Related papers: Information Sources on a Bratteli diagram
We connect several notions relating the structural and dynamical properties of a graph. Among them are the topological entropy coming from the vertex shift, which is related to the spectral radius of the graph's adjacency matrix, the…
This paper is a survey on general (simple and non-simple) Bratteli diagrams which focuses on the following topics: finite and infinite tail invariant measures on the path space $X_B$ of a Bratteli diagram $B$, existence of continuous…
For a Bratteli diagram $B$, we study the simplex $\mathcal{M}_1(B)$ of probability measures on the path space of $B$ which are invariant with respect to the tail equivalence relation. Equivalently, $\mathcal{M}_1(B)$ is formed by…
Recalling the construction of a flat surface from a Bratteli diagram, this paper considers the dynamics of the shift map on the space of all bi-infinite Bratteli diagrams as the renormalizing dynamics on a moduli space of flat surfaces of…
Separated graphs provide a powerful combinatorial tool for approximating dynamical systems. This paper details the explicit construction of Bratteli-like separated graphs -- a generalization of classical Bratteli diagrams -- that encode the…
Graphlets are subgraphs rooted at a fixed vertex. The number of occurrences of graphlets aligned to a particular vertex, called graphlet degree sequence (gds), gives a topological description of the surrounding of the analyzed vertex.…
In the paper we study aperiodic substitutional dynamical systems arisen from non-primitive substitutions. We prove that the Vershik homeomorphism $\phi$ of a stationary ordered Bratteli diagram is homeomorphic to an aperiodic substitutional…
Feed-forward deep neural networks have been used extensively in various machine learning applications. Developing a precise understanding of the underling behavior of neural networks is crucial for their efficient deployment. In this paper,…
Characterisations of interval graphs, comparability graphs, co-comparability graphs, permutation graphs, and split graphs in terms of linear orderings of the vertex set are presented. As an application, it is proved that interval graphs,…
Graph covers are a way to describe continuous maps (and homeomorphisms) of a Cantor set, more generally than e.g.\ Bratteli-Vershik systems. Every continuous map on a zero-dimensional compact set can be expressed by a graph cover (e.g.\…
A bargraph is a self-avoiding lattice path with steps $U=(0,1)$, $H=(1,0)$ and $D=(0,-1)$ that starts at the origin and ends on the $x$-axis, and stays strictly above the $x$-axis everywhere except at the endpoints. Bargraphs have been…
We study the problem of distributed information bottleneck, in which multiple encoders separately compress their observations in a manner such that, collectively, the compressed signals preserve as much information as possible about another…
The Information bottleneck method is an unsupervised non-parametric data organization technique. Given a joint distribution P(A,B), this method constructs a new variable T that extracts partitions, or clusters, over the values of A that are…
Based on our previous graph covering method, we introduce weighted graph covering models and flexible graph covering models that are almost equivalent to the well-known Bratteli--Vershik models. These models play important roles in showing…
We study the problem of inferring network topology from information cascades, in which the amount of time taken for information to diffuse across an edge in the network follows an unknown distribution. Unlike previous studies, which assume…
The spectral radius of a graph is the spectral radius of its adjacency matrix. A threshold graph is a simple graph whose vertices can be ordered as $v_1, v_2, \ldots, v_n$, so that for each $2 \le i \le n$, vertex $v_i$ is either adjacent…
We consider a time-continuous branching random walk on a one-dimensional lattice on which there is one center (lattice point) of particle generation, called branching source. The generation of particles in the branching source is described…
We introduce and study dynamical systems and measures on stationary generalized Bratteli diagrams $B$ that are represented as the union of countably many classical Pascal-Bratteli diagrams. We describe all ergodic tail invariant measures on…
A class of models describing the flow of information within networks via routing processes is proposed and investigated, concentrating on the effects of memory traces on the global properties. The long-term flow of information is governed…
We show that every topological factoring between two zero dimensional dynamical systems can be represented by a sequence of morphisms between the levels of the associated ordered Bratteli diagrams. Conversely, we will prove that given an…