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Slicing the Truth

Slicing the Truth Author Denis R Hirschfeldt
ISBN-10 9789814612630
Release 2014-07-18
Pages 232
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This book is a brief and focused introduction to the reverse mathematics and computability theory of combinatorial principles, an area of research which has seen a particular surge of activity in the last few years. It provides an overview of some fundamental ideas and techniques, and enough context to make it possible for students with at least a basic knowledge of computability theory and proof theory to appreciate the exciting advances currently happening in the area, and perhaps make contributions of their own. It adopts a case-study approach, using the study of versions of Ramsey's Theorem (for colorings of tuples of natural numbers) and related principles as illustrations of various aspects of computability theoretic and reverse mathematical analysis. This book contains many exercises and open questions. Contents:Setting Off: An IntroductionGathering Our Tools: Basic Concepts and NotationFinding Our Path: König's Lemma and ComputabilityGauging Our Strength: Reverse MathematicsIn Defense of DisarrayAchieving Consensus: Ramsey's TheoremPreserving Our Power: ConservativityDrawing a Map: Five DiagramsExploring Our Surroundings: The World Below RT22Charging Ahead: Further TopicsLagniappe: A Proof of Liu's Theorem Readership: Graduates and researchers in mathematical logic. Key Features:This book assumes minimal background in mathematical logic and takes the reader all the way to current research in a highly active areaIt is the first detailed introduction to this particular approach to this area of researchThe combination of fully worked out arguments and exercises make this book well suited to self-study by graduate students and other researchers unfamiliar with the areaKeywords:Reverse Mathematics;Computability Theory;Computable Mathematics;Computable Combinatorics

Induction Bounding Weak Combinatorial Principles and the Homogeneous Model Theorem

Induction  Bounding  Weak Combinatorial Principles  and the Homogeneous Model Theorem Author Denis R. Hirschfeldt
ISBN-10 9781470426576
Release 2017-09-25
Pages 101
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Goncharov and Peretyat'kin independently gave necessary and sufficient conditions for when a set of types of a complete theory is the type spectrum of some homogeneous model of . Their result can be stated as a principle of second order arithmetic, which is called the Homogeneous Model Theorem (HMT), and analyzed from the points of view of computability theory and reverse mathematics. Previous computability theoretic results by Lange suggested a close connection between HMT and the Atomic Model Theorem (AMT), which states that every complete atomic theory has an atomic model. The authors show that HMT and AMT are indeed equivalent in the sense of reverse mathematics, as well as in a strong computability theoretic sense and do the same for an analogous result of Peretyat'kin giving necessary and sufficient conditions for when a set of types is the type spectrum of some model.

Computability and Complexity

Computability and Complexity Author Adam Day
ISBN-10 9783319500621
Release 2016-11-30
Pages 755
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This Festschrift is published in honor of Rodney G. Downey, eminent logician and computer scientist, surfer and Scottish country dancer, on the occasion of his 60th birthday. The Festschrift contains papers and laudations that showcase the broad and important scientific, leadership and mentoring contributions made by Rod during his distinguished career. The volume contains 42 papers presenting original unpublished research, or expository and survey results in Turing degrees, computably enumerable sets, computable algebra, computable model theory, algorithmic randomness, reverse mathematics, and parameterized complexity, all areas in which Rod Downey has had significant interests and influence. The volume contains several surveys that make the various areas accessible to non-specialists while also including some proofs that illustrate the flavor of the fields.

Algorithmic Randomness and Complexity

Algorithmic Randomness and Complexity Author Rodney G. Downey
ISBN-10 9780387684413
Release 2010-10-29
Pages 855
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Computability and complexity theory are two central areas of research in theoretical computer science. This book provides a systematic, technical development of "algorithmic randomness" and complexity for scientists from diverse fields.

