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Sample records for standard arithmetic algorithms

  1. Four (Algorithms) in One (Bag): An Integrative Framework of Knowledge for Teaching the Standard Algorithms of the Basic Arithmetic Operations

    Science.gov (United States)

    Raveh, Ira; Koichu, Boris; Peled, Irit; Zaslavsky, Orit

    2016-01-01

    In this article we present an integrative framework of knowledge for teaching the standard algorithms of the four basic arithmetic operations. The framework is based on a mathematical analysis of the algorithms, a connectionist perspective on teaching mathematics and an analogy with previous frameworks of knowledge for teaching arithmetic…

  2. The Cognitive Correlates of Third-Grade Skill in Arithmetic, Algorithmic Computation, and Arithmetic Word Problems

    Science.gov (United States)

    Fuchs, Lynn S.; Fuchs, Douglas; Compton, Donald L.; Powell, Sarah R.; Seethaler, Pamela M.; Capizzi, Andrea M.; Schatschneider, Christopher; Fletcher, Jack M.

    2006-01-01

    The purpose of this study was to examine the cognitive correlates of RD-grade skill in arithmetic, algorithmic computation, and arithmetic word problems. Third graders (N = 312) were measured on language, nonverbal problem solving, concept formation, processing speed, long-term memory, working memory, phonological decoding, and sight word…

  3. 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...

  4. Handbook of floating-point arithmetic

    CERN Document Server

    Muller, Jean-Michel; de Dinechin, Florent; Jeannerod, Claude-Pierre; Joldes, Mioara; Lefèvre, Vincent; Melquiond, Guillaume; Revol, Nathalie; Torres, Serge

    2018-01-01

    This handbook is a definitive guide to the effective use of modern floating-point arithmetic, which has considerably evolved, from the frequently inconsistent floating-point number systems of early computing to the recent IEEE 754-2008 standard. Most of computational mathematics depends on floating-point numbers, and understanding their various implementations will allow readers to develop programs specifically tailored for the standard’s technical features. Algorithms for floating-point arithmetic are presented throughout the book and illustrated where possible by example programs which show how these techniques appear in actual coding and design. The volume itself breaks its core topic into four parts: the basic concepts and history of floating-point arithmetic; methods of analyzing floating-point algorithms and optimizing them; implementations of IEEE 754-2008 in hardware and software; and useful extensions to the standard floating-point system, such as interval arithmetic, double- and triple-word arithm...

  5. An algorithm for the arithmetic classification of multilattices.

    Science.gov (United States)

    Indelicato, Giuliana

    2013-01-01

    A procedure for the construction and the classification of monoatomic multilattices in arbitrary dimension is developed. The algorithm allows one to determine the location of the points of all monoatomic multilattices with a given symmetry, or to determine whether two assigned multilattices are arithmetically equivalent. This approach is based on ideas from integral matrix theory, in particular the reduction to the Smith normal form, and can be coded to provide a classification software package.

  6. A software framework for pipelined arithmetic algorithms in field programmable gate arrays

    Science.gov (United States)

    Kim, J. B.; Won, E.

    2018-03-01

    Pipelined algorithms implemented in field programmable gate arrays are extensively used for hardware triggers in the modern experimental high energy physics field and the complexity of such algorithms increases rapidly. For development of such hardware triggers, algorithms are developed in C++, ported to hardware description language for synthesizing firmware, and then ported back to C++ for simulating the firmware response down to the single bit level. We present a C++ software framework which automatically simulates and generates hardware description language code for pipelined arithmetic algorithms.

  7. An Asynchronous IEEE Floating-Point Arithmetic Unit

    Directory of Open Access Journals (Sweden)

    Joel R. Noche

    2007-12-01

    Full Text Available An asynchronous floating-point arithmetic unit is designed and tested at the transistor level usingCadence software. It uses CMOS (complementary metal oxide semiconductor and DCVS (differentialcascode voltage switch logic in a 0.35 µm process using a 3.3 V supply voltage, with dual-rail data andsingle-rail control signals using four-phase handshaking.Using 17,085 transistors, the unit handles single-precision (32-bit addition/subtraction, multiplication,division, and remainder using the IEEE 754-1985 Standard for Binary Floating-Point Arithmetic, withrounding and other operations to be handled by separate hardware or software. Division and remainderare done using a restoring subtractive algorithm; multiplication uses an additive algorithm. Exceptionsare noted by flags (and not trap handlers and the output is in single-precision.Previous work on asynchronous floating-point arithmetic units have mostly focused on single operationssuch as division. This is the first work to the authors' knowledge that can perform floating-point addition,multiplication, division, and remainder using a common datapath.

  8. Image Steganography In Securing Sound File Using Arithmetic Coding Algorithm, Triple Data Encryption Standard (3DES) and Modified Least Significant Bit (MLSB)

    Science.gov (United States)

    Nasution, A. B.; Efendi, S.; Suwilo, S.

    2018-04-01

    The amount of data inserted in the form of audio samples that use 8 bits with LSB algorithm, affect the value of PSNR which resulted in changes in image quality of the insertion (fidelity). So in this research will be inserted audio samples using 5 bits with MLSB algorithm to reduce the number of data insertion where previously the audio sample will be compressed with Arithmetic Coding algorithm to reduce file size. In this research will also be encryption using Triple DES algorithm to better secure audio samples. The result of this research is the value of PSNR more than 50dB so it can be concluded that the image quality is still good because the value of PSNR has exceeded 40dB.

  9. Algorithmic solution of arithmetic problems and operands-answer associations in long-term memory.

    Science.gov (United States)

    Thevenot, C; Barrouillet, P; Fayol, M

    2001-05-01

    Many developmental models of arithmetic problem solving assume that any algorithmic solution of a given problem results in an association of the two operands and the answer in memory (Logan & Klapp, 1991; Siegler, 1996). In this experiment, adults had to perform either an operation or a comparison on the same pairs of two-digit numbers and then a recognition task. It is shown that unlike comparisons, the algorithmic solution of operations impairs the recognition of operands in adults. Thus, the postulate of a necessary and automatic storage of operands-answer associations in memory when young children solve additions by algorithmic strategies needs to be qualified.

  10. Digital Arithmetic: Division Algorithms

    DEFF Research Database (Denmark)

    Montuschi, Paolo; Nannarelli, Alberto

    2017-01-01

    Division is one of the basic arithmetic operations supported by every computer system. The operation can be performed and implemented by either hardware or software, or by a combination of the two. Although division is not as frequent as addition and multiplication, nowadays, most processors impl...... significant hardware resources and is more suitable for software implementation on the existing multiply units. The purpose of this entry is to provide an introductory survey using a presentation style suitable for the interested non-specialist readers as well....

  11. 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.

  12. Simple Exact Algorithm for Transistor Sizing of Low-Power High-Speed Arithmetic Circuits

    Directory of Open Access Journals (Sweden)

    Tooraj Nikoubin

    2010-01-01

    Full Text Available A new transistor sizing algorithm, SEA (Simple Exact Algorithm, for optimizing low-power and high-speed arithmetic integrated circuits is proposed. In comparison with other transistor sizing algorithms, simplicity, accuracy, independency of order and initial sizing factors of transistors, and flexibility in choosing the optimization parameters such as power consumption, delay, Power-Delay Product (PDP, chip area or the combination of them are considered as the advantages of this new algorithm. More exhaustive rules of grouping transistors are the main trait of our algorithm. Hence, the SEA algorithm dominates some major transistor sizing metrics such as optimization rate, simulation speed, and reliability. According to approximate comparison of the SEA algorithm with MDE and ADC for a number of conventional full adder circuits, delay and PDP have been improved 55.01% and 57.92% on an average, respectively. By comparing the SEA and Chang's algorithm, 25.64% improvement in PDP and 33.16% improvement in delay have been achieved. All the simulations have been performed with 0.13 m technology based on the BSIM3v3 model using HSpice simulator software.

  13. Face Recognition using Approximate Arithmetic

    DEFF Research Database (Denmark)

    Marso, Karol

    Face recognition is image processing technique which aims to identify human faces and found its use in various different fields for example in security. Throughout the years this field evolved and there are many approaches and many different algorithms which aim to make the face recognition as effective...... processing applications the results do not need to be completely precise and use of the approximate arithmetic can lead to reduction in terms of delay, space and power consumption. In this paper we examine possible use of approximate arithmetic in face recognition using Eigenfaces algorithm....

  14. Development of arithmetical abilities

    Directory of Open Access Journals (Sweden)

    Tatjana Levstek

    2014-02-01

    Full Text Available Arithmetic (from the word 'arithmos' which means 'numbers' is an elementary branch of mathematics. Numeracy is essential for understanding mathematics, so the development of arithmetic abilities has been an area of scientific research for a long time. Recent research has shown that the development of arithmetic abilities is not based only on gaining experience and learning. Some arithmetic abilities, especially the sense of quantity, are innate. Even babies are able to distinguish between groups with different number of elements and they perceive numeracy amodally. Six-month-olds distinguish between two groups with the numeracy ratio of 1 : 2. With age this ratio improves rapidly. Five-year-old children already distinguish between groups with the number ratio 7 : 8. The ability to compare two quantities begins to develop after 15 months of age and children learn how to count spontaneously, together with the acquisition of language. Speech enables children to understand number in its abstract, symbolic sense, thus opening the way to symbolic arithmetic. During the preschool period children use intuition when doing calculations, but in school the arithmetic is based on the knowledge of arithmetical algorithms. So, in order to acquire mathematical knowledge, it is necessary to incorporate memory and automate arithmetical processes, without the use of intuition. However, research has shown that intuition is very important and is even a predictive factor for the development of mathematical abilities throughout the schooling process.

  15. Reversible arithmetic logic unit for quantum arithmetic

    DEFF Research Database (Denmark)

    Thomsen, Michael Kirkedal; Glück, Robert; Axelsen, Holger Bock

    2010-01-01

    This communication presents the complete design of a reversible arithmetic logic unit (ALU) that can be part of a programmable reversible computing device such as a quantum computer. The presented ALU is garbage free and uses reversible updates to combine the standard reversible arithmetic...... and logical operations in one unit. Combined with a suitable control unit, the ALU permits the construction of an r-Turing complete computing device. The garbage-free ALU developed in this communication requires only 6n elementary reversible gates for five basic arithmetic-logical operations on two n......-bit operands and does not use ancillae. This remarkable low resource consumption was achieved by generalizing the V-shape design first introduced for quantum ripple-carry adders and nesting multiple V-shapes in a novel integrated design. This communication shows that the realization of an efficient reversible...

  16. Using the Variable-Length Arithmetic for an Accurate Poles-Zeros Analysis

    Directory of Open Access Journals (Sweden)

    J. Michal

    2003-09-01

    Full Text Available In the paper, a reduction algorithm for transforming the generaleigenvalue problem to the standard one is presented for both classicalfull-matrix methods and a sparse-matrix technique appropriate forlarge-scale circuits. An optimal pivoting strategy for the two methodsis proposed to increase the precision of the computations. The accuracyof the algorithms is furthermore increased using longer numerical data.First, a ORQJ.GRXEOH precision sparse algorithm is compared with theGRXEOH precision sparse and full-matrix ones. Finally, the applicationof a suitable multiple-precision arithmetic library is evaluated.

  17. Segment LLL Reduction of Lattice Bases Using Modular Arithmetic

    Directory of Open Access Journals (Sweden)

    Sanjay Mehrotra

    2010-07-01

    Full Text Available The algorithm of Lenstra, Lenstra, and Lovász (LLL transforms a given integer lattice basis into a reduced basis. Storjohann improved the worst case complexity of LLL algorithms by a factor of O(n using modular arithmetic. Koy and Schnorr developed a segment-LLL basis reduction algorithm that generates lattice basis satisfying a weaker condition than the LLL reduced basis with O(n improvement than the LLL algorithm. In this paper we combine Storjohann’s modular arithmetic approach with the segment-LLL approach to further improve the worst case complexity of the segment-LLL algorithms by a factor of n0.5.

  18. A fast fractional difference algorithm

    DEFF Research Database (Denmark)

    Jensen, Andreas Noack; Nielsen, Morten Ørregaard

    2014-01-01

    We provide a fast algorithm for calculating the fractional difference of a time series. In standard implementations, the calculation speed (number of arithmetic operations) is of order T 2, where T is the length of the time series. Our algorithm allows calculation speed of order T log...

  19. A Fast Fractional Difference Algorithm

    DEFF Research Database (Denmark)

    Jensen, Andreas Noack; Nielsen, Morten Ørregaard

    We provide a fast algorithm for calculating the fractional difference of a time series. In standard implementations, the calculation speed (number of arithmetic operations) is of order T 2, where T is the length of the time series. Our algorithm allows calculation speed of order T log...

  20. An efficient adaptive arithmetic coding image compression technology

    International Nuclear Information System (INIS)

    Wang Xing-Yuan; Yun Jiao-Jiao; Zhang Yong-Lei

    2011-01-01

    This paper proposes an efficient lossless image compression scheme for still images based on an adaptive arithmetic coding compression algorithm. The algorithm increases the image coding compression rate and ensures the quality of the decoded image combined with the adaptive probability model and predictive coding. The use of adaptive models for each encoded image block dynamically estimates the probability of the relevant image block. The decoded image block can accurately recover the encoded image according to the code book information. We adopt an adaptive arithmetic coding algorithm for image compression that greatly improves the image compression rate. The results show that it is an effective compression technology. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)

  1. Arithmetic the foundation of mathematics

    CERN Document Server

    2015-01-01

    Arithmetic factors into our lives on a daily basis, so it's hard to imagine a world without the six basic operations: addition, subtraction, multiplication, division, raising to powers, and finding roots. Readers will get a solid overview of arithmetic, while offering useful examples of how they are used in routine activities, such as social media applications. It reinforces Common Core math standards, including understanding basic math concepts and how they apply to students' daily lives and challenges. A history of arithmetic helps provide a contextual framework for the course of its develop

  2. Guest Editors' Introduction: Special Section on Computer Arithmetic

    DEFF Research Database (Denmark)

    Nannarelli, Alberto; Seidel, Peter-Michael; Tang, Ping Tak Peter

    2014-01-01

    and their subsequent testing and verification. Many practitioners of the field also focus on the art and science of using computer arithmetic to carry out scientific and engineering computations. Computer arithmetic is therefore an interdisciplinary field that draws upon mathematics, computer science and electrical......The articles in this special issue focus on current trends and developments in the field of computer arithmetic. This is a field that encompasses the definition and standardization of arithmetic system for computers. The field also deals with issues of hardware and software implementations...

  3. Lattice for FPGAs using logarithmic arithmetic

    Czech Academy of Sciences Publication Activity Database

    Kadlec, Jiří; Matoušek, Rudolf; Heřmánek, Antonín; Líčko, Miroslav; Tichý, Milan

    2002-01-01

    Roč. 74, č. 906 (2002), s. 53-56 ISSN 0013-4902 Grant - others: ESPRIT (XE) 33544 Institutional research plan: CEZ:AV0Z1075907 Keywords : lattice Rls algorithm * FPGA * logarithmic arithmetic Subject RIV: JC - Computer Hardware ; Software Impact factor: 0.039, year: 2002

  4. Optimal Design of Fixed-Point and Floating-Point Arithmetic Units for Scientific Applications

    OpenAIRE

    Pongyupinpanich, Surapong

    2012-01-01

    The challenge in designing a floating-point arithmetic co-processor/processor for scientific and engineering applications is to improve the performance, efficiency, and computational accuracy of the arithmetic unit. The arithmetic unit should efficiently support several mathematical functions corresponding to scientific and engineering computation demands. Moreover, the computations should be performed as fast as possible with a high degree of accuracy. Thus, this thesis proposes algorithm, d...

  5. Algorithmic-Reducibility = Renormalization-Group Fixed-Points; ``Noise''-Induced Phase-Transitions (NITs) to Accelerate Algorithmics (``NIT-Picking'') Replacing CRUTCHES!!!: Gauss Modular/Clock-Arithmetic Congruences = Signal X Noise PRODUCTS..

    Science.gov (United States)

    Siegel, J.; Siegel, Edward Carl-Ludwig

    2011-03-01

    Cook-Levin computational-"complexity"(C-C) algorithmic-equivalence reduction-theorem reducibility equivalence to renormalization-(semi)-group phase-transitions critical-phenomena statistical-physics universality-classes fixed-points, is exploited with Gauss modular/clock-arithmetic/model congruences = signal X noise PRODUCT reinterpretation. Siegel-Baez FUZZYICS=CATEGORYICS(SON of ``TRIZ''): Category-Semantics(C-S) tabular list-format truth-table matrix analytics predicts and implements "noise"-induced phase-transitions (NITs) to accelerate versus to decelerate Harel [Algorithmics(1987)]-Sipser[Intro. Theory Computation(1997) algorithmic C-C: "NIT-picking" to optimize optimization-problems optimally(OOPO). Versus iso-"noise" power-spectrum quantitative-only amplitude/magnitude-only variation stochastic-resonance, this "NIT-picking" is "noise" power-spectrum QUALitative-type variation via quantitative critical-exponents variation. Computer-"science" algorithmic C-C models: Turing-machine, finite-state-models/automata, are identified as early-days once-workable but NOW ONLY LIMITING CRUTCHES IMPEDING latter-days new-insights!!!

  6. Hybrid content addressable memory MSD arithmetic

    Science.gov (United States)

    Li, Yao; Kim, Dai Hyun; Kostrzewski, Andrew A.; Eichmann, George

    1990-07-01

    The modified signed-digit (MSD) number system, because of its inherent weak interdigit dependance, has been suggested as a useful means for a fast and parallel digital arithmetic. To maintain a fast processing speed, a single-stage holographic optical content-addressable memory (CAM) based MSD algorithm was suggested. In this paper, a novel non-holographic opto-electronic CAM based fast MSD addition processing architecture is proposed. The proposed concept has been verified with our first-order proof-of-principle experiments. A figure of merit comparison of this and other existing approaches is also presented. Based on this key opto-electronic CAM element, implementation of more sophisticated I'VISD arithmetic, such as optical MSD subtraction and multiplication operations, are proposed.

  7. Towards an arithmetical logic the arithmetical foundations of logic

    CERN Document Server

    Gauthier, Yvon

    2015-01-01

    This book offers an original contribution to the foundations of logic and mathematics, and focuses on the internal logic of mathematical theories, from arithmetic or number theory to algebraic geometry. Arithmetical logic is the term used to refer to the internal logic of classical arithmetic, here called Fermat-Kronecker arithmetic, and combines Fermat’s method of infinite descent with Kronecker’s general arithmetic of homogeneous polynomials. The book also includes a treatment of theories in physics and mathematical physics to underscore the role of arithmetic from a constructivist viewpoint. The scope of the work intertwines historical, mathematical, logical and philosophical dimensions in a unified critical perspective; as such, it will appeal to a broad readership from mathematicians to logicians, to philosophers interested in foundational questions. Researchers and graduate students in the fields of philosophy and mathematics will benefit from the author’s critical approach to the foundations of l...

  8. A Unified Formal Description of Arithmetic and Set Theoretical Data Types

    OpenAIRE

    Tarau, Paul

    2010-01-01

    We provide a "shared axiomatization" of natural numbers and hereditarily finite sets built around a polymorphic abstraction of bijective base-2 arithmetics. The "axiomatization" is described as a progressive refinement of Haskell type classes with examples of instances converging to an efficient implementation in terms of arbitrary length integers and bit operations. As an instance, we derive algorithms to perform arithmetic operations efficiently directly with hereditarily finite sets. The s...

  9. The Lanczos and Conjugate Gradient Algorithms in Finite Precision Arithmetic

    Czech Academy of Sciences Publication Activity Database

    Meurant, G.; Strakoš, Zdeněk

    2006-01-01

    Roč. 15, - (2006), s. 471-542 ISSN 0962-4929 R&D Projects: GA AV ČR 1ET400300415 Institutional research plan: CEZ:AV0Z10300504 Keywords : Lanczos method * conjugate gradient method * finite precision arithmetic * numerical stability * iterative methods Subject RIV: BA - General Mathematics

  10. Arithmetic noncommutative geometry

    CERN Document Server

    Marcolli, Matilde

    2005-01-01

    Arithmetic noncommutative geometry denotes the use of ideas and tools from the field of noncommutative geometry, to address questions and reinterpret in a new perspective results and constructions from number theory and arithmetic algebraic geometry. This general philosophy is applied to the geometry and arithmetic of modular curves and to the fibers at archimedean places of arithmetic surfaces and varieties. The main reason why noncommutative geometry can be expected to say something about topics of arithmetic interest lies in the fact that it provides the right framework in which the tools of geometry continue to make sense on spaces that are very singular and apparently very far from the world of algebraic varieties. This provides a way of refining the boundary structure of certain classes of spaces that arise in the context of arithmetic geometry, such as moduli spaces (of which modular curves are the simplest case) or arithmetic varieties (completed by suitable "fibers at infinity"), by adding boundaries...

  11. Adelic divisors on arithmetic varieties

    CERN Document Server

    Moriwaki, Atsushi

    2016-01-01

    In this article, the author generalizes several fundamental results for arithmetic divisors, such as the continuity of the volume function, the generalized Hodge index theorem, Fujita's approximation theorem for arithmetic divisors, Zariski decompositions for arithmetic divisors on arithmetic surfaces and a special case of Dirichlet's unit theorem on arithmetic varieties, to the case of the adelic arithmetic divisors.

  12. Elementary functions algorithms and implementation

    CERN Document Server

    Muller, Jean-Michel

    2016-01-01

    This textbook presents the concepts and tools necessary to understand, build, and implement algorithms for computing elementary functions (e.g., logarithms, exponentials, and the trigonometric functions). Both hardware- and software-oriented algorithms are included, along with issues related to accurate floating-point implementation. This third edition has been updated and expanded to incorporate the most recent advances in the field, new elementary function algorithms, and function software. After a preliminary chapter that briefly introduces some fundamental concepts of computer arithmetic, such as floating-point arithmetic and redundant number systems, the text is divided into three main parts. Part I considers the computation of elementary functions using algorithms based on polynomial or rational approximations and using table-based methods; the final chapter in this section deals with basic principles of multiple-precision arithmetic. Part II is devoted to a presentation of “shift-and-add” algorithm...

  13. A functional interpretation for nonstandard arithmetic

    NARCIS (Netherlands)

    van den Berg, B.; Briseid, E.; Safarik, P.

    2012-01-01

    We introduce constructive and classical systems for nonstandard arithmetic and show how variants of the functional interpretations due to Gödel and Shoenfield can be used to rewrite proofs performed in these systems into standard ones. These functional interpretations show in particular that our

  14. If Gravity is Geometry, is Dark Energy just Arithmetic?

    Science.gov (United States)

    Czachor, Marek

    2017-04-01

    Arithmetic operations (addition, subtraction, multiplication, division), as well as the calculus they imply, are non-unique. The examples of four-dimensional spaces, R+4 and (- L/2, L/2)4, are considered where different types of arithmetic and calculus coexist simultaneously. In all the examples there exists a non-Diophantine arithmetic that makes the space globally Minkowskian, and thus the laws of physics are formulated in terms of the corresponding calculus. However, when one switches to the `natural' Diophantine arithmetic and calculus, the Minkowskian character of the space is lost and what one effectively obtains is a Lorentzian manifold. I discuss in more detail the problem of electromagnetic fields produced by a pointlike charge. The solution has the standard form when expressed in terms of the non-Diophantine formalism. When the `natural' formalsm is used, the same solution looks as if the fields were created by a charge located in an expanding universe, with nontrivially accelerating expansion. The effect is clearly visible also in solutions of the Friedman equation with vanishing cosmological constant. All of this suggests that phenomena attributed to dark energy may be a manifestation of a miss-match between the arithmetic employed in mathematical modeling, and the one occurring at the level of natural laws. Arithmetic is as physical as geometry.

  15. Computer arithmetic and validity theory, implementation, and applications

    CERN Document Server

    Kulisch, Ulrich

    2013-01-01

    This is the revised and extended second edition of the successful basic book on computer arithmetic. It is consistent with the newest recent standard developments in the field. The book shows how the arithmetic capability of the computer can be enhanced. The work is motivated by the desire and the need to improve the accuracy of numerical computing and to control the quality of the computed results (validity). The accuracy requirements for the elementary floating-point operations are extended to the customary product spaces of computations including interval spaces. The mathematical properties

  16. [Acquisition of arithmetic knowledge].

    Science.gov (United States)

    Fayol, Michel

    2008-01-01

    The focus of this paper is on contemporary research on the number counting and arithmetical competencies that emerge during infancy, the preschool years, and the elementary school. I provide a brief overview of the evolution of children's conceptual knowledge of arithmetic knowledge, the acquisition and use of counting and how they solve simple arithmetic problems (e.g. 4 + 3).

  17. Arithmetic Abilities in Children with Developmental Dyslexia: Performance on French ZAREKI-R Test

    Science.gov (United States)

    De Clercq-Quaegebeur, Maryse; Casalis, Séverine; Vilette, Bruno; Lemaitre, Marie-Pierre; Vallée, Louis

    2018-01-01

    A high comorbidity between reading and arithmetic disabilities has already been reported. The present study aims at identifying more precisely patterns of arithmetic performance in children with developmental dyslexia, defined with severe and specific criteria. By means of a standardized test of achievement in mathematics ("Calculation and…

  18. Arithmetic functions in torus and tree networks

    Science.gov (United States)

    Bhanot, Gyan; Blumrich, Matthias A.; Chen, Dong; Gara, Alan G.; Giampapa, Mark E.; Heidelberger, Philip; Steinmacher-Burow, Burkhard D.; Vranas, Pavlos M.

    2007-12-25

    Methods and systems for performing arithmetic functions. In accordance with a first aspect of the invention, methods and apparatus are provided, working in conjunction of software algorithms and hardware implementation of class network routing, to achieve a very significant reduction in the time required for global arithmetic operation on the torus. Therefore, it leads to greater scalability of applications running on large parallel machines. The invention involves three steps in improving the efficiency and accuracy of global operations: (1) Ensuring, when necessary, that all the nodes do the global operation on the data in the same order and so obtain a unique answer, independent of roundoff error; (2) Using the topology of the torus to minimize the number of hops and the bidirectional capabilities of the network to reduce the number of time steps in the data transfer operation to an absolute minimum; and (3) Using class function routing to reduce latency in the data transfer. With the method of this invention, every single element is injected into the network only once and it will be stored and forwarded without any further software overhead. In accordance with a second aspect of the invention, methods and systems are provided to efficiently implement global arithmetic operations on a network that supports the global combining operations. The latency of doing such global operations are greatly reduced by using these methods.

  19. Arithmetic circuits for DSP applications

    CERN Document Server

    Stouraitis, Thanos

    2017-01-01

    Arithmetic Circuits for DSP Applications is a complete resource on arithmetic circuits for digital signal processing (DSP). It covers the key concepts, designs and developments of different types of arithmetic circuits, which can be used for improving the efficiency of implementation of a multitude of DSP applications. Each chapter includes various applications of the respective class of arithmetic circuits along with information on the future scope of research. Written for students, engineers, and researchers in electrical and computer engineering, this comprehensive text offers a clear understanding of different types of arithmetic circuits used for digital signal processing applications. The text includes contributions from noted researchers on a wide range of topics, including a review o circuits used in implementing basic operations like additions and multiplications; distributed arithmetic as a technique for the multiplier-less implementation of inner products for DSP applications; discussions on look ...

  20. PaCAL: A Python Package for Arithmetic Computations with Random Variables

    Directory of Open Access Journals (Sweden)

    Marcin Korze?

    2014-05-01

    Full Text Available In this paper we present PaCAL, a Python package for arithmetical computations on random variables. The package is capable of performing the four arithmetic operations: addition, subtraction, multiplication and division, as well as computing many standard functions of random variables. Summary statistics, random number generation, plots, and histograms of the resulting distributions can easily be obtained and distribution parameter ?tting is also available. The operations are performed numerically and their results interpolated allowing for arbitrary arithmetic operations on random variables following practically any probability distribution encountered in practice. The package is easy to use, as operations on random variables are performed just as they are on standard Python variables. Independence of random variables is, by default, assumed on each step but some computations on dependent random variables are also possible. We demonstrate on several examples that the results are very accurate, often close to machine precision. Practical applications include statistics, physical measurements or estimation of error distributions in scienti?c computations.

  1. 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

  2. Synthesis of logic circuits with evolutionary algorithms

    Energy Technology Data Exchange (ETDEWEB)

    JONES,JAKE S.; DAVIDSON,GEORGE S.

    2000-01-26

    In the last decade there has been interest and research in the area of designing circuits with genetic algorithms, evolutionary algorithms, and genetic programming. However, the ability to design circuits of the size and complexity required by modern engineering design problems, simply by specifying required outputs for given inputs has as yet eluded researchers. This paper describes current research in the area of designing logic circuits using an evolutionary algorithm. The goal of the research is to improve the effectiveness of this method and make it a practical aid for design engineers. A novel method of implementing the algorithm is introduced, and results are presented for various multiprocessing systems. In addition to evolving standard arithmetic circuits, work in the area of evolving circuits that perform digital signal processing tasks is described.

  3. Sets with Prescribed Arithmetic Densities

    Czech Academy of Sciences Publication Activity Database

    Luca, F.; Pomerance, C.; Porubský, Štefan

    2008-01-01

    Roč. 3, č. 2 (2008), s. 67-80 ISSN 1336-913X R&D Projects: GA ČR GA201/07/0191 Institutional research plan: CEZ:AV0Z10300504 Keywords : generalized arithmetic density * generalized asymptotic density * generalized logarithmic density * arithmetical semigroup * weighted arithmetic mean * ratio set * R-dense set * Axiom A * delta-regularly varying function Subject RIV: BA - General Mathematics

  4. Floating-point geometry: toward guaranteed geometric computations with approximate arithmetics

    Science.gov (United States)

    Bajard, Jean-Claude; Langlois, Philippe; Michelucci, Dominique; Morin, Géraldine; Revol, Nathalie

    2008-08-01

    Geometric computations can fail because of inconsistencies due to floating-point inaccuracy. For instance, the computed intersection point between two curves does not lie on the curves: it is unavoidable when the intersection point coordinates are non rational, and thus not representable using floating-point arithmetic. A popular heuristic approach tests equalities and nullities up to a tolerance ɛ. But transitivity of equality is lost: we can have A approx B and B approx C, but A not approx C (where A approx B means ||A - B|| < ɛ for A,B two floating-point values). Interval arithmetic is another, self-validated, alternative; the difficulty is to limit the swell of the width of intervals with computations. Unfortunately interval arithmetic cannot decide equality nor nullity, even in cases where it is decidable by other means. A new approach, developed in this paper, consists in modifying the geometric problems and algorithms, to account for the undecidability of the equality test and unavoidable inaccuracy. In particular, all curves come with a non-zero thickness, so two curves (generically) cut in a region with non-zero area, an inner and outer representation of which is computable. This last approach no more assumes that an equality or nullity test is available. The question which arises is: which geometric problems can still be solved with this last approach, and which cannot? This paper begins with the description of some cases where every known arithmetic fails in practice. Then, for each arithmetic, some properties of the problems they can solve are given. We end this work by proposing the bases of a new approach which aims to fulfill the geometric computations requirements.

  5. Arithmetic soft-core accelerators

    NARCIS (Netherlands)

    Calderon Rocabado, D.R.H.

    2007-01-01

    In this dissertation, we address the design of multi-functional arithmetic units working with the most common fixed-point number representations, namely: unsigned, sign-magnitude, fractional, ten's and two's complement notations. The main design goal is to collapse multiple complex arithmetic

  6. Use of trapezoidal shaping algorithm in the digital multi-channel system

    International Nuclear Information System (INIS)

    Wang Jihong; Wang Lianghou; Fang Zongliang

    2011-01-01

    It discusses one kind of digital filter technology-trapezoidal algorithm based on actual need of studying the digital multi-channel. Firstly, demonstrating the feasibility of the arithmetic with theoretical analysis; secondly, predigesting the process of the arithmetic; thirdly, simulating with MATLAB; lastly, using the arithmetic to measure data. The result of testing indicates trapezoidal shaping algorithm accords with the need of digital multi-channel shaping extraordinary. The best filter can be obtained by means of setting parameter due to superiority of digital multi-channel. (authors)

  7. Cognitive precursors of arithmetic development in primary school children with cerebral palsy.

    Science.gov (United States)

    Van Rooijen, M; Verhoeven, L; Smits, D W; Dallmeijer, A J; Becher, J G; Steenbergen, B

    2014-04-01

    The aim of this study was to examine the development of arithmetic performance and its cognitive precursors in children with CP from 7 till 9 years of age. Previous research has shown that children with CP are generally delayed in arithmetic performance compared to their typically developing peers. In children with CP, the developmental trajectory of the ability to solve addition- and subtraction tasks has, however, rarely been studied, as well as the cognitive factors affecting this trajectory. Sixty children (M=7.2 years, SD=.23 months at study entry) with CP participated in this study. Standardized tests were administered to assess arithmetic performance, word decoding skills, non-verbal intelligence, and working memory. The results showed that the ability to solve addition- and subtraction tasks increased over a two year period. Word decoding skills were positively related to the initial status of arithmetic performance. In addition, non-verbal intelligence and working memory were associated with the initial status and growth rate of arithmetic performance from 7 till 9 years of age. The current study highlights the importance of non-verbal intelligence and working memory to the development of arithmetic performance of children with CP. Copyright © 2014 Elsevier Ltd. All rights reserved.

  8. Pricing and hedging of arithmetic Asian options via the Edgeworth series expansion approach

    Directory of Open Access Journals (Sweden)

    Weiping Li

    2016-03-01

    Full Text Available In this paper, we derive a pricing formula for arithmetic Asian options by using the Edgeworth series expansion. Our pricing formula consists of a Black-Scholes-Merton type formula and a finite sum with the estimation of the remainder term. Moreover, we present explicitly a method to compute each term in our pricing formula. The hedging formulas (greek letters for the arithmetic Asian options are obtained as well. Our formulas for the long lasting question on pricing and hedging arithmetic Asian options are easy to implement with enough accuracy. Our numerical illustration shows that the arithmetic Asian options worths less than the European options under the standard Black-Scholes assumptions, verifies theoretically that the volatility of the arithmetic average is less than the one of the underlying assets, and also discovers an interesting phenomena that the arithmetic Asian option for large fixed strikes such as stocks has higher volatility (elasticity than the plain European option. However, the elasticity of the arithmetic Asian options for small fixed strikes as trading in currencies and commodity products is much less than the elasticity of the plain European option. These findings are consistent with the ones from the hedgings with respect to the time to expiration, the strike, the present underlying asset price, the interest rate and the volatility.

  9. Energy efficient smartphone-based activity recognition using fixed-point arithmetic

    OpenAIRE

    Anguita, Davide; Ghio, Alessandro; Oneto, Luca; Llanas Parra, Francesc Xavier; Reyes Ortiz, Jorge Luis

    2013-01-01

    In this paper we propose a novel energy efficient approach for the recognition of human activities using smartphones as wearable sensing devices, targeting assisted living applications such as remote patient activity monitoring for the disabled and the elderly. The method exploits fixed-point arithmetic to propose a modified multiclass Support Vector Machine (SVM) learning algorithm, allowing to better pre- serve the smartphone battery lifetime with respect to the conventional flo...

  10. Construction of Quasi-Cyclic LDPC Codes Based on Fundamental Theorem of Arithmetic

    Directory of Open Access Journals (Sweden)

    Hai Zhu

    2018-01-01

    Full Text Available Quasi-cyclic (QC LDPC codes play an important role in 5G communications and have been chosen as the standard codes for 5G enhanced mobile broadband (eMBB data channel. In this paper, we study the construction of QC LDPC codes based on an arbitrary given expansion factor (or lifting degree. First, we analyze the cycle structure of QC LDPC codes and give the necessary and sufficient condition for the existence of short cycles. Based on the fundamental theorem of arithmetic in number theory, we divide the integer factorization into three cases and present three classes of QC LDPC codes accordingly. Furthermore, a general construction method of QC LDPC codes with girth of at least 6 is proposed. Numerical results show that the constructed QC LDPC codes perform well over the AWGN channel when decoded with the iterative algorithms.

  11. Cryptanalysis of a chaos-based cryptosystem with an embedded adaptive arithmetic coder

    International Nuclear Information System (INIS)

    Wang Xing-Yuan; Xie Yi-Xin

    2011-01-01

    In this paper, we analyse a new chaos-based cryptosystem with an embedded adaptive arithmetic coder, which was proposed by Li Heng-Jian and Zhang J S (Li H J and Zhang J S 2010 Chin. Phys. B 19 050508). Although this new method has a better compression performance than its original version, it is found that there are some problems with its security and decryption processes. In this paper, it is shown how to obtain a great deal of plain text from the cipher text without prior knowledge of the secret key. After discussing the security and decryption problems of the Li Heng-Jian et al. algorithm, we propose an improved chaos-based cryptosystem with an embedded adaptive arithmetic coder that is more secure. (general)

  12. Multiple Paths to Mathematics Practice in Al-Kashi's Key to Arithmetic

    Science.gov (United States)

    Taani, Osama

    2014-01-01

    In this paper, I discuss one of the most distinguishing features of Jamshid al-Kashi's pedagogy from his Key to Arithmetic, a well-known Arabic mathematics textbook from the fifteenth century. This feature is the multiple paths that he includes to find a desired result. In the first section light is shed on al-Kashi's life and his contributions to mathematics and astronomy. Section 2 starts with a brief discussion of the contents and pedagogy of the Key to Arithmetic. Al-Kashi's multiple approaches are discussed through four different examples of his versatility in presenting a topic from multiple perspectives. These examples are multiple definitions, multiple algorithms, multiple formulas, and multiple methods for solving word problems. Section 3 is devoted to some benefits that can be gained by implementing al-Kashi's multiple paths approach in modern curricula. For this discussion, examples from two teaching modules taken from the Key to Arithmetic and implemented in Pre-Calculus and mathematics courses for preservice teachers are discussed. Also, the conclusions are supported by some aspects of these modules. This paper is an attempt to help mathematics educators explore more benefits from reading from original sources.

  13. Strategies of solving arithmetic word problems in students with learning difficulties in mathematics

    OpenAIRE

    Kalan, Marko

    2015-01-01

    Problem solving as an important skill is, beside arithmetic, measure and algebra, included in standards of school mathematics (National Council of Teachers of Mathematics) (NCTM, 2000) and needed as a necessary skill for successfulness in science, technology, engineering and mathematics (STEM) (National Mathematics Advisory Panel, 2008). Since solving of human problems is connected to the real life, the arithmetic word problems (in short AWP) are an important kind of mathematics tasks in scho...

  14. Weak Arithmetic Completeness of Object-Oriented First-Order Assertion Networks

    NARCIS (Netherlands)

    C.P.T. de Gouw (Stijn); F.S. de Boer (Frank); W. Ahrendt (Wolfgang); R. Bubel (Richard); P. van Emde Boas; F.C.A. Groen; G.F. Italiano; J.R. Nawrocki; H. Sack

    2013-01-01

    htmlabstractWe present a completeness proof of the inductive assertion method for object-oriented programs extended with auxiliary variables. The class of programs considered are assumed to compute over structures which include the standard interpretation of Presburger arithmetic. Further, the

  15. Curiosities of arithmetic gases

    International Nuclear Information System (INIS)

    Bakas, I.; Bowick, M.J.

    1991-01-01

    Statistical mechanical systems with an exponential density of states are considered. The arithmetic analog of parafermions of arbitrary order is constructed and a formula for boson-parafermion equivalence is obtained using properties of the Riemann zeta function. Interactions (nontrivial mixing) among arithmetic gases using the concept of twisted convolutions are also introduced. Examples of exactly solvable models are discussed in detail

  16. Arithmetic learning in advanced age.

    Science.gov (United States)

    Zamarian, Laura; Scherfler, Christoph; Kremser, Christian; Pertl, Marie-Theres; Gizewski, Elke; Benke, Thomas; Delazer, Margarete

    2018-01-01

    Acquisition of numerical knowledge and understanding of numerical information are crucial for coping with the changing demands of our digital society. In this study, we assessed arithmetic learning in older and younger individuals in a training experiment including brain imaging. In particular, we assessed age-related effects of training intensity, prior arithmetic competence, and neuropsychological variables on the acquisition of new arithmetic knowledge and on the transfer to new, unknown problems. Effects were assessed immediately after training and after 3 months. Behavioural results showed higher training effects for younger individuals than for older individuals and significantly better performance after 90 problem repetitions than after 30 repetitions in both age groups. A correlation analysis indicated that older adults with lower memory and executive functions at baseline could profit more from intensive training. Similarly, training effects in the younger group were higher for those individuals who had lower arithmetic competence and executive functions prior to intervention. In younger adults, successful transfer was associated with higher executive functions. Memory and set-shifting emerged as significant predictors of training effects in the older group. For the younger group, prior arithmetic competence was a significant predictor of training effects, while cognitive flexibility was a predictor of transfer effects. After training, a subgroup of participants underwent an MRI assessment. A voxel-based morphometry analysis showed a significant interaction between training effects and grey matter volume of the right middle temporal gyrus extending to the angular gyrus for the younger group relative to the older group. The reverse contrast (older group vs. younger group) did not yield any significant results. These results suggest that improvements in arithmetic competence are supported by temporo-parietal areas in the right hemisphere in younger

  17. 0011-0030.Data Representation amp Computer Arithmetic6 IEEE ...

    Indian Academy of Sciences (India)

    Home; public; Volumes; reso; 021; 01; 0011-0030.Data Representation amp Computer Arithmetic6 IEEE Standard Double Precision FormatIn.pdf. 404! error. The page your are looking for can not be found! Please check the link or use the navigation bar at the top. YouTube; Twitter; Facebook; Blog. Academy News.

  18. Knowing, Applying, and Reasoning about Arithmetic: Roles of Domain-General and Numerical Skills in Multiple Domains of Arithmetic Learning

    Science.gov (United States)

    Zhang, Xiao; Räsänen, Pekka; Koponen, Tuire; Aunola, Kaisa; Lerkkanen, Marja-Kristiina; Nurmi, Jari-Erik

    2017-01-01

    The longitudinal relations of domain-general and numerical skills at ages 6-7 years to 3 cognitive domains of arithmetic learning, namely knowing (written computation), applying (arithmetic word problems), and reasoning (arithmetic reasoning) at age 11, were examined for a representative sample of 378 Finnish children. The results showed that…

  19. Conceptual Knowledge of Fraction Arithmetic

    Science.gov (United States)

    Siegler, Robert S.; Lortie-Forgues, Hugues

    2015-01-01

    Understanding an arithmetic operation implies, at minimum, knowing the direction of effects that the operation produces. However, many children and adults, even those who execute arithmetic procedures correctly, may lack this knowledge on some operations and types of numbers. To test this hypothesis, we presented preservice teachers (Study 1),…

  20. Lossless Authentication Watermarking Based on Adaptive Modular Arithmetic

    Directory of Open Access Journals (Sweden)

    H. Yang

    2010-04-01

    Full Text Available Reversible watermarking schemes based on modulo-256 addition may cause annoying salt-and-pepper noise. To avoid the salt-and-pepper noise, a reversible watermarking scheme using human visual perception characteristics and adaptive modular arithmetic is proposed. First, a high-bit residual image is obtained by extracting the most significant bits (MSB of the original image, and a new spatial visual perception model is built according to the high-bit residual image features. Second, the watermark strength and the adaptive divisor of modulo operation for each pixel are determined by the visual perception model. Finally, the watermark is embedded into different least significant bits (LSB of original image with adaptive modulo addition. The original image can be losslessly recovered if the stego-image has not been altered. Extensive experiments show that the proposed algorithm eliminates the salt-and-pepper noise effectively, and the visual quality of the stego-image with the proposed algorithm has been dramatically improved over some existing reversible watermarking algorithms. Especially, the stegoimage of this algorithm has about 9.9864 dB higher PSNR value than that of modulo-256 addition based reversible watermarking scheme.

  1. An Arithmetic-Algebraic Work Space for the Promotion of Arithmetic and Algebraic Thinking: Triangular Numbers

    Science.gov (United States)

    Hitt, Fernando; Saboya, Mireille; Cortés Zavala, Carlos

    2016-01-01

    This paper presents an experiment that attempts to mobilise an arithmetic-algebraic way of thinking in order to articulate between arithmetic thinking and the early algebraic thinking, which is considered a prelude to algebraic thinking. In the process of building this latter way of thinking, researchers analysed pupils' spontaneous production…

  2. On Chudnovsky-Based Arithmetic Algorithms in Finite Fields

    OpenAIRE

    Atighehchi, Kevin; Ballet, Stéphane; Bonnecaze, Alexis; Rolland, Robert

    2015-01-01

    Thanks to a new construction of the so-called Chudnovsky-Chudnovsky multiplication algorithm, we design efficient algorithms for both the exponentiation and the multiplication in finite fields. They are tailored to hardware implementation and they allow computations to be parallelized while maintaining a low number of bilinear multiplications. We give an example with the finite field ${\\mathbb F}_{16^{13}}$.

  3. Conceptual Knowledge of Decimal Arithmetic

    Science.gov (United States)

    Lortie-Forgues, Hugues; Siegler, Robert S.

    2017-01-01

    In 2 studies (Ns = 55 and 54), the authors examined a basic form of conceptual understanding of rational number arithmetic, the direction of effect of decimal arithmetic operations, at a level of detail useful for informing instruction. Middle school students were presented tasks examining knowledge of the direction of effects (e.g., "True or…

  4. Quality of Arithmetic Education for Children with Cerebral Palsy

    Science.gov (United States)

    Jenks, Kathleen M.; de Moor, Jan; van Lieshout, Ernest C. D. M.; Withagen, Floortje

    2010-01-01

    The aim of this exploratory study was to investigate the quality of arithmetic education for children with cerebral palsy. The use of individual educational plans, amount of arithmetic instruction time, arithmetic instructional grouping, and type of arithmetic teaching method were explored in three groups: children with cerebral palsy (CP) in…

  5. Improved FHT Algorithms for Fast Computation of the Discrete Hartley Transform

    Directory of Open Access Journals (Sweden)

    M. T. Hamood

    2013-05-01

    Full Text Available In this paper, by using the symmetrical properties of the discrete Hartley transform (DHT, an improved radix-2 fast Hartley transform (FHT algorithm with arithmetic complexity comparable to that of the real-valued fast Fourier transform (RFFT is developed. It has a simple and regular butterfly structure and possesses the in-place computation property. Furthermore, using the same principles, the development can be extended to more efficient radix-based FHT algorithms. An example for the improved radix-4 FHT algorithm is given to show the validity of the presented method. The arithmetic complexity for the new algorithms are computed and then compared with the existing FHT algorithms. The results of these comparisons have shown that the developed algorithms reduce the number of multiplications and additions considerably.

