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Sample records for algorithmic number theory

  1. Higher arithmetic an algorithmic introduction to number theory

    CERN Document Server

    Edwards, Harold M

    2008-01-01

    Although number theorists have sometimes shunned and even disparaged computation in the past, today's applications of number theory to cryptography and computer security demand vast arithmetical computations. These demands have shifted the focus of studies in number theory and have changed attitudes toward computation itself. The important new applications have attracted a great many students to number theory, but the best reason for studying the subject remains what it was when Gauss published his classic Disquisitiones Arithmeticae in 1801: Number theory is the equal of Euclidean geometry--some would say it is superior to Euclidean geometry--as a model of pure, logical, deductive thinking. An arithmetical computation, after all, is the purest form of deductive argument. Higher Arithmetic explains number theory in a way that gives deductive reasoning, including algorithms and computations, the central role. Hands-on experience with the application of algorithms to computational examples enables students to m...

  2. Algorithmic and experimental methods in algebra, geometry, and number theory

    CERN Document Server

    Decker, Wolfram; Malle, Gunter

    2017-01-01

    This book presents state-of-the-art research and survey articles that highlight work done within the Priority Program SPP 1489 “Algorithmic and Experimental Methods in Algebra, Geometry and Number Theory”, which was established and generously supported by the German Research Foundation (DFG) from 2010 to 2016. The goal of the program was to substantially advance algorithmic and experimental methods in the aforementioned disciplines, to combine the different methods where necessary, and to apply them to central questions in theory and practice. Of particular concern was the further development of freely available open source computer algebra systems and their interaction in order to create powerful new computational tools that transcend the boundaries of the individual disciplines involved.  The book covers a broad range of topics addressing the design and theoretical foundations, implementation and the successful application of algebraic algorithms in order to solve mathematical research problems. It off...

  3. The mathematics of ciphers number theory and RSA cryptography

    CERN Document Server

    Coutinho, S C

    1999-01-01

    This book is an introduction to the algorithmic aspects of number theory and its applications to cryptography, with special emphasis on the RSA cryptosys-tem. It covers many of the familiar topics of elementary number theory, all with an algorithmic twist. The text also includes many interesting historical notes.

  4. Number theory an introduction via the density of primes

    CERN Document Server

    Fine, Benjamin

    2016-01-01

    Now in its second edition, this textbook provides an introduction and overview of number theory based on the density and properties of the prime numbers. This unique approach offers both a firm background in the standard material of number theory, as well as an overview of the entire discipline. All of the essential topics are covered, such as the fundamental theorem of arithmetic, theory of congruences, quadratic reciprocity, arithmetic functions, and the distribution of primes. New in this edition are coverage of p-adic numbers, Hensel's lemma, multiple zeta-values, and elliptic curve methods in primality testing. Key topics and features include: A solid introduction to analytic number theory, including full proofs of Dirichlet's Theorem and the Prime Number Theorem Concise treatment of algebraic number theory, including a complete presentation of primes, prime factorizations in algebraic number fields, and unique factorization of ideals Discussion of the AKS algorithm, which shows that primality testing is...

  5. Algorithms in invariant theory

    CERN Document Server

    Sturmfels, Bernd

    2008-01-01

    J. Kung and G.-C. Rota, in their 1984 paper, write: "Like the Arabian phoenix rising out of its ashes, the theory of invariants, pronounced dead at the turn of the century, is once again at the forefront of mathematics". The book of Sturmfels is both an easy-to-read textbook for invariant theory and a challenging research monograph that introduces a new approach to the algorithmic side of invariant theory. The Groebner bases method is the main tool by which the central problems in invariant theory become amenable to algorithmic solutions. Students will find the book an easy introduction to this "classical and new" area of mathematics. Researchers in mathematics, symbolic computation, and computer science will get access to a wealth of research ideas, hints for applications, outlines and details of algorithms, worked out examples, and research problems.

  6. Applied number theory

    CERN Document Server

    Niederreiter, Harald

    2015-01-01

    This textbook effectively builds a bridge from basic number theory to recent advances in applied number theory. It presents the first unified account of the four major areas of application where number theory plays a fundamental role, namely cryptography, coding theory, quasi-Monte Carlo methods, and pseudorandom number generation, allowing the authors to delineate the manifold links and interrelations between these areas.  Number theory, which Carl-Friedrich Gauss famously dubbed the queen of mathematics, has always been considered a very beautiful field of mathematics, producing lovely results and elegant proofs. While only very few real-life applications were known in the past, today number theory can be found in everyday life: in supermarket bar code scanners, in our cars’ GPS systems, in online banking, etc.  Starting with a brief introductory course on number theory in Chapter 1, which makes the book more accessible for undergraduates, the authors describe the four main application areas in Chapters...

  7. Number theory

    CERN Document Server

    Andrews, George E

    1994-01-01

    Although mathematics majors are usually conversant with number theory by the time they have completed a course in abstract algebra, other undergraduates, especially those in education and the liberal arts, often need a more basic introduction to the topic.In this book the author solves the problem of maintaining the interest of students at both levels by offering a combinatorial approach to elementary number theory. In studying number theory from such a perspective, mathematics majors are spared repetition and provided with new insights, while other students benefit from the consequent simpl

  8. Positive approach: Implications for the relation between number theory and geometry, including connection to Santilli mathematics, from Fibonacci reconstitution of natural numbers and of prime numbers

    International Nuclear Information System (INIS)

    Johansen, Stein E.

    2014-01-01

    The paper recapitulates some key elements in previously published results concerning exact and complete reconstitution of the field of natural numbers, both as ordinal and as cardinal numbers, from systematic unfoldment of the Fibonacci algorithm. By this natural numbers emerge as Fibonacci 'atoms' and 'molecules' consistent with the notion of Zeckendorf sums. Here, the sub-set of prime numbers appears not as the primary numbers, but as an epistructure from a deeper Fibonacci constitution, and is thus targeted from a 'positive approach'. In the Fibonacci reconstitution of number theory natural numbers show a double geometrical aspect: partly as extension in space and partly as position in a successive structuring of space. More specifically, the natural numbers are shown to be distributed by a concise 5:3 code structured from the Fibonacci algorithm via Pascal's triangle. The paper discusses possible implications for the more general relation between number theory and geometry, as well as more specifically in relation to hadronic mathematics, initiated by R.M. Santilli, and also briefly to some other recent science linking number theory more directly to geometry and natural systems

  9. Positive approach: Implications for the relation between number theory and geometry, including connection to Santilli mathematics, from Fibonacci reconstitution of natural numbers and of prime numbers

    Energy Technology Data Exchange (ETDEWEB)

    Johansen, Stein E., E-mail: stein.johansen@svt.ntnu.no [Institute for Basic Research, Division of Physics, Palm Harbor, Florida, USA and Norwegian University of Science and Technology, Department of Social Anthropology, Trondheim (Norway)

    2014-12-10

    The paper recapitulates some key elements in previously published results concerning exact and complete reconstitution of the field of natural numbers, both as ordinal and as cardinal numbers, from systematic unfoldment of the Fibonacci algorithm. By this natural numbers emerge as Fibonacci 'atoms' and 'molecules' consistent with the notion of Zeckendorf sums. Here, the sub-set of prime numbers appears not as the primary numbers, but as an epistructure from a deeper Fibonacci constitution, and is thus targeted from a 'positive approach'. In the Fibonacci reconstitution of number theory natural numbers show a double geometrical aspect: partly as extension in space and partly as position in a successive structuring of space. More specifically, the natural numbers are shown to be distributed by a concise 5:3 code structured from the Fibonacci algorithm via Pascal's triangle. The paper discusses possible implications for the more general relation between number theory and geometry, as well as more specifically in relation to hadronic mathematics, initiated by R.M. Santilli, and also briefly to some other recent science linking number theory more directly to geometry and natural systems.

  10. Inference algorithms and learning theory for Bayesian sparse factor analysis

    International Nuclear Information System (INIS)

    Rattray, Magnus; Sharp, Kevin; Stegle, Oliver; Winn, John

    2009-01-01

    Bayesian sparse factor analysis has many applications; for example, it has been applied to the problem of inferring a sparse regulatory network from gene expression data. We describe a number of inference algorithms for Bayesian sparse factor analysis using a slab and spike mixture prior. These include well-established Markov chain Monte Carlo (MCMC) and variational Bayes (VB) algorithms as well as a novel hybrid of VB and Expectation Propagation (EP). For the case of a single latent factor we derive a theory for learning performance using the replica method. We compare the MCMC and VB/EP algorithm results with simulated data to the theoretical prediction. The results for MCMC agree closely with the theory as expected. Results for VB/EP are slightly sub-optimal but show that the new algorithm is effective for sparse inference. In large-scale problems MCMC is infeasible due to computational limitations and the VB/EP algorithm then provides a very useful computationally efficient alternative.

  11. Inference algorithms and learning theory for Bayesian sparse factor analysis

    Energy Technology Data Exchange (ETDEWEB)

    Rattray, Magnus; Sharp, Kevin [School of Computer Science, University of Manchester, Manchester M13 9PL (United Kingdom); Stegle, Oliver [Max-Planck-Institute for Biological Cybernetics, Tuebingen (Germany); Winn, John, E-mail: magnus.rattray@manchester.ac.u [Microsoft Research Cambridge, Roger Needham Building, Cambridge, CB3 0FB (United Kingdom)

    2009-12-01

    Bayesian sparse factor analysis has many applications; for example, it has been applied to the problem of inferring a sparse regulatory network from gene expression data. We describe a number of inference algorithms for Bayesian sparse factor analysis using a slab and spike mixture prior. These include well-established Markov chain Monte Carlo (MCMC) and variational Bayes (VB) algorithms as well as a novel hybrid of VB and Expectation Propagation (EP). For the case of a single latent factor we derive a theory for learning performance using the replica method. We compare the MCMC and VB/EP algorithm results with simulated data to the theoretical prediction. The results for MCMC agree closely with the theory as expected. Results for VB/EP are slightly sub-optimal but show that the new algorithm is effective for sparse inference. In large-scale problems MCMC is infeasible due to computational limitations and the VB/EP algorithm then provides a very useful computationally efficient alternative.

  12. The theory of hybrid stochastic algorithms

    International Nuclear Information System (INIS)

    Duane, S.; Kogut, J.B.

    1986-01-01

    The theory of hybrid stochastic algorithms is developed. A generalized Fokker-Planck equation is derived and is used to prove that the correct equilibrium distribution is generated by the algorithm. Systematic errors following from the discrete time-step used in the numerical implementation of the scheme are computed. Hybrid algorithms which simulate lattice gauge theory with dynamical fermions are presented. They are optimized in computer simulations and their systematic errors and efficiencies are studied. (orig.)

  13. Advanced number theory

    CERN Document Server

    Cohn, Harvey

    1980-01-01

    ""A very stimulating book ... in a class by itself."" - American Mathematical MonthlyAdvanced students, mathematicians and number theorists will welcome this stimulating treatment of advanced number theory, which approaches the complex topic of algebraic number theory from a historical standpoint, taking pains to show the reader how concepts, definitions and theories have evolved during the last two centuries. Moreover, the book abounds with numerical examples and more concrete, specific theorems than are found in most contemporary treatments of the subject.The book is divided into three parts

  14. A random-matrix theory of the number sense.

    Science.gov (United States)

    Hannagan, T; Nieder, A; Viswanathan, P; Dehaene, S

    2017-02-19

    Number sense, a spontaneous ability to process approximate numbers, has been documented in human adults, infants and newborns, and many other animals. Species as distant as monkeys and crows exhibit very similar neurons tuned to specific numerosities. How number sense can emerge in the absence of learning or fine tuning is currently unknown. We introduce a random-matrix theory of self-organized neural states where numbers are coded by vectors of activation across multiple units, and where the vector codes for successive integers are obtained through multiplication by a fixed but random matrix. This cortical implementation of the 'von Mises' algorithm explains many otherwise disconnected observations ranging from neural tuning curves in monkeys to looking times in neonates and cortical numerotopy in adults. The theory clarifies the origin of Weber-Fechner's Law and yields a novel and empirically validated prediction of multi-peak number neurons. Random matrices constitute a novel mechanism for the emergence of brain states coding for quantity.This article is part of a discussion meeting issue 'The origins of numerical abilities'. © 2017 The Author(s).

  15. Learning theory of distributed spectral algorithms

    International Nuclear Information System (INIS)

    Guo, Zheng-Chu; Lin, Shao-Bo; Zhou, Ding-Xuan

    2017-01-01

    Spectral algorithms have been widely used and studied in learning theory and inverse problems. This paper is concerned with distributed spectral algorithms, for handling big data, based on a divide-and-conquer approach. We present a learning theory for these distributed kernel-based learning algorithms in a regression framework including nice error bounds and optimal minimax learning rates achieved by means of a novel integral operator approach and a second order decomposition of inverse operators. Our quantitative estimates are given in terms of regularity of the regression function, effective dimension of the reproducing kernel Hilbert space, and qualification of the filter function of the spectral algorithm. They do not need any eigenfunction or noise conditions and are better than the existing results even for the classical family of spectral algorithms. (paper)

  16. Introduction to number theory

    CERN Document Server

    Vazzana, Anthony; Garth, David

    2007-01-01

    One of the oldest branches of mathematics, number theory is a vast field devoted to studying the properties of whole numbers. Offering a flexible format for a one- or two-semester course, Introduction to Number Theory uses worked examples, numerous exercises, and two popular software packages to describe a diverse array of number theory topics.

  17. The theory of hybrid stochastic algorithms

    International Nuclear Information System (INIS)

    Kennedy, A.D.

    1989-01-01

    These lectures introduce the family of Hybrid Stochastic Algorithms for performing Monte Carlo calculations in Quantum Field Theory. After explaining the basic concepts of Monte Carlo integration we discuss the properties of Markov processes and one particularly useful example of them: the Metropolis algorithm. Building upon this framework we consider the Hybrid and Langevin algorithms from the viewpoint that they are approximate versions of the Hybrid Monte Carlo method; and thus we are led to consider Molecular Dynamics using the Leapfrog algorithm. The lectures conclude by reviewing recent progress in these areas, explaining higher-order integration schemes, the asymptotic large-volume behaviour of the various algorithms, and some simple exact results obtained by applying them to free field theory. It is attempted throughout to give simple yet correct proofs of the various results encountered. 38 refs

  18. Number theory via Representation theory

    Indian Academy of Sciences (India)

    2014-11-09

    Number theory via Representation theory. Eknath Ghate. November 9, 2014. Eightieth Annual Meeting, Chennai. Indian Academy of Sciences1. 1. This is a non-technical 20 minute talk intended for a general Academy audience.

  19. 2016 Gainesville Number Theory Conference

    CERN Document Server

    Garvan, Frank

    2017-01-01

    Gathered from the 2016 Gainesville Number Theory Conference honoring Krishna Alladi on his 60th birthday, these proceedings present recent research in number theory. Extensive and detailed, this volume features 40 articles by leading researchers on topics in analytic number theory, probabilistic number theory, irrationality and transcendence, Diophantine analysis, partitions, basic hypergeometric series, and modular forms. Readers will also find detailed discussions of several aspects of the path-breaking work of Srinivasa Ramanujan and its influence on current research. Many of the papers were motivated by Alladi's own research on partitions and q-series as well as his earlier work in number theory.  Alladi is well known for his contributions in number theory and mathematics. His research interests include combinatorics, discrete mathematics, sieve methods, probabilistic and analytic number theory, Diophantine approximations, partitions and q-series identities. Graduate students and researchers will find th...

  20. Generalization of the Lord-Wingersky Algorithm to Computing the Distribution of Summed Test Scores Based on Real-Number Item Scores

    Science.gov (United States)

    Kim, Seonghoon

    2013-01-01

    With known item response theory (IRT) item parameters, Lord and Wingersky provided a recursive algorithm for computing the conditional frequency distribution of number-correct test scores, given proficiency. This article presents a generalized algorithm for computing the conditional distribution of summed test scores involving real-number item…

  1. Algorithms in combinatorial design theory

    CERN Document Server

    Colbourn, CJ

    1985-01-01

    The scope of the volume includes all algorithmic and computational aspects of research on combinatorial designs. Algorithmic aspects include generation, isomorphism and analysis techniques - both heuristic methods used in practice, and the computational complexity of these operations. The scope within design theory includes all aspects of block designs, Latin squares and their variants, pairwise balanced designs and projective planes and related geometries.

  2. Interior point algorithms theory and analysis

    CERN Document Server

    Ye, Yinyu

    2011-01-01

    The first comprehensive review of the theory and practice of one of today's most powerful optimization techniques. The explosive growth of research into and development of interior point algorithms over the past two decades has significantly improved the complexity of linear programming and yielded some of today's most sophisticated computing techniques. This book offers a comprehensive and thorough treatment of the theory, analysis, and implementation of this powerful computational tool. Interior Point Algorithms provides detailed coverage of all basic and advanced aspects of the subject.

  3. Algebraic number theory

    CERN Document Server

    Weiss, Edwin

    1998-01-01

    Careful organization and clear, detailed proofs characterize this methodical, self-contained exposition of basic results of classical algebraic number theory from a relatively modem point of view. This volume presents most of the number-theoretic prerequisites for a study of either class field theory (as formulated by Artin and Tate) or the contemporary treatment of analytical questions (as found, for example, in Tate's thesis).Although concerned exclusively with algebraic number fields, this treatment features axiomatic formulations with a considerable range of applications. Modem abstract te

  4. Analytic number theory

    CERN Document Server

    Iwaniec, Henryk

    2004-01-01

    Analytic Number Theory distinguishes itself by the variety of tools it uses to establish results, many of which belong to the mainstream of arithmetic. One of the main attractions of analytic number theory is the vast diversity of concepts and methods it includes. The main goal of the book is to show the scope of the theory, both in classical and modern directions, and to exhibit its wealth and prospects, its beautiful theorems and powerful techniques. The book is written with graduate students in mind, and the authors tried to balance between clarity, completeness, and generality. The exercis

  5. Elementary number theory

    CERN Document Server

    Dudley, Underwood

    2008-01-01

    Ideal for a first course in number theory, this lively, engaging text requires only a familiarity with elementary algebra and the properties of real numbers. Author Underwood Dudley, who has written a series of popular mathematics books, maintains that the best way to learn mathematics is by solving problems. In keeping with this philosophy, the text includes nearly 1,000 exercises and problems-some computational and some classical, many original, and some with complete solutions. The opening chapters offer sound explanations of the basics of elementary number theory and develop the fundamenta

  6. Invitation to number theory

    CERN Document Server

    Ore, Oystein

    2017-01-01

    Number theory is the branch of mathematics concerned with the counting numbers, 1, 2, 3, … and their multiples and factors. Of particular importance are odd and even numbers, squares and cubes, and prime numbers. But in spite of their simplicity, you will meet a multitude of topics in this book: magic squares, cryptarithms, finding the day of the week for a given date, constructing regular polygons, pythagorean triples, and many more. In this revised edition, John Watkins and Robin Wilson have updated the text to bring it in line with contemporary developments. They have added new material on Fermat's Last Theorem, the role of computers in number theory, and the use of number theory in cryptography, and have made numerous minor changes in the presentation and layout of the text and the exercises.

  7. Elementary number theory with programming

    CERN Document Server

    Lewinter, Marty

    2015-01-01

    A successful presentation of the fundamental concepts of number theory and computer programming Bridging an existing gap between mathematics and programming, Elementary Number Theory with Programming provides a unique introduction to elementary number theory with fundamental coverage of computer programming. Written by highly-qualified experts in the fields of computer science and mathematics, the book features accessible coverage for readers with various levels of experience and explores number theory in the context of programming without relying on advanced prerequisite knowledge and con

  8. Recognition algorithms in knot theory

    International Nuclear Information System (INIS)

    Dynnikov, I A

    2003-01-01

    In this paper the problem of constructing algorithms for comparing knots and links is discussed. A survey of existing approaches and basic results in this area is given. In particular, diverse combinatorial methods for representing links are discussed, the Haken algorithm for recognizing a trivial knot (the unknot) and a scheme for constructing a general algorithm (using Haken's ideas) for comparing links are presented, an approach based on representing links by closed braids is described, the known algorithms for solving the word problem and the conjugacy problem for braid groups are described, and the complexity of the algorithms under consideration is discussed. A new method of combinatorial description of knots is given together with a new algorithm (based on this description) for recognizing the unknot by using a procedure for monotone simplification. In the conclusion of the paper several problems are formulated whose solution could help to advance towards the 'algorithmization' of knot theory

  9. Algorithm Theory - SWAT 2006

    DEFF Research Database (Denmark)

    This book constitutes the refereed proceedings of the 10th Scandinavian Workshop on Algorithm Theory, SWAT 2006, held in Riga, Latvia, in July 2006. The 36 revised full papers presented together with 3 invited papers were carefully reviewed and selected from 154 submissions. The papers address all...

  10. Nonequilibrium molecular dynamics theory, algorithms and applications

    CERN Document Server

    Todd, Billy D

    2017-01-01

    Written by two specialists with over twenty-five years of experience in the field, this valuable text presents a wide range of topics within the growing field of nonequilibrium molecular dynamics (NEMD). It introduces theories which are fundamental to the field - namely, nonequilibrium statistical mechanics and nonequilibrium thermodynamics - and provides state-of-the-art algorithms and advice for designing reliable NEMD code, as well as examining applications for both atomic and molecular fluids. It discusses homogenous and inhomogenous flows and pays considerable attention to highly confined fluids, such as nanofluidics. In addition to statistical mechanics and thermodynamics, the book covers the themes of temperature and thermodynamic fluxes and their computation, the theory and algorithms for homogenous shear and elongational flows, response theory and its applications, heat and mass transport algorithms, applications in molecular rheology, highly confined fluids (nanofluidics), the phenomenon of slip and...

  11. Accuracy verification methods theory and algorithms

    CERN Document Server

    Mali, Olli; Repin, Sergey

    2014-01-01

    The importance of accuracy verification methods was understood at the very beginning of the development of numerical analysis. Recent decades have seen a rapid growth of results related to adaptive numerical methods and a posteriori estimates. However, in this important area there often exists a noticeable gap between mathematicians creating the theory and researchers developing applied algorithms that could be used in engineering and scientific computations for guaranteed and efficient error control.   The goals of the book are to (1) give a transparent explanation of the underlying mathematical theory in a style accessible not only to advanced numerical analysts but also to engineers and students; (2) present detailed step-by-step algorithms that follow from a theory; (3) discuss their advantages and drawbacks, areas of applicability, give recommendations and examples.

  12. Planar graphs theory and algorithms

    CERN Document Server

    Nishizeki, T

    1988-01-01

    Collected in this volume are most of the important theorems and algorithms currently known for planar graphs, together with constructive proofs for the theorems. Many of the algorithms are written in Pidgin PASCAL, and are the best-known ones; the complexities are linear or 0(nlogn). The first two chapters provide the foundations of graph theoretic notions and algorithmic techniques. The remaining chapters discuss the topics of planarity testing, embedding, drawing, vertex- or edge-coloring, maximum independence set, subgraph listing, planar separator theorem, Hamiltonian cycles, and single- or multicommodity flows. Suitable for a course on algorithms, graph theory, or planar graphs, the volume will also be useful for computer scientists and graph theorists at the research level. An extensive reference section is included.

  13. Sequences, groups, and number theory

    CERN Document Server

    Rigo, Michel

    2018-01-01

    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.

  14. Entanglement distillation protocols and number theory

    International Nuclear Information System (INIS)

    Bombin, H.; Martin-Delgado, M.A.

    2005-01-01

    We show that the analysis of entanglement distillation protocols for qudits of arbitrary dimension D benefits from applying basic concepts from number theory, since the set Z D n associated with Bell diagonal states is a module rather than a vector space. We find that a partition of Z D n into divisor classes characterizes the invariant properties of mixed Bell diagonal states under local permutations. We construct a very general class of recursion protocols by means of unitary operations implementing these local permutations. We study these distillation protocols depending on whether we use twirling operations in the intermediate steps or not, and we study them both analytically and numerically with Monte Carlo methods. In the absence of twirling operations, we construct extensions of the quantum privacy algorithms valid for secure communications with qudits of any dimension D. When D is a prime number, we show that distillation protocols are optimal both qualitatively and quantitatively

  15. Number Theory and Applications : Proceedings of the International Conferences on Number Theory and Cryptography

    CERN Document Server

    Ramakrishnan, B

    2009-01-01

    This collection of articles contains the proceedings of the two international conferences (on Number Theory and Cryptography) held at the Harish - Chandra Research Institute. In recent years the interest in number theory has increased due to its applications in areas like error-correcting codes and cryptography. These proceedings contain papers in various areas of number theory, such as combinatorial, algebraic, analytic and transcendental aspects, arithmetic algebraic geometry, as well as graph theory and cryptography. While some papers do contain new results, several of the papers are expository articles that mention open questions, which will be useful to young researchers.

  16. The discrete Fourier transform theory, algorithms and applications

    CERN Document Server

    Sundaraajan, D

    2001-01-01

    This authoritative book provides comprehensive coverage of practical Fourier analysis. It develops the concepts right from the basics and gradually guides the reader to the advanced topics. It presents the latest and practically efficient DFT algorithms, as well as the computation of discrete cosine and Walsh-Hadamard transforms. The large number of visual aids such as figures, flow graphs and flow charts makes the mathematical topic easy to understand. In addition, the numerous examples and the set of C-language programs (a supplement to the book) help greatly in understanding the theory and

  17. Classical theory of algebraic numbers

    CERN Document Server

    Ribenboim, Paulo

    2001-01-01

    Gauss created the theory of binary quadratic forms in "Disquisitiones Arithmeticae" and Kummer invented ideals and the theory of cyclotomic fields in his attempt to prove Fermat's Last Theorem These were the starting points for the theory of algebraic numbers, developed in the classical papers of Dedekind, Dirichlet, Eisenstein, Hermite and many others This theory, enriched with more recent contributions, is of basic importance in the study of diophantine equations and arithmetic algebraic geometry, including methods in cryptography This book has a clear and thorough exposition of the classical theory of algebraic numbers, and contains a large number of exercises as well as worked out numerical examples The Introduction is a recapitulation of results about principal ideal domains, unique factorization domains and commutative fields Part One is devoted to residue classes and quadratic residues In Part Two one finds the study of algebraic integers, ideals, units, class numbers, the theory of decomposition, iner...

  18. Unsolved problems in number theory

    CERN Document Server

    Guy, Richard K

    1994-01-01

    Unsolved Problems in Number Theory contains discussions of hundreds of open questions, organized into 185 different topics. They represent numerous aspects of number theory and are organized into six categories: prime numbers, divisibility, additive number theory, Diophantine equations, sequences of integers, and miscellaneous. To prevent repetition of earlier efforts or duplication of previously known results, an extensive and up-to-date collection of references follows each problem. In the second edition, not only extensive new material has been added, but corrections and additions have been included throughout the book.

  19. Linear programming mathematics, theory and algorithms

    CERN Document Server

    1996-01-01

    Linear Programming provides an in-depth look at simplex based as well as the more recent interior point techniques for solving linear programming problems. Starting with a review of the mathematical underpinnings of these approaches, the text provides details of the primal and dual simplex methods with the primal-dual, composite, and steepest edge simplex algorithms. This then is followed by a discussion of interior point techniques, including projective and affine potential reduction, primal and dual affine scaling, and path following algorithms. Also covered is the theory and solution of the linear complementarity problem using both the complementary pivot algorithm and interior point routines. A feature of the book is its early and extensive development and use of duality theory. Audience: The book is written for students in the areas of mathematics, economics, engineering and management science, and professionals who need a sound foundation in the important and dynamic discipline of linear programming.

  20. Fundamental number theory with applications

    CERN Document Server

    Mollin, Richard A

    2008-01-01

    An update of the most accessible introductory number theory text available, Fundamental Number Theory with Applications, Second Edition presents a mathematically rigorous yet easy-to-follow treatment of the fundamentals and applications of the subject. The substantial amount of reorganizing makes this edition clearer and more elementary in its coverage. New to the Second Edition           Removal of all advanced material to be even more accessible in scope           New fundamental material, including partition theory, generating functions, and combinatorial number theory           Expa

  1. Elementary theory of numbers

    CERN Document Server

    Sierpinski, Waclaw

    1988-01-01

    Since the publication of the first edition of this work, considerable progress has been made in many of the questions examined. This edition has been updated and enlarged, and the bibliography has been revised.The variety of topics covered here includes divisibility, diophantine equations, prime numbers (especially Mersenne and Fermat primes), the basic arithmetic functions, congruences, the quadratic reciprocity law, expansion of real numbers into decimal fractions, decomposition of integers into sums of powers, some other problems of the additive theory of numbers and the theory of Gaussian

  2. Fundamentals of number theory

    CERN Document Server

    LeVeque, William J

    1996-01-01

    This excellent textbook introduces the basics of number theory, incorporating the language of abstract algebra. A knowledge of such algebraic concepts as group, ring, field, and domain is not assumed, however; all terms are defined and examples are given - making the book self-contained in this respect.The author begins with an introductory chapter on number theory and its early history. Subsequent chapters deal with unique factorization and the GCD, quadratic residues, number-theoretic functions and the distribution of primes, sums of squares, quadratic equations and quadratic fields, diopha

  3. Parallelization of a spherical Sn transport theory algorithm

    International Nuclear Information System (INIS)

    Haghighat, A.

    1989-01-01

    The work described in this paper derives a parallel algorithm for an R-dependent spherical S N transport theory algorithm and studies its performance by testing different sample problems. The S N transport method is one of the most accurate techniques used to solve the linear Boltzmann equation. Several studies have been done on the vectorization of the S N algorithms; however, very few studies have been performed on the parallelization of this algorithm. Weinke and Hommoto have looked at the parallel processing of the different energy groups, and Azmy recently studied the parallel processing of the inner iterations of an X-Y S N nodal transport theory method. Both studies have reported very encouraging results, which have prompted us to look at the parallel processing of an R-dependent S N spherical geometry algorithm. This geometry was chosen because, in spite of its simplicity, it contains the complications of the curvilinear geometries (i.e., redistribution of neutrons over the discretized angular bins)

  4. The theory of algebraic numbers

    CERN Document Server

    Pollard, Harry

    1998-01-01

    An excellent introduction to the basics of algebraic number theory, this concise, well-written volume examines Gaussian primes; polynomials over a field; algebraic number fields; and algebraic integers and integral bases. After establishing a firm introductory foundation, the text explores the uses of arithmetic in algebraic number fields; the fundamental theorem of ideal theory and its consequences; ideal classes and class numbers; and the Fermat conjecture. 1975 edition. References. List of Symbols. Index.

  5. Topics from the theory of numbers

    CERN Document Server

    Grosswald, Emil

    1984-01-01

    Many of the important and creative developments in modern mathematics resulted from attempts to solve questions that originate in number theory. The publication of Emil Grosswald’s classic text presents an illuminating introduction to number theory. Combining the historical developments with the analytical approach, Topics from the Theory of Numbers offers the reader a diverse range of subjects to investigate, including: * divisibility * congruences * the Riemann zeta function * Diophantine equations and Fermat’s conjecture * the theory of partitions Comprehensive in nature, Topics from the Theory of Numbers is an ideal text for advanced undergraduates and graduate students alike. "In my opinion it is excellent. It is carefully written and represents clearly a work of a scholar who loves and understands his subject. One can only wish more authors would take such pains and would be as good and honest expositors as Grosswald." — Marc Kac "This book is designed for use in a first course in number theory at...

  6. Optimisation combinatoire Theorie et algorithmes

    CERN Document Server

    Korte, Bernhard; Fonlupt, Jean

    2010-01-01

    Ce livre est la traduction fran aise de la quatri me et derni re dition de Combinatorial Optimization: Theory and Algorithms crit par deux minents sp cialistes du domaine: Bernhard Korte et Jens Vygen de l'universit de Bonn en Allemagne. Il met l accent sur les aspects th oriques de l'optimisation combinatoire ainsi que sur les algorithmes efficaces et exacts de r solution de probl mes. Il se distingue en cela des approches heuristiques plus simples et souvent d crites par ailleurs. L ouvrage contient de nombreuses d monstrations, concises et l gantes, de r sultats difficiles. Destin aux tudia

  7. Algebraic theory of numbers

    CERN Document Server

    Samuel, Pierre

    2008-01-01

    Algebraic number theory introduces students not only to new algebraic notions but also to related concepts: groups, rings, fields, ideals, quotient rings and quotient fields, homomorphisms and isomorphisms, modules, and vector spaces. Author Pierre Samuel notes that students benefit from their studies of algebraic number theory by encountering many concepts fundamental to other branches of mathematics - algebraic geometry, in particular.This book assumes a knowledge of basic algebra but supplements its teachings with brief, clear explanations of integrality, algebraic extensions of fields, Gal

  8. Law and Order in Algorithmics

    NARCIS (Netherlands)

    Fokkinga, M.M.

    1992-01-01

    An algorithm is the input-output effect of a computer program; mathematically, the notion of algorithm comes close to the notion of function. Just as arithmetic is the theory and practice of calculating with numbers, so is ALGORITHMICS the theory and practice of calculating with algorithms. Just as

  9. A portable high-quality random number generator for lattice field theory simulations

    International Nuclear Information System (INIS)

    Luescher, M.

    1993-09-01

    The theory underlying a proposed random number generator for numerical simulations in elementary particle physics and statistical mechanics is discussed. The generator is based on an algorithm introduced by Marsaglia and Zaman, with an important added feature leading to demonstrably good statistical properties. It can be implemented exactly on any computer complying with the IEEE-754 standard for single precision floating point arithmetic. (orig.)

  10. Computer and machine vision theory, algorithms, practicalities

    CERN Document Server

    Davies, E R

    2012-01-01

    Computer and Machine Vision: Theory, Algorithms, Practicalities (previously entitled Machine Vision) clearly and systematically presents the basic methodology of computer and machine vision, covering the essential elements of the theory while emphasizing algorithmic and practical design constraints. This fully revised fourth edition has brought in more of the concepts and applications of computer vision, making it a very comprehensive and up-to-date tutorial text suitable for graduate students, researchers and R&D engineers working in this vibrant subject. Key features include: Practical examples and case studies give the 'ins and outs' of developing real-world vision systems, giving engineers the realities of implementing the principles in practice New chapters containing case studies on surveillance and driver assistance systems give practical methods on these cutting-edge applications in computer vision Necessary mathematics and essential theory are made approachable by careful explanations and well-il...

  11. Relativistic theory of tidal Love numbers

    International Nuclear Information System (INIS)

    Binnington, Taylor; Poisson, Eric

    2009-01-01

    In Newtonian gravitational theory, a tidal Love number relates the mass multipole moment created by tidal forces on a spherical body to the applied tidal field. The Love number is dimensionless, and it encodes information about the body's internal structure. We present a relativistic theory of Love numbers, which applies to compact bodies with strong internal gravities; the theory extends and completes a recent work by Flanagan and Hinderer, which revealed that the tidal Love number of a neutron star can be measured by Earth-based gravitational-wave detectors. We consider a spherical body deformed by an external tidal field, and provide precise and meaningful definitions for electric-type and magnetic-type Love numbers; and these are computed for polytropic equations of state. The theory applies to black holes as well, and we find that the relativistic Love numbers of a nonrotating black hole are all zero.

  12. Additive theory of prime numbers

    CERN Document Server

    Hua, L K

    2009-01-01

    Loo-Keng Hua was a master mathematician, best known for his work using analytic methods in number theory. In particular, Hua is remembered for his contributions to Waring's Problem and his estimates of trigonometric sums. Additive Theory of Prime Numbers is an exposition of the classic methods as well as Hua's own techniques, many of which have now also become classic. An essential starting point is Vinogradov's mean-value theorem for trigonometric sums, which Hua usefully rephrases and improves. Hua states a generalized version of the Waring-Goldbach problem and gives asymptotic formulas for the number of solutions in Waring's Problem when the monomial x^k is replaced by an arbitrary polynomial of degree k. The book is an excellent entry point for readers interested in additive number theory. It will also be of value to those interested in the development of the now classic methods of the subject.

  13. Topics in the theory of numbers

    CERN Document Server

    Erdős, Paul

    2003-01-01

    This rather unique book is a guided tour through number theory. While most introductions to number theory provide a systematic and exhaustive treatment of the subject, the authors have chosen instead to illustrate the many varied subjects by associating recent discoveries, interesting methods, and unsolved problems. In particular, we read about combinatorial problems in number theory, a branch of mathematics co-founded and popularized by Paul Erdös. Janos Suranyis vast teaching experience successfully complements Paul Erdös'ability to initiate new directions of research by suggesting new problems and approaches. This book will surely arouse the interest of the student and the teacher alike. Until his death in 1996, Professor Paul Erdös was one of the most prolific mathematicians ever, publishing close to 1,500 papers. While his papers contributed to almost every area of mathematics, his main research interest was in the area of combinatorics, graph theory, and number theory. He is most famous for proposing...

  14. From algorithmic computing to direct retrieval: evidence from number and alphabetic arithmetic in children and adults.

    Science.gov (United States)

    Barrouillet, P; Fayol, M

    1998-03-01

    A number of theories of mental arithmetic suggest that the ability to solve simple addition and subtraction problems develops from an algorithmic strategy toward a strategy based on the direct retrieval of the result from memory. In the experiment presented here, 2nd and 12th graders were asked to solve two tasks of number and alphabet arithmetic. The subjects transformed series of 1 to 4 numbers or letters (item span) by adding or subtracting an operand varying from 1 to 4 (operation span). Although both the item and operation span were associated with major and identical effects in the case of both numbers and letters at 2nd grade, such effects were clearly observable only in the case of letters for the adult subjects. This suggests the use of an algorithmic strategy for both types of material in the case of the children and for the letters only in the case of the adults, who retrieved numerical results directly from memory.

  15. On factoring RSA modulus using random-restart hill-climbing algorithm and Pollard’s rho algorithm

    Science.gov (United States)

    Budiman, M. A.; Rachmawati, D.

    2017-12-01

    The security of the widely-used RSA public key cryptography algorithm depends on the difficulty of factoring a big integer into two large prime numbers. For many years, the integer factorization problem has been intensively and extensively studied in the field of number theory. As a result, a lot of deterministic algorithms such as Euler’s algorithm, Kraitchik’s, and variants of Pollard’s algorithms have been researched comprehensively. Our study takes a rather uncommon approach: rather than making use of intensive number theories, we attempt to factorize RSA modulus n by using random-restart hill-climbing algorithm, which belongs the class of metaheuristic algorithms. The factorization time of RSA moduli with different lengths is recorded and compared with the factorization time of Pollard’s rho algorithm, which is a deterministic algorithm. Our experimental results indicates that while random-restart hill-climbing algorithm is an acceptable candidate to factorize smaller RSA moduli, the factorization speed is much slower than that of Pollard’s rho algorithm.

  16. New MPPT algorithm based on hybrid dynamical theory

    KAUST Repository

    Elmetennani, Shahrazed

    2014-11-01

    This paper presents a new maximum power point tracking algorithm based on the hybrid dynamical theory. A multiceli converter has been considered as an adaptation stage for the photovoltaic chain. The proposed algorithm is a hybrid automata switching between eight different operating modes, which has been validated by simulation tests under different working conditions. © 2014 IEEE.

  17. New MPPT algorithm based on hybrid dynamical theory

    KAUST Repository

    Elmetennani, Shahrazed; Laleg-Kirati, Taous-Meriem; Benmansour, K.; Boucherit, M. S.; Tadjine, M.

    2014-01-01

    This paper presents a new maximum power point tracking algorithm based on the hybrid dynamical theory. A multiceli converter has been considered as an adaptation stage for the photovoltaic chain. The proposed algorithm is a hybrid automata switching between eight different operating modes, which has been validated by simulation tests under different working conditions. © 2014 IEEE.

  18. New topological structures of Skyrme theory: baryon number and monopole number

    Energy Technology Data Exchange (ETDEWEB)

    Cho, Y.M. [Chinese Academy of Science, Institute of Modern Physics, Lanzhou (China); Konkuk University, Seoul (Korea, Republic of); Seoul National University, School of Physics and Astronomy, Seoul (Korea, Republic of); Kimm, Kyoungtae [Seoul National University, Faculty of Liberal Education, Seoul (Korea, Republic of); Yoon, J.H. [Konkuk University, Department of Physics, Seoul (Korea, Republic of); Zhang, Pengming [Chinese Academy of Science, Institute of Modern Physics, Lanzhou (China)

    2017-02-15

    Based on the observation that the skyrmion in Skyrme theory can be viewed as a dressed monopole, we show that the skyrmions have two independent topology, the baryon topology π{sub 3}(S{sup 3}) and the monopole topology π{sub 2}(S{sup 2}). With this we propose to classify the skyrmions by two topological numbers (m, n), the monopole number m and the shell (radial) number n. In this scheme the popular (non spherically symmetric) skyrmions are classified as the (m, 1) skyrmions but the spherically symmetric skyrmions are classified as the (1, n) skyrmions, and the baryon number B is given by B = mn. Moreover, we show that the vacuum of the Skyrme theory has the structure of the vacuum of the Sine-Gordon theory and QCD combined together, which can also be classified by two topological numbers (p, q). This puts the Skyrme theory in a totally new perspective. (orig.)

  19. An adventurer's guide to number theory

    CERN Document Server

    Friedberg, Richard

    1995-01-01

    In this delightful guide, a noted mathematician and teacher offers a witty, historically oriented introduction to number theory, dealing with properties of numbers and with numbers as abstract concepts. Written for readers with an understanding of arithmetic and beginning algebra, the book presents the classical discoveries of number theory, including the work of Pythagoras, Euclid, Diophantus, Fermat, Euler, Lagrange and Gauss.Unlike many authors, however, Mr. Friedberg encourages students to think about the imaginative, playful qualities of numbers as they consider such subjects as primes

  20. Grand canonical electronic density-functional theory: Algorithms and applications to electrochemistry

    International Nuclear Information System (INIS)

    Sundararaman, Ravishankar; Goddard, William A. III; Arias, Tomas A.

    2017-01-01

    First-principles calculations combining density-functional theory and continuum solvation models enable realistic theoretical modeling and design of electrochemical systems. When a reaction proceeds in such systems, the number of electrons in the portion of the system treated quantum mechanically changes continuously, with a balancing charge appearing in the continuum electrolyte. A grand-canonical ensemble of electrons at a chemical potential set by the electrode potential is therefore the ideal description of such systems that directly mimics the experimental condition. We present two distinct algorithms: a self-consistent field method and a direct variational free energy minimization method using auxiliary Hamiltonians (GC-AuxH), to solve the Kohn-Sham equations of electronic density-functional theory directly in the grand canonical ensemble at fixed potential. Both methods substantially improve performance compared to a sequence of conventional fixed-number calculations targeting the desired potential, with the GC-AuxH method additionally exhibiting reliable and smooth exponential convergence of the grand free energy. Lastly, we apply grand-canonical density-functional theory to the under-potential deposition of copper on platinum from chloride-containing electrolytes and show that chloride desorption, not partial copper monolayer formation, is responsible for the second voltammetric peak.

  1. Grand canonical electronic density-functional theory: Algorithms and applications to electrochemistry

    Science.gov (United States)

    Sundararaman, Ravishankar; Goddard, William A.; Arias, Tomas A.

    2017-03-01

    First-principles calculations combining density-functional theory and continuum solvation models enable realistic theoretical modeling and design of electrochemical systems. When a reaction proceeds in such systems, the number of electrons in the portion of the system treated quantum mechanically changes continuously, with a balancing charge appearing in the continuum electrolyte. A grand-canonical ensemble of electrons at a chemical potential set by the electrode potential is therefore the ideal description of such systems that directly mimics the experimental condition. We present two distinct algorithms: a self-consistent field method and a direct variational free energy minimization method using auxiliary Hamiltonians (GC-AuxH), to solve the Kohn-Sham equations of electronic density-functional theory directly in the grand canonical ensemble at fixed potential. Both methods substantially improve performance compared to a sequence of conventional fixed-number calculations targeting the desired potential, with the GC-AuxH method additionally exhibiting reliable and smooth exponential convergence of the grand free energy. Finally, we apply grand-canonical density-functional theory to the under-potential deposition of copper on platinum from chloride-containing electrolytes and show that chloride desorption, not partial copper monolayer formation, is responsible for the second voltammetric peak.

  2. Monte Carlo algorithms for lattice gauge theory

    International Nuclear Information System (INIS)

    Creutz, M.

    1987-05-01

    Various techniques are reviewed which have been used in numerical simulations of lattice gauge theories. After formulating the problem, the Metropolis et al. algorithm and some interesting variations are discussed. The numerous proposed schemes for including fermionic fields in the simulations are summarized. Langevin, microcanonical, and hybrid approaches to simulating field theories via differential evolution in a fictitious time coordinate are treated. Some speculations are made on new approaches to fermionic simulations

  3. Stream ciphers and number theory

    CERN Document Server

    Cusick, Thomas W; Renvall, Ari R

    2004-01-01

    This is the unique book on cross-fertilisations between stream ciphers and number theory. It systematically and comprehensively covers known connections between the two areas that are available only in research papers. Some parts of this book consist of new research results that are not available elsewhere. In addition to exercises, over thirty research problems are presented in this book. In this revised edition almost every chapter was updated, and some chapters were completely rewritten. It is useful as a textbook for a graduate course on the subject, as well as a reference book for researchers in related fields. · Unique book on interactions of stream ciphers and number theory. · Research monograph with many results not available elsewhere. · A revised edition with the most recent advances in this subject. · Over thirty research problems for stimulating interactions between the two areas. · Written by leading researchers in stream ciphers and number theory.

  4. Fourier analysis in combinatorial number theory

    International Nuclear Information System (INIS)

    Shkredov, Il'ya D

    2010-01-01

    In this survey applications of harmonic analysis to combinatorial number theory are considered. Discussion topics include classical problems of additive combinatorics, colouring problems, higher-order Fourier analysis, theorems about sets of large trigonometric sums, results on estimates for trigonometric sums over subgroups, and the connection between combinatorial and analytic number theory. Bibliography: 162 titles.

  5. Fourier analysis in combinatorial number theory

    Energy Technology Data Exchange (ETDEWEB)

    Shkredov, Il' ya D [M. V. Lomonosov Moscow State University, Moscow (Russian Federation)

    2010-09-16

    In this survey applications of harmonic analysis to combinatorial number theory are considered. Discussion topics include classical problems of additive combinatorics, colouring problems, higher-order Fourier analysis, theorems about sets of large trigonometric sums, results on estimates for trigonometric sums over subgroups, and the connection between combinatorial and analytic number theory. Bibliography: 162 titles.

  6. Advanced number theory with applications

    CERN Document Server

    Mollin, Richard A

    2009-01-01

    Algebraic Number Theory and Quadratic Fields Algebraic Number Fields The Gaussian Field Euclidean Quadratic Fields Applications of Unique Factorization Ideals The Arithmetic of Ideals in Quadratic Fields Dedekind Domains Application to Factoring Binary Quadratic Forms Basics Composition and the Form Class Group Applications via Ambiguity Genus Representation Equivalence Modulo p Diophantine Approximation Algebraic and Transcendental Numbers Transcendence Minkowski's Convex Body Theorem Arithmetic Functions The Euler-Maclaurin Summation Formula Average Orders The Riemann zeta-functionIntroduction to p-Adic AnalysisSolving Modulo pn Introduction to Valuations Non-Archimedean vs. Archimedean Valuations Representation of p-Adic NumbersDirichlet: Characters, Density, and Primes in Progression Dirichlet Characters Dirichlet's L-Function and Theorem Dirichlet DensityApplications to Diophantine Equations Lucas-Lehmer Theory Generalized Ramanujan-Nagell Equations Bachet's Equation The Fermat Equation Catalan and the A...

  7. Conferences on Combinatorial and Additive Number Theory

    CERN Document Server

    2014-01-01

    This proceedings volume is based on papers presented at the Workshops on Combinatorial and Additive Number Theory (CANT), which were held at the Graduate Center of the City University of New York in 2011 and 2012. The goal of the workshops is to survey recent progress in combinatorial number theory and related parts of mathematics. The workshop attracts researchers and students who discuss the state-of-the-art, open problems, and future challenges in number theory.

  8. Fixed Orientation Interconnection Problems: Theory, Algorithms and Applications

    DEFF Research Database (Denmark)

    Zachariasen, Martin

    Interconnection problems have natural applications in the design of integrated circuits (or chips). A modern chip consists of billions of transistors that are connected by metal wires on the surface of the chip. These metal wires are routed on a (fairly small) number of layers in such a way...... that electrically independent nets do not intersect each other. Traditional manufacturing technology limits the orientations of the wires to be either horizontal or vertical — and is known as Manhattan architecture. Over the last decade there has been a growing interest in general architectures, where more than two...... a significant step forward, both concerning theory and algorithms, for the fixed orientation Steiner tree problem. In addition, the work maintains a close link to applications and generalizations motivated by chip design....

  9. Theory and Algorithms for Global/Local Design Optimization

    National Research Council Canada - National Science Library

    Watson, Layne T; Guerdal, Zafer; Haftka, Raphael T

    2005-01-01

    The motivating application for this research is the global/local optimal design of composite aircraft structures such as wings and fuselages, but the theory and algorithms are more widely applicable...

  10. Galois theory and algorithms for linear differential equations

    NARCIS (Netherlands)

    Put, Marius van der

    2005-01-01

    This paper is an informal introduction to differential Galois theory. It surveys recent work on differential Galois groups, related algorithms and some applications. (c) 2005 Elsevier Ltd. All rights reserved.

  11. History of the theory of numbers

    CERN Document Server

    Dickson, Leonard Eugene

    2005-01-01

    The three-volume series History of the Theory of Numbers is the work of the distinguished mathematician Leonard Eugene Dickson, who taught at the University of Chicago for four decades and is celebrated for his many contributions to number theory and group theory. This second volume in the series, which is suitable for upper-level undergraduates and graduate students, is devoted to the subject of diophantine analysis. It can be read independently of the preceding volume, which explores divisibility and primality, and volume III, which examines quadratic and higher forms.Featured topics include

  12. Prime Numbers Comparison using Sieve of Eratosthenes and Sieve of Sundaram Algorithm

    Science.gov (United States)

    Abdullah, D.; Rahim, R.; Apdilah, D.; Efendi, S.; Tulus, T.; Suwilo, S.

    2018-03-01

    Prime numbers are numbers that have their appeal to researchers due to the complexity of these numbers, many algorithms that can be used to generate prime numbers ranging from simple to complex computations, Sieve of Eratosthenes and Sieve of Sundaram are two algorithm that can be used to generate Prime numbers of randomly generated or sequential numbered random numbers, testing in this study to find out which algorithm is better used for large primes in terms of time complexity, the test also assisted with applications designed using Java language with code optimization and Maximum memory usage so that the testing process can be simultaneously and the results obtained can be objective

  13. Nonsmooth Optimization Algorithms, System Theory, and Software Tools

    Science.gov (United States)

    1993-04-13

    Optimization Algorithms, System Theory , and Scftware Tools" AFOSR-90-OO68 L AUTHOR($) Elijah Polak -Professor and Principal Investigator 7. PERFORMING...NSN 754Q-01-2W0-S500 Standard Form 295 (69O104 Draft) F’wsa*W by hA Sit 230.1""V AFOSR-90-0068 NONSMO0 TH OPTIMIZA TION A L GORI THMS, SYSTEM THEORY , AND

  14. Characteristics of Complexity: Clique Number of a Polytope Graph and Rectangle Covering Number

    Directory of Open Access Journals (Sweden)

    A. N. Maksimenko

    2014-01-01

    Full Text Available In the 1980s V.A. Bondarenko found that the clique number of the graph of a polytope in many cases corresponds to the actual complexity of the optimization problem on the vertices of the polytope. For an explanation of this phenomenon he proposed the theory of direct type algorithms. This theory asserts that the clique number of the graph of a polytope is the lower bound of the complexity of the corresponding problem in the so-called class of direct type algorithms. Moreover, it was argued that this class is wide enough and includes many classical combinatorial algorithms. In this paper we present a few examples, designed to identify the limits of applicability of this theory. In particular, we describe a modification of algorithms that is quite frequently used in practice. This modification takes the algorithms out of the specified class, while the complexity is not changed. Another, much closer to reality combinatorial characteristic of complexity is the rectangle covering number of the facet-vertex incidence matrix, introduced into consideration by M. Yannakakis in 1988. We give an example of a polytope with a polynomial (with respect to the dimension of the polytope value of this characteristic, while the corresponding optimization problem is NP-hard.

