Related papers: Mass generation in graphs
The effect of introducing a mass dependent diffusion rate ~ m^{-alpha} in a model of coagulation with single-particle break up is studied both analytically and numerically. The model with alpha=0 is known to undergo a nonequilibrium phase…
We propose a combination of a variational autoencoder and a transformer based model which fully utilises graph convolutional and graph pooling layers to operate directly on graphs. The transformer model implements a novel node encoding…
We present an effective model for particle mass generation in which we extract generic features of the Higgs mechanism that do not depend on its interpretation in terms of a Higgs field. In this model the physical vacuum is assumed as a…
We examine the fundamental question whether a random discrete structure with the minimal number of restrictions can converge to continuous metric space. We study the geometrical properties such as the dimensionality and the curvature…
Probability models on graphs are becoming increasingly important in many applications, but statistical tools for fitting such models are not yet well developed. Here we propose a general method of moments approach that can be used to fit a…
One of the biggest huddles faced by researchers studying algorithms for massive graphs is the lack of large input graphs that are essential for the development and test of the graph algorithms. This paper proposes two efficient and highly…
A kinetic theory of vacuum particle creation under the action of an inertial mechanism is constructed within a nonpertrubative dynamical approach. At the semi-phenomenological level, the inertial mechanism corresponds to quantum field…
We study the spread of information on multi-type directed random graphs. In such graphs the vertices are partitioned into distinct types (communities) that have different transmission rates between themselves and with other types. We…
We describe a simple and efficient mechanism by which very heavy particles are copiously created from a primordial inflationary epoch. It works for scalar fields which are massless or very light during inflation and acquire a large mass…
We present a conceptually new approach to describe state-of-the-art photonic quantum experiments using Graph Theory. There, the quantum states are given by the coherent superpositions of perfect matchings. The crucial observation is that…
Large graphs can be found in a wide array of scientific fields ranging from sociology and biology to scientometrics and computer science. Their analysis is by no means a trivial task due to their sheer size and complex structure. Such…
We consider two measures of entanglement, the logarithmic negativity and the entanglement entropy, between regions of space in excited states of many-body systems formed by a finite number of particle excitations. In parts I and II of the…
The inducibility of a graph $H$ measures the maximum number of induced copies of $H$ a large graph $G$ can have. Generalizing this notion, we study how many induced subgraphs of fixed order $k$ and size $\ell$ a large graph $G$ on $n$…
We study the properties of random graphs where for each vertex a {\it neighbourhood} has been previously defined. The probability of an edge joining two vertices depends on whether the vertices are neighbours or not, as happens in Small…
Analyzing massive complex networks yields promising insights about our everyday lives. Building scalable algorithms to do so is a challenging task that requires a careful analysis and an extensive evaluation. However, engineering such…
We analyze the quantum entanglement properties of bosonic particles hopping over graph structures.Mode-entanglement of a graph vertex with respect the rest of the graph is generated, starting from a product state, by turning on for a finite…
Paper proposes a model of large networks based on a random preferential attachment graph with addition of complete subgraphs (cliques). The proposed model refers to models of random graphs following the nonlinear preferential attachment…
We study connected graphs with a fixed degree sequence, in the sparse setting where the number of edges grows linearly in the number of vertices. Using the relation to the configuration model, we identify the number of such connected graphs…
Given a quantum (or statistical) system with a very large number of degrees of freedom and a preferred tensor product factorization of the Hilbert space (or of a space of distributions) we describe how it can be approximated with a very…
Graphity models are characterized by configuration spaces in which states correspond to graphs and Hamiltonians that depend on local properties of graphs such as the degrees of vertices and numbers of short cycles. As statistical systems,…