Book
xvi, 293 pages : illustrations (some color) ; 26 cm.
  • * Preface* Acknowledgements* Commonly Used Symbols* Chapter 1: Phylogeny* Chapter 2: Basic combinatorics of discrete phylogenies* Chapter 3: Tree shape and random discrete phylogenies* Chapter 4: Pulling trees apart and putting trees together* Chapter 5: Phylogenies based on discrete characters* Chapter 6: Continuous phylogenies and distance-based tree reconstruction* Chapter 7: Evolution on a tree: Part one* Chapter 8: Evolution on a tree: Part two* Chapter 9: Evolution of trees* Chapter 10: Introduction to phylogenetic networks* Bibliography* Index.
  • (source: Nielsen Book Data)9781611974478 20170731
Phylogenetics is a topical and growing area of research. Phylogenies (phylogenetic trees and networks) allow biologists to study and graph evolutionary relationships between different species. These are also used to investigate other evolutionary processes - for example, how languages developed or how different strains of a virus (such as HIV or influenza) are related to each other. This self-contained book addresses the underlying mathematical theory behind the reconstruction and analysis of phylogenies. The theory is grounded in classical concepts from discrete mathematics and probability theory as well as techniques from other branches of mathematics (algebra, topology, differential equations). The biological relevance of the results is highlighted throughout. In Phylogeny: Discrete and Random Processes in Evolution, the author:* Supplies proofs of key classical theorems and includes results not covered in existing boosk* Emphasizes relevant mathematical results derived over the past 20 years. * Provides numerous exercises, examples, and figures.
(source: Nielsen Book Data)9781611974478 20170731
Science Library (Li and Ma)
Book
xvi, 240 pages : illustrations (some color) ; 26 cm.
  • List of figures-- Preface-- Part I. Introduction: 1. Why use mathematics in medical imaging?-- 2. A brief and incomplete history of CT-- 3. Some major CT modalities and their features to watch for-- 4. Organization of the book-- Part II. Traditional Computed Tomography Techniques and Integral Geometry: 5. 'Standard' CT and X-ray and Radon transforms-- 6. Emission tomography-- 7. Artifacts, incomplete data, microlocal analysis, and such-- 8. More about 3D Radon and X-ray transforms-- 9. A brief overview of numerical methods-- 10. MRI, EIT, OT, elastography, UT-- Part III. Hybrid (Coupled Physics) Imaging Techniques: 11. Thermo-, photo-, and optoacoustic tomography (TAT/PAT/OAT)-- 12. Ultrasound modulation in EIT and OT-- 13. Inverse problems with interior information-- Part IV. Appendices: A. Notation-- B. Brief notes on the Fourier transform and harmonic analysis-- C. Geometric rays, trapping, energy decay-- D. Some classes of linear operators and operator functions-- E. Recommended books and surveys-- Bibliography-- Index.
  • (source: Nielsen Book Data)9781611973280 20160612
The Radon transform, which represents the scattering data arising from a tomographic scan, underpins the mathematical foundations of medical imaging. This book surveys the mathematics behind some well-established imaging modalities such as X-ray CT and emission tomography, as well as a variety of newly developing coupled physics or hybrid techniques, including thermoacoustic tomography. Presented in this treatment are explanations of important concepts such as inversion, stability, incomplete data effects, the role of interior information, and other critical issues. In addition to emphasising mathematical ideas from across the spectrum of medical imaging modalities, the author provides a vast bibliography, and appendices covering notation, Fourier analysis, geometric rays, and linear operators. Graduate students and researchers in mathematics, physics, and engineering who are interested in medical imaging will find this book to be an invaluable resource.
(source: Nielsen Book Data)9781611973280 20160612
Science Library (Li and Ma)
Book
xviii, 270 p. : ill. (some col.) ; 25 cm.
  • Preface-- 1. Compartmental epidemic models-- 2. Models for endemic diseases-- 3. Heterogeneity in epidemic models-- 4. Models structured by age-- 5. Models for diseases in highly mobile populations-- 6. Modeling influenza-- 7. Models for the dynamics of influenza-- 8. Models for the transmission dynamics of HIV-- 9. Dynamical models of tuberculosis and applications-- 10. Models for sexually transmitted diseases-- Index.
