相关论文: Non-separable graphs meet Ledoux's polynomials

We investigate the entropy $H(\mu,t)$ of a probability measure $\mu$ along the heat flow and more precisely we seek for closed algebraic representations of its derivatives. Provided that $\mu$ admits moments of any order, it is indeed…

We introduce an algorithmic model of heat conduction, the thermodynamic graph. The thermodynamic graph is analogous to meshes in the finite difference method in the sense that the calculation of temperature is carried out at the vertices of…

Information theoretic quantities play an important role in various settings in machine learning, including causality testing, structure inference in graphical models, time-series problems, feature selection as well as in providing privacy…

In this paper, we study random embeddings of polymer networks distributed according to any potential energy which can be expressed in terms of distances between pairs of monomers. This includes freely jointed chains, steric effects,…

Mutual visibility in graphs provides a framework for analysing how vertices can observe one another along shortest paths free of internal obstructions. The visibility polynomial, which enumerates mutual-visibility sets of all orders, has…

We study evolution equations on metric graphs with reservoirs, that is graphs where a one-dimensional interval is associated to each edge and, in addition, the vertices are able to store and exchange mass with these intervals. Focusing on…

We study a family of dissections of flow polytopes arising from the subdivision algebra. To each dissection of a flow polytope, we associate a polynomial, called the left-degree polynomial, which we show is invariant of the dissection…

We introduce the notion of combinatorial encoding of continuous dynamical systems and suggest the first examples, which are the most interesting and important, namely, the combinatorial encoding of a Bernoulli process with continuous state…

Graphical models represent multivariate and generally not normalized probability distributions. Computing the normalization factor, called the partition function, is the main inference challenge relevant to multiple statistical and…

Dynamical processes can be transformed into graphs through a family of mappings called visibility algorithms, enabling the possibility of (i) making empirical data analysis and signal processing and (ii) characterising classes of dynamical…

The graph polynomial for the number of independent sets of size $k$ in a general undirected graph is shown to be equal to an elementary symmetric polynomial of the vertex monomials, which are determined by the edges incident at the…

Recently a variety of methods have been developed to encode graphs into low-dimensional vectors that can be easily exploited by machine learning algorithms. The majority of these methods start by embedding the graph nodes into a…

A new conceptual foundation for the notion of "information" is proposed, based on the concept of a "distinction graph": a graph in which two nodes are connected iff they cannot be distinguished by a particular observer. The "graphtropy" of…

In this paper, we focus on the study of immanantal polynomials for linear combination matrices composed of the degree matrix and adjacency matrix of a graph. First, applying the concept of vertex orientation for general graphs, we provide a…

We consider sufficient conditions for the existence of $k$-th powers of Hamiltonian cycles in $n$-vertex graphs $G$ with minimum degree $\mu n$ for arbitrarily small $\mu>0$. About 20 years ago Koml\'os, Sark\"ozy, and Szemer\'edi resolved…

The entropy of random graph ensembles has gained widespread attention in the field of graph theory and network science. We consider microcanonical ensembles of simple graphs with prescribed degree sequences. We demonstrate that the…

We present a comprehensive extension of the latent position network model known as the random dot product graph to accommodate multiple graphs -- both undirected and directed -- which share a common subset of nodes, and propose a method for…

We investigate novel random graph embeddings that can be computed in expected polynomial time and that are able to distinguish all non-isomorphic graphs in expectation. Previous graph embeddings have limited expressiveness and either cannot…

The step-growth polymerisation of a mixture of arbitrary-functional monomers is viewed as a time-continuos random graph process with degree bounds that are not necessarily the same for different vertices. The sequence of degree bounds acts…

An unsplittable multiflow routes the demand of each commodity along a single path from its source to its sink node. As our main result, we prove that in series-parallel digraphs, any given multiflow can be expressed as a convex combination…