Download or read book Sets And Computations written by Raghavan Dilip and published by World Scientific. This book was released on 2017-06-22 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: The contents in this volume are based on the program Sets and Computations that was held at the Institute for Mathematical Sciences, National University of Singapore from 30 March until 30 April 2015. This special collection reports on important and recent interactions between the fields of Set Theory and Computation Theory. This includes the new research areas of computational complexity in set theory, randomness beyond the hyperarithmetic, powerful extensions of Goodstein's theorem and the capturing of large fragments of set theory via elementary-recursive structures. Further chapters are concerned with central topics within Set Theory, including cardinal characteristics, Fraïssé limits, the set-generic multiverse and the study of ideals. Also Computation Theory, which includes computable group theory and measure-theoretic aspects of Hilbert's Tenth Problem. A volume of this broad scope will appeal to a wide spectrum of researchers in mathematical logic.
Download or read book Basis Sets in Computational Chemistry written by Eva Perlt and published by Springer Nature. This book was released on 2021-05-06 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book addresses the construction and application of the major types of basis sets for computational chemistry calculations. In addition to a general introduction, it includes mathematical basics and a discussion of errors arising from incomplete or inappropriate basis sets. The different chapters introduce local orbitals and orbital localization as well as Slater-type orbitals and review basis sets for special applications, such as those for correlated methods, solid-state calculations, heavy atoms and time-dependent adaptable Gaussian bases for quantum dynamics simulations. This detailed review of the purpose of basis sets, their design, applications, possible problems and available solutions provides graduate students and beginning researchers with information not easily obtained from the available textbooks and offers valuable supporting material for any quantum chemistry or computational chemistry course at the graduate and/or undergraduate level. This book is also useful as a guide for researchers who are new to computational chemistry but are willing to extend their research tools by applying such methods.
Download or read book Mathematics and Computation written by Avi Wigderson and published by Princeton University Press. This book was released on 2019-10-29 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences, technology, and philosophy Mathematics and Computation provides a broad, conceptual overview of computational complexity theory—the mathematical study of efficient computation. With important practical applications to computer science and industry, computational complexity theory has evolved into a highly interdisciplinary field, with strong links to most mathematical areas and to a growing number of scientific endeavors. Avi Wigderson takes a sweeping survey of complexity theory, emphasizing the field’s insights and challenges. He explains the ideas and motivations leading to key models, notions, and results. In particular, he looks at algorithms and complexity, computations and proofs, randomness and interaction, quantum and arithmetic computation, and cryptography and learning, all as parts of a cohesive whole with numerous cross-influences. Wigderson illustrates the immense breadth of the field, its beauty and richness, and its diverse and growing interactions with other areas of mathematics. He ends with a comprehensive look at the theory of computation, its methodology and aspirations, and the unique and fundamental ways in which it has shaped and will further shape science, technology, and society. For further reading, an extensive bibliography is provided for all topics covered. Mathematics and Computation is useful for undergraduate and graduate students in mathematics, computer science, and related fields, as well as researchers and teachers in these fields. Many parts require little background, and serve as an invitation to newcomers seeking an introduction to the theory of computation. Comprehensive coverage of computational complexity theory, and beyond High-level, intuitive exposition, which brings conceptual clarity to this central and dynamic scientific discipline Historical accounts of the evolution and motivations of central concepts and models A broad view of the theory of computation's influence on science, technology, and society Extensive bibliography
Download or read book Sets Logic Computation written by Richard Zach and published by . This book was released on 2021-07-13 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: A textbook on the semantics, proof theory, and metatheory of first-order logic. It covers naive set theory, first-order logic, sequent calculus and natural deduction, the completeness, compactness, and Löwenheim-Skolem theorems, Turing machines, and the undecidability of the halting problem and of first-order logic. It is based on the Open Logic project, and available for free download at slc.openlogicproject.org.
Download or read book Computational Logic and Set Theory written by Jacob T. Schwartz and published by Springer Science & Business Media. This book was released on 2011-07-16 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: This must-read text presents the pioneering work of the late Professor Jacob (Jack) T. Schwartz on computational logic and set theory and its application to proof verification techniques, culminating in the ÆtnaNova system, a prototype computer program designed to verify the correctness of mathematical proofs presented in the language of set theory. Topics and features: describes in depth how a specific first-order theory can be exploited to model and carry out reasoning in branches of computer science and mathematics; presents an unique system for automated proof verification in large-scale software systems; integrates important proof-engineering issues, reflecting the goals of large-scale verifiers; includes an appendix showing formalized proofs of ordinals, of various properties of the transitive closure operation, of finite and transfinite induction principles, and of Zorn’s lemma.
