Series: Springer Handbooks of Computational Statistics
1st Edition., 2011, IV, 846 p., Hardcover
ISBN: 978-3-642-16344-9
Due: December 15, 2010
Numerous fascinating breakthroughs in biotechnology have generated large volumes and diverse types of high throughput data that demand the development of efficient and appropriate tools in computational statistics integrated with biological knowledge and computational algorithms. This volume collects contributed chapters from leading researchers to survey the many active research topics and promote the visibility of this research area. This volume is intended to provide an introductory and reference book for students and researchers who are interested in the recent developments of computational statistics in computational biology.
I: Accuracy Assessment of Consensus Sequence from Shotgun Sequencing.- Statistical and Computational Studies on Alternative Splicing.- Using Sequence Information to Predict TF-DNA Binding.- Computational Promoter Prediction in a Vertebrate Genome.- Discovering Influential Variables: A General Computer Intensive Method for Common Genetic Disorders.- STORMSeq: A Method for Ranking Regulatory Sequences by Integrating Experimental Datasets with Diverse Computational Predictions.- Mixture Tree Construction and Its Applications.- II: Experimental Designs and ANOVA for Microarray Data.- MAQC and Cross Platform Analysis of Microarray Data.- A Survey of Classification Techniques for Microarray Analysis.- Statistical Analysis of Single Nucleotide Polymorphism Microarrays in Cancer Studies.- Computational Analysis of ChIP-chip Data.- eQTL Mapping for Functional Classes of Saccharomyces Cerevisiae Genes with Multivariate Sparse Partial Least Squares Regression.- Analysis of Time Course Data.- III: Kernel Methods in Bioinformatics.- Graph Classification Methods in Chemoinformatics.- Hidden Markov Random Field Models for Network-based Analysis of Genomic Data.- Review of Weighted Gene Coexpression Network Analysis.- Liquid Association.- Boolean Networks.- Protein Interaction Networks: Protein Domain Interaction and Protein Function Prediction.- Regulatory Networks.- Inferring Signaling and Gene Regulatory Network from Genetic and Genomic Information.- Computational Drug Target Pathway Discovery: A Bayesian Network Approach.- Cancer Systems Biology.- Comparative Genomics and Molecular Evolution.- Robust Control of Immune Systems under Noises: Stochastic Game Approach.
Series: Algebra and Applications, Vol. 14
1st Edition., 2011, X, 302 p. 23 illus., Hardcover
ISBN: 978-0-85729-176-9
Due: November 2010
The study of free resolutions is a core and beautiful area in Commutative Algebra. The main goal of this book is to inspire the readers and develop their intuition about syzygies and Hilbert functions. Many examples are given in order to illustrate ideas and key concepts.
A valuable feature of the book is the inclusion of open problems and conjectures; these provide a glimpse of exciting, and often challenging, research directions in the field. Three types of problems are presented: Conjectures, Problems, and Open-Ended Problems. The latter do not describe specific problems but point to interesting directions for exploration.
The first part of the monograph contains basic background material on graded free resolutions. Further coverage of topics includes syzygies over a polynomial ring, resolutions over quotient rings, lex ideals and Hilbert functions, compression, resolutions of monomial ideals, and syzygies of toric ideals. With a clear and self-contained exposition this text is intended for advanced graduate students and postdoctorates; it will be also of interest to senior mathematicians.
Graded Free Resolutions.- Hilbert Functions.- Monomial Resolutions.- Syzygies of Toric Ideals
Series: Developments in Mathematics, Vol. 21
1st Edition., 2011, XVIII, 354 p., Hardcover
ISBN: 978-1-4419-7846-2
Due: November 29, 2010
This book provides a comprehensive overview of the theory of theta functions, as applied to compact Riemann surfaces, as well as the necessary background for understanding and proving the Thomae formulae.
The exposition examines the properties of a particular class of compact Riemann surfaces, i.e., the Zn curves, and thereafter focuses on how to prove the Thomae formulae, which give a relation between the algebraic parameters of the Zn curve, and the theta constants associated with the Zn curve.
