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601
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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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
ALTERNATING SIGN MATRICES AND SYMMETRY
, 2007
"... An Alternating Sign Matrix (or ASM) is an n × n matrix whose entries are each 0, 1, or1 with the property that the sum of each row or column is 1, and the nonzero entries in ..."
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An Alternating Sign Matrix (or ASM) is an n × n matrix whose entries are each 0, 1, or1 with the property that the sum of each row or column is 1, and the nonzero entries in
Optimizing Sparse Graph Codes over GF(q)
, 2003
"... This note explains the method used by Davey and MacKay to set the nonzero entries in lowdensity paritycheck codes over GF (q), and gives explicit prescriptions. ..."
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Cited by 2 (0 self)
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This note explains the method used by Davey and MacKay to set the nonzero entries in lowdensity paritycheck codes over GF (q), and gives explicit prescriptions.
Proof of the alternating sign matrix conjecture
, 1995
"... The number of n × n matrices whose entries are either −1, 0, or 1, whose row and column sums are all 1, and such that in every row and every column the nonzero entries alternate in sign, is proved to be [1!4!... (3n −2)!]/[n!(n+1)!... (2n −1)!], as conjectured by Mills, Robbins, and Rumsey. ..."
Abstract

Cited by 121 (4 self)
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The number of n × n matrices whose entries are either −1, 0, or 1, whose row and column sums are all 1, and such that in every row and every column the nonzero entries alternate in sign, is proved to be [1!4!... (3n −2)!]/[n!(n+1)!... (2n −1)!], as conjectured by Mills, Robbins, and Rumsey.
F01 – Matrix Operations and Distribution
"... Note: before using this routine, please read the Users ’ Note for your implementation to check for implementationdependent details. You are advised to enclose any calls to NAG Parallel Library routines between calls to Z01AAFP and Z01ABFP. 1 Description F01XPFP distributes an n by n complex sparse ..."
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of the nonzero entries of the matrix A or (ii) only the numerical values of the nonzero entries. The latter option should be used if the matrix A has the same pattern of nonzero entries as a previously generated matrix.
F01 – Matrix Operations and Distribution
"... Note: before using this routine, please read the Users ’ Note for your implementation to check for implementationdependent details. You are advised to enclose any calls to NAG Parallel Library routines between calls to Z01AAFP and Z01ABFP. 1 Description F01YBFP generates an n by n real sparse matri ..."
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matrix A, in coordinate storage format and distributed in cyclic row block fashion (see Section 2.5 of the F11 Chapter Introduction). Depending on the value of the input parameter WHAT, F01YBFP generates either (i) both the numerical values and the row and column coordinates of the nonzero entries
F01 – Matrix Operations and Distribution
"... Note: before using this routine, please read the Users ’ Note for your implementation to check for implementationdependent details. You are advised to enclose any calls to NAG Parallel Library routines between calls to Z01AAFP and Z01ABFP. 1 Description F01XAFP distributes an n by n real sparse mat ..."
Abstract
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of the nonzero entries of the matrix A or (ii) only the numerical values of the nonzero entries.The latter option should be used if the matrix A has the same pattern of nonzero entries as a previously generated matrix.
F01 – Matrix Operations and Distribution
"... Note: before using this routine, please read the Users ’ Note for your implementation to check for implementationdependent details. You are advised to enclose any calls to NAG Parallel Library routines between calls to Z01AAFP and Z01ABFP. 1 Description F01YQFP generates an n by n complex sparse ma ..."
Abstract
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matrix A, in coordinate storage format and distributed in cyclic row block fashion (see Section 2.5 of the F11 Chapter Introduction). Depending on the value of the input parameter WHAT, F01YQFP generates either (i) both the numerical values and the row and column coordinates of the nonzero entries
INTEGER
"... Note: before using this routine, please read the Users ’ Note for your implementation to check for implementationdependent details. You are advised to enclose any calls to NAG Parallel Library routines between calls to Z01AAFP and Z01ABFP. 1 Description F11YNFP reorders the nonzero entries of an n ..."
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Note: before using this routine, please read the Users ’ Note for your implementation to check for implementationdependent details. You are advised to enclose any calls to NAG Parallel Library routines between calls to Z01AAFP and Z01ABFP. 1 Description F11YNFP reorders the nonzero entries
DOUBLE PRECISION A(*) INTEGER
"... Note: before using this routine, please read the Users ’ Note for your implementation to check for implementationdependent details. You are advised to enclose any calls to NAG Parallel Library routines between calls to Z01AAFP and Z01ABFP. 1 Description F11YAFP reorders the nonzero entries of an n ..."
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Note: before using this routine, please read the Users ’ Note for your implementation to check for implementationdependent details. You are advised to enclose any calls to NAG Parallel Library routines between calls to Z01AAFP and Z01ABFP. 1 Description F11YAFP reorders the nonzero entries
Results 1  10
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601