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Lectures on Inductive Logic
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<table><tr><td width="200px"><img width="150px" src="/view/covers/9780199666478.jpg" alt="Lectures on Inductive Logic"/><br/></td><td><dl><dt>Author:</dt><dd>Jon Williamson</dd><dt>ISBN:</dt><dd>9780199666478</dd><dt>Publisher:</dt><dd>Oxford University Press</dd><dt>Subjects:</dt><dd>Mathematics, Logic / Computer Science / Mathematical Philosophy</dd><dt>DOI:</dt><dd>10.1093/acprof:oso/9780199666478.001.0001</dd><dt>Published in print:</dt><dd>2017</dd><dt>Published Online:</dt><dd>2017-03-23</dd></dl></td></tr></table><p>Inductive logic (also known as confirmation theory) seeks to determine the extent to which the premisses of an argument entail its conclusion. This book offers an introduction to the field of inductive logic and develops a new Bayesian inductive logic. Chapter 1 introduces perhaps the simplest and most natural account of inductive logic, classical inductive logic, which is attributable to Ludwig Wittgenstein. Classical inductive logic is seen to fail in a crucial way, so there is a need to develop more sophisticated inductive logics. Chapter 2 presents enough logic and probability theory for the reader to begin to study inductive logic, while Chapter 3 introduces the ways in which logic and probability can be combined in an inductive logic. Chapter 4 analyses the most influential approach to inductive logic, due to W.E. Johnson and Rudolf Carnap. Again, this logic is seen to be inadequate. Chapter 5 shows how an alternative approach to inductive logic follows naturally from the philosophical theory of objective Bayesian epistemology. This approach preserves the inferences that classical inductive logic gets right (Chapter 6). On the other hand, it also offers a way out of the problems that beset classical inductive logic (Chapter 7). Chapter 8 defends the approach by tackling several key criticisms that are often levelled at inductive logic. Chapter 9 presents a formal justification of the version of objective Bayesianism which underpins the approach. Chapter 10 explains what has been achieved and poses some open questions.</p>Jon Williamson2017-03-23Everyday Cryptography
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<table><tr><td width="200px"><img width="150px" src="/view/covers/9780199695591.jpg" alt="Everyday CryptographyFundamental Principles and Applications"/><br/></td><td><dl><dt>Author:</dt><dd>Keith M. Martin</dd><dt>ISBN:</dt><dd>9780199695591</dd><dt>Publisher:</dt><dd>Oxford University Press</dd><dt>Subjects:</dt><dd>Mathematics, Applied Mathematics</dd><dt>DOI:</dt><dd>10.1093/acprof:oso/9780199695591.001.0001</dd><dt>Published in print:</dt><dd>2012</dd><dt>Published Online:</dt><dd>2013-12-17</dd></dl></td></tr></table><p>Cryptography is a vital technology that underpins the security of information in computer networks. This book presents an introduction to the role that cryptography plays in providing information security for technologies such as the Internet, mobile phones, payment cards, and wireless local area networks. Focusing on the fundamental principles that ground modern cryptography as they arise in modern applications, it avoids both an over-reliance on transient current technologies and over-whelming theoretical research. A short appendix is included for those looking for a deeper appreciation of some of the concepts involved. By the end of this book, the reader will not only be able to understand the practical issues concerned with the deployment of cryptographic mechanisms, including the management of cryptographic keys, but will also be able to interpret future developments in this increasingly important area of technology.</p>Keith M. Martin2013-12-17Spectral/hp Element Methods for Computational Fluid Dynamics
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<table><tr><td width="200px"><img width="150px" src="/view/covers/9780198528692.jpg" alt="Spectral/hp Element Methods for Computational Fluid Dynamics"/><br/></td><td><dl><dt>Author:</dt><dd>George Karniadakis, Spencer Sherwin</dd><dt>ISBN:</dt><dd>9780198528692</dd><dt>Publisher:</dt><dd>Oxford University Press</dd><dt>Subjects:</dt><dd>Mathematics, Numerical Analysis</dd><dt>DOI:</dt><dd>10.1093/acprof:oso/9780198528692.001.0001</dd><dt>Published in print:</dt><dd>2005</dd><dt>Published Online:</dt><dd>2007-09-01</dd></dl></td></tr></table><p>Spectral methods have long been popular in direct and large eddy simulation of turbulent flows, but their use in areas with complex-geometry computational domains has historically been much more limited. More recently, the need to find accurate solutions to the viscous flow equations