Lattice Rules

Author : Josef Dick,Peter Kritzer,Friedrich Pillichshammer
Publisher : Springer Nature
Page : 584 pages
File Size : 43,9 Mb
Release : 2022-08-24
Category : Mathematics
ISBN : 9783031099519

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Lattice Rules by Josef Dick,Peter Kritzer,Friedrich Pillichshammer Pdf

Lattice rules are a powerful and popular form of quasi-Monte Carlo rules based on multidimensional integration lattices. This book provides a comprehensive treatment of the subject with detailed explanations of the basic concepts and the current methods used in research. This comprises, for example, error analysis in reproducing kernel Hilbert spaces, fast component-by-component constructions, the curse of dimensionality and tractability, weighted integration and approximation problems, and applications of lattice rules.

Author : I. H. Sloan,S. Joe
Publisher : Oxford University Press
Page : 256 pages
File Size : 42,9 Mb
Release : 1994
Category : Mathematics
ISBN : 0198534728

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Lattice Methods for Multiple Integration by I. H. Sloan,S. Joe Pdf

This is the first book devoted to lattice methods, a recently developed way of calculating multiple integrals in many variables. Multiple integrals of this kind arise in fields such as quantum physics and chemistry, statistical mechanics, Bayesian statistics and many others. Lattice methods are an effective tool when the number of integrals are large. The book begins with a review of existing methods before presenting lattice theory in a thorough, self-contained manner, with numerous illustrations and examples. Group and number theory are included, but the treatment is such that no prior knowledge is needed. Not only the theory but the practical implementation of lattice methods is covered. An algorithm is presented alongside tables not available elsewhere, which together allow the practical evaluation of multiple integrals in many variables. Most importantly, the algorithm produces an error estimate in a very efficient manner. The book also provides a fast track for readers wanting to move rapidly to using lattice methods in practical calculations. It concludes with extensive numerical tests which compare lattice methods with other methods, such as the Monte Carlo.

Author : Vassilis G. Kaburlasos,Gerhard X. Ritter
Publisher : Springer
Page : 375 pages
File Size : 55,8 Mb
Release : 2007-06-26
Category : Computers
ISBN : 9783540726876

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Computational Intelligence Based on Lattice Theory by Vassilis G. Kaburlasos,Gerhard X. Ritter Pdf

This eighteen-chapter book presents the latest applications of lattice theory in Computational Intelligence (CI). The book focuses on neural computation, mathematical morphology, machine learning, and (fuzzy) inference/logic. The book comes out of a special session held during the World Council for Curriculum and Instruction World Conference (WCCI 2006). The articles presented here demonstrate how lattice theory may suggest viable alternatives in practical clustering, classification, pattern analysis, and regression applications.

Author : Ovidiu Carja,Ioan I Vrabie
Publisher : World Scientific
Page : 364 pages
File Size : 49,6 Mb
Release : 2007-03-27
Category : Mathematics
ISBN : 9789814475723

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Applied Analysis And Differential Equations by Ovidiu Carja,Ioan I Vrabie Pdf

This volume contains refereed research articles written by experts in the field of applied analysis, differential equations and related topics. Well-known leading mathematicians worldwide and prominent young scientists cover a diverse range of topics, including the most exciting recent developments.A broad range of topics of recent interest are treated: existence, uniqueness, viability, asymptotic stability, viscosity solutions, controllability and numerical analysis for ODE, PDE and stochastic equations. The scope of the book is wide, ranging from pure mathematics to various applied fields such as classical mechanics, biomedicine, and population dynamics.

Author : Gary Doolen
Publisher : CRC Press
Page : 584 pages
File Size : 52,5 Mb
Release : 2019-03-01
Category : Mathematics
ISBN : 9780429697494

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Lattice Gas Methods For Partial Differential Equations by Gary Doolen Pdf

Although the idea of using discrete methods for modeling partial differential equations occurred very early, the actual statement that cellular automata techniques can approximate the solutions of hydrodynamic partial differential equations was first discovered by Frisch, Hasslacher, and Pomeau. Their description of the derivation, which assumes the validity of the Boltzmann equation, appeared in the Physical Review Letters in April 1986. It is the intent of this book to provide some overview of the directions that lattice gas research has taken from 1986 to early 1989.

Author : Nick Bassiliades,Guido Governatori,Adrian Paschke
Publisher : Springer Science & Business Media
Page : 397 pages
File Size : 40,5 Mb
Release : 2011-07-12
Category : Computers
ISBN : 9783642225451

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Rule-Based Reasoning, Programming, and Applications by Nick Bassiliades,Guido Governatori,Adrian Paschke Pdf

This book constitutes the refereed proceedings of the 5th International Symposium on Rules, RuleML 2011 - Europe, held in Barcelona, Spain, in July 2011 - collocated with the 22nd International Joint Conference on Artificial Intelligence, IJCAI 2011. It is the first of two RuleML events that take place in 2011. The second RuleML Symposium - RuleML 2011 - America - will be held in Fort Lauderdale, FL, USA, in November 2011. The 18 revised full papers, 8 revised short papers and 3 invited track papers presented together with the abstracts of 2 keynote talks were carefully reviewed and selected from 58 submissions. The papers are organized in the following topical sections: rule-based distributed/multi-agent systems; rules, agents and norms; rule-based event processing and reaction rules; fuzzy rules and uncertainty; rules and the semantic Web; rule learning and extraction; rules and reasoning; and rule-based applications.

