Series: Lecture Notes in Mathematics, Vol. 1936
Subseries: Mathematical Biosciences Subseries
2008, Approx. 345 p., Softcover
ISBN: 978-3-540-78272-8
Due: May 7, 2008
About this book
This book consists of six chapters written by leading researchers in mathematical biology. These chapters present recent and important developments in the study of structured population models in biology and epidemiology. Topics include population models structured by age, size, and spatial position; size-structured models for metapopulations, macroparasitc diseases, and prion proliferation; models for transmission of microparasites between host populations living on non-coincident spatial domains; spatiotemporal patterns of disease spread; method of aggregation of variables in population dynamics; and biofilm models.
It is suitable as a textbook for a mathematical biology course or a summer school at the advanced undergraduate and graduate level. It can also serve as a reference book for researchers looking for either interesting and specific problems to work on or useful techniques and discussions of some particular problems.
Table of contents
Population Models Structured by Age, Size, and Spatial Position (Glenn Webb).- Infinite ODE Systems Modeling Size-structured Metapopulations, Macroparasitic Diseases, and Prion Proliferation (Maia Martcheva and Horst Thieme).- Simple Models for the Transmission of Microparasites between Host Populations Living on Non-coincident Spatial Domains (William E. Fitzgibbon and Michel Langlais).- Spatiotemporal Patterns of Disease Spread: Interaction of Physiological Structure, Spatial Movements, Disease Progression and Human Intervention (Stephen A. Gourley, Rongsong Liu, and Jianhong Wu).- Aggregation of Variables and Applications to Population Dynamics (Pierre Auger, Rafael Bravo de la Parra, Jean-Christophe Poggiale, Eva Sanchez, and T. Nguyen-Huu).- The Biofilm Model of Freter: A Review (Mary Ballyk, Don Jones, and Hal Smith).
Series: Lecture Notes in Mathematics , Vol. 1941
2008, Approx. 190 p., Softcover
ISBN: 978-3-540-78378-7
Due: May 7, 2008
About this book
In this volume the author further develops his philosophy of quantum interpolation between the real numbers and the p-adic numbers. The p-adic numbers contain the p-adic integers $Zp$ which are the inverse limit of the finite rings $Z/pn$. This gives rise to a tree, and probability measures w on $Zp$ correspond to Markov chains on this tree. From the tree structure one obtains special basis for the Hilbert space $L2(Zp,w)$. The real analogue of the p-adic integers is the interval [-1,1], and a probability measure w on it gives rise to a special basis for $L2([-1,1],w)$ - the orthogonal polynomials, and to a Markov chain on "finite approximations" of [-1,1]. For special (gamma and beta) measures there is a "quantum" or "q-analogue" Markov chain, and a special basis, that within certain limits yield the real and the p-adic theories. This idea can be generalized variously. In representation theory, it is the quantum general linear group $GLn(q)$ that interpolates between the p-adic group $GLn(Zp)$, and between its real (and complex) analogue -the orthogonal $On$ (and unitary $Un$ )groups. There is a similar quantum interpolation between the real and p-adic Fourier transform and between the real and p-adic (local unramified part of) Tate thesis, and Weil explicit sums.
Table of contents
Introduction: Motivations from Geometry.- Gamma and Beta Measures.- Markov Chains.- Real Beta cchain and q-Interpolation.- Ladder Structure.- q-Interpolation of Local Tate Thesis.- Pure Basis and Semi-group.- Higher Dimentional Theory.- Real Grassmann Manifold.- p-Adic Grasmann Manifold.- q-Grassmann Manifold.- Quantum Group Uq(su1,1) and the q-Hahn Basis.- Problems and Questions.- Orthogonal Polynomials.- Record.- Bibliography.- Index
Series: Springer Series in Statistics
2008, Approx. 370 p., Hardcover
ISBN: 978-0-387-77500-5
Due: June 2008
About this book
-An Accesible discussion of statistical learning procedures for practitioners.
-Lots of real applications discussed.
-Intuitive explanations and visual representation of underlying statistical concepts.
Statistical Learning from a Regression Perspective considers statistical learning applications when interest centers on the conditional distribution of the response variable, given a set of predictors, and when it is important to characterize how the predictors are related to the response. As a first approximation, this is can be seen as an extension of nonparametric regression. Among the statistical learning procedures examined are bagging, random forests, boosting, and support vector machines. Response variables may be quantitative or categorical.
Real applications are emphasized, especially those with practical implications. One important theme is the need to explicitly take into account asymmetric costs in the fitting process. For example, in some situations false positives may be far less costly than false negatives. Another important theme is to not automatically cede modeling decisions to a fitting algorithm. In many settings, subject-matter knowledge should trump formal fitting criteria. Yet another important theme is to appreciate the limitation of one’s data and not apply statistical learning procedures that require more than the data can provide.
The material is written for graduate students in the social and life sciences and for researchers who want to apply statistical learning procedures to scientific and policy problems. Intuitive explanations and visual representations are prominent. All of the analyses included are done in R.
