Algorithms in Bioinformatics

Algorithms in Bioinformatics

An improved model for statistical alignment (I. Mikls, Z. Toroczkai). Improving profile-profile alignments via log average scoring (N. von ohsen, R. Zimmer). False positive s in genomic map assembly and sequence validation (T. Anantharaman, B. Mishra). Boosting EM for radiation hybrid and genetic mapping (T. Schiex, P. Chabrier, M. Bouchez, D. Milan). Placing probes along the genome using pairwise distance data (W. Casey, B. Mishra, M. Wigler). Comparing a Hidden Markov model and a stochastic context-free grammar (A. Jagota, R. B. Lyngso, C. N. S. Pedersen). Assessing the statistical significance of overrepresented oligonucleotides (A. Denise, M. Rgnier, M. vandenbogaert). Pattern matching and pattern discovery algorithms for protein topologies (J. Viksna, D. Gilbert). Computing linking numbers of a filtration (H. Edelsbrusnner, A. Zomorodian). Side chain-positioning as an integer programming problem (O. Eriksson, Y. Zhou, A. Elofsson). A chemical-distance-based test for positive darwinian selection (T. Pupko, R. Sharan, M. Hasegawa, R. Shamir, D. Graur). Finding a maximum compatible tree for a bounded number of trees with bounded degree is solvable in polynominal time (G. Ganapathysaravanabavan, T. Warnow). Experiments in computing sequences of reversals (A. Bergeron, Franois Strasbourg). Exact-IEBP: a new technique for estimating evolutionary distances between whole genomes (Li-San Wang). Finding an optimal inversion median: experimental results (A. C. Siepel, B. M. E. Moret). Analytic solutions for three-taxon MLMC trees with variable rates across sites (B. Chor, M. Hendy, D. Penny). The performance of phylogenetic methods on trees of bounded diameter (L. nakhleh, U. Roshan, K. St. John, J. Sun, T. Warnow). (1+E)- approximation of sorting by reversals and transpositions (N. Eriksen). On the practical solution of the reversal median problem (A. Caprara). Algorithms for finding gene clusters (S. Heber, J. Stoye). Determination of binding amino acids based on random peptide array screening data (P. J. van der Veen, L. F. A. Wessels, J. W. Sloostra, R. H. Meloen, M. J. T. Reinders, J. Hellendoorn). A simple hyper-geometric approach for discovering putative transcription factor binding sites (Y. Barash, G. Bejerano, N. Friedman). Comparing assemblies using fragments and mate-pairs (D. H. Huson, A. L. Halpern, Z. Lai, E. W. myers, K. Reinert, G. G. Sutton). Author index.

Algorithms in Bioinformatics

Numerical Methods for Controlled Stochastic Delay Systems

Numerical Methods for Controlled Stochastic Delay Systems

The Markov chain approximation methods are widely used for the numerical solution of nonlinear stochastic control problems in continuous time. This book extends the methods to stochastic systems with delays. Because such problems are infinite-dimensional, many new issues arise in getting good numerical approximations and in the convergence proofs. Useful forms of numerical algorithms and system approximations are developed in this work, and the convergence proofs are given. All of the usual cost functions are treated as well as singular and impulsive controls. A major concern is on representations and approximations that use minimal memory. Featuring numerical algorithms and examples with applications to control and modern communications systems, this book is the first on the subject and will be of great interest to all those who work with stochastic delay equations and whose main interest is in either the use of the algorithms or in the underlying mathematics. An excellent resource for graduate students, researchers, and practitioners, the work may be used as a graduate-level textbook for a special topics course or seminar on numerical methods in stochastic control.

