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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


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