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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. 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

  4. 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.

  5. 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.

  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. 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.

  8. 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

  9. 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.

  10. 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...

  11. 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

  12. 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

  13. 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

  14. 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

  15. 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

  16. 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

  17. 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

  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. 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

  20. 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...

  1. 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.

  2. 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.

  3. 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

  4. 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.,.

  5. 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.

  6. 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

  7. 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...

  8. 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.

  9. 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.

  10. 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.

  11. 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.

  12. 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

  13. 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.

  14. 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.

  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. 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.

  17. 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...

  18. 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.

  19. 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...

  20. 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).

  1. 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).

  2. 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 ...

  3. 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. ...

  4. 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...

  5. 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.)

  6. 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

  7. 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

  8. 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...

  9. 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.

  10. 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

  11. 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...

  12. 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)

  13. 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

  14. 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.

  15. 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.

  16. 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 ...

  17. 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...

  18. 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.

  19. 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.

  20. 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.

  1. 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.

  2. 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...

  3. 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.

  4. 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.

  5. 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

  6. 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...

  7. 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

  8. 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.

  9. 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.

  10. 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

  11. 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...

  12. 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.

  13. 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

  14. 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)

  15. 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.

  16. 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.

  17. 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...

  18. 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.

  19. 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...

  20. 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.

  1. 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.

  2. 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.

  3. 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...

  4. 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.

  5. 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.

  6. 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

  7. 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...

  8. 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

  9. 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

  10. 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, ...

  11. 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-...

  12. 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

  13. 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).

  14. 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.

  15. 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

  16. 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.

  17. 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.

  18. 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

  19. 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)

  20. 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...

  1. 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.

  2. 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.

  3. 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...

  4. 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.

  5. 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.

  6. 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.

  7. 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.

  8. 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.

  9. 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....

  10. 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.

  11. 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

  12. 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%.

  13. A Geometrical Application of Number Theory

    Science.gov (United States)

    Srinivasan, V. K.

    2013-01-01

    Any quadruple of natural numbers {a, b, c, d} is called a "Pythagorean quadruple" if it satisfies the relationship "a[superscript 2] + b[superscript 2] + c[superscript 2]". This "Pythagorean quadruple" can always be identified with a rectangular box of dimensions "a greater than 0," "b greater than…

  14. 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

  15. 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

  16. Residue number systems theory and applications

    CERN Document Server

    Mohan, P V Ananda

    2016-01-01

    This new and expanded monograph improves upon Mohan's earlier book, Residue Number Systems (Springer, 2002) with a state of the art treatment of the subject. Replete with detailed illustrations and helpful examples, this book covers a host of cutting edge topics such as the core function, the quotient function, new Chinese Remainder theorems, and large integer operations. It also features many significant applications to practical communication systems and cryptography such as FIR filters and elliptic curve cryptography. Starting with a comprehensive introduction to the basics and leading up to current research trends that are not yet widely distributed in other publications, this book will be of interest to both researchers and students alike.

  17. 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.

  18. Nonlinear model predictive control theory and algorithms

    CERN Document Server

    Grüne, Lars

    2017-01-01

    This book offers readers a thorough and rigorous introduction to nonlinear model predictive control (NMPC) for discrete-time and sampled-data systems. NMPC schemes with and without stabilizing terminal constraints are detailed, and intuitive examples illustrate the performance of different NMPC variants. NMPC is interpreted as an approximation of infinite-horizon optimal control so that important properties like closed-loop stability, inverse optimality and suboptimality can be derived in a uniform manner. These results are complemented by discussions of feasibility and robustness. An introduction to nonlinear optimal control algorithms yields essential insights into how the nonlinear optimization routine—the core of any nonlinear model predictive controller—works. Accompanying software in MATLAB® and C++ (downloadable from extras.springer.com/), together with an explanatory appendix in the book itself, enables readers to perform computer experiments exploring the possibilities and limitations of NMPC. T...

  19. 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...

  20. 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

  1. 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 ...

  2. On a connection of number theory with graph theory

    Czech Academy of Sciences Publication Activity Database

    Somer, L.; Křížek, Michal

    2004-01-01

    Roč. 54, č. 2 (2004), s. 465-485 ISSN 0011-4642 R&D Projects: GA ČR GA201/02/1058 Institutional research plan: CEZ:AV0Z1019905 Keywords : Fermat numbers * Chinese remainder theorem * primality Subject RIV: BA - General Mathematics Impact factor: 0.131, year: 2004

  3. 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

  4. 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.)

  5. 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

  6. 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. .

  7. 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...

  8. 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…

  9. 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.

  10. 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.

  11. 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.)

  12. 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…

  13. 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)

  14. 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

  15. 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.

  16. 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…

  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. 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

  19. 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

  20. 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

  1. 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

  2. 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...

  3. 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...

  4. 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...

  5. 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.

  6. 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: ...

  7. 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.

  8. 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, ...

  9. 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

  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. 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

  12. 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.

  13. 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.

  14. 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 ...

  15. 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...

  16. 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.

  17. 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.

  18. 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)

  19. 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.

  20. 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.

  1. 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.

  2. 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.

  3. 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...

  4. 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.

  5. 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

  6. 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.

  7. 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

  8. 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

  9. 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.

  10. 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.

  11. 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.

  12. 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...

  13. 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...

  14. 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.

  15. 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.

  16. 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.

  17. 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.

  18. 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.

  19. 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

  20. 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...

  1. Turing’s algorithmic lens: From computability to complexity theory

    Directory of Open Access Journals (Sweden)

    Díaz, Josep

    2013-12-01

    Full Text Available The decidability question, i.e., whether any mathematical statement could be computationally proven true or false, was raised by Hilbert and remained open until Turing answered it in the negative. Then, most efforts in theoretical computer science turned to complexity theory and the need to classify decidable problems according to their difficulty. Among others, the classes P (problems solvable in polynomial time and NP (problems solvable in non-deterministic polynomial time were defined, and one of the most challenging scientific quests of our days arose: whether P = NP. This still open question has implications not only in computer science, mathematics and physics, but also in biology, sociology and economics, and it can be seen as a direct consequence of Turing’s way of looking through the algorithmic lens at different disciplines to discover how pervasive computation is.La cuestión de la decidibilidad, es decir, si es posible demostrar computacionalmente que una expresión matemática es verdadera o falsa, fue planteada por Hilbert y permaneció abierta hasta que Turing la respondió de forma negativa. Establecida la no-decidibilidad de las matemáticas, los esfuerzos en informática teórica se centraron en el estudio de la complejidad computacional de los problemas decidibles. En este artículo presentamos una breve introducción a las clases P (problemas resolubles en tiempo polinómico y NP (problemas resolubles de manera no determinista en tiempo polinómico, al tiempo que exponemos la dificultad de establecer si P = NP y las consecuencias que se derivarían de que ambas clases de problemas fueran iguales. Esta cuestión tiene implicaciones no solo en los campos de la informática, las matemáticas y la física, sino también para la biología, la sociología y la economía. La idea seminal del estudio de la complejidad computacional es consecuencia directa del modo en que Turing abordaba problemas en diferentes ámbitos mediante lo

  2. 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.

  3. 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.

  4. 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...

  5. 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...

  6. [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.

  7. Optimization and Control of Bilinear Systems Theory, Algorithms, and Applications

    CERN Document Server

    Pardalos, Panos M

    2008-01-01

    Covers developments in bilinear systems theory Focuses on the control of open physical processes functioning in a non-equilibrium mode Emphasis is on three primary disciplines: modern differential geometry, control of dynamical systems, and optimization theory Includes applications to the fields of quantum and molecular computing, control of physical processes, biophysics, superconducting magnetism, and physical information science

  8. 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.

  9. 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)

  10. 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...

  11. 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)

  12. 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.

  13. 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

  14. Similarity Theory and Dimensionless Numbers in Heat Transfer

    Science.gov (United States)

    Marin, E.; Calderon, A.; Delgado-Vasallo, O.

    2009-01-01

    We present basic concepts underlying the so-called similarity theory that in our opinion should be explained in basic undergraduate general physics courses when dealing with heat transport problems, in particular with those involving natural or free convection. A simple example is described that can be useful in showing a criterion for neglecting…

  15. Cell Formation in Industrial Engineering : Theory, Algorithms and Experiments

    NARCIS (Netherlands)

    Goldengorin, B.; Krushynskyi, D.; Pardalos, P.M.

    2013-01-01

    This book focuses on a development of optimal, flexible, and efficient models and algorithms for cell formation in group technology. Its main aim is to provide a reliable tool that can be used by managers and engineers to design manufacturing cells based on their own preferences and constraints

  16. Foundations of digital signal processing theory, algorithms and hardware design

    CERN Document Server

    Gaydecki, Patrick

    2005-01-01

    An excellent introductory text, this book covers the basic theoretical, algorithmic and real-time aspects of digital signal processing (DSP). Detailed information is provided on off-line, real-time and DSP programming and the reader is effortlessly guided through advanced topics such as DSP hardware design, FIR and IIR filter design and difference equation manipulation.

  17. Bilevel programming problems theory, algorithms and applications to energy networks

    CERN Document Server

    Dempe, Stephan; Pérez-Valdés, Gerardo A; Kalashnykova, Nataliya; Kalashnikova, Nataliya

    2015-01-01

    This book describes recent theoretical findings relevant to bilevel programming in general, and in mixed-integer bilevel programming in particular. It describes recent applications in energy problems, such as the stochastic bilevel optimization approaches used in the natural gas industry. New algorithms for solving linear and mixed-integer bilevel programming problems are presented and explained.

  18. Computation and theory of Euler sums of generalized hyperharmonic numbers

    OpenAIRE

    Xu, Ce

    2017-01-01

    Recently, Dil and Boyadzhiev \\cite{AD2015} proved an explicit formula for the sum of multiple harmonic numbers whose indices are the sequence $\\left( {{{\\left\\{ 0 \\right\\}}_r},1} \\right)$. In this paper we show that the sums of multiple harmonic numbers whose indices are the sequence $\\left( {{{\\left\\{ 0 \\right\\}}_r,1};{{\\left\\{ 1 \\right\\}}_{k-1}}} \\right)$ can be expressed in terms of (multiple) zeta values, multiple harmonic numbers and Stirling numbers of the first kind, and give an explic...

  19. 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.

  20. Gauge theory for baryon and lepton numbers with leptoquarks.

    Science.gov (United States)

    Duerr, Michael; Fileviez Pérez, Pavel; Wise, Mark B

    2013-06-07

    Models where the baryon (B) and lepton (L) numbers are local gauge symmetries that are spontaneously broken at a low scale are revisited. We find new extensions of the standard model which predict the existence of fermions that carry both baryon and lepton numbers (i.e., leptoquarks). The local baryonic and leptonic symmetries can be broken at a scale close to the electroweak scale and we do not need to postulate the existence of a large desert to satisfy the experimental constraints on baryon number violating processes like proton decay.

  1. Algorithmic information theory mathematics of digital information processing

    CERN Document Server

    Seibt, Peter

    2007-01-01

    Treats the Mathematics of many important areas in digital information processing. This book covers, in a unified presentation, five topics: Data Compression, Cryptography, Sampling (Signal Theory), Error Control Codes, Data Reduction. It is useful for teachers, students and practitioners in Electronic Engineering, Computer Science and Mathematics.

  2. 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.

  3. 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.

  4. 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)

  5. The logical syntax of number words: theory, acquisition and processing.

    Science.gov (United States)

    Musolino, Julien

    2009-04-01

    Recent work on the acquisition of number words has emphasized the importance of integrating linguistic and developmental perspectives [Musolino, J. (2004). The semantics and acquisition of number words: Integrating linguistic and developmental perspectives. Cognition93, 1-41; Papafragou, A., Musolino, J. (2003). Scalar implicatures: Scalar implicatures: Experiments at the semantics-pragmatics interface. Cognition, 86, 253-282; Hurewitz, F., Papafragou, A., Gleitman, L., Gelman, R. (2006). Asymmetries in the acquisition of numbers and quantifiers. Language Learning and Development, 2, 76-97; Huang, Y. T., Snedeker, J., Spelke, L. (submitted for publication). What exactly do numbers mean?]. Specifically, these studies have shown that data from experimental investigations of child language can be used to illuminate core theoretical issues in the semantic and pragmatic analysis of number terms. In this article, I extend this approach to the logico-syntactic properties of number words, focusing on the way numerals interact with each other (e.g. Three boys are holding two balloons) as well as with other quantified expressions (e.g. Three boys are holding each balloon). On the basis of their intuitions, linguists have claimed that such sentences give rise to at least four different interpretations, reflecting the complexity of the linguistic structure and syntactic operations involved. Using psycholinguistic experimentation with preschoolers (n=32) and adult speakers of English (n=32), I show that (a) for adults, the intuitions of linguists can be verified experimentally, (b) by the age of 5, children have knowledge of the core aspects of the logical syntax of number words, (c) in spite of this knowledge, children nevertheless differ from adults in systematic ways, (d) the differences observed between children and adults can be accounted for on the basis of an independently motivated, linguistically-based processing model [Geurts, B. (2003). Quantifying kids. Language

  6. 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)

  7. 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)

  8. 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.

  9. 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.

  10. 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

  11. Blind source separation advances in theory, algorithms and applications

    CERN Document Server

    Wang, Wenwu

    2014-01-01

    Blind Source Separation intends to report the new results of the efforts on the study of Blind Source Separation (BSS). The book collects novel research ideas and some training in BSS, independent component analysis (ICA), artificial intelligence and signal processing applications. Furthermore, the research results previously scattered in many journals and conferences worldwide are methodically edited and presented in a unified form. The book is likely to be of interest to university researchers, R&D engineers and graduate students in computer science and electronics who wish to learn the core principles, methods, algorithms, and applications of BSS. Dr. Ganesh R. Naik works at University of Technology, Sydney, Australia; Dr. Wenwu Wang works at University of Surrey, UK.

  12. Muon number violation in some horizontal gauge theories

    International Nuclear Information System (INIS)

    Shanker, O.

    1980-11-01

    Horizontal gauge models have been studied which have a mechanism for suppressing flavour changing processes involving only two flavours, i.e., processes like μ→eγ, μ→ ee anti e and the K 0 - anti K 0 transition. It is found that the rates for some muon-number violating processes, in particular for μe conversion and kaon decays, can be close to experimental upper limits. This is in contrast to horizontal gauge models in which the K 0 - anti K 0 transition is not suppressed. (auth)

  13. 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.

  14. 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.

  15. 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.

  16. 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.

  17. 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.

  18. 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.

  19. Cognitive Radio for Smart Grid: Theory, Algorithms, and Security

    Directory of Open Access Journals (Sweden)

    Raghuram Ranganathan

    2011-01-01

    Full Text Available Recently, cognitive radio and smart grid are two areas which have received considerable research impetus. Cognitive radios are intelligent software defined radios (SDRs that efficiently utilize the unused regions of the spectrum, to achieve higher data rates. The smart grid is an automated electric power system that monitors and controls grid activities. In this paper, the novel concept of incorporating a cognitive radio network as the communications infrastructure for the smart grid is presented. A brief overview of the cognitive radio, IEEE 802.22 standard and smart grid, is provided. Experimental results obtained by using dimensionality reduction techniques such as principal component analysis (PCA, kernel PCA, and landmark maximum variance unfolding (LMVU on Wi-Fi signal measurements are presented in a spectrum sensing context. Furthermore, compressed sensing algorithms such as Bayesian compressed sensing and the compressed sensing Kalman filter is employed for recovering the sparse smart meter transmissions. From the power system point of view, a supervised learning method called support vector machine (SVM is used for the automated classification of power system disturbances. The impending problem of securing the smart grid is also addressed, in addition to the possibility of applying FPGA-based fuzzy logic intrusion detection for the smart grid.

  20. Technology Corner: Calculating the Number of Android Lock Patterns: An Unfinished Study in Number Theory

    Directory of Open Access Journals (Sweden)

    Gary Kessler

    2013-12-01

    Full Text Available Although one is unlikely to ever want to brute-force an Android lock pattern, many do wonder about the relative strength of the lock pattern versus a multi-digit personal identification number (PIN. It becomes obvious pretty quickly that there are many more lock patterns than the 10,000 possible four-digit PINs.(see PDF for full technology corner

  1. 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.

  2. 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.

  3. 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)

  4. Algorithms

    Indian Academy of Sciences (India)

    polynomial) division have been found in Vedic Mathematics which are dated much before Euclid's algorithm. A programming language Is used to describe an algorithm for execution on a computer. An algorithm expressed using a programming.

  5. Ensemble Bayesian forecasting system Part I: Theory and algorithms

    Science.gov (United States)

    Herr, Henry D.; Krzysztofowicz, Roman

    2015-05-01

    The ensemble Bayesian forecasting system (EBFS), whose theory was published in 2001, is developed for the purpose of quantifying the total uncertainty about a discrete-time, continuous-state, non-stationary stochastic process such as a time series of stages, discharges, or volumes at a river gauge. The EBFS is built of three components: an input ensemble forecaster (IEF), which simulates the uncertainty associated with random inputs; a deterministic hydrologic model (of any complexity), which simulates physical processes within a river basin; and a hydrologic uncertainty processor (HUP), which simulates the hydrologic uncertainty (an aggregate of all uncertainties except input). It works as a Monte Carlo simulator: an ensemble of time series of inputs (e.g., precipitation amounts) generated by the IEF is transformed deterministically through a hydrologic model into an ensemble of time series of outputs, which is next transformed stochastically by the HUP into an ensemble of time series of predictands (e.g., river stages). Previous research indicated that in order to attain an acceptable sampling error, the ensemble size must be on the order of hundreds (for probabilistic river stage forecasts and probabilistic flood forecasts) or even thousands (for probabilistic stage transition forecasts). The computing time needed to run the hydrologic model this many times renders the straightforward simulations operationally infeasible. This motivates the development of the ensemble Bayesian forecasting system with randomization (EBFSR), which takes full advantage of the analytic meta-Gaussian HUP and generates multiple ensemble members after each run of the hydrologic model; this auxiliary randomization reduces the required size of the meteorological input ensemble and makes it operationally feasible to generate a Bayesian ensemble forecast of large size. Such a forecast quantifies the total uncertainty, is well calibrated against the prior (climatic) distribution of

  6. 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.

