Related papers: Self-Correlation and Maximum Independence in Finit…
We use an entropy based method to study two graph maximization problems. We upper bound the number of matchings of fixed size $\ell$ in a $d$-regular graph on $N$ vertices. For $\frac{2\ell}{N}$ bounded away from 0 and 1, the logarithm of…
We describe a construction that maps any connected graph G on three or more vertices into a larger graph, H(G), whose independence number is strictly smaller than its Lov\'asz number which is equal to its fractional packing number. The…
The paper investigates how correlations can completely specify a uniformly discrete point process. The setting is that of uniformly discrete point sets in real space for which the corresponding dynamical hull is ergodic. The first result is…
In this paper we discuss the concept of relational system with involution. This system is called orthogonal if, for every pair of non-zero orthogonal elements, there exists a supremal element in their upper cone and the upper cone of…
We presents an independence relation on sets, one can define dimension by it, assuming that we have an abstract elementary class with a forking notion that satisfies the axioms of a good frame minus stability.
The concept of self-similarity on subsets of algebraic varieties is defined by considering algebraic endomorphisms of the variety as `similarity' maps. Self-similar fractals are subsets of algebraic varieties which can be written as a…
A concentration graph associated with a random vector is an undirected graph where each vertex corresponds to one random variable in the vector. The absence of an edge between any pair of vertices (or variables) is equivalent to full…
Correlation between nodes is found to be a common and important property in many complex networks. Here we investigate degree correlations of the Barabasi-Albert (BA) Scale-Free model with both analytical results and simulations, and find…
We present a method for evaluating the partition function in a varying external field. Specifically, we look at the case of a non-interacting, charged, massive scalar field at finite temperature with an associated chemical potential in the…
Conditional independence is a crucial concept supporting adequate modelling and efficient reasoning in probabilistics. In knowledge representation, the idea of conditional independence has also been introduced for specific formalisms, such…
The representation of independence relations generally builds upon the well-known semigraphoid axioms of independence. Recently, a representation has been proposed that captures a set of dominant statements of an independence relation from…
The rules of d-separation provide a framework for deriving conditional independence facts from model structure. However, this theory only applies to simple directed graphical models. We introduce relational d-separation, a theory for…
The size of a largest independent set of vertices in a given graph $G$ is denoted by $\alpha(G)$ and is called its independence number (or stability number). Given a graph $G$ and an integer $K,$ it is NP-complete to decide whether…
Given integers $\Delta\ge 2$ and $t\ge 2\Delta$, suppose there is a graph of maximum degree $\Delta$ and a partition of its vertices into blocks of size at least $t$. By a seminal result of Haxell, there must be some independent set of the…
We introduce an independence criterion based on entropy regularized optimal transport. Our criterion can be used to test for independence between two samples. We establish non-asymptotic bounds for our test statistic and study its…
Algebraic independence is an advanced notion in commutative algebra that generalizes independence of linear polynomials to higher degree. Polynomials {f_1, ..., f_m} \subset \F[x_1, ..., x_n] are called algebraically independent if there is…
Given a finite and non-empty set $X$ and randomly selected specific functions and relations on $X$, we investigate the existence and non-existence of fixed points and reflexive points, respectively. First, we consider the class of…
Independence testing plays a central role in statistical and causal inference from observational data. Standard independence tests assume that the data samples are independent and identically distributed (i.i.d.) but that assumption is…
It seems that the index theory for non-compact spaces has found its ultimate formulation in realm of coarse spaces and $K$-theory of related operator algebras. Relative and partitioned index theorems may be mentioned as two important and…
A continuous infinite system of point particles with strong superstable interaction is considered in the framework of classical statistical mechanics. The family of approximated correlation functions is determined in such a way, that they…