  15. Machine vision theory, algorithms, practicalities

    CERN Document Server

    Davies, E R

    2005-01-01

    In the last 40 years, machine vision has evolved into a mature field embracing a wide range of applications including surveillance, automated inspection, robot assembly, vehicle guidance, traffic monitoring and control, signature verification, biometric measurement, and analysis of remotely sensed images. While researchers and industry specialists continue to document their work in this area, it has become increasingly difficult for professionals and graduate students to understand the essential theory and practicalities well enough to design their own algorithms and systems. This book directl

  16. A conversational introduction to algebraic number theory

    CERN Document Server

    Pollack, Paul

    2017-01-01

    Gauss famously referred to mathematics as the "queen of the sciences" and to number theory as the "queen of mathematics". This book is an introduction to algebraic number theory, meaning the study of arithmetic in finite extensions of the rational number field \\mathbb{Q}. Originating in the work of Gauss, the foundations of modern algebraic number theory are due to Dirichlet, Dedekind, Kronecker, Kummer, and others. This book lays out basic results, including the three "fundamental theorems": unique factorization of ideals, finiteness of the class number, and Dirichlet's unit theorem. While these theorems are by now quite classical, both the text and the exercises allude frequently to more recent developments. In addition to traversing the main highways, the book reveals some remarkable vistas by exploring scenic side roads. Several topics appear that are not present in the usual introductory texts. One example is the inclusion of an extensive discussion of the theory of elasticity, which provides a precise w...

  17. Theory of analogous force on number sets

    Energy Technology Data Exchange (ETDEWEB)

    Canessa, Enrique [Abdus Salam International Centre for Theoretical Physics, Trieste (Italy)

    2003-08-01

    A general statistical thermodynamic theory that considers given sequences of x-integers to play the role of particles of known type in an isolated elastic system is proposed. By also considering some explicit discrete probability distributions p{sub x} for natural numbers, we claim that they lead to a better understanding of probabilistic laws associated with number theory. Sequences of numbers are treated as the size measure of finite sets. By considering p{sub x} to describe complex phenomena, the theory leads to derive a distinct analogous force f{sub x} on number sets proportional to ({partial_derivative}p{sub x}/{partial_derivative}x){sub T} at an analogous system temperature T. In particular, this yields to an understanding of the uneven distribution of integers of random sets in terms of analogous scale invariance and a screened inverse square force acting on the significant digits. The theory also allows to establish recursion relations to predict sequences of Fibonacci numbers and to give an answer to the interesting theoretical question of the appearance of the Benford's law in Fibonacci numbers. A possible relevance to prime numbers is also analyzed. (author)

  18. Distribution theory of algebraic numbers

    CERN Document Server

    Yang, Chung-Chun

    2008-01-01

    The book timely surveys new research results and related developments in Diophantine approximation, a division of number theory which deals with the approximation of real numbers by rational numbers. The book is appended with a list of challenging open problems and a comprehensive list of references. From the contents: Field extensions Algebraic numbers Algebraic geometry Height functions The abc-conjecture Roth''s theorem Subspace theorems Vojta''s conjectures L-functions.

  19. Algorithmic cryptanalysis

    CERN Document Server

    Joux, Antoine

    2009-01-01

    Illustrating the power of algorithms, Algorithmic Cryptanalysis describes algorithmic methods with cryptographically relevant examples. Focusing on both private- and public-key cryptographic algorithms, it presents each algorithm either as a textual description, in pseudo-code, or in a C code program.Divided into three parts, the book begins with a short introduction to cryptography and a background chapter on elementary number theory and algebra. It then moves on to algorithms, with each chapter in this section dedicated to a single topic and often illustrated with simple cryptographic applic

  20. Number theory in the spirit of Ramanujan

    CERN Document Server

    Berndt, Bruce C

    2006-01-01

    Ramanujan is recognized as one of the great number theorists of the twentieth century. Here now is the first book to provide an introduction to his work in number theory. Most of Ramanujan's work in number theory arose out of q-series and theta functions. This book provides an introduction to these two important subjects and to some of the topics in number theory that are inextricably intertwined with them, including the theory of partitions, sums of squares and triangular numbers, and the Ramanujan tau function. The majority of the results discussed here are originally due to Ramanujan or were rediscovered by him. Ramanujan did not leave us proofs of the thousands of theorems he recorded in his notebooks, and so it cannot be claimed that many of the proofs given in this book are those found by Ramanujan. However, they are all in the spirit of his mathematics. The subjects examined in this book have a rich history dating back to Euler and Jacobi, and they continue to be focal points of contemporary mathematic...

  1. Promoting Number Theory in High Schools or Birthday Problem and Number Theory

    Science.gov (United States)

    Srinivasan, V. K.

    2010-01-01

    The author introduces the birthday problem in this article. This can amuse willing members of any birthday party. This problem can also be used as the motivational first day lecture in number theory for the gifted students in high schools or in community colleges or in undergraduate classes in colleges.

  2. Number theory and its history

    CERN Document Server

    Ore, Oystein

    1988-01-01

    A prominent mathematician presents the principal ideas and methods of number theory within a historical and cultural framework. Oystein Ore's fascinating, accessible treatment requires only a basic knowledge of algebra. Topics include prime numbers, the Aliquot parts, linear indeterminate problems, congruences, Euler's theorem, classical construction problems, and many other subjects.

  3. Algebraic Geometry and Number Theory Summer School

    CERN Document Server

    Sarıoğlu, Celal; Soulé, Christophe; Zeytin, Ayberk

    2017-01-01

    This lecture notes volume presents significant contributions from the “Algebraic Geometry and Number Theory” Summer School, held at Galatasaray University, Istanbul, June 2-13, 2014. It addresses subjects ranging from Arakelov geometry and Iwasawa theory to classical projective geometry, birational geometry and equivariant cohomology. Its main aim is to introduce these contemporary research topics to graduate students who plan to specialize in the area of algebraic geometry and/or number theory. All contributions combine main concepts and techniques with motivating examples and illustrative problems for the covered subjects. Naturally, the book will also be of interest to researchers working in algebraic geometry, number theory and related fields.

  4. Muon number nonconservation in gauge theories

    International Nuclear Information System (INIS)

    Cheng, T.P.; Li, L.F.

    1977-01-01

    The question of separate conservation of muon and electron number is considered in the context of unified gauge theories of weak and electromagnetic interactions. Theories with heavy neutral leptons, Higgs scalars, and doubly charged heavy leptons are discussed. 28 references

  5. Introduction to $p$-adic analytic number theory

    CERN Document Server

    Murty, M Ram

    2002-01-01

    This book is an elementary introduction to p-adic analysis from the number theory perspective. With over 100 exercises included, it will acquaint the non-expert to the basic ideas of the theory and encourage the novice to enter this fertile field of research. The main focus of the book is the study of p-adic L-functions and their analytic properties. It begins with a basic introduction to Bernoulli numbers and continues with establishing the Kummer congruences. These congruences are then used to construct the p-adic analog of the Riemann zeta function and p-adic analogs of Dirichlet's L-functions. Featured is a chapter on how to apply the theory of Newton polygons to determine Galois groups of polynomials over the rational number field. As motivation for further study, the final chapter introduces Iwasawa theory.

  6. Multiscale Monte Carlo algorithms in statistical mechanics and quantum field theory

    Energy Technology Data Exchange (ETDEWEB)

    Lauwers, P G

    1990-12-01

    Conventional Monte Carlo simulation algorithms for models in statistical mechanics and quantum field theory are afflicted by problems caused by their locality. They become highly inefficient if investigations of critical or nearly-critical systems, i.e., systems with important large scale phenomena, are undertaken. We present two types of multiscale approaches that alleveate problems of this kind: Stochastic cluster algorithms and multigrid Monte Carlo simulation algorithms. Another formidable computational problem in simulations of phenomenologically relevant field theories with fermions is the need for frequently inverting the Dirac operator. This inversion can be accelerated considerably by means of deterministic multigrid methods, very similar to the ones used for the numerical solution of differential equations. (orig.).

  7. Inverse problems with Poisson data: statistical regularization theory, applications and algorithms

    International Nuclear Information System (INIS)

    Hohage, Thorsten; Werner, Frank

    2016-01-01

    Inverse problems with Poisson data arise in many photonic imaging modalities in medicine, engineering and astronomy. The design of regularization methods and estimators for such problems has been studied intensively over the last two decades. In this review we give an overview of statistical regularization theory for such problems, the most important applications, and the most widely used algorithms. The focus is on variational regularization methods in the form of penalized maximum likelihood estimators, which can be analyzed in a general setup. Complementing a number of recent convergence rate results we will establish consistency results. Moreover, we discuss estimators based on a wavelet-vaguelette decomposition of the (necessarily linear) forward operator. As most prominent applications we briefly introduce Positron emission tomography, inverse problems in fluorescence microscopy, and phase retrieval problems. The computation of a penalized maximum likelihood estimator involves the solution of a (typically convex) minimization problem. We also review several efficient algorithms which have been proposed for such problems over the last five years. (topical review)

  8. Support vector machines optimization based theory, algorithms, and extensions

    CERN Document Server

    Deng, Naiyang; Zhang, Chunhua

    2013-01-01

    Support Vector Machines: Optimization Based Theory, Algorithms, and Extensions presents an accessible treatment of the two main components of support vector machines (SVMs)-classification problems and regression problems. The book emphasizes the close connection between optimization theory and SVMs since optimization is one of the pillars on which SVMs are built.The authors share insight on many of their research achievements. They give a precise interpretation of statistical leaning theory for C-support vector classification. They also discuss regularized twi

  9. Parallel/vector algorithms for the spherical SN transport theory method

    International Nuclear Information System (INIS)

    Haghighat, A.; Mattis, R.E.

    1990-01-01

    This paper discusses vector and parallel processing of a 1-D curvilinear (i.e. spherical) S N transport theory algorithm on the Cornell National SuperComputer Facility (CNSF) IBM 3090/600E. Two different vector algorithms were developed and parallelized based on angular decomposition. It is shown that significant speedups are attainable. For example, for problems with large granularity, using 4 processors, the parallel/vector algorithm achieves speedups (for wall-clock time) of more than 4.5 relative to the old serial/scalar algorithm. Furthermore, this work has demonstrated the existing potential for the development of faster processing vector and parallel algorithms for multidimensional curvilinear geometries. (author)

  10. Number Worlds: Visual and Experimental Access to Elementary Number Theory Concepts

    Science.gov (United States)

    Sinclair, Nathalie; Zazkis, Rina; Liljedahl, Peter

    2004-01-01

    Recent research demonstrates that many issues related to the structure of natural numbers and the relationship among numbers are not well grasped by students. In this article, we describe a computer-based learning environment called "Number Worlds" that was designed to support the exploration of elementary number theory concepts by…

  11. A New GCD Algorithm for Quadratic Number Rings with Unique Factorization

    DEFF Research Database (Denmark)

    Agarwal, Saurabh; Frandsen, Gudmund Skovbjerg

    2006-01-01

    We present an algorithm to compute a greatest common divisor of two integers in a quadratic number ring that is a unique factorization domain. The algorithm uses bit operations in a ring of discriminant Δ. This appears to be the first gcd algorithm of complexity o(n 2) for any fixed non-Euclidean...

  12. Alternative analysis: the prime numbers theory and an extension of the real numbers set

    OpenAIRE

    Sukhotin A.; Zvyagin M.

    2016-01-01

    Here we consider the theory of prime numbers at a new methodology. The theory of prime numbers is one of the most ancient mathematical branches. We found an estimate of the all prime numbers sum using the notions of infinite lager numbers and infinitely small numbers, farther we estimated the value of the maximal prime number. We proved that Hardy–Littlewood Hypothesis has the positive decision too. The infinite small numbers define a new methodology of the well–known function o(x) applicatio...

  13. Relativistic theory of surficial Love numbers

    Science.gov (United States)

    Landry, Philippe; Poisson, Eric

    2014-06-01

    A relativistic theory of surficial Love numbers, which characterize the surface deformation of a body subjected to tidal forces, was initiated by Damour and Nagar. We revisit this effort in order to extend it, clarify some of its aspects, and simplify its computational implementation. First, we refine the definition of surficial Love numbers proposed by Damour and Nagar and formulate it directly in terms of the deformed curvature of the body's surface, a meaningful geometrical quantity. Second, we develop a unified theory of surficial Love numbers that applies equally well to material bodies and black holes. Third, we derive a compactness-dependent relation between the surficial and (electric-type) gravitational Love numbers of a perfect-fluid body and show that it reduces to the familiar Newtonian relation when the compactness is small. And fourth, we simplify the tasks associated with the practical computation of the surficial and gravitational Love numbers for a material body.

  14. The distribution of prime numbers and associated problems in number theory

    International Nuclear Information System (INIS)

    Nair, M.

    1991-01-01

    Some problems in number theory, namely the gaps between consecutive primes, the distribution of primes in arithmetic progressions, Brun-Titchmarsh theorem, Fermat's last theorem, The Thue equation, the gaps between square-free numbers are discussed

  15. 13th Conference of the Canadian Number Theory Association

    CERN Document Server

    Alaca, Şaban; Williams, Kenneth

    2015-01-01

    The theory of numbers continues to occupy a central place in modern mathematics because of both its long history over many centuries as well as its many diverse applications to other fields such as discrete mathematics, cryptography, and coding theory. The proof by Andrew Wiles (with Richard Taylor) of Fermat’s last theorem published in 1995 illustrates the high level of difficulty of problems encountered in number-theoretic research as well as the usefulness of the new ideas arising from its proof. The thirteenth conference of the Canadian Number Theory Association was held at Carleton University, Ottawa, Ontario, Canada from June 16 to 20, 2014. Ninety-nine talks were presented at the conference on the theme of advances in the theory of numbers. Topics of the talks reflected the diversity of current trends and activities in modern number theory. These topics included modular forms, hypergeometric functions, elliptic curves, distribution of prime numbers, diophantine equations, L-functions, Diophantine app...

  16. Generating log-normally distributed random numbers by using the Ziggurat algorithm

    International Nuclear Information System (INIS)

    Choi, Jong Soo

    2016-01-01

    Uncertainty analyses are usually based on the Monte Carlo method. Using an efficient random number generator(RNG) is a key element in success of Monte Carlo simulations. Log-normal distributed variates are very typical in NPP PSAs. This paper proposes an approach to generate log normally distributed variates based on the Ziggurat algorithm and evaluates the efficiency of the proposed Ziggurat RNG. The proposed RNG can be helpful to improve the uncertainty analysis of NPP PSAs. This paper focuses on evaluating the efficiency of the Ziggurat algorithm from a NPP PSA point of view. From this study, we can draw the following conclusions. - The Ziggurat algorithm is one of perfect random number generators to product normal distributed variates. - The Ziggurat algorithm is computationally much faster than the most commonly used method, Marsaglia polar method

  17. Seniority Number in Valence Bond Theory.

    Science.gov (United States)

    Chen, Zhenhua; Zhou, Chen; Wu, Wei

    2015-09-08

    In this work, a hierarchy of valence bond (VB) methods based on the concept of seniority number, defined as the number of singly occupied orbitals in a determinant or an orbital configuration, is proposed and applied to the studies of the potential energy curves (PECs) of H8, N2, and C2 molecules. It is found that the seniority-based VB expansion converges more rapidly toward the full configuration interaction (FCI) or complete active space self-consistent field (CASSCF) limit and produces more accurate PECs with smaller nonparallelity errors than its molecular orbital (MO) theory-based analogue. Test results reveal that the nonorthogonal orbital-based VB theory provides a reverse but more efficient way to truncate the complete active Hilbert space by seniority numbers.

  18. John Knopfmacher, [Abstract] Analytic Number Theory, and the ...

    African Journals Online (AJOL)

    Abstract. In this paper some important contributions of John Knopfmacher to ' Analytic Number Theory' are described. This theory investigates semigroups with countably many generators (generalized 'primes'), with a norm map (or a 'degree map'), and satisfying certain conditions on the number of elements with norm less

  19. A Note on "A polynomial-time algorithm for global value numbering"

    OpenAIRE

    Nabeezath, Saleena; Paleri, Vineeth

    2013-01-01

    Global Value Numbering(GVN) is a popular method for detecting redundant computations. A polynomial time algorithm for GVN is presented by Gulwani and Necula(2006). Here we present two limitations of this GVN algorithm due to which detection of certain kinds of redundancies can not be done using this algorithm. The first one is concerning the use of this algorithm in detecting some instances of the classical global common subexpressions, and the second is concerning its use in the detection of...

  20. String fields, higher spins and number theory

    CERN Document Server

    Polyakov, Dimitri

    2018-01-01

    The book aims to analyze and explore deep and profound relations between string field theory, higher spin gauge theories and holography the disciplines that have been on the cutting edge of theoretical high energy physics and other fields. These intriguing relations and connections involve some profound ideas in number theory, which appear to be part of a unifying language to describe these connections.

  1. [Prediction of regional soil quality based on mutual information theory integrated with decision tree algorithm].

    Science.gov (United States)

    Lin, Fen-Fang; Wang, Ke; Yang, Ning; Yan, Shi-Guang; Zheng, Xin-Yu

    2012-02-01

    In this paper, some main factors such as soil type, land use pattern, lithology type, topography, road, and industry type that affect soil quality were used to precisely obtain the spatial distribution characteristics of regional soil quality, mutual information theory was adopted to select the main environmental factors, and decision tree algorithm See 5.0 was applied to predict the grade of regional soil quality. The main factors affecting regional soil quality were soil type, land use, lithology type, distance to town, distance to water area, altitude, distance to road, and distance to industrial land. The prediction accuracy of the decision tree model with the variables selected by mutual information was obviously higher than that of the model with all variables, and, for the former model, whether of decision tree or of decision rule, its prediction accuracy was all higher than 80%. Based on the continuous and categorical data, the method of mutual information theory integrated with decision tree could not only reduce the number of input parameters for decision tree algorithm, but also predict and assess regional soil quality effectively.

  2. Contributions to Analytic Number Theory | Lucht | Quaestiones ...

    African Journals Online (AJOL)

    This paper reports on some recent contributions to the theory of multiplicative arithmetic semigroups, which have been initiated by John Knopfmacher's work on analytic number theory. They concern weighted inversion theorems of the. Wiener type, mean-value theorems for multiplicative functions, and, Ramanujan

  3. String amplitudes: from field theories to number theory

    CERN Multimedia

    CERN. Geneva

    2017-01-01

    In a variety of recent developments, scattering amplitudes hint at new symmetries of and unexpected connections between physical theories which are otherwise invisible in their conventional description via Feynman diagrams or Lagrangians. Yet, many of these hidden structures are conveniently accessible to string theory where gauge interactions and gravity arise as the low-energy excitations of open and closed strings. In this talk, I will give an intuitive picture of gravity as a double copy of gauge interactions and extend the web of relations to scalar field theories including chiral Lagrangians for Goldstone bosons. The string corrections to gauge and gravity amplitudes beyond their point-particle limit exhibit elegant mathematical structures and offer a convenient laboratory to explore modern number-theoretic concepts in a simple context. As a common theme with Feynman integrals, string amplitudes introduce a variety of periods and special functions including multiple zeta values and polylogarithms, orga...

  4. Number theory III Diophantine geometry

    CERN Document Server

    1991-01-01

    From the reviews of the first printing of this book, published as Volume 60 of the Encyclopaedia of Mathematical Sciences: "Between number theory and geometry there have been several stimulating influences, and this book records of these enterprises. This author, who has been at the centre of such research for many years, is one of the best guides a reader can hope for. The book is full of beautiful results, open questions, stimulating conjectures and suggestions where to look for future developments. This volume bears witness of the broad scope of knowledge of the author, and the influence of several people who have commented on the manuscript before publication ... Although in the series of number theory, this volume is on diophantine geometry, and the reader will notice that algebraic geometry is present in every chapter. ... The style of the book is clear. Ideas are well explained, and the author helps the reader to pass by several technicalities. Reading and rereading this book I noticed that the topics ...

  5. Topics in Number Theory Conference

    CERN Document Server

    Andrews, George; Ono, Ken

    1999-01-01

    From July 31 through August 3,1997, the Pennsylvania State University hosted the Topics in Number Theory Conference. The conference was organized by Ken Ono and myself. By writing the preface, I am afforded the opportunity to express my gratitude to Ken for beng the inspiring and driving force behind the whole conference. Without his energy, enthusiasm and skill the entire event would never have occurred. We are extremely grateful to the sponsors of the conference: The National Sci­ ence Foundation, The Penn State Conference Center and the Penn State Depart­ ment of Mathematics. The object in this conference was to provide a variety of presentations giving a current picture of recent, significant work in number theory. There were eight plenary lectures: H. Darmon (McGill University), "Non-vanishing of L-functions and their derivatives modulo p. " A. Granville (University of Georgia), "Mean values of multiplicative functions. " C. Pomerance (University of Georgia), "Recent results in primality testing. " C. ...

  6. Distributed k-Means Algorithm and Fuzzy c-Means Algorithm for Sensor Networks Based on Multiagent Consensus Theory.

    Science.gov (United States)

    Qin, Jiahu; Fu, Weiming; Gao, Huijun; Zheng, Wei Xing

    2016-03-03

    This paper is concerned with developing a distributed k-means algorithm and a distributed fuzzy c-means algorithm for wireless sensor networks (WSNs) where each node is equipped with sensors. The underlying topology of the WSN is supposed to be strongly connected. The consensus algorithm in multiagent consensus theory is utilized to exchange the measurement information of the sensors in WSN. To obtain a faster convergence speed as well as a higher possibility of having the global optimum, a distributed k-means++ algorithm is first proposed to find the initial centroids before executing the distributed k-means algorithm and the distributed fuzzy c-means algorithm. The proposed distributed k-means algorithm is capable of partitioning the data observed by the nodes into measure-dependent groups which have small in-group and large out-group distances, while the proposed distributed fuzzy c-means algorithm is capable of partitioning the data observed by the nodes into different measure-dependent groups with degrees of membership values ranging from 0 to 1. Simulation results show that the proposed distributed algorithms can achieve almost the same results as that given by the centralized clustering algorithms.

  7. A Simple But Effective Canonical Dual Theory Unified Algorithm for Global Optimization

    OpenAIRE

    Zhang, Jiapu

    2011-01-01

    Numerical global optimization methods are often very time consuming and could not be applied for high-dimensional nonconvex/nonsmooth optimization problems. Due to the nonconvexity/nonsmoothness, directly solving the primal problems sometimes is very difficult. This paper presents a very simple but very effective canonical duality theory (CDT) unified global optimization algorithm. This algorithm has convergence is proved in this paper. More important, for this CDT-unified algorithm, numerous...

  8. CUNY Graduate Center Workshops on Combinatorial and Additive Number Theory

    CERN Document Server

    2017-01-01

    Based on talks from the 2015 and 2016 Combinatorial and Additive Number Theory (CANT) workshops at the City University of New York, these proceedings offer 19 peer-reviewed and edited papers on current topics in number theory. Held every year since 2003, the workshop series surveys state-of-the-art open problems in combinatorial and additive number theory and related parts of mathematics. Sumsets, partitions, convex polytopes and discrete geometry, Ramsey theory, primality testing, and cryptography are among the topics featured in this volume. Each contribution is dedicated to a specific topic that reflects the latest results by experts in the field. Researchers and graduate students interested in the current progress in number theory will find this selection of articles relevant and compelling. .

  9. Some functional equations originating from number theory

    Indian Academy of Sciences (India)

    R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22

    Moreover, we will also study some stability problems of those equations. ... Wisconsin in which he discussed a number of important unsolved problems [18]. ... According to a well-known theorem in number theory, a positive integer of the form.

  10. Women in numbers Europe II contributions to number theory and arithmetic geometry

    CERN Document Server

    Ozman, Ekin; Johnson-Leung, Jennifer; Newton, Rachel

    2018-01-01

    Inspired by the September 2016 conference of the same name, this second volume highlights recent research in a wide range of topics in contemporary number theory and arithmetic geometry. Research reports from projects started at the conference, expository papers describing ongoing research, and contributed papers from women number theorists outside the conference make up this diverse volume. Topics cover a broad range of topics such as arithmetic dynamics, failure of local-global principles, geometry in positive characteristics, and heights of algebraic integers. The use of tools from algebra, analysis and geometry, as well as computational methods exemplifies the wealth of techniques available to modern researchers in number theory. Exploring connections between different branches of mathematics and combining different points of view, these papers continue the tradition of supporting and highlighting the contributions of women number theorists at a variety of career stages. Perfect for students and researche...

  11. Number theory and the periodicity of matter

    CERN Document Server

    Boeyens, Jan C A

    2008-01-01

    Presents a fully scientific account of the use of the golden ratio and explores the observation that stable nucleides obey a number theory based general lawThe interest in number theory is worldwide and covers the entire spectrum of human knowledge. Those aspects covered here will not be immediately accessible to the general lay readership, but, scientists of all pursuations immediately appreciate the importance of the applications described hereThe well-known interest of engineers, medical practitioners and information technologists in popular scientific matters, should make this an attractive buy for such individuals. Undergraduate students in these disciplines should be equally interested.

  12. FAST-PT: a novel algorithm to calculate convolution integrals in cosmological perturbation theory

    Energy Technology Data Exchange (ETDEWEB)

    McEwen, Joseph E.; Fang, Xiao; Hirata, Christopher M.; Blazek, Jonathan A., E-mail: mcewen.24@osu.edu, E-mail: fang.307@osu.edu, E-mail: hirata.10@osu.edu, E-mail: blazek@berkeley.edu [Center for Cosmology and AstroParticle Physics, Department of Physics, The Ohio State University, 191 W Woodruff Ave, Columbus OH 43210 (United States)

    2016-09-01

    We present a novel algorithm, FAST-PT, for performing convolution or mode-coupling integrals that appear in nonlinear cosmological perturbation theory. The algorithm uses several properties of gravitational structure formation—the locality of the dark matter equations and the scale invariance of the problem—as well as Fast Fourier Transforms to describe the input power spectrum as a superposition of power laws. This yields extremely fast performance, enabling mode-coupling integral computations fast enough to embed in Monte Carlo Markov Chain parameter estimation. We describe the algorithm and demonstrate its application to calculating nonlinear corrections to the matter power spectrum, including one-loop standard perturbation theory and the renormalization group approach. We also describe our public code (in Python) to implement this algorithm. The code, along with a user manual and example implementations, is available at https://github.com/JoeMcEwen/FAST-PT.

  13. Anomalous quantum numbers and topological properties of field theories

    International Nuclear Information System (INIS)

    Polychronakos, A.P.

    1987-01-01

    We examine the connection between anomalous quantum numbers, symmetry breaking patterns and topological properties of some field theories. The main results are the following: In three dimensions the vacuum in the presence of abelian magnetic field configurations behaves like a superconductor. Its quantum numbers are exactly calculable and are connected with the Atiyah-Patodi-Singer index theorem. Boundary conditions, however, play a nontrivial role in this case. Local conditions were found to be physically preferable than the usual global ones. Due to topological reasons, only theories for which the gauge invariant photon mass in three dimensions obeys a quantization condition can support states of nonzero magnetic flux. For similar reasons, this mass induces anomalous angular momentum quantum numbers to the states of the theory. Parity invariance and global flavor symmetry were shown to be incompatible in such theories. In the presence of mass less flavored fermions, parity will always break for an odd number of fermion flavors, while for even fermion flavors it may not break but only at the expense of maximally breaking the flavor symmetry. Finally, a connection between these theories and the quantum Hall effect was indicated

  14. Introduction to number theory with cryptography

    CERN Document Server

    Kraft, James S

    2013-01-01

    IntroductionDiophantine EquationsModular ArithmeticPrimes and the Distribution of PrimesCryptographyDivisibilityDivisibilityEuclid's Theorem Euclid's Original Proof The Sieve of Eratosthenes The Division Algorithm The Greatest Common Divisor The Euclidean Algorithm Other BasesLinear Diophantine EquationsThe Postage Stamp Problem Fermat and Mersenne Numbers Chapter Highlights Problems Unique FactorizationPreliminary Results The Fundamental Theorem of Arithmetic Euclid and the Fundamental Theorem of ArithmeticChapter Highlights Problems Applications of Unique Factorization A Puzzle Irrationality Proofs The Rational Root Theorem Pythagorean Triples Differences of Squares Prime Factorization of Factorials The Riemann Zeta Function Chapter Highlights Problems CongruencesDefinitions and Examples Modular Exponentiation Divisibility TestsLinear Congruences The Chinese Remainder TheoremFractions mod m Fermat's Theorem Euler's Theorem Wilson's Theorem Queens on a Chessboard Chapter Highlights Problems Cryptographic App...

  15. Number-theory dark matter

    International Nuclear Information System (INIS)

    Nakayama, Kazunori; Takahashi, Fuminobu; Yanagida, Tsutomu T.

    2011-01-01

    We propose that the stability of dark matter is ensured by a discrete subgroup of the U(1) B-L gauge symmetry, Z 2 (B-L). We introduce a set of chiral fermions charged under the U(1) B-L in addition to the right-handed neutrinos, and require the anomaly-cancellation conditions associated with the U(1) B-L gauge symmetry. We find that the possible number of fermions and their charges are tightly constrained, and that non-trivial solutions appear when at least five additional chiral fermions are introduced. The Fermat theorem in the number theory plays an important role in this argument. Focusing on one of the solutions, we show that there is indeed a good candidate for dark matter, whose stability is guaranteed by Z 2 (B-L).

  16. Phenomenology of muon number violation in spontaneously broken gauge theories

    International Nuclear Information System (INIS)

    Shanker, O.U.

    1980-01-01

    The phenomenology of muon number violation in gauge theories of weak and electromagnetic interactions is studied. In the first chapter a brief introduction to the concept of muon number and to spontaneously broken gauge theories is given. A review of the phenomenology and experimental situation regarding different muon number violating processes is made in the second chapter. A detailed phenomenological study of the μe conversion process μ - + (A,Z) → e - + (A,Z) is given in the third chapter. In the fourth chapter some specific gauge theories incorporating spontaneously broken horizontal gauge symmetries between different fermion generations are discussed with special reference to muon number violation in the theories. The μe conversion process seems to be a good process to search for muon number violation if it occurs. The K/sub L/-K/sub S/ mass difference is likely to constrain muon number violating rates to lie far below present experimental limits unless strangeness changing neutral currents changing strangeness by two units are suppressed

  17. Fermi-Dirac statistics and the number theory

    OpenAIRE

    Kubasiak, A.; Korbicz, J.; Zakrzewski, J.; Lewenstein, M.

    2005-01-01

    We relate the Fermi-Dirac statistics of an ideal Fermi gas in a harmonic trap to partitions of given integers into distinct parts, studied in number theory. Using methods of quantum statistical physics we derive analytic expressions for cumulants of the probability distribution of the number of different partitions.

  18. 7th International Conference on Elementary and Analytic Number Theory

    CERN Document Server

    Steuding, Jörn; Steuding, Rasa

    2016-01-01

    This book collects more than thirty contributions in memory of Wolfgang Schwarz, most of which were presented at the seventh International Conference on Elementary and Analytic Number Theory (ELAZ), held July 2014 in Hildesheim, Germany. Ranging from the theory of arithmetical functions to diophantine problems, to analytic aspects of zeta-functions, the various research and survey articles cover the broad interests of the well-known number theorist and cherished colleague Wolfgang Schwarz (1934-2013), who contributed over one hundred articles on number theory, its history and related fields. Readers interested in elementary or analytic number theory and related fields will certainly find many fascinating topical results among the contributions from both respected mathematicians and up-and-coming young researchers. In addition, some biographical articles highlight the life and mathematical works of Wolfgang Schwarz.

  19. Number-theory dark matter

    Energy Technology Data Exchange (ETDEWEB)

    Nakayama, Kazunori [Theory Center, KEK, 1-1 Oho, Tsukuba, Ibaraki 305-0801 (Japan); Takahashi, Fuminobu, E-mail: fumi@tuhep.phys.tohoku.ac.jp [Department of Physics, Tohoku University, Sendai 980-8578 (Japan); Institute for the Physics and Mathematics of the Universe, University of Tokyo, Kashiwa 277-8568 (Japan); Yanagida, Tsutomu T. [Institute for the Physics and Mathematics of the Universe, University of Tokyo, Kashiwa 277-8568 (Japan); Department of Physics, University of Tokyo, Tokyo 113-0033 (Japan)

    2011-05-23

    We propose that the stability of dark matter is ensured by a discrete subgroup of the U(1){sub B-L} gauge symmetry, Z{sub 2}(B-L). We introduce a set of chiral fermions charged under the U(1){sub B-L} in addition to the right-handed neutrinos, and require the anomaly-cancellation conditions associated with the U(1){sub B-L} gauge symmetry. We find that the possible number of fermions and their charges are tightly constrained, and that non-trivial solutions appear when at least five additional chiral fermions are introduced. The Fermat theorem in the number theory plays an important role in this argument. Focusing on one of the solutions, we show that there is indeed a good candidate for dark matter, whose stability is guaranteed by Z{sub 2}(B-L).

  20. The Work of Lagrange in Number Theory and Algebra

    Indian Academy of Sciences (India)

    GENERAL I ARTICLE. The Work of Lagrange in Number Theory and Algebra. D P Patil, C R Pranesachar and Renuka RafJindran. (left) D P Patil got his Ph.D from the School of Math- ematics, TIFR and joined. IISc in 1992. His interests are commutative algebra, algebraic geometry and algebraic number theory. (right) C R ...

  1. Topics in number theory

    CERN Document Server

    LeVeque, William J

    2002-01-01

    Classic two-part work now available in a single volume assumes no prior theoretical knowledge on reader's part and develops the subject fully. Volume I is a suitable first course text for advanced undergraduate and beginning graduate students. Volume II requires a much higher level of mathematical maturity, including a working knowledge of the theory of analytic functions. Contents range from chapters on binary quadratic forms to the Thue-Siegel-Roth Theorem and the Prime Number Theorem. Includes numerous problems and hints for their solutions. 1956 edition. Supplementary Reading. List of Symb

  2. A Self-Adaptive Fuzzy c-Means Algorithm for Determining the Optimal Number of Clusters

    Science.gov (United States)

    Wang, Zhihao; Yi, Jing

    2016-01-01

    For the shortcoming of fuzzy c-means algorithm (FCM) needing to know the number of clusters in advance, this paper proposed a new self-adaptive method to determine the optimal number of clusters. Firstly, a density-based algorithm was put forward. The algorithm, according to the characteristics of the dataset, automatically determined the possible maximum number of clusters instead of using the empirical rule n and obtained the optimal initial cluster centroids, improving the limitation of FCM that randomly selected cluster centroids lead the convergence result to the local minimum. Secondly, this paper, by introducing a penalty function, proposed a new fuzzy clustering validity index based on fuzzy compactness and separation, which ensured that when the number of clusters verged on that of objects in the dataset, the value of clustering validity index did not monotonically decrease and was close to zero, so that the optimal number of clusters lost robustness and decision function. Then, based on these studies, a self-adaptive FCM algorithm was put forward to estimate the optimal number of clusters by the iterative trial-and-error process. At last, experiments were done on the UCI, KDD Cup 1999, and synthetic datasets, which showed that the method not only effectively determined the optimal number of clusters, but also reduced the iteration of FCM with the stable clustering result. PMID:28042291

  3. Genetic algorithm based on virus theory of evolution for traveling salesman problem; Virus shinkaron ni motozuku identeki algorithm no junkai salesman mondai eno oyo

    Energy Technology Data Exchange (ETDEWEB)

    Kubota, N. [Osaka Inst. of Technology, Osaka (Japan); Fukuda, T. [Nagoya University, Nagoya (Japan)

    1998-05-31

    This paper deals with virus evolutionary genetic algorithm. The genetic algorithms (GAs) have been demonstrated its effectiveness in optimization problems in these days. In general, the GAs simulate the survival of fittest by natural selection and the heredity of the Darwin`s theory of evolution. However, some types of evolutionary hypotheses such as neutral theory of molecular evolution, Imanishi`s evolutionary theory, serial symbiosis theory, and virus theory of evolution, have been proposed in addition to the Darwinism. Virus theory of evolution is based on the view that the virus transduction is a key mechanism for transporting segments of DNA across species. This paper proposes genetic algorithm based on the virus theory of evolution (VE-GA), which has two types of populations: host population and virus population. The VE-GA is composed of genetic operators and virus operators such as reverse transcription and incorporation. The reverse transcription operator transcribes virus genes on the chromosome of host individual and the incorporation operator creates new genotype of virus from host individual. These operators by virus population make it possible to transmit segment of DNA between individuals in the host population. Therefore, the VE-GA realizes not only vertical but also horizontal propagation of genetic information. Further, the VE-GA is applied to the traveling salesman problem in order to show the effectiveness. 20 refs., 10 figs., 3 tabs.

  4. Number theory an approach through history from Hammurapi to Legendre

    CERN Document Server

    Weil, André

    2007-01-01

    Number Theory or arithmetic, as some prefer to call it, is the oldest, purest, liveliest, most elementary yet sophisticated field of mathematics. It is no coincidence that the fundamental science of numbers has come to be known as the "Queen of Mathematics." Indeed some of the most complex conventions of the mathematical mind have evolved from the study of basic problems of number theory. André Weil, one of the outstanding contributors to number theory, has written an historical exposition of this subject; his study examines texts that span roughly thirty-six centuries of arithmetical work — from an Old Babylonian tablet, datable to the time of Hammurapi to Legendre’s Essai sur la Théorie des Nombres (1798). Motivated by a desire to present the substance of his field to the educated reader, Weil employs an historical approach in the analysis of problems and evolving methods of number theory and their significance within mathematics. In the course of his study Weil accompanies the reader into the worksho...

  5. Automation of Algorithmic Tasks for Virtual Laboratories Based on Automata Theory

    Directory of Open Access Journals (Sweden)

    Evgeniy A. Efimchik

    2016-03-01

    Full Text Available In the work a description of an automata model of standard algorithm for constructing a correct solution of algorithmic tests is given. The described model allows a formal determination of the variant complexity of algorithmic test and serves as a basis for determining the complexity functions, including the collision concept – the situation of uncertainty, when a choice must be made upon fulfilling the task between the alternatives with various priorities. The influence of collisions on the automata model and its inner structure is described. The model and complexity functions are applied for virtual laboratories upon designing the algorithms of constructing variant with a predetermined complexity in real time and algorithms of the estimation procedures of students’ solution with respect to collisions. The results of the work are applied to the development of virtual laboratories, which are used in the practical part of massive online course on graph theory.

  6. ID card number detection algorithm based on convolutional neural network

    Science.gov (United States)

    Zhu, Jian; Ma, Hanjie; Feng, Jie; Dai, Leiyan

    2018-04-01

    In this paper, a new detection algorithm based on Convolutional Neural Network is presented in order to realize the fast and convenient ID information extraction in multiple scenarios. The algorithm uses the mobile device equipped with Android operating system to locate and extract the ID number; Use the special color distribution of the ID card, select the appropriate channel component; Use the image threshold segmentation, noise processing and morphological processing to take the binary processing for image; At the same time, the image rotation and projection method are used for horizontal correction when image was tilting; Finally, the single character is extracted by the projection method, and recognized by using Convolutional Neural Network. Through test shows that, A single ID number image from the extraction to the identification time is about 80ms, the accuracy rate is about 99%, It can be applied to the actual production and living environment.

  7. The logic of logistics: theory, algorithms and applications for logistics management

    Directory of Open Access Journals (Sweden)

    Claudio Barbieri da Cunha

    2010-04-01

    Full Text Available

    Nesse texto o autor apresenta uma resenha acerca do livro "The logic of logistics: theory, algorithms and applications for logistics management", de autoria de Julien Bramel e David Simchi-Levi, publicado pela Springer-Verlag, em 1997.

  8. Bilinear Inverse Problems: Theory, Algorithms, and Applications

    Science.gov (United States)

    Ling, Shuyang

    guarantees and stability theory are derived and the number of sampling complexity is nearly optimal (up to a poly-log factor). Applications in imaging sciences and signal processing are discussed and numerical simulations are presented to demonstrate the effectiveness and efficiency of our approach.

  9. Experimental determination of Ramsey numbers.

    Science.gov (United States)

    Bian, Zhengbing; Chudak, Fabian; Macready, William G; Clark, Lane; Gaitan, Frank

    2013-09-27

    Ramsey theory is a highly active research area in mathematics that studies the emergence of order in large disordered structures. Ramsey numbers mark the threshold at which order first appears and are extremely difficult to calculate due to their explosive rate of growth. Recently, an algorithm that can be implemented using adiabatic quantum evolution has been proposed that calculates the two-color Ramsey numbers R(m,n). Here we present results of an experimental implementation of this algorithm and show that it correctly determines the Ramsey numbers R(3,3) and R(m,2) for 4≤m≤8. The R(8,2) computation used 84 qubits of which 28 were computational qubits. This computation is the largest experimental implementation of a scientifically meaningful adiabatic evolution algorithm that has been done to date.

  10. Number theory meets Higgs physics

    CERN Multimedia

    CERN. Geneva

    2014-01-01

    Inspired by results from modern number theory and algebraic geometry, a lot of progress has recently been made regarding the computation of multi-loop integrals and scattering amplitudes. I will discuss various new approaches to the computation of loop integrals, and illustrate them on the first computation of a quantity at N3LO in perturbative QCD, the soft-virtual part of the inclusive Higgs-boson cross section in gluon fusion at N3LO.

  11. Lepton number violation in theories with a large number of standard model copies

    International Nuclear Information System (INIS)

    Kovalenko, Sergey; Schmidt, Ivan; Paes, Heinrich

    2011-01-01

    We examine lepton number violation (LNV) in theories with a saturated black hole bound on a large number of species. Such theories have been advocated recently as a possible solution to the hierarchy problem and an explanation of the smallness of neutrino masses. On the other hand, the violation of the lepton number can be a potential phenomenological problem of this N-copy extension of the standard model as due to the low quantum gravity scale black holes may induce TeV scale LNV operators generating unacceptably large rates of LNV processes. We show, however, that this issue can be avoided by introducing a spontaneously broken U 1(B-L) . Then, due to the existence of a specific compensation mechanism between contributions of different Majorana neutrino states, LNV processes in the standard model copy become extremely suppressed with rates far beyond experimental reach.

  12. Scheduling theory, algorithms, and systems

    CERN Document Server

    Pinedo, Michael L

    2016-01-01

    This new edition of the well-established text Scheduling: Theory, Algorithms, and Systems provides an up-to-date coverage of important theoretical models in the scheduling literature as well as important scheduling problems that appear in the real world. The accompanying website includes supplementary material in the form of slide-shows from industry as well as movies that show actual implementations of scheduling systems. The main structure of the book, as per previous editions, consists of three parts. The first part focuses on deterministic scheduling and the related combinatorial problems. The second part covers probabilistic scheduling models; in this part it is assumed that processing times and other problem data are random and not known in advance. The third part deals with scheduling in practice; it covers heuristics that are popular with practitioners and discusses system design and implementation issues. All three parts of this new edition have been revamped, streamlined, and extended. The reference...

  13. From c-number to q-numbers the classical analogy in the history of quantum theory

    CERN Document Server

    Darrigol, Olivier

    1992-01-01

    The history of quantum theory is a maze of conceptual problems, through which Olivier Darrigol provides a lucid and learned guide, tracking the role of formal analogies between classical and quantum theory. From Planck's first introduction of the quantum of action to Dirac's formulation of quantum mechanics, Darrigol illuminates not only the history of quantum theory but also the role of analogies in scientific thinking and theory change. Unlike previous works, which have tended to focus on qualitative, global arguments, Darrigol's study follows the lines of mathematical reasoning and symbolizing and so is able to show the motivations of early quantum theorists more precisely—and provocatively—than ever before. Erudite and original, From c-Numbers to q-Numbers sets a new standard as a philosophically perceptive and mathematically precise history of quantum mechanics. For years to come it will influence historical and philosophical discussions of twentieth-century physics.

  14. Some Functional Equations Originating from Number Theory

    Indian Academy of Sciences (India)

    We will introduce new functional equations (3) and (4) which are strongly related to well-known formulae (1) and (2) of number theory, and investigate the solutions of the equations. Moreover, we will also study some stability problems of those equations.

  15. Rational hybrid Monte Carlo algorithm for theories with unknown spectral bounds

    International Nuclear Information System (INIS)

    Kogut, J. B.; Sinclair, D. K.

    2006-01-01

    The Rational Hybrid Monte Carlo (RHMC) algorithm extends the Hybrid Monte Carlo algorithm for lattice QCD simulations to situations involving fractional powers of the determinant of the quadratic Dirac operator. This avoids the updating increment (dt) dependence of observables which plagues the Hybrid Molecular-dynamics (HMD) method. The RHMC algorithm uses rational approximations to fractional powers of the quadratic Dirac operator. Such approximations are only available when positive upper and lower bounds to the operator's spectrum are known. We apply the RHMC algorithm to simulations of 2 theories for which a positive lower spectral bound is unknown: lattice QCD with staggered quarks at finite isospin chemical potential and lattice QCD with massless staggered quarks and chiral 4-fermion interactions (χQCD). A choice of lower bound is made in each case, and the properties of the RHMC simulations these define are studied. Justification of our choices of lower bounds is made by comparing measurements with those from HMD simulations, and by comparing different choices of lower bounds

  16. Contributions to the founding of the theory of transfinite numbers

    CERN Document Server

    Cantor, Georg

    1955-01-01

    One of the greatest mathematical classics of all time, this work established a new field of mathematics which was to be of incalculable importance in topology, number theory, analysis, theory of functions, etc., as well as in the entire field of modern logic. It is rare that a theory of such fundamental mathematical importance is expressed so simply and clearly: the reader with a good grasp of college mathematics will be able to understand most of the basic ideas and many of the proofs.Cantor first develops the elementary definitions and operations of cardinal and ordinal numbers and analyzes

  17. Polynomial hybrid Monte Carlo algorithm for lattice QCD with an odd number of flavors

    International Nuclear Information System (INIS)

    Aoki, S.; Burkhalter, R.; Ishikawa, K-I.; Tominaga, S.; Fukugita, M.; Hashimoto, S.; Kaneko, T.; Kuramashi, Y.; Okawa, M.; Tsutsui, N.; Yamada, N.; Ishizuka, N.; Iwasaki, Y.; Kanaya, K.; Ukawa, A.; Yoshie, T.; Onogi, T.

    2002-01-01

    We present a polynomial hybrid Monte Carlo (PHMC) algorithm for lattice QCD with odd numbers of flavors of O(a)-improved Wilson quark action. The algorithm makes use of the non-Hermitian Chebyshev polynomial to approximate the inverse square root of the fermion matrix required for an odd number of flavors. The systematic error from the polynomial approximation is removed by a noisy Metropolis test for which a new method is developed. Investigating the property of our PHMC algorithm in the N f =2 QCD case, we find that it is as efficient as the conventional HMC algorithm for a moderately large lattice size (16 3 x48) with intermediate quark masses (m PS /m V ∼0.7-0.8). We test our odd-flavor algorithm through extensive simulations of two-flavor QCD treated as an N f =1+1 system, and comparing the results with those of the established algorithms for N f =2 QCD. These tests establish that our PHMC algorithm works on a moderately large lattice size with intermediate quark masses (16 3 x48,m PS /m V ∼0.7-0.8). Finally we experiment with the (2+1)-flavor QCD simulation on small lattices (4 3 x8 and 8 3 x16), and confirm the agreement of our results with those obtained with the R algorithm and extrapolated to a zero molecular dynamics step size

  18. The large numbers hypothesis and a relativistic theory of gravitation

    International Nuclear Information System (INIS)

    Lau, Y.K.; Prokhovnik, S.J.

    1986-01-01

    A way to reconcile Dirac's large numbers hypothesis and Einstein's theory of gravitation was recently suggested by Lau (1985). It is characterized by the conjecture of a time-dependent cosmological term and gravitational term in Einstein's field equations. Motivated by this conjecture and the large numbers hypothesis, we formulate here a scalar-tensor theory in terms of an action principle. The cosmological term is required to be spatially dependent as well as time dependent in general. The theory developed is appled to a cosmological model compatible with the large numbers hypothesis. The time-dependent form of the cosmological term and the scalar potential are then deduced. A possible explanation of the smallness of the cosmological term is also given and the possible significance of the scalar field is speculated

  19. Mathematical conversations multicolor problems, problems in the theory of numbers, and random walks

    CERN Document Server

    Dynkin, E B

    2006-01-01

    Comprises Multicolor Problems, dealing with map-coloring problems; Problems in the Theory of Numbers, an elementary introduction to algebraic number theory; Random Walks, addressing basic problems in probability theory. 1963 edition.

  20. Selected papers on number theory and algebraic geometry

    CERN Document Server

    Nomizu, Katsumi

    1996-01-01

    This book presents papers that originally appeared in the Japanese journal Sugaku from the Mathematical Society of Japan. The papers explore the relationship between number theory and algebraic geometry.

  1. Numerical Test of Analytical Theories for Perpendicular Diffusion in Small Kubo Number Turbulence

    Energy Technology Data Exchange (ETDEWEB)

    Heusen, M.; Shalchi, A., E-mail: husseinm@myumanitoba.ca, E-mail: andreasm4@yahoo.com [Department of Physics and Astronomy, University of Manitoba, Winnipeg, MB R3T 2N2 (Canada)

    2017-04-20

    In the literature, one can find various analytical theories for perpendicular diffusion of energetic particles interacting with magnetic turbulence. Besides quasi-linear theory, there are different versions of the nonlinear guiding center (NLGC) theory and the unified nonlinear transport (UNLT) theory. For turbulence with high Kubo numbers, such as two-dimensional turbulence or noisy reduced magnetohydrodynamic turbulence, the aforementioned nonlinear theories provide similar results. For slab and small Kubo number turbulence, however, this is not the case. In the current paper, we compare different linear and nonlinear theories with each other and test-particle simulations for a noisy slab model corresponding to small Kubo number turbulence. We show that UNLT theory agrees very well with all performed test-particle simulations. In the limit of long parallel mean free paths, the perpendicular mean free path approaches asymptotically the quasi-linear limit as predicted by the UNLT theory. For short parallel mean free paths we find a Rechester and Rosenbluth type of scaling as predicted by UNLT theory as well. The original NLGC theory disagrees with all performed simulations regardless what the parallel mean free path is. The random ballistic interpretation of the NLGC theory agrees much better with the simulations, but compared to UNLT theory the agreement is inferior. We conclude that for this type of small Kubo number turbulence, only the latter theory allows for an accurate description of perpendicular diffusion.

  2. Numerical Test of Analytical Theories for Perpendicular Diffusion in Small Kubo Number Turbulence

    International Nuclear Information System (INIS)

    Heusen, M.; Shalchi, A.

    2017-01-01

    In the literature, one can find various analytical theories for perpendicular diffusion of energetic particles interacting with magnetic turbulence. Besides quasi-linear theory, there are different versions of the nonlinear guiding center (NLGC) theory and the unified nonlinear transport (UNLT) theory. For turbulence with high Kubo numbers, such as two-dimensional turbulence or noisy reduced magnetohydrodynamic turbulence, the aforementioned nonlinear theories provide similar results. For slab and small Kubo number turbulence, however, this is not the case. In the current paper, we compare different linear and nonlinear theories with each other and test-particle simulations for a noisy slab model corresponding to small Kubo number turbulence. We show that UNLT theory agrees very well with all performed test-particle simulations. In the limit of long parallel mean free paths, the perpendicular mean free path approaches asymptotically the quasi-linear limit as predicted by the UNLT theory. For short parallel mean free paths we find a Rechester and Rosenbluth type of scaling as predicted by UNLT theory as well. The original NLGC theory disagrees with all performed simulations regardless what the parallel mean free path is. The random ballistic interpretation of the NLGC theory agrees much better with the simulations, but compared to UNLT theory the agreement is inferior. We conclude that for this type of small Kubo number turbulence, only the latter theory allows for an accurate description of perpendicular diffusion.

  3. A potential theory approach to an algorithm of conceptual space partitioning

    Directory of Open Access Journals (Sweden)

    Roman Urban

    2017-12-01

    Full Text Available A potential theory approach to an algorithm of conceptual space partitioning This paper proposes a new classification algorithm for the partitioning of a conceptual space. All the algorithms which have been used until now have mostly been based on the theory of Voronoi diagrams. This paper proposes an approach based on potential theory, with the criteria for measuring similarities between objects in the conceptual space being based on the Newtonian potential function. The notion of a fuzzy prototype, which generalizes the previous definition of a prototype, is introduced. Furthermore, the necessary conditions that a natural concept must meet are discussed. Instead of convexity, as proposed by Gärdenfors, the notion of geodesically convex sets is used. Thus, if a concept corresponds to a set which is geodesically convex, it is a natural concept. This definition applies, for example, if the conceptual space is an Euclidean space. As a by-product of the construction of the algorithm, an extension of the conceptual space to d-dimensional Riemannian manifolds is obtained.   Algorytm podziału przestrzeni konceptualnych przy użyciu teorii potencjału W niniejszej pracy zaproponowany został nowy algorytm podziału przestrzeni konceptualnej. Dotąd podział taki zazwyczaj wykorzystywał teorię diagramów Voronoi. Nasze podejście do problemu oparte jest na teorii potencjału Miara podobieństwa pomiędzy elementami przestrzeni konceptualnej bazuje na Newtonowskiej funkcji potencjału. Definiujemy pojęcie rozmytego prototypu, który uogólnia dotychczas stosowane definicje prototypu. Ponadto zajmujemy się warunkiem koniecznym, który musi spełniać naturalny koncept. Zamiast wypukłości zaproponowanej przez Gärdenforsa, rozważamy linie geodezyjne w obszarze odpowiadającym danemu konceptowi naturalnemu, otrzymując warunek mówiący, że koncept jest konceptem naturalnym, jeżeli zbiór odpowiadający temu konceptowi jest geodezyjnie wypuk

  4. Algorithms for Monte Carlo calculations with fermions

    International Nuclear Information System (INIS)

    Weingarten, D.