  6. Arithmetic Training Does Not Improve Approximate Number System Acuity

    Directory of Open Access Journals (Sweden)

    Marcus Lindskog

    2016-10-01

    Full Text Available The Approximate Number System (ANS is thought to support non-symbolic representations of numerical magnitudes in humans. Recently much debate has focused on the causal direction for an observed relation between ANS acuity and arithmetic fluency. Here we investigate if arithmetic training can improve ANS acuity. We show with an experimental training study consisting of six 45-minute training sessions that although feedback during arithmetic training improves arithmetic performance substantially, it does not influence ANS acuity. Hence, we find no support for a causal link where symbolic arithmetic training influences the ANS acuity. Further, although short-term number memory is likely involved in arithmetic tasks we did not find that short-term memory capacity for numbers, measured by a digit-span test, was effected by arithmetic training. This suggests that the improvement in arithmetic fluency may have occurred independent of short-term memory efficiency, but rather due to long-term memory processes and/or mental calculation strategy development. The theoretical implications of these findings are discussed.

  7. Image Steganography of Multiple File Types with Encryption and Compression Algorithms

    Directory of Open Access Journals (Sweden)

    Ernest Andreigh C. Centina

    2017-05-01

    Full Text Available The goals of this study were to develop a system intended for securing files through the technique of image steganography integrated with cryptography by utilizing ZLIB Algorithm for compressing and decompressing secret files, DES Algorithm for encryption and decryption, and Least Significant Bit Algorithm for file embedding and extraction to avoid compromise on highly confidential files from exploits of unauthorized persons. Ensuing to this, the system is in acc ordance with ISO 9126 international quality standards. Every quality criteria of the system was evaluated by 10 Information Technology professionals, and the arithmetic Mean and Standard Deviation of the survey were computed. The result exhibits that m ost of them strongly agreed that the system is excellently effective based on Functionality, Reliability, Usability, Efficiency, Maintainability and Portability conformance to ISO 9126 standards. The system was found to be a useful tool for both governmen t agencies and private institutions for it could keep not only the message secret but also the existence of that particular message or file et maintaining the privacy of highly confidential and sensitive files from unauthorized access.

  8. Personal Experience and Arithmetic Meaning in Semantic Dementia

    Science.gov (United States)

    Julien, Camille L.; Neary, David; Snowden, Julie S.

    2010-01-01

    Arithmetic skills are generally claimed to be preserved in semantic dementia (SD), suggesting functional independence of arithmetic knowledge from other aspects of semantic memory. However, in a recent case series analysis we showed that arithmetic performance in SD is not entirely normal. The finding of a direct association between severity of…

  9. Improvement of Frequency Locking Algorithm for Atomic Frequency Standards

    Science.gov (United States)

    Park, Young-Ho; Kang, Hoonsoo; Heyong Lee, Soo; Eon Park, Sang; Lee, Jong Koo; Lee, Ho Seong; Kwon, Taeg Yong

    2010-09-01

    The authors describe a novel method of frequency locking algorithm for atomic frequency standards. The new algorithm for locking the microwave frequency to the Ramsey resonance is compared with the old one that had been employed in the cesium atomic beam frequency standards such as NIST-7 and KRISS-1. Numerical simulations for testing the performance of the algorithm show that the new method has a noise filtering performance superior to the old one by a factor of 1.2 for the flicker signal noise and 1.4 for random-walk signal noise. The new algorithm can readily be used to enhance the frequency stability for a digital servo employing the slow square wave frequency modulation.

  10. Optical modular arithmetic

    Science.gov (United States)

    Pavlichin, Dmitri S.; Mabuchi, Hideo

    2014-06-01

    Nanoscale integrated photonic devices and circuits offer a path to ultra-low power computation at the few-photon level. Here we propose an optical circuit that performs a ubiquitous operation: the controlled, random-access readout of a collection of stored memory phases or, equivalently, the computation of the inner product of a vector of phases with a binary selector" vector, where the arithmetic is done modulo 2pi and the result is encoded in the phase of a coherent field. This circuit, a collection of cascaded interferometers driven by a coherent input field, demonstrates the use of coherence as a computational resource, and of the use of recently-developed mathematical tools for modeling optical circuits with many coupled parts. The construction extends in a straightforward way to the computation of matrix-vector and matrix-matrix products, and, with the inclusion of an optical feedback loop, to the computation of a weighted" readout of stored memory phases. We note some applications of these circuits for error correction and for computing tasks requiring fast vector inner products, e.g. statistical classification and some machine learning algorithms.

  11. Numerical Magnitude Representations Influence Arithmetic Learning

    Science.gov (United States)

    Booth, Julie L.; Siegler, Robert S.

    2008-01-01

    This study examined whether the quality of first graders' (mean age = 7.2 years) numerical magnitude representations is correlated with, predictive of, and causally related to their arithmetic learning. The children's pretest numerical magnitude representations were found to be correlated with their pretest arithmetic knowledge and to be…

  12. Effective arithmetic in finite fields based on Chudnovsky's multiplication algorithm

    OpenAIRE

    Atighehchi , Kévin; Ballet , Stéphane; Bonnecaze , Alexis; Rolland , Robert

    2016-01-01

    International audience; Thanks to a new construction of the Chudnovsky and Chudnovsky multiplication algorithm, we design efficient algorithms for both the exponentiation and the multiplication in finite fields. They are tailored to hardware implementation and they allow computations to be parallelized, while maintaining a low number of bilinear multiplications.À partir d'une nouvelle construction de l'algorithme de multiplication de Chudnovsky et Chudnovsky, nous concevons des algorithmes ef...

  13. A Computational Model of Fraction Arithmetic

    Science.gov (United States)

    Braithwaite, David W.; Pyke, Aryn A.; Siegler, Robert S.

    2017-01-01

    Many children fail to master fraction arithmetic even after years of instruction, a failure that hinders their learning of more advanced mathematics as well as their occupational success. To test hypotheses about why children have so many difficulties in this area, we created a computational model of fraction arithmetic learning and presented it…

  14. Specificity and Overlap in Skills Underpinning Reading and Arithmetical Fluency

    Science.gov (United States)

    van Daal, Victor; van der Leij, Aryan; Ader, Herman

    2013-01-01

    The aim of this study was to examine unique and common causes of problems in reading and arithmetic fluency. 13- to 14-year-old students were placed into one of five groups: reading disabled (RD, n = 16), arithmetic disabled (AD, n = 34), reading and arithmetic disabled (RAD, n = 17), reading, arithmetic, and listening comprehension disabled…

  15. The Structure of Models of Peano Arithmetic

    CERN Document Server

    Kossak, Roman

    2006-01-01

    Aimed at graduate students and research logicians and mathematicians, this much-awaited text covers over forty years of work on relative classification theory for non-standard models of arithmetic. With graded exercises at the end of each chapter, the book covers basic isomorphism invariants: families of types realized in a model, lattices of elementary substructures and automorphism groups. Many results involve applications of the powerful technique of minimal types due to HaimGaifman, and some of the results are classical but have never been published in a book form before.

  16. ASIC For Complex Fixed-Point Arithmetic

    Science.gov (United States)

    Petilli, Stephen G.; Grimm, Michael J.; Olson, Erlend M.

    1995-01-01

    Application-specific integrated circuit (ASIC) performs 24-bit, fixed-point arithmetic operations on arrays of complex-valued input data. High-performance, wide-band arithmetic logic unit (ALU) designed for use in computing fast Fourier transforms (FFTs) and for performing ditigal filtering functions. Other applications include general computations involved in analysis of spectra and digital signal processing.

  17. Arithmetic groups and their generalizations what, why, and how

    CERN Document Server

    Ji, Lizhen

    2010-01-01

    In one guise or another, many mathematicians are familiar with certain arithmetic groups, such as \\mathbf{Z} or \\mathrm{SL}(n,\\mathbf{Z}). Yet, many applications of arithmetic groups and many connections to other subjects within mathematics are less well known. Indeed, arithmetic groups admit many natural and important generalizations. The purpose of this expository book is to explain, through some brief and informal comments and extensive references, what arithmetic groups and their generalizations are, why they are important to study, and how they can be understood and applied to many fields, such as analysis, geometry, topology, number theory, representation theory, and algebraic geometry. It is hoped that such an overview will shed a light on the important role played by arithmetic groups in modern mathematics.

  18. Inversion of the fermion matrix and the equivalence of the conjugate gradient and Lanczos algorithms

    International Nuclear Information System (INIS)

    Burkitt, A.N.; Irving, A.C.

    1990-01-01

    The Lanczos and conjugate gradient algorithms are widely used in lattice QCD calculations. The previously known close relationship between the two methods is explored and two commonly used implementations are shown to give identically the same results at each iteration, in exact arithmetic, for matrix inversion. The identities between the coefficients of the two algorithms are given, and many of the features of the two algorithms can now be combined. The effects of finite arithmetic are investigated and the particular Lanczos formulation is found to be most stable with respect to rounding errors. (orig.)

  19. A CABAC codec of H.264AVC with secure arithmetic coding

    Science.gov (United States)

    Neji, Nihel; Jridi, Maher; Alfalou, Ayman; Masmoudi, Nouri

    2013-02-01

    This paper presents an optimized H.264/AVC coding system for HDTV displays based on a typical flow with high coding efficiency and statics adaptivity features. For high quality streaming, the codec uses a Binary Arithmetic Encoding/Decoding algorithm with high complexity and a JVCE (Joint Video compression and encryption) scheme. In fact, particular attention is given to simultaneous compression and encryption applications to gain security without compromising the speed of transactions [1]. The proposed design allows us to encrypt the information using a pseudo-random number generator (PRNG). Thus we achieved the two operations (compression and encryption) simultaneously and in a dependent manner which is a novelty in this kind of architecture. Moreover, we investigated the hardware implementation of CABAC (Context-based adaptive Binary Arithmetic Coding) codec. The proposed architecture is based on optimized binarizer/de-binarizer to handle significant pixel rates videos with low cost and high performance for most frequent SEs. This was checked using HD video frames. The obtained synthesis results using an FPGA (Xilinx's ISE) show that our design is relevant to code main profile video stream.

  20. An approach to multicore parallelism using functional programming: A case study based on Presburger Arithmetic

    DEFF Research Database (Denmark)

    Dung, Phan Anh; Hansen, Michael Reichhardt

    2015-01-01

    In this paper we investigate multicore parallelism in the context of functional programming by means of two quantifier-elimination procedures for Presburger Arithmetic: one is based on Cooper’s algorithm and the other is based on the Omega Test. We first develop correct-by-construction prototype...... platform executing on an 8-core machine. A speedup of approximately 4 was obtained for Cooper’s algorithm and a speedup of approximately 6 was obtained for the exact-shadow part of the Omega Test. The considered procedures are complex, memory-intense algorithms on huge formula trees and the case study...... reveals more general applicable techniques and guideline for deriving parallel algorithms from sequential ones in the context of data-intensive tree algorithms. The obtained insights should apply for any strict and impure functional programming language. Furthermore, the results obtained for the exact...

  1. 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.

  2. New technological design of arithmetics

    International Nuclear Information System (INIS)

    Hanitriarivo, R.

    2008-01-01

    There are illogical and irrational rules in numbers writing and pronunciation in almost of languages. A part of the aim is to show the electronic applications possibility of logical and systematic rules which are proposed by Raoelina Andriambololona to write and pronounce numbers; we had studied and created the arithmetic operations representation corresponding in binary basis and in hexadecimal basis. The brand new found concept corresponds as well as the method which uses the matrix product calculation, in according with the writing and the pronunciation of numbers. It was shown how to concept the arithmetic operators in digital electronics; and we proposed and assumed to make headway and to do amelioration for technical conception of calculator and arithmetic unite those are at the basic function of all computers and almost domestic sophisticated machine. The left hand side- right hand side and increasing order writing of number is exploited to build a new computer programming for a scientific calculator. [fr

  3. Perceiving fingers in single-digit arithmetic problems.

    Science.gov (United States)

    Berteletti, Ilaria; Booth, James R

    2015-01-01

    In this study, we investigate in children the neural underpinnings of finger representation and finger movement involved in single-digit arithmetic problems. Evidence suggests that finger representation and finger-based strategies play an important role in learning and understanding arithmetic. Because different operations rely on different networks, we compared activation for subtraction and multiplication problems in independently localized finger somatosensory and motor areas and tested whether activation was related to skill. Brain activations from children between 8 and 13 years of age revealed that only subtraction problems significantly activated finger motor areas, suggesting reliance on finger-based strategies. In addition, larger subtraction problems yielded greater somatosensory activation than smaller problems, suggesting a greater reliance on finger representation for larger numerical values. Interestingly, better performance in subtraction problems was associated with lower activation in the finger somatosensory area. Our results support the importance of fine-grained finger representation in arithmetical skill and are the first neurological evidence for a functional role of the somatosensory finger area in proficient arithmetical problem solving, in particular for those problems requiring quantity manipulation. From an educational perspective, these results encourage investigating whether different finger-based strategies facilitate arithmetical understanding and encourage educational practices aiming at integrating finger representation and finger-based strategies as a tool for instilling stronger numerical sense.

  4. Baby Arithmetic: One Object Plus One Tone

    Science.gov (United States)

    Kobayashi, Tessei; Hiraki, Kazuo; Mugitani, Ryoko; Hasegawa, Toshikazu

    2004-01-01

    Recent studies using a violation-of-expectation task suggest that preverbal infants are capable of recognizing basic arithmetical operations involving visual objects. There is still debate, however, over whether their performance is based on any expectation of the arithmetical operations, or on a general perceptual tendency to prefer visually…

  5. Trace formulae for arithmetical systems

    International Nuclear Information System (INIS)

    Bogomolny, E.B.; Georgeot, B.; Giannoni, M.J.; Schmit, C.

    1992-09-01

    For quantum problems on the pseudo-sphere generated by arithmetic groups there exist special trace formulae, called trace formulae for Hecke operators, which permit the reconstruction of wave functions from the knowledge of periodic orbits. After a short discussion of this subject, the Hecke operators trace formulae are presented for the Dirichlet problem on the modular billiard, which is a prototype of arithmetical systems. The results of numerical computations for these semiclassical type relations are in good agreement with the directly computed eigenfunctions. (author) 23 refs.; 2 figs

  6. 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.

  7. Perceiving fingers in single-digit arithmetic problems

    Directory of Open Access Journals (Sweden)

    Ilaria eBerteletti

    2015-03-01

    Full Text Available In this study, we investigate in children the neural underpinnings of finger representation and finger movement involved in single-digit arithmetic problems. Evidence suggests that finger representation and finger-based strategies play an important role in learning and understanding arithmetic. Because different operations rely on different networks, we compared activation for subtraction and multiplication problems in independently localized finger somatosensory and motor areas and tested whether activation was related to skill. Brain activations from children between 8 and 13 years of age revealed that only subtraction problems significantly activated finger motor areas, suggesting reliance on finger-based strategies. In addition, larger subtraction problems yielded greater somatosensory activation than smaller problems, suggesting a greater reliance on finger representation for larger numerical values. Interestingly, better performance in subtraction problems was associated with lower activation in the finger somatosensory area. Our results support the importance of fine-grained finger representation in arithmetical skill and are the first neurological evidence for a functional role of the somatosensory finger area in proficient arithmetical problem solving, in particular for those problems requiring quantity manipulation. From an educational perspective, these results encourage investigating whether different finger-based strategies facilitate arithmetical understanding and encourage educational practices aiming at integrating finger representation and finger-based strategies as a tool for instilling stronger numerical sense.

  8. Digital image processing an algorithmic approach with Matlab

    CERN Document Server

    Qidwai, Uvais

    2009-01-01

    Introduction to Image Processing and the MATLAB EnvironmentIntroduction Digital Image Definitions: Theoretical Account Image Properties MATLAB Algorithmic Account MATLAB CodeImage Acquisition, Types, and File I/OImage Acquisition Image Types and File I/O Basics of Color Images Other Color Spaces Algorithmic Account MATLAB CodeImage ArithmeticIntroduction Operator Basics Theoretical TreatmentAlgorithmic Treatment Coding ExamplesAffine and Logical Operations, Distortions, and Noise in ImagesIntroduction Affine Operations Logical Operators Noise in Images Distortions in ImagesAlgorithmic Account

  9. Specificity and overlap in skills underpinning reading and arithmetical fluency

    NARCIS (Netherlands)

    van Daal, V.; van der Leij, A.; Adèr, H.

    2013-01-01

    The aim of this study was to examine unique and common causes of problems in reading and arithmetic fluency. 13- to 14-year-old students were placed into one of five groups: reading disabled (RD, n = 16), arithmetic disabled (AD, n = 34), reading and arithmetic disabled (RAD, n = 17), reading,

  10. GSM Channel Equalization Algorithm - Modern DSP Coprocessor Approach

    Directory of Open Access Journals (Sweden)

    M. Drutarovsky

    1999-12-01

    Full Text Available The paper presents basic equations of efficient GSM Viterbi equalizer algorithm based on approximation of GMSK modulation by linear superposition of amplitude modulated pulses. This approximation allows to use Ungerboeck form of channel equalizer with significantly reduced arithmetic complexity. Proposed algorithm can be effectively implemented on the Viterbi and Filter coprocessors of new Motorola DSP56305 digital signal processor. Short overview of coprocessor features related to the proposed algorithm is included.

  11. Arithmetic geometry over global function fields

    CERN Document Server

    Longhi, Ignazio; Trihan, Fabien

    2014-01-01

    This volume collects the texts of five courses given in the Arithmetic Geometry Research Programme 2009–2010 at the CRM Barcelona. All of them deal with characteristic p global fields; the common theme around which they are centered is the arithmetic of L-functions (and other special functions), investigated in various aspects. Three courses examine some of the most important recent ideas in the positive characteristic theory discovered by Goss (a field in tumultuous development, which is seeing a number of spectacular advances): they cover respectively crystals over function fields (with a number of applications to L-functions of t-motives), gamma and zeta functions in characteristic p, and the binomial theorem. The other two are focused on topics closer to the classical theory of abelian varieties over number fields: they give respectively a thorough introduction to the arithmetic of Jacobians over function fields (including the current status of the BSD conjecture and its geometric analogues, and the con...

  12. Training of Attention in Children With Low Arithmetical Achievement

    Directory of Open Access Journals (Sweden)

    Maria Guarnera

    2014-05-01

    Full Text Available This study focuses on the role of attentional processes in arithmetical skills and examines if training of basic attentive skills may improve also working memory abilities reducing arithmetic difficulties. In order to study the efficacy of attentional treatment in arithmetic achievement and in enhancing working memory abilities a test-treatment-retest quasi experimental design was adopted. The research involved 14 children, attending fourth and fifth grades, with Arithmetical Learning Disabilities (ALD assigned to experimental and control conditions. The numerical comprehension and calculation processes were assessed using the ABCA battery (Lucangeli, Tressoldi, & Fiore, 1998. Attentional abilities were evaluated using a multitask computerized assessment battery Attenzione e Concentrazione (Di Nuovo, 2000. WM abilities were evaluated by Listening span task, Digit span backward, Making verbal trails and Making colour trails. The results showed that intensive computerized attention training increased basic attentive skills and arithmetical performances with respect to numeric system in children with ALD. No effect on working memory abilities was found. Results are also important from a clinical perspective, since they may suggest strategies for planning individualized training programs.

  13. Approximate Arithmetic Training Improves Informal Math Performance in Low Achieving Preschoolers

    Directory of Open Access Journals (Sweden)

    Emily Szkudlarek

    2018-05-01

    Full Text Available Recent studies suggest that practice with approximate and non-symbolic arithmetic problems improves the math performance of adults, school aged children, and preschoolers. However, the relative effectiveness of approximate arithmetic training compared to available educational games, and the type of math skills that approximate arithmetic targets are unknown. The present study was designed to (1 compare the effectiveness of approximate arithmetic training to two commercially available numeral and letter identification tablet applications and (2 to examine the specific type of math skills that benefit from approximate arithmetic training. Preschool children (n = 158 were pseudo-randomly assigned to one of three conditions: approximate arithmetic, letter identification, or numeral identification. All children were trained for 10 short sessions and given pre and post tests of informal and formal math, executive function, short term memory, vocabulary, alphabet knowledge, and number word knowledge. We found a significant interaction between initial math performance and training condition, such that children with low pretest math performance benefited from approximate arithmetic training, and children with high pretest math performance benefited from symbol identification training. This effect was restricted to informal, and not formal, math problems. There were also effects of gender, socio-economic status, and age on post-test informal math score after intervention. A median split on pretest math ability indicated that children in the low half of math scores in the approximate arithmetic training condition performed significantly better than children in the letter identification training condition on post-test informal math problems when controlling for pretest, age, gender, and socio-economic status. Our results support the conclusion that approximate arithmetic training may be especially effective for children with low math skills, and that

  14. Approximate Arithmetic Training Improves Informal Math Performance in Low Achieving Preschoolers.

    Science.gov (United States)

    Szkudlarek, Emily; Brannon, Elizabeth M

    2018-01-01

    Recent studies suggest that practice with approximate and non-symbolic arithmetic problems improves the math performance of adults, school aged children, and preschoolers. However, the relative effectiveness of approximate arithmetic training compared to available educational games, and the type of math skills that approximate arithmetic targets are unknown. The present study was designed to (1) compare the effectiveness of approximate arithmetic training to two commercially available numeral and letter identification tablet applications and (2) to examine the specific type of math skills that benefit from approximate arithmetic training. Preschool children ( n = 158) were pseudo-randomly assigned to one of three conditions: approximate arithmetic, letter identification, or numeral identification. All children were trained for 10 short sessions and given pre and post tests of informal and formal math, executive function, short term memory, vocabulary, alphabet knowledge, and number word knowledge. We found a significant interaction between initial math performance and training condition, such that children with low pretest math performance benefited from approximate arithmetic training, and children with high pretest math performance benefited from symbol identification training. This effect was restricted to informal, and not formal, math problems. There were also effects of gender, socio-economic status, and age on post-test informal math score after intervention. A median split on pretest math ability indicated that children in the low half of math scores in the approximate arithmetic training condition performed significantly better than children in the letter identification training condition on post-test informal math problems when controlling for pretest, age, gender, and socio-economic status. Our results support the conclusion that approximate arithmetic training may be especially effective for children with low math skills, and that approximate arithmetic

  15. Arithmetical meadows

    OpenAIRE

    Bergstra, J.A.; Middelburg, C.A.

    2009-01-01

    An inversive meadow is a commutative ring with identity equipped with a multiplicative inverse operation made total by choosing 0 as its value at 0. Previously, inversive meadows were shortly called meadows. A divisive meadow is an inversive meadows with the multiplicative inverse operation replaced by a division operation. In the spirit of Peacock's arithmetical algebra, we introduce variants of inversive and divisive meadows without an additive identity element and an additive inverse opera...

  16. Arithmetic differential equations on $GL_n$, I: differential cocycles

    OpenAIRE

    Buium, Alexandru; Dupuy, Taylor

    2013-01-01

    The theory of differential equations has an arithmetic analogue in which derivatives are replaced by Fermat quotients. One can then ask what is the arithmetic analogue of a linear differential equation. The study of usual linear differential equations is the same as the study of the differential cocycle from $GL_n$ into its Lie algebra given by the logarithmic derivative. However we prove here that there are no such cocycles in the context of arithmetic differential equations. In sequels of t...

  17. [Standard algorithm of molecular typing of Yersinia pestis strains].

    Science.gov (United States)

    Eroshenko, G A; Odinokov, G N; Kukleva, L M; Pavlova, A I; Krasnov, Ia M; Shavina, N Iu; Guseva, N P; Vinogradova, N A; Kutyrev, V V

    2012-01-01

    Development of the standard algorithm of molecular typing of Yersinia pestis that ensures establishing of subspecies, biovar and focus membership of the studied isolate. Determination of the characteristic strain genotypes of plague infectious agent of main and nonmain subspecies from various natural foci of plague of the Russian Federation and the near abroad. Genotyping of 192 natural Y. pestis strains of main and nonmain subspecies was performed by using PCR methods, multilocus sequencing and multilocus analysis of variable tandem repeat number. A standard algorithm of molecular typing of plague infectious agent including several stages of Yersinia pestis differentiation by membership: in main and nonmain subspecies, various biovars of the main subspecies, specific subspecies; natural foci and geographic territories was developed. The algorithm is based on 3 typing methods--PCR, multilocus sequence typing and multilocus analysis of variable tandem repeat number using standard DNA targets--life support genes (terC, ilvN, inv, glpD, napA, rhaS and araC) and 7 loci of variable tandem repeats (ms01, ms04, ms06, ms07, ms46, ms62, ms70). The effectiveness of the developed algorithm is shown on the large number of natural Y. pestis strains. Characteristic sequence types of Y. pestis strains of various subspecies and biovars as well as MLVA7 genotypes of strains from natural foci of plague of the Russian Federation and the near abroad were established. The application of the developed algorithm will increase the effectiveness of epidemiologic monitoring of plague infectious agent, and analysis of epidemics and outbreaks of plague with establishing the source of origin of the strain and routes of introduction of the infection.

  18. Interactive Realizability and the elimination of Skolem functions in Peano Arithmetic

    Directory of Open Access Journals (Sweden)

    Federico Aschieri

    2012-10-01

    Full Text Available We present a new syntactical proof that first-order Peano Arithmetic with Skolem axioms is conservative over Peano Arithmetic alone for arithmetical formulas. This result – which shows that the Excluded Middle principle can be used to eliminate Skolem functions – has been previously proved by other techniques, among them the epsilon substitution method and forcing. In our proof, we employ Interactive Realizability, a computational semantics for Peano Arithmetic which extends Kreisel's modified realizability to the classical case.

  19. Assessing Adult Learner’s Numeracy as Related to Gender and Performance in Arithmetic

    Directory of Open Access Journals (Sweden)

    Adeneye O. A. Awofala

    2014-07-01

    Full Text Available The study investigated adult learner numeracy as related to gender and performance in arithmetic among 32 Nigerian adult learners from one government accredited adult literacy centre in Lagos State using the quantitative research method within the blueprint of descriptive survey design. Data collected were analysed using the descriptive statistics of percentages, mean, and standard deviation and inferential statistics of factor analysis, independent samples t-test, and multiple regression analysis. Findings revealed that numeracy skill assessed by the numeracy self-assessment scale was a multi-dimensional construct (numeracy in everyday life, numeracy in workplace, and numeracy in mathematical tasks. Adult learners showed average numeracy strength as gender differences in perception of numeracy skills and performance in arithmetic among adult learners reached zero-tolerance level. Numeracy in workplace and numeracy in mathematical tasks made statistically significant contributions to the variance in adult learners’ performance in arithmetic. Based on this base line study, it was thus, recommended that future studies in Nigeria should investigate adult learners’ numeracy skills using more robust and psychometrically sound instruments such as the Adult Literacy and Life Skills Survey (ALLS and the International Adult Literacy Survey (IALS.

  20. Cognitive mechanisms underlying third graders' arithmetic skills: Expanding the pathways to mathematics model.

    Science.gov (United States)

    Träff, Ulf; Olsson, Linda; Skagerlund, Kenny; Östergren, Rickard

    2018-03-01

    A modified pathways to mathematics model was used to examine the cognitive mechanisms underlying arithmetic skills in third graders. A total of 269 children were assessed on tasks tapping the four pathways and arithmetic skills. A path analysis showed that symbolic number processing was directly supported by the linguistic and approximate quantitative pathways. The direct contribution from the four pathways to arithmetic proficiency varied; the linguistic pathway supported single-digit arithmetic and word problem solving, whereas the approximate quantitative pathway supported only multi-digit calculation. The spatial processing and verbal working memory pathways supported only arithmetic word problem solving. The notion of hierarchical levels of arithmetic was supported by the results, and the different levels were supported by different constellations of pathways. However, the strongest support to the hierarchical levels of arithmetic were provided by the proximal arithmetic skills. Copyright © 2017 Elsevier Inc. All rights reserved.

  1. Studi Kompresi Data dengan Metode Arithmetic Coding

    OpenAIRE

    Santoso, Petrus

    2001-01-01

    In Bahasa Indonesia : Ada banyak sekali metode kompresi data yang ada saat ini. Sebagian besar metode tersebut bisa dikelompokkan ke dalam salah satu dari dua kelompok besar, statistical based dan dictionary based. Contoh dari dictionary based coding adalah Lempel Ziv Welch dan contoh dari statistical based coding adalah Huffman Coding dan Arithmetic Coding yang merupakan algoritma terbaru. Makalah ini mengulas prinsip-prinsip dari Arithmetic Coding serta keuntungan-keuntungannya dibandi...

  2. Alignment of Custom Standards by Machine Learning Algorithms

    Directory of Open Access Journals (Sweden)

    Adela Sirbu

    2010-09-01

    Full Text Available Building an efficient model for automatic alignment of terminologies would bring a significant improvement to the information retrieval process. We have developed and compared two machine learning based algorithms whose aim is to align 2 custom standards built on a 3 level taxonomy, using kNN and SVM classifiers that work on a vector representation consisting of several similarity measures. The weights utilized by the kNN were optimized with an evolutionary algorithm, while the SVM classifier's hyper-parameters were optimized with a grid search algorithm. The database used for train was semi automatically obtained by using the Coma++ tool. The performance of our aligners is shown by the results obtained on the test set.

  3. Mental Computation or Standard Algorithm? Children's Strategy Choices on Multi-Digit Subtractions

    Science.gov (United States)

    Torbeyns, Joke; Verschaffel, Lieven

    2016-01-01

    This study analyzed children's use of mental computation strategies and the standard algorithm on multi-digit subtractions. Fifty-eight Flemish 4th graders of varying mathematical achievement level were individually offered subtractions that either stimulated the use of mental computation strategies or the standard algorithm in one choice and two…

  4. Operator Arithmetic-Harmonic Mean Inequality on Krein Spaces

    Directory of Open Access Journals (Sweden)

    M. Dehghani

    2014-03-01

    Full Text Available We prove an operator arithmetic-harmonic mean type inequality in Krein space setting, by using some block matrix techniques of indefinite type. We also give an example which shows that the operator arithmetic-geometric-harmonic mean inequality for two invertible selfadjoint operators on Krein spaces is not valid, in general.

  5. Digital speech processing arithmetic and its realization on ADSP-2191 system

    International Nuclear Information System (INIS)

    Zhang Wansheng; Wang Yonggang

    2005-01-01

    The paper reports the realization of LPC arithmetic in fixed-point DSP system. First we introduce the theory of LPC arithmetic and describe the chip (ADSP-2191)'s structure and function relating to the LPC arithmetic; emphasized on the realization process of LPC in ADSP-2191 and its result. (authors)

  6. Matrix inequalities for the difference between arithmetic mean and harmonic mean

    OpenAIRE

    Liao, Wenshi; Wu, Junliang

    2015-01-01

    Motivated by the refinements and reverses of arithmetic-geometric mean and arithmetic-harmonic mean inequalities for scalars and matrices, in this article, we generalize the scalar and matrix inequalities for the difference between arithmetic mean and harmonic mean. In addition, relevant inequalities for the Hilbert-Schmidt norm and determinant are established.

  7. Some studies on arithmetical chaos in classical and quantum mechanics

    International Nuclear Information System (INIS)

    Bolte, J.

    1993-04-01

    Several aspects of classical and quantum mechanics applied to a class of strongly chaotic systems are studied. The latter consists of single particles moving without external forces on surfaces of constant negative Gaussian curvature whose corresponding fundamental groups are supplied with an arithmetic structure. It is shown that the arithmetical features of the considered systems lead to exceptional properties of the corresponding spectra of lengths of closed geodesics (periodic orbits). The most significant one is an exponential growth of degeneracies in these geodesic length spectra. Furthermore, the arithmetical systems are distinguished by a structure that appears as a generalization of geometric symmetries. These pseudosymmetries occur in the quantization of the classical arithmetic systems as Hecke operators, which form an infinite algebra of self-adjoint operators commuting with the Hamiltonian. The statistical properties of quantum energies in the arithmetical systems have previously been identified as exceptional. They do not fit into the general scheme of random matrix theory. It is shown with the help of a simplified model for the spectral form factor how the spectral statistics in arithmetical quantum chaos can be understood by the properties of the corresponding classical geodesic length spectra. A decisive role is played by the exponentially increasing multiplicities of lengths. The model developed for the level spacings distribution and for the number variance is compared to the corresponding quantities obtained from quantum energies for a specific arithmetical system. Finally, the convergence properties of a representation for the Selberg zeta function as a Dirichlet series are studied. It turns out that the exceptional classical and quantum mechanical properties shared by the arithmetical systems prohibit a convergence of this important function in the physically interesting domain. (orig.)

  8. Some uses of the symmetric Lanczos algorithm - and why it works!

    Energy Technology Data Exchange (ETDEWEB)

    Druskin, V.L. [Schlumberger-Doll Research, Ridgefield, CT (United States); Greenbaum, A. [Courant Institute of Mathematical Sciences, New York, NY (United States); Knizhnerman, L.A. [Central Geophysical Expedition, Moscow (Russian Federation)

    1996-12-31

    The Lanczos algorithm uses a three-term recurrence to construct an orthonormal basis for the Krylov space corresponding to a symmetric matrix A and a starting vector q{sub 1}. The vectors and recurrence coefficients produced by this algorithm can be used for a number of purposes, including solving linear systems Au = {var_phi} and computing the matrix exponential e{sup -tA}{var_phi}. Although the vectors produced in finite precision arithmetic are not orthogonal, we show why they can still be used effectively for these purposes. The reason is that the 2-norm of the residual is essentially determined by the tridiagonal matrix and the next recurrence coefficient produced by the finite precision Lanczos computation. It follows that if the same tridiagonal matrix and recurrence coefficient are produced by the exact Lanczos algorithm applied to some other problem, then exact arithmetic bounds on the residual for that problem will hold for the finite precision computation. In order to establish exact arithmetic bounds for the different problem, it is necessary to have some information about the eigenvalues of the new coefficient matrix. Here we make use of information already established in the literature, and we also prove a new result for indefinite matrices.

  9. Extreme-Scale Algorithms & Software Resilience (EASIR) Architecture-Aware Algorithms for Scalable Performance and Resilience on Heterogeneous Architectures

    Energy Technology Data Exchange (ETDEWEB)

    Demmel, James W. [Univ. of California, Berkeley, CA (United States)

    2017-09-14

    This project addresses both communication-avoiding algorithms, and reproducible floating-point computation. Communication, i.e. moving data, either between levels of memory or processors over a network, is much more expensive per operation than arithmetic (measured in time or energy), so we seek algorithms that greatly reduce communication. We developed many new algorithms for both dense and sparse, and both direct and iterative linear algebra, attaining new communication lower bounds, and getting large speedups in many cases. We also extended this work in several ways: (1) We minimize writes separately from reads, since writes may be much more expensive than reads on emerging memory technologies, like Flash, sometimes doing asymptotically fewer writes than reads. (2) We extend the lower bounds and optimal algorithms to arbitrary algorithms that may be expressed as perfectly nested loops accessing arrays, where the array subscripts may be arbitrary affine functions of the loop indices (eg A(i), B(i,j+k, k+3*m-7, …) etc.). (3) We extend our communication-avoiding approach to some machine learning algorithms, such as support vector machines. This work has won a number of awards. We also address reproducible floating-point computation. We define reproducibility to mean getting bitwise identical results from multiple runs of the same program, perhaps with different hardware resources or other changes that should ideally not change the answer. Many users depend on reproducibility for debugging or correctness. However, dynamic scheduling of parallel computing resources, combined with nonassociativity of floating point addition, makes attaining reproducibility a challenge even for simple operations like summing a vector of numbers, or more complicated operations like the Basic Linear Algebra Subprograms (BLAS). We describe an algorithm that computes a reproducible sum of floating point numbers, independent of the order of summation. The algorithm depends only on a

  10. How to be Brilliant at Mental Arithmetic

    CERN Document Server

    Webber, Beryl

    2010-01-01

    How to be Brilliant at Mental Arithmetic addresses the twin pillars of mental arithmetic - mental recall and mental agility. Mental recall depends on familiarity with number bonds and plenty of opportunity to practise. Mental agility depends more on confidence with the number system and the four operations. Using the worksheets in this book, students will learn about: tens and units; addition, subtraction, multiplication and division; addition shortcuts; product squares; quick recall; number se

  11. Highly Efficient Compression Algorithms for Multichannel EEG.

    Science.gov (United States)

    Shaw, Laxmi; Rahman, Daleef; Routray, Aurobinda

    2018-05-01

    The difficulty associated with processing and understanding the high dimensionality of electroencephalogram (EEG) data requires developing efficient and robust compression algorithms. In this paper, different lossless compression techniques of single and multichannel EEG data, including Huffman coding, arithmetic coding, Markov predictor, linear predictor, context-based error modeling, multivariate autoregression (MVAR), and a low complexity bivariate model have been examined and their performances have been compared. Furthermore, a high compression algorithm named general MVAR and a modified context-based error modeling for multichannel EEG have been proposed. The resulting compression algorithm produces a higher relative compression ratio of 70.64% on average compared with the existing methods, and in some cases, it goes up to 83.06%. The proposed methods are designed to compress a large amount of multichannel EEG data efficiently so that the data storage and transmission bandwidth can be effectively used. These methods have been validated using several experimental multichannel EEG recordings of different subjects and publicly available standard databases. The satisfactory parametric measures of these methods, namely percent-root-mean square distortion, peak signal-to-noise ratio, root-mean-square error, and cross correlation, show their superiority over the state-of-the-art compression methods.

  12. Individual differences in children's understanding of inversion and arithmetical skill.

    Science.gov (United States)

    Gilmore, Camilla K; Bryant, Peter

    2006-06-01

    Background and aims. In order to develop arithmetic expertise, children must understand arithmetic principles, such as the inverse relationship between addition and subtraction, in addition to learning calculation skills. We report two experiments that investigate children's understanding of the principle of inversion and the relationship between their conceptual understanding and arithmetical skills. A group of 127 children from primary schools took part in the study. The children were from 2 age groups (6-7 and 8-9 years). Children's accuracy on inverse and control problems in a variety of presentation formats and in canonical and non-canonical forms was measured. Tests of general arithmetic ability were also administered. Children consistently performed better on inverse than control problems, which indicates that they could make use of the inverse principle. Presentation format affected performance: picture presentation allowed children to apply their conceptual understanding flexibly regardless of the problem type, while word problems restricted their ability to use their conceptual knowledge. Cluster analyses revealed three subgroups with different profiles of conceptual understanding and arithmetical skill. Children in the 'high ability' and 'low ability' groups showed conceptual understanding that was in-line with their arithmetical skill, whilst a 3rd group of children had more advanced conceptual understanding than arithmetical skill. The three subgroups may represent different points along a single developmental path or distinct developmental paths. The discovery of the existence of the three groups has important consequences for education. It demonstrates the importance of considering the pattern of individual children's conceptual understanding and problem-solving skills.

  13. Design and Implementation of Numerical Linear Algebra Algorithms on Fixed Point DSPs

    Directory of Open Access Journals (Sweden)

    Gene Frantz

    2007-01-01

    Full Text Available Numerical linear algebra algorithms use the inherent elegance of matrix formulations and are usually implemented using C/C++ floating point representation. The system implementation is faced with practical constraints because these algorithms usually need to run in real time on fixed point digital signal processors (DSPs to reduce total hardware costs. Converting the simulation model to fixed point arithmetic and then porting it to a target DSP device is a difficult and time-consuming process. In this paper, we analyze the conversion process. We transformed selected linear algebra algorithms from floating point to fixed point arithmetic, and compared real-time requirements and performance between the fixed point DSP and floating point DSP algorithm implementations. We also introduce an advanced code optimization and an implementation by DSP-specific, fixed point C code generation. By using the techniques described in the paper, speed can be increased by a factor of up to 10 compared to floating point emulation on fixed point hardware.

  14. Reading instead of reasoning? Predictors of arithmetic skills in children with cochlear implants.

    Science.gov (United States)

    Huber, Maria; Kipman, Ulrike; Pletzer, Belinda

    2014-07-01

    The aim of the present study was to evaluate whether the arithmetic achievement of children with cochlear implants (CI) was lower or comparable to that of their normal hearing peers and to identify predictors of arithmetic achievement in children with CI. In particular we related the arithmetic achievement of children with CI to nonverbal IQ, reading skills and hearing variables. 23 children with CI (onset of hearing loss in the first 24 months, cochlear implantation in the first 60 months of life, atleast 3 years of hearing experience with the first CI) and 23 normal hearing peers matched by age, gender, and social background participated in this case control study. All attended grades two to four in primary schools. To assess their arithmetic achievement, all children completed the "Arithmetic Operations" part of the "Heidelberger Rechentest" (HRT), a German arithmetic test. To assess reading skills and nonverbal intelligence as potential predictors of arithmetic achievement, all children completed the "Salzburger Lesetest" (SLS), a German reading screening, and the Culture Fair Intelligence Test (CFIT), a nonverbal intelligence test. Children with CI did not differ significantly from hearing children in their arithmetic achievement. Correlation and regression analyses revealed that in children with CI, arithmetic achievement was significantly (positively) related to reading skills, but not to nonverbal IQ. Reading skills and nonverbal IQ were not related to each other. In normal hearing children, arithmetic achievement was significantly (positively) related to nonverbal IQ, but not to reading skills. Reading skills and nonverbal IQ were positively correlated. Hearing variables were not related to arithmetic achievement. Children with CI do not show lower performance in non-verbal arithmetic tasks, compared to normal hearing peers. Copyright © 2014. Published by Elsevier Ireland Ltd.

  15. Learning, Realizability and Games in Classical Arithmetic

    Science.gov (United States)

    Aschieri, Federico

    2010-12-01

    In this dissertation we provide mathematical evidence that the concept of learning can be used to give a new and intuitive computational semantics of classical proofs in various fragments of Predicative Arithmetic. First, we extend Kreisel modified realizability to a classical fragment of first order Arithmetic, Heyting Arithmetic plus EM1 (Excluded middle axiom restricted to Sigma^0_1 formulas). We introduce a new realizability semantics we call "Interactive Learning-Based Realizability". Our realizers are self-correcting programs, which learn from their errors and evolve through time. Secondly, we extend the class of learning based realizers to a classical version PCFclass of PCF and, then, compare the resulting notion of realizability with Coquand game semantics and prove a full soundness and completeness result. In particular, we show there is a one-to-one correspondence between realizers and recursive winning strategies in the 1-Backtracking version of Tarski games. Third, we provide a complete and fully detailed constructive analysis of learning as it arises in learning based realizability for HA+EM1, Avigad's update procedures and epsilon substitution method for Peano Arithmetic PA. We present new constructive techniques to bound the length of learning processes and we apply them to reprove - by means of our theory - the classic result of Godel that provably total functions of PA can be represented in Godel's system T. Last, we give an axiomatization of the kind of learning that is needed to computationally interpret Predicative classical second order Arithmetic. Our work is an extension of Avigad's and generalizes the concept of update procedure to the transfinite case. Transfinite update procedures have to learn values of transfinite sequences of non computable functions in order to extract witnesses from classical proofs.

  16. Frege, Dedekind, and Peano on the foundations of arithmetic

    CERN Document Server

    Gillies, Donald

    2013-01-01

    First published in 1982, this reissue contains a critical exposition of the views of Frege, Dedekind and Peano on the foundations of arithmetic. The last quarter of the 19th century witnessed a remarkable growth of interest in the foundations of arithmetic. This work analyses both the reasons for this growth of interest within both mathematics and philosophy and the ways in which this study of the foundations of arithmetic led to new insights in philosophy and striking advances in logic. This historical-critical study provides an excellent introduction to the problems of the philosop

  17. Patterns of problem-solving in children's literacy and arithmetic.

    Science.gov (United States)

    Farrington-Flint, Lee; Vanuxem-Cotterill, Sophie; Stiller, James

    2009-11-01

    Patterns of problem-solving among 5-to-7 year-olds' were examined on a range of literacy (reading and spelling) and arithmetic-based (addition and subtraction) problem-solving tasks using verbal self-reports to monitor strategy choice. The results showed higher levels of variability in the children's strategy choice across Years I and 2 on the arithmetic (addition and subtraction) than literacy-based tasks (reading and spelling). However, across all four tasks, the children showed a tendency to move from less sophisticated procedural-based strategies, which included phonological strategies for reading and spelling and counting-all and finger modellingfor addition and subtraction, to more efficient retrieval methods from Years I to 2. Distinct patterns in children's problem-solving skill were identified on the literacy and arithmetic tasks using two separate cluster analyses. There was a strong association between these two profiles showing that those children with more advanced problem-solving skills on the arithmetic tasks also showed more advanced profiles on the literacy tasks. The results highlight how different-aged children show flexibility in their use of problem-solving strategies across literacy and arithmetical contexts and reinforce the importance of studying variations in children's problem-solving skill across different educational contexts.

  18. PDES, Fips Standard Data Encryption Algorithm

    Energy Technology Data Exchange (ETDEWEB)

    Nessett, D N [Lawrence Livermore National Laboratory (United States)

    1991-03-26

    Description of program or function: PDES performs the National Bureau of Standards FIPS Pub. 46 data encryption/decryption algorithm used for the cryptographic protection of computer data. The DES algorithm is designed to encipher and decipher blocks of data consisting of 64 bits under control of a 64-bit key. The key is generated in such a way that each of the 56 bits used directly by the algorithm are random and the remaining 8 error-detecting bits are set to make the parity of each 8-bit byte of the key odd, i. e. there is an odd number of '1' bits in each 8-bit byte. Each member of a group of authorized users of encrypted computer data must have the key that was used to encipher the data in order to use it. Data can be recovered from cipher only by using exactly the same key used to encipher it, but with the schedule of addressing the key bits altered so that the deciphering process is the reverse of the enciphering process. A block of data to be enciphered is subjected to an initial permutation, then to a complex key-dependent computation, and finally to a permutation which is the inverse of the initial permutation. Two PDES routines are included; both perform the same calculation. One, identified as FDES.MAR, is designed to achieve speed in execution, while the other identified as PDES.MAR, presents a clearer view of how the algorithm is executed

  19. PDES, Fips Standard Data Encryption Algorithm

    International Nuclear Information System (INIS)

    Nessett, D.N.

