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Optimization

Sergey N. Dorogovtsev

in Lectures on Complex Networks

Published in print:
2010
Published Online:
May 2010
ISBN:
9780199548927
eISBN:
9780191720574
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199548927.003.0014
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter demonstrates how a universal requirement for optimality leads to the complex structural organization of a network. It discusses a long-lasting criticism of the preferential concept and ... More


THEORY OF RANDOM SOLID STATES

M. Mézard

in Stealing the Gold: A celebration of the pioneering physics of Sam Edwards

Published in print:
2004
Published Online:
September 2007
ISBN:
9780198528531
eISBN:
9780191713415
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198528531.003.0017
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter is a non-technical, elementary introduction to the theory of glassy phases and their ubiquity. The aim is to provide a guide and some kind of coherent view to the various topics that ... More


Bridges: Inference and the Monte Carlo method

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/9780198570837.003.0013
Subject:
Physics, Theoretical, Computational, and Statistical Physics

The mathematical structure highlighted in this chapter by the factor graph representation is the locality of probabilistic dependencies between variables. Locality also emerges in many problems of ... More


Optimization Problems

Hidetoshi Nishimori

in Statistical Physics of Spin Glasses and Information Processing: An Introduction

Published in print:
2001
Published Online:
January 2010
ISBN:
9780198509417
eISBN:
9780191709081
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198509417.003.0009
Subject:
Physics, Theoretical, Computational, and Statistical Physics

A decision-making problem is often formulated as the minimization or maximization of a multivariable function, an optimization problem. This chapter shows that the methods of statistical mechanics ... More


The Nature of Computation

Cristopher Moore and Stephan Mertens

Published in print:
2011
Published Online:
December 2013
ISBN:
9780199233212
eISBN:
9780191775079
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199233212.001.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Computational complexity is one of the most beautiful fields of modern mathematics, and it is increasingly relevant to other sciences ranging from physics to biology. However, this beauty is often ... More


Optimization and Approximation

Christopher Moore and Stephan Mertens

in The Nature of Computation

Published in print:
2011
Published Online:
December 2013
ISBN:
9780199233212
eISBN:
9780191775079
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199233212.003.0009
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter focuses on the relationships between decision problems and their optimisation versions. It shows that, for most problems, the optimal solution can be realised in polynomial time if and ... More


Models of network formation

Mark Newman

in Networks

Published in print:
2018
Published Online:
October 2018
ISBN:
9780198805090
eISBN:
9780191843235
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198805090.003.0013
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter describes models of the growth or formation of networks, with a particular focus on preferential attachment models. It starts with a discussion of the classic preferential attachment ... More


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