around complex configurations has led to the development of high-order discretization procedures on unstructured meshes, which are also recognized as more efficient for solution of time-dependent oscillatory solutions over long time periods. This book, an updated edition on the original text, presents the recent and significant progress in multi-domain spectral methods at both the fundamental and application level. Containing material on discontinuous Galerkin methods, non-tensorial nodal spectral element methods in simplex domains, and stabilization and filtering techniques, this text introduces the use of spectral/hp element methods with particular emphasis on their application to unstructured meshes. It provides a detailed explanation of the key concepts underlying the methods along with practical examples of their derivation and application.</p>George Karniadakis and Spencer Sherwin2007-09-01Numerical Methods for Image Registration
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<table><tr><td width="200px"><img width="150px" src="/view/covers/9780198528418.jpg" alt="Numerical Methods for Image Registration"/><br/></td><td><dl><dt>Author:</dt><dd>Jan Modersitzki</dd><dt>ISBN:</dt><dd>9780198528418</dd><dt>Publisher:</dt><dd>Oxford University Press</dd><dt>Subjects:</dt><dd>Mathematics, Applied Mathematics</dd><dt>DOI:</dt><dd>10.1093/acprof:oso/9780198528418.001.0001</dd><dt>Published in print:</dt><dd>2003</dd><dt>Published Online:</dt><dd>2007-09-01</dd></dl></td></tr></table><p>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 image, the goal of image registration is to find a reasonable transformation such that the transformed template is similar to the reference image. Image registration is utilized whenever information obtained from different viewpoints times and sensors needs to be combined or compared, and unwanted distortion needs to be eliminated. The book provides a systematic introduction to image registration and discusses the basic mathematical principles, including aspects from approximations theory, image processing, numerics, optimization, partial differential equations, and statistics, with a strong focus on numerical methods. A unified variational approach is introduced and enables a separation into data-related issues like image feature or image intensity-based similarity measures, and problem inherent regularization like elastic or diffusion registration. This general framework is further used for the explanation and classification of established methods as well as the design of new schemes and building blocks including landmark-, thin-plate-spline, mutual information, elastic, fluid, demon, diffusion, and curvature registration.</p>Jan Modersitzki2007-09-01An Introduction to Model-Based Survey Sampling with Applications
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<table><tr><td width="200px"><img width="150px" src="/view/covers/9780198566625.jpg" alt="An Introduction to Model-Based Survey Sampling with Applications"/><br/></td><td><dl><dt>Author:</dt><dd>Ray Chambers, Robert Clark</dd><dt>ISBN:</dt><dd>9780198566625</dd><dt>Publisher:</dt><dd>Oxford University Press</dd><dt>Subjects:</dt><dd>Mathematics, Probability / Statistics</dd><dt>DOI:</dt><dd>10.1093/acprof:oso/9780198566625.001.0001</dd><dt>Published in print:</dt><dd>2012</dd><dt>Published Online:</dt><dd>2012-05-24</dd></dl></td></tr></table><p>This book is an introduction to the model-based approach to survey sampling. It consists of three parts, with Part I focusing on estimation of population totals. Chapters 1 and 2 introduce survey sampling, and the model-based approach, respectively. Chapter 3 considers the simplest possible model, the homogenous population model, which is then extended to stratified populations in Chapter 4. Chapter 5 discusses simple linear regression models for populations, and Chapter 6 considers clustered populations. The general linear population model is then used to integrate these results in Chapter 7. Part II of this book considers the properties of estimators based on incorrectly specified models. Chapter 8 develops robust sample designs that lead to unbiased predictors under model misspecification, and shows how flexible modelling methods like non-parametric regression can be used in survey sampling. Chapter 9 extends this development to misspecfication robust prediction variance estimators and Chapter 10 completes Part II of the book with an exploration of outlier robust sample survey estimation. Chapters 11 to 17 constitute Part III of the book and show how model-based methods can be used in a variety of problem areas of modern survey sampling. They cover (in order) prediction of non-linear population quantities, sub-sampling approaches to prediction variance estimation, design and estimation for multipurpose surveys, prediction for domains, small area estimation, efficient prediction of population distribution functions and the use of transformations in survey inference. The book is designed to be accessible to undergraduate and graduate level students with a good grounding in statistics and applied survey statisticians seeking an introduction to model-based survey design and estimation.</p>Ray Chambers and Robert Clark2012-05-24Proving in the Elementary Mathematics Classroom
