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This text presents mathematical biology as a field with a unity of its own, rather than only the intrusion of one science into another. It updates an earlier successful edition and greatly expands the concept of the "computer biology laboratory," giving students a general perspective of the field before proceeding to more specialized topics. The book focuses on problems of contemporary interest, such as cancer, genetics, and the rapidly growing field of genomics. It includes new chapters on parasites, cancer, and phylogenetics, along with an introduction to online resources for DNA, protein lookups, and popular pattern matching tools such as BLAST. In addition, the emerging field of algebraic statistics is introduced and its power illustrated in the context of phylogenetics. A unique feature of the book is the integration of a computer algebra system into the flow of ideas in a supporting but unobtrusive role. Syntax for both the Maple and Matlab systems is provided in a tandem format. The use of a computer algebra system gives the students the opportunity to examine "what if" scenarios, allowing them to investigate biological systems in a way never before possible. For students without access to Maple or Matlab, each topic presented is complete. Graphic visualizations are provided for all mathematical results. Mathematical Biology includes extensive exercises, problems and examples. A year of calculus with linear algebra is required to understand the material presented. The biology presented proceeds from the study of populations down to the molecular level; no previous coursework in biology is necessary. The book is appropriate for undergraduate and graduate students studying mathematics or biology and for scientists and researchers who wish to study the applications of mathematics and computers in the natural sciences.

Biomathematics. Biometry. Biostatistics --- Mathematics. --- Mathematical Biology in General. --- Computer Appl. in Life Sciences. --- Probability Theory and Stochastic Processes. --- Applications of Mathematics. --- Computer Applications. --- Computer science. --- Biology --- Distribution (Probability theory). --- Mathématiques --- Informatique --- Biologie --- Distribution (Théorie des probabilités) --- Data processing.

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This book is the fourth in a multidisciplinary series which brings together leading researchers in the STEAM-H disciplines (Science, Technology, Engineering, Agriculture, Mathematics and Health) to present their perspective on advances in their own specific fields, and to generate a genuinely interdisciplinary collaboration that transcends parochial subject-matter boundaries. All contributions are carefully edited, peer-reviewed, reasonably self-contained, and pedagogically crafted for a multidisciplinary readership. Contributions are drawn from a variety of fields including mathematics, statistics, game theory and behavioral sciences, biomathematics and physical chemistry, computer science and human-centered computing. This volume is dedicated to Professor Christiane Rousseau, whose work inspires the STEAM-H series, in recognition of her passion for the mathematical sciences and her on-going initiative, the Mathematics of Planet Earth paradigm of interdisciplinarity. The volume's primary goal is to enhance interdisciplinary understanding between these areas of research by showing how new advances in a particular field can be relevant to open problems in another and how many disciplines contribute to a better understanding of relevant issues at the interface of mathematics and the sciences. The main emphasis is on important methods, research directions and applications of analysis within and beyond each field. As such, the volume aims to foster student interest and participation in the STEAM-H domain, as well as promote interdisciplinary research collaborations. The volume is valuable as a reference of choice and a source of inspiration for a broad spectrum of scientists, mathematicians, research students and postdoctoral fellows.

Mathematics. --- Game theory. --- Mathematical physics. --- Mathematical models. --- Mathematical Modeling and Industrial Mathematics. --- Game Theory, Economics, Social and Behav. Sciences. --- Mathematical Applications in the Physical Sciences. --- Mathematical Biology in General. --- Mathematics --- Mathematical and Computational Biology. --- Math --- Science --- Biomathematics. --- Physical mathematics --- Physics --- Games, Theory of --- Theory of games --- Mathematical models --- Models, Mathematical --- Simulation methods --- Biology