  7. 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.).

  8. Algorithms

    Indian Academy of Sciences (India)

    to as 'divide-and-conquer'. Although there has been a large effort in realizing efficient algorithms, there are not many universally accepted algorithm design paradigms. In this article, we illustrate algorithm design techniques such as balancing, greedy strategy, dynamic programming strategy, and backtracking or traversal of ...

  9. 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.

  10. 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.)

  11. 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...

  12. 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

  13. 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

  14. 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 ...

  15. 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.

  16. [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…

  17. 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…

  18. 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)

  19. 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.

  20. 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)

  1. 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...

  2. PARTIAL TRAINING METHOD FOR HEURISTIC ALGORITHM OF POSSIBLE CLUSTERIZATION UNDER UNKNOWN NUMBER OF CLASSES

    Directory of Open Access Journals (Sweden)

    D. A. Viattchenin

    2009-01-01

    Full Text Available A method for constructing a subset of labeled objects which is used in a heuristic algorithm of possible  clusterization with partial  training is proposed in the  paper.  The  method  is  based  on  data preprocessing by the heuristic algorithm of possible clusterization using a transitive closure of a fuzzy tolerance. Method efficiency is demonstrated by way of an illustrative example.

  3. 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.

  4. 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.

  5. 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.

  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. 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.

  8. 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.

  9. Algorithms

    Indian Academy of Sciences (India)

    ticians but also forms the foundation of computer science. Two ... with methods of developing algorithms for solving a variety of problems but ... applications of computers in science and engineer- ... numerical calculus are as important. We will ...

  10. 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.

  11. 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.)

  12. 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.

  13. 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...

  14. Polynomial Approximation Algorithms for the TSP and the QAP with a Factorial Domination Number

    DEFF Research Database (Denmark)

    Gutin, Gregory; Yeo, Anders

    2002-01-01

    Glover and Punnen (J. Oper. Res. Soc. 48 (1997) 502) asked whether there exists a polynomial time algorithm that always produces a tour which is not worse than at least n!/p(n) tours for some polynomial p(n) for every TSP instance on n cities. They conjectured that, unless P = NP, the answer to t...

  15. 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.

  16. 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

  17. 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.

  18. 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.

  19. 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.

  20. 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

  1. 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.

  2. 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

  3. 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.

  4. 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…

  5. 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,…

  6. 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…

  7. 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

  8. 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

  9. 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.

  10. 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.

  11. Study of high speed complex number algorithms. [for determining antenna for field radiation patterns

    Science.gov (United States)

    Heisler, R.

    1981-01-01

    A method of evaluating the radiation integral on the curved surface of a reflecting antenna is presented. A three dimensional Fourier transform approach is used to generate a two dimensional radiation cross-section along a planer cut at any angle phi through the far field pattern. Salient to the method is an algorithm for evaluating a subset of the total three dimensional discrete Fourier transform results. The subset elements are selectively evaluated to yield data along a geometric plane of constant. The algorithm is extremely efficient so that computation of the induced surface currents via the physical optics approximation dominates the computer time required to compute a radiation pattern. Application to paraboloid reflectors with off-focus feeds in presented, but the method is easily extended to offset antenna systems and reflectors of arbitrary shapes. Numerical results were computed for both gain and phase and are compared with other published work.

  12. 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.

  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. Algorithms

    Indian Academy of Sciences (India)

    algorithm design technique called 'divide-and-conquer'. One of ... Turtle graphics, September. 1996. 5. ... whole list named 'PO' is a pointer to the first element of the list; ..... Program for computing matrices X and Y and placing the result in C *).

  15. Algorithms

    Indian Academy of Sciences (India)

    algorithm that it is implicitly understood that we know how to generate the next natural ..... Explicit comparisons are made in line (1) where maximum and minimum is ... It can be shown that the function T(n) = 3/2n -2 is the solution to the above ...

  16. 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.

  17. 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

  18. An algorithm for the 〈r, s〉-domination number of a tree

    African Journals Online (AJOL)

    Dedication to Emeritus Professor Gerhard Geldenhuys. Dedicated to my friend and colleague Professor Gerhard Geldenhuys, a gentleman and scholar, on the occasion of his 70th birthday. This friendship has led to twenty years of fruitful research collaborations on practical aspects of graph theory involving scientists from.

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

    Czech Academy of Sciences Publication Activity Database

    Chlumecký, M.; Buchtele, Josef; Richta, K.

    2017-01-01

    Roč. 553, October (2017), s. 350-355 ISSN 0022-1694 Institutional support: RVO:67985874 Keywords : genetic algorithm * optimisation * rainfall-runoff modeling * random generator Subject RIV: DA - Hydrology ; Limnology OBOR OECD: Hydrology Impact factor: 3.483, year: 2016 https://ac.els-cdn.com/S0022169417305516/1-s2.0-S0022169417305516-main.pdf?_tid=fa1bad8a-bd6a-11e7-8567-00000aab0f27&acdnat=1509365462_a1335d3d997e9eab19e23b1eee977705

  20. 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”.

  1. 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

  2. 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.

  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. 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.

  5. Algorithms

    Indian Academy of Sciences (India)

    will become clear in the next article when we discuss a simple logo like programming language. ... Rod B may be used as an auxiliary store. The problem is to find an algorithm which performs this task. ... No disks are moved from A to Busing C as auxiliary rod. • move _disk (A, C);. (No + l)th disk is moved from A to C directly ...

  6. 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).

  7. 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.

  8. 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.

  9. 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.

  10. 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...

  11. Using pseudo-random number generator for making iterative algorithms of hashing data

    International Nuclear Information System (INIS)

    Ivanov, M.A.; Vasil'ev, N.P.; Kozyrskij, B.L.

    2014-01-01

    The method of stochastic data transformation made for usage in cryptographic methods of information protection has been analyzed. The authors prove the usage of cryptographically strong pseudo-random number generators as a basis for Sponge construction. This means that the analysis of the quality of the known methods and tools for assessing the statistical security of pseudo-random number generators can be used effectively [ru

  12. 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.

  13. 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.

  14. A practical approximation algorithm for solving massive instances of hybridization number

    NARCIS (Netherlands)

    Iersel, van L.J.J.; Kelk, S.M.; Lekic, N.; Scornavacca, C.; Raphael, B.; Tang, J.

    2012-01-01

    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. In practice, exact solvers struggle to solve instances with

  15. 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).

  16. 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.

  17. 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.

  18. 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

  19. 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.

  20. 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.)

  1. 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.

  2. 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)

  3. 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

  4. 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.)

  5. 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.

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. 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...

  11. 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.

  12. 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

  13. Voltage equalization of an ultracapacitor module by cell grouping using number partitioning algorithm

    Science.gov (United States)

    Oyarbide, E.; Bernal, C.; Molina, P.; Jiménez, L. A.; Gálvez, R.; Martínez, A.

    2016-01-01

    Ultracapacitors are low voltage devices and therefore, for practical applications, they need to be used in modules of series-connected cells. Because of the inherent manufacturing tolerance of the capacitance parameter of each cell, and as the maximum voltage value cannot be exceeded, the module requires inter-cell voltage equalization. If the intended application suffers repeated fast charging/discharging cycles, active equalization circuits must be rated to full power, and thus the module becomes expensive. Previous work shows that a series connection of several sets of paralleled ultracapacitors minimizes the dispersion of equivalent capacitance values, and also the voltage differences between capacitors. Thus the overall life expectancy is improved. This paper proposes a method to distribute ultracapacitors with a number partitioning-based strategy to reduce the dispersion between equivalent submodule capacitances. Thereafter, the total amount of stored energy and/or the life expectancy of the device can be considerably improved.

  14. 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.

  15. 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.

  16. 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.

  17. 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

  18. 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

  19. 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.

  20. 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.

  1. 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.

  2. 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.

  3. 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.

  4. Designing mixed metal halide ammines for ammonia storage using density functional theory and genetic algorithms.

    Science.gov (United States)

    Jensen, Peter Bjerre; Lysgaard, Steen; Quaade, Ulrich J; Vegge, Tejs

    2014-09-28

    Metal halide ammines have great potential as a future, high-density energy carrier in vehicles. So far known materials, e.g. Mg(NH3)6Cl2 and Sr(NH3)8Cl2, are not suitable for automotive, fuel cell applications, because the release of ammonia is a multi-step reaction, requiring too much heat to be supplied, making the total efficiency lower. Here, we apply density functional theory (DFT) calculations to predict new mixed metal halide ammines with improved storage capacities and the ability to release the stored ammonia in one step, at temperatures suitable for system integration with polymer electrolyte membrane fuel cells (PEMFC). We use genetic algorithms (GAs) to search for materials containing up to three different metals (alkaline-earth, 3d and 4d) and two different halides (Cl, Br and I) - almost 27,000 combinations, and have identified novel mixtures, with significantly improved storage capacities. The size of the search space and the chosen fitness function make it possible to verify that the found candidates are the best possible candidates in the search space, proving that the GA implementation is ideal for this kind of computational materials design, requiring calculations on less than two percent of the candidates to identify the global optimum.

  5. Imitation Monte Carlo methods for problems of the Boltzmann equation with small Knudsen numbers, parallelizing algorithms with splitting

    International Nuclear Information System (INIS)

    Khisamutdinov, A I; Velker, N N

    2014-01-01

    The talk examines a system of pairwise interaction particles, which models a rarefied gas in accordance with the nonlinear Boltzmann equation, the master equations of Markov evolution of this system and corresponding numerical Monte Carlo methods. Selection of some optimal method for simulation of rarefied gas dynamics depends on the spatial size of the gas flow domain. For problems with the Knudsen number K n of order unity 'imitation', or 'continuous time', Monte Carlo methods ([2]) are quite adequate and competitive. However if K n ≤ 0.1 (the large sizes), excessive punctuality, namely, the need to see all the pairs of particles in the latter, leads to a significant increase in computational cost(complexity). We are interested in to construct the optimal methods for Boltzmann equation problems with large enough spatial sizes of the flow. Speaking of the optimal, we mean that we are talking about algorithms for parallel computation to be implemented on high-performance multi-processor computers. The characteristic property of large systems is the weak dependence of sub-parts of each other at a sufficiently small time intervals. This property is taken into account in the approximate methods using various splittings of operator of corresponding master equations. In the paper, we develop the approximate method based on the splitting of the operator of master equations system 'over groups of particles' ([7]). The essence of the method is that the system of particles is divided into spatial subparts which are modeled independently for small intervals of time, using the precise 'imitation' method. The type of splitting used is different from other well-known type 'over collisions and displacements', which is an attribute of the known Direct simulation Monte Carlo methods. The second attribute of the last ones is the grid of the 'interaction cells', which is completely absent in the imitation methods. The

  6. 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...

  7. The remote ischemic preconditioning algorithm: effect of number of cycles, cycle duration and effector organ mass on efficacy of protection.

    Science.gov (United States)

    Johnsen, Jacob; Pryds, Kasper; Salman, Rasha; Løfgren, Bo; Kristiansen, Steen Buus; Bøtker, Hans Erik

    2016-03-01

    Remote ischemic preconditioning (rIPC), induced by cycles of transient limb ischemia and reperfusion (IR), is cardioprotective. The optimal rIPC-algorithm is not established. We investigated the effect of cycle numbers and ischemia duration within each rIPC-cycle and the influence of effector organ mass on the efficacy of cardioprotection. Furthermore, the duration of the early phase of protection by rIPC was investigated. Using a tourniquet tightened at the inguinal level, we subjected C57Bl/6NTac mice to intermittent hind-limb ischemia and reperfusion. The rIPC-protocols consisted of (I) two, four, six or eight cycles, (II) 2, 5 or 10 min of ischemia in each cycle, (III) single or two hind-limb occlusions and (IV) 0.5, 1.5, 2.0 or 2.5 h intervals from rIPC to index cardiac ischemia. All rIPC algorithms were followed by 5 min of reperfusion. The hearts were subsequently exposed to 25 min of global ischemia and 60 min of reperfusion in an ex vivo Langendorff model. Cardioprotection was evaluated by infarct size and post-ischemic hemodynamic recovery. Four to six rIPC cycles yielded significant cardioprotection with no further protection by eight cycles. Ischemic cycles lasting 2 min offered the same protection as cycles of 5 min ischemia, whereas prolonged cycles lasting 10 min abrogated protection. One and two hind-limb preconditioning were equally protective. In our mouse model, the duration of protection by rIPC was 1.5 h. These findings indicate that the number and duration of cycles rather than the tissue mass exposed to rIPC determines the efficacy of rIPC.

  8. 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

  9. Assessment of various failure theories for weight and cost optimized laminated composites using genetic algorithm

    Energy Technology Data Exchange (ETDEWEB)

    Goyal, T. [Indian Institute of Technology Kanpur. Dept. of Aerospace Engineering, UP (India); Gupta, R. [Infotech Enterprises Ltd., Hyderabad (India)

    2012-07-01

    In this work, minimum weight-cost design for laminated composites is presented. A genetic algorithm has been developed for the optimization process. Maximum-Stress, Tsai-Wu and Tsai-Hill failure criteria have been used along with buckling analysis parameter for the margin of safety calculations. The design variables include three materials; namely Carbon-Epoxy, Glass-Epoxy, Kevlar-Epoxy; number of plies; ply orientation angles, varying from -75 deg. to 90 deg. in the intervals of 15 deg. and ply thicknesses which depend on the material in use. The total cost is a sum of material cost and layup cost. Layup cost is a function of the ply angle. Validation studies for solution convergence and weight-cost inverse proportionality are carried out. One set of results for shear loading are also validated from literature for a particular case. A Pareto-Optimal solution set is demonstrated for biaxial loading conditions. It is then extended to applied moments. It is found that global optimum for a given loading condition is a function of the failure criteria for shear loading, with Maximum Stress criteria giving the lightest-cheapest and Tsai-Wu criteria giving the heaviest-costliest optimized laminates. Optimized weight results are plotted from the three criteria to do a comparative study. This work gives a global optimized laminated composite and also a set of other local optimum laminates for a given set of loading conditions. The current algorithm also provides with adequate data to supplement the use of different failure criteria for varying loadings. This work can find use in the industry and/or academia considering the increased use of laminated composites in modern wind blades. (Author)

  10. On the continuum theory of the one-fluid solar wind for small Prandtl number

    International Nuclear Information System (INIS)

    Johnson, R.S.

    1976-01-01

    The continuum theory for a single-species gas expanding into a vacuum (or near vacuum) is considered. The gas is assumed compressible, viscous and heat conducting with a constant Prandtl number and viscosity proportional to (temperature) sup(ω), ω > 1. The gas is under the influence of a gravitational field centred on the Sun. For small Prandtl number (which is realistic for the one-fluid solar wind), the method of matched asymptotic expansions is used to construct a solution describing the complete flow field from the surface of the Sun to infinity. The first two regions correspond to those found by Roberts and Soward (Proc. R. Soc. Lond.; A328:185 (1972)) for large thermal conductivity; the next involves the viscous terms, and in the fourth the viscous terms dominate. It it shown from the fourth region that either the flow remains supersonic but terminates at a finite point, or the flow becomes subsonic through a diffuse shock layer and approaches a non-zero pressure at infinity. It is seen that the existence of a critical point (subsonic/supersonic transition) together with a known pressure at infinity can uniquely determine the complete solution. However, to correspond with typical results near the Sun and at the Earth's orbit the pressure at infinity is found to be very much larger than that generally accepted. (author)

  11. 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).

  12. 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.

  13. Neutrinoless double beta decay in chiral effective field theory: lepton number violation at dimension seven

    Science.gov (United States)

    Cirigliano, V.; Dekens, W.; de Vries, J.; Graesser, M. L.; Mereghetti, E.

    2017-12-01

    We analyze neutrinoless double beta decay (0 νββ) within the framework of the Standard Model Effective Field Theory. Apart from the dimension-five Weinberg operator, the first contributions appear at dimension seven. We classify the operators and evolve them to the electroweak scale, where we match them to effective dimension-six, -seven, and -nine operators. In the next step, after renormalization group evolution to the QCD scale, we construct the chiral Lagrangian arising from these operators. We develop a power-counting scheme and derive the two-nucleon 0 νββ currents up to leading order in the power counting for each lepton-number-violating operator. We argue that the leading-order contribution to the decay rate depends on a relatively small number of nuclear matrix elements. We test our power counting by comparing nuclear matrix elements obtained by various methods and by different groups. We find that the power counting works well for nuclear matrix elements calculated from a specific method, while, as in the case of light Majorana neutrino exchange, the overall magnitude of the matrix elements can differ by factors of two to three between methods. We calculate the constraints that can be set on dimension-seven lepton-number-violating operators from 0 νββ experiments and study the interplay between dimension-five and -seven operators, discussing how dimension-seven contributions affect the interpretation of 0 νββ in terms of the effective Majorana mass m ββ .

  14. Splitting turbulence algorithm for mixing parameterization embedded in the ocean climate model. Examples of data assimilation and Prandtl number variations.

