reaction networks
Under suitable assumptions, the dynamic behaviour of a chemical reaction network is governed by an autonomous set of polynomial ordinary differential equations over continuous variables representing the concentrations of the reactant…
We study the response of chemical reaction networks driven far from equilibrium to logarithmic perturbations of reaction rates. The response of the mean number of a chemical species is observed to be quantitively limited by number…
The metabolic network of a living cell involves several hundreds or thousands of interconnected biochemical reactions. Previous research has shown that under realistic conditions only a fraction of these reactions is concurrently active in…
Zero-one biochemical reaction networks play key roles in cell signalling such as signalling pathways regulated by protein phosphorylation. Multistability of reaction networks is a crucial dynamics feature enabling decision-making in cells.…
We describe a large class of chemical reaction networks, those endowed with a subtle structural property called concordance. We show that the class of concordant networks coincides precisely with the class of networks which, when taken with…
Dynamical system models of complex biochemical reaction networks are usually high-dimensional, nonlinear, and contain many unknown parameters. In some cases the reaction network structure dictates that positive equilibria must be unique for…
A major challenge in network science is to determine parameters governing complex network dynamics from experimental observations and theoretical models. In complex chemical reaction networks, for example, such as those describing processes…
Siphons in a chemical reaction system are subsets of the species that have the potential of being absent in a steady state. We present a characterization of minimal siphons in terms of primary decomposition of binomial ideals, we explore…
We analyze a class of chemical reaction networks under mass-action kinetics and involving multiple time-scales, whose deterministic and stochastic models display qualitative differences. The networks are inspired by gene-regulatory…
The nonlinearities found in molecular networks usually prevent mathematical analysis of network behaviour, which has largely been studied by numerical simulation. This can lead to difficult problems of parameter determination. However,…
The problem of of how many entangled or, respectively, separable states there are in the set of all quantum states is investigated. We study to what extent the choice of a measure in the space of density matrices describing N--dimensional…
For three typical sets of small reaction networks (networks with two reactions, one irreversible and one reversible reaction, or two reversible-reaction pairs), we completely answer the challenging question: what is the smallest subset of…
Arguing about the equilibrium distribution of continuous-time Markov chains can be vital for showing properties about the underlying systems. For example in biological systems, bistability of a chemical reaction network can hint at its…
In the first part of this paper, we propose new optimization-based methods for the computation of preferred (dense, sparse, reversible, detailed and complex balanced) linearly conjugate reaction network structures with mass action dynamics.…
Polynomial dynamical systems are widely used to model and study real phenomena. In biochemistry, they are the preferred choice for modelling the concentration of chemical species in reaction networks with mass-action kinetics. These systems…
A reaction network is a chemical system involving multiple reactions and chemical species. Stochastic models of such networks treat the system as a continuous time Markov chain on the number of molecules of each species with reactions as…
We extend a recent method to detect lower bounds to the quantum capacity of quantum communication channels by considering realistic scenarios with general input probe states and arbitrary detection procedures at the output. Realistic…
Chemical reaction networks taken with mass-action kinetics are dynamical systems that arise in chemical engineering and systems biology. In general, determining whether a chemical reaction network admits multiple steady states is difficult,…
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…
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…