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<table><tr><td width="200px"><img width="150px" src="/view/covers/9780198723066.jpg" alt="Proving in the Elementary Mathematics Classroom"/><br/></td><td><dl><dt>Author:</dt><dd>Andreas J. Stylianides</dd><dt>ISBN:</dt><dd>9780198723066</dd><dt>Publisher:</dt><dd>Oxford University Press</dd><dt>Subjects:</dt><dd>Mathematics, Educational Mathematics</dd><dt>DOI:</dt><dd>10.1093/acprof:oso/9780198723066.001.0001</dd><dt>Published in print:</dt><dd>2016</dd><dt>Published Online:</dt><dd>2016-09-22</dd></dl></td></tr></table><p>Proving in the Elementary Mathematics Classroom addresses a fundamental problem in children’s learning that has received relatively little research attention: Although proving and related concepts (e.g., proof, argumentation, conjecturing) are core to mathematics as a sense-making activity, they currently have a marginal place in elementary classrooms internationally. This book takes a step toward addressing this problem by examining how the place of proving in elementary students’ mathematical work can be elevated through the purposeful design and implementation of mathematics tasks, specifically proving tasks. In particular, the book draws on relevant research and theory and classroom episodes with 8–9-year-olds from England and the United States to examine different kinds of proving tasks and the proving activity they can help generate in the elementary classroom. It examines further the role of elementary teachers in mediating the relationship between proving tasks and proving activity, including major mathematical and pedagogical issues that can arise for them as they implement each kind of proving task in the classroom. In addition to its research contribution in the intersection of the scholarly areas of teaching/learning proving and task design/implementation, the book has important implications for teaching, curricular resources, and teacher education. For example, the book identifies different kinds of proving tasks whose balanced representation in the mathematics classroom and in curricular resources can support a rounded set of learning experiences for elementary students related to proving. It identifies further important mathematical ideas and pedagogical practices related to proving that can be studied in teacher education.</p>Andreas J. Stylianides2016-09-22Electromagnetism of Continuous Media
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<table><tr><td width="200px"><img width="150px" src="/view/covers/9780198527008.jpg" alt="Electromagnetism of Continuous MediaMathematical Modelling and Applications"/><br/></td><td><dl><dt>Author:</dt><dd>Mauro Fabrizio, Angelo Morro</dd><dt>ISBN:</dt><dd>9780198527008</dd><dt>Publisher:</dt><dd>Oxford University Press</dd><dt>Subjects:</dt><dd>Mathematics, Applied Mathematics</dd><dt>DOI:</dt><dd>10.1093/acprof:oso/9780198527008.001.0001</dd><dt>Published in print:</dt><dd>2003</dd><dt>Published Online:</dt><dd>2007-09-01</dd></dl></td></tr></table><p>This book is devoted to the mathematical modelling of electromagnetic materials. Electromagnetism in matter is developed with particular emphasis on material effects, which are ascribed to memory in time and nonlocality. Within the mathematical modelling, thermodynamics of continuous media plays a central role in that it places significant restrictions on the constitutive equations. Further, as shown in connection with uniqueness, existence and stability, variational settings, and wave propagation, a correct formulation of the pertinent problems is based on the knowledge of the thermodynamic restrictions for the material. The book is divided into four parts. Part I (chapters 1 to 4) reviews the basic concepts of electromagnetism, starting from the integral form of Maxwell’s equations and then addressing attention to the physical motivation for materials with memory. Part II (chapers 5 to 9) deals with thermodynamics of systems with memory and applications to evolution and initial/boundary-value problems. It contains developments and results which are unusual in textbooks on electromagnetism and arise from the research literature, mainly post-1960s. Part III (chapters 10 to 12) outlines some topics of materials modelling — nonlinearity, nonlocality, superconductivity, and magnetic hysteresis — which are of great interest both in mathematics and in applications.</p>Mauro Fabrizio and Angelo Morro2007-09-01Sasakian Geometry
