## The Fourth Janko Group

*Alexander A. Ivanov*

- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198527596
- eISBN:
- 9780191713163
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198527596.001.0001
- Subject:
- Mathematics, Pure Mathematics

This book illustrates how different methods of finite group theory including representation theory, cohomology theory, combinatorial group theory, and local analysis, are combined to construct one of ... More

## Invitation to Fixed-Parameter Algorithms

*Rolf Niedermeier*

- Published in print:
- 2006
- Published Online:
- September 2007
- ISBN:
- 9780198566076
- eISBN:
- 9780191713910
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198566076.001.0001
- Subject:
- Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This book provides an introduction to the concept of fixed-parameter tractability. The corresponding design and analysis of efficient fixed-parameter algorithms for optimally solving combinatorially ... More

## Spin Glasses and Complexity

*Daniel L. Stein and Charles M. Newman*

- Published in print:
- 2013
- Published Online:
- October 2017
- ISBN:
- 9780691147338
- eISBN:
- 9781400845637
- Item type:
- book

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691147338.001.0001
- Subject:
- Sociology, Science, Technology and Environment

Spin glasses are disordered magnetic systems that have led to the development of mathematical tools with an array of real-world applications, from airline scheduling to neural networks. This book ... More

## PARAMETERIZED COMPLEXITY THEORY—A PRIMER

*Rolf Niedermeier*

### in Invitation to Fixed-Parameter Algorithms

- Published in print:
- 2006
- Published Online:
- September 2007
- ISBN:
- 9780198566076
- eISBN:
- 9780191713910
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198566076.003.0003
- Subject:
- Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter introduces basic concepts which are necessary for an understanding of this subject, beginning with a close look at parameterized algorithmics. It briefly highlights the central aspects ... More

## Applications to Other Fields

*Daniel L. Stein and Charles M. Newman*

### in Spin Glasses and Complexity

- Published in print:
- 2013
- Published Online:
- October 2017
- ISBN:
- 9780691147338
- eISBN:
- 9781400845637
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691147338.003.0007
- Subject:
- Sociology, Science, Technology and Environment

This chapter explores how spin glass concepts have found use in and, in some cases, further advanced areas such as computational complexity, combinatorial optimization, neural networks, protein ... More

## Outline of the Proof

*Ben Brubaker, Daniel Bump, and Solomon Friedberg*

### in Weyl Group Multiple Dirichlet Series: Type A Combinatorial Theory (AM-175)

- Published in print:
- 2011
- Published Online:
- October 2017
- ISBN:
- 9780691150659
- eISBN:
- 9781400838998
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691150659.003.0006
- Subject:
- Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter presents the proof of the equivalence of the two definitions for the λ-parts in terms of Gelfand-Tsetlin patterns. The equivalence of these two descriptions is a deep fact that uses ... More

## Combinatorics of Genome Rearrangements

*Guillaume Fertin, Anthony Labarre, Irena Rusu, Eric Tannier, and Stéphane Vialette*

- Published in print:
- 2009
- Published Online:
- August 2013
- ISBN:
- 9780262062824
- eISBN:
- 9780262258753
- Item type:
- book

- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262062824.001.0001
- Subject:
- Mathematics, Mathematical Biology

From one cell to another, from one individual to another, and from one species to another, the content of DNA molecules is often similar. The organization of these molecules, however, differs ... More

## Ideas, Pioneers, and Precursors

*Kumaraswamy Velupillai*

### in Computable Economics: The Arne Ryde Memorial Lectures

- Published in print:
- 2000
- Published Online:
- November 2003
- ISBN:
- 9780198295273
- eISBN:
- 9780191596988
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198295278.003.0002
- Subject:
- Economics and Finance, Macro- and Monetary Economics

In this chapter, a first, tentative attempt is made to define the nature and scope of what is meant by computable economics. From a study of the way economics was mathematized in the modern era, – ... More

## How Analysis and Synthesis are Related

*Kurt Smith*

### in Matter Matters: Metaphysics and Methodology in the Early Modern Period

- Published in print:
- 2010
- Published Online:
- September 2010
- ISBN:
- 9780199583652
- eISBN:
- 9780191723155
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199583652.003.0013
- Subject:
- Philosophy, History of Philosophy, Metaphysics/Epistemology

This chapter shows how the combinatorial nature of bodies expresses the permutation group concept, the latter expressing the conditions underwriting a genuine mathematical system. The chapter ... More

