الصفحة 1
الصفحة 1
Weighted Littlewood-Paley Theory and Exponential-Square Integrability
Littlewood-Paley theory is an essential tool of Fourier analysis, with applications and connections to PDEs, signal processing, and probability. It extends some of the benefits of orthogonality to situations where orthogonality doesn’t really make sense. It does so by letting us control certain oscillatory infinite series of functions in terms of infinite series of non-negative functions.
Weak Links : The Universal Key to the Stability of Networks and Complex Systems
How can our societies be stabilized in a crisis? Why can we enjoy and understand Shakespeare? Why are fruitflies uniform? How do omnivorous eating habits aid our survival? What makes the Mona Lisa’s smile beautiful? How do women keep our social structures intact? – Could there possibly be a single answer to all these questions? This book shows that the statement: "weak links stabilize complex systems" provides the key to understanding each of these intriguing puzzles, and many others too. The author (recipient of several distinguished science communication prizes) uses weak (low affinity, low probability) interactions as a thread to introduce a vast variety of networks from proteins to economics and ecosystems.
Wave Propagation and Time Reversal in Randomly Layered Media
Wave propagation in random media is an interdisciplinary field that has emerged from the need in physics and engineering to model and analyze wave energy transport in complex environments.This book gives a systematic and self-contained presentation of wave propagation in randomly layered media using the asymptotic theory of ordinary differential equations with random coefficients.
Variant Construction from Theoretical Foundation to Applications
This book presents theoretical framework and sample applications of variant construction. The first part includes the components variant logic, variant measurements, and variant maps, while the second part covers sample applications such as variation with functions, variant stream ciphers, quantum interference, classical/quantum random sequences, whole DNA sequences, and multiple-valued pulse sequences. Addressing topics ranging from logic and measuring foundation to typical applications and including various illustrated maps.
Value-Distribution of L-Functions
This book presents recent results in the value-distribution theory of L-functions with emphasis on the phenomenon of universality. In this book the author proves universality for polynomial Euler products.is written in a narrative and reader friendly language. The author gives many examples, presents main hypotheses and problems in the recent theory of universality. There is a large bibliography of 372 entries. The book is recommended for everybody wanting to see the current panorama of the universality theory.
Validation of Risk Management Models for Financial Institutions : Theory and Practice
Covers all of the major risk areas that a financial institution is exposed to and uses models for, including market risk, interest rate risk, retail credit risk, wholesale credit risk, compliance risk, and investment management. The book discusses current practices and pitfalls that model risk users need to be aware of and identifies areas where validation can be advanced in the future. This provides the first unified framework for validating risk management models.
Using SPSS for Windows : Data Analysis and Graphics
The second edition of this popular guide demonstrates the process of entering and analyzing data using the latest version of SPSS (12.0), and is also appropriate for those using earlier versions of SPSS. The book is easy to follow because all procedures are outlined in a step-by-step format designed for the novice user. Students are introduced to the rationale of statistical tests and detailed explanations of results are given through clearly annotated examples of SPSS output. Topics covered range from descriptive statistics through multiple regression analysis. In addition, this guide includes topics not typically covered in other books such as probability theory, interaction effects in analysis of variance, factor analysis, and scale reliability. Chapter exercises reinforce the text examples and may be performed for further practice, for homework assignments, or in computer laboratory sessions.
Universal Artificial Intelligence : Sequential Decisions Based on Algorithmic Probability
This book presents sequential decision theory from a novel algorithmic information theory perspective. While the former is suited for active agents in known environments, the latter is suited for passive prediction in unknown environments. The book introduces these two well-known but very different ideas and removes the limitations by unifying them to one parameter-free theory of an optimal reinforcement learning agent embedded in an arbitrary unknown environment. Most if not all AI problems can easily be formulated within this theory, which reduces the conceptual problems to pure computational ones. Considered problem classes include sequence prediction, strategic games, function minimization, reinforcement and supervised learning. The discussion includes formal definitions of intelligence order relations, the horizon problem and relations to other approaches to AI.
Univariate Stable Distributions : Models for Heavy Tailed Data
Highlights the many practical uses of stable distributions, exploring the theory, numerical algorithms, and statistical methods used to work with stable laws. Because of the author’s accessible and comprehensive approach, readers will be able to understand and use these methods. Both mathematicians and non-mathematicians will find this a valuable resource for more accurately modelling and predicting large values in a number of real-world scenarios.The following chapters present the theory of stable distributions, a wide range of applications, and statistical methods, with the final chapters focusing on regression, signal processing, and related distributions. Each chapter ends with a number of carefully chosen exercises. Links to free software are included as well, where readers can put these methods into practice.
Understanding Planning Tasks : Domain Complexity and Heuristic Decomposition
Action planning has always played a central role in Artificial Intelligence. Given a description of the current situation, a description of possible actions and a description of the goals to be achieved, the task is to identify a sequence of actions, i.e., a plan that transforms the current situation into one that satisfies the goal description. The book contains an exhaustive analysis of the computational complexity of the benchmark problems that have been used in the past decade, namely the standard benchmark domains of the International Planning Competitions (IPC). At the same time, it contributes to the practice of solving planning tasks by presenting a powerful new approach to heuristic planning. The author also provides an in-depth analysis of so-called routing and transportation problems.