Richard Berk is Distinguished Professor of Statistics Emeritus from the Department of Statistics at UCLA and currently a Professor at the University of Pennsylvania in the Department of Statistics and in the Department of Criminology. He is an elected fellow of the American Statistical Association and the American Association for the Advancement of Science and has served in a professional capacity with a number of organizations such as the Committee on Applied and Theoretical Statistics for the National Research Council and the Board of Directors of the Social Science Research Council. His research has ranged across a variety of applications in the social and natural sciences.
Table of contents
Statistical learning as a regression problem - Regression splines and regression smoothers - Classification and regression trees (CART) - Bagging - Random forests - Boosting - Support vector machines - Broader implications and a bit of craft lore.
Series: Applied and Numerical Harmonic Analysis
2008, Approx. 350 p. 10 illus., Hardcover
ISBN: 978-0-8176-4682-0
Due: July 2008
About this book
The work of Lawrence Baggett has had a profound impact on the field of abstract harmonic analysis and the many areas of mathematics that use its techniques. His sphere of influence ranges from purely theoretical results regarding the representations of locally compact groups to recent applications of wavelets and frames to problems in sampling theory and image compression. Contributions in this volume reflect this broad scope, and Larry’s unusual ability to bring together techniques from disparate fields.
Topics in theoretical harmonic analysis, wavelets and frames include: groups with atomic regular representations, Gelfand pairs associated with finite Heisenberg groups, convergence of Riemann sums, the density theorem for Gabor frames, applications of sampling in multiresolution spaces, and oblique extension principles on dual wavelet frames.
Table of contents
Foreword.-Preface.-Mathematical Family Tree of Lawrence W. Baggett.-Publications of Lawrence W. Baggett.-Co-Workers of Lawrence W. Baggett.-Titles of All Talks.-Part I. Classical and Abstract Harmonic Analysis.- Some Riemann Sums Are Better than Others by V.W. Gullemin and D.W. Stroock.-Gelfand Pairs Associated with Finite Heisenberg Groups by C. Benson and G. Ratcliff.-Groups with Atomic Regular Representation by K.F. Taylor.-Wavelet Transforms and Admissible Group Representations by E. Weber.-Part II: Frames and Multiresolution Structures.-The Density Theorem and the Homogeneous Approximation Property for Gabor Frames by C. Heil.-Recent Developments on Dual Wavelet Frames by Bin Han.-Characteristic Wavelet Equations and Generalizations of the Spectral Function by V. Furst.-Baggett’s Problem for Frame Wavelets by M. Bownik.-Part III: Wavelet Sets.-Simple Wavelet Sets for Scalar Dilations in R^2 by K.D. Merrill.-Interpolation Maps and Congruence Domains for Wavelet Sets by X. Zhang and D.R. Larson.-Part IV: Applications to Dynamical Systems and C*-Algebras.-Orthogonal Exponentials for Bernoulli Iterated Function Systems by P. E.T. Jorgensen, K. Kornelson, and K. Shuman.-A Survey of Projective Multiresolution Analysis Corresponding with the Quincunx Lattice by J.A. Packer.-Part V: Signal and Image Processing.-Sampling and Time-Frequency Localization of Bandlimited and Multiband Signals by J.A. Hogan and J.D. Lakey.-Entropy Encoding in Wavelet Image Compression by M.-S. Song.-Index.
Series: Operator Theory: Advances and Applications, Vol. 183
Subseries: Advances in Partial Differential Equations
2008, Approx. 240 p., Hardcover
ISBN: 978-3-7643-8774-7
Due: June 2008
About this book
The book deals with nonlocal elliptic differential operators. These are operators whose coefficients involve shifts generated by diffeomorphisms of the manifold on which the operators are defined. The main goal of the study is to relate analytical invariants (in particular, the index) of such operators to topological invariants of the manifold itself. This problem can be solved by modern methods of noncommutative geometry. To make the book self-contained, the authors have included necessary geometric material (C*-algebras and their K-theory, cyclic homology, etc.).
Table of contents
Preface.- Introduction.- I. Analysis of Nonlocal Elliptic Operators.- 1. Nonlocal Functions and Bundles.- 2. Nonlocal Elliptic Operators.- 3. Elliptic Operators over C*-Algebras.- II. Homotopy Invariants of Nonlocal Elliptic Operators.- 5. Analytic Invariants.- 6. Bott Periodicity.- 7. Direct Image and Index Formulas in K-Theory.- 8. Chern Character.- 9. Cohomological Index Formula.- 10. Cohomological Formula for the Lambda-Index.- 11. Index of Nonlocal Operators over C*-Algebras.- III. Examples.- 12. Index Formula on the Noncommutative Torus.- 13. An Application of Higher Traces.- 14. Index Formula for a Finite Group Gamma.- IV. Appendices.- A. C*-Algebras.- A.1 Basic Notions.- A.2 Representations of C*-Algebras.- A.3 Tensor Products and Nuclear Algebras.- B. K-Theory of Operator Algebras.- B.1 Covariant K-Theory.- B.2 K-Homology.- C. Cyclic Homology and Cohomology.- C.1 Cyclic Cohomology.- C.2 Cyclic Homology.- Concise Bibliographical Remarks.- Bibliography.- Index