  • (source: Nielsen Book Data)9781611972412 20160610
This self-contained textbook provides a comprehensive guide to the mathematical theory of disease transmission models. General theory is presented alongside models for specific diseases and related phenomena, with exposition that is accessible to those who are comfortable with calculus, elementary differential equations and linear algebra. The reader will gain insight into the modeling of: cross-immunity between different disease strains (such as influenza); synergistic interactions between multiple diseases (such as HIV and tuberculosis); diseases transmitted by viral agents, bacteria and vectors; and, both epidemic and endemic disease occurrences. This text is ideal for a graduate level course for students in mathematics, or for students of epidemiology with strong mathematics backgrounds. The material within will also be of interest to researchers in epidemiology and related areas, and those involved with the development of public health policy.
(source: Nielsen Book Data)9781611972412 20160610
Science Library (Li and Ma)
Book
ix, 127 p. : ill. ; 26 cm.
  • Preface-- 1. Introduction-- 2. Overview on spaces-- 3. The MAP on subspaces-- 4. Row-action methods-- 5. Projecting on convex sets-- 6. Applications of MAP for matrix problems-- Bibliography-- Author index-- Subject index.
  • (source: Nielsen Book Data)9781611971934 20160608
This comprehensive textbook describes and analyzes all available alternating projection methods for solving the general problem of finding a point in the intersection of several given sets that belong to a Hilbert space. For each method, the authors describe and analyze the issues of convergence, speed of convergence, acceleration techniques, stopping criteria and applications. Different types of algorithms and applications are studied for subspaces, linear varieties and general convex sets. The authors also unify these algorithms in a common theoretical framework. Many examples and problems are included in order to reinforce student learning. This book can be used as a textbook for graduate or advanced undergraduate students. Because it is comprehensive, it can also be used as a tutorial or a reference by mathematicians and non-mathematicians from many fields of applications who need to solve alternating projection problems in their work.
(source: Nielsen Book Data)9781611971934 20160608
Science Library (Li and Ma)
Book
xii, 213 p. : ill. ; 26 cm.
  • Preface-- List of symbols-- 1. Introduction and motivation-- 2. Meet the Fredholm integral equation of the first kind-- 3. Getting to business: discretizations of linear inverse problems-- 4. Computational aspects: regularization methods-- 5. Getting serious: choosing the regularization parameter-- 6. Toward real-world problems: iterative regularization-- 7. Regularization methods at work: solving real problems-- 8. Beyond the 2-norm: the use of discrete smoothing norms-- Appendix A. Linear algebra stuff-- Appendix B. Symmetric Toeplitz-plus-Hankel matrices and the DCT-- Appendix C. Early work on 'Tikhonov regularization'-- Bibliography-- Index.
  • (source: Nielsen Book Data)9780898716962 20160604
This acclaimed book introduces the practical treatment of inverse problems by means of numerical methods, with a focus on basic mathematical and computational aspects. To solve inverse problems, it demonstrates that insight about them and algorithms go hand in hand. Discrete Inverse Problems includes a number of tutorial exercises that give the reader hands-on experience with the methods, and challenges associated with the treatment of inverse problems. It includes carefully constructed illustrative computed examples and figures that highlight the important issues in the theory and algorithms. This book is written for graduate students, researchers, and professionals in engineering and other areas that depend on solving inverse problems with noisy data. It aims to provide readers with enough background that they can solve simple inverse problems and read more advanced literature on the subject.
(source: Nielsen Book Data)9780898716962 20160604
Science Library (Li and Ma)
Book
xi, 336 p. : ill. ; 26 cm.
  • Preface-- 1. Introduction to MATLAB-- 2. Linear equations-- 3. Interpolation-- 4. Zeros and roots-- 5. Least squares-- 6. Quadrature-- 7. Ordinary differential equations-- 8. Fourier analysis-- 9. Random numbers-- 10. Eigenvalues and singular values-- 11. Partial differential equations-- Bibliography-- Index.
  • (source: Nielsen Book Data)9780898716603 20160609
This is a lively textbook for an introductory course in numerical methods, MATLAB and technical computing, which emphasises the informed use of mathematical software. Numerical Computing with MATLAB helps readers learn about the mathematical functions in MATLAB, how to appreciate their limitations, and how to use and modify them appropriately. The book makes extensive use of computer graphics, and provides more than 70 M-files, which can be downloaded from the text website www.mathworks.com/moler. Many of the numerous exercises involve modifying and extending these programs. The theory can be adapted to apply to modern problems from cryptography, touch-tone dialing, Google page-ranking, atmospheric science and image processing, as well as classical problems from physics and engineering. This book will appeal to advanced undergraduate and beginning graduate students in science and engineering. This revision includes changes and corrections made since the book was originally published in 2004.