    1985-01-01

    We describe a fermion Monte Carlo algorithm due to Petcher and the present author and another due to Fucito, Marinari, Parisi and Rebbi. For the first algorithm we estimate the number of arithmetic operations required to evaluate a vacuum expectation value grows as N 11 /msub(q) on an N 4 lattice with fixed periodicity in physical units and renormalized quark mass msub(q). For the second algorithm the rate of growth is estimated to be N 8 /msub(q) 2 . Numerical experiments are presented comparing the two algorithms on a lattice of size 2 4 . With a hopping constant K of 0.15 and β of 4.0 we find the number of operations for the second algorithm is about 2.7 times larger than for the first and about 13 000 times larger than for corresponding Monte Carlo calculations with a pure gauge theory. An estimate is given for the number of operations required for more realistic calculations by each algorithm on a larger lattice. (orig.)

  5. Indonesian Sign Language Number Recognition using SIFT Algorithm

    Science.gov (United States)

    Mahfudi, Isa; Sarosa, Moechammad; Andrie Asmara, Rosa; Azrino Gustalika, M.

    2018-04-01

    Indonesian sign language (ISL) is generally used for deaf individuals and poor people communication in communicating. They use sign language as their primary language which consists of 2 types of action: sign and finger spelling. However, not all people understand their sign language so that this becomes a problem for them to communicate with normal people. this problem also becomes a factor they are isolated feel from the social life. It needs a solution that can help them to be able to interacting with normal people. Many research that offers a variety of methods in solving the problem of sign language recognition based on image processing. SIFT (Scale Invariant Feature Transform) algorithm is one of the methods that can be used to identify an object. SIFT is claimed very resistant to scaling, rotation, illumination and noise. Using SIFT algorithm for Indonesian sign language recognition number result rate recognition to 82% with the use of a total of 100 samples image dataset consisting 50 sample for training data and 50 sample images for testing data. Change threshold value get affect the result of the recognition. The best value threshold is 0.45 with rate recognition of 94%.

  6. Conference on Representation Theory, Number Theory and Invariant Theory: on the Occasion of Roger Howe’s 70th Birthday

    CERN Document Server

    Kim, Ju-Lee; Zhu, Chen-Bo

    2017-01-01

    This book contains selected papers based on talks given at the "Representation Theory, Number Theory, and Invariant Theory" conference held at Yale University from June 1 to June 5, 2015. The meeting and this resulting volume are in honor of Professor Roger Howe, on the occasion of his 70th birthday, whose work and insights have been deeply influential in the development of these fields. The speakers who contributed to this work include Roger Howe's doctoral students, Roger Howe himself, and other world renowned mathematicians. Topics covered include automorphic forms, invariant theory, representation theory of reductive groups over local fields, and related subjects.

  7. Two-colour QCD at finite fundamental quark-number density and related theories

    International Nuclear Information System (INIS)

    Hands, S.J.; Kogut, J.B.; Morrison, S.E.; Sinclair, D.K.

    2001-01-01

    We are simulating SU(2) Yang-Mills theory with four flavours of dynamical quarks in the fundamental representation of SU(2) 'colour' at finite chemical potential, μ for quark number, as a model for QCD at finite baryon number density. In particular we observe that for μ large enough this theory undergoes a phase transition to a state with a diquark condensate which breaks quark-number symmetry. In this phase we examine the spectrum of light scalar and pseudoscalar bosons and see evidence for the Goldstone boson associated with this spontaneous symmetry breaking. This theory is closely related to QCD at finite chemical potential for isospin, a theory which we are now studying for SU(3) colour

  8. Two-colour QCD at finite fundamental quark-number density and related theories

    International Nuclear Information System (INIS)

    Hands, S. J.; Kogut, J. B.; Morrison, S. E.; Sinclair, D. K.

    2000-01-01

    We are simulating SU(2) Yang-Mills theory with four flavours of dynamical quarks in the fundamental representation of SU(2) colour at finite chemical potential, p for quark number, as a model for QCD at finite baryon number density. In particular we observe that for p large enough this theory undergoes a phase transition to a state with a diquark condensate which breaks quark-number symmetry. In this phase we examine the spectrum of light scalar and pseudoscalar bosons and see evidence for the Goldstone boson associated with this spontaneous symmetry breaking. This theory is closely related to QCD at finite chemical potential for isospin, a theory which we are now studying for SU(3) colour

  9. Python algorithms mastering basic algorithms in the Python language

    CERN Document Server

    Hetland, Magnus Lie

    2014-01-01

    Python Algorithms, Second Edition explains the Python approach to algorithm analysis and design. Written by Magnus Lie Hetland, author of Beginning Python, this book is sharply focused on classical algorithms, but it also gives a solid understanding of fundamental algorithmic problem-solving techniques. The book deals with some of the most important and challenging areas of programming and computer science in a highly readable manner. It covers both algorithmic theory and programming practice, demonstrating how theory is reflected in real Python programs. Well-known algorithms and data struc

  10. Quantum Computations: Fundamentals and Algorithms

    International Nuclear Information System (INIS)

    Duplij, S.A.; Shapoval, I.I.

    2007-01-01

    Basic concepts of quantum information theory, principles of quantum calculations and the possibility of creation on this basis unique on calculation power and functioning principle device, named quantum computer, are concerned. The main blocks of quantum logic, schemes of quantum calculations implementation, as well as some known today effective quantum algorithms, called to realize advantages of quantum calculations upon classical, are presented here. Among them special place is taken by Shor's algorithm of number factorization and Grover's algorithm of unsorted database search. Phenomena of decoherence, its influence on quantum computer stability and methods of quantum errors correction are described

  11. Cryptography and computational number theory

    CERN Document Server

    Shparlinski, Igor; Wang, Huaxiong; Xing, Chaoping; Workshop on Cryptography and Computational Number Theory, CCNT'99

    2001-01-01

    This volume contains the refereed proceedings of the Workshop on Cryptography and Computational Number Theory, CCNT'99, which has been held in Singapore during the week of November 22-26, 1999. The workshop was organized by the Centre for Systems Security of the Na­ tional University of Singapore. We gratefully acknowledge the financial support from the Singapore National Science and Technology Board under the grant num­ ber RP960668/M. The idea for this workshop grew out of the recognition of the recent, rapid development in various areas of cryptography and computational number the­ ory. The event followed the concept of the research programs at such well-known research institutions as the Newton Institute (UK), Oberwolfach and Dagstuhl (Germany), and Luminy (France). Accordingly, there were only invited lectures at the workshop with plenty of time for informal discussions. It was hoped and successfully achieved that the meeting would encourage and stimulate further research in information and computer s...

  12. A universal algorithm to generate pseudo-random numbers based on uniform mapping as homeomorphism

    International Nuclear Information System (INIS)

    Fu-Lai, Wang

    2010-01-01

    A specific uniform map is constructed as a homeomorphism mapping chaotic time series into [0,1] to obtain sequences of standard uniform distribution. With the uniform map, a chaotic orbit and a sequence orbit obtained are topologically equivalent to each other so the map can preserve the most dynamic properties of chaotic systems such as permutation entropy. Based on the uniform map, a universal algorithm to generate pseudo random numbers is proposed and the pseudo random series is tested to follow the standard 0–1 random distribution both theoretically and experimentally. The algorithm is not complex, which does not impose high requirement on computer hard ware and thus computation speed is fast. The method not only extends the parameter spaces but also avoids the drawback of small function space caused by constraints on chaotic maps used to generate pseudo random numbers. The algorithm can be applied to any chaotic system and can produce pseudo random sequence of high quality, thus can be a good universal pseudo random number generator. (general)

  13. A universal algorithm to generate pseudo-random numbers based on uniform mapping as homeomorphism

    Science.gov (United States)

    Wang, Fu-Lai

    2010-09-01

    A specific uniform map is constructed as a homeomorphism mapping chaotic time series into [0,1] to obtain sequences of standard uniform distribution. With the uniform map, a chaotic orbit and a sequence orbit obtained are topologically equivalent to each other so the map can preserve the most dynamic properties of chaotic systems such as permutation entropy. Based on the uniform map, a universal algorithm to generate pseudo random numbers is proposed and the pseudo random series is tested to follow the standard 0-1 random distribution both theoretically and experimentally. The algorithm is not complex, which does not impose high requirement on computer hard ware and thus computation speed is fast. The method not only extends the parameter spaces but also avoids the drawback of small function space caused by constraints on chaotic maps used to generate pseudo random numbers. The algorithm can be applied to any chaotic system and can produce pseudo random sequence of high quality, thus can be a good universal pseudo random number generator.

  14. An Integrated Theory of Whole Number and Fractions Development

    Science.gov (United States)

    Siegler, Robert S.; Thompson, Clarissa A.; Schneider, Michael

    2011-01-01

    This article proposes an integrated theory of acquisition of knowledge about whole numbers and fractions. Although whole numbers and fractions differ in many ways that influence their development, an important commonality is the centrality of knowledge of numerical magnitudes in overall understanding. The present findings with 11- and 13-year-olds…

  15. Conference on Number Theory and Arithmetic Geometry

    CERN Document Server

    Silverman, Joseph; Stevens, Glenn; Modular forms and Fermat’s last theorem

    1997-01-01

    This volume contains expanded versions of lectures given at an instructional conference on number theory and arithmetic geometry held August 9 through 18, 1995 at Boston University. Contributor's includeThe purpose of the conference, and of this book, is to introduce and explain the many ideas and techniques used by Wiles in his proof that every (semi-stable) elliptic curve over Q is modular, and to explain how Wiles' result can be combined with Ribet's theorem and ideas of Frey and Serre to show, at long last, that Fermat's Last Theorem is true. The book begins with an overview of the complete proof, followed by several introductory chapters surveying the basic theory of elliptic curves, modular functions, modular curves, Galois cohomology, and finite group schemes. Representation theory, which lies at the core of Wiles' proof, is dealt with in a chapter on automorphic representations and the Langlands-Tunnell theorem, and this is followed by in-depth discussions of Serre's conjectures, Galois deformations, ...

  16. WSNs Microseismic Signal Subsection Compression Algorithm Based on Compressed Sensing

    Directory of Open Access Journals (Sweden)

    Zhouzhou Liu

    2015-01-01

    Full Text Available For wireless network microseismic monitoring and the problems of low compression ratio and high energy consumption of communication, this paper proposes a segmentation compression algorithm according to the characteristics of the microseismic signals and the compression perception theory (CS used in the transmission process. The algorithm will be collected as a number of nonzero elements of data segmented basis, by reducing the number of combinations of nonzero elements within the segment to improve the accuracy of signal reconstruction, while taking advantage of the characteristics of compressive sensing theory to achieve a high compression ratio of the signal. Experimental results show that, in the quantum chaos immune clone refactoring (Q-CSDR algorithm for reconstruction algorithm, under the condition of signal sparse degree higher than 40, to be more than 0.4 of the compression ratio to compress the signal, the mean square error is less than 0.01, prolonging the network life by 2 times.

  17. Study on recognition algorithm for paper currency numbers based on neural network

    Science.gov (United States)

    Li, Xiuyan; Liu, Tiegen; Li, Yuanyao; Zhang, Zhongchuan; Deng, Shichao

    2008-12-01

    Based on the unique characteristic, the paper currency numbers can be put into record and the automatic identification equipment for paper currency numbers is supplied to currency circulation market in order to provide convenience for financial sectors to trace the fiduciary circulation socially and provide effective supervision on paper currency. Simultaneously it is favorable for identifying forged notes, blacklisting the forged notes numbers and solving the major social problems, such as armor cash carrier robbery, money laundering. For the purpose of recognizing the paper currency numbers, a recognition algorithm based on neural network is presented in the paper. Number lines in original paper currency images can be draw out through image processing, such as image de-noising, skew correction, segmentation, and image normalization. According to the different characteristics between digits and letters in serial number, two kinds of classifiers are designed. With the characteristics of associative memory, optimization-compute and rapid convergence, the Discrete Hopfield Neural Network (DHNN) is utilized to recognize the letters; with the characteristics of simple structure, quick learning and global optimum, the Radial-Basis Function Neural Network (RBFNN) is adopted to identify the digits. Then the final recognition results are obtained by combining the two kinds of recognition results in regular sequence. Through the simulation tests, it is confirmed by simulation results that the recognition algorithm of combination of two kinds of recognition methods has such advantages as high recognition rate and faster recognition simultaneously, which is worthy of broad application prospect.

  18. Partial Fractions in Calculus, Number Theory, and Algebra

    Science.gov (United States)

    Yackel, C. A.; Denny, J. K.

    2007-01-01

    This paper explores the development of the method of partial fraction decomposition from elementary number theory through calculus to its abstraction in modern algebra. This unusual perspective makes the topic accessible and relevant to readers from high school through seasoned calculus instructors.

  19. On two functional equations originating from number theory

    Indian Academy of Sciences (India)

    On two functional equations originating from number theory. JAEYOUNG CHUNG1 and JEONGWOOK CHANG2,∗. 1Department of Mathematics, Kunsan National University, Kunsan, 573-701, Korea. 2Department of Mathematics Education, Dankook University, Yongin 448-701, Korea. *Corresponding author. E-mail: ...

  20. Generalized Net Model of the Cognitive and Neural Algorithm for Adaptive Resonance Theory 1

    Directory of Open Access Journals (Sweden)

    Todor Petkov

    2013-12-01

    Full Text Available The artificial neural networks are inspired by biological properties of human and animal brains. One of the neural networks type is called ART [4]. The abbreviation of ART stands for Adaptive Resonance Theory that has been invented by Stephen Grossberg in 1976 [5]. ART represents a family of Neural Networks. It is a cognitive and neural theory that describes how the brain autonomously learns to categorize, recognize and predict objects and events in the changing world. In this paper we introduce a GN model that represent ART1 Neural Network learning algorithm [1]. The purpose of this model is to explain when the input vector will be clustered or rejected among all nodes by the network. It can also be used for explanation and optimization of ART1 learning algorithm.

  1. Small numbers in supersymmetric theories of nature

    International Nuclear Information System (INIS)

    Graesser, Michael L.

    1999-01-01

    The Standard Model of particle interactions is a successful theory for describing the interactions of quarks, leptons and gauge bosons at microscopic distance scales. Despite these successes, the theory contains many unsatisfactory features. The origin of particle masses is a central mystery that has eluded experimental elucidation. In the Standard Model the known particles obtain their mass from the condensate of the so-called Higgs particle. Quantum corrections to the Higgs mass require an unnatural fine tuning in the Higgs mass of one part in 10 -32 to obtain the correct mass scale of electroweak physics. In addition, the origin of the vast hierarchy between the mass scales of the electroweak and quantum gravity physics is not explained in the current theory. Supersymmetric extensions to the Standard Model are not plagued by this fine tuning issue and may therefore be relevant in Nature. In the minimal supersymmetric Standard Model there is also a natural explanation for electroweak symmetry breaking. Supersymmetric Grand Unified Theories also correctly predict a parameter of the Standard Model. This provides non-trivial indirect evidence for these theories. The most general supersymmetric extension to the Standard Model however, is excluded by many physical processes, such as rare flavor changing processes, and the non-observation of the instability of the proton. These processes provide important information about the possible structure such a theory. In particular, certain parameters in this theory must be rather small. A physics explanation for why this is the case would be desirable. It is striking that the gauge couplings of the Standard Model unify if there is supersymmetry close to the weak scale. This suggests that at high energies Nature is described by a supersymmetric Grand Unified Theory. But the mass scale of unification must be introduced into the theory since it does not coincide with the probable mass scale of strong quantum gravity. The subject

  2. Linear programming algorithms and applications

    CERN Document Server

    Vajda, S

    1981-01-01

    This text is based on a course of about 16 hours lectures to students of mathematics, statistics, and/or operational research. It is intended to introduce readers to the very wide range of applicability of linear programming, covering problems of manage­ ment, administration, transportation and a number of other uses which are mentioned in their context. The emphasis is on numerical algorithms, which are illustrated by examples of such modest size that the solutions can be obtained using pen and paper. It is clear that these methods, if applied to larger problems, can also be carried out on automatic (electronic) computers. Commercially available computer packages are, in fact, mainly based on algorithms explained in this book. The author is convinced that the user of these algorithms ought to be knowledgeable about the underlying theory. Therefore this volume is not merely addressed to the practitioner, but also to the mathematician who is interested in relatively new developments in algebraic theory and in...

  3. An efficient algorithm for generating random number pairs drawn from a bivariate normal distribution

    Science.gov (United States)

    Campbell, C. W.

    1983-01-01

    An efficient algorithm for generating random number pairs from a bivariate normal distribution was developed. Any desired value of the two means, two standard deviations, and correlation coefficient can be selected. Theoretically the technique is exact and in practice its accuracy is limited only by the quality of the uniform distribution random number generator, inaccuracies in computer function evaluation, and arithmetic. A FORTRAN routine was written to check the algorithm and good accuracy was obtained. Some small errors in the correlation coefficient were observed to vary in a surprisingly regular manner. A simple model was developed which explained the qualities aspects of the errors.

  4. Selfish Gene Algorithm Vs Genetic Algorithm: A Review

    Science.gov (United States)

    Ariff, Norharyati Md; Khalid, Noor Elaiza Abdul; Hashim, Rathiah; Noor, Noorhayati Mohamed

    2016-11-01

    Evolutionary algorithm is one of the algorithms inspired by the nature. Within little more than a decade hundreds of papers have reported successful applications of EAs. In this paper, the Selfish Gene Algorithms (SFGA), as one of the latest evolutionary algorithms (EAs) inspired from the Selfish Gene Theory which is an interpretation of Darwinian Theory ideas from the biologist Richards Dawkins on 1989. In this paper, following a brief introduction to the Selfish Gene Algorithm (SFGA), the chronology of its evolution is presented. It is the purpose of this paper is to present an overview of the concepts of Selfish Gene Algorithm (SFGA) as well as its opportunities and challenges. Accordingly, the history, step involves in the algorithm are discussed and its different applications together with an analysis of these applications are evaluated.

  5. Intercept Algorithm for Maneuvering Targets Based on Differential Geometry and Lyapunov Theory

    Directory of Open Access Journals (Sweden)

    Yunes Sh. ALQUDSI

    2018-03-01

    Full Text Available Nowadays, the homing guidance is utilized in the existed and under development air defense systems (ADS to effectively intercept the targets. The targets became smarter and capable to fly and maneuver professionally and the tendency to design missile with a small warhead became greater, then there is a pressure to produce a more precise and accurate missile guidance system based on intelligent algorithms to ensure effective interception of highly maneuverable targets. The aim of this paper is to present an intelligent guidance algorithm that effectively and precisely intercept the maneuverable and smart targets by virtue of the differential geometry (DG concepts. The intercept geometry and engagement kinematics, in addition to the direct intercept condition are developed and expressed in DG terms. The guidance algorithm is then developed by virtue of DG and Lyapunov theory. The study terminates with 2D engagement simulation with illustrative examples, to demonstrate that, the derived DG guidance algorithm is a generalized guidance approach and the well-known proportional navigation (PN guidance law is a subset of this approach.

  6. Cryptographic applications of analytic number theory complexity lower bounds and pseudorandomness

    CERN Document Server

    2003-01-01

    The book introduces new ways of using analytic number theory in cryptography and related areas, such as complexity theory and pseudorandom number generation. Key topics and features: - various lower bounds on the complexity of some number theoretic and cryptographic problems, associated with classical schemes such as RSA, Diffie-Hellman, DSA as well as with relatively new schemes like XTR and NTRU - a series of very recent results about certain important characteristics (period, distribution, linear complexity) of several commonly used pseudorandom number generators, such as the RSA generator, Blum-Blum-Shub generator, Naor-Reingold generator, inversive generator, and others - one of the principal tools is bounds of exponential sums, which are combined with other number theoretic methods such as lattice reduction and sieving - a number of open problems of different level of difficulty and proposals for further research - an extensive and up-to-date bibliography Cryptographers and number theorists will find th...

  7. International Conference on Automorphic Forms and Number Theory

    CERN Document Server

    Al-Baali, Mehiddin; Ibukiyama, Tomoyoshi; Rupp, Florian

    2014-01-01

    This edited volume presents a collection of carefully refereed articles covering the latest advances in Automorphic Forms and Number Theory, that were primarily developed from presentations given at the 2012 “International Conference on Automorphic Forms and Number Theory,” held in Muscat, Sultanate of Oman. The present volume includes original research as well as some surveys and outlines of research altogether providing a contemporary snapshot on the latest activities in the field and covering the topics of: Borcherds products Congruences and Codes Jacobi forms Siegel and Hermitian modular forms Special values of L-series Recently, the Sultanate of Oman became a member of the International Mathematical Society. In view of this development, the conference provided the platform for scientific exchange and collaboration between scientists of different countries from all over the world. In particular, an opportunity was established for a close exchange between scientists and students of Germany, Oman, and J...

  8. Elementary number theory an algebraic approach

    CERN Document Server

    Bolker, Ethan D

    2007-01-01

    This text uses the concepts usually taught in the first semester of a modern abstract algebra course to illuminate classical number theory: theorems on primitive roots, quadratic Diophantine equations, and the Fermat conjecture for exponents three and four. The text contains abundant numerical examples and a particularly helpful collection of exercises, many of which are small research problems requiring substantial study or outside reading. Some problems call for new proofs for theorems already covered or for inductive explorations and proofs of theorems found in later chapters.Ethan D. Bolke

  9. Number-theoretic properties of hyperelliptic fields and the torsion problem in Jacobians of hyperelliptic curves over the rational number field

    International Nuclear Information System (INIS)

    Platonov, V P

    2014-01-01

    In the past four years a theory has been developed for finding fundamental units in hyperelliptic fields, and on basis of this theory innovative and efficient algorithms for computing them have been constructed and implemented. A new local-global principle was discovered which gives a criterion for the existence of non-trivial units in hyperelliptic fields. The natural connection between the problem of computing fundamental units and the problem of torsion in Jacobian varieties of hyperelliptic curves over the rational number field has led to breakthrough results in the solution of this problem. The main results in the present survey were largely obtained using a symbiosis of deep theory, efficient algorithms, and supercomputing. Such a symbiosis will play an ever increasing role in the mathematics of the 21st century. Bibliography: 27 titles

  10. Additional operations in algebra of structural numbers for control algorithm development

    Directory of Open Access Journals (Sweden)

    Morhun A.V.

    2016-12-01

    Full Text Available The structural numbers and the algebra of the structural numbers due to the simplicity of representation, flexibility and current algebraic operations are the powerful tool for a wide range of applications. In autonomous power supply systems and systems with distributed generation (Micro Grid mathematical apparatus of structural numbers can be effectively used for the calculation of the parameters of the operating modes of consumption of electric energy. The purpose of the article is the representation of the additional algebra of structural numbers. The standard algebra was proposed to be extended by the additional operations and modification current in order to expand the scope of their use, namely to construct a flexible, adaptive algorithms of control systems. It is achieved due to the possibility to consider each individual component of the system with its parameters and provide easy management of entire system and each individual component. Thus, structural numbers and extended algebra are the perspective line of research and further studying is required.

  11. Additive Number Theory Festschrift in Honor of the Sixtieth Birthday of Melvyn B Nathanson

    CERN Document Server

    Chudnovsky, David

    2010-01-01

    This impressive volume is dedicated to Mel Nathanson, a leading authoritative expert for several decades in the area of combinatorial and additive number theory. For several decades, Mel Nathanson's seminal ideas and results in combinatorial and additive number theory have influenced graduate students and researchers alike. The invited survey articles in this volume reflect the work of distinguished mathematicians in number theory, and represent a wide range of important topics in current research.

  12. Optimal interconnection trees in the plane theory, algorithms and applications

    CERN Document Server

    Brazil, Marcus

    2015-01-01

    This book explores fundamental aspects of geometric network optimisation with applications to a variety of real world problems. It presents, for the first time in the literature, a cohesive mathematical framework within which the properties of such optimal interconnection networks can be understood across a wide range of metrics and cost functions. The book makes use of this mathematical theory to develop efficient algorithms for constructing such networks, with an emphasis on exact solutions.  Marcus Brazil and Martin Zachariasen focus principally on the geometric structure of optimal interconnection networks, also known as Steiner trees, in the plane. They show readers how an understanding of this structure can lead to practical exact algorithms for constructing such trees.  The book also details numerous breakthroughs in this area over the past 20 years, features clearly written proofs, and is supported by 135 colour and 15 black and white figures. It will help graduate students, working mathematicians, ...

  13. Fringe pattern analysis for optical metrology theory, algorithms, and applications

    CERN Document Server

    Servin, Manuel; Padilla, Moises

    2014-01-01

    The main objective of this book is to present the basic theoretical principles and practical applications for the classical interferometric techniques and the most advanced methods in the field of modern fringe pattern analysis applied to optical metrology. A major novelty of this work is the presentation of a unified theoretical framework based on the Fourier description of phase shifting interferometry using the Frequency Transfer Function (FTF) along with the theory of Stochastic Process for the straightforward analysis and synthesis of phase shifting algorithms with desired properties such

  14. BootGraph: probabilistic fiber tractography using bootstrap algorithms and graph theory.

    Science.gov (United States)

    Vorburger, Robert S; Reischauer, Carolin; Boesiger, Peter

    2013-02-01

    Bootstrap methods have recently been introduced to diffusion-weighted magnetic resonance imaging to estimate the measurement uncertainty of ensuing diffusion parameters directly from the acquired data without the necessity to assume a noise model. These methods have been previously combined with deterministic streamline tractography algorithms to allow for the assessment of connection probabilities in the human brain. Thereby, the local noise induced disturbance in the diffusion data is accumulated additively due to the incremental progression of streamline tractography algorithms. Graph based approaches have been proposed to overcome this drawback of streamline techniques. For this reason, the bootstrap method is in the present work incorporated into a graph setup to derive a new probabilistic fiber tractography method, called BootGraph. The acquired data set is thereby converted into a weighted, undirected graph by defining a vertex in each voxel and edges between adjacent vertices. By means of the cone of uncertainty, which is derived using the wild bootstrap, a weight is thereafter assigned to each edge. Two path finding algorithms are subsequently applied to derive connection probabilities. While the first algorithm is based on the shortest path approach, the second algorithm takes all existing paths between two vertices into consideration. Tracking results are compared to an established algorithm based on the bootstrap method in combination with streamline fiber tractography and to another graph based algorithm. The BootGraph shows a very good performance in crossing situations with respect to false negatives and permits incorporating additional constraints, such as a curvature threshold. By inheriting the advantages of the bootstrap method and graph theory, the BootGraph method provides a computationally efficient and flexible probabilistic tractography setup to compute connection probability maps and virtual fiber pathways without the drawbacks of

  15. Quantum algorithms and learning theory

    NARCIS (Netherlands)

    Arunachalam, S.

    2018-01-01

    This thesis studies strengths and weaknesses of quantum computers. In the first part we present three contributions to quantum algorithms. 1) consider a search space of N elements. One of these elements is "marked" and our goal is to find this. We describe a quantum algorithm to solve this problem

  16. Analytic number theory, approximation theory, and special functions in honor of Hari M. Srivastava

    CERN Document Server

    Rassias, Michael

    2014-01-01

    This book, in honor of Hari M. Srivastava, discusses essential developments in mathematical research in a variety of problems. It contains thirty-five articles, written by eminent scientists from the international mathematical community, including both research and survey works. Subjects covered include analytic number theory, combinatorics, special sequences of numbers and polynomials, analytic inequalities and applications, approximation of functions and quadratures, orthogonality, and special and complex functions. The mathematical results and open problems discussed in this book are presented in a simple and self-contained manner. The book contains an overview of old and new results, methods, and theories toward the solution of longstanding problems in a wide scientific field, as well as new results in rapidly progressing areas of research. The book will be useful for researchers and graduate students in the fields of mathematics, physics, and other computational and applied sciences.

  17. Fast half-sibling population reconstruction: theory and algorithms.

    Science.gov (United States)

    Dexter, Daniel; Brown, Daniel G

    2013-07-12

    Kinship inference is the task of identifying genealogically related individuals. Kinship information is important for determining mating structures, notably in endangered populations. Although many solutions exist for reconstructing full sibling relationships, few exist for half-siblings. We consider the problem of determining whether a proposed half-sibling population reconstruction is valid under Mendelian inheritance assumptions. We show that this problem is NP-complete and provide a 0/1 integer program that identifies the minimum number of individuals that must be removed from a population in order for the reconstruction to become valid. We also present SibJoin, a heuristic-based clustering approach based on Mendelian genetics, which is strikingly fast. The software is available at http://github.com/ddexter/SibJoin.git+. Our SibJoin algorithm is reasonably accurate and thousands of times faster than existing algorithms. The heuristic is used to infer a half-sibling structure for a population which was, until recently, too large to evaluate.

  18. Elementary theory of numbers

    CERN Document Server

    LeVeque, William J

    1990-01-01

    Superb introduction to Euclidean algorithm and its consequences, congruences, continued fractions, powers of an integer modulo m, Gaussian integers, Diophantine equations, more. Problems, with answers. Bibliography.

  19. Number theory and modular forms papers in memory of Robert A Rankin

    CERN Document Server

    Ono, Ken

    2003-01-01

    Robert A. Rankin, one of the world's foremost authorities on modular forms and a founding editor of The Ramanujan Journal, died on January 27, 2001, at the age of 85. Rankin had broad interests and contributed fundamental papers in a wide variety of areas within number theory, geometry, analysis, and algebra. To commemorate Rankin's life and work, the editors have collected together 25 papers by several eminent mathematicians reflecting Rankin's extensive range of interests within number theory. Many of these papers reflect Rankin's primary focus in modular forms. It is the editors' fervent hope that mathematicians will be stimulated by these papers and gain a greater appreciation for Rankin's contributions to mathematics. This volume would be an inspiration to students and researchers in the areas of number theory and modular forms.

  20. Genetic algorithm to solve the problems of lectures and practicums scheduling

    Science.gov (United States)

    Syahputra, M. F.; Apriani, R.; Sawaluddin; Abdullah, D.; Albra, W.; Heikal, M.; Abdurrahman, A.; Khaddafi, M.

    2018-02-01

    Generally, the scheduling process is done manually. However, this method has a low accuracy level, along with possibilities that a scheduled process collides with another scheduled process. When doing theory class and practicum timetable scheduling process, there are numerous problems, such as lecturer teaching schedule collision, schedule collision with another schedule, practicum lesson schedules that collides with theory class, and the number of classrooms available. In this research, genetic algorithm is implemented to perform theory class and practicum timetable scheduling process. The algorithm will be used to process the data containing lists of lecturers, courses, and class rooms, obtained from information technology department at University of Sumatera Utara. The result of scheduling process using genetic algorithm is the most optimal timetable that conforms to available time slots, class rooms, courses, and lecturer schedules.

  1. Efficient Algorithms for Searching the Minimum Information Partition in Integrated Information Theory

    Science.gov (United States)

    Kitazono, Jun; Kanai, Ryota; Oizumi, Masafumi

    2018-03-01

    The ability to integrate information in the brain is considered to be an essential property for cognition and consciousness. Integrated Information Theory (IIT) hypothesizes that the amount of integrated information ($\\Phi$) in the brain is related to the level of consciousness. IIT proposes that to quantify information integration in a system as a whole, integrated information should be measured across the partition of the system at which information loss caused by partitioning is minimized, called the Minimum Information Partition (MIP). The computational cost for exhaustively searching for the MIP grows exponentially with system size, making it difficult to apply IIT to real neural data. It has been previously shown that if a measure of $\\Phi$ satisfies a mathematical property, submodularity, the MIP can be found in a polynomial order by an optimization algorithm. However, although the first version of $\\Phi$ is submodular, the later versions are not. In this study, we empirically explore to what extent the algorithm can be applied to the non-submodular measures of $\\Phi$ by evaluating the accuracy of the algorithm in simulated data and real neural data. We find that the algorithm identifies the MIP in a nearly perfect manner even for the non-submodular measures. Our results show that the algorithm allows us to measure $\\Phi$ in large systems within a practical amount of time.

  2. Antieigenvalue analysis for continuum mechanics, economics, and number theory

    Directory of Open Access Journals (Sweden)

    Gustafson Karl

    2016-01-01

    Full Text Available My recent book Antieigenvalue Analysis, World-Scientific, 2012, presented the theory of antieigenvalues from its inception in 1966 up to 2010, and its applications within those forty-five years to Numerical Analysis, Wavelets, Statistics, Quantum Mechanics, Finance, and Optimization. Here I am able to offer three further areas of application: Continuum Mechanics, Economics, and Number Theory. In particular, the critical angle of repose in a continuum model of granular materials is shown to be exactly my matrix maximum turning angle of the stress tensor of the material. The important Sharpe ratio of the Capital Asset Pricing Model is now seen in terms of my antieigenvalue theory. Euclid’s Formula for Pythagorean triples becomes a special case of my operator trigonometry.

  3. Recreations in the theory of numbers the queen of mathematics entertains

    CERN Document Server

    Beiler, Albert H

    1966-01-01

    Number theory, the Queen of Mathematics, is an almost purely theoretical science. Yet it can be the source of endlessly intriguing puzzle problems, as this remarkable book demonstrates. This is the first book to deal exclusively with the recreational aspects of the subject and it is certain to be a delightful surprise to all devotees of the mathematical puzzle, from the rawest beginner to the most practiced expert. Almost every aspect of the theory of numbers that could conceivably be of interest to the layman is dealt with, all from the recreational point of view. Readers will become acquainted with divisors, perfect numbers, the ingenious invention of congruences by Gauss, scales of notation, endless decimals, Pythagorean triangles (there is a list of the first 100 with consecutive legs; the 100th has a leg of 77 digits), oddities about squares, methods of factoring, mysteries of prime numbers, Gauss's Golden Theorem, polygonal and pyramidal numbers, the Pell Equation, the unsolved Last Theorem of Fermat, a...

  4. A Successful Senior Seminar: Unsolved Problems in Number Theory

    Science.gov (United States)

    Styer, Robert

    2014-01-01

    The "Unsolved Problems in Number Theory" book by Richard Guy provides nice problems suitable for a typical math major. We give examples of problems that have worked well in our senior seminar course and some nice results that senior math majors can obtain.

  5. Assessment of a transitional boundary layer theory at low hypersonic Mach numbers

    Science.gov (United States)

    Shamroth, S. J.; Mcdonald, H.

    1972-01-01

    An investigation was carried out to assess the accuracy of a transitional boundary layer theory in the low hypersonic Mach number regime. The theory is based upon the simultaneous numerical solution of the boundary layer partial differential equations for the mean motion and an integral form of the turbulence kinetic energy equation which controls the magnitude and development of the Reynolds stress. Comparisions with experimental data show the theory is capable of accurately predicting heat transfer and velocity profiles through the transitional regime and correctly predicts the effects of Mach number and wall cooling on transition Reynolds number. The procedure shows promise of predicting the initiation of transition for given free stream disturbance levels. The effects on transition predictions of the pressure dilitation term and of direct absorption of acoustic energy by the boundary layer were evaluated.

  6. A molecular dynamics algorithm for simulation of field theories in the canonical ensemble

    International Nuclear Information System (INIS)

    Kogut, J.B.; Sinclair, D.K.

    1986-01-01

    We add a single scalar degree of freedom (''demon'') to the microcanonical ensemble which converts its molecular dynamics into a simulation method for the canonical ensemble (euclidean path integral) of the underlying field theory. This generalization of the microcanonical molecular dynamics algorithm simulates the field theory at fixed coupling with a completely deterministic procedure. We discuss the finite size effects of the method, the equipartition theorem and ergodicity. The method is applied to the planar model in two dimensions and SU(3) lattice gauge theory with four species of light, dynamical quarks in four dimensions. The method is much less sensitive to its discrete time step than conventional Langevin equation simulations of the canonical ensemble. The method is a straightforward generalization of a procedure introduced by S. Nose for molecular physics. (orig.)

  7. Securing mobile ad hoc networks using danger theory-based artificial immune algorithm.

    Science.gov (United States)

    Abdelhaq, Maha; Alsaqour, Raed; Abdelhaq, Shawkat

    2015-01-01

    A mobile ad hoc network (MANET) is a set of mobile, decentralized, and self-organizing nodes that are used in special cases, such as in the military. MANET properties render the environment of this network vulnerable to different types of attacks, including black hole, wormhole and flooding-based attacks. Flooding-based attacks are one of the most dangerous attacks that aim to consume all network resources and thus paralyze the functionality of the whole network. Therefore, the objective of this paper is to investigate the capability of a danger theory-based artificial immune algorithm called the mobile dendritic cell algorithm (MDCA) to detect flooding-based attacks in MANETs. The MDCA applies the dendritic cell algorithm (DCA) to secure the MANET with additional improvements. The MDCA is tested and validated using Qualnet v7.1 simulation tool. This work also introduces a new simulation module for a flooding attack called the resource consumption attack (RCA) using Qualnet v7.1. The results highlight the high efficiency of the MDCA in detecting RCAs in MANETs.

  8. Geometric invariant theory over the real and complex numbers

    CERN Document Server

    Wallach, Nolan R

    2017-01-01

    Geometric Invariant Theory (GIT) is developed in this text within the context of algebraic geometry over the real and complex numbers. This sophisticated topic is elegantly presented with enough background theory included to make the text accessible to advanced graduate students in mathematics and physics with diverse backgrounds in algebraic and differential geometry.  Throughout the book, examples are emphasized. Exercises add to the reader’s understanding of the material; most are enhanced with hints. The exposition is divided into two parts. The first part, ‘Background Theory’, is organized as a reference for the rest of the book. It contains two chapters developing material in complex and real algebraic geometry and algebraic groups that are difficult to find in the literature. Chapter 1 emphasizes the relationship between the Zariski topology and the canonical Hausdorff topology of an algebraic variety over the complex numbers. Chapter 2 develops the interaction between Lie groups and algebraic ...

  9. Symbolic Computation, Number Theory, Special Functions, Physics and Combinatorics

    CERN Document Server

    Ismail, Mourad

    2001-01-01

    These are the proceedings of the conference "Symbolic Computation, Number Theory, Special Functions, Physics and Combinatorics" held at the Department of Mathematics, University of Florida, Gainesville, from November 11 to 13, 1999. The main emphasis of the conference was Com­ puter Algebra (i. e. symbolic computation) and how it related to the fields of Number Theory, Special Functions, Physics and Combinatorics. A subject that is common to all of these fields is q-series. We brought together those who do symbolic computation with q-series and those who need q-series in­ cluding workers in Physics and Combinatorics. The goal of the conference was to inform mathematicians and physicists who use q-series of the latest developments in the field of q-series and especially how symbolic computa­ tion has aided these developments. Over 60 people were invited to participate in the conference. We ended up having 45 participants at the conference, including six one hour plenary speakers and 28 half hour speakers. T...

  10. Fast algorithm for computing complex number-theoretic transforms

    Science.gov (United States)

    Reed, I. S.; Liu, K. Y.; Truong, T. K.

    1977-01-01

    A high-radix FFT algorithm for computing transforms over FFT, where q is a Mersenne prime, is developed to implement fast circular convolutions. This new algorithm requires substantially fewer multiplications than the conventional FFT.

  11. Detection of Cheating by Decimation Algorithm

    Science.gov (United States)

    Yamanaka, Shogo; Ohzeki, Masayuki; Decelle, Aurélien

    2015-02-01

    We expand the item response theory to study the case of "cheating students" for a set of exams, trying to detect them by applying a greedy algorithm of inference. This extended model is closely related to the Boltzmann machine learning. In this paper we aim to infer the correct biases and interactions of our model by considering a relatively small number of sets of training data. Nevertheless, the greedy algorithm that we employed in the present study exhibits good performance with a few number of training data. The key point is the sparseness of the interactions in our problem in the context of the Boltzmann machine learning: the existence of cheating students is expected to be very rare (possibly even in real world). We compare a standard approach to infer the sparse interactions in the Boltzmann machine learning to our greedy algorithm and we find the latter to be superior in several aspects.

  12. Introduction to the Interface of Probability and Algorithms

    OpenAIRE

    Aldous, David; Steele, J. Michael

    1993-01-01

    Probability and algorithms enjoy an almost boisterous interaction that has led to an active, extensive literature that touches fields as diverse as number theory and the design of computer hardware. This article offers a gentle introduction to the simplest, most basic ideas that underlie this development.

  13. An extension theory-based maximum power tracker using a particle swarm optimization algorithm

    International Nuclear Information System (INIS)

    Chao, Kuei-Hsiang

    2014-01-01

    Highlights: • We propose an adaptive maximum power point tracking (MPPT) approach for PV systems. • Transient and steady state performances in tracking process are improved. • The proposed MPPT can automatically tune tracking step size along a P–V curve. • A PSO algorithm is used to determine the weighting values of extension theory. - Abstract: The aim of this work is to present an adaptive maximum power point tracking (MPPT) approach for photovoltaic (PV) power generation system. Integrating the extension theory as well as the conventional perturb and observe method, an maximum power point (MPP) tracker is made able to automatically tune tracking step size by way of the category recognition along a P–V characteristic curve. Accordingly, the transient and steady state performances in tracking process are improved. Furthermore, an optimization approach is proposed on the basis of a particle swarm optimization (PSO) algorithm for the complexity reduction in the determination of weighting values. At the end of this work, a simulated improvement in the tracking performance is experimentally validated by an MPP tracker with a programmable system-on-chip (PSoC) based controller

  14. Elliptic Tales Curves, Counting, and Number Theory

    CERN Document Server

    Ash, Avner

    2012-01-01

    Elliptic Tales describes the latest developments in number theory by looking at one of the most exciting unsolved problems in contemporary mathematics--the Birch and Swinnerton-Dyer Conjecture. The Clay Mathematics Institute is offering a prize of 1 million to anyone who can discover a general solution to the problem. In this book, Avner Ash and Robert Gross guide readers through the mathematics they need to understand this captivating problem. The key to the conjecture lies in elliptic curves, which are cubic equations in two variables. These equations may appear simple, yet they arise from

  15. An efficient reconstruction algorithm for differential phase-contrast tomographic images from a limited number of views

    International Nuclear Information System (INIS)

    Sunaguchi, Naoki; Yuasa, Tetsuya; Gupta, Rajiv; Ando, Masami

    2015-01-01

    The main focus of this paper is reconstruction of tomographic phase-contrast image from a set of projections. We propose an efficient reconstruction algorithm for differential phase-contrast computed tomography that can considerably reduce the number of projections required for reconstruction. The key result underlying this research is a projection theorem that states that the second derivative of the projection set is linearly related to the Laplacian of the tomographic image. The proposed algorithm first reconstructs the Laplacian image of the phase-shift distribution from the second-derivative of the projections using total variation regularization. The second step is to obtain the phase-shift distribution by solving a Poisson equation whose source is the Laplacian image previously reconstructed under the Dirichlet condition. We demonstrate the efficacy of this algorithm using both synthetically generated simulation data and projection data acquired experimentally at a synchrotron. The experimental phase data were acquired from a human coronary artery specimen using dark-field-imaging optics pioneered by our group. Our results demonstrate that the proposed algorithm can reduce the number of projections to approximately 33% as compared with the conventional filtered backprojection method, without any detrimental effect on the image quality

  16. Algorithmic crystal chemistry: A cellular automata approach

    International Nuclear Information System (INIS)

    Krivovichev, S. V.

    2012-01-01

    Atomic-molecular mechanisms of crystal growth can be modeled based on crystallochemical information using cellular automata (a particular case of finite deterministic automata). In particular, the formation of heteropolyhedral layered complexes in uranyl selenates can be modeled applying a one-dimensional three-colored cellular automaton. The use of the theory of calculations (in particular, the theory of automata) in crystallography allows one to interpret crystal growth as a computational process (the realization of an algorithm or program with a finite number of steps).

  17. Feature extraction algorithm for space targets based on fractal theory

    Science.gov (United States)

    Tian, Balin; Yuan, Jianping; Yue, Xiaokui; Ning, Xin

    2007-11-01

    In order to offer a potential for extending the life of satellites and reducing the launch and operating costs, satellite servicing including conducting repairs, upgrading and refueling spacecraft on-orbit become much more frequently. Future space operations can be more economically and reliably executed using machine vision systems, which can meet real time and tracking reliability requirements for image tracking of space surveillance system. Machine vision was applied to the research of relative pose for spacecrafts, the feature extraction algorithm was the basis of relative pose. In this paper fractal geometry based edge extraction algorithm which can be used in determining and tracking the relative pose of an observed satellite during proximity operations in machine vision system was presented. The method gets the gray-level image distributed by fractal dimension used the Differential Box-Counting (DBC) approach of the fractal theory to restrain the noise. After this, we detect the consecutive edge using Mathematical Morphology. The validity of the proposed method is examined by processing and analyzing images of space targets. The edge extraction method not only extracts the outline of the target, but also keeps the inner details. Meanwhile, edge extraction is only processed in moving area to reduce computation greatly. Simulation results compared edge detection using the method which presented by us with other detection methods. The results indicate that the presented algorithm is a valid method to solve the problems of relative pose for spacecrafts.

  18. The large number hypothesis and Einstein's theory of gravitation

    International Nuclear Information System (INIS)

    Yun-Kau Lau

    1985-01-01

    In an attempt to reconcile the large number hypothesis (LNH) with Einstein's theory of gravitation, a tentative generalization of Einstein's field equations with time-dependent cosmological and gravitational constants is proposed. A cosmological model consistent with the LNH is deduced. The coupling formula of the cosmological constant with matter is found, and as a consequence, the time-dependent formulae of the cosmological constant and the mean matter density of the Universe at the present epoch are then found. Einstein's theory of gravitation, whether with a zero or nonzero cosmological constant, becomes a limiting case of the new generalized field equations after the early epoch

  19. Algorithms for detecting and analysing autocatalytic sets.

    Science.gov (United States)

    Hordijk, Wim; Smith, Joshua I; Steel, Mike

    2015-01-01

    Autocatalytic sets are considered to be fundamental to the origin of life. Prior theoretical and computational work on the existence and properties of these sets has relied on a fast algorithm for detectingself-sustaining autocatalytic sets in chemical reaction systems. Here, we introduce and apply a modified version and several extensions of the basic algorithm: (i) a modification aimed at reducing the number of calls to the computationally most expensive part of the algorithm, (ii) the application of a previously introduced extension of the basic algorithm to sample the smallest possible autocatalytic sets within a reaction network, and the application of a statistical test which provides a probable lower bound on the number of such smallest sets, (iii) the introduction and application of another extension of the basic algorithm to detect autocatalytic sets in a reaction system where molecules can also inhibit (as well as catalyse) reactions, (iv) a further, more abstract, extension of the theory behind searching for autocatalytic sets. (i) The modified algorithm outperforms the original one in the number of calls to the computationally most expensive procedure, which, in some cases also leads to a significant improvement in overall running time, (ii) our statistical test provides strong support for the existence of very large numbers (even millions) of minimal autocatalytic sets in a well-studied polymer model, where these minimal sets share about half of their reactions on average, (iii) "uninhibited" autocatalytic sets can be found in reaction systems that allow inhibition, but their number and sizes depend on the level of inhibition relative to the level of catalysis. (i) Improvements in the overall running time when searching for autocatalytic sets can potentially be obtained by using a modified version of the algorithm, (ii) the existence of large numbers of minimal autocatalytic sets can have important consequences for the possible evolvability of

  20. Treatment of the intrinsic Hamiltonian in particle-number nonconserving theories

    International Nuclear Information System (INIS)

    Hergert, H.; Roth, R.

    2009-01-01

    We discuss the implications of using an intrinsic Hamiltonian in theories without particle-number conservation, e.g., the Hartree-Fock-Bogoliubov approximation, where the Hamiltonian's particle-number dependence leads to discrepancies if one naively replaces the particle-number operator by its expectation value. We develop a systematic expansion that fixes this problem and leads to an a posteriori justification of the widely-used one- plus two-body form of the intrinsic kinetic energy in nuclear self-consistent field methods. The expansion's convergence properties as well as its practical applications are discussed for several sample nuclei.

  1. Studying the varied shapes of gold clusters by an elegant optimization algorithm that hybridizes the density functional tight-binding theory and the density functional theory

    Science.gov (United States)

    Yen, Tsung-Wen; Lim, Thong-Leng; Yoon, Tiem-Leong; Lai, S. K.

    2017-11-01

    We combined a new parametrized density functional tight-binding (DFTB) theory (Fihey et al. 2015) with an unbiased modified basin hopping (MBH) optimization algorithm (Yen and Lai 2015) and applied it to calculate the lowest energy structures of Au clusters. From the calculated topologies and their conformational changes, we find that this DFTB/MBH method is a necessary procedure for a systematic study of the structural development of Au clusters but is somewhat insufficient for a quantitative study. As a result, we propose an extended hybridized algorithm. This improved algorithm proceeds in two steps. In the first step, the DFTB theory is employed to calculate the total energy of the cluster and this step (through running DFTB/MBH optimization for given Monte-Carlo steps) is meant to efficiently bring the Au cluster near to the region of the lowest energy minimum since the cluster as a whole has explicitly considered the interactions of valence electrons with ions, albeit semi-quantitatively. Then, in the second succeeding step, the energy-minimum searching process will continue with a skilledly replacement of the energy function calculated by the DFTB theory in the first step by one calculated in the full density functional theory (DFT). In these subsequent calculations, we couple the DFT energy also with the MBH strategy and proceed with the DFT/MBH optimization until the lowest energy value is found. We checked that this extended hybridized algorithm successfully predicts the twisted pyramidal structure for the Au40 cluster and correctly confirms also the linear shape of C8 which our previous DFTB/MBH method failed to do so. Perhaps more remarkable is the topological growth of Aun: it changes from a planar (n =3-11) → an oblate-like cage (n =12-15) → a hollow-shape cage (n =16-18) and finally a pyramidal-like cage (n =19, 20). These varied forms of the cluster's shapes are consistent with those reported in the literature.

  2. Comparative analysis of different variants of the Uzawa algorithm in problems of the theory of elasticity for incompressible materials

    Directory of Open Access Journals (Sweden)

    Nikita E. Styopin

    2016-09-01

    Full Text Available Different variants of the Uzawa algorithm are compared with one another. The comparison is performed for the case in which this algorithm is applied to large-scale systems of linear algebraic equations. These systems arise in the finite-element solution of the problems of elasticity theory for incompressible materials. A modification of the Uzawa algorithm is proposed. Computational experiments show that this modification improves the convergence of the Uzawa algorithm for the problems of solid mechanics. The results of computational experiments show that each variant of the Uzawa algorithm considered has its advantages and disadvantages and may be convenient in one case or another.

  3. A Convergent Differential Evolution Algorithm with Hidden Adaptation Selection for Engineering Optimization

    Directory of Open Access Journals (Sweden)

    Zhongbo Hu

    2014-01-01

    Full Text Available Many improved differential Evolution (DE algorithms have emerged as a very competitive class of evolutionary computation more than a decade ago. However, few improved DE algorithms guarantee global convergence in theory. This paper developed a convergent DE algorithm in theory, which employs a self-adaptation scheme for the parameters and two operators, that is, uniform mutation and hidden adaptation selection (haS operators. The parameter self-adaptation and uniform mutation operator enhance the diversity of populations and guarantee ergodicity. The haS can automatically remove some inferior individuals in the process of the enhancing population diversity. The haS controls the proposed algorithm to break the loop of current generation with a small probability. The breaking probability is a hidden adaptation and proportional to the changes of the number of inferior individuals. The proposed algorithm is tested on ten engineering optimization problems taken from IEEE CEC2011.

  4. Efficient multitasking of the SU(3) lattice gauge theory algorithm on the CRAY X-MP

    International Nuclear Information System (INIS)

    Kuba, D.W.; Moriarty, K.J.M.