Author : Shih-Kung Lai
Publisher : Routledge
Page : 284 pages
File Size : 44,8 Mb
Release : 2020-12-18
Category : Business & Economics
ISBN : 9781000206227

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Planning within Complex Urban Systems by Shih-Kung Lai Pdf

Imagine living in a city where people could move freely and buildings could be replaced at minimal cost. Reality cannot be further from such. Despite this imperfect world in which we live, urban planning has become integral and critical especially in the face of rapid urbanization in many developing and developed countries. This book introduces the axiomatic/experimental approach to urban planning and addresses the criticism of the lack of a theoretical foundation in urban planning. With the rise of the complexity movement, the book is timely in its depiction of cities as complex systems and explains why planning from within is useful in the face of urban complexity. It also includes policy implications for the Chinese cities in the context of axiomatic/experimental planning theory.

Author : Jan von Plato
Publisher : Princeton University Press
Page : 392 pages
File Size : 48,7 Mb
Release : 2017-08-02
Category : Science
ISBN : 9780691174174

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The Great Formal Machinery Works by Jan von Plato Pdf

The information age owes its existence to a little-known but crucial development, the theoretical study of logic and the foundations of mathematics. The Great Formal Machinery Works draws on original sources and rare archival materials to trace the history of the theories of deduction and computation that laid the logical foundations for the digital revolution. Jan von Plato examines the contributions of figures such as Aristotle; the nineteenth-century German polymath Hermann Grassmann; George Boole, whose Boolean logic would prove essential to programming languages and computing; Ernst Schröder, best known for his work on algebraic logic; and Giuseppe Peano, cofounder of mathematical logic. Von Plato shows how the idea of a formal proof in mathematics emerged gradually in the second half of the nineteenth century, hand in hand with the notion of a formal process of computation. A turning point was reached by 1930, when Kurt Gödel conceived his celebrated incompleteness theorems. They were an enormous boost to the study of formal languages and computability, which were brought to perfection by the end of the 1930s with precise theories of formal languages and formal deduction and parallel theories of algorithmic computability. Von Plato describes how the first theoretical ideas of a computer soon emerged in the work of Alan Turing in 1936 and John von Neumann some years later. Shedding new light on this crucial chapter in the history of science, The Great Formal Machinery Works is essential reading for students and researchers in logic, mathematics, and computer science.

Author : Erich Novak,H. Woźniakowski
Publisher : European Mathematical Society
Page : 684 pages
File Size : 53,7 Mb
Release : 2008
Category : Approximation theory
ISBN : 3037190841

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Tractability of Multivariate Problems: Standard information for functionals by Erich Novak,H. Woźniakowski Pdf

This is the second volume of a three-volume set comprising a comprehensive study of the tractability of multivariate problems. The second volume deals with algorithms using standard information consisting of function values for the approximation of linear and selected nonlinear functionals. An important example is numerical multivariate integration. The proof techniques used in volumes I and II are quite different. It is especially hard to establish meaningful lower error bounds for the approximation of functionals by using finitely many function values. Here, the concept of decomposable reproducing kernels is helpful, allowing it to find matching lower and upper error bounds for some linear functionals. It is then possible to conclude tractability results from such error bounds. Tractability results, even for linear functionals, are very rich in variety. There are infinite-dimensional Hilbert spaces for which the approximation with an arbitrarily small error of all linear functionals requires only one function value. There are Hilbert spaces for which all nontrivial linear functionals suffer from the curse of dimensionality. This holds for unweighted spaces, where the role of all variables and groups of variables is the same. For weighted spaces one can monitor the role of all variables and groups of variables. Necessary and sufficient conditions on the decay of the weights are given to obtain various notions of tractability. The text contains extensive chapters on discrepancy and integration, decomposable kernels and lower bounds, the Smolyak/sparse grid algorithms, lattice rules and the CBC (component-by-component) algorithms. This is done in various settings. Path integration and quantum computation are also discussed. This volume is of interest to researchers working in computational mathematics, especially in approximation of high-dimensional problems. It is also well suited for graduate courses and seminars. There are 61 open problems listed to stimulate future research in tractability.

Author : Kyle Gorman,Richard Sproat
Publisher : Springer Nature
Page : 140 pages
File Size : 49,7 Mb
Release : 2022-06-01
Category : Computers
ISBN : 9783031021794

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Finite-State Text Processing by Kyle Gorman,Richard Sproat Pdf

Weighted finite-state transducers (WFSTs) are commonly used by engineers and computational linguists for processing and generating speech and text. This book first provides a detailed introduction to this formalism. It then introduces Pynini, a Python library for compiling finite-state grammars and for combining, optimizing, applying, and searching finite-state transducers. This book illustrates this library's conventions and use with a series of case studies. These include the compilation and application of context-dependent rewrite rules, the construction of morphological analyzers and generators, and text generation and processing applications.