    Science.gov (United States)

    Moshonkin, Sergey; Gusev, Anatoly; Zalesny, Vladimir; Diansky, Nikolay

    2017-04-01

    Series of experiments were performed with a three-dimensional, free surface, sigma coordinate eddy-permitting ocean circulation model for Atlantic (from 30°S) - Arctic and Bering sea domain (0.25 degrees resolution, Institute of Numerical Mathematics Ocean Model or INMOM) using vertical grid refinement in the zone of fully developed turbulence (40 sigma-levels). The model variables are horizontal velocity components, potential temperature, and salinity as well as free surface height. For parameterization of viscosity and diffusivity, the original splitting turbulence algorithm (STA) is used when total evolutionary equations for the turbulence kinetic energy (TKE) and turbulence dissipation frequency (TDF) split into the stages of transport-diffusion and generation-dissipation. For the generation-dissipation stage the analytical solution was obtained for TKE and TDF as functions of the buoyancy and velocity shift frequencies (BF and VSF). The proposed model with STA is similar to the contemporary differential turbulence models, concerning the physical formulations. At the same time, its algorithm has high enough computational efficiency. For mixing simulation in the zone of turbulence decay, the two kind numerical experiments were carried out, as with assimilation of annual mean climatic buoyancy frequency, as with variation of Prandtl number function dependence upon the BF, VSF, TKE and TDF. The CORE-II data for 1948-2009 were used for experiments. Quality of temperature T and salinity S structure simulation is estimated by the comparison of model monthly profiles T and S averaged for 1980-2009, with T and S monthly data from the World Ocean Atlas 2013. Form of coefficients in equations for TKE and TDF on the generation-dissipation stage makes it possible to assimilate annual mean climatic buoyancy frequency in a varying degree that cardinally improves adequacy of model results to climatic data in all analyzed model domain. The numerical experiments with modified

  15. An automatic optimum number of well-distributed ground control lines selection procedure based on genetic algorithm

    Science.gov (United States)

    Yavari, Somayeh; Valadan Zoej, Mohammad Javad; Salehi, Bahram

    2018-05-01

    The procedure of selecting an optimum number and best distribution of ground control information is important in order to reach accurate and robust registration results. This paper proposes a new general procedure based on Genetic Algorithm (GA) which is applicable for all kinds of features (point, line, and areal features). However, linear features due to their unique characteristics are of interest in this investigation. This method is called Optimum number of Well-Distributed ground control Information Selection (OWDIS) procedure. Using this method, a population of binary chromosomes is randomly initialized. The ones indicate the presence of a pair of conjugate lines as a GCL and zeros specify the absence. The chromosome length is considered equal to the number of all conjugate lines. For each chromosome, the unknown parameters of a proper mathematical model can be calculated using the selected GCLs (ones in each chromosome). Then, a limited number of Check Points (CPs) are used to evaluate the Root Mean Square Error (RMSE) of each chromosome as its fitness value. The procedure continues until reaching a stopping criterion. The number and position of ones in the best chromosome indicate the selected GCLs among all conjugate lines. To evaluate the proposed method, a GeoEye and an Ikonos Images are used over different areas of Iran. Comparing the obtained results by the proposed method in a traditional RFM with conventional methods that use all conjugate lines as GCLs shows five times the accuracy improvement (pixel level accuracy) as well as the strength of the proposed method. To prevent an over-parametrization error in a traditional RFM due to the selection of a high number of improper correlated terms, an optimized line-based RFM is also proposed. The results show the superiority of the combination of the proposed OWDIS method with an optimized line-based RFM in terms of increasing the accuracy to better than 0.7 pixel, reliability, and reducing systematic

  16. A statistical mechanical interpretation of algorithmic information theory: Total statistical mechanical interpretation based on physical argument

    International Nuclear Information System (INIS)

    Tadaki, Kohtaro

    2010-01-01

    The statistical mechanical interpretation of algorithmic information theory (AIT, for short) was introduced and developed by our former works [K. Tadaki, Local Proceedings of CiE 2008, pp. 425-434, 2008] and [K. Tadaki, Proceedings of LFCS'09, Springer's LNCS, vol. 5407, pp. 422-440, 2009], where we introduced the notion of thermodynamic quantities, such as partition function Z(T), free energy F(T), energy E(T), statistical mechanical entropy S(T), and specific heat C(T), into AIT. We then discovered that, in the interpretation, the temperature T equals to the partial randomness of the values of all these thermodynamic quantities, where the notion of partial randomness is a stronger representation of the compression rate by means of program-size complexity. Furthermore, we showed that this situation holds for the temperature T itself, which is one of the most typical thermodynamic quantities. Namely, we showed that, for each of the thermodynamic quantities Z(T), F(T), E(T), and S(T) above, the computability of its value at temperature T gives a sufficient condition for T is an element of (0,1) to satisfy the condition that the partial randomness of T equals to T. In this paper, based on a physical argument on the same level of mathematical strictness as normal statistical mechanics in physics, we develop a total statistical mechanical interpretation of AIT which actualizes a perfect correspondence to normal statistical mechanics. We do this by identifying a microcanonical ensemble in the framework of AIT. As a result, we clarify the statistical mechanical meaning of the thermodynamic quantities of AIT.

  17. 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.)

  18. 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...

  19. 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.

  20. 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.)

  1. 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

  2. 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

  3. 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

  4. Approximate Bayesian algorithm to estimate the basic reproduction number in an influenza pandemic using arrival times of imported cases.

    Science.gov (United States)

    Chong, Ka Chun; Zee, Benny Chung Ying; Wang, Maggie Haitian

    2018-04-10

    In an influenza pandemic, arrival times of cases are a proxy of the epidemic size and disease transmissibility. Because of intense surveillance of travelers from infected countries, detection is more rapid and complete than on local surveillance. Travel information can provide a more reliable estimation of transmission parameters. We developed an Approximate Bayesian Computation algorithm to estimate the basic reproduction number (R 0 ) in addition to the reporting rate and unobserved epidemic start time, utilizing travel, and routine surveillance data in an influenza pandemic. A simulation was conducted to assess the sampling uncertainty. The estimation approach was further applied to the 2009 influenza A/H1N1 pandemic in Mexico as a case study. In the simulations, we showed that the estimation approach was valid and reliable in different simulation settings. We also found estimates of R 0 and the reporting rate to be 1.37 (95% Credible Interval [CI]: 1.26-1.42) and 4.9% (95% CI: 0.1%-18%), respectively, in the 2009 influenza pandemic in Mexico, which were robust to variations in the fixed parameters. The estimated R 0 was consistent with that in the literature. This method is useful for officials to obtain reliable estimates of disease transmissibility for strategic planning. We suggest that improvements to the flow of reporting for confirmed cases among patients arriving at different countries are required. Copyright © 2018 Elsevier Ltd. All rights reserved.

  5. Parallel Fokker–Planck-DSMC algorithm for rarefied gas flow simulation in complex domains at all Knudsen numbers

    Energy Technology Data Exchange (ETDEWEB)

    Küchlin, Stephan, E-mail: kuechlin@ifd.mavt.ethz.ch; Jenny, Patrick

    2017-01-01

    A major challenge for the conventional Direct Simulation Monte Carlo (DSMC) technique lies in the fact that its computational cost becomes prohibitive in the near continuum regime, where the Knudsen number (Kn)—characterizing the degree of rarefaction—becomes small. In contrast, the Fokker–Planck (FP) based particle Monte Carlo scheme allows for computationally efficient simulations of rarefied gas flows in the low and intermediate Kn regime. The Fokker–Planck collision operator—instead of performing binary collisions employed by the DSMC method—integrates continuous stochastic processes for the phase space evolution in time. This allows for time step and grid cell sizes larger than the respective collisional scales required by DSMC. Dynamically switching between the FP and the DSMC collision operators in each computational cell is the basis of the combined FP-DSMC method, which has been proven successful in simulating flows covering the whole Kn range. Until recently, this algorithm had only been applied to two-dimensional test cases. In this contribution, we present the first general purpose implementation of the combined FP-DSMC method. Utilizing both shared- and distributed-memory parallelization, this implementation provides the capability for simulations involving many particles and complex geometries by exploiting state of the art computer cluster technologies.

  6. Consensus embedding: theory, algorithms and application to segmentation and classification of biomedical data

    Directory of Open Access Journals (Sweden)

    Viswanath Satish

    2012-02-01

    Full Text Available Abstract Background Dimensionality reduction (DR enables the construction of a lower dimensional space (embedding from a higher dimensional feature space while preserving object-class discriminability. However several popular DR approaches suffer from sensitivity to choice of parameters and/or presence of noise in the data. In this paper, we present a novel DR technique known as consensus embedding that aims to overcome these problems by generating and combining multiple low-dimensional embeddings, hence exploiting the variance among them in a manner similar to ensemble classifier schemes such as Bagging. We demonstrate theoretical properties of consensus embedding which show that it will result in a single stable embedding solution that preserves information more accurately as compared to any individual embedding (generated via DR schemes such as Principal Component Analysis, Graph Embedding, or Locally Linear Embedding. Intelligent sub-sampling (via mean-shift and code parallelization are utilized to provide for an efficient implementation of the scheme. Results Applications of consensus embedding are shown in the context of classification and clustering as applied to: (1 image partitioning of white matter and gray matter on 10 different synthetic brain MRI images corrupted with 18 different combinations of noise and bias field inhomogeneity, (2 classification of 4 high-dimensional gene-expression datasets, (3 cancer detection (at a pixel-level on 16 image slices obtained from 2 different high-resolution prostate MRI datasets. In over 200 different experiments concerning classification and segmentation of biomedical data, consensus embedding was found to consistently outperform both linear and non-linear DR methods within all applications considered. Conclusions We have presented a novel framework termed consensus embedding which leverages ensemble classification theory within dimensionality reduction, allowing for application to a wide range

  7. A kinetic theory for nonanalog Monte Carlo algorithms: Exponential transform with angular biasing

    International Nuclear Information System (INIS)

    Ueki, T.; Larsen, E.W.

    1998-01-01

    A new Boltzmann Monte Carlo (BMC) equation is proposed to describe the transport of Monte Carlo particles governed by a set of nonanalog rules for the transition of space, velocity, and weight. The BMC equation is a kinetic equation that includes weight as an extra independent variable. The solution of the BMC equation is the pointwise distribution of velocity and weight throughout the physical system. The BMC equation is derived for the simulation of a transmitted current, utilizing the exponential transform with angular biasing. The weight moments of the solution of the BMC equation are used to predict the score moments of the transmission current. (Also, it is shown that an adjoint BMC equation can be used for this purpose.) Integrating the solution of the forward BMC equation over space, velocity, and weight, the mean number of flights per history is obtained. This is used to determine theoretically the figure of merit for any choice of biasing parameters. Also, a maximum safe value of the exponential transform parameter is proposed, which ensure the finite variance of variance estimate (sample variance) for any penetration distance. Finally, numerical results that validate the new theory are provided

  8. Finite element methods for viscous incompressible flows a guide to theory, practice, and algorithms

    CERN Document Server

    Gunzburger, Max D

    2012-01-01

    In this book, the author examines mathematical aspects of finite element methods for the approximate solution of incompressible flow problems. The principal goal is to present some of the important mathematical results that are relevant to practical computations. In so doing, useful algorithms are also discussed. Although rigorous results are stated, no detailed proofs are supplied; rather, the intention is to present these results so that they can serve as a guide for the selection and, in certain respects, the implementation of algorithms.

  9. 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.

  10. 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.

  11. 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.

  12. Behavioral data requirements for translating cognitive theories into computer software algorithms

    International Nuclear Information System (INIS)

    Meister, D.

    1992-01-01

    This paper reviews the characteristics of cognitive theories and their links to behavioral science and advanced intelligent systems. Cognitive theories model human cognition, perception, and communication. They suggest the human functions the system should have, serve as a philosophical basis for system development, and provide abstract design guidelines. The underlying assumption behind this paper is that if the cognitive theories are to have any value at all, they must be translated into usable systems. A process for testing a cognitive theory in terms of conceptual criteria, behavioral predictions and tests, and software development and tests, is suggested. Criteria for measuring the problem solving success of the advanced system are described. A theory of the system as an intelligent problem solver is presented. (author)

  13. A dual communicator and dual grid-resolution algorithm for petascale simulations of turbulent mixing at high Schmidt number

    Science.gov (United States)

    Clay, M. P.; Buaria, D.; Gotoh, T.; Yeung, P. K.

    2017-10-01

    A new dual-communicator algorithm with very favorable performance characteristics has been developed for direct numerical simulation (DNS) of turbulent mixing of a passive scalar governed by an advection-diffusion equation. We focus on the regime of high Schmidt number (S c), where because of low molecular diffusivity the grid-resolution requirements for the scalar field are stricter than those for the velocity field by a factor √{ S c }. Computational throughput is improved by simulating the velocity field on a coarse grid of Nv3 points with a Fourier pseudo-spectral (FPS) method, while the passive scalar is simulated on a fine grid of Nθ3 points with a combined compact finite difference (CCD) scheme which computes first and second derivatives at eighth-order accuracy. A static three-dimensional domain decomposition and a parallel solution algorithm for the CCD scheme are used to avoid the heavy communication cost of memory transposes. A kernel is used to evaluate several approaches to optimize the performance of the CCD routines, which account for 60% of the overall simulation cost. On the petascale supercomputer Blue Waters at the University of Illinois, Urbana-Champaign, scalability is improved substantially with a hybrid MPI-OpenMP approach in which a dedicated thread per NUMA domain overlaps communication calls with computational tasks performed by a separate team of threads spawned using OpenMP nested parallelism. At a target production problem size of 81923 (0.5 trillion) grid points on 262,144 cores, CCD timings are reduced by 34% compared to a pure-MPI implementation. Timings for 163843 (4 trillion) grid points on 524,288 cores encouragingly maintain scalability greater than 90%, although the wall clock time is too high for production runs at this size. Performance monitoring with CrayPat for problem sizes up to 40963 shows that the CCD routines can achieve nearly 6% of the peak flop rate. The new DNS code is built upon two existing FPS and CCD codes

  14. Improved PSO algorithm based on chaos theory and its application to design flood hydrograph

    Directory of Open Access Journals (Sweden)

    Si-Fang Dong

    2010-06-01

    Full Text Available The deficiencies of basic particle swarm optimization (bPSO are its ubiquitous prematurity and its inability to seek the global optimal solution when optimizing complex high-dimensional functions. To overcome such deficiencies, the chaos-PSO (COSPSO algorithm was established by introducing the chaos optimization mechanism and a global particle stagnation-disturbance strategy into bPSO. In the improved algorithm, chaotic movement was adopted for the particles' initial movement trajectories to replace the former stochastic movement, and the chaos factor was used to guide the particles' path. When the global particles were stagnant, the disturbance strategy was used to keep the particles in motion. Five benchmark optimizations were introduced to test COSPSO, and they proved that COSPSO can remarkably improve efficiency in optimizing complex functions. Finally, a case study of COSPSO in calculating design flood hydrographs demonstrated the applicability of the improved algorithm.

  15. Using game theory for perceptual tuned rate control algorithm in video coding

    Science.gov (United States)

    Luo, Jiancong; Ahmad, Ishfaq

    2005-03-01

    This paper proposes a game theoretical rate control technique for video compression. Using a cooperative gaming approach, which has been utilized in several branches of natural and social sciences because of its enormous potential for solving constrained optimization problems, we propose a dual-level scheme to optimize the perceptual quality while guaranteeing "fairness" in bit allocation among macroblocks. At the frame level, the algorithm allocates target bits to frames based on their coding complexity. At the macroblock level, the algorithm distributes bits to macroblocks by defining a bargaining game. Macroblocks play cooperatively to compete for shares of resources (bits) to optimize their quantization scales while considering the Human Visual System"s perceptual property. Since the whole frame is an entity perceived by viewers, macroblocks compete cooperatively under a global objective of achieving the best quality with the given bit constraint. The major advantage of the proposed approach is that the cooperative game leads to an optimal and fair bit allocation strategy based on the Nash Bargaining Solution. Another advantage is that it allows multi-objective optimization with multiple decision makers (macroblocks). The simulation results testify the algorithm"s ability to achieve accurate bit rate with good perceptual quality, and to maintain a stable buffer level.

  16. Who Owns Educational Theory? Big Data, Algorithms and the Expert Power of Education Data Science

    Science.gov (United States)

    Williamson, Ben

    2017-01-01

    "Education data science" is an emerging methodological field which possesses the algorithm-driven technologies required to generate insights and knowledge from educational big data. This article consists of an analysis of the Lytics Lab, Stanford University's laboratory for research and development in learning analytics, and the Center…

  17. A Novel Control Algorithm for Static Series Compensators by Use of PQR Instantaneous Power Theory

    DEFF Research Database (Denmark)

    Lee, Sang-Joon; Kim, Hyosung; Sul, Seung-Ki

    2004-01-01

    in coordinates is very simple and clear, has better steady state and dynamic performance. The controlled variables in coordinates are then inversely transformed to the original coordinates without time delay, generating control signals to SSCs. The control algorithm can be used for various kinds of SSCs...

  18. A Global Convergence Theory for General Trust-Region-Based Algorithms for Equality Constrained Optimization

    National Research Council Canada - National Science Library

    Dennis, John E; El-Alem, Mahmoud; Maciel, Maria C

    1995-01-01

    .... The normal Component need not be computed accurately. The theory requires a quasi-normal component to satisfy a fraction of Cauchy decrease condition on the quadratic model of the linearized constraints...

  19. On Equality and Natural Numbers in Cantor-Lukasiewicz Set Theory

    Czech Academy of Sciences Publication Activity Database

    Hájek, Petr

    2013-01-01

    Roč. 21, č. 1 (2013), s. 91-100 ISSN 1367-0751 R&D Projects: GA MŠk(CZ) 1M0545 Institutional research plan: CEZ:AV0Z10300504 Keywords : Lukasiewicz logic * Cantor set theory * full comprehension Subject RIV: BA - General Mathematics Impact factor: 0.530, year: 2013

  20. Noniterative accurate algorithm for the exact exchange potential of density-functional theory

    International Nuclear Information System (INIS)

    Cinal, M.; Holas, A.