    1991-01-01

    Description of program or function: PDES performs the National Bureau of Standards FIPS Pub. 46 data encryption/decryption algorithm used for the cryptographic protection of computer data. The DES algorithm is designed to encipher and decipher blocks of data consisting of 64 bits under control of a 64-bit key. The key is generated in such a way that each of the 56 bits used directly by the algorithm are random and the remaining 8 error-detecting bits are set to make the parity of each 8-bit byte of the key odd, i. e. there is an odd number of '1' bits in each 8-bit byte. Each member of a group of authorized users of encrypted computer data must have the key that was used to encipher the data in order to use it. Data can be recovered from cipher only by using exactly the same key used to encipher it, but with the schedule of addressing the key bits altered so that the deciphering process is the reverse of the enciphering process. A block of data to be enciphered is subjected to an initial permutation, then to a complex key-dependent computation, and finally to a permutation which is the inverse of the initial permutation. Two PDES routines are included; both perform the same calculation. One, identified as FDES.MAR, is designed to achieve speed in execution, while the other identified as PDES.MAR, presents a clearer view of how the algorithm is executed

  20. The bilinear complexity and practical algorithms for matrix multiplication

    Science.gov (United States)

    Smirnov, A. V.

    2013-12-01

    A method for deriving bilinear algorithms for matrix multiplication is proposed. New estimates for the bilinear complexity of a number of problems of the exact and approximate multiplication of rectangular matrices are obtained. In particular, the estimate for the boundary rank of multiplying 3 × 3 matrices is improved and a practical algorithm for the exact multiplication of square n × n matrices is proposed. The asymptotic arithmetic complexity of this algorithm is O( n 2.7743).

  1. Classified one-step high-radix signed-digit arithmetic units

    Science.gov (United States)

    Cherri, Abdallah K.

    1998-08-01

    High-radix number systems enable higher information storage density, less complexity, fewer system components, and fewer cascaded gates and operations. A simple one-step fully parallel high-radix signed-digit arithmetic is proposed for parallel optical computing based on new joint spatial encodings. This reduces hardware requirements and improves throughput by reducing the space-bandwidth produce needed. The high-radix signed-digit arithmetic operations are based on classifying the neighboring input digit pairs into various groups to reduce the computation rules. A new joint spatial encoding technique is developed to present both the operands and the computation rules. This technique increases the spatial bandwidth product of the spatial light modulators of the system. An optical implementation of the proposed high-radix signed-digit arithmetic operations is also presented. It is shown that our one-step trinary signed-digit and quaternary signed-digit arithmetic units are much simpler and better than all previously reported high-radix signed-digit techniques.

  2. Algorithms for worst-case tolerance optimization

    DEFF Research Database (Denmark)

    Schjær-Jacobsen, Hans; Madsen, Kaj

    1979-01-01

    New algorithms are presented for the solution of optimum tolerance assignment problems. The problems considered are defined mathematically as a worst-case problem (WCP), a fixed tolerance problem (FTP), and a variable tolerance problem (VTP). The basic optimization problem without tolerances...... is denoted the zero tolerance problem (ZTP). For solution of the WCP we suggest application of interval arithmetic and also alternative methods. For solution of the FTP an algorithm is suggested which is conceptually similar to algorithms previously developed by the authors for the ZTP. Finally, the VTP...... is solved by a double-iterative algorithm in which the inner iteration is performed by the FTP- algorithm. The application of the algorithm is demonstrated by means of relatively simple numerical examples. Basic properties, such as convergence properties, are displayed based on the examples....

  3. Chaotically encoded particle swarm optimization algorithm and its applications

    International Nuclear Information System (INIS)

    Alatas, Bilal; Akin, Erhan

    2009-01-01

    This paper proposes a novel particle swarm optimization (PSO) algorithm, chaotically encoded particle swarm optimization algorithm (CENPSOA), based on the notion of chaos numbers that have been recently proposed for a novel meaning to numbers. In this paper, various chaos arithmetic and evaluation measures that can be used in CENPSOA have been described. Furthermore, CENPSOA has been designed to be effectively utilized in data mining applications.

  4. Children's Acquisition of Arithmetic Principles: The Role of Experience

    Science.gov (United States)

    Prather, Richard; Alibali, Martha W.

    2011-01-01

    The current study investigated how young learners' experiences with arithmetic equations can lead to learning of an arithmetic principle. The focus was elementary school children's acquisition of the Relation to Operands principle for subtraction (i.e., for natural numbers, the difference must be less than the minuend). In Experiment 1, children…

  5. Task-based evaluation of segmentation algorithms for diffusion-weighted MRI without using a gold standard

    International Nuclear Information System (INIS)

    Jha, Abhinav K; Kupinski, Matthew A; Rodríguez, Jeffrey J; Stephen, Renu M; Stopeck, Alison T

    2012-01-01

    In many studies, the estimation of the apparent diffusion coefficient (ADC) of lesions in visceral organs in diffusion-weighted (DW) magnetic resonance images requires an accurate lesion-segmentation algorithm. To evaluate these lesion-segmentation algorithms, region-overlap measures are used currently. However, the end task from the DW images is accurate ADC estimation, and the region-overlap measures do not evaluate the segmentation algorithms on this task. Moreover, these measures rely on the existence of gold-standard segmentation of the lesion, which is typically unavailable. In this paper, we study the problem of task-based evaluation of segmentation algorithms in DW imaging in the absence of a gold standard. We first show that using manual segmentations instead of gold-standard segmentations for this task-based evaluation is unreliable. We then propose a method to compare the segmentation algorithms that does not require gold-standard or manual segmentation results. The no-gold-standard method estimates the bias and the variance of the error between the true ADC values and the ADC values estimated using the automated segmentation algorithm. The method can be used to rank the segmentation algorithms on the basis of both the ensemble mean square error and precision. We also propose consistency checks for this evaluation technique. (paper)

  6. Bit-wise arithmetic coding for data compression

    Science.gov (United States)

    Kiely, A. B.

    1994-01-01

    This article examines the problem of compressing a uniformly quantized independent and identically distributed (IID) source. We present a new compression technique, bit-wise arithmetic coding, that assigns fixed-length codewords to the quantizer output and uses arithmetic coding to compress the codewords, treating the codeword bits as independent. We examine the performance of this method and evaluate the overhead required when used block-adaptively. Simulation results are presented for Gaussian and Laplacian sources. This new technique could be used as the entropy coder in a transform or subband coding system.

  7. Optimized 4-bit Quantum Reversible Arithmetic Logic Unit

    Science.gov (United States)

    Ayyoub, Slimani; Achour, Benslama

    2017-08-01

    Reversible logic has received a great attention in the recent years due to its ability to reduce the power dissipation. The main purposes of designing reversible logic are to decrease quantum cost, depth of the circuits and the number of garbage outputs. The arithmetic logic unit (ALU) is an important part of central processing unit (CPU) as the execution unit. This paper presents a complete design of a new reversible arithmetic logic unit (ALU) that can be part of a programmable reversible computing device such as a quantum computer. The proposed ALU based on a reversible low power control unit and small performance parameters full adder named double Peres gates. The presented ALU can produce the largest number (28) of arithmetic and logic functions and have the smallest number of quantum cost and delay compared with existing designs.

  8. Cognitive Processes that Account for Mental Addition Fluency Differences between Children Typically Achieving in Arithmetic and Children At-Risk for Failure in Arithmetic

    Science.gov (United States)

    Berg, Derek H.; Hutchinson, Nancy L.

    2010-01-01

    This study investigated whether processing speed, short-term memory, and working memory accounted for the differential mental addition fluency between children typically achieving in arithmetic (TA) and children at-risk for failure in arithmetic (AR). Further, we drew attention to fluency differences in simple (e.g., 5 + 3) and complex (e.g., 16 +…

  9. Early but not late blindness leads to enhanced arithmetic and working memory abilities.

    Science.gov (United States)

    Dormal, Valérie; Crollen, Virginie; Baumans, Christine; Lepore, Franco; Collignon, Olivier

    2016-10-01

    Behavioural and neurophysiological evidence suggest that vision plays an important role in the emergence and development of arithmetic abilities. However, how visual deprivation impacts on the development of arithmetic processing remains poorly understood. We compared the performances of early (EB), late blind (LB) and sighted control (SC) individuals during various arithmetic tasks involving addition, subtraction and multiplication of various complexities. We also assessed working memory (WM) performances to determine if they relate to a blind person's arithmetic capacities. Results showed that EB participants performed better than LB and SC in arithmetic tasks, especially in conditions in which verbal routines and WM abilities are needed. Moreover, EB participants also showed higher WM abilities. Together, our findings demonstrate that the absence of developmental vision does not prevent the development of refined arithmetic skills and can even trigger the refinement of these abilities in specific tasks. Copyright © 2016 Elsevier Ltd. All rights reserved.

  10. Prospective relations between resting-state connectivity of parietal subdivisions and arithmetic competence.

    Science.gov (United States)

    Price, Gavin R; Yeo, Darren J; Wilkey, Eric D; Cutting, Laurie E

    2018-04-01

    The present study investigates the relation between resting-state functional connectivity (rsFC) of cytoarchitectonically defined subdivisions of the parietal cortex at the end of 1st grade and arithmetic performance at the end of 2nd grade. Results revealed a dissociable pattern of relations between rsFC and arithmetic competence among subdivisions of intraparietal sulcus (IPS) and angular gyrus (AG). rsFC between right hemisphere IPS subdivisions and contralateral IPS subdivisions positively correlated with arithmetic competence. In contrast, rsFC between the left hIP1 and the right medial temporal lobe, and rsFC between the left AG and left superior frontal gyrus, were negatively correlated with arithmetic competence. These results suggest that strong inter-hemispheric IPS connectivity is important for math development, reflecting either neurocognitive mechanisms specific to arithmetic processing, domain-general mechanisms that are particularly relevant to arithmetic competence, or structural 'cortical maturity'. Stronger connectivity between IPS, and AG, subdivisions and frontal and temporal cortices, however, appears to be negatively associated with math development, possibly reflecting the ability to disengage suboptimal problem-solving strategies during mathematical processing, or to flexibly reorient task-based networks. Importantly, the reported results pertain even when controlling for reading, spatial attention, and working memory, suggesting that the observed rsFC-behavior relations are specific to arithmetic competence. Copyright © 2017 The Authors. Published by Elsevier Ltd.. All rights reserved.

  11. Performance evaluation of grid-enabled registration algorithms using bronze-standards

    CERN Document Server

    Glatard, T; Montagnat, J

    2006-01-01

    Evaluating registration algorithms is difficult due to the lack of gold standard in most clinical procedures. The bronze standard is a real-data based statistical method providing an alternative registration reference through a computationally intensive image database registration procedure. We propose in this paper an efficient implementation of this method through a grid-interfaced workflow enactor enabling the concurrent processing of hundreds of image registrations in a couple of hours only. The performances of two different grid infrastructures were compared. We computed the accuracy of 4 different rigid registration algorithms on longitudinal MRI images of brain tumors. Results showed an average subvoxel accuracy of 0.4 mm and 0.15 degrees in rotation.

  12. Rewrite systems for integer arithmetic

    NARCIS (Netherlands)

    H.R. Walters (Pum); H. Zantema (Hans)

    1995-01-01

    textabstractWe present three term rewrite systems for integer arithmetic with addition, multiplication, and, in two cases, subtraction. All systems are ground confluent and terminating; termination is proved by semantic labelling and recursive path order. The first system represents numbers by

  13. Number processing and arithmetic skills in children with cochlear implants

    Directory of Open Access Journals (Sweden)

    Silvia ePixner

    2014-12-01

    Full Text Available Though previous findings report that hearing impaired children exhibit impaired language and arithmetic skills, our current understanding of how hearing and the associated language impairments may influence the development of arithmetic skills is still limited. In the current study numerical/arithmetic performance of 45 children with a cochlea implant were compared to that of controls matched for hearing age, intelligence and sex. Our main results were twofold disclosing that children with CI show general as well as specific numerical/arithmetic impairments. On the one hand, we found an increased percentage of children with CI with an indication of dyscalculia symptoms, a general slowing in multiplication and subtraction as well as less accurate number line estimations. On the other hand, however, children with CI exhibited very circumscribed difficulties associated with place-value processing. Performance declined specifically when subtraction required a borrow procedure and number line estimation required the integration of units, tens, and hundreds instead of only units and tens. Thus, it seems that despite initially atypical language development, children with CI are able to acquire arithmetic skills in a qualitatively similar fashion as their normal hearing peers. Nonetheless, when demands on place-value understanding, which has only recently been proposed to be language mediated, hearing impaired children experience specific difficulties.

  14. Advanced topics in the arithmetic of elliptic curves

    CERN Document Server

    Silverman, Joseph H

    1994-01-01

    In the introduction to the first volume of The Arithmetic of Elliptic Curves (Springer-Verlag, 1986), I observed that "the theory of elliptic curves is rich, varied, and amazingly vast," and as a consequence, "many important topics had to be omitted." I included a brief introduction to ten additional topics as an appendix to the first volume, with the tacit understanding that eventually there might be a second volume containing the details. You are now holding that second volume. it turned out that even those ten topics would not fit Unfortunately, into a single book, so I was forced to make some choices. The following material is covered in this book: I. Elliptic and modular functions for the full modular group. II. Elliptic curves with complex multiplication. III. Elliptic surfaces and specialization theorems. IV. Neron models, Kodaira-Neron classification of special fibers, Tate's algorithm, and Ogg's conductor-discriminant formula. V. Tate's theory of q-curves over p-adic fields. VI. Neron's theory of can...

  15. Investigation of an American Arithmetic Text Book (I)

    OpenAIRE

    植村, 憲治; UEMURA, Kenji

    2006-01-01

    The teaching method of mathematics and/or arithmetic essentially does not depend on language or culture. In this paper we introduce and investigate an American arithmetic text book and teacher's book of kindergarten, named "Mathematics" published by McGraw-Hill Company. And we point out the difference of Japanese teaching methods from those of the U.S. especially from the point of the Problem Solving Method which is still not taught in Japan as a system.

  16. Multi-objective optimization in the presence of practical constraints using non-dominated sorting hybrid cuckoo search algorithm

    Directory of Open Access Journals (Sweden)

    M. Balasubbareddy

    2015-12-01

    Full Text Available A novel optimization algorithm is proposed to solve single and multi-objective optimization problems with generation fuel cost, emission, and total power losses as objectives. The proposed method is a hybridization of the conventional cuckoo search algorithm and arithmetic crossover operations. Thus, the non-linear, non-convex objective function can be solved under practical constraints. The effectiveness of the proposed algorithm is analyzed for various cases to illustrate the effect of practical constraints on the objectives' optimization. Two and three objective multi-objective optimization problems are formulated and solved using the proposed non-dominated sorting-based hybrid cuckoo search algorithm. The effectiveness of the proposed method in confining the Pareto front solutions in the solution region is analyzed. The results for single and multi-objective optimization problems are physically interpreted on standard test functions as well as the IEEE-30 bus test system with supporting numerical and graphical results and also validated against existing methods.

  17. Modifying a numerical algorithm for solving the matrix equation X + AX T B = C

    Science.gov (United States)

    Vorontsov, Yu. O.

    2013-06-01

    Certain modifications are proposed for a numerical algorithm solving the matrix equation X + AX T B = C. By keeping the intermediate results in storage and repeatedly using them, it is possible to reduce the total complexity of the algorithm from O( n 4) to O( n 3) arithmetic operations.

  18. A novel chaotic encryption scheme based on arithmetic coding

    International Nuclear Information System (INIS)

    Mi Bo; Liao Xiaofeng; Chen Yong

    2008-01-01

    In this paper, under the combination of arithmetic coding and logistic map, a novel chaotic encryption scheme is presented. The plaintexts are encrypted and compressed by using an arithmetic coder whose mapping intervals are changed irregularly according to a keystream derived from chaotic map and plaintext. Performance and security of the scheme are also studied experimentally and theoretically in detail

  19. Relating arithmetical techniques of proportion to geometry

    DEFF Research Database (Denmark)

    Wijayanti, Dyana

    2015-01-01

    The purpose of this study is to investigate how textbooks introduce and treat the theme of proportion in geometry (similarity) and arithmetic (ratio and proportion), and how these themes are linked to each other in the books. To pursue this aim, we use the anthropological theory of the didactic....... Considering 6 common Indonesian textbooks in use, we describe how proportion is explained and appears in examples and exercises, using an explicit reference model of the mathematical organizations of both themes. We also identify how the proportion themes of the geometry and arithmetic domains are linked. Our...

  20. Rewrite systems for integer arithmetic

    NARCIS (Netherlands)

    Walters, H.R.; Zantema, H.

    1994-01-01

    We present three term rewrite systems for integer arithmetic with addition, multiplication, and, in two cases, subtraction. All systems are ground con uent and terminating; termination is proved by semantic labelling and recursive path order. The first system represents numbers by successor and

  1. RSFQ logic arithmetic

    International Nuclear Information System (INIS)

    Mukhanov, O.A.; Rylov, S.V.; Semenov, V.K.; Vyshenskii, S.V.

    1989-01-01

    Several ways of local timing of the Josephson-junction RSFQ (Rapid Single Flux Quantum) logic elements are proposed, and their peculiarities are discussed. Several examples of serial and parallel pipelined arithmetic blocks using various types of timing are suggested and their possible performance is discussed. Serial devices enable one to perform n-bit functions relatively slowly but using integrated circuits of a moderate integration scale, while parallel pipelined devices are more hardware-wasteful but promise extremely high productivity

  2. Quantifying the Impact of Single Bit Flips on Floating Point Arithmetic

    Energy Technology Data Exchange (ETDEWEB)

    Elliott, James J [ORNL; Mueller, Frank [North Carolina State University; Stoyanov, Miroslav K [ORNL; Webster, Clayton G [ORNL

    2013-08-01

    In high-end computing, the collective surface area, smaller fabrication sizes, and increasing density of components have led to an increase in the number of observed bit flips. If mechanisms are not in place to detect them, such flips produce silent errors, i.e. the code returns a result that deviates from the desired solution by more than the allowed tolerance and the discrepancy cannot be distinguished from the standard numerical error associated with the algorithm. These phenomena are believed to occur more frequently in DRAM, but logic gates, arithmetic units, and other circuits are also susceptible to bit flips. Previous work has focused on algorithmic techniques for detecting and correcting bit flips in specific data structures, however, they suffer from lack of generality and often times cannot be implemented in heterogeneous computing environment. Our work takes a novel approach to this problem. We focus on quantifying the impact of a single bit flip on specific floating-point operations. We analyze the error induced by flipping specific bits in the most widely used IEEE floating-point representation in an architecture-agnostic manner, i.e., without requiring proprietary information such as bit flip rates and the vendor-specific circuit designs. We initially study dot products of vectors and demonstrate that not all bit flips create a large error and, more importantly, expected value of the relative magnitude of the error is very sensitive on the bit pattern of the binary representation of the exponent, which strongly depends on scaling. Our results are derived analytically and then verified experimentally with Monte Carlo sampling of random vectors. Furthermore, we consider the natural resilience properties of solvers based on the fixed point iteration and we demonstrate how the resilience of the Jacobi method for linear equations can be significantly improved by rescaling the associated matrix.

  3. Predicting Arithmetical Achievement from Neuro-Psychological Performance: A Longitudinal Study.

    Science.gov (United States)

    Fayol, Michel; Barrouillet, Pierre; Marinthe, Catherine

    1998-01-01

    Assessed whether performances of 5- and 6-year olds in arithmetic tests can be predicted from their performances in neuropsychological tests. Participants completed neuropsychological, drawing, and arithmetic tests at 5 and 6 years of age. Findings at older age were correctly assumed by conclusions of first evaluation. (LBT)

  4. PandA : pairings and arithmetic

    NARCIS (Netherlands)

    Chuengsatiansup, C.; Naehrig, M.; Ribarski, P.; Schwabe, P.; Cao, Z.; Zhang, F.

    2014-01-01

    This paper introduces PandA, a software framework for Pairings and Arithmetic. It is designed to bring together advances in the efficient computation of cryptographic pairings and the development and implementation of pairing-based protocols. The intention behind the PandA framework is to give

  5. Kodiak: An Implementation Framework for Branch and Bound Algorithms

    Science.gov (United States)

    Smith, Andrew P.; Munoz, Cesar A.; Narkawicz, Anthony J.; Markevicius, Mantas

    2015-01-01

    Recursive branch and bound algorithms are often used to refine and isolate solutions to several classes of global optimization problems. A rigorous computation framework for the solution of systems of equations and inequalities involving nonlinear real arithmetic over hyper-rectangular variable and parameter domains is presented. It is derived from a generic branch and bound algorithm that has been formally verified, and utilizes self-validating enclosure methods, namely interval arithmetic and, for polynomials and rational functions, Bernstein expansion. Since bounds computed by these enclosure methods are sound, this approach may be used reliably in software verification tools. Advantage is taken of the partial derivatives of the constraint functions involved in the system, firstly to reduce the branching factor by the use of bisection heuristics and secondly to permit the computation of bifurcation sets for systems of ordinary differential equations. The associated software development, Kodiak, is presented, along with examples of three different branch and bound problem types it implements.

  6. Children learn spurious associations in their math textbooks: Examples from fraction arithmetic.

    Science.gov (United States)

    Braithwaite, David W; Siegler, Robert S

    2018-04-26

    Fraction arithmetic is among the most important and difficult topics children encounter in elementary and middle school mathematics. Braithwaite, Pyke, and Siegler (2017) hypothesized that difficulties learning fraction arithmetic often reflect reliance on associative knowledge-rather than understanding of mathematical concepts and procedures-to guide choices of solution strategies. They further proposed that this associative knowledge reflects distributional characteristics of the fraction arithmetic problems children encounter. To test these hypotheses, we examined textbooks and middle school children in the United States (Experiments 1 and 2) and China (Experiment 3). We asked the children to predict which arithmetic operation would accompany a specified pair of operands, to generate operands to accompany a specified arithmetic operation, and to match operands and operations. In both countries, children's responses indicated that they associated operand pairs having equal denominators with addition and subtraction, and operand pairs having a whole number and a fraction with multiplication and division. The children's associations paralleled the textbook input in both countries, which was consistent with the hypothesis that children learned the associations from the practice problems. Differences in the effects of such associative knowledge on U.S. and Chinese children's fraction arithmetic performance are discussed, as are implications of these differences for educational practice. (PsycINFO Database Record (c) 2018 APA, all rights reserved).

  7. Evolving aerodynamic airfoils for wind turbines through a genetic algorithm

    Science.gov (United States)

    Hernández, J. J.; Gómez, E.; Grageda, J. I.; Couder, C.; Solís, A.; Hanotel, C. L.; Ledesma, JI

    2017-01-01

    Nowadays, genetic algorithms stand out for airfoil optimisation, due to the virtues of mutation and crossing-over techniques. In this work we propose a genetic algorithm with arithmetic crossover rules. The optimisation criteria are taken to be the maximisation of both aerodynamic efficiency and lift coefficient, while minimising drag coefficient. Such algorithm shows greatly improvements in computational costs, as well as a high performance by obtaining optimised airfoils for Mexico City's specific wind conditions from generic wind turbines designed for higher Reynolds numbers, in few iterations.

  8. Algorithms: economical computation of functions of real matrices

    International Nuclear Information System (INIS)

    Weiss, Z.

    1991-01-01

    An algorithm is presented which economizes on the calculation of F(a), where A is a real matrix and F(x) a real valued function of x, using spectral analysis. Assuming the availability of the software for the calculation of the complete set of eigenvalues and eigen vectors of A, it is shown that the complex matrix arithmetics involved in subsequent operations leading from A to F(A) can be reduced to the size comparable with the analogous problem in real matrix arithmetics. Saving in CPU time and storage has been achieved by utilizing explicitly the property that complex eigenvalues of a real matrix appear in pairs of complex conjugated numbers. (author)

  9. Distributed Arithmetic for Efficient Base-Band Processing in Real-Time GNSS Software Receivers

    Directory of Open Access Journals (Sweden)

    Grégoire Waelchli

    2010-01-01

    Full Text Available The growing market of GNSS capable mobile devices is driving the interest of GNSS software solutions, as they can share many system resources (processor, memory, reducing both the size and the cost of their integration. Indeed, with the increasing performance of modern processors, it becomes now feasible to implement in software a multichannel GNSS receiver operating in real time. However, a major issue with this approach is the large computing resources required for the base-band processing, in particular for the correlation operations. Therefore, new algorithms need to be developed in order to reduce the overall complexity of the receiver architecture. Towards that aim, this paper first introduces the challenges of the software implementation of a GPS receiver, with a main focus given to the base-band processing and correlation operations. It then describes the already existing solutions and, from this, introduces a new algorithm based on distributed arithmetic.

  10. An administrative data validation study of the accuracy of algorithms for identifying rheumatoid arthritis: the influence of the reference standard on algorithm performance.

    Science.gov (United States)

    Widdifield, Jessica; Bombardier, Claire; Bernatsky, Sasha; Paterson, J Michael; Green, Diane; Young, Jacqueline; Ivers, Noah; Butt, Debra A; Jaakkimainen, R Liisa; Thorne, J Carter; Tu, Karen

    2014-06-23

    We have previously validated administrative data algorithms to identify patients with rheumatoid arthritis (RA) using rheumatology clinic records as the reference standard. Here we reassessed the accuracy of the algorithms using primary care records as the reference standard. We performed a retrospective chart abstraction study using a random sample of 7500 adult patients under the care of 83 family physicians contributing to the Electronic Medical Record Administrative data Linked Database (EMRALD) in Ontario, Canada. Using physician-reported diagnoses as the reference standard, we computed and compared the sensitivity, specificity, and predictive values for over 100 administrative data algorithms for RA case ascertainment. We identified 69 patients with RA for a lifetime RA prevalence of 0.9%. All algorithms had excellent specificity (>97%). However, sensitivity varied (75-90%) among physician billing algorithms. Despite the low prevalence of RA, most algorithms had adequate positive predictive value (PPV; 51-83%). The algorithm of "[1 hospitalization RA diagnosis code] or [3 physician RA diagnosis codes with ≥1 by a specialist over 2 years]" had a sensitivity of 78% (95% CI 69-88), specificity of 100% (95% CI 100-100), PPV of 78% (95% CI 69-88) and NPV of 100% (95% CI 100-100). Administrative data algorithms for detecting RA patients achieved a high degree of accuracy amongst the general population. However, results varied slightly from our previous report, which can be attributed to differences in the reference standards with respect to disease prevalence, spectrum of disease, and type of comparator group.

  11. Knowing right from wrong in mental arithmetic judgments: calibration of confidence predicts the development of accuracy.

    Science.gov (United States)

    Rinne, Luke F; Mazzocco, Michèle M M

    2014-01-01

    Does knowing when mental arithmetic judgments are right--and when they are wrong--lead to more accurate judgments over time? We hypothesize that the successful detection of errors (and avoidance of false alarms) may contribute to the development of mental arithmetic performance. Insight into error detection abilities can be gained by examining the "calibration" of mental arithmetic judgments-that is, the alignment between confidence in judgments and the accuracy of those judgments. Calibration may be viewed as a measure of metacognitive monitoring ability. We conducted a developmental longitudinal investigation of the relationship between the calibration of children's mental arithmetic judgments and their performance on a mental arithmetic task. Annually between Grades 5 and 8, children completed a problem verification task in which they rapidly judged the accuracy of arithmetic expressions (e.g., 25 + 50 = 75) and rated their confidence in each judgment. Results showed that calibration was strongly related to concurrent mental arithmetic performance, that calibration continued to develop even as mental arithmetic accuracy approached ceiling, that poor calibration distinguished children with mathematics learning disability from both low and typically achieving children, and that better calibration in Grade 5 predicted larger gains in mental arithmetic accuracy between Grades 5 and 8. We propose that good calibration supports the implementation of cognitive control, leading to long-term improvement in mental arithmetic accuracy. Because mental arithmetic "fluency" is critical for higher-level mathematics competence, calibration of confidence in mental arithmetic judgments may represent a novel and important developmental predictor of future mathematics performance.

  12. Numbers in action: individual differences and interactivity in mental arithmetic.

    Science.gov (United States)

    Guthrie, Lisa G; Vallée-Tourangeau, Frédéric

    2018-02-03

    Previous research indicates that interactive arithmetic tasks may alleviate the deleterious impact of maths anxiety on arithmetic performance. Our aim here was to further test the impact of interactivity on maths-anxious individuals and those with poorer numeracy skills. In the experiment reported here participants completed sums in two interactivity contexts. In a low-interactivity condition, sums were completed with hands down. In a second, high-interactivity condition, participants used moveable number tokens. As anticipated, accuracy and efficiency were greater in the high compared to the low-interactivity condition. Correlational analyses indicated that maths anxiety, objective numeracy, measures of maths expertise and working memory were stronger predictors of performance in the low- than in the high-interactivity conditions. Interactivity transformed the deployment of arithmetic skills, improved performance, and reduced the gap between high- and low-ability individuals. These findings suggest that traditional psychometric efforts that identify the cognitive capacities and dispositions involved in mental arithmetic should take into account the degree of interactivity afforded by the task environment.

  13. Examining the relationship between rapid automatized naming and arithmetic fluency in Chinese kindergarten children.

    Science.gov (United States)

    Cui, Jiaxin; Georgiou, George K; Zhang, Yiyun; Li, Yixun; Shu, Hua; Zhou, Xinlin

    2017-02-01

    Rapid automatized naming (RAN) has been found to predict mathematics. However, the nature of their relationship remains unclear. Thus, the purpose of this study was twofold: (a) to examine how RAN (numeric and non-numeric) predicts a subdomain of mathematics (arithmetic fluency) and (b) to examine what processing skills may account for the RAN-arithmetic fluency relationship. A total of 160 third-year kindergarten Chinese children (83 boys and 77 girls, mean age=5.11years) were assessed on RAN (colors, objects, digits, and dice), nonverbal IQ, visual-verbal paired associate learning, phonological awareness, short-term memory, speed of processing, approximate number system acuity, and arithmetic fluency (addition and subtraction). The results indicated first that RAN was a significant correlate of arithmetic fluency and the correlations did not vary as a function of type of RAN or arithmetic fluency tasks. In addition, RAN continued to predict addition and subtraction fluency even after controlling for all other processing skills. Taken together, these findings challenge the existing theoretical accounts of the RAN-arithmetic fluency relationship and suggest that, similar to reading fluency, multiple processes underlie the RAN-arithmetic fluency relationship. Copyright © 2016 Elsevier Inc. All rights reserved.

  14. Neuroanthropological Understanding of Complex Cognition – Numerosity and Arithmetics

    Directory of Open Access Journals (Sweden)

    Zarja Mursic

    2013-10-01

    Full Text Available Humankind has a long evolutionary history. When we are trying to understand human complex cognition, it is as well important to look back to entire evolution. I will present the thesis that our biological predispositions and culture, together with natural and social environment, are tightly connected. During ontogenetically development we are shaped by various factors, and they enabled humans to develop some aspects of complex cognition, such as mathematics.In the beginning of the article I present the importance of natural and cultural evolution in other animals. In the following part, I briefly examine the field of mathematics – numerosity and arithmetic. Presentation of comparative animal studies, mainly made on primates, provides some interesting examples in animals’ abilities to separate between different quantities. From abilities for numerosity in animals I continue to neuroscientific studies of humans and our ability to solve simple arithmetic tasks. I also mention cross-cultural studies of arithmetic skills. In the final part of the text I present the field neuroanthropology as a possible new pillar of cognitive science. Finally, it is important to connect human evolution and development with animal cognition studies, but as well with cross-cultural studies in shaping of human ability for numerosity and arithmetic.

  15. Torsionfree Sheaves over a Nodal Curve of Arithmetic Genus One

    Indian Academy of Sciences (India)

    We classify all isomorphism classes of stable torsionfree sheaves on an irreducible nodal curve of arithmetic genus one defined over C C . Let be a nodal curve of arithmetic genus one defined over R R , with exactly one node, such that does not have any real points apart from the node. We classify all isomorphism ...

  16. ANALYSIS OF THE CHARACTERISTICS OF INTERNATIONAL STANDARD ALGORITHMS «LIGHTWEIGHT CRYPTOGRAPHY» – ISO/IEC 29192-3:2012

    Directory of Open Access Journals (Sweden)

    A. S. Poljakov

    2014-01-01

    Full Text Available The data on the characteristics of international standard algorithms «lightweight cryptography» while application in hardware implementation based on microchips of FPGA are provided. A compari-son of the characteristics of these algorithms with the characteristics of several widely-used standard encryption algorithms is made and possibilities of lightweight cryptography algorithms are evaluated.

  17. Groups and fields in arithmetic

    NARCIS (Netherlands)

    Kosters, Michiel F.

    2014-01-01

    This thesis consists of 8 chapters in which we discuss various aspects of arithmetic. In the first chapter, we give an introduction to the algebraic theory of valued fields. In the second chapter, we give an introduction to the theory of normal projective curves. In particular, we study curves over

  18. Transcranial direct current stimulation of the posterior parietal cortex modulates arithmetic learning.

    Science.gov (United States)

    Grabner, Roland H; Rütsche, Bruno; Ruff, Christian C; Hauser, Tobias U

    2015-07-01

    The successful acquisition of arithmetic skills is an essential step in the development of mathematical competencies and has been associated with neural activity in the left posterior parietal cortex (PPC). It is unclear, however, whether this brain region plays a causal role in arithmetic skill acquisition and whether arithmetic learning can be modulated by means of non-invasive brain stimulation of this key region. In the present study we addressed these questions by applying transcranial direct current stimulation (tDCS) over the left PPC during a short-term training that simulates the typical path of arithmetic skill acquisition (specifically the transition from effortful procedural to memory-based problem-solving strategies). Sixty participants received either anodal, cathodal or sham tDCS while practising complex multiplication and subtraction problems. The stability of the stimulation-induced learning effects was assessed in a follow-up test 24 h after the training. Learning progress was modulated by tDCS. Cathodal tDCS (compared with sham) decreased learning rates during training and resulted in poorer performance which lasted over 24 h after stimulation. Anodal tDCS showed an operation-specific improvement for subtraction learning. Our findings extend previous studies by demonstrating that the left PPC is causally involved in arithmetic learning (and not only in arithmetic performance) and that even a short-term tDCS application can modulate the success of arithmetic knowledge acquisition. Moreover, our finding of operation-specific anodal stimulation effects suggests that the enhancing effects of tDCS on learning can selectively affect just one of several cognitive processes mediated by the stimulated area. © 2015 Federation of European Neuroscience Societies and John Wiley & Sons Ltd.

  19. An Elementary Algorithm to Evaluate Trigonometric Functions to High Precision

    Science.gov (United States)

    Johansson, B. Tomas

    2018-01-01

    Evaluation of the cosine function is done via a simple Cordic-like algorithm, together with a package for handling arbitrary-precision arithmetic in the computer program Matlab. Approximations to the cosine function having hundreds of correct decimals are presented with a discussion around errors and implementation.

  20. Sabrewing: A lightweight architecture for combined floating-point and integer arithmetic

    NARCIS (Netherlands)

    Bruintjes, Tom; Walters, K.H.G.; Gerez, Sabih H.; Molenkamp, Egbert; Smit, Gerardus Johannes Maria

    In spite of the fact that floating-point arithmetic is costly in terms of silicon area, the joint design of hardware for floating-point and integer arithmetic is seldom considered. While components like multipliers and adders can potentially be shared, floating-point and integer units in

  1. The unique and shared contributions of arithmetic operation understanding and numerical magnitude representation to children's mathematics achievement.

    Science.gov (United States)

    Wong, Terry Tin-Yau

    2017-12-01

    The current study examined the unique and shared contributions of arithmetic operation understanding and numerical magnitude representation to children's mathematics achievement. A sample of 124 fourth graders was tested on their arithmetic operation understanding (as reflected by their understanding of arithmetic principles and the knowledge about the application of arithmetic operations) and their precision of rational number magnitude representation. They were also tested on their mathematics achievement and arithmetic computation performance as well as the potential confounding factors. The findings suggested that both arithmetic operation understanding and numerical magnitude representation uniquely predicted children's mathematics achievement. The findings highlight the significance of arithmetic operation understanding in mathematics learning. Copyright © 2017 Elsevier Inc. All rights reserved.

  2. Dictionary of algebra, arithmetic, and trigonometry

    CERN Document Server

    Krantz, Steven G

    2000-01-01

    Clear, rigorous definitions of mathematical terms are crucial to good scientific and technical writing-and to understanding the writings of others. Scientists, engineers, mathematicians, economists, technical writers, computer programmers, along with teachers, professors, and students, all have the need for comprehensible, working definitions of mathematical expressions. To meet that need, CRC Press proudly introduces its Dictionary of Algebra, Arithmetic, and Trigonometry- the second published volume in the CRC Comprehensive Dictionary of Mathematics. More than three years in development, top academics and professionals from prestigious institutions around the world bring you more than 2,800 detailed definitions, written in a clear, readable style, complete with alternative meanings, and related references.From Abelian cohomology to zero ring and from the very basic to the highly advanced, this unique lexicon includes terms associated with arithmetic, algebra, and trigonometry, with natural overlap into geom...

  3. Self-reference in Arithmetic I

    NARCIS (Netherlands)

    Halbach, Volker; Visser, Albert|info:eu-repo/dai/nl/068579985

    2014-01-01

    A Gödel sentence is often described as a sentence saying about itself that it is not provable, and a Henkin sentence as a sentence stating its own provability. We discuss what it could mean for a sentence of arithmetic to ascribe to itself a property such as provability or unprovability. The

  4. Individual structural differences in left inferior parietal area are associated with schoolchildrens’ arithmetic scores

    Directory of Open Access Journals (Sweden)

    Yongxin eLi

    2013-12-01

    Full Text Available Arithmetic skill is of critical importance for academic achievement, professional success and everyday life, and childhood is the key period to acquire this skill. Neuroimaging studies have identified that left parietal regions are a key neural substrate for representing arithmetic skill. Although the relationship between functional brain activity in left parietal regions and arithmetic skill has been studied in detail, it remains unclear about the relationship between arithmetic achievement and structural properties in left inferior parietal area in schoolchildren. The current study employed a combination of voxel-based morphometry (VBM for high-resolution T1-weighted images and fiber tracking on diffusion tensor imaging (DTI to examine the relationship between structural properties in the inferior parietal area and arithmetic achievement in 10-year-old schoolchildren. VBM of the T1-weighted images revealed that individual differences in arithmetic scores were significantly and positively correlated with the grey matter (GM volume in the left intraparietal sulcus (IPS. Fiber tracking analysis revealed that the forceps major, left superior longitudinal fasciculus (SLF, bilateral inferior longitudinal fasciculus (ILF and inferior fronto-occipital fasciculus (IFOF were the primary pathways connecting the left IPS with other brain areas. Furthermore, the regression analysis of the probabilistic pathways revealed a significant and positive correlation between the fractional anisotropy (FA values in the left SLF, ILF and bilateral IFOF and arithmetic scores. The brain structure-behavior correlation analyses indicated that the GM volumes in the left IPS and the FA values in the tract pathways connecting left IPS were both related to children’s arithmetic achievement. The present findings provide evidence that individual structural differences in the left IPS are associated with arithmetic scores in schoolchildren.

  5. Fast Combinatorial Algorithm for the Solution of Linearly Constrained Least Squares Problems

    Science.gov (United States)

    Van Benthem, Mark H.; Keenan, Michael R.

    2008-11-11

    A fast combinatorial algorithm can significantly reduce the computational burden when solving general equality and inequality constrained least squares problems with large numbers of observation vectors. The combinatorial algorithm provides a mathematically rigorous solution and operates at great speed by reorganizing the calculations to take advantage of the combinatorial nature of the problems to be solved. The combinatorial algorithm exploits the structure that exists in large-scale problems in order to minimize the number of arithmetic operations required to obtain a solution.

  6. Equations for arithmetic pointed tori

    NARCIS (Netherlands)

    Sijsling, J.R.

    2010-01-01

    In 1983, Kisao Takeuchi enumerated all 71 arithmetic (1;e)-groups. This is a special set of discrete subgroups of SL(2,R) of finite covolume and signature (1;e). The corresponding quotients of the upper half plane (called (1;e)-curves) have genus equal to 1 and a single elliptic point of order e.

  7. Solutions to Arithmetic Convolution Equations

    Czech Academy of Sciences Publication Activity Database

    Glöckner, H.; Lucht, L.G.; Porubský, Štefan

    2007-01-01

    Roč. 135, č. 6 (2007), s. 1619-1629 ISSN 0002-9939 R&D Projects: GA ČR GA201/04/0381 Institutional research plan: CEZ:AV0Z10300504 Keywords : arithmetic functions * Dirichlet convolution * polynomial equations * analytic equations * topological algebras * holomorphic functional calculus Subject RIV: BA - General Mathematics Impact factor: 0.520, year: 2007

  8. Memory updating and mental arithmetic

    Directory of Open Access Journals (Sweden)

    Cheng-Ching eHan

    2016-02-01

    Full Text Available Is domain-general memory updating ability predictive of calculation skills or are such skills better predicted by the capacity for updating specifically numerical information? Here, we used multidigit mental multiplication (MMM as a measure for calculating skill as this operation requires the accurate maintenance and updating of information in addition to skills needed for arithmetic more generally. In Experiment 1, we found that only individual differences with regard to a task updating numerical information following addition (MUcalc could predict the performance of MMM, perhaps owing to common elements between the task and MMM. In Experiment 2, new updating tasks were designed to clarify this: a spatial updating task with no numbers, a numerical task with no calculation, and a word task. The results showed that both MUcalc and the spatial task were able to predict the performance of MMM but only with the more difficult problems, while other updating tasks did not predict performance. It is concluded that relevant processes involved in updating the contents of working memory support mental arithmetic in adults.

  9. Language-specific memory for everyday arithmetic facts in Chinese-English bilinguals.

    Science.gov (United States)

    Chen, Yalin; Yanke, Jill; Campbell, Jamie I D

    2016-04-01

    The role of language in memory for arithmetic facts remains controversial. Here, we examined transfer of memory training for evidence that bilinguals may acquire language-specific memory stores for everyday arithmetic facts. Chinese-English bilingual adults (n = 32) were trained on different subsets of simple addition and multiplication problems. Each operation was trained in one language or the other. The subsequent test phase included all problems with addition and multiplication alternating across trials in two blocks, one in each language. Averaging over training language, the response time (RT) gains for trained problems relative to untrained problems were greater in the trained language than in the untrained language. Subsequent analysis showed that English training produced larger RT gains for trained problems relative to untrained problems in English at test relative to the untrained Chinese language. In contrast, there was no evidence with Chinese training that problem-specific RT gains differed between Chinese and the untrained English language. We propose that training in Chinese promoted a translation strategy for English arithmetic (particularly multiplication) that produced strong cross-language generalization of practice, whereas training in English strengthened relatively weak, English-language arithmetic memories and produced little generalization to Chinese (i.e., English training did not induce an English translation strategy for Chinese language trials). The results support the existence of language-specific strengthening of memory for everyday arithmetic facts.

  10. Functional Neuroanatomy Involved in Automatic order Mental Arithmetic and Recitation of the Multiplication Table

    Science.gov (United States)

    Wang, Li-Qun; Saito, Masao

    We used 1.5T functional magnetic resonance imaging (fMRI) to explore that which brain areas contribute uniquely to numeric computation. The BOLD effect activation pattern of metal arithmetic task (successive subtraction: actual calculation task) was compared with multiplication tables repetition task (rote verbal arithmetic memory task) response. The activation found in right parietal lobule during metal arithmetic task suggested that quantitative cognition or numeric computation may need the assistance of sensuous convert, such as spatial imagination and spatial sensuous convert. In addition, this mechanism may be an ’analog algorithm’ in the simple mental arithmetic processing.

  11. Common brain regions underlying different arithmetic operations as revealed by conjunct fMRI-BOLD activation.

    Science.gov (United States)

    Fehr, Thorsten; Code, Chris; Herrmann, Manfred

    2007-10-03

    The issue of how and where arithmetic operations are represented in the brain has been addressed in numerous studies. Lesion studies suggest that a network of different brain areas are involved in mental calculation. Neuroimaging studies have reported inferior parietal and lateral frontal activations during mental arithmetic using tasks of different complexities and using different operators (addition, subtraction, etc.). Indeed, it has been difficult to compare brain activation across studies because of the variety of different operators and different presentation modalities used. The present experiment examined fMRI-BOLD activity in participants during calculation tasks entailing different arithmetic operations -- addition, subtraction, multiplication and division -- of different complexities. Functional imaging data revealed a common activation pattern comprising right precuneus, left and right middle and superior frontal regions during all arithmetic operations. All other regional activations were operation specific and distributed in prominently frontal, parietal and central regions when contrasting complex and simple calculation tasks. The present results largely confirm former studies suggesting that activation patterns due to mental arithmetic appear to reflect a basic anatomical substrate of working memory, numerical knowledge and processing based on finger counting, and derived from a network originally related to finger movement. We emphasize that in mental arithmetic research different arithmetic operations should always be examined and discussed independently of each other in order to avoid invalid generalizations on arithmetics and involved brain areas.

  12. Working Memory in Dutch Children with Reading- and Arithmetic-Related LD

    Science.gov (United States)

    van der Sluis, Sophie; van der Leij, Aryan; de Jong, Peter F.

    2005-01-01

    The aim of the two studies presented in this article was to examine working memory performance in Dutch children with various subtypes of learning disabilities. The performance of children with reading disabilities (RD) was compared to that of children with arithmetic disabilities (AD), children with both reading and arithmetic disabilities (RAD),…

  13. Lossless Image Compression Based on Multiple-Tables Arithmetic Coding

    Directory of Open Access Journals (Sweden)

    Rung-Ching Chen

    2009-01-01

    Full Text Available This paper is intended to present a lossless image compression method based on multiple-tables arithmetic coding (MTAC method to encode a gray-level image f. First, the MTAC method employs a median edge detector (MED to reduce the entropy rate of f. The gray levels of two adjacent pixels in an image are usually similar. A base-switching transformation approach is then used to reduce the spatial redundancy of the image. The gray levels of some pixels in an image are more common than those of others. Finally, the arithmetic encoding method is applied to reduce the coding redundancy of the image. To promote high performance of the arithmetic encoding method, the MTAC method first classifies the data and then encodes each cluster of data using a distinct code table. The experimental results show that, in most cases, the MTAC method provides a higher efficiency in use of storage space than the lossless JPEG2000 does.

  14. Some arithmetically symmetrical bandpass filters

    Science.gov (United States)

    Paranasi, P.; Roy, S. C. D.