Combinatorial Set Theory

Combinatorial Set Theory Author Lorenz J. Halbeisen
ISBN-10 9783319602318
Release 2017-12-20
Pages 594
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This book, now in a thoroughly revised second edition, provides a comprehensive and accessible introduction to modern set theory. Following an overview of basic notions in combinatorics and first-order logic, the author outlines the main topics of classical set theory in the second part, including Ramsey theory and the axiom of choice. The revised edition contains new permutation models and recent results in set theory without the axiom of choice. The third part explains the sophisticated technique of forcing in great detail, now including a separate chapter on Suslin’s problem. The technique is used to show that certain statements are neither provable nor disprovable from the axioms of set theory. In the final part, some topics of classical set theory are revisited and further developed in light of forcing, with new chapters on Sacks Forcing and Shelah’s astonishing construction of a model with finitely many Ramsey ultrafilters. Written for graduate students in axiomatic set theory, Combinatorial Set Theory will appeal to all researchers interested in the foundations of mathematics. With extensive reference lists and historical remarks at the end of each chapter, this book is suitable for self-study.

Partition Problems in Topology

Partition Problems in Topology Author Stevo Todorcevic
ISBN-10 9780821850916
Release 1989
Pages 116
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This book presents results on the case of the Ramsey problem for the uncountable: When does a partition of a square of an uncountable set have an uncountable homogeneous set? This problem most frequently appears in areas of general topology, measure theory, and functional analysis. Building on his solution of one of the two most basic partition problems in general topology, the ``S-space problem,'' the author has unified most of the existing results on the subject and made many improvements and simplifications. The first eight sections of the book require basic knowldege of naive set theory at the level of a first year graduate or advanced undergraduate student. The book may also be of interest to the exclusively set-theoretic reader, for it provides an excellent introduction to the subject of forcing axioms of set theory, such as Martin's axiom and the Proper forcing axiom.

Effective Mathematics of the Uncountable

Effective Mathematics of the Uncountable Author Noam Greenberg
ISBN-10 9781107512009
Release 2013-10-31
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Classical computable model theory is most naturally concerned with countable domains. There are, however, several methods – some old, some new – that have extended its basic concepts to uncountable structures. Unlike in the classical case, however, no single dominant approach has emerged, and different methods reveal different aspects of the computable content of uncountable mathematics. This book contains introductions to eight major approaches to computable uncountable mathematics: descriptive set theory; infinite time Turing machines; Blum-Shub-Smale computability; Sigma-definability; computability theory on admissible ordinals; E-recursion theory; local computability; and uncountable reverse mathematics. This book provides an authoritative and multifaceted introduction to this exciting new area of research that is still in its early stages. It is ideal as both an introductory text for graduate and advanced undergraduate students and a source of interesting new approaches for researchers in computability theory and related areas.

On Fuzziness

On Fuzziness Author Rudolf Seising
ISBN-10 9783642356414
Release 2013-01-12
Pages 431
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The notion of Fuzziness stands as one of the really new concepts that have recently enriched the world of Science. Science grows not only through technical and formal advances on one side and useful applications on the other side, but also as consequence of the introduction and assimilation of new concepts in its corpus. These, in turn, produce new developments and applications. And this is what Fuzziness, one of the few new concepts arisen in the XX Century, has been doing so far. This book aims at paying homage to Professor Lotfi A. Zadeh, the “father of fuzzy logic” and also at giving credit to his exceptional work and personality. In a way, this is reflected in the variety of contributions collected in the book. In some of them the authors chose to speak of personal meetings with Lotfi; in others, they discussed how certain papers of Zadeh were able to open for them a new research horizon. Some contributions documented results obtained from the author/s after taking inspiration from a particular idea of Zadeh, thus implicitly acknowledging him. Finally, there are contributions of several “third generation fuzzysists or softies” who were firstly led into the world of Fuzziness by a disciple of Lotfi Zadeh, who, following his example, took care of opening for them a new road in science. Rudolf Seising is Adjoint Researcher at the European Centre for Soft Computing in Mieres, Asturias (Spain). Enric Trillas and Claudio Moraga are Emeritus Researchers at the European Centre for Soft Computing, Mieres, Asturias (Spain). Settimo Termini is Professor of Theoretical Computer Science at the University of Palermo, Italy and Affiliated Researcher at the European Centre for Soft Computing, Mieres, Asturias (Spain)

