Algebraic Computability and Enumeration Models

Recursion Theory and Descriptive Complexity

Author: Cyrus F. Nourani

Publisher: CRC Press

ISBN: 1771882484

Category: Mathematics

Page: 310

View: 4021

This book, Algebraic Computability and Enumeration Models: Recursion Theory and Descriptive Complexity, presents new techniques with functorial models to address important areas on pure mathematics and computability theory from the algebraic viewpoint. The reader is first introduced to categories and functorial models, with Kleene algebra examples for languages. Functorial models for Peano arithmetic are described toward important computational complexity areas on a Hilbert program, leading to computability with initial models. Infinite language categories are also introduced to explain descriptive complexity with recursive computability with admissible sets and urelements. Algebraic and categorical realizability is staged on several levels, addressing new computability questions with omitting types realizably. Further applications to computing with ultrafilters on sets and Turing degree computability are examined. Functorial models computability is presented with algebraic trees realizing intuitionistic types of models. New homotopy techniques are applied to Marin Lof types of computations with model categories. Functorial computability, induction, and recursion are examined in view of the above, presenting new computability techniques with monad transformations and projective sets. This informative volume will give readers a complete new feel for models, computability, recursion sets, complexity, and realizability. This book pulls together functorial thoughts, models, computability, sets, recursion, arithmetic hierarchy, filters, with real tree computing areas, presented in a very intuitive manner for university teaching, with exercises for every chapter. The book will also prove valuable for faculty in computer science and mathematics.

An Invitation to Model Theory

Author: Jonathan Kirby

Publisher: Cambridge University Press

ISBN: 1107163889

Category: Mathematics

Page: 195

View: 5480

An innovative and largely self-contained textbook bringing model theory to an undergraduate audience.

Generalized Descriptive Set Theory and Classification Theory

Author: Sy-David Friedman,Tapani Hyttinen, Vadim Kulikov

Publisher: American Mathematical Soc.

ISBN: 0821894757

Category: Mathematics

Page: 80

View: 804

Descriptive set theory is mainly concerned with studying subsets of the space of all countable binary sequences. In this paper the authors study the generalization where countable is replaced by uncountable. They explore properties of generalized Baire and Cantor spaces, equivalence relations and their Borel reducibility. The study shows that the descriptive set theory looks very different in this generalized setting compared to the classical, countable case. They also draw the connection between the stability theoretic complexity of first-order theories and the descriptive set theoretic complexity of their isomorphism relations. The authors' results suggest that Borel reducibility on uncountable structures is a model theoretically natural way to compare the complexity of isomorphism relations.

Models and Games

Author: Jouko Väänänen

Publisher: Cambridge University Press

ISBN: 1139496336

Category: Mathematics

Page: N.A

View: 7036

This gentle introduction to logic and model theory is based on a systematic use of three important games in logic: the semantic game; the Ehrenfeucht–Fraïssé game; and the model existence game. The third game has not been isolated in the literature before but it underlies the concepts of Beth tableaux and consistency properties. Jouko Väänänen shows that these games are closely related and in turn govern the three interrelated concepts of logic: truth, elementary equivalence and proof. All three methods are developed not only for first order logic but also for infinitary logic and generalized quantifiers. Along the way, the author also proves completeness theorems for many logics, including the cofinality quantifier logic of Shelah, a fully compact extension of first order logic. With over 500 exercises this book is ideal for graduate courses, covering the basic material as well as more advanced applications.

Fluid Mechanics

A Short Course for Physicists

Author: Gregory Falkovich

Publisher: Cambridge University Press

ISBN: 9781139497510

Category: Science

Page: N.A

View: 6301

The multidisciplinary field of fluid mechanics is one of the most actively developing fields of physics, mathematics and engineering. In this book, the fundamental ideas of fluid mechanics are presented from a physics perspective. Using examples taken from everyday life, from hydraulic jumps in a kitchen sink to Kelvin–Helmholtz instabilities in clouds, the book provides readers with a better understanding of the world around them. It teaches the art of fluid-mechanical estimates and shows how the ideas and methods developed to study the mechanics of fluids are used to analyze other systems with many degrees of freedom in statistical physics and field theory. Aimed at undergraduate and graduate students, the book assumes no prior knowledge of the subject and only a basic understanding of vector calculus and analysis. It contains 32 exercises of varying difficulties, from simple estimates to elaborate calculations, with detailed solutions to help readers understand fluid mechanics.

Geometric Analysis

Author: Peter Li

Publisher: Cambridge University Press

ISBN: 1107020646

Category: Mathematics

Page: 406

View: 7350

Basic techniques for researchers interested in the field of geometric analysis.