    1985-01-01

    The Monte Carlo lattice gauge theory algorithm with the Metropolis et.al. updating procedure is vectorized and multitasked on the four processor CRAY X-MP and results in a code with a link-update-time, in 64-bit arithmetic and 10 hits-per-link, of 11.0 μs on a 16 4 lattice, the fastest link-update-time so far achieved. The program calculates the Wilson loops of size up to L/2.L/2 for an L 4 lattice for SU(3) gauge theory. (orig./HSI)

  5. A panorama of discrepancy theory

    CERN Document Server

    Srivastav, Anand; Travaglini, Giancarlo

    2014-01-01

    Discrepancy theory concerns the problem of replacing a continuous object with a discrete sampling. Discrepancy theory is currently at a crossroads between number theory, combinatorics, Fourier analysis, algorithms and complexity, probability theory and numerical analysis. There are several excellent books on discrepancy theory but perhaps no one of them actually shows the present variety of points of view and applications covering the areas "Classical and Geometric Discrepancy Theory", "Combinatorial Discrepancy Theory" and "Applications and Constructions". Our book consists of several chapters, written by experts in the specific areas, and focused on the different aspects of the theory. The book should also be an invitation to researchers and students to find a quick way into the different methods and to motivate interdisciplinary research.

  6. Mean field theory of EM algorithm for Bayesian grey scale image restoration

    International Nuclear Information System (INIS)

    Inoue, Jun-ichi; Tanaka, Kazuyuki

    2003-01-01

    The EM algorithm for the Bayesian grey scale image restoration is investigated in the framework of the mean field theory. Our model system is identical to the infinite range random field Q-Ising model. The maximum marginal likelihood method is applied to the determination of hyper-parameters. We calculate both the data-averaged mean square error between the original image and its maximizer of posterior marginal estimate, and the data-averaged marginal likelihood function exactly. After evaluating the hyper-parameter dependence of the data-averaged marginal likelihood function, we derive the EM algorithm which updates the hyper-parameters to obtain the maximum likelihood estimate analytically. The time evolutions of the hyper-parameters and so-called Q function are obtained. The relation between the speed of convergence of the hyper-parameters and the shape of the Q function is explained from the viewpoint of dynamics

  7. Improved Inverse Kinematics Algorithm Using Screw Theory for a Six-DOF Robot Manipulator

    Directory of Open Access Journals (Sweden)

    Qingcheng Chen

    2015-10-01

    Full Text Available Based on screw theory, a novel improved inverse-kinematics approach for a type of six-DOF serial robot, “Qianjiang I”, is proposed in this paper. The common kinematics model of the robot is based on the Denavit-Hartenberg (D-H notation method while its inverse kinematics has inefficient calculation and complicated solution, which cannot meet the demands of online real-time application. To solve this problem, this paper presents a new method to improve the efficiency of the inverse kinematics solution by introducing the screw theory. Unlike other methods, the proposed method only establishes two coordinates, namely the inertial coordinate and the tool coordinate; the screw motion of each link is carried out based on the inertial coordinate, ensuring definite geometric meaning. Furthermore, we adopt a new inverse kinematics algorithm, developing an improved sub-problem method along with Paden-Kahan sub-problems. This method has high efficiency and can be applied in real-time industrial operation. It is convenient to select the desired solutions directly from among multiple solutions by examining clear geometric meaning. Finally, the effectiveness and reliability performance of the new algorithm are analysed and verified in comparative experiments carried out on the six-DOF serial robot “Qianjiang I”.

  8. Density functional theory and evolution algorithm calculations of elastic properties of AlON

    Energy Technology Data Exchange (ETDEWEB)

    Batyrev, I. G.; Taylor, D. E.; Gazonas, G. A.; McCauley, J. W. [U.S. Army Research Laboratory, Aberdeen Proving Ground, Maryland 21005 (United States)

    2014-01-14

    Different models for aluminum oxynitride (AlON) were calculated using density functional theory and optimized using an evolutionary algorithm. Evolutionary algorithm and density functional theory (DFT) calculations starting from several models of AlON with different Al or O vacancy locations and different positions for the N atoms relative to the vacancy were carried out. The results show that the constant anion model [McCauley et al., J. Eur. Ceram. Soc. 29(2), 223 (2009)] with a random distribution of N atoms not adjacent to the Al vacancy has the lowest energy configuration. The lowest energy structure is in a reasonable agreement with experimental X-ray diffraction spectra. The optimized structure of a 55 atom unit cell was used to construct 220 and 440 atom models for simulation cells using DFT with a Gaussian basis set. Cubic elastic constant predictions were found to approach the experimentally determined AlON single crystal elastic constants as the model size increased from 55 to 440 atoms. The pressure dependence of the elastic constants found from simulated stress-strain relations were in overall agreement with experimental measurements of polycrystalline and single crystal AlON. Calculated IR intensity and Raman spectra are compared with available experimental data.

  9. Genetic algorithm for lattice gauge theory on SU(2) and U(1) on 4 dimensional lattice, how to hitchhike to thermal equilibrium state

    International Nuclear Information System (INIS)

    Yamaguchi, A.; Sugamoto, A.

    2000-01-01

    Applying Genetic Algorithm for the Lattice Gauge Theory is formed to be an effective method to minimize the action of gauge field on a lattice. In 4 dimensions, the critical point and the Wilson loop behaviour of SU(2) lattice gauge theory as well as the phase transition of U(1) theory have been studied. The proper coding methodi has been developed in order to avoid the increase of necessary memory and the overload of calculation for Genetic Algorithm. How hichhikers toward equilibrium appear against kidnappers is clarified

  10. From the social learning theory to a social learning algorithm for global optimization

    OpenAIRE

    Gong, Yue-Jiao; Zhang, Jun; Li, Yun

    2014-01-01

    Traditionally, the Evolutionary Computation (EC) paradigm is inspired by Darwinian evolution or the swarm intelligence of animals. Bandura's Social Learning Theory pointed out that the social learning behavior of humans indicates a high level of intelligence in nature. We found that such intelligence of human society can be implemented by numerical computing and be utilized in computational algorithms for solving optimization problems. In this paper, we design a novel and generic optimization...

  11. Performance of multiobjective computational intelligence algorithms for the routing and wavelength assignment problem

    Directory of Open Access Journals (Sweden)

    Jorge Patiño

    2016-01-01

    Full Text Available This paper presents an evaluation performance of computational intelligence algorithms based on the multiobjective theory for the solution of the Routing and Wavelength Assignment problem (RWA in optical networks. The study evaluates the Firefly Algorithm, the Differential Evolutionary Algorithm, the Simulated Annealing Algorithm and two versions of the Particle Swarm Optimization algorithm. The paper provides a description of the multiobjective algorithms; then, an evaluation based on the performance provided by the multiobjective algorithms versus mono-objective approaches when dealing with different traffic loads, different numberof wavelengths and wavelength conversion process over the NSFNet topology is presented. Simulation results show that monoobjective algorithms properly solve the RWA problem for low values of data traffic and low number of wavelengths. However, the multiobjective approaches adapt better to online traffic when the number of wavelengths available in the network increases as well as when wavelength conversion is implemented in the nodes.

  12. A multilevel algorithm for flow observables in gauge theories

    International Nuclear Information System (INIS)

    Garcia Vera, Miguel; Humboldt-Universitaet, Berlin; Schaefer, Stefan

    2016-03-01

    We study the possibility of using multilevel algorithms for the computation of correlation functions of gradient flow observables. For each point in the correlation function an approximate flow is defined which depends only on links in a subset of the lattice. Together with a local action this allows for independent updates and consequently a convergence of the Monte Carlo process faster than the inverse square root of the number of measurements. We demonstrate the feasibility of this idea in the correlation functions of the topological charge and the energy density.

  13. Problems in particle theory

    International Nuclear Information System (INIS)

    Adler, S.L.; Wilczek, F.

    1992-11-01

    Members of the Institute have worked on a number of problems including the following: acceleration algorithms for the Monte Carlo analysis of lattice field, and gauge and spin theories, based on changes of variables specific to lattices of dimension 2 ell ; construction of quaternionic generalizations of complex quantum mechanics and field theory; wave functions for paired Hall states; black hole quantum mechanics; generalized target-space duality in curved string backgrounds; gauge symnmetry algebra of the N = 2 string; two-dimensional quantum gravity and associated string theories; organizing principles from which the signal processing of neural networks in the retina and cortex can be deduced; integrable systems of KdV type; and a theory for Kondo insulators

  14. Algorithm for the real-structure design of neutron supermirrors

    International Nuclear Information System (INIS)

    Pleshanov, N.K.

    2004-01-01

    The effect of structure imperfections of neutron supermirrors on their performance is well known. Nevertheless, supermirrors are designed with the algorithms based on the theories of reflection from perfect layered structures. In the present paper an approach is suggested, in which the design of a supermirror is made on the basis of its real-structure model (the RSD algorithm) with the use of exact numerical methods. It allows taking the growth laws and the reflectance of real structures into account. The new algorithm was compared with the Gukasov-Ruban-Bedrizova (GRB) algorithm and with the most frequently used algorithm of Hayter and Mook (HM). Calculations showed that, when the parameters of the algorithms are chosen so that the supermirrors designed for a given angular acceptance m have the same number of bilayers, (a) for perfect layers the GRB, HM and RSD algorithms generate sequences of practically the same reflectance; (b) for real structures with rough interfaces and interdiffusion the GRB and HM algorithms generate sequences with insufficient number of thinner layers and the RSD algorithm turns out to be more responsive and efficient. The efficiency of the RSD algorithm increases for larger m. In addition, calculations have been carried out to demonstrate the effect of fabrication errors and absorption on the reflectance of Ni/Ti supermirrors

  15. Describing Pre-Service Teachers' Developing Understanding of Elementary Number Theory Topics

    Science.gov (United States)

    Feldman, Ziv

    2012-01-01

    Although elementary number theory topics are closely linked to foundational topics in number and operations and are prevalent in elementary and middle grades mathematics curricula, little is currently known about how students and teachers make sense of them. This study investigated pre-service elementary teachers' developing understanding of…

  16. Data clustering theory, algorithms, and applications

    CERN Document Server

    Gan, Guojun; Wu, Jianhong

    2007-01-01

    Cluster analysis is an unsupervised process that divides a set of objects into homogeneous groups. This book starts with basic information on cluster analysis, including the classification of data and the corresponding similarity measures, followed by the presentation of over 50 clustering algorithms in groups according to some specific baseline methodologies such as hierarchical, center-based, and search-based methods. As a result, readers and users can easily identify an appropriate algorithm for their applications and compare novel ideas with existing results. The book also provides examples of clustering applications to illustrate the advantages and shortcomings of different clustering architectures and algorithms. Application areas include pattern recognition, artificial intelligence, information technology, image processing, biology, psychology, and marketing. Readers also learn how to perform cluster analysis with the C/C++ and MATLAB® programming languages.

  17. Mean-field theory of spin-glasses with finite coordination number

    Science.gov (United States)

    Kanter, I.; Sompolinsky, H.

    1987-01-01

    The mean-field theory of dilute spin-glasses is studied in the limit where the average coordination number is finite. The zero-temperature phase diagram is calculated and the relationship between the spin-glass phase and the percolation transition is discussed. The present formalism is applicable also to graph optimization problems.

  18. Cuckoo search and firefly algorithm theory and applications

    CERN Document Server

    2014-01-01

    Nature-inspired algorithms such as cuckoo search and firefly algorithm have become popular and widely used in recent years in many applications. These algorithms are flexible, efficient and easy to implement. New progress has been made in the last few years, and it is timely to summarize the latest developments of cuckoo search and firefly algorithm and their diverse applications. This book will review both theoretical studies and applications with detailed algorithm analysis, implementation and case studies so that readers can benefit most from this book.  Application topics are contributed by many leading experts in the field. Topics include cuckoo search, firefly algorithm, algorithm analysis, feature selection, image processing, travelling salesman problem, neural network, GPU optimization, scheduling, queuing, multi-objective manufacturing optimization, semantic web service, shape optimization, and others.   This book can serve as an ideal reference for both graduates and researchers in computer scienc...

  19. Quantum computation and Shor close-quote s factoring algorithm

    International Nuclear Information System (INIS)

    Ekert, A.; Jozsa, R.

    1996-01-01

    Current technology is beginning to allow us to manipulate rather than just observe individual quantum phenomena. This opens up the possibility of exploiting quantum effects to perform computations beyond the scope of any classical computer. Recently Peter Shor discovered an efficient algorithm for factoring whole numbers, which uses characteristically quantum effects. The algorithm illustrates the potential power of quantum computation, as there is no known efficient classical method for solving this problem. The authors give an exposition of Shor close-quote s algorithm together with an introduction to quantum computation and complexity theory. They discuss experiments that may contribute to its practical implementation. copyright 1996 The American Physical Society

  20. Edge Detection Algorithm Based on Fuzzy Logic Theory for a Local Vision System of Robocup Humanoid League

    Directory of Open Access Journals (Sweden)

    Andrea K. Perez-Hernandez

    2013-06-01

    Full Text Available At this paper we shown the development of an algorithm to perform edges extraction based on fuzzy logic theory. This method allows recognizing landmarks on the game field for Humanoid League of RoboCup. The proposed algorithm describes the creation of a fuzzy inference system that permit evaluate the existent relationship between image pixels, finding variations on grey levels of related neighbor pixels. Subsequently, it shows an implementation of OTSU method to binarize an image that was obtained from fuzzy process and so generate an image containing only extracted edges, validating the algorithm with Humanoid League images. Later, we analyze obtained results that evidence a good performance of algorithm, considering that this proposal only takes an extra 35% processing time that will be required by traditional methods, whereas extracted edges are 52% less noise susceptible.

  1. Generation Expansion Planning in pool market: A hybrid modified game theory and improved genetic algorithm

    International Nuclear Information System (INIS)

    Shayanfar, H.A.; Lahiji, A. Saliminia; Aghaei, J.; Rabiee, A.

    2009-01-01

    Unlike the traditional policy, Generation Expansion Planning (GEP) problem in competitive framework is complicated. In the new policy, each Generation Company (GENCO) decides to invest in such a way that obtains as much profit as possible. This paper presents a new hybrid algorithm to determine GEP in a Pool market. The proposed algorithm is divided in two programming levels: master and slave. In the master level a Modified Game Theory (MGT) is proposed to evaluate the contrast of GENCOs by the Independent System Operator (ISO). In the slave level, an Improved Genetic Algorithm (IGA) method is used to find the best solution of each GENCO for decision-making of investment. The validity of the proposed method is examined in the case study including three GENCOs with multi-type of power plants. The results show that the presented method is both satisfactory and consistent with expectation. (author)

  2. Fermion number non-conservation and cold neutral fermionic matter in (V-A) gauge theories

    International Nuclear Information System (INIS)

    Matveev, V.A.; Rubakov, V.A.; Tavkhelidze, A.N.; Tokarev, V.F.

    1987-01-01

    It is shown that in four-dimensional abelian (V-A) theories, the ground state of cold neutral fermionic matter is an anomalous state containing domains of abnormal phase surrounded by the normal vacuum. Inside these domains, there exists a gauge field condensate which makes real fermions disappear both inside and outside the domains. In non-abelian theories, the abnormal matter is unstable in its turn, and the system rolls back down into the normal state with a small number of fermions above the topologically non-trivial vacuum. Thus, in several non-abelian gauge theories, the fermion number density of cold neutral matter cannot exceed some critical value. (orig.)

  3. Baryon and lepton number violation in the Weinberg-Salam theory

    International Nuclear Information System (INIS)

    Mottola, E.

    1989-01-01

    This report discusses the concept of baryon and lepton number violation in the Weinberg-Salam theory. The topics discussed are: periodic vacua in quantum mechanics; tunnelling at finite temperature and classical thermal activation; calculation of the rate; an O(3) nonlinear sigma model; and the transition rate in the O(3) model

  4. Multi-objective random search algorithm for simultaneously optimizing wind farm layout and number of turbines

    DEFF Research Database (Denmark)

    Feng, Ju; Shen, Wen Zhong; Xu, Chang

    2016-01-01

    A new algorithm for multi-objective wind farm layout optimization is presented. It formulates the wind turbine locations as continuous variables and is capable of optimizing the number of turbines and their locations in the wind farm simultaneously. Two objectives are considered. One is to maximi...

  5. Glowworm swarm optimization theory, algorithms, and applications

    CERN Document Server

    Kaipa, Krishnanand N

    2017-01-01

    This book provides a comprehensive account of the glowworm swarm optimization (GSO) algorithm, including details of the underlying ideas, theoretical foundations, algorithm development, various applications, and MATLAB programs for the basic GSO algorithm. It also discusses several research problems at different levels of sophistication that can be attempted by interested researchers. The generality of the GSO algorithm is evident in its application to diverse problems ranging from optimization to robotics. Examples include computation of multiple optima, annual crop planning, cooperative exploration, distributed search, multiple source localization, contaminant boundary mapping, wireless sensor networks, clustering, knapsack, numerical integration, solving fixed point equations, solving systems of nonlinear equations, and engineering design optimization. The book is a valuable resource for researchers as well as graduate and undergraduate students in the area of swarm intelligence and computational intellige...

  6. Optimized Bayesian dynamic advising theory and algorithms

    CERN Document Server

    Karny, Miroslav

    2006-01-01

    Written by one of the world's leading groups in the area of Bayesian identification, control, and decision making, this book provides the theoretical and algorithmic basis of optimized probabilistic advising. Starting from abstract ideas and formulations, and culminating in detailed algorithms, the book comprises a unified treatment of an important problem of the design of advisory systems supporting supervisors of complex processes. It introduces the theoretical and algorithmic basis of developed advising, relying on novel and powerful combination black-box modelling by dynamic mixture models

  7. Theory and applications of numerical analysis

    CERN Document Server

    Phillips, G M

    1996-01-01

    This text is a self-contained Second Edition, providing an introductory account of the main topics in numerical analysis. The book emphasizes both the theorems which show the underlying rigorous mathematics andthe algorithms which define precisely how to program the numerical methods. Both theoretical and practical examples are included.* a unique blend of theory and applications* two brand new chapters on eigenvalues and splines* inclusion of formal algorithms* numerous fully worked examples* a large number of problems, many with solutions

  8. Very high Mach number shocks - Theory. [in space plasmas

    Science.gov (United States)

    Quest, Kevin B.

    1986-01-01

    The theory and simulation of collisionless perpendicular supercritical shock structure is reviewed, with major emphasis on recent research results. The primary tool of investigation is the hybrid simulation method, in which the Newtonian orbits of a large number of ion macroparticles are followed numerically, and in which the electrons are treated as a charge neutralizing fluid. The principal results include the following: (1) electron resistivity is not required to explain the observed quasi-stationarity of the earth's bow shock, (2) the structure of the perpendicular shock at very high Mach numbers depends sensitively on the upstream value of beta (the ratio of the thermal to magnetic pressure) and electron resistivity, (3) two-dimensional turbulence will become increasingly important as the Mach number is increased, and (4) nonadiabatic bulk electron heating will result when a thermal electron cannot complete a gyrorbit while transiting the shock.

  9. Phenomenological aspects of theories for baryon and lepton number violation

    International Nuclear Information System (INIS)

    Duerr, Michael

    2013-01-01

    The renormalizable couplings of the Standard Model are invariant under two accidental global symmetries, which correspond to conserved baryon and lepton numbers. In this thesis, we discuss possible roles of these symmetries in extension of the Standard Model. Two approaches are considered: explicit violation of lepton number by two units in the renormalizable couplings of the Lagrangian, and promotion of the global symmetries to local gauge symmetries that are spontaneously broken. The former approach directly leads to Majorana neutrino masses and neutrinoless double beta decay. We discuss the interplay of the contributions to this decay in a one-loop neutrino mass model, the colored seesaw mechanism. We find that, depending on the parameters of the model, both the light Majorana neutrino exchange and the contribution of the new colored particles may be dominant. Additionally, an experimental test is presented, which allows for a discrimination of neutrinoless double beta decay from unknown nuclear background using only one isotope. In the latter approach, fascinating implications originate from the attempt to write down an anomaly-free and spontaneously broken gauge theory for baryon and lepton numbers, such as an automatically stable dark matter candidate. When gauging the symmetries in a left-right symmetric setup, the same fields that allow for an anomaly-free theory generate neutrino masses via the type III seesaw mechanism.

  10. Abelian Chern-Simons theory and linking numbers via oscillatory integrals

    International Nuclear Information System (INIS)

    Albeverio, S.; Schaefer, J.

    1994-06-01

    We introduce a rigorous mathematical model of abelian Chern-Simons theory based on the theory of infinite dimensional oscillatory integrals developed by Albeverio and Hoeegh-Krohn. We construct a gauge-fixed Chern-Simons path integral as a Fresnel integral in a certain Hilbert space. Wilson loop variables are defined as Fresnel integrable functions and it is shown in this context that the expectation value of products of Wilson loops w.r.t. the Chern-Simons path integral is a topological invariant which can be computed in terms of pairwise linking numbers of the loops, as conjectured by Witten. We also propose a lattice Chern-Simons action which converges to the continuum limit. (orig.)

  11. Theory of affine projection algorithms for adaptive filtering

    CERN Document Server

    Ozeki, Kazuhiko

    2016-01-01

    This book focuses on theoretical aspects of the affine projection algorithm (APA) for adaptive filtering. The APA is a natural generalization of the classical, normalized least-mean-squares (NLMS) algorithm. The book first explains how the APA evolved from the NLMS algorithm, where an affine projection view is emphasized. By looking at those adaptation algorithms from such a geometrical point of view, we can find many of the important properties of the APA, e.g., the improvement of the convergence rate over the NLMS algorithm especially for correlated input signals. After the birth of the APA in the mid-1980s, similar algorithms were put forward by other researchers independently from different perspectives. This book shows that they are variants of the APA, forming a family of APAs. Then it surveys research on the convergence behavior of the APA, where statistical analyses play important roles. It also reviews developments of techniques to reduce the computational complexity of the APA, which are important f...

  12. A general rough-surface inversion algorithm: Theory and application to SAR data

    Science.gov (United States)

    Moghaddam, M.

    1993-01-01

    Rough-surface inversion has significant applications in interpretation of SAR data obtained over bare soil surfaces and agricultural lands. Due to the sparsity of data and the large pixel size in SAR applications, it is not feasible to carry out inversions based on numerical scattering models. The alternative is to use parameter estimation techniques based on approximate analytical or empirical models. Hence, there are two issues to be addressed, namely, what model to choose and what estimation algorithm to apply. Here, a small perturbation model (SPM) is used to express the backscattering coefficients of the rough surface in terms of three surface parameters. The algorithm used to estimate these parameters is based on a nonlinear least-squares criterion. The least-squares optimization methods are widely used in estimation theory, but the distinguishing factor for SAR applications is incorporating the stochastic nature of both the unknown parameters and the data into formulation, which will be discussed in detail. The algorithm is tested with synthetic data, and several Newton-type least-squares minimization methods are discussed to compare their convergence characteristics. Finally, the algorithm is applied to multifrequency polarimetric SAR data obtained over some bare soil and agricultural fields. Results will be shown and compared to ground-truth measurements obtained from these areas. The strength of this general approach to inversion of SAR data is that it can be easily modified for use with any scattering model without changing any of the inversion steps. Note also that, for the same reason it is not limited to inversion of rough surfaces, and can be applied to any parameterized scattering process.

  13. Phase transition and computational complexity in a stochastic prime number generator

    Energy Technology Data Exchange (ETDEWEB)

    Lacasa, L; Luque, B [Departamento de Matematica Aplicada y EstadIstica, ETSI Aeronauticos, Universidad Politecnica de Madrid, Plaza Cardenal Cisneros 3, Madrid 28040 (Spain); Miramontes, O [Departamento de Sistemas Complejos, Instituto de FIsica, Universidad Nacional Autonoma de Mexico, Mexico 01415 DF (Mexico)], E-mail: lucas@dmae.upm.es

    2008-02-15

    We introduce a prime number generator in the form of a stochastic algorithm. The character of this algorithm gives rise to a continuous phase transition which distinguishes a phase where the algorithm is able to reduce the whole system of numbers into primes and a phase where the system reaches a frozen state with low prime density. In this paper, we firstly present a broader characterization of this phase transition, both in analytical and numerical terms. Critical exponents are calculated, and data collapse is provided. Further on, we redefine the model as a search problem, fitting it in the hallmark of computational complexity theory. We suggest that the system belongs to the class NP. The computational cost is maximal around the threshold, as is common in many algorithmic phase transitions, revealing the presence of an easy-hard-easy pattern. We finally relate the nature of the phase transition to an average-case classification of the problem.

  14. Development of an image reconstruction algorithm for a few number of projection data

    International Nuclear Information System (INIS)

    Vieira, Wilson S.; Brandao, Luiz E.; Braz, Delson

    2007-01-01

    An image reconstruction algorithm was developed for specific cases of radiotracer applications in industry (rotating cylindrical mixers), involving a very few number of projection data. The algorithm was planned for imaging radioactive isotope distributions around the center of circular planes. The method consists of adapting the original expectation maximization algorithm (EM) to solve the ill-posed emission tomography inverse problem in order to reconstruct transversal 2D images of an object with only four projections. To achieve this aim, counts of photons emitted by selected radioactive sources in the plane, after they had been simulated using the commercial software MICROSHIELD 5.05, constitutes the projections and a computational code (SPECTEM) was developed to generate activity vectors or images related to those sources. SPECTEM is flexible to support simultaneous changes of the detectors's geometry, the medium under investigation and the properties of the gamma radiation. As a consequence of the code had been followed correctly the proposed method, good results were obtained and they encouraged us to continue the next step of the research: the validation of SPECTEM utilizing experimental data to check its real performance. We aim this code will improve considerably radiotracer methodology, making easier the diagnosis of fails in industrial processes. (author)

  15. Development of an image reconstruction algorithm for a few number of projection data

    Energy Technology Data Exchange (ETDEWEB)

    Vieira, Wilson S.; Brandao, Luiz E. [Instituto de Engenharia Nuclear (IEN-CNEN/RJ), Rio de Janeiro , RJ (Brazil)]. E-mails: wilson@ien.gov.br; brandao@ien.gov.br; Braz, Delson [Universidade Federal do Rio de Janeiro (UFRJ), RJ (Brazil). Coordenacao dos Programa de Pos-graduacao de Engenharia (COPPE). Lab. de Instrumentacao Nuclear]. E-mail: delson@mailhost.lin.ufrj.br

    2007-07-01

    An image reconstruction algorithm was developed for specific cases of radiotracer applications in industry (rotating cylindrical mixers), involving a very few number of projection data. The algorithm was planned for imaging radioactive isotope distributions around the center of circular planes. The method consists of adapting the original expectation maximization algorithm (EM) to solve the ill-posed emission tomography inverse problem in order to reconstruct transversal 2D images of an object with only four projections. To achieve this aim, counts of photons emitted by selected radioactive sources in the plane, after they had been simulated using the commercial software MICROSHIELD 5.05, constitutes the projections and a computational code (SPECTEM) was developed to generate activity vectors or images related to those sources. SPECTEM is flexible to support simultaneous changes of the detectors's geometry, the medium under investigation and the properties of the gamma radiation. As a consequence of the code had been followed correctly the proposed method, good results were obtained and they encouraged us to continue the next step of the research: the validation of SPECTEM utilizing experimental data to check its real performance. We aim this code will improve considerably radiotracer methodology, making easier the diagnosis of fails in industrial processes. (author)

  16. Algorithmic mathematics

    CERN Document Server

    Hougardy, Stefan

    2016-01-01

    Algorithms play an increasingly important role in nearly all fields of mathematics. This book allows readers to develop basic mathematical abilities, in particular those concerning the design and analysis of algorithms as well as their implementation. It presents not only fundamental algorithms like the sieve of Eratosthenes, the Euclidean algorithm, sorting algorithms, algorithms on graphs, and Gaussian elimination, but also discusses elementary data structures, basic graph theory, and numerical questions. In addition, it provides an introduction to programming and demonstrates in detail how to implement algorithms in C++. This textbook is suitable for students who are new to the subject and covers a basic mathematical lecture course, complementing traditional courses on analysis and linear algebra. Both authors have given this "Algorithmic Mathematics" course at the University of Bonn several times in recent years.

  17. An algorithm for high order strong coupling expansions: The mass gap in 3d pure Z2 lattice gauge theory

    International Nuclear Information System (INIS)

    Decker, K.; Hamburg Univ.

    1985-12-01

    An efficient description of all clusters contributing to the strong coupling expansion of the mass gap in three-dimensional pure Z 2 lattice gauge theory is presented. This description is correct to all orders in the strong coupling expansion and is chosen in such a way that it remains valid in four dimensions for gauge group Z 2 . Relying on this description an algorithm has been constructed which generates and processes all the contributing graphs to the exact strong coupling expansion of the mass gap in the three-dimensional model in a fully automatic fashion. A major component of this algorithm can also be used to generate exact strong coupling expansions for the free energy logZ. The algorithm is correct to any order; thus the order of these expansions is only limited by the available computing power. The presentation of the algorithm is such that it can serve as a guide-line for the construction of a generalized one which would also generate exact strong coupling expansions for the masses of low-lying excited states of four-dimensional pure Yang-Mills theories. (orig.)

  18. Multi-SOM: an Algorithm for High-Dimensional, Small Size Datasets

    Directory of Open Access Journals (Sweden)

    Shen Lu

    2013-04-01

    Full Text Available Since it takes time to do experiments in bioinformatics, biological datasets are sometimes small but with high dimensionality. From probability theory, in order to discover knowledge from a set of data, we have to have a sufficient number of samples. Otherwise, the error bounds can become too large to be useful. For the SOM (Self- Organizing Map algorithm, the initial map is based on the training data. In order to avoid the bias caused by the insufficient training data, in this paper we present an algorithm, called Multi-SOM. Multi-SOM builds a number of small self-organizing maps, instead of just one big map. Bayesian decision theory is used to make the final decision among similar neurons on different maps. In this way, we can better ensure that we can get a real random initial weight vector set, the map size is less of consideration and errors tend to average out. In our experiments as applied to microarray datasets which are highly intense data composed of genetic related information, the precision of Multi-SOMs is 10.58% greater than SOMs, and its recall is 11.07% greater than SOMs. Thus, the Multi-SOMs algorithm is practical.

  19. FAST-PT II: an algorithm to calculate convolution integrals of general tensor quantities in cosmological perturbation theory

    Energy Technology Data Exchange (ETDEWEB)

    Fang, Xiao; Blazek, Jonathan A.; McEwen, Joseph E.; Hirata, Christopher M., E-mail: fang.307@osu.edu, E-mail: blazek@berkeley.edu, E-mail: mcewen.24@osu.edu, E-mail: hirata.10@osu.edu [Center for Cosmology and AstroParticle Physics, Department of Physics, The Ohio State University, 191 W Woodruff Ave, Columbus OH 43210 (United States)

    2017-02-01

    Cosmological perturbation theory is a powerful tool to predict the statistics of large-scale structure in the weakly non-linear regime, but even at 1-loop order it results in computationally expensive mode-coupling integrals. Here we present a fast algorithm for computing 1-loop power spectra of quantities that depend on the observer's orientation, thereby generalizing the FAST-PT framework (McEwen et al., 2016) that was originally developed for scalars such as the matter density. This algorithm works for an arbitrary input power spectrum and substantially reduces the time required for numerical evaluation. We apply the algorithm to four examples: intrinsic alignments of galaxies in the tidal torque model; the Ostriker-Vishniac effect; the secondary CMB polarization due to baryon flows; and the 1-loop matter power spectrum in redshift space. Code implementing this algorithm and these applications is publicly available at https://github.com/JoeMcEwen/FAST-PT.

  20. Number Theory, Dialogue, and the Use of Spreadsheets in Teacher Education

    Directory of Open Access Journals (Sweden)

    Sergei Abramovich

    2011-04-01

    Full Text Available This paper demonstrates the use of a spreadsheet in teaching topics in elementary number theory. It emphasizes both the power and deficiency of inductive reasoning using a number of historically significant examples. The notion of computational experiment as a modern approach to the teaching of mathematics is discussed. The paper, grounded in a teacher-student dialogue as an instructional method, is a reflection on the author’s work over the years with prospective teachers of secondary mathematics.

  1. A Theory of Evolving Natural Constants Based on the Unification of General Theory of Relativity and Dirac's Large Number Hypothesis

    International Nuclear Information System (INIS)

    Peng Huanwu

    2005-01-01

    Taking Dirac's large number hypothesis as true, we have shown [Commun. Theor. Phys. (Beijing, China) 42 (2004) 703] the inconsistency of applying Einstein's theory of general relativity with fixed gravitation constant G to cosmology, and a modified theory for varying G is found, which reduces to Einstein's theory outside the gravitating body for phenomena of short duration in small distances, thereby agrees with all the crucial tests formerly supporting Einstein's theory. The modified theory, when applied to the usual homogeneous cosmological model, gives rise to a variable cosmological tensor term determined by the derivatives of G, in place of the cosmological constant term usually introduced ad hoc. Without any free parameter the theoretical Hubble's relation obtained from the modified theory seems not in contradiction to observations, as Dr. Wang's preliminary analysis of the recent data indicates [Commun. Theor. Phys. (Beijing, China) 42 (2004) 703]. As a complement to Commun. Theor. Phys. (Beijing, China) 42 (2004) 703 we shall study in this paper the modification of electromagnetism due to Dirac's large number hypothesis in more detail to show that the approximation of geometric optics still leads to null geodesics for the path of light, and that the general relation between the luminosity distance and the proper geometric distance is still valid in our theory as in Einstein's theory, and give the equations for homogeneous cosmological model involving matter plus electromagnetic radiation. Finally we consider the impact of the modification to quantum mechanics and statistical mechanics, and arrive at a systematic theory of evolving natural constants including Planck's h-bar as well as Boltzmann's k B by finding out their cosmologically combined counterparts with factors of appropriate powers of G that may remain truly constant to cosmologically long time.

  2. Combinatorial optimization theory and algorithms

    CERN Document Server

    Korte, Bernhard

    2018-01-01

    This comprehensive textbook on combinatorial optimization places special emphasis on theoretical results and algorithms with provably good performance, in contrast to heuristics. It is based on numerous courses on combinatorial optimization and specialized topics, mostly at graduate level. This book reviews the fundamentals, covers the classical topics (paths, flows, matching, matroids, NP-completeness, approximation algorithms) in detail, and proceeds to advanced and recent topics, some of which have not appeared in a textbook before. Throughout, it contains complete but concise proofs, and also provides numerous exercises and references. This sixth edition has again been updated, revised, and significantly extended. Among other additions, there are new sections on shallow-light trees, submodular function maximization, smoothed analysis of the knapsack problem, the (ln 4+ɛ)-approximation for Steiner trees, and the VPN theorem. Thus, this book continues to represent the state of the art of combinatorial opti...

  3. Algorithmic Principles of Mathematical Programming

    NARCIS (Netherlands)

    Faigle, Ulrich; Kern, Walter; Still, Georg

    2002-01-01

    Algorithmic Principles of Mathematical Programming investigates the mathematical structures and principles underlying the design of efficient algorithms for optimization problems. Recent advances in algorithmic theory have shown that the traditionally separate areas of discrete optimization, linear

  4. The large numbers hypothesis and the Einstein theory of gravitation

    International Nuclear Information System (INIS)

    Dirac, P.A.M.

    1979-01-01

    A study of the relations between large dimensionless numbers leads to the belief that G, expressed in atomic units, varies with the epoch while the Einstein theory requires G to be constant. These two requirements can be reconciled by supposing that the Einstein theory applies with a metric that differs from the atomic metric. The theory can be developed with conservation of mass by supposing that the continual increase in the mass of the observable universe arises from a continual slowing down of the velocity of recession of the galaxies. This leads to a model of the Universe that was first proposed by Einstein and de Sitter (the E.S. model). The observations of the microwave radiation fit in with this model. The static Schwarzchild metric has to be modified to fit in with the E.S. model for large r. The modification is worked out, and also the motion of planets with the new metric. It is found that there is a difference between ephemeris time and atomic time, and also that there should be an inward spiralling of the planets, referred to atomic units, superposed on the motion given by ordinary gravitational theory. These are effects that can be checked by observation, but there is no conclusive evidence up to the present. (author)

  5. Numerical linear algebra theory and applications

    CERN Document Server

    Beilina, Larisa; Karchevskii, Mikhail

    2017-01-01

    This book combines a solid theoretical background in linear algebra with practical algorithms for numerical solution of linear algebra problems. Developed from a number of courses taught repeatedly by the authors, the material covers topics like matrix algebra, theory for linear systems of equations, spectral theory, vector and matrix norms combined with main direct and iterative numerical methods, least squares problems, and eigen problems. Numerical algorithms illustrated by computer programs written in MATLAB® are also provided as supplementary material on SpringerLink to give the reader a better understanding of professional numerical software for the solution of real-life problems. Perfect for a one- or two-semester course on numerical linear algebra, matrix computation, and large sparse matrices, this text will interest students at the advanced undergraduate or graduate level.

  6. A Game Theory Algorithm for Intra-Cluster Data Aggregation in a Vehicular Ad Hoc Network.

    Science.gov (United States)

    Chen, Yuzhong; Weng, Shining; Guo, Wenzhong; Xiong, Naixue

    2016-02-19

    Vehicular ad hoc networks (VANETs) have an important role in urban management and planning. The effective integration of vehicle information in VANETs is critical to traffic analysis, large-scale vehicle route planning and intelligent transportation scheduling. However, given the limitations in the precision of the output information of a single sensor and the difficulty of information sharing among various sensors in a highly dynamic VANET, effectively performing data aggregation in VANETs remains a challenge. Moreover, current studies have mainly focused on data aggregation in large-scale environments but have rarely discussed the issue of intra-cluster data aggregation in VANETs. In this study, we propose a multi-player game theory algorithm for intra-cluster data aggregation in VANETs by analyzing the competitive and cooperative relationships among sensor nodes. Several sensor-centric metrics are proposed to measure the data redundancy and stability of a cluster. We then study the utility function to achieve efficient intra-cluster data aggregation by considering both data redundancy and cluster stability. In particular, we prove the existence of a unique Nash equilibrium in the game model, and conduct extensive experiments to validate the proposed algorithm. Results demonstrate that the proposed algorithm has advantages over typical data aggregation algorithms in both accuracy and efficiency.

  7. A Game Theory Algorithm for Intra-Cluster Data Aggregation in a Vehicular Ad Hoc Network

    Directory of Open Access Journals (Sweden)

    Yuzhong Chen

    2016-02-01

    Full Text Available Vehicular ad hoc networks (VANETs have an important role in urban management and planning. The effective integration of vehicle information in VANETs is critical to traffic analysis, large-scale vehicle route planning and intelligent transportation scheduling. However, given the limitations in the precision of the output information of a single sensor and the difficulty of information sharing among various sensors in a highly dynamic VANET, effectively performing data aggregation in VANETs remains a challenge. Moreover, current studies have mainly focused on data aggregation in large-scale environments but have rarely discussed the issue of intra-cluster data aggregation in VANETs. In this study, we propose a multi-player game theory algorithm for intra-cluster data aggregation in VANETs by analyzing the competitive and cooperative relationships among sensor nodes. Several sensor-centric metrics are proposed to measure the data redundancy and stability of a cluster. We then study the utility function to achieve efficient intra-cluster data aggregation by considering both data redundancy and cluster stability. In particular, we prove the existence of a unique Nash equilibrium in the game model, and conduct extensive experiments to validate the proposed algorithm. Results demonstrate that the proposed algorithm has advantages over typical data aggregation algorithms in both accuracy and efficiency.

  8. Evaluation of Origin Ensemble algorithm for image reconstruction for pixelated solid-state detectors with large number of channels

    Science.gov (United States)

    Kolstein, M.; De Lorenzo, G.; Mikhaylova, E.; Chmeissani, M.; Ariño, G.; Calderón, Y.; Ozsahin, I.; Uzun, D.

    2013-04-01

    The Voxel Imaging PET (VIP) Pathfinder project intends to show the advantages of using pixelated solid-state technology for nuclear medicine applications. It proposes designs for Positron Emission Tomography (PET), Positron Emission Mammography (PEM) and Compton gamma camera detectors with a large number of signal channels (of the order of 106). For PET scanners, conventional algorithms like Filtered Back-Projection (FBP) and Ordered Subset Expectation Maximization (OSEM) are straightforward to use and give good results. However, FBP presents difficulties for detectors with limited angular coverage like PEM and Compton gamma cameras, whereas OSEM has an impractically large time and memory consumption for a Compton gamma camera with a large number of channels. In this article, the Origin Ensemble (OE) algorithm is evaluated as an alternative algorithm for image reconstruction. Monte Carlo simulations of the PET design are used to compare the performance of OE, FBP and OSEM in terms of the bias, variance and average mean squared error (MSE) image quality metrics. For the PEM and Compton camera designs, results obtained with OE are presented.

  9. Number Theory in Science and Communication With Applications in Cryptography, Physics, Digital Information, Computing, and Self-Similarity

    CERN Document Server

    Schroeder, Manfred

    2009-01-01

    "Number Theory in Science and Communication" is a well-known introduction for non-mathematicians to this fascinating and useful branch of applied mathematics . It stresses intuitive understanding rather than abstract theory and highlights important concepts such as continued fractions, the golden ratio, quadratic residues and Chinese remainders, trapdoor functions, pseudoprimes and primitive elements. Their applications to problems in the real world are one of the main themes of the book. This revised fifth edition is augmented by recent advances in coding theory, permutations and derangements and a chapter in quantum cryptography. From reviews of earlier editions – "I continue to find [Schroeder’s] Number Theory a goldmine of valuable information. It is a marvellous book, in touch with the most recent applications of number theory and written with great clarity and humor.’ Philip Morrison (Scientific American) "A light-hearted and readable volume with a wide range of applications to which the author ha...

  10. Coding theory and cryptography the essentials

    CERN Document Server

    Hankerson, DC; Leonard, DA; Phelps, KT; Rodger, CA; Wall, JR; Wall, J R

    2000-01-01

    Containing data on number theory, encryption schemes, and cyclic codes, this highly successful textbook, proven by the authors in a popular two-quarter course, presents coding theory, construction, encoding, and decoding of specific code families in an ""easy-to-use"" manner appropriate for students with only a basic background in mathematics offering revised and updated material on the Berlekamp-Massey decoding algorithm and convolutional codes. Introducing the mathematics as it is needed and providing exercises with solutions, this edition includes an extensive section on cryptography, desig

  11. Computational invariant theory

    CERN Document Server

    Derksen, Harm

    2015-01-01

    This book is about the computational aspects of invariant theory. Of central interest is the question how the invariant ring of a given group action can be calculated. Algorithms for this purpose form the main pillars around which the book is built. There are two introductory chapters, one on Gröbner basis methods and one on the basic concepts of invariant theory, which prepare the ground for the algorithms. Then algorithms for computing invariants of finite and reductive groups are discussed. Particular emphasis lies on interrelations between structural properties of invariant rings and computational methods. Finally, the book contains a chapter on applications of invariant theory, covering fields as disparate as graph theory, coding theory, dynamical systems, and computer vision. The book is intended for postgraduate students as well as researchers in geometry, computer algebra, and, of course, invariant theory. The text is enriched with numerous explicit examples which illustrate the theory and should be ...

  12. Analytic theory for the selection of 2-D needle crystal at arbitrary Peclet number

    Science.gov (United States)

    Tanveer, Saleh

    1989-01-01

    An accurate analytic theory is presented for the velocity selection of a two-dimensional needle crystal for arbitrary Peclet number for small values of the surface tension parameter. The velocity selection is caused by the effect of transcendentally small terms which are determined by analytic continuation to the complex plane and analysis of nonlinear equations. The work supports the general conclusion of previous small Peclet number analytical results of other investigators, though there are some discrepancies in details. It also addresses questions raised on the validity of selection theory owing to assumptions made on shape corrections at large distances from the tip.

  13. Extended symmetries of the kinetic plasma theory models

    International Nuclear Information System (INIS)

    Taranov, V.B.

    2005-01-01

    Symmetry extension of the kinetic theory of collisionless plasma containing particles with equal charge to mass ratio is considered. It is shown that this symmetry allows us to reduce the number of equations. Symmetries obtained for the integro-differential equations of the kinetic theory by the indirect algorithm are compared to those obtained by direct methods. The importance of additional conditions - positiveness and integrability of distribution functions, existence of their moments - is underlined

  14. Genetic Algorithm and Graph Theory Based Matrix Factorization Method for Online Friend Recommendation

    Directory of Open Access Journals (Sweden)

    Qu Li

    2014-01-01

    Full Text Available Online friend recommendation is a fast developing topic in web mining. In this paper, we used SVD matrix factorization to model user and item feature vector and used stochastic gradient descent to amend parameter and improve accuracy. To tackle cold start problem and data sparsity, we used KNN model to influence user feature vector. At the same time, we used graph theory to partition communities with fairly low time and space complexity. What is more, matrix factorization can combine online and offline recommendation. Experiments showed that the hybrid recommendation algorithm is able to recommend online friends with good accuracy.

  15. Blink Number Forecasting Based on Improved Bayesian Fusion Algorithm for Fatigue Driving Detection

    Directory of Open Access Journals (Sweden)

    Wei Sun

    2015-01-01

    Full Text Available An improved Bayesian fusion algorithm (BFA is proposed for forecasting the blink number in a continuous video. It assumes that, at one prediction interval, the blink number is correlated with the blink numbers of only a few previous intervals. With this assumption, the weights of the component predictors in the improved BFA are calculated according to their prediction performance only from a few intervals rather than from all intervals. Therefore, compared with the conventional BFA, the improved BFA is more sensitive to the disturbed condition of the component predictors for adjusting their weights more rapidly. To determine the most relevant intervals, the grey relation entropy-based analysis (GREBA method is proposed, which can be used analyze the relevancy between the historical data flows of blink number and the data flow at the current interval. Three single predictors, that is, the autoregressive integrated moving average (ARIMA, radial basis function neural network (RBFNN, and Kalman filter (KF, are designed and incorporated linearly into the BFA. Experimental results demonstrate that the improved BFA obviously outperforms the conventional BFA in both accuracy and stability; also fatigue driving can be accurately warned against in advance based on the blink number forecasted by the improved BFA.

  16. Application of random number generators in genetic algorithms to improve rainfall-runoff modelling

    Science.gov (United States)

    Chlumecký, Martin; Buchtele, Josef; Richta, Karel

    2017-10-01

    The efficient calibration of rainfall-runoff models is a difficult issue, even for experienced hydrologists. Therefore, fast and high-quality model calibration is a valuable improvement. This paper describes a novel methodology and software for the optimisation of a rainfall-runoff modelling using a genetic algorithm (GA) with a newly prepared concept of a random number generator (HRNG), which is the core of the optimisation. The GA estimates model parameters using evolutionary principles, which requires a quality number generator. The new HRNG generates random numbers based on hydrological information and it provides better numbers compared to pure software generators. The GA enhances the model calibration very well and the goal is to optimise the calibration of the model with a minimum of user interaction. This article focuses on improving the internal structure of the GA, which is shielded from the user. The results that we obtained indicate that the HRNG provides a stable trend in the output quality of the model, despite various configurations of the GA. In contrast to previous research, the HRNG speeds up the calibration of the model and offers an improvement of rainfall-runoff modelling.

  17. Number Theory : A Seminar held at the Graduate School and University Center of the City University of New York

    CERN Document Server

    Chudnovsky, Gregory; Cohn, Harvey; Nathanson, Melvyn

    1989-01-01

    The New York Number Theory Seminar was organized in 1982 to provide a forum for the presentation and discussion of recent advances in higher arithmetic and its applications. Papers included in this volume are based on the lectures presented by their authors at the Seminar at the Graduate Center of C.U.N.Y. in 1985-88. Papers in the volume cover a wide spectrum of number theoretic topics ranging from additive number theory and diophantine approximations to algebraic number theory and relations with algebraic geometry and topology.

  18. The queen of mathematics a historically motivated guide to number theory

    CERN Document Server

    Goldman, Jay R

    2004-01-01

    This book takes the unique approach of examining number theory as it emerged in the 17th through 19th centuries. It leads to an understanding of today's research problems on the basis of their historical development. This book is a contribution to cultural history and brings a difficult subject within the reach of the serious reader.

  19. Odd number of coupled antiferromagnetic anisotropic Heisenberg chains: Spin wave theory

    International Nuclear Information System (INIS)

    Benyoussef, A.

    1996-10-01

    The effect of the chain and perpendicular anisotropies on the energy gap for odd number of coupled quantum spin-1/2 antiferromagnetic anisotropic Heisenberg chains is investigated using a spin wave theory. The energy gap opens above a critical anisotropic value. The known results of the isotropic case have been obtained. (author). 11 refs, 4 figs

  20. Algorithmic Self

    DEFF Research Database (Denmark)

    Markham, Annette

    This paper takes an actor network theory approach to explore some of the ways that algorithms co-construct identity and relational meaning in contemporary use of social media. Based on intensive interviews with participants as well as activity logging and data tracking, the author presents a richly...... layered set of accounts to help build our understanding of how individuals relate to their devices, search systems, and social network sites. This work extends critical analyses of the power of algorithms in implicating the social self by offering narrative accounts from multiple perspectives. It also...... contributes an innovative method for blending actor network theory with symbolic interaction to grapple with the complexity of everyday sensemaking practices within networked global information flows....

  1. CFD simulation with Code-Saturne of the light gas stratification erosion by a vertical air gas injection using a Low Mach number algorithm

    International Nuclear Information System (INIS)

    Hou Bingxu; Yu Jiyang; Senechal, Dorothee; Mechitoua, Namane; Min Jiesheng; Chen Guofei

    2015-01-01

    During CFD simulations of the flows at low Mach number regime, the classical assumption which neglects the dilatable effect of gas is no longer applicable when the temperature variation or the concentration variation of the mixture's components is too large in the fluid domain. To be able to correctly predict the flow at such a regime, some authors have recourse to a Low Mach number algorithm. This algorithm is based on the well-known pressure-based algorithm or elliptic solver for incompressible flows, SIMPLE, with a modification for the treatment of the pressure which is split into two parts (the hydrodynamic pressure and the thermodynamic pressure) and a dilatable term added in the mass equation. This algorithm has been implemented in the CFD code, Code_—Saturne, developed by EDF R and D, and applied for the CFD simulations of the erosion phenomena of light gas stratification by air injection. This paper is devoted to the analytical work with the Low Mach number algorithm based on the ST1 series of the SETH-2 campaign provided by the OECD project on the PANDA test facility of PSI. The first part is focused on a mesh sensitivity analysis, which is a common procedure for CFD codes validation. The second part of the paper presents a comparison between the CFD results obtained with the standard algorithms used for incompressible flows and the Low Mach number algorithm. The third part is an analysis of the CFD results obtained on the reference mesh with both different Froude numbers corresponding to the tests ST1_—7 (Fr=6.04) and ST1_—10 (Fr=7.95) from the ST1 series. In the last part the authors perform the knowledge of the initial light gas distribution effect on the stratification erosion and the capability of the CFD codes to predict this phenomenon with an area governed by diffusion regime (at the top of the vessel) and another one by forced convection near the injection. (author)

  2. The reconstruction algorithm used for ["6"8Ga]PSMA-HBED-CC PET/CT reconstruction significantly influences the number of detected lymph node metastases and coeliac ganglia

    International Nuclear Information System (INIS)

    Krohn, Thomas; Birmes, Anita; Winz, Oliver H.; Drude, Natascha I.; Mottaghy, Felix M.; Behrendt, Florian F.; Verburg, Frederik A.

    2017-01-01

    To investigate whether the numbers of lymph node metastases and coeliac ganglia delineated on ["6"8Ga]PSMA-HBED-CC PET/CT scans differ among datasets generated using different reconstruction algorithms. Data were constructed using the BLOB-OS-TF, BLOB-OS and 3D-RAMLA algorithms. All reconstructions were assessed by two nuclear medicine physicians for the number of pelvic/paraaortal lymph node metastases as well the number of coeliac ganglia. Standardized uptake values (SUV) were also calculated in different regions. At least one ["6"8Ga]PSMA-HBED-CC PET/CT-positive pelvic or paraaortal lymph node metastasis was found in 49 and 35 patients using the BLOB-OS-TF algorithm, in 42 and 33 patients using the BLOB-OS algorithm, and in 41 and 31 patients using the 3D-RAMLA algorithm, respectively, and a positive ganglion was found in 92, 59 and 24 of 100 patients using the three algorithms, respectively. Quantitatively, the SUVmean and SUVmax were significantly higher with the BLOB-OS algorithm than with either the BLOB-OS-TF or the 3D-RAMLA algorithm in all measured regions (p < 0.001 for all comparisons). The differences between the SUVs with the BLOB-OS-TF- and 3D-RAMLA algorithms were not significant in the aorta (SUVmean, p = 0.93; SUVmax, p = 0.97) but were significant in all other regions (p < 0.001 in all cases). The SUVmean ganglion/gluteus ratio was significantly higher with the BLOB-OS-TF algorithm than with either the BLOB-OS or the 3D-RAMLA algorithm and was significantly higher with the BLOB-OS than with the 3D-RAMLA algorithm (p < 0.001 in all cases). The results of ["6"8Ga]PSMA-HBED-CC PET/CT are affected by the reconstruction algorithm used. The highest number of lesions and physiological structures will be visualized using a modern algorithm employing time-of-flight information. (orig.)

