Download or read book Foundations of Garside Theory written by Patrick Dehornoy and published by Erich Schmidt Verlag GmbH & Co. KG. This book was released on 2015 with total page 714 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is a monograph on algebra, with connections to geometry and low-dimensional topology. It mainly involves groups, monoids, and categories, and aims to provide a unified treatment for those situations in which one can find distinguished decompositions by iteratively extracting a maximal fragment lying in a prescribed family. Initiated in 1969 by F. A. Garside in the case of Artin's braid groups, this approach led to interesting results in a number of cases, the central notion being what the authors call a Garside family. The study is far from complete, and the purpose of this book is to present the current state of the theory and to invite further research. The book has two parts: In Part A, the bases of a general theory, including many easy examples, are developed. In Part B, various more sophisticated examples are specifically addressed. To make the content accessible to a wide audience of nonspecialists, the book's exposition is essentially self-contained and very few prerequisites are needed. In particular, it should be easy to use this as a textbook both for Garside theory and for the more specialized topics investigated in Part B: Artin-Tits groups, Deligne-Lusztig varieties, groups of algebraic laws, ordered groups, and structure groups of set-theoretic solutions of the Yang-Baxter equation. The first part of the book can be used as the basis for a graduate or advanced undergraduate course.
Download or read book Geometric and Cohomological Group Theory written by Peter H. Kropholler and published by Cambridge University Press. This book was released on 2018 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: Surveys the state of the art in geometric and cohomological group theory. Ideal entry point for young researchers.
Download or read book Sequences Groups and Number Theory written by Valérie Berthé and published by Birkhäuser. This book was released on 2018-04-09 with total page 591 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collaborative book presents recent trends on the study of sequences, including combinatorics on words and symbolic dynamics, and new interdisciplinary links to group theory and number theory. Other chapters branch out from those areas into subfields of theoretical computer science, such as complexity theory and theory of automata. The book is built around four general themes: number theory and sequences, word combinatorics, normal numbers, and group theory. Those topics are rounded out by investigations into automatic and regular sequences, tilings and theory of computation, discrete dynamical systems, ergodic theory, numeration systems, automaton semigroups, and amenable groups. This volume is intended for use by graduate students or research mathematicians, as well as computer scientists who are working in automata theory and formal language theory. With its organization around unified themes, it would also be appropriate as a supplemental text for graduate level courses.
Download or read book Developments in Language Theory written by Igor Potapov and published by Springer. This book was released on 2015-07-17 with total page 459 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 19th International Conference on Developments in Language Theory, DLT 2015, held in Liverpool, UK. The 31 papers presented together with 5 invited talks were carefully reviewed and selected from 54 submissions. Its scope is very general and includes, among others, the following topics and areas: combinatorial and algebraic properties of words and languages, grammars, acceptors and transducers for strings, trees, graphs, arrays, algebraic theories for automata and languages, codes, efficient text algorithms, symbolic dynamics, decision problems, relationships to complexity theory and logic, picture description and analysis, polyominoes and bidimensional patterns, cryptography, concurrency, cellular automata, bio-inspired computing, and quantum computing.
Download or read book Interactions between Group Theory Symmetry and Cryptology written by María Isabel González Vasco and published by MDPI. This book was released on 2020-04-22 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: Cryptography lies at the heart of most technologies deployed today for secure communications. At the same time, mathematics lies at the heart of cryptography, as cryptographic constructions are based on algebraic scenarios ruled by group or number theoretical laws. Understanding the involved algebraic structures is, thus, essential to design robust cryptographic schemes. This Special Issue is concerned with the interplay between group theory, symmetry and cryptography. The book highlights four exciting areas of research in which these fields intertwine: post-quantum cryptography, coding theory, computational group theory and symmetric cryptography. The articles presented demonstrate the relevance of rigorously analyzing the computational hardness of the mathematical problems used as a base for cryptographic constructions. For instance, decoding problems related to algebraic codes and rewriting problems in non-abelian groups are explored with cryptographic applications in mind. New results on the algebraic properties or symmetric cryptographic tools are also presented, moving ahead in the understanding of their security properties. In addition, post-quantum constructions for digital signatures and key exchange are explored in this Special Issue, exemplifying how (and how not) group theory may be used for developing robust cryptographic tools to withstand quantum attacks.
Download or read book Fundamentals of Computation Theory written by Henning Fernau and published by Springer Nature. This book was released on 2023-09-21 with total page 451 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 24th International Symposium on Fundamentals of Computation Theory, FCT 2023, held in Trier, Germany, in September 2023. The __ full papers included in this volume were carefully reviewed and selected from __ submissions. In addition, the book contains ____ invited talks. The papers cover topics of all aspects of theoretical computer science, in particular algorithms, complexity, formal and logical methods.
