Related papers: On (Anti)Conditional Independence in Dempster-Shaf…

We give a category-theoretic construction of simple and NSOP$_1$-like independence relations in locally finitely presentable categories, and in the more general locally finitely multipresentable categories. We do so by identifying…

Given $d>0$ and a positive integer $n$, let $G$ be a triangle-free graph on $n$ vertices with average degree $d$. With an elegant induction, Shearer (1983) tightened a seminal result of Ajtai, Koml\'os and Szemer\'edi (1980/1981) by proving…

Let $\Gamma$ be a function that maps two arbitrary graphs $G$ and $H$ to a non-negative real number such that $$\alpha(G^{\boxtimes n})\leq \alpha(H^{\boxtimes n})\Gamma(G,H)^n$$ where $n$ is any natural number and $G^{\boxtimes n}$ is the…

We introduce a new dependence order, termed the conditional convex order, whose minimal and maximal elements characterize independence and perfect dependence. Moreover, it characterizes conditional independence, satisfies information…

Let X be a solenoid, that is, a compact finite dimensional connected abelian group with normalized Haar measure m, and let G be a countable discrete group acting on X by continuous affine transformations. We show that the probability…

In this paper we study different concepts of independence for convex sets of probabilities. There will be two basic ideas for independence. The first is irrelevance. Two variables are independent when a change on the knowledge about one…

In this comment we discuss relative strengths and weaknesses of simplex and Dirichlet Dempster-Shafer inference as applied to multi-resolution tests of independence.

The enumeration of independent sets of regular graphs is of interest in statistical mechanics, as it corresponds to the solution of hard-particle models. In 2004, it was conjectured by Fendleyet al. that for some rectangular grids, with…

We show that the d -separation criterion constitutes a valid test for conditional independence relationships that are induced by feedback systems involving discrete variables.

We give lower bounds for the degree of multiplicative combinations of iterates of rational functions (with certain exceptions) over a general field, establishing the multiplicative independence of said iterates. This leads to a…

By a theorem of Chevalley the image of a morphism of varieties is a constructible set. The algebraic version of this fact is usually stated as a result on "extension of specializations" or "lifting of prime ideals". We present a difference…

Suppose $G$ is a controllable graph of order $n$ with adjacency matrix $A$. Let $W=[e,Ae,\ldots,A^{n-1}e]$ ($e$ is the all-one vector) and $\Delta=\prod_{i>j}(\alpha_i-\alpha_j)^2$ ($\alpha_i$'s are eigenvalues of $A$) be the walk matrix…

We study the independence structure of finitely exchangeable distributions over random vectors and random networks. In particular, we provide necessary and sufficient conditions for an exchangeable vector so that its elements are completely…

In probability theory, the independence is a very fundamental concept, but with a little mystery. People can always easily manipulate it logistically but not geometrically, especially when it comes to the independence relationships among…

Measurements of systems taken along a continuous functional dimension, such as time or space, are ubiquitous in many fields, from the physical and biological sciences to economics and engineering.Such measurements can be viewed as…

We generalize two main theorems of matching polynomials of undirected simple graphs, namely, real-rootedness and the Heilmann-Lieb root bound. Viewing the matching polynomial of a graph $G$ as the independence polynomial of the line graph…

We prove general de Finetti type theorems for classical and free independence. The de Finetti type theorems work for all non-easy quantum groups, which generalize a recent work of Banica, Curran and Speicher. We determine maximal…

We give a new consistent scoring function for structure learning of Bayesian networks. In contrast to traditional approaches to score-based structure learning, such as BDeu or MDL, the complexity penalty that we propose is data-dependent…

In this paper we extend the classical Glivenko-Cantelli theorem to real-valued empirical functions under dependence structures characterised by $\alpha$-mixing and $\beta$-mixing conditions. We investigate sufficient conditions ensuring…

Connections between structural graph theory and finite model theory recently gained a lot of attention. In this setting, many interesting questions remain on the properties of dependent (NIP) hereditary classes of graphs, in particular…