Related papers: Hypergraph Laplace Operators for Chemical Reaction…

In this paper we derive a compact mathematical formulation describing the dynamics of chemical reaction networks that are complex-balanced and are governed by mass action kinetics. The formulation is based on the graph of (substrate and…

We study two different types of gluing for graphs: interface (obtained by choosing a common subgraph as the gluing component) and bridge gluing (obtained by adding a set of edges to the given subgraphs). We introduce formulae for computing…

Recent applications of large network models to machine learning, and to neural network suggest a need for a systematic study of the general correspondence, (i) discrete vs (ii) continuous. Even if the starting point is (i), limit…

We study the existence of a common hypercyclic vector for different families of composition operators.

Several new spectral properties of the normalized Laplacian defined for oriented hypergraphs are shown. The eigenvalue $1$ and the case of duplicate vertices are discussed; two Courant nodal domain theorems are established; new quantities…

This paper considers the comparison between the eigenvalues of Laplace operators with the standard conditions and the anti-standard conditions on non-bipartite graphs which are equilateral or inequilateral. First of all, we show the…

In this paper we introduce a new representation for the multistationarity region of a reaction network, using polynomial superlevel sets. The advantages of using this polynomial superlevel set representation over the already existing…

Spectral graph convolutional networks are generalizations of standard convolutional networks for graph-structured data using the Laplacian operator. A common misconception is the instability of spectral filters, i.e. the impossibility to…

For the investigation of chemical reaction networks, the identification of all relevant intermediates and elementary reactions is mandatory. Many algorithmic approaches exist that perform explorations efficiently and automatedly. These…

Lattice structures play a central role in spectral graph theory, offering analytical insight into diffusion, synchronization, and transport processes on regular discrete spaces. While their spectral properties are completely characterized…

In the study of dynamical systems on networks/graphs, a key theme is how the network topology influences stability for steady states or synchronized states. Ideally, one would like to derive conditions for stability or instability that…

Many neural networks for graphs are based on the graph convolution operator, proposed more than a decade ago. Since then, many alternative definitions have been proposed, that tend to add complexity (and non-linearity) to the model. In this…

We consider a generalization of the diffusion equation on graphs. This generalized diffusion equation gives rise to both normal and superdiffusive processes on infinite one-dimensional graphs. The generalization is based on the $k$-path…

We study Laplace-type operators on hybrid manifolds, i.e. on configurations consisting of closed two-dimensional manifolds and one-dimensional segments. Such an operator can be constructed by using the Laplace-Beltrami operators on each…

The main objective of the present work is to study the negative spectrum of (differential) Laplace operators on metric graphs as well as their resolvents and associated heat semigroups. We prove an upper bound on the number of negative…

Many variants of join operations of graphs have been introduced and their spectral properties have been studied extensively by many researchers. This paper mainly focuses on the Laplacian spectra of some double join operations of graphs. We…

In this paper, we introduce three operations on hypergraphs by using tensors. We show that these three formulations are equivalent and we commonly call them as the tensor join. We show that any hypergraph can be viewed as a tensor join of…

Notions of interpolating variational splines and Paley-Wiener spaces are introduced on a combinatorial graph G. Both of these definitions explore existence of a combinatorial Laplace operator onG. The existence and uniqueness of…

In this study, we explore the interrelation between hypergraph symmetries represented by equivalence relations on the vertex set and the spectra of operators associated with the hypergraph. We introduce the idea of equivalence relation…

Motivated by recent progress on the interplay between graph theory, dynamics, and systems theory, we revisit the analysis of chemical reaction networks described by mass action kinetics. For reaction networks possessing a thermodynamic…