## NON-PARAMETRIC IMAGE REGISTRATION

*Jan Modersitzki*

### in Numerical Methods for Image Registration

- Published in print:
- 2003
- Published Online:
- September 2007
- ISBN:
- 9780198528418
- eISBN:
- 9780191713583
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198528418.003.0008
- Subject:
- Mathematics, Applied Mathematics

This chapter introduces non-parametric registrations. The idea behind this type of registration is to come up with an appropriate measure both for the similarity as well as for the likelihood of a ... More

## Numerical Solution

*W. Otto Friesen and Jonathon A. Friesen*

### in NeuroDynamix II: Concepts of Neurophysiology Illustrated by Computer Simulations

- Published in print:
- 2009
- Published Online:
- February 2010
- ISBN:
- 9780195371833
- eISBN:
- 9780199865178
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195371833.003.0024
- Subject:
- Psychology, Cognitive Neuroscience

This chapter describes the method for numerical integration of the equations that underlie NeuroDynamix II models.

## Outlook

*Sergey N. Dorogovtsev*

### in Lectures on Complex Networks

- Published in print:
- 2010
- Published Online:
- May 2010
- ISBN:
- 9780199548927
- eISBN:
- 9780191720574
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199548927.003.0015
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

In this concluding section of the text, the three major milestones marking the history of the exploration of networks are indicated. These are: Leonhard Euler's work (1735), the introduction of ... More

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

*Ben Brubaker, Daniel Bump, and Solomon Friedberg*

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

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691150659.001.0001
- Subject:
- Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

Weyl group multiple Dirichlet series are generalizations of the Riemann zeta function. Like the Riemann zeta function, they are Dirichlet series with analytic continuation and functional equations, ... More

## o n e The Vis Viva Debate Kant's Starting Point

*Martin Schönfeld*

### in The Philosophy of the Young Kant: The Precritical Project

- Published in print:
- 2000
- Published Online:
- May 2006
- ISBN:
- 9780195132182
- eISBN:
- 9780199786336
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0195132181.003.0002
- Subject:
- Philosophy, History of Philosophy

This chapter explores the context of Kant’s first and original puzzle: what actually is force? It is an account of the debate over kinetic energy (Leibniz’s “living force” or vis viva) and the ... More

## s e v e n The Physical Monadology and theElements of Nature

*Martin Schöneld*

### in The Philosophy of the Young Kant: The Precritical Project

- Published in print:
- 2000
- Published Online:
- May 2006
- ISBN:
- 9780195132182
- eISBN:
- 9780199786336
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0195132181.003.0008
- Subject:
- Philosophy, History of Philosophy

This chapter explores Kant’s professorial thesis, The Joint Use of Metaphysics and Geometry in Natural Philosophy, the First Example of Which Contains the Physical Monadology (1756). Section 1 ... More

## n i n e The Newtonian Program of thePrize Essay and Kant's Crisis The Struggle for Freedom

*Martin Schöneld*

### in The Philosophy of the Young Kant: The Precritical Project

- Published in print:
- 2000
- Published Online:
- May 2006
- ISBN:
- 9780195132182
- eISBN:
- 9780199786336
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0195132181.003.0010
- Subject:
- Philosophy, History of Philosophy

This chapter explores the aftermath of Only Possible Argument and the Prize Essay (1764). Section 1 examines the curious preface of Kant’s third book, the exchange with Mendelssohn, and Kant’s ... More

## Catalan Numbers with Applications

*Thomas Koshy*

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

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195334548.001.0001
- Subject:
- Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

Fibonacci and Lucas sequences are “two shining stars in the vast array of integer sequences,” and because of their ubiquitousness, tendency to appear in quite unexpected and unrelated places, ... More

## RADON TRANSFORM AS THE INTERRELATION OF GEOMETRY AND ANALYSIS

*Leon Ehrenpreis*

### in The Universality of the Radon Transform

- Published in print:
- 2003
- Published Online:
- September 2007
- ISBN:
- 9780198509783
- eISBN:
- 9780191709166
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198509783.003.0008
- Subject:
- Mathematics, Mathematical Physics

This chapter deals with various questions which are related to the Radon transform, for example, the analog for forms, Selberg's trace formula. It gives a sharpening of the classical Euler-Maclaurin ... More

## Existence of Ball Quotients Covering Line Arrangements

*Paula Tretkoff*

### in Complex Ball Quotients and Line Arrangements in the Projective Plane (MN-51)

- Published in print:
- 2016
- Published Online:
- October 2017
- ISBN:
- 9780691144771
- eISBN:
- 9781400881253
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691144771.003.0007
- Subject:
- Mathematics, Geometry / Topology

This chapter justifies the assumption that ball quotients covering line arrangements exist. It begins with the general case on the existence of finite covers by ball quotients of weighted ... More

## HYPERBOLIC CONSERVATION LAWS

*George Em Karniadakis and Spencer J. Sherwin*

### in Spectral/hp Element Methods for Computational Fluid Dynamics

- Published in print:
- 2005
- Published Online:
- September 2007
- ISBN:
- 9780198528692
- eISBN:
- 9780191713491
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198528692.003.0010
- Subject:
- Mathematics, Numerical Analysis