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<table><tr><td width="200px"><img width="150px" src="/view/covers/9780198564959.jpg" alt="Sasakian Geometry"/><br/></td><td><dl><dt>Author:</dt><dd>Charles Boyer, Krzysztof Galicki</dd><dt>ISBN:</dt><dd>9780198564959</dd><dt>Publisher:</dt><dd>Oxford University Press</dd><dt>Subjects:</dt><dd>Mathematics, Geometry / Topology</dd><dt>DOI:</dt><dd>10.1093/acprof:oso/9780198564959.001.0001</dd><dt>Published in print:</dt><dd>2007</dd><dt>Published Online:</dt><dd>2008-01-01</dd></dl></td></tr></table><p>Sasakian manifolds were first introduced in 1962. This book's main focus is on the intricate relationship between Sasakian and Kähler geometries, especially when the Kähler structure is that of an algebraic variety. The book is divided into three parts. The first five chapters carefully prepare the stage for the proper introduction of the subject. After a brief discussion of G-structures, the reader is introduced to the theory of Riemannian foliations. A concise review of complex and Kähler geometry precedes a fairly detailed treatment of compact complex Kähler orbifolds. A discussion of the existence and obstruction theory of Kähler-Einstein metrics (Monge-Ampère problem) on complex compact orbifolds follows. The second part gives a careful discussion of contact structures in the Riemannian setting. Compact quasi-regular Sasakian manifolds emerge here as algebraic objects: they are orbifold circle bundles over compact projective algebraic orbifolds. After a discussion of symmetries of Sasakian manifolds in Chapter 8, the book looks at Sasakian structures on links of isolated hypersurface singularities in Chapter 9. What follows is a study of compact Sasakian manifolds in dimensions three and five focusing on the important notion of positivity. The latter is crucial in understanding the existence of Sasaki-Einstein and 3-Sasakian metrics, which are studied in Chapters 11 and 13. Chapter 12 gives a fairly brief description of quaternionic geometry which is a prerequisite for Chapter 13. The study of Sasaki-Einstein geometry was the original motivation for the book. The final chapter on Killing spinors discusses the properties of Sasaki-Einstein manifolds, which allow them to play an important role as certain models in the supersymmetric field theories of theoretical physics.</p>Charles Boyer and Krzysztof Galicki2008-01-01Thiele: Pioneer in Statistics
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<table><tr><td width="200px"><img width="150px" src="/view/covers/9780198509721.jpg" alt="Thiele: Pioneer in Statistics"/><br/></td><td><dl><dt>Author:</dt><dd>Steffen L. Lauritzen</dd><dt>ISBN:</dt><dd>9780198509721</dd><dt>Publisher:</dt><dd>Oxford University Press</dd><dt>Subjects:</dt><dd>Mathematics, Probability / Statistics</dd><dt>DOI:</dt><dd>10.1093/acprof:oso/9780198509721.001.0001</dd><dt>Published in print:</dt><dd>2002</dd><dt>Published Online:</dt><dd>2007-09-01</dd></dl></td></tr></table><p>Thorvald Nicolai Thiele was a brilliant Danish researcher of the 19th century. He was a professor of Astronomy at the University of Copenhagen and the founder of Hafnia, the first Danish private insurance company. Thiele worked in astronomy, mathematics, actuarial science, and statistics, his most spectacular contributions were in the latter two areas, where his published work was far ahead of his time. This book is concerned with his statistical work. It evolves around his three main statistical masterpieces, which are now translated into English for the first time: 1) his article from 1880 where he derives the Kalman filter; 2) his book from 1889, where he lays out the subject of statistics in a highly original way, derives the half-invariants (today known as cumulants), the notion of likelihood in the case of binomial experiments, the canonical form of the linear normal model, and develops model criticism via analysis of residuals; and 3) an article from 1899 where he completes the theory of the half-invariants. This book also contains three chapters, written by A. Hald and S. L. Lauritzen, which describe Thiele's statistical work in modern terms and puts it into an historical perspective.</p>Steffen L. Lauritzen2007-09-01The Theory of Infinite Soluble Groups