    2007-01-01

    An algorithm for determination of the exchange potential is constructed and tested. It represents a one-step procedure based on the equations derived by Krieger, Li, and Iafrate (KLI) [Phys. Rev. A 46, 5453 (1992)], implemented already as an iterative procedure by Kuemmel and Perdew [Phys. Rev. Lett. 90, 043004 (2003)]. Due to suitable transformation of the KLI equations, we can solve them avoiding iterations. Our algorithm is applied to the closed-shell atoms, from Be up to Kr, within the DFT exchange-only approximation. Using pseudospectral techniques for representing orbitals, we obtain extremely accurate values of total and orbital energies with errors at least four orders of magnitude smaller than known in the literature

  1. Practical mathematical optimization basic optimization theory and gradient-based algorithms

    CERN Document Server

    Snyman, Jan A

    2018-01-01

    This textbook presents a wide range of tools for a course in mathematical optimization for upper undergraduate and graduate students in mathematics, engineering, computer science, and other applied sciences. Basic optimization principles are presented with emphasis on gradient-based numerical optimization strategies and algorithms for solving both smooth and noisy discontinuous optimization problems. Attention is also paid to the difficulties of expense of function evaluations and the existence of multiple minima that often unnecessarily inhibit the use of gradient-based methods. This second edition addresses further advancements of gradient-only optimization strategies to handle discontinuities in objective functions. New chapters discuss the construction of surrogate models as well as new gradient-only solution strategies and numerical optimization using Python. A special Python module is electronically available (via springerlink) that makes the new algorithms featured in the text easily accessible and dir...

  2. Sparse representation, modeling and learning in visual recognition theory, algorithms and applications

    CERN Document Server

    Cheng, Hong

    2015-01-01

    This unique text/reference presents a comprehensive review of the state of the art in sparse representations, modeling and learning. The book examines both the theoretical foundations and details of algorithm implementation, highlighting the practical application of compressed sensing research in visual recognition and computer vision. Topics and features: provides a thorough introduction to the fundamentals of sparse representation, modeling and learning, and the application of these techniques in visual recognition; describes sparse recovery approaches, robust and efficient sparse represen

  3. Perfect blind restoration of images blurred by multiple filters: theory and efficient algorithms.

    Science.gov (United States)

    Harikumar, G; Bresler, Y

    1999-01-01

    We address the problem of restoring an image from its noisy convolutions with two or more unknown finite impulse response (FIR) filters. We develop theoretical results about the existence and uniqueness of solutions, and show that under some generically true assumptions, both the filters and the image can be determined exactly in the absence of noise, and stably estimated in its presence. We present efficient algorithms to estimate the blur functions and their sizes. These algorithms are of two types, subspace-based and likelihood-based, and are extensions of techniques proposed for the solution of the multichannel blind deconvolution problem in one dimension. We present memory and computation-efficient techniques to handle the very large matrices arising in the two-dimensional (2-D) case. Once the blur functions are determined, they are used in a multichannel deconvolution step to reconstruct the unknown image. The theoretical and practical implications of edge effects, and "weakly exciting" images are examined. Finally, the algorithms are demonstrated on synthetic and real data.

  4. The number of elementary particles in a fractal M-theory of 11.2360667977 dimensions

    International Nuclear Information System (INIS)

    He, J.-H.

    2007-01-01

    It is generally accepted that there are 60 experimentally found particles. The standard model strongly predicts two more hypothetical particles, the Higgs and the graviton. This paper reveals other possible scenario for predicting 69 particles at different energy scales in 11+φ 3 fractal dimensions of a fractal M theory, where φ=(5-1)/2. A modified Newton's law is suggested to experimentally verify our predictions at extremely small quantum scales. The modified Newton's law is in harmony with Heisenberg's uncertainty principle

  5. 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.

  6. 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.

  7. 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.

  8. A new free-surface stabilization algorithm for geodynamical modelling: Theory and numerical tests

    Science.gov (United States)

    Andrés-Martínez, Miguel; Morgan, Jason P.; Pérez-Gussinyé, Marta; Rüpke, Lars

    2015-09-01

    The surface of the solid Earth is effectively stress free in its subaerial portions, and hydrostatic beneath the oceans. Unfortunately, this type of boundary condition is difficult to treat computationally, and for computational convenience, numerical models have often used simpler approximations that do not involve a normal stress-loaded, shear-stress free top surface that is free to move. Viscous flow models with a computational free surface typically confront stability problems when the time step is bigger than the viscous relaxation time. The small time step required for stability (develop strategies that mitigate the stability problem by making larger (at least ∼10 Kyr) time steps stable and accurate. Here we present a new free-surface stabilization algorithm for finite element codes which solves the stability problem by adding to the Stokes formulation an intrinsic penalization term equivalent to a portion of the future load at the surface nodes. Our algorithm is straightforward to implement and can be used with both Eulerian or Lagrangian grids. It includes α and β parameters to respectively control both the vertical and the horizontal slope-dependent penalization terms, and uses Uzawa-like iterations to solve the resulting system at a cost comparable to a non-stress free surface formulation. Four tests were carried out in order to study the accuracy and the stability of the algorithm: (1) a decaying first-order sinusoidal topography test, (2) a decaying high-order sinusoidal topography test, (3) a Rayleigh-Taylor instability test, and (4) a steep-slope test. For these tests, we investigate which α and β parameters give the best results in terms of both accuracy and stability. We also compare the accuracy and the stability of our algorithm with a similar implicit approach recently developed by Kaus et al. (2010). We find that our algorithm is slightly more accurate and stable for steep slopes, and also conclude that, for longer time steps, the optimal

  9. 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)

  10. 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.

  11. Symmetry numbers for rigid, flexible, and fluxional molecules: theory and applications.

    Science.gov (United States)

    Gilson, Michael K; Irikura, Karl K

    2010-12-16

    The use of molecular simulations and ab initio calculations to predict thermodynamic properties of molecules has become routine. Such methods rely upon an accurate representation of the molecular partition function or configurational integral, which in turn often includes a rotational symmetry number. However, the reason for including the symmetry number is unclear to many practitioners, and there is also a need for a general prescription for evaluating the symmetry numbers of flexible molecules, i.e., for molecules with thermally active internal degrees of freedom, such as internal rotors. Surprisingly, we have been unable to find any complete and convincing explanations of these important issues in textbooks or the journal literature. The present paper aims to explain why symmetry numbers are needed and how their values should be determined. Both classical and quantum approaches are provided.

  12. Application of a transitional boundary-layer theory in the low hypersonic Mach number regime

    Science.gov (United States)

    Shamroth, S. J.; Mcdonald, H.

    1975-01-01

    An investigation is made to assess the capability of a finite-difference boundary-layer procedure to predict the mean profile development across a transition from laminar to turbulent flow in the low hypersonic Mach-number regime. The boundary-layer procedure uses an integral form of the turbulence kinetic-energy equation to govern the development of the Reynolds apparent shear stress. The present investigation shows the ability of this procedure to predict Stanton number, velocity profiles, and density profiles through the transition region and, in addition, to predict the effect of wall cooling and Mach number on transition Reynolds number. The contribution of the pressure-dilatation term to the energy balance is examined and it is suggested that transition can be initiated by the direct absorption of acoustic energy even if only a small amount (1 per cent) of the incident acoustic energy is absorbed.

  13. 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

  14. Parallel algorithm of real-time infrared image restoration based on total variation theory

    Science.gov (United States)

    Zhu, Ran; Li, Miao; Long, Yunli; Zeng, Yaoyuan; An, Wei

    2015-10-01

    Image restoration is a necessary preprocessing step for infrared remote sensing applications. Traditional methods allow us to remove the noise but penalize too much the gradients corresponding to edges. Image restoration techniques based on variational approaches can solve this over-smoothing problem for the merits of their well-defined mathematical modeling of the restore procedure. The total variation (TV) of infrared image is introduced as a L1 regularization term added to the objective energy functional. It converts the restoration process to an optimization problem of functional involving a fidelity term to the image data plus a regularization term. Infrared image restoration technology with TV-L1 model exploits the remote sensing data obtained sufficiently and preserves information at edges caused by clouds. Numerical implementation algorithm is presented in detail. Analysis indicates that the structure of this algorithm can be easily implemented in parallelization. Therefore a parallel implementation of the TV-L1 filter based on multicore architecture with shared memory is proposed for infrared real-time remote sensing systems. Massive computation of image data is performed in parallel by cooperating threads running simultaneously on multiple cores. Several groups of synthetic infrared image data are used to validate the feasibility and effectiveness of the proposed parallel algorithm. Quantitative analysis of measuring the restored image quality compared to input image is presented. Experiment results show that the TV-L1 filter can restore the varying background image reasonably, and that its performance can achieve the requirement of real-time image processing.

  15. Parallel scientific computing theory, algorithms, and applications of mesh based and meshless methods

    CERN Document Server

    Trobec, Roman

    2015-01-01

    This book is concentrated on the synergy between computer science and numerical analysis. It is written to provide a firm understanding of the described approaches to computer scientists, engineers or other experts who have to solve real problems. The meshless solution approach is described in more detail, with a description of the required algorithms and the methods that are needed for the design of an efficient computer program. Most of the details are demonstrated on solutions of practical problems, from basic to more complicated ones. This book will be a useful tool for any reader interes

  16. Designing mixed metal halide ammines for ammonia storage using density functional theory and genetic algorithms

    DEFF Research Database (Denmark)

    Jensen, Peter Bjerre; Lysgaard, Steen; Quaade, Ulrich J.

    2014-01-01

    electrolyte membrane fuel cells (PEMFC). We use genetic algorithms (GAs) to search for materials containing up to three different metals (alkaline-earth, 3d and 4d) and two different halides (Cl, Br and I) – almost 27000 combinations, and have identified novel mixtures, with significantly improved storage......Metal halide ammines have great potential as a future, high-density energy carrier in vehicles. So far known materials, e.g. Mg(NH3)6Cl2 and Sr(NH3)8Cl2, are not suitable for automotive, fuel cell applications, because the release of ammonia is a multi-step reaction, requiring too much heat...

  17. Combinatorial theory of the semiclassical evaluation of transport moments II: Algorithmic approach for moment generating functions

    Energy Technology Data Exchange (ETDEWEB)

    Berkolaiko, G. [Department of Mathematics, Texas A and M University, College Station, Texas 77843-3368 (United States); Kuipers, J. [Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg (Germany)

    2013-12-15

    Electronic transport through chaotic quantum dots exhibits universal behaviour which can be understood through the semiclassical approximation. Within the approximation, calculation of transport moments reduces to codifying classical correlations between scattering trajectories. These can be represented as ribbon graphs and we develop an algorithmic combinatorial method to generate all such graphs with a given genus. This provides an expansion of the linear transport moments for systems both with and without time reversal symmetry. The computational implementation is then able to progress several orders further than previous semiclassical formulae as well as those derived from an asymptotic expansion of random matrix results. The patterns observed also suggest a general form for the higher orders.

  18. Sphalerons, small fluctuations, and baryon-number violation in electroweak theory

    International Nuclear Information System (INIS)

    Arnold, P.; McLerran, L.

    1987-01-01

    We study the formalism of the sphaleron approximation to baryon-number violation in the standard model at temperatures near 1 TeV. We investigate small fluctuations of the sphaleron, the competition of large-scale sphalerons with thermal fluctuations, and the damping of the transition rate in the plasma. We find a suppression of the rate due to Landau damping and due to factors arising from zero modes. Our approximations are valid in the regime 2M/sub W/(T) 2 . We find that the rate of baryon-number violation is still significantly larger than the expansion rate of the Universe

  19. 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

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

    CERN Document Server

    Simchi-Levi, David; Bramel, Julien

    2014-01-01

    Fierce competition in today's global market provides a powerful motivation for developing ever more sophisticated logistics systems. This book, written for the logistics manager and researcher, presents a survey of the modern theory and application of logistics. The goal of the book is to present the state of the art in the science of logistics management. This third edition includes new chapters on the subjects of game theory, the power of process flexibility, supply chain competition and collaboration. Among the other materials new to the edition are sections on discrete convex analysis and its applications to stochastic inventory models, as well as extended discussions of integrated inventory and pricing models. The material presents a timely and authoritative survey of the field that will make an invaluable companion to the work of many researchers and practitioners.   Review of earlier edition:   "The present book focuses on the application of operational research and mathematical modelling technique...

  1. A Bayes Theory-Based Modeling Algorithm to End-to-end Network Traffic

    Directory of Open Access Journals (Sweden)

    Zhao Hong-hao

    2016-01-01

    Full Text Available Recently, network traffic has exponentially increasing due to all kind of applications, such as mobile Internet, smart cities, smart transportations, Internet of things, and so on. the end-to-end network traffic becomes more important for traffic engineering. Usually end-to-end traffic estimation is highly difficult. This paper proposes a Bayes theory-based method to model the end-to-end network traffic. Firstly, the end-to-end network traffic is described as a independent identically distributed normal process. Then the Bases theory is used to characterize the end-to-end network traffic. By calculating the parameters, the model is determined correctly. Simulation results show that our approach is feasible and effective.

  2. A Bayes Theory-Based Modeling Algorithm to End-to-end Network Traffic

    OpenAIRE

    Zhao Hong-hao; Meng Fan-bo; Zhao Si-wen; Zhao Si-hang; Lu Yi

    2016-01-01

    Recently, network traffic has exponentially increasing due to all kind of applications, such as mobile Internet, smart cities, smart transportations, Internet of things, and so on. the end-to-end network traffic becomes more important for traffic engineering. Usually end-to-end traffic estimation is highly difficult. This paper proposes a Bayes theory-based method to model the end-to-end network traffic. Firstly, the end-to-end network traffic is described as a independent identically distrib...

  3. Characterizing the Development of Specialized Mathematical Content Knowledge for Teaching in Algebraic Reasoning and Number Theory

    Science.gov (United States)

    Bair, Sherry L.; Rich, Beverly S.

    2011-01-01

    This article characterizes the development of a deep and connected body of mathematical knowledge categorized by Ball and Bass' (2003b) model of Mathematical Knowledge for Teaching (MKT), as Specialized Content Knowledge for Teaching (SCK) in algebraic reasoning and number sense. The research employed multiple cases across three years from two…

  4. Theory of wire number scaling in wire-array Z pinches

    International Nuclear Information System (INIS)

    Desjarlais, M.P.; Marder, B.M.

    1999-01-01

    Pulsed-power-driven Z pinches, produced by imploding cylindrical arrays of many wires, have generated very high x-ray radiation powers (>200 TW) and energies (2 MJ). Experiments have revealed a steady improvement in Z-pinch performance with increasing wire number at fixed total mass and array radius. The dominant mechanism acting to limit the performance of these devices is believed to be the Rayleigh-Taylor instability which broadens the radially imploding plasma sheath and consequently reduces the peak radiation power. A model is presented which describes an amplification over the two-dimensional Rayleigh-Taylor growth rate brought about by kink-like forces on the individual wires. This amplification factor goes to zero as the number of wires approaches infinity. This model gives results which are in good agreement with the experimental data and provides a scaling for wire-array Z pinches. copyright 1999 American Institute of Physics

  5. A Non-Perturbative, Finite Particle Number Approach to Relativistic Scattering Theory

    Energy Technology Data Exchange (ETDEWEB)

    Lindesay, James V

    2001-05-11

    We present integral equations for the scattering amplitudes of three scalar particles, using the Faddeev channel decomposition, which can be readily extended to any finite number of particles of any helicity. The solution of these equations, which have been demonstrated to be calculable, provide a non-perturbative way of obtaining relativistic scattering amplitudes for any finite number of particles that are Lorentz invariant, unitary, cluster decomposable and reduce unambiguously in the non-relativistic limit to the non-relativistic Faddeev equations. The aim of this program is to develop equations which explicitly depend upon physically observable input variables, and do not require ''renormalization'' or ''dressing'' of these parameters to connect them to the boundary states.

  6. Theory and applications of ordered fuzzy numbers a tribute to professor Witold Kosiński

    CERN Document Server

    Czerniak, Jacek; Mikołajewski, Dariusz; Apiecionek, Łukasz; Ślȩzak, Dominik

    2017-01-01

    This book is open access under a CC BY 4.0 license. This open access book offers comprehensive coverage on Ordered Fuzzy Numbers, providing readers with both the basic information and the necessary expertise to use them in a variety of real-world applications. The respective chapters, written by leading researchers, discuss the main techniques and applications, together with the advantages and shortcomings of these tools in comparison to other fuzzy number representation models. Primarily intended for engineers and researchers in the field of fuzzy arithmetic, the book also offers a valuable source of basic information on fuzzy models and an easy-to-understand reference guide to their applications for advanced undergraduate students, operations researchers, modelers and managers alike.

  7. Quasi-Decidability of a Fragment of the First-Order Theory of Real Numbers

    Czech Academy of Sciences Publication Activity Database

    Franek, Peter; Ratschan, Stefan; Zgliczynski, P.