(source: Nielsen Book Data)9780898716603 20160609
Science Library (Li and Ma)
Video
1 videodisc (26 min.) : sd., col. ; 4 3/4 in.
Contains interviews with mathematicians working in industry, business and government. The purpose of the video is to allow the viewer to hear from people working outside academia what their day-to-day work life is like and how their background in mathematics contributes to their ability to do their job. Interviews were conducted on site, showing the work environment and some of the projects mathematicians were contributing to as part of multidisciplinary teams. People interviewed come from industrial based firms such as Kodak and Boeing, business and financial firms such as Price Waterhouse and D.E. Shaw & Co., and government agencies such as the National Institute of Standards and Technology and the Naval Sea System Command.
Science Library (Li and Ma)
Book
353 p. : ill. ; 26 cm.
Science Library (Li and Ma)
Book
xiv, 157 p. : ill. ; 26 cm.
  • Preface-- 1. Introduction J .E. Castillo and S. Steinberg-- 2. Elliptic Grid Generation and Conformal Mapping C. W. Mastin-- 3. Continuum Variational Formulation J. E. Castillo-- 4. Discrete Variational Grid Generation J. E. Castillo-- 5. Bifurcation of Grids on Curves S. Steinberg and P. J. Roache-- 6. Intrinsic Algebraic Grid Generation P. M. Knupp-- 7. Surface Grid Generation and Differential Geometry Z. U. A. Warsi-- 8. Harmonic Maps in Grid Generation A. Dvinsky-- 9. On Harmonic Maps G. Liao-- 10. Mathematical Aspects of Harmonic Grid Generation S. S. Sritharan-- References-- Index.
  • (source: Nielsen Book Data)9780898712674 20160528
Numerical grid generation plays a critical role in any scientific computing problem when the geometry of the underlying region is complex or when the solution has a complex structure. The mathematical aspects of grid generation are discussed to provide a deeper understanding of the algorithms and their imitations. Variational methods are emphasized because they are more robust, but elliptic and transcendental algebraic methods are also considered.
(source: Nielsen Book Data)9780898712674 20160528
Science Library (Li and Ma)
Book
xxxv, 730 p. : ill. ; 25 cm.
  • A construction of integrable differential system associated with braid groups by K. Aomoto Mapping class groups of surfaces by J. S. Birman Automorphic sets and braids and singularities by E. Brieskorn The operator algebras of the two-dimensional Ising model by A. L. Carey and D. E. Evans Artin's braid groups, classical homotopy theory, and sundry other curiosities by F. R. Cohen Classification of solvorbifolds in dimension three, I by W. D. Dunbar Pure braid groups and products of free groups by M. Falk and R. Randell Polynomial covering maps by L. V.Hansen Arithmetic analogues of braid groups and Galois representations by Y. Ihara Application of braids to fixed points of surface maps by B. Jiang Statistical mechanics and the Jones polynomial by L. H. Kauffman Hurwitz action and finite quotients of braid groups by P. Kluitmann Heights of simple loops and pseudo-Anosov homeomorphisms by T. Kobayashi Linear representations of braid groups and classical Yang-Baxter equations by T. Kohno A survey of Hecke algebras and the Artin braid groups by G. I. Lehrer On divisibility properties of braids associated with algebraic curves by A. Libgober The panorama of polynomials for knots, links, and skeins by W. B. R. Lickorish The structure of deleted symmetric products by R. J. Milgram and P. Loffler Braid group technique in complex geometry, I: Line arrangements in $CP^2$ by B. Moishezon and M. Teicher Problems by H. R. Morton Polynomials from braids by H. R. Morton The Jones polynomial of satellite links around mutants by H. R. Morton and P. Traczyk On the deformation of certain type of algebraic varieties by M. Oka Braids and discriminants by P. Orlik and L. Solomon $t_k$ moves on links by J. H. Przytycki Mutually braided open books and new invariants of fibered links by L. Rudolph Generalized braid groups and self-energy Feynman integrals by M. Salvetti Markov classes in certain finite symplectic representations of braid groups by B. Wajnryb The braid index of an algebraic link by R. F. Williams Markov algebras by D. N. Yetter.
