Related papers: Correlation between residual entropy and spanning …
We consider the entanglement entropy for the 2D Ising model at the conformal fixed point in the presence of interfaces. More precisely, we investigate the situation where the two subsystems are separated by a defect line that preserves…
We establish an exact analytic relation between random spanning forests and the heat-kernel partition function. This identity enables estimation of partition functions, energies, and the Von Neumann entropy by Wilson sampling of forests,…
Graph based entropy, an index of the diversity of events in their distribution to parts of a co-occurrence graph, is proposed for detecting signs of structural changes in the data that are informative in explaining latent dynamics of…
Entropy is a measure of heterogeneity widely used in applied sciences, often when data are collected over space. Recently, a number of approaches has been proposed to include spatial information in entropy. The aim of entropy is to…
The long-standing question of whether the residual entropy of hexagonal ice ($S_h$) equals that of cubic ice ($S_c$) remains unresolved despite decades of research on ice-type models. While analytical studies have established the inequality…
The topological entropy of piecewise affine maps is studied. It is shown that singularities may contribute to the entropy only if there is angular expansion and we bound the entropy via the expansion rates of the map. As a corollary we…
We study the evolution of graphs densifying by adding edges: Two vertices are chosen randomly, and an edge is (i) established if each vertex belongs to a tree; (ii) established with probability $p$ if only one vertex belongs to a tree;…
We prove a theorem computing the number of solutions to a system of equations which is generic subject to the sparsity conditions embodied in a graph. We apply this theorem to games obeying graphical models and to extensive-form games. We…
The von Neumann entropy of a graph is a spectral complexity measure that has recently found applications in complex networks analysis and pattern recognition. Two variants of the von Neumann entropy exist based on the graph Laplacian and…
We establish a connection between barcode entropy and metric entropy. Namely, we show that the barcode entropy bounds the metric entropy from below for a measure from a specific class of invariant measures associated with a pair of…
In this paper, we develop the notion of entropy for uniform hypergraphs via tensor theory. We employ the probability distribution of the generalized singular values, calculated from the higher-order singular value decomposition of the…
We study the dependence of the topological entropy of piecewise monotonic maps with holes under perturbations, for example sliding a hole of fixed size at uniform speed or expanding a hole with uniform expansion. We show that under suitable…
In this thesis, we study a new disordered system called random spanning tree in random environment (RSTRE) across different families of graphs with varying disorder distributions. We examine several observables as functions of the disorder…
We compute the complexity of two infinite families of finite graphs: the Sierpi\'{n}ski graphs, which are finite approximations of the well-known Sierpi\'nsky gasket, and the Schreier graphs of the Hanoi Towers group $H^{(3)}$ acting on the…
Let $\mathcal{H}$ be a hypergraph with $n$ vertices. Suppose that $d_1,d_2,\ldots,d_n$ are degrees of the vertices of $\mathcal{H}$. The $t$-th graph entropy based on degrees of $\mathcal{H}$ is defined as $$ I_d^t(\mathcal{H})…
Spatially embedded networks are important in several disciplines. The prototypical spatial net- work we assume is the Random Geometric Graph of which many properties are known. Here we present new results for the two-point degree…
Volume entropy is an important invariant of metric graphs as well as Riemannian manifolds. In this note, we calculate the change of volume entropy when an edge is added to a metric graph. Using the first result, we investigate the change of…
Exponential random graph models have attracted significant research attention over the past decades. These models are maximum-entropy ensembles under the constraints that the expected values of a set of graph observables are equal to given…
The total reciprocal edge-eccentricity is a novel graph invariant with vast potential in structure activity/property relationships. This graph invariant displays high discriminating power with respect to both biological activity and…
Quantifying the complexity of large graphs requires measures that extend beyond predefined structural features and scale efficiently with graph size. This work adopts a generative perspective, modeling large networks as exchangeable graphs…