Edited by Andrea Prosperetti / The Johns Hopkins University
Gretar Tryggvason / Worcester Polytechnic Institute, Massachusetts

Computational Methods for Multiphase Flow

Hardback (ISBN-13: 9780521847643 | ISBN-10: 0521847648)

Predicting the behavior of multiphase flows is a problem of immense importance for both industrial and natural processes. Thanks to high-speed computers and advanced algorithms, it is starting to be possible to simulate such flows numerically. Researchers and students alike need to have a one-stop account of the area, and this book is that: it's a comprehensive and self-contained, graduate-level introduction to the computational modeling of multiphase flows. Each chapter is written by a recognized expert in the field and contains extensive references to current research. The book is organized so that the chapters are fairly independent to enable it to be used for a range of advanced courses. No other book offers the simultaneous coverage of so many topics related to multiphase flow. It will be welcomed by researchers and graduate students in engineering, physics, and applied mathematics.

* Unique coverage for a single volume book
* Comprehensive and self-contained
* Features extensive references to current research

Contents

Preface; 1. Introduction: A computational approach to multiphase flow A. Prosperetti and G. Tryggvason; 2. Direct numerical simulations of finite Reynolds number flows G. Tryggvason and S. Balachandar; 3. Immersed boundary methods for fluid Iinterfaces G. Tryggvason, M. Sussman and M. Y. Hussaini; 4. Structured grid methods for solid particles S. Balachandar; 5. Finite element methods for particulate flows H. Hu; 6. Lattice Boltzmann methods for multiphase flows S. Chen, X. He and L. S. Luo; 7. Boundary integral methods for Stokes flows J. Blawzdziewic; 8. Averaged equations for multiphase flows A. Prosperetti; 9. Point particle methods for disperse flows K. Squires; 10. Segregated methods for two-fluid models A. Prosperetti, S. Sundaresan, S. Pannala and D. Z. Zhang; 11. Coupled methods for multi-fluid models A. Prosperetti.

David J. Benson /University of Aberdeen

Music: A Mathematical Offering

Hardback (ISBN-13: 9780521853873 | ISBN-10: 0521853877)
Paperback (ISBN-13: 9780521619998 | ISBN-10: 0521619998)

Since the time of the Ancient Greeks, much has been written about the relation between mathematics and music: from harmony and number theory, to musical patterns and group theory. Benson provides a wealth of information here to enable the teacher, the student, or the interested amateur to understand, at varying levels of technicality, the real interplay between these two ancient disciplines. The story is long as well as broad and involves physics, biology, psycho acoustics, the history of science, and digital technology as well as, of course, mathematics and music. Starting with the structure of the human ear and its relationship with Fourier analysis, the story proceeds via the mathematics of musical instruments to the ideas of consonance and dissonance, and then to scales and temperaments. This is a must-have book if you want to know about the music of the spheres or digital music and many things in between.

* The only modern account that is comprehensive and thorough
* Lots of musical examples that make the mathematical ideas concrete; lots of illustrations
* Self-contained for the enthusiast but also usable as a course text in mathematics, physics and engineering departments

Contents

Preface; Introduction; Acknowledgements; 1. Waves and harmonics; 2. Fourier theory; 3. A mathematician's guide to the orchestra; 4. Consonance and dissonance; 5. Scales and temperaments: the fivefold way; 6. More scales and temperaments; 7. Digital music; 8. Synthesis; 9. Symmetry in music; Appendix A. Bessel functions; Appendix B. Equal tempered scales; Appendix C. Frequency and MIDI chart; Appendix D. Intervals; Appendix E. Just, equal and meantone scales compared; Appendix F. Music theory; Appendix G. Recordings; Bibliography; Index.

Terence Tao / University of California, Los Angeles
Van H. Vu / Rutgers University, New Jersey

Additive Combinatorics

Series: Cambridge Studies in Advanced Mathematics (No. 105)
Hardback (ISBN-13: 9780521853866 | ISBN-10: 0521853869)

Additive combinatorics is the theory of counting additive structures in sets. This theory has seen exciting developments and dramatic changes in direction in recent years thanks to its connections with areas such as number theory, ergodic theory and graph theory. This graduate level textbook will allow students and researchers easy entry into this fascinating field. Here, for the first time, the authors bring together in a self-contained and systematic manner the many different tools and ideas that are used in the modern theory, presenting them in an accessible, coherent, and intuitively clear manner, and providing immediate applications to problems in additive combinatorics. The power of these tools is well demonstrated in the presentation of recent advances such as Szemeri's theorem on arithmetic progressions, the Kakeya conjecture and Erdos distance problems, and the developing field of sum-product estimates. The text is supplemented by a large number of exercises and new results.

