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Loopy belief propagation for approximate inference: An empirical study. In:
 Proceedings of Uncertainty in AI,
, 1999
"... Abstract Recently, researchers have demonstrated that "loopy belief propagation" the use of Pearl's polytree algorithm in a Bayesian network with loops can perform well in the context of errorcorrecting codes. The most dramatic instance of this is the near Shannonlimit performanc ..."
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Cited by 676 (15 self)
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likelihood weighting 3.1 The PYRAMID network All nodes were binary and the conditional probabilities were represented by tablesentries in the conditional probability tables (CPTs) were chosen uniformly in the range (0, 1]. 3.2 The toyQMR network All nodes were binary and the conditional probabilities
Dense Minors in Graphs of Large Girth
 Combinatorica
"... this paper is to reduce the upper bound for the required girth to the correct order of magnitude: Theorem 1. For any inte k,e ve graph G of girth g(G) > 6 log k +3and #(G) # 3 has a minor H with #(H) >k. The best lower bound we have found is 8 3 log c, but we note that existing conjectu ..."
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Cited by 8 (0 self)
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conjectures about cubic graphs of large girth would raise this to about 4 log . Since an average degree of at least cr # log r forces a K r minor [ 5, 8 ], Theorem 1 has the following consequence: Corollary 2.The ee a constant c # R such thate ea graph G of girth g(G) # 6 log r<F1
Graph minors. X. Obstructions to treedecomposition
 J. COMB. THEORY, SERIES B
, 1991
"... Roughly, a graph has small “treewidth” if it can be constructed by piecing small graphs together in a tree structure. Here we study the obstructions to the existence of such a tree structure. We find, for instance: (i) a minimax formula relating treewidth with the largest such obstructions (ii) an ..."
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Cited by 207 (10 self)
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) an association between such obstructions and large grid minors of the graph (iii) a “treedecomposition” of the graph into pieces corresponding with the obstructions. These results will be of use in later papers.
MINORITIES
, 2009
"... ii The Dissertation Committee for Vicki L. CollieAkers certifies that this is the approved version of the following dissertation: ..."
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ii The Dissertation Committee for Vicki L. CollieAkers certifies that this is the approved version of the following dissertation:
Small minors in dense graphs
 European J. Combin
"... Abstract. A fundamental result in structural graph theory states that every graph with large average degree contains a large complete graph as a minor. We prove this result with the extra property that the minor is small with respect to the order of the whole graph. More precisely, we describe funct ..."
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Cited by 3 (0 self)
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(t); in particular f(3) = 2 + ε and f(4) = 4 + ε. For t ≤ 4, we establish similar results for graphs embedded on surfaces, where the size of the Ktmodel is bounded (for fixed t). 1.
E.: Stochastic minority on graphs
, 2008
"... Abstract. Cellular automata have been mainly studied on very regular graphs carrying the vertices (like lines or grids) and under synchronous dynamics (all vertices update simultaneously). In this paper, we study how the asynchronism and the graph act upon the dynamics of the classical Minority rul ..."
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Cited by 1 (1 self)
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Abstract. Cellular automata have been mainly studied on very regular graphs carrying the vertices (like lines or grids) and under synchronous dynamics (all vertices update simultaneously). In this paper, we study how the asynchronism and the graph act upon the dynamics of the classical Minority
Minors in Graphs of Large Girth
 J. Combin. Theory B
, 1988
"... We show that for every odd integer g 5 there exists a constant c such that every graph of minimum degree r and girth at least g contains a minor of minimum degree at least cr . This is best possible up to the value of the constant c for g = 5; 7 and 11. More generally, a wellknown conjecture ..."
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Cited by 5 (0 self)
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We show that for every odd integer g 5 there exists a constant c such that every graph of minimum degree r and girth at least g contains a minor of minimum degree at least cr . This is best possible up to the value of the constant c for g = 5; 7 and 11. More generally, a wellknown
Results 1  10
of
1,079,909