Network Economics and the Allocation of Savings

A Model of Peering in the Voice-over-IP Telecommunications Market

Author: Philipp Servatius

Publisher: Springer Science & Business Media

ISBN: 9783642210969

Category: Business & Economics

Page: 297

View: 5241

This book provides a game theoretic model of interaction among VoIP telecommunications providers regarding their willingness to enter peering agreements with one another. The author shows that the incentive to peer is generally based on savings from otherwise payable long distance fees. At the same time, termination fees can have a countering and dominant effect, resulting in an environment in which VoIP firms decide against peering. Various scenarios of peering and rules for allocation of the savings are considered. The first part covers the relevant aspects of game theory and network theory, trying to give an overview of the concepts required in the subsequent application. The second part of the book introduces first a model of how the savings from peering can be calculated and then turns to the actual formation of peering relationships between VoIP firms. The conditions under which firms are willing to peer are then described, considering the possible influence of a regulatory body.

Generative Social Science: Studies in Agent-Based Computational Modeling

Studies in Agent-Based Computational Modeling

Author: Joshua M. Epstein

Publisher: Princeton University Press

ISBN: 1400842875

Category: Business & Economics

Page: 384

View: 2826

Agent-based computational modeling is changing the face of social science. In Generative Social Science, Joshua Epstein argues that this powerful, novel technique permits the social sciences to meet a fundamentally new standard of explanation, in which one "grows" the phenomenon of interest in an artificial society of interacting agents: heterogeneous, boundedly rational actors, represented as mathematical or software objects. After elaborating this notion of generative explanation in a pair of overarching foundational chapters, Epstein illustrates it with examples chosen from such far-flung fields as archaeology, civil conflict, the evolution of norms, epidemiology, retirement economics, spatial games, and organizational adaptation. In elegant chapter preludes, he explains how these widely diverse modeling studies support his sweeping case for generative explanation. This book represents a powerful consolidation of Epstein's interdisciplinary research activities in the decade since the publication of his and Robert Axtell's landmark volume, Growing Artificial Societies. Beautifully illustrated, Generative Social Science includes a CD that contains animated movies of core model runs, and programs allowing users to easily change assumptions and explore models, making it an invaluable text for courses in modeling at all levels.

Analytical Network and System Administration

Managing Human-Computer Systems

Author: Mark Burgess

Publisher: Wiley


Category: Technology & Engineering

Page: 382

View: 9639

Network and system administration usually refers to the skill of keeping computers and networks running properly. But in truth, the skill needed is that of managing complexity. This book describes the science behind these complex systems, independent of the actual operating systems they work on. It provides a theoretical approach to systems administration that: saves time in performing common system administration tasks. allows safe utilization of untrained and trained help in maintaining mission-critical systems. allows efficient and safe centralized network administration. Managing Human-Computer Networks: Will show how to make informed analyses and decisions about systems, how to diagnose faults and weaknesses Gives advice/guidance as to how to determine optimal policies for system management Includes exercises that illustrate the key points of the book The book provides a unique approach to an old problem and will become a classic for researchers and graduate students in Networking and Computer Science, as well as practicing system managers and system administrators.

Conference Record of FPCA '95

SIGPLAN-SIGARCH-WG2.8 Conference on Functional Programming Languages and Computer Architecture : Papers Presented at the Conference, La Jolla, California, 25-28 June 1995

Author: N.A

Publisher: Assn for Computing Machinery


Category: Computer architecture

Page: 333

View: 8341


Debt Games

Strategic Interaction in International Debt Rescheduling

Author: Vinod K. Aggarwal,Aggarwal Vinod K.

Publisher: Cambridge University Press

ISBN: 9780521555524

Category: Business & Economics

Page: 613

View: 2768

This book explains the significant variation that has emerged over time and across cases in international debt rescheduling during the past one hundred and seventy years. Based on a novel situational theory of bargaining, Professor Aggarwal's study provides a method to deduce actors' payoffs in different bargaining situations to develop "debt games," which are then used to predict negotiating outcomes. This integrated political-economic approach to analyze bargaining episodes goes beyond simple economic models or purely descriptive studies. In doing so, it contributes to international political and economic theory, game theory, and historical research on debt negotiations.

Formal Models of Domestic Politics

Author: Scott Gehlbach

Publisher: Cambridge University Press

ISBN: 0521767156

Category: Mathematics

Page: 228

View: 4203

A unified and accessible treatment of important formal models of domestic politics appropriate for students in political science and economics.

Social Behaviour

Genes, Ecology and Evolution

Author: Tamás Székely,Allen J. Moore,Jan Komdeur

Publisher: Cambridge University Press

ISBN: 0521883172

Category: Medical

Page: 562

View: 9059

A comprehensive analysis of the genetic, ecological and phylogenetic aspects of social behaviour, by experts in the field.

The World in the Model

How Economists Work and Think

Author: Mary S. Morgan

Publisher: Cambridge University Press

ISBN: 0521176190

Category: Business & Economics

Page: 421

View: 5726

Describes the radical shift in the study of economic science; where arguing with words was replaced by reasoning with mathematical models.