Related papers: Information Sources on a Bratteli diagram
A Q-system is a unitary version of a separable Frobenius algebra object in a C*-tensor category. In a recent joint work with P. Das, S. Ghosh and C. Jones, the author has categorified Bratteli diagrams and unitary connections by building a…
The middle-levels graph $M_k$ ($0<k\in\mathbb{Z}$) has a dihedral quotient pseudograph $R_k$ whose vertices are the $k$-edge ordered trees $T$, each $T$ encoded as a $(2k+1)$-string $F(T)$ formed via $\rightarrow$DFS by: {\bf(i)}…
Information hierarchies are organizational structures that often used to organize and present large and complex information as well as provide a mechanism for effective human navigation. Fortunately, many statistical and computational…
In the context of statistical learning, the Information Bottleneck method seeks a right balance between accuracy and generalization capability through a suitable tradeoff between compression complexity, measured by minimum description…
A cyclic base ordering of a connected graph $G$, is a cyclic ordering of $E(G)$ such that every cyclically consecutive $|V(G)|-1$ edges form a spanning tree. In this project, we study cyclic base ordering of various families of graphs,…
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…
Graphs are widely used for describing systems made up of many interacting components and for understanding the structure of their interactions. Various statistical models exist, which describe this structure as the result of a combination…
The present paper explores substitution minimal systems and their relation to stationary Bratteli diagrams and stationary dimension groups. The constructions involved are algorithmic and explicit, and render an effective method to compute…
Percolation is perhaps the simplest example of a process exhibiting a phase transition and one of the most studied phenomena in statistical physics. The percolation transition is continuous if sites/bonds are occupied independently with the…
Graph is a highly generic and diverse representation, suitable for almost any data processing problem. Spectral graph theory has been shown to provide powerful algorithms, backed by solid linear algebra theory. It thus can be extremely…
Vertex deletion problems for graphs are studied intensely in classical and parameterized complexity theory. They ask whether we can delete at most k vertices from an input graph such that the resulting graph has a certain property.…
Let $F$ be a probability distribution with support on the non-negative integers. Two algorithms are described for generating a stationary random graph, with vertex set $\mathbb{Z}$, so that the degrees of the vertices are i.i.d.\ random…
Voronoi diagrams appear in many areas in science and technology and have numerous applications. They have been the subject of extensive investigation during the last decades. Roughly speaking, they are a certain decomposition of a given…
From any given sequence of finite or infinite graphs, a nonstandard graph is constructed. The procedure is similar to an ultrapower construction of an internal set from a sequence of subsets of the real line, but now the individual entities…
A graph is a mathematical object consisting of a set of vertices and a set of edges connecting vertices. Graphs can be drawn on paper in various ways, but until recently all published methods of drawing graphs have had undesirable…
In this paper we describe a triple correspondence between graph limits, information theory and group theory. We put forward a new graph limit concept called log-convergence that is closely connected to dense graph limits but its main…
In many applications, the two-dimensional trajectories of fluid particles are available, but little is known about the underlying flow. Oceanic floats are a clear example. To extract quantitative information from such data, one can measure…
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…
The Information Bottleneck (IB) is a method of lossy compression of relevant information. Its rate-distortion (RD) curve describes the fundamental tradeoff between input compression and the preservation of relevant information embedded in…
We derive mean-field information Hessian matrices on finite graphs. The "information" refers to entropy functions on the probability simplex. And the "mean-field" means nonlinear weight functions of probabilities supported on graphs. These…