  3. The reconstruction algorithm used for [{sup 68}Ga]PSMA-HBED-CC PET/CT reconstruction significantly influences the number of detected lymph node metastases and coeliac ganglia

    Energy Technology Data Exchange (ETDEWEB)

    Krohn, Thomas [RWTH University Hospital Aachen, Department of Nuclear Medicine, Aachen (Germany); Ulm University, Department of Nuclear Medicine, Ulm (Germany); Birmes, Anita; Winz, Oliver H.; Drude, Natascha I. [RWTH University Hospital Aachen, Department of Nuclear Medicine, Aachen (Germany); Mottaghy, Felix M. [RWTH University Hospital Aachen, Department of Nuclear Medicine, Aachen (Germany); Maastricht UMC+, Department of Nuclear Medicine, Maastricht (Netherlands); Behrendt, Florian F. [RWTH University Hospital Aachen, Department of Nuclear Medicine, Aachen (Germany); Radiology Institute ' ' Aachen Land' ' , Wuerselen (Germany); Verburg, Frederik A. [RWTH University Hospital Aachen, Department of Nuclear Medicine, Aachen (Germany); University Hospital Giessen and Marburg, Department of Nuclear Medicine, Marburg (Germany)

    2017-04-15

    To investigate whether the numbers of lymph node metastases and coeliac ganglia delineated on [{sup 68}Ga]PSMA-HBED-CC PET/CT scans differ among datasets generated using different reconstruction algorithms. Data were constructed using the BLOB-OS-TF, BLOB-OS and 3D-RAMLA algorithms. All reconstructions were assessed by two nuclear medicine physicians for the number of pelvic/paraaortal lymph node metastases as well the number of coeliac ganglia. Standardized uptake values (SUV) were also calculated in different regions. At least one [{sup 68}Ga]PSMA-HBED-CC PET/CT-positive pelvic or paraaortal lymph node metastasis was found in 49 and 35 patients using the BLOB-OS-TF algorithm, in 42 and 33 patients using the BLOB-OS algorithm, and in 41 and 31 patients using the 3D-RAMLA algorithm, respectively, and a positive ganglion was found in 92, 59 and 24 of 100 patients using the three algorithms, respectively. Quantitatively, the SUVmean and SUVmax were significantly higher with the BLOB-OS algorithm than with either the BLOB-OS-TF or the 3D-RAMLA algorithm in all measured regions (p < 0.001 for all comparisons). The differences between the SUVs with the BLOB-OS-TF- and 3D-RAMLA algorithms were not significant in the aorta (SUVmean, p = 0.93; SUVmax, p = 0.97) but were significant in all other regions (p < 0.001 in all cases). The SUVmean ganglion/gluteus ratio was significantly higher with the BLOB-OS-TF algorithm than with either the BLOB-OS or the 3D-RAMLA algorithm and was significantly higher with the BLOB-OS than with the 3D-RAMLA algorithm (p < 0.001 in all cases). The results of [{sup 68}Ga]PSMA-HBED-CC PET/CT are affected by the reconstruction algorithm used. The highest number of lesions and physiological structures will be visualized using a modern algorithm employing time-of-flight information. (orig.)

  4. Introduction to analytic and probabilistic number theory

    CERN Document Server

    Tenenbaum, Gérald

    2015-01-01

    This book provides a self contained, thorough introduction to the analytic and probabilistic methods of number theory. The prerequisites being reduced to classical contents of undergraduate courses, it offers to students and young researchers a systematic and consistent account on the subject. It is also a convenient tool for professional mathematicians, who may use it for basic references concerning many fundamental topics. Deliberately placing the methods before the results, the book will be of use beyond the particular material addressed directly. Each chapter is complemented with bibliographic notes, useful for descriptions of alternative viewpoints, and detailed exercises, often leading to research problems. This third edition of a text that has become classical offers a renewed and considerably enhanced content, being expanded by more than 50 percent. Important new developments are included, along with original points of view on many essential branches of arithmetic and an accurate perspective on up-to-...

  5. A practical approximation algorithm for solving massive instances of hybridization number for binary and nonbinary trees.

    Science.gov (United States)

    van Iersel, Leo; Kelk, Steven; Lekić, Nela; Scornavacca, Celine

    2014-05-05

    Reticulate events play an important role in determining evolutionary relationships. The problem of computing the minimum number of such events to explain discordance between two phylogenetic trees is a hard computational problem. Even for binary trees, exact solvers struggle to solve instances with reticulation number larger than 40-50. Here we present CycleKiller and NonbinaryCycleKiller, the first methods to produce solutions verifiably close to optimality for instances with hundreds or even thousands of reticulations. Using simulations, we demonstrate that these algorithms run quickly for large and difficult instances, producing solutions that are very close to optimality. As a spin-off from our simulations we also present TerminusEst, which is the fastest exact method currently available that can handle nonbinary trees: this is used to measure the accuracy of the NonbinaryCycleKiller algorithm. All three methods are based on extensions of previous theoretical work (SIDMA 26(4):1635-1656, TCBB 10(1):18-25, SIDMA 28(1):49-66) and are publicly available. We also apply our methods to real data.

  6. Number Theory in Science and Communication With Applications in Cryptography, Physics, Digital Information, Computing, and Self-Similarity

    CERN Document Server

    Schroeder, Manfred R

    2006-01-01

    "Number Theory in Science and Communication" is a well-known introduction for non-mathematicians to this fascinating and useful branch of applied mathematics . It stresses intuitive understanding rather than abstract theory and highlights important concepts such as continued fractions, the golden ratio, quadratic residues and Chinese remainders, trapdoor functions, pseudoprimes and primitive elements. Their applications to problems in the real world are one of the main themes of the book. This revised fourth edition is augmented by recent advances in primes in progressions, twin primes, prime triplets, prime quadruplets and quintruplets, factoring with elliptic curves, quantum factoring, Golomb rulers and "baroque" integers. From reviews of earlier editions – "I continue to find [Schroeder’s] Number Theory a goldmine of valuable information. It is a marvellous book, in touch with the most recent applications of number theory and written with great clarity and humor.’ Philip Morrison (Scientific American...

  7. Algorithmic approach to diagram techniques

    International Nuclear Information System (INIS)

    Ponticopoulos, L.

    1980-10-01

    An algorithmic approach to diagram techniques of elementary particles is proposed. The definition and axiomatics of the theory of algorithms are presented, followed by the list of instructions of an algorithm formalizing the construction of graphs and the assignment of mathematical objects to them. (T.A.)

  8. Look-ahead fermion algorithm

    International Nuclear Information System (INIS)

    Grady, M.

    1986-01-01

    I describe a fast fermion algorithm which utilizes pseudofermion fields but appears to have little or no systematic error. Test simulations on two-dimensional gauge theories are described. A possible justification for the algorithm being exact is discussed. 8 refs

  9. Markov chains theory and applications

    CERN Document Server

    Sericola, Bruno

    2013-01-01

    Markov chains are a fundamental class of stochastic processes. They are widely used to solve problems in a large number of domains such as operational research, computer science, communication networks and manufacturing systems. The success of Markov chains is mainly due to their simplicity of use, the large number of available theoretical results and the quality of algorithms developed for the numerical evaluation of many metrics of interest.The author presents the theory of both discrete-time and continuous-time homogeneous Markov chains. He carefully examines the explosion phenomenon, the

  10. Number Theory and Public-Key Cryptography.

    Science.gov (United States)

    Lefton, Phyllis

    1991-01-01

    Described are activities in the study of techniques used to conceal the meanings of messages and data. Some background information and two BASIC programs that illustrate the algorithms used in a new cryptographic system called "public-key cryptography" are included. (CW)

  11. Modified large number theory with constant G

    International Nuclear Information System (INIS)

    Recami, E.

    1983-01-01

    The inspiring ''numerology'' uncovered by Dirac, Eddington, Weyl, et al. can be explained and derived when it is slightly modified so to connect the ''gravitational world'' (cosmos) with the ''strong world'' (hadron), rather than with the electromagnetic one. The aim of this note is to show the following. In the present approach to the ''Large Number Theory,'' cosmos and hadrons are considered to be (finite) similar systems, so that the ratio R-bar/r-bar of the cosmos typical length R-bar to the hadron typical length r-bar is constant in time (for instance, if both cosmos and hadrons undergo an expansion/contraction cycle: according to the ''cyclical big-bang'' hypothesis: then R-bar and r-bar can be chosen to be the maximum radii, or the average radii). As a consequence, then gravitational constant G results to be independent of time. The present note is based on work done in collaboration with P.Caldirola, G. D. Maccarrone, and M. Pavsic

  12. Swarm size and iteration number effects to the performance of PSO algorithm in RFID tag coverage optimization

    Science.gov (United States)

    Prathabrao, M.; Nawawi, Azli; Sidek, Noor Azizah

    2017-04-01

    Radio Frequency Identification (RFID) system has multiple benefits which can improve the operational efficiency of the organization. The advantages are the ability to record data systematically and quickly, reducing human errors and system errors, update the database automatically and efficiently. It is often more readers (reader) is needed for the installation purposes in RFID system. Thus, it makes the system more complex. As a result, RFID network planning process is needed to ensure the RFID system works perfectly. The planning process is also considered as an optimization process and power adjustment because the coordinates of each RFID reader to be determined. Therefore, algorithms inspired by the environment (Algorithm Inspired by Nature) is often used. In the study, PSO algorithm is used because it has few number of parameters, the simulation time is fast, easy to use and also very practical. However, PSO parameters must be adjusted correctly, for robust and efficient usage of PSO. Failure to do so may result in disruption of performance and results of PSO optimization of the system will be less good. To ensure the efficiency of PSO, this study will examine the effects of two parameters on the performance of PSO Algorithm in RFID tag coverage optimization. The parameters to be studied are the swarm size and iteration number. In addition to that, the study will also recommend the most optimal adjustment for both parameters that is, 200 for the no. iterations and 800 for the no. of swarms. Finally, the results of this study will enable PSO to operate more efficiently in order to optimize RFID network planning system.

  13. Modelling Problem-Solving Situations into Number Theory Tasks: The Route towards Generalisation

    Science.gov (United States)

    Papadopoulos, Ioannis; Iatridou, Maria

    2010-01-01

    This paper examines the way two 10th graders cope with a non-standard generalisation problem that involves elementary concepts of number theory (more specifically linear Diophantine equations) in the geometrical context of a rectangle's area. Emphasis is given on how the students' past experience of problem solving (expressed through interplay…

  14. Analytic theory for the selection of a two-dimensional needle crystal at arbitrary Peclet number

    Science.gov (United States)

    Tanveer, S.

    1989-01-01

    An accurate analytic theory is presented for the velocity selection of a two-dimensional needle crystal for arbitrary Peclet number for small values of the surface tension parameter. The velocity selection is caused by the effect of transcendentally small terms which are determined by analytic continuation to the complex plane and analysis of nonlinear equations. The work supports the general conclusion of previous small Peclet number analytical results of other investigators, though there are some discrepancies in details. It also addresses questions raised on the validity of selection theory owing to assumptions made on shape corrections at large distances from the tip.

  15. An Efficient Rank Adaptation Algorithm for Cellular MIMO Systems with IRC Receivers

    DEFF Research Database (Denmark)

    Mahmood, Nurul Huda; Berardinelli, Gilberto; Tavares, Fernando Menezes Leitão

    2014-01-01

    Multiple transmit and receive antennas introduce additional degrees of freedom, which can be used to increase the number of spatial channels between a transmitter-receiver pair. Alternately, the additional degrees of freedom can be used to improve the interference resilience property with the help...... algorithm based on an estimate of the mean signal-to-interference-plus-noise ratio (SINR) at an IRC receiver; wherein, we use results from random matrix theory to derive the expression for the mean post-IRC SINR in the presence of interferers with unequal powers. The performance of the proposed algorithm...

  16. Geometric approximation algorithms

    CERN Document Server

    Har-Peled, Sariel

    2011-01-01

    Exact algorithms for dealing with geometric objects are complicated, hard to implement in practice, and slow. Over the last 20 years a theory of geometric approximation algorithms has emerged. These algorithms tend to be simple, fast, and more robust than their exact counterparts. This book is the first to cover geometric approximation algorithms in detail. In addition, more traditional computational geometry techniques that are widely used in developing such algorithms, like sampling, linear programming, etc., are also surveyed. Other topics covered include approximate nearest-neighbor search, shape approximation, coresets, dimension reduction, and embeddings. The topics covered are relatively independent and are supplemented by exercises. Close to 200 color figures are included in the text to illustrate proofs and ideas.

  17. Systematic errors due to linear congruential random-number generators with the Swendsen-Wang algorithm: a warning.

    Science.gov (United States)

    Ossola, Giovanni; Sokal, Alan D

    2004-08-01

    We show that linear congruential pseudo-random-number generators can cause systematic errors in Monte Carlo simulations using the Swendsen-Wang algorithm, if the lattice size is a multiple of a very large power of 2 and one random number is used per bond. These systematic errors arise from correlations within a single bond-update half-sweep. The errors can be eliminated (or at least radically reduced) by updating the bonds in a random order or in an aperiodic manner. It also helps to use a generator of large modulus (e.g., 60 or more bits).

  18. Projective block Lanczos algorithm for dense, Hermitian eigensystems

    International Nuclear Information System (INIS)

    Webster, F.; Lo, G.C.

    1996-01-01

    Projection operators are used to effect open-quotes deflation by restrictionclose quotes and it is argued that this is an optimal Lanczos algorithm for memory minimization. Algorithmic optimization is constrained to dense, Hermitian eigensystems where a significant number of the extreme eigenvectors must be obtained reliably and completely. The defining constraints are operator algebra without a matrix representation and semi-orthogonalization without storage of Krylov vectors. other semi-orthogonalization strategies for Lanczos algorithms and conjugate gradient techniques are evaluated within these constraints. Large scale, sparse, complex numerical experiments are performed on clusters of magnetic dipoles, a quantum many-body system that is not block-diagonalizable. Plane-wave, density functional theory of beryllium clusters provides examples of dense complex eigensystems. Use of preconditioners and spectral transformations is evaluated in a preprocessor prior to a high accuracy self-consistent field calculation. 25 refs., 3 figs., 5 tabs

  19. Anomalies, sphalerons and baryon number violation in electro-weak theory

    International Nuclear Information System (INIS)

    Mclerran, L.

    1989-01-01

    In series of three lectures, baryon number violation at high temperatures in the Weinberg-Salam model is discussed. The first lecture presents a discussion of anomalies, and how this is related to level crossing of energy levels in the Dirac equation for fermions in an external field. The second lecture discusses topological aspects of the Weinberg-Salam theory, and some related two dimensional models. The sphaleron solution of these theories is constructed. In the final lecture, the sphaleron is related to transition rates at finite temperature. In a simple quantum mechanics model, it is shown that sphalerons, not instantons, are responsible for transitions at high temperature. The sphaleron induced rate is then discussed in a solvable 1+1 dimensional model, which has many similarities to the Weinberg-Salam model. Finally, the result for the Weinberg-Salam model is derived and is shown to be large for temperatures T ≥ 1 TeV. 35 refs., 9 figs. (author)

  20. A Simulated Annealing-Based Heuristic Algorithm for Job Shop Scheduling to Minimize Lateness

    Directory of Open Access Journals (Sweden)

    Rui Zhang

    2013-04-01

    Full Text Available A decomposition-based optimization algorithm is proposed for solving large job shop scheduling problems with the objective of minimizing the maximum lateness. First, we use the constraint propagation theory to derive the orientation of a portion of disjunctive arcs. Then we use a simulated annealing algorithm to find a decomposition policy which satisfies the maximum number of oriented disjunctive arcs. Subsequently, each subproblem (corresponding to a subset of operations as determined by the decomposition policy is successively solved with a simulated annealing algorithm, which leads to a feasible solution to the original job shop scheduling problem. Computational experiments are carried out for adapted benchmark problems, and the results show the proposed algorithm is effective and efficient in terms of solution quality and time performance.

  1. An Instructional Model for Teaching Proof Writing in the Number Theory Classroom

    Science.gov (United States)

    Schabel, Carmen

    2005-01-01

    I discuss an instructional model that I have used in my number theory classes. Facets of the model include using small group work and whole class discussion, having students generate examples and counterexamples, and giving students the opportunity to write proofs and make conjectures in class. The model is designed to actively engage students in…

  2. Algebraic Algorithm Design and Local Search

    National Research Council Canada - National Science Library

    Graham, Robert

    1996-01-01

    .... Algebraic techniques have been applied successfully to algorithm synthesis by the use of algorithm theories and design tactics, an approach pioneered in the Kestrel Interactive Development System (KIDS...

  3. Stochastic Reformulations of Linear Systems: Algorithms and Convergence Theory

    KAUST Repository

    Richtarik, Peter; Taká č, Martin

    2017-01-01

    We develop a family of reformulations of an arbitrary consistent linear system into a stochastic problem. The reformulations are governed by two user-defined parameters: a positive definite matrix defining a norm, and an arbitrary discrete or continuous distribution over random matrices. Our reformulation has several equivalent interpretations, allowing for researchers from various communities to leverage their domain specific insights. In particular, our reformulation can be equivalently seen as a stochastic optimization problem, stochastic linear system, stochastic fixed point problem and a probabilistic intersection problem. We prove sufficient, and necessary and sufficient conditions for the reformulation to be exact. Further, we propose and analyze three stochastic algorithms for solving the reformulated problem---basic, parallel and accelerated methods---with global linear convergence rates. The rates can be interpreted as condition numbers of a matrix which depends on the system matrix and on the reformulation parameters. This gives rise to a new phenomenon which we call stochastic preconditioning, and which refers to the problem of finding parameters (matrix and distribution) leading to a sufficiently small condition number. Our basic method can be equivalently interpreted as stochastic gradient descent, stochastic Newton method, stochastic proximal point method, stochastic fixed point method, and stochastic projection method, with fixed stepsize (relaxation parameter), applied to the reformulations.

  4. Stochastic Reformulations of Linear Systems: Algorithms and Convergence Theory

    KAUST Repository

    Richtarik, Peter

    2017-06-04

    We develop a family of reformulations of an arbitrary consistent linear system into a stochastic problem. The reformulations are governed by two user-defined parameters: a positive definite matrix defining a norm, and an arbitrary discrete or continuous distribution over random matrices. Our reformulation has several equivalent interpretations, allowing for researchers from various communities to leverage their domain specific insights. In particular, our reformulation can be equivalently seen as a stochastic optimization problem, stochastic linear system, stochastic fixed point problem and a probabilistic intersection problem. We prove sufficient, and necessary and sufficient conditions for the reformulation to be exact. Further, we propose and analyze three stochastic algorithms for solving the reformulated problem---basic, parallel and accelerated methods---with global linear convergence rates. The rates can be interpreted as condition numbers of a matrix which depends on the system matrix and on the reformulation parameters. This gives rise to a new phenomenon which we call stochastic preconditioning, and which refers to the problem of finding parameters (matrix and distribution) leading to a sufficiently small condition number. Our basic method can be equivalently interpreted as stochastic gradient descent, stochastic Newton method, stochastic proximal point method, stochastic fixed point method, and stochastic projection method, with fixed stepsize (relaxation parameter), applied to the reformulations.

  5. A new fast algorithm for computing a complex number: Theoretic transforms

    Science.gov (United States)

    Reed, I. S.; Liu, K. Y.; Truong, T. K.

    1977-01-01

    A high-radix fast Fourier transformation (FFT) algorithm for computing transforms over GF(sq q), where q is a Mersenne prime, is developed to implement fast circular convolutions. This new algorithm requires substantially fewer multiplications than the conventional FFT.

  6. Fast clustering algorithm for large ECG data sets based on CS theory in combination with PCA and K-NN methods.

    Science.gov (United States)

    Balouchestani, Mohammadreza; Krishnan, Sridhar

    2014-01-01

    Long-term recording of Electrocardiogram (ECG) signals plays an important role in health care systems for diagnostic and treatment purposes of heart diseases. Clustering and classification of collecting data are essential parts for detecting concealed information of P-QRS-T waves in the long-term ECG recording. Currently used algorithms do have their share of drawbacks: 1) clustering and classification cannot be done in real time; 2) they suffer from huge energy consumption and load of sampling. These drawbacks motivated us in developing novel optimized clustering algorithm which could easily scan large ECG datasets for establishing low power long-term ECG recording. In this paper, we present an advanced K-means clustering algorithm based on Compressed Sensing (CS) theory as a random sampling procedure. Then, two dimensionality reduction methods: Principal Component Analysis (PCA) and Linear Correlation Coefficient (LCC) followed by sorting the data using the K-Nearest Neighbours (K-NN) and Probabilistic Neural Network (PNN) classifiers are applied to the proposed algorithm. We show our algorithm based on PCA features in combination with K-NN classifier shows better performance than other methods. The proposed algorithm outperforms existing algorithms by increasing 11% classification accuracy. In addition, the proposed algorithm illustrates classification accuracy for K-NN and PNN classifiers, and a Receiver Operating Characteristics (ROC) area of 99.98%, 99.83%, and 99.75% respectively.

  7. An algorithm for gluinos on the lattice

    International Nuclear Information System (INIS)

    Montvay, I.

    1995-10-01

    Luescher's local bosonic algorithm for Monte Carlo simulations of quantum field theories with fermions is applied to the simulation of a possibly supersymmetric Yang-Mills theory with a Majorana fermion in the adjoint representation. Combined with a correction step in a two-step polynomial approximation scheme, the obtained algorithm seems to be promising and could be competitive with more conventional algorithms based on discretized classical (''molecular dynamics'') equations of motion. The application of the considered polynomial approximation scheme to optimized hopping parameter expansions is also discussed. (orig.)

  8. A demand response modeling for residential consumers in smart grid environment using game theory based energy scheduling algorithm

    Directory of Open Access Journals (Sweden)

    S. Sofana Reka

    2016-06-01

    Full Text Available In this paper, demand response modeling scheme is proposed for residential consumers using game theory algorithm as Generalized Tit for Tat (GTFT Dominant Game based Energy Scheduler. The methodology is established as a work flow domain model between the utility and the user considering the smart grid framework. It exhibits an algorithm which schedules load usage by creating several possible tariffs for consumers such that demand is never raised. This can be done both individually and among multiple users of a community. The uniqueness behind the demand response proposed is that, the tariff is calculated for all hours and the load during the peak hours which can be rescheduled is shifted based on the Peak Average Ratio. To enable the vitality of the work simulation results of a general case of three domestic consumers are modeled extended to a comparative performance and evaluation with other algorithms and inference is analyzed.

  9. A trust evaluation algorithm for wireless sensor networks based on node behaviors and D-S evidence theory.

    Science.gov (United States)

    Feng, Renjian; Xu, Xiaofeng; Zhou, Xiang; Wan, Jiangwen

    2011-01-01

    For wireless sensor networks (WSNs), many factors, such as mutual interference of wireless links, battlefield applications and nodes exposed to the environment without good physical protection, result in the sensor nodes being more vulnerable to be attacked and compromised. In order to address this network security problem, a novel trust evaluation algorithm defined as NBBTE (Node Behavioral Strategies Banding Belief Theory of the Trust Evaluation Algorithm) is proposed, which integrates the approach of nodes behavioral strategies and modified evidence theory. According to the behaviors of sensor nodes, a variety of trust factors and coefficients related to the network application are established to obtain direct and indirect trust values through calculating weighted average of trust factors. Meanwhile, the fuzzy set method is applied to form the basic input vector of evidence. On this basis, the evidence difference is calculated between the indirect and direct trust values, which link the revised D-S evidence combination rule to finally synthesize integrated trust value of nodes. The simulation results show that NBBTE can effectively identify malicious nodes and reflects the characteristic of trust value that 'hard to acquire and easy to lose'. Furthermore, it is obvious that the proposed scheme has an outstanding advantage in terms of illustrating the real contribution of different nodes to trust evaluation.

  10. A density distribution algorithm for bone incorporating local orthotropy, modal analysis and theories of cellular solids.

    Science.gov (United States)

    Impelluso, Thomas J

    2003-06-01

    An algorithm for bone remodeling is presented which allows for both a redistribution of density and a continuous change of principal material directions for the orthotropic material properties of bone. It employs a modal analysis to add density for growth and a local effective strain based analysis to redistribute density. General re-distribution functions are presented. The model utilizes theories of cellular solids to relate density and strength. The code predicts the same general density distributions and local orthotropy as observed in reality.

  11. Control Systems and Number Theory

    Directory of Open Access Journals (Sweden)

    Fuhuo Li

    2012-01-01

    and PID-controllers are applied successfully in the EV control by J.-Y. Cao and B.-G. Cao 2006 and Cao et al. 2007, which we may unify in our framework. Finally, we mention some similarities between control theory and zeta-functions.

  12. Reference Frame Fields based on Quantum Theory Representations of Real and Complex Numbers

    OpenAIRE

    Benioff, Paul

    2007-01-01

    A quantum theory representations of real (R) and complex (C) numbers is given that is based on states of single, finite strings of qukits for any base k > 1. Both unary representations and the possibility that qukits with k a prime number are elementary and the rest composite are discussed. Cauchy sequences of qukit string states are defined from the arithmetic properties. The representations of R and C, as equivalence classes of these sequences, differ from classical kit string state represe...

  13. Combinatorial optimization algorithms and complexity

    CERN Document Server

    Papadimitriou, Christos H

    1998-01-01

    This clearly written, mathematically rigorous text includes a novel algorithmic exposition of the simplex method and also discusses the Soviet ellipsoid algorithm for linear programming; efficient algorithms for network flow, matching, spanning trees, and matroids; the theory of NP-complete problems; approximation algorithms, local search heuristics for NP-complete problems, more. All chapters are supplemented by thought-provoking problems. A useful work for graduate-level students with backgrounds in computer science, operations research, and electrical engineering.

  14. A Refined Self-Tuning Filter-Based Instantaneous Power Theory Algorithm for Indirect Current Controlled Three-Level Inverter-Based Shunt Active Power Filters under Non-sinusoidal Source Voltage Conditions

    Directory of Open Access Journals (Sweden)

    Yap Hoon

    2017-02-01

    Full Text Available In this paper, a refined reference current generation algorithm based on instantaneous power (pq theory is proposed, for operation of an indirect current controlled (ICC three-level neutral-point diode clamped (NPC inverter-based shunt active power filter (SAPF under non-sinusoidal source voltage conditions. SAPF is recognized as one of the most effective solutions to current harmonics due to its flexibility in dealing with various power system conditions. As for its controller, pq theory has widely been applied to generate the desired reference current due to its simple implementation features. However, the conventional dependency on self-tuning filter (STF in generating reference current has significantly limited mitigation performance of SAPF. Besides, the conventional STF-based pq theory algorithm is still considered to possess needless features which increase computational complexity. Furthermore, the conventional algorithm is mostly designed to suit operation of direct current controlled (DCC SAPF which is incapable of handling switching ripples problems, thereby leading to inefficient mitigation performance. Therefore, three main improvements are performed which include replacement of STF with mathematical-based fundamental real power identifier, removal of redundant features, and generation of sinusoidal reference current. To validate effectiveness and feasibility of the proposed algorithm, simulation work in MATLAB-Simulink and laboratory test utilizing a TMS320F28335 digital signal processor (DSP are performed. Both simulation and experimental findings demonstrate superiority of the proposed algorithm over the conventional algorithm.

  15. Lattice gauge calculation in particle theory

    International Nuclear Information System (INIS)

    Barkai, D.; Moriarty, K.J.M.; Rebbi, C.; Brookhaven National Lab., Upton, NY

    1985-01-01

    There are many problems in particle physics which cannot be treated analytically, but are amenable to numcerical solution using today's most powerful computers. Prominent among such problems are those encountered in the theory of strong interactions, where the resolution of fundamental issues such as demonstrating quark confinement or evaluating hadronic structure is rooted in a successful description of the behaviour of a very large number of dynamical variables in non-linear interaction. This paper briefly outlines the mathematical problems met in the formulation of the quantum field theory for strong interactions, the motivation for numerical methods of resolution and the algorithms which are currently being used. Such algorithms require very large amounts of memory and computation and, because of their organized structure, are ideally suited for implementation on mainframes with vectorized architecture. While the details of the actual implementation will be coverd in other contributions to this conference, this paper will present an account of the most important physics results obtained up to now and will conclude with a survey of open problems in particle theory which could be solved numerically in the near future. (orig.)

  16. Lattice gauge calculation in particle theory

    International Nuclear Information System (INIS)

    Barkai, D.; Moriarity, K.J.M.; Rebbi, C.

    1985-01-01

    There are many problems in particle physics which cannot be treated analytically, but are amenable to numerical solution using today's most powerful computers. Prominent among such problems are those encountered in the theory of strong interactions, where the resolution of fundamental issues such as demonstrating quark confinement or evaluating hadronic structure is rooted in a successful description of the behavior of a very large number of dynamical variables in non-linear interaction. This paper briefly outlines the mathematical problems met in the formulation of the quantum field theory for strong interactions, the motivation for numerical methods of resolution and the algorithms which are currently being used. Such algorithms require very large amounts of memory and computation and, because of their organized structure, are ideally suited for implementation on mainframes with vectorized architecture. While the details of the actual implementation will be covered in other contributions to this conference, this paper will present an account of the most important physics results obtained up to now and will conclude with a survey of open problems in particle theory which could be solved numerically in the near future

  17. Lattice gauge calculation in particle theory

    Energy Technology Data Exchange (ETDEWEB)

    Barkai, D [Control Data Corp., Fort Collins, CO (USA); Moriarty, K J.M. [Dalhousie Univ., Halifax, Nova Scotia (Canada). Inst. for Computational Studies; Rebbi, C [European Organization for Nuclear Research, Geneva (Switzerland); Brookhaven National Lab., Upton, NY (USA). Physics Dept.)

    1985-05-01

    There are many problems in particle physics which cannot be treated analytically, but are amenable to numcerical solution using today's most powerful computers. Prominent among such problems are those encountered in the theory of strong interactions, where the resolution of fundamental issues such as demonstrating quark confinement or evaluating hadronic structure is rooted in a successful description of the behaviour of a very large number of dynamical variables in non-linear interaction. This paper briefly outlines the mathematical problems met in the formulation of the quantum field theory for strong interactions, the motivation for numerical methods of resolution and the algorithms which are currently being used. Such algorithms require very large amounts of memory and computation and, because of their organized structure, are ideally suited for implementation on mainframes with vectorized architecture. While the details of the actual implementation will be coverd in other contributions to this conference, this paper will present an account of the most important physics results obtained up to now and will conclude with a survey of open problems in particle theory which could be solved numerically in the near future.

  18. A methodology for finding the optimal iteration number of the SIRT algorithm for quantitative Electron Tomography

    Energy Technology Data Exchange (ETDEWEB)

    Okariz, Ana, E-mail: ana.okariz@ehu.es [eMERG, Fisika Aplikatua I Saila, Faculty of Engineering, University of the Basque Country, UPV/EHU, Rafael Moreno “Pitxitxi” Pasealekua 3, 48013 Bilbao (Spain); Guraya, Teresa [eMERG, Departamento de Ingeniería Minera y Metalúrgica y Ciencia de los Materiales, Faculty of Engineering, University of the Basque Country, UPV/EHU, Rafael Moreno “Pitxitxi” Pasealekua 3, 48013 Bilbao (Spain); Iturrondobeitia, Maider [eMERG, Departamento de Expresión Gráfica y Proyectos de Ingeniería, Faculty of Engineering, University of the Basque Country, UPV/EHU, Rafael Moreno “Pitxitxi” Pasealekua 3, 48013 Bilbao (Spain); Ibarretxe, Julen [eMERG, Fisika Aplikatua I Saila, Faculty of Engineering,University of the Basque Country, UPV/EHU, Rafael Moreno “Pitxitxi” Pasealekua 2, 48013 Bilbao (Spain)

    2017-02-15

    The SIRT (Simultaneous Iterative Reconstruction Technique) algorithm is commonly used in Electron Tomography to calculate the original volume of the sample from noisy images, but the results provided by this iterative procedure are strongly dependent on the specific implementation of the algorithm, as well as on the number of iterations employed for the reconstruction. In this work, a methodology for selecting the iteration number of the SIRT reconstruction that provides the most accurate segmentation is proposed. The methodology is based on the statistical analysis of the intensity profiles at the edge of the objects in the reconstructed volume. A phantom which resembles a a carbon black aggregate has been created to validate the methodology and the SIRT implementations of two free software packages (TOMOJ and TOMO3D) have been used. - Highlights: • The non uniformity of the resolution in electron tomography reconstructions has been demonstrated. • An overall resolution for the evaluation of the quality of electron tomography reconstructions has been defined. • Parameters for estimating an overall resolution across the reconstructed volume have been proposed. • The overall resolution of the reconstructions of a phantom has been estimated from the probability density functions. • It has been proven that reconstructions with the best overall resolutions have provided the most accurate segmentations.

  19. A methodology for finding the optimal iteration number of the SIRT algorithm for quantitative Electron Tomography

    International Nuclear Information System (INIS)

    Okariz, Ana; Guraya, Teresa; Iturrondobeitia, Maider; Ibarretxe, Julen

    2017-01-01

    The SIRT (Simultaneous Iterative Reconstruction Technique) algorithm is commonly used in Electron Tomography to calculate the original volume of the sample from noisy images, but the results provided by this iterative procedure are strongly dependent on the specific implementation of the algorithm, as well as on the number of iterations employed for the reconstruction. In this work, a methodology for selecting the iteration number of the SIRT reconstruction that provides the most accurate segmentation is proposed. The methodology is based on the statistical analysis of the intensity profiles at the edge of the objects in the reconstructed volume. A phantom which resembles a a carbon black aggregate has been created to validate the methodology and the SIRT implementations of two free software packages (TOMOJ and TOMO3D) have been used. - Highlights: • The non uniformity of the resolution in electron tomography reconstructions has been demonstrated. • An overall resolution for the evaluation of the quality of electron tomography reconstructions has been defined. • Parameters for estimating an overall resolution across the reconstructed volume have been proposed. • The overall resolution of the reconstructions of a phantom has been estimated from the probability density functions. • It has been proven that reconstructions with the best overall resolutions have provided the most accurate segmentations.

  20. [Experimental Course in Elementary Number Theory, Cambridge Conference on School Mathematics Feasibility Study No. 35.

    Science.gov (United States)

    Hatch, Mary Jacqueline

    In the winter of 1965, an experimental course in Elementary Number Theory was presented to a 6th grade class in the Hosmer School, Watertown, Massachusetts. Prior to the introduction of the present material, students had been exposed in class to such topics from the University of Illinois Arithmetic Project as lattices, number lines, frame…

  1. Time-dependent quantum many-body theory of identical bosons in a double well: Early-time ballistic interferences of fragmented and number entangled states

    International Nuclear Information System (INIS)

    Masiello, David J.; Reinhardt, William P.

    2007-01-01

    A time-dependent multiconfigurational self-consistent field theory is presented to describe the many-body dynamics of a gas of identical bosonic atoms confined to an external trapping potential at zero temperature from first principles. A set of generalized evolution equations are developed, through the time-dependent variational principle, which account for the complete and self-consistent coupling between the expansion coefficients of each configuration and the underlying one-body wave functions within a restricted two state Fock space basis that includes the full effects of the condensate's mean field as well as atomic correlation. The resulting dynamical equations are a classical Hamiltonian system and, by construction, form a well-defined initial value problem. They are implemented in an efficient numerical algorithm. An example is presented, highlighting the generality of the theory, in which the ballistic expansion of a fragmented condensate ground state is compared to that of a macroscopic quantum superposition state, taken here to be a highly entangled number state, upon releasing the external trapping potential. Strikingly different many-body matter-wave dynamics emerge in each case, accentuating the role of both atomic correlation and mean-field effects in the two condensate states

  2. Graph theory

    CERN Document Server

    Gould, Ronald

    2012-01-01

    This introduction to graph theory focuses on well-established topics, covering primary techniques and including both algorithmic and theoretical problems. The algorithms are presented with a minimum of advanced data structures and programming details. This thoroughly corrected 1988 edition provides insights to computer scientists as well as advanced undergraduates and graduate students of topology, algebra, and matrix theory. Fundamental concepts and notation and elementary properties and operations are the first subjects, followed by examinations of paths and searching, trees, and networks. S

  3. Majorization arrow in quantum-algorithm design

    International Nuclear Information System (INIS)

    Latorre, J.I.; Martin-Delgado, M.A.

    2002-01-01

    We apply majorization theory to study the quantum algorithms known so far and find that there is a majorization principle underlying the way they operate. Grover's algorithm is a neat instance of this principle where majorization works step by step until the optimal target state is found. Extensions of this situation are also found in algorithms based in quantum adiabatic evolution and the family of quantum phase-estimation algorithms, including Shor's algorithm. We state that in quantum algorithms the time arrow is a majorization arrow

  4. How random are random numbers generated using photons?

    International Nuclear Information System (INIS)

    Solis, Aldo; Angulo Martínez, Alí M; Ramírez Alarcón, Roberto; Cruz Ramírez, Hector; U’Ren, Alfred B; Hirsch, Jorge G

    2015-01-01

    Randomness is fundamental in quantum theory, with many philosophical and practical implications. In this paper we discuss the concept of algorithmic randomness, which provides a quantitative method to assess the Borel normality of a given sequence of numbers, a necessary condition for it to be considered random. We use Borel normality as a tool to investigate the randomness of ten sequences of bits generated from the differences between detection times of photon pairs generated by spontaneous parametric downconversion. These sequences are shown to fulfil the randomness criteria without difficulties. As deviations from Borel normality for photon-generated random number sequences have been reported in previous work, a strategy to understand these diverging findings is outlined. (paper)

  5. Coding theory on the m-extension of the Fibonacci p-numbers

    International Nuclear Information System (INIS)

    Basu, Manjusri; Prasad, Bandhu

    2009-01-01

    In this paper, we introduce a new Fibonacci G p,m matrix for the m-extension of the Fibonacci p-numbers where p (≥0) is integer and m (>0). Thereby, we discuss various properties of G p,m matrix and the coding theory followed from the G p,m matrix. In this paper, we establish the relations among the code elements for all values of p (nonnegative integer) and m(>0). We also show that the relation, among the code matrix elements for all values of p and m=1, coincides with the relation among the code matrix elements for all values of p [Basu M, Prasad B. The generalized relations among the code elements for Fibonacci coding theory. Chaos, Solitons and Fractals (2008). doi: 10.1016/j.chaos.2008.09.030]. In general, correct ability of the method increases as p increases but it is independent of m.

  6. A robust variant of block Jacobi-Davidson for extracting a large number of eigenpairs: Application to grid-based real-space density functional theory

    Science.gov (United States)

    Lee, M.; Leiter, K.; Eisner, C.; Breuer, A.; Wang, X.

    2017-09-01

    In this work, we investigate a block Jacobi-Davidson (J-D) variant suitable for sparse symmetric eigenproblems where a substantial number of extremal eigenvalues are desired (e.g., ground-state real-space quantum chemistry). Most J-D algorithm variations tend to slow down as the number of desired eigenpairs increases due to frequent orthogonalization against a growing list of solved eigenvectors. In our specification of block J-D, all of the steps of the algorithm are performed in clusters, including the linear solves, which allows us to greatly reduce computational effort with blocked matrix-vector multiplies. In addition, we move orthogonalization against locked eigenvectors and working eigenvectors outside of the inner loop but retain the single Ritz vector projection corresponding to the index of the correction vector. Furthermore, we minimize the computational effort by constraining the working subspace to the current vectors being updated and the latest set of corresponding correction vectors. Finally, we incorporate accuracy thresholds based on the precision required by the Fermi-Dirac distribution. The net result is a significant reduction in the computational effort against most previous block J-D implementations, especially as the number of wanted eigenpairs grows. We compare our approach with another robust implementation of block J-D (JDQMR) and the state-of-the-art Chebyshev filter subspace (CheFSI) method for various real-space density functional theory systems. Versus CheFSI, for first-row elements, our method yields competitive timings for valence-only systems and 4-6× speedups for all-electron systems with up to 10× reduced matrix-vector multiplies. For all-electron calculations on larger elements (e.g., gold) where the wanted spectrum is quite narrow compared to the full spectrum, we observe 60× speedup with 200× fewer matrix-vector multiples vs. CheFSI.

  7. Optimal solution for travelling salesman problem using heuristic shortest path algorithm with imprecise arc length

    Science.gov (United States)

    Bakar, Sumarni Abu; Ibrahim, Milbah

    2017-08-01

    The shortest path problem is a popular problem in graph theory. It is about finding a path with minimum length between a specified pair of vertices. In any network the weight of each edge is usually represented in a form of crisp real number and subsequently the weight is used in the calculation of shortest path problem using deterministic algorithms. However, due to failure, uncertainty is always encountered in practice whereby the weight of edge of the network is uncertain and imprecise. In this paper, a modified algorithm which utilized heuristic shortest path method and fuzzy approach is proposed for solving a network with imprecise arc length. Here, interval number and triangular fuzzy number in representing arc length of the network are considered. The modified algorithm is then applied to a specific example of the Travelling Salesman Problem (TSP). Total shortest distance obtained from this algorithm is then compared with the total distance obtained from traditional nearest neighbour heuristic algorithm. The result shows that the modified algorithm can provide not only on the sequence of visited cities which shown to be similar with traditional approach but it also provides a good measurement of total shortest distance which is lesser as compared to the total shortest distance calculated using traditional approach. Hence, this research could contribute to the enrichment of methods used in solving TSP.

  8. An IDS Alerts Aggregation Algorithm Based on Rough Set Theory

    Science.gov (United States)

    Zhang, Ru; Guo, Tao; Liu, Jianyi

    2018-03-01

    Within a system in which has been deployed several IDS, a great number of alerts can be triggered by a single security event, making real alerts harder to be found. To deal with redundant alerts, we propose a scheme based on rough set theory. In combination with basic concepts in rough set theory, the importance of attributes in alerts was calculated firstly. With the result of attributes importance, we could compute the similarity of two alerts, which will be compared with a pre-defined threshold to determine whether these two alerts can be aggregated or not. Also, time interval should be taken into consideration. Allowed time interval for different types of alerts is computed individually, since different types of alerts may have different time gap between two alerts. In the end of this paper, we apply proposed scheme on DAPRA98 dataset and the results of experiment show that our scheme can efficiently reduce the redundancy of alerts so that administrators of security system could avoid wasting time on useless alerts.

  9. Fuzzy 2-partition entropy threshold selection based on Big Bang–Big Crunch Optimization algorithm

    Directory of Open Access Journals (Sweden)

    Baljit Singh Khehra

    2015-03-01

    Full Text Available The fuzzy 2-partition entropy approach has been widely used to select threshold value for image segmenting. This approach used two parameterized fuzzy membership functions to form a fuzzy 2-partition of the image. The optimal threshold is selected by searching an optimal combination of parameters of the membership functions such that the entropy of fuzzy 2-partition is maximized. In this paper, a new fuzzy 2-partition entropy thresholding approach based on the technology of the Big Bang–Big Crunch Optimization (BBBCO is proposed. The new proposed thresholding approach is called the BBBCO-based fuzzy 2-partition entropy thresholding algorithm. BBBCO is used to search an optimal combination of parameters of the membership functions for maximizing the entropy of fuzzy 2-partition. BBBCO is inspired by the theory of the evolution of the universe; namely the Big Bang and Big Crunch Theory. The proposed algorithm is tested on a number of standard test images. For comparison, three different algorithms included Genetic Algorithm (GA-based, Biogeography-based Optimization (BBO-based and recursive approaches are also implemented. From experimental results, it is observed that the performance of the proposed algorithm is more effective than GA-based, BBO-based and recursion-based approaches.

  10. Automated computation of one-loop integrals in massless theories

    International Nuclear Information System (INIS)

    Hameren, A. van; Vollinga, J.; Weinzierl, S.

    2005-01-01

    We consider one-loop tensor and scalar integrals, which occur in a massless quantum field theory, and we report on the implementation into a numerical program of an algorithm for the automated computation of these one-loop integrals. The number of external legs of the loop integrals is not restricted. All calculations are done within dimensional regularization. (orig.)

  11. Multi objective optimization of horizontal axis tidal current turbines, using Meta heuristics algorithms

    International Nuclear Information System (INIS)

    Tahani, Mojtaba; Babayan, Narek; Astaraei, Fatemeh Razi; Moghadam, Ali

    2015-01-01

    Highlights: • The performance of four different Meta heuristic optimization algorithms was studied. • Power coefficient and produced torque on stationary blade were selected as objective functions. • Chord and twist distributions were selected as decision variables. • All optimization algorithms were combined with blade element momentum theory. • The best Pareto front was obtained by multi objective flower pollination algorithm for HATCTs. - Abstract: The performance of horizontal axis tidal current turbines (HATCT) strongly depends on their geometry. According to this fact, the optimum performance will be achieved by optimized geometry. In this research study, the multi objective optimization of the HATCT is carried out by using four different multi objective optimization algorithms and their performance is evaluated in combination with blade element momentum theory (BEM). The second version of non-dominated sorting genetic algorithm (NSGA-II), multi objective particle swarm optimization algorithm (MOPSO), multi objective cuckoo search algorithm (MOCS) and multi objective flower pollination algorithm (MOFPA) are the selected algorithms. The power coefficient and the produced torque on stationary blade are selected as objective functions and chord and twist distributions along the blade span are selected as decision variables. These algorithms are combined with the blade element momentum (BEM) theory for the purpose of achieving the best Pareto front. The obtained Pareto fronts are compared with each other. Different sets of experiments are carried out by considering different numbers of iterations, population size and tip speed ratios. The Pareto fronts which are achieved by MOFPA and NSGA-II have better quality in comparison to MOCS and MOPSO, but on the other hand a detail comparison between the first fronts of MOFPA and NSGA-II indicated that MOFPA algorithm can obtain the best Pareto front and can maximize the power coefficient up to 4.3% and the

  12. Perspective: Ring-polymer instanton theory

    Science.gov (United States)

    Richardson, Jeremy O.

    2018-05-01

    Since the earliest explorations of quantum mechanics, it has been a topic of great interest that quantum tunneling allows particles to penetrate classically insurmountable barriers. Instanton theory provides a simple description of these processes in terms of dominant tunneling pathways. Using a ring-polymer discretization, an efficient computational method is obtained for applying this theory to compute reaction rates and tunneling splittings in molecular systems. Unlike other quantum-dynamics approaches, the method scales well with the number of degrees of freedom, and for many polyatomic systems, the method may provide the most accurate predictions which can be practically computed. Instanton theory thus has the capability to produce useful data for many fields of low-temperature chemistry including spectroscopy, atmospheric and astrochemistry, as well as surface science. There is however still room for improvement in the efficiency of the numerical algorithms, and new theories are under development for describing tunneling in nonadiabatic transitions.

  13. Ortega y Gasset on Georg Cantor’s Theory of Transfinite Numbers

    Directory of Open Access Journals (Sweden)

    Rabi Lior

    2016-04-01

    Full Text Available Ortega y Gasset is known for his philosophy of life and his effort to propose an alternative to both realism and idealism. The goal of this article is to focus on an unfamiliar aspect of his thought. The focus will be given to Ortega’s interpretation of the advancements in modern mathematics in general and Cantor’s theory of transfinite numbers in particular. The main argument is that Ortega acknowledged the historical importance of the Cantor’s Set Theory, analyzed it and articulated a response to it. In his writings he referred many times to the advancements in modern mathematics and argued that mathematics should be based on the intuition of counting. In response to Cantor’s mathematics Ortega presented what he defined as an ‘absolute positivism’. In this theory he did not mean to naturalize cognition or to follow the guidelines of the Comte’s positivism, on the contrary. His aim was to present an alternative to Cantor’s mathematics by claiming that mathematicians are allowed to deal only with objects that are immediately present and observable to intuition. Ortega argued that the infinite set cannot be present to the intuition and therefore there is no use to differentiate between cardinals of different infinite sets.

  14. Triangular Numbers

    Indian Academy of Sciences (India)

    Admin

    Triangular number, figurate num- ber, rangoli, Brahmagupta–Pell equation, Jacobi triple product identity. Figure 1. The first four triangular numbers. Left: Anuradha S Garge completed her PhD from. Pune University in 2008 under the supervision of Prof. S A Katre. Her research interests include K-theory and number theory.

  15. Two- and three-dimensional nonlocal density functional theory for inhomogeneous fluids. 1. Algorithms and parallelization

    International Nuclear Information System (INIS)

    Frink, L.J.D.; Salinger, A.G.

    2000-01-01

    Fluids adsorbed near surfaces, near macromolecules, and in porous materials are inhomogeneous, exhibiting spatially varying density distributions. This inhomogeneity in the fluid plays an important role in controlling a wide variety of complex physical phenomena including wetting, self-assembly, corrosion, and molecular recognition. One of the key methods for studying the properties of inhomogeneous fluids in simple geometries has been density functional theory (DFT). However, there has been a conspicuous lack of calculations in complex two- and three-dimensional geometries. The computational difficulty arises from the need to perform nested integrals that are due to nonlocal terms in the free energy functional. These integral equations are expensive both in evaluation time and in memory requirements; however, the expense can be mitigated by intelligent algorithms and the use of parallel computers. This paper details the efforts to develop efficient numerical algorithms so that nonlocal DFT calculations in complex geometries that require two or three dimensions can be performed. The success of this implementation will enable the study of solvation effects at heterogeneous surfaces, in zeolites, in solvated (bio)polymers, and in colloidal suspensions

  16. Computing molecular fluctuations in biochemical reaction systems based on a mechanistic, statistical theory of irreversible processes.

    Science.gov (United States)

    Kulasiri, Don

    2011-01-01

    We discuss the quantification of molecular fluctuations in the biochemical reaction systems within the context of intracellular processes associated with gene expression. We take the molecular reactions pertaining to circadian rhythms to develop models of molecular fluctuations in this chapter. There are a significant number of studies on stochastic fluctuations in intracellular genetic regulatory networks based on single cell-level experiments. In order to understand the fluctuations associated with the gene expression in circadian rhythm networks, it is important to model the interactions of transcriptional factors with the E-boxes in the promoter regions of some of the genes. The pertinent aspects of a near-equilibrium theory that would integrate the thermodynamical and particle dynamic characteristics of intracellular molecular fluctuations would be discussed, and the theory is extended by using the theory of stochastic differential equations. We then model the fluctuations associated with the promoter regions using general mathematical settings. We implemented ubiquitous Gillespie's algorithms, which are used to simulate stochasticity in biochemical networks, for each of the motifs. Both the theory and the Gillespie's algorithms gave the same results in terms of the time evolution of means and variances of molecular numbers. As biochemical reactions occur far away from equilibrium-hence the use of the Gillespie algorithm-these results suggest that the near-equilibrium theory should be a good approximation for some of the biochemical reactions. © 2011 Elsevier Inc. All rights reserved.

  17. A Combined Algorithm for Optimization: Application for Optimization of the Transition Gas-Liquid in Stirred Tank Bioreactors

    Directory of Open Access Journals (Sweden)

    Mitko Petrov

    2005-12-01

    Full Text Available A combined algorithm for static optimization is developed. The algorithm includes a method for random search of optimal an initial point and a method based on fuzzy sets theory, combined in order to be found for the best solution of the optimization problem. The application of the combined algorithm eliminates the main disadvantage of the used fuzzy optimization method, namely decreases the number of discrete values of control variables. In this way, the algorithm allows problems with larger scale to be solved. The combined algorithm is used for optimization of gas-liquid transition in dependence on some constructive and regime parameters of a laboratory scale stirred tank bioreactor. After the application of developed optimization algorithm significant increase of mass-transfer effectiveness, aeration and mixing processes in the bioreactor are observed.

  18. Autonomous intelligent vehicles theory, algorithms, and implementation

    CERN Document Server

    Cheng, Hong

    2011-01-01

    Here is the latest on intelligent vehicles, covering object and obstacle detection and recognition and vehicle motion control. Includes a navigation approach using global views; introduces algorithms for lateral and longitudinal motion control and more.

  19. Parallel Algorithms for Switching Edges in Heterogeneous Graphs.

    Science.gov (United States)

    Bhuiyan, Hasanuzzaman; Khan, Maleq; Chen, Jiangzhuo; Marathe, Madhav

    2017-06-01

    An edge switch is an operation on a graph (or network) where two edges are selected randomly and one of their end vertices are swapped with each other. Edge switch operations have important applications in graph theory and network analysis, such as in generating random networks with a given degree sequence, modeling and analyzing dynamic networks, and in studying various dynamic phenomena over a network. The recent growth of real-world networks motivates the need for efficient parallel algorithms. The dependencies among successive edge switch operations and the requirement to keep the graph simple (i.e., no self-loops or parallel edges) as the edges are switched lead to significant challenges in designing a parallel algorithm. Addressing these challenges requires complex synchronization and communication among the processors leading to difficulties in achieving a good speedup by parallelization. In this paper, we present distributed memory parallel algorithms for switching edges in massive networks. These algorithms provide good speedup and scale well to a large number of processors. A harmonic mean speedup of 73.25 is achieved on eight different networks with 1024 processors. One of the steps in our edge switch algorithms requires the computation of multinomial random variables in parallel. This paper presents the first non-trivial parallel algorithm for the problem, achieving a speedup of 925 using 1024 processors.