  • (source: Nielsen Book Data)9780821850886 20160528
Artin introduced braid groups into mathematical literature in 1925. In the years since, and particularly in the last five to ten years, braid groups have played diverse and unexpected roles in widely different areas of mathematics, including knot theory, homotopy theory, singularity theory, and dynamical systems. Most recently, the area of operator algebras has brought striking new applications to knots and links. This volume contains the proceedings of the AMS-IMS-SIAM Joint Summer Research Conference on Artin's Braid Group, held at the University of California, Santa Cruz, in July 1986. This interdisciplinary conference brought together leading specialists in diverse areas of mathematics to discuss their discoveries and to exchange ideas and problems concerning this important and fundamental group.Because the proceedings present a mix of expository articles and new research, this volume will be of interest to graduate students and researchers who wish to learn more about braids, as well as more experienced workers in this area. The required background includes the basics of knot theory, group theory, and low-dimensional topology.
(source: Nielsen Book Data)9780821850886 20160528
Science Library (Li and Ma)
Book
xi, 394 p. : ill. ; 26 cm.
  • Dilators, generalized Goodstein sequences, independence results: A survey by V. M. Abrusci Some uses of dilators in combinatorial problems, part I by V. M. Abrusci, J.-Y. Girard, and J. Van de Wiele Cross products of Souslin trees by B. Ackman and J. Owings Ergodic Ramsey theory by V. Bergelson Ultrafilters related to Hindman's finite unions theorem and its extensions by A. Blass Logical analysis of some theorems of combinatorics and topological dynamics by A. R. Blass, J. L. Hirst, and S. G. Simpson A remark on partition relations for infinite ordinals, with an application to finite combinatorics by J. E. Baumgartner and A. Hajnal A summary of "On Ramsey-type Theorems and Their Provability in Weak Formal Systems" by S. H. Brackin Provably computable functions and the fast growing hierarchy by W. Buchholz and S. Wainer Rigid Borel sets and better quasiorder theory by F. van Engelen, A. W. Miller, and J. Steel Some problems on finite and infinite graphs by P. Erdos The metamathematics of the graph minor theorem by H. Friedman, N. Robertson, and P. D. Seymour Summable ultrafilters and finite sums by N. Hindman On undecidability of the weakened Kruskal theorem by M. Loebl and J. Matousek Well quasi orderings, long games, and a combinatorial study of undecidability by J. Nesetril and R. Thomas On the theory of quasi ordinal diagrams by M. Okada and G. Takeuti Improved bounds to the length of proofs of finitistic consistency statements by P. Pudlak Non standard universes with strong embeddings, and their finite approximations by J.-P. Ressayre Unprovable theorems and fast-growing functions by S. G. Simpson.
  • (source: Nielsen Book Data)9780821850527 20160528
In recent years, several remarkable results have shown that certain theorems of finite combinatorics are unprovable in certain logical systems. These developments have been instrumental in stimulating research in both areas, with the interface between logic and combinatorics being especially important because of its relation to crucial issues in the foundations of mathematics which were raised by the work of Kurt Godel. Because of the diversity of the lines of research that have begun to shed light on these issues, there was a need for a comprehensive overview which would tie the lines together. This volume fills that need by presenting a balanced mixture of high quality expository and research articles that were presented at the August 1985 AMS-IMS-SIAM Joint Summer Research Conference, held at Humboldt State University in Arcata, California.With an introductory survey to put the works into an appropriate context, the collection consists of papers dealing with various aspects of 'unprovable theorems and fast-growing functions'. Among the topics addressed are: ordinal notations, the dynamical systems approach to Ramsey theory, Hindman's finite sums theorem and related ultrafilters, well quasiordering theory, uncountable combinatorics, nonstandard models of set theory, and a length-of-proof analysis of Godel's incompleteness theorem. Many of the articles bring the reader to the frontiers of research in this area, and most assume familiarity with combinatorics and/or mathematical logic only at the senior undergraduate or first-year graduate level.
(source: Nielsen Book Data)9780821850527 20160528
Science Library (Li and Ma)
Book
xvi, 448 p. : ill. ; 25 cm.
