Results 1  10
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825
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 ..."
Abstract

Cited by 676 (15 self)
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with loops (undirected cycles). The algorithm is an exact inference algorithm for singly connected networks the beliefs converge to the cor rect marginals in a number of iterations equal to the diameter of the graph.1 However, as Pearl noted, the same algorithm will not give the correct beliefs for mul
Random Graph Dynamics
, 2007
"... Chapter 1 will explain what this book is about. Here I will explain why I chose to write the book, how it is written, where and when the work was done, and who helped. Why. It would make a good story if I was inspired to write this book by an image of Paul Erdös magically appearing on a cheese ques ..."
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Cited by 203 (2 self)
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Chapter 1 will explain what this book is about. Here I will explain why I chose to write the book, how it is written, where and when the work was done, and who helped. Why. It would make a good story if I was inspired to write this book by an image of Paul Erdös magically appearing on a cheese
Some Properties of Strongly Regular Graphs
, 2011
"... An approach to the enumeration of feasible parameters for strongly regular graphs is described, based on the pair of structural parameters (a, c) and the positive eigenvalue e. The Krein bound ensures that there are only finitely many possibilities for c, given a and e, and the standard divisibility ..."
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An approach to the enumeration of feasible parameters for strongly regular graphs is described, based on the pair of structural parameters (a, c) and the positive eigenvalue e. The Krein bound ensures that there are only finitely many possibilities for c, given a and e, and the standard
Random Regular Graphs: Asymptotic Distributions And Contiguity
 Combinatorics, Probability and Computing
, 1993
"... . The asymptotic distribution of the number of Hamilton cycles in a random regular graph is determined. The limit distribution is of an unusual type; it is the distribution of a variable whose logarithm can be written as an infinite linear combination of independent Poisson variables, and thus the l ..."
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Cited by 52 (3 self)
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. For example, if r 3, then the usual (uniformly distributed) random rregular graph is contiguous to the one constructed by taking the union of r perfect matchings on the same vertex set (assumed to be of even cardinality), conditioned on there being no multiple edges. Some consequences of contiguity
Conditional diagnosability measures for large multiprocessor Systems
 IEEE Trans. Comput
"... Abstract—Diagnosability has played an important role in the reliability of an interconnection network. The classical problem of fault diagnosis is discussed widely and the diagnosability of many wellknown networks have been explored. In this paper, we introduce a new measure of diagnosability, call ..."
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Cited by 12 (2 self)
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, called conditional diagnosability, by restricting that any faulty set cannot contain all the neighbors of any vertex in the graph. Based on this requirement, the conditional diagnosability of the ndimensional hypercube is shown to be 4ðn 2Þ þ 1, which is about four times as large as the classical
On Regular Fuzzy Graphs
, 2007
"... In this paper, regular fuzzy graphs, total degree and totally regular fuzzy graphs are introduced. Regular fuzzy graphs and totally regular fuzzy graphs are compared through various examples. A necessary and sufficient condition under which they are equivalent is provided. A characterization of regu ..."
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Cited by 3 (1 self)
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In this paper, regular fuzzy graphs, total degree and totally regular fuzzy graphs are introduced. Regular fuzzy graphs and totally regular fuzzy graphs are compared through various examples. A necessary and sufficient condition under which they are equivalent is provided. A characterization
On quasistrongly regular graphs
, 2004
"... We study the quasistrongly regular graphs, which are a combinatorial generalization of the strongly regular and the distance regular graphs. Our main focus is on quasistrongly regular graphs of grade 2. We prove a ‘‘spectral gap’’type result for them which generalizes Seidel’s wellknown formula ..."
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for the eigenvalues of a strongly regular graph. We also obtain a number of necessary conditions for the feasibility of parameter sets and some structural results. We propose the heuristic principle that quasistrongly regular graphs can be viewed as a ‘‘lowerorder approximation’ ’ to the distance regular graphs
Graphs of some CAT(0) complexes
 Adv. Appl. Math
, 1998
"... In this note, we characterize the graphs (1skeletons) of some piecewise Euclidean simplicial and cubical complexes having nonpositive curvature in the sense of Gromov’s CAT(0) inequality. Each such cell complex K is simply connected and obeys a certain flag condition. It turns out that if, in addit ..."
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Cited by 47 (19 self)
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In this note, we characterize the graphs (1skeletons) of some piecewise Euclidean simplicial and cubical complexes having nonpositive curvature in the sense of Gromov’s CAT(0) inequality. Each such cell complex K is simply connected and obeys a certain flag condition. It turns out that if
DistanceRegular Cayley Graphs on . . .
"... The main result of this article is a classification of distanceregular Cayley graphs on dihedral groups. There exist four obvious families of such graphs, which are called trivial. These are: complete graphs, complete bipartite graphs, complete bipartite graphs with the edges of a 1factor removed, ..."
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, and cycles. It is proved that every nontrivial distanceregular Cayley graph on a dihedral group is bipartite, nonantipodal, has diameter 3 and arises either from a cyclic difference set, or possibly (if any such exists) from a dihedral difference set satisfying some additional conditions. Finally, all
Highdimensional graphical model selection using ℓ1regularized logistic regression
 Advances in Neural Information Processing Systems 19
, 2007
"... We consider the problem of estimating the graph structure associated with a discrete Markov random field. We describe a method based on ℓ1regularized logistic regression, in which the neighborhood of any given node is estimated by performing logistic regression subject to an ℓ1constraint. Our fram ..."
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Cited by 102 (2 self)
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We consider the problem of estimating the graph structure associated with a discrete Markov random field. We describe a method based on ℓ1regularized logistic regression, in which the neighborhood of any given node is estimated by performing logistic regression subject to an ℓ1constraint. Our
Results 1  10
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825