Related papers: Complex-linear invariants of biochemical networks
Biological regulatory networks depend upon chemical interactions to process information. Engineering such molecular computing systems is a major challenge for synthetic biology and related fields. The chemical reaction network (CRN) model…
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…
We consider the problem of binomiality of the steady state ideals of biochemical reaction networks. We are interested in finding polynomial conditions on the parameters such that the steady state ideal of a chemical reaction network is…
The goal of this paper is to gather and develop some necessary and sufficient criteria for injectivity and multistationarity in vector fields associated with a chemical reaction network under a variety of more or less general assumptions on…
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…
Equivariant neural networks have shown improved performance, expressiveness and sample complexity on symmetrical domains. But for some specific symmetries, representations, and choice of coordinates, the most common point-wise activations,…
The fundamental decomposition of a chemical reaction network (CRN) is induced by partitioning the reaction set into "fundamental classes". It was the basis of the Higher Deficiency Algorithm for mass action systems of Ji and Feinberg, and…
We address several questions in reduced versus extended networks via the elimination or addition of intermediate complexes in the framework of chemical reaction networks with mass-action kinetics. We clarify and extend advances in the…
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…
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…
The development of chemical reaction models aids understanding and prediction in areas ranging from biology to electrochemistry and combustion. A systematic approach to building reaction network models uses observational data not only to…
We introduce a mixed-integer linear programming (MILP) framework capable of determining whether a chemical reaction network possesses the property of being endotactic or strongly endotactic. The network property of being strongly endotactic…
A complex-valued convolutional network (convnet) implements the repeated application of the following composition of three operations, recursively applying the composition to an input vector of nonnegative real numbers: (1) convolution with…
Many biochemical and industrial applications involve complicated networks of simultaneously occurring chemical reactions. Under the assumption of mass action kinetics, the dynamics of these chemical reaction networks are governed by systems…
Counting the number of isomers of a chemical molecule is one of the formative problems of graph theory. However, recent progress has been slow, and the problem has largely been ignored in modern network science. Here we provide an…
Reconstruction of biochemical reaction networks is a central topic in systems biology which raises crucial theoretical challenges in system identification. Nonlinear Ordinary Differential Equations (ODEs) that involve polynomial and…
We propose a method of analysis of dynamical networks based on a recent measure of Granger causality between time series, based on kernel methods. The generalization of kernel Granger causality to the multivariate case, here presented,…
Despite the recent advances in optical character recognition (OCR), mathematical expressions still face a great challenge to recognize due to their two-dimensional graphical layout. In this paper, we propose a convolutional sequence…
Complex networks provide a powerful mathematical representation of complex systems in nature and society. To understand complex networks, it is crucial to explore their internal structures, also called structural regularities. The task of…
Models of biochemical networks are usually presented as connected graphs where vertices indicate proteins and edges are drawn to indicate activation or inhibition relationships. These diagrams are useful for drawing qualitative conclusions…