Unconstrained Face Recognition
This volume provides a comprehensive view of unconstrained face recognition, especially face recognition from multiple still images and/or video sequences, assembling a collection of novel approaches able to recognize human faces under various unconstrained situations. The underlying basis of these approaches is that, unlike conventional face recognition algorithms, they exploit the inherent characteristics of the unconstrained situation and thus improve the recognition performance when compared with conventional algorithms. Unconstrained Face Recognition is accessible to a wide audience with an elementary level of linear algebra, probability and statistics, and signal processing.
Uncertainty Theory
Uncertainty theory is a branch of mathematics based on normality, monotonicity, self-duality, and countable subadditivity axioms. The goal of uncertainty theory is to study the behavior of uncertain phenomena such as fuzziness and randomness. The main topics include probability theory, credibility theory, and chance theory. For this new edition the entire text has been totally rewritten. More importantly, the chapters on chance theory and uncertainty theory are completely new. This book provides a self-contained, comprehensive and up-to-date presentation of uncertainty theory. The purpose is to equip the readers with an axiomatic approach to deal with uncertainty. Mathematicians, researchers, engineers, designers, and students in the field of mathematics, information science, operations research, industrial engineering, computer science, artificial intelligence, and management science will find this work a stimulating and useful reference.
Uncertainty Reasoning for the Semantic Web I ; ISWC International Workshops, URSW 2005-2007, Revised Selected and Invited Papers
Represents the first comprehensive compilation of state-of-the-art research approaches to uncertainty reasoning in the context of the semantic Web, capturing different models of uncertainty and approaches to deductive as well as inductive reasoning with uncertain formal knowledge.
Uncertainty and Risk : Mental, Formal, Experimental Representations
This book tries to sort out the different meanings of uncertainty and to discover their foundations. It shows that uncertainty can be represented using various tools and mental guidelines. Some decision criteria are then related to each case and assessed. Alternative ways to deal with risk - and risk attitude concepts - are then examined in the above perspective. Behavior under uncertainty emerges from this book as something to base more on inquiry and reflection than on mere intuition.
Transactions on Computational Systems Biology X
The first three papers describe the applicability of bio-inspired techniques in the technical domain of computing and communication. The following two papers focus on molecular communication and the properties of such communication channels. Two further papers demonstrate techniques for the analysis of genes, and these are followed by a paper outlining an evolutionary approach to the non-unique oligonucleotide probe selection problem. The final paper, which is a regular paper, describes a stochastic pi-calculus model of the PHO pathway.
Theory of Random Sets
Theory of Random Sets presents a state of the art treatment of the modern theory, but it does not neglect to recall and build on the foundations laid by Matheron and others, including the vast advances in stochastic geometry, probability theory, set-valued analysis, and statistical inference of the 1990s. The book is entirely self-contained, systematic and exhaustive, with the full proofs that are necessary to gain insight. It shows the various interdisciplinary relationships of random set theory within other parts of mathematics, and at the same time, fixes terminology and notation that are often varying in the current literature to establish it as a natural part of modern probability theory, and to provide a platform for future development.
Theory of Probability and Random Processes
A one-year course in probability theory and the theory of random processes, taught at Princeton University to undergraduate and graduate students, forms the core of the content of this bookIt is structured in two parts: the first part providing a detailed discussion of Lebesgue integration, Markov chains, random walks, laws of large numbers, limit theorems, and their relation to Renormalization Group theory. The second part includes the theory of stationary random processes, martingales, generalized random processes, Brownian motion, stochastic integrals, and stochastic differential equations. One section is devoted to the theory of Gibbs random fields.
The Teleological and Kalam Cosmological Arguments Revisited
This book moves the discussion ahead in a significant way by devising an original deductive formulation of the Teleological Argument (TA) which demonstrates that the following are the only possible categories of hypotheses concerning fine-tuning and order: (i) chance, (ii) regularity, (iii) combinations of regularity and chance, (iv) uncaused, and (v) design. This book also demonstrates that there are essential features of each category such that, while the alternatives to design are unlikely, the Design Hypothesis is not, and that one can argue for design by exclusion without having to first assign a prior probability for design.
The Structure of Physics
Carl Friedrich von Weizsäcker‘s "Aufbau der Physik", first published in 1985, was intended as an overview of his lifelong concern: an understanding of the unity of physics. That is, the idea of a quantum theory of binary alternatives (the so-called ur-theory), a unified quantum theoretical framework in which spinorial symmetry groups are considered to give rise to the structure of space and time.
The Strength of Nonstandard Analysis
This book reflects the progress made in the forty years since the appearance of Robinson’s revolutionary book Nonstandard Analysis: in the foundations of mathematics and logic, number theory, statistics and probability, in ordinary, partial and stochastic differential equations and in education. The contributions are clear and essentially self-contained.