## Creative Combination of Representations: Scientific Discovery and Technological Invention

*Paul Thagard*

### in Psychology of Science: Implicit and Explicit Processes

- Published in print:
- 2012
- Published Online:
- September 2012
- ISBN:
- 9780199753628
- eISBN:
- 9780199950027
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199753628.003.0016
- Subject:
- Psychology, Cognitive Psychology, Social Psychology

This chapter describes two studies that help evaluate the combinatorial conjecture that all creativity results from combinations of mental representations. The first study examines 100 examples of ... 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

## Combination and Specialization in the Evolution of the Internet

*Ilkka Tuomi*

### in Networks of Innovation: Change and Meaning in the Age of the Internet

- Published in print:
- 2006
- Published Online:
- October 2011
- ISBN:
- 9780199269051
- eISBN:
- 9780191699337
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199269051.003.0008
- Subject:
- Business and Management, Knowledge Management, Innovation

This chapter returns to the history of the Internet. It briefly discusses email as an example of combinatorial innovation, and describes the evolution of the social structure that provided the basis ... More

## Frontiers in Complex Dynamics: In Celebration of John Milnor's 80th Birthday

*Araceli Bonifant, Misha Lyubich, and Scott Sutherland*

- Published in print:
- 2014
- Published Online:
- October 2017
- ISBN:
- 9780691159294
- eISBN:
- 9781400851317
- Item type:
- book

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691159294.001.0001
- Subject:
- Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

John Milnor, best known for his work in differential topology, K-theory, and dynamical systems, is one of only three mathematicians to have won the Fields medal, the Abel prize, and the Wolf prize, ... 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

## Introduction

*Stephen J. Blundell and Katherine M. Blundell*

### in Concepts in Thermal Physics

- Published in print:
- 2009
- Published Online:
- February 2010
- ISBN:
- 9780199562091
- eISBN:
- 9780191718236
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199562091.003.0001
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

This introductory chapter explores the concept of large numbers, showing why large numbers appear in thermal physics and explaining how to handle them. Large numbers arise in thermal physics because ... More

## Combining Sounds to Reinvent the World: World Music, Sociology, and Musical Analysis

*Simha Arom and Denis-Constant Martin*

### in Analytical and Cross-Cultural Studies in World Music

- Published in print:
- 2011
- Published Online:
- January 2012
- ISBN:
- 9780195384581
- eISBN:
- 9780199918331
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195384581.003.0011
- Subject:
- Music, Ethnomusicology, World Music

The success of the expression “world music,” a commercial label coined during the 1980s to refer to certain types of music, provokes an inquiry into the conditions underlying its invention and ... More

## Linguistic Forms, Properties, and Efficient Signaling

*John A. Hawkins*

### in Efficiency and Complexity in Grammars

- Published in print:
- 2004
- Published Online:
- January 2010
- ISBN:
- 9780199252695
- eISBN:
- 9780191719301
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199252695.003.002
- Subject:
- Linguistics, Syntax and Morphology

The previous chapter proposed an efficiency-complexity hypothesis and presented three general principles that will give substance to it: Minimize Domains, Minimize Forms, and Maximize On-line ... More

## Tractarian Nominalism: (for Wilfrid Sellars)

*Brian Skyrms*

### in From Zeno to Arbitrage: Essays on Quantity, Coherence, and Induction

- Published in print:
- 2012
- Published Online:
- January 2013
- ISBN:
- 9780199652808
- eISBN:
- 9780191745829
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199652808.003.0003
- Subject:
- Philosophy, Philosophy of Science, Metaphysics/Epistemology

This gives a reading of one of the main ideas of the Tractatus. The emphasis on facts deflates the importance both of ontology and of ideology. A given fact can be parsed in different ways. If we ... More

## Logical Atoms and Combinatorial Possibility

*Brian Skyrms*

### in From Zeno to Arbitrage: Essays on Quantity, Coherence, and Induction

- Published in print:
- 2012
- Published Online:
- January 2013
- ISBN:
- 9780199652808
- eISBN:
- 9780191745829
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199652808.003.0004
- Subject:
- Philosophy, Philosophy of Science, Metaphysics/Epistemology

What would the philosophy of logical atomism be like without logical atoms? The question was raised but not answered by Russell. Here I give an answer, using atomless Boolean algebras. In particular, ... More

## Direct Methods for Sparse Matrices

*I. S. Duff, A. M. Erisman, and J. K. Reid*

- Published in print:
- 2017
- Published Online:
- April 2017
- ISBN:
- 9780198508380
- eISBN:
- 9780191746420
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198508380.001.0001
- Subject:
- Mathematics, Numerical Analysis

Direct Methods for Sparse Matrices, second edition, is a complete rewrite of the first edition published 30 years ago. Much has changed since that time. Problems have grown greatly in size and ... More