    2016-01-01

    Roč. 57, č. 2 (2016), s. 157-185 ISSN 0168-7433 R&D Projects: GA ČR GCP202/12/J060; GA MŠk OC10048; GA ČR GA15-14484S Institutional support: RVO:67985807 Keywords : decidability * decision procedure * real numbers Subject RIV: IN - Informatics, Computer Science Impact factor: 1.636, year: 2016

  8. Metaheuristic Algorithms Applied to Bioenergy Supply Chain Problems: Theory, Review, Challenges, and Future

    Directory of Open Access Journals (Sweden)

    Krystel K. Castillo-Villar

    2014-11-01

    Full Text Available Bioenergy is a new source of energy that accounts for a substantial portion of the renewable energy production in many countries. The production of bioenergy is expected to increase due to its unique advantages, such as no harmful emissions and abundance. Supply-related problems are the main obstacles precluding the increase of use of biomass (which is bulky and has low energy density to produce bioenergy. To overcome this challenge, large-scale optimization models are needed to be solved to enable decision makers to plan, design, and manage bioenergy supply chains. Therefore, the use of effective optimization approaches is of great importance. The traditional mathematical methods (such as linear, integer, and mixed-integer programming frequently fail to find optimal solutions for non-convex and/or large-scale models whereas metaheuristics are efficient approaches for finding near-optimal solutions that use less computational resources. This paper presents a comprehensive review by studying and analyzing the application of metaheuristics to solve bioenergy supply chain models as well as the exclusive challenges of the mathematical problems applied in the bioenergy supply chain field. The reviewed metaheuristics include: (1 population approaches, such as ant colony optimization (ACO, the genetic algorithm (GA, particle swarm optimization (PSO, and bee colony algorithm (BCA; and (2 trajectory approaches, such as the tabu search (TS and simulated annealing (SA. Based on the outcomes of this literature review, the integrated design and planning of bioenergy supply chains problem has been solved primarily by implementing the GA. The production process optimization was addressed primarily by using both the GA and PSO. The supply chain network design problem was treated by utilizing the GA and ACO. The truck and task scheduling problem was solved using the SA and the TS, where the trajectory-based methods proved to outperform the population

  9. Quantum numbers of anti-grand-unified-theory Higgs fields from the quark-lepton spectrum

    International Nuclear Information System (INIS)

    Froggatt, C.D.; Nielsen, H.B.; Smith, D.J.

    2002-01-01

    A series of Higgs field quantum numbers in the anti-grand-unification model, based on the gauge group SMG 3 xU(1) f , is tested against the spectrum of quark and lepton masses and mixing angles. A more precise formulation of the statement that the couplings are assumed of order unity is given. It is found that the corrections coming from this more precise assumption do not contain factors of the order of the number of colors, N c =3, as one could have feared. We also include a combinatorial correction factor, taking account of the distinct internal orderings within the chain Feynman diagrams in our statistical estimates. Strictly speaking our model predicts that the uncertainty in its predictions and thus the accuracy of our fits should be ±60%. Many of the best fitting quantum numbers give a higher accuracy fit to the masses and mixing angles, although within the expected fluctuations in a χ 2 . This means that our fit is as good as it can possibly be

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

    OpenAIRE

    Chen, Qingcheng; Zhu, Shiqiang; Zhang, Xuequn

    2015-01-01

    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...

  11. The logic of logistics theory, algorithms, and applications for logistics and supply chain management

    CERN Document Server

    Simchi-Levi, David; Bramel, Julien

    2005-01-01

    Fierce competition in today's global market provides a powerful motivation for developing ever more sophisticated logistics systems. This book, written for the logistics manager and researcher, presents a survey of the modern theory and application of logistics. The goal of the book is to present the state of the art in the science of logistics management. As a result, the authors have written a timely and authoritative survey of this field that many practitioners and researchers will find makes an invaluable companion to their work.

  12. Robust algorithms and system theory applied to the reconstruction of primary and secondary vertices

    International Nuclear Information System (INIS)

    Fruehwirth, R.; Liko, D.; Mitaroff, W.; Regler, M.

    1990-01-01

    Filter techniques from system theory have recently been applied to the estimation of track and vertex parameters. In this paper, vertex fitting by the Kalman filter method is discussed. These techniques have been applied to the identification of short-lived decay vertices in the case of high multiplicities as expected at LEP (Monte Carlo data in the DELPHI detector). Then in this context the need of further rebustification of the Kalman filter method is discussed. Finally results of an application with real data at a heavy ion experiment (NA36) will be presented. Here the vertex fit is used to select the interaction point among possible targets

  13. Fractal geometry and number theory complex dimensions of fractal strings and zeros of zeta functions

    CERN Document Server

    Lapidus, Michael L

    1999-01-01

    A fractal drum is a bounded open subset of R. m with a fractal boundary. A difficult problem is to describe the relationship between the shape (geo­ metry) of the drum and its sound (its spectrum). In this book, we restrict ourselves to the one-dimensional case of fractal strings, and their higher dimensional analogues, fractal sprays. We develop a theory of complex di­ mensions of a fractal string, and we study how these complex dimensions relate the geometry with the spectrum of the fractal string. We refer the reader to [Berrl-2, Lapl-4, LapPol-3, LapMal-2, HeLapl-2] and the ref­ erences therein for further physical and mathematical motivations of this work. (Also see, in particular, Sections 7. 1, 10. 3 and 10. 4, along with Ap­ pendix B. ) In Chapter 1, we introduce the basic object of our research, fractal strings (see [Lapl-3, LapPol-3, LapMal-2, HeLapl-2]). A 'standard fractal string' is a bounded open subset of the real line. Such a set is a disjoint union of open intervals, the lengths of which ...

  14. 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

  15. Basic Knowledge for Market Principle: Approaches to the Price Coordination Mechanism by Using Optimization Theory and Algorithm

    Science.gov (United States)

    Aiyoshi, Eitaro; Masuda, Kazuaki

    On the basis of market fundamentalism, new types of social systems with the market mechanism such as electricity trading markets and carbon dioxide (CO2) emission trading markets have been developed. However, there are few textbooks in science and technology which present the explanation that Lagrange multipliers can be interpreted as market prices. This tutorial paper explains that (1) the steepest descent method for dual problems in optimization, and (2) Gauss-Seidel method for solving the stationary conditions of Lagrange problems with market principles, can formulate the mechanism of market pricing, which works even in the information-oriented modern society. The authors expect readers to acquire basic knowledge on optimization theory and algorithms related to economics and to utilize them for designing the mechanism of more complicated markets.

  16. The unified neutral theory of biodiversity: do the numbers add up?

    Science.gov (United States)

    Ricklefs, Robert E

    2006-06-01

    Hubbell's unified neutral theory is a zero-sum ecological drift model in which population sizes change at random in a process resembling genetic drift, eventually leading to extinction. Diversity is maintained within the community by speciation. Hubbell's model makes predictions about the distribution of species abundances within communities and the turnover of species from place to place (beta diversity). However, ecological drift cannot be tested adequately against these predictions without independent estimates of speciation rates, population sizes, and dispersal distances. A more practical prediction from ecological drift is that time to extinction of a population of size N is approximately 2N generations. I test this prediction here using data for passerine birds (Passeriformes). Waiting times to speciation and extinction were estimated from genetic divergence between sister populations and a lineage-through-time plot for endemic South American suboscine passerines. Population sizes were estimated from local counts of birds in two large forest plots extrapolated to the area of wet tropical forest in South America and from atlas data on European passerines. Waiting times to extinction (ca. 2 Ma) are much less than twice the product of average population size (4.0 and 14.4 x 10(6) individuals in South America and Europe) and generation length (five and three years) for songbirds, that is, 40 and 86 Ma, respectively. Thus, drift is too slow to account for turnover in regional avifaunas. Presumably, other processes, involving external drivers, such as climate and physiographic change, and internal drivers, such as evolutionary change in antagonistic interactions, predominate. Hubbell's model is historical and geographic, and his perspective importantly links local and regional process and pattern. Ecological reality can be added to the mix while retaining Hubbell's concept of continuity of communities in space and time.

  17. Vertex operators, semiclassical limit for soliton S-matrices and the number of bound states in Affine Toda Field Theories

    International Nuclear Information System (INIS)

    Kneipp, Marco A.C.

    1999-10-01

    Soliton time delays and the semiclassical limit for soliton S-matrices are calculated for non-simply laced Affine Toda Field Theories. The phase shift is written as a sum over bilinears on the soliton conserved charges. The results apply to any two solitons of any Affine Toda Field Theory. As a by-product, a general expression for the number of bound states and the values of the coupling in which the S-matrix can be diagonal are obtained. In order to arrive at these results, a vertex operator is constructed, in the principal gradation, for non-simply laced affine Lie algebras, extending the previous constructions for simply laced and twisted affine Lie algebras. (author)

  18. Analytic number theory in honor of Helmut Maier’s 60th birthday

    CERN Document Server

    Rassias, Michael

    2015-01-01

    This volume contains a collection of research and survey papers written by some of the most eminent mathematicians in the international community and is dedicated to Helmut Maier, whose own research has been groundbreaking and deeply influential to the field. Specific emphasis is given to topics regarding exponential and  trigonometric sums and their behavior in short intervals, anatomy of integers and cyclotomic polynomials, small gaps in sequences of sifted prime numbers, oscillation theorems for primes in arithmetic progressions, inequalities related to the distribution of primes in short intervals, the Möbius function, Euler’s totient function, the Riemann zeta function and the Riemann Hypothesis. Graduate students, research mathematicians, as well as computer scientists and engineers who are interested in pure and interdisciplinary research, will find this volume a useful resource. Contributors to this volume: Bill Allombert, Levent Alpoge, Nadine Amersi, Yuri Bilu, Régis de la Bretèche, Christian ...

  19. Algorithms and computer codes for atomic and molecular quantum scattering theory. Volume I

    Energy Technology Data Exchange (ETDEWEB)

    Thomas, L. (ed.)

    1979-01-01

    The goals of this workshop are to identify which of the existing computer codes for solving the coupled equations of quantum molecular scattering theory perform most efficiently on a variety of test problems, and to make tested versions of those codes available to the chemistry community through the NRCC software library. To this end, many of the most active developers and users of these codes have been invited to discuss the methods and to solve a set of test problems using the LBL computers. The first volume of this workshop report is a collection of the manuscripts of the talks that were presented at the first meeting held at the Argonne National Laboratory, Argonne, Illinois June 25-27, 1979. It is hoped that this will serve as an up-to-date reference to the most popular methods with their latest refinements and implementations.

  20. Algorithms and computer codes for atomic and molecular quantum scattering theory. Volume I

    International Nuclear Information System (INIS)

    Thomas, L.

    1979-01-01

    The goals of this workshop are to identify which of the existing computer codes for solving the coupled equations of quantum molecular scattering theory perform most efficiently on a variety of test problems, and to make tested versions of those codes available to the chemistry community through the NRCC software library. To this end, many of the most active developers and users of these codes have been invited to discuss the methods and to solve a set of test problems using the LBL computers. The first volume of this workshop report is a collection of the manuscripts of the talks that were presented at the first meeting held at the Argonne National Laboratory, Argonne, Illinois June 25-27, 1979. It is hoped that this will serve as an up-to-date reference to the most popular methods with their latest refinements and implementations

  1. 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.

  2. 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.

  3. A dynamo theory prediction for solar cycle 22: Sunspot number, radio flux, exospheric temperature, and total density at 400 km

    Science.gov (United States)

    Schatten, K. H.; Hedin, A. E.

    1986-01-01

    Using the dynamo theory method to predict solar activity, a value for the smoothed sunspot number of 109 + or - 20 is obtained for solar cycle 22. The predicted cycle is expected to peak near December, 1990 + or - 1 year. Concommitantly, F(10.7) radio flux is expected to reach a smoothed value of 158 + or - 18 flux units. Global mean exospheric temperature is expected to reach 1060 + or - 50 K and global total average total thermospheric density at 400 km is expected to reach 4.3 x 10 to the -15th gm/cu cm + or - 25 percent.

  4. A dynamo theory prediction for solar cycle 22 - Sunspot number, radio flux, exospheric temperature, and total density at 400 km

    Science.gov (United States)

    Schatten, K. H.; Hedin, A. E.

    1984-01-01

    Using the 'dynamo theory' method to predict solar activity, a value for the smoothed sunspot number of 109 + or - 20 is obtained for solar cycle 22. The predicted cycle is expected to peak near December, 1990 + or - 1 year. Concommitantly, F(10.7) radio flux is expected to reach a smoothed value of 158 + or - 18 flux units. Global mean exospheric temperature is expected to reach 1060 + or - 50 K and global total average total thermospheric density at 400 km is expected to reach 4.3 x 10 to the -15th gm/cu cm + or - 25 percent.

  5. Automated multi-camera surveillance algorithms and practice : theory and practice

    CERN Document Server

    Javed, Omar

    2008-01-01

    The deployment of surveillance systems has captured the interest of both the research and the industrial worlds in recent years. The aim of this effort is to increase security and safety in several application domains such as national security, home and bank safety, traffic monitoring and navigation, tourism, and military applications. The video surveillance systems currently in use share one feature: A human operator must monitor them at all times, thus limiting the number of cameras and the area under surveillance and increasing cost. A more advantageous system would have continuous active w

  6. Nonlinear theory of nonstationary low Mach number channel flows of freely cooling nearly elastic granular gases.

    Science.gov (United States)

    Meerson, Baruch; Fouxon, Itzhak; Vilenkin, Arkady

    2008-02-01

    We employ hydrodynamic equations to investigate nonstationary channel flows of freely cooling dilute gases of hard and smooth spheres with nearly elastic particle collisions. This work focuses on the regime where the sound travel time through the channel is much shorter than the characteristic cooling time of the gas. As a result, the gas pressure rapidly becomes almost homogeneous, while the typical Mach number of the flow drops well below unity. Eliminating the acoustic modes and employing Lagrangian coordinates, we reduce the hydrodynamic equations to a single nonlinear and nonlocal equation of a reaction-diffusion type. This equation describes a broad class of channel flows and, in particular, can follow the development of the clustering instability from a weakly perturbed homogeneous cooling state to strongly nonlinear states. If the heat diffusion is neglected, the reduced equation becomes exactly soluble, and the solution develops a finite-time density blowup. The blowup has the same local features at singularity as those exhibited by the recently found family of exact solutions of the full set of ideal hydrodynamic equations [I. Fouxon, Phys. Rev. E 75, 050301(R) (2007); I. Fouxon,Phys. Fluids 19, 093303 (2007)]. The heat diffusion, however, always becomes important near the attempted singularity. It arrests the density blowup and brings about previously unknown inhomogeneous cooling states (ICSs) of the gas, where the pressure continues to decay with time, while the density profile becomes time-independent. The ICSs represent exact solutions of the full set of granular hydrodynamic equations. Both the density profile of an ICS and the characteristic relaxation time toward it are determined by a single dimensionless parameter L that describes the relative role of the inelastic energy loss and heat diffusion. At L>1 the intermediate cooling dynamics proceeds as a competition between "holes": low-density regions of the gas. This competition resembles Ostwald

  7. On the Transfer of a Number of Concepts of Statistical Radiophysics to the Theory of One-dimensional Point Mappings

    Directory of Open Access Journals (Sweden)

    Agalar M. Agalarov

    2018-01-01

    Full Text Available In the article, the possibility of using a bispectrum under the investigation of regular and chaotic behaviour of one-dimensional point mappings is discussed. The effectiveness of the transfer of this concept to nonlinear dynamics was demonstrated by an example of the Feigenbaum mapping. Also in the work, the application of the Kullback-Leibler entropy in the theory of point mappings is considered. It has been shown that this information-like value is able to describe the behaviour of statistical ensembles of one-dimensional mappings. In the framework of this theory some general properties of its behaviour were found out. Constructivity of the Kullback-Leibler entropy in the theory of point mappings was shown by means of its direct calculation for the ”saw tooth” mapping with linear initial probability density. Moreover, for this mapping the denumerable set of initial probability densities hitting into its stationary probability density after a finite number of steps was pointed out. 

  8. An analytical multigroup benchmark for (n, γ) and (n, n', γ) verification of diffusion theory algorithms

    International Nuclear Information System (INIS)

    Ganapol, B.D.

    2011-01-01

    Highlights: → Coupled neutron and gamma transport is considered in the multigroup diffusion approximation. → The model accommodates fission, up- and down-scattering and common neutron-gamma interactions. → The exact solution to the diffusion equation in a heterogeneous media of any number of regions is found. → The solution is shown to parallel the one-group case in a homogeneous medium. → The discussion concludes with a heterogeneous, 2 fuel-plate 93.2% enriched reactor fuel benchmark demonstration. - Abstract: The angular flux for the 'rod model' describing coupled neutron/gamma (n, γ) diffusion has a particularly straightforward analytical representation when viewed from the perspective of a one-group homogeneous medium. Cast in the form of matrix functions of a diagonalizable matrix, the solution to the multigroup equations in heterogeneous media is greatly simplified. We shall show exactly how the one-group homogeneous medium solution leads to the multigroup solution.

  9. Explaining the large numbers by a hierarchy of ''universes'': a unified theory of strong and gravitational interactions

    International Nuclear Information System (INIS)

    Caldirola, P.; Recami, E.

    1978-01-01

    By assuming covariance of physical laws under (discrete) dilatations, strong and gravitational interactions have been described in a unified way. In terms of the (additional, discrete) ''dilatational'' degree of freedom, our cosmos as well as hadrons can be considered as different states of the same system, or rather as similar systems. Moreover, a discrete hierarchy can be defined of ''universes'' which are governed by force fields with strengths inversely proportional to the ''universe'' radii. Inside each ''universe'' an equivalence principle holds, so that its characteristic field can be geometrized there. It is thus easy to derive a whole ''numerology'', i.e. relations among numbers analogous to the so-called Weyl-Eddington-Dirac ''large numbers''. For instance, the ''Planck mass'' happens to be nothing but the (average) magnitude of the strong charge of the hadron quarks. However, our ''numerology'' connects the (gravitational) macrocosmos with the (strong) microcosmos, rather than with the electromagnetic ones (as, e.g., in Dirac's version). Einstein-type scaled equations (with ''cosmological'' term) are suggested for the hadron interior, which - incidentally - yield a (classical) quark confinement in a very natural way and are compatible with the ''asymptotic freedom''. At last, within a ''bi-scale'' theory, further equations are proposed that provide a priori a classical field theory of strong interactions (between different hadrons). The relevant sections are 5.2, 7 and 8. (author)

  10. 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.

