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The Factorization Method for Inverse Problems

Andreas Kirsch and Natalia Grinberg

Published in print:
2007
Published Online:
September 2008
ISBN:
9780199213535
eISBN:
9780191707629
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199213535.001.0001
Subject:
Mathematics, Applied Mathematics

This book is devoted to problems of shape identification in the context of (inverse) scattering problems and problems of impedance tomography. In contrast to traditional methods which are based on ... More


Numerical Methods for Image Registration

Jan Modersitzki

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198528418
eISBN:
9780191713583
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198528418.001.0001
Subject:
Mathematics, Applied Mathematics

This text provides an introduction to the theoretical, practical, and numerical aspects of image registration, with special emphasis on medical imaging. Given a so-called reference and template ... More


The Mean Duration of Cabinets

Rein Taagepera

in Predicting Party Sizes: The Logic of Simple Electoral Systems

Published in print:
2007
Published Online:
September 2007
ISBN:
9780199287741
eISBN:
9780191713408
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199287741.003.0010
Subject:
Political Science, Democratization

Again the quantity to watch is the ‘seat product’. The inverse square law of cabinet durations says that the mean cabinet duration in a country is approximately forty-two years divided by the square ... More


The Fundamental Theorem of Linear Algebra

Gidon Eshel

in Spatiotemporal Data Analysis

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691128917
eISBN:
9781400840632
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691128917.003.0010
Subject:
Environmental Science, Environmental Studies

This chapter summarizes pictorially some of the linear algebraic foundations discussed thus far by revisiting the fundamental theorem of linear algebra, the unifying view of matrices, vectors, and ... More


MEG: An Introduction to Methods

Peter Hansen, Morten Kringelbach, and Riitta Salmelin (eds)

Published in print:
2010
Published Online:
September 2010
ISBN:
9780195307238
eISBN:
9780199863990
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195307238.001.0001
Subject:
Neuroscience, Behavioral Neuroscience, Techniques

Magnetoencephalography (MEG) is an exciting brain imaging technology that allows real-time tracking of neural activity, making it an invaluable tool for advancing our understanding of brain function. ... More


The MUSIC algorithm and scattering by an inhomogeneous medium

Andreas Kirsch and Natalia Grinberg

in The Factorization Method for Inverse Problems

Published in print:
2007
Published Online:
September 2008
ISBN:
9780199213535
eISBN:
9780191707629
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199213535.003.0004
Subject:
Mathematics, Applied Mathematics

This chapter examines the case of a penetrable scatterer with an index of refraction that can be space-dependent and is assumed to be different from the constant background index. The inverse ... More


Alternative sampling and probe methods

Andreas Kirsch and Natalia Grinberg

in The Factorization Method for Inverse Problems

Published in print:
2007
Published Online:
September 2008
ISBN:
9780199213535
eISBN:
9780191707629
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199213535.003.0007
Subject:
Mathematics, Applied Mathematics

The Factorization Method is not the only sampling method. This final chapter introduces three alternative methods which belong to this class but, in contrast to the Factorization Method, are based on ... More


Inverse Problems

Peter Monk

in Finite Element Methods for Maxwell's Equations

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198508885
eISBN:
9780191708633
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198508885.003.0014
Subject:
Mathematics, Numerical Analysis

This final chapter introduces an inverse electromagnetic reconstruction problem of finding the shape of a scatterer from far field data. It focuses on the Linear Sampling Method that reduces the ... More


INTRODUCTION

Moody T. Chu and Gene H. Golub

in Inverse Eigenvalue Problems: Theory, Algorithms, and Applications

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198566649
eISBN:
9780191718021
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198566649.003.0001
Subject:
Mathematics, Applied Mathematics

This chapter introduces the underlying difference between a forward problem and an inverse problem. Fundamental issues such as solvability, computability, sensitivity, and feasibility are raised. ... More


APPLICATIONS

Moody T. Chu and Gene H. Golub

in Inverse Eigenvalue Problems: Theory, Algorithms, and Applications

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198566649
eISBN:
9780191718021
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198566649.003.0002
Subject:
Mathematics, Applied Mathematics

Inverse eigenvalue problems arise in a remarkable variety of applications. This chapter briefly highlights a few applications. The discussion is divided into six categories of applications: feedback ... More