Graduate students in mathematics will benefit from the classical material, connecting Riemann surfaces, algebraic curves, and theta functions, while young researchers, whose interests are related to complex analysis, algebraic geometry, and number theory, will find new rich areas to explore. Mathematical physicists and physicists with interests also in conformal field theory will surely appreciate the beauty of this subject.
- Introduction.- 1. Riemann Surfaces.- 2. Zn Curves.- 3. Examples of Thomae Formulae.- 4. Thomae Formulae for Nonsingular Zn Curves.- 5. Thomae Formulae for Singular Zn Curves.-6. Some More Singular Zn Curves.-Appendix A. Constructions and Generalizations for the Nonsingular and Singular Cases.-Appendix B. The Construction and Basepoint Change Formulae for the Symmetric Equation Case.-References.-List of Symbols.-Index.
Series: Applied Mathematical Sciences, Vol. 174
1st Edition., 2011, XVIII, 470 p. 121 illus., 7 in color., Hardcover
ISBN: 978-1-4419-7915-5
Due: November 29, 2010
Moving mesh methods are an effective, mesh-adaptation-based approach for the numerical solution of mathematical models of physical phenomena. Currently there exist three main strategies for mesh adaptation, namely, to use mesh subdivision, local high order approximation (sometimes combined with mesh subdivision), and mesh movement. The latter type of adaptive mesh method has been less well studied, both computationally and theoretically.
This book is about adaptive mesh generation and moving mesh methods for the numerical solution of time-dependent partial differential equations. It presents a general framework and theory for adaptive mesh generation and gives a comprehensive treatment of moving mesh methods and their basic components, along with their application for a number of nontrivial physical problems. Many explicit examples with computed figures illustrate the various methods and the effects of parameter choices for those methods. The partial differential equations considered are mainly parabolic (diffusion-dominated, rather than convection-dominated).
The extensive bibliography provides an invaluable guide to the literature in this field. Each chapter contains useful exercises. Graduate students, researchers and practitioners working in this area will benefit from this book.
Preface.- Introduction.- Adaptive Mesh Movement in 1D.- Discretization of PDEs on Time-Varying Meshes.- Basic Principles of Multidimensional Mesh Adaption.- Monitor Functions.- Variational Mesh Adaptive Methods.- Velocity-Based Adaptive Methods.- Appendix: Sobolev Spaces.- Appendix: Arithmetic Mean Geometric Mean Inequality and Jensen's Inequality.- Bibliography.
Series: Grundlehren der mathematischen Wissenschaften, Vol. 343
1st Edition., 2011, XVI, 522 p., Hardcover
ISBN: 978-3-642-16829-1
Due: January 12, 2011
In recent years, the Fourier analysis methods have expereinced a growing interest in the study of partial differential equations. In particular, those techniques based on the Littlewood-Paley decomposition have proved to be very efficient for the study of evolution equations. The present book aims at presenting self-contained, state- of- the- art models of those techniques with applications to different classes of partial differential equations: transport, heat, wave and Schrodinger equations. It also offers more sophisticated models originating from fluid mechanics (in particular the incompressible and compressible Navier-Stokes equations) or general relativity.
It is either directed to anyone with a good undergraduate level of knowledge in analysis or useful for experts who are eager to know the benefit that one might gain from Fourier analysis when dealing with nonlinear partial differential equations.
Preface.- 1. Basic analysis.- 2. Littlewood-Paley theory.- 3. Transport and transport-diffusion equations.- 4. Quasilinear symmetric systems.- 5. Incompressible Navier-Stokes system.- 6. Anisotropic viscosity.- 7. Euler system for perfect incompressible fluids.- 8. Strichartz estimates and applications to semilinear dispersive equations.- 9. Smoothing effect in quasilinear wave equations.- 10.- The compressible Navier-Stokes system.- References. - List of notations.- Index.