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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

*Cristopher 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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