Download or read book Grobner shirshov Bases Normal Forms Combinatorial And Decision Problems In Algebra written by Leonid Bokut and published by World Scientific. This book was released on 2020-06-16 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is about (associative, Lie and other) algebras, groups, semigroups presented by generators and defining relations. They play a great role in modern mathematics. It is enough to mention the quantum groups and Hopf algebra theory, the Kac-Moody and Borcherds algebra theory, the braid groups and Hecke algebra theory, the Coxeter groups and semisimple Lie algebra theory, the plactic monoid theory. One of the main problems for such presentations is the problem of normal forms of their elements. Classical examples of such normal forms give the Poincaré-Birkhoff-Witt theorem for universal enveloping algebras and Artin-Markov normal form theorem for braid groups in Burau generators.What is now called Gröbner-Shirshov bases theory is a general approach to the problem. It was created by a Russian mathematician A I Shirshov (1921-1981) for Lie algebras (explicitly) and associative algebras (implicitly) in 1962. A few years later, H Hironaka created a theory of standard bases for topological commutative algebra and B Buchberger initiated this kind of theory for commutative algebras, the Gröbner basis theory. The Shirshov paper was largely unknown outside Russia. The book covers this gap in the modern mathematical literature. Now Gröbner-Shirshov bases method has many applications both for classical algebraic structures (associative, Lie algebra, groups, semigroups) and new structures (dialgebra, pre-Lie algebra, Rota-Baxter algebra, operads). This is a general and powerful method in algebra.
Download or read book Perspectives in Lie Theory written by Filippo Callegaro and published by Springer. This book was released on 2017-12-07 with total page 465 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lie theory is a mathematical framework for encoding the concept of symmetries of a problem, and was the central theme of an INdAM intensive research period at the Centro de Giorgi in Pisa, Italy, in the academic year 2014-2015. This book gathers the key outcomes of this period, addressing topics such as: structure and representation theory of vertex algebras, Lie algebras and superalgebras, as well as hyperplane arrangements with different approaches, ranging from geometry and topology to combinatorics.
Download or read book Application and Theory of Petri Nets and Concurrency written by Didier Buchs and published by Springer Nature. This book was released on 2021-06-16 with total page 487 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 42nd International Conference on Application and Theory of Petri Nets and Concurrency, PETRI NETS 2021, which was held virtually in June 2021. The 22 full papers presented together with 2 keynote papers in this volume were carefully reviewed and selected from 39 submissions. The focus of the conference is on the following topics: application of concurrency to system design; games; verification; synthesis and mining; reachability and partial order; semantics; and tools.
Download or read book Foundations of Statistical Natural Language Processing written by Christopher Manning and published by MIT Press. This book was released on 1999-05-28 with total page 722 pages. Available in PDF, EPUB and Kindle. Book excerpt: Statistical approaches to processing natural language text have become dominant in recent years. This foundational text is the first comprehensive introduction to statistical natural language processing (NLP) to appear. The book contains all the theory and algorithms needed for building NLP tools. It provides broad but rigorous coverage of mathematical and linguistic foundations, as well as detailed discussion of statistical methods, allowing students and researchers to construct their own implementations. The book covers collocation finding, word sense disambiguation, probabilistic parsing, information retrieval, and other applications.
Download or read book Bayesian Nets and Causality Philosophical and Computational Foundations written by Jon Williamson and published by Oxford University Press. This book was released on 2005 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bayesian nets are used in artificial intelligence as a calculus for causal reasoning, enabling machines to make predictions perform diagnoses, take decisions and even to discover causal relationships. This book brings together how to automate reasoning in artificial intelligence, and the nature of causality and probability in philosophy.
Download or read book Theoretical Foundations of Behavior Therapy written by Hans J. Eysenck and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book we have attempted to confront a number of issues that are intimately related to the theoretical basis of behavior therapy. We believe that behavior therapy is an extremely efficient procedure for the treatment of neurotic disorders; that it is based on certain principles derived from learning theory; and that it is unique in using basic scientific principles in psychology in the service of applied and practical ends. We believe that we are here dealing with much more than the advantageous use of serendipitous borrowings from nonexistent principles, the cookbook collection of precepts, methods, and working rules that happen to have lasting effects. We also believe that there is truly a general principle unde. rlying behavior therapy, rather than a varied mass of nonintegrated therapies that have little in common other than a name. These beliefs are often contes ted, but usually those who oppose them do so on the basis of misconceptions and misunderstandings that indicate a lack of knowledge of fundamental facts. It is the purpose of this book to remove these misconceptions and misunderstandings, and to bring up to date our knowledge in certain fundamental areas of learning theory, behavior therapy, and the biological foundations of per sonality and individual differences. There are three major groups of misconceptions and misunderstandings. The first of these relates to beliefs held by many psychiatrists and cognitive psychologists relating to behavior therapy.