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<table><tr><td width="200px"><img width="150px" src="/view/covers/9780198507284.jpg" alt="The Theory of Infinite Soluble Groups"/><br/></td><td><dl><dt>Author:</dt><dd>John C. Lennox, Derek J. S. Robinson</dd><dt>ISBN:</dt><dd>9780198507284</dd><dt>Publisher:</dt><dd>Oxford University Press</dd><dt>Subjects:</dt><dd>Mathematics, Pure Mathematics</dd><dt>DOI:</dt><dd>10.1093/acprof:oso/9780198507284.001.0001</dd><dt>Published in print:</dt><dd>2004</dd><dt>Published Online:</dt><dd>2007-09-01</dd></dl></td></tr></table><p>This book provides a comprehensive account of the theory of infinite soluble groups, from its foundations up to research level. Topics covered include: polycyclic groups, Cernikov groups, Mal’cev completions, soluble linear groups, P. Hall’s theory of finitely generated soluble groups, soluble groups with finite rank, soluble groups whose abelian subgroups satisfy finiteness conditions, simple modules over polycyclic groups, the Jategaonkar-Roseblade theorem, centrality in finitely generated soluble groups and the Lennox-Roseblade theorem, algorithmic problems for polycyclic and metabelian groups, cohomological topics including groups with finite (co)homological dimension and vanishing theorems, finitely presented soluble groups, constructible soluble groups, the Bieri-Strebel invariant, subnormality, and soluble groups.</p>John C. Lennox and Derek J. S. Robinson2007-09-01Riemann Surfaces
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<table><tr><td width="200px"><img width="150px" src="/view/covers/9780198526391.jpg" alt="Riemann Surfaces"/><br/></td><td><dl><dt>Author:</dt><dd>Simon Donaldson</dd><dt>ISBN:</dt><dd>9780198526391</dd><dt>Publisher:</dt><dd>Oxford University Press</dd><dt>Subjects:</dt><dd>Mathematics, Geometry / Topology, Analysis</dd><dt>DOI:</dt><dd>10.1093/acprof:oso/9780198526391.001.0001</dd><dt>Published in print:</dt><dd>2011</dd><dt>Published Online:</dt><dd>2013-12-17</dd></dl></td></tr></table><p>The theory of Riemann surfaces occupies a very special place in mathematics. It is a culmination of much of traditional calculus, making surprising connections with geometry and arithmetic. It is an extremely useful part of mathematics, knowledge of which is needed by specialists in many other fields. It provides a model for a large number of more recent developments in areas including manifold topology, global analysis, algebraic geometry, Riemannian geometry, and diverse topics in mathematical physics. This text on Riemann surface theory proves the fundamental analytical results on the existence of meromorphic functions and the Uniformisation Theorem. The approach taken emphasises PDE methods, applicable more generally in global analysis. The connection with geometric topology, and in particular the role of the mapping class group, is also explained. To this end, some more sophisticated topics have been included, compared with traditional texts at this level. While the treatment is novel, the roots of the subject in traditional calculus and complex analysis are kept well in mind. Part I sets up the interplay between complex analysis and topology, with the latter treated informally. Part II works as a rapid first course in Riemann surface theory, including elliptic curves. The core of the book is contained in Part III, where the fundamental analytical results are proved.</p>Simon Donaldson2013-12-17The Factorization Method for Inverse Problems
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<table><tr><td width="200px"><img width="150px" src="/view/covers/9780199213535.jpg" alt="The Factorization Method for Inverse Problems"/><br/></td><td><dl><dt>Author:</dt><dd>Andreas Kirsch, Natalia Grinberg</dd><dt>ISBN:</dt><dd>9780199213535</dd><dt>Publisher:</dt><dd>Oxford University Press</dd><dt>Subjects:</dt><dd>Mathematics, Applied Mathematics</dd><dt>DOI:</dt><dd>10.1093/acprof:oso/9780199213535.001.0001</dd><dt>Published in print:</dt><dd>2007</dd><dt>Published Online:</dt><dd>2008-09-01</dd></dl></td></tr></table><p>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 iterative schemes of solving sequences of corresponding direct problems, this book presents a completely different method. The Factorization Method avoids the need to solve the (time consuming) direct problems. Furthermore, no a-priori information about the type of scatterer (penetrable or impenetrable), type of boundary condition, or number of components is needed. The Factorization Method can be considered as an example of a Sampling Method. The book aims to construct a binary criterium on the known data to decide whether or not a given point z is inside or outside the unknown domain D. By choosing a grid of sampling points z in a region known to contain D, the characteristic function of D can be computed (in the case of finite data only approximately). The book also introduces some alternative Sampling Methods.</p>Andreas Kirsch and Natalia Grinberg2008-09-01Stochastic Population Processes