    1981-01-01

    A combination of the conventional and Matthaei lowpass-bandpass transformations is shown to result in some bandpass filters having very good arithmetic symmetry. The technique presented is applicable to the Butterworth and inverse Chebyshev types of magnitude approximations and the Bessel type of delay approximations. It is not valid, however, for the Chebyshev and elliptic varieties of filters.

  15. Executive function in relation to arithmetic development in children with cerebral palsy

    NARCIS (Netherlands)

    Jenks, K.M.; de Moor, J.; van Lieshout, E.C.D.M.

    2009-01-01

    Background: Although it is believed that children with cerebral palsy are at high risk for learning difficulties and arithmetic difficulties in particular, few studies have investigated this issue. Methods: Arithmetic ability was longitudinally assessed in children with cerebral palsy in special (n

  16. Domain-General Factors Influencing Numerical and Arithmetic Processing

    Directory of Open Access Journals (Sweden)

    André Knops

    2017-12-01

    Full Text Available This special issue contains 18 articles that address the question how numerical processes interact with domain-general factors. We start the editorial with a discussion of how to define domain-general versus domain-specific factors and then discuss the contributions to this special issue grouped into two core numerical domains that are subject to domain-general influences (see Figure 1. The first group of contributions addresses the question how numbers interact with spatial factors. The second group of contributions is concerned with factors that determine and predict arithmetic understanding, performance and development. This special issue shows that domain-general (Table 1a as well as domain-specific (Table 1b abilities influence numerical and arithmetic performance virtually at all levels and make it clear that for the field of numerical cognition a sole focus on one or several domain-specific factors like the approximate number system or spatial-numerical associations is not sufficient. Vice versa, in most studies that included domain-general and domain-specific variables, domain-specific numerical variables predicted arithmetic performance above and beyond domain-general variables. Therefore, a sole focus on domain-general aspects such as, for example, working memory, to explain, predict and foster arithmetic learning is also not sufficient. Based on the articles in this special issue we conclude that both domain-general and domain-specific factors contribute to numerical cognition. But the how, why and when of their contribution still needs to be better understood. We hope that this special issue may be helpful to readers in constraining future theory and model building about the interplay of domain-specific and domain-general factors.

  17. Non-commutative arithmetic circuits with division

    Czech Academy of Sciences Publication Activity Database

    Hrubeš, Pavel; Wigderson, A.

    2015-01-01

    Roč. 11, Article 14 (2015), s. 357-393 ISSN 1557-2862 EU Projects: European Commission(XE) 339691 - FEALORA Institutional support: RVO:67985840 Keywords : arithmetic circuits * non-commutative rational function * skew field Subject RIV: BA - General Mathematics http://theoryofcomputing.org/articles/v011a014/

  18. Relational thinking: The bridge between arithmetic and algebra

    Directory of Open Access Journals (Sweden)

    Ayhan Kızıltoprak

    2017-09-01

    Full Text Available The purpose of this study is to investigate the development of relational thinking skill, which is an important component of the transition from arithmetic to algebra, of 5th grade students. In the study, the qualitative research method of teaching experiment was used. The research data were collected from six secondary school 5th grade students by means of clinical interviews and teaching episodes. For observing the development of relational thinking, pre and post clinical interviews were also conducted before and after the eight-session teaching experiment. Qualitative analysis of the research data revealed that the relational thinking skills of all the students developed. It was also found that there was an interaction between the development of fundamental arithmetic concepts and relational thinking; that the students developed concepts related to arithmetical operations such as addend and sum; minuend, subtrahend and difference; multiplicator and product; and dividend, divisor and quotient. Moreover, students were able to use these concepts effectivelyalthough they failed to provide formal explanations about the relations between them. In addition, the students perceived the equal sign not only finding a result but also as a symbol used to establish a relation between operations and expressions.

  19. Encryption of Stereo Images after Compression by Advanced Encryption Standard (AES

    Directory of Open Access Journals (Sweden)

    Marwah k Hussien

    2018-04-01

    Full Text Available New partial encryption schemes are proposed, in which a secure encryption algorithm is used to encrypt only part of the compressed data. Partial encryption applied after application of image compression algorithm. Only 0.0244%-25% of the original data isencrypted for two pairs of dif-ferent grayscale imageswiththe size (256 ´ 256 pixels. As a result, we see a significant reduction of time in the stage of encryption and decryption. In the compression step, the Orthogonal Search Algorithm (OSA for motion estimation (the dif-ferent between stereo images is used. The resulting disparity vector and the remaining image were compressed by Discrete Cosine Transform (DCT, Quantization and arithmetic encoding. The image compressed was encrypted by Advanced Encryption Standard (AES. The images were then decoded and were compared with the original images. Experimental results showed good results in terms of Peak Signal-to-Noise Ratio (PSNR, Com-pression Ratio (CR and processing time. The proposed partial encryption schemes are fast, se-cure and do not reduce the compression performance of the underlying selected compression methods

  20. Teachers’ Beliefs and Practices Regarding the Role of Executive Functions in Reading and Arithmetic

    Directory of Open Access Journals (Sweden)

    Shirley Rapoport

    2016-10-01

    Full Text Available The current study investigated early elementary school teachers’ beliefs and practices regarding the role of Executive Functions in reading and arithmetic. A new research questionnaire was developed and judged by professionals in the academia and the field. Reponses were obtained from 144 teachers from Israel. Factor analysis divided the questionnaire into three valid and reliable subscales, reflecting (1 beliefs regarding the contribution of executive functions to reading and arithmetic, (2 pedagogical practices, and (3 a connection between the cognitive mechanisms of reading and arithmetic. Findings indicate that teachers believe executive functions affect students’ performance in reading and arithmetic. These beliefs were also correlated with pedagogical practices. Additionally, special education teachers’ scored higher on the different subscales compared to general education teachers. These findings shed light on the way teachers perceive the cognitive foundations of reading and arithmetic and indicate to which extent these perceptions guide their teaching practices.

  1. Teachers’ Beliefs and Practices Regarding the Role of Executive Functions in Reading and Arithmetic

    Science.gov (United States)

    Rapoport, Shirley; Rubinsten, Orly; Katzir, Tami

    2016-01-01

    The current study investigated early elementary school teachers’ beliefs and practices regarding the role of Executive Functions (EFs) in reading and arithmetic. A new research questionnaire was developed and judged by professionals in the academia and the field. Reponses were obtained from 144 teachers from Israel. Factor analysis divided the questionnaire into three valid and reliable subscales, reflecting (1) beliefs regarding the contribution of EFs to reading and arithmetic, (2) pedagogical practices, and (3) a connection between the cognitive mechanisms of reading and arithmetic. Findings indicate that teachers believe EFs affect students’ performance in reading and arithmetic. These beliefs were also correlated with pedagogical practices. Additionally, special education teachers’ scored higher on the different subscales compared to general education teachers. These findings shed light on the way teachers perceive the cognitive foundations of reading and arithmetic and indicate to which extent these perceptions guide their teaching practices. PMID:27799917

  2. Teachers' Beliefs and Practices Regarding the Role of Executive Functions in Reading and Arithmetic.

    Science.gov (United States)

    Rapoport, Shirley; Rubinsten, Orly; Katzir, Tami

    2016-01-01

    The current study investigated early elementary school teachers' beliefs and practices regarding the role of Executive Functions (EFs) in reading and arithmetic. A new research questionnaire was developed and judged by professionals in the academia and the field. Reponses were obtained from 144 teachers from Israel. Factor analysis divided the questionnaire into three valid and reliable subscales, reflecting (1) beliefs regarding the contribution of EFs to reading and arithmetic, (2) pedagogical practices, and (3) a connection between the cognitive mechanisms of reading and arithmetic. Findings indicate that teachers believe EFs affect students' performance in reading and arithmetic. These beliefs were also correlated with pedagogical practices. Additionally, special education teachers' scored higher on the different subscales compared to general education teachers. These findings shed light on the way teachers perceive the cognitive foundations of reading and arithmetic and indicate to which extent these perceptions guide their teaching practices.

  3. Simple arithmetic: not so simple for highly math anxious individuals.

    Science.gov (United States)

    Chang, Hyesang; Sprute, Lisa; Maloney, Erin A; Beilock, Sian L; Berman, Marc G

    2017-12-01

    Fluency with simple arithmetic, typically achieved in early elementary school, is thought to be one of the building blocks of mathematical competence. Behavioral studies with adults indicate that math anxiety (feelings of tension or apprehension about math) is associated with poor performance on cognitively demanding math problems. However, it remains unclear whether there are fundamental differences in how high and low math anxious individuals approach overlearned simple arithmetic problems that are less reliant on cognitive control. The current study used functional magnetic resonance imaging to examine the neural correlates of simple arithmetic performance across high and low math anxious individuals. We implemented a partial least squares analysis, a data-driven, multivariate analysis method to measure distributed patterns of whole-brain activity associated with performance. Despite overall high simple arithmetic performance across high and low math anxious individuals, performance was differentially dependent on the fronto-parietal attentional network as a function of math anxiety. Specifically, low-compared to high-math anxious individuals perform better when they activate this network less-a potential indication of more automatic problem-solving. These findings suggest that low and high math anxious individuals approach even the most fundamental math problems differently. © The Author (2017). Published by Oxford University Press.

  4. Children Learn Spurious Associations in Their Math Textbooks: Examples from Fraction Arithmetic

    Science.gov (United States)

    Braithwaite, David W.; Siegler, Robert S.

    2018-01-01

    Fraction arithmetic is among the most important and difficult topics children encounter in elementary and middle school mathematics. Braithwaite, Pyke, and Siegler (2017) hypothesized that difficulties learning fraction arithmetic often reflect reliance on associative knowledge--rather than understanding of mathematical concepts and procedures--to…

  5. Uncertainty analysis for dynamic properties of MEMS resonator supported by fuzzy arithmetics

    Directory of Open Access Journals (Sweden)

    A Martowicz

    2016-04-01

    Full Text Available In the paper the application of uncertainty analysis performed formicroelectromechanical resonator is presented. Main objective ofundertaken analysis is to assess the propagation of considered uncertaintiesin the variation of chosen dynamic characteristics of Finite Element model ofmicroresonator. Many different model parameters have been assumed tobe uncertain: geometry and material properties. Apart from total uncertaintypropagation, sensitivity analysis has been carried out to study separateinfluences of all input uncertain characteristics. Uncertainty analysis has beenperformed by means of fuzzy arithmetics in which alpha-cut strategy hasbeen applied to assemble output fuzzy number. Monte Carlo Simulation andGenetic Algorithms have been employed to calculate intervals connectedwith each alpha-cut of searched fuzzy number. Elaborated model ofmicroresonator has taken into account in a simplified way the presence ofsurrounding air and constant electrostatic field.

  6. Arithmetic of Complex Manifolds

    CERN Document Server

    Lange, Herbert

    1989-01-01

    It was the aim of the Erlangen meeting in May 1988 to bring together number theoretists and algebraic geometers to discuss problems of common interest, such as moduli problems, complex tori, integral points, rationality questions, automorphic forms. In recent years such problems, which are simultaneously of arithmetic and geometric interest, have become increasingly important. This proceedings volume contains 12 original research papers. Its main topics are theta functions, modular forms, abelian varieties and algebraic three-folds.

  7. MM Algorithms for Geometric and Signomial Programming.

    Science.gov (United States)

    Lange, Kenneth; Zhou, Hua

    2014-02-01

    This paper derives new algorithms for signomial programming, a generalization of geometric programming. The algorithms are based on a generic principle for optimization called the MM algorithm. In this setting, one can apply the geometric-arithmetic mean inequality and a supporting hyperplane inequality to create a surrogate function with parameters separated. Thus, unconstrained signomial programming reduces to a sequence of one-dimensional minimization problems. Simple examples demonstrate that the MM algorithm derived can converge to a boundary point or to one point of a continuum of minimum points. Conditions under which the minimum point is unique or occurs in the interior of parameter space are proved for geometric programming. Convergence to an interior point occurs at a linear rate. Finally, the MM framework easily accommodates equality and inequality constraints of signomial type. For the most important special case, constrained quadratic programming, the MM algorithm involves very simple updates.

  8. Should we naturalize mind, or should we arithmetize matter?

    Directory of Open Access Journals (Sweden)

    Marchal Bruno

    2017-12-01

    Full Text Available We provide an argument showing that once we assume the mechanist hypothesis in the cognitive science then we have to explain physics from intensional number theory and/or mathematical computer science alone. The proof is constructive. It shows how to derive the physical laws from elementary arithmetic. It makes the computationalist thesis empirically refutable, by comparing the physics extracted from numbers and the inferred physics from observation. The proof shows that if mechanism is true, we cannot naturalize the mind, and we have to arithmetize matter, or beliefs in matter, instead.

  9. Trinary signed-digit arithmetic using an efficient encoding scheme

    Science.gov (United States)

    Salim, W. Y.; Alam, M. S.; Fyath, R. S.; Ali, S. A.

    2000-09-01

    The trinary signed-digit (TSD) number system is of interest for ultrafast optoelectronic computing systems since it permits parallel carry-free addition and borrow-free subtraction of two arbitrary length numbers in constant time. In this paper, a simple coding scheme is proposed to encode the decimal number directly into the TSD form. The coding scheme enables one to perform parallel one-step TSD arithmetic operation. The proposed coding scheme uses only a 5-combination coding table instead of the 625-combination table reported recently for recoded TSD arithmetic technique.

  10. Circuit lower bounds in bounded arithmetics

    Czech Academy of Sciences Publication Activity Database

    Pich, Ján

    2015-01-01

    Roč. 166, č. 1 (2015), s. 29-45 ISSN 0168-0072 R&D Projects: GA AV ČR IAA100190902 Keywords : bounded arithmetic * circuit lower bounds Subject RIV: BA - General Mathematics Impact factor: 0.582, year: 2015 http://www.sciencedirect.com/science/article/pii/S0168007214000888

  11. Fuzzy Logic and Arithmetical Hierarchy III

    Czech Academy of Sciences Publication Activity Database

    Hájek, Petr

    2001-01-01

    Roč. 68, č. 1 (2001), s. 129-142 ISSN 0039-3215 R&D Projects: GA AV ČR IAA1030004 Institutional research plan: AV0Z1030915 Keywords : fuzzy logic * basic fuzzy logic * Lukasiewicz logic * Godel logic * product logic * arithmetical hierarchy Subject RIV: BA - General Mathematics

  12. Inhibition and Shifting in Children with Learning Deficits in Arithmetic and Reading

    Science.gov (United States)

    van der Sluis, Sophie; de Jong, Peter F.; van der Leij, Aryan

    2004-01-01

    The executive functions of inhibition and shifting were studied in arithmetic-disabled children, reading-disabled children, reading plus arithmetic-disabled children, and controls (N = 74). Measures involved the rapid naming of objects, digits, letters, or quantities with or without additional task requirements that reflected inhibition or…

  13. Medical image registration algorithms assesment Bronze Standard application enactment on grids using the MOTEUR workflow engine

    CERN Document Server

    Glatard, T; Pennec, X

    2006-01-01

    Medical image registration is pre-processing needed for many medical image analysis procedures. A very large number of registration algorithms are available today, but their performance is often not known and very difficult to assess due to the lack of gold standard. The Bronze Standard algorithm is a very data and compute intensive statistical approach for quantifying registration algorithms accuracy. In this paper, we describe the Bronze Standard application and we discuss the need for grids to tackle such computations on medical image databases. We demonstrate MOTEUR, a service-based workflow engine optimized for dealing with data intensive applications. MOTEUR eases the enactment of the Bronze Standard and similar applications on the EGEE production grid infrastructure. It is a generic workflow engine, based on current standards and freely available, that can be used to instrument legacy application code at low cost.

  14. A Non-Arithmetical Gödel Logic

    Czech Academy of Sciences Publication Activity Database

    Hájek, Petr

    2005-01-01

    Roč. 13, č. 4 (2005), s. 435-441 ISSN 1367-0751 R&D Projects: GA AV ČR IAA100300503 Institutional research plan: CEZ:AV0Z10300504 Keywords : fuzzy logic * Gödel logic * arithmetical hierarchy Subject RIV: BA - General Mathematics Impact factor: 0.382, year: 2005

  15. An algorithm for solving an arbitrary triangular fully fuzzy Sylvester matrix equations

    Science.gov (United States)

    Daud, Wan Suhana Wan; Ahmad, Nazihah; Malkawi, Ghassan

    2017-11-01

    Sylvester matrix equations played a prominent role in various areas including control theory. Considering to any un-certainty problems that can be occurred at any time, the Sylvester matrix equation has to be adapted to the fuzzy environment. Therefore, in this study, an algorithm for solving an arbitrary triangular fully fuzzy Sylvester matrix equation is constructed. The construction of the algorithm is based on the max-min arithmetic multiplication operation. Besides that, an associated arbitrary matrix equation is modified in obtaining the final solution. Finally, some numerical examples are presented to illustrate the proposed algorithm.

  16. Quantile arithmetic methodology for uncertainty propagation in fault trees

    International Nuclear Information System (INIS)

    Abdelhai, M.; Ragheb, M.

    1986-01-01

    A methodology based on quantile arithmetic, the probabilistic analog to interval analysis, is proposed for the computation of uncertainties propagation in fault tree analysis. The basic events' continuous probability density functions (pdf's) are represented by equivalent discrete distributions by dividing them into a number of quantiles N. Quantile arithmetic is then used to performthe binary arithmetical operations corresponding to the logical gates in the Boolean expression of the top event expression of a given fault tree. The computational advantage of the present methodology as compared with the widely used Monte Carlo method was demonstrated for the cases of summation of M normal variables through the efficiency ratio defined as the product of the labor and error ratios. The efficiency ratio values obtained by the suggested methodology for M = 2 were 2279 for N = 5, 445 for N = 25, and 66 for N = 45 when compared with the results for 19,200 Monte Carlo samples at the 40th percentile point. Another advantage of the approach is that the exact analytical value of the median is always obtained for the top event

  17. Binary Arithmetic From Hariot (CA, 1600 A.D.) to the Computer Age.

    Science.gov (United States)

    Glaser, Anton

    This history of binary arithmetic begins with details of Thomas Hariot's contribution and includes specific references to Hariot's manuscripts kept at the British Museum. A binary code developed by Sir Francis Bacon is discussed. Briefly mentioned are contributions to binary arithmetic made by Leibniz, Fontenelle, Gauss, Euler, Benzout, Barlow,…

  18. Age-related changes in strategic variations during arithmetic problem solving: The role of executive control.

    Science.gov (United States)

    Hinault, T; Lemaire, P

    2016-01-01

    In this review, we provide an overview of how age-related changes in executive control influence aging effects in arithmetic processing. More specifically, we consider the role of executive control in strategic variations with age during arithmetic problem solving. Previous studies found that age-related differences in arithmetic performance are associated with strategic variations. That is, when they accomplish arithmetic problem-solving tasks, older adults use fewer strategies than young adults, use strategies in different proportions, and select and execute strategies less efficiently. Here, we review recent evidence, suggesting that age-related changes in inhibition, cognitive flexibility, and working memory processes underlie age-related changes in strategic variations during arithmetic problem solving. We discuss both behavioral and neural mechanisms underlying age-related changes in these executive control processes. © 2016 Elsevier B.V. All rights reserved.

  19. 多重随机序列在算术编码中的应用%Application of Multiple Random Sequence in Arithmetic Coding

    Institute of Scientific and Technical Information of China (English)

    周明; 冯民富

    2012-01-01

    Arithmetic coding, for its high compression ratio and moderate coding efficiency, plays an important role in the standard of image compression technology. This algorithm depends on only one argument: the occurrence probability of information source symbols. This probability determines the efficiency of compression, and the interval of information source symbols as well. However, the classical arithmetic coding considers no internal structure of the input sequence of information source symbols, but only the probability of single symbols. Finally to which special combinations the coding intervals should be allocated, and whether there exists an effective allocation algorithm, these are still problems to been considered and settled.%算术编码凭借其高效的压缩比以及适度的编码效率,在图像压缩技术标准(比如JPEG等)中有着重要的地位。该算法仅仅依赖于一个参数:信源符号出现的概率。该概率决定了压缩编码的效率,同时也决定了编码过程中信源符号的间隔。然而,经典的算术编码都没有考虑信源符号输入序列的内在结构,仅仅是考虑单个的符号。这些连续的输入组合中的某些组合若大量出现在信源符号中,就有必要考虑这些组合的出现概率了。而最终需要给哪些特定的组合分配编码区间,以及是否有行之有效的分配算法,都需要考虑。

  20. Nonverbal arithmetic in humans: light from noise.

    Science.gov (United States)

    Cordes, Sara; Gallistel, C R; Gelman, Rochel; Latham, Peter

    2007-10-01

    Animal and human data suggest the existence of a cross-species system of analog number representation (e.g., Cordes, Gelman, Gallistel, & Whalen, 2001; Meeck & Church, 1983), which may mediate the computation of statistical regularities in the environment (Gallistel, Gelman, & Cordes, 2006). However, evidence of arithmetic manipulation of these nonverbal magnitude representations is sparse and lacking in depth. This study uses the analysis of variability as a tool for understanding properties of these combinatorial processes. Human subjects participated in tasks requiring responses dependent upon the addition, subtraction, or reproduction of nonverbal counts. Variance analyses revealed that the magnitude of both inputs and answer contributed to the variability in the arithmetic responses, with operand variability dominating. Other contributing factors to the observed variability and implications for logarithmic versus scalar models of magnitude representation are discussed in light of these results.

  1. An arithmetic transference proof of a relative Szemer\\'edi theorem

    OpenAIRE

    Zhao, Yufei

    2013-01-01

    Recently Conlon, Fox, and the author gave a new proof of a relative Szemer\\'edi theorem, which was the main novel ingredient in the proof of the celebrated Green-Tao theorem that the primes contain arbitrarily long arithmetic progressions. Roughly speaking, a relative Szemer\\'edi theorem says that if S is a set of integers satisfying certain conditions, and A is a subset of S with positive relative density, then A contains long arithmetic progressions, and our recent results show that S only ...

  2. A parallel row-based algorithm for standard cell placement with integrated error control

    Science.gov (United States)

    Sargent, Jeff S.; Banerjee, Prith

    1989-01-01

    A new row-based parallel algorithm for standard-cell placement targeted for execution on a hypercube multiprocessor is presented. Key features of this implementation include a dynamic simulated-annealing schedule, row-partitioning of the VLSI chip image, and two novel approaches to control error in parallel cell-placement algorithms: (1) Heuristic Cell-Coloring; (2) Adaptive Sequence Length Control.

  3. The effect of illustrations in arithmetic problem-solving: Effects of increased cognitive load

    NARCIS (Netherlands)

    Berends, I.E.; van Lieshout, E.C.D.M.

    2009-01-01

    Arithmetic word problems are often presented accompanied by illustrations. The present study examined how different types of illustrations influence the speed and accuracy of performance of both good (n = 67) and poor arithmeticians (n = 63). Twenty-four arithmetic word problems were presented with

  4. SeqCompress: an algorithm for biological sequence compression.

    Science.gov (United States)

    Sardaraz, Muhammad; Tahir, Muhammad; Ikram, Ataul Aziz; Bajwa, Hassan

    2014-10-01

    The growth of Next Generation Sequencing technologies presents significant research challenges, specifically to design bioinformatics tools that handle massive amount of data efficiently. Biological sequence data storage cost has become a noticeable proportion of total cost in the generation and analysis. Particularly increase in DNA sequencing rate is significantly outstripping the rate of increase in disk storage capacity, which may go beyond the limit of storage capacity. It is essential to develop algorithms that handle large data sets via better memory management. This article presents a DNA sequence compression algorithm SeqCompress that copes with the space complexity of biological sequences. The algorithm is based on lossless data compression and uses statistical model as well as arithmetic coding to compress DNA sequences. The proposed algorithm is compared with recent specialized compression tools for biological sequences. Experimental results show that proposed algorithm has better compression gain as compared to other existing algorithms. Copyright © 2014 Elsevier Inc. All rights reserved.

  5. An Evaluation of the Sniffer Global Optimization Algorithm Using Standard Test Functions

    Science.gov (United States)

    Butler, Roger A. R.; Slaminka, Edward E.

    1992-03-01

    The performance of Sniffer—a new global optimization algorithm—is compared with that of Simulated Annealing. Using the number of function evaluations as a measure of efficiency, the new algorithm is shown to be significantly better at finding the global minimum of seven standard test functions. Several of the test functions used have many local minima and very steep walls surrounding the global minimum. Such functions are intended to thwart global minimization algorithms.

  6. Acoustic simulation in architecture with parallel algorithm

    Science.gov (United States)

    Li, Xiaohong; Zhang, Xinrong; Li, Dan

    2004-03-01

    In allusion to complexity of architecture environment and Real-time simulation of architecture acoustics, a parallel radiosity algorithm was developed. The distribution of sound energy in scene is solved with this method. And then the impulse response between sources and receivers at frequency segment, which are calculated with multi-process, are combined into whole frequency response. The numerical experiment shows that parallel arithmetic can improve the acoustic simulating efficiency of complex scene.

  7. Arithmetic difficulties in children with cerebral palsy are related to executive function and working memory.

    Science.gov (United States)

    Jenks, Kathleen M; de Moor, Jan; van Lieshout, Ernest C D M

    2009-07-01

    Although it is believed that children with cerebral palsy are at high risk for learning difficulties and arithmetic difficulties in particular, few studies have investigated this issue. Arithmetic ability was longitudinally assessed in children with cerebral palsy in special (n = 41) and mainstream education (n = 16) and controls in mainstream education (n = 16). Second grade executive function and working memory scores were used to predict third grade arithmetic accuracy and response time. Children with cerebral palsy in special education were less accurate and slower than their peers on all arithmetic tests, even after controlling for IQ, whereas children with cerebral palsy in mainstream education performed as well as controls. Although the performance gap became smaller over time, it did not disappear. Children with cerebral palsy in special education showed evidence of executive function and working memory deficits in shifting, updating, visuospatial sketchpad and phonological loop (for digits, not words) whereas children with cerebral palsy in mainstream education only had a deficit in visuospatial sketchpad. Hierarchical regression revealed that, after controlling for intelligence, components of executive function and working memory explained large proportions of unique variance in arithmetic accuracy and response time and these variables were sufficient to explain group differences in simple, but not complex, arithmetic. Children with cerebral palsy are at risk for specific executive function and working memory deficits that, when present, increase the risk for arithmetic difficulties in these children.

  8. Secret Codes, Remainder Arithmetic, and Matrices.

    Science.gov (United States)

    Peck, Lyman C.

    This pamphlet is designed for use as enrichment material for able junior and senior high school students who are interested in mathematics. No more than a clear understanding of basic arithmetic is expected. Students are introduced to ideas from number theory and modern algebra by learning mathematical ways of coding and decoding secret messages.…

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

    International Nuclear Information System (INIS)

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

    2015-01-01

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

  10. The Arithmetic Project Course for Teachers - 8. Topic: Lower Brackets and Upper Brackets. Supplement: Arithmetic With Frames.

    Science.gov (United States)

    Education Development Center, Inc., Newton, MA.

    This is one of a series of 20 booklets designed for participants in an in-service course for teachers of elementary mathematics. The course, developed by the University of Illinois Arithmetic Project, is designed to be conducted by local school personnel. In addition to these booklets, a course package includes films showing mathematics being…

  11. 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.)

  12. Algorithm for Automatic Generation of Curved and Compound Twills

    Institute of Scientific and Technical Information of China (English)

    WANG Mei-zhen; WANG Fu-mei; WANG Shan-yuan

    2005-01-01

    A new arithmetic using matrix left-shift functions for the quicker generation of curved and compound twills is introduced in this paper. A matrix model for the generation of regular, curved and compound twill structures is established and its computing simulation realization are elaborated. Examples of the algorithm applying in the simulation and the automatic generation of curved and compound twills in fabric CAD are obtained.

  13. Rapid mental computation system as a tool for algorithmic thinking of elementary school students development

    OpenAIRE

    Ziatdinov, Rushan; Musa, Sajid

    2013-01-01

    In this paper, we describe the possibilities of using a rapid mental computation system in elementary education. The system consists of a number of readily memorized operations that allow one to perform arithmetic computations very quickly. These operations are actually simple algorithms which can develop or improve the algorithmic thinking of pupils. Using a rapid mental computation system allows forming the basis for the study of computer science in secondary school.

  14. Hippocampal spatial mechanisms relate to the development of arithmetic symbol processing in children.

    Science.gov (United States)

    Mathieu, Romain; Epinat-Duclos, Justine; Léone, Jessica; Fayol, Michel; Thevenot, Catherine; Prado, Jérôme

    2017-06-13

    Understanding the meaning of abstract mathematical symbols is a cornerstone of arithmetic learning in children. Studies have long focused on the role of spatial intuitions in the processing of numerals. However, it has been argued that such intuitions may also underlie symbols that convey fundamental arithmetic concepts, such as arithmetic operators. In the present cross-sectional study, we used fMRI to investigate how and when associations between arithmetic operators and brain regions processing spatial information emerge in children from 3 rd to 10 th grade. We found that the mere perception of a '+' sign elicited grade-related increases of spatial activity in the right hippocampus. That is, merely perceiving '+' signs - without any operands - elicited enhanced hippocampal activity after around 7 th grade (12-13 years old). In these children, hippocampal activity in response to a '+' sign was further correlated with the degree to which calculation performance was facilitated by the preview of that sign before an addition problem, an effect termed operator-priming. Grade-related increases of hippocampal spatial activity were operation-specific because they were not observed with '×' signs, which might evoke rote retrieval rather than numerical manipulation. Our study raises the possibility that hippocampal spatial mechanisms help build associations between some arithmetic operators and space throughout age and/or education. Copyright © 2017 The Authors. Published by Elsevier Ltd.. All rights reserved.

  15. When problem size matters: differential effects of brain stimulation on arithmetic problem solving and neural oscillations.

    Directory of Open Access Journals (Sweden)

    Bruno Rütsche

    Full Text Available The problem size effect is a well-established finding in arithmetic problem solving and is characterized by worse performance in problems with larger compared to smaller operand size. Solving small and large arithmetic problems has also been shown to involve different cognitive processes and distinct electroencephalography (EEG oscillations over the left posterior parietal cortex (LPPC. In this study, we aimed to provide further evidence for these dissociations by using transcranial direct current stimulation (tDCS. Participants underwent anodal (30min, 1.5 mA, LPPC and sham tDCS. After the stimulation, we recorded their neural activity using EEG while the participants solved small and large arithmetic problems. We found that the tDCS effects on performance and oscillatory activity critically depended on the problem size. While anodal tDCS improved response latencies in large arithmetic problems, it decreased solution rates in small arithmetic problems. Likewise, the lower-alpha desynchronization in large problems increased, whereas the theta synchronization in small problems decreased. These findings reveal that the LPPC is differentially involved in solving small and large arithmetic problems and demonstrate that the effects of brain stimulation strikingly differ depending on the involved neuro-cognitive processes.

  16. The problem of complex eigensystems in the semianalytical solution for advancement of time in solute transport simulations: a new method using real arithmetic

    Science.gov (United States)

    Umari, Amjad M.J.; Gorelick, Steven M.

    1986-01-01

    In the numerical modeling of groundwater solute transport, explicit solutions may be obtained for the concentration field at any future time without computing concentrations at intermediate times. The spatial variables are discretized and time is left continuous in the governing differential equation. These semianalytical solutions have been presented in the literature and involve the eigensystem of a coefficient matrix. This eigensystem may be complex (i.e., have imaginary components) due to the asymmetry created by the advection term in the governing advection-dispersion equation. Previous investigators have either used complex arithmetic to represent a complex eigensystem or chosen large dispersivity values for which the imaginary components of the complex eigenvalues may be ignored without significant error. It is shown here that the error due to ignoring the imaginary components of complex eigenvalues is large for small dispersivity values. A new algorithm that represents the complex eigensystem by converting it to a real eigensystem is presented. The method requires only real arithmetic.

  17. Cross-cultural investigation into cognitive underpinnings of individual differences in early arithmetic.

    Science.gov (United States)

    Rodic, Maja; Zhou, Xinlin; Tikhomirova, Tatiana; Wei, Wei; Malykh, Sergei; Ismatulina, Victoria; Sabirova, Elena; Davidova, Yulia; Tosto, Maria Grazia; Lemelin, Jean-Pascal; Kovas, Yulia

    2015-01-01

    The present study evaluated 626 5-7-year-old children in the UK, China, Russia, and Kyrgyzstan on a cognitive test battery measuring: (1) general skills; (2) non-symbolic number sense; (3) symbolic number understanding; (4) simple arithmetic - operating with numbers; and (5) familiarity with numbers. Although most inter-population differences were small, 13% of the variance in arithmetic skills could be explained by the sample, replicating the pattern, previously found with older children in PISA. Furthermore, the same cognitive skills were related to early arithmetic in these diverse populations. Only understanding of symbolic number explained variation in mathematical performance in all samples. We discuss the results in terms of potential influences of socio-demographic, linguistic and genetic factors on individual differences in mathematics. © 2014 John Wiley & Sons Ltd.

  18. Introduction to cardinal arithmetic

    CERN Document Server

    Holz, M; Weitz, E

    1999-01-01

    This book is an introduction into modern cardinal arithmetic in the frame of the axioms of Zermelo-Fraenkel set theory together with the axiom of choice (ZFC). A first part describes the classical theory developed by Bernstein, Cantor, Hausdorff, König and Tarski between 1870 and 1930. Next, the development in the 1970s led by Galvin, Hajnal and Silver is characterized. The third part presents the fundamental investigations in pcf theory which have been worked out by Shelah to answer the questions left open in the 1970s.Reviews:'The authors aim their text at beginners in set theory. They start

  19. Language, arithmetic word problems, and deaf students: Linguistic strategies used to solve tasks

    Science.gov (United States)

    Zevenbergen, Robyn; Hyde, Merv; Power, Des

    2001-12-01

    There has been limited examination of the intersection between language and arithmetic in the performance of deaf students, although some previous research has shown that deaf and hearing-impaired1 students are delayed in both their language acquisition and arithmetic performance. This paper examines the performance of deaf and hearing-impaired students in South-East Queensland, Australia, in solving arithmetic word problems. It was found that the subjects' solutions of word problems confirmed trends for hearing students, but that their performance was delayed in comparison. The results confirm other studies where deaf and hearing-impaired students are delayed in their language acquisition and this impacts on their capacity to successfully undertake the resolution of word problems.

  20. Arithmetic of quantum entropy function

    International Nuclear Information System (INIS)

    Sen, Ashoke

    2009-01-01

    Quantum entropy function is a proposal for computing the entropy associated with the horizon of a black hole in the extremal limit, and is related via AdS/CFT correspondence to the dimension of the Hilbert space in a dual quantum mechanics. We show that in N = 4 supersymmetric string theories, quantum entropy function formalism naturally explains the origin of the subtle differences between the microscopic degeneracies of quarter BPS dyons carrying different torsion, i.e. different arithmetical properties. These arise from additional saddle points in the path integral - whose existence depends on the arithmetical properties of the black hole charges - constructed as freely acting orbifolds of the original AdS 2 x S 2 near horizon geometry. During this analysis we demonstrate that the quantum entropy function is insensitive to the details of the infrared cutoff used in the computation, and the details of the boundary terms added to the action. We also discuss the role of the asymptotic symmetries of AdS 2 in carrying out the path integral in the definition of quantum entropy function. Finally we show that even though quantum entropy function is expected to compute the absolute degeneracy in a given charge and angular momentum sector, it can also be used to compute the index. This can then be compared with the microscopic computation of the index.

  1. Retrieval or nonretrieval strategies in mental arithmetic? An operand recognition paradigm.

    Science.gov (United States)

    Thevenot, Catherine; Fanget, Muriel; Fayol, Michel

    2007-09-01

    According to LeFevre, Sadesky, and Bisanz, averaging solution latencies in order to study individuals' arithmetic strategies can result in misleading conclusions. Therefore, in addition to classical chronometric data, they collected verbal reports and challenged the assumption that adults rely systematically on retrieval of arithmetic facts from memory to solve simple addition problems. However, Kirk and Ashcraft questioned the validity of such a methodology and concluded that a more appropriate method has to be found. Thus, we developed an operand recognition paradigm that does not rely on verbal reports or on solution latencies. In accordance with LeFevre et al., we show in a first experiment that adults resort to nonretrieval strategies to solve addition problems involving medium numbers. However, in a second experiment, we show that high-skilled individuals can solve the same problems using a retrieval strategy. The benefits of our paradigm to the study of arithmetic strategies are discussed.

  2. Tower of London test performance in children with poor arithmetic skills.

    Science.gov (United States)

    Sikora, M Darryn; Haley, Pat; Edwards, Jay; Butler, Robert W

    2002-01-01

    The Tower of London (TOL) has been used to assess executive functions in both children and adults with documented brain dysfunction. Like many other measures of executive function, it has not been widely used in the assessment of learning disabilities in children. However, if performance on the TOL discriminated among groups of children with different academic strengths and weaknesses, then it may be useful in identifying learning disability subtypes. The purpose of this study was to determine whether performance on the TOL would differ among 3 groups of children: those with arithmetic difficulties, those with reading difficulties, and those with no academic difficulties. The group with arithmetic difficulties exhibited significantly greater impairment on the TOL than either the group with reading difficulties or the group with no difficulties. The latter 2 groups performed similarly. The clinical utility of the TOL, as well as the relation between arithmetic deficits and executive functions, are discussed.

  3. Arithmetic convergent sequence space defined by modulus function

    Directory of Open Access Journals (Sweden)

    Taja Yaying

    2019-10-01

    Full Text Available The aim of this article is to introduce the sequence spaces $AC(f$ and $AS(f$ using arithmetic convergence and modulus function, and study algebraic and topological properties of this space, and certain inclusion results.

  4. Taming the Wild: A Unified Analysis of Hogwild!-Style Algorithms.

    Science.gov (United States)

    De Sa, Christopher; Zhang, Ce; Olukotun, Kunle; Ré, Christopher

    2015-12-01

    Stochastic gradient descent (SGD) is a ubiquitous algorithm for a variety of machine learning problems. Researchers and industry have developed several techniques to optimize SGD's runtime performance, including asynchronous execution and reduced precision. Our main result is a martingale-based analysis that enables us to capture the rich noise models that may arise from such techniques. Specifically, we use our new analysis in three ways: (1) we derive convergence rates for the convex case (Hogwild!) with relaxed assumptions on the sparsity of the problem; (2) we analyze asynchronous SGD algorithms for non-convex matrix problems including matrix completion; and (3) we design and analyze an asynchronous SGD algorithm, called Buckwild!, that uses lower-precision arithmetic. We show experimentally that our algorithms run efficiently for a variety of problems on modern hardware.

  5. Cloud Computing Security Model with Combination of Data Encryption Standard Algorithm (DES) and Least Significant Bit (LSB)

    Science.gov (United States)

    Basri, M.; Mawengkang, H.; Zamzami, E. M.

    2018-03-01

    Limitations of storage sources is one option to switch to cloud storage. Confidentiality and security of data stored on the cloud is very important. To keep up the confidentiality and security of such data can be done one of them by using cryptography techniques. Data Encryption Standard (DES) is one of the block cipher algorithms used as standard symmetric encryption algorithm. This DES will produce 8 blocks of ciphers combined into one ciphertext, but the ciphertext are weak against brute force attacks. Therefore, the last 8 block cipher will be converted into 8 random images using Least Significant Bit (LSB) algorithm which later draws the result of cipher of DES algorithm to be merged into one.

  6. Public Conceptions of Algorithms and Representations in the Common Core State Standards for Mathematics

    Science.gov (United States)

    Nanna, Robert J.

    2016-01-01

    Algorithms and representations have been an important aspect of the work of mathematics, especially for understanding concepts and communicating ideas about concepts and mathematical relationships. They have played a key role in various mathematics standards documents, including the Common Core State Standards for Mathematics. However, there have…

  7. A sorting network in bounded arithmetic

    Czech Academy of Sciences Publication Activity Database

    Jeřábek, Emil

    2011-01-01

    Roč. 162, č. 4 (2011), s. 341-355 ISSN 0168-0072 R&D Projects: GA AV ČR IAA1019401; GA MŠk(CZ) 1M0545 Institutional research plan: CEZ:AV0Z10190503 Keywords : bounded arithmetic * sorting network * proof complexity * monotone sequent calculus Subject RIV: BA - General Mathematics Impact factor: 0.450, year: 2011 http://www.sciencedirect.com/science/article/pii/S0168007210001272

  8. Philosophy of arithmetic psychological and logical investigations with supplementary texts from 1887–1901

    CERN Document Server

    Husserl, Edmund

    2003-01-01

    In his first book, Philosophy of Arithmetic, Edmund Husserl provides a carefully worked out account of number as a categorial or formal feature of the objective world, and of arithmetic as a symbolic technique for mastering the infinite field of numbers for knowledge. It is a realist account of numbers and number relations that interweaves them into the basic structure of the universe and into our knowledge of reality. It provides an answer to the question of how arithmetic applies to reality, and gives an account of how, in general, formalized systems of symbols work in providing access to the world. The "appendices" to this book provide some of Husserl's subsequent discussions of how formalisms work, involving David Hilbert's program of completeness for arithmetic. "Completeness" is integrated into Husserl's own problematic of the "imaginary", and allows him to move beyond the analysis of "representations" in his understanding of the logic of mathematics. Husserl's work here provides an alternative model of...

  9. Canonical algorithms for numerical integration of charged particle motion equations

    Science.gov (United States)

    Efimov, I. N.; Morozov, E. A.; Morozova, A. R.

    2017-02-01

    A technique for numerically integrating the equation of charged particle motion in a magnetic field is considered. It is based on the canonical transformations of the phase space in Hamiltonian mechanics. The canonical transformations make the integration process stable against counting error accumulation. The integration algorithms contain a minimum possible amount of arithmetics and can be used to design accelerators and devices of electron and ion optics.

  10. Identity of the conjugate gradient and Lanczos algorithms for matrix inversion in lattice fermion calculations

    International Nuclear Information System (INIS)

    Burkitt, A.N.; Irving, A.C.

    1988-01-01

    Two of the methods that are widely used in lattice gauge theory calculations requiring inversion of the fermion matrix are the Lanczos and the conjugate gradient algorithms. Those algorithms are already known to be closely related. In fact for matrix inversion, in exact arithmetic, they give identical results at each iteration and are just alternative formulations of a single algorithm. This equivalence survives rounding errors. We give the identities between the coefficients of the two formulations, enabling many of the best features of them to be combined. (orig.)

  11. From numeracy to arithmetic: Precursors of arithmetic performance in children with cerebral palsy from 6 till 8 years of age

    NARCIS (Netherlands)

    Rooijen, M. van; Verhoeven, L.T.W.; Steenbergen, B.

    2015-01-01

    Children with cerebral palsy (CP) are generally delayed in arithmetic compared to their peers. The development of early numeracy performance in children with CP is not yet evident, nor have the factors associated with change over time been identified. Therefore, we examined the development of

  12. Symbolic Numerical Magnitude Processing Is as Important to Arithmetic as Phonological Awareness Is to Reading.

    Directory of Open Access Journals (Sweden)

    Kiran Vanbinst

    Full Text Available In this article, we tested, using a 1-year longitudinal design, whether symbolic numerical magnitude processing or children's numerical representation of Arabic digits, is as important to arithmetic as phonological awareness is to reading. Children completed measures of symbolic comparison, phonological awareness, arithmetic, reading at the start of third grade and the latter two were retested at the start of fourth grade. Cross-sectional and longitudinal correlations indicated that symbolic comparison was a powerful domain-specific predictor of arithmetic and that phonological awareness was a unique predictor of reading. Crucially, the strength of these independent associations was not significantly different. This indicates that symbolic numerical magnitude processing is as important to arithmetic development as phonological awareness is to reading and suggests that symbolic numerical magnitude processing is a good candidate for screening children at risk for developing mathematical difficulties.

  13. A review of lossless audio compression standards and algorithms

    Science.gov (United States)

    Muin, Fathiah Abdul; Gunawan, Teddy Surya; Kartiwi, Mira; Elsheikh, Elsheikh M. A.

    2017-09-01

    Over the years, lossless audio compression has gained popularity as researchers and businesses has become more aware of the need for better quality and higher storage demand. This paper will analyse various lossless audio coding algorithm and standards that are used and available in the market focusing on Linear Predictive Coding (LPC) specifically due to its popularity and robustness in audio compression, nevertheless other prediction methods are compared to verify this. Advanced representation of LPC such as LSP decomposition techniques are also discussed within this paper.

  14. DNA Microarray Data Analysis: A Novel Biclustering Algorithm Approach

    Directory of Open Access Journals (Sweden)

    Tewfik Ahmed H

    2006-01-01

    Full Text Available Biclustering algorithms refer to a distinct class of clustering algorithms that perform simultaneous row-column clustering. Biclustering problems arise in DNA microarray data analysis, collaborative filtering, market research, information retrieval, text mining, electoral trends, exchange analysis, and so forth. When dealing with DNA microarray experimental data for example, the goal of biclustering algorithms is to find submatrices, that is, subgroups of genes and subgroups of conditions, where the genes exhibit highly correlated activities for every condition. In this study, we develop novel biclustering algorithms using basic linear algebra and arithmetic tools. The proposed biclustering algorithms can be used to search for all biclusters with constant values, biclusters with constant values on rows, biclusters with constant values on columns, and biclusters with coherent values from a set of data in a timely manner and without solving any optimization problem. We also show how one of the proposed biclustering algorithms can be adapted to identify biclusters with coherent evolution. The algorithms developed in this study discover all valid biclusters of each type, while almost all previous biclustering approaches will miss some.

  15. One-step trinary signed-digit arithmetic using an efficient encoding scheme

    Science.gov (United States)

    Salim, W. Y.; Fyath, R. S.; Ali, S. A.; Alam, Mohammad S.

    2000-11-01

    The trinary signed-digit (TSD) number system is of interest for ultra fast optoelectronic computing systems since it permits parallel carry-free addition and borrow-free subtraction of two arbitrary length numbers in constant time. In this paper, a simple coding scheme is proposed to encode the decimal number directly into the TSD form. The coding scheme enables one to perform parallel one-step TSD arithmetic operation. The proposed coding scheme uses only a 5-combination coding table instead of the 625-combination table reported recently for recoded TSD arithmetic technique.