  20. Theory of viscous transonic flow over airfoils at high Reynolds number

    Science.gov (United States)

    Melnik, R. E.; Chow, R.; Mead, H. R.

    1977-01-01

    This paper considers viscous flows with unseparated turbulent boundary layers over two-dimensional airfoils at transonic speeds. Conventional theoretical methods are based on boundary layer formulations which do not account for the effect of the curved wake and static pressure variations across the boundary layer in the trailing edge region. In this investigation an extended viscous theory is developed that accounts for both effects. The theory is based on a rational analysis of the strong turbulent interaction at airfoil trailing edges. The method of matched asymptotic expansions is employed to develop formal series solutions of the full Reynolds equations in the limit of Reynolds numbers tending to infinity. Procedures are developed for combining the local trailing edge solution with numerical methods for solving the full potential flow and boundary layer equations. Theoretical results indicate that conventional boundary layer methods account for only about 50% of the viscous effect on lift, the remaining contribution arising from wake curvature and normal pressure gradient effects.

  1. A Trust Evaluation Algorithm for Wireless Sensor Networks Based on Node Behaviors and D-S Evidence Theory

    Directory of Open Access Journals (Sweden)

    Jiangwen Wan

    2011-01-01

    Full Text Available For wireless sensor networks (WSNs, many factors, such as mutual interference of wireless links, battlefield applications and nodes exposed to the environment without good physical protection, result in the sensor nodes being more vulnerable to be attacked and compromised. In order to address this network security problem, a novel trust evaluation algorithm defined as NBBTE (Node Behavioral Strategies Banding Belief Theory of the Trust Evaluation Algorithm is proposed, which integrates the approach of nodes behavioral strategies and modified evidence theory. According to the behaviors of sensor nodes, a variety of trust factors and coefficients related to the network application are established to obtain direct and indirect trust values through calculating weighted average of trust factors. Meanwhile, the fuzzy set method is applied to form the basic input vector of evidence. On this basis, the evidence difference is calculated between the indirect and direct trust values, which link the revised D-S evidence combination rule to finally synthesize integrated trust value of nodes. The simulation results show that NBBTE can effectively identify malicious nodes and reflects the characteristic of trust value that ‘hard to acquire and easy to lose’. Furthermore, it is obvious that the proposed scheme has an outstanding advantage in terms of illustrating the real contribution of different nodes to trust evaluation.

  2. Statistical behaviour of adaptive multilevel splitting algorithms in simple models

    International Nuclear Information System (INIS)

    Rolland, Joran; Simonnet, Eric

    2015-01-01

    Adaptive multilevel splitting algorithms have been introduced rather recently for estimating tail distributions in a fast and efficient way. In particular, they can be used for computing the so-called reactive trajectories corresponding to direct transitions from one metastable state to another. The algorithm is based on successive selection–mutation steps performed on the system in a controlled way. It has two intrinsic parameters, the number of particles/trajectories and the reaction coordinate used for discriminating good or bad trajectories. We investigate first the convergence in law of the algorithm as a function of the timestep for several simple stochastic models. Second, we consider the average duration of reactive trajectories for which no theoretical predictions exist. The most important aspect of this work concerns some systems with two degrees of freedom. They are studied in detail as a function of the reaction coordinate in the asymptotic regime where the number of trajectories goes to infinity. We show that during phase transitions, the statistics of the algorithm deviate significatively from known theoretical results when using non-optimal reaction coordinates. In this case, the variance of the algorithm is peaking at the transition and the convergence of the algorithm can be much slower than the usual expected central limit behaviour. The duration of trajectories is affected as well. Moreover, reactive trajectories do not correspond to the most probable ones. Such behaviour disappears when using the optimal reaction coordinate called committor as predicted by the theory. We finally investigate a three-state Markov chain which reproduces this phenomenon and show logarithmic convergence of the trajectory durations

  3. Transportation optimization with fuzzy trapezoidal numbers based on possibility theory.

    Science.gov (United States)

    He, Dayi; Li, Ran; Huang, Qi; Lei, Ping

    2014-01-01

    In this paper, a parametric method is introduced to solve fuzzy transportation problem. Considering that parameters of transportation problem have uncertainties, this paper develops a generalized fuzzy transportation problem with fuzzy supply, demand and cost. For simplicity, these parameters are assumed to be fuzzy trapezoidal numbers. Based on possibility theory and consistent with decision-makers' subjectiveness and practical requirements, the fuzzy transportation problem is transformed to a crisp linear transportation problem by defuzzifying fuzzy constraints and objectives with application of fractile and modality approach. Finally, a numerical example is provided to exemplify the application of fuzzy transportation programming and to verify the validity of the proposed methods.

  4. Designing and implementing of improved cryptographic algorithm using modular arithmetic theory

    Directory of Open Access Journals (Sweden)

    Maryam Kamarzarrin

    2015-05-01

    Full Text Available Maintaining the privacy and security of people information are two most important principles of electronic health plan. One of the methods of creating privacy and securing of information is using Public key cryptography system. In this paper, we compare two algorithms, Common And Fast Exponentiation algorithms, for enhancing the efficiency of public key cryptography. We express that a designed system by Fast Exponentiation Algorithm has high speed and performance but low power consumption and space occupied compared with Common Exponentiation algorithm. Although designed systems by Common Exponentiation algorithm have slower speed and lower performance, designing by this algorithm has less complexity, and easier designing compared with Fast Exponentiation algorithm. In this paper, we will try to examine and compare two different methods of exponentiation, also observe performance Impact of these two approaches in the form of hardware with VHDL language on FPGA.

  5. Dynamic route guidance algorithm based algorithm based on artificial immune system

    Institute of Scientific and Technical Information of China (English)

    2007-01-01

    To improve the performance of the K-shortest paths search in intelligent traffic guidance systems,this paper proposes an optimal search algorithm based on the intelligent optimization search theory and the memphor mechanism of vertebrate immune systems.This algorithm,applied to the urban traffic network model established by the node-expanding method,can expediently realize K-shortest paths search in the urban traffic guidance systems.Because of the immune memory and global parallel search ability from artificial immune systems,K shortest paths can be found without any repeat,which indicates evidently the superiority of the algorithm to the conventional ones.Not only does it perform a better parallelism,the algorithm also prevents premature phenomenon that often occurs in genetic algorithms.Thus,it is especially suitable for real-time requirement of the traffic guidance system and other engineering optimal applications.A case study verifies the efficiency and the practicability of the algorithm aforementioned.

  6. Machine Learning an algorithmic perspective

    CERN Document Server

    Marsland, Stephen

    2009-01-01

    Traditional books on machine learning can be divided into two groups - those aimed at advanced undergraduates or early postgraduates with reasonable mathematical knowledge and those that are primers on how to code algorithms. The field is ready for a text that not only demonstrates how to use the algorithms that make up machine learning methods, but also provides the background needed to understand how and why these algorithms work. Machine Learning: An Algorithmic Perspective is that text.Theory Backed up by Practical ExamplesThe book covers neural networks, graphical models, reinforcement le

  7. The Orthogonally Partitioned EM Algorithm: Extending the EM Algorithm for Algorithmic Stability and Bias Correction Due to Imperfect Data.

    Science.gov (United States)

    Regier, Michael D; Moodie, Erica E M

    2016-05-01

    We propose an extension of the EM algorithm that exploits the common assumption of unique parameterization, corrects for biases due to missing data and measurement error, converges for the specified model when standard implementation of the EM algorithm has a low probability of convergence, and reduces a potentially complex algorithm into a sequence of smaller, simpler, self-contained EM algorithms. We use the theory surrounding the EM algorithm to derive the theoretical results of our proposal, showing that an optimal solution over the parameter space is obtained. A simulation study is used to explore the finite sample properties of the proposed extension when there is missing data and measurement error. We observe that partitioning the EM algorithm into simpler steps may provide better bias reduction in the estimation of model parameters. The ability to breakdown a complicated problem in to a series of simpler, more accessible problems will permit a broader implementation of the EM algorithm, permit the use of software packages that now implement and/or automate the EM algorithm, and make the EM algorithm more accessible to a wider and more general audience.

  8. Integrality of the monopole number in SU(2) Yang-Mills-Higgs theory on R3

    International Nuclear Information System (INIS)

    Groisser, D.

    1984-01-01

    We prove that in classical SU(2) Yang-Mills-Higgs theories on R 3 with a Higgs field in the adjoint representation, an integer-valued monopole number (magnetic charge) is canonically defined for any finite-action L 2 sub(1,loc) configuration. In particular the result is true for smooth configurations. The monopole number is shown to decompose the configuration space into path components. (orig.)

  9. On the instabilities of supersonic mixing layers - A high-Mach-number asymptotic theory

    Science.gov (United States)

    Balsa, Thomas F.; Goldstein, M. E.

    1990-01-01

    The stability of a family of tanh mixing layers is studied at large Mach numbers using perturbation methods. It is found that the eigenfunction develops a multilayered structure, and the eigenvalue is obtained by solving a simplified version of the Rayleigh equation (with homogeneous boundary conditions) in one of these layers which lies in either of the external streams. This analysis leads to a simple hypersonic similarity law which explains how spatial and temporal phase speeds and growth rates scale with Mach number and temperature ratio. Comparisons are made with numerical results, and it is found that this similarity law provides a good qualitative guide for the behavior of the instability at high Mach numbers. In addition to this asymptotic theory, some fully numerical results are also presented (with no limitation on the Mach number) in order to explain the origin of the hypersonic modes (through mode splitting) and to discuss the role of oblique modes over a very wide range of Mach number and temperature ratio.

  10. Research about the number of D-points of -tiling in given ellipse

    Directory of Open Access Journals (Sweden)

    Xianglin WEI

    2017-04-01

    Full Text Available An Archimedean tiling is a tiling of the plane by one type of regular polygon or several types of regular polygons, and every vertex of the tiling has the same vertex characteristics. There are 11 Archimedean tiling, and this paper studies -tiling, which is an Archimedean tiling generated by squares and regular octagons in the plane, and every vertex is associated with one square and two octagons. This paper studies the number of vertices contained in an ellipse in -tiling. Through analysing the sequence of vertices lying on half chord in the ellipse, and using the method of the geometry of number and congruence in number theory, it presents an algorithm about the value of the number of vertices contained in the ellipse, and obtains a formula of limit about the number of vertices and the square of short semi-axis of the ellipse. It is proved that the value of limit is connected with the area of the corresponding central polygon. The algorithm and the formula of limit are very useful for the study of related problems in other Archimedean tilings.

  11. Fragmented metastable states exist in an attractive bose-einstein condensate for atom numbers well above the critical number of the Gross-Pitaevskii theory.

    Science.gov (United States)

    Cederbaum, Lorenz S; Streltsov, Alexej I; Alon, Ofir E

    2008-02-01

    It is well known that attractive condensates do not posses a stable ground state in three dimensions. The widely used Gross-Pitaevskii theory predicts the existence of metastable states up to some critical number N(cr)(GP) of atoms. It is demonstrated here that fragmented metastable states exist for atom numbers well above N(cr)(GP). The fragments are strongly overlapping in space. The results are obtained and analyzed analytically as well as numerically. The implications are discussed.

  12. Analytic operator approach to fermionic lattice field theories

    International Nuclear Information System (INIS)

    Duncan, A.

    1985-01-01

    An analytic Lanczos algorithm previously used to extract the spectrum of bosonic lattice field theories in the continuum region is extended to theories with fermions. The method is illustrated in detail for the (1+1)-dimensional Gross-Neveu model. All parameters in the model (coupling, lattice size N, number of fermion flavors Nsub(F), etc.) appear explicitly in analytic formulas for matrix elements of the hamiltonian. The method is applied to the calculation of the collective field vacuum expectation value and the mass gap, and excellent agreement obtained with explicit results available from the large Nsub(F) solution of the model. (orig.)

  13. Number-Theory in Nuclear-Physics in Number-Theory: Non-Primality Factorization As Fission VS. Primality As Fusion; Composites' Islands of INstability: Feshbach-Resonances?

    Science.gov (United States)

    Siegel, Edward

    2011-10-01

    Numbers: primality/indivisibility/non-factorization versus compositeness/divisibility /factor-ization, often in tandem but not always, provocatively close analogy to nuclear-physics: (2 + 1)=(fusion)=3; (3+1)=(fission)=4[=2 × 2]; (4+1)=(fusion)=5; (5 +1)=(fission)=6[=2 × 3]; (6 + 1)=(fusion)=7; (7+1)=(fission)=8[= 2 × 4 = 2 × 2 × 2]; (8 + 1) =(non: fission nor fusion)= 9[=3 × 3]; then ONLY composites' Islands of fusion-INstability: 8, 9, 10; then 14, 15, 16,... Could inter-digit Feshbach-resonances exist??? Applications to: quantum-information/computing non-Shore factorization, millennium-problem Riemann-hypotheses proof as Goodkin BEC intersection with graph-theory ``short-cut'' method: Rayleigh(1870)-Polya(1922)-``Anderson'' (1958)-localization, Goldbach-conjecture, financial auditing/accounting as quantum-statistical-physics;... abound!!!

  14. Optimization of the solution of the problem of scheduling theory ...

    African Journals Online (AJOL)

    This article describes the genetic algorithm used to solve the problem related to the scheduling theory. A large number of different methods is described in the scientific literature. The main issue that faced the problem in question is that it is necessary to search the optimal solution in a large search space for the set of ...

  15. Extreme Value Theory Applied to the Millennial Sunspot Number Series

    Science.gov (United States)

    Acero, F. J.; Gallego, M. C.; García, J. A.; Usoskin, I. G.; Vaquero, J. M.

    2018-01-01

    In this work, we use two decadal sunspot number series reconstructed from cosmogenic radionuclide data (14C in tree trunks, SN 14C, and 10Be in polar ice, SN 10Be) and the extreme value theory to study variability of solar activity during the last nine millennia. The peaks-over-threshold technique was used to compute, in particular, the shape parameter of the generalized Pareto distribution for different thresholds. Its negative value implies an upper bound of the extreme SN 10Be and SN 14C timeseries. The return level for 1000 and 10,000 years were estimated leading to values lower than the maximum observed values, expected for the 1000 year, but not for the 10,000 year return levels, for both series. A comparison of these results with those obtained using the observed sunspot numbers from telescopic observations during the last four centuries suggests that the main characteristics of solar activity have already been recorded in the telescopic period (from 1610 to nowadays) which covers the full range of solar variability from a Grand minimum to a Grand maximum.

  16. A Novel Dynamic Algorithm for IT Outsourcing Risk Assessment Based on Transaction Cost Theory

    Directory of Open Access Journals (Sweden)

    Guodong Cong

    2015-01-01

    Full Text Available With the great risk exposed in IT outsourcing, how to assess IT outsourcing risk becomes a critical issue. However, most of approaches to date need to further adapt to the particular complexity of IT outsourcing risk for either falling short in subjective bias, inaccuracy, or efficiency. This paper proposes a dynamic algorithm of risk assessment. It initially forwards extended three layers (risk factors, risks, and risk consequences of transferring mechanism based on transaction cost theory (TCT as the framework of risk analysis, which bridges the interconnection of components in three layers with preset transferring probability and impact. Then, it establishes an equation group between risk factors and risk consequences, which assures the “attribution” more precisely to track the specific sources that lead to certain loss. Namely, in each phase of the outsourcing lifecycle, both the likelihood and the loss of each risk factor and those of each risk are acquired through solving equation group with real data of risk consequences collected. In this “reverse” way, risk assessment becomes a responsive and interactive process with real data instead of subjective estimation, which improves the accuracy and alleviates bias in risk assessment. The numerical case proves the effectiveness of the algorithm compared with the approach forwarded by other references.

  17. Some ideas for learning CP-theories

    OpenAIRE

    Fierens, Daan

    2008-01-01

    Causal Probabilistic logic (CP-logic) is a language for describing complex probabilistic processes. In this talk we consider the problem of learning CP-theories from data. We briefly discuss three possible approaches. First, we review the existing algorithm by Meert et al. Second, we show how simple CP-theories can be learned by using the learning algorithm for Logical Bayesian Networks and converting the result into a CP-theory. Third, we argue that for learning more complex CP-theories, an ...

  18. Learning algorithms and automatic processing of languages; Algorithmes a apprentissage et traitement automatique des langues

    Energy Technology Data Exchange (ETDEWEB)

    Fluhr, Christian Yves Andre

    1977-06-15

    This research thesis concerns the field of artificial intelligence. It addresses learning algorithms applied to automatic processing of languages. The author first briefly describes some mechanisms of human intelligence in order to describe how these mechanisms are simulated on a computer. He outlines the specific role of learning in various manifestations of intelligence. Then, based on the Markov's algorithm theory, the author discusses the notion of learning algorithm. Two main types of learning algorithms are then addressed: firstly, an 'algorithm-teacher dialogue' type sanction-based algorithm which aims at learning how to solve grammatical ambiguities in submitted texts; secondly, an algorithm related to a document system which structures semantic data automatically obtained from a set of texts in order to be able to understand by references to any question on the content of these texts.

  19. Problems of the processing of nuclear magnetic logging signals (identification of fluid-containing strata from a number of measurements)

    International Nuclear Information System (INIS)

    Aliev, T.M.; Orlov, G.L.; Lof, V.M.; Mityushin, E.M.; Ragimova, E.K.

    1978-01-01

    Problems of the processing of nuclear magnetic logging signals to identification of fluid-containing strata from a number of measurements. Problems of application statistical decision theory to discovery of fluid-containing beds from a number of measurements are considered. Using the technique possibilities of nuclear magnetic logging method the necessary volume of samples is motivated, the rational algorithm for processing of sequential measurements is obtained

  20. A subexponential lower bound for the Random Facet algorithm for Parity Games

    DEFF Research Database (Denmark)

    Friedmann, Oliver; Hansen, Thomas Dueholm; Zwick, Uri

    2011-01-01

    Parity Games form an intriguing family of infinite duration games whose solution is equivalent to the solution of important problems in automatic verification and automata theory. They also form a very natural subclass of Deterministic Mean Payoff Games, which in turn is a very natural subclass...... of turn-based Stochastic Mean Payoff Games. It is a major open problem whether these game families can be solved in polynomial time. The currently theoretically fastest algorithms for the solution of all these games are adaptations of the randomized algorithms of Kalai and of Matouˇsek, Sharir and Welzl...... for LP-type problems, an abstract generalization of linear programming. The expected running time of both algorithms is subexponential in the size of the game, i.e., 2O(√n log n), where n is the number of vertices in the game. We focus in this paper on the algorithm of Matouˇsek, Sharir and Welzl...

  1. A projected preconditioned conjugate gradient algorithm for computing many extreme eigenpairs of a Hermitian matrix

    International Nuclear Information System (INIS)

    Vecharynski, Eugene; Yang, Chao; Pask, John E.

    2015-01-01

    We present an iterative algorithm for computing an invariant subspace associated with the algebraically smallest eigenvalues of a large sparse or structured Hermitian matrix A. We are interested in the case in which the dimension of the invariant subspace is large (e.g., over several hundreds or thousands) even though it may still be small relative to the dimension of A. These problems arise from, for example, density functional theory (DFT) based electronic structure calculations for complex materials. The key feature of our algorithm is that it performs fewer Rayleigh–Ritz calculations compared to existing algorithms such as the locally optimal block preconditioned conjugate gradient or the Davidson algorithm. It is a block algorithm, and hence can take advantage of efficient BLAS3 operations and be implemented with multiple levels of concurrency. We discuss a number of practical issues that must be addressed in order to implement the algorithm efficiently on a high performance computer

  2. Baryon and lepton number violation in the electroweak theory at TeV energies

    International Nuclear Information System (INIS)

    Mottola, E.

    1990-01-01

    In the standard Weinberg-Salam electroweak theory baryon and lepton number (B and L) are NOT exactly conserved. The nonconservation of B and L can be traced to the existence of parity violation in the electroweak theory, together with the chiral current anomaly. This subtle effect gives negligibly small amplitudes for B and L violation at energies and temperatures significantly smaller than M w sin 2 θ w /α ∼ 10 TeV. However, recent theoretical work shows that the rate for B and L nonconservation is unsuppressed at higher energies. The consequences of this for cosmology and the baryon asymmetry of the universe, as well as the prospects for direct verification at the SSC are discussed. 13 refs., 3 figs

  3. Maximum-entropy clustering algorithm and its global convergence analysis

    Institute of Scientific and Technical Information of China (English)

    2001-01-01

    Constructing a batch of differentiable entropy functions touniformly approximate an objective function by means of the maximum-entropy principle, a new clustering algorithm, called maximum-entropy clustering algorithm, is proposed based on optimization theory. This algorithm is a soft generalization of the hard C-means algorithm and possesses global convergence. Its relations with other clustering algorithms are discussed.

  4. NLSE: Parameter-Based Inversion Algorithm

    Science.gov (United States)

    Sabbagh, Harold A.; Murphy, R. Kim; Sabbagh, Elias H.; Aldrin, John C.; Knopp, Jeremy S.

    Chapter 11 introduced us to the notion of an inverse problem and gave us some examples of the value of this idea to the solution of realistic industrial problems. The basic inversion algorithm described in Chap. 11 was based upon the Gauss-Newton theory of nonlinear least-squares estimation and is called NLSE in this book. In this chapter we will develop the mathematical background of this theory more fully, because this algorithm will be the foundation of inverse methods and their applications during the remainder of this book. We hope, thereby, to introduce the reader to the application of sophisticated mathematical concepts to engineering practice without introducing excessive mathematical sophistication.

  5. A modified large number theory with constant G

    Science.gov (United States)

    Recami, Erasmo

    1983-03-01

    The inspiring “numerology” uncovered by Dirac, Eddington, Weyl, et al. can be explained and derived when it is slightly modified so to connect the “gravitational world” (cosmos) with the “strong world” (hadron), rather than with the electromagnetic one. The aim of this note is to show the following. In the present approach to the “Large Number Theory,” cosmos and hadrons are considered to be (finite) similar systems, so that the ratio{{bar R} / {{bar R} {bar r}} of the cosmos typical lengthbar R to the hadron typical lengthbar r is constant in time (for instance, if both cosmos and hadrons undergo an expansion/contraction cycle—according to the “cyclical bigbang” hypothesis—thenbar R andbar r can be chosen to be the maximum radii, or the average radii). As a consequence, then gravitational constant G results to be independent of time. The present note is based on work done in collaboration with P. Caldirola, G. D. Maccarrone, and M. Pavšič.

  6. A spectral algorithm for the seriation problem

    Energy Technology Data Exchange (ETDEWEB)

    Atkins, J.E. [Michigan Univ., Ann Arbor, MI (United States). Dept. of Mathematics; Boman, E.G. [Stanford Univ., CA (United States). Dept. of Computer Science; Hendrickson, B. [Sandia National Labs., Albuquerque, NM (United States)

    1994-11-01

    Given a set of objects and a correlation function f reflecting the desire for two items to be near each other, find all sequences {pi} of the items so that correlation preferences are preserved; that is if {pi}(i) < {pi}(j) < {pi}(k) then f(i,j) {ge} f(i,k) and f(j,k) {ge} f(i,k). This seriation problem has numerous applications, for instance, solving it yields a solution to the consecutive ones problem. We present a spectral algorithm for this problem that has a number of interesting features. Whereas most previous applications of spectral techniques provided bounds or heuristics, our result is an algorithm for a nontrivial combinatorial problem. Our analysis introduces powerful tools from matrix theory to the theoretical computer science community. Also, spectral methods are being applied as heuristics for a variety of sequencing problems and our result helps explain and justify these applications. Although the worst case running time for our approach is not competitive with that of existing methods for well posed problem instances, unlike combinatorial approaches our algorithm remains a credible heuristic for the important cases where there are errors in the data.

  7. Algorithms in Singular

    Directory of Open Access Journals (Sweden)

    Hans Schonemann

    1996-12-01

    Full Text Available Some algorithms for singularity theory and algebraic geometry The use of Grobner basis computations for treating systems of polynomial equations has become an important tool in many areas. This paper introduces of the concept of standard bases (a generalization of Grobner bases and the application to some problems from algebraic geometry. The examples are presented as SINGULAR commands. A general introduction to Grobner bases can be found in the textbook [CLO], an introduction to syzygies in [E] and [St1]. SINGULAR is a computer algebra system for computing information about singularities, for use in algebraic geometry. The basic algorithms in SINGULAR are several variants of a general standard basis algorithm for general monomial orderings (see [GG]. This includes wellorderings (Buchberger algorithm ([B1], [B2] and tangent cone orderings (Mora algorithm ([M1], [MPT] as special cases: It is able to work with non-homogeneous and homogeneous input and also to compute in the localization of the polynomial ring in 0. Recent versions include algorithms to factorize polynomials and a factorizing Grobner basis algorithm. For a complete description of SINGULAR see [Si].

  8. Conjecture of twin primes (Still unsolved problem in Number Theory. An expository essay

    Directory of Open Access Journals (Sweden)

    Hayat Rezgui

    2017-12-01

    Full Text Available The purpose of this paper is to gather as much results of advances, recent and previous works as possible concerning the oldest outstanding still unsolved problem in Number Theory (and the most elusive open problem in prime numbers called "Twin primes conjecture" (8th problem of David Hilbert, stated in 1900 which has eluded many gifted mathematicians. This conjecture has been circulating for decades, even with the progress of contemporary technology that puts the whole world within our reach. So, simple to state, yet so hard to prove. Basic Concepts, many and varied topics regarding the Twin prime conjecture will be cover.

  9. Not always buried deep a second course in elementary number theory

    CERN Document Server

    Pollack, Paul

    2009-01-01

    Number theory is one of the few areas of mathematics where problems of substantial interest can be fully described to someone with minimal mathematical background. Solving such problems sometimes requires difficult and deep methods. But this is not a universal phenomenon; many engaging problems can be successfully attacked with little more than one's mathematical bare hands. In this case one says that the problem can be solved in an elementary way. Such elementary methods and the problems to which they apply are the subject of this book. Not Always Buried Deep is designed to be read and enjoye

  10. How to implement a quantum algorithm on a large number of qubits by controlling one central qubit

    Science.gov (United States)

    Zagoskin, Alexander; Ashhab, Sahel; Johansson, J. R.; Nori, Franco

    2010-03-01

    It is desirable to minimize the number of control parameters needed to perform a quantum algorithm. We show that, under certain conditions, an entire quantum algorithm can be efficiently implemented by controlling a single central qubit in a quantum computer. We also show that the different system parameters do not need to be designed accurately during fabrication. They can be determined through the response of the central qubit to external driving. Our proposal is well suited for hybrid architectures that combine microscopic and macroscopic qubits. More details can be found in: A.M. Zagoskin, S. Ashhab, J.R. Johansson, F. Nori, Quantum two-level systems in Josephson junctions as naturally formed qubits, Phys. Rev. Lett. 97, 077001 (2006); and S. Ashhab, J.R. Johansson, F. Nori, Rabi oscillations in a qubit coupled to a quantum two-level system, New J. Phys. 8, 103 (2006).

  11. Influence of Extrinsic Information Scaling Coefficient on Double-Iterative Decoding Algorithm for Space-Time Turbo Codes with Large Number of Antennas

    Directory of Open Access Journals (Sweden)

    TRIFINA, L.

    2011-02-01

    Full Text Available This paper analyzes the extrinsic information scaling coefficient influence on double-iterative decoding algorithm for space-time turbo codes with large number of antennas. The max-log-APP algorithm is used, scaling both the extrinsic information in the turbo decoder and the one used at the input of the interference-canceling block. Scaling coefficients of 0.7 or 0.75 lead to a 0.5 dB coding gain compared to the no-scaling case, for one or more iterations to cancel the spatial interferences.

  12. The Effects of Number Theory Study on High School Students' Metacognition and Mathematics Attitudes

    Science.gov (United States)

    Miele, Anthony M.

    2014-01-01

    The purpose of this study was to determine how the study of number theory might affect high school students' metacognitive functioning, mathematical curiosity, and/or attitudes towards mathematics. The study utilized questionnaire and/or interview responses of seven high school students from New York City and 33 high school students from Dalian,…

  13. Genetic algorithms: Theory and applications in the safety domain

    International Nuclear Information System (INIS)

    Marseguerra, M.; Zio, E.

    2001-01-01

    This work illustrates the fundamentals underlying optimization by genetic algorithms. All the steps of the procedure are sketched in details for both the traditional breeding algorithm as well as for more sophisticated breeding procedures. The necessity of affine transforming the fitness function, object of the optimization, is discussed in detail, together with the transformation itself. Procedures for the inducement of species and niches are also presented. The theoretical aspects of the work are corroborated by a demonstration of the potential of genetic algorithm optimization procedures on three different case studies. The first case study deals with the design of the pressure stages of a natural gas pipeline system; the second one treats a reliability allocation problem in system configuration design; the last case regards the selection of maintenance and repair strategies for the logistic management of a risky plant. (author)

  14. Study and discretization of kinetic models and fluid models at low Mach number

    International Nuclear Information System (INIS)

    Dellacherie, Stephane

    2011-01-01

    This thesis summarizes our work between 1995 and 2010. It concerns the analysis and the discretization of Fokker-Planck or semi-classical Boltzmann kinetic models and of Euler or Navier-Stokes fluid models at low Mach number. The studied Fokker-Planck equation models the collisions between ions and electrons in a hot plasma, and is here applied to the inertial confinement fusion. The studied semi-classical Boltzmann equations are of two types. The first one models the thermonuclear reaction between a deuterium ion and a tritium ion producing an α particle and a neutron particle, and is also in our case used to describe inertial confinement fusion. The second one (known as the Wang-Chang and Uhlenbeck equations) models the transitions between electronic quantified energy levels of uranium and iron atoms in the AVLIS isotopic separation process. The basic properties of these two Boltzmann equations are studied, and, for the Wang-Chang and Uhlenbeck equations, a kinetic-fluid coupling algorithm is proposed. This kinetic-fluid coupling algorithm incited us to study the relaxation concept for gas and immiscible fluids mixtures, and to underline connections with classical kinetic theory. Then, a diphasic low Mach number model without acoustic waves is proposed to model the deformation of the interface between two immiscible fluids induced by high heat transfers at low Mach number. In order to increase the accuracy of the results without increasing computational cost, an AMR algorithm is studied on a simplified interface deformation model. These low Mach number studies also incited us to analyse on cartesian meshes the inaccuracy at low Mach number of Godunov schemes. Finally, the LBM algorithm applied to the heat equation is justified

  15. Automatic bounding estimation in modified NLMS algorithm

    International Nuclear Information System (INIS)

    Shahtalebi, K.; Doost-Hoseini, A.M.

    2002-01-01

    Modified Normalized Least Mean Square algorithm, which is a sign form of Nlm based on set-membership (S M) theory in the class of optimal bounding ellipsoid (OBE) algorithms, requires a priori knowledge of error bounds that is unknown in most applications. In a special but popular case of measurement noise, a simple algorithm has been proposed. With some simulation examples the performance of algorithm is compared with Modified Normalized Least Mean Square

  16. Lyapunov vectors and assimilation in the unstable subspace: theory and applications

    International Nuclear Information System (INIS)

    Palatella, Luigi; Carrassi, Alberto; Trevisan, Anna

    2013-01-01

    Based on a limited number of noisy observations, estimation algorithms provide a complete description of the state of a system at current time. Estimation algorithms that go under the name of assimilation in the unstable subspace (AUS) exploit the nonlinear stability properties of the forecasting model in their formulation. Errors that grow due to sensitivity to initial conditions are efficiently removed by confining the analysis solution in the unstable and neutral subspace of the system, the subspace spanned by Lyapunov vectors with positive and zero exponents, while the observational noise does not disturb the system along the stable directions. The formulation of the AUS approach in the context of four-dimensional variational assimilation (4DVar-AUS) and the extended Kalman filter (EKF-AUS) and its application to chaotic models is reviewed. In both instances, the AUS algorithms are at least as efficient but simpler to implement and computationally less demanding than their original counterparts. As predicted by the theory when error dynamics is linear, the optimal subspace dimension for 4DVar-AUS is given by the number of positive and null Lyapunov exponents, while the EKF-AUS algorithm, using the same unstable and neutral subspace, recovers the solution of the full EKF algorithm, but dealing with error covariance matrices of a much smaller dimension and significantly reducing the computational burden. Examples of the application to a simplified model of the atmospheric circulation and to the optimal velocity model for traffic dynamics are given. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Lyapunov analysis: from dynamical systems theory to applications’. (paper)

  17. Testing a Fourier Accelerated Hybrid Monte Carlo Algorithm

    OpenAIRE

    Catterall, S.; Karamov, S.

    2001-01-01

    We describe a Fourier Accelerated Hybrid Monte Carlo algorithm suitable for dynamical fermion simulations of non-gauge models. We test the algorithm in supersymmetric quantum mechanics viewed as a one-dimensional Euclidean lattice field theory. We find dramatic reductions in the autocorrelation time of the algorithm in comparison to standard HMC.

  18. An On-Demand Optical Quantum Random Number Generator with In-Future Action and Ultra-Fast Response.

    Science.gov (United States)

    Stipčević, Mario; Ursin, Rupert

    2015-06-09

    Random numbers are essential for our modern information based society e.g. in cryptography. Unlike frequently used pseudo-random generators, physical random number generators do not depend on complex algorithms but rather on a physical process to provide true randomness. Quantum random number generators (QRNG) do rely on a process, which can be described by a probabilistic theory only, even in principle. Here we present a conceptually simple implementation, which offers a 100% efficiency of producing a random bit upon a request and simultaneously exhibits an ultra low latency. A careful technical and statistical analysis demonstrates its robustness against imperfections of the actual implemented technology and enables to quickly estimate randomness of very long sequences. Generated random numbers pass standard statistical tests without any post-processing. The setup described, as well as the theory presented here, demonstrate the maturity and overall understanding of the technology.

  19. Matching theory

    CERN Document Server

    Plummer, MD

    1986-01-01

    This study of matching theory deals with bipartite matching, network flows, and presents fundamental results for the non-bipartite case. It goes on to study elementary bipartite graphs and elementary graphs in general. Further discussed are 2-matchings, general matching problems as linear programs, the Edmonds Matching Algorithm (and other algorithmic approaches), f-factors and vertex packing.

  20. Algorithmic alternatives

    International Nuclear Information System (INIS)

    Creutz, M.

    1987-11-01

    A large variety of Monte Carlo algorithms are being used for lattice gauge simulations. For purely bosonic theories, present approaches are generally adequate; nevertheless, overrelaxation techniques promise savings by a factor of about three in computer time. For fermionic fields the situation is more difficult and less clear. Algorithms which involve an extrapolation to a vanishing step size are all quite closely related. Methods which do not require such an approximation tend to require computer time which grows as the square of the volume of the system. Recent developments combining global accept/reject stages with Langevin or microcanonical updatings promise to reduce this growth to V/sup 4/3/

  1. Theory and Algorithms for Global/Local Design Optimization

    National Research Council Canada - National Science Library

    Haftka, Raphael T

    2004-01-01

    ... the component and overall design as well as on exploration of global optimization algorithms. In the former category, heuristic decomposition was followed with proof that it solves the original problem...

  2. Scoping review identifies significant number of knowledge translation theories, models and frameworks with limited use.

    Science.gov (United States)

    Strifler, Lisa; Cardoso, Roberta; McGowan, Jessie; Cogo, Elise; Nincic, Vera; Khan, Paul A; Scott, Alistair; Ghassemi, Marco; MacDonald, Heather; Lai, Yonda; Treister, Victoria; Tricco, Andrea C; Straus, Sharon E

    2018-04-13

    To conduct a scoping review of knowledge translation (KT) theories, models and frameworks that have been used to guide dissemination or implementation of evidence-based interventions targeted to prevention and/or management of cancer or other chronic diseases. We used a comprehensive multistage search process from 2000-2016, which included traditional bibliographic database searching, searching using names of theories, models and frameworks, and cited reference searching. Two reviewers independently screened the literature and abstracted data. We found 596 studies reporting on the use of 159 KT theories, models or frameworks. A majority (87%) of the identified theories, models or frameworks were used in five or fewer studies, with 60% used once. The theories, models and frameworks were most commonly used to inform planning/design, implementation and evaluation activities, and least commonly used to inform dissemination and sustainability/scalability activities. Twenty-six were used across the full implementation spectrum (from planning/design to sustainability/scalability) either within or across studies. All were used for at least individual-level behavior change, while 48% were used for organization-level, 33% for community-level and 17% for system-level change. We found a significant number of KT theories, models and frameworks with a limited evidence base describing their use. Copyright © 2018. Published by Elsevier Inc.

  3. Low Rank Approximation Algorithms, Implementation, Applications

    CERN Document Server

    Markovsky, Ivan

    2012-01-01

    Matrix low-rank approximation is intimately related to data modelling; a problem that arises frequently in many different fields. Low Rank Approximation: Algorithms, Implementation, Applications is a comprehensive exposition of the theory, algorithms, and applications of structured low-rank approximation. Local optimization methods and effective suboptimal convex relaxations for Toeplitz, Hankel, and Sylvester structured problems are presented. A major part of the text is devoted to application of the theory. Applications described include: system and control theory: approximate realization, model reduction, output error, and errors-in-variables identification; signal processing: harmonic retrieval, sum-of-damped exponentials, finite impulse response modeling, and array processing; machine learning: multidimensional scaling and recommender system; computer vision: algebraic curve fitting and fundamental matrix estimation; bioinformatics for microarray data analysis; chemometrics for multivariate calibration; ...

  4. Field-Split Preconditioned Inexact Newton Algorithms

    KAUST Repository

    Liu, Lulu

    2015-06-02

    The multiplicative Schwarz preconditioned inexact Newton (MSPIN) algorithm is presented as a complement to additive Schwarz preconditioned inexact Newton (ASPIN). At an algebraic level, ASPIN and MSPIN are variants of the same strategy to improve the convergence of systems with unbalanced nonlinearities; however, they have natural complementarity in practice. MSPIN is naturally based on partitioning of degrees of freedom in a nonlinear PDE system by field type rather than by subdomain, where a modest factor of concurrency can be sacrificed for physically motivated convergence robustness. ASPIN, originally introduced for decompositions into subdomains, is natural for high concurrency and reduction of global synchronization. We consider both types of inexact Newton algorithms in the field-split context, and we augment the classical convergence theory of ASPIN for the multiplicative case. Numerical experiments show that MSPIN can be significantly more robust than Newton methods based on global linearizations, and that MSPIN can be more robust than ASPIN and maintain fast convergence even for challenging problems, such as high Reynolds number Navier--Stokes equations.

  5. Field-Split Preconditioned Inexact Newton Algorithms

    KAUST Repository

    Liu, Lulu; Keyes, David E.

    2015-01-01

    The multiplicative Schwarz preconditioned inexact Newton (MSPIN) algorithm is presented as a complement to additive Schwarz preconditioned inexact Newton (ASPIN). At an algebraic level, ASPIN and MSPIN are variants of the same strategy to improve the convergence of systems with unbalanced nonlinearities; however, they have natural complementarity in practice. MSPIN is naturally based on partitioning of degrees of freedom in a nonlinear PDE system by field type rather than by subdomain, where a modest factor of concurrency can be sacrificed for physically motivated convergence robustness. ASPIN, originally introduced for decompositions into subdomains, is natural for high concurrency and reduction of global synchronization. We consider both types of inexact Newton algorithms in the field-split context, and we augment the classical convergence theory of ASPIN for the multiplicative case. Numerical experiments show that MSPIN can be significantly more robust than Newton methods based on global linearizations, and that MSPIN can be more robust than ASPIN and maintain fast convergence even for challenging problems, such as high Reynolds number Navier--Stokes equations.

  6. Set Theory Correlation Free Algorithm for HRRR Target Tracking

    National Research Council Canada - National Science Library

    Blasch, Erik

    1999-01-01

    .... Recently a few fusionists including Mahler 1 and Mori 2 are using a set theory approach for a unified data fusion theory which is a correlation free paradigm 3 This paper uses the set theory approach...

  7. Numerical approach of the quantum circuit theory

    Energy Technology Data Exchange (ETDEWEB)

    Silva, J.J.B., E-mail: jaedsonfisica@hotmail.com; Duarte-Filho, G.C.; Almeida, F.A.G.

    2017-03-15

    In this paper we develop a numerical method based on the quantum circuit theory to approach the coherent electronic transport in a network of quantum dots connected with arbitrary topology. The algorithm was employed in a circuit formed by quantum dots connected each other in a shape of a linear chain (associations in series), and of a ring (associations in series, and in parallel). For both systems we compute two current observables: conductance and shot noise power. We find an excellent agreement between our numerical results and the ones found in the literature. Moreover, we analyze the algorithm efficiency for a chain of quantum dots, where the mean processing time exhibits a linear dependence with the number of quantum dots in the array.

  8. Numerical approach of the quantum circuit theory

    International Nuclear Information System (INIS)

    Silva, J.J.B.; Duarte-Filho, G.C.; Almeida, F.A.G.

    2017-01-01

    In this paper we develop a numerical method based on the quantum circuit theory to approach the coherent electronic transport in a network of quantum dots connected with arbitrary topology. The algorithm was employed in a circuit formed by quantum dots connected each other in a shape of a linear chain (associations in series), and of a ring (associations in series, and in parallel). For both systems we compute two current observables: conductance and shot noise power. We find an excellent agreement between our numerical results and the ones found in the literature. Moreover, we analyze the algorithm efficiency for a chain of quantum dots, where the mean processing time exhibits a linear dependence with the number of quantum dots in the array.

  9. Numerical approach of the quantum circuit theory

    Science.gov (United States)

    Silva, J. J. B.; Duarte-Filho, G. C.; Almeida, F. A. G.

    2017-03-01

    In this paper we develop a numerical method based on the quantum circuit theory to approach the coherent electronic transport in a network of quantum dots connected with arbitrary topology. The algorithm was employed in a circuit formed by quantum dots connected each other in a shape of a linear chain (associations in series), and of a ring (associations in series, and in parallel). For both systems we compute two current observables: conductance and shot noise power. We find an excellent agreement between our numerical results and the ones found in the literature. Moreover, we analyze the algorithm efficiency for a chain of quantum dots, where the mean processing time exhibits a linear dependence with the number of quantum dots in the array.

  10. Periodic-orbit theory of the number variance Σ2(L) of strongly chaotic systems

    International Nuclear Information System (INIS)

    Aurich, R.; Steiner, F.

    1994-03-01

    We discuss the number variance Σ 2 (L) and the spectral form factor F(τ) of the energy levels of bound quantum systems whose classical counterparts are strongly chaotic. Exact periodic-orbit representations of Σ 2 (L) and F(τ) are derived which explain the breakdown of universality, i.e., the deviations from the predictions of random-matrix theory. The relation of the exact spectral form factor F(τ) to the commonly used approximation K(τ) is clarified. As an illustration the periodic-orbit representations are tested in the case of a strongly chaotic system at low and high energies including very long-range correlations up to L=700. Good agreement between 'experimental' data and theory is obtained. (orig.)

  11. Extension of anisotropic effective medium theory to account for an arbitrary number of inclusion types

    Science.gov (United States)

    Myles, Timothy D.; Peracchio, Aldo A.; Chiu, Wilson K. S.

    2015-01-01

    The purpose of this work is to extend, to multi-components, a previously reported theory for calculating the effective conductivity of a two component mixture. The previously reported theory involved preferentially oriented spheroidal inclusions contained in a continuous matrix, with inclusions oriented relative to a principle axis. This approach was based on Bruggeman's unsymmetrical theory, and is extended to account for an arbitrary number of different inclusion types. The development begins from two well-known starting points; the Maxwell approach and the Maxwell-Garnett approach for dilute mixtures. It is shown that despite these two different starting points, the final Bruggeman type equation is the same. As a means of validating the developed expression, comparisons are made to several existing effective medium theories. It is shown that these existing theories coincide with the developed equations for the appropriate parameter set. Finally, a few example mixtures are considered to demonstrate the effect of multiple inclusions on the calculated effective property. Inclusion types of different conductivities, shapes, and orientations are considered and each of the aforementioned properties is shown to have a potentially significant impact on the calculated mixture property.

  12. Beurling generalized numbers

    CERN Document Server

    Diamond, Harold G; Cheung, Man Ping

    2016-01-01

    "Generalized numbers" is a multiplicative structure introduced by A. Beurling to study how independent prime number theory is from the additivity of the natural numbers. The results and techniques of this theory apply to other systems having the character of prime numbers and integers; for example, it is used in the study of the prime number theorem (PNT) for ideals of algebraic number fields. Using both analytic and elementary methods, this book presents many old and new theorems, including several of the authors' results, and many examples of extremal behavior of g-number systems. Also, the authors give detailed accounts of the L^2 PNT theorem of J. P. Kahane and of the example created with H. L. Montgomery, showing that additive structure is needed for proving the Riemann hypothesis. Other interesting topics discussed are propositions "equivalent" to the PNT, the role of multiplicative convolution and Chebyshev's prime number formula for g-numbers, and how Beurling theory provides an interpretation of the ...

  13. Generalized phase retrieval algorithm based on information measures

    OpenAIRE

    Shioya, Hiroyuki; Gohara, Kazutoshi

    2006-01-01

    An iterative phase retrieval algorithm based on the maximum entropy method (MEM) is presented. Introducing a new generalized information measure, we derive a novel class of algorithms which includes the conventionally used error reduction algorithm and a MEM-type iterative algorithm which is presented for the first time. These different phase retrieval methods are unified on the basis of the framework of information measures used in information theory.

  14. Using dynamo theory to predict the sunspot number during solar cycle 21

    Science.gov (United States)

    Schatten, K. H.; Scherrer, P. H.; Svalgaard, L.; Wilcox, J. M.

    1978-01-01

    On physical grounds it is suggested that the polar field strength of the sun near a solar minimum is closely related to the solar activity of the following cycle. Four methods of estimating the polar magnetic field strength of the sun near solar minimum are employed to provide an estimate of the yearly mean sunspot number of cycle 21 at solar maximum of 140 + or - 20. This estimate may be considered a first-order attempt to predict the cycle activity using one parameter of physical importance based upon dynamo theory.

  15. Quantum algorithm for linear regression

    Science.gov (United States)

    Wang, Guoming

    2017-07-01

    We present a quantum algorithm for fitting a linear regression model to a given data set using the least-squares approach. Differently from previous algorithms which yield a quantum state encoding the optimal parameters, our algorithm outputs these numbers in the classical form. So by running it once, one completely determines the fitted model and then can use it to make predictions on new data at little cost. Moreover, our algorithm works in the standard oracle model, and can handle data sets with nonsparse design matrices. It runs in time poly( log2(N ) ,d ,κ ,1 /ɛ ) , where N is the size of the data set, d is the number of adjustable parameters, κ is the condition number of the design matrix, and ɛ is the desired precision in the output. We also show that the polynomial dependence on d and κ is necessary. Thus, our algorithm cannot be significantly improved. Furthermore, we also give a quantum algorithm that estimates the quality of the least-squares fit (without computing its parameters explicitly). This algorithm runs faster than the one for finding this fit, and can be used to check whether the given data set qualifies for linear regression in the first place.

  16. Ramsey numbers and adiabatic quantum computing.

    Science.gov (United States)

    Gaitan, Frank; Clark, Lane

    2012-01-06

    The graph-theoretic Ramsey numbers are notoriously difficult to calculate. In fact, for the two-color Ramsey numbers R(m,n) with m, n≥3, only nine are currently known. We present a quantum algorithm for the computation of the Ramsey numbers R(m,n). We show how the computation of R(m,n) can be mapped to a combinatorial optimization problem whose solution can be found using adiabatic quantum evolution. We numerically simulate this adiabatic quantum algorithm and show that it correctly determines the Ramsey numbers R(3,3) and R(2,s) for 5≤s≤7. We then discuss the algorithm's experimental implementation, and close by showing that Ramsey number computation belongs to the quantum complexity class quantum Merlin Arthur.

  17. Tenth workshop on the algorithmic foundations of robotics (WAFR)

    CERN Document Server

    Lozano-Perez, Tomas; Roy, Nicholas; Rus, Daniela; Algorithmic foundations of robotics X

    2013-01-01

    Algorithms are a fundamental component of robotic systems. Robot algorithms process inputs from sensors that provide noisy and partial data, build geometric and physical models of the world, plan high-and low-level actions at different time horizons, and execute these actions on actuators with limited precision. The design and analysis of robot algorithms raise a unique combination of questions from many elds, including control theory, computational geometry and topology, geometrical and physical modeling, reasoning under uncertainty, probabilistic algorithms, game theory, and theoretical computer science. The Workshop on Algorithmic Foundations of Robotics (WAFR) is a single-track meeting of leading researchers in the eld of robot algorithms. Since its inception in 1994, WAFR has been held every other year, and has provided one of the premiere venues for the publication of some of the eld's most important and lasting contributions. This books contains the proceedings of the tenth WAFR, held on June 13{15 201...

  18. Sorting a distribution theory

    CERN Document Server

    Mahmoud, Hosam M

    2011-01-01

    A cutting-edge look at the emerging distributional theory of sorting Research on distributions associated with sorting algorithms has grown dramatically over the last few decades, spawning many exact and limiting distributions of complexity measures for many sorting algorithms. Yet much of this information has been scattered in disparate and highly specialized sources throughout the literature. In Sorting: A Distribution Theory, leading authority Hosam Mahmoud compiles, consolidates, and clarifies the large volume of available research, providing a much-needed, comprehensive treatment of the

  19. Essays on the theory of numbers

    CERN Document Server

    Dedekind, Richard

    1963-01-01

    Two classic essays by great German mathematician: one provides an arithmetic, rigorous foundation for the irrational numbers, the other is an attempt to give the logical basis for transfinite numbers and properties of the natural numbers.

  20. Number theory Diophantine problems, uniform distribution and applications : festschrift in honour of Robert F. Tichy’s 60th birthday

    CERN Document Server

    Grabner, Peter

    2017-01-01

    This volume is dedicated to Robert F. Tichy on the occasion of his 60th birthday. Presenting 22 research and survey papers written by leading experts in their respective fields, it focuses on areas that align with Tichy’s research interests and which he significantly shaped, including Diophantine problems, asymptotic counting, uniform distribution and discrepancy of sequences (in theory and application), dynamical systems, prime numbers, and actuarial mathematics. Offering valuable insights into recent developments in these areas, the book will be of interest to researchers and graduate students engaged in number theory and its applications.

  1. Fast algorithm for Morphological Filters

    International Nuclear Information System (INIS)

    Lou Shan; Jiang Xiangqian; Scott, Paul J

    2011-01-01

    In surface metrology, morphological filters, which evolved from the envelope filtering system (E-system) work well for functional prediction of surface finish in the analysis of surfaces in contact. The naive algorithms are time consuming, especially for areal data, and not generally adopted in real practice. A fast algorithm is proposed based on the alpha shape. The hull obtained by rolling the alpha ball is equivalent to the morphological opening/closing in theory. The algorithm depends on Delaunay triangulation with time complexity O(nlogn). In comparison to the naive algorithms it generates the opening and closing envelope without combining dilation and erosion. Edge distortion is corrected by reflective padding for open profiles/surfaces. Spikes in the sample data are detected and points interpolated to prevent singularities. The proposed algorithm works well both for morphological profile and area filters. Examples are presented to demonstrate the validity and superiority on efficiency of this algorithm over the naive algorithm.

  2. A Family of Algorithms for Computing Consensus about Node State from Network Data

    Science.gov (United States)

    Brush, Eleanor R.; Krakauer, David C.; Flack, Jessica C.