Download or read book Sets Logic and Maths for Computing written by David Makinson and published by Springer Science & Business Media. This book was released on 2012-02-27 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: This easy-to-follow textbook introduces the mathematical language, knowledge and problem-solving skills that undergraduates need to study computing. The language is in part qualitative, with concepts such as set, relation, function and recursion/induction; but it is also partly quantitative, with principles of counting and finite probability. Entwined with both are the fundamental notions of logic and their use for representation and proof. Features: teaches finite math as a language for thinking, as much as knowledge and skills to be acquired; uses an intuitive approach with a focus on examples for all general concepts; brings out the interplay between the qualitative and the quantitative in all areas covered, particularly in the treatment of recursion and induction; balances carefully the abstract and concrete, principles and proofs, specific facts and general perspectives; includes highlight boxes that raise common queries and clear confusions; provides numerous exercises, with selected solutions.
Download or read book Control of Stochastic Hybrid Systems based on Probabilistic Reachable Set Computation written by Leonhard Asselborn and published by kassel university press GmbH. This book was released on 2018-09-17 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis proposes an algorithmic controller synthesis based on the computation of probabilistic reachable sets for stochastic hybrid systems. Hybrid systems consist in general of a composition of discrete and continuous valued dynamics, and are able to capture a wide range of physical phenomena. The stochasticity is considered in form of normally distributed initial continuous states and normally distributed disturbances, resulting in stochastic hybrid systems. The reachable sets describe all states, which are reachable by a system for a given initialization of the system state, inputs, disturbances, and time horizon. For stochastic hybrid systems, these sets are probabilistic, since the system state and disturbance are random variables. This thesis introduces probabilistic reachable sets with a predefined confidence, which are used in an optimization based procedure for the determination of stabilizing control inputs. Besides the stabilizing property, the controlled dynamics also observes input constraints, as well as, so-called chance constraints for the continuous state. The main contribution of this thesis is the formulation of an algorithmic control procedure for each considerd type of stochastic hybrid systems, where different discrete dynamics are considered. First, a control procedure for a deterministic system with bounded disturbances is introduced, and thereafter a probabilistic distribution of the system state and the disturbance is assumed. The formulation of probabilistic reachable sets with a predefined confidence is subsequently used in a control procedure for a stochastic hybrid system, in which the switch of the continuous dynamics is externally induced. Finally, the control procedure based on reachable set computation is extended to a type of stochastic hybrid systems with autonomously switching of the continuous dynamics.
Download or read book Computability of Julia Sets written by Mark Braverman and published by Springer Science & Business Media. This book was released on 2009-02-08 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: Among all computer-generated mathematical images, Julia sets of rational maps occupy one of the most prominent positions. Their beauty and complexity can be fascinating. They also hold a deep mathematical content. Computational hardness of Julia sets is the main subject of this book. By definition, a computable set in the plane can be visualized on a computer screen with an arbitrarily high magnification. There are countless programs to draw Julia sets. Yet, as the authors have discovered, it is possible to constructively produce examples of quadratic polynomials, whose Julia sets are not computable. This result is striking - it says that while a dynamical system can be described numerically with an arbitrary precision, the picture of the dynamics cannot be visualized. The book summarizes the present knowledge (most of it from the authors' own work) about the computational properties of Julia sets in a self-contained way. It is accessible to experts and students with interest in theoretical computer science or dynamical systems.
Download or read book Algorithms and Theory of Computation Handbook 2 Volume Set written by Mikhail J. Atallah and published by CRC Press. This book was released on 2022-05-30 with total page 1944 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algorithms and Theory of Computation Handbook, Second Edition in a two volume set, provides an up-to-date compendium of fundamental computer science topics and techniques. It also illustrates how the topics and techniques come together to deliver efficient solutions to important practical problems. New to the Second Edition: Along with updating and revising many of the existing chapters, this second edition contains more than 20 new chapters. This edition now covers external memory, parameterized, self-stabilizing, and pricing algorithms as well as the theories of algorithmic coding, privacy and anonymity, databases, computational games, and communication networks. It also discusses computational topology, computational number theory, natural language processing, and grid computing and explores applications in intensity-modulated radiation therapy, voting, DNA research, systems biology, and financial derivatives. This best-selling handbook continues to help computer professionals and engineers find significant information on various algorithmic topics. The expert contributors clearly define the terminology, present basic results and techniques, and offer a number of current references to the in-depth literature. They also provide a glimpse of the major research issues concerning the relevant topics
Download or read book A Book of Set Theory written by Charles C Pinter and published by Courier Corporation. This book was released on 2014-07-23 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This accessible approach to set theory for upper-level undergraduates poses rigorous but simple arguments. Each definition is accompanied by commentary that motivates and explains new concepts. A historical introduction is followed by discussions of classes and sets, functions, natural and cardinal numbers, the arithmetic of ordinal numbers, and related topics. 1971 edition with new material by the author"--
Download or read book EVOLVE A Bridge between Probability Set Oriented Numerics and Evolutionary Computation V written by Alexandru-Adrian Tantar and published by Springer. This book was released on 2014-06-04 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume encloses research articles that were presented at the EVOLVE 2014 International Conference in Beijing, China, July 1–4, 2014. The book gathers contributions that emerged from the conference tracks, ranging from probability to set oriented numerics and evolutionary computation; all complemented by the bridging purpose of the conference, e.g. Complex Networks and Landscape Analysis, or by the more application oriented perspective. The novelty of the volume, when considering the EVOLVE series, comes from targeting also the practitioner’s view. This is supported by the Machine Learning Applied to Networks and Practical Aspects of Evolutionary Algorithms tracks, providing surveys on new application areas, as in the networking area and useful insights in the development of evolutionary techniques, from a practitioner’s perspective. Complementary to these directions, the conference tracks supporting the volume, follow on the individual advancements of the subareas constituting the scope of the conference, through the Computational Game Theory, Local Search and Optimization, Genetic Programming, Evolutionary Multi-objective optimization tracks.