  16. Arithmetic difficulties in children with cerebral palsy are related to executive function and working memory

    NARCIS (Netherlands)

    Jenks, K.M.; Moor, J.M.H. de; Lieshout, E.C.D.M. van

    2009-01-01

    Background - Although it is believed that children with cerebral palsy are at high risk for learning difficulties and arithmetic difficulties in particular, few studies have investigated this issue. Methods - Arithmetic ability was longitudinally assessed in children with cerebral palsy in special

  17. File compression and encryption based on LLS and arithmetic coding

    Science.gov (United States)

    Yu, Changzhi; Li, Hengjian; Wang, Xiyu

    2018-03-01

    e propose a file compression model based on arithmetic coding. Firstly, the original symbols, to be encoded, are input to the encoder one by one, we produce a set of chaotic sequences by using the Logistic and sine chaos system(LLS), and the values of this chaotic sequences are randomly modified the Upper and lower limits of current symbols probability. In order to achieve the purpose of encryption, we modify the upper and lower limits of all character probabilities when encoding each symbols. Experimental results show that the proposed model can achieve the purpose of data encryption while achieving almost the same compression efficiency as the arithmetic coding.

  18. Partial sums of arithmetical functions with absolutely convergent ...

    Indian Academy of Sciences (India)

    For an arithmetical function f with absolutely convergent Ramanujan expansion, we derive an asymptotic formula for the ∑ n ≤ N f(n)$ with explicit error term. As a corollary we obtain new results about sum-of-divisors functions and Jordan's totient functions.

  19. When is working memory important for arithmetic? The impact of strategy and age.

    Science.gov (United States)

    Cragg, Lucy; Richardson, Sophie; Hubber, Paula J; Keeble, Sarah; Gilmore, Camilla

    2017-01-01

    Our ability to perform arithmetic relies heavily on working memory, the manipulation and maintenance of information in mind. Previous research has found that in adults, procedural strategies, particularly counting, rely on working memory to a greater extent than retrieval strategies. During childhood there are changes in the types of strategies employed, as well as an increase in the accuracy and efficiency of strategy execution. As such it seems likely that the role of working memory in arithmetic may also change, however children and adults have never been directly compared. This study used traditional dual-task methodology, with the addition of a control load condition, to investigate the extent to which working memory requirements for different arithmetic strategies change with age between 9-11 years, 12-14 years and young adulthood. We showed that both children and adults employ working memory when solving arithmetic problems, no matter what strategy they choose. This study highlights the importance of considering working memory in understanding the difficulties that some children and adults have with mathematics, as well as the need to include working memory in theoretical models of mathematical cognition.

  20. Children, algorithm and the decimal numeral system

    Directory of Open Access Journals (Sweden)

    Clélia Maria Ignatius Nogueira

    2010-08-01

    Full Text Available A large number of studies in Mathematics Education approach some possible problems in the study of algorithms in the early school years of arithmetic teaching. However, this discussion is not exhausted. In this feature, this article presents the results of a research which proposed to investigate if the arithmetic’s teaching, with emphasis in the fundamental operation’s algorithm, cooperate to build the mathematics knowledge, specifically of the Decimal Numeral System. In order to achieve this purpose, we interviewed, using the Piaget Critique Clinical Method, twenty students from a public school. The result’s analysis indicates that they mechanically reproduce the regular algorithm’s techniques without notice the relations between the techniques and the principle and the Decimal Numeral System’s properties.

  1. Arithmetic difficulties in children with cerebral palsy are related to executive function and working memory.

    NARCIS (Netherlands)

    Jenks, K.M.; Moor, J.M.H. de; Lieshout, E.C. van

    2009-01-01

    BACKGROUND: Although it is believed that children with cerebral palsy are at high risk for learning difficulties and arithmetic difficulties in particular, few studies have investigated this issue. METHODS: Arithmetic ability was longitudinally assessed in children with cerebral palsy in special (n

  2. SCALCE: boosting sequence compression algorithms using locally consistent encoding.

    Science.gov (United States)

    Hach, Faraz; Numanagic, Ibrahim; Alkan, Can; Sahinalp, S Cenk

    2012-12-01

    The high throughput sequencing (HTS) platforms generate unprecedented amounts of data that introduce challenges for the computational infrastructure. Data management, storage and analysis have become major logistical obstacles for those adopting the new platforms. The requirement for large investment for this purpose almost signalled the end of the Sequence Read Archive hosted at the National Center for Biotechnology Information (NCBI), which holds most of the sequence data generated world wide. Currently, most HTS data are compressed through general purpose algorithms such as gzip. These algorithms are not designed for compressing data generated by the HTS platforms; for example, they do not take advantage of the specific nature of genomic sequence data, that is, limited alphabet size and high similarity among reads. Fast and efficient compression algorithms designed specifically for HTS data should be able to address some of the issues in data management, storage and communication. Such algorithms would also help with analysis provided they offer additional capabilities such as random access to any read and indexing for efficient sequence similarity search. Here we present SCALCE, a 'boosting' scheme based on Locally Consistent Parsing technique, which reorganizes the reads in a way that results in a higher compression speed and compression rate, independent of the compression algorithm in use and without using a reference genome. Our tests indicate that SCALCE can improve the compression rate achieved through gzip by a factor of 4.19-when the goal is to compress the reads alone. In fact, on SCALCE reordered reads, gzip running time can improve by a factor of 15.06 on a standard PC with a single core and 6 GB memory. Interestingly even the running time of SCALCE + gzip improves that of gzip alone by a factor of 2.09. When compared with the recently published BEETL, which aims to sort the (inverted) reads in lexicographic order for improving bzip2, SCALCE + gzip

  3. Rapid Mental Сomputation System as a Tool for Algorithmic Thinking of Elementary School Students Development

    Directory of Open Access Journals (Sweden)

    Rushan Ziatdinov

    2012-07-01

    Full Text Available In this paper, we describe the possibilities of using a rapid mental computation system in elementary education. The system consists of a number of readily memorized operations that allow one to perform arithmetic computations very quickly. These operations are actually simple algorithms which can develop or improve the algorithmic thinking of pupils. Using a rapid mental computation system allows forming the basis for the study of computer science in secondary school.

  4. Adaptive Binary Arithmetic Coder-Based Image Feature and Segmentation in the Compressed Domain

    Directory of Open Access Journals (Sweden)

    Hsi-Chin Hsin

    2012-01-01

    Full Text Available Image compression is necessary in various applications, especially for efficient transmission over a band-limited channel. It is thus desirable to be able to segment an image in the compressed domain directly such that the burden of decompressing computation can be avoided. Motivated by the adaptive binary arithmetic coder (MQ coder of JPEG2000, we propose an efficient scheme to segment the feature vectors that are extracted from the code stream of an image. We modify the Compression-based Texture Merging (CTM algorithm to alleviate the influence of overmerging problem by making use of the rate distortion information. Experimental results show that the MQ coder-based image segmentation is preferable in terms of the boundary displacement error (BDE measure. It has the advantage of saving computational cost as the segmentation results even at low rates of bits per pixel (bpp are satisfactory.

  5. The relation between language and arithmetic in bilinguals: insights from different stages of language acquisition

    Directory of Open Access Journals (Sweden)

    Amandine eVan Rinsveld

    2015-03-01

    Full Text Available Solving arithmetic problems is a cognitive task that heavily relies on language processing. One might thus wonder whether this language-reliance leads to qualitative differences (e.g. greater difficulties, error types, etc. in arithmetic for bilingual individuals who frequently have to solve arithmetic problems in more than one language. The present study investigated how proficiency in two languages interacts with arithmetic problem solving throughout language acquisition in adolescents and young adults. Additionally, we examined whether the number word structure that is specific to a given language plays a role in number processing over and above bilingual proficiency. We addressed these issues in a German-French educational bilingual setting, where there is a progressive transition from German to French as teaching language. Importantly, German and French number naming structures differ clearly, as two-digit number names follow a unit-ten order in German, but a ten-unit order in French. We implemented a transversal developmental design in which bilingual pupils from grades 7, 8, 10, 11, and young adults were asked to solve simple and complex additions in both languages. The results confirmed that language proficiency is crucial especially for complex addition computation. Simple additions in contrast can be retrieved equally well in both languages after extended language practice. Additional analyses revealed that over and above language proficiency, language-specific number word structures (e.g. unit-ten vs. ten-unit also induced significant modulations of bilinguals’ arithmetic performances. Taken together, these findings support the view of a strong relation between language and arithmetic in bilinguals.

  6. VIRTEX-5 Fpga Implementation of Advanced Encryption Standard Algorithm

    Science.gov (United States)

    Rais, Muhammad H.; Qasim, Syed M.

    2010-06-01

    In this paper, we present an implementation of Advanced Encryption Standard (AES) cryptographic algorithm using state-of-the-art Virtex-5 Field Programmable Gate Array (FPGA). The design is coded in Very High Speed Integrated Circuit Hardware Description Language (VHDL). Timing simulation is performed to verify the functionality of the designed circuit. Performance evaluation is also done in terms of throughput and area. The design implemented on Virtex-5 (XC5VLX50FFG676-3) FPGA achieves a maximum throughput of 4.34 Gbps utilizing a total of 399 slices.

  7. Quantum arithmetic with the Quantum Fourier Transform

    OpenAIRE

    Ruiz-Perez, Lidia; Garcia-Escartin, Juan Carlos

    2014-01-01

    The Quantum Fourier Transform offers an interesting way to perform arithmetic operations on a quantum computer. We review existing Quantum Fourier Transform adders and multipliers and propose some modifications that extend their capabilities. Among the new circuits, we propose a quantum method to compute the weighted average of a series of inputs in the transform domain.

  8. Processing the Order of Symbolic Numbers: A Reliable and Unique Predictor of Arithmetic Fluency

    Directory of Open Access Journals (Sweden)

    Stephan E. Vogel

    2017-12-01

    Full Text Available A small but growing body of evidence suggests a link between individual differences in processing the order of numerical symbols (e.g., deciding whether a set of digits is arranged in ascending/descending order or not and arithmetic achievement. However, the reliability of behavioral correlates measuring symbolic and non-symbolic numerical order processing and their relationship to arithmetic abilities remain poorly understood. The present study aims to fill this knowledge gap by examining the behavioral correlates of numerical and non-numerical order processing and their unique associations with arithmetic fluency at two different time points within the same sample of individuals. Thirty-two right-handed adults performed three order judgment tasks consisting of symbolic numbers (i.e., digits, non-symbolic numbers (i.e., dots, and letters of the alphabet. Specifically, participants had to judge as accurately and as quickly as possible whether stimuli were ordered correctly (in ascending/descending order, e.g., 2-3-4; ●●●●-●●●-●●; B-C-D or not (e.g., 4-5-3; ●●●●-●●●●●-●●●; D-E-C. Results of this study demonstrate that numerical order judgments are reliable measurements (i.e., high test-retest reliability, and that the observed relationship between symbolic number processing and arithmetic fluency accounts for a unique and reliable portion of variance over and above the non-symbolic number and the letter conditions. The differential association of symbolic and non-symbolic numbers with arithmetic support the view that processing the order of symbolic and non-symbolic numbers engages different cognitive mechanisms, and that the ability to process ordinal relationships of symbolic numbers is a reliable and unique predictor of arithmetic fluency.

  9. A case study of arithmetic facts dyscalculia caused by a hypersensitivity-to-interference in memory.

    Science.gov (United States)

    De Visscher, Alice; Noël, Marie-Pascale

    2013-01-01

    While the heterogeneity of developmental dyscalculia is increasingly recognized, the different profiles have not yet been clearly established. Among the features underpinning types of developmental dyscalculia suggested in the literature, an impairment in arithmetic fact retrieval is particularly prominent. In this paper, we present a case study of an adult woman (DB) with very good cognitive capacities suffering from a specific and developmental arithmetic fact retrieval deficit. We test the main hypotheses about developmental dyscalculia derived from literature. We first explore the influential hypothesis of an approximate number system deficit, through estimation tasks, comparison tasks and a priming comparison task. Secondly, we evaluate whether DB's mathematical deficiencies are caused by a rote verbal memory deficit, using tasks involving completion of expressions, and reciting automatic series such as the alphabet and the months of the year. Alternatively, taking into account the extreme similarity of the arithmetic facts, we propose that a heightened sensitivity to interference could have prevented DB from memorizing the arithmetic facts. The pattern of DB's results on different tasks supports this hypothesis. Our findings identify a new etiology of a specific impairment of arithmetic facts storage, namely a hypersensitivity-to-interference. Copyright © 2012 Elsevier Ltd. All rights reserved.

  10. The Duality Principle in Teaching Arithmetic and Geometric Series

    Science.gov (United States)

    Yeshurun, Shraga

    1978-01-01

    The author discusses the use of the duality principle in combination with the hierarchy of algebraic operations in helping students to retain and use definitions and rules for arithmetic and geometric sequences and series. (MN)

  11. Verification of Linear (In)Dependence in Finite Precision Arithmetic

    Czech Academy of Sciences Publication Activity Database

    Rohn, Jiří

    2014-01-01

    Roč. 8, č. 3-4 (2014), s. 323-328 ISSN 1661-8289 Institutional support: RVO:67985807 Keywords : linear dependence * linear independence * pseudoinverse matrix * finite precision arithmetic * verification * MATLAB file Subject RIV: BA - General Mathematics

  12. Coherent states, pseudodifferential analysis and arithmetic

    Science.gov (United States)

    Unterberger, André

    2012-06-01

    Basic questions regarding families of coherent states include describing some constructions of such and the way they can be applied to operator theory or partial differential equations. In both questions, pseudodifferential analysis is important. Recent developments indicate that they can contribute to methods in arithmetic, especially modular form theory. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Coherent states: mathematical and physical aspects’.

  13. Sex Differences in Mental Arithmetic, Digit Span, and "g" Defined as Working Memory Capacity

    Science.gov (United States)

    Lynn, Richard; Irwing, Paul

    2008-01-01

    Meta-analyses are presented of sex differences in (1) the (mental) arithmetic subtest of the Wechsler intelligence tests for children and adolescents (the WISC and WPPSI tests), showing that boys obtained a mean advantage of 0.11d; (2) the (mental) arithmetic subtest of the Wechsler intelligence tests for adults (the WAIS tests) showing a mean…

  14. RAID-6 reed-solomon codes with asymptotically optimal arithmetic complexities

    KAUST Repository

    Lin, Sian-Jheng

    2016-12-24

    In computer storage, RAID 6 is a level of RAID that can tolerate two failed drives. When RAID-6 is implemented by Reed-Solomon (RS) codes, the penalty of the writing performance is on the field multiplications in the second parity. In this paper, we present a configuration of the factors of the second-parity formula, such that the arithmetic complexity can reach the optimal complexity bound when the code length approaches infinity. In the proposed approach, the intermediate data used for the first parity is also utilized to calculate the second parity. To the best of our knowledge, this is the first approach supporting the RAID-6 RS codes to approach the optimal arithmetic complexity.

  15. A novel high-frequency encoding algorithm for image compression

    Science.gov (United States)

    Siddeq, Mohammed M.; Rodrigues, Marcos A.

    2017-12-01

    In this paper, a new method for image compression is proposed whose quality is demonstrated through accurate 3D reconstruction from 2D images. The method is based on the discrete cosine transform (DCT) together with a high-frequency minimization encoding algorithm at compression stage and a new concurrent binary search algorithm at decompression stage. The proposed compression method consists of five main steps: (1) divide the image into blocks and apply DCT to each block; (2) apply a high-frequency minimization method to the AC-coefficients reducing each block by 2/3 resulting in a minimized array; (3) build a look up table of probability data to enable the recovery of the original high frequencies at decompression stage; (4) apply a delta or differential operator to the list of DC-components; and (5) apply arithmetic encoding to the outputs of steps (2) and (4). At decompression stage, the look up table and the concurrent binary search algorithm are used to reconstruct all high-frequency AC-coefficients while the DC-components are decoded by reversing the arithmetic coding. Finally, the inverse DCT recovers the original image. We tested the technique by compressing and decompressing 2D images including images with structured light patterns for 3D reconstruction. The technique is compared with JPEG and JPEG2000 through 2D and 3D RMSE. Results demonstrate that the proposed compression method is perceptually superior to JPEG with equivalent quality to JPEG2000. Concerning 3D surface reconstruction from images, it is demonstrated that the proposed method is superior to both JPEG and JPEG2000.

  16. Heuristics and representational change in two-move matchstick arithmetic tasks

    Directory of Open Access Journals (Sweden)

    Michael Öllinger

    2006-01-01

    Full Text Available Insight problems are problems where the problem solver struggles to find a solution until * aha! * the solution suddenly appears. Two contemporary theories suggest that insight problems are difficult either because problem solvers begin with an incorrect representation of the problem, or that problem solvers apply inappropriate heuristics to the problem. The relative contributions of representational change and inappropriate heuristics on the process of insight problem solving was studied with a task that required the problem solver to move two matchsticks in order to transform an incorrect arithmetic statement into a correct one. Problem solvers (N = 120 worked on two different types of two-move matchstick arithmetic problems that both varied with respect to the effectiveness of heuristics and to the degree of a necessary representational change of the problem representation. A strong influence of representational change on solution rates was found whereas the influence of heuristics hadminimal effects on solution rates. That is, the difficulty of insight problems within the two-move matchstick arithmetic domain is governed by the degree of representational change required. A model is presented that details representational change as the necessary condition for ensuring that appropriate heuristics can be applied on the proper problem representation.

  17. Model Theory in Algebra, Analysis and Arithmetic

    CERN Document Server

    Dries, Lou; Macpherson, H Dugald; Pillay, Anand; Toffalori, Carlo; Wilkie, Alex J

    2014-01-01

    Presenting recent developments and applications, the book focuses on four main topics in current model theory: 1) the model theory of valued fields; 2) undecidability in arithmetic; 3) NIP theories; and 4) the model theory of real and complex exponentiation. Young researchers in model theory will particularly benefit from the book, as will more senior researchers in other branches of mathematics.

  18. High performance integer arithmetic circuit design on FPGA architecture, implementation and design automation

    CERN Document Server

    Palchaudhuri, Ayan

    2016-01-01

    This book describes the optimized implementations of several arithmetic datapath, controlpath and pseudorandom sequence generator circuits for realization of high performance arithmetic circuits targeted towards a specific family of the high-end Field Programmable Gate Arrays (FPGAs). It explores regular, modular, cascadable, and bit-sliced architectures of these circuits, by directly instantiating the target FPGA-specific primitives in the HDL. Every proposed architecture is justified with detailed mathematical analyses. Simultaneously, constrained placement of the circuit building blocks is performed, by placing the logically related hardware primitives in close proximity to one another by supplying relevant placement constraints in the Xilinx proprietary “User Constraints File”. The book covers the implementation of a GUI-based CAD tool named FlexiCore integrated with the Xilinx Integrated Software Environment (ISE) for design automation of platform-specific high-performance arithmetic circuits from us...

  19. Stochastic approach for round-off error analysis in computing application to signal processing algorithms

    International Nuclear Information System (INIS)

    Vignes, J.

    1986-01-01

    Any result of algorithms provided by a computer always contains an error resulting from floating-point arithmetic round-off error propagation. Furthermore signal processing algorithms are also generally performed with data containing errors. The permutation-perturbation method, also known under the name CESTAC (controle et estimation stochastique d'arrondi de calcul) is a very efficient practical method for evaluating these errors and consequently for estimating the exact significant decimal figures of any result of algorithms performed on a computer. The stochastic approach of this method, its probabilistic proof, and the perfect agreement between the theoretical and practical aspects are described in this paper [fr

  20. Bi-amalgamations subject to the arithmetical property

    OpenAIRE

    Kabbaj, S.; Mahdou, N.; Moutui, M. A. S.

    2016-01-01

    This paper establishes necessary and sufficient conditions for a bi-amalgamation to inherit the arithmetical property, with applications on the weak global dimension and transfer of the semihereditary property. The new results compare to previous works carried on various settings of duplications and amalgamations, and capitalize on recent results on bi-amalgamations. All results are backed with new and illustrative examples arising as bi-amalgamations.

  1. The association between arithmetic and reading performance in school: A meta-analytic study.

    Science.gov (United States)

    Singer, Vivian; Strasser, Kathernie

    2017-12-01

    Many studies of school achievement find a significant association between reading and arithmetic achievement. The magnitude of the association varies widely across the studies, but the sources of this variation have not been identified. The purpose of this paper is to examine the magnitude and determinants of the relation between arithmetic and reading performance during elementary and middle school years. We meta-analyzed 210 correlations between math and reading measures, coming from 68 independent samples (the overall sample size was 58923 participants). The meta-analysis yielded an average correlation of 0.55 between math and reading measures. Among the moderators tested, only transparency of orthography and use of timed or untimed tests were significant in explaining the size of the correlation, with the largest correlations observed between timed measures of arithmetic and reading and between math and reading in opaque orthographies. (PsycINFO Database Record (c) 2017 APA, all rights reserved).

  2. Fractionating the neural correlates of individual working memory components underlying arithmetic problem solving skills in children

    Science.gov (United States)

    Metcalfe, Arron W. S.; Ashkenazi, Sarit; Rosenberg-Lee, Miriam; Menon, Vinod

    2013-01-01

    Baddeley and Hitch’s multi-component working memory (WM) model has played an enduring and influential role in our understanding of cognitive abilities. Very little is known, however, about the neural basis of this multi-component WM model and the differential role each component plays in mediating arithmetic problem solving abilities in children. Here, we investigate the neural basis of the central executive (CE), phonological (PL) and visuo-spatial (VS) components of WM during a demanding mental arithmetic task in 7–9 year old children (N=74). The VS component was the strongest predictor of math ability in children and was associated with increased arithmetic complexity-related responses in left dorsolateral and right ventrolateral prefrontal cortices as well as bilateral intra-parietal sulcus and supramarginal gyrus in posterior parietal cortex. Critically, VS, CE and PL abilities were associated with largely distinct patterns of brain response. Overlap between VS and CE components was observed in left supramarginal gyrus and no overlap was observed between VS and PL components. Our findings point to a central role of visuo-spatial WM during arithmetic problem-solving in young grade-school children and highlight the usefulness of the multi-component Baddeley and Hitch WM model in fractionating the neural correlates of arithmetic problem solving during development. PMID:24212504

  3. Weak task-related modulation and stimulus representations during arithmetic problem solving in children with developmental dyscalculia.

    Science.gov (United States)

    Ashkenazi, Sarit; Rosenberg-Lee, Miriam; Tenison, Caitlin; Menon, Vinod

    2012-02-15

    Developmental dyscalculia (DD) is a disability that impacts math learning and skill acquisition in school-age children. Here we investigate arithmetic problem solving deficits in young children with DD using univariate and multivariate analysis of fMRI data. During fMRI scanning, 17 children with DD (ages 7-9, grades 2 and 3) and 17 IQ- and reading ability-matched typically developing (TD) children performed complex and simple addition problems which differed only in arithmetic complexity. While the TD group showed strong modulation of brain responses with increasing arithmetic complexity, children with DD failed to show such modulation. Children with DD showed significantly reduced activation compared to TD children in the intraparietal sulcus, superior parietal lobule, supramarginal gyrus and bilateral dorsolateral prefrontal cortex in relation to arithmetic complexity. Critically, multivariate representational similarity revealed that brain response patterns to complex and simple problems were less differentiated in the DD group in bilateral anterior IPS, independent of overall differences in signal level. Taken together, these results show that children with DD not only under-activate key brain regions implicated in mathematical cognition, but they also fail to generate distinct neural responses and representations for different arithmetic problems. Our findings provide novel insights into the neural basis of DD. Copyright © 2011 Elsevier Ltd. All rights reserved.

  4. The effects of auditory stimulation on the arithmetic performance of children with ADHD and nondisabled children.

    Science.gov (United States)

    Abikoff, H; Courtney, M E; Szeibel, P J; Koplewicz, H S

    1996-05-01

    This study evaluated the impact of extra-task stimulation on the academic task performance of children with attention-deficit/hyperactivity disorder (ADHD). Twenty boys with ADHD and 20 nondisabled boys worked on an arithmetic task during high stimulation (music), low stimulation (speech), and no stimulation (silence). The music "distractors" were individualized for each child, and the arithmetic problems were at each child's ability level. A significant Group x Condition interaction was found for number of correct answers. Specifically, the nondisabled youngsters performed similarly under all three auditory conditions. In contrast, the children with ADHD did significantly better under the music condition than speech or silence conditions. However, a significant Group x Order interaction indicated that arithmetic performance was enhanced only for those children with ADHD who received music as the first condition. The facilitative effects of salient auditory stimulation on the arithmetic performance of the children with ADHD provide some support for the underarousal/optimal stimulation theory of ADHD.

  5. The Speech multi features fusion perceptual hash algorithm based on tensor decomposition

    Science.gov (United States)

    Huang, Y. B.; Fan, M. H.; Zhang, Q. Y.

    2018-03-01

    With constant progress in modern speech communication technologies, the speech data is prone to be attacked by the noise or maliciously tampered. In order to make the speech perception hash algorithm has strong robustness and high efficiency, this paper put forward a speech perception hash algorithm based on the tensor decomposition and multi features is proposed. This algorithm analyses the speech perception feature acquires each speech component wavelet packet decomposition. LPCC, LSP and ISP feature of each speech component are extracted to constitute the speech feature tensor. Speech authentication is done by generating the hash values through feature matrix quantification which use mid-value. Experimental results showing that the proposed algorithm is robust for content to maintain operations compared with similar algorithms. It is able to resist the attack of the common background noise. Also, the algorithm is highly efficiency in terms of arithmetic, and is able to meet the real-time requirements of speech communication and complete the speech authentication quickly.

  6. Hardware realization of an SVM algorithm implemented in FPGAs

    Science.gov (United States)

    Wiśniewski, Remigiusz; Bazydło, Grzegorz; Szcześniak, Paweł

    2017-08-01

    The paper proposes a technique of hardware realization of a space vector modulation (SVM) of state function switching in matrix converter (MC), oriented on the implementation in a single field programmable gate array (FPGA). In MC the SVM method is based on the instantaneous space-vector representation of input currents and output voltages. The traditional computation algorithms usually involve digital signal processors (DSPs) which consumes the large number of power transistors (18 transistors and 18 independent PWM outputs) and "non-standard positions of control pulses" during the switching sequence. Recently, hardware implementations become popular since computed operations may be executed much faster and efficient due to nature of the digital devices (especially concurrency). In the paper, we propose a hardware algorithm of SVM computation. In opposite to the existing techniques, the presented solution applies COordinate Rotation DIgital Computer (CORDIC) method to solve the trigonometric operations. Furthermore, adequate arithmetic modules (that is, sub-devices) used for intermediate calculations, such as code converters or proper sectors selectors (for output voltages and input current) are presented in detail. The proposed technique has been implemented as a design described with the use of Verilog hardware description language. The preliminary results of logic implementation oriented on the Xilinx FPGA (particularly, low-cost device from Artix-7 family from Xilinx was used) are also presented.

  7. Arithmetic learning with the use of graphic organiser

    Science.gov (United States)

    Sai, F. L.; Shahrill, M.; Tan, A.; Han, S. H.

    2018-01-01

    For this study, Zollman’s four corners-and-a-diamond mathematics graphic organiser embedded with Polya’s Problem Solving Model was used to investigate secondary school students’ performance in arithmetic word problems. This instructional learning tool was used to help students break down the given information into smaller units for better strategic planning. The participants were Year 7 students, comprised of 21 male and 20 female students, aged between 11-13 years old, from a co-ed secondary school in Brunei Darussalam. This study mainly adopted a quantitative approach to investigate the types of differences found in the arithmetic word problem pre- and post-tests results from the use of the learning tool. Although the findings revealed slight improvements in the overall comparisons of the students’ test results, the in-depth analysis of the students’ responses in their activity worksheets shows a different outcome. Some students were able to make good attempts in breaking down the key points into smaller information in order to solve the word problems.

  8. Multistate Memristive Tantalum Oxide Devices for Ternary Arithmetic

    Science.gov (United States)

    Kim, Wonjoo; Chattopadhyay, Anupam; Siemon, Anne; Linn, Eike; Waser, Rainer; Rana, Vikas

    2016-11-01

    Redox-based resistive switching random access memory (ReRAM) offers excellent properties to implement future non-volatile memory arrays. Recently, the capability of two-state ReRAMs to implement Boolean logic functionality gained wide interest. Here, we report on seven-states Tantalum Oxide Devices, which enable the realization of an intrinsic modular arithmetic using a ternary number system. Modular arithmetic, a fundamental system for operating on numbers within the limit of a modulus, is known to mathematicians since the days of Euclid and finds applications in diverse areas ranging from e-commerce to musical notations. We demonstrate that multistate devices not only reduce the storage area consumption drastically, but also enable novel in-memory operations, such as computing using high-radix number systems, which could not be implemented using two-state devices. The use of high radix number system reduces the computational complexity by reducing the number of needed digits. Thus the number of calculation operations in an addition and the number of logic devices can be reduced.

  9. Simplification of integrity constraints with aggregates and arithmetic built-ins

    DEFF Research Database (Denmark)

    Martinenghi, Davide

    2004-01-01

    Both aggregates and arithmetic built-ins are widely used in current database query languages: Aggregates are second-order constructs such as CNT and SUM of SQL; arithmetic built-ins include relational and other mathematical operators that apply to numbers, such as < and +. These features are also...... time, simplified versions of such integrity constraints that can be tested before the execution of any update. In this way, virtually no time is spent for optimization or rollbacks at run time. Both set and bag semantics are considered....... of interest in the context of database integrity constraints: correct and efficient integrity checking is crucial, as, without any guarantee of data consistency, the answers to queries cannot be trusted. In this paper we propose a method of practical relevance that can be used to derive, at database design...

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

    Science.gov (United States)

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

    2015-08-01

    Among all kinds of wavefront control algorithms in adaptive optics systems, the direct gradient wavefront control algorithm is the most widespread and common method. This control algorithm obtains the actuator voltages directly from wavefront slopes through pre-measuring the relational matrix between deformable mirror actuators and Hartmann wavefront sensor with perfect real-time characteristic and stability. However, with increasing the number of sub-apertures in wavefront sensor and deformable mirror actuators of adaptive optics systems, the matrix operation in direct gradient algorithm takes too much time, which becomes a major factor influencing control effect of adaptive optics systems. In this paper we apply an iterative wavefront control algorithm to high-resolution adaptive optics systems, in which the voltages of each actuator are obtained through iteration arithmetic, which gains great advantage in calculation and storage. For AO system with thousands of actuators, the computational complexity estimate is about O(n2) ˜ O(n3) in direct gradient wavefront control algorithm, while the computational complexity estimate in iterative wavefront control algorithm is about O(n) ˜ (O(n)3/2), in which n is the number of actuators of AO system. And the more the numbers of sub-apertures and deformable mirror actuators, the more significant advantage the iterative wavefront control algorithm exhibits. Project supported by the National Key Scientific and Research Equipment Development Project of China (Grant No. ZDYZ2013-2), the National Natural Science Foundation of China (Grant No. 11173008), and the Sichuan Provincial Outstanding Youth Academic Technology Leaders Program, China (Grant No. 2012JQ0012).

  11. Bit-Wise Arithmetic Coding For Compression Of Data

    Science.gov (United States)

    Kiely, Aaron

    1996-01-01

    Bit-wise arithmetic coding is data-compression scheme intended especially for use with uniformly quantized data from source with Gaussian, Laplacian, or similar probability distribution function. Code words of fixed length, and bits treated as being independent. Scheme serves as means of progressive transmission or of overcoming buffer-overflow or rate constraint limitations sometimes arising when data compression used.

  12. The optimal algorithm for Multi-source RS image fusion.

    Science.gov (United States)

    Fu, Wei; Huang, Shui-Guang; Li, Zeng-Shun; Shen, Hao; Li, Jun-Shuai; Wang, Peng-Yuan

    2016-01-01

    In order to solve the issue which the fusion rules cannot be self-adaptively adjusted by using available fusion methods according to the subsequent processing requirements of Remote Sensing (RS) image, this paper puts forward GSDA (genetic-iterative self-organizing data analysis algorithm) by integrating the merit of genetic arithmetic together with the advantage of iterative self-organizing data analysis algorithm for multi-source RS image fusion. The proposed algorithm considers the wavelet transform of the translation invariance as the model operator, also regards the contrast pyramid conversion as the observed operator. The algorithm then designs the objective function by taking use of the weighted sum of evaluation indices, and optimizes the objective function by employing GSDA so as to get a higher resolution of RS image. As discussed above, the bullet points of the text are summarized as follows.•The contribution proposes the iterative self-organizing data analysis algorithm for multi-source RS image fusion.•This article presents GSDA algorithm for the self-adaptively adjustment of the fusion rules.•This text comes up with the model operator and the observed operator as the fusion scheme of RS image based on GSDA. The proposed algorithm opens up a novel algorithmic pathway for multi-source RS image fusion by means of GSDA.

  13. Fractionating the neural correlates of individual working memory components underlying arithmetic problem solving skills in children.

    Science.gov (United States)

    Metcalfe, Arron W S; Ashkenazi, Sarit; Rosenberg-Lee, Miriam; Menon, Vinod

    2013-10-01

    Baddeley and Hitch's multi-component working memory (WM) model has played an enduring and influential role in our understanding of cognitive abilities. Very little is known, however, about the neural basis of this multi-component WM model and the differential role each component plays in mediating arithmetic problem solving abilities in children. Here, we investigate the neural basis of the central executive (CE), phonological (PL) and visuo-spatial (VS) components of WM during a demanding mental arithmetic task in 7-9 year old children (N=74). The VS component was the strongest predictor of math ability in children and was associated with increased arithmetic complexity-related responses in left dorsolateral and right ventrolateral prefrontal cortices as well as bilateral intra-parietal sulcus and supramarginal gyrus in posterior parietal cortex. Critically, VS, CE and PL abilities were associated with largely distinct patterns of brain response. Overlap between VS and CE components was observed in left supramarginal gyrus and no overlap was observed between VS and PL components. Our findings point to a central role of visuo-spatial WM during arithmetic problem-solving in young grade-school children and highlight the usefulness of the multi-component Baddeley and Hitch WM model in fractionating the neural correlates of arithmetic problem solving during development. Copyright © 2013 Elsevier Ltd. All rights reserved.

  14. Unpacking symbolic number comparison and its relation with arithmetic in adults.

    Science.gov (United States)

    Sasanguie, Delphine; Lyons, Ian M; De Smedt, Bert; Reynvoet, Bert

    2017-08-01

    Symbolic number - or digit - comparison has been a central tool in the domain of numerical cognition for decades. More recently, individual differences in performance on this task have been shown to robustly relate to individual differences in more complex math processing - a result that has been replicated across many different age groups. In this study, we 'unpack' the underlying components of digit comparison (i.e. digit identification, digit to number-word matching, digit ordering and general comparison) in a sample of adults. In a first experiment, we showed that digit comparison performance was most strongly related to digit ordering ability - i.e., the ability to judge whether symbolic numbers are in numerical order. Furthermore, path analyses indicated that the relation between digit comparison and arithmetic was partly mediated by digit ordering and fully mediated when non-numerical (letter) ordering was also entered into the model. In a second experiment, we examined whether a general order working memory component could account for the relation between digit comparison and arithmetic. It could not. Instead, results were more consistent with the notion that fluent access and activation of long-term stored associations between numbers explains the relation between arithmetic and both digit comparison and digit ordering tasks. Copyright © 2017 Elsevier B.V. All rights reserved.

  15. Non-Archimedean L-functions and arithmetical Siegel modular forms

    CERN Document Server

    1991-01-01

    This book is devoted to the arithmetical theory of Siegel modular forms and their L-functions. The central object are L-functions of classical Siegel modular forms whose special values are studied using the Rankin-Selberg method and the action of certain differential operators on modular forms which have nice arithmetical properties. A new method of p-adic interpolation of these critical values is presented. An important class of p-adic L-functions treated in the present book are p-adic L-functions of Siegel modular forms having logarithmic growth (which were first introduced by Amice, Velu and Vishik in the elliptic modular case when they come from a good supersingular reduction of ellptic curves and abelian varieties). The given construction of these p-adic L-functions uses precise algebraic properties of the arihmetical Shimura differential operator. The book could be very useful for postgraduate students and for non-experts giving a quick access to a rapidly developping domain of algebraic number theory: ...

  16. A standard deviation selection in evolutionary algorithm for grouper fish feed formulation

    Science.gov (United States)

    Cai-Juan, Soong; Ramli, Razamin; Rahman, Rosshairy Abdul

    2016-10-01

    Malaysia is one of the major producer countries for fishery production due to its location in the equatorial environment. Grouper fish is one of the potential markets in contributing to the income of the country due to its desirable taste, high demand and high price. However, the demand of grouper fish is still insufficient from the wild catch. Therefore, there is a need to farm grouper fish to cater to the market demand. In order to farm grouper fish, there is a need to have prior knowledge of the proper nutrients needed because there is no exact data available. Therefore, in this study, primary data and secondary data are collected even though there is a limitation of related papers and 30 samples are investigated by using standard deviation selection in Evolutionary algorithm. Thus, this study would unlock frontiers for an extensive research in respect of grouper fish feed formulation. Results shown that the fitness of standard deviation selection in evolutionary algorithm is applicable. The feasible and low fitness, quick solution can be obtained. These fitness can be further predicted to minimize cost in farming grouper fish.

  17. Competing Biases in Mental Arithmetic: When Division Is More and Multiplication Is Less.

    Science.gov (United States)

    Shaki, Samuel; Fischer, Martin H

    2017-01-01

    Mental arithmetic exhibits various biases. Among those is a tendency to overestimate addition and to underestimate subtraction outcomes. Does such "operational momentum" (OM) also affect multiplication and division? Twenty-six adults produced lines whose lengths corresponded to the correct outcomes of multiplication and division problems shown in symbolic format. We found a reliable tendency to over-estimate division outcomes, i.e., reverse OM. We suggest that anchoring on the first operand (a tendency to use this number as a reference for further quantitative reasoning) contributes to cognitive biases in mental arithmetic.

  18. On the Organization of Parallel Operation of Some Algorithms for Finding the Shortest Path on a Graph on a Computer System with Multiple Instruction Stream and Single Data Stream

    Directory of Open Access Journals (Sweden)

    V. E. Podol'skii

    2015-01-01

    Full Text Available The paper considers the implementing Bellman-Ford and Lee algorithms to find the shortest graph path on a computer system with multiple instruction stream and single data stream (MISD. The MISD computer is a computer that executes commands of arithmetic-logical processing (on the CPU and commands of structures processing (on the structures processor in parallel on a single data stream. Transformation of sequential programs into the MISD programs is a labor intensity process because it requires a stream of the arithmetic-logical processing to be manually separated from that of the structures processing. Algorithms based on the processing of data structures (e.g., algorithms on graphs show high performance on a MISD computer. Bellman-Ford and Lee algorithms for finding the shortest path on a graph are representatives of these algorithms. They are applied to robotics for automatic planning of the robot movement in-situ. Modification of Bellman-Ford and Lee algorithms for finding the shortest graph path in coprocessor MISD mode and the parallel MISD modification of these algorithms were first obtained in this article. Thus, this article continues a series of studies on the transformation of sequential algorithms into MISD ones (Dijkstra and Ford-Fulkerson 's algorithms and has a pronouncedly applied nature. The article also presents the analysis results of Bellman-Ford and Lee algorithms in MISD mode. The paper formulates the basic trends of a technique for parallelization of algorithms into arithmetic-logical processing stream and structures processing stream. Among the key areas for future research, development of the mathematical approach to provide a subsequently formalized and automated process of parallelizing sequential algorithms between the CPU and structures processor is highlighted. Among the mathematical models that can be used in future studies there are graph models of algorithms (e.g., dependency graph of a program. Due to the high

  19. Oscillatory EEG correlates of arithmetic strategies: A training study

    Directory of Open Access Journals (Sweden)

    Roland H. Grabner

    2012-10-01

    Full Text Available There has been a long tradition of research on mathematics education showing that children and adults use different strategies to solve arithmetic problems. Neurophysiological studies have recently begun to investigate the brain correlates of these strategies. The existing body of data, however, reflect static end points of the learning process and do not provide information on how brain activity changes in response to training or intervention. In this study, we explicitly address this issue by training participants in using fact retrieval strategies. We also investigate whether brain activity related to arithmetic fact learning is domain-specific or whether this generalizes to other learning materials, such as the solution of figural-spatial problems. Twenty adult students were trained on sets of two-digit multiplication problems and figural-spatial problems. After the training, they were presented with the trained and untrained problems while their brain activity was recorded by means of electroencephalography (EEG . In both problem types, the training resulted in accuracies over 90 % and significant decreases in solution times. Analyses of the oscillatory EEG data also revealed training effects across both problem types. Specifically, we observed training-related activity increases in the theta band (3-6 Hz and decreases in the lower alpha band (8-10 Hz, especially over parieto-occipital and parietal brain regions. These results provide the first evidence that a short term fact retrieval training results in significant changes in oscillatory EEG activity. These findings further corroborate the role of the theta band in the retrieval of semantic information from memory and suggest that theta activity is not only sensitive to fact retrieval in mental arithmetic but also in other domains.

  20. RAID-6 reed-solomon codes with asymptotically optimal arithmetic complexities

    KAUST Repository

    Lin, Sian-Jheng; Alloum, Amira; Al-Naffouri, Tareq Y.

    2016-01-01

    present a configuration of the factors of the second-parity formula, such that the arithmetic complexity can reach the optimal complexity bound when the code length approaches infinity. In the proposed approach, the intermediate data used for the first

  1. Why Is Learning Fraction and Decimal Arithmetic so Difficult?

    Science.gov (United States)

    Lortie-Forgues, Hugues; Tian, Jing; Siegler, Robert S.

    2015-01-01

    Fraction and decimal arithmetic are crucial for later mathematics achievement and for ability to succeed in many professions. Unfortunately, these capabilities pose large difficulties for many children and adults, and students' proficiency in them has shown little sign of improvement over the past three decades. To summarize what is known about…

  2. A wild model of linear arithmetic and discretely ordered modules

    Czech Academy of Sciences Publication Activity Database

    Glivický, Petr; Pudlák, Pavel

    2017-01-01

    Roč. 63, č. 6 (2017), s. 501-508 ISSN 0942-5616 EU Projects: European Commission(XE) 339691 - FEALORA Institutional support: RVO:67985840 Keywords : linear arithmetics Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 0.250, year: 2016

  3. Parallel algorithms for interactive manipulation of digital terrain models

    Science.gov (United States)

    Davis, E. W.; Mcallister, D. F.; Nagaraj, V.

    1988-01-01

    Interactive three-dimensional graphics applications, such as terrain data representation and manipulation, require extensive arithmetic processing. Massively parallel machines are attractive for this application since they offer high computational rates, and grid connected architectures provide a natural mapping for grid based terrain models. Presented here are algorithms for data movement on the massive parallel processor (MPP) in support of pan and zoom functions over large data grids. It is an extension of earlier work that demonstrated real-time performance of graphics functions on grids that were equal in size to the physical dimensions of the MPP. When the dimensions of a data grid exceed the processing array size, data is packed in the array memory. Windows of the total data grid are interactively selected for processing. Movement of packed data is needed to distribute items across the array for efficient parallel processing. Execution time for data movement was found to exceed that for arithmetic aspects of graphics functions. Performance figures are given for routines written in MPP Pascal.

  4. The arithmetic of supersymmetric vacua

    Energy Technology Data Exchange (ETDEWEB)

    Bourget, Antoine; Troost, Jan [Laboratoire de Physique Théorique de l’École Normale Supérieure, CNRS, PSL Research University, Sorbonne Universités,75005 Paris (France)

    2016-07-07

    We provide explicit formulas for the number of vacua of four-dimensional pure N=1 super Yang-Mills theories on a circle, with any simple gauge algebra and any choice of center and spectrum of line operators. The formula for the (SU(N)/ℤ{sub m}){sub n} theory is a key ingredient in the semi-classical calculation of the number of massive vacua of N=1{sup ∗} gauge theories with gauge algebra su(n), compactified on a circle. Using arithmetic, we express that number in an SL(2,ℤ) duality invariant manner. We confirm our tally of massive vacua of the N=1{sup ∗} theories by a count of inequivalent extrema of the exact superpotential.

  5. Numeral words and arithmetic operations in the Alor-Pantar languages

    NARCIS (Netherlands)

    Schapper, Antoinette; Holton, Gary; Klamer, Marian; Kratochvíl, František; Robinson, Laura; Klamer, Marian

    2014-01-01

    The indigenous numerals of the AP languages, as well as the indigenous structures for arithmetic operations are currently under pressure from Indonesian, and will inevitably be replaced with Indonesian forms and structures. This chapter presents a documentary record of the forms and patterns

  6. A fast direct sampling algorithm for equilateral closed polygons

    International Nuclear Information System (INIS)

    Cantarella, Jason; Duplantier, Bertrand; Shonkwiler, Clayton; Uehara, Erica

    2016-01-01

    Sampling equilateral closed polygons is of interest in the statistical study of ring polymers. Over the past 30 years, previous authors have proposed a variety of simple Markov chain algorithms (but have not been able to show that they converge to the correct probability distribution) and complicated direct samplers (which require extended-precision arithmetic to evaluate numerically unstable polynomials). We present a simple direct sampler which is fast and numerically stable, and analyze its runtime using a new formula for the volume of equilateral polygon space as a Dirichlet-type integral. (paper)

  7. A Learning Trajectory for Teaching Social Arithmetic using RME Approach

    Science.gov (United States)

    Fauzan, A.; Armiati, A.; Ceria, C.

    2018-04-01

    This paper discusses the role of a learning trajectory (LT) in promoting students’ reasoning when they learn social arithmetic using Realistic Mathematics Education (RME) approach. In our LT, we built the intertwining of the concepts such as profit, loss, percentage, discount, and interest rate, so that the students understand the relations among them. The LT was developed through a design research that consisted of a cyclic process of preparing for the experiment, conducting the experiment, and retrospective analysis. The research’s subject was 32 students at grade 7 MTsN Sintoga, Pariaman, Indonesia. Data were collected through observations, interviews, checklist, videotaping, and analyzing the students' works. The results showed that the LT could help the students to reinvent the concepts in social arithmetic. The students had more confidence to use their own strategies in solving contextual problems. The most important thing, we discovered the growth in the students’ mathematical reasoning.