Numerical Methods for Controlled Stochastic Delay Systems

Algorithms on Trees and Graphs

Algorithms on Trees and Graphs

Graph algorithms is a well-established subject in mathematics and computer science. Beyond classical application fields, like approximation, combinatorial optimization, graphics, and operations research, graph algorithms have recently attracted increased attention from computational molecular biology and computational chemistry. Centered around the fundamental issue of graph isomorphism, this text goes beyond classical graph problems of shortest paths, spanning trees, flows in networks, and matchings in bipartite graphs. Advanced algorithmic results and techniques of practical relevance are presented in a coherent and consolidated way. This book introduces graph algorithms on an intuitive basis followed by a detailed exposition in a literate programming style, with correctness proofs as well as worst-case analyses. Furthermore, full C++ implementations of all algorithms presented are given using the LEDA library of efficient data structures and algorithms. Numerous illustrations, examples, and exercises, and a comprehensive bibliography support students and professionals in using the book as a text and source of reference

Algorithms on Trees and Graphs

Partial Differential Equations

Partial Differential Equations

This book collects papers mainly presented at the ‘International Conference on Partial Differential Equations: Theory, Control and Approximation’ (May 28 to June 1, 2012 in Shanghai) in honor of the scientific legacy of the exceptional mathematician Jacques-Louis Lions. The contributors are leading experts from all over the world, including members of the Academies of Sciences in France, the USA and China etc., and their papers cover key fields of research, e.g. partial differential equations, control theory and numerical analysis, that Jacques-Louis Lions created or contributed so much to establishing.

Partial Differential Equations

Knapsack Problems

Knapsack Problems

This book provides a full-scale presentation of all methods and techniques available for the solution of the Knapsack problem. This most basic combinatorial optimization problem appears explicitly or as a subproblem in a wide range of optimization models with backgrounds such diverse as cutting and packing, finance, logistics or general integer programming. This monograph spans the range from a comprehensive introduction of classical algorithmic methods to the unified presentation of the most recent and advanced results in this area many of them originating from the authors. The chapters dealing with particular versions and extensions of the Knapsack problem are self-contained to a high degree and provide a valuable source of reference for researchers. Due to its simple structure, the Knapsack problem is an ideal model for introducing solution techniques to students of computer science, mathematics and economics. The first three chapters give an in-depth treatment of several basic techniques, making the book also suitable as underlying literature for courses in combinatorial optimization and approximation.

Knapsack Problems

A Course in Modern Analysis and Its Applications

A Course in Modern Analysis and Its Applications

Designed for one-semester courses at the senior undergraduate level, this book will appeal to mathematics majors, to mathematics teachers, and to others who need to learn some mathematical analysis for use in other areas such as engineering, physics, biology or finance.Nominal divisions of pure and applied mathematics have been merged, leaving enough for students of either inclination to have a feeling for further developments. Applications have been included from such fields as differential and integral equations, systems of linear algebraic equations, approximation theory, numerical analysis and quantum mechanics.

A Course in Modern Analysis and Its Applications

Random Perturbation Methods with Applications in Science and Engineering, Volume 150

Random Perturbation Methods with Applications in Science and Engineering, Volume 150

As systems evolve, they are subjected to random operating environments. In addition, random errors occur in measurements of their outputs and in their design and fabrication where tolerances are not precisely met. This book develops methods for describing random dynamical systems, and it illustrates how the methods can be used in a variety of applications. The first half of the book concentrates on finding approximations to random processes using the methodologies of probability theory. The second half of the book derives approximations to solutions of various problems in mechanics, electronic circuits, population biology, and genetics. In each example, the underlying physical or biological phenomenon is described in terms of nonrandom models taken from the literature, and the impact of random noise on the solutions is investigated. The mathematical problems in these applicitons involve random pertubations of gradient systems, Hamiltonian systems, toroidal flows, Markov chains, difference equations, filters, and nonlinear renewal equations. The models are analyzed using the approximation methods described here and are visualized using MATLAB-based computer simulations.

Random Perturbation Methods with Applications in Science and Engineering, Volume 150

Essential Quantum Physics

Essential Quantum Physics

This is a first course on quantum mechanics and describes simple applications to physical phenomena that are of immediate and everyday interest. The first five chapters introduce the fundamentals of quantum mechanics and are followed by a quiz so readers can test themselves. The remaining chapters describe applications, including the physics of lasers, molecular binding, simple properties of crystalline solids arising from their band structure, and the operation of junction transistors. This new expanded edition now includes a chapter on the theory of spin and its application to magnetic resonance imaging, as well as a description of the WKB approximation and its application to alpha decay. Ideal either as a course text or a self-study text, the book contains nearly 100 exercises and hints to their solution.

Essential Quantum Physics