Download or read book EVOLVE A Bridge between Probability Set Oriented Numerics and Evolutionary Computation III written by Oliver Schuetze and published by Springer. This book was released on 2013-07-23 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book comprises a selection of extended abstracts and papers presented at the EVOLVE 2012 held in Mexico City, Mexico. The aim of the EVOLVE is to build a bridge between probability, set oriented numerics, and evolutionary computation as to identify new common and challenging research aspects. The conference is also intended to foster a growing interest for robust and efficient methods with a sound theoretical background. EVOLVE aims to unify theory-inspired methods and cutting-edge techniques ensuring performance guarantee factors. By gathering researchers with different backgrounds, a unified view and vocabulary can emerge where the theoretical advancements may echo in different domains. Summarizing, the EVOLVE conference focuses on challenging aspects arising at the passage from theory to new paradigms and aims to provide a unified view while raising questions related to reliability, performance guarantees, and modeling. The extended papers of the EVOLVE 2012 make a contribution to this goal.
Download or read book A neutrosophic set based computational model for a time dependent decision support system with multi attribute criteria written by Andy St. Fort and published by Infinite Study. This book was released on with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt: We present a neutrosophic set-based model for a time-dependent decision-support system (DSS) with multiattribute criteria decision-making.We describe such DSS as one that includes multiple conflicting objectives having strategies spanning over several time-periods. In this paper, we utilize the concept of neutrosophic sets and some of its operations to present a computational model that captures decision trees with various imprecise preferences for a time-dependent DSS.
Download or read book Set Theory for Computing written by Domenico Cantone and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: An up-to-date and comprehensive account of set-oriented symbolic manipulation and automated reasoning methods. This book is of interest to graduates and researchers in theoretical computer science and computational logic and automated reasoning.
Download or read book Annual Report of the Commissioners of the District of Columbia written by District of Columbia. Board of Commissioners and published by . This book was released on 1903 with total page 1260 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book EVOLVE A Bridge between Probability Set Oriented Numerics and Evolutionary Computation IV written by Michael Emmerich and published by Springer Science & Business Media. This book was released on 2013-06-12 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical and computational methods are nowadays used in a wide range of contexts in complex systems research, biology, physics, and engineering. Over the last decades different methodological schools have emerged with emphasis on different aspects of computation, such as nature-inspired algorithms, set oriented numerics, probabilistic systems and Monte Carlo methods. Due to the use of different terminologies and emphasis on different aspects of algorithmic performance there is a strong need for a more integrated view and opportunities for cross-fertilization across particular disciplines. These proceedings feature 20 original publications from distinguished authors in the cross-section of computational sciences, such as machine learning algorithms and probabilistic models, complex networks and fitness landscape analysis, set oriented numerics and cell mapping, evolutionary multiobjective optimization, diversity-oriented search, and the foundations of genetic programming algorithms. By presenting cutting edge results with a strong focus on foundations and integration aspects this work presents a stepping stone towards efficient, reliable, and well-analyzed methods for complex systems management and analysis.
Download or read book EVOLVE A Bridge between Probability Set Oriented Numerics and Evolutionary Computation written by Emilia Tantar and published by Springer. This book was released on 2012-09-14 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to provide a strong theoretical support for understanding and analyzing the behavior of evolutionary algorithms, as well as for creating a bridge between probability, set-oriented numerics and evolutionary computation. The volume encloses a collection of contributions that were presented at the EVOLVE 2011 international workshop, held in Luxembourg, May 25-27, 2011, coming from invited speakers and also from selected regular submissions. The aim of EVOLVE is to unify the perspectives offered by probability, set oriented numerics and evolutionary computation. EVOLVE focuses on challenging aspects that arise at the passage from theory to new paradigms and practice, elaborating on the foundations of evolutionary algorithms and theory-inspired methods merged with cutting-edge techniques that ensure performance guarantee factors. EVOLVE is also intended to foster a growing interest for robust and efficient methods with a sound theoretical background. The chapters enclose challenging theoretical findings, concrete optimization problems as well as new perspectives. By gathering contributions from researchers with different backgrounds, the book is expected to set the basis for a unified view and vocabulary where theoretical advancements may echo in different domains.
