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Bioinformatics and Computational Biology Solutions Using R and Bioconductor
Bioconductor is a widely used open source and open development software project for the analysis and comprehension of data arising from high-throughput experimentation in genomics and molecular biology. Bioconductor is rooted in the open source statistical computing environment R. This volume's coverage is broad and ranges across most of the key capabilities of the Bioconductor project, including: Importation and preprocessing of high-throughput data from microarray, proteomic, and flow cytometry platforms / Curation and delivery of biological metadata for use in statistical modeling and interpretation. / Statistical analysis of high-throughput data, including machine learning and visualization,modeling and visualization of graphs and networks. This book is a dynamic document. Code underlying all of the computations that are shown is made available on a companion website, and readers can reproduce every number, figure, and table on their own computers.
Binomial models in finance
This book deals with many topics in modern financial mathematics in a way that does not use advanced mathematical tools and shows how these models can be numerically implemented in a practical way. The book is aimed at undergraduate students, MBA students, and executives who wish to understand and apply financial models in the spreadsheet computing environment.The basic building block is the one-step binomial model where a known price today can take one of two possible values at the next time. In this simple situation, risk neutral pricing can be defined and the model can be applied to price forward contracts, exchange rate contracts, and interest rate derivatives.
Binary Quadratic Forms: An Algorithmic Approach
This book deals with algorithmic problems concerning binary quadratic forms 2 2 f(X,Y)= aX +bXY +cY with integer coe?cients a, b, c, the mathem- ical theories that permit the solution of these problems, and applications to cryptography.
Beyond partial differential equations : On linear and Quasi-Linear abstract hyperbolic evolution equations
The present volume is self-contained and introduces to the treatment of linear and nonlinear (quasi-linear) abstract evolution equations by methods from the theory of strongly continuous semigroups.
Benchmarking, Temporal Distribution, and Reconciliation Methods for Time Series
This book discusses the statistical methods most often applied for such adjustments, ranging from ad hoc procedures to regression-based models. The latter are emphasized, because of their clarity, ease of application, and superior results. Each topic is illustrated with many real case examples. In order to facilitate understanding of their properties and limitations of the methods discussed, a real data example, the Canada Total Retail Trade Series, is followed throughout the book.This book brings together the scattered literature on these topics and presents them using a consistent notation and a unifying view.
Bayesian reliability
Bayesian Reliability presents modern methods and techniques for analyzing reliability data from a Bayesian perspective. The adoption and application of Bayesian methods in virtually all branches of science and engineering have significantly increased over the past few decades. This increase is largely due to advances in simulation-based computational tools for implementing Bayesian methods. The authors extensively use such tools throughout this book, focusing on assessing the reliability of components and systems with particular attention to hierarchical models and models incorporating explanatory variables. Such models include failure time regression models, accelerated testing models, and degradation models. The authors pay special attention to Bayesian goodness-of-fit testing, model validation, reliability test design, and assurance test planning. Throughout the book, the authors use Markov chain Monte Carlo (MCMC) algorithms for implementing Bayesian analyses--algorithms that make the Bayesian approach to reliability computationally feasible and conceptually straightforward.
Bayesian core : A practical approach to computational Bayesian statistics
This Bayesian modeling book provides an operational methodology for conducting Bayesian inference, rather than focusing on its theoretical justifications. Special attention is paid to the derivation of prior distributions in each case and specific reference solutions are given for each of the models.
Bayesian computation with R : Introduces Bayesian modeling by use of computation using the R language
R's open source nature, free availability, and large number of contributor packages have made R the software of choice for many statisticians in education and industry. Bayesian Computation with R introduces Bayesian modeling by the use of computation using the R language.
Basic Real Analysis
Basic Real Analysis and Advanced Real Analysis (available separately or together as a Set) systematically develop those concepts and tools in real analysis that are vital to every mathematician, whether pure or applied, aspiring or established. These works present a comprehensive treatment with a global view of the subject, emphasizing the connections between real analysis and other branches of mathematics.
Basic Probability Theory with Applications
This book presents elementary probability theory with interesting and well-chosen applications that illustrate the theory. An introductory chapter reviews the basic elements of differential calculus which are used in the material to follow. The theory is presented systematically, beginning with the main results in elementary probability theory. This is followed by material on random variables. Random vectors, including the all important central limit theorem, are treated next. The last three chapters concentrate on applications of this theory in the areas of reliability theory, basic queuing models, and time series. Examples are elegantly woven into the text and over 400 exercises reinforce the material and provide students with ample practice.
