Related papers: Lattice supported distributions and graphical mode…
The paper develop a new approach to the justification of Gibbs canonical distribution for Hamiltonian systems with finite number of degrees of freedom. It uses the condition of nonintegrability of the ensemble of weak interacting…
For irreducible, time-homogeneous Markov networks, mutual linearity has recently been established for both occupation probabilities and network currents in the stationary regime as well as in the non-stationary regime in Laplace space. The…
We establish a topological duality for bounded lattices. The two main features of our duality are that it generalizes Stone duality for bounded distributive lattices, and that the morphisms on either side are not the standard ones. A…
We locate gaps in the spectrum of a Hamiltonian on a periodic cuboidal (and generally hyperrectangular) lattice graph with $\delta$ couplings in the vertices. We formulate sufficient conditions under which the number of gaps is finite. As…
We present an algorithm to identify sparse dependence structure in continuous and non-Gaussian probability distributions, given a corresponding set of data. The conditional independence structure of an arbitrary distribution can be…
The well-known Hammersley-Clifford theorem states (under certain conditions) that any Markov random field is a Gibbs state for a nearest neighbor interaction. In this paper we study Markov random fields for which the proof of the…
Motivated by Gentzen disjunction elimination rule in his Natural Deduction calculus and reading inequalities with meet in a natural way, we conceive a notion of distributivity for join-semilattices. We prove that it is equivalent to a…
It has been suggested that the distribution of the suitably normalized number of zeros of Laplacian eigenfunctions contains information about the geometry of the underlying domain. We study this distribution (more precisely, the…
Propagation of coherent light through a disordered network is accompanied by randomization and possible conversion into thermal light. Here, we show that network topology plays a decisive role in determining the statistics of the emerging…
In this second part of our survey on the social and natural distributions, we investigate some models, which intend to explain the statistical regularity of the natural and social distributions. There is a large variety of models and in…
We develop a theoretical framework for the diffusion of a single unconstrained species of atoms on a crystal lattice that provides a generalization of the classical theories of atomic diffusion and diffusion-induced phase separation to…
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…
Let $G$ be an acylic directed graph. For each vertex $g \in G$, we define an involution on the independent sets of $G$. We call these involutions flips, and use them to define a new partial order on independent sets of $G$. Trim lattices…
We study bases of the lattice generated by the cycles of an undirected graph, defined as the integer linear combinations of the 0/1-incidence vectors of cycles. We prove structural results for this lattice, including explicit formulas for…
We study conditional independence relationships for random networks and their interplay with exchangeability. We show that, for finitely exchangeable network models, the empirical subgraph densities are maximum likelihood estimates of their…
We give the cumulative distribution functions, the expected values, and the moments of weighted lattice polynomials when regarded as real functions of independent random variables. Since weighted lattice polynomial functions include…
We describe a framework and an algorithm for solving hybrid influence diagrams with discrete, continuous, and deterministic chance variables, and discrete and continuous decision variables. A continuous chance variable in an influence…
For a directed acyclic graph, there are two known criteria to decide whether any specific conditional independence statement is implied for all distributions factorized according to the given graph. Both criteria are based on special types…
We show central limit theorems (CLT) for the Stieltjes transforms or more general analytic functions of symmetric matrices with independent heavy tailed entries, including entries in the domain of attraction of $\alpha$-stable laws and…
The methods of non-homogeneous random graphs calibration are developed for social networks simulation. The graphs are calibrated by the degree distributions of the vertices and the edges. The mathematical foundation of the methods is formed…