  11. A multithreaded and GPU-optimized compact finite difference algorithm for turbulent mixing at high Schmidt number using petascale computing

    Science.gov (United States)

    Clay, M. P.; Yeung, P. K.; Buaria, D.; Gotoh, T.

    2017-11-01

    Turbulent mixing at high Schmidt number is a multiscale problem which places demanding requirements on direct numerical simulations to resolve fluctuations down the to Batchelor scale. We use a dual-grid, dual-scheme and dual-communicator approach where velocity and scalar fields are computed by separate groups of parallel processes, the latter using a combined compact finite difference (CCD) scheme on finer grid with a static 3-D domain decomposition free of the communication overhead of memory transposes. A high degree of scalability is achieved for a 81923 scalar field at Schmidt number 512 in turbulence with a modest inertial range, by overlapping communication with computation whenever possible. On the Cray XE6 partition of Blue Waters, use of a dedicated thread for communication combined with OpenMP locks and nested parallelism reduces CCD timings by 34% compared to an MPI baseline. The code has been further optimized for the 27-petaflops Cray XK7 machine Titan using GPUs as accelerators with the latest OpenMP 4.5 directives, giving 2.7X speedup compared to CPU-only execution at the largest problem size. Supported by NSF Grant ACI-1036170, the NCSA Blue Waters Project with subaward via UIUC, and a DOE INCITE allocation at ORNL.

  12. Number Theory and Combinatorics

    Indian Academy of Sciences (India)

    2012-02-24

    Feb 24, 2012 ... Primarily directed at students and teachers at the un- dergraduate .... ate good mathematics (irrespective of whether I could originally contribute to it or not). ..... The cyclotomic polynomials are useful in many ways and have.

  13. Elementary number theory

    CERN Document Server

    Kraft, James S

    2014-01-01

    Introduction. Divisibility. Linear Diophantine Equations. Unique Factorization. Applications of Unique Factorization. Congruences. Fermat, Euler, Wilson. Cryptographic Applications. Order and Primitive Roots. More Cryptographic Applications. Quadratic Reciprocity. Primality and Factorization. Sums of Squares. Arithmetic Functions. Continued Fractions. Recent Developments. Appendices. Index.

  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. Applying Probability Theory for the Quality Assessment of a Wildfire Spread Prediction Framework Based on Genetic Algorithms

    Directory of Open Access Journals (Sweden)

    Andrés Cencerrado

    2013-01-01

    Full Text Available This work presents a framework for assessing how the existing constraints at the time of attending an ongoing forest fire affect simulation results, both in terms of quality (accuracy obtained and the time needed to make a decision. In the wildfire spread simulation and prediction area, it is essential to properly exploit the computational power offered by new computing advances. For this purpose, we rely on a two-stage prediction process to enhance the quality of traditional predictions, taking advantage of parallel computing. This strategy is based on an adjustment stage which is carried out by a well-known evolutionary technique: Genetic Algorithms. The core of this framework is evaluated according to the probability theory principles. Thus, a strong statistical study is presented and oriented towards the characterization of such an adjustment technique in order to help the operation managers deal with the two aspects previously mentioned: time and quality. The experimental work in this paper is based on a region in Spain which is one of the most prone to forest fires: El Cap de Creus.

  16. Coupling graph perturbation theory with scalable parallel algorithms for large-scale enumeration of maximal cliques in biological graphs

    International Nuclear Information System (INIS)

    Samatova, N F; Schmidt, M C; Hendrix, W; Breimyer, P; Thomas, K; Park, B-H

    2008-01-01

    Data-driven construction of predictive models for biological systems faces challenges from data intensity, uncertainty, and computational complexity. Data-driven model inference is often considered a combinatorial graph problem where an enumeration of all feasible models is sought. The data-intensive and the NP-hard nature of such problems, however, challenges existing methods to meet the required scale of data size and uncertainty, even on modern supercomputers. Maximal clique enumeration (MCE) in a graph derived from such biological data is often a rate-limiting step in detecting protein complexes in protein interaction data, finding clusters of co-expressed genes in microarray data, or identifying clusters of orthologous genes in protein sequence data. We report two key advances that address this challenge. We designed and implemented the first (to the best of our knowledge) parallel MCE algorithm that scales linearly on thousands of processors running MCE on real-world biological networks with thousands and hundreds of thousands of vertices. In addition, we proposed and developed the Graph Perturbation Theory (GPT) that establishes a foundation for efficiently solving the MCE problem in perturbed graphs, which model the uncertainty in the data. GPT formulates necessary and sufficient conditions for detecting the differences between the sets of maximal cliques in the original and perturbed graphs and reduces the enumeration time by more than 80% compared to complete recomputation

  17. Development of Theory of Mind in Mentally Retarded Students and its Relation with the Number of the Siblings

    Directory of Open Access Journals (Sweden)

    Mehdi Abdollah-Zadeh Rafi

    2011-01-01

    Conclusion: Theory of mind development of mental retarded students varies based on that type of task being used to assess. In total, the claim of Theory-Theory approach, that says theory of mind development is on the basis of necessary processes, could be accepted. Also those theories which are based on cultural-social approaches calming that experience with other people causes development of mind understanding need to be more examined.

  18. CTC-ask: a new algorithm for conversion of CT numbers to tissue parameters for Monte Carlo dose calculations applying DICOM RS knowledge

    International Nuclear Information System (INIS)

    Ottosson, Rickard O; Behrens, Claus F

    2011-01-01

    One of the building blocks in Monte Carlo (MC) treatment planning is to convert patient CT data to MC compatible phantoms, consisting of density and media matrices. The resulting dose distribution is highly influenced by the accuracy of the conversion. Two major contributing factors are precise conversion of CT number to density and proper differentiation between air and lung. Existing tools do not address this issue specifically. Moreover, their density conversion may depend on the number of media used. Differentiation between air and lung is an important task in MC treatment planning and misassignment may lead to local dose errors on the order of 10%. A novel algorithm, CTC-ask, is presented in this study. It enables locally confined constraints for the media assignment and is independent of the number of media used for the conversion of CT number to density. MC compatible phantoms were generated for two clinical cases using a CT-conversion scheme implemented in both CTC-ask and the DICOM-RT toolbox. Full MC dose calculation was subsequently conducted and the resulting dose distributions were compared. The DICOM-RT toolbox inaccurately assigned lung in 9.9% and 12.2% of the voxels located outside of the lungs for the two cases studied, respectively. This was completely avoided by CTC-ask. CTC-ask is able to reduce anatomically irrational media assignment. The CTC-ask source code can be made available upon request to the authors. (note)

  19. 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

  20. Construction of a system using a deep learning algorithm to count cell numbers in nanoliter wells for viable single-cell experiments.

    Science.gov (United States)

    Kamatani, Takashi; Fukunaga, Koichi; Miyata, Kaede; Shirasaki, Yoshitaka; Tanaka, Junji; Baba, Rie; Matsusaka, Masako; Kamatani, Naoyuki; Moro, Kazuyo; Betsuyaku, Tomoko; Uemura, Sotaro

    2017-12-04

    For single-cell experiments, it is important to accurately count the number of viable cells in a nanoliter well. We used a deep learning-based convolutional neural network (CNN) on a large amount of digital data obtained as microscopic images. The training set consisted of 103 019 samples, each representing a microscopic grayscale image. After extensive training, the CNN was able to classify the samples into four categories, i.e., 0, 1, 2, and more than 2 cells per well, with an accuracy of 98.3% when compared to determination by two trained technicians. By analyzing the samples for which judgments were discordant, we found that the judgment by technicians was relatively correct although cell counting was often difficult by the images of discordant samples. Based on the results, the system was further enhanced by introducing a new algorithm in which the highest outputs from CNN were used, increasing the accuracy to higher than 99%. Our system was able to classify the data even from wells with a different shape. No other tested machine learning algorithm showed a performance higher than that of our system. The presented CNN system is expected to be useful for various single-cell experiments, and for high-throughput and high-content screening.

  1. Gyrokinetic theory of fast-wave transmission with arbitrary parallel wave number in a non-uniformly magnetized plasma

    International Nuclear Information System (INIS)

    Lashmore-Davies, C.N.; Dendy, R.O.

    1990-01-01

    The gyrokinetic theory of ion cyclotron resonance is extended to include propagation at arbitrary angles to a straight equilibrium magnetic field with a linear perpendicular gradient in strength. The case of the compressional Alfven wave propagating in a D( 3 He) plasma is analyzed in detail, for arbitrary concentrations of the two species. A self-consistent local dispersion relation is obtained using a single mode description; this approach enables three-dimensional effects to be included and permits efficient calculation of the transmission coefficient. The dependence of this quantity on the species density ratio, minority temperature, plasma density, magnetic field and equilibrium scale length is obtained. A self-consistent treatment of the variation of the field polarization across the resonant region is included. Families of transmission curves are given as a function of the normalized parallel wave number for parameters relevant to Joint European Torus. Perpendicular absorption by the minority ions is also discussed, and shown to depend on a single parameter, the ratio of the ion thermal velocity to the Alfven speed. (author)

  2. The self-preserving size distribution theory. I. Effects of the Knudsen number on aerosol agglomerate growth.

    Science.gov (United States)

    Dekkers, Petrus J; Friedlander, Sheldon K

    2002-04-15

    Gas-phase synthesis of fine solid particles leads to fractal-like structures whose transport and light scattering properties differ from those of their spherical counterparts. Self-preserving size distribution theory provides a useful methodology for analyzing the asymptotic behavior of such systems. Apparent inconsistencies in previous treatments of the self-preserving size distributions in the free molecule regime are resolved. Integro-differential equations for fractal-like particles in the continuum and near continuum regimes are derived and used to calculate the self-preserving and quasi-self-preserving size distributions for agglomerates formed by Brownian coagulation. The results for the limiting case (the continuum regime) were compared with the results of other authors. For these cases the finite difference method was in good in agreement with previous calculations in the continuum regime. A new analysis of aerosol agglomeration for the entire Knudsen number range was developed and compared with a monodisperse model; Higher agglomeration rates were found for lower fractal dimensions, as expected from previous studies. Effects of fractal dimension, pressure, volume loading and temperature on agglomerate growth were investigated. The agglomeration rate can be reduced by decreasing volumetric loading or by increasing the pressure. In laminar flow, an increase in pressure can be used to control particle growth and polydispersity. For D(f)=2, an increase in pressure from 1 to 4 bar reduces the collision radius by about 30%. Varying the temperature has a much smaller effect on agglomerate coagulation.

  3. 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.

  4. 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.)

  5. 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

  6. Application of supersonic linear theory and hypersonic impact methods to three nonslender hypersonic airplane concepts at Mach numbers from 1.10 to 2.86

    Science.gov (United States)

    Pittman, J. L.

    1979-01-01

    Aerodynamic predictions from supersonic linear theory and hypersonic impact theory were compared with experimental data for three hypersonic research airplane concepts over a Mach number range from 1.10 to 2.86. The linear theory gave good lift prediction and fair to good pitching-moment prediction over the Mach number (M) range. The tangent-cone theory predictions were good for lift and fair to good for pitching moment for M more than or equal to 2.0. The combined tangent-cone theory predictions were good for lift and fair to good for pitching moment for M more than or equal to 2.0. The combined tangent-cone/tangent-wedge method gave the least accurate prediction of lift and pitching moment. The zero-lift drag was overestimated, especially for M less than 2.0. The linear theory drag prediction was generally poor, with areas of good agreement only for M less than or equal to 1.2. For M more than or equal to 2.), the tangent-cone method predicted the zero-lift drag most accurately.

  7. Theory and algorithms for solving large-scale numerical problems. Application to the management of electricity production

    International Nuclear Information System (INIS)

    Chiche, A.

    2012-01-01

    This manuscript deals with large-scale optimization problems, and more specifically with solving the electricity unit commitment problem arising at EDF. First, we focused on the augmented Lagrangian algorithm. The behavior of that algorithm on an infeasible convex quadratic optimization problem is analyzed. It is shown that the algorithm finds a point that satisfies the shifted constraints with the smallest possible shift in the sense of the Euclidean norm and that it minimizes the objective on the corresponding shifted constrained set. The convergence to such a point is realized at a global linear rate, which depends explicitly on the augmentation parameter. This suggests us a rule for determining the augmentation parameter to control the speed of convergence of the shifted constraint norm to zero. This rule has the advantage of generating bounded augmentation parameters even when the problem is infeasible. As a by-product, the algorithm computes the smallest translation in the Euclidean norm that makes the constraints feasible. Furthermore, this work provides solution methods for stochastic optimization industrial problems decomposed on a scenario tree, based on the progressive hedging algorithm introduced by [Rockafellar et Wets, 1991]. We also focus on the convergence of that algorithm. On the one hand, we offer a counter-example showing that the algorithm could diverge if its augmentation parameter is iteratively updated. On the other hand, we show how to recover the multipliers associated with the non-dualized constraints defined on the scenario tree from those associated with the corresponding constraints of the scenario subproblems. Their convergence is also analyzed for convex problems. The practical interest of theses solutions techniques is corroborated by numerical experiments performed on the electric production management problem. We apply the progressive hedging algorithm to a realistic industrial problem. More precisely, we solve the French medium

  8. A study of the application of singular perturbation theory. [development of a real time algorithm for optimal three dimensional aircraft maneuvers

    Science.gov (United States)

    Mehra, R. K.; Washburn, R. B.; Sajan, S.; Carroll, J. V.

    1979-01-01

    A hierarchical real time algorithm for optimal three dimensional control of aircraft is described. Systematic methods are developed for real time computation of nonlinear feedback controls by means of singular perturbation theory. The results are applied to a six state, three control variable, point mass model of an F-4 aircraft. Nonlinear feedback laws are presented for computing the optimal control of throttle, bank angle, and angle of attack. Real Time capability is assessed on a TI 9900 microcomputer. The breakdown of the singular perturbation approximation near the terminal point is examined Continuation methods are examined to obtain exact optimal trajectories starting from the singular perturbation solutions.

  9. 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/

  10. Increasing the Number of Replications in Item Response Theory Simulations: Automation through SAS and Disk Operating System

    Science.gov (United States)

    Gagne, Phill; Furlow, Carolyn; Ross, Terris

    2009-01-01

    In item response theory (IRT) simulation research, it is often necessary to use one software package for data generation and a second software package to conduct the IRT analysis. Because this can substantially slow down the simulation process, it is sometimes offered as a justification for using very few replications. This article provides…

  11. Enhancement in Evaluating Small Group Work in Courses with Large Number of Students. Machine Theory at Industrial Engineering Degrees

    Science.gov (United States)

    Jordi Nebot, Lluïsa; Pàmies-Vilà, Rosa; Català Calderon, Pau; Puig-Ortiz, Joan

    2013-01-01

    This article examines new tutoring evaluation methods to be adopted in the course, Machine Theory, in the Escola Tècnica Superior d'Enginyeria Industrial de Barcelona (ETSEIB, Universitat Politècnica de Catalunya). These new methods have been developed in order to facilitate teaching staff work and include students in the evaluation process.…

  12. An Integrated Decision-Making Model for Transformer Condition Assessment Using Game Theory and Modified Evidence Combination Extended by D Numbers

    Directory of Open Access Journals (Sweden)

    Lingjie Sun

    2016-08-01

    Full Text Available The power transformer is one of the most critical and expensive components for the stable operation of the power system. Hence, how to obtain the health condition of transformer is of great importance for power utilities. Multi-attribute decision-making (MADM, due to its ability of solving multi-source information problems, has become a quite effective tool to evaluate the health condition of transformers. Currently, the analytic hierarchy process (AHP and Dempster–Shafer theory are two popular methods to solve MADM problems; however, these techniques rarely consider one-sidedness of the single weighting method and the exclusiveness hypothesis of the Dempster–Shafer theory. To overcome these limitations, this paper introduces a novel decision-making model, which integrates the merits of fuzzy set theory, game theory and modified evidence combination extended by D numbers, to evaluate the health condition of transformers. A four-level framework, which includes three factors and seventeen sub-factors, is put forward to facilitate the evaluation model. The model points out the following: First, the fuzzy set theory is employed to obtain the original basic probability assignments for all indices. Second, the subjective and objective weights of indices, which are calculated by fuzzy AHP and entropy weight, respectively, are integrated to generate the comprehensive weights based on game theory. Finally, based on the above two steps, the modified evidence combination extended by D numbers, which avoids the limitation of the exclusiveness hypothesis in the application of Dempster–Shafer theory, is proposed to obtain the final assessment results of transformers. Case studies are given to demonstrate the proposed modeling process. The results show the effectiveness and engineering practicability of the model in transformer condition assessment.

  13. On two-primary algebraic K-theory of quadratic number rings with focus on K_2

    NARCIS (Netherlands)

    Crainic, M.; Østvær, Paul Arne

    1999-01-01

    We give explicit formulas for the 2-rank of the algebraic K-groups of quadratic number rings. A 4-rank formula for K2 of quadratic number rings given in [1] provides further information about the actual group structure. The K2 claculations are based on 2- and 4-rank formulas for Picard groups of

  14. Transfinite Numbers

    Indian Academy of Sciences (India)

    Transfinite Numbers. What is Infinity? S M Srivastava. In a series of revolutionary articles written during the last quarter of the nineteenth century, the great Ger- man mathematician Georg Cantor removed the age-old mistrust of infinity and created an exceptionally beau- tiful and useful theory of transfinite numbers. This is.

  15. 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....