    2013-01-01

    Biological and social networks are composed of heterogeneous nodes that contribute differentially to network structure and function. A number of algorithms have been developed to measure this variation. These algorithms have proven useful for applications that require assigning scores to individual nodes–from ranking websites to determining critical species in ecosystems–yet the mechanistic basis for why they produce good rankings remains poorly understood. We show that a unifying property of these algorithms is that they quantify consensus in the network about a node's state or capacity to perform a function. The algorithms capture consensus by either taking into account the number of a target node's direct connections, and, when the edges are weighted, the uniformity of its weighted in-degree distribution (breadth), or by measuring net flow into a target node (depth). Using data from communication, social, and biological networks we find that that how an algorithm measures consensus–through breadth or depth– impacts its ability to correctly score nodes. We also observe variation in sensitivity to source biases in interaction/adjacency matrices: errors arising from systematic error at the node level or direct manipulation of network connectivity by nodes. Our results indicate that the breadth algorithms, which are derived from information theory, correctly score nodes (assessed using independent data) and are robust to errors. However, in cases where nodes “form opinions” about other nodes using indirect information, like reputation, depth algorithms, like Eigenvector Centrality, are required. One caveat is that Eigenvector Centrality is not robust to error unless the network is transitive or assortative. In these cases the network structure allows the depth algorithms to effectively capture breadth as well as depth. Finally, we discuss the algorithms' cognitive and computational demands. This is an important consideration in systems in which

  3. Littlewood and Number Theory

    Indian Academy of Sciences (India)

    IAS Admin

    improved by Selberg [4] in 1941 who showed that a pos- ... be seen by entries of his first letter to G H Hardy in ... tary in the technical sense of the word, employed com- ..... III: On the expression of a number as a sum of primes, Acta Math.,.

  4. Recursive algorithms for phylogenetic tree counting.

    Science.gov (United States)

    Gavryushkina, Alexandra; Welch, David; Drummond, Alexei J

    2013-10-28

    In Bayesian phylogenetic inference we are interested in distributions over a space of trees. The number of trees in a tree space is an important characteristic of the space and is useful for specifying prior distributions. When all samples come from the same time point and no prior information available on divergence times, the tree counting problem is easy. However, when fossil evidence is used in the inference to constrain the tree or data are sampled serially, new tree spaces arise and counting the number of trees is more difficult. We describe an algorithm that is polynomial in the number of sampled individuals for counting of resolutions of a constraint tree assuming that the number of constraints is fixed. We generalise this algorithm to counting resolutions of a fully ranked constraint tree. We describe a quadratic algorithm for counting the number of possible fully ranked trees on n sampled individuals. We introduce a new type of tree, called a fully ranked tree with sampled ancestors, and describe a cubic time algorithm for counting the number of such trees on n sampled individuals. These algorithms should be employed for Bayesian Markov chain Monte Carlo inference when fossil data are included or data are serially sampled.

  5. Comparison between iterative wavefront control algorithm and direct gradient wavefront control algorithm for adaptive optics system

    International Nuclear Information System (INIS)

    Cheng Sheng-Yi; Liu Wen-Jin; Chen Shan-Qiu; Dong Li-Zhi; Yang Ping; Xu Bing

    2015-01-01

    Among all kinds of wavefront control algorithms in adaptive optics systems, the direct gradient wavefront control algorithm is the most widespread and common method. This control algorithm obtains the actuator voltages directly from wavefront slopes through pre-measuring the relational matrix between deformable mirror actuators and Hartmann wavefront sensor with perfect real-time characteristic and stability. However, with increasing the number of sub-apertures in wavefront sensor and deformable mirror actuators of adaptive optics systems, the matrix operation in direct gradient algorithm takes too much time, which becomes a major factor influencing control effect of adaptive optics systems. In this paper we apply an iterative wavefront control algorithm to high-resolution adaptive optics systems, in which the voltages of each actuator are obtained through iteration arithmetic, which gains great advantage in calculation and storage. For AO system with thousands of actuators, the computational complexity estimate is about O(n 2 ) ∼ O(n 3 ) in direct gradient wavefront control algorithm, while the computational complexity estimate in iterative wavefront control algorithm is about O(n) ∼ (O(n) 3/2 ), in which n is the number of actuators of AO system. And the more the numbers of sub-apertures and deformable mirror actuators, the more significant advantage the iterative wavefront control algorithm exhibits. (paper)

  6. Certain number-theoretic episodes in algebra

    CERN Document Server

    Sivaramakrishnan, R

    2006-01-01

    Many basic ideas of algebra and number theory intertwine, making it ideal to explore both at the same time. Certain Number-Theoretic Episodes in Algebra focuses on some important aspects of interconnections between number theory and commutative algebra. Using a pedagogical approach, the author presents the conceptual foundations of commutative algebra arising from number theory. Self-contained, the book examines situations where explicit algebraic analogues of theorems of number theory are available. Coverage is divided into four parts, beginning with elements of number theory and algebra such as theorems of Euler, Fermat, and Lagrange, Euclidean domains, and finite groups. In the second part, the book details ordered fields, fields with valuation, and other algebraic structures. This is followed by a review of fundamentals of algebraic number theory in the third part. The final part explores links with ring theory, finite dimensional algebras, and the Goldbach problem.

  7. Perturbation theory of the quark-gluon plasma at finite temperature and baryon number density

    International Nuclear Information System (INIS)

    Anon.

    1984-01-01

    At very high energy densities, hadronic matter becomes an almost ideal gas of quarks and gluons. In these circumstances, the effects of particle interactions are small, and to some order in perturbation theory are computable by methods involving weak coupling expansions. To illustrate the perturbative methods which may be used to compute the thermodynamic potential, the results and methods which are employed to compute to first order in α/sub s/ are reviewed. The problem of the plasmon effect, and the necessity of using non-perturbative methods when going beyond first order in α/sub s/ in evaluating the thermodynamic potential are discussed. The results at zero temperature and finite baryon number density to second order in α/sub s/ are also reviewed. The method of renormalization group improving the weak coupling expansions by replacing the expansion by an expansion in a temperature and baryon number density dependent coupling which approaches zero at high energy densities is discussed. Non-perturbative effects such as instantons are briefly mentioned and the breakdown of perturbation theory for the thermodynamical at order α/sub s/ 3 for finite temperature is presented

  8. Algorithmic Algebraic Combinatorics and Gröbner Bases

    CERN Document Server

    Klin, Mikhail; Jurisic, Aleksandar

    2009-01-01

    This collection of tutorial and research papers introduces readers to diverse areas of modern pure and applied algebraic combinatorics and finite geometries with a special emphasis on algorithmic aspects and the use of the theory of Grobner bases. Topics covered include coherent configurations, association schemes, permutation groups, Latin squares, the Jacobian conjecture, mathematical chemistry, extremal combinatorics, coding theory, designs, etc. Special attention is paid to the description of innovative practical algorithms and their implementation in software packages such as GAP and MAGM

  9. Autonomous algorithms for image restoration

    OpenAIRE

    Griniasty , Meir

    1994-01-01

    We describe a general theoretical framework for algorithms that adaptively tune all their parameters during the restoration of a noisy image. The adaptation procedure is based on a mean field approach which is known as ``Deterministic Annealing'', and is reminiscent of the ``Deterministic Bolzmann Machiné'. The algorithm is less time consuming in comparison with its simulated annealing alternative. We apply the theory to several architectures and compare their performances.

  10. Shape reconstruction from apparent contours theory and algorithms

    CERN Document Server

    Bellettini, Giovanni; Paolini, Maurizio

    2015-01-01

    Motivated by a variational model concerning the depth of the objects in a picture and the problem of hidden and illusory contours, this book investigates one of the central problems of computer vision: the topological and algorithmic reconstruction of a smooth three dimensional scene starting from the visible part of an apparent contour. The authors focus their attention on the manipulation of apparent contours using a finite set of elementary moves, which correspond to diffeomorphic deformations of three dimensional scenes. A large part of the book is devoted to the algorithmic part, with implementations, experiments, and computed examples. The book is intended also as a user's guide to the software code appcontour, written for the manipulation of apparent contours and their invariants. This book is addressed to theoretical and applied scientists working in the field of mathematical models of image segmentation.

  11. Algorithmic Relative Complexity

    Directory of Open Access Journals (Sweden)

    Daniele Cerra

    2011-04-01

    Full Text Available Information content and compression are tightly related concepts that can be addressed through both classical and algorithmic information theories, on the basis of Shannon entropy and Kolmogorov complexity, respectively. The definition of several entities in Kolmogorov’s framework relies upon ideas from classical information theory, and these two approaches share many common traits. In this work, we expand the relations between these two frameworks by introducing algorithmic cross-complexity and relative complexity, counterparts of the cross-entropy and relative entropy (or Kullback-Leibler divergence found in Shannon’s framework. We define the cross-complexity of an object x with respect to another object y as the amount of computational resources needed to specify x in terms of y, and the complexity of x related to y as the compression power which is lost when adopting such a description for x, compared to the shortest representation of x. Properties of analogous quantities in classical information theory hold for these new concepts. As these notions are incomputable, a suitable approximation based upon data compression is derived to enable the application to real data, yielding a divergence measure applicable to any pair of strings. Example applications are outlined, involving authorship attribution and satellite image classification, as well as a comparison to similar established techniques.

  12. Framelets and wavelets algorithms, analysis, and applications

    CERN Document Server

    Han, Bin

    2017-01-01

    Marking a distinct departure from the perspectives of frame theory and discrete transforms, this book provides a comprehensive mathematical and algorithmic introduction to wavelet theory. As such, it can be used as either a textbook or reference guide. As a textbook for graduate mathematics students and beginning researchers, it offers detailed information on the basic theory of framelets and wavelets, complemented by self-contained elementary proofs, illustrative examples/figures, and supplementary exercises. Further, as an advanced reference guide for experienced researchers and practitioners in mathematics, physics, and engineering, the book addresses in detail a wide range of basic and advanced topics (such as multiwavelets/multiframelets in Sobolev spaces and directional framelets) in wavelet theory, together with systematic mathematical analysis, concrete algorithms, and recent developments in and applications of framelets and wavelets. Lastly, the book can also be used to teach on or study selected spe...

  13. New Insights into the RLS Algorithm

    Directory of Open Access Journals (Sweden)

    Gänsler Tomas

    2004-01-01

    Full Text Available The recursive least squares (RLS algorithm is one of the most popular adaptive algorithms that can be found in the literature, due to the fact that it is easily and exactly derived from the normal equations. In this paper, we give another interpretation of the RLS algorithm and show the importance of linear interpolation error energies in the RLS structure. We also give a very efficient way to recursively estimate the condition number of the input signal covariance matrix thanks to fast versions of the RLS algorithm. Finally, we quantify the misalignment of the RLS algorithm with respect to the condition number.

  14. Improvement of the Gravitational Search Algorithm by means of Low-Discrepancy Sobol Quasi Random-Number Sequence Based Initialization

    Directory of Open Access Journals (Sweden)

    ALTINOZ, O. T.

    2014-08-01

    Full Text Available Nature-inspired optimization algorithms can obtain the optima by updating the position of each member in the population. At the beginning of the algorithm, the particles of the population are spread into the search space. The initial distribution of particles corresponds to the beginning points of the search process. Hence, the aim is to alter the position for each particle beginning with this initial position until the optimum solution will be found with respect to the pre-determined conditions like maximum iteration, and specific error value for the fitness function. Therefore, initial positions of the population have a direct effect on both accuracy of the optima and the computational cost. If any member in the population is close enough to the optima, this eases the achievement of the exact solution. On the contrary, individuals grouped far away from the optima might yield pointless efforts. In this study, low-discrepancy quasi-random number sequence is preferred for the localization of the population at the initialization phase. By this way, the population is distributed into the search space in a more uniform manner at the initialization phase. The technique is applied to the Gravitational Search Algorithm and compared via the performance on benchmark function solutions.

  15. Hybrid Cryptosystem Using Tiny Encryption Algorithm and LUC Algorithm

    Science.gov (United States)

    Rachmawati, Dian; Sharif, Amer; Jaysilen; Andri Budiman, Mohammad

    2018-01-01

    Security becomes a very important issue in data transmission and there are so many methods to make files more secure. One of that method is cryptography. Cryptography is a method to secure file by writing the hidden code to cover the original file. Therefore, if the people do not involve in cryptography, they cannot decrypt the hidden code to read the original file. There are many methods are used in cryptography, one of that method is hybrid cryptosystem. A hybrid cryptosystem is a method that uses a symmetric algorithm to secure the file and use an asymmetric algorithm to secure the symmetric algorithm key. In this research, TEA algorithm is used as symmetric algorithm and LUC algorithm is used as an asymmetric algorithm. The system is tested by encrypting and decrypting the file by using TEA algorithm and using LUC algorithm to encrypt and decrypt the TEA key. The result of this research is by using TEA Algorithm to encrypt the file, the cipher text form is the character from ASCII (American Standard for Information Interchange) table in the form of hexadecimal numbers and the cipher text size increase by sixteen bytes as the plaintext length is increased by eight characters.

  16. Power Load Prediction Based on Fractal Theory

    OpenAIRE

    Jian-Kai, Liang; Cattani, Carlo; Wan-Qing, Song

    2015-01-01

    The basic theories of load forecasting on the power system are summarized. Fractal theory, which is a new algorithm applied to load forecasting, is introduced. Based on the fractal dimension and fractal interpolation function theories, the correlation algorithms are applied to the model of short-term load forecasting. According to the process of load forecasting, the steps of every process are designed, including load data preprocessing, similar day selecting, short-term load forecasting, and...

  17. Determining the number of clusters for kernelized fuzzy C-means algorithms for automatic medical image segmentation

    Directory of Open Access Journals (Sweden)

    E.A. Zanaty

    2012-03-01

    Full Text Available In this paper, we determine the suitable validity criterion of kernelized fuzzy C-means and kernelized fuzzy C-means with spatial constraints for automatic segmentation of magnetic resonance imaging (MRI. For that; the original Euclidean distance in the FCM is replaced by a Gaussian radial basis function classifier (GRBF and the corresponding algorithms of FCM methods are derived. The derived algorithms are called as the kernelized fuzzy C-means (KFCM and kernelized fuzzy C-means with spatial constraints (SKFCM. These methods are implemented on eighteen indexes as validation to determine whether indexes are capable to acquire the optimal clusters number. The performance of segmentation is estimated by applying these methods independently on several datasets to prove which method can give good results and with which indexes. Our test spans various indexes covering the classical and the rather more recent indexes that have enjoyed noticeable success in that field. These indexes are evaluated and compared by applying them on various test images, including synthetic images corrupted with noise of varying levels, and simulated volumetric MRI datasets. Comparative analysis is also presented to show whether the validity index indicates the optimal clustering for our datasets.

  18. Upper Bounds on the Number of Errors Corrected by the Koetter–Vardy Algorithm

    DEFF Research Database (Denmark)

    Justesen, Jørn

    2007-01-01

    By introducing a few simplifying assumptions we derive a simple condition for successful decoding using the Koetter-Vardy algorithm for soft-decision decoding of Reed-Solomon codes. We show that the algorithm has a significant advantage over hard decision decoding when the code rate is low, when ...

  19. Lattice implementation of Abelian gauge theories with Chern-Simons number and an axion field

    Science.gov (United States)

    Figueroa, Daniel G.; Shaposhnikov, Mikhail

    2018-01-01

    Real time evolution of classical gauge fields is relevant for a number of applications in particle physics and cosmology, ranging from the early Universe to dynamics of quark-gluon plasma. We present an explicit non-compact lattice formulation of the interaction between a shift-symmetric field and some U (1) gauge sector, a (x)FμνF˜μν, reproducing the continuum limit to order O (dxμ2) and obeying the following properties: (i) the system is gauge invariant and (ii) shift symmetry is exact on the lattice. For this end we construct a definition of the topological number density K =FμνF˜μν that admits a lattice total derivative representation K = Δμ+ Kμ, reproducing to order O (dxμ2) the continuum expression K =∂μKμ ∝ E → ṡ B → . If we consider a homogeneous field a (x) = a (t), the system can be mapped into an Abelian gauge theory with Hamiltonian containing a Chern-Simons term for the gauge fields. This allow us to study in an accompanying paper the real time dynamics of fermion number non-conservation (or chirality breaking) in Abelian gauge theories at finite temperature. When a (x) = a (x → , t) is inhomogeneous, the set of lattice equations of motion do not admit however a simple explicit local solution (while preserving an O (dxμ2) accuracy). We discuss an iterative scheme allowing to overcome this difficulty.

  20. Lattice implementation of Abelian gauge theories with Chern–Simons number and an axion field

    Directory of Open Access Journals (Sweden)

    Daniel G. Figueroa

    2018-01-01

    Full Text Available Real time evolution of classical gauge fields is relevant for a number of applications in particle physics and cosmology, ranging from the early Universe to dynamics of quark–gluon plasma. We present an explicit non-compact lattice formulation of the interaction between a shift-symmetric field and some U(1 gauge sector, a(xFμνF˜μν, reproducing the continuum limit to order O(dxμ2 and obeying the following properties: (i the system is gauge invariant and (ii shift symmetry is exact on the lattice. For this end we construct a definition of the topological number density K=FμνF˜μν that admits a lattice total derivative representation K=Δμ+Kμ, reproducing to order O(dxμ2 the continuum expression K=∂μKμ∝E→⋅B→. If we consider a homogeneous field a(x=a(t, the system can be mapped into an Abelian gauge theory with Hamiltonian containing a Chern–Simons term for the gauge fields. This allow us to study in an accompanying paper the real time dynamics of fermion number non-conservation (or chirality breaking in Abelian gauge theories at finite temperature. When a(x=a(x→,t is inhomogeneous, the set of lattice equations of motion do not admit however a simple explicit local solution (while preserving an O(dxμ2 accuracy. We discuss an iterative scheme allowing to overcome this difficulty.

  1. From Enumerating to Generating: A Linear Time Algorithm for Generating 2D Lattice Paths with a Given Number of Turns

    Directory of Open Access Journals (Sweden)

    Ting Kuo

    2015-05-01

    Full Text Available We propose a linear time algorithm, called G2DLP, for generating 2D lattice L(n1, n2 paths, equivalent to two-item  multiset permutations, with a given number of turns. The usage of turn has three meanings: in the context of multiset permutations, it means that two consecutive elements of a permutation belong to two different items; in lattice path enumerations, it means that the path changes its direction, either from eastward to northward or from northward to eastward; in open shop scheduling, it means that we transfer a job from one type of machine to another. The strategy of G2DLP is divide-and-combine; the division is based on the enumeration results of a previous study and is achieved by aid of an integer partition algorithm and a multiset permutation algorithm; the combination is accomplished by a concatenation algorithm that constructs the paths we require. The advantage of G2DLP is twofold. First, it is optimal in the sense that it directly generates all feasible paths without visiting an infeasible one. Second, it can generate all paths in any specified order of turns, for example, a decreasing order or an increasing order. In practice, two applications, scheduling and cryptography, are discussed.

  2. The mGA1.0: A common LISP implementation of a messy genetic algorithm

    Science.gov (United States)

    Goldberg, David E.; Kerzic, Travis

    1990-01-01

    Genetic algorithms (GAs) are finding increased application in difficult search, optimization, and machine learning problems in science and engineering. Increasing demands are being placed on algorithm performance, and the remaining challenges of genetic algorithm theory and practice are becoming increasingly unavoidable. Perhaps the most difficult of these challenges is the so-called linkage problem. Messy GAs were created to overcome the linkage problem of simple genetic algorithms by combining variable-length strings, gene expression, messy operators, and a nonhomogeneous phasing of evolutionary processing. Results on a number of difficult deceptive test functions are encouraging with the mGA always finding global optima in a polynomial number of function evaluations. Theoretical and empirical studies are continuing, and a first version of a messy GA is ready for testing by others. A Common LISP implementation called mGA1.0 is documented and related to the basic principles and operators developed by Goldberg et. al. (1989, 1990). Although the code was prepared with care, it is not a general-purpose code, only a research version. Important data structures and global variations are described. Thereafter brief function descriptions are given, and sample input data are presented together with sample program output. A source listing with comments is also included.

  3. BQP-completeness of scattering in scalar quantum field theory

    Directory of Open Access Journals (Sweden)

    Stephen P. Jordan

    2018-01-01

    Full Text Available Recent work has shown that quantum computers can compute scattering probabilities in massive quantum field theories, with a run time that is polynomial in the number of particles, their energy, and the desired precision. Here we study a closely related quantum field-theoretical problem: estimating the vacuum-to-vacuum transition amplitude, in the presence of spacetime-dependent classical sources, for a massive scalar field theory in (1+1 dimensions. We show that this problem is BQP-hard; in other words, its solution enables one to solve any problem that is solvable in polynomial time by a quantum computer. Hence, the vacuum-to-vacuum amplitude cannot be accurately estimated by any efficient classical algorithm, even if the field theory is very weakly coupled, unless BQP=BPP. Furthermore, the corresponding decision problem can be solved by a quantum computer in a time scaling polynomially with the number of bits needed to specify the classical source fields, and this problem is therefore BQP-complete. Our construction can be regarded as an idealized architecture for a universal quantum computer in a laboratory system described by massive phi^4 theory coupled to classical spacetime-dependent sources.

  4. New technique for number-plate recognition

    Science.gov (United States)

    Guo, Jie; Shi, Peng-Fei

    2001-09-01

    This paper presents an alternative algorithm for number plate recognition. The algorithm consists of three modules. Respectively, they are number plate location module, character segmentation module and character recognition module. Number plate location module extracts the number plate from the detected car image by analyzing the color and the texture properties. Different from most license plate location methods, the algorithm has fewer limits to the car size, the car position in the image and the image background. Character segmentation module applies connected region algorithm both to eliminate noise points and to segment characters. Touching characters and broken characters can be processed correctly. Character recognition module recognizes characters with HHIC (Hierarchical Hybrid Integrated Classifier). The system has been tested with 100 images obtained from crossroad and parking lot, etc, where the cars have different size, position, background and illumination. Successful recognition rate is about 92%. The average processing time is 1.2 second.

  5. Parallel algorithms for numerical linear algebra

    CERN Document Server

    van der Vorst, H

    1990-01-01

    This is the first in a new series of books presenting research results and developments concerning the theory and applications of parallel computers, including vector, pipeline, array, fifth/future generation computers, and neural computers.All aspects of high-speed computing fall within the scope of the series, e.g. algorithm design, applications, software engineering, networking, taxonomy, models and architectural trends, performance, peripheral devices.Papers in Volume One cover the main streams of parallel linear algebra: systolic array algorithms, message-passing systems, algorithms for p

  6. Biased Monte Carlo algorithms on unitary groups

    International Nuclear Information System (INIS)

    Creutz, M.; Gausterer, H.; Sanielevici, S.

    1989-01-01

    We introduce a general updating scheme for the simulation of physical systems defined on unitary groups, which eliminates the systematic errors due to inexact exponentiation of algebra elements. The essence is to work directly with group elements for the stochastic noise. Particular cases of the scheme include the algorithm of Metropolis et al., overrelaxation algorithms, and globally corrected Langevin and hybrid algorithms. The latter are studied numerically for the case of SU(3) theory

  7. Quantum Computation and Algorithms

    International Nuclear Information System (INIS)

    Biham, O.; Biron, D.; Biham, E.; Grassi, M.; Lidar, D.A.

    1999-01-01

    It is now firmly established that quantum algorithms provide a substantial speedup over classical algorithms for a variety of problems, including the factorization of large numbers and the search for a marked element in an unsorted database. In this talk I will review the principles of quantum algorithms, the basic quantum gates and their operation. The combination of superposition and interference, that makes these algorithms efficient, will be discussed. In particular, Grover's search algorithm will be presented as an example. I will show that the time evolution of the amplitudes in Grover's algorithm can be found exactly using recursion equations, for any initial amplitude distribution

  8. Fast algorithms for chiral fermions in 2 dimensions

    Directory of Open Access Journals (Sweden)

    Hyka (Xhako Dafina

    2018-01-01

    Full Text Available In lattice QCD simulations the formulation of the theory in lattice should be chiral in order that symmetry breaking happens dynamically from interactions. In order to guarantee this symmetry on the lattice one uses overlap and domain wall fermions. On the other hand high computational cost of lattice QCD simulations with overlap or domain wall fermions remains a major obstacle of research in the field of elementary particles. We have developed the preconditioned GMRESR algorithm as fast inverting algorithm for chiral fermions in U(1 lattice gauge theory. In this algorithm we used the geometric multigrid idea along the extra dimension.The main result of this work is that the preconditioned GMRESR is capable to accelerate the convergence 2 to 12 times faster than the other optimal algorithms (SHUMR for different coupling constant and lattice 32x32. Also, in this paper we tested it for larger lattice size 64x64. From the results of simulations we can see that our algorithm is faster than SHUMR. This is a very promising result that this algorithm can be adapted also in 4 dimension.

  9. Viability Theory

    CERN Document Server

    Aubin, Jean-Pierre; Saint-Pierre, Patrick

    2011-01-01

    Viability theory designs and develops mathematical and algorithmic methods for investigating the adaptation to viability constraints of evolutions governed by complex systems under uncertainty that are found in many domains involving living beings, from biological evolution to economics, from environmental sciences to financial markets, from control theory and robotics to cognitive sciences. It involves interdisciplinary investigations spanning fields that have traditionally developed in isolation. The purpose of this book is to present an initiation to applications of viability theory, explai

  10. Bernoulli numbers and zeta functions

    CERN Document Server

    Arakawa, Tsuneo; Kaneko, Masanobu

    2014-01-01

    Two major subjects are treated in this book. The main one is the theory of Bernoulli numbers and the other is the theory of zeta functions. Historically, Bernoulli numbers were introduced to give formulas for the sums of powers of consecutive integers. The real reason that they are indispensable for number theory, however, lies in the fact that special values of the Riemann zeta function can be written by using Bernoulli numbers. This leads to more advanced topics, a number of which are treated in this book: Historical remarks on Bernoulli numbers and the formula for the sum of powers of consecutive integers; a formula for Bernoulli numbers by Stirling numbers; the Clausen–von Staudt theorem on the denominators of Bernoulli numbers; Kummer's congruence between Bernoulli numbers and a related theory of p-adic measures; the Euler–Maclaurin summation formula; the functional equation of the Riemann zeta function and the Dirichlet L functions, and their special values at suitable integers; various formulas of ...

  11. Interactive animation of fault-tolerant parallel algorithms

    Energy Technology Data Exchange (ETDEWEB)

    Apgar, S.W.

    1992-02-01

    Animation of algorithms makes understanding them intuitively easier. This paper describes the software tool Raft (Robust Animator of Fault Tolerant Algorithms). The Raft system allows the user to animate a number of parallel algorithms which achieve fault tolerant execution. In particular, we use it to illustrate the key Write-All problem. It has an extensive user-interface which allows a choice of the number of processors, the number of elements in the Write-All array, and the adversary to control the processor failures. The novelty of the system is that the interface allows the user to create new on-line adversaries as the algorithm executes.

  12. An optimized routing algorithm for the automated assembly of standard multimode ribbon fibers in a full-mesh optical backplane

    Science.gov (United States)

    Basile, Vito; Guadagno, Gianluca; Ferrario, Maddalena; Fassi, Irene

    2018-03-01

    In this paper a parametric, modular and scalable algorithm allowing a fully automated assembly of a backplane fiber-optic interconnection circuit is presented. This approach guarantees the optimization of the optical fiber routing inside the backplane with respect to specific criteria (i.e. bending power losses), addressing both transmission performance and overall costs issues. Graph theory has been exploited to simplify the complexity of the NxN full-mesh backplane interconnection topology, firstly, into N independent sub-circuits and then, recursively, into a limited number of loops easier to be generated. Afterwards, the proposed algorithm selects a set of geometrical and architectural parameters whose optimization allows to identify the optimal fiber optic routing for each sub-circuit of the backplane. The topological and numerical information provided by the algorithm are then exploited to control a robot which performs the automated assembly of the backplane sub-circuits. The proposed routing algorithm can be extended to any array architecture and number of connections thanks to its modularity and scalability. Finally, the algorithm has been exploited for the automated assembly of an 8x8 optical backplane realized with standard multimode (MM) 12-fiber ribbons.

  13. Evaluation of imaging protocol for ECT based on CS image reconstruction algorithm

    International Nuclear Information System (INIS)

    Zhou Xiaolin; Yun Mingkai; Cao Xuexiang; Liu Shuangquan; Wang Lu; Huang Xianchao; Wei Long

    2014-01-01

    Single-photon emission computerized tomography and positron emission tomography are essential medical imaging tools, for which the sampling angle number and scan time should be carefully chosen to give a good compromise between image quality and radiopharmaceutical dose. In this study, the image quality of different acquisition protocols was evaluated via varied angle number and count number per angle with Monte Carlo simulation data. It was shown that, when similar imaging counts were used, the factor of acquisition counts was more important than that of the sampling number in emission computerized tomography. To further reduce the activity requirement and the scan duration, an iterative image reconstruction algorithm for limited-view and low-dose tomography based on compressed sensing theory has been developed. The total variation regulation was added to the reconstruction process to improve the signal to noise Ratio and reduce artifacts caused by the limited angle sampling. Maximization of the maximum likelihood of the estimated image and the measured data and minimization of the total variation of the image are alternatively implemented. By using this advanced algorithm, the reconstruction process is able to achieve image quality matching or exceed that of normal scans with only half of the injection radiopharmaceutical dose. (authors)

  14. Network-Oblivious Algorithms

    DEFF Research Database (Denmark)

    Bilardi, Gianfranco; Pietracaprina, Andrea; Pucci, Geppino

    2016-01-01

    A framework is proposed for the design and analysis of network-oblivious algorithms, namely algorithms that can run unchanged, yet efficiently, on a variety of machines characterized by different degrees of parallelism and communication capabilities. The framework prescribes that a network......-oblivious algorithm be specified on a parallel model of computation where the only parameter is the problem’s input size, and then evaluated on a model with two parameters, capturing parallelism granularity and communication latency. It is shown that for a wide class of network-oblivious algorithms, optimality...... of cache hierarchies, to the realm of parallel computation. Its effectiveness is illustrated by providing optimal network-oblivious algorithms for a number of key problems. Some limitations of the oblivious approach are also discussed....

  15. Correlation of theory to wind-tunnel data at Reynolds numbers below 500,000

    Science.gov (United States)

    Evangelista, Raquel; Mcghee, Robert J.; Walker, Betty S.

    1989-01-01

    This paper presents results obtained from two airfoil analysis methods compared with previously published wind tunnel test data at chord Reynolds numbers below 500,000. The analysis methods are from the Eppler-Somers airfoil design/analysis code and from ISES, the Drela-Giles Airfoil design/analysis code. The experimental data are from recent tests of the Eppler 387 airfoil in the NASA Langley Low Turbulence Pressure Tunnel. For R not less than 200,000, lift and pitching moment predictions from both theories compare well with experiment. Drag predictions from both theories also agree with experiment, although to different degrees. However, most of the drag predictions from the Eppler-Somers code are accompanied with separation bubble warnings which indicate that the drag predictions are too low. With the Drela-Giles code, there is a large discrepancy between the computed and experimental pressure distributions in cases with laminar separation bubbles, although the drag polar predictions are similar in trend to experiment.

  16. A deep cut ellipsoid algorithm for convex programming : Theory and applications

    NARCIS (Netherlands)

    J.B.G. Frenk (Hans); J.A.S. Gromicho (Joaquim); S. Zhang (Shuzhong)

    1994-01-01

    textabstractThis paper proposes a deep cut version of the ellipsoid algorithm for solving a general class of continuous convex programming problems. In each step the algorithm does not require more computational effort to construct these deep cuts than its corresponding central cut version. Rules

  17. Economic dispatch using chaotic bat algorithm

    International Nuclear Information System (INIS)

    Adarsh, B.R.; Raghunathan, T.; Jayabarathi, T.; Yang, Xin-She

    2016-01-01

    This paper presents the application of a new metaheuristic optimization algorithm, the chaotic bat algorithm for solving the economic dispatch problem involving a number of equality and inequality constraints such as power balance, prohibited operating zones and ramp rate limits. Transmission losses and multiple fuel options are also considered for some problems. The chaotic bat algorithm, a variant of the basic bat algorithm, is obtained by incorporating chaotic sequences to enhance its performance. Five different example problems comprising 6, 13, 20, 40 and 160 generating units are solved to demonstrate the effectiveness of the algorithm. The algorithm requires little tuning by the user, and the results obtained show that it either outperforms or compares favorably with several existing techniques reported in literature. - Highlights: • The chaotic bat algorithm, a new metaheuristic optimization algorithm has been used. • The problem solved – the economic dispatch problem – is nonlinear, discontinuous. • It has number of equality and inequality constraints. • The algorithm has been demonstrated to be applicable on high dimensional problems.

  18. Boosting foundations and algorithms

    CERN Document Server

    Schapire, Robert E

    2012-01-01

    Boosting is an approach to machine learning based on the idea of creating a highly accurate predictor by combining many weak and inaccurate "rules of thumb." A remarkably rich theory has evolved around boosting, with connections to a range of topics, including statistics, game theory, convex optimization, and information geometry. Boosting algorithms have also enjoyed practical success in such fields as biology, vision, and speech processing. At various times in its history, boosting has been perceived as mysterious, controversial, even paradoxical.

  19. Maximization Network Throughput Based on Improved Genetic Algorithm and Network Coding for Optical Multicast Networks

    Science.gov (United States)

    Wei, Chengying; Xiong, Cuilian; Liu, Huanlin

    2017-12-01

    Maximal multicast stream algorithm based on network coding (NC) can improve the network's throughput for wavelength-division multiplexing (WDM) networks, which however is far less than the network's maximal throughput in terms of theory. And the existing multicast stream algorithms do not give the information distribution pattern and routing in the meantime. In the paper, an improved genetic algorithm is brought forward to maximize the optical multicast throughput by NC and to determine the multicast stream distribution by hybrid chromosomes construction for multicast with single source and multiple destinations. The proposed hybrid chromosomes are constructed by the binary chromosomes and integer chromosomes, while the binary chromosomes represent optical multicast routing and the integer chromosomes indicate the multicast stream distribution. A fitness function is designed to guarantee that each destination can receive the maximum number of decoding multicast streams. The simulation results showed that the proposed method is far superior over the typical maximal multicast stream algorithms based on NC in terms of network throughput in WDM networks.

  20. Unconventional Algorithms: Complementarity of Axiomatics and Construction

    Directory of Open Access Journals (Sweden)

    Gordana Dodig Crnkovic

    2012-10-01

    Full Text Available In this paper, we analyze axiomatic and constructive issues of unconventional computations from a methodological and philosophical point of view. We explain how the new models of algorithms and unconventional computations change the algorithmic universe, making it open and allowing increased flexibility and expressive power that augment creativity. At the same time, the greater power of new types of algorithms also results in the greater complexity of the algorithmic universe, transforming it into the algorithmic multiverse and demanding new tools for its study. That is why we analyze new powerful tools brought forth by local mathematics, local logics, logical varieties and the axiomatic theory of algorithms, automata and computation. We demonstrate how these new tools allow efficient navigation in the algorithmic multiverse. Further work includes study of natural computation by unconventional algorithms and constructive approaches.

  1. DISCRETE MATHEMATICS/NUMBER THEORY

    OpenAIRE

    Mrs. Manju Devi*

    2017-01-01

    Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. In contrast to real numbers that have the property of varying "smoothly", the objects studied in discrete mathematics such as integers, graphs, and statements do not vary smoothly in this way, but have distinct, separated values. Discrete mathematics therefore excludes topics in "continuous mathematics" such as calculus and analysis. Discrete objects can often be enumerated by ...

  2. Learning algorithms and automatic processing of languages

    International Nuclear Information System (INIS)

    Fluhr, Christian Yves Andre

    1977-01-01

    This research thesis concerns the field of artificial intelligence. It addresses learning algorithms applied to automatic processing of languages. The author first briefly describes some mechanisms of human intelligence in order to describe how these mechanisms are simulated on a computer. He outlines the specific role of learning in various manifestations of intelligence. Then, based on the Markov's algorithm theory, the author discusses the notion of learning algorithm. Two main types of learning algorithms are then addressed: firstly, an 'algorithm-teacher dialogue' type sanction-based algorithm which aims at learning how to solve grammatical ambiguities in submitted texts; secondly, an algorithm related to a document system which structures semantic data automatically obtained from a set of texts in order to be able to understand by references to any question on the content of these texts

  3. An Algorithmic Information Calculus for Causal Discovery and Reprogramming Systems

    KAUST Repository

    Zenil, Hector

    2017-09-08

    We introduce a conceptual framework and an interventional calculus to steer and manipulate systems based on their intrinsic algorithmic probability using the universal principles of the theory of computability and algorithmic information. By applying sequences of controlled interventions to systems and networks, we estimate how changes in their algorithmic information content are reflected in positive/negative shifts towards and away from randomness. The strong connection between approximations to algorithmic complexity (the size of the shortest generating mechanism) and causality induces a sequence of perturbations ranking the network elements by the steering capabilities that each of them is capable of. This new dimension unmasks a separation between causal and non-causal components providing a suite of powerful parameter-free algorithms of wide applicability ranging from optimal dimension reduction, maximal randomness analysis and system control. We introduce methods for reprogramming systems that do not require the full knowledge or access to the system\\'s actual kinetic equations or any probability distributions. A causal interventional analysis of synthetic and regulatory biological networks reveals how the algorithmic reprogramming qualitatively reshapes the system\\'s dynamic landscape. For example, during cellular differentiation we find a decrease in the number of elements corresponding to a transition away from randomness and a combination of the system\\'s intrinsic properties and its intrinsic capabilities to be algorithmically reprogrammed can reconstruct an epigenetic landscape. The interventional calculus is broadly applicable to predictive causal inference of systems such as networks and of relevance to a variety of machine and causal learning techniques driving model-based approaches to better understanding and manipulate complex systems.

  4. A DEEP CUT ELLIPSOID ALGORITHM FOR CONVEX-PROGRAMMING - THEORY AND APPLICATIONS

    NARCIS (Netherlands)

    FRENK, JBG; GROMICHO, J; ZHANG, S

    1994-01-01

    This paper proposes a deep cut version of the ellipsoid algorithm for solving a general class of continuous convex programming problems. In each step the algorithm does not require more computational effort to construct these deep cuts than its corresponding central cut version. Rules that prevent

  5. A Deep Cut Ellipsoid Algorithm for convex Programming: theory and Applications

    NARCIS (Netherlands)

    Frenk, J.B.G.; Gromicho Dos Santos, J.A.; Zhang, S.

    1994-01-01

    This paper proposes a deep cut version of the ellipsoid algorithm for solving a general class of continuous convex programming problems. In each step the algorithm does not require more computational effort to construct these deep cuts than its corresponding central cut version. Rules that prevent

  6. Free vibration analysis of delaminated composite shells using different shell theories

    International Nuclear Information System (INIS)

    Nanda, Namita; Sahu, S.K.

    2012-01-01

    Free vibration response of laminated composite shells with delamination is presented using the finite element method based on first order shear deformation theory. The shell theory used is the extension of dynamic, shear deformable theory according to the Sanders' first approximation for doubly curved shells, which can be reduced to Love's and Donnell's theories by means of tracers. An eight-noded C 0 continuity, isoparametric quadrilateral element with five degrees of freedom per node is used in the formulation. For modeling the delamination, multipoint constraint algorithm is incorporated in the finite element code. The natural frequencies of the delaminated cylindrical (CYL), spherical (SPH) and hyperbolic paraboloid (HYP) shells are determined by using the above mentioned shell theories, namely Sanders', Love's, and Donnell's. The validity of the present approach is established by comparing the authors' results with those available in the literature. Additional studies on free vibration response of CYL, SPH and HYP shells are conducted to assess the effects of delamination size and number of layers considering all three shell theories. It is shown that shell theories according to Sanders and Love always predict practically identical frequencies. Donnell's theory gives reliable results only for shallow shells. Moreover, the natural frequency is found to be very sensitive to delamination size and number of layers in the shell.

  7. A novel algorithm of artificial immune system for high-dimensional function numerical optimization

    Institute of Scientific and Technical Information of China (English)

    DU Haifeng; GONG Maoguo; JIAO Licheng; LIU Ruochen

    2005-01-01

    Based on the clonal selection theory and immune memory theory, a novel artificial immune system algorithm, immune memory clonal programming algorithm (IMCPA), is put forward. Using the theorem of Markov chain, it is proved that IMCPA is convergent. Compared with some other evolutionary programming algorithms (like Breeder genetic algorithm), IMCPA is shown to be an evolutionary strategy capable of solving complex machine learning tasks, like high-dimensional function optimization, which maintains the diversity of the population and avoids prematurity to some extent, and has a higher convergence speed.

  8. New Optimization Algorithms in Physics

    CERN Document Server

    Hartmann, Alexander K

    2004-01-01

    Many physicists are not aware of the fact that they can solve their problems by applying optimization algorithms. Since the number of such algorithms is steadily increasing, many new algorithms have not been presented comprehensively until now. This presentation of recently developed algorithms applied in physics, including demonstrations of how they work and related results, aims to encourage their application, and as such the algorithms selected cover concepts and methods from statistical physics to optimization problems emerging in theoretical computer science.

  9. Digital and discrete geometry theory and algorithms

    CERN Document Server

    Chen, Li

    2014-01-01

    This book provides comprehensive coverage of the modern methods for geometric problems in the computing sciences. It also covers concurrent topics in data sciences including geometric processing, manifold learning, Google search, cloud data, and R-tree for wireless networks and BigData.The author investigates digital geometry and its related constructive methods in discrete geometry, offering detailed methods and algorithms. The book is divided into five sections: basic geometry; digital curves, surfaces and manifolds; discretely represented objects; geometric computation and processing; and a

  10. Parameterized Algorithms for Survivable Network Design with Uniform Demands

    DEFF Research Database (Denmark)

    Bang-Jensen, Jørgen; Klinkby Knudsen, Kristine Vitting; Saurabh, Saket

    2018-01-01

    problem in combinatorial optimization that captures numerous well-studied problems in graph theory and graph algorithms. Consequently, there is a long line of research into exact-polynomial time algorithms as well as approximation algorithms for various restrictions of this problem. An important...... that SNDP is W[1]-hard for both arc and vertex connectivity versions on digraphs. The core of our algorithms is composed of new combinatorial results on connectivity in digraphs and undirected graphs....

  11. Algorithm FIRE-Feynman Integral REduction

    International Nuclear Information System (INIS)

    Smirnov, A.V.

    2008-01-01

    The recently developed algorithm FIRE performs the reduction of Feynman integrals to master integrals. It is based on a number of strategies, such as applying the Laporta algorithm, the s-bases algorithm, region-bases and integrating explicitly over loop momenta when possible. Currently it is being used in complicated three-loop calculations.

  12. Analyzing the evolutionary mechanisms of the Air Transportation System-of-Systems using network theory and machine learning algorithms

    Science.gov (United States)

    Kotegawa, Tatsuya

    Complexity in the Air Transportation System (ATS) arises from the intermingling of many independent physical resources, operational paradigms, and stakeholder interests, as well as the dynamic variation of these interactions over time. Currently, trade-offs and cost benefit analyses of new ATS concepts are carried out on system-wide evaluation simulations driven by air traffic forecasts that assume fixed airline routes. However, this does not well reflect reality as airlines regularly add and remove routes. A airline service route network evolution model that projects route addition and removal was created and combined with state-of-the-art air traffic forecast methods to better reflect the dynamic properties of the ATS in system-wide simulations. Guided by a system-of-systems framework, network theory metrics and machine learning algorithms were applied to develop the route network evolution models based on patterns extracted from historical data. Constructing the route addition section of the model posed the greatest challenge due to the large pool of new link candidates compared to the actual number of routes historically added to the network. Of the models explored, algorithms based on logistic regression, random forests, and support vector machines showed best route addition and removal forecast accuracies at approximately 20% and 40%, respectively, when validated with historical data. The combination of network evolution models and a system-wide evaluation tool quantified the impact of airline route network evolution on air traffic delay. The expected delay minutes when considering network evolution increased approximately 5% for a forecasted schedule on 3/19/2020. Performance trade-off studies between several airline route network topologies from the perspectives of passenger travel efficiency, fuel burn, and robustness were also conducted to provide bounds that could serve as targets for ATS transformation efforts. The series of analysis revealed that high

  13. New algorithms derived from the synthesis method. Application to diffusion problems

    International Nuclear Information System (INIS)

    Rouzaud, Philippe.

    1976-05-01

    Two algorithms to compute the neutron distribution in a nuclear reactor are presented. These algorithms, the iterative synthesis method (MSI) and the synthesis method by deflation (MSD), are derived from the classical synthesis method (MSC). They retain the most important advantages of MSC (computing time and memory storage reduced with regard to finite difference methods) and avoid its drawbacks: choice of trial functions; choice of weighting functions; choice of the number of terms (for MSD only). Extensive numerical checks of the three methods (MSC, MSI, MSD) were carried out on two fast reactor configurations described in plane geometry (X,Y). Monoenergetic and multigroup theories were successively used. The use of MSI and MSD allows a significant reduction of the discrepancies between the finite difference method and the synthesis method for the reactivity values and the flux distribution [fr

  14. Control algorithms for autonomous robot navigation

    International Nuclear Information System (INIS)

    Jorgensen, C.C.

    1985-01-01

    This paper examines control algorithm requirements for autonomous robot navigation outside laboratory environments. Three aspects of navigation are considered: navigation control in explored terrain, environment interactions with robot sensors, and navigation control in unanticipated situations. Major navigation methods are presented and relevance of traditional human learning theory is discussed. A new navigation technique linking graph theory and incidental learning is introduced

  15. Golden Sine Algorithm: A Novel Math-Inspired Algorithm

    Directory of Open Access Journals (Sweden)

    TANYILDIZI, E.

    2017-05-01

    Full Text Available In this study, Golden Sine Algorithm (Gold-SA is presented as a new metaheuristic method for solving optimization problems. Gold-SA has been developed as a new search algorithm based on population. This math-based algorithm is inspired by sine that is a trigonometric function. In the algorithm, random individuals are created as many as the number of search agents with uniform distribution for each dimension. The Gold-SA operator searches to achieve a better solution in each iteration by trying to bring the current situation closer to the target value. The solution space is narrowed by the golden section so that the areas that are supposed to give only good results are scanned instead of the whole solution space scan. In the tests performed, it is seen that Gold-SA has better results than other population based methods. In addition, Gold-SA has fewer algorithm-dependent parameters and operators than other metaheuristic methods, increasing the importance of this method by providing faster convergence of this new method.

  16. A hybrid intelligent algorithm for portfolio selection problem with fuzzy returns

    Science.gov (United States)

    Li, Xiang; Zhang, Yang; Wong, Hau-San; Qin, Zhongfeng

    2009-11-01

    Portfolio selection theory with fuzzy returns has been well developed and widely applied. Within the framework of credibility theory, several fuzzy portfolio selection models have been proposed such as mean-variance model, entropy optimization model, chance constrained programming model and so on. In order to solve these nonlinear optimization models, a hybrid intelligent algorithm is designed by integrating simulated annealing algorithm, neural network and fuzzy simulation techniques, where the neural network is used to approximate the expected value and variance for fuzzy returns and the fuzzy simulation is used to generate the training data for neural network. Since these models are used to be solved by genetic algorithm, some comparisons between the hybrid intelligent algorithm and genetic algorithm are given in terms of numerical examples, which imply that the hybrid intelligent algorithm is robust and more effective. In particular, it reduces the running time significantly for large size problems.

  17. Problems in particle theory

    International Nuclear Information System (INIS)

    Adler, S.L.; Wilczek, F.

    1993-11-01

    Areas of emphasis include acceleration algorithms for the Monte Carlo analysis of lattice field and gauge theories, quaternionic generalizations of complex quantum mechanics and field theory, application of the renormalization group to the QCD phase transition, the quantum Hall effect, and black holes. Other work involved string theory, statistical properties of energy levels in integrable quantum systems, baryon asymmetry and the electroweak phase transition, anisotropies of the cosmic microwave background, and theory of superconductors

  18. Partial Evaluation of the Euclidian Algorithm

    DEFF Research Database (Denmark)

    Danvy, Olivier; Goldberg, Mayer

    1997-01-01

    -like behavior. Each of them presents a challenge for partial evaluation. The Euclidian algorithm is one of them, and in this article, we make it amenable to partial evaluation. We observe that the number of iterations in the Euclidian algorithm is bounded by a number that can be computed given either of the two...... arguments. We thus rephrase this algorithm using bounded recursion. The resulting program is better suited for automatic unfolding and thus for partial evaluation. Its specialization is efficient....

  19. Numerical studies of fermionic field theories at large-N

    International Nuclear Information System (INIS)

    Dickens, T.A.

    1987-01-01

    A description of an algorithm, which may be used to study large-N theories with or without fermions, is presented. As an initial test of the method, the spectrum of continuum QCD in 1 + 1 dimensions is determined and compared to previously obtained results. Exact solutions of 1 + 1 dimensional lattice versions of the free fermion theory, the Gross-Neveu model, and QCD are obtained. Comparison of these exact results with results from the numerical algorithm is used to test the algorithms, and more importantly, to determine the errors incurred from the approximations used in the numerical technique. Numerical studies of the above three lattice theories in higher dimensions are also presented. The results are again compared to exact solutions for free fermions and the Gross-Neveu model; perturbation theory is used to derive expansions with which the numerical results for QCD may be compared. The numerical algorithm may also be used to study the euclidean formulation of lattice gauge theories. Results for 1 + 1 dimensional euclidean lattice QCD are compared to the exact solution of this model

  20. Application of Mathematical Symmetrical Group Theory in the Creation Process of Digital Holograms

    Directory of Open Access Journals (Sweden)

    Agustín Pérez-Ramírez

    2017-01-01

    Full Text Available This work presents an algorithm to reduce the multiplicative computational complexity in the creation of digital holograms, where an object is considered as a set of point sources using mathematical symmetry properties of both the core in the Fresnel integral and the image. The image is modeled using group theory. This algorithm has multiplicative complexity equal to zero and an additive complexity (k-1N2 for the case of sparse matrices or binary images, where k is the number of pixels other than zero and N2 is the total of points in the image.

  1. Analytic MHD Theory for Earth's Bow Shock at Low Mach Numbers

    Science.gov (United States)

    Grabbe, Crockett L.; Cairns, Iver H.

    1995-01-01

    A previous MHD theory for the density jump at the Earth's bow shock, which assumed the Alfven M(A) and sonic M(s) Mach numbers are both much greater than 1, is reanalyzed and generalized. It is shown that the MHD jump equation can be analytically solved much more directly using perturbation theory, with the ordering determined by M(A) and M(s), and that the first-order perturbation solution is identical to the solution found in the earlier theory. The second-order perturbation solution is calculated, whereas the earlier approach cannot be used to obtain it. The second-order terms generally are important over most of the range of M(A) and M(s) in the solar wind when the angle theta between the normal to the bow shock and magnetic field is not close to 0 deg or 180 deg (the solutions are symmetric about 90 deg). This new perturbation solution is generally accurate under most solar wind conditions at 1 AU, with the exception of low Mach numbers when theta is close to 90 deg. In this exceptional case the new solution does not improve on the first-order solutions obtained earlier, and the predicted density ratio can vary by 10-20% from the exact numerical MHD solutions. For theta approx. = 90 deg another perturbation solution is derived that predicts the density ratio much more accurately. This second solution is typically accurate for quasi-perpendicular conditions. Taken together, these two analytical solutions are generally accurate for the Earth's bow shock, except in the rare circumstance that M(A) is less than or = 2. MHD and gasdynamic simulations have produced empirical models in which the shock's standoff distance a(s) is linearly related to the density jump ratio X at the subsolar point. Using an empirical relationship between a(s) and X obtained from MHD simulations, a(s) values predicted using the MHD solutions for X are compared with the predictions of phenomenological models commonly used for modeling observational data, and with the predictions of a

  2. The coherent state variational algorithm and the QCD deconfinement phase transition

    International Nuclear Information System (INIS)

    Somsky, W.R.

    1989-01-01

    This thesis describes the coherent state variational algorithm, its implementation in a recently completed set of computer programs, and its application to the study of the QCD deconfinement phase transition. The coherent state variational algorithm is a computational method for studying the large-N limit of non-abelian gauge theories by direct exploitation of the classical nature of this limit. Unlike Monte Carlo methods, this technique is applicable to both euclidean and hamiltonian formulations of lattice gauge theories and is deterministic, rather than statistical, in nature. The first part of this thesis presents the theoretical basis of the coherent state algorithm and describes the application of the algorithm, to non-abelian lattice gauge theories. The second part describes the symbolic methods involved in the computer implementation of the coherent state algorithm and gives an overview of the programs which form the full coherent state implementation. The final part of this thesis discusses the application of the coherent state algorithm to the study of the QCD deconfinement phase transition at large N. The results obtained are indicative of a second-order transition for lattices of temporal extent N ν = 1 and N τ = 2 in both three and four space-time dimensions

  3. Tradeoffs Between Branch Mispredictions and Comparisons for Sorting Algorithms

    DEFF Research Database (Denmark)

    Brodal, Gerth Stølting; Moruz, Gabriel

    2005-01-01

    Branch mispredictions is an important factor affecting the running time in practice. In this paper we consider tradeoffs between the number of branch mispredictions and the number of comparisons for sorting algorithms in the comparison model. We prove that a sorting algorithm using O(dnlog n......) comparisons performs Omega(nlogd n) branch mispredictions. We show that Multiway MergeSort achieves this tradeoff by adopting a multiway merger with a low number of branch mispredictions. For adaptive sorting algorithms we similarly obtain that an algorithm performing O(dn(1+log (1+Inv/n))) comparisons must...... perform Omega(nlogd (1+Inv/n)) branch mispredictions, where Inv is the number of inversions in the input. This tradeoff can be achieved by GenericSort by Estivill-Castro and Wood by adopting a multiway division protocol and a multiway merging algorithm with a low number of branch mispredictions....