Every Thing Must Go

Every Thing Must Go Author James Ladyman
ISBN-10 9780199276196
Release 2007-07-05
Pages 346
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Every Thing Must Go argues that the only kind of metaphysics that can contribute to objective knowledge is one based specifically on contemporary science as it really is, and not on philosophers' a priori intuitions, common sense, or simplifications of science. In addition to showing how recent metaphysics has drifted away from connection with all other serious scholarly inquiry as a result of not heeding this restriction, they demonstrate how to build a metaphysicscompatible with current fundamental physics ('ontic structural realism'), which, when combined with their metaphysics of the special sciences ('rainforest realism'), can be used to unify physics with the other sciences without reducing these sciences to physics itself. Taking science metaphysically seriously,Ladyman and Ross argue, means that metaphysicians must abandon the picture of the world as composed of self-subsistent individual objects, and the paradigm of causation as the collision of such objects.Everything Must Go also assesses the role of information theory and complex systems theory in attempts to explain the relationship between the special sciences and physics, treading a middle road between the grand synthesis of thermodynamics and information, and eliminativism about information. The consequences of the author's metaphysical theory for central issues in the philosophy of science are explored, including the implications for the realism vs. empiricism debate, the role ofcausation in scientific explanations, the nature of causation and laws, the status of abstract and virtual objects, and the objective reality of natural kinds.

Self organization and Emergence in Life Sciences

Self organization and Emergence in Life Sciences Author Bernard Feltz
ISBN-10 9781402039171
Release 2006-07-10
Pages 352
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Self-organization constitutes one of the most important theoretical debates in contemporary life sciences. The present book explores the relevance of the concept of self-organization and its impact on such scientific fields as: immunology, neurosciences, ecology and theories of evolution. Historical aspects of the issue are also broached. Intuitions relative to self-organization can be found in the works of such key western philosophical figures as Aristotle, Leibniz and Kant. Interacting with more recent authors and cybernetics, self-organization represents a notion in keeping with the modern world's discovery of radical complexity. The themes of teleology and emergence are analyzed by philosophers of sciences with regards to the issues of modelization and scientific explanation. The implications of self-organization for life sciences are here approached from an interdisciplinary angle, revealing the notion as already rewarding and full of promise for the future.

The Unity of Mind Brain and World

The Unity of Mind  Brain and World Author Alfredo Pereira, Jr
ISBN-10 9781107026292
Release 2013-09-12
Pages 368
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This book on consciousness spans the relation of individuals with the world and the individual's constitution at different organizational levels. Covering a diversity of perspectives and presenting a theoretical synthesis, the book will stimulate the current debate on the nature of consciousness, strengthening a more systematic approach to the phenomenon.

Complex Quantum Systems

Complex Quantum Systems Author Heinz Siedentop
ISBN-10 9814460141
Release 2013
Pages 290
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This volume is based on lectures given during the program Complex Quantum Systems held at the National University of Singapore's Institute for Mathematical Sciences from 17 February to 27 March 2010. It guides the reader through two introductory expositions on large Coulomb systems to five of the most important developments in the field: derivation of mean field equations, derivation of effective Hamiltonians, alternative high precision methods in quantum chemistry, modern many body methods originating from quantum information, and - the most complex - semirelativistic quantum electrodynamics. These introductions are written by leaders in their fields; amongst them are Volker Bach, Rafael Benguria, Thomas Chen, and Jan Philip Solovej. Together, they fill a gap between current textbooks and the vast modern literature on complex quantum systems.