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<table><tr><td width="200px"><img width="150px" src="/view/covers/9780199575312.jpg" alt="Stochastic Population ProcessesAnalysis, Approximations, Simulations"/><br/></td><td><dl><dt>Author:</dt><dd>Eric Renshaw</dd><dt>ISBN:</dt><dd>9780199575312</dd><dt>Publisher:</dt><dd>Oxford University Press</dd><dt>Subjects:</dt><dd>Mathematics, Applied Mathematics, Mathematical Biology</dd><dt>DOI:</dt><dd>10.1093/acprof:oso/9780199575312.001.0001</dd><dt>Published in print:</dt><dd>2011</dd><dt>Published Online:</dt><dd>2011-09-22</dd></dl></td></tr></table><p>The vast majority of random processes in the real world have no memory — the next step in their development depends purely on their current state. Stochastic realizations are therefore defined purely in terms of successive event-time pairs, and such systems are easy to simulate irrespective of their degree of complexity. However, whilst the associated probability equations are straightforward to write down, their solution usually requires the use of approximation and perturbation procedures. Traditional books, heavy in mathematical theory, often ignore such methods and attempt to force problems into a rigid framework of closed-form solutions.</p>Eric Renshaw2011-09-22Inverse Eigenvalue Problems
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<table><tr><td width="200px"><img width="150px" src="/view/covers/9780198566649.jpg" alt="Inverse Eigenvalue ProblemsTheory, Algorithms, and Applications"/><br/></td><td><dl><dt>Author:</dt><dd>Moody Chu, Gene Golub</dd><dt>ISBN:</dt><dd>9780198566649</dd><dt>Publisher:</dt><dd>Oxford University Press</dd><dt>Subjects:</dt><dd>Mathematics, Applied Mathematics</dd><dt>DOI:</dt><dd>10.1093/acprof:oso/9780198566649.001.0001</dd><dt>Published in print:</dt><dd>2005</dd><dt>Published Online:</dt><dd>2007-09-01</dd></dl></td></tr></table><p>The basic goal of an inverse eigenvalue problem is to reconstruct the physical parameters of a certain system from the knowledge or desire of its dynamical behavior. Depending on the application, inverse eigenvalue problems appear in many different forms. This book discusses the fundamental questions, some known results, many applications, mathematical properties, a variety of numerical techniques, as well as several open problems.</p>Moody Chu and Gene Golub2007-09-01Procrustes Problems
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<table><tr><td width="200px"><img width="150px" src="/view/covers/9780198510581.jpg" alt="Procrustes Problems"/><br/></td><td><dl><dt>Author:</dt><dd>John C Gower, Garmt B Dijksterhuis</dd><dt>ISBN:</dt><dd>9780198510581</dd><dt>Publisher:</dt><dd>Oxford University Press</dd><dt>Subjects:</dt><dd>Mathematics, Probability / Statistics</dd><dt>DOI:</dt><dd>10.1093/acprof:oso/9780198510581.001.0001</dd><dt>Published in print:</dt><dd>2004</dd><dt>Published Online:</dt><dd>2007-09-01</dd></dl></td></tr></table><p>Procrustean methods are used to transform one set of data to represent another set of data as closely as possible. This book unifies several strands in the literature and contains new algorithms. It focuses on matching two or more configurations by using orthogonal, projection, and oblique axes transformations. Group-average summaries play an important part, and links with other group-average methods are discussed. The text is multi-disciplinary and also presents a unifying ANOVA framework.</p>John C Gower and Garmt B Dijksterhuis2007-09-01Mathematical Methods for the Magnetohydrodynamics of Liquid Metals
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<table><tr><td width="200px"><img width="150px" src="/view/covers/9780198566656.jpg" alt="Mathematical Methods for the Magnetohydrodynamics of Liquid Metals"/><br/></td><td><dl><dt>Author:</dt><dd>Jean-Frédéric Gerbeau, Claude Le Bris, Tony Lelièvre</dd><dt>ISBN:</dt><dd>9780198566656</dd><dt>Publisher:</dt><dd>Oxford University Press</dd><dt>Subjects:</dt><dd>Mathematics, Mathematical Physics</dd><dt>DOI:</dt><dd>10.1093/acprof:oso/9780198566656.001.0001</dd><dt>Published in print:</dt><dd>2006</dd><dt>Published Online:</dt><dd>2007-09-01</dd></dl></td></tr></table><p>This text focuses on mathematical and numerical techniques for the simulation of magnetohydrodynamic phenomena, with an emphasis on the magnetohydrodynamics of liquid metals, on two-fluid flows, and on a prototypical industrial application. The approach is a highly mathematical one, based on the rigorous analysis of the equations at hand, and a solid numerical analysis of the discretization methods. Up-to-date techniques, both on the theoretical side and the numerical side, are introduced to deal with the nonlinearities of the multifluid magnetohydrodynamics equations. At each stage of the exposition, examples of numerical simulations are provided, first on academic test cases to illustrate the approach, next on benchmarks well documented in the professional literature, and finally on real industrial cases. The simulation of aluminium electrolysis cells is used as a guideline throughout the book to motivate the study of a particular setting of the magnetohydrodynamics equations.</p>Jean-Frédéric Gerbeau, Claude Le Bris, and Tony Lelièvre2007-09-01Random Geometric Graphs