  4. Analytic number theory an introductory course

    CERN Document Server

    Bateman, Paul T

    2004-01-01

    This valuable book focuses on a collection of powerful methods ofanalysis that yield deep number-theoretical estimates. Particularattention is given to counting functions of prime numbers andmultiplicative arithmetic functions. Both real variable ("elementary")and complex variable ("analytic") methods are employed.

  5. Understanding how replication processes can maintain systems away from equilibrium using Algorithmic Information Theory.

    Science.gov (United States)

    Devine, Sean D

    2016-02-01

    Replication can be envisaged as a computational process that is able to generate and maintain order far-from-equilibrium. Replication processes, can self-regulate, as the drive to replicate can counter degradation processes that impact on a system. The capability of replicated structures to access high quality energy and eject disorder allows Landauer's principle, in conjunction with Algorithmic Information Theory, to quantify the entropy requirements to maintain a system far-from-equilibrium. Using Landauer's principle, where destabilising processes, operating under the second law of thermodynamics, change the information content or the algorithmic entropy of a system by ΔH bits, replication processes can access order, eject disorder, and counter the change without outside interventions. Both diversity in replicated structures, and the coupling of different replicated systems, increase the ability of the system (or systems) to self-regulate in a changing environment as adaptation processes select those structures that use resources more efficiently. At the level of the structure, as selection processes minimise the information loss, the irreversibility is minimised. While each structure that emerges can be said to be more entropically efficient, as such replicating structures proliferate, the dissipation of the system as a whole is higher than would be the case for inert or simpler structures. While a detailed application to most real systems would be difficult, the approach may well be useful in understanding incremental changes to real systems and provide broad descriptions of system behaviour. Copyright © 2016 The Author. Published by Elsevier Ireland Ltd.. All rights reserved.

  6. Technical Note: Modification of the standard gain correction algorithm to compensate for the number of used reference flat frames in detector performance studies

    International Nuclear Information System (INIS)

    Konstantinidis, Anastasios C.; Olivo, Alessandro; Speller, Robert D.

    2011-01-01

    Purpose: The x-ray performance evaluation of digital x-ray detectors is based on the calculation of the modulation transfer function (MTF), the noise power spectrum (NPS), and the resultant detective quantum efficiency (DQE). The flat images used for the extraction of the NPS should not contain any fixed pattern noise (FPN) to avoid contamination from nonstochastic processes. The ''gold standard'' method used for the reduction of the FPN (i.e., the different gain between pixels) in linear x-ray detectors is based on normalization with an average reference flat-field. However, the noise in the corrected image depends on the number of flat frames used for the average flat image. The aim of this study is to modify the standard gain correction algorithm to make it independent on the used reference flat frames. Methods: Many publications suggest the use of 10-16 reference flat frames, while other studies use higher numbers (e.g., 48 frames) to reduce the propagated noise from the average flat image. This study quantifies experimentally the effect of the number of used reference flat frames on the NPS and DQE values and appropriately modifies the gain correction algorithm to compensate for this effect. Results: It is shown that using the suggested gain correction algorithm a minimum number of reference flat frames (i.e., down to one frame) can be used to eliminate the FPN from the raw flat image. This saves computer memory and time during the x-ray performance evaluation. Conclusions: The authors show that the method presented in the study (a) leads to the maximum DQE value that one would have by using the conventional method and very large number of frames and (b) has been compared to an independent gain correction method based on the subtraction of flat-field images, leading to identical DQE values. They believe this provides robust validation of the proposed method.

  7. Engineering a Cache-Oblivious Sorting Algorithm

    DEFF Research Database (Denmark)

    Brodal, Gerth Stølting; Fagerberg, Rolf; Vinther, Kristoffer

    2007-01-01

    This paper is an algorithmic engineering study of cache-oblivious sorting. We investigate by empirical methods a number of implementation issues and parameter choices for the cache-oblivious sorting algorithm Lazy Funnelsort, and compare the final algorithm with Quicksort, the established standard...

  8. Aerodynamic characteristics of wings designed with a combined-theory method to cruise at a Mach number of 4.5

    Science.gov (United States)

    Mack, Robert J.

    1988-01-01

    A wind-tunnel study was conducted to determine the capability of a method combining linear theory and shock-expansion theory to design optimum camber surfaces for wings that will fly at high-supersonic/low-hypersonic speeds. Three force models (a flat-plate reference wing and two cambered and twisted wings) were used to obtain aerodynamic lift, drag, and pitching-moment data. A fourth pressure-orifice model was used to obtain surface-pressure data. All four wing models had the same planform, airfoil section, and centerbody area distribution. The design Mach number was 4.5, but data were also obtained at Mach numbers of 3.5 and 4.0. Results of these tests indicated that the use of airfoil thickness as a theoretical optimum, camber-surface design constraint did not improve the aerodynamic efficiency or performance of a wing as compared with a wing that was designed with a zero-thickness airfoil (linear-theory) constraint.

  9. FFLP problem with symmetric trapezoidal fuzzy numbers

    Directory of Open Access Journals (Sweden)

    Reza Daneshrad

    2015-04-01

    Full Text Available The most popular approach for solving fully fuzzy linear programming (FFLP problems is to convert them into the corresponding deterministic linear programs. Khan et al. (2013 [Khan, I. U., Ahmad, T., & Maan, N. (2013. A simplified novel technique for solving fully fuzzy linear programming problems. Journal of Optimization Theory and Applications, 159(2, 536-546.] claimed that there had been no method in the literature to find the fuzzy optimal solution of a FFLP problem without converting it into crisp linear programming problem, and proposed a technique for the same. Others showed that the fuzzy arithmetic operation used by Khan et al. (2013 had some problems in subtraction and division operations, which could lead to misleading results. Recently, Ezzati et al. (2014 [Ezzati, R., Khorram, E., & Enayati, R. (2014. A particular simplex algorithm to solve fuzzy lexicographic multi-objective linear programming problems and their sensitivity analysis on the priority of the fuzzy objective functions. Journal of Intelligent and Fuzzy Systems, 26(5, 2333-2358.] defined a new operation on symmetric trapezoidal fuzzy numbers and proposed a new algorithm to find directly a lexicographic/preemptive fuzzy optimal solution of a fuzzy lexicographic multi-objective linear programming problem by using new fuzzy arithmetic operations, but their model was not fully fuzzy optimization. In this paper, a new method, by using Ezzati et al. (2014’s fuzzy arithmetic operation and a fuzzy version of simplex algorithm, is proposed for solving FFLP problem whose parameters are represented by symmetric trapezoidal fuzzy number without converting the given problem into crisp equivalent problem. By using the proposed method, the fuzzy optimal solution of FFLP problem can be easily obtained. A numerical example is provided to illustrate the proposed method.

  10. Adaptive testing with equated number-correct scoring

    NARCIS (Netherlands)

    van der Linden, Willem J.

    1999-01-01

    A constrained CAT algorithm is presented that automatically equates the number-correct scores on adaptive tests. The algorithm can be used to equate number-correct scores across different administrations of the same adaptive test as well as to an external reference test. The constraints are derived

  11. Contribution from the interaction Hamiltonian to the expectation value of particle number with the non-equilibrium quantum field theory

    International Nuclear Information System (INIS)

    Hotta, Ryuuichi; Morozumi, Takuya; Takata, Hiroyuki

    2012-01-01

    We develop the method analyzing particle number non-conserving phenomena with non-equilibrium quantum field-theory. In this study, we consider a CP violating model with interaction Hamiltonian that breaks particle number conservation. To derive the quantum Boltzmann equation for the particle number, we solve Schwinger-Dyson equation, which are obtained from two particle irreducible closed-time-path (2PI CTP) effective action. In this calculation, we show the contribution from interaction Hamiltonian to the time evolution of expectation value of particle number.

  12. Another higher order Langevin algorithm for QCD

    International Nuclear Information System (INIS)

    Kronfeld, A.S.

    1986-01-01

    This note provides an algorithm for integrating the Langevin equation which is second order. It introduces a term into the drift force which is a product of the Gaussian noise and a second derivative of the action. The specific application presented here is for nonabelian gauge theories interacting with fermions, e.g. QCD, for which it requires less memory than the Runge-Kutta algorithm of the same order. The memory and computational requirements of Euler, Runge-Kutta, and the present algorithm are compared. (orig.)

  13. A Novel Hierarchical Model to Locate Health Care Facilities with Fuzzy Demand Solved by Harmony Search Algorithm

    Directory of Open Access Journals (Sweden)

    Mehdi Alinaghian

    2014-08-01

    Full Text Available In the field of health losses resulting from failure to establish the facilities in a suitable location and the required number, beyond the cost and quality of service will result in an increase in mortality and the spread of diseases. So the facility location models have special importance in this area. In this paper, a successively inclusive hierarchical model for location of health centers in term of the transfer of patients from a lower level to a higher level of health centers has been developed. Since determination the exact number of demand for health care in the future is difficult and in order to make the model close to the real conditions of demand uncertainty, a fuzzy programming model based on credibility theory is considered. To evaluate the proposed model, several numerical examples are solved in small size. In order to solve large scale problems, a meta-heuristic algorithm based on harmony search algorithm was developed in conjunction with the GAMS software which indicants the performance of the proposed algorithm.

  14. Consensus algorithm in smart grid and communication networks

    Science.gov (United States)

    Alfagee, Husain Abdulaziz

    On a daily basis, consensus theory attracts more and more researches from different areas of interest, to apply its techniques to solve technical problems in a way that is faster, more reliable, and even more precise than ever before. A power system network is one of those fields that consensus theory employs extensively. The use of the consensus algorithm to solve the Economic Dispatch and Load Restoration Problems is a good example. Instead of a conventional central controller, some researchers have explored an algorithm to solve the above mentioned problems, in a distribution manner, using the consensus algorithm, which is based on calculation methods, i.e., non estimation methods, for updating the information consensus matrix. Starting from this point of solving these types of problems mentioned, specifically, in a distribution fashion, using the consensus algorithm, we have implemented a new advanced consensus algorithm. It is based on the adaptive estimation techniques, such as the Gradient Algorithm and the Recursive Least Square Algorithm, to solve the same problems. This advanced work was tested on different case studies that had formerly been explored, as seen in references 5, 7, and 18. Three and five generators, or agents, with different topologies, correspond to the Economic Dispatch Problem and the IEEE 16-Bus power system corresponds to the Load Restoration Problem. In all the cases we have studied, the results met our expectations with extreme accuracy, and completely matched the results of the previous researchers. There is little question that this research proves the capability and dependability of using the consensus algorithm, based on the estimation methods as the Gradient Algorithm and the Recursive Least Square Algorithm to solve such power problems.

  15. Comparison between iterative wavefront control algorithm and direct gradient wavefront control algorithm for adaptive optics system

    Science.gov (United States)

    Cheng, Sheng-Yi; Liu, Wen-Jin; Chen, Shan-Qiu; Dong, Li-Zhi; Yang, Ping; Xu, Bing

    2015-08-01

    Among all kinds of wavefront control algorithms in adaptive optics systems, the direct gradient wavefront control algorithm is the most widespread and common method. This control algorithm obtains the actuator voltages directly from wavefront slopes through pre-measuring the relational matrix between deformable mirror actuators and Hartmann wavefront sensor with perfect real-time characteristic and stability. However, with increasing the number of sub-apertures in wavefront sensor and deformable mirror actuators of adaptive optics systems, the matrix operation in direct gradient algorithm takes too much time, which becomes a major factor influencing control effect of adaptive optics systems. In this paper we apply an iterative wavefront control algorithm to high-resolution adaptive optics systems, in which the voltages of each actuator are obtained through iteration arithmetic, which gains great advantage in calculation and storage. For AO system with thousands of actuators, the computational complexity estimate is about O(n2) ˜ O(n3) in direct gradient wavefront control algorithm, while the computational complexity estimate in iterative wavefront control algorithm is about O(n) ˜ (O(n)3/2), in which n is the number of actuators of AO system. And the more the numbers of sub-apertures and deformable mirror actuators, the more significant advantage the iterative wavefront control algorithm exhibits. Project supported by the National Key Scientific and Research Equipment Development Project of China (Grant No. ZDYZ2013-2), the National Natural Science Foundation of China (Grant No. 11173008), and the Sichuan Provincial Outstanding Youth Academic Technology Leaders Program, China (Grant No. 2012JQ0012).

  16. Search for a perfect generator of random numbers

    International Nuclear Information System (INIS)

    Musyck, E.

    1977-01-01

    Theoretical tests have been carried out by COVEYOU and MAC PHERSON to verify the applications of the LEHMER algorithm. In a similar way, a theoretical method is proposed to evaluate in a rigorous way the random character of numbers generated by a shift register. This theory introduces the concept of ''degree of randomness'' of the elements, taken in a definite order, of a shift register. It permits making the judicious choice of the elements of the shift register which will produce the bits of the random numbers. On the other hand, a calculation method is developed in order to verify the primitive character of any shift register of high complexity. A new test, called ''slice test'', of empirical and theoretical use is also described; it constitutes a significant contribution to the understanding of certain properties of pseudo-random sequences. As a practical example, a random number generator structure formed with 32 bits, built out of a shift register with 61 elements and 60 modulo-2 adder circuits was made. The author is convinced that this generator can be considered to be practically perfect for all empirical applications of random numbers, particularly for the solution of Monte-Carlo problems. (author)

  17. Reactive Collision Avoidance Algorithm

    Science.gov (United States)

    Scharf, Daniel; Acikmese, Behcet; Ploen, Scott; Hadaegh, Fred

    2010-01-01

    The reactive collision avoidance (RCA) algorithm allows a spacecraft to find a fuel-optimal trajectory for avoiding an arbitrary number of colliding spacecraft in real time while accounting for acceleration limits. In addition to spacecraft, the technology can be used for vehicles that can accelerate in any direction, such as helicopters and submersibles. In contrast to existing, passive algorithms that simultaneously design trajectories for a cluster of vehicles working to achieve a common goal, RCA is implemented onboard spacecraft only when an imminent collision is detected, and then plans a collision avoidance maneuver for only that host vehicle, thus preventing a collision in an off-nominal situation for which passive algorithms cannot. An example scenario for such a situation might be when a spacecraft in the cluster is approaching another one, but enters safe mode and begins to drift. Functionally, the RCA detects colliding spacecraft, plans an evasion trajectory by solving the Evasion Trajectory Problem (ETP), and then recovers after the collision is avoided. A direct optimization approach was used to develop the algorithm so it can run in real time. In this innovation, a parameterized class of avoidance trajectories is specified, and then the optimal trajectory is found by searching over the parameters. The class of trajectories is selected as bang-off-bang as motivated by optimal control theory. That is, an avoiding spacecraft first applies full acceleration in a constant direction, then coasts, and finally applies full acceleration to stop. The parameter optimization problem can be solved offline and stored as a look-up table of values. Using a look-up table allows the algorithm to run in real time. Given a colliding spacecraft, the properties of the collision geometry serve as indices of the look-up table that gives the optimal trajectory. For multiple colliding spacecraft, the set of trajectories that avoid all spacecraft is rapidly searched on

  18. Information theoretic methods for image processing algorithm optimization

    Science.gov (United States)

    Prokushkin, Sergey F.; Galil, Erez

    2015-01-01

    Modern image processing pipelines (e.g., those used in digital cameras) are full of advanced, highly adaptive filters that often have a large number of tunable parameters (sometimes > 100). This makes the calibration procedure for these filters very complex, and the optimal results barely achievable in the manual calibration; thus an automated approach is a must. We will discuss an information theory based metric for evaluation of algorithm adaptive characteristics ("adaptivity criterion") using noise reduction algorithms as an example. The method allows finding an "orthogonal decomposition" of the filter parameter space into the "filter adaptivity" and "filter strength" directions. This metric can be used as a cost function in automatic filter optimization. Since it is a measure of a physical "information restoration" rather than perceived image quality, it helps to reduce the set of the filter parameters to a smaller subset that is easier for a human operator to tune and achieve a better subjective image quality. With appropriate adjustments, the criterion can be used for assessment of the whole imaging system (sensor plus post-processing).

  19. An efficient central DOA tracking algorithm for multiple incoherently distributed sources

    Science.gov (United States)

    Hassen, Sonia Ben; Samet, Abdelaziz

    2015-12-01

    In this paper, we develop a new tracking method for the direction of arrival (DOA) parameters assuming multiple incoherently distributed (ID) sources. The new approach is based on a simple covariance fitting optimization technique exploiting the central and noncentral moments of the source angular power densities to estimate the central DOAs. The current estimates are treated as measurements provided to the Kalman filter that model the dynamic property of directional changes for the moving sources. Then, the covariance-fitting-based algorithm and the Kalman filtering theory are combined to formulate an adaptive tracking algorithm. Our algorithm is compared to the fast approximated power iteration-total least square-estimation of signal parameters via rotational invariance technique (FAPI-TLS-ESPRIT) algorithm using the TLS-ESPRIT method and the subspace updating via FAPI-algorithm. It will be shown that the proposed algorithm offers an excellent DOA tracking performance and outperforms the FAPI-TLS-ESPRIT method especially at low signal-to-noise ratio (SNR) values. Moreover, the performances of the two methods increase as the SNR values increase. This increase is more prominent with the FAPI-TLS-ESPRIT method. However, their performances degrade when the number of sources increases. It will be also proved that our method depends on the form of the angular distribution function when tracking the central DOAs. Finally, it will be shown that the more the sources are spaced, the more the proposed method can exactly track the DOAs.

  20. A Functional Programming Approach to AI Search Algorithms

    Science.gov (United States)

    Panovics, Janos

    2012-01-01

    The theory and practice of search algorithms related to state-space represented problems form the major part of the introductory course of Artificial Intelligence at most of the universities and colleges offering a degree in the area of computer science. Students usually meet these algorithms only in some imperative or object-oriented language…

  1. Random number generators and the Metropolis algorithm: application to various problems in physics and mechanics as an introduction to computational physics

    International Nuclear Information System (INIS)

    Calvayrac, Florent

    2005-01-01

    We present known and new applications of pseudo random numbers and of the Metropolis algorithm to phenomena of physical and mechanical interest, such as the search of simple clusters isomers with interactive visualization, or vehicle motion planning. The progression towards complicated problems was used with first-year graduate students who wrote most of the programs presented here. We argue that the use of pseudo random numbers in simulation and extrema research programs in teaching numerical methods in physics allows one to get quick programs and physically meaningful and demonstrative results without recurring to the advanced numerical analysis methods

  2. Multiscale System Theory

    Science.gov (United States)

    1990-02-21

    LIDS-P-1953 Multiscale System Theory Albert Benveniste IRISA-INRIA, Campus de Beaulieu 35042 RENNES CEDEX, FRANCE Ramine Nikoukhah INRIA...TITLE AND SUBTITLE Multiscale System Theory 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d. PROJECT NUMBER 5e...the development of a corresponding system theory and a theory of stochastic processes and their estimation. The research presented in this and several

  3. Analytical and Algorithmic Approaches to Determine the Number of Sensor Nodes for Minimum Power Consumption in LWSNs

    Directory of Open Access Journals (Sweden)

    Ali Soner Kilinc

    2017-08-01

    Full Text Available A Linear Wireless Sensor Network (LWSN is a kind of wireless sensor network where the nodes are deployed in a line. Since the sensor nodes are energy restricted, energy efficiency becomes one of the most significant design issues for LWSNs as well as wireless sensor networks. With the proper deployment, the power consumption could be minimized by adjusting the distance between the sensor nodes which is known as hop length. In this paper, analytical and algorithmic approaches are presented to determine the number of hops and sensor nodes for minimum power consumption in a linear wireless sensor network including equidistantly placed sensor nodes.

  4. An Improved Fruit Fly Optimization Algorithm and Its Application in Heat Exchange Fouling Ultrasonic Detection

    Directory of Open Access Journals (Sweden)

    Xia Li

    2018-01-01

    Full Text Available Inspired by the basic theory of Fruit Fly Optimization Algorithm, in this paper, cat mapping was added to the original algorithm, and the individual distribution and evolution mechanism of fruit fly population were improved in order to increase the search speed and accuracy. The flowchart of the improved algorithm was drawn to show its procedure. Using classical test functions, simulation optimization results show that the improved algorithm has faster and more reliable optimization ability. The algorithm was then combined with sparse decomposition theory and used in processing fouling detection ultrasonic signals to verify the validity and practicability of the improved algorithm.

  5. Using random matrix theory to determine the number of endmembers in a hyperspectral image

    CSIR Research Space (South Africa)

    Cawse, K

    2010-06-01

    Full Text Available apply our method to synthetic images, including a standard test image developed by Chein-I Chang, with good results for Gaussian independent noise. Index Terms— Hyperspectral Unmixing, Random Ma- trix Theory, Linear Mixture Model, Virtual Dimension... function, and K is the number of endmembers. We assume Gaussian noise following the methods of [1] [5]. The first step in unmixing the image is to determine how many endmembers or constituents are contained in the scene. This is known as the Virtual...

  6. Introduction to lattice theory with computer science applications

    CERN Document Server

    Garg, Vijay K

    2015-01-01

    A computational perspective on partial order and lattice theory, focusing on algorithms and their applications This book provides a uniform treatment of the theory and applications of lattice theory. The applications covered include tracking dependency in distributed systems, combinatorics, detecting global predicates in distributed systems, set families, and integer partitions. The book presents algorithmic proofs of theorems whenever possible. These proofs are written in the calculational style advocated by Dijkstra, with arguments explicitly spelled out step by step. The author's intent

  7. A Dependable Localization Algorithm for Survivable Belt-Type Sensor Networks.

    Science.gov (United States)

    Zhu, Mingqiang; Song, Fei; Xu, Lei; Seo, Jung Taek; You, Ilsun

    2017-11-29

    As the key element, sensor networks are widely investigated by the Internet of Things (IoT) community. When massive numbers of devices are well connected, malicious attackers may deliberately propagate fake position information to confuse the ordinary users and lower the network survivability in belt-type situation. However, most existing positioning solutions only focus on the algorithm accuracy and do not consider any security aspects. In this paper, we propose a comprehensive scheme for node localization protection, which aims to improve the energy-efficient, reliability and accuracy. To handle the unbalanced resource consumption, a node deployment mechanism is presented to satisfy the energy balancing strategy in resource-constrained scenarios. According to cooperation localization theory and network connection property, the parameter estimation model is established. To achieve reliable estimations and eliminate large errors, an improved localization algorithm is created based on modified average hop distances. In order to further improve the algorithms, the node positioning accuracy is enhanced by using the steepest descent method. The experimental simulations illustrate the performance of new scheme can meet the previous targets. The results also demonstrate that it improves the belt-type sensor networks' survivability, in terms of anti-interference, network energy saving, etc.

  8. A new quantum inspired chaotic artificial bee colony algorithm for optimal power flow problem

    International Nuclear Information System (INIS)

    Yuan, Xiaohui; Wang, Pengtao; Yuan, Yanbin; Huang, Yuehua; Zhang, Xiaopan

    2015-01-01

    Highlights: • Quantum theory is introduced to artificial bee colony algorithm (ABC) to increase population diversity. • A chaotic local search operator is used to enhance local search ability of ABC. • Quantum inspired chaotic ABC method (QCABC) is proposed to solve optimal power flow. • The feasibility and effectiveness of the proposed QCABC is verified by examples. - Abstract: This paper proposes a new artificial bee colony algorithm with quantum theory and the chaotic local search strategy (QCABC), and uses it to solve the optimal power flow (OPF) problem. Under the quantum computing theory, the QCABC algorithm encodes each individual with quantum bits to form a corresponding quantum bit string. By determining each quantum bits value, we can get the value of the individual. After the scout bee stage of the artificial bee colony algorithm, we begin the chaotic local search in the vicinity of the best individual found so far. Finally, the quantum rotation gate is used to process each quantum bit so that all individuals can update toward the direction of the best individual. The QCABC algorithm is carried out to deal with the OPF problem in the IEEE 30-bus and IEEE 118-bus standard test systems. The results of the QCABC algorithm are compared with other algorithms (artificial bee colony algorithm, genetic algorithm, particle swarm optimization algorithm). The comparison shows that the QCABC algorithm can effectively solve the OPF problem and it can get the better optimal results than those of other algorithms

  9. Law of Large Numbers: the Theory, Applications and Technology-based Education.

    Science.gov (United States)

    Dinov, Ivo D; Christou, Nicolas; Gould, Robert

    2009-03-01

    Modern approaches for technology-based blended education utilize a variety of recently developed novel pedagogical, computational and network resources. Such attempts employ technology to deliver integrated, dynamically-linked, interactive-content and heterogeneous learning environments, which may improve student comprehension and information retention. In this paper, we describe one such innovative effort of using technological tools to expose students in probability and statistics courses to the theory, practice and usability of the Law of Large Numbers (LLN). We base our approach on integrating pedagogical instruments with the computational libraries developed by the Statistics Online Computational Resource (www.SOCR.ucla.edu). To achieve this merger we designed a new interactive Java applet and a corresponding demonstration activity that illustrate the concept and the applications of the LLN. The LLN applet and activity have common goals - to provide graphical representation of the LLN principle, build lasting student intuition and present the common misconceptions about the law of large numbers. Both the SOCR LLN applet and activity are freely available online to the community to test, validate and extend (Applet: http://socr.ucla.edu/htmls/exp/Coin_Toss_LLN_Experiment.html, and Activity: http://wiki.stat.ucla.edu/socr/index.php/SOCR_EduMaterials_Activities_LLN).

  10. Contributions to Persistence Theory

    Directory of Open Access Journals (Sweden)

    Du Dong

    2014-12-01

    Full Text Available Persistence theory discussed in this paper is an application of algebraic topology (Morse Theory [29] to Data Analysis, precisely to qualitative understanding of point cloud data, or PCD for short. PCD can be geometrized as a filtration of simplicial complexes (Vietoris-Rips complex [25] [36] and the homology changes of these complexes provide qualitative information about the data. Bar codes describe the changes in homology with coefficients in a fixed field. When the coefficient field is ℤ2, the calculation of bar codes is done by ELZ algorithm (named after H. Edelsbrunner, D. Letscher, and A. Zomorodian [20]. When the coefficient field is ℝ, we propose an algorithm based on the Hodge decomposition [17]. With Dan Burghelea and Tamal K. Dey we developed a persistence theory which involves level sets discussed in Section 4. We introduce and discuss new computable invariants, the “relevant level persistence numbers” and the “positive and negative bar codes”, and explain how they are related to the bar codes for level persistence. We provide enhancements and modifications of ELZ algorithm to calculate such invariants and illustrate them by examples.

  11. An efficient non-dominated sorting method for evolutionary algorithms.

    Science.gov (United States)

    Fang, Hongbing; Wang, Qian; Tu, Yi-Cheng; Horstemeyer, Mark F

    2008-01-01

    We present a new non-dominated sorting algorithm to generate the non-dominated fronts in multi-objective optimization with evolutionary algorithms, particularly the NSGA-II. The non-dominated sorting algorithm used by NSGA-II has a time complexity of O(MN(2)) in generating non-dominated fronts in one generation (iteration) for a population size N and M objective functions. Since generating non-dominated fronts takes the majority of total computational time (excluding the cost of fitness evaluations) of NSGA-II, making this algorithm faster will significantly improve the overall efficiency of NSGA-II and other genetic algorithms using non-dominated sorting. The new non-dominated sorting algorithm proposed in this study reduces the number of redundant comparisons existing in the algorithm of NSGA-II by recording the dominance information among solutions from their first comparisons. By utilizing a new data structure called the dominance tree and the divide-and-conquer mechanism, the new algorithm is faster than NSGA-II for different numbers of objective functions. Although the number of solution comparisons by the proposed algorithm is close to that of NSGA-II when the number of objectives becomes large, the total computational time shows that the proposed algorithm still has better efficiency because of the adoption of the dominance tree structure and the divide-and-conquer mechanism.

  12. Algorithmic phase diagrams

    Science.gov (United States)

    Hockney, Roger

    1987-01-01

    Algorithmic phase diagrams are a neat and compact representation of the results of comparing the execution time of several algorithms for the solution of the same problem. As an example, the recent results are shown of Gannon and Van Rosendale on the solution of multiple tridiagonal systems of equations in the form of such diagrams. The act of preparing these diagrams has revealed an unexpectedly complex relationship between the best algorithm and the number and size of the tridiagonal systems, which was not evident from the algebraic formulae in the original paper. Even so, for a particular computer, one diagram suffices to predict the best algorithm for all problems that are likely to be encountered the prediction being read directly from the diagram without complex calculation.

  13. Unified path integral approach to theories of diffusion-influenced reactions

    Science.gov (United States)

    Prüstel, Thorsten; Meier-Schellersheim, Martin

    2017-08-01

    Building on mathematical similarities between quantum mechanics and theories of diffusion-influenced reactions, we develop a general approach for computational modeling of diffusion-influenced reactions that is capable of capturing not only the classical Smoluchowski picture but also alternative theories, as is here exemplified by a volume reactivity model. In particular, we prove the path decomposition expansion of various Green's functions describing the irreversible and reversible reaction of an isolated pair of molecules. To this end, we exploit a connection between boundary value and interaction potential problems with δ - and δ'-function perturbation. We employ a known path-integral-based summation of a perturbation series to derive a number of exact identities relating propagators and survival probabilities satisfying different boundary conditions in a unified and systematic manner. Furthermore, we show how the path decomposition expansion represents the propagator as a product of three factors in the Laplace domain that correspond to quantities figuring prominently in stochastic spatially resolved simulation algorithms. This analysis will thus be useful for the interpretation of current and the design of future algorithms. Finally, we discuss the relation between the general approach and the theory of Brownian functionals and calculate the mean residence time for the case of irreversible and reversible reactions.

  14. An approach to solve group-decision-making problems with ordinal interval numbers.

    Science.gov (United States)

    Fan, Zhi-Ping; Liu, Yang

    2010-10-01

    The ordinal interval number is a form of uncertain preference information in group decision making (GDM), while it is seldom discussed in the existing research. This paper investigates how the ranking order of alternatives is determined based on preference information of ordinal interval numbers in GDM problems. When ranking a large quantity of ordinal interval numbers, the efficiency and accuracy of the ranking process are critical. A new approach is proposed to rank alternatives using ordinal interval numbers when every ranking ordinal in an ordinal interval number is thought to be uniformly and independently distributed in its interval. First, we give the definition of possibility degree on comparing two ordinal interval numbers and the related theory analysis. Then, to rank alternatives, by comparing multiple ordinal interval numbers, a collective expectation possibility degree matrix on pairwise comparisons of alternatives is built, and an optimization model based on this matrix is constructed. Furthermore, an algorithm is also presented to rank alternatives by solving the model. Finally, two examples are used to illustrate the use of the proposed approach.

  15. A numerical study of super-resolution through fast 3D wideband algorithm for scattering in highly-heterogeneous media

    KAUST Repository

    Létourneau, Pierre-David

    2016-09-19

    We present a wideband fast algorithm capable of accurately computing the full numerical solution of the problem of acoustic scattering of waves by multiple finite-sized bodies such as spherical scatterers in three dimensions. By full solution, we mean that no assumption (e.g. Rayleigh scattering, geometrical optics, weak scattering, Born single scattering, etc.) is necessary regarding the properties of the scatterers, their distribution or the background medium. The algorithm is also fast in the sense that it scales linearly with the number of unknowns. We use this algorithm to study the phenomenon of super-resolution in time-reversal refocusing in highly-scattering media recently observed experimentally (Lemoult et al., 2011), and provide numerical arguments towards the fact that such a phenomenon can be explained through a homogenization theory.

  16. Analysis of entropy extraction efficiencies in random number generation systems

    Science.gov (United States)

    Wang, Chao; Wang, Shuang; Chen, Wei; Yin, Zhen-Qiang; Han, Zheng-Fu

    2016-05-01

    Random numbers (RNs) have applications in many areas: lottery games, gambling, computer simulation, and, most importantly, cryptography [N. Gisin et al., Rev. Mod. Phys. 74 (2002) 145]. In cryptography theory, the theoretical security of the system calls for high quality RNs. Therefore, developing methods for producing unpredictable RNs with adequate speed is an attractive topic. Early on, despite the lack of theoretical support, pseudo RNs generated by algorithmic methods performed well and satisfied reasonable statistical requirements. However, as implemented, those pseudorandom sequences were completely determined by mathematical formulas and initial seeds, which cannot introduce extra entropy or information. In these cases, “random” bits are generated that are not at all random. Physical random number generators (RNGs), which, in contrast to algorithmic methods, are based on unpredictable physical random phenomena, have attracted considerable research interest. However, the way that we extract random bits from those physical entropy sources has a large influence on the efficiency and performance of the system. In this manuscript, we will review and discuss several randomness extraction schemes that are based on radiation or photon arrival times. We analyze the robustness, post-processing requirements and, in particular, the extraction efficiency of those methods to aid in the construction of efficient, compact and robust physical RNG systems.

  17. FASTSIM2: a second-order accurate frictional rolling contact algorithm

    Science.gov (United States)

    Vollebregt, E. A. H.; Wilders, P.

    2011-01-01

    In this paper we consider the frictional (tangential) steady rolling contact problem. We confine ourselves to the simplified theory, instead of using full elastostatic theory, in order to be able to compute results fast, as needed for on-line application in vehicle system dynamics simulation packages. The FASTSIM algorithm is the leading technology in this field and is employed in all dominant railway vehicle system dynamics packages (VSD) in the world. The main contribution of this paper is a new version "FASTSIM2" of the FASTSIM algorithm, which is second-order accurate. This is relevant for VSD, because with the new algorithm 16 times less grid points are required for sufficiently accurate computations of the contact forces. The approach is based on new insights in the characteristics of the rolling contact problem when using the simplified theory, and on taking precise care of the contact conditions in the numerical integration scheme employed.

  18. Large scale tracking algorithms

    Energy Technology Data Exchange (ETDEWEB)

    Hansen, Ross L. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Love, Joshua Alan [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Melgaard, David Kennett [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Karelitz, David B. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Pitts, Todd Alan [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Zollweg, Joshua David [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Anderson, Dylan Z. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Nandy, Prabal [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Whitlow, Gary L. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Bender, Daniel A. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Byrne, Raymond Harry [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

    2015-01-01

    Low signal-to-noise data processing algorithms for improved detection, tracking, discrimination and situational threat assessment are a key research challenge. As sensor technologies progress, the number of pixels will increase signi cantly. This will result in increased resolution, which could improve object discrimination, but unfortunately, will also result in a significant increase in the number of potential targets to track. Many tracking techniques, like multi-hypothesis trackers, suffer from a combinatorial explosion as the number of potential targets increase. As the resolution increases, the phenomenology applied towards detection algorithms also changes. For low resolution sensors, "blob" tracking is the norm. For higher resolution data, additional information may be employed in the detection and classfication steps. The most challenging scenarios are those where the targets cannot be fully resolved, yet must be tracked and distinguished for neighboring closely spaced objects. Tracking vehicles in an urban environment is an example of such a challenging scenario. This report evaluates several potential tracking algorithms for large-scale tracking in an urban environment.

  19. From natural numbers to quaternions

    CERN Document Server

    Kramer, Jürg

    2017-01-01

    This textbook offers an invitation to modern algebra through number systems of increasing complexity, beginning with the natural numbers and culminating with Hamilton's quaternions. Along the way, the authors carefully develop the necessary concepts and methods from abstract algebra: monoids, groups, rings, fields, and skew fields. Each chapter ends with an appendix discussing related topics from algebra and number theory, including recent developments reflecting the relevance of the material to current research. The present volume is intended for undergraduate courses in abstract algebra or elementary number theory. The inclusion of exercises with solutions also makes it suitable for self-study and accessible to anyone with an interest in modern algebra and number theory.

  20. High speed railway track dynamics models, algorithms and applications

    CERN Document Server

    Lei, Xiaoyan

    2017-01-01

    This book systematically summarizes the latest research findings on high-speed railway track dynamics, made by the author and his research team over the past decade. It explores cutting-edge issues concerning the basic theory of high-speed railways, covering the dynamic theories, models, algorithms and engineering applications of the high-speed train and track coupling system. Presenting original concepts, systematic theories and advanced algorithms, the book places great emphasis on the precision and completeness of its content. The chapters are interrelated yet largely self-contained, allowing readers to either read through the book as a whole or focus on specific topics. It also combines theories with practice to effectively introduce readers to the latest research findings and developments in high-speed railway track dynamics. It offers a valuable resource for researchers, postgraduates and engineers in the fields of civil engineering, transportation, highway & railway engineering.

  1. Behavioural modelling using the MOESP algorithm, dynamic neural networks and the Bartels-Stewart algorithm

    NARCIS (Netherlands)

    Schilders, W.H.A.; Meijer, P.B.L.; Ciggaar, E.

    2008-01-01

    In this paper we discuss the use of the state-space modelling MOESP algorithm to generate precise information about the number of neurons and hidden layers in dynamic neural networks developed for the behavioural modelling of electronic circuits. The Bartels–Stewart algorithm is used to transform

  2. Exact Algorithms for Solving Stochastic Games

    DEFF Research Database (Denmark)

    Hansen, Kristoffer Arnsfelt; Koucky, Michal; Lauritzen, Niels

    2012-01-01

    Shapley's discounted stochastic games, Everett's recursive games and Gillette's undiscounted stochastic games are classical models of game theory describing two-player zero-sum games of potentially infinite duration. We describe algorithms for exactly solving these games....

  3. Adaptive Algorithms for Automated Processing of Document Images

    Science.gov (United States)

    2011-01-01

    ABSTRACT Title of dissertation: ADAPTIVE ALGORITHMS FOR AUTOMATED PROCESSING OF DOCUMENT IMAGES Mudit Agrawal, Doctor of Philosophy, 2011...2011 4. TITLE AND SUBTITLE Adaptive Algorithms for Automated Processing of Document Images 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM...ALGORITHMS FOR AUTOMATED PROCESSING OF DOCUMENT IMAGES by Mudit Agrawal Dissertation submitted to the Faculty of the Graduate School of the University

  4. Genetic algorithm for project time-cost optimization in fuzzy environment

    Directory of Open Access Journals (Sweden)

    Khan Md. Ariful Haque

    2012-12-01

    Full Text Available Purpose: The aim of this research is to develop a more realistic approach to solve project time-cost optimization problem under uncertain conditions, with fuzzy time periods. Design/methodology/approach: Deterministic models for time-cost optimization are never efficient considering various uncertainty factors. To make such problems realistic, triangular fuzzy numbers and the concept of a-cut method in fuzzy logic theory are employed to model the problem. Because of NP-hard nature of the project scheduling problem, Genetic Algorithm (GA has been used as a searching tool. Finally, Dev-C++ 4.9.9.2 has been used to code this solver. Findings: The solution has been performed under different combinations of GA parameters and after result analysis optimum values of those parameters have been found for the best solution. Research limitations/implications: For demonstration of the application of the developed algorithm, a project on new product (Pre-paid electric meter, a project under government finance launching has been chosen as a real case. The algorithm is developed under some assumptions. Practical implications: The proposed model leads decision makers to choose the desired solution under different risk levels. Originality/value: Reports reveal that project optimization problems have never been solved under multiple uncertainty conditions. Here, the function has been optimized using Genetic Algorithm search technique, with varied level of risks and fuzzy time periods.

  5. From Calculus to Number Theory

    Indian Academy of Sciences (India)

    A. Raghuram

    2016-11-04

    Nov 4, 2016 ... diverges to infinity. This means given any number M, however large, we can add sufficiently many terms in the above series to make the sum larger than M. This was first proved by Nicole Oresme (1323-1382), a brilliant. French philosopher of his times.

  6. Implementation of ternary Shor’s algorithm based on vibrational states of an ion in anharmonic potential

    Science.gov (United States)

    Liu, Wei; Chen, Shu-Ming; Zhang, Jian; Wu, Chun-Wang; Wu, Wei; Chen, Ping-Xing

    2015-03-01

    It is widely believed that Shor’s factoring algorithm provides a driving force to boost the quantum computing research. However, a serious obstacle to its binary implementation is the large number of quantum gates. Non-binary quantum computing is an efficient way to reduce the required number of elemental gates. Here, we propose optimization schemes for Shor’s algorithm implementation and take a ternary version for factorizing 21 as an example. The optimized factorization is achieved by a two-qutrit quantum circuit, which consists of only two single qutrit gates and one ternary controlled-NOT gate. This two-qutrit quantum circuit is then encoded into the nine lower vibrational states of an ion trapped in a weakly anharmonic potential. Optimal control theory (OCT) is employed to derive the manipulation electric field for transferring the encoded states. The ternary Shor’s algorithm can be implemented in one single step. Numerical simulation results show that the accuracy of the state transformations is about 0.9919. Project supported by the National Natural Science Foundation of China (Grant No. 61205108) and the High Performance Computing (HPC) Foundation of National University of Defense Technology, China.

  7. Winding numbers in homotopy theory from integers to reals

    International Nuclear Information System (INIS)

    Mekhfi, M.

    1993-07-01

    In Homotopy Theory (HT) we define paths on a given topological space. Closed paths prove to be construction elements of a group (the fundamental group) Π 1 and carry charges, the winding numbers. The charges are integers as they indicate how many times closed paths encircle a given hole (or set of holes). Open paths as they are defined in (HT) do not possess any groups structure and as such they are less useful in topology. In the present paper we enlarge the concept of a path in such a way that both types of paths do possess a group structure. In this broad sense we have two fundamental groups the Π i = Z group and the SO(2) group of rotations but the latter has the global property that there is no periodicity in the rotation angle. There is also two charge operators W and W λ whose eigenvalues are either integers or reals depending respectively on the paths being closed or open. Also the SO(2) group and the real charge operator W λ are not independently defined but directly related respectively to the Π i group and to the integer charge operator W. Thus well defined links can be established between seemingly different groups and charges. (author). 3 refs, 1 fig

  8. Automatic motor task selection via a bandit algorithm for a brain-controlled button

    Science.gov (United States)

    Fruitet, Joan; Carpentier, Alexandra; Munos, Rémi; Clerc, Maureen

    2013-02-01

    Objective. Brain-computer interfaces (BCIs) based on sensorimotor rhythms use a variety of motor tasks, such as imagining moving the right or left hand, the feet or the tongue. Finding the tasks that yield best performance, specifically to each user, is a time-consuming preliminary phase to a BCI experiment. This study presents a new adaptive procedure to automatically select (online) the most promising motor task for an asynchronous brain-controlled button. Approach. We develop for this purpose an adaptive algorithm UCB-classif based on the stochastic bandit theory and design an EEG experiment to test our method. We compare (offline) the adaptive algorithm to a naïve selection strategy which uses uniformly distributed samples from each task. We also run the adaptive algorithm online to fully validate the approach. Main results. By not wasting time on inefficient tasks, and focusing on the most promising ones, this algorithm results in a faster task selection and a more efficient use of the BCI training session. More precisely, the offline analysis reveals that the use of this algorithm can reduce the time needed to select the most appropriate task by almost half without loss in precision, or alternatively, allow us to investigate twice the number of tasks within a similar time span. Online tests confirm that the method leads to an optimal task selection. Significance. This study is the first one to optimize the task selection phase by an adaptive procedure. By increasing the number of tasks that can be tested in a given time span, the proposed method could contribute to reducing ‘BCI illiteracy’.

  9. Renormalization of gauge theories without cohomology

    International Nuclear Information System (INIS)

    Anselmi, Damiano

    2013-01-01

    We investigate the renormalization of gauge theories without assuming cohomological properties. We define a renormalization algorithm that preserves the Batalin-Vilkovisky master equation at each step and automatically extends the classical action till it contains sufficiently many independent parameters to reabsorb all divergences into parameter-redefinitions and canonical transformations. The construction is then generalized to the master functional and the field-covariant proper formalism for gauge theories. Our results hold in all manifestly anomaly-free gauge theories, power-counting renormalizable or not. The extension algorithm allows us to solve a quadratic problem, such as finding a sufficiently general solution of the master equation, even when it is not possible to reduce it to a linear (cohomological) problem. (orig.)

  10. Instance-specific algorithm configuration

    CERN Document Server

    Malitsky, Yuri

    2014-01-01

    This book presents a modular and expandable technique in the rapidly emerging research area of automatic configuration and selection of the best algorithm for the instance at hand. The author presents the basic model behind ISAC and then details a number of modifications and practical applications. In particular, he addresses automated feature generation, offline algorithm configuration for portfolio generation, algorithm selection, adaptive solvers, online tuning, and parallelization.    The author's related thesis was honorably mentioned (runner-up) for the ACP Dissertation Award in 2014,

  11. Parallel Algorithms for Model Checking

    NARCIS (Netherlands)

    van de Pol, Jaco; Mousavi, Mohammad Reza; Sgall, Jiri

    2017-01-01

    Model checking is an automated verification procedure, which checks that a model of a system satisfies certain properties. These properties are typically expressed in some temporal logic, like LTL and CTL. Algorithms for LTL model checking (linear time logic) are based on automata theory and graph

  12. MVDR Algorithm Based on Estimated Diagonal Loading for Beamforming

    Directory of Open Access Journals (Sweden)

    Yuteng Xiao

    2017-01-01

    Full Text Available Beamforming algorithm is widely used in many signal processing fields. At present, the typical beamforming algorithm is MVDR (Minimum Variance Distortionless Response. However, the performance of MVDR algorithm relies on the accurate covariance matrix. The MVDR algorithm declines dramatically with the inaccurate covariance matrix. To solve the problem, studying the beamforming array signal model and beamforming MVDR algorithm, we improve MVDR algorithm based on estimated diagonal loading for beamforming. MVDR optimization model based on diagonal loading compensation is established and the interval of the diagonal loading compensation value is deduced on the basis of the matrix theory. The optimal diagonal loading value in the interval is also determined through the experimental method. The experimental results show that the algorithm compared with existing algorithms is practical and effective.

  13. Complexity Theory

    Science.gov (United States)

    Lee, William H K.

    2016-01-01

    A complex system consists of many interacting parts, generates new collective behavior through self organization, and adaptively evolves through time. Many theories have been developed to study complex systems, including chaos, fractals, cellular automata, self organization, stochastic processes, turbulence, and genetic algorithms.

  14. Discussion: The Forward Search: Theory and Data Analysis

    DEFF Research Database (Denmark)

    Johansen, Søren; Nielsen, Bent

    2010-01-01

    The Forward Search Algorithm is a statistical algorithm for obtaining robust estimators of regression coefficients in the presence of outliers. The algorithm selects a succession of subsets of observations from which the parameters are estimated. The present note shows how the theory of empirical...

  15. A comparison of three self-tuning control algorithms developed for the Bristol-Babcock controller

    International Nuclear Information System (INIS)

    Tapp, P.A.

    1992-04-01

    A brief overview of adaptive control methods relating to the design of self-tuning proportional-integral-derivative (PID) controllers is given. The methods discussed include gain scheduling, self-tuning, auto-tuning, and model-reference adaptive control systems. Several process identification and parameter adjustment methods are discussed. Characteristics of the two most common types of self-tuning controllers implemented by industry (i.e., pattern recognition and process identification) are summarized. The substance of the work is a comparison of three self-tuning proportional-plus-integral (STPI) control algorithms developed to work in conjunction with the Bristol-Babcock PID control module. The STPI control algorithms are based on closed-loop cycling theory, pattern recognition theory, and model-based theory. A brief theory of operation of these three STPI control algorithms is given. Details of the process simulations developed to test the STPI algorithms are given, including an integrating process, a first-order system, a second-order system, a system with initial inverse response, and a system with variable time constant and delay. The STPI algorithms' performance with regard to both setpoint changes and load disturbances is evaluated, and their robustness is compared. The dynamic effects of process deadtime and noise are also considered. Finally, the limitations of each of the STPI algorithms is discussed, some conclusions are drawn from the performance comparisons, and a few recommendations are made. 6 refs

  16. Fast algorithm of adaptive Fourier series

    Science.gov (United States)

    Gao, You; Ku, Min; Qian, Tao

    2018-05-01

    Adaptive Fourier decomposition (AFD, precisely 1-D AFD or Core-AFD) was originated for the goal of positive frequency representations of signals. It achieved the goal and at the same time offered fast decompositions of signals. There then arose several types of AFDs. AFD merged with the greedy algorithm idea, and in particular, motivated the so-called pre-orthogonal greedy algorithm (Pre-OGA) that was proven to be the most efficient greedy algorithm. The cost of the advantages of the AFD type decompositions is, however, the high computational complexity due to the involvement of maximal selections of the dictionary parameters. The present paper offers one formulation of the 1-D AFD algorithm by building the FFT algorithm into it. Accordingly, the algorithm complexity is reduced, from the original $\\mathcal{O}(M N^2)$ to $\\mathcal{O}(M N\\log_2 N)$, where $N$ denotes the number of the discretization points on the unit circle and $M$ denotes the number of points in $[0,1)$. This greatly enhances the applicability of AFD. Experiments are carried out to show the high efficiency of the proposed algorithm.

  17. Deep Learning in Intermediate Microeconomics: Using Scaffolding Assignments to Teach Theory and Promote Transfer

    Science.gov (United States)

    Green, Gareth P.; Bean, John C.; Peterson, Dean J.

    2013-01-01

    Intermediate microeconomics is typically viewed as a theory and tools course that relies on algorithmic problems to help students learn and apply economic theory. However, the authors' assessment research suggests that algorithmic problems by themselves do not encourage students to think about where the theory comes from, why the theory is…

  18. A Dynamic Neighborhood Learning-Based Gravitational Search Algorithm.

    Science.gov (United States)

    Zhang, Aizhu; Sun, Genyun; Ren, Jinchang; Li, Xiaodong; Wang, Zhenjie; Jia, Xiuping

    2018-01-01

    Balancing exploration and exploitation according to evolutionary states is crucial to meta-heuristic search (M-HS) algorithms. Owing to its simplicity in theory and effectiveness in global optimization, gravitational search algorithm (GSA) has attracted increasing attention in recent years. However, the tradeoff between exploration and exploitation in GSA is achieved mainly by adjusting the size of an archive, named , which stores those superior agents after fitness sorting in each iteration. Since the global property of remains unchanged in the whole evolutionary process, GSA emphasizes exploitation over exploration and suffers from rapid loss of diversity and premature convergence. To address these problems, in this paper, we propose a dynamic neighborhood learning (DNL) strategy to replace the model and thereby present a DNL-based GSA (DNLGSA). The method incorporates the local and global neighborhood topologies for enhancing the exploration and obtaining adaptive balance between exploration and exploitation. The local neighborhoods are dynamically formed based on evolutionary states. To delineate the evolutionary states, two convergence criteria named limit value and population diversity, are introduced. Moreover, a mutation operator is designed for escaping from the local optima on the basis of evolutionary states. The proposed algorithm was evaluated on 27 benchmark problems with different characteristic and various difficulties. The results reveal that DNLGSA exhibits competitive performances when compared with a variety of state-of-the-art M-HS algorithms. Moreover, the incorporation of local neighborhood topology reduces the numbers of calculations of gravitational force and thus alleviates the high computational cost of GSA.

  19. Algorithmic Foundation of Spectral Rarefaction for Measuring Satellite Imagery Heterogeneity at Multiple Spatial Scales

    Science.gov (United States)

    Rocchini, Duccio

    2009-01-01

    Measuring heterogeneity in satellite imagery is an important task to deal with. Most measures of spectral diversity have been based on Shannon Information theory. However, this approach does not inherently address different scales, ranging from local (hereafter referred to alpha diversity) to global scales (gamma diversity). The aim of this paper is to propose a method for measuring spectral heterogeneity at multiple scales based on rarefaction curves. An algorithmic solution of rarefaction applied to image pixel values (Digital Numbers, DNs) is provided and discussed. PMID:22389600

  20. Fast geometric algorithms

    International Nuclear Information System (INIS)

    Noga, M.T.

    1984-01-01

    This thesis addresses a number of important problems that fall within the framework of the new discipline of Computational Geometry. The list of topics covered includes sorting and selection, convex hull algorithms, the L 1 hull, determination of the minimum encasing rectangle of a set of points, the Euclidean and L 1 diameter of a set of points, the metric traveling salesman problem, and finding the superrange of star-shaped and monotype polygons. The main theme of all the work was to develop a set of very fast state-of-the-art algorithms that supersede any rivals in terms of speed and ease of implementation. In some cases existing algorithms were refined; for others new techniques were developed that add to the present database of fast adaptive geometric algorithms. What emerges is a collection of techniques that is successful at merging modern tools developed in analysis of algorithms with those of classical geometry