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Information, Physics, and Computation

Marc Mézard and Andrea Montanari

Published in print:
2009
Published Online:
September 2009
ISBN:
9780198570837
eISBN:
9780191718755
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198570837.001.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This book presents a unified approach to a rich and rapidly evolving research domain at the interface between statistical physics, theoretical computer science/discrete mathematics, and ... More


Ising models on random graph

Marc Mézard and Andrea Montanari

in Information, Physics, and Computation

Published in print:
2009
Published Online:
September 2009
ISBN:
9780198570837
eISBN:
9780191718755
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198570837.003.0017
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter studies two problems of statistical physics: the ferromagnet and the spin glass, on large random graphs with fixed degree profile. It describes the use of the replica symmetric cavity ... More


The assignment problem

Marc Mézard and Andrea Montanari

in Information, Physics, and Computation

Published in print:
2009
Published Online:
September 2009
ISBN:
9780198570837
eISBN:
9780191718755
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198570837.003.0016
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter discusses the use of message passing techniques in a combinatorial optimization problem assignment. Given N ‘agents’ and N ‘jobs’, and the cost matrix E(i,j) for having job i executed by ... More


Belief propogation

Marc Mézard and Andrea Montanari

in Information, Physics, and Computation

Published in print:
2009
Published Online:
September 2009
ISBN:
9780198570837
eISBN:
9780191718755
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198570837.003.0014
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter discusses a general method for approximating marginals of large graphical models. This powerful technique has been discovered independently in various fields: statistical physics (under ... More


Cavity method: message-passing from a physics perspective

Marc Mézard

in Statistical Physics, Optimization, Inference, and Message-Passing Algorithms: Lecture Notes of the Les Houches School of Physics: Special Issue, October 2013

Published in print:
2015
Published Online:
March 2016
ISBN:
9780198743736
eISBN:
9780191803802
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198743736.003.0004
Subject:
Physics, Theoretical, Computational, and Statistical Physics

The cavity method is introduced as a heuristic framework from a physics perspective to solve probabilistic graphical models and is presented at both the replica symmetry (RS) and one-step replica ... More


Statistical Physics, Optimization, Inference, and Message-Passing Algorithms: Lecture Notes of the Les Houches School of Physics: Special Issue, October 2013

Florent Krzakala, Federico Ricci-Tersenghi, Lenka Zdeborova, Riccardo Zecchina, Eric W. Tramel, and Leticia F. Cugliandolo (eds)

Published in print:
2015
Published Online:
March 2016
ISBN:
9780198743736
eISBN:
9780191803802
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198743736.001.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This book contains a collection of the presentations that were given in October 2013 at the Les Houches Autumn School on statistical physics, optimization, inference, and message-passing algorithms. ... More


Constraint satisfaction: random regular k-SAT

Amin Coja-Oghlan

in Statistical Physics, Optimization, Inference, and Message-Passing Algorithms: Lecture Notes of the Les Houches School of Physics: Special Issue, October 2013

Published in print:
2015
Published Online:
March 2016
ISBN:
9780198743736
eISBN:
9780191803802
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198743736.003.0007
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter discusses the random regular k-SAT problem, i.e., a random k-CNF formula Φ‎ = Φ‎k(n,d) on n variables such that each of the 2n literals appears exactly d times. With k0 a certain ... More


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