Author : Joseph Désiré Hubert Donnay
Publisher : Unknown
Page : 1328 pages
File Size : 50,8 Mb
Release : 1978
Category : Crystallography
ISBN : UCLA:L0064459183

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Crystal Data: Inorganic compounds 1967-1969 by Joseph Désiré Hubert Donnay Pdf

Author : Da Ruan
Publisher : World Scientific
Page : 560 pages
File Size : 55,7 Mb
Release : 2000
Category : Technology & Engineering
ISBN : 9810243561

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Intelligent Techniques and Soft Computing for Nuclear Science and Engineering by Da Ruan Pdf

This book is divided into three parts. The first part, ?Mathematical Tools and New Developments?, provides basic tools to treat fuzzy set theory, rough set theory, fuzzy control, fuzzy modelling, decision support systems, and related applications. The second part, ?Intelligent Engineering Applications?, reports on engineering problems such as man-machine interface, risk analysis, image processing, robotics, knowledge-based engineering, expert systems, process control integration, diagnosis, measurements and interpretation by intelligent techniques and soft computing used for general engineering applications. The third part, ?Nuclear Engineering Applications?, concentrates on nuclear applications and covers several topics such as nuclear energy, nuclear safety assessment, radioactive waste management, nuclear measurements, nuclear safeguards, nuclear reactor operation, reactor controller design, fuel reload pattern design, signal validation, nuclear power plants, and optimizations in nuclear applications.

Author : Mathieu Capcarrere,Alex A. Freitas,Peter J. Bentley,Colin G. Johnson,Jon Timmis
Publisher : Springer
Page : 949 pages
File Size : 51,6 Mb
Release : 2005-09-19
Category : Computers
ISBN : 9783540318163

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Advances in Artificial Life by Mathieu Capcarrere,Alex A. Freitas,Peter J. Bentley,Colin G. Johnson,Jon Timmis Pdf

TheArti?cialLifetermappearedmorethan20yearsagoinasmallcornerofNew Mexico, USA. Since then the area has developed dramatically, many researchers joining enthusiastically and research groups sprouting everywhere. This frenetic activity led to the emergence of several strands that are now established ?elds in themselves. We are now reaching a stage that one may describe as maturer: with more rigour, more benchmarks, more results, more stringent acceptance criteria, more applications, in brief, more sound science. This, which is the n- ural path of all new areas, comes at a price, however. A certain enthusiasm, a certain adventurousness from the early years is fading and may have been lost on the way. The ?eld has become more reasonable. To counterbalance this and to encourage lively discussions, a conceptual track, where papers were judged on criteria like importance and/or novelty of the concepts proposed rather than the experimental/theoretical results, has been introduced this year. A conference on a theme as broad as Arti?cial Life is bound to be very - verse,but a few tendencies emerged. First, ?elds like ‘Robotics and Autonomous Agents’ or ‘Evolutionary Computation’ are still extremely active and keep on bringing a wealth of results to the A-Life community. Even there, however, new tendencies appear, like collective robotics, and more speci?cally self-assembling robotics, which represent now a large subsection. Second, new areas appear.

Author : United States. National Bureau of Standards
Publisher : Unknown
Page : 588 pages
File Size : 49,6 Mb
Release : 1962
Category : Chemistry
ISBN : UOM:39015019019077

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Journal of Research of the National Bureau of Standards by United States. National Bureau of Standards Pdf

Author : Gabriel A. Wainer
Publisher : CRC Press
Page : 691 pages
File Size : 48,7 Mb
Release : 2017-12-19
Category : Technology & Engineering
ISBN : 9781351835350

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Discrete-Event Modeling and Simulation by Gabriel A. Wainer Pdf

Complex artificial dynamic systems require advanced modeling techniques that can accommodate their asynchronous, concurrent, and highly non-linear nature. Discrete Event systems Specification (DEVS) provides a formal framework for hierarchical construction of discrete-event models in a modular manner, allowing for model re-use and reduced development time. Discrete Event Modeling and Simulation presents a practical approach focused on the creation of discrete-event applications. The book introduces the CD++ tool, an open-source framework that enables the simulation of discrete-event models. After setting up the basic theory of DEVS and Cell-DEVS, the author focuses on how to use the CD++ tool to define a variety of models in biology, physics, chemistry, and artificial systems. They also demonstrate how to map different modeling techniques, such as Finite State Machines and VHDL, to DEVS. The in-depth coverage elaborates on the creation of simulation software for DEVS models and the 3D visualization environments associated with these tools. A much-needed practical approach to creating discrete-event applications, this book offers world-class instruction on the field’s most useful modeling tools.