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This volume is dedicated to the memory of the late Professor C.C. (Chris) Heyde (1939-2008), distinguished statistician, mathematician and scientist. Chris worked at a time when many of the foundational building blocks of probability and statistics were being put in place by a phalanx of eminent scientists around the world. He contributed significantly to this effort and took his place deservedly among the top-most rank of researchers. Throughout his career, Chris maintained also a keen interest in applications of probability and statistics, and in the history of the subject. The magnitude of his impact on his chosen area of research, both in Australia and internationally, was well recognised by the abundance of honours he received within and without the profession. The book is comprised of a number of Chris's papers covering each one of four major topics to which he contributed. These papers are reproduced herein. The topics, and the papers in them, were selected by four of Chris's friends and collaborators: Ishwar Basawa, Peter Hall, Ross Maller (overall Editor of the volume) and Eugene Seneta. Each topic is provided with an overview by the selecting editor. The topics cover a range of areas to which Chris made especially important contributions: Inference in Stochastic Processes, Rates of Convergence in the Central Limit Theorem, the Law of the Iterated Logarithm, and Branching Processes and Population Genetics. The Editor and the other contributors to the volume include well known researchers in probability and statistics. The collection begins with an author's pick  of a number of his papers which Chris considered most interesting and significant, chosen by him shortly before his death. A biography of Chris by his close friend and collaborator, Joe Gani, is also included. An introduction by the Editor and a comprehensive bibliography of Chris's publications complete the volume. The book will be of especial interest to researchers in probability and statistics, and in the history of these subjects.

Statistics. --- Statistical Theory and Methods. --- Probability Theory and Stochastic Processes. --- Econometrics. --- Mathematical Biology in General. --- Quantitative Finance. --- Biology --- Finance. --- Distribution (Probability theory). --- Mathematical statistics. --- Statistique --- Finances --- Distribution (Théorie des probabilités) --- Statistique mathématique --- Econométrie --- Mathematics. --- AA / International- internationaal --- 301 --- 300 --- 08 --- Techniek van statistische inlichtingen. Organisatie van de statistische enquêtes. Statistische kritiek. --- Algemene statistische naslagwerken. --- Biografieën en memoires. --- Branching processes --- Limit theorems (Probability theory) --- Mathematical statistics --- Probabilities --- Stochastic processes --- Random processes --- Probability --- Statistical inference --- Mathematics --- Statistics, Mathematical --- Processes, Branching --- Biografieën en memoires --- Algemene statistische naslagwerken --- Techniek van statistische inlichtingen. Organisatie van de statistische enquêtes. Statistische kritiek --- Statistical methods --- Combinations --- Chance --- Least squares --- Risk --- Statistics --- Sampling (Statistics)

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Cardiovascular diseases have a major impact in Western countries. Mathematical models and numerical simulations can help the understanding of physiological and pathological processes, complementing the information provided to medical doctors by medical imaging and other non-invasive means, and opening the possibility of a better diagnosis and more in-depth surgical planning.This book offers a mathematically sound and up-to-date foundation to the training of researchers, and serves as a useful reference for the development of mathematical models and numerical simulation codes. It is structured into different chapters, written by recognized experts in the field, and however it features a common thread, with consistency of notation and expressions and systematic cross-referencing. Many fundamental issues are faced, such as: the mathematical representation of vascular geometries extracted from medical images, modelling blood rheology and the complex multilayer structure of the vascular tissue, and its possible pathologies, the mechanical and chemical interaction between blood and vascular walls; the different scales coupling local and systemic dynamics. All of these topics introduce challenging mathematical and numerical problems, demanding for advanced analysis and simulation techniques. This book is addressed to graduate students and researchers in the field of bioengineering, applied mathematics and medicine, wishing to engage themselves in the fascinating task of modeling how the cardiovascular system works.

Mathematics. --- Applications of Mathematics. --- Cardiology. --- Mathematical Biology in General. --- Physiological, Cellular and Medical Topics. --- Mathematical Modeling and Industrial Mathematics. --- Partial Differential Equations. --- Differential equations, partial. --- Biology --- Physiology --- Mathématiques --- Cardiologie --- Cardiovascular system --- Mathematical models. --- Blood -- Diseases. --- Blood flow -- Mathematical models. --- Blood flow. --- Cardiovascular System --- Cardiovascular Physiological Processes --- Blood Physiological Phenomena --- Blood Physiological Processes --- Models, Biological --- Cardiovascular Physiological Phenomena --- Rheology --- Anatomy --- Investigative Techniques --- Circulatory and Respiratory Physiological Phenomena --- Models, Theoretical --- Blood Circulation --- Hemorheology --- Hemodynamics --- Models, Cardiovascular --- Blood Vessels --- Phenomena and Processes --- Analytical, Diagnostic and Therapeutic Techniques and Equipment --- Engineering & Applied Sciences --- Human Anatomy & Physiology --- Health & Biological Sciences --- Applied Mathematics --- Circulatory system --- Vascular system --- Partial differential equations. --- Applied mathematics. --- Engineering mathematics. --- Biomathematics. --- Mathematical and Computational Biology. --- Blood --- Circulation --- Animal physiology --- Animals --- Heart --- Internal medicine --- Math --- Science --- Partial differential equations --- Diseases --- Models, Mathematical --- Simulation methods --- Mathematics --- Engineering --- Engineering analysis --- Mathematical analysis