* Comprehensive graduate level textbook for a highly active current area of research
* The authors bring together for the first time the many different tools and ideas that are used in the modern theory of additive combinatorics
* The text is supplemented with a large number of exercises

Contents

Prologue; 1. The probabilistic method; 2. Sum set estimates; 3. Additive geometry; 4. Fourier analytic methods; 5. Inverse sumset theorems; 6. Graph theoretic methods; 7. The Littlewood-Offord problem; 8. Incidence geometry; 9. Algebraic methods; 10. Szemeri's theorem for k = 3; 11. Szemeri's theorem for k > 3; 12. Long arithmetic progressions in sumsets; Bibliography.

Edited by Kim-Anh Do / University of Texas, Houston
Peter Muller / University of Texas, Houston
Marina Vannucci / Texas A & M University

Bayesian Inference for Gene Expression and Proteomics

Hardback (ISBN-13: 9780521860925 | ISBN-10: 052186092X)

The interdisciplinary nature of bioinformatics presents a challenge in integrating concepts, methods, software, and multi-platform data. Although there have been rapid developments in new technology and an inundation of statistical methodology and software for the analysis of microarray gene expression arrays, there exist few rigorous statistical methods for addressing other types of high-throughput data, such as proteomic profiles that arise from mass spectrometry experiments. This book discusses the development and application of Bayesian methods in the analysis of high-throughput bioinformatics data, from medical research and molecular and structural biology. The Bayesian approach has the advantage that evidence can be easily and flexibly incorporated into statistical models. A basic overview of the biological and technical principles behind multi-platform high-throughput experimentation is followed by expert reviews of Bayesian methodology, tools, and software for single group inference, group comparisons, classification and clustering, motif discovery and regulatory networks, and Bayesian networks and gene interactions.

* Novel Bayesian methods for the analysis of high throughput bioinformatics data
* Applications to translational research
* Special case studies

Contents

1. An introduction to high-throughput bioinformatics data Keith Baggerly, Kevin Coombes and Jeffrey S. Morris; 2. Hierarchical mixture models for expression profiles Michael Newton, Ping Wang and Christina Kendziorski; 3. Bayesian hierarchical models for inference in microarray data Anne-Mette K. Hein, Alex Lewin and Sylvia Richardson; 4. Bayesian process-based modeling of two-channel microarray experiments estimating absolute mRNA concentrations Mark A. van de Wiel, Marit Holden, Ingrid K. Glad, Heidi Lyng and Arnoldo Frigessi; 5. Identification of biomarkers in classification and clustering of high-throughput data Mahlet Tadesse, Marina Vannucci, Naijun Sha and Sinae Kim; 6. Modeling nonlinear gene interactions using Bayesian MARS Veerabhadran Baladandayuthapani Chris C. Holmes, Bani K. Mallick and Raymond J. Carroll; 7. Models for probability of under- and overexpression: the POE scale Elizabeth Garrett-Mayer and Robert Scharpf; 8. Sparse statistical modelling in gene expression genomics Joseph Lucas, Carlos Carvalho, Quanli Wang, Andrea Bild, Joseph Nevins and Mike West; 9. Bayesian analysis of cell-cycle gene expression Chuan Zhou, Jon Wakefield and Linda L. Breeden; 10. Model-based clustering for expression data via a Dirichlet process mixture model David Dahl; 11. Interval mapping for Expression Quantitative Trait Loci mapping Meng Chen and Christina Kendziorski; 12. Bayesian mixture model for gene expression and protein profiles Michele Guindani, Kim-Anh Do, Peter Muller and Jeffrey S. Morris; 13. Shrinkage estimation for SAGE data using a mixture Dirichlet prior Jeffrey S. Morris, Kevin Coombes and Keith Baggerly; 14. Analysis of mass spectrometry data using Bayesian wavelet-based functional mixed models Jeffrey S. Morris, Philip J. Brown, Keith Baggerly and Kevin Coombes; 15. Nonparametric models for proteomic peak identification and quantification Merlise Clyde, Leanna House and Robert Wolpert; 16. Bayesian modeling and inference for sequence motif discovery Mayetri Gupta and Jun S. Liu; 17. Identifying of DNA regulatory motifs and regulators by integrating gene expression and sequence data Deuk Woo Kwon, Sinae Kim, David Dahl, Michael Swartz, Mahlet Tadesse and Marina Vannucci; 18. A misclassification model for inferring transcriptional regulatory networks Ning Sun and Hongyu Zhao; 19. Estimating cellular signaling from transcription data Andrew V. Kossenkov, Ghislain Bidaut and Michael Ochs; 20. Computational methods for learning Bayesian networks from high-throughput biological data Bradley Broom and Devika Subramanian; 21. Modeling transcriptional regulation: Bayesian networks and informative priors Alexander J. Hartemink; 22. Sample size choice for microarray experiments Peter Muller, Christian Robert and Judith Rousseau.