Computer Vision ACCV 2010

Computer Vision   ACCV 2010 Author Ron Kimmel
ISBN-10 9783642192821
Release 2011-02-28
Pages 722
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The four-volume set LNCS 6492-6495 constitutes the thoroughly refereed post-proceedings of the 10th Asian Conference on Computer Vision, ACCV 2009, held in Queenstown, New Zealand in November 2010. All together the four volumes present 206 revised papers selected from a total of 739 Submissions. All current issues in computer vision are addressed ranging from algorithms that attempt to automatically understand the content of images, optical methods coupled with computational techniques that enhance and improve images, and capturing and analyzing the world's geometry while preparing the higher level image and shape understanding. Novel gemometry techniques, statistical learning methods, and modern algebraic procedures are dealt with as well.

Computational Intelligence

Computational Intelligence Author Russell C. Eberhart
ISBN-10 9780080553832
Release 2011-04-18
Pages 496
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Computational Intelligence: Concepts to Implementations provides the most complete and practical coverage of computational intelligence tools and techniques to date. This book integrates various natural and engineering disciplines to establish Computational Intelligence. This is the first comprehensive textbook on the subject, supported with lots of practical examples. It asserts that computational intelligence rests on a foundation of evolutionary computation. This refreshing view has set the book apart from other books on computational intelligence. This book lays emphasis on practical applications and computational tools, which are very useful and important for further development of the computational intelligence field. Focusing on evolutionary computation, neural networks, and fuzzy logic, the authors have constructed an approach to thinking about and working with computational intelligence that has, in their extensive experience, proved highly effective. The book moves clearly and efficiently from concepts and paradigms to algorithms and implementation techniques by focusing, in the early chapters, on the specific con. It explores a number of key themes, including self-organization, complex adaptive systems, and emergent computation. It details the metrics and analytical tools needed to assess the performance of computational intelligence tools. The book concludes with a series of case studies that illustrate a wide range of successful applications. This book will appeal to professional and academic researchers in computational intelligence applications, tool development, and systems. Moves clearly and efficiently from concepts and paradigms to algorithms and implementation techniques by focusing, in the early chapters, on the specific concepts and paradigms that inform the authors' methodologies Explores a number of key themes, including self-organization, complex adaptive systems, and emergent computation Details the metrics and analytical tools needed to assess the performance of computational intelligence tools Concludes with a series of case studies that illustrate a wide range of successful applications Presents code examples in C and C++ Provides, at the end of each chapter, review questions and exercises suitable for graduate students, as well as researchers and practitioners engaged in self-study

Countable Boolean Algebras and Decidability

Countable Boolean Algebras and Decidability Author S. S. Goncharov
ISBN-10 030611061X
Release 1997-01-31
Pages 318
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This book describes the latest Russian research covering the structure and algorithmic properties of Boolean algebras from the algebraic and model-theoretic points of view. A significantly revised version of the author's Countable Boolean Algebras (Nauka, Novosibirsk, 1989), the text presents new results as well as a selection of open questions on Boolean algebras. Other current features include discussions of the Kottonen algebras in enrichments by ideals and automorphisms, and the properties of the automorphism groups.

Unveiling Dynamics and Complexity

Unveiling Dynamics and Complexity Author Jarkko Kari
ISBN-10 9783319587417
Release 2017-06-07
Pages 401
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This book constitutes the refereed proceedings of the 13th Conference on Computability in Europe, CiE 2017, held in Turku, Finland, in June 2017. The 24 revised full papers and 12 invited papers were carefully reviewed and selected from 69 submissions. The conference CiE 2016 has six special sessions, namly: algorithmics for biology; combinatorics and algorithmics on words; computability in analysis, algebra, and geometry; cryptography and information theory; formal languages and automata theory; and history and philosophy of computing.

Category Theory in Context

Category Theory in Context Author Emily Riehl
ISBN-10 9780486820804
Release 2017-03-09
Pages 272
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Introduction to concepts of category theory — categories, functors, natural transformations, the Yoneda lemma, limits and colimits, adjunctions, monads — revisits a broad range of mathematical examples from the categorical perspective. 2016 edition.