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<table><tr><td width="200px"><img width="150px" src="/view/covers/9780198506263.jpg" alt="Random Geometric Graphs"/><br/></td><td><dl><dt>Author:</dt><dd>Mathew Penrose</dd><dt>ISBN:</dt><dd>9780198506263</dd><dt>Publisher:</dt><dd>Oxford University Press</dd><dt>Subjects:</dt><dd>Mathematics, Probability / Statistics</dd><dt>DOI:</dt><dd>10.1093/acprof:oso/9780198506263.001.0001</dd><dt>Published in print:</dt><dd>2003</dd><dt>Published Online:</dt><dd>2007-09-01</dd></dl></td></tr></table><p>This book sets out a body of rigorous mathematical theory for finite graphs with nodes placed randomly in Euclidean d-space according to a common probability density, and edges added to connect points that are close to each other. As an alternative to classical random graph models, these geometric graphs are relevant to the modelling of real networks having spatial content, arising for example in wireless communications, parallel processing, classification, epidemiology, astronomy, and the internet. Their study illustrates numerous techniques of modern stochastic geometry, including Stein's method, martingale methods, and continuum percolation. Typical results in the book concern properties of a graph G on n random points with edges included for interpoint distances up to r, with the parameter r dependent on n and typically small for large n. Asymptotic distributional properties are derived for numerous graph quantities. These include the number of copies of a given finite graph embedded in G, the number of isolated components isomorphic to a given graph, the empirical distributions of vertex degrees, the clique number, the chromatic number, the maximum and minimum degree, the size of the largest component, the total number of components, and the connectivity of the graph.</p>Mathew Penrose2007-09-01Probabilistic Graphical Models for Genetics, Genomics, and Postgenomics
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<table><tr><td width="200px"><img width="150px" src="/view/covers/9780198709022.jpg" alt="Probabilistic Graphical Models for Genetics, Genomics, and Postgenomics"/><br/></td><td><dl><dt>Author:</dt><dd>ChristineSinoquetChristine SinoquetUniversity of NantesRaphaëlMouradRaphaël MouradDepartment of Human Genetics, University of Chicago</dd><dt>ISBN:</dt><dd>9780198709022</dd><dt>Publisher:</dt><dd>Oxford University Press</dd><dt>Subjects:</dt><dd>Mathematics, Probability / Statistics, Biostatistics</dd><dt>DOI:</dt><dd>10.1093/acprof:oso/9780198709022.001.0001</dd><dt>Published in print:</dt><dd>2014</dd><dt>Published Online:</dt><dd>2014-12-18</dd></dl></td></tr></table><p>At the crossroads between statistics and machine learning, probabilistic graphical models provide a powerful formal framework to model complex data. Probabilistic graphical models are probabilistic models whose graphical components denote conditional independence structures between random variables. The probabilistic framework makes it possible to deal with data uncertainty while the conditional independence assumption helps process high dimensional and complex data. Examples of probabilistic graphical models are Bayesian networks and Markov random fields, which represent two of the most popular classes of such models. With the rapid advancements of high-throughput technologies and the ever decreasing costs of these next generation technologies, a fast-growing volume of biological data of various types—the so-called omics—is in need of accurate and efficient methods for modeling, prior to further downstream analysis. Network reconstruction from gene expression data represents perhaps the most emblematic area of research where probabilistic graphical models have been successfully applied. However these models have also created renew interest in genetics, in particular: association genetics, causality discovery, prediction of outcomes, detection of copy number variations, epigenetics, etc.. For all these reasons, it is foreseeable that such models will have a prominent role to play in advances in genome-wide analyses.</p>Christine Sinoquet and Raphaël Mourad2014-12-18Bayesian Statistics 9