Basic principles and applications of probability theory
This introductory chapter discusses such notions as determinism, chaos and randomness, p- dictibility and unpredictibility, some initial approaches to formalizing r- domness and it surveys certain problems that can be solved by probability theory. This will perhaps give one an idea to what extent the theory can - swer questions arising in speci?c random occurrences and the character of the answers provided by the theory. 1. 1 The Nature of Randomness The phrase “by chance” has no single meaning in ordinary language. For instance, it may mean unpremeditated, nonobligatory, unexpected, and so on. Its opposite sense is simpler: “not by chance” signi?es obliged to or bound to (happen). In philosophy, necessity counteracts randomness. Necessity signi?es conforming to law – it can be expressed by an exact law. The basic laws of mechanics, physics and astronomy can be formulated in terms of precise quantitativerelationswhichmustholdwithironcladnecessity.
Basic Notions of Algebra
Aims to present a general survey of algebra, of its basic notions and main branches.Those parts of the book devoted to the systematic treatment of notions and results of algebra make very limited demands on the reader: we presuppose only that the reader knows calculus, analytic geometry and linear algebra in the form taught in many high schools and colleges. The extent of the prerequisites required in our treatment of examples is harder to state; an acquaintance with projective space, topological spaces, differentiable and complex analytic manifolds and the basic theory of functions of a complex variable is desirable, but the reader should bear in mind that difficulties arising in the treatment of some specific example are likely to be purely local in nature, and not to affect the understanding of the rest of the book.
Basic Algebra
Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Together, the two books give the reader a global view of algebra and its role in mathematics as a whole.Basic Algebra presents the subject matter in a forward-looking way that takes into account its historical development. It is suitable as a text in a two-semester advanced undergraduate or first-year graduate sequence in algebra, possibly supplemented by some material from Advanced Algebra at the graduate level. It requires of the reader only familiarity with matrix algebra, an understanding of the geometry and reduction of linear equations, and an acquaintance with proofs.
Axiom of Choice
AC, the axiom of choice, because of its non-constructive character, is the most controversial mathematical axiom, shunned by some, used indiscriminately by others. This treatise shows paradigmatically that:Disasters happen without AC: Many fundamental mathematical results fail (being equivalent in ZF to AC or to some weak form of AC).Disasters happen with AC: Many undesirable mathematical monsters are being created (e.g., non measurable sets and undeterminate games).Illuminating examples are drawn from diverse areas of mathematics, particularly from general topology, but also from algebra, order theory, elementary analysis, measure theory, game theory, and graph theory.
Averaging Methods in Nonlinear Dynamical Systems
The authors have presented an extensive revision of the first edition of the Averaging Methods in Nonlinear Dynamical Systems book. There are many changes, corrections and updates in chapters on Basic Material and Asymptotics, Averaging, and Attraction.
Average-Cost Control of Stochastic Manufacturing Systems
This book is concerned with hierarchical control of manufacturing systems under uncertainty. It focuses on system performance measured in long-run average cost criteria, exploring the relationship between control problems with a discounted cost and that with a long-run average cost in connection with hierarchical control. A new theory is articulated that shows that hierarchical decision making in the context of a goal-seeking manufacturing system can lead to a near optimization of its objective. The approach in the book considers manufacturing systems in which events occur at different time scales.
Automorphic Forms and Lie Superalgebras
Most known examples of Lie superalgebras with a related automorphic form such as the Fake Monster Lie algebra whose reflection group is given by the Leech lattice arise from (super)string theory and can be derived from lattice vertex algebras. The No-Ghost Theorem from dual resonance theory and a conjecture of Berger-Li-Sarnak on the eigenvalues of the hyperbolic Laplacian provide strong evidence that they are of rank at most 26.The aim of this book is to give the reader the tools to understand the ongoing classification and construction project of this class of Lie superalgebras and is ideal for a graduate course.
Automatic Differentiation : Applications, Theory, and Implementations
This collection covers the state of the art in automatic differentiation theory and practice. Practitioners and students will learn about advances in automatic differentiation techniques and strategies for the implementation of robust and powerful tools. Computational scientists and engineers will benefit from the discussion of applications, which provide insight into effective strategies for using automatic differentiation for design optimization, sensitivity analysis, and uncertainty quantification.
Attractivity and bifurcation for nonautonomous dynamical systems
Although, bifurcation theory of equations with autonomous and periodic time dependence is a major object of research in the study of dynamical systems since decades, the notion of a nonautonomous bifurcation is not yet established. In this book, two different approaches are developed which are based on special definitions of local attractivity and repulsivity.
Asymptotics for Dissipative Nonlinear Equations
Many of problems of the natural sciences lead to nonlinear partial differential equations. However, only a few of them have succeeded in being solved explicitly. Therefore different methods of qualitative analysis such as the asymptotic methods play a very important role. This is the first book in the world literature giving a systematic development of a general asymptotic theory for nonlinear partial differential equations with dissipation. Many typical well-known equations are considered as examples, such as: nonlinear heat equation, KdVB equation, nonlinear damped wave equation, Landau-Ginzburg equation, Sobolev type equations, systems of equations of Boussinesq, Navier-Stokes and others.
