相关论文: Coassociativity breaking and oriented graphs

Coalescing random walk on a unimodular random rooted graph for which the root has finite expected degree visits each site infinitely often almost surely. A corollary is that an opinion in the voter model on such graphs has infinite expected…

We present analytical treatment of quantum walks on a cycle graph. The investigation is based on a realistic physical model of the graph in which decoherence is induced by continuous monitoring of each graph vertex with nearby quantum point…

Several interesting approaches have been reported in the literature on complex networks, random walks, and hierarchy of graphs. While many of these works perform random walks on stable, fixed networks, in the present work we address the…

In this paper, we present an explicit construction of twisted traces for quantum Coulomb branches of conical theories. We develop an operator representation of the Coulomb branch algebra and use it to derive integral formulas for the…

We give a construction of a family of (weighted) graphs that are pairwise cospectral with respect to the normalized Laplacian matrix, or equivalently probability transition matrix. This construction can be used to form pairs of cospectral…

We show how to construct discrete-time quantum walks on directed, Eulerian graphs. These graphs have tails on which the particle making the walk propagates freely, and this makes it possible to analyze the walks in terms of scattering…

We introduce a new cohomology theory related to deformations of Lie algebra morphisms. This notion involves simultaneous deformations of two Lie algebras and a homomorphism between them.

Cohomologies of nonassociative metagroup algebras are investigated. Extensions of metagroup algebras are studied. Examples are given.

Clustering trajectory data attracted considerable attention in the last few years. Most of prior work assumed that moving objects can move freely in an euclidean space and did not consider the eventual presence of an underlying road network…

We give a short overview over recent developments on quantum graphs and outline the connection between general quantum graphs and so-called quantum random walks.

In this paper we study the structure of $k$-transitive closures of directed paths and formulate several properties. Concept of $k$-transitive orientation generalize the traditional concept of transitive orientation of a graph.

Evolution algebras are non-associative algebras inspired from biological phenomena, with applications to or connections with different mathematical fields. There are two natural ways to define an evolution algebra associated to a given…

We address the correspondence search problem among multiple graphs with complex properties while considering the matching consistency. We describe each pair of graphs by combining multiple attributes, then jointly match them in a unified…

We develop a generalised gauge theory in which the role of gauge group is played by a coalgebra and the role of principal bundle by an algebra. The theory provides a unifying point of view which includes quantum group gauge theory,…

The goal of this paper is to consider some relations between varieties of representations of groups and varieties of associative algebras. The main emphasis is put on the varieties of representations of groups induced by the varieties of…

The present paper is a review of the current state of Graph-Link Theory (graph-links are also closely related to homotopy classes of looped interlacement graphs), dealing with a generalisation of knots obtained by translating the…

We obtain expected number of arrivals, absorption probabilities and expected time until absorption for an asymmetric discrete random walk on a graph in the presence of multiple function barriers. On each edge of the graph and in each vertex…

Focusing on coupling between edges, we generalize the relationship between the normalized graph Laplacian and random walks on graphs by devising an appropriate normalization for the Hodge Laplacian -- the generalization of the graph…

In the theory of coalgebras, trace semantics can be defined in various distinct ways, including through algebraic logics, the Kleisli category of a monad or its Eilenberg-Moore category. This paper elaborates two new unifying ideas: 1)…

In a coalescing random walk, a set of particles make independent random walks on a graph. Whenever one or more particles meet at a vertex, they unite to form a single particle, which then continues the random walk through the graph.…