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Graphical models are popular statistical tools which are used to represent dependent or causal complex systems. Statistically equivalent causal or directed graphical models are said to belong to a Mar...
The orientation preserving topological symmetry group of a graph embedded in the 3-sphere is the subgroup of the automorphism group of the graph consisting of those automorphisms which can be induc...
We prove that for every closed, connected, orientable, irreducible 3-manifold, there exists an alternating group An which is not the topological symmetry group of any graph embedded in the manifold. ...
We present an adaptive finite element method (AFEM) of any polynomial degree for the Laplace-Beltrami operator on C 1 graphs Γ in R d (d ≥ 2). We first derive residual-type a posteri...
We develop a new approach to formulate and prove the weak uncertainty inequality which was recently introduced by Okoudjou and Strichartz.We assume either an appropriate measure growth condition with ...
Given a sequence {αn} in (0, 1) converging to a rational, we examine the model theoretic properties of structures obtained as limits of ShelahSpencer graphs G(m, m−αn ). We show that in most c...
A spanning tree T in a finite planar connected graph G determines a dual spanning tree T* in the dual graph G* such that T and T* do not intersect. We show that it is not always possible to find T in ...
We show that for integers k > 1 and n > 2, the diameter of the Cayley graph of SLn(Z/kZ) with respect to a standard two-element generating set, is at most a constant times n2 ln k. This answers a ques...
We give a non-deterministic algorithm that expresses elements of SLN(Z), for N>2, as words in a finite set of generators, with the length of these words at most a constant times the word metric. We sh...
We pose some graph theoretic conjectures about duality and the diameter of maximal trees in planar graphs, and we describe innovations in the following two topics in Geometric Group Theory, where the ...
Consider a collection of random variables attached to the vertices of a graph. The reconstruction problem requires to estimate one of them given ‘far away’ observations. Several theoretical results (a...
We present a simple and efficient algorithm for randomly generating simple graphs without small cycles. These graphs can be used to design high performance Low-Density Parity-Check (LDPC) codes. ...
We consider Ising models on graphs that converge locally to trees. Examples include random regular graphs with bounded degree and uniformly random graphs with bounded average degree. We prove that the...
We consider the Ising model with inverse temperature β and without external field on sequences of graphs Gn which converge locally to the k-regular tree. We show that for such graphs the Ising m...
We consider homogeneous factor models on uniformly sparse graph sequences converg-ing locally to a (unimodular) random tree T, and study the existence of the free energy density ,the limit of the log...

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