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Abstrak :
[This book summarizes a line of research that maps certain classical problems of discrete mathematics and operations research, such as the Hamiltonian cycle and the Travelling Salesman problems, into convex domains where continuum analysis can be carried out., This book summarizes a line of research that maps certain classical problems of discrete mathematics and operations research, such as the Hamiltonian cycle and the Travelling Salesman problems, into convex domains where continuum analysis can be carried out.]

Abstrak :
This book focuses on the different steps involved in the conception, implementation and application of EDAs that use Markov networks, and undirected models in general. It can serve as a general introduction to EDAs but covers also an important current void in the study of these algorithms by explaining the specificities and benefits of modeling optimization problems by means of undirected probabilistic models. All major developments to date in the progressive introduction of Markov networks based EDAs are reviewed in the book. Hot current research trends and future perspectives in the enhancement and applicability of EDAs are also covered. The contributions included in the book address topics as relevant as the application of probabilistic-based fitness models, the use of belief propagation algorithms in EDAs and the application of Markov network based EDAs to real-world optimization problems.

Abstrak :
This self-contained, practical, entry-level text integrates the basic principles of applied mathematics, applied probability, and computational science for a clear presentation of stochastic processes and control for jump diffusions in continuous time. The author covers the important problem of controlling these systems and, through the use of a jump calculus construction, discusses the strong role of discontinuous and nonsmooth properties versus random properties in stochastic systems. The book emphasizes modeling and problem solving and presents sample applications in financial engineering and biomedical modeling. Computational and analytic exercises and examples are included throughout. While classical applied mathematics is used in most of the chapters to set up systematic derivations and essential proofs, the final chapter bridges the gap between the applied and the abstract worlds to give readers an understanding of the more abstract literature on jump diffusions.

Abstrak :
Matrix analytic methods are popular as modeling tools because they give one the ability to construct and analyze a wide class of queuing models in a unified and algorithmically tractable way. The authors present the basic mathematical ideas and algorithms of the matrix analytic theory in a readable, up-to-date, and comprehensive manner. In the current literature, a mixed bag of techniques is used-some probabilistic, some from linear algebra, and some from transform methods. Here, many new proofs that emphasize the unity of the matrix analytic approach are included. The authors begin by describing several examples of quasi-birth-and-death (QBD) processes. These examples give the reader an idea of the variety of models which are hidden by the general block notation as well as reinforce some of the terminology and notation used throughout the text. These same examples are used as illustrations later. The second part of the book deals with phase-type distributions and related-point processes, which provide a versatile set of tractable models for applied probability. Part three reviews birth-and-death processes, and points out that the arguments for these processes carry over to more general processes in a parallel manner and are based on Markov renewal theory. Part four covers material where algorithmic and probabilistic reasoning are most intimately connected. In three steps, the authors take you from one of the simplest iterative procedures to the fastest, relating the successive approximations to the dynamic behavior of the stochastic process itself. The final part goes beyond simple QBDs with a sequence of short chapters where the authors discuss various extensions to the analyzed processes. Their intention is to show that the fundamental ideas extend beyond simple homogeneous QBD.

Abstrak :
This book is intended for statisticians with minimal backgrounds in algebra. As we ourselves learned algebraic notions through working on statistical problems and collaborating with notable algebraists, we hope that this book with many practical statistical problems is useful for statisticians to start working on the field