Related papers: Self-Correlation and Maximum Independence in Finit…
Let $X$ be $k$-regular graph on $v$ vertices and let $\tau$ denote the least eigenvalue of its adjacency matrix $A(X)$. If $\alpha(X)$ denotes the maximum size of an independent set in $X$, we have the following well known bound: \[…
In set theory without the Axiom of Choice (AC), we observe new relations of the following statements with weak choice principles. 1. Every locally finite connected graph has a maximal independent set. 2. Every locally countable connected…
Let $G$ be a simple, connected and finite graph with order $n$. Denote the independence number, edge independence number and total independence number by $\alpha(G), \alpha'(G)$ and $\alpha"(G)$ respectively. This paper establishes a…
Let G=(V,E) be a graph. A set S is independent if no two vertices from S are adjacent. The independence number alpha(G) is the cardinality of a maximum independent set, and mu(G) is the size of a maximum matching. The number…
An independent vertex set of a graph is a set of vertices of the graph in which no two vertices are adjacent, and a maximal independent set is one that is not a proper subset of any other independent set. In this paper we count the number…
In random cellular systems, both observation and maximum entropy inference give a specific form to the topological pair correlation: it is bi-affine in the cells number of edges with coefficients depending on the distance between the two…
It is well-known in thermodynamics that the creation of correlations costs work. It seems then a truism that if a thermodynamic transformation A->B is impossible, so will be any transformation that in sending A to B also correlates among…
A new notion of vertex independence and rank for a finite graph G is introduced. The independence of vertices is based on the boolean independence of columns of a natural boolean matrix associated to G. Rank is the cardinality of the…
We study the problem of deterministic approximate counting of matchings and independent sets in graphs of bounded connective constant. More generally, we consider the problem of evaluating the partition functions of the monomer-dimer model…
We study a combinatorial property of subsets in finite groups that is analogous to the notion of independence in graphs. Given a group $G$ and a non-empty subset $A\subset G$, we define a (right) $s$-factor as a subset $B\subset G$…
Superdeterminism - where the Measurement Independence assumption in Bell's Theorem is violated - is frequently assumed to imply implausibly conspiratorial correlations between properties $\lambda$ of particles being measured and measurement…
Independent Component Analysis (ICA) offers interpretable semantic components of embeddings. While ICA theory assumes that embeddings can be linearly decomposed into independent components, real-world data often do not satisfy this…
In the context of many-fermion systems, "correlation" refers to the inadequacy of an independent-particle model. Using "free" states as archetypes of our independent-particle model, we have proposed a measure of correlation that we called…
Structural independence is the (conditional) independence that arises from the structure rather than the precise numerical values of a distribution. We develop this concept and relate it to $d$-separation and structural causal models.…
Completely determining the relationship between quantum correlation sets is a long-standing open problem, known as Tsirelson's problem. Following recent progress by Slofstra [arXiv:1606.03140 (2016), arXiv:1703.08618 (2017)] only two…
The maximal correlation coefficient is a well-established generalization of the Pearson correlation coefficient for measuring non-linear dependence between random variables. It is appealing from a theoretical standpoint, satisfying…
We study the properties of algebraic independence and pointwise algebraic independence in a class of continuous theories, the randomizations $T^R$ of complete first order theories $T$. If algebraic and definable closure coincide in $T$,…
As a simple model for single-file diffusion of hard core particles we investigate the one-dimensional symmetric exclusion process. We consider an open semi-infinite system where one end is coupled to an external reservoir of constant…
We consider a symmetric exclusion process on a discrete interval of $S$ points with various boundary conditions at the endpoints. We study the asymptotic decay of correlations as $S\to\infty$. The main result is asymptotic independence of a…
We give a characterization for the extreme points of the convex set of correlation matrices with a countable index set. A Hermitian matrix is called a correlation matrix if it is positive semidefinite with unit diagonal entries. Using the…