Related papers: Chemical Reaction Networks in a Laplacian Framewor…
Chemical systems are interpreted through the species they contain and the reactions they may undergo, i.e., their chemical reaction network (CRN). In spite of their central importance to chemistry, the structure of CRNs continues to be…
Chemical reaction networks (CRNs) are fundamental computational models used to study the behavior of chemical reactions in well-mixed solutions. They have been used extensively to model a broad range of biological systems, and are primarily…
Power law dynamics is used to describe the stability behavior in metabolic networks such as chemical reaction networks (CRN's). These systems allow multiple steady states within a single stoichiometric class. On the other side thermodynamic…
We introduce a new model of \emph{step} Chemical Reaction Networks (step CRNs), motivated by the step-wise addition of materials in standard lab procedures. Step CRNs have ordered reactants that transform into products via reaction rules…
Stochastic evolution of Chemical Reactions Networks (CRNs) over time is usually analysed through solving the Chemical Master Equation (CME) or performing extensive simulations. Analysing stochasticity is often needed, particularly when some…
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…
Recent developments in deep learning have revolutionized the paradigm of image restoration. However, its applications on real image denoising are still limited, due to its sensitivity to training data and the complex nature of real image…
The theory of pattern formation in reaction-diffusion systems is extended to the case of a directed network. Due to the structure of the network Laplacian of the scrutinised system, the dispersion relation has both real and imaginary parts,…
Linearized catalytic reaction equations modeling e.g. the dynamics of genetic regulatory networks under the constraint that expression levels, i.e. molecular concentrations of nucleic material are positive, exhibit nontrivial dynamical…
Continuous-time Markov chains are frequently used as stochastic models for chemical reaction networks, especially in the growing field of systems biology. A fundamental problem for these Stochastic Chemical Reaction Networks (SCRNs) is to…
We lay the foundation of a circuit theory for chemical reaction networks. Chemical reactions are grouped into chemical modules solely characterized by their current-concentration characteristic, as electrical devices by their…
The purpose of this paper is to infer a global (collective) model of time-varying responses of a set of nodes as a dynamic graph, where the individual time series are respectively observed at each of the nodes. The motivation of this work…
Recent advances in event-based research prioritize sparsity and temporal precision. Approaches using dense frame-based representations processed via well-pretrained CNNs are being replaced by the use of sparse point-based representations…
Complex real-world phenomena across a wide range of scales, from aviation and internet traffic to signal propagation in electronic and gene regulatory circuits, can be efficiently described through dynamic network models. In many such…
Some results are presented on how oscillation is inherited by chemical reaction networks (CRNs) when they are built in natural ways from smaller oscillatory networks. The main results describe four important ways in which a CRN can be…
Chemical reaction networks in living cells maintain precise control over thousands of metabolites despite operating far from equilibrium under constant perturbations. While mass action kinetics accurately describe the underlying dynamics,…
Graph Convolutional Networks (GCNs) have recently become the primary choice for learning from graph-structured data, superseding hash fingerprints in representing chemical compounds. However, GCNs lack the ability to take into account the…
Spectral graph convolutional networks (GCNs) are particular deep models which aim at extending neural networks to arbitrary irregular domains. The principle of these networks consists in projecting graph signals using the…
We study the model of continuous chemical reaction networks (CRNs), consisting of reactions such as $A+B \to C+D$ that can transform some continuous, nonnegative real-valued quantity (called a *concentration*) of chemical species $A$ and…
The large-scale properties of chemical reaction systems, such as the metabolism, can be studied with graph-based methods. To do this, one needs to reduce the information -- lists of chemical reactions -- available in databases. Even for the…