This chapter discusses compressible Euler and Navier-Stokes equations as well as general hyperbolic conservation laws. The principle issue is how effectively to use the high-order expansions of the ... More

## THE MATHEMATICAL SETTING

*Jan Modersitzki*

### in Numerical Methods for Image Registration

- Published in print:
- 2003
- Published Online:
- September 2007
- ISBN:
- 9780198528418
- eISBN:
- 9780191713583
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198528418.003.0003
- Subject:
- Mathematics, Applied Mathematics

The basic mathematical notation is introduced, including formal definitions of images and digital images, midpoint and meshpoint grids. Local and global interpolation techniques such as ... More

## ELASTIC REGISTRATION

*Jan Modersitzki*

### in Numerical Methods for Image Registration

- Published in print:
- 2003
- Published Online:
- September 2007
- ISBN:
- 9780198528418
- eISBN:
- 9780191713583
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198528418.003.0009
- Subject:
- Mathematics, Applied Mathematics

This chapter introduces elastic registration using the general framework introduced in Chapter 8. A physical motivation for this particular regularizer is given. The two images are viewed as two ... More

## Topological Invariants and Differential Geometry

*Paula Tretkoff*

### in Complex Ball Quotients and Line Arrangements in the Projective Plane (MN-51)

- Published in print:
- 2016
- Published Online:
- October 2017
- ISBN:
- 9780691144771
- eISBN:
- 9781400881253
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691144771.003.0002
- Subject:
- Mathematics, Geometry / Topology

This chapter deals with topological invariants and differential geometry. It first considers a topological space X for which singular homology and cohomology are defined, along with the Euler number ... More

## Riemann Surfaces, Coverings, and Hypergeometric Functions

*Paula Tretkoff*

### in Complex Ball Quotients and Line Arrangements in the Projective Plane (MN-51)

- Published in print:
- 2016
- Published Online:
- October 2017
- ISBN:
- 9780691144771
- eISBN:
- 9781400881253
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691144771.003.0003
- Subject:
- Mathematics, Geometry / Topology

This chapter deals with Riemann surfaces, coverings, and hypergeometric functions. It first considers the genus and Euler number of a Riemann surface before discussing Möbius transformations and ... More

## The Case of <i>SL</i>(2); the Examples of Evans and Rudnick

*Nicholas M. Katz*

### in Convolution and Equidistribution: Sato-Tate Theorems for Finite-Field Mellin Transforms (AM-180)

- Published in print:
- 2012
- Published Online:
- October 2017
- ISBN:
- 9780691153308
- eISBN:
- 9781400842704
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691153308.003.0015
- Subject:
- Mathematics, Number Theory

This chapter treats both of these examples, as well as all the examples to come, using the Euler–Poincaré formula, cf. [Ray, Thm. 1] or [Ka-GKM, 2.3.1] or [Ka-SE, 4.6, (v) atop p. 113] or [De-ST, ... More

## Tic-tac-toe on Affine Planes

*Maureen T. Carroll and Steven T. Dougherty*

### 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/9780691164038.003.0013
- Subject:
- Mathematics, History of Mathematics

This chapter introduces a new game of tic-tac-toe that fits squarely within the body of work inspired by mathematician Leonhard Euler's findings on the so-called “Graeco-Latin squares” and the ... More

## Partial differential equations for fluids

*Bijan Mohammadi and Olivier Pironneau*

### in Applied Shape Optimization for Fluids

- Published in print:
- 2009
- Published Online:
- February 2010
- ISBN:
- 9780199546909
- eISBN:
- 9780191720482
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199546909.003.0003
- Subject:
- Mathematics, Mathematical Physics

This chapter describes the governing equations considered throughout the book. The equations of fluid dynamics are recalled, together with the k-epsilon turbulence model, which is used later on for ... More

## Relativistic Fluids

*Yvonne Choquet-Bruhat*

### in General Relativity and the Einstein Equations

- Published in print:
- 2008
- Published Online:
- May 2009
- ISBN:
- 9780199230723
- eISBN:
- 9780191710872
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199230723.003.0009
- Subject:
- Mathematics, Applied Mathematics

This chapter presents general properties of perfect fluids. When appropriate definitions are given, some of these properties generalize well-known properties of non-relativistic perfect fluids. ... More

## Introduction: From Pipeline Economics to Computational Economics

*Ramon Marimon and Andrew Scott*

### in Computational Methods for the Study of Dynamic Economies

- Published in print:
- 2001
- Published Online:
- November 2003
- ISBN:
- 9780199248278
- eISBN:
- 9780191596605
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199248273.003.0001
- Subject:
- Economics and Finance, Macro- and Monetary Economics

Starts by looking at the advances in macroeconomics that have been made since A. W. Phillips's 1958 Economica paper and his physical economic model (made of piping and valves) designed to teach ... More