  8. Visuo–spatial working memory is an important source of domain-general vulnerability in the development of arithmetic cognition

    Science.gov (United States)

    Ashkenazi, Sarit; Rosenberg-Lee, Miriam; Metcalfe, Arron W.S.; Swigart, Anna G.; Menon, Vinod

    2014-01-01

    The study of developmental disorders can provide a unique window into the role of domain-general cognitive abilities and neural systems in typical and atypical development. Mathematical disabilities (MD) are characterized by marked difficulty in mathematical cognition in the presence of preserved intelligence and verbal ability. Although studies of MD have most often focused on the role of core deficits in numerical processing, domain-general cognitive abilities, in particular working memory (WM), have also been implicated. Here we identify specific WM components that are impaired in children with MD and then examine their role in arithmetic problem solving. Compared to typically developing (TD) children, the MD group demonstrated lower arithmetic performance and lower visuo-spatial working memory (VSWM) scores with preserved abilities on the phonological and central executive components of WM. Whole brain analysis revealed that, during arithmetic problem solving, left posterior parietal cortex, bilateral dorsolateral and ventrolateral prefrontal cortex, cingulate gyrus and precuneus, and fusiform gyrus responses were positively correlated with VSWM ability in TD children, but not in the MD group. Additional analyses using a priori posterior parietal cortex regions previously implicated in WM tasks, demonstrated a convergent pattern of results during arithmetic problem solving. These results suggest that MD is characterized by a common locus of arithmetic and VSWM deficits at both the cognitive and functional neuroanatomical levels. Unlike TD children, children with MD do not use VSWM resources appropriately during arithmetic problem solving. This work advances our understanding of VSWM as an important domain-general cognitive process in both typical and atypical mathematical skill development. PMID:23896444

  9. Design of Improved Arithmetic Logic Unit in Quantum-Dot Cellular Automata

    Science.gov (United States)

    Heikalabad, Saeed Rasouli; Gadim, Mahya Rahimpour

    2018-06-01

    The quantum-dot cellular automata (QCA) can be replaced to overcome the limitation of CMOS technology. An arithmetic logic unit (ALU) is a basic structure of any computer devices. In this paper, design of improved single-bit arithmetic logic unit in quantum dot cellular automata is presented. The proposed structure for ALU has AND, OR, XOR and ADD operations. A unique 2:1 multiplexer, an ultra-efficient two-input XOR and a low complexity full adder are used in the proposed structure. Also, an extended design of this structure is provided for two-bit ALU in this paper. The proposed structure of ALU is simulated by QCADesigner and simulation result is evaluated. Evaluation results show that the proposed design has best performance in terms of area, complexity and delay compared to the previous designs.

  10. Decidable and undecidable arithmetic functions in actin filament networks

    Science.gov (United States)

    Schumann, Andrew

    2018-01-01

    The plasmodium of Physarum polycephalum is very sensitive to its environment, and reacts to stimuli with appropriate motions. Both the sensory and motor stages of these reactions are explained by hydrodynamic processes, based on fluid dynamics, with the participation of actin filament networks. This paper is devoted to actin filament networks as a computational medium. The point is that actin filaments, with contributions from many other proteins like myosin, are sensitive to extracellular stimuli (attractants as well as repellents), and appear and disappear at different places in the cell to change aspects of the cell structure—e.g. its shape. By assembling and disassembling actin filaments, some unicellular organisms, like Amoeba proteus, can move in response to various stimuli. As a result, these organisms can be considered a simple reversible logic gate—extracellular signals being its inputs and motions its outputs. In this way, we can implement various logic gates on amoeboid behaviours. These networks can embody arithmetic functions within p-adic valued logic. Furthermore, within these networks we can define the so-called diagonalization for deducing undecidable arithmetic functions.

  11. Brauer groups and obstruction problems moduli spaces and arithmetic

    CERN Document Server

    Hassett, Brendan; Várilly-Alvarado, Anthony; Viray, Bianca

    2017-01-01

    The contributions in this book explore various contexts in which the derived category of coherent sheaves on a variety determines some of its arithmetic. This setting provides new geometric tools for interpreting elements of the Brauer group. With a view towards future arithmetic applications, the book extends a number of powerful tools for analyzing rational points on elliptic curves, e.g., isogenies among curves, torsion points, modular curves, and the resulting descent techniques, as well as higher-dimensional varieties like K3 surfaces. Inspired by the rapid recent advances in our understanding of K3 surfaces, the book is intended to foster cross-pollination between the fields of complex algebraic geometry and number theory. Contributors: · Nicolas Addington · Benjamin Antieau · Kenneth Ascher · Asher Auel · Fedor Bogomolov · Jean-Louis Colliot-Thélène · Krishna Dasaratha · Brendan Hassett · Colin Ingalls · Martí Lahoz · Emanuele Macrì · Kelly McKinnie · Andrew Obus · Ekin Ozman · Raman...

  12. Low Power S-Box Architecture for AES Algorithm using Programmable Second Order Reversible Cellular Automata: An Application to WBAN.

    Science.gov (United States)

    Gangadari, Bhoopal Rao; Ahamed, Shaik Rafi

    2016-12-01

    In this paper, we presented a novel approach of low energy consumption architecture of S-Box used in Advanced Encryption Standard (AES) algorithm using programmable second order reversible cellular automata (RCA 2 ). The architecture entails a low power implementation with minimal delay overhead and the performance of proposed RCA 2 based S-Box in terms of security is evaluated using the cryptographic properties such as nonlinearity, correlation immunity bias, strict avalanche criteria, entropy and also found that the proposed architecture is secure enough for cryptographic applications. Moreover, the proposed AES algorithm architecture simulation studies show that energy consumption of 68.726 nJ, power dissipation of 3.856 mW for 0.18- μm at 13.69 MHz and energy consumption of 29.408 nJ, power dissipation of 1.65 mW for 0.13- μm at 13.69 MHz. The proposed AES algorithm with RCA 2 based S-Box shows a reduction power consumption by 50 % and energy consumption by 5 % compared to best classical S-Box and composite field arithmetic based AES algorithm. Apart from that, it is also shown that RCA 2 based S-Boxes are dynamic in nature, invertible, low power dissipation compared to that of LUT based S-Box and hence suitable for Wireless Body Area Network (WBAN) applications.

  13. Early language and executive skills predict variations in number and arithmetic skills in children at family-risk of dyslexia and typically developing controls.

    Science.gov (United States)

    Moll, Kristina; Snowling, Margaret J; Göbel, Silke M; Hulme, Charles

    2015-08-01

    Two important foundations for learning are language and executive skills. Data from a longitudinal study tracking the development of 93 children at family-risk of dyslexia and 76 controls was used to investigate the influence of these skills on the development of arithmetic. A two-group longitudinal path model assessed the relationships between language and executive skills at 3-4 years, verbal number skills (counting and number knowledge) and phonological processing skills at 4-5 years, and written arithmetic in primary school. The same cognitive processes accounted for variability in arithmetic skills in both groups. Early language and executive skills predicted variations in preschool verbal number skills, which in turn, predicted arithmetic skills in school. In contrast, phonological awareness was not a predictor of later arithmetic skills. These results suggest that verbal and executive processes provide the foundation for verbal number skills, which in turn influence the development of formal arithmetic skills. Problems in early language development may explain the comorbidity between reading and mathematics disorder.

  14. Alternating minima and maxima, Nash equilibria and bounded arithmetic

    Czech Academy of Sciences Publication Activity Database

    Pudlák, Pavel; Thapen, Neil

    2012-01-01

    Roč. 163, č. 5 (2012), s. 604-614 ISSN 0168-0072 R&D Projects: GA AV ČR IAA100190902 Institutional research plan: CEZ:AV0Z10190503 Keywords : proof complexity * bounded arithmetic * search problems Subject RIV: BA - General Mathematics Impact factor: 0.504, year: 2012 http://www.sciencedirect.com/science/article/pii/S016800721100090X

  15. Practical considerations for the implantation of a fuzzy control algorithm in a DSP

    International Nuclear Information System (INIS)

    Perez C, B.; Benitez R, J.S.; Pacheco S, J.O.

    2003-01-01

    The development of a digital system based on a DSP to implant a Mamdani type algorithm of fuzzy control whose objective is to regulate the neutron power in a nuclear research reactor Type TRIGA Mark III is presented. Its are simultaneously carried out the aggregation des fuzzy stages discreeting the universe of the output variable. The format MPF for the handling of the floating point in the arithmetic operations is used. (Author)

  16. Gas Source Localization via Behaviour Based Mobile Robot and Weighted Arithmetic Mean

    Science.gov (United States)

    Yeon, Ahmad Shakaff Ali; Kamarudin, Kamarulzaman; Visvanathan, Retnam; Mamduh Syed Zakaria, Syed Muhammad; Zakaria, Ammar; Munirah Kamarudin, Latifah

    2018-03-01

    This work is concerned with the localization of gas source in dynamic indoor environment using a single mobile robot system. Algorithms such as Braitenberg, Zig-Zag and the combination of the two were implemented on the mobile robot as gas plume searching and tracing behaviours. To calculate the gas source location, a weighted arithmetic mean strategy was used. All experiments were done on an experimental testbed consisting of a large gas sensor array (LGSA) to monitor real-time gas concentration within the testbed. Ethanol gas was released within the testbed and the source location was marked using a pattern that can be tracked by a pattern tracking system. A pattern template was also mounted on the mobile robot to track the trajectory of the mobile robot. Measurements taken by the mobile robot and the LGSA were then compared to verify the experiments. A combined total of 36.5 hours of real time experimental runs were done and the typical results from such experiments were presented in this paper. From the results, we obtained gas source localization errors between 0.4m to 1.2m from the real source location.

  17. Math anxiety differentially affects WAIS-IV arithmetic performance in undergraduates.

    Science.gov (United States)

    Buelow, Melissa T; Frakey, Laura L

    2013-06-01

    Previous research has shown that math anxiety can influence the math performance level; however, to date, it is unknown whether math anxiety influences performance on working memory tasks during neuropsychological evaluation. In the present study, 172 undergraduate students completed measures of math achievement (the Math Computation subtest from the Wide Range Achievement Test-IV), math anxiety (the Math Anxiety Rating Scale-Revised), general test anxiety (from the Adult Manifest Anxiety Scale-College version), and the three Working Memory Index tasks from the Wechsler Adult Intelligence Scale-IV Edition (WAIS-IV; Digit Span [DS], Arithmetic, Letter-Number Sequencing [LNS]). Results indicated that math anxiety predicted performance on Arithmetic, but not DS or LNS, above and beyond the effects of gender, general test anxiety, and math performance level. Our findings suggest that math anxiety can negatively influence WAIS-IV working memory subtest scores. Implications for clinical practice include the utilization of LNS in individuals expressing high math anxiety.

  18. Students creative thinking skills in solving two dimensional arithmetic series through research-based learning

    Science.gov (United States)

    Tohir, M.; Abidin, Z.; Dafik; Hobri

    2018-04-01

    Arithmetics is one of the topics in Mathematics, which deals with logic and detailed process upon generalizing formula. Creativity and flexibility are needed in generalizing formula of arithmetics series. This research aimed at analyzing students creative thinking skills in generalizing arithmetic series. The triangulation method and research-based learning was used in this research. The subjects were students of the Master Program of Mathematics Education in Faculty of Teacher Training and Education at Jember University. The data was collected by giving assignments to the students. The data collection was done by giving open problem-solving task and documentation study to the students to arrange generalization pattern based on the dependent function formula i and the function depend on i and j. Then, the students finished the next problem-solving task to construct arithmetic generalization patterns based on the function formula which depends on i and i + n and the sum formula of functions dependent on i and j of the arithmetic compiled. The data analysis techniques operative in this study was Miles and Huberman analysis model. Based on the result of data analysis on task 1, the levels of students creative thinking skill were classified as follows; 22,22% of the students categorized as “not creative” 38.89% of the students categorized as “less creative” category; 22.22% of the students categorized as “sufficiently creative” and 16.67% of the students categorized as “creative”. By contrast, the results of data analysis on task 2 found that the levels of students creative thinking skills were classified as follows; 22.22% of the students categorized as “sufficiently creative”, 44.44% of the students categorized as “creative” and 33.33% of the students categorized as “very creative”. This analysis result can set the basis for teaching references and actualizing a better teaching model in order to increase students creative thinking skills.

  19. Visuo-spatial working memory is an important source of domain-general vulnerability in the development of arithmetic cognition.

    Science.gov (United States)

    Ashkenazi, Sarit; Rosenberg-Lee, Miriam; Metcalfe, Arron W S; Swigart, Anna G; Menon, Vinod

    2013-09-01

    The study of developmental disorders can provide a unique window into the role of domain-general cognitive abilities and neural systems in typical and atypical development. Mathematical disabilities (MD) are characterized by marked difficulty in mathematical cognition in the presence of preserved intelligence and verbal ability. Although studies of MD have most often focused on the role of core deficits in numerical processing, domain-general cognitive abilities, in particular working memory (WM), have also been implicated. Here we identify specific WM components that are impaired in children with MD and then examine their role in arithmetic problem solving. Compared to typically developing (TD) children, the MD group demonstrated lower arithmetic performance and lower visuo-spatial working memory (VSWM) scores with preserved abilities on the phonological and central executive components of WM. Whole brain analysis revealed that, during arithmetic problem solving, left posterior parietal cortex, bilateral dorsolateral and ventrolateral prefrontal cortex, cingulate gyrus and precuneus, and fusiform gyrus responses were positively correlated with VSWM ability in TD children, but not in the MD group. Additional analyses using a priori posterior parietal cortex regions previously implicated in WM tasks, demonstrated a convergent pattern of results during arithmetic problem solving. These results suggest that MD is characterized by a common locus of arithmetic and VSWM deficits at both the cognitive and functional neuroanatomical levels. Unlike TD children, children with MD do not use VSWM resources appropriately during arithmetic problem solving. This work advances our understanding of VSWM as an important domain-general cognitive process in both typical and atypical mathematical skill development. © 2013 Elsevier Ltd. All rights reserved.

  20. Arithmetic properties of $\\ell$-regular overpartition pairs

    OpenAIRE

    NAIKA, MEGADAHALLI SIDDA MAHADEVA; SHIVASHANKAR, CHANDRAPPA

    2017-01-01

    In this paper, we investigate the arithmetic properties of $\\ell$-regular overpartition pairs. Let $\\overline{B}_{\\ell}(n)$ denote the number of $\\ell$-regular overpartition pairs of $n$. We will prove the number of Ramanujan-like congruences and infinite families of congruences modulo 3, 8, 16, 36, 48, 96 for $\\overline{B}_3(n)$ and modulo 3, 16, 64, 96 for $\\overline{B}_4(n)$. For example, we find that for all nonnegative integers $\\alpha$ and $n$, $\\overline{B}_{3}(3^{\\alpha}(3n+2))\\equiv ...

  1. Fourier transforms on Cantor sets: A study in non-Diophantine arithmetic and calculus

    International Nuclear Information System (INIS)

    Aerts, Diederik; Czachor, Marek; Kuna, Maciej

    2016-01-01

    Highlights: • Fractal arithmetic allows to define Fourier transforms on Cantor-like sets. • General construction is illustrated on the example of a sawtooth signal. • The formalism is much simpler than the approaches discussed so far in the literature. - Abstract: Fractals equipped with intrinsic arithmetic lead to a natural definition of differentiation, integration, and complex structure. Applying the formalism to the problem of a Fourier transform on fractals we show that the resulting transform has all the required basic properties. As an example we discuss a sawtooth signal on the ternary middle-third Cantor set. The formalism works also for fractals that are not self-similar.

  2. Effects of cold-pressor and mental arithmetic on pupillary light reflex

    International Nuclear Information System (INIS)

    Davis, B C; Daluwatte, C; Colona, N C; Yao, D G

    2013-01-01

    Dynamic pupillary light reflex (PLR) is a simple neurological test that can be useful for assessment of autonomic disorders. In this study, we investigated the changes in PLR induced by mental arithmetic task and cold pressor trials which are often applied in research as model systems to elicit autonomic responses. PLR was recorded before, during and after mental arithmetic and cold pressor tasks in 20 healthy adults (ten males and ten females). Stress-induced sympathetic activation was evident as shown in the increased blood pressure during both tasks. Although the pupillary constriction amplitude did not show significant changes, both constriction time and redilation time changed during the tasks. A significant gender effect was observed in cold pressor that suggested more sympathetic activation in males and faster parasympathetic activation in females in response to light stimulation under cold pressor. (paper)

  3. Schema Knowledge for Solving Arithmetic Story Problems: Some Affective Components.

    Science.gov (United States)

    Marshall, Sandra P.

    This report discusses the role of affect in cognitive processing. The importance of affect in processing mathematical information is described in the context of solving arithmetic story problems. Some ideas are offered about the way affective responses to mathematical problem solving situations influence the development, maintenance, and retrieval…

  4. Fleeting footsteps tracing the conception of arithmetic and algebra in ancient China

    CERN Document Server

    Yong, Lam Lay

    2004-01-01

    The Hindu-Arabic numeral system (1, 2, 3,...) is one of mankind''sgreatest achievements and one of its most commonly usedinventions. How did it originate? Those who have written about thenumeral system have hypothesized that it originated in India; however,there is little evidence to support this claim. This book provides considerable evidence to show that theHindu-Arabic numeral system, despite its commonly accepted name,has its origins in the Chinese rod numeral system. This system waswidely used in China from antiquity till the 16th century. It was usedby officials, astronomers, traders and others to perform addition,subtraction, multiplication, division and other arithmetic operations,and also used by mathematicians to develop arithmetic andalgebra. Based on this system, numerous mathematical treatises werewritten.

  5. On the arithmetic of fractal dimension using hyperhelices

    International Nuclear Information System (INIS)

    Toledo-Suarez, Carlos D.

    2009-01-01

    A hyperhelix is a fractal curve generated by coiling a helix around a rect line, then another helix around the first one, a third around the second... an infinite number of times. A way to generate hyperhelices with any desired fractal dimension is presented, leading to the result that they have embedded an algebraic structure that allows making arithmetic with fractal dimensions and to the idea of an infinitesimal of fractal dimension

  6. Enhancing performance in numerical magnitude processing and mental arithmetic using transcranial Direct Current Stimulation (tDCS

    Directory of Open Access Journals (Sweden)

    Tobias U. Hauser

    2013-06-01

    Full Text Available The ability to accurately process numerical magnitudes and solve mental arithmetic is of highest importance for schooling and professional career. Although impairments in these domains in disorders such as developmental dyscalculia (DD are highly detrimental, remediation is still sparse. In recent years, transcranial brain stimulation methods such as transcranial Direct Current Stimulation (tDCS have been suggested as a treatment for various neurologic and neuropsychiatric disorders. The posterior parietal cortex (PPC is known to be crucially involved in numerical magnitude processing and mental arithmetic. In this study, we evaluated whether tDCS has a beneficial effect on numerical magnitude processing and mental arithmetic. Due to the unclear lateralization, we stimulated the left, right as well as both hemispheres simultaneously in two experiments. We found that left anodal tDCS significantly enhanced performance in a number comparison and a subtraction task, while bilateral and right anodal tDCS did not induce any improvements compared to sham. Our findings demonstrate that the left PPC is causally involved in numerical magnitude processing and mental arithmetic. Furthermore, we show that these cognitive functions can be enhanced by means of tDCS. These findings encourage to further investigate the beneficial effect of tDCS in the domain of mathematics in healthy and impaired humans.

  7. Alternative proposal of arithmetic and image operations in optical parallel computation

    Science.gov (United States)

    Ghosh, Partha; Das, Partha P.; Mukhopadhay, Sourangshu

    2001-10-01

    Here, we refer our new proposal of applying multi-valued logic (particularly tristate logic) to develop logic gates and systems for arithmetic operation. Space-variant approach is used here to implement the functioning. Also triple input image detection is done here.

  8. Early language and executive skills predict variations in number and arithmetic skills in children at family-risk of dyslexia and typically developing controls

    Science.gov (United States)

    Moll, Kristina; Snowling, Margaret J.; Göbel, Silke M.; Hulme, Charles

    2015-01-01

    Two important foundations for learning are language and executive skills. Data from a longitudinal study tracking the development of 93 children at family-risk of dyslexia and 76 controls was used to investigate the influence of these skills on the development of arithmetic. A two-group longitudinal path model assessed the relationships between language and executive skills at 3–4 years, verbal number skills (counting and number knowledge) and phonological processing skills at 4–5 years, and written arithmetic in primary school. The same cognitive processes accounted for variability in arithmetic skills in both groups. Early language and executive skills predicted variations in preschool verbal number skills, which in turn, predicted arithmetic skills in school. In contrast, phonological awareness was not a predictor of later arithmetic skills. These results suggest that verbal and executive processes provide the foundation for verbal number skills, which in turn influence the development of formal arithmetic skills. Problems in early language development may explain the comorbidity between reading and mathematics disorder. PMID:26412946

  9. Relational Thinking: Learning Arithmetic in Order to Promote Algebraic Thinking

    Science.gov (United States)

    Napaphun, Vishnu

    2012-01-01

    Trends in the curriculum reform propose that algebra should be taught throughout the grades, starting in elementary school. The aim should be to decrease the discontinuity between the arithmetic in elementary school and the algebra in upper grades. This study was conducted to investigate and characterise upper elementary school students…

  10. Algebra 1 groups, rings, fields and arithmetic

    CERN Document Server

    Lal, Ramji

    2017-01-01

    This is the first in a series of three volumes dealing with important topics in algebra. It offers an introduction to the foundations of mathematics together with the fundamental algebraic structures, namely groups, rings, fields, and arithmetic. Intended as a text for undergraduate and graduate students of mathematics, it discusses all major topics in algebra with numerous motivating illustrations and exercises to enable readers to acquire a good understanding of the basic algebraic structures, which they can then use to find the exact or the most realistic solutions to their problems.

  11. Arithmetic fundamental groups and moduli of curves

    International Nuclear Information System (INIS)

    Makoto Matsumoto

    2000-01-01

    This is a short note on the algebraic (or sometimes called arithmetic) fundamental groups of an algebraic variety, which connects classical fundamental groups with Galois groups of fields. A large part of this note describes the algebraic fundamental groups in a concrete manner. This note gives only a sketch of the fundamental groups of the algebraic stack of moduli of curves. Some application to a purely topological statement, i.e., an obstruction to the subjectivity of Johnson homomorphisms in the mapping class groups, which comes from Galois group of Q, is explained. (author)

  12. Pipeline Implementation of Polyphase PSO for Adaptive Beamforming Algorithm

    Directory of Open Access Journals (Sweden)

    Shaobing Huang

    2017-01-01

    Full Text Available Adaptive beamforming is a powerful technique for anti-interference, where searching and tracking optimal solutions are a great challenge. In this paper, a partial Particle Swarm Optimization (PSO algorithm is proposed to track the optimal solution of an adaptive beamformer due to its great global searching character. Also, due to its naturally parallel searching capabilities, a novel Field Programmable Gate Arrays (FPGA pipeline architecture using polyphase filter bank structure is designed. In order to perform computations with large dynamic range and high precision, the proposed implementation algorithm uses an efficient user-defined floating-point arithmetic. In addition, a polyphase architecture is proposed to achieve full pipeline implementation. In the case of PSO with large population, the polyphase architecture can significantly save hardware resources while achieving high performance. Finally, the simulation results are presented by cosimulation with ModelSim and SIMULINK.

  13. Angular quadrature generator for neutron transport SN calculations in slab geometry with arbitrary arithmetic precision

    International Nuclear Information System (INIS)

    Dominguez, Dany S.; Oliveira, Francisco B.S.; Barros, Ricardo C.

    2003-01-01

    We present in this paper a multiplatform computational code to calculate elements of Gauss-Legendre angular quadrature sets of arbitrary order used in slab-geometry discrete ordinates (S N ) formulation of neutron transport equation. In the code, the values can be computed with arbitrary arithmetic precision based on the approach of exact computing floating-point numbers. Calculation routines have been developed in the common language ANSI C using standard compiler gcc and the libraries of the open code GMP (GNU Multi precision Library). The code has a graphical interface in order to facilitate user interaction and numerical results analysis. The code architecture allows it to run on different platforms such as Unix, Linux and Windows. Numerical results and performance measures are also given. (author)

  14. Optoelectronic switch matrix as a look-up table for residue arithmetic.

    Science.gov (United States)

    Macdonald, R I

    1987-10-01

    The use of optoelectronic matrix switches to perform look-up table functions in residue arithmetic processors is proposed. In this application, switchable detector arrays give the advantage of a greatly reduced requirement for optical sources by comparison with previous optoelectronic residue processors.

  15. Interactivity And Mental Arithmetic: Coupling Mind And World Transforms And Enhances Performance

    Directory of Open Access Journals (Sweden)

    Guthrie Lisa G.

    2015-06-01

    Full Text Available Interactivity has been linked to better performance in problem solving, due in part to a more efficient allocation of attentional resources, a better distribution of cognitive load, but perhaps more important by enabling the reasoner to shape and reshape the physical problem presentation to promote the development of the problem solution. Interactivity in solving quotidian arithmetic problems involves gestures, pointing, and the recruitment of artefacts to facilitate computation and augment efficiency. In the experiment reported here, different types of interactivity were examined with a series of mental arithmetic problems. Using a repeated-measures design, participants solved series of five 11-digit sums in four conditions that varied in the type of interactivity: (i no interactivity (participants solved the problems with their hands on the table top, (ii pointing (participants could point at the numbers, (iii pen and paper (participants could note interim totals with a pen, and (iv tokens (the sums were presented as 11 numbered tokens the arrangement of which participants were free to modify as they proceeded to the solution. Performance in the four conditions was measured in terms of accuracy, calculation error, and efficiency (a ratio composed of the proportion correct over the proportion of time invested in working on the sums. These quantitative analyses were supplemented by a detailed qualitative examination of a participant’s actions in the different conditions. The integration of artefacts, such as tokens or a pen, offered reasoners the opportunity to reconfigure the physical presentation of the problem, enacting different arithmetic strategies: the affordance landscape shifts as the problem trajectory is enacted through interactivity, and this generally produced better “mental” arithmetic performance. Participants also felt more positive about and better engaged with the task when they could reconfigure the problem presentation

  16. Attention Contributes to Arithmetic Deficits in New-Onset Childhood Absence Epilepsy.

    Science.gov (United States)

    Cheng, Dazhi; Yan, Xiuxian; Gao, Zhijie; Xu, Keming; Chen, Qian

    2017-01-01

    Neuropsychological studies indicate that new-onset childhood absence epilepsy (CAE) is associated with deficits in attention and executive functioning. However, the contribution of these deficits to impaired academic performance remains unclear. We aimed to examine whether attention and executive functioning deficits account for the academic difficulties prevalent in patients with new-onset CAE. We analyzed cognitive performance in several domains, including language, mathematics, psychomotor speed, spatial ability, memory, general intelligence, attention, and executive functioning, in 35 children with new-onset CAE and 33 control participants. Patients with new-onset CAE exhibited deficits in mathematics, general intelligence, attention, and executive functioning. Furthermore, attention deficits, as measured by a visual tracing task, accounted for impaired arithmetic performance in the new-onset CAE group. Therefore, attention deficits, rather than impaired general intelligence or executive functioning, may be responsible for arithmetic performance deficits in patients with new-onset CAE.

  17. How Do Different Aspects of Spatial Skills Relate to Early Arithmetic and Number Line Estimation?

    Directory of Open Access Journals (Sweden)

    Véronique Cornu

    2017-12-01

    Full Text Available The present study investigated the predictive role of spatial skills for arithmetic and number line estimation in kindergarten children (N = 125. Spatial skills are known to be related to mathematical development, but due to the construct’s non-unitary nature, different aspects of spatial skills need to be differentiated. In the present study, a spatial orientation task, a spatial visualization task and visuo-motor integration task were administered to assess three different aspects of spatial skills. Furthermore, we assessed counting abilities, knowledge of Arabic numerals, quantitative knowledge, as well as verbal working memory and verbal intelligence in kindergarten. Four months later, the same children performed an arithmetic and a number line estimation task to evaluate how the abilities measured at Time 1 predicted early mathematics outcomes. Hierarchical regression analysis revealed that children’s performance in arithmetic was predicted by their performance on the spatial orientation and visuo-motor integration task, as well as their knowledge of the Arabic numerals. Performance in number line estimation was significantly predicted by the children’s spatial orientation performance. Our findings emphasize the role of spatial skills, notably spatial orientation, in mathematical development. The relation between spatial orientation and arithmetic was partially mediated by the number line estimation task. Our results further show that some aspects of spatial skills might be more predictive of mathematical development than others, underlining the importance to differentiate within the construct of spatial skills when it comes to understanding numerical development.

  18. Automatically Proving Termination and Memory Safety for Programs with Pointer Arithmetic

    DEFF Research Database (Denmark)

    Ströder, Thomas; Giesl, Jürgen; Brockschmidt, Marc

    2017-01-01

    While automated verification of imperative programs has been studied intensively, proving termination of programs with explicit pointer arithmetic fully automatically was still an open problem. To close this gap, we introduce a novel abstract domain that can track allocated memory in detail. We use...

  19. Arithmetic Facts Storage Deficit: The Hypersensitivity-to-Interference in Memory Hypothesis

    Science.gov (United States)

    De Visscher, Alice; Noël, Marie-Pascale

    2014-01-01

    Dyscalculia, or mathematics learning disorders, is currently known to be heterogeneous (Wilson & Dehaene, 2007). While various profiles of dyscalculia coexist, a general and persistent hallmark of this math learning disability is the difficulty in memorizing arithmetic facts (Geary, Hoard & Hamson, 1999; Jordan & Montani, 1997; Slade…

  20. Comparing and Transforming: An Application of Piaget's Morphisms Theory to the Development of Class Inclusion and Arithmetic Problem Solving.

    Science.gov (United States)

    Barrouillet, Pierre; Poirier, Louise

    1997-01-01

    Outlines Piaget's late ideas on categories and morphisms and the impact of these ideas on the comprehension of the inclusion relationship and the solution of arithmetic problems. Reports a study in which fourth through sixth graders were given arithmetic problems involving two known quantities associated with changes rather than states. Identified…

  1. Design of arithmetic circuits in quantum dot cellular automata nanotechnology

    CERN Document Server

    Sridharan, K

    2015-01-01

    This research monograph focuses on the design of arithmetic circuits in Quantum Dot Cellular Automata (QCA). Using the fact that the 3-input majority gate is a primitive in QCA, the book sets out to discover hitherto unknown properties of majority logic in the context of arithmetic circuit designs. The pursuit for efficient adders in QCA takes two forms. One involves application of the new results in majority logic to existing adders. The second involves development of a custom adder for QCA technology. A QCA adder named as hybrid adder is proposed and it is shown that it outperforms existing multi-bit adders with respect to area and delay. The work is extended to the design of a low-complexity multiplier for signed numbers in QCA. Furthermore the book explores two aspects unique to QCA technology, namely thermal robustness and the role of interconnects. In addition, the book introduces the reader to QCA layout design and simulation using QCADesigner. Features & Benefits: This research-based book: ·  �...

  2. Online EEG-Based Workload Adaptation of an Arithmetic Learning Environment.

    Science.gov (United States)

    Walter, Carina; Rosenstiel, Wolfgang; Bogdan, Martin; Gerjets, Peter; Spüler, Martin

    2017-01-01

    In this paper, we demonstrate a closed-loop EEG-based learning environment, that adapts instructional learning material online, to improve learning success in students during arithmetic learning. The amount of cognitive workload during learning is crucial for successful learning and should be held in the optimal range for each learner. Based on EEG data from 10 subjects, we created a prediction model that estimates the learner's workload to obtain an unobtrusive workload measure. Furthermore, we developed an interactive learning environment that uses the prediction model to estimate the learner's workload online based on the EEG data and adapt the difficulty of the learning material to keep the learner's workload in an optimal range. The EEG-based learning environment was used by 13 subjects to learn arithmetic addition in the octal number system, leading to a significant learning effect. The results suggest that it is feasible to use EEG as an unobtrusive measure of cognitive workload to adapt the learning content. Further it demonstrates that a promptly workload prediction is possible using a generalized prediction model without the need for a user-specific calibration.

  3. Comparison of 30-2 Standard and Fast programs of Swedish Interactive Threshold Algorithm of Humphrey Field Analyzer for perimetry in patients with intracranial tumors.

    Science.gov (United States)

    Singh, Manav Deep; Jain, Kanika

    2017-11-01

    To find out whether 30-2 Swedish Interactive Threshold Algorithm (SITA) Fast is comparable to 30-2 SITA Standard as a tool for perimetry among the patients with intracranial tumors. This was a prospective cross-sectional study involving 80 patients aged ≥18 years with imaging proven intracranial tumors and visual acuity better than 20/60. The patients underwent multiple visual field examinations using the two algorithms till consistent and repeatable results were obtained. A total of 140 eyes of 80 patients were analyzed. Almost 60% of patients undergoing perimetry with SITA Standard required two or more sessions to obtain consistent results, whereas the same could be obtained in 81.42% with SITA Fast in the first session itself. Of 140 eyes, 70 eyes had recordable field defects and the rest had no defects as detected by either of the two algorithms. Mean deviation (MD) (P = 0.56), pattern standard deviation (PSD) (P = 0.22), visual field index (P = 0.83) and number of depressed points at P 0.5% on MD and PSD probability plots showed no statistically significant difference between two algorithms. Bland-Altman test showed that considerable variability existed between two algorithms. Perimetry performed by SITA Standard and SITA Fast algorithm of Humphrey Field Analyzer gives comparable results among the patients of intracranial tumors. Being more time efficient and with a shorter learning curve, SITA Fast my be recommended as a standard test for the purpose of perimetry among these patients.

  4. What's Behind a "+" Sign? Perceiving an Arithmetic Operator Recruits Brain Circuits for Spatial Orienting.

    Science.gov (United States)

    Mathieu, Romain; Epinat-Duclos, Justine; Sigovan, Monica; Breton, Audrey; Cheylus, Anne; Fayol, Michel; Thevenot, Catherine; Prado, Jérôme

    2018-05-01

    Do mathematical symbols evoke spatial representations? Although behavioral studies have long demonstrated interactions between space and the processing of Arabic digits, how to interpret these results remains controversial. Here, we tested whether activity in regions supporting spatial processing contributes to the processing of symbols conveying fundamental arithmetic concepts-such as operation signs-even in the absence of associated digits. Using functional magnetic resonance imaging, we show that merely perceiving a "+" sign triggers activity in brain regions that support the orienting of spatial attention in adults. Activity in these regions was greater for "+" than for "×" signs, indicating that it is modulated by whether an operator reflects an operation that evokes numerical manipulation (rather than rote memorization). Finally, the degree to which subjects activated a spatial region in response to a "+" sign was correlated with the degree to which subjects benefited from being briefly presented with that sign before having to calculate a single-digit addition problem, an effect termed operator-priming. Therefore, not only are some arithmetic operators linked to spatial intuitions, but such intuitions might also have an important role during arithmetic calculation. More generally, our findings support the view that mathematical symbols inherently evoke spatial representations.

  5. Standardized evaluation framework for evaluating coronary artery stenosis detection, stenosis quantification and lumen segmentation algorithms in computed tomography angiography.

    Science.gov (United States)

    Kirişli, H A; Schaap, M; Metz, C T; Dharampal, A S; Meijboom, W B; Papadopoulou, S L; Dedic, A; Nieman, K; de Graaf, M A; Meijs, M F L; Cramer, M J; Broersen, A; Cetin, S; Eslami, A; Flórez-Valencia, L; Lor, K L; Matuszewski, B; Melki, I; Mohr, B; Oksüz, I; Shahzad, R; Wang, C; Kitslaar, P H; Unal, G; Katouzian, A; Örkisz, M; Chen, C M; Precioso, F; Najman, L; Masood, S; Ünay, D; van Vliet, L; Moreno, R; Goldenberg, R; Vuçini, E; Krestin, G P; Niessen, W J; van Walsum, T

    2013-12-01

    Though conventional coronary angiography (CCA) has been the standard of reference for diagnosing coronary artery disease in the past decades, computed tomography angiography (CTA) has rapidly emerged, and is nowadays widely used in clinical practice. Here, we introduce a standardized evaluation framework to reliably evaluate and compare the performance of the algorithms devised to detect and quantify the coronary artery stenoses, and to segment the coronary artery lumen in CTA data. The objective of this evaluation framework is to demonstrate the feasibility of dedicated algorithms to: (1) (semi-)automatically detect and quantify stenosis on CTA, in comparison with quantitative coronary angiography (QCA) and CTA consensus reading, and (2) (semi-)automatically segment the coronary lumen on CTA, in comparison with expert's manual annotation. A database consisting of 48 multicenter multivendor cardiac CTA datasets with corresponding reference standards are described and made available. The algorithms from 11 research groups were quantitatively evaluated and compared. The results show that (1) some of the current stenosis detection/quantification algorithms may be used for triage or as a second-reader in clinical practice, and that (2) automatic lumen segmentation is possible with a precision similar to that obtained by experts. The framework is open for new submissions through the website, at http://coronary.bigr.nl/stenoses/. Copyright © 2013 Elsevier B.V. All rights reserved.

  6. High-performers use the phonological loop less to process mental arithmetic during working memory tasks.

    Science.gov (United States)

    Otsuka, Yuki; Osaka, Naoyuki

    2015-01-01

    This study investigated the effects of three working memory components-the central executive, phonological loop, and visuospatial sketchpad-on performance differences in complex mental arithmetic between individuals. Using the dual-task method, we examined how performance during two-digit addition was affected by load on the central executive (random tapping condition), phonological loop (articulatory suppression condition), and visuospatial sketchpad (spatial tapping condition) compared to that under no load (control condition) in high- and low-performers of complex mental arithmetic in Experiment 1. Low-performers showed an increase in errors under the random tapping and articulatory suppression conditions, whereas high-performers showed an increase of errors only under the random tapping condition. In Experiment 2, we conducted similar experiments on only the high-performers but used a shorter presentation time of each number. We found the same pattern for performing complex mental arithmetic as seen in Experiment 1. These results indicate that high-performers might reduce their dependence on the phonological loop, because the central executive enables them to choose a strategy in which they use less working memory capacity.

  7. The geometric and arithmetic volume of Shimura varieties of orthogonal type

    CERN Document Server

    Hörmann, Fritz

    2015-01-01

    This book outlines a functorial theory of integral models of (mixed) Shimura varieties and of their toroidal compactifications, for odd primes of good reduction. This is the integral version, developed in the author's thesis, of the theory invented by Deligne and Pink in the rational case. In addition, the author develops a theory of arithmetic Chern classes of integral automorphic vector bundles with singular metrics using the work of Burgos, Kramer and Kühn. The main application is calculating arithmetic volumes or "heights" of Shimura varieties of orthogonal type using Borcherds' famous modular forms with their striking product formula-an idea due to Bruinier-Burgos-Kühn and Kudla. This should be seen as an Arakelov analogue of the classical calculation of volumes of orthogonal locally symmetric spaces by Siegel and Weil. In the latter theory, the volumes are related to special values of (normalized) Siegel Eisenstein series. In this book, it is proved that the Arakelov analogues are related to special d...

  8. The Arithmetic of Elliptic Fibrations in Gauge Theories on a Circle

    CERN Document Server

    Grimm, Thomas W.; Klevers, Denis

    2016-01-01

    The geometry of elliptic fibrations translates to the physics of gauge theories in F-theory. We systematically develop the dictionary between arithmetic structures on elliptic curves as well as desingularized elliptic fibrations and symmetries of gauge theories on a circle. We show that the Mordell-Weil group law matches integral large gauge transformations around the circle in Abelian gauge theories and explain the significance of Mordell-Weil torsion in this context. We also use Higgs transitions and circle large gauge transformations to introduce a group law for genus-one fibrations with multi-sections. Finally, we introduce a novel arithmetic structure on elliptic fibrations with non-Abelian gauge groups in F-theory. It is defined on the set of exceptional divisors resolving the singularities and divisor classes of sections of the fibration. This group structure can be matched with certain integral non-Abelian large gauge transformations around the circle when studying the theory on the lower-dimensional ...

  9. General Dirichlet Series, Arithmetic Convolution Equations and Laplace Transforms

    Czech Academy of Sciences Publication Activity Database

    Glöckner, H.; Lucht, L.G.; Porubský, Štefan

    2009-01-01

    Roč. 193, č. 2 (2009), s. 109-129 ISSN 0039-3223 R&D Projects: GA ČR GA201/07/0191 Institutional research plan: CEZ:AV0Z10300504 Keywords : arithmetic function * Dirichlet convolution * polynomial equation * analytic equation * topological algebra * holomorphic functional calculus * implicit function theorem * Laplace transform * semigroup * complex measure Subject RIV: BA - General Mathematics Impact factor: 0.645, year: 2009 http://arxiv.org/abs/0712.3172

  10. Geometric computations with interval and new robust methods applications in computer graphics, GIS and computational geometry

    CERN Document Server

    Ratschek, H

    2003-01-01

    This undergraduate and postgraduate text will familiarise readers with interval arithmetic and related tools to gain reliable and validated results and logically correct decisions for a variety of geometric computations plus the means for alleviating the effects of the errors. It also considers computations on geometric point-sets, which are neither robust nor reliable in processing with standard methods. The authors provide two effective tools for obtaining correct results: (a) interval arithmetic, and (b) ESSA the new powerful algorithm which improves many geometric computations and makes th

  11. Fixed-point image orthorectification algorithms for reduced computational cost

    Science.gov (United States)

    French, Joseph Clinton

    Imaging systems have been applied to many new applications in recent years. With the advent of low-cost, low-power focal planes and more powerful, lower cost computers, remote sensing applications have become more wide spread. Many of these applications require some form of geolocation, especially when relative distances are desired. However, when greater global positional accuracy is needed, orthorectification becomes necessary. Orthorectification is the process of projecting an image onto a Digital Elevation Map (DEM), which removes terrain distortions and corrects the perspective distortion by changing the viewing angle to be perpendicular to the projection plane. Orthorectification is used in disaster tracking, landscape management, wildlife monitoring and many other applications. However, orthorectification is a computationally expensive process due to floating point operations and divisions in the algorithm. To reduce the computational cost of on-board processing, two novel algorithm modifications are proposed. One modification is projection utilizing fixed-point arithmetic. Fixed point arithmetic removes the floating point operations and reduces the processing time by operating only on integers. The second modification is replacement of the division inherent in projection with a multiplication of the inverse. The inverse must operate iteratively. Therefore, the inverse is replaced with a linear approximation. As a result of these modifications, the processing time of projection is reduced by a factor of 1.3x with an average pixel position error of 0.2% of a pixel size for 128-bit integer processing and over 4x with an average pixel position error of less than 13% of a pixel size for a 64-bit integer processing. A secondary inverse function approximation is also developed that replaces the linear approximation with a quadratic. The quadratic approximation produces a more accurate approximation of the inverse, allowing for an integer multiplication calculation

  12. To what extent are stochastic the arithmetical progressions of the fractional parts?

    International Nuclear Information System (INIS)

    Arnold, V.

    2008-01-01

    For the residues of the division of the n members of an arithmetical progression by a real number N is proved the tending to 0 of the Kolmogorov's stochasticity parameter λ n , when n tends to infinity, providing that the progression step is commensurable with N. On the contrary, when the step is incommensurable with N, the paper describes some examples, where the stochasticity parameter λ n does not tend to zero, and even attains (infrequently) some arbitrary large values. Both the too small and the too large values of the stochasticity parameter show the small probability of the randomness of the sequence, for which they have been counted. Thus, the long arithmetical progressions' stochasticity degree is much smaller than that of the geometrical progressions (which provide temperate values of the stochasticity parameter, similarly to its value for the genuinely random sequences). (author)

  13. Fast parallel molecular algorithms for DNA-based computation: factoring integers.

    Science.gov (United States)

    Chang, Weng-Long; Guo, Minyi; Ho, Michael Shan-Hui

    2005-06-01

    The RSA public-key cryptosystem is an algorithm that converts input data to an unrecognizable encryption and converts the unrecognizable data back into its original decryption form. The security of the RSA public-key cryptosystem is based on the difficulty of factoring the product of two large prime numbers. This paper demonstrates to factor the product of two large prime numbers, and is a breakthrough in basic biological operations using a molecular computer. In order to achieve this, we propose three DNA-based algorithms for parallel subtractor, parallel comparator, and parallel modular arithmetic that formally verify our designed molecular solutions for factoring the product of two large prime numbers. Furthermore, this work indicates that the cryptosystems using public-key are perhaps insecure and also presents clear evidence of the ability of molecular computing to perform complicated mathematical operations.

  14. Characterization and Comparison of the 10-2 SITA-Standard and Fast Algorithms

    Directory of Open Access Journals (Sweden)

    Yaniv Barkana

    2012-01-01

    Full Text Available Purpose: To compare the 10-2 SITA-standard and SITA-fast visual field programs in patients with glaucoma. Methods: We enrolled 26 patients with open angle glaucoma with involvement of at least one paracentral location on 24-2 SITA-standard field test. Each subject performed 10-2 SITA-standard and SITA-fast tests. Within 2 months this sequence of tests was repeated. Results: SITA-fast was 30% shorter than SITA-standard (5.5±1.1 vs 7.9±1.1 minutes, <0.001. Mean MD was statistically significantly higher for SITA-standard compared with SITA-fast at first visit (Δ=0.3 dB, =0.017 but not second visit. Inter-visit difference in MD or in number of depressed points was not significant for both programs. Bland-Altman analysis showed that clinically significant variations can exist in individual instances between the 2 programs and between repeat tests with the same program. Conclusions: The 10-2 SITA-fast algorithm is significantly shorter than SITA-standard. The two programs have similar long-term variability. Average same-visit between-program and same-program between-visit sensitivity results were similar for the study population, but clinically significant variability was observed for some individual test pairs. Group inter- and intra-program test results may be comparable, but in the management of the individual patient field change should be verified by repeat testing.

  15. Lógica y Pensamiento Aritmético (Logic and Arithmetic Thinking

    Directory of Open Access Journals (Sweden)

    Alfonso Ortiz

    2009-01-01

    Full Text Available Presentamos los resultados obtenidos en una prueba sobre razonamiento inductivo numérico finito y unas entrevistas clínicas posteriores realizadas a escolares de educación primaria. La primera fue respondida por 400 escolares. Con base en los resultados obtenidos, se seleccionaron 28 alumnos para realizarles entrevistas clínicas individualizadas con el fin de determinar la evolución de las relaciones lógicas que estos escolares pueden establecer en el campo de los números naturales finitos. El origen de este estudio está en problemas históricos sobre los fundamentos lógicos de la aritmética. Buscamos determinar de forma empírica hasta qué punto la lógica juega un papel determinante en el origen de la aritmética o, por el contrario, si los orígenes de la lógica están predeterminados por la aritmética y otros conocimientos. We present the results of two tests performed by primary school students. The first one was on finite numeric inductive reasoning and was performed by 400 students. According to its results, we selected 28 students to whom we clinically interviewed aiming to determine the evolution of the logic relations that they can establish in the field of finite natural numbers. This study originates on historic problems of the logical foundation of arithmetic. We aim to empirically determine the extent to which logic plays a key role in the origin of arithmetic or, on the contrary, if the origins of logic are predetermined by arithmetic and other fields.

