Related papers: Thuston's Teapots and Graph Directed Systems
Graph fractional Fourier transform (GFRFT) is an extension of graph Fourier transform (GFT) that provides an additional fractional analysis tool for graph signal processing (GSP) by generalizing temporal-vertex domain Fourier analysis to…
Transformers were originally proposed as a sequence-to-sequence model for text but have become vital for a wide range of modalities, including images, audio, video, and undirected graphs. However, transformers for directed graphs are a…
In this paper we construct a correspondence between the parameter spaces of two families of one-dimensional dynamical systems, the alpha-continued fraction transformations T_alpha and unimodal maps. This correspondence identifies…
We propose an algorithm to estimate the topology of an embedded metric graph from a well-sampled finite subset of the underlying graph.
In this paper we will modify the Milnor--Thurston map, which maps a one dimensional mapping to a piece-wise linear of the same entropy, and study its properties. This will allow us to give a simple proof of monotonicity of topological…
Transfer entropy (TE) is an information theoretic measure that reveals the directional flow of information between processes, providing valuable insights for a wide range of real-world applications. This work proposes Transfer Entropy…
Directed graphs have been widely used in Community Question Answering services (CQAs) to model asymmetric relationships among different types of nodes in CQA graphs, e.g., question, answer, user. Asymmetric transitivity is an essential…
In his paper, Thurston shows that a positive real number $h$ is the topological entropy for an ergodic traintrack representative of an outer automorphism of a free group if and only if its expansion constant $\lambda = e^h$ is a weak Perron…
We investigate the family of marked Thurston maps that are defined everywhere on the topological sphere $S^2$, potentially excluding at most countable closed set of essential singularities. We show that when an unmarked Thurston map $f$ is…
Intrinsic computation refers to how dynamical systems store, structure, and transform historical and spatial information. By graphing a measure of structural complexity against a measure of randomness, complexity-entropy diagrams display…
In this paper we define unstable topological entropy for any subsets (not necessarily compact or invariant) in partially hyperbolic systems as a Carath\'{e}odory dimension characteristic, motivated by the work of Bowen and Pesin etc. We…
Building upon [1], this study aims to introduce fractal geometry into graph theory, and to establish a potential theoretical foundation for complex networks. Specifically, we employ the method of substitution to create and explore…
A general investigation is made into the intrinsic Riemannian geometry for complex systems, from the perspective of statistical mechanics. The entropic formulation of statistical mechanics is the ingredient which enables a connection…
In connection with the Entropy Conjecture it is known that the topological entropy of a continuous graph map is bounded from below by the spectral radius of the induced map on the first homology group. We show that in the case of a…
The Unrelated Parallel Machine Scheduling Problem (UPMSP) with release dates, setups, and eligibility constraints presents a significant multi-objective challenge. Traditional methods struggle to balance minimizing Total Weighted Tardiness…
Topological mating is an combination that takes two same-degree polynomials and produces a new map with dynamics inherited from this initial pair. This process frequently yields a map that is Thurston-equivalent to a rational map $F$ on the…
A computation of the dynamical structure factor of topologically disordered systems, where the disorder can be described in terms of euclidean random matrices, is presented. Among others, structural glasses and supercooled liquids belong to…
Graphs are a representation of structured data that captures the relationships between sets of objects. With the ubiquity of available network data, there is increasing industrial and academic need to quickly analyze graphs with billions of…
Directed Algebraic Topology studies spaces equipped with a form of direction, to include models of non-reversible processes. In the present extension we also want to cover critical processes, indecomposable and unstoppable. The first part…
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…