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How is genetic variability shaped by natural selection, demographic factors, and random genetic drift? To approach this question, we introduce and analyze a number of probability models beginning with the basics, and ending at the frontiers of current research. Throughout the book, the theory is developed in close connection with examples from the biology literature that illustrate the use of these results. Along the way, there are many numerical examples and graphs to illustrate the conclusions. This is the second edition and is twice the size of the first one. The material on recombination and the stepping stone model have been greatly expanded, there are many results form the last five years, and two new chapters on diffusion processes develop that viewpoint. This book is written for mathematicians and for biologists alike. No previous knowledge of concepts from biology is assumed, and only a basic knowledge of probability, including some familiarity with Markov chains and Poisson processes. The book has been restructured into a large number of subsections and written in a theorem-proof style, to more clearly highlight the main results and allow readers to find the results they need and to skip the proofs if they desire. Rick Durrett received his Ph.D. in operations research from Stanford University in 1976. He taught in the UCLA mathematics department before coming to Cornell in 1985. He is the author of eight books and 160 research papers, most of which concern the use of probability models in genetics and ecology. He is the academic father of 39 Ph.D. students and was recently elected to the National Academy of Sciences.

Mathematics. --- Evolutionary Biology. --- Genetics and Population Dynamics. --- Mathematical Biology in General. --- Statistics for Life Sciences, Medicine, Health Sciences. --- Probability Theory and Stochastic Processes. --- Evolution (Biology). --- Genetics --- Biology --- Distribution (Probability theory). --- Statistics. --- Mathématiques --- Evolution (Biologie) --- Distribution (Théorie des probabilités) --- Statistique --- Evolutionary genetics --Statistical methods. --- Nucleotide sequence --Statistical methods. --- Probabilities. --- Variation (Biology) --Statistical methods. --- Evolutionary genetics --- Nucleotide sequence --- Probabilities --- Variation (Biology) --- Probability --- Evolution, Molecular --- Base Sequence --- Models, Genetic --- Molecular Structure --- Mathematical Concepts --- Models, Biological --- Biological Evolution --- Molecular Sequence Data --- Statistics as Topic --- Genetic Structures --- Documentation --- Biological Processes --- Genetic Processes --- Models, Theoretical --- Health Care Evaluation Mechanisms --- Epidemiologic Methods --- Phenomena and Processes --- Biochemical Phenomena --- Genetic Phenomena --- Biological Phenomena --- Chemical Phenomena --- Quality of Health Care --- Investigative Techniques --- Information Services --- Public Health --- Environment and Public Health --- Analytical, Diagnostic and Therapeutic Techniques and Equipment --- Information Science --- Health Care Quality, Access, and Evaluation --- Health Care --- Health & Biological Sciences --- Statistical methods --- Statistical methods. --- Biological variation --- Statistical inference --- Analysis, Nucleic acid sequence --- Analysis, Nucleotide sequence --- Base sequence (Nucleic acids) --- DNA sequence --- Nucleic acid sequence analysis --- Nucleotide sequence analysis --- RNA sequence --- Sequence, Nucleotide --- Genetic evolution --- Biochemistry. --- Evolutionary biology. --- Biomathematics. --- Biochemistry, general. --- Mathematical and Computational Biology. --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Heredity --- Mutation (Biology) --- Nucleic acids --- Nucleotides --- Sequence alignment (Bioinformatics) --- Evolution (Biology) --- Analysis --- Distribution (Probability theory. --- Embryology --- Mendel's law --- Adaptation (Biology) --- Breeding --- Chromosomes --- Statistical analysis --- Statistical data --- Statistical science --- Econometrics --- Biological chemistry --- Chemical composition of organisms --- Organisms --- Physiological chemistry --- Chemistry --- Medical sciences --- Animal evolution --- Animals --- Biological evolution --- Darwinism --- Evolutionary biology --- Evolutionary science --- Origin of species --- Evolution --- Biological fitness --- Homoplasy --- Natural selection --- Phylogeny --- Distribution functions --- Frequency distribution --- Characteristic functions --- Composition --- Statistics .