Download or read book Handbook of Teichm ller Theory written by Athanase Papadopoulos and published by European Mathematical Society. This book was released on 2007 with total page 888 pages. Available in PDF, EPUB and Kindle. Book excerpt: This multi-volume set deals with Teichmuller theory in the broadest sense, namely, as the study of moduli space of geometric structures on surfaces, with methods inspired or adapted from those of classical Teichmuller theory. The aim is to give a complete panorama of this generalized Teichmuller theory and of its applications in various fields of mathematics. The volumes consist of chapters, each of which is dedicated to a specific topic. The volume has 19 chapters and is divided into four parts: The metric and the analytic theory (uniformization, Weil-Petersson geometry, holomorphic families of Riemann surfaces, infinite-dimensional Teichmuller spaces, cohomology of moduli space, and the intersection theory of moduli space). The group theory (quasi-homomorphisms of mapping class groups, measurable rigidity of mapping class groups, applications to Lefschetz fibrations, affine groups of flat surfaces, braid groups, and Artin groups). Representation spaces and geometric structures (trace coordinates, invariant theory, complex projective structures, circle packings, and moduli spaces of Lorentz manifolds homeomorphic to the product of a surface with the real line). The Grothendieck-Teichmuller theory (dessins d'enfants, Grothendieck's reconstruction principle, and the Teichmuller theory of the solenoid). This handbook is an essential reference for graduate students and researchers interested in Teichmuller theory and its ramifications, in particular for mathematicians working in topology, geometry, algebraic geometry, dynamical systems and complex analysis. The authors are leading experts in the field.
Download or read book Quantum Lie Theory written by Vladislav Kharchenko and published by Springer. This book was released on 2015-12-24 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an introduction to the mathematics behind the phrase “quantum Lie algebra”. The numerous attempts over the last 15-20 years to define a quantum Lie algebra as an elegant algebraic object with a binary “quantum” Lie bracket have not been widely accepted. In this book, an alternative approach is developed that includes multivariable operations. Among the problems discussed are the following: a PBW-type theorem; quantum deformations of Kac--Moody algebras; generic and symmetric quantum Lie operations; the Nichols algebras; the Gurevich--Manin Lie algebras; and Shestakov--Umirbaev operations for the Lie theory of nonassociative products. Opening with an introduction for beginners and continuing as a textbook for graduate students in physics and mathematics, the book can also be used as a reference by more advanced readers. With the exception of the introductory chapter, the content of this monograph has not previously appeared in book form.
Download or read book Foundations of Computational Linguistics written by Roland Hausser and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 585 pages. Available in PDF, EPUB and Kindle. Book excerpt: As an interdisciplinary field, computational linguistics has its sources in several areas of science, each with its own goals, methods, and historical background. Thereby, it has remained unclear which components fit together and which do not. This suggests three possible approaches to designing a computational linguistics textbook. The first approach proceeds from one's own school of thought, usually determined of study, rather than by a well-informed, delib by chance, such as one's initial place erate choice. The goal is to extend the inherited theoretical framework or method to as many aspects of language analysis as possible. As a consequence, the issue of com pat ibility with other approaches in the field need not be addressed and one's assumptions are questioned at best in connection with 'puzzling problems. ' The second approach takes the viewpoint of an objective observer and aims to survey the field as completely as possible. However, the large number of different schools, methods, and tasks necessitates a subjective selection. Furthermore, the pre sumed neutrality provides no incentive to investigate the compatibility between the elements selected. The third approach aims at solving a comprehensive functional task, with the differ To arrive at the desired solution, suitability ent approaches being ordered relative to it. and compatibility of the different elements adopted must be investigated with regard to the task at hand.
Download or read book Foundations of Computational Linguistics written by Roland R. Hausser and published by Springer Science & Business Media. This book was released on 2001 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt: The central task of a future-oriented computational linguistics is the development of cognitive machines which humans can freely talk with in their respective natural language. In the long run, this task will ensure the development of a functional theory of language, an objective method of verification, and a wide range of practical applications. Natural communication requires not only verbal processing, but also non-verbal perception and action. Therefore the content of this textbook is organized as a theory of language for the construction of talking robots. The main topic is the mechanism of natural language communication in both the speaker and the hearer. The content is divided into four parts: Theory of Language, Theory of Grammar, Morphology and Syntax, Semantics and Pragmatics. The book contains more than 700 exercises for reviewing key ideas and important problems. In the Second Edition, changes are most noticeable in Chapters 22-24, which have been completely rewritten. They present a declarative outline for programming the semantic and pragmatic interpretation of natural language communication. The presentation is now simpler and more comprehensive. It is defined as a formal fragment and includes a new control structure, an analysis of spatio-temporal infer-encing, and an analysis of internal matching based on the notion of a task analysis. Examples and explanations which were contained in the old versions of Chapters 22-24 have been moved to the new Appendix. A schematic summary and a conclusion have been added as well.
Download or read book Introducing Writing Across the Curriculum into China written by Dan Wu and published by Springer Science & Business Media. This book was released on 2012-09-19 with total page 143 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dr. Wu Dan’s Introducing Writing Across the Curriculum into China is an important and provocative research study that is broadly international in scope. Of particular significance for education in China, this book provides a historical analysis of writing instruction in China and an original application of activity theory used to analyze problems and possibilities for Writing Across the Curriculum (WAC) in higher education. Through an examination of important aspects of WAC as it has developed in the United States, Dr. Wu Dan brings together various perspectives in support of developing and sustaining WAC programs in China and by analogy throughout the world. Her work opens new avenues for research in writing and for the teaching of courses throughout the curriculum using a writing-in-the-disciplines approach. A major contribution to international WAC scholarship, Introducing Writing Across the Curriculum into China will be invaluable to English faculty and to all readers interested in educational innovations in China.
