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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


Adaptive Diversification and Speciation as Pattern Formation in Partial Differential Equation Models

Michael Doebeli

in Adaptive Diversification (MPB-48)

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691128931
eISBN:
9781400838936
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691128931.003.0009
Subject:
Biology, Biodiversity / Conservation Biology

This chapter discusses partial differential equation models. Partial differential equations can describe the dynamics of phenotype distributions of polymorphic populations, and they allow for a ... More


Wavelet Methods for Elliptic Partial Differential Equations

Karsten Urban

Published in print:
2008
Published Online:
May 2009
ISBN:
9780198526056
eISBN:
9780191712340
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198526056.001.0001
Subject:
Mathematics, Applied Mathematics, Mathematical Finance

Wavelets have become a powerful tool in several applications by now. Their use for the numerical solution of operator equations has been investigated more recently. By now the theoretical ... More


The Porous Medium Equation: Mathematical Theory

Juan Luis Vazquez

Published in print:
2006
Published Online:
September 2007
ISBN:
9780198569039
eISBN:
9780191717468
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198569039.001.0001
Subject:
Mathematics, Mathematical Physics

The heat equation is one of the three classical linear partial differential equations of second order that form the basis of any elementary introduction to the area of PDEs, and only recently has it ... More


EXTENSION OF SOLUTIONS OF DIFFERENTIAL EQUATIONS

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/9780198509783.003.0009
Subject:
Mathematics, Mathematical Physics

This chapter shows how the book's main theory allows for the treatment of extension problems for partial differential equations. The culmination of this is a solution of the asymptotic edge of the ... More


HARMONIC FUNCTIONS IN R n

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/9780198509783.003.0003
Subject:
Mathematics, Mathematical Physics

This chapter looks at a variation of “harmonic function” which was introduced by Chevalley. Ordinary harmonic functions are solutions of the Laplace equation; Chevalley harmonic functions are ... More


Finite‐Difference Methods for Continuous‐Time Dynamic Programming

Graham V. Candler

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:
10.1093/0199248273.003.0008
Subject:
Economics and Finance, Macro- and Monetary Economics

Introduces some of the methods and underlying ideas behind computational fluid dynamics—in particular, the use is discussed of finite‐difference methods for the simulation of dynamic economies. A ... More


Mathematical and computational modelling tools

Baltazar D. Aguda and Avner Friedman

in Models of Cellular Regulation

Published in print:
2008
Published Online:
September 2008
ISBN:
9780198570912
eISBN:
9780191718717
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198570912.003.0003
Subject:
Physics, Soft Matter / Biological Physics

This chapter reviews chemical kinetics to illustrate the formulation of model equations for a given reaction mechanism. For spatially uniform systems, these model equations are usually ordinary ... 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


Differential equations in physics

Chun Wa Wong

in Introduction to Mathematical Physics: Methods & Concepts

Published in print:
2013
Published Online:
May 2013
ISBN:
9780199641390
eISBN:
9780191747786
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199641390.003.0005
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Ordinary and partial differential equations appear in physics as equations of motion or of state. They are often linear differential equations for which a sum of solutions remains a solution. The ... More


Appell 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/9780691144771.003.0008
Subject:
Mathematics, Geometry / Topology

This chapter discusses the complete quadrilateral line arrangement, and especially its relationship with the space of regular points of the system of partial differential equations defining the ... More


Generalized Fokker–Planck equation

Melvin Lax, Wei Cai, and Min Xu

in Random Processes in Physics and Finance

Published in print:
2006
Published Online:
January 2010
ISBN:
9780198567769
eISBN:
9780191718359
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198567769.003.0008
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Thermal noise and Gaussian noise sources combine to create a category of Markovian processes known as Fokker–Planck processes. This chapter discusses Fokker–Planck processes such as ... More


