Finite-dimensional optimization problems occur throughout the mathematical sciences. The majority of these problems cannot be solved analytically. This introduction to optimization attempts to strike a balance between presentation of mathematical theory and development of numerical algorithms. Building on students’ skills in calculus and linear algebra, the text provides a rigorous exposition without undue abstraction. Its stress on statistical applications will be especially appealing to graduate students of statistics and biostatistics. The intended audience also includes students in applied mathematics, computational biology, computer science, economics, and physics who want to see rigorous mathematics combined with real applications. In this second edition the emphasis remains on finite-dimensional optimization. New material has been added on the MM algorithm, block descent and ascent, and the calculus of variations. Convex calculus is now treated in much greater depth. Advanced topics such as the Fenchel conjugate, subdifferentials, duality, feasibility, alternating projections, projected gradient methods, exact penalty methods, and Bregman iteration will equip students with the essentials for understanding modern data mining techniques in high dimensions.
MM Optimization Algorithms offers an overview of the MM principle, a device for deriving optimization algorithms satisfying the ascent or descent property. These algorithms can separate the variables of a problem, avoid large matrix inversions, linearize a problem, restore symmetry, deal with equality and inequality constraints gracefully, and turn a nondifferentiable problem into a smooth problem. The author presents the first extended treatment of MM algorithms, which are ideal for high-dimensional optimization problems in data mining, imaging, and genomics; derives numerous algorithms from a broad diversity of application areas, with a particular emphasis on statistics, biology, and data mining; and summarizes a large amount of literature that has not reached book form before.
Applied Probability presents a unique blend of theory and applications, with special emphasis on mathematical modeling, computational techniques, and examples from the biological sciences. It can serve as a textbook for graduate students in applied mathematics, biostatistics, computational biology, computer science, physics, and statistics. Readers should have a working knowledge of multivariate calculus, linear algebra, ordinary differential equations, and elementary probability theory. Chapter 1 reviews elementary probability and provides a brief survey of relevant results from measure theory. Chapter 2 is an extended essay on calculating expectations. Chapter 3 deals with probabilistic applications of convexity, inequalities, and optimization theory. Chapters 4 and 5 touch on combinatorics and combinatorial optimization. Chapters 6 through 11 present core material on stochastic processes. If supplemented with appropriate sections from Chapters 1 and 2, there is sufficient material for a traditional semester-long course in stochastic processes covering the basics of Poisson processes, Markov chains, branching processes, martingales, and diffusion processes. The second edition adds two new chapters on asymptotic and numerical methods and an appendix that separates some of the more delicate mathematical theory from the steady flow of examples in the main text. Besides the two new chapters, the second edition includes a more extensive list of exercises, many additions to the exposition of combinatorics, new material on rates of convergence to equilibrium in reversible Markov chains, a discussion of basic reproduction numbers in population modeling, and better coverage of Brownian motion. Because many chapters are nearly self-contained, mathematical scientists from a variety of backgrounds will find Applied Probability useful as a reference
Written to equip students in the mathematical siences to understand and model the epidemiological and experimental data encountered in genetics research. This second edition expands the original edition by over 100 pages and includes new material. Sprinkled throughout the chapters are many new problems.
Algorithms are a dominant force in modern culture, and every indication is that they will become more pervasive, not less. The best algorithms are undergirded by beautiful mathematics. This text cuts across discipline boundaries to highlight some of the most famous and successful algorithms. Readers are exposed to the principles behind these examples and guided in assembling complex algorithms from simpler building blocks. Written in clear, instructive language within the constraints of mathematical rigor, Algorithms from THE BOOK includes a large number of classroom-tested exercises at the end of each chapter. The appendices cover background material often omitted from undergraduate courses. Most of the algorithm descriptions are accompanied by Julia code, an ideal language for scientific computing. This code is immediately available for experimentation. Algorithms from THE BOOK is aimed at first-year graduate and advanced undergraduate students. It will also serve as a convenient reference for professionals throughout the mathematical sciences, physical sciences, engineering, and the quantitative sectors of the biological and social sciences.
The fun, fast, portable way to review microbiology and infectious diseases Market: Medical Students (18,750); Physician Assistant Students (3,000); Nurse Practitioner Programs Great review tool for the boards and course exams Every card includes a board-style clinical vignette Format allows students to compare and contrast diseases 220 High Yield Cards Kenneth D. Somers, Ph.D. Eastern Virginia Medical School, Norfolk, VA, and Stephen Morse, Center for Infectious Diseases, Center of Disease Control, Atlanta GA
The most practical and efficient guide to the diagnosis and management of blood disorders – now in full color 200 full-color illustrations! Hematology in Clinical Practice is a succinct, cutting-edge guide to the diagnosis and treatment of disorders of red blood cells, white blood cells, and hemostasis, and the use of blood components for transfusion. Each disease state is discussed in detail, incorporating the pathophysiology, clinical features, up-to-date laboratory testing, and current management strategies into a comprehensive and practical approach to hematologic disorders. Features: New full-color presentation includes over 200 superb illustrations and classic images of blood morphology, tissue pathology, and clinical findings New Case Histories introduce and continue through relevant chapters, highlighting critical clinical points for diagnosis and management New end-of-chapter Points to Remember encapsulate key clinical information New chapters include Anemia in the Elderly and expanded and updated coverage of Transplantation and treatment of hematologic malignancies Outstanding collection of tables, charts, and illustrations that translate basic science into valuable clinical context Strong focus on practical clinical management and supportive care Coverage of state-of-the-art drugs and chemotherapies and the latest advances in genetic testing and molecular pathways Conveniently organized into sections on Red Cells, White Cells, Hemostasis, and Transfusion Medicine
This book investigates whether and why social structure influences cooperative organizational strategic decision making in an international relations context. It looks in particular at the United Nations General Assembly (UNGA).
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