Related papers: Graph theoretical approach to evaluate molecular i…
Graph neural networks are widely used to learn global representations of graphs, which are then used for regression or classification tasks. Typically, the graphs in such data sets are connected, i.e. each training sample consists of a…
The near-infinite chemical diversity of natural and artificial macromolecules arises from the vast range of possible component monomers, linkages, and polymers topologies. This enormous variety contributes to the ubiquity and…
This book collects the lectures about graph theory and its applications which were given to students of mathematical departments of Moscow State University and Peking University. Graph theory is a very wide field with a lot of applications…
In a coupled network cells can interact in several ways. There is a vast literature from the last twenty years that investigates this interacting dynamics under a graph theory formalism, namely as a graph endowed with an input-equivalence…
In this paper we investigate the spectral and scattering theory for operators acting on topological crystals and on their perturbations. A special attention is paid to perturbations obtained by the addition of an infinite number of edges,…
We analyze the interaction of two conducting, charged polymer chains in solution using a minimal model for their electronic degrees of freedom. We show that a crossing of the two chains in which the polymers pass within Angstroms of each…
We investigate the pairing and crystalline instabilities of bosonic and fermionic polar molecules confined to a ladder geometry. By means of analytical and quasi-exact numerical techniques, we show that gases of composite molecular dimers…
Formation of clusters of interlayer interstitial carbon atoms in graphite is studied by means of molecular dynamics simulation. It is shown that the deformation potential is attractive for interstitials located in one interlayer region and…
Graphs are commonly used to characterise interactions between objects of interest. Because they are based on a straightforward formalism, they are used in many scientific fields from computer science to historical sciences. In this paper,…
A method for considering a weighted directed graph with an accuracy of up to a given partition of the set of vertices is proposed. The resulting digraph (the splitting graph) does not contain arcs inside each partition element, and the arcs…
Chemical reactions can be understood as transformations of multigraphs (molecules) that preserve vertex labels (atoms) and degrees (sums of bonding and non-bonding electrons), thereby implying the atom-atom map of a reaction. The…
The general formalism of the multipolar expansion of electrostatic interactions is applied to the calculation the potential energy between an excited atom (without fine structure) and a ground state diatomic molecule at large separations.…
We investigate theoretically the long-range electrostatic interactions between a ground-state homonuclear alkali-metal dimer and an excited alkali-metal atom taking into account its fine-structure. The interaction involves the combination…
We develop a microscopic large-$N$ theory of electron-electron interaction corrections to multi-legged Feynman diagrams describing second- and third-order nonlinear response functions. Our theory, which reduces to the well-known random…
In this article we formulate and solve the problem of molecular beam diffraction when each molecule consists of two interacting bodies. Then, using our results, we present the diffraction patterns for various molecular sizes employing the…
We study numerically the Casimir interaction between dielectrics in both two and three dimensions. We demonstrate how sparse matrix factorizations enable one to study torsional interactions in three dimensions. In two dimensions we study…
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…
Topology identification and inference of processes evolving over graphs arise in timely applications involving brain, transportation, financial, power, as well as social and information networks. This chapter provides an overview of graph…
Consider a connected graph $G$ and let $T$ be a spanning tree of $G$. Every edge $e \in G-T$ induces a cycle in $T \cup \{e\}$. The intersection of two distinct such cycles is the set of edges of $T$ that belong to both cycles. The MSTCI…
In this paper, we demonstrate a useful interaction between the theory of clique partitions, edge clique covers of a graph, and the spectra of graphs. Using a clique partition and an edge clique cover of a graph we introduce the notion of a…