  • Part I. Geometric-Analytic Methods: Stability of Poisson-Hamilton equilibria by A. Weinstein Stability of rigid body motion using the energy-Casimir method by D. Holm, J. Marsden, T. Ratiu, and A. Weinstein Stability of planar multifluid plasma equilibria by Arnold's method by D. Holm Canonical derivation of the Vlasov-Coulomb noncanonical Poisson structure by A. Kaufman and R. Dewar Reduction and Hamiltonian structures on duals of semidirect product Lie algebras by J. Marsden, T. Ratiu, and A. Weinstein Gauged Lie-Poisson structures by R. Montgomery, J. Marsden, and T. Ratiu The Hamiltonian structure of the BBGKY hierarchy equations by J. Marsden, P. Morrison, and A. Weinstein Particle and bracket formulations of kinetic equations by M. Grmela Noncanonical Hamiltonian field theory and reduced MHD by J. Marsden and P. Morrison Geometry and guiding center motion by R. Littlejohn Lie-transform derivation of the gyrokinetic Hamiltonian system by A. Kaufman and B. Boghosian Poisson structures for relativistic systems by M. Mayer Diffeomorphism groups, semidirect products and quantum theory by G. Goldin-- Part II. Analytic and Numerical Methods: Contour dynamics for two dimensional flows by N. Zabusky On the nonlinear stability of circular vortex patches by Y. Wan Vortex methods for fluid flow in two or three dimensions by T. Beale and A. Majda Hamiltonian perturbation theory and water waves by P. Olver Results on existence and uniqueness of solutions to the Vlasov equation by S. Wollman Remarks on collisionless plasmas by R. Glassey and W. Strauss Toward a new kinetic theory for resonant triads by H. Segur A spectral method for external viscous flows by P. Spalart Forecasting the ocean's weather: numerical models for application to oceanographic data by R. Miller-- Part III. Bifurcation and Dynamical Systems: Geometry and dynamics in experiments on chaotic systems by H. Swinney Dimension estimates for attractors by J. Guckenheimer Solitary waves as fixed points of infinite-dimensional maps in an optical bistable ring cavity by D. McLaughlin, J. Moloney, and A. Newell Hopf bifurcation and the beam-plasma instability by J. Crawford Some remarks on chaotic particle paths in time-periodic, three-dimensional swirling flows by P. Holmes A universal transition from quasi-periodicity to chaos by E. Siggia On the nonpathological behavior of Newton's method by J. Curry and E. Wayne Successive bifurcations in the interaction of steady state and Hopf bifurcation by J. Scheurle Convection in a rotating fluid layer by J. Swift.
  • (source: Nielsen Book Data)9780821850282 20160528
Science Library (Li and Ma)
Book
xiii, 156 p. ; 25 cm.
Science Library (Li and Ma)
Book
75 p. ; 25 cm.
  • Weak convergence-- Markov processes and their generators-- Convergence to Markov processes-- Diffusion Approximations-- Branching Markov processes-- Markov processes as random time changes-- Approximations of density dependent Jump Markov processes-- Epidemic models-- Random replication with errors.
  • (source: Nielsen Book Data)9780898711691 20160528
Population processes are stochastic models for systems involving a number of similar particles. Examples include models for chemical reactions and for epidemics. The model may involve a finite number of attributes, or even a continuum. This monograph considers approximations that are possible when the number of particles is large. The models considered will involve a finite number of different types of particles.
(source: Nielsen Book Data)9780898711691 20160528
Science Library (Li and Ma)
Book
ca. 320 p. in various pagings ; 28 cm.
  • General matrices-- Band matrices-- Positive definite matrices-- Positive definite band matrices-- Symmetric Indefinite Matrices-- Triangular matrices-- Tridiagonal matrices-- The Cholesky decomposition-- The QR decomposition-- Updating QR and Cholesky decompositions-- The singular value decomposition-- References-- Basic linear algebra subprograms-- Timing data-- Program listings-- BLA Listings.
  • (source: Nielsen Book Data)9780898711721 20160528
The authors of this carefully structured guide are the principal developers of LINPACK, a unique package of Fortran subroutines for analyzing and solving various systems of simultaneous linear algebraic equations and linear least squares problems. This guide supports both the casual user of LINPACK who simply requires a library subroutine, and the specialist who wishes to modify or extend the code to handle special problems. It is also recommended for classroom work.
(source: Nielsen Book Data)9780898711721 20160528
SAL3 (off-campus storage), Science Library (Li and Ma)
Book
viii, 490 p. illus. 24 cm.
Science Library (Li and Ma)
Book
v, 48 p. illus. 25 cm.
Science Library (Li and Ma)
Book
v, 31 p. 25 cm.
Science Library (Li and Ma)