  16. Using the Binomial Series to Prove the Arithmetic Mean-Geometric Mean Inequality

    Science.gov (United States)

    Persky, Ronald L.

    2003-01-01

    In 1968, Leon Gerber compared (1 + x)[superscript a] to its kth partial sum as a binomial series. His result is stated and, as an application of this result, a proof of the arithmetic mean-geometric mean inequality is presented.

  17. Abelian groups and quadratic residues in weak arithmetic

    Czech Academy of Sciences Publication Activity Database

    Jeřábek, Emil

    2010-01-01

    Roč. 56, č. 3 (2010), s. 262-278 ISSN 0942-5616 R&D Projects: GA AV ČR IAA1019401; GA MŠk(CZ) 1M0545 Institutional research plan: CEZ:AV0Z10190503 Keywords : bounded arithmetic * abelian group * Fermat's little theorem * quadratic reciprocity Subject RIV: BA - General Mathematics Impact factor: 0.361, year: 2010 http://onlinelibrary.wiley.com/doi/10.1002/malq.200910009/abstract;jsessionid=9F636FFACB84C025FD90C7E6880350DD.f03t03

  18. General and Specific Contributions of RAN to Reading and Arithmetic Fluency in First Graders: A Longitudinal Latent Variable Approach

    Directory of Open Access Journals (Sweden)

    Caroline Hornung

    2017-10-01

    Full Text Available In the present study, we opted for a longitudinal design and examined rapid automatized naming (RAN performance from two perspectives. In a first step, we examined the structure of RAN performance from a general cognitive perspective. We investigated whether rapid naming measures (e.g., digit RAN and color RAN reflect a mainly domain-general factor or domain-specific factors. In a second step, we examined how the best fitting RAN model was related to reading and arithmetic outcomes, assessed several months later. Finally in a third step we took a clinical perspective and investigated specific contributions of RAN measures to reading and arithmetic outcomes. While RAN has emerged as a promising predictor of reading, the relationship between RAN and arithmetic has been less examined in the past. Hundred and twenty-two first graders completed seven RAN tasks, each comprising visually familiar stimuli such as digits, vowels, consonants, dice, finger-numeral configurations, objects, and colors. Four months later the same children completed a range of reading and arithmetic tasks. From a general descriptive perspective, structural equation modeling supports a one-dimensional RAN factor in 6- to -7-year-old children. However, from a clinical perspective, our findings emphasize the specific contributions of RANs. Interestingly, alphanumeric RANs (i.e., vowel RAN were most promising when predicting reading skills and number-specific RANs (i.e., finger-numeral configuration RAN were most promising when predicting arithmetic fluency. The implications for clinical and educational practices will be discussed.

  19. General and Specific Contributions of RAN to Reading and Arithmetic Fluency in First Graders: A Longitudinal Latent Variable Approach.

    Science.gov (United States)

    Hornung, Caroline; Martin, Romain; Fayol, Michel

    2017-01-01

    In the present study, we opted for a longitudinal design and examined rapid automatized naming (RAN) performance from two perspectives. In a first step, we examined the structure of RAN performance from a general cognitive perspective. We investigated whether rapid naming measures (e.g., digit RAN and color RAN) reflect a mainly domain-general factor or domain-specific factors. In a second step, we examined how the best fitting RAN model was related to reading and arithmetic outcomes, assessed several months later. Finally in a third step we took a clinical perspective and investigated specific contributions of RAN measures to reading and arithmetic outcomes. While RAN has emerged as a promising predictor of reading, the relationship between RAN and arithmetic has been less examined in the past. Hundred and twenty-two first graders completed seven RAN tasks, each comprising visually familiar stimuli such as digits, vowels, consonants, dice, finger-numeral configurations, objects, and colors. Four months later the same children completed a range of reading and arithmetic tasks. From a general descriptive perspective, structural equation modeling supports a one-dimensional RAN factor in 6- to -7-year-old children. However, from a clinical perspective, our findings emphasize the specific contributions of RANs. Interestingly, alphanumeric RANs (i.e., vowel RAN) were most promising when predicting reading skills and number-specific RANs (i.e., finger-numeral configuration RAN) were most promising when predicting arithmetic fluency. The implications for clinical and educational practices will be discussed.

  20. Gaussian width bounds with applications to arithmetic progressions in random settings

    NARCIS (Netherlands)

    J. Briët (Jop); S. Gopi (Sivakanth)

    2017-01-01

    textabstractMotivated by two problems on arithmetic progressions (APs)—concerning large deviations for AP counts in random sets and random differences in Szemer´edi’s theorem— we prove upper bounds on the Gaussian width of the image of the n-dimensional Boolean hypercube under a mapping ψ : Rn →

  1. The arithmetic basis of special relativity

    International Nuclear Information System (INIS)

    Greenspan, D.

    1976-01-01

    Under relatively general particle and rocket frame motions, it is shown that, for special relativity, the basic concepts can be formulated and the basic properties deduced using only arithmetic. Particular attention is directed toward velocity, acceleration, proper time, momentum, energy, and 4-vectors in both space-time and Minkowski space, and to relativistic generalizations of Newton's second law. The resulting mathematical simplification is not only completely compatible with modern computer technology, but it yields dynamical equations that can be solved directly by such computers. Particular applications of the numerical equations, which are either Lorentz invariant or are directly related to Lorentz-invariant formulas, are made to the study of a relativistic harmonic oscillator and to the motion of an electric particle in a magnetic field. (author)

  2. The Influence of verbalization on the pattern of cortical activation during mental arithmetic

    Directory of Open Access Journals (Sweden)

    Zarnhofer Sabrina

    2012-03-01

    Full Text Available Abstract Background The aim of the present functional magnetic resonance imaging (fMRI study at 3 T was to investigate the influence of the verbal-visual cognitive style on cerebral activation patterns during mental arithmetic. In the domain of arithmetic, a visual style might for example mean to visualize numbers and (intermediate results, and a verbal style might mean, that numbers and (intermediate results are verbally repeated. In this study, we investigated, first, whether verbalizers show activations in areas for language processing, and whether visualizers show activations in areas for visual processing during mental arithmetic. Some researchers have proposed that the left and right intraparietal sulcus (IPS, and the left angular gyrus (AG, two areas involved in number processing, show some domain or modality specificity. That is, verbal for the left AG, and visual for the left and right IPS. We investigated, second, whether the activation in these areas implied in number processing depended on an individual's cognitive style. Methods 42 young healthy adults participated in the fMRI study. The study comprised two functional sessions. In the first session, subtraction and multiplication problems were presented in an event-related design, and in the second functional session, multiplications were presented in two formats, as Arabic numerals and as written number words, in an event-related design. The individual's habitual use of visualization and verbalization during mental arithmetic was assessed by a short self-report assessment. Results We observed in both functional sessions that the use of verbalization predicts activation in brain areas associated with language (supramarginal gyrus and auditory processing (Heschl's gyrus, Rolandic operculum. However, we found no modulation of activation in the left AG as a function of verbalization. Conclusions Our results confirm that strong verbalizers use mental speech as a form of mental

  3. Semiotic mediation: from multiplication properties to arithmetical expressions

    Directory of Open Access Journals (Sweden)

    Andrea Maffia

    2016-04-01

    Full Text Available Multiplication is introduced early in primary school, but its properties are usually introduced after the rote memorization of multiplicative facts. In this paper we present a teaching experiment aimed to early introducing arithmetical properties of multiplication. It is realized through an artefact built on the rectangle model for multiplication. Children activity is designed and analyzed using Theory of Semiotic Mediation. The development of the relational meaning of arithmetical expressions is shown through the enchaining of representations from signs related to the activity with the artefact to mathematical ones. In particular, the role of the teacher in the process of semiotic mediation results as crucial. Mediazione semiotica: dalle proprietà della moltiplicazione alle espressioni aritmeticheLa moltiplicazione viene presentata presto nella scuola primaria, ma le sue proprietà sono introdotte solo dopo che le cosiddette tabelline sono state memorizzate. Nell’articolo si presenta un teaching experiment volto a introdurre precocemente le proprietà della moltiplicazione per facilitare la memorizzazione di fatti moltiplicativi. L’esperimento è centrato sull’uso di un artefatto costruito sul modello rettangolare della moltiplicazione. L’attività degli studenti è progettata e analizzata nel quadro della Teoria della Mediazione Semiotica (TMS. Lo sviluppo del significato relazionale delle espressioni aritmetiche viene mostrato attraverso la concatenazione di rappresentazioni che vanno da segni strettamente legati all’attività con l’artefatto fino a segni matematici. In particolare, si evidenzia il ruolo dell’insegnante nello sviluppo del processo di mediazione semiotica.

  4. Scatter-Reducing Sounding Filtration Using a Genetic Algorithm and Mean Monthly Standard Deviation

    Science.gov (United States)

    Mandrake, Lukas

    2013-01-01

    Retrieval algorithms like that used by the Orbiting Carbon Observatory (OCO)-2 mission generate massive quantities of data of varying quality and reliability. A computationally efficient, simple method of labeling problematic datapoints or predicting soundings that will fail is required for basic operation, given that only 6% of the retrieved data may be operationally processed. This method automatically obtains a filter designed to reduce scatter based on a small number of input features. Most machine-learning filter construction algorithms attempt to predict error in the CO2 value. By using a surrogate goal of Mean Monthly STDEV, the goal is to reduce the retrieved CO2 scatter rather than solving the harder problem of reducing CO2 error. This lends itself to improved interpretability and performance. This software reduces the scatter of retrieved CO2 values globally based on a minimum number of input features. It can be used as a prefilter to reduce the number of soundings requested, or as a post-filter to label data quality. The use of the MMS (Mean Monthly Standard deviation) provides a much cleaner, clearer filter than the standard ABS(CO2-truth) metrics previously employed by competitor methods. The software's main strength lies in a clearer (i.e., fewer features required) filter that more efficiently reduces scatter in retrieved CO2 rather than focusing on the more complex (and easily removed) bias issues.

  5. A hand full of numbers: a role for offloading in arithmetics learning?

    Directory of Open Access Journals (Sweden)

    Annelise Júlio Costa

    2011-12-01

    Full Text Available Finger counting has been associated to arithmetic learning in children. We examined children with (n = 14 and without (n = 84 mathematics learning difficulties with ages between 8 to 11 years. Deficits in finger gnosia were found in association to mathematical difficulties. Finger gnosia is particularly relevant for the performance in word problems requiring active manipulation of small magnitudes in the range between 1 and 10. Moreover, the deficits in finger gnosia cannot be attributed to a shortage in working memory capacity but rather to a specific inability to use fingers to transiently represent magnitudes, tagging to be counted objects and reducing the cognitive load necessary to solve arithmetic problems. Since finger gnosia is more related to symbolic than to nonsymbolic magnitude processing, finger-related representation of magnitude seems to be an important link for learning the mapping of analog onto discrete symbolic magnitudes.

  6. 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...

  7. Using fuzzy arithmetic in containment event trees

    International Nuclear Information System (INIS)

    Rivera, S.S.; Baron, Jorge H.

    2000-01-01

    The use of fuzzy arithmetic is proposed for the evaluation of containment event trees. Concepts such as improbable, very improbable, and so on, which are subjective by nature, are represented by fuzzy numbers. The quantitative evaluation of containment event trees is based on the extension principle, by which operations on real numbers are extended to operations on fuzzy numbers. Expert knowledge is considered as state of the base variable with a normal distribution, which is considered to represent the membership function. Finally, this paper presents results of an example calculation of a containment event tree for the CAREM-25 nuclear power plant, presently under detailed design stage at Argentina. (author)

  8. Deriving causes of child mortality by re–analyzing national verbal autopsy data applying a standardized computer algorithm in Uganda, Rwanda and Ghana

    Directory of Open Access Journals (Sweden)

    Li Liu

    2015-06-01

    Full Text Available Background To accelerate progress toward the Millennium Development Goal 4, reliable information on causes of child mortality is critical. With more national verbal autopsy (VA studies becoming available, how to improve consistency of national VA derived child causes of death should be considered for the purpose of global comparison. We aimed to adapt a standardized computer algorithm to re–analyze national child VA studies conducted in Uganda, Rwanda and Ghana recently, and compare our results with those derived from physician review to explore issues surrounding the application of the standardized algorithm in place of physician review. Methods and Findings We adapted the standardized computer algorithm considering the disease profile in Uganda, Rwanda and Ghana. We then derived cause–specific mortality fractions applying the adapted algorithm and compared the results with those ascertained by physician review by examining the individual– and population–level agreement. Our results showed that the leading causes of child mortality in Uganda, Rwanda and Ghana were pneumonia (16.5–21.1% and malaria (16.8–25.6% among children below five years and intrapartum–related complications (6.4–10.7% and preterm birth complications (4.5–6.3% among neonates. The individual level agreement was poor to substantial across causes (kappa statistics: –0.03 to 0.83, with moderate to substantial agreement observed for injury, congenital malformation, preterm birth complications, malaria and measles. At the population level, despite fairly different cause–specific mortality fractions, the ranking of the leading causes was largely similar. Conclusions The standardized computer algorithm produced internally consistent distribution of causes of child mortality. The results were also qualitatively comparable to those based on physician review from the perspective of public health policy. The standardized computer algorithm has the advantage of

  9. Numerical Algorithm for Delta of Asian Option

    Directory of Open Access Journals (Sweden)

    Boxiang Zhang

    2015-01-01

    Full Text Available We study the numerical solution of the Greeks of Asian options. In particular, we derive a close form solution of Δ of Asian geometric option and use this analytical form as a control to numerically calculate Δ of Asian arithmetic option, which is known to have no explicit close form solution. We implement our proposed numerical method and compare the standard error with other classical variance reduction methods. Our method provides an efficient solution to the hedging strategy with Asian options.

  10. Temporal Comparison Between NIRS and EEG Signals During a Mental Arithmetic Task Evaluated with Self-Organizing Maps.

    Science.gov (United States)

    Oyama, Katsunori; Sakatani, Kaoru

    2016-01-01

    Simultaneous monitoring of brain activity with near-infrared spectroscopy and electroencephalography allows spatiotemporal reconstruction of the hemodynamic response regarding the concentration changes in oxyhemoglobin and deoxyhemoglobin that are associated with recorded brain activity such as cognitive functions. However, the accuracy of state estimation during mental arithmetic tasks is often different depending on the length of the segment for sampling of NIRS and EEG signals. This study compared the results of a self-organizing map and ANOVA, which were both used to assess the accuracy of state estimation. We conducted an experiment with a mental arithmetic task performed by 10 participants. The lengths of the segment in each time frame for observation of NIRS and EEG signals were compared with the 30-s, 1-min, and 2-min segment lengths. The optimal segment lengths were different for NIRS and EEG signals in the case of classification of feature vectors into the states of performing a mental arithmetic task and being at rest.

  11. Fermat’s ‘primitive solutions’ and some arithmetic of elliptic curves

    NARCIS (Netherlands)

    Top, Jaap

    1993-01-01

    In his work on Diophantine equations of the form y2=ax4+bx3+cx2+dx+e, Fermat introduced the notion of primitive solutions. In this expository note we intend to interpret this notion more geometrically, and explain what it means in terms of the arithmetic of elliptic curves. The specific equation

  12. Design and evaluation of online arithmetic for signal processing applications on FPGAs

    Science.gov (United States)

    Galli, Reto; Tenca, Alexandre F.

    2001-11-01

    This paper shows the design and the evaluation of on-line arithmetic modules for the most common operators used in DSP applications, using FPGAs as the target technology. The designs are highly optimized for the target technology and the common range of precision in DSP. The results are based on experimental data collected using CAD tools. All designs are synthesized for the same type of devices (Xilinx XC4000) for comparison, avoiding rough estimates of the system performance, and generating a more reliable and detailed comparison of on-line signal processing solutions with other state of the art approaches, such as distributed arithmetic. We show that on-line designs have a hard stand for basic DSP applications that use only addition and multiplication. However, we also show that on-line designs are able to overtake other approaches as the applications become more sophisticated, e.g. when data dependencies exist, or when non constant multiplicands restrict the use of other approaches.

  13. GSFAP Adaptive Filtering Using Log Arithmetic for Resource-Constrained Embedded Systems

    Czech Academy of Sciences Publication Activity Database

    Tichý, Milan; Schier, Jan; Gregg, D.

    2010-01-01

    Roč. 9, č. 3 (2010), s. 1-31 ISSN 1539-9087 R&D Projects: GA MŠk 7H09005 Institutional research plan: CEZ:AV0Z10750506 Keywords : FPGA * DSP * logarithmic arithmetic * affine projection Subject RIV: BD - Theory of Information Impact factor: 1.057, year: 2010 http://library.utia.cas.cz/separaty/2010/ZS/tichy-0341115.pdf

  14. Foundations of arithmetic differential geometry

    CERN Document Server

    Buium, Alexandru

    2017-01-01

    The aim of this book is to introduce and develop an arithmetic analogue of classical differential geometry. In this new geometry the ring of integers plays the role of a ring of functions on an infinite dimensional manifold. The role of coordinate functions on this manifold is played by the prime numbers. The role of partial derivatives of functions with respect to the coordinates is played by the Fermat quotients of integers with respect to the primes. The role of metrics is played by symmetric matrices with integer coefficients. The role of connections (respectively curvature) attached to metrics is played by certain adelic (respectively global) objects attached to the corresponding matrices. One of the main conclusions of the theory is that the spectrum of the integers is "intrinsically curved"; the study of this curvature is then the main task of the theory. The book follows, and builds upon, a series of recent research papers. A significant part of the material has never been published before.

  15. Efficient Solving of Large Non-linear Arithmetic Constraint Systems with Complex Boolean Structure

    Czech Academy of Sciences Publication Activity Database

    Fränzle, M.; Herde, C.; Teige, T.; Ratschan, Stefan; Schubert, T.

    2007-01-01

    Roč. 1, - (2007), s. 209-236 ISSN 1574-0617 Grant - others:AVACS(DE) SFB/TR 14 Institutional research plan: CEZ:AV0Z10300504 Keywords : interval-based arithmetic constraint solving * SAT modulo theories Subject RIV: BA - General Mathematics

  16. Assessing Adult Learner's Numeracy as Related to Gender and Performance in Arithmetic

    Science.gov (United States)

    Awofala, Adeneye O. A.; Anyikwa, Blessing E.

    2014-01-01

    The study investigated adult learner numeracy as related to gender and performance in arithmetic among 32 Nigerian adult learners from one government accredited adult literacy centre in Lagos State using the quantitative research method within the blueprint of descriptive survey design. Data collected were analysed using the descriptive statistics…

  17. Constant savings rates and quasi-arithmetic population growth under exhaustible resource constraints

    NARCIS (Netherlands)

    Asheim, G.B.; Buchholz, W.; Hartwick, J.M.; Mitra, T.; Withagen, C.A.A.M.

    2007-01-01

    In the Dasgupta–Heal–Solow–Stiglitz (DHSS) model of capital accumulation and resource depletion we show the following equivalence: if an efficient path has constant (gross and net of population growth) savings rates, then population growth must be quasi-arithmetic and the path is a maximin or a

  18. FAST (Four chamber view And Swing Technique) Echo: a Novel and Simple Algorithm to Visualize Standard Fetal Echocardiographic Planes

    Science.gov (United States)

    Yeo, Lami; Romero, Roberto; Jodicke, Cristiano; Oggè, Giovanna; Lee, Wesley; Kusanovic, Juan Pedro; Vaisbuch, Edi; Hassan, Sonia S.

    2010-01-01

    Objective To describe a novel and simple algorithm (FAST Echo: Four chamber view And Swing Technique) to visualize standard diagnostic planes of fetal echocardiography from dataset volumes obtained with spatiotemporal image correlation (STIC) and applying a new display technology (OmniView). Methods We developed an algorithm to image standard fetal echocardiographic planes by drawing four dissecting lines through the longitudinal view of the ductal arch contained in a STIC volume dataset. Three of the lines are locked to provide simultaneous visualization of targeted planes, and the fourth line (unlocked) “swings” through the ductal arch image (“swing technique”), providing an infinite number of cardiac planes in sequence. Each line generated the following plane(s): 1) Line 1: three-vessels and trachea view; 2) Line 2: five-chamber view and long axis view of the aorta (obtained by rotation of the five-chamber view on the y-axis); 3) Line 3: four-chamber view; and 4) “Swing” line: three-vessels and trachea view, five-chamber view and/or long axis view of the aorta, four-chamber view, and stomach. The algorithm was then tested in 50 normal hearts (15.3 – 40 weeks of gestation) and visualization rates for cardiac diagnostic planes were calculated. To determine if the algorithm could identify planes that departed from the normal images, we tested the algorithm in 5 cases with proven congenital heart defects. Results In normal cases, the FAST Echo algorithm (3 locked lines and rotation of the five-chamber view on the y-axis) was able to generate the intended planes (longitudinal view of the ductal arch, pulmonary artery, three-vessels and trachea view, five-chamber view, long axis view of the aorta, four-chamber view): 1) individually in 100% of cases [except for the three-vessel and trachea view, which was seen in 98% (49/50)]; and 2) simultaneously in 98% (49/50). The “swing technique” was able to generate the three-vessels and trachea view, five

  19. Four-chamber view and 'swing technique' (FAST) echo: a novel and simple algorithm to visualize standard fetal echocardiographic planes.

    Science.gov (United States)

    Yeo, L; Romero, R; Jodicke, C; Oggè, G; Lee, W; Kusanovic, J P; Vaisbuch, E; Hassan, S

    2011-04-01

    To describe a novel and simple algorithm (four-chamber view and 'swing technique' (FAST) echo) for visualization of standard diagnostic planes of fetal echocardiography from dataset volumes obtained with spatiotemporal image correlation (STIC) and applying a new display technology (OmniView). We developed an algorithm to image standard fetal echocardiographic planes by drawing four dissecting lines through the longitudinal view of the ductal arch contained in a STIC volume dataset. Three of the lines are locked to provide simultaneous visualization of targeted planes, and the fourth line (unlocked) 'swings' through the ductal arch image (swing technique), providing an infinite number of cardiac planes in sequence. Each line generates the following plane(s): (a) Line 1: three-vessels and trachea view; (b) Line 2: five-chamber view and long-axis view of the aorta (obtained by rotation of the five-chamber view on the y-axis); (c) Line 3: four-chamber view; and (d) 'swing line': three-vessels and trachea view, five-chamber view and/or long-axis view of the aorta, four-chamber view and stomach. The algorithm was then tested in 50 normal hearts in fetuses at 15.3-40 weeks' gestation and visualization rates for cardiac diagnostic planes were calculated. To determine whether the algorithm could identify planes that departed from the normal images, we tested the algorithm in five cases with proven congenital heart defects. In normal cases, the FAST echo algorithm (three locked lines and rotation of the five-chamber view on the y-axis) was able to generate the intended planes (longitudinal view of the ductal arch, pulmonary artery, three-vessels and trachea view, five-chamber view, long-axis view of the aorta, four-chamber view) individually in 100% of cases (except for the three-vessels and trachea view, which was seen in 98% (49/50)) and simultaneously in 98% (49/50). The swing technique was able to generate the three-vessels and trachea view, five-chamber view and/or long

  20. Robustness and precision of an automatic marker detection algorithm for online prostate daily targeting using a standard V-EPID.

    Science.gov (United States)

    Aubin, S; Beaulieu, L; Pouliot, S; Pouliot, J; Roy, R; Girouard, L M; Martel-Brisson, N; Vigneault, E; Laverdière, J

    2003-07-01

    An algorithm for the daily localization of the prostate using implanted markers and a standard video-based electronic portal imaging device (V-EPID) has been tested. Prior to planning, three gold markers were implanted in the prostate of seven patients. The clinical images were acquired with a BeamViewPlus 2.1 V-EPID for each field during the normal course radiotherapy treatment and are used off-line to determine the ability of the automatic marker detection algorithm to adequately and consistently detect the markers. Clinical images were obtained with various dose levels from ranging 2.5 to 75 MU. The algorithm is based on marker attenuation characterization in the portal image and spatial distribution. A total of 1182 clinical images were taken. The results show an average efficiency of 93% for the markers detected individually and 85% for the group of markers. This algorithm accomplishes the detection and validation in 0.20-0.40 s. When the center of mass of the group of implanted markers is used, then all displacements can be corrected to within 1.0 mm in 84% of the cases and within 1.5 mm in 97% of cases. The standard video-based EPID tested provides excellent marker detection capability even with low dose levels. The V-EPID can be used successfully with radiopaque markers and the automatic detection algorithm to track and correct the daily setup deviations due to organ motions.

  1. Number comparison and number ordering as predictors of arithmetic performance in adults: Exploring the link between the two skills, and investigating the question of domain-specificity.

    Science.gov (United States)

    Morsanyi, Kinga; O'Mahony, Eileen; McCormack, Teresa

    2017-12-01

    Recent evidence has highlighted the important role that number-ordering skills play in arithmetic abilities, both in children and adults. In the current study, we demonstrated that number comparison and ordering skills were both significantly related to arithmetic performance in adults, and the effect size was greater in the case of ordering skills. Additionally, we found that the effect of number comparison skills on arithmetic performance was mediated by number-ordering skills. Moreover, performance on comparison and ordering tasks involving the months of the year was also strongly correlated with arithmetic skills, and participants displayed similar (canonical or reverse) distance effects on the comparison and ordering tasks involving months as when the tasks included numbers. This suggests that the processes responsible for the link between comparison and ordering skills and arithmetic performance are not specific to the domain of numbers. Finally, a factor analysis indicated that performance on comparison and ordering tasks loaded on a factor that included performance on a number line task and self-reported spatial thinking styles. These results substantially extend previous research on the role of order processing abilities in mental arithmetic.

  2. Validation of the Welch Allyn SureBP (inflation) and StepBP (deflation) algorithms by AAMI standard testing and BHS data analysis.

    Science.gov (United States)

    Alpert, Bruce S

    2011-04-01

    We evaluated two new Welch Allyn automated blood pressure (BP) algorithms. The first, SureBP, estimates BP during cuff inflation; the second, StepBP, does so during deflation. We followed the American National Standards Institute/Association for the Advancement of Medical Instrumentation SP10:2006 standard for testing and data analysis. The data were also analyzed using the British Hypertension Society analysis strategy. We tested children, adolescents, and adults. The requirements of the American National Standards Institute/Association for the Advancement of Medical Instrumentation SP10:2006 standard were fulfilled with respect to BP levels, arm sizes, and ages. Association for the Advancement of Medical Instrumentation SP10 Method 1 data analysis was used. The mean±standard deviation for the device readings compared with auscultation by paired, trained, blinded observers in the SureBP mode were -2.14±7.44 mmHg for systolic BP (SBP) and -0.55±5.98 mmHg for diastolic BP (DBP). In the StepBP mode, the differences were -3.61±6.30 mmHg for SBP and -2.03±5.30 mmHg for DBP. Both algorithms achieved an A grade for both SBP and DBP by British Hypertension Society analysis. The SureBP inflation-based algorithm will be available in many new-generation Welch Allyn monitors. Its use will reduce the time it takes to estimate BP in critical patient care circumstances. The device will not need to inflate to excessive suprasystolic BPs to obtain the SBP values. Deflation is rapid once SBP has been determined, thus reducing the total time of cuff inflation and reducing patient discomfort. If the SureBP fails to obtain a BP value, the StepBP algorithm is activated to estimate BP by traditional deflation methodology.

  3. Executive Functioning in Children, and Its Relations with Reasoning, Reading, and Arithmetic

    Science.gov (United States)

    van der Sluis, Sophie; de Jong, Peter F.; van der Leij, Aryan

    2007-01-01

    The aims of this study were to investigate whether the executive functions, inhibition, shifting, and updating, are distinguishable as latent variables (common factors) in children aged 9 to 12, and to examine the relations between these executive functions and reading, arithmetic, and (non)verbal reasoning. Confirmatory factor analysis was used…

  4. The Algorithm for Algorithms: An Evolutionary Algorithm Based on Automatic Designing of Genetic Operators

    Directory of Open Access Journals (Sweden)

    Dazhi Jiang

    2015-01-01

    Full Text Available At present there is a wide range of evolutionary algorithms available to researchers and practitioners. Despite the great diversity of these algorithms, virtually all of the algorithms share one feature: they have been manually designed. A fundamental question is “are there any algorithms that can design evolutionary algorithms automatically?” A more complete definition of the question is “can computer construct an algorithm which will generate algorithms according to the requirement of a problem?” In this paper, a novel evolutionary algorithm based on automatic designing of genetic operators is presented to address these questions. The resulting algorithm not only explores solutions in the problem space like most traditional evolutionary algorithms do, but also automatically generates genetic operators in the operator space. In order to verify the performance of the proposed algorithm, comprehensive experiments on 23 well-known benchmark optimization problems are conducted. The results show that the proposed algorithm can outperform standard differential evolution algorithm in terms of convergence speed and solution accuracy which shows that the algorithm designed automatically by computers can compete with the algorithms designed by human beings.

  5. Design and evaluation of basic standard encryption algorithm modules using nanosized complementary metal oxide semiconductor molecular circuits

    Science.gov (United States)

    Masoumi, Massoud; Raissi, Farshid; Ahmadian, Mahmoud; Keshavarzi, Parviz

    2006-01-01

    We are proposing that the recently proposed semiconductor-nanowire-molecular architecture (CMOL) is an optimum platform to realize encryption algorithms. The basic modules for the advanced encryption standard algorithm (Rijndael) have been designed using CMOL architecture. The performance of this design has been evaluated with respect to chip area and speed. It is observed that CMOL provides considerable improvement over implementation with regular CMOS architecture even with a 20% defect rate. Pseudo-optimum gate placement and routing are provided for Rijndael building blocks and the possibility of designing high speed, attack tolerant and long key encryptions are discussed.

  6. Algorithms for the rapid simulation of Rutherford backscattering spectra

    Energy Technology Data Exchange (ETDEWEB)

    Doolittle, L.R.

    1985-06-01

    A computer program which simulates Rutherford backscattering spectra is currently in use at Cornell University and other institutions. Straggling and detector resolution are among the effects included. Samples are considered to be made up of a finite number of layers, each with uniform composition. The emphasis in the mathematics is on accuracy beyond that of iterated surface approximation methods. Thicker layers can thus be analyzed without a net loss in accuracy. The mathematical description of the sample can then have fewer layers, and fewer calculations are required. This paper provides estimates of the number of arithmetic operations used by the program for any simulation to demonstrate the tradeoffs between accuracy, computation time, and algorithm sophistication.

  7. Algorithms for the rapid simulation of Rutherford backscattering spectra

    International Nuclear Information System (INIS)

    Doolittle, L.R.

    1985-01-01

    A computer program which simulates Rutherford backscattering spectra is currently in use at Cornell University and other institutions. Straggling and detector resolution are among the effects included. Samples are considered to be made up of a finite number of layers, each with uniform composition. The emphasis in the mathematics is on accuracy beyond that of iterated surface approximation methods. Thicker layers can thus be analyzed without a net loss in accuracy. The mathematical description of the sample can then have fewer layers, and fewer calculations are required. This paper provides estimates of the number of arithmetic operations used by the program for any simulation to demonstrate the tradeoffs between accuracy, computation time, and algorithm sophistication. (orig.)

  8. Using text adventure games to entice learners to practice arithmetic skills over Mxit

    CSIR Research Space (South Africa)

    Butgereit, L

    2009-01-01

    Full Text Available examines a project where text adventure games with a mathematical twist are deployed over Mxit which participants can play on their cell phones. In order to complete the puzzles laid out in the game, participants must do various arithmetic calculations....

  9. A practical approach to model checking Duration Calculus using Presburger Arithmetic

    DEFF Research Database (Denmark)

    Hansen, Michael Reichhardt; Dung, Phan Anh; Brekling, Aske Wiid

    2014-01-01

    This paper investigates the feasibility of reducing a model-checking problem K ⊧ ϕ for discrete time Duration Calculus to the decision problem for Presburger Arithmetic. Theoretical results point at severe limitations of this approach: (1) the reduction in Fränzle and Hansen (Int J Softw Inform 3...... limits of the approach are illustrated by a family of examples....

  10. Implementation of an Evidence-Based and Content Validated Standardized Ostomy Algorithm Tool in Home Care: A Quality Improvement Project.

    Science.gov (United States)

    Bare, Kimberly; Drain, Jerri; Timko-Progar, Monica; Stallings, Bobbie; Smith, Kimberly; Ward, Naomi; Wright, Sandra

    Many nurses have limited experience with ostomy management. We sought to provide a standardized approach to ostomy education and management to support nurses in early identification of stomal and peristomal complications, pouching problems, and provide standardized solutions for managing ostomy care in general while improving utilization of formulary products. This article describes development and testing of an ostomy algorithm tool.

  11. DEBT AMORTIZATION AND SIMPLE INTEREST: THE CASE OF PAYMENTS IN AN ARITHMETIC PROGRESSION

    Directory of Open Access Journals (Sweden)

    Clovis José Daudt Lyra Darrigue Faro

    2014-12-01

    Full Text Available With the argument that, necessarily, compound interest implies anatocism, the Brazilian Judiciary has been determining that, specially for the case of  debt amortization in accordance with the so called Tabela Price, when we have constant payments, the use of simple interest. With the same determination occurring in the case of the Constant Amortization Scheme, when the payments follow arithmetic progressions.  However, as simple interest lacks the property of time subdivision, it is shown that as in the case of constant payments, the adoption of simple interest in the case of payments following an arithmetic progression results in amortization schemes that are financially inconsistent. In the sense that the determination of the outstanding principal in accordance with the prospective, retrospective and of recurrence methods lead to conflicting  results. To this end, four different variations of the use of simple interest are numerically analyzed.

  12. Energy footprint of advanced dense numerical linear algebra using tile algorithms on multicore architectures

    KAUST Repository

    Dongarra, Jack

    2012-11-01

    We propose to study the impact on the energy footprint of two advanced algorithmic strategies in the context of high performance dense linear algebra libraries: (1) mixed precision algorithms with iterative refinement allow to run at the peak performance of single precision floating-point arithmetic while achieving double precision accuracy and (2) tree reduction technique exposes more parallelism when factorizing tall and skinny matrices for solving over determined systems of linear equations or calculating the singular value decomposition. Integrated within the PLASMA library using tile algorithms, which will eventually supersede the block algorithms from LAPACK, both strategies further excel in performance in the presence of a dynamic task scheduler while targeting multicore architecture. Energy consumption measurements are reported along with parallel performance numbers on a dual-socket quad-core Intel Xeon as well as a quad-socket quad-core Intel Sandy Bridge chip, both providing component-based energy monitoring at all levels of the system, through the Power Pack framework and the Running Average Power Limit model, respectively. © 2012 IEEE.

  13. Energy footprint of advanced dense numerical linear algebra using tile algorithms on multicore architectures

    KAUST Repository

    Dongarra, Jack; Ltaief, Hatem; Luszczek, Piotr R.; Weaver, Vincent M.

    2012-01-01

    We propose to study the impact on the energy footprint of two advanced algorithmic strategies in the context of high performance dense linear algebra libraries: (1) mixed precision algorithms with iterative refinement allow to run at the peak performance of single precision floating-point arithmetic while achieving double precision accuracy and (2) tree reduction technique exposes more parallelism when factorizing tall and skinny matrices for solving over determined systems of linear equations or calculating the singular value decomposition. Integrated within the PLASMA library using tile algorithms, which will eventually supersede the block algorithms from LAPACK, both strategies further excel in performance in the presence of a dynamic task scheduler while targeting multicore architecture. Energy consumption measurements are reported along with parallel performance numbers on a dual-socket quad-core Intel Xeon as well as a quad-socket quad-core Intel Sandy Bridge chip, both providing component-based energy monitoring at all levels of the system, through the Power Pack framework and the Running Average Power Limit model, respectively. © 2012 IEEE.

  14. Energy efficient data sorting using standard sorting algorithms

    KAUST Repository

    Bunse, Christian; Hö pfner, Hagen; Roychoudhury, Suman; Mansour, Essam

    2011-01-01

    Protecting the environment by saving energy and thus reducing carbon dioxide emissions is one of todays hottest and most challenging topics. Although the perspective for reducing energy consumption, from ecological and business perspectives is clear, from a technological point of view, the realization especially for mobile systems still falls behind expectations. Novel strategies that allow (software) systems to dynamically adapt themselves at runtime can be effectively used to reduce energy consumption. This paper presents a case study that examines the impact of using an energy management component that dynamically selects and applies the "optimal" sorting algorithm, from an energy perspective, during multi-party mobile communication. Interestingly, the results indicate that algorithmic performance is not key and that dynamically switching algorithms at runtime does have a significant impact on energy consumption. © Springer-Verlag Berlin Heidelberg 2011.

  15. The relationship between medical impairments and arithmetic development in children with cerebral palsy.

    NARCIS (Netherlands)

    Jenks, K.M.; Lieshout, E.C. van; Moor, J.M.H. de

    2009-01-01

    Arithmetic ability was tested in children with cerebral palsy without severe intellectual impairment (verbal IQ >or= 70) attending special (n = 41) or mainstream education (n = 16) as well as control children in mainstream education (n = 16) throughout first and second grade. Children with cerebral

  16. The arithmetic of elliptic fibrations in gauge theories on a circle

    Energy Technology Data Exchange (ETDEWEB)

    Grimm, Thomas W. [Max-Planck-Institut für Physik,Föhringer Ring 6, 80805 Munich (Germany); Institute for Theoretical Physics,Utrecht University, Leuvenlaan 4, 3584 CE Utrecht (Netherlands); Center for Extreme Matter and Emergent Phenomena,Utrecht University, Leuvenlaan 4, 3584 CE Utrecht (Netherlands); Kapfer, Andreas [Max-Planck-Institut für Physik,Föhringer Ring 6, 80805 Munich (Germany); Klevers, Denis [Theory Group, Physics Department, CERN,CH-1211, Geneva 23 (Switzerland)

    2016-06-20

    The geometry of elliptic fibrations translates to the physics of gauge theories in F-theory. We systematically develop the dictionary between arithmetic structures on elliptic curves as well as desingularized elliptic fibrations and symmetries of gauge theories on a circle. We show that the Mordell-Weil group law matches integral large gauge transformations around the circle in Abelian gauge theories and explain the significance of Mordell-Weil torsion in this context. We also use Higgs transitions and circle large gauge transformations to introduce a group law for genus-one fibrations with multi-sections. Finally, we introduce a novel arithmetic structure on elliptic fibrations with non-Abelian gauge groups in F-theory. It is defined on the set of exceptional divisors resolving the singularities and divisor classes of sections of the fibration. This group structure can be matched with certain integral non-Abelian large gauge transformations around the circle when studying the theory on the lower-dimensional Coulomb branch. Its existence is required by consistency with Higgs transitions from the non-Abelian theory to its Abelian phases in which it becomes the Mordell-Weil group. This hints towards the existence of a new underlying geometric symmetry.

  17. The arithmetic of elliptic fibrations in gauge theories on a circle

    Science.gov (United States)

    Grimm, Thomas W.; Kapfer, Andreas; Klevers, Denis

    2016-06-01

    The geometry of elliptic fibrations translates to the physics of gauge theories in F-theory. We systematically develop the dictionary between arithmetic structures on elliptic curves as well as desingularized elliptic fibrations and symmetries of gauge theories on a circle. We show that the Mordell-Weil group law matches integral large gauge transformations around the circle in Abelian gauge theories and explain the significance of Mordell-Weil torsion in this context. We also use Higgs transitions and circle large gauge transformations to introduce a group law for genus-one fibrations with multi-sections. Finally, we introduce a novel arithmetic structure on elliptic fibrations with non-Abelian gauge groups in F-theory. It is defined on the set of exceptional divisors resolving the singularities and divisor classes of sections of the fibration. This group structure can be matched with certain integral non-Abelian large gauge transformations around the circle when studying the theory on the lower-dimensional Coulomb branch. Its existence is required by consistency with Higgs transitions from the non-Abelian theory to its Abelian phases in which it becomes the Mordell-Weil group. This hints towards the existence of a new underlying geometric symmetry.

  18. The arithmetic of elliptic fibrations in gauge theories on a circle

    International Nuclear Information System (INIS)

    Grimm, Thomas W.; Kapfer, Andreas; Klevers, Denis

    2016-01-01

    The geometry of elliptic fibrations translates to the physics of gauge theories in F-theory. We systematically develop the dictionary between arithmetic structures on elliptic curves as well as desingularized elliptic fibrations and symmetries of gauge theories on a circle. We show that the Mordell-Weil group law matches integral large gauge transformations around the circle in Abelian gauge theories and explain the significance of Mordell-Weil torsion in this context. We also use Higgs transitions and circle large gauge transformations to introduce a group law for genus-one fibrations with multi-sections. Finally, we introduce a novel arithmetic structure on elliptic fibrations with non-Abelian gauge groups in F-theory. It is defined on the set of exceptional divisors resolving the singularities and divisor classes of sections of the fibration. This group structure can be matched with certain integral non-Abelian large gauge transformations around the circle when studying the theory on the lower-dimensional Coulomb branch. Its existence is required by consistency with Higgs transitions from the non-Abelian theory to its Abelian phases in which it becomes the Mordell-Weil group. This hints towards the existence of a new underlying geometric symmetry.

  19. Is the SNARC effect related to the level of mathematics? No systematic relationship observed despite more power, more repetitions, and more direct assessment of arithmetic skill.

    Science.gov (United States)

    Cipora, Krzysztof; Nuerk, Hans-Christoph

    2013-01-01

    The SNARC (spatial-numerical association of response codes) described that larger numbers are responded faster with the right hand and smaller numbers with the left hand. It is held in the literature that arithmetically skilled and nonskilled adults differ in the SNARC. However, the respective data are descriptive, and the decisive tests are nonsignificant. Possible reasons for this nonsignificance could be that in previous studies (a) very small samples were used, (b) there were too few repetitions producing too little power and, consequently, reliabilities that were too small to reach conventional significance levels for the descriptive skill differences in the SNARC, and (c) general mathematical ability was assessed by the field of study of students, while individual arithmetic skills were not examined. Therefore we used a much bigger sample, a lot more repetitions, and direct assessment of arithmetic skills to explore relations between the SNARC effect and arithmetic skills. Nevertheless, a difference in SNARC effect between arithmetically skilled and nonskilled participants was not obtained. Bayesian analysis showed positive evidence of a true null effect, not just a power problem. Hence we conclude that the idea that arithmetically skilled and nonskilled participants generally differ in the SNARC effect is not warranted by our data.

  20. Algorithms in Singular

    Directory of Open Access Journals (Sweden)

    Hans Schonemann

    1996-12-01

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

  1. Improved Accuracy of Nonlinear Parameter Estimation with LAV and Interval Arithmetic Methods

    Directory of Open Access Journals (Sweden)

    Humberto Muñoz

    2009-06-01

    Full Text Available The reliable solution of nonlinear parameter es- timation problems is an important computational problem in many areas of science and engineering, including such applications as real time optimization. Its goal is to estimate accurate model parameters that provide the best fit to measured data, despite small- scale noise in the data or occasional large-scale mea- surement errors (outliers. In general, the estimation techniques are based on some kind of least squares or maximum likelihood criterion, and these require the solution of a nonlinear and non-convex optimiza- tion problem. Classical solution methods for these problems are local methods, and may not be reliable for finding the global optimum, with no guarantee the best model parameters have been found. Interval arithmetic can be used to compute completely and reliably the global optimum for the nonlinear para- meter estimation problem. Finally, experimental re- sults will compare the least squares, l2, and the least absolute value, l1, estimates using interval arithmetic in a chemical engineering application.

  2. Mothers, Intrinsic Math Motivation, Arithmetic Skills, and Math Anxiety in Elementary School.

    Science.gov (United States)

    Daches Cohen, Lital; Rubinsten, Orly

    2017-01-01

    Math anxiety is influenced by environmental, cognitive, and personal factors. Yet, the concurrent relationships between these factors have not been examined. To this end, the current study investigated how the math anxiety of 30 sixth graders is affected by: (a) mother's math anxiety and maternal behaviors (environmental factors); (b) children's arithmetic skills (cognitive factors); and (c) intrinsic math motivation (personal factor). A rigorous assessment of children's math anxiety was made by using both explicit and implicit measures. The results indicated that accessible self-representations of math anxiety, as reflected by the explicit self-report questionnaire, were strongly affected by arithmetic skills. However, unconscious cognitive constructs of math anxiety, as reflected by the numerical dot-probe task, were strongly affected by environmental factors, such as maternal behaviors and mothers' attitudes toward math. Furthermore, the present study provided preliminary evidence of intergenerational transmission of math anxiety. The conclusions are that in order to better understand the etiology of math anxiety, multiple facets of parenting and children's skills should be taken into consideration. Implications for researchers, parents, and educators are discussed.

  3. Positive and Negative Consequences in Contingency Contracts: Their Relative Effectiveness on Arithmetic Performance.

    Science.gov (United States)

    Kidd, Teresa A.; Saudargas, Richard A.