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<table><tr><td width="200px"><img width="150px" src="/view/covers/9780199694587.jpg" alt="Bayesian Statistics 9"/><br/></td><td><dl><dt>Author:</dt><dd>José M.BernardoJosé M. BernardoUniversitat de ValènciaM. J.BayarriM. J. BayarriUniversitat de ValènciaJames O.BergerJames O. BergerDuke UniversityA. P.DawidA. P. DawidUniversity of CambridgeDavidHeckermanDavid HeckermanMicrosoft ResearchAdrian F. M.SmithAdrian F. M. SmithUK Department of Business, Innovation and SkillsMikeWestMike WestDuke University</dd><dt>ISBN:</dt><dd>9780199694587</dd><dt>Publisher:</dt><dd>Oxford University Press</dd><dt>Subjects:</dt><dd>Mathematics, Probability / Statistics</dd><dt>DOI:</dt><dd>10.1093/acprof:oso/9780199694587.001.0001</dd><dt>Published in print:</dt><dd>2011</dd><dt>Published Online:</dt><dd>2012-01-19</dd></dl></td></tr></table><p>The Valencia International Meetings on Bayesian Statistics – established in 1979 and held every four years – have been the forum for a definitive overview of current concerns and activities in Bayesian statistics. These are the edited Proceedings of the Ninth meeting, and contain the invited papers each followed by their discussion and a rejoinder by the author(s). In the tradition of the earlier editions, this encompasses an enormous range of theoretical and applied research, highlighting the breadth, vitality and impact of Bayesian thinking in interdisciplinary research across many fields as well as the corresponding growth and vitality of core theory and methodology. The Valencia 9 invited papers cover a broad range of topics, including foundational and core theoretical issues in statistics, the continued development of new and refined computational methods for complex Bayesian modelling, substantive applications of flexible Bayesian modelling, and new developments in the theory and methodology of graphical modelling. They also describe advances in methodology for specific applied fields, including financial econometrics and portfolio decision making, public policy applications for drug surveillance, studies in the physical and environmental sciences, astronomy and astrophysics, climate change studies, molecular biosciences, statistical genetics or stochastic dynamic networks in systems biology.</p>José M. Bernardo, M. J. Bayarri, James O. Berger, A. P. Dawid, David Heckerman, Adrian F. M. Smith, and Mike West2012-01-19Numerical Methods for Structured Markov Chains
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<table><tr><td width="200px"><img width="150px" src="/view/covers/9780198527688.jpg" alt="Numerical Methods for Structured Markov Chains"/><br/></td><td><dl><dt>Author:</dt><dd>Dario A. Bini, Guy Latouche, Beatrice Meini</dd><dt>ISBN:</dt><dd>9780198527688</dd><dt>Publisher:</dt><dd>Oxford University Press</dd><dt>Subjects:</dt><dd>Mathematics, Numerical Analysis</dd><dt>DOI:</dt><dd>10.1093/acprof:oso/9780198527688.001.0001</dd><dt>Published in print:</dt><dd>2005</dd><dt>Published Online:</dt><dd>2007-09-01</dd></dl></td></tr></table><p>The book deals with the numerical solution of structured Markov chains which include M/G/1 and G/M/1-type Markov chains, QBD processes, non-skip-free queues, and tree-like stochastic processes and has a wide applicability in queueing theory and stochastic modeling. It presents in a unified language the most up to date algorithms, which are so far scattered in diverse papers, written with different languages and notation. It contains a thorough treatment of numerical algorithms to solve these problems, from the simplest to the most advanced and most efficient. Nonlinear matrix equations are at the heart of the analysis of structured Markov chains, they are analysed both from the theoretical, from the probabilistic, and from the computational point of view. The set of methods for solution contains functional iterations, doubling methods, logarithmic reduction, cyclic reduction, and subspace iteration, all are described and analysed in detail. They are also adapted to interesting specific queueing models coming from applications. The book also offers a comprehensive and self-contained treatment of the structured matrix tools which are at the basis of the fastest algorithmic techniques for structured Markov chains. Results about Toeplitz matrices, displacement operators, and Wiener-Hopf factorizations are reported to the extent that they are useful for the numerical treatment of Markov chains. Every and all solution methods are reported in detailed algorithmic form so that they can be coded in a high-level language with minimum effort.</p>Dario A. Bini, Guy Latouche, and Beatrice Meini2007-09-01