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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


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