    1988-01-01

    The study with two elementary students who had low levels of completion and accuracy on daily arithmetic assignments found that a negative consequence was not necessary and that use of a positive component alone was sufficient to maintain high levels of completion and accuracy. (Author/DB)

  4. Model, analysis, and evaluation of the effects of analog VLSI arithmetic on linear subspace-based image recognition.

    Science.gov (United States)

    Carvajal, Gonzalo; Figueroa, Miguel

    2014-07-01

    Typical image recognition systems operate in two stages: feature extraction to reduce the dimensionality of the input space, and classification based on the extracted features. Analog Very Large Scale Integration (VLSI) is an attractive technology to achieve compact and low-power implementations of these computationally intensive tasks for portable embedded devices. However, device mismatch limits the resolution of the circuits fabricated with this technology. Traditional layout techniques to reduce the mismatch aim to increase the resolution at the transistor level, without considering the intended application. Relating mismatch parameters to specific effects in the application level would allow designers to apply focalized mismatch compensation techniques according to predefined performance/cost tradeoffs. This paper models, analyzes, and evaluates the effects of mismatched analog arithmetic in both feature extraction and classification circuits. For the feature extraction, we propose analog adaptive linear combiners with on-chip learning for both Least Mean Square (LMS) and Generalized Hebbian Algorithm (GHA). Using mathematical abstractions of analog circuits, we identify mismatch parameters that are naturally compensated during the learning process, and propose cost-effective guidelines to reduce the effect of the rest. For the classification, we derive analog models for the circuits necessary to implement Nearest Neighbor (NN) approach and Radial Basis Function (RBF) networks, and use them to emulate analog classifiers with standard databases of face and hand-writing digits. Formal analysis and experiments show how we can exploit adaptive structures and properties of the input space to compensate the effects of device mismatch at the application level, thus reducing the design overhead of traditional layout techniques. Results are also directly extensible to multiple application domains using linear subspace methods. Copyright © 2014 Elsevier Ltd. All rights

  5. Penambahan Chinese Reminder Theorem Untuk Mempercepat Proses Enkripsi Dan Dekripsi Pada RSA

    OpenAIRE

    Hasibuan, Andi Hazri

    2015-01-01

    Many methods are used to protect digital data stored or transmitted via electronic media. One way is to use a cryptographic algorithm RSA (Rivest-Shamir-Adleman). Standard RSA uses modular arithmetic to perform the encryption and decryption. In this thesis discussed the addition of Chinese Remainder Theorem to speed up the RSA. 100823021

  6. Fast parallel DNA-based algorithms for molecular computation: quadratic congruence and factoring integers.

    Science.gov (United States)

    Chang, Weng-Long

    2012-03-01

    Assume that n is a positive integer. If there is an integer such that M (2) ≡ C (mod n), i.e., the congruence has a solution, then C is said to be a quadratic congruence (mod n). If the congruence does not have a solution, then C is said to be a quadratic noncongruence (mod n). The task of solving the problem is central to many important applications, the most obvious being cryptography. In this article, we describe a DNA-based algorithm for solving quadratic congruence and factoring integers. In additional to this novel contribution, we also show the utility of our encoding scheme, and of the algorithm's submodules. We demonstrate how a variety of arithmetic, shifted and comparative operations, namely bitwise and full addition, subtraction, left shifter and comparison perhaps are performed using strands of DNA.

  7. Do Birth Order, Family Size and Gender Affect Arithmetic Achievement in Elementary School?

    Science.gov (United States)

    Desoete, Annemie

    2008-01-01

    Introduction: For decades birth order and gender differences have attracted research attention. Method: Birth order, family size and gender, and the relationship with arithmetic achievement is studied among 1152 elementary school children (540 girls, 612 boys) in Flanders. Children were matched on socioeconomic status of the parents and…

  8. Theory of ratios in Nicomachus' Arithmetica and series of arithmetical problems in Pachymeres' Quadrivium: Reflections about a possible relationship

    Directory of Open Access Journals (Sweden)

    Megremi Athanasia

    2015-01-01

    Full Text Available The voluminous Treatise of the four mathematical sciences of Georgios Pachymeres is the most renowned quadrivium produced in Byzantium. Among its specific features, historians of mathematics have pointed out, is the inclusion of Diophantus, besides Nicomachus and Euclid, in the sources for the arithmetical section and, accordingly, the incorporation of series of problems and problem-solving in its contents. The present paper investigates the “Diophantine portion” of Pachymeres' treatise and it shows that it is structured according to two criteria intrinsically characterized by seriality: on one hand, the arrangement in which the problems are presented in book I of Diophantus' Arithmetica; on the other hand, for those problems of which the enunciation involves ratio, the order in which Nicomachus discusses the kinds of ratios in his Arithmetical introduction. Furthermore, it analyses the solutions that Pachymeres offers and argues that Nicomachus' Arithmetical introduction provides the necessary tools for pursuing them.

  9. Logical NAND and NOR Operations Using Algorithmic Self-assembly of DNA Molecules

    Science.gov (United States)

    Wang, Yanfeng; Cui, Guangzhao; Zhang, Xuncai; Zheng, Yan

    DNA self-assembly is the most advanced and versatile system that has been experimentally demonstrated for programmable construction of patterned systems on the molecular scale. It has been demonstrated that the simple binary arithmetic and logical operations can be computed by the process of self assembly of DNA tiles. Here we report a one-dimensional algorithmic self-assembly of DNA triple-crossover molecules that can be used to execute five steps of a logical NAND and NOR operations on a string of binary bits. To achieve this, abstract tiles were translated into DNA tiles based on triple-crossover motifs. Serving as input for the computation, long single stranded DNA molecules were used to nucleate growth of tiles into algorithmic crystals. Our method shows that engineered DNA self-assembly can be treated as a bottom-up design techniques, and can be capable of designing DNA computer organization and architecture.

  10. Sex differences in prefrontal hemodynamic response to mental arithmetic as assessed by near-infrared spectroscopy.

    Science.gov (United States)

    Yang, Hongyu; Wang, Ying; Zhou, Zhenyu; Gong, Hui; Luo, Qingming; Wang, Yiwen; Lu, Zuhong

    2009-12-01

    Sex differences in cognitive tasks have been widely investigated. With brain-imaging techniques, the functions of the brain during the performance of tasks can be examined. Mental arithmetic and near-infrared spectroscopy (NIRS) were used to assess sex differences in prefrontal area activation in a functional brain study. Healthy college students were recruited to perform 2 mental arithmetic tasks. In the first (easy) task, students had to subtract a 1-digit number from a 3-digit number. In the second (difficult) task, they had to subtract a 2-digit number from a 3-digit number. Changes in the concentration of oxygenated hemoglobin (oxy-Hgb) in the prefrontal area during the tasks were measured with NIRS. Thirty students (15 men, 15 women; mean [SD] age: 24.9 [2.2] and 24.3 [2.6] years, respectively) were recruited from Southeast University, Nanjing, China, to participate in the study. The concentration of oxy-Hgb increased during both mental arithmetic tasks (difficult task vs easy task, mean [SD] % arbitrary units: 4.36 [4.38] vs 2.26 [2.82]; F(1,28) = 222.80; P men and women were observed in the mean (SD) response time (men vs women, sec: 3.60 [0.74] vs 3.56 [0.49] for the easy task, 6.55 [0.77] vs 6.44 [0.75] for the difficult task; F(1,28) = 0.67; P = NS) or accuracy rate (men vs women, %: 95.33 [7.40] vs 92.77 [8.80] for the easy task, 62.67 [28.56] vs 54.67 [18.75] for the difficult task; F(1,28) = 0.54; P = NS). Male students showed neural efficiency (less prefrontal activation in subjects with better performance) during the difficult task. In these subjects, sex differences in prefrontal response when performing mental arithmetic were associated with the intensity of the task. Compared with men, women had greater efficiency in task performance (ie, less activation or oxygen consumption for equal performance). Copyright 2009 Excerpta Medica Inc. All rights reserved.

  11. Interference and problem size effect in multiplication fact solving: Individual differences in brain activations and arithmetic performance.

    Science.gov (United States)

    De Visscher, Alice; Vogel, Stephan E; Reishofer, Gernot; Hassler, Eva; Koschutnig, Karl; De Smedt, Bert; Grabner, Roland H

    2018-05-15

    In the development of math ability, a large variability of performance in solving simple arithmetic problems is observed and has not found a compelling explanation yet. One robust effect in simple multiplication facts is the problem size effect, indicating better performance for small problems compared to large ones. Recently, behavioral studies brought to light another effect in multiplication facts, the interference effect. That is, high interfering problems (receiving more proactive interference from previously learned problems) are more difficult to retrieve than low interfering problems (in terms of physical feature overlap, namely the digits, De Visscher and Noël, 2014). At the behavioral level, the sensitivity to the interference effect is shown to explain individual differences in the performance of solving multiplications in children as well as in adults. The aim of the present study was to investigate the individual differences in multiplication ability in relation to the neural interference effect and the neural problem size effect. To that end, we used a paradigm developed by De Visscher, Berens, et al. (2015) that contrasts the interference effect and the problem size effect in a multiplication verification task, during functional magnetic resonance imaging (fMRI) acquisition. Forty-two healthy adults, who showed high variability in an arithmetic fluency test, participated in our fMRI study. In order to control for the general reasoning level, the IQ was taken into account in the individual differences analyses. Our findings revealed a neural interference effect linked to individual differences in multiplication in the left inferior frontal gyrus, while controlling for the IQ. This interference effect in the left inferior frontal gyrus showed a negative relation with individual differences in arithmetic fluency, indicating a higher interference effect for low performers compared to high performers. This region is suggested in the literature to be

  12. 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)

  13. Selection and determination of beam weights based on genetic algorithms for conformal radiotherapy treatment planning

    International Nuclear Information System (INIS)

    Xingen Wu; Zunliang Wang

    2000-01-01

    A genetic algorithm has been used to optimize the selection of beam weights for external beam three-dimensional conformal radiotherapy treatment planning. A fitness function is defined, which includes a difference function to achieve a least-square fit to doses at preselected points in a planning target volume, and a penalty item to constrain the maximum allowable doses delivered to critical organs. Adjustment between the dose uniformity within the target volume and the dose constraint to the critical structures can be achieved by varying the beam weight variables in the fitness function. A floating-point encoding schema and several operators, like uniform crossover, arithmetical crossover, geometrical crossover, Gaussian mutation and uniform mutation, have been used to evolve the population. Three different cases were used to verify the correctness of the algorithm and quality assessment based on dose-volume histograms and three-dimensional dose distributions were given. The results indicate that the genetic algorithm presented here has considerable potential. (author)

  14. Measuring Acetabular Cup Orientation on Antero-Posterior Radiographs of the Hip after Total Hip Arthroplasty with a Vector Arithmetic Radiological Method. Is It Valid and Verified for Daily Clinical Practice?

    Science.gov (United States)

    Craiovan, B; Weber, M; Worlicek, M; Schneider, M; Springorum, H R; Zeman, F; Grifka, J; Renkawitz, T

    2016-06-01

    The aim of this prospective study is to validate a vector arithmetic method for measuring acetabular cup orientation after total hip arthroplasty (THA) and to verify the clinical practice. We measured cup anteversion and inclination of 123 patients after cementless primary THA twice by two examiners on AP pelvic radiographs with a vector arithmetic method and compared with a 3D-CT based reconstruction model within the same radiographic coronal plane. The mean difference between the radiographic and the 3D-CT measurements was - 1.4° ± 3.9° for inclination and 0.8°± 7.9° for anteversion with excellent correlation for inclination (r = 0.81, p cup position after THA on pelvic radiographs by this vector arithmetic method, there is a need for a correct postoperative ap view, with special regards to the pelvic tilt for the future. • Measuring acetabular cup orientation on anteroposterior radiographs of the hip after THA is a helpful procedure in everyday clinical practice as a first-line imaging modality• CT remains the golden standard to accurately determine acetabular cup position.• Future measuring on radiographs for cup orientation after THA should account for integration of the pelvic tilt in order to maximize the measurement accuracy. Citation Format: • Craiovan B, Weber M, Worlicek M et al. Measuring Acetabular Cup Orientation on Antero-Posterior Radiographs of the Hip after Total Hip Arthroplasty with a Vector Arithmetic Radiological Method. Is It Valid and Verified for Daily Clinical Practice?. Fortschr Röntgenstr 2016; 188: 574 - 581. © Georg Thieme Verlag KG Stuttgart · New York.

  15. Comparing Repetition Priming Effects in Words and Arithmetic Equations: Robust Priming Regardless of Color or Response Hand Change

    Directory of Open Access Journals (Sweden)

    Ailsa Humphries

    2018-01-01

    Full Text Available Previous studies have shown that stimulus repetition can lead to reliable behavioral improvements. Although this repetition priming (RP effect has been reported in a number of paradigms using a variety of stimuli including words, objects, and faces, only a few studies have investigated mathematical cognition involving arithmetic computation, and no prior research has directly compared RP effects in a linguistic task with an arithmetic task. In two experiments, we used a within-subjects design to investigate and compare the magnitude of RP, and the effects of changing the color or the response hand for repeated, otherwise identical, stimuli in a word and an arithmetic categorization task. The results show that the magnitude of RP was comparable between the two tasks and that changing the color or the response hand had a negligible effect on priming in either task. These results extended previous findings in mathematical cognition. They also indicate that priming does not vary with stimulus domain. The implications of the results were discussed with reference to both facilitation of component processes and episodic memory retrieval of stimulus–response binding.

  16. Comparing Repetition Priming Effects in Words and Arithmetic Equations: Robust Priming Regardless of Color or Response Hand Change.

    Science.gov (United States)

    Humphries, Ailsa; Chen, Zhe; Neumann, Ewald

    2017-01-01

    Previous studies have shown that stimulus repetition can lead to reliable behavioral improvements. Although this repetition priming (RP) effect has been reported in a number of paradigms using a variety of stimuli including words, objects, and faces, only a few studies have investigated mathematical cognition involving arithmetic computation, and no prior research has directly compared RP effects in a linguistic task with an arithmetic task. In two experiments, we used a within-subjects design to investigate and compare the magnitude of RP, and the effects of changing the color or the response hand for repeated, otherwise identical, stimuli in a word and an arithmetic categorization task. The results show that the magnitude of RP was comparable between the two tasks and that changing the color or the response hand had a negligible effect on priming in either task. These results extended previous findings in mathematical cognition. They also indicate that priming does not vary with stimulus domain. The implications of the results were discussed with reference to both facilitation of component processes and episodic memory retrieval of stimulus-response binding.

  17. STAR Algorithm Integration Team - Facilitating operational algorithm development

    Science.gov (United States)

    Mikles, V. J.

    2015-12-01

    The NOAA/NESDIS Center for Satellite Research and Applications (STAR) provides technical support of the Joint Polar Satellite System (JPSS) algorithm development and integration tasks. Utilizing data from the S-NPP satellite, JPSS generates over thirty Environmental Data Records (EDRs) and Intermediate Products (IPs) spanning atmospheric, ocean, cryosphere, and land weather disciplines. The Algorithm Integration Team (AIT) brings technical expertise and support to product algorithms, specifically in testing and validating science algorithms in a pre-operational environment. The AIT verifies that new and updated algorithms function in the development environment, enforces established software development standards, and ensures that delivered packages are functional and complete. AIT facilitates the development of new JPSS-1 algorithms by implementing a review approach based on the Enterprise Product Lifecycle (EPL) process. Building on relationships established during the S-NPP algorithm development process and coordinating directly with science algorithm developers, the AIT has implemented structured reviews with self-contained document suites. The process has supported algorithm improvements for products such as ozone, active fire, vegetation index, and temperature and moisture profiles.

  18. Strategy Choice in Solving Arithmetic Word Problems: Are There Differences between Students with Learning Disabilities, G-V Poor Performance, and Typical Achievement Students?

    Science.gov (United States)

    Gonzalez, Juan E. Jimenez; Espinel, Ana Isabel Garcia

    2002-01-01

    A study was designed to test whether there are differences between Spanish children (ages 7-9) with arithmetic learning disabilities (n=60), garden-variety (G-V) poor performance (n=44), and typical children (n=44) in strategy choice when solving arithmetic word problems. No significant differences were found between children with dyscalculia and…

  19. Hard Lessons: Why Rational Number Arithmetic Is so Difficult for so Many People

    Science.gov (United States)

    Siegler, Robert S.; Lortie-Forgues, Hugues

    2017-01-01

    Fraction and decimal arithmetic pose large difficulties for many children and adults. This is a serious problem, because proficiency with these skills is crucial for learning more advanced mathematics and science and for success in many occupations. This review identifies two main classes of difficulties that underlie poor understanding of…

  20. Automatic Circuit Design and Optimization Using Modified PSO Algorithm

    Directory of Open Access Journals (Sweden)

    Subhash Patel

    2016-04-01

    Full Text Available In this work, we have proposed modified PSO algorithm based optimizer for automatic circuit design. The performance of the modified PSO algorithm is compared with two other evolutionary algorithms namely ABC algorithm and standard PSO algorithm by designing two stage CMOS operational amplifier and bulk driven OTA in 130nm technology. The results show the robustness of the proposed algorithm. With modified PSO algorithm, the average design error for two stage op-amp is only 0.054% in contrast to 3.04% for standard PSO algorithm and 5.45% for ABC algorithm. For bulk driven OTA, average design error is 1.32% with MPSO compared to 4.70% with ABC algorithm and 5.63% with standard PSO algorithm.

  1. A parallel row-based algorithm with error control for standard-cell replacement on a hypercube multiprocessor

    Science.gov (United States)

    Sargent, Jeff Scott

    1988-01-01

    A new row-based parallel algorithm for standard-cell placement targeted for execution on a hypercube multiprocessor is presented. Key features of this implementation include a dynamic simulated-annealing schedule, row-partitioning of the VLSI chip image, and two novel new approaches to controlling error in parallel cell-placement algorithms; Heuristic Cell-Coloring and Adaptive (Parallel Move) Sequence Control. Heuristic Cell-Coloring identifies sets of noninteracting cells that can be moved repeatedly, and in parallel, with no buildup of error in the placement cost. Adaptive Sequence Control allows multiple parallel cell moves to take place between global cell-position updates. This feedback mechanism is based on an error bound derived analytically from the traditional annealing move-acceptance profile. Placement results are presented for real industry circuits and the performance is summarized of an implementation on the Intel iPSC/2 Hypercube. The runtime of this algorithm is 5 to 16 times faster than a previous program developed for the Hypercube, while producing equivalent quality placement. An integrated place and route program for the Intel iPSC/2 Hypercube is currently being developed.

  2. Acute appendicitis: prospective evaluation of a diagnostic algorithm integrating ultrasound and low-dose CT to reduce the need of standard CT

    International Nuclear Information System (INIS)

    Poletti, Pierre-Alexandre; Platon, Alexandra; Perrot, Thomas de; Becker, Christoph D.; Sarasin, Francois; Rutschmann, Olivier; Andereggen, Elisabeth; Dupuis-Lozeron, Elise; Perneger, Thomas; Gervaz, Pascal

    2011-01-01

    To evaluate an algorithm integrating ultrasound and low-dose unenhanced CT with oral contrast medium (LDCT) in the assessment of acute appendicitis, to reduce the need of conventional CT. Ultrasound was performed upon admission in 183 consecutive adult patients (111 women, 72 men, mean age 32) with suspicion of acute appendicitis and a BMI between 18.5 and 30 (step 1). No further examination was recommended when ultrasound was positive for appendicitis, negative with low clinical suspicion, or demonstrated an alternative diagnosis. All other patients underwent LDCT (30 mAs) (step 2). Standard intravenously enhanced CT (180 mAs) was performed after indeterminate LDCT (step 3). No further imaging was recommended after ultrasound in 84 (46%) patients; LDCT was obtained in 99 (54%). LDCT was positive or negative for appendicitis in 81 (82%) of these 99 patients, indeterminate in 18 (18%) who underwent standard CT. Eighty-six (47%) of the 183 patients had a surgically proven appendicitis. The sensitivity and specificity of the algorithm were 98.8% and 96.9%. The proposed algorithm achieved high sensitivity and specificity for detection of acute appendicitis, while reducing the need for standard CT and thus limiting exposition to radiation and to intravenous contrast media. (orig.)

  3. Acute appendicitis: prospective evaluation of a diagnostic algorithm integrating ultrasound and low-dose CT to reduce the need of standard CT

    Energy Technology Data Exchange (ETDEWEB)

    Poletti, Pierre-Alexandre; Platon, Alexandra [University Hospital of Geneva, Department of Radiology, Geneva (Switzerland); University Hospital of Geneva, Emergency Center, Geneva (Switzerland); Perrot, Thomas de; Becker, Christoph D. [University Hospital of Geneva, Department of Radiology, Geneva (Switzerland); Sarasin, Francois; Rutschmann, Olivier [University Hospital of Geneva, Emergency Center, Geneva (Switzerland); Andereggen, Elisabeth [University Hospital of Geneva, Emergency Center, Geneva (Switzerland); University Hospital of Geneva, Department of Surgery, Geneva (Switzerland); Dupuis-Lozeron, Elise; Perneger, Thomas [University Hospital of Geneva, Division of Clinical Epidemiology, Geneva (Switzerland); Gervaz, Pascal [University Hospital of Geneva, Department of Surgery, Geneva (Switzerland)

    2011-12-15

    To evaluate an algorithm integrating ultrasound and low-dose unenhanced CT with oral contrast medium (LDCT) in the assessment of acute appendicitis, to reduce the need of conventional CT. Ultrasound was performed upon admission in 183 consecutive adult patients (111 women, 72 men, mean age 32) with suspicion of acute appendicitis and a BMI between 18.5 and 30 (step 1). No further examination was recommended when ultrasound was positive for appendicitis, negative with low clinical suspicion, or demonstrated an alternative diagnosis. All other patients underwent LDCT (30 mAs) (step 2). Standard intravenously enhanced CT (180 mAs) was performed after indeterminate LDCT (step 3). No further imaging was recommended after ultrasound in 84 (46%) patients; LDCT was obtained in 99 (54%). LDCT was positive or negative for appendicitis in 81 (82%) of these 99 patients, indeterminate in 18 (18%) who underwent standard CT. Eighty-six (47%) of the 183 patients had a surgically proven appendicitis. The sensitivity and specificity of the algorithm were 98.8% and 96.9%. The proposed algorithm achieved high sensitivity and specificity for detection of acute appendicitis, while reducing the need for standard CT and thus limiting exposition to radiation and to intravenous contrast media. (orig.)

  4. Design and algorithm research of high precision airborne infrared touch screen

    Science.gov (United States)

    Zhang, Xiao-Bing; Wang, Shuang-Jie; Fu, Yan; Chen, Zhao-Quan

    2016-10-01

    There are shortcomings of low precision, touch shaking, and sharp decrease of touch precision when emitting and receiving tubes are failure in the infrared touch screen. A high precision positioning algorithm based on extended axis is proposed to solve these problems. First, the unimpeded state of the beam between emitting and receiving tubes is recorded as 0, while the impeded state is recorded as 1. Then, the method of oblique scan is used, in which the light of one emitting tube is used for five receiving tubes. The impeded information of all emitting and receiving tubes is collected as matrix. Finally, according to the method of arithmetic average, the position of the touch object is calculated. The extended axis positioning algorithm is characteristic of high precision in case of failure of individual infrared tube and affects slightly the precision. The experimental result shows that the 90% display area of the touch error is less than 0.25D, where D is the distance between adjacent emitting tubes. The conclusion is gained that the algorithm based on extended axis has advantages of high precision, little impact when individual infrared tube is failure, and using easily.

  5. A codesign case study: implementing arithmetic functions in FPGAs

    DEFF Research Database (Denmark)

    Klotchkov, I. V.; Pedersen, Steen

    1996-01-01

    Different ways of implementing and designing arithmetic functions for 16/32 bit integers in FPGA technology are studied. A comparison of four different design methods is also included. The results are used to increase the overall system performance in a dedicated 3D image analysis prototype system...... by moving a vector length calculation from software to hardware. The conclusion is that by adding one relatively simple board containing two FPGAs in the prototype setup, the total computing time is reduced by 30%. The total amount of image data, in this case 300 Mbyte, which has to be transmitted via...

  6. Naming Speed and Effortful and Automatic Inhibition in Children with Arithmetic Learning Disabilities

    Science.gov (United States)

    D'Amico, Antonella; Passolunghi, Maria Chiara

    2009-01-01

    We report a two-year longitudinal study aimed at investigating the rate of access to numerical and non-numerical information in long-term memory and the functioning of automatic and effortful cognitive inhibition processes in children with arithmetical learning disabilities (ALDs). Twelve children with ALDs, of age 9.3 years, and twelve…

  7. Enhancing Arithmetic and Word-Problem Solving Skills Efficiently by Individualized Computer-Assisted Practice

    Science.gov (United States)

    Schoppek, Wolfgang; Tulis, Maria

    2010-01-01

    The fluency of basic arithmetical operations is a precondition for mathematical problem solving. However, the training of skills plays a minor role in contemporary mathematics instruction. The authors proposed individualization of practice as a means to improve its efficiency, so that the time spent with the training of skills is minimized. As a…

  8. THE EFFECT OF PLAYING SNAKE AND LADDER TOWARD THE RESULT STUDY OF ARITHMETIC ADDITION FOR STUDENT WITH MENTALLY RETARDED STUDENT

    Directory of Open Access Journals (Sweden)

    Arianti Iman Sari

    2016-12-01

    Full Text Available The purpose of this research were to describe: (1 the study result of arithmetic addition operation for fourth grade student with mentally retarded in SDLB before playing the Snake and Ladder activity (2 the study result of arithmetic addition operation for fourth grade student with mentally retarded in SDLB after playing the Snake and Ladder activity (3 the effect of Snake and Ladder playing toward the result study of arithmetic addition for fourth grade student with mentally retarded SDLB. This research used SSR (Single Subject Research with A-B-A design. Collecting the data was done by using assessment instrument, tests and observations. The result of this research showed that playing Snake and Ladder affected the study result of arithmetic addition operation for fourth-grade children with mentally retarded student in SDLB. Tujuan penelitian ini adalah mendeskripsikan (1 Hasil belajar penjumlahan siswa kelas 4 SDLB sebelum melakukan kegiatan bermain Ular Tangga (2 Hasil belajar penjumlahan siswa kelas 4 SDLB sesudah melakukan kegiatan bermain Ular Tangga (3 Pengaruh bermain Ular Tangga terhadap hasil belajar penjumlahan siswa kelas 4 SDLB. Penelitian ini menggunakan rancangan penelitian SSR (Single Subject Research dengan desain A-B-A. Pengumpulan data menggunakan instrumen assesmen, tes dan observasi. Hasil penelitian menunjukkan bermain ular tangga berpengaruh terhadap hasil belajar penjumlahan siswa tunagrahita kelas 4 SDLB.

  9. On the form of the forgetting function: the effects of arithmetic and logarithmic distributions of delays.

    Science.gov (United States)

    Sargisson, Rebecca J; White, K Geoffrey

    2003-11-01

    Forgetting functions with 18 delay intervals were generated for delayed matching-to-sample performance in pigeons. Delay interval variation was achieved by arranging five different sets of five delays across daily sessions. In different conditions, the delays were distributed in arithmetic or logarithmic series. There was no convincing evidence for different effects on discriminability of the distributions of different delays. The mean data were better fitted by some mathematical functions than by others, but the best-fitting functions depended on the distribution of delays. In further conditions with a fixed set of five delays, discriminability was higher with a logarithmic distribution of delays than with an arithmetic distribution. This result is consistent with the treatment of the forgetting function in terms of generalization decrement.

  10. Mothers, Intrinsic Math Motivation, Arithmetic Skills, and Math Anxiety in Elementary School

    Science.gov (United States)

    Daches Cohen, Lital; Rubinsten, Orly

    2017-01-01

    Math anxiety is influenced by environmental, cognitive, and personal factors. Yet, the concurrent relationships between these factors have not been examined. To this end, the current study investigated how the math anxiety of 30 sixth graders is affected by: (a) mother’s math anxiety and maternal behaviors (environmental factors); (b) children’s arithmetic skills (cognitive factors); and (c) intrinsic math motivation (personal factor). A rigorous assessment of children’s math anxiety was made by using both explicit and implicit measures. The results indicated that accessible self-representations of math anxiety, as reflected by the explicit self-report questionnaire, were strongly affected by arithmetic skills. However, unconscious cognitive constructs of math anxiety, as reflected by the numerical dot-probe task, were strongly affected by environmental factors, such as maternal behaviors and mothers’ attitudes toward math. Furthermore, the present study provided preliminary evidence of intergenerational transmission of math anxiety. The conclusions are that in order to better understand the etiology of math anxiety, multiple facets of parenting and children’s skills should be taken into consideration. Implications for researchers, parents, and educators are discussed. PMID:29180973

  11. Mothers, Intrinsic Math Motivation, Arithmetic Skills, and Math Anxiety in Elementary School

    Directory of Open Access Journals (Sweden)

    Lital Daches Cohen

    2017-11-01

    Full Text Available Math anxiety is influenced by environmental, cognitive, and personal factors. Yet, the concurrent relationships between these factors have not been examined. To this end, the current study investigated how the math anxiety of 30 sixth graders is affected by: (a mother’s math anxiety and maternal behaviors (environmental factors; (b children’s arithmetic skills (cognitive factors; and (c intrinsic math motivation (personal factor. A rigorous assessment of children’s math anxiety was made by using both explicit and implicit measures. The results indicated that accessible self-representations of math anxiety, as reflected by the explicit self-report questionnaire, were strongly affected by arithmetic skills. However, unconscious cognitive constructs of math anxiety, as reflected by the numerical dot-probe task, were strongly affected by environmental factors, such as maternal behaviors and mothers’ attitudes toward math. Furthermore, the present study provided preliminary evidence of intergenerational transmission of math anxiety. The conclusions are that in order to better understand the etiology of math anxiety, multiple facets of parenting and children’s skills should be taken into consideration. Implications for researchers, parents, and educators are discussed.

  12. The Arithmetical Machine Zero + 1 in Mathematics Laboratory: Instrumental Genesis and Semiotic Mediation

    Science.gov (United States)

    Maschietto, Michela

    2015-01-01

    This paper presents the analysis of two teaching experiments carried out in the context of the mathematics laboratory in a primary school (grades 3 and 4) with the use of the pascaline Zero + 1, an arithmetical machine. The teaching experiments are analysed by coordinating two theoretical frameworks, i.e. the instrumental approach and the Theory…

  13. Solution Strategies and Achievement in Dutch Complex Arithmetic: Latent Variable Modeling of Change

    Science.gov (United States)

    Hickendorff, Marian; Heiser, Willem J.; van Putten, Cornelis M.; Verhelst, Norman D.

    2009-01-01

    In the Netherlands, national assessments at the end of primary school (Grade 6) show a decline of achievement on problems of complex or written arithmetic over the last two decades. The present study aims at contributing to an explanation of the large achievement decrease on complex division, by investigating the strategies students used in…

  14. Development of Working Memory and Performance in Arithmetic: A Longitudinal Study with Children

    Science.gov (United States)

    López, Magdalena

    2014-01-01

    Introduction: This study has aimed to investigate the relationship between the development of working memory and performance on arithmetic activities. Method: We conducted a 3-year longitudinal study of a sample of 90 children, that was followed during the first, second and third year of primary school. All children were tested on measures of WM…

  15. Instrument for bone mineral measurement using a microprocessor as the control and arithmetic element

    International Nuclear Information System (INIS)

    Alberi, J.L.; Hardy, W.H. II.

    1975-11-01

    A self-contained instrument for the determination of bone mineral content by photon absorptometry is described. A high-resolution detection system allows measurements to be made at up to 16 photon energies. Control and arithmetic functions are performed by a microprocessor. Analysis capability and limitations are discussed

  16. Realization of two-dimensional transformations by the arithmetical module of an intelligent graphics terminal

    International Nuclear Information System (INIS)

    Leich, A.; Polyntsev, A.D.

    1982-01-01

    The structure and software of the arithmetical module for the multi-microprocessor intelligent graphics terminal designed for realization of the world coordinate two-dimensional transformation are described. The module performs the operations like coordinate system displacement, scaling and rotation as well as transformations for window/viewport separation

  17. Metacognition for strategy selection during arithmetic problem-solving in young and older adults.

    Science.gov (United States)

    Geurten, Marie; Lemaire, Patrick

    2018-04-19

    We examined participants' strategy choices and metacognitive judgments during arithmetic problem-solving. Metacognitive judgments were collected either prospectively or retrospectively. We tested whether metacognitive judgments are related to strategy choices on the current problems and on the immediately following problems, and age-related differences in relations between metacognition and strategy choices. Data showed that both young and older adults were able to make accurate retrospective, but not prospective, judgments. Moreover, the accuracy of retrospective judgments was comparable in young and older adults when participants had to select and execute the better strategy. Metacognitive accuracy was even higher in older adults when participants had to only select the better strategy. Finally, low-confidence judgments on current items were more frequently followed by better strategy selection on immediately succeeding items than high-confidence judgments in both young and older adults. Implications of these findings to further our understanding of age-related differences and similarities in adults' metacognitive monitoring and metacognitive regulation for strategy selection in the context of arithmetic problem solving are discussed.

  18. Modified LMI condition for the realization of limit cycle-free digital filters using saturation arithmetic

    International Nuclear Information System (INIS)

    Singh, Vimal

    2007-01-01

    A criterion in the form of linear matrix inequality for the elimination of limit cycles in a class of state-space digital filters using saturation arithmetic is presented. The criterion is a modified form of a previously reported criterion

  19. Age-related differences in strategic monitoring during arithmetic problem solving.

    Science.gov (United States)

    Geurten, Marie; Lemaire, Patrick

    2017-10-01

    We examined the role of metacognitive monitoring in strategic behavior during arithmetic problem solving, a process that is expected to shed light on age-related differences in strategy selection. Young and older adults accomplished better strategy-judgment, better strategy-selection, and strategy-execution tasks. Data showed that participants made better strategy judgments when problems were problems with homogeneous unit digits (i.e., problems with both unit digits smaller or larger than 5; 31×62) relative to problems with heterogeneous unit digits (i.e., problems with one unit digit smaller or larger than 5; 31×67) and when the better strategy was cued on rounding-up problems (e.g., 68×23) compared to rounding-down problems (e.g., 36×53). Results also indicated higher rates of better strategy judgment in young than in older adults. These aging effects differed across problem types. Older adults made more accurate judgments on rounding-up problems than on rounding-down problems when the cued strategy was rounding-up, while young adults did not show such problem-related differences. Moreover, strategy selection correlated with strategy judgment, and even more so in older adults than in young adults. To discuss the implications of these findings, we propose a theoretical framework of how strategy judgments occur in young and older adults and discuss how this framework enables to understand relationships between metacognitive monitoring and strategic behaviors when participants solve arithmetic problems. Copyright © 2017 Elsevier B.V. All rights reserved.

  20. Deficits in working memory, reading comprehension and arithmetic skills in children with mouth breathing syndrome: analytical cross-sectional study.

    Science.gov (United States)

    Kuroishi, Rita Cristina Sadako; Garcia, Ricardo Basso; Valera, Fabiana Cardoso Pereira; Anselmo-Lima, Wilma Terezinha; Fukuda, Marisa Tomoe Hebihara

    2015-01-01

    Mouth breathing syndrome is very common among school-age children, and it is possibly related to learning difficulties and low academic achievement. In this study, we investigated working memory, reading comprehension and arithmetic skills in children with nasal and mouth breathing. Analytical cross-sectional study with control group conducted in a public university hospital. 42 children (mean age = 8.7 years) who had been identified as mouth breathers were compared with a control group (mean age = 8.4 years) matched for age and schooling. All the participants underwent a clinical interview, tone audiometry, otorhinolaryngological evaluation and cognitive assessment of phonological working memory (numbers and pseudowords), reading comprehension and arithmetic skills. Children with mouth breathing had poorer performance than controls, regarding reading comprehension (P = 0.006), arithmetic (P = 0.025) and working memory for pseudowords (P = 0.002), but not for numbers (P = 0.76). Children with mouth breathing have low academic achievement and poorer phonological working memory than controls. Teachers and healthcare professionals should be aware of the association of mouth breathing with children's physical and cognitive health.

  1. Short-term memory impairment and arithmetical ability.

    Science.gov (United States)

    Butterworth, B; Cipolotti, L; Warrington, E K

    1996-02-01

    We document the dissociation of preserved calculation skills in a patient with impaired auditory short-term memory. The patient (MRF) had a memory span of three digits. Furthermore, he showed rapid decrement in performance of single digits and letters with both auditory and visual presentation in the Brown-Peterson forgetting task. Analysis of his calculation skills revealed a normal ability to solve auditorily presented multidigit addition and subtraction problems such as 173 + 68 and to execute the Paced Auditory Serial Addition Task (Sampson, 1956, 1958; Gronwall, 1977). In addition, his performance on other tests, including arithmetic manipulation of natural numbers, decimals and fractions, approximation, magnitude, ratio, and percentage, appeared to be normal (Hitch, 1978b). It is argued that these findings require a revision of Baddeley and Hitch's (1974) concept of the function of working memory.

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

    Science.gov (United States)

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

    2018-03-01

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

  3. Neurocognitive Effects of Transcranial Direct Current Stimulation in Arithmetic Learning and Performance: A Simultaneous tDCS-fMRI Study.

    Science.gov (United States)

    Hauser, Tobias U; Rütsche, Bruno; Wurmitzer, Karoline; Brem, Silvia; Ruff, Christian C; Grabner, Roland H

    A small but increasing number of studies suggest that non-invasive brain stimulation by means of transcranial direct current stimulation (tDCS) can modulate arithmetic processes that are essential for higher-order mathematical skills and that are impaired in dyscalculic individuals. However, little is known about the neural mechanisms underlying such stimulation effects, and whether they are specific to cognitive processes involved in different arithmetic tasks. We addressed these questions by applying tDCS during simultaneous functional magnetic resonance imaging (fMRI) while participants were solving two types of complex subtraction problems: repeated problems, relying on arithmetic fact learning and problem-solving by fact retrieval, and novel problems, requiring calculation procedures. Twenty participants receiving left parietal anodal plus right frontal cathodal stimulation were compared with 20 participants in a sham condition. We found a strong cognitive and neural dissociation between repeated and novel problems. Repeated problems were solved more accurately and elicited increased activity in the bilateral angular gyri and medial plus lateral prefrontal cortices. Solving novel problems, in contrast, was accompanied by stronger activation in the bilateral intraparietal sulci and the dorsomedial prefrontal cortex. Most importantly, tDCS decreased the activation of the right inferior frontal cortex while solving novel (compared to repeated) problems, suggesting that the cathodal stimulation rendered this region unable to respond to the task-specific cognitive demand. The present study revealed that tDCS during arithmetic problem-solving can modulate the neural activity in proximity to the electrodes specifically when the current demands lead to an engagement of this area. Copyright © 2016 Elsevier Inc. All rights reserved.

  4. Batched QR and SVD Algorithms on GPUs with Applications in Hierarchical Matrix Compression

    KAUST Repository

    Halim Boukaram, Wajih

    2017-09-14

    We present high performance implementations of the QR and the singular value decomposition of a batch of small matrices hosted on the GPU with applications in the compression of hierarchical matrices. The one-sided Jacobi algorithm is used for its simplicity and inherent parallelism as a building block for the SVD of low rank blocks using randomized methods. We implement multiple kernels based on the level of the GPU memory hierarchy in which the matrices can reside and show substantial speedups against streamed cuSOLVER SVDs. The resulting batched routine is a key component of hierarchical matrix compression, opening up opportunities to perform H-matrix arithmetic efficiently on GPUs.

  5. Batched QR and SVD Algorithms on GPUs with Applications in Hierarchical Matrix Compression

    KAUST Repository

    Halim Boukaram, Wajih; Turkiyyah, George; Ltaief, Hatem; Keyes, David E.

    2017-01-01

    We present high performance implementations of the QR and the singular value decomposition of a batch of small matrices hosted on the GPU with applications in the compression of hierarchical matrices. The one-sided Jacobi algorithm is used for its simplicity and inherent parallelism as a building block for the SVD of low rank blocks using randomized methods. We implement multiple kernels based on the level of the GPU memory hierarchy in which the matrices can reside and show substantial speedups against streamed cuSOLVER SVDs. The resulting batched routine is a key component of hierarchical matrix compression, opening up opportunities to perform H-matrix arithmetic efficiently on GPUs.

  6. A Teachable Agent Game Engaging Primary School Children to Learn Arithmetic Concepts and Reasoning

    Science.gov (United States)

    Pareto, Lena

    2014-01-01

    In this paper we will describe a learning environment designed to foster conceptual understanding and reasoning in mathematics among younger school children. The learning environment consists of 48 2-player game variants based on a graphical model of arithmetic where the mathematical content is intrinsically interwoven with the game idea. The…

  7. Syntactic Awareness and Arithmetic Word Problem Solving in Children with and without Learning Disabilities

    Science.gov (United States)

    Peake, Christian; Jiménez, Juan E.; Rodríguez, Cristina; Bisschop, Elaine; Villarroel, Rebeca

    2015-01-01

    Arithmetic word problem (AWP) solving is a highly demanding task for children with learning disabilities (LD) since verbal and mathematical information have to be integrated. This study examines specifically how syntactic awareness (SA), the ability to manage the grammatical structures of language, affects AWP solving. Three groups of children in…

  8. Brain potentials during mental arithmetic: effects of extensive practice and problem difficulty

    OpenAIRE

    Pauli, Paul; Lutzenberger, W.; Rau, H.; Birbaumer, N.; Rickard, T. C.; Yaroush, R. A.; Bourne, L. E. J.

    2011-01-01

    Recent behavioral investigations indicate that the processes underlying mental arithmetic change systematically with practice from deliberate, conscious calculation to automatic, direct retrieval of answers from memory [Bourne, L.E.Jr. and Rickard, T.C., Mental calculation: The development of a cognitive skill, Paper presented at the Interamerican Congress of Psychology, San Jose, Costa Rica, 1991; Psychol. Rev., 95 (1988) 492-527]. Results reviewed by Moscovitch and Winocur [In: The handbook...

  9. Assessing flood forecast uncertainty with fuzzy arithmetic

    Directory of Open Access Journals (Sweden)

    de Bruyn Bertrand

    2016-01-01

    Full Text Available Providing forecasts for flow rates and water levels during floods have to be associated with uncertainty estimates. The forecast sources of uncertainty are plural. For hydrological forecasts (rainfall-runoff performed using a deterministic hydrological model with basic physics, two main sources can be identified. The first obvious source is the forcing data: rainfall forecast data are supplied in real time by meteorological forecasting services to the Flood Forecasting Service within a range between a lowest and a highest predicted discharge. These two values define an uncertainty interval for the rainfall variable provided on a given watershed. The second source of uncertainty is related to the complexity of the modeled system (the catchment impacted by the hydro-meteorological phenomenon, the number of variables that may describe the problem and their spatial and time variability. The model simplifies the system by reducing the number of variables to a few parameters. Thus it contains an intrinsic uncertainty. This model uncertainty is assessed by comparing simulated and observed rates for a large number of hydro-meteorological events. We propose a method based on fuzzy arithmetic to estimate the possible range of flow rates (and levels of water making a forecast based on possible rainfalls provided by forcing and uncertainty model. The model uncertainty is here expressed as a range of possible values. Both rainfall and model uncertainties are combined with fuzzy arithmetic. This method allows to evaluate the prediction uncertainty range. The Flood Forecasting Service of Oise and Aisne rivers, in particular, monitors the upstream watershed of the Oise at Hirson. This watershed’s area is 310 km2. Its response time is about 10 hours. Several hydrological models are calibrated for flood forecasting in this watershed and use the rainfall forecast. This method presents the advantage to be easily implemented. Moreover, it permits to be carried out

  10. Arithmetic difficulties in children with cerebral palsy are related to executive function and working memory

    NARCIS (Netherlands)

    Jenks, K.M.; van Lieshout, E.C.D.M.; de Moor, J.

    2009-01-01

    Arithmetic ability was tested in children with cerebral palsy without severe intellectual impairment (verbal IQ ≥ 70) attending special (n = 41) or mainstream education (n = 16) as well as control children in mainstream education (n = 16) throughout first and second grade. Children with cerebral

  11. Learning Arithmetic Outdoors in Junior High School--Influence on Performance and Self-Regulating Skills

    Science.gov (United States)

    Fägerstam, Emilia; Samuelsson, Joakim

    2014-01-01

    This study aims to explore the influence of outdoor teaching among students, aged 13, on arithmetic performance and self-regulation skills as previous research concerning outdoor mathematics learning is limited. This study had a quasi-experimental design. An outdoor and a traditional group answered a test and a self-regulation skills questionnaire…

  12. A flexible algorithm for calculating pair interactions on SIMD architectures

    Science.gov (United States)

    Páll, Szilárd; Hess, Berk

    2013-12-01

    Calculating interactions or correlations between pairs of particles is typically the most time-consuming task in particle simulation or correlation analysis. Straightforward implementations using a double loop over particle pairs have traditionally worked well, especially since compilers usually do a good job of unrolling the inner loop. In order to reach high performance on modern CPU and accelerator architectures, single-instruction multiple-data (SIMD) parallelization has become essential. Avoiding memory bottlenecks is also increasingly important and requires reducing the ratio of memory to arithmetic operations. Moreover, when pairs only interact within a certain cut-off distance, good SIMD utilization can only be achieved by reordering input and output data, which quickly becomes a limiting factor. Here we present an algorithm for SIMD parallelization based on grouping a fixed number of particles, e.g. 2, 4, or 8, into spatial clusters. Calculating all interactions between particles in a pair of such clusters improves data reuse compared to the traditional scheme and results in a more efficient SIMD parallelization. Adjusting the cluster size allows the algorithm to map to SIMD units of various widths. This flexibility not only enables fast and efficient implementation on current CPUs and accelerator architectures like GPUs or Intel MIC, but it also makes the algorithm future-proof. We present the algorithm with an application to molecular dynamics simulations, where we can also make use of the effective buffering the method introduces.

  13. A self-adaptive genetic algorithm to estimate JA model parameters considering minor loops

    Energy Technology Data Exchange (ETDEWEB)

    Lu, Hai-liang; Wen, Xi-shan; Lan, Lei; An, Yun-zhu; Li, Xiao-ping

    2015-01-15

    A self-adaptive genetic algorithm for estimating Jiles–Atherton (JA) magnetic hysteresis model parameters is presented. The fitness function is established based on the distances between equidistant key points of normalized hysteresis loops. Linearity function and logarithm function are both adopted to code the five parameters of JA model. Roulette wheel selection is used and the selection pressure is adjusted adaptively by deducting a proportional which depends on current generation common value. The Crossover operator is established by combining arithmetic crossover and multipoint crossover. Nonuniform mutation is improved by adjusting the mutation ratio adaptively. The algorithm is used to estimate the parameters of one kind of silicon-steel sheet’s hysteresis loops, and the results are in good agreement with published data. - Highlights: • We present a method to find JA parameters for both major and minor loops. • Fitness function is based on distances between key points of normalized loops. • The selection pressure is adjusted adaptively based on generations.

  14. A self-adaptive genetic algorithm to estimate JA model parameters considering minor loops

    International Nuclear Information System (INIS)

    Lu, Hai-liang; Wen, Xi-shan; Lan, Lei; An, Yun-zhu; Li, Xiao-ping

    2015-01-01

    A self-adaptive genetic algorithm for estimating Jiles–Atherton (JA) magnetic hysteresis model parameters is presented. The fitness function is established based on the distances between equidistant key points of normalized hