## 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 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

## 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

## 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

## 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

## 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