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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...
TOPOLOGICAL SYMMETRY GROUPS OF COMPLETE GRAPHS IN THE 3-SPHERE     TOPOLOGICAL SYMMETRY  THE 3-SPHERE       font style='font-size:12px;'> 2015/12/17
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...
TOPOLOGICAL SYMMETRY GROUPS OF GRAPHS IN 3-MANIFOLDS     GRAPHS IN 3-MANIFOLDS  SYMMETRY GROUPS       font style='font-size:12px;'> 2015/12/17
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 ...
On rational limits of Shelah-Spencer graphs     rational limits  Shelah-Spencer graphs       font style='font-size:12px;'> 2015/9/28
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...
The absence of efficient dual pairs of spanning trees in planar graphs     planar graphs  cells       font style='font-size:12px;'> 2015/8/26
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 ...
Diameters of Cayley Graphs of Chevalley Groups     Chevalley Groups  Cayley       font style='font-size:12px;'> 2015/8/26
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...
Navigating in the Cayley Graphs of SLN(Z) and SLN(Fp)     Cayley Graphs  constant       font style='font-size:12px;'> 2015/8/26
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 ...
Reconstruction for models on random graphs     Random variables  algorithms  the random sequence diagram       font style='font-size:12px;'> 2015/8/21
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...
Generating Random Graphs with Large Girth     Cient  algorithm  random  small cycle  constant       font style='font-size:12px;'> 2015/8/21
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...
Linkage and association analysis based on haplotype transmission disequilibrium can be more informative than single marker analysis. Several works have been proposed in recent years to extend the tra...
The weak limit of Ising models on locally tree-like graphs     Ising model  the temperature  the last beta  sequence       font style='font-size:12px;'> 2015/8/20
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...

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