SPECTRALLY CONSTRAINED APPROXIMATION

Moody T. Chu and Gene H. Golub

in Inverse Eigenvalue Problems: Theory, Algorithms, and Applications

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198566649
eISBN:
9780191718021
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198566649.003.0007
Subject:
Mathematics, Applied Mathematics

This chapter shows that the problems of computing least squares approximations for various types of real and symmetric matrices subject to spectral constraints share a common structure. A general ... More


INTRODUCTION

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/9780198528418.003.0001
Subject:
Mathematics, Applied Mathematics

This chapter states the problem of image registration and presents various applications, including remote sensing and medical image registration. Three examples which serve as test cases throughout ... More


Seeing in the cyclopean domain

Ian P. Howard and Brian J. Rogers

in Seeing in Depth: Volume 1: Basic Mechanics/ Volume 2: Depth Perception 2-Volume Set

Published in print:
2008
Published Online:
May 2009
ISBN:
9780195367607
eISBN:
9780199867264
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195367607.003.0017
Subject:
Psychology, Cognitive Neuroscience, Cognitive Psychology

Images in the two eyes may be superimposed or juxtaposed to produce a perceptual effect not evident when either image is presented alone. Any such effect is known as a cyclopean effect. This chapter ... More


Voice and transitivity in Guaraní

Maura Velázquez‐castillo

in The Typology of Semantic Alignment

Published in print:
2008
Published Online:
January 2009
ISBN:
9780199238385
eISBN:
9780191716768
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199238385.003.0015
Subject:
Linguistics, Semantics and Pragmatics

This chapter shows that the closest equivalents to voice alternations in Guarani cut across the transitive divide and respond to spatial relations between events and event participants. The ... More


Stevens' Power Law

Donald Laming

in The Measurement of Sensation

Published in print:
1997
Published Online:
January 2008
ISBN:
9780198523420
eISBN:
9780191712425
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198523420.003.0005
Subject:
Psychology, Cognitive Neuroscience

This chapter introduces Stevens' direct methods of magnitude estimation, magnitude production, and cross-modality matching. It summarizes Stevens' estimates of exponent values for twenty-four ... More


The Voice Continuum

William Croft

in Radical Construction Grammar: Syntactic Theory in Typological Perspective

Published in print:
2001
Published Online:
September 2007
ISBN:
9780198299554
eISBN:
9780191708091
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198299554.003.0008
Subject:
Linguistics, Syntax and Morphology

Some constructions are claimed to be universal, including the passive and the inverse voice constructions. In fact, the syntactic properties used to define passive and inverse constructions, and ... More


Statistical Models of Spike Trains

Liam Paninski, Emery N. Brown, Satish Iyengar, and Robert E. Kass

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/9780199235070.003.0010
Subject:
Mathematics, Biostatistics

Spiking neurons make inviting targets for analytical methods based on stochastic processes: spike trains carry information in their temporal patterning, yet they are often highly irregular across ... More


Optimal Commodity Taxation

Chris Jones

in Applied Welfare Economics

Published in print:
2005
Published Online:
July 2005
ISBN:
9780199281978
eISBN:
9780191602535
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0199281971.003.0009
Subject:
Economics and Finance, Public and Welfare

Rules for setting Ramsey (1927) optimal commodity taxes are derived in this chapter using the conventional welfare analysis presented in Ch. 6. When these tax rules apply, Diamond and Mirrlees (1971) ... More


Parliament and Congress: Representation and Scrutiny in the Twenty-First Century

William McKay and Charles W. Johnson

Published in print:
2010
Published Online:
September 2010
ISBN:
9780199273621
eISBN:
9780191594281
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199273621.001.0001
Subject:
Political Science, American Politics, UK Politics

The constitutional background of both legislatures and their procedures are described and where possible compared. Currently unsolved problems often have much in common, in vexed areas such as ethics ... More


The Inequality–Growth Nexus in the Short and Long Run: Empirical Evidence from China *

Guanghua Wan, Ming Lu, and Zhao Chen

in Inequality and Growth in Modern China

Published in print:
2008
Published Online:
May 2008
ISBN:
9780199535194
eISBN:
9780191715730
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199535194.003.0001
Subject:
Economics and Finance, Development, Growth, and Environmental

This chapter argues that the conventional approach of data averaging is problematic for exploring the growth-inequality nexus. It introduces the polynominal inverse lag (PIL) framework so that the ... More


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