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Lectures on Probability Theory and Statistics
This volume contains lectures given at the 31st Probability Summer School in Saint-Flour (July 8-25, 2001). Simon Tavaré’s lectures serve as an introduction to the coalescent, and to inference for ancestral processes in population genetics. The stochastic computation methods described include rejection methods, importance sampling, Markov chain Monte Carlo, and approximate Bayesian methods. Ofer Zeitouni’s course on "Random Walks in Random Environment" presents systematically the tools that have been introduced to study the model. A fairly complete description of available results in dimension 1 is given. For higher dimension, the basic techniques and a discussion of some of the available results are provided. The contribution also includes an updated annotated bibliography and suggestions for further reading. Olivier Catoni's course appears separately.
Monte Carlo and Quasi-Monte Carlo Methods 2002
This book represents the refereed proceedings of the Fifth International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing which was held at the National University of Singapore in the year 2002. An important feature are invited surveys of the state of the art in key areas such as multidimensional numerical integration, low-discrepancy point sets, computational complexity, finance, and other applications of Monte Carlo and quasi-Monte Carlo methods. These proceedings also include carefully selected contributed papers on all aspects of Monte Carlo and quasi-Monte Carlo methods. The reader will be informed about current research in this very active area.
Logarithmic Combinatorial Structures
This book explains similarities in asymptotic behavior as the result of two basic properties shared by the structures: the conditioning relation and the logarithmic condition. The discussion is conducted in the language of probability, enabling the theory to be developed under rather general and explicit conditions; for the finer conclusions, Stein's method emerges as the key ingredient.
Convergence of Probability Measures
A new look at weak-convergence methods in metric spaces-from a master of probability theory In this new edition, Patrick Billingsley updates his classic work Convergence of Probability Measures to reflect developments of the past thirty years. Widely known for his straightforward approach and reader-friendly style, Dr. Billingsley presents a clear, precise, up-to-date account of probability limit theory in metric spaces. He incorporates many examples and applications that illustrate the power and utility of this theory in a range of disciplines-from analysis and number theory to statistics, engineering, economics, and population biology. With an emphasis on the simplicity of the mathematics ...
Branching Processes
This book covers the mathematical idea of branching processes, and tailors it for a biological audience.
The 100 Most Outrageous Hoaxes and Mistakes
Scientific breakthroughs are often regarded with suspicion, especially those that diverge substantially from established theories. New ideas are tested by scientists around the world to ensure that they hold up to scrutiny. This book takes a look at the instances when, despite these precautions, the scientific community got it wrong. The book includes the most infamous cases of fraud and famous mistakes that initially had scientists fooled.
Some Mathematical Questions in Biology
Several data banks around the world are accumulating DNA sequences at a feverish rate, with tremendous potential for furthering our knowledge of how biological systems code and pass on information. The sophisticated mathematical analysis of that data is just beginning. The Eighteenth Annual Symposium on Some Mathematical Questions in Biology was held in conjunction with the Annual Meeting of the AAAS and brought together speakers knowledgeable in both biology and mathematics to discuss these developments and to emphasize the need for rigorous, efficient computational tools. These computational tools include biologically relevant definitions of sequence similarity and string matching algorithms. The solutions for some of these problems have great generality; the string matching methods first developed for biological sequences have now been applied to areas such as geology, linguistics, and speech recognition. There is a great potential here for creating of new mathematics to handle this growing data base, with new applications for many areas of mathematics, computer science, and statistics.
Highly Structured Stochastic Systems
Through this text, the author aims to make recent developments in the title subject (a modern strategy for the creation of statistical models to solve 'real world' problems) accessible to graduate students and researchers in the field of statistics.
Natural Locomotion in Fluids and on Surfaces
This volume developed from a Workshop on Natural Locomotion in Fluids and on Surfaces: Swimming, Flying, and Sliding which was held at the Institute for Mathematics and its Applications (IMA) at the University of Minnesota, from June 1-5, 2010. The subject matter ranged widely from observational data to theoretical mechanics, and reflected the broad scope of the workshop. In both the prepared presentations and in the informal discussions, the workshop engaged exchanges across disciplines and invited a lively interaction between modelers and observers. The articles in this volume were invited and fully refereed. They provide a representative if necessarily incomplete account of the field of natural locomotion during a period of rapid growth and expansion. The papers presented at the workshop, and the contributions to the present volume, can be roughly divided into those pertaining to swimming on the scale of marine organisms, swimming of microorganisms at low Reynolds numbers, animal flight, and sliding and other related examples of locomotion.
Calculating the Secrets of Life
As researchers have pursued biology's secrets to the molecular level, mathematical and computer sciences have played an increasingly important roleâ€"in genome mapping, population genetics, and even the controversial search for "Eve," hypothetical mother of the human race. In this first-ever survey of the partnership between the two fields, leading experts look at how mathematical research and methods have made possible important discoveries in biology. The volume explores how differential geometry, topology, and differential mechanics have allowed researchers to "wind" and "unwind" DNA's double helix to understand the phenomenon of supercoiling. It explains how mathematical tools are revealing the workings of enzymes and proteins. And it describes how mathematicians are detecting echoes from the origin of life by applying stochastic and statistical theory to the study of DNA sequences. This informative and motivational book will be of interest to researchers, research administrators, and educators and students in mathematics, computer sciences, and biology.
