A mixture of survey and research articles by leading experts that will be of interest to specialists in permutation patterns and other researchers in combinatorics and related fields. In addition, the volume provides plenty of material accessible to advanced undergraduates and is a suitable reference for projects and dissertations.

There has been considerable interest recently in the subject of patterns in permutations and words, a new branch of combinatorics with its roots in the works of Rotem, Rogers, and Knuth in the 1970s. Consideration of the patterns in question has been extremely interesting from the combinatorial point of view, and it has proved to be a useful language in a variety of seemingly unrelated problems, including the theory of Kazhdan—Lusztig polynomials, singularities of Schubert varieties, interval orders, Chebyshev polynomials, models in statistical mechanics, and various sorting algorithms, including sorting stacks and sortable permutations. The author collects the main results in the field in this up-to-date, comprehensive reference volume. He highlights significant achievements in the area, and points to research directions and open problems. The book will be of interest to researchers and graduate students in theoretical computer science and mathematics, in particular those working in algebraic combinatorics and combinatorics on words. It will also be of interest to specialists in other branches of mathematics, theoretical physics, and computational biology. The author collects the main results in the field in this up-to-date, comprehensive reference volume. He highlights significant achievements in the area, and points to research directions and open problems. The book will be of interest to researchers and graduate students in theoretical computer science and mathematics, in particular those working in algebraic combinatorics and combinatorics on words. It will also be of interest to specialists in other branches of mathematics, theoretical physics, and computational biology.

A Unified Account of Permutations in Modern Combinatorics A 2006 CHOICE Outstanding Academic Title, the first edition of this bestseller was lauded for its detailed yet engaging treatment of permutations. Providing more than enough material for a one-semester course, Combinatorics of Permutations, Second Edition continues to clearly show the usefulness of this subject for both students and researchers and is recommended for undergraduate libraries by the MAA. Expanded Chapters Much of the book has been significantly revised and extended. This edition includes a new section on alternating permutations and new material on multivariate applications of the exponential formula. It also discusses several important results in pattern avoidance as well as the concept of asymptotically normal distributions. New Chapter An entirely new chapter focuses on three sorting algorithms from molecular biology. This emerging area of combinatorics is known for its easily stated and extremely difficult problems, which sometimes can be solved using deep techniques from seemingly remote branches of mathematics. Additional Exercises and Problems All chapters in the second edition have more exercises and problems. Exercises are marked according to level of difficulty and many of the problems encompass results from the last eight years.

This volume contains the proceedings of the AMS Special Sessions on Algorithmic Probability and Combinatories held at DePaul University on October 5-6, 2007 and at the University of British Columbia on October 4-5, 2008. This volume collects cutting-edge research and expository on algorithmic probability and combinatories. It includes contributions by well-established experts and younger researchers who use generating functions, algebraic and probabilistic methods as well as asymptotic analysis on a daily basis. Walks in the quarter-plane and random walks (quantum, rotor and self-avoiding), permutation tableaux, and random permutations are considered. In addition, articles in the volume present a variety of saddle-point and geometric methods for the asymptotic analysis of the coefficients of single-and multivariable generating functions associated with combinatorial objects and discrete random structures. The volume should appeal to pure and applied mathematicians, as well as mathematical physicists; in particular, anyone interested in computational aspects of probability, combinatories and enumeration. Furthermore, the expository or partly expository papers included in this volume should serve as an entry point to this literature not only to experts in other areas, but also to graduate students.

Surveys of recent important developments in combinatorics covering a wide range of areas in the field.

Info-metrics is a framework for modeling, reasoning, and drawing inferences under conditions of noisy and insufficient information. It is an interdisciplinary framework situated at the intersection of information theory, statistical inference, and decision-making under uncertainty. In Advances in Info-Metrics, Min Chen, J. Michael Dunn, Amos Golan, and Aman Ullah bring together a group of thirty experts to expand the study of info-metrics across the sciences and demonstrate how to solve problems using this interdisciplinary framework. Building on the theoretical underpinnings of info-metrics, the volume sheds new light on statistical inference, information, and general problem solving. The book explores the basis of information-theoretic inference and its mathematical and philosophical foundations. It emphasizes the interrelationship between information and inference and includes explanations of model building, theory creation, estimation, prediction, and decision making. Each of the nineteen chapters provides the necessary tools for using the info-metrics framework to solve a problem. The collection covers recent developments in the field, as well as many new cross-disciplinary case studies and examples. Designed to be accessible for researchers, graduate students, and practitioners across disciplines, this book provides a clear, hands-on experience for readers interested in solving problems when presented with incomplete and imperfect information.

A One-Stop Source of Known Results, a Bibliography of Papers on the Subject, and Novel Research Directions Focusing on a very active area of research in the last decade, Combinatorics of Compositions and Words provides an introduction to the methods used in the combinatorics of pattern avoidance and pattern enumeration in compositions and words. It

Complex Systems are natural systems that science is unable to describe exhaustively. Examples of Complex Systems are both unicellular and multicellular living beings; human brains; human immune systems; ecosystems; human societies; the global economy; the climate and geology of our planet. This book is an account of a marvelous interdisciplinary journey the author made to understand properties of the Complex Systems. He has undertaken his trip, equipped with the fundamental principles of physical chemistry, in particular, the Second Law of Thermodynamics that describes the spontaneous evolution of our universe, and the tools of Non-linear dynamics. By dealing with many disciplines, in particular, chemistry, biology, physics, economy, and philosophy, the author demonstrates that Complex Systems are intertwined networks, working in out-of-equilibrium conditions, which exhibit emergent properties, such as self-organization phenomena and chaotic behaviors in time and space.

The Pacific Symposium on Biocomputing (PSB) 2010 is an international, multidisciplinary conference for the presentation and discussion of current research in the theory and application of computational methods in problems of biological significance. Presentations are rigorously peer reviewed and are published in an archival proceedings volume. PSB 2010 will be held on January 4 - 8, 2010 in Kohala Coast, Hawaii. Tutorials and workshops will be offered prior to the start of the conference. PSB 2010 will bring together top researchers from the US, Asia Pacific, and around the world to exchange research results and address pertinent issues in all aspects of computational biology. It is a forum for the presentation of work in databases, algorithms, interfaces, visualization, modeling, and other computational methods, as applied to biological problems, with emphasis on applications in data-rich areas of molecular biology. The PSB has been designed to be responsive to the need for critical mass in sub-disciplines within biocomputing. For that reason, it is the only meeting whose sessions are defined dynamically each year in response to specific proposals. PSB sessions are organized by leaders of research in biocomputing's "hot topics". In this way, the meeting provides an early forum for serious examination of emerging methods and approaches in this rapidly changing field.