BIFURCATIONS AND INSTABILITIES

Nasr M. Ghoniem and Daniel D. Walgraef

in Instabilities and Self-Organization in Materials: Volume I: Fundamentals of Nanoscience, Volume II: Applications in Materials Design and Nanotechnology

Published in print:
2008
Published Online:
May 2008
ISBN:
9780199298686
eISBN:
9780191720222
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199298686.003.0007
Subject:
Physics, Condensed Matter Physics / Materials

This chapter focuses on the mathematical structures underlying the notions of stability, bifurcation, and instabilities in complex nonlinear dynamical systems described by sets of ordinary or partial ... More


Population Density Methods in Large-Scale Neural Network Modelling

Daniel Tranchina

in Stochastic Methods in Neuroscience

Published in print:
2009
Published Online:
February 2010
ISBN:
9780199235070
eISBN:
9780191715778
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199235070.003.0007
Subject:
Mathematics, Biostatistics

Population density methods have a rich history in theoretical and computational neuroscience. In earlier years, these methods were used in large part to study the statistics of spike trains. Starting ... More


Introduction

Karsten Urban

in Wavelet Methods for Elliptic Partial Differential Equations

Published in print:
2008
Published Online:
May 2009
ISBN:
9780198526056
eISBN:
9780191712340
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198526056.003.0001
Subject:
Mathematics, Applied Mathematics, Mathematical Finance

This chapter gives an outline of the history of wavelets, in particular with respect to their use to numerically solve partial differential equations. The scope of the book and its outline is ... More


Differential Equations

Bard Ermentrout and John Rinzel

in Computational Modeling Methods for Neuroscientists

Published in print:
2009
Published Online:
August 2013
ISBN:
9780262013277
eISBN:
9780262258722
Item type:
chapter
Publisher:
The MIT Press
DOI:
10.7551/mitpress/9780262013277.003.0002
Subject:
Neuroscience, Techniques

This chapter, which addresses the partial differential equations (PDEs) with the example of finding the speed and profile of a propagating impulse for a Hodgkin-Huxley-like cable equation, highlights ... More


Stochastic Homogenization and Energy of Infinite Sets of Points

Xavier Blanc

in Analysis and Stochastics of Growth Processes and Interface Models

Published in print:
2008
Published Online:
September 2008
ISBN:
9780199239252
eISBN:
9780191716911
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199239252.003.0004
Subject:
Mathematics, Probability / Statistics, Analysis

This chapter presents, in a synthetic way, a series of recent works by X. Blanc, C. Le Bris, and P-L. Lions on homogenization of an elliptic partial differential equation under certain periodic or ... More


Looking at the World Sideways

Craig Callender

in What Makes Time Special?

Published in print:
2017
Published Online:
July 2017
ISBN:
9780198797302
eISBN:
9780191839603
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198797302.003.0008
Subject:
Philosophy, Metaphysics/Epistemology

When physics tells its story of the world, it writes on spatial pages and we flip pages in the temporal directions. The present moment contains the seeds of what happens next. Relativity challenges ... More


Fundamentals of fluid dynamics with an introduction to the importance of interfaces

H. A. Stone

in Soft Interfaces: Lecture Notes of the Les Houches Summer School: Volume 98, July 2012

Published in print:
2017
Published Online:
November 2017
ISBN:
9780198789352
eISBN:
9780191831201
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198789352.003.0001
Subject:
Physics, Soft Matter / Biological Physics

The topics discussed are all related to basic fluid mechanics. In these introductory notes I highlight some of the main features of fluid flows and their mathematical characterization. There is much ... More


A Review of General Asset Pricing Theory

Claus Munk

in Fixed Income Modelling

Published in print:
2011
Published Online:
September 2011
ISBN:
9780199575084
eISBN:
9780191728648
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199575084.003.0004
Subject:
Economics and Finance, Financial Economics

The pricing of fixed income securities follows the same general principles as the pricing of all other financial assets. This chapter explains some important general concepts and results in asset ... More


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