  16. Unified theory to evaluate the effect of concentration difference and Peclet number on electroosmotic mobility error of micro electroosmotic flow

    KAUST Repository

    Wang, Wentao; Lee, Yi Kuen

    2012-01-01

    Both theoretical analysis and nonlinear 2D numerical simulations are used to study the concentration difference and Peclet number effect on the measurement error of electroosmotic mobility in microchannels. We propose a compact analytical model

  17. A modification to linearized theory for prediction of pressure loadings on lifting surfaces at high supersonic Mach numbers and large angles of attack

    Science.gov (United States)

    Carlson, H. W.

    1979-01-01

    A new linearized-theory pressure-coefficient formulation was studied. The new formulation is intended to provide more accurate estimates of detailed pressure loadings for improved stability analysis and for analysis of critical structural design conditions. The approach is based on the use of oblique-shock and Prandtl-Meyer expansion relationships for accurate representation of the variation of pressures with surface slopes in two-dimensional flow and linearized-theory perturbation velocities for evaluation of local three-dimensional aerodynamic interference effects. The applicability and limitations of the modification to linearized theory are illustrated through comparisons with experimental pressure distributions for delta wings covering a Mach number range from 1.45 to 4.60 and angles of attack from 0 to 25 degrees.

  18. Microcanonical algorithm of carged roteting dilatonic black holes from the viewpoint of the Kaluza-Klein theory

    CERN Document Server

    Fujisaki, H

    2003-01-01

    Microcanonical ensemble paradigm is described in proper reference to the thermal aspect of the extremal state for a dilute gas of charged rotating black holes coupled to a dilaton field on the basis of the boosted Kerr solution of the Kaluza-Klein theory.

  19. Unified theory to evaluate the effect of concentration difference and Peclet number on electroosmotic mobility error of micro electroosmotic flow

    KAUST Repository

    Wang, Wentao

    2012-03-01

    Both theoretical analysis and nonlinear 2D numerical simulations are used to study the concentration difference and Peclet number effect on the measurement error of electroosmotic mobility in microchannels. We propose a compact analytical model for this error as a function of normalized concentration difference and Peclet number in micro electroosmotic flow. The analytical predictions of the errors are consistent with the numerical simulations. © 2012 IEEE.

  20. Theoretical Aspects of the Patterns Recognition Statistical Theory Used for Developing the Diagnosis Algorithms for Complicated Technical Systems

    Science.gov (United States)

    Obozov, A. A.; Serpik, I. N.; Mihalchenko, G. S.; Fedyaeva, G. A.

    2017-01-01

    In the article, the problem of application of the pattern recognition (a relatively young area of engineering cybernetics) for analysis of complicated technical systems is examined. It is shown that the application of a statistical approach for hard distinguishable situations could be the most effective. The different recognition algorithms are based on Bayes approach, which estimates posteriori probabilities of a certain event and an assumed error. Application of the statistical approach to pattern recognition is possible for solving the problem of technical diagnosis complicated systems and particularly big powered marine diesel engines.

  1. ASSOCIATION AMONG MATHEMATICAL CRITICAL THINKING SKILL, COMMUNICATION, AND CURIOSITY ATTITUDE AS THE IMPACT OF PROBLEM-BASED LEARNING AND COGNITIVE CONFLICT STRATEGY (PBLCCS) IN NUMBER THEORY COURSE

    OpenAIRE

    Zetriuslita Zetriuslita; Wahyudin Wahyudin; Jarnawi Afgani Dahlan

    2018-01-01

    This research aims to find out the association amongMathematical Critical Thinking (MCT) ability, Mathematical Communication, and Mathematical Curiosity Attitude (MCA) as the impact of applying Problem-Based Learning Cognitive Conflict Strategy(PBLCCS) in Number Theory course. The research method is correlative study. The instruments include a test for mathematical critical thinking skill and communication, and questionnaire to obtain the scores of mathematical curiosity attitude. The finding...

  2. Time-dependent occupation numbers in reduced-density-matrix-functional theory: Application to an interacting Landau-Zener model

    International Nuclear Information System (INIS)

    Requist, Ryan; Pankratov, Oleg

    2011-01-01

    We prove that if the two-body terms in the equation of motion for the one-body reduced density matrix are approximated by ground-state functionals, the eigenvalues of the one-body reduced density matrix (occupation numbers) remain constant in time. This deficiency is related to the inability of such an approximation to account for relative phases in the two-body reduced density matrix. We derive an exact differential equation giving the functional dependence of these phases in an interacting Landau-Zener model and study their behavior in short- and long-time regimes. The phases undergo resonances whenever the occupation numbers approach the boundaries of the interval [0,1]. In the long-time regime, the occupation numbers display correlation-induced oscillations and the memory dependence of the functionals assumes a simple form.

  3. Restricted active space spin-flip configuration interaction: theory and examples for multiple spin flips with odd numbers of electrons.

    Science.gov (United States)

    Zimmerman, Paul M; Bell, Franziska; Goldey, Matthew; Bell, Alexis T; Head-Gordon, Martin

    2012-10-28

    The restricted active space spin flip (RAS-SF) method is extended to allow ground and excited states of molecular radicals to be described at low cost (for small numbers of spin flips). RAS-SF allows for any number of spin flips and a flexible active space while maintaining pure spin eigenfunctions for all states by maintaining a spin complete set of determinants and using spin-restricted orbitals. The implementation supports both even and odd numbers of electrons, while use of resolution of the identity integrals and a shared memory parallel implementation allow for fast computation. Examples of multiple-bond dissociation, excited states in triradicals, spin conversions in organic multi-radicals, and mixed-valence metal coordination complexes demonstrate the broad usefulness of RAS-SF.

  4. 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.

  5. The application of cryogenics to high Reynolds number testing in wind tunnels. I - Evolution, theory, and advantages

    Science.gov (United States)

    Kilgore, R. A.; Dress, D. A.

    1984-01-01

    During the time which has passed since the construction of the first wind tunnel in 1870, wind tunnels have been developed to a high degree of sophistication. However, their development has consistently failed to keep pace with the demands placed on them. One of the more serious problems to be found with existing transonic wind tunnels is their inability to test subscale aircraft models at Reynolds numbers sufficiently near full-scale values to ensure the validity of using the wind tunnel data to predict flight characteristics. The Reynolds number capability of a wind tunnel may be increased by a number of different approaches. However, the best solution in terms of model, balance, and model support loads, as well as in terms of capital and operating cost appears to be related to the reduction of the temperature of the test gas to cryogenic temperatures. The present paper has the objective to review the evolution of the cryogenic wind tunnel concept and to describe its more important advantages.

  6. A source-initiated on-demand routing algorithm based on the Thorup-Zwick theory for mobile wireless sensor networks.

    Science.gov (United States)

    Mao, Yuxin; Zhu, Ping

    2013-01-01

    The unreliability and dynamics of mobile wireless sensor networks make it hard to perform end-to-end communications. This paper presents a novel source-initiated on-demand routing mechanism for efficient data transmission in mobile wireless sensor networks. It explores the Thorup-Zwick theory to achieve source-initiated on-demand routing with time efficiency. It is able to find out shortest routing path between source and target in a network and transfer data in linear time. The algorithm is easy to be implemented and performed in resource-constrained mobile wireless sensor networks. We also evaluate the approach by analyzing its cost in detail. It can be seen that the approach is efficient to support data transmission in mobile wireless sensor networks.

  7. 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.

  8. Prediction of crack growth direction by Strain Energy Sih's Theory on specimens SEN under tension-compression biaxial loading employing Genetic Algorithms

    Energy Technology Data Exchange (ETDEWEB)

    Rodriguez-MartInez R; Lugo-Gonzalez E; Urriolagoitia-Calderon G; Urriolagoitia-Sosa G; Hernandez-Gomez L H; Romero-Angeles B; Torres-San Miguel Ch, E-mail: rrodriguezm@ipn.mx, E-mail: urrio332@hotmail.com, E-mail: guiurri@hotmail.com, E-mail: luishector56@hotmail.com, E-mail: romerobeatriz98@hotmail.com, E-mail: napor@hotmail.com [INSTITUTO POLITECNICO NACIONAL Seccion de Estudios de Posgrado e Investigacion (SEPI), Escuela Superior de Ingenieria Mecanica y Electrica (ESIME), Edificio 5. 2do Piso, Unidad Profesional Adolfo Lopez Mateos ' Zacatenco' Col. Lindavista, C.P. 07738, Mexico, D.F. (Mexico)

    2011-07-19

    Crack growth direction has been studied in many ways. Particularly Sih's strain energy theory predicts that a fracture under a three-dimensional state of stress spreads in direction of the minimum strain energy density. In this work a study for angle of fracture growth was made, considering a biaxial stress state at the crack tip on SEN specimens. The stress state applied on a tension-compression SEN specimen is biaxial one on crack tip, as it can observed in figure 1. A solution method proposed to obtain a mathematical model considering genetic algorithms, which have demonstrated great capacity for the solution of many engineering problems. From the model given by Sih one can deduce the density of strain energy stored for unit of volume at the crack tip as dW = [1/2E({sigma}{sup 2}{sub x} + {sigma}{sup 2}{sub y}) - {nu}/E({sigma}{sub x}{sigma}{sub y})]dV (1). From equation (1) a mathematical deduction to solve in terms of {theta} of this case was developed employing Genetic Algorithms, where {theta} is a crack propagation direction in plane x-y. Steel and aluminium mechanical properties to modelled specimens were employed, because they are two of materials but used in engineering design. Obtained results show stable zones of fracture propagation but only in a range of applied loading.

  9. Estimation of Bridge Height over Water from Polarimetric SAR Image Data Using Mapping and Projection Algorithm and De-Orientation Theory

    Science.gov (United States)

    Wang, Haipeng; Xu, Feng; Jin, Ya-Qiu; Ouchi, Kazuo

    An inversion method of bridge height over water by polarimetric synthetic aperture radar (SAR) is developed. A geometric ray description to illustrate scattering mechanism of a bridge over water surface is identified by polarimetric image analysis. Using the mapping and projecting algorithm, a polarimetric SAR image of a bridge model is first simulated and shows that scattering from a bridge over water can be identified by three strip lines corresponding to single-, double-, and triple-order scattering, respectively. A set of polarimetric parameters based on the de-orientation theory is applied to analysis of three types scattering, and the thinning-clustering algorithm and Hough transform are then employed to locate the image positions of these strip lines. These lines are used to invert the bridge height. Fully polarimetric image data of airborne Pi-SAR at X-band are applied to inversion of the height and width of the Naruto Bridge in Japan. Based on the same principle, this approach is also applicable to spaceborne ALOSPALSAR single-polarization data of the Eastern Ocean Bridge in China. The results show good feasibility to realize the bridge height inversion.

  10. Prediction of crack growth direction by Strain Energy Sih's Theory on specimens SEN under tension-compression biaxial loading employing Genetic Algorithms

    International Nuclear Information System (INIS)

    Rodriguez-MartInez R; Lugo-Gonzalez E; Urriolagoitia-Calderon G; Urriolagoitia-Sosa G; Hernandez-Gomez L H; Romero-Angeles B; Torres-San Miguel Ch

    2011-01-01

    Crack growth direction has been studied in many ways. Particularly Sih's strain energy theory predicts that a fracture under a three-dimensional state of stress spreads in direction of the minimum strain energy density. In this work a study for angle of fracture growth was made, considering a biaxial stress state at the crack tip on SEN specimens. The stress state applied on a tension-compression SEN specimen is biaxial one on crack tip, as it can observed in figure 1. A solution method proposed to obtain a mathematical model considering genetic algorithms, which have demonstrated great capacity for the solution of many engineering problems. From the model given by Sih one can deduce the density of strain energy stored for unit of volume at the crack tip as dW = [1/2E(σ 2 x + σ 2 y ) - ν/E(σ x σy)]dV (1). From equation (1) a mathematical deduction to solve in terms of θ of this case was developed employing Genetic Algorithms, where θ is a crack propagation direction in plane x-y. Steel and aluminium mechanical properties to modelled specimens were employed, because they are two of materials but used in engineering design. Obtained results show stable zones of fracture propagation but only in a range of applied loading.

  11. Drug repositioning for non-small cell lung cancer by using machine learning algorithms and topological graph theory.

    Science.gov (United States)

    Huang, Chien-Hung; Chang, Peter Mu-Hsin; Hsu, Chia-Wei; Huang, Chi-Ying F; Ng, Ka-Lok

    2016-01-11

    Non-small cell lung cancer (NSCLC) is one of the leading causes of death globally, and research into NSCLC has been accumulating steadily over several years. Drug repositioning is the current trend in the pharmaceutical industry for identifying potential new uses for existing drugs and accelerating the development process of drugs, as well as reducing side effects. This work integrates two approaches--machine learning algorithms and topological parameter-based classification--to develop a novel pipeline of drug repositioning to analyze four lung cancer microarray datasets, enriched biological processes, potential therapeutic drugs and targeted genes for NSCLC treatments. A total of 7 (8) and 11 (12) promising drugs (targeted genes) were discovered for treating early- and late-stage NSCLC, respectively. The effectiveness of these drugs is supported by the literature, experimentally determined in-vitro IC50 and clinical trials. This work provides better drug prediction accuracy than competitive research according to IC50 measurements. With the novel pipeline of drug repositioning, the discovery of enriched pathways and potential drugs related to NSCLC can provide insight into the key regulators of tumorigenesis and the treatment of NSCLC. Based on the verified effectiveness of the targeted drugs predicted by this pipeline, we suggest that our drug-finding pipeline is effective for repositioning drugs.

  12. 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...

  13. Correlation between catalytic activity and bonding and coordination number of atoms and molecules on transition metal surfaces: theory and experimental evidence

    International Nuclear Information System (INIS)

    Falicov, L.M.; Somorjai, G.A.

    1985-01-01

    Correlation between catalytic activity and low-energy local electronic fluctuation in transition metals is proposed. A theory and calculations are presented which indicate that maximum electronic fluctuants take place at high-coordination metal sites. Either (i) atomically rough surfaces that expose to the reactant molecules atoms with large numbers of nonmagnetic or weakly magnetic neighbors in the first or second layer at the surface or (ii) stepped and kinked surfaces are the most active in carrying out structure-sensitive catalytic reactions. The synthesis of ammonia from N 2 and H 2 over iron and rhenium surfaces, 1 H 2 / 2 H 2 exchange over stepped platinum crystal surfaces at low pressures, and the hydrogenolysis (C - C bond breaking) of isobutane at kinked platinum crystal surfaces are presented as experimental evidence in support of the theory

  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. Theory and implementation of a very high throughput true random number generator in field programmable gate array

    Energy Technology Data Exchange (ETDEWEB)

    Wang, Yonggang, E-mail: wangyg@ustc.edu.cn; Hui, Cong; Liu, Chong; Xu, Chao [Department of Modern Physics, University of Science and Technology of China, Hefei 230026 (China)

    2016-04-15

    The contribution of this paper is proposing a new entropy extraction mechanism based on sampling phase jitter in ring oscillators to make a high throughput true random number generator in a field programmable gate array (FPGA) practical. Starting from experimental observation and analysis of the entropy source in FPGA, a multi-phase sampling method is exploited to harvest the clock jitter with a maximum entropy and fast sampling speed. This parametrized design is implemented in a Xilinx Artix-7 FPGA, where the carry chains in the FPGA are explored to realize the precise phase shifting. The generator circuit is simple and resource-saving, so that multiple generation channels can run in parallel to scale the output throughput for specific applications. The prototype integrates 64 circuit units in the FPGA to provide a total output throughput of 7.68 Gbps, which meets the requirement of current high-speed quantum key distribution systems. The randomness evaluation, as well as its robustness to ambient temperature, confirms that the new method in a purely digital fashion can provide high-speed high-quality random bit sequences for a variety of embedded applications.

  16. 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.

  17. 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.

  18. An Laudau-Lifschitz theory based algorithm on calculating post-buckling configuration of a rod buckling in elastic media

    Science.gov (United States)

    Huang, Shicheng; Tan, Likun; Hu, Nan; Grover, Hannah; Chu, Kevin; Chen, Zi

    This reserach introduces a new numerical approach of calculating the post-buckling configuration of a thin rod embedded in elastic media. The theoretical base is the governing ODEs describing the balance of forces and moments, the length conservation, and the physics of bending and twisting by Laudau and Lifschitz. The numerical methods applied in the calculation are continuation method and Newton's method of iteration in combination with spectrum method. To the authors' knowledge, it is the first trial of directly applying the L-L theory to numerically studying the phenomenon of rod buckling in elastic medium. This method accounts for nonlinearity of geometry, thus is capable of calculating large deformation. The stability of this method is another advantage achieved by expressing the governing equations in a set of first-order derivative form. The wave length, amplitude, and decay effect all agree with the experiment without any further assumptions. This program can be applied to different occasions with varying stiffness of the elastic medai and rigidity of the rod.

  19. COMBINATION OF GENETIC ALGORITHM AND DEMPSTER-SHAFER THEORY OF EVIDENCE FOR LAND COVER CLASSIFICATION USING INTEGRATION OF SAR AND OPTICAL SATELLITE IMAGERY

    Directory of Open Access Journals (Sweden)

    H. T. Chu

    2012-07-01

    Full Text Available The integration of different kinds of remotely sensed data, in particular Synthetic Aperture Radar (SAR and optical satellite imagery, is considered a promising approach for land cover classification because of the complimentary properties of each data source. However, the challenges are: how to fully exploit the capabilities of these multiple data sources, which combined datasets should be used and which data processing and classification techniques are most appropriate in order to achieve the best results. In this paper an approach, in which synergistic use of a feature selection (FS methods with Genetic Algorithm (GA and multiple classifiers combination based on Dempster-Shafer Theory of Evidence, is proposed and evaluated for classifying land cover features in New South Wales, Australia. Multi-date SAR data, including ALOS/PALSAR, ENVISAT/ASAR and optical (Landsat 5 TM+ images, were used for this study. Textural information were also derived and integrated with the original images. Various combined datasets were generated for classification. Three classifiers, namely Artificial Neural Network (ANN, Support Vector Machines (SVMs and Self-Organizing Map (SOM were employed. Firstly, feature selection using GA was applied for each classifier and dataset to determine the optimal input features and parameters. Then the results of three classifiers on particular datasets were combined using the Dempster-Shafer theory of Evidence. Results of this study demonstrate the advantages of the proposed method for land cover mapping using complex datasets. It is revealed that the use of GA in conjunction with the Dempster-Shafer Theory of Evidence can significantly improve the classification accuracy. Furthermore, integration of SAR and optical data often outperform single-type datasets.

  20. The new electromagnetic tetrads, infinite tetrad nesting and the non-trivial emergence of complex numbers in real theories of gravitation

    Science.gov (United States)

    Garat, Alcides

    How complex numbers get into play in a non-trivial way in real theories of gravitation is relevant since in a unified structure they should be able to relate in a natural way with quantum theories. For a long time this issue has been lingering on both relativistic formulations and quantum theories. We will analyze this fundamental subject under the light of new group isomorphism theorems linking local internal groups of transformations and local groups of spacetime transformations. The bridge between these two kinds of transformations is represented by new tetrads introduced previously. It is precisely through these local tetrad structures that we will provide a non-trivial answer to this old issue. These new tetrads have two fundamental building components, the skeletons and the gauge vectors. It is these constructive elements that provide the mathematical support that allows to prove group isomorphism theorems. In addition to this, we will prove a unique new property, the infinite tetrad nesting, alternating the nesting with non-Abelian tetrads in the construction of the tetrad gauge vectors. As an application we will demonstrate an alternative proof of a new group isomorphism theorem.

  1. Performance comparison of machine learning algorithms and number of independent components used in fMRI decoding of belief vs. disbelief.

    Science.gov (United States)

    Douglas, P K; Harris, Sam; Yuille, Alan; Cohen, Mark S

    2011-05-15

    Machine learning (ML) has become a popular tool for mining functional neuroimaging data, and there are now hopes of performing such analyses efficiently in real-time. Towards this goal, we compared accuracy of six different ML algorithms applied to neuroimaging data of persons engaged in a bivariate task, asserting their belief or disbelief of a variety of propositional statements. We performed unsupervised dimension reduction and automated feature extraction using independent component (IC) analysis and extracted IC time courses. Optimization of classification hyperparameters across each classifier occurred prior to assessment. Maximum accuracy was achieved at 92% for Random Forest, followed by 91% for AdaBoost, 89% for Naïve Bayes, 87% for a J48 decision tree, 86% for K*, and 84% for support vector machine. For real-time decoding applications, finding a parsimonious subset of diagnostic ICs might be useful. We used a forward search technique to sequentially add ranked ICs to the feature subspace. For the current data set, we determined that approximately six ICs represented a meaningful basis set for classification. We then projected these six IC spatial maps forward onto a later scanning session within subject. We then applied the optimized ML algorithms to these new data instances, and found that classification accuracy results were reproducible. Additionally, we compared our classification method to our previously published general linear model results on this same data set. The highest ranked IC spatial maps show similarity to brain regions associated with contrasts for belief > disbelief, and disbelief < belief. Copyright © 2010 Elsevier Inc. All rights reserved.

  2. On the truncation of the number of excited states in density functional theory sum-over-states calculations of indirect spin spin coupling constants

    International Nuclear Information System (INIS)

    Zarycz, M. Natalia C.; Provasi, Patricio F.; Sauer, Stephan P. A.

    2015-01-01

    It is investigated, whether the number of excited (pseudo)states can be truncated in the sum-over-states expression for indirect spin-spin coupling constants (SSCCs), which is used in the Contributions from Localized Orbitals within the Polarization Propagator Approach and Inner Projections of the Polarization Propagator (IPPP-CLOPPA) approach to analyzing SSCCs in terms of localized orbitals. As a test set we have studied the nine simple compounds, CH 4 , NH 3 , H 2 O, SiH 4 , PH 3 , SH 2 , C 2 H 2 , C 2 H 4 , and C 2 H 6 . The excited (pseudo)states were obtained from time-dependent density functional theory (TD-DFT) calculations with the B3LYP exchange-correlation functional and the specialized core-property basis set, aug-cc-pVTZ-J. We investigated both how the calculated coupling constants depend on the number of (pseudo)states included in the summation and whether the summation can be truncated in a systematic way at a smaller number of states and extrapolated to the total number of (pseudo)states for the given one-electron basis set. We find that this is possible and that for some of the couplings it is sufficient to include only about 30% of the excited (pseudo)states

  3. On the truncation of the number of excited states in density functional theory sum-over-states calculations of indirect spin spin coupling constants

    Energy Technology Data Exchange (ETDEWEB)

    Zarycz, M. Natalia C., E-mail: mnzarycz@gmail.com; Provasi, Patricio F., E-mail: patricio@unne.edu.ar [Department of Physics, University of Northeastern - CONICET, Av. Libertad 5500, Corrientes W3404AAS (Argentina); Sauer, Stephan P. A., E-mail: sauer@kiku.dk [Department of Chemistry, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen Ø (Denmark)

    2015-12-28

    It is investigated, whether the number of excited (pseudo)states can be truncated in the sum-over-states expression for indirect spin-spin coupling constants (SSCCs), which is used in the Contributions from Localized Orbitals within the Polarization Propagator Approach and Inner Projections of the Polarization Propagator (IPPP-CLOPPA) approach to analyzing SSCCs in terms of localized orbitals. As a test set we have studied the nine simple compounds, CH{sub 4}, NH{sub 3}, H{sub 2}O, SiH{sub 4}, PH{sub 3}, SH{sub 2}, C{sub 2}H{sub 2}, C{sub 2}H{sub 4}, and C{sub 2}H{sub 6}. The excited (pseudo)states were obtained from time-dependent density functional theory (TD-DFT) calculations with the B3LYP exchange-correlation functional and the specialized core-property basis set, aug-cc-pVTZ-J. We investigated both how the calculated coupling constants depend on the number of (pseudo)states included in the summation and whether the summation can be truncated in a systematic way at a smaller number of states and extrapolated to the total number of (pseudo)states for the given one-electron basis set. We find that this is possible and that for some of the couplings it is sufficient to include only about 30% of the excited (pseudo)states.

  4. 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

  5. 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

  6. One-particle many-body Green's function theory: Algebraic recursive definitions, linked-diagram theorem, irreducible-diagram theorem, and general-order algorithms.

    Science.gov (United States)

    Hirata, So; Doran, Alexander E; Knowles, Peter J; Ortiz, J V

    2017-07-28

    A thorough analytical and numerical characterization of the whole perturbation series of one-particle many-body Green's function (MBGF) theory is presented in a pedagogical manner. Three distinct but equivalent algebraic (first-quantized) recursive definitions of the perturbation series of the Green's function are derived, which can be combined with the well-known recursion for the self-energy. Six general-order algorithms of MBGF are developed, each implementing one of the three recursions, the ΔMPn method (where n is the perturbation order) [S. Hirata et al., J. Chem. Theory Comput. 11, 1595 (2015)], the automatic generation and interpretation of diagrams, or the numerical differentiation of the exact Green's function with a perturbation-scaled Hamiltonian. They all display the identical, nondivergent perturbation series except ΔMPn, which agrees with MBGF in the diagonal and frequency-independent approximations at 1≤n≤3 but converges at the full-configuration-interaction (FCI) limit at n=∞ (unless it diverges). Numerical data of the perturbation series are presented for Koopmans and non-Koopmans states to quantify the rate of convergence towards the FCI limit and the impact of the diagonal, frequency-independent, or ΔMPn approximation. The diagrammatic linkedness and thus size-consistency of the one-particle Green's function and self-energy are demonstrated at any perturbation order on the basis of the algebraic recursions in an entirely time-independent (frequency-domain) framework. The trimming of external lines in a one-particle Green's function to expose a self-energy diagram and the removal of reducible diagrams are also justified mathematically using the factorization theorem of Frantz and Mills. Equivalence of ΔMPn and MBGF in the diagonal and frequency-independent approximations at 1≤n≤3 is algebraically proven, also ascribing the differences at n = 4 to the so-called semi-reducible and linked-disconnected diagrams.

  7. Development of constraint algorithm for the number of electrons in molecular orbitals consisting mainly 4f atomic orbitals of rare-earth elements and its introduction to tight-binding quantum chemical molecular dynamics method

    International Nuclear Information System (INIS)

    Endou, Akira; Onuma, Hiroaki; Jung, Sun-ho

    2007-01-01

    Our original tight-binding quantum chemical molecular dynamics code, Colors', has been successfully applied to the theoretical investigation of complex materials including rare-earth elements, e.g., metal catalysts supported on a CeO 2 surface. To expand our code so as to obtain a good convergence for the electronic structure of a calculation system including a rare-earth element, we developed a novel algorithm to provide a constraint condition for the number of electrons occupying the selected molecular orbitals that mainly consist of 4f atomic orbitals of the rare-earth element. This novel algorithm was introduced in Colors. Using Colors, we succeeded in obtaining the classified electronic configurations of the 4f atomic orbitals of Ce 4+ and reduced Ce ions in a CeO 2 bulk model with one oxygen defect, which makes it difficult to obtain a good convergence using a conventional first-principles quantum chemical calculation code. (author)

  8. From symmetries to number theory

    International Nuclear Information System (INIS)

    Tempesta, P.

    2009-01-01

    It is shown that the finite-operator calculus provides a simple formalism useful for constructing symmetry-preserving discretizations of quantum-mechanical integrable models. A related algebraic approach can also be used to define a class of Appell polynomials and of L series.

  9. 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

  10. 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.

  11. Transcendental numbers

    CERN Document Server

    Murty, M Ram

    2014-01-01

    This book provides an introduction to the topic of transcendental numbers for upper-level undergraduate and graduate students. The text is constructed to support a full course on the subject, including descriptions of both relevant theorems and their applications. While the first part of the book focuses on introducing key concepts, the second part presents more complex material, including applications of Baker’s theorem, Schanuel’s conjecture, and Schneider’s theorem. These later chapters may be of interest to researchers interested in examining the relationship between transcendence and L-functions. Readers of this text should possess basic knowledge of complex analysis and elementary algebraic number theory.

  12. Locating structures and evolution pathways of reconstructed rutile TiO2(011) using genetic algorithm aided density functional theory calculations.

    Science.gov (United States)

    Ding, Pan; Gong, Xue-Qing

    2016-05-01

    Titanium dioxide (TiO2) is an important metal oxide that has been used in many different applications. TiO2 has also been widely employed as a model system to study basic processes and reactions in surface chemistry and heterogeneous catalysis. In this work, we investigated the (011) surface of rutile TiO2 by focusing on its reconstruction. Density functional theory calculations aided by a genetic algorithm based optimization scheme were performed to extensively sample the potential energy surfaces of reconstructed rutile TiO2 structures that obey (2 × 1) periodicity. A lot of stable surface configurations were located, including the global-minimum configuration that was proposed previously. The wide variety of surface structures determined through the calculations performed in this work provide insight into the relationship between the atomic configuration of a surface and its stability. More importantly, several analytical schemes were proposed and tested to gauge the differences and similarities among various surface structures, aiding the construction of the complete pathway for the reconstruction process.

  13. Direct Index Method of Beam Damage Location Detection Based on Difference Theory of Strain Modal Shapes and the Genetic Algorithms Application

    Directory of Open Access Journals (Sweden)

    Bao Zhenming

    2012-01-01

    Full Text Available Structural damage identification is to determine the structure health status and analyze the test results. The three key problems to be solved are as follows: the existence of damage in structure, to detect the damage location, and to confirm the damage degree or damage form. Damage generally changes the structure physical properties (i.e., stiffness, mass, and damping corresponding with the modal characteristics of the structure (i.e., natural frequencies, modal shapes, and modal damping. The research results show that strain mode can be more sensitive and effective for local damage. The direct index method of damage location detection is based on difference theory, without the modal parameter of the original structure. FEM numerical simulation to partial crack with different degree is done. The criteria of damage location detection can be obtained by strain mode difference curve through cubic spline interpolation. Also the genetic algorithm box in Matlab is used. It has been possible to identify the damage to a reasonable level of accuracy.

  14. 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

  15. 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.)

  16. 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.

  17. Algorithms in behavioral systems theory

    NARCIS (Netherlands)

    Cotroneo, Tommaso

    2001-01-01

    Een van de belangrijkste eigenschappen van systemen is hun complexiteit en hun interconnectiviteit. Een manier om dergelijke systemen te bestuderen is door ze te beschouwen als bestaande uit interacterende deelsystemen. Typische voorbeelden van complexe systemen die opgebouwd zijn uit eenvoudige

  18. 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

  19. 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.

  20. Algorithming the Algorithm

    DEFF Research Database (Denmark)

    Mahnke, Martina; Uprichard, Emma

    2014-01-01

    Imagine sailing across the ocean. The sun is shining, vastness all around you. And suddenly [BOOM] you’ve hit an invisible wall. Welcome to the Truman Show! Ever since Eli Pariser published his thoughts on a potential filter bubble, this movie scenario seems to have become reality, just with slight...... changes: it’s not the ocean, it’s the internet we’re talking about, and it’s not a TV show producer, but algorithms that constitute a sort of invisible wall. Building on this assumption, most research is trying to ‘tame the algorithmic tiger’. While this is a valuable and often inspiring approach, we...

  1. 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

  2. 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

  3. 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.)

  4. 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...

  5. 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.

  6. 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

  7. 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).

  8. 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

  9. 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

  10. 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.

  11. Sound algorithms

    OpenAIRE

    De Götzen , Amalia; Mion , Luca; Tache , Olivier

    2007-01-01

    International audience; We call sound algorithms the categories of algorithms that deal with digital sound signal. Sound algorithms appeared in the very infancy of computer. Sound algorithms present strong specificities that are the consequence of two dual considerations: the properties of the digital sound signal itself and its uses, and the properties of auditory perception.

  12. Genetic algorithms

    Science.gov (United States)

    Wang, Lui; Bayer, Steven E.

    1991-01-01

    Genetic algorithms are mathematical, highly parallel, adaptive search procedures (i.e., problem solving methods) based loosely on the processes of natural genetics and Darwinian survival of the fittest. Basic genetic algorithms concepts are introduced, genetic algorithm applications are introduced, and results are presented from a project to develop a software tool that will enable the widespread use of genetic algorithm technology.

  13. 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.

  14. 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.

  15. 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.

  16. Building Numbers from Primes

    Science.gov (United States)

    Burkhart, Jerry

    2009-01-01

    Prime numbers are often described as the "building blocks" of natural numbers. This article shows how the author and his students took this idea literally by using prime factorizations to build numbers with blocks. In this activity, students explore many concepts of number theory, including the relationship between greatest common factors and…

  17. A Whitham-Theory Sonic-Boom Analysis of the TU-144 Aircraft at a Mach Number of 2.2

    Science.gov (United States)

    Mack, Robert J.

    1999-01-01

    . Therefore, an analysis of the Tu-144 was made to obtain predictions of pressure signature shape and shock strengths at cruise conditions so that the range and characteristics of the required pressure gages could be determined well in advance of the tests. Cancellation of the sonic-boom signature measurement part of the tests removed the need for these pressure gages. Since CFD methods would be used to analyze the aerodynamic performance of the Tu-144 and make similar pressure signature predictions, the relatively quick and simple Whitham-theory pressure signature predictions presented in this paper could be used for comparisons. Pressure signature predictions of sonic-boom disturbances from the Tu- 144 aircraft were obtained from geometry derived from a three-view description of the production aircraft. The geometry was used to calculate aerodynamic performance characteristics at supersonic-cruise conditions. These characteristics and Whitham/Walkden sonic-boom theory were employed to obtain F-functions and flow-field pressure signature predictions at a Mach number of 2.2, at a cruise altitude of 61000 feet, and at a cruise weight of 350000 pounds.

  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. Semioptimal practicable algorithmic cooling

    International Nuclear Information System (INIS)

    Elias, Yuval; Mor, Tal; Weinstein, Yossi

    2011-01-01

    Algorithmic cooling (AC) of spins applies entropy manipulation algorithms in open spin systems in order to cool spins far beyond Shannon's entropy bound. Algorithmic cooling of nuclear spins was demonstrated experimentally and may contribute to nuclear magnetic resonance spectroscopy. Several cooling algorithms were suggested in recent years, including practicable algorithmic cooling (PAC) and exhaustive AC. Practicable algorithms have simple implementations, yet their level of cooling is far from optimal; exhaustive algorithms, on the other hand, cool much better, and some even reach (asymptotically) an optimal level of cooling, but they are not practicable. We introduce here semioptimal practicable AC (SOPAC), wherein a few cycles (typically two to six) are performed at each recursive level. Two classes of SOPAC algorithms are proposed and analyzed. Both attain cooling levels significantly better than PAC and are much more efficient than the exhaustive algorithms. These algorithms are shown to bridge the gap between PAC and exhaustive AC. In addition, we calculated the number of spins required by SOPAC in order to purify qubits for quantum computation. As few as 12 and 7 spins are required (in an ideal scenario) to yield a mildly pure spin (60% polarized) from initial polarizations of 1% and 10%, respectively. In the latter case, about five more spins are sufficient to produce a highly pure spin (99.99% polarized), which could be relevant for fault-tolerant quantum computing.

  20. Total algorithms

    NARCIS (Netherlands)

    Tel, G.

    We define the notion of total algorithms for networks of processes. A total algorithm enforces that a "decision" is taken by a subset of the processes, and that participation of all processes is required to reach this decision. Total algorithms are an important building block in the design of