## The Mathematics of Non-Individuality

*Steven French and Décio Krause*

### in Identity in Physics: A Historical, Philosophical, and Formal Analysis

- Published in print:
- 2006
- Published Online:
- September 2006
- ISBN:
- 9780199278244
- eISBN:
- 9780191603952
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199278245.003.0007
- Subject:
- Philosophy, Philosophy of Science

This chapter presents the theory of quasi-sets, and argues that this offers an appropriate set-theoretic formalism for non-individual quantum objects. The basic idea is that in a quasi-set, there may ... More

## Putnam's Model‐Theoretic Arguments

*Barry Taylor*

### in Models, Truth, and Realism

- Published in print:
- 2006
- Published Online:
- September 2006
- ISBN:
- 9780199286690
- eISBN:
- 9780191604065
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199286698.003.0003
- Subject:
- Philosophy, Metaphysics/Epistemology

This chapter sets out the relevant core of Putnam’s case. Section 3.1 extracts three arguments from Putnam’s writings: the Arguments from Cardinality, Completeness, and Permutation. Of these, section ... More

## The Ubiquity of Catalan Numbers II

*Thomas Koshy*

### in Catalan Numbers with Applications

- Published in print:
- 2008
- Published Online:
- January 2009
- ISBN:
- 9780195334548
- eISBN:
- 9780199868766
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195334548.003.0007
- Subject:
- Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter continues the investigation of the ubiquitous occurrences of Catalan numbers. It includes permutations, the ballot problem, multisets, noncrossing matchings, LIFO, staircase ... More

## Statistical Inference in MEG Distributed Source Imaging

*Dimitrios Pantazis and Richard M. Leahy*

### in MEG: An Introduction to Methods

- Published in print:
- 2010
- Published Online:
- September 2010
- ISBN:
- 9780195307238
- eISBN:
- 9780199863990
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195307238.003.0010
- Subject:
- Neuroscience, Behavioral Neuroscience, Techniques

This chapter reviews the statistical tools available for the analysis of distributed activation maps defined either on the 2D cortical surface or throughout the 3D brain volume. Statistical analysis ... More

## Other two-sets Procrustes problems

*J. C. Gower and G. B. Dijksterhuis*

### in Procrustes Problems

- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198510581
- eISBN:
- 9780191708961
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198510581.003.0007
- Subject:
- Mathematics, Probability / Statistics

This chapter briefly reviews other choices of T, such as when T is of given rank or is a permutation, symmetric, or positive matrix. It discusses double Procrustes problems of the form: where S and ... More

## Exchangeability and regression models

*Peter McCullagh*

### in Celebrating Statistics: Papers in honour of Sir David Cox on his 80th birthday

- Published in print:
- 2005
- Published Online:
- September 2007
- ISBN:
- 9780198566540
- eISBN:
- 9780191718038
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198566540.003.0005
- Subject:
- Mathematics, Probability / Statistics

This chapter explores the relation between exchangeability, a concept from stochastic processes, and regression models in which the observed process is modulated by a covariate. A stochastic process ... More

## THE FAST FOURIER TRANSFORM

*Rob H. Bisseling*

### in Parallel Scientific Computation: A Structured Approach using BSP and MPI

- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198529392
- eISBN:
- 9780191712869
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198529392.003.0003
- Subject:
- Mathematics, Applied Mathematics

This chapter demonstrates the use of different data distributions in different phases of a computation: both the block and cyclic distributions of a vector are used and the intermediates between ... More

## Accuracy and stability

*J. C. Gower and G. B. Dijksterhuis*

### in Procrustes Problems

- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198510581
- eISBN:
- 9780191708961
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198510581.003.0012
- Subject:
- Mathematics, Probability / Statistics

This chapter discusses what little is known about probability models for Procrustes problems. For most practical purposes, it relies on data sampling procedures like permutation tests, jack-knifing, ... More

## Formal Models in Narrative Analysis

*David Herman*

*Apostolos Doxiadis and Barry Mazur (eds)*

### in Circles Disturbed: The Interplay of Mathematics and Narrative

- Published in print:
- 2012
- Published Online:
- October 2017
- ISBN:
- 9780691149042
- eISBN:
- 9781400842681
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691149042.003.0013
- Subject:
- Mathematics, History of Mathematics

This chapter considers formal models of narrative and the nature of the theory of narrative. After discussing the diachronic and synchronic approaches to investigating the role of formal models in ... More

## Finding the Roots of Algebraic Equations

*Victor J. Katz and Karen Hunger Parshall*

### in Taming the Unknown: A History of Algebra from Antiquity to the Early Twentieth Century

- Published in print:
- 2014
- Published Online:
- October 2017
- ISBN:
- 9780691149059
- eISBN:
- 9781400850525
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691149059.003.0011
- Subject:
- Mathematics, History of Mathematics

This chapter highlights some of the struggles to solve fifth-degree polynomials as well as the development of the idea of a group and its application to answering the question of solvability of ... More

## An Introduction to Gilbreath Numbers

*Robert W. Vallin*

### in The Mathematics of Various Entertaining Subjects: Research in Recreational Math

- Published in print:
- 2015
- Published Online:
- October 2017
- ISBN:
- 9780691164038
- eISBN:
- 9781400881338
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691164038.003.0012
- Subject:
- Mathematics, History of Mathematics

This chapter mathematically analyzes the behavior of a card trick described by an undergraduate math major at the University of California, Los Angeles, named Norman Gilbreath. Stated succinctly, ... 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

## Graph-Theoretic and Linear Algebra Formulations

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

### in Combinatorics of Genome Rearrangements

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

- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262062824.003.0006
- Subject:
- Mathematics, Mathematical Biology

This chapter demonstrates the expansion of genome rearrangement problems to a wide mathematical field, including long-standing problems in algebra. It discusses simple permutations and the ... More

## Inscrutability of Reference 285

*Ernie Lepore and Kirk Ludwig*

### in Donald Davidson: Meaning, Truth, Language, and Reality

- Published in print:
- 2005
- Published Online:
- July 2005
- ISBN:
- 9780199251346
- eISBN:
- 9780191602634
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199251347.003.0023
- Subject:
- Philosophy, General

Examines Davidson’s thesis of the inscrutability of reference, according to which any two different assignments of referents to singular terms and extensions to predicates which preserve the ... More

## Genomes as Permutations

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

### in Combinatorics of Genome Rearrangements

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

- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262062824.003.0002
- Subject:
- Mathematics, Mathematical Biology

Permutations were the first mathematical objects to serve as formal models for studying arrangements of DNA fragments among several species. This chapter discusses the following: the symmetric group; ... More

## Indeterminism and Probability

*Bas C. van Fraassen*

### in Quantum Mechanics: An Empiricist View

- Published in print:
- 1991
- Published Online:
- November 2003
- ISBN:
- 9780198239802
- eISBN:
- 9780191597466
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198239807.003.0003
- Subject:
- Philosophy, Philosophy of Science

Pure indeterminism is simply the denial of determinism; a theory may augment this with models in which the uncertain events have definite probabilities. De Finetti's representation theorem, which ... More

## The Problem of Identical Particles

*Bas C. van Fraassen*

### in Quantum Mechanics: An Empiricist View

- Published in print:
- 1991
- Published Online:
- November 2003
- ISBN:
- 9780198239802
- eISBN:
- 9780191597466
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198239807.003.0011
- Subject:
- Philosophy, Philosophy of Science

Do the properties of a compound or aggregate supervene on the properties of its parts? Theories that imply a negative answer (or the states they attribute) are called ’holistic’. Besides the EPR ... More

## Pacta and Innominate Real Contracts

*Reinhard Zimmermann*

### in The Law of Obligations: Roman Foundations of the Civilian Tradition

- Published in print:
- 1996
- Published Online:
- March 2012
- ISBN:
- 9780198764267
- eISBN:
- 9780191695247
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198764267.003.0017
- Subject:
- Law, Law of Obligations

This chapter discusses pacta and innominate real contracts. The first section looks at pacta in general. The second section discusses two types of pacta praetorian: the constitutum debiti and the ... More

## Distances between Signed Permutations

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

### in Combinatorics of Genome Rearrangements

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

- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262062824.003.0004
- Subject:
- Mathematics, Mathematical Biology

Signed permutations allow the relative orientation of homologous markers to be taken into account and constitute a more biologically relevant model for genomes. Reversals, for instance, always change ... More

## Distances between Arbitrary Strings

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

### in Combinatorics of Genome Rearrangements

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

- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262062824.003.0008
- Subject:
- Mathematics, Mathematical Biology

This chapter presents two main ideas to deal with arbitrary (that is, not necessarily balanced) strings. The first idea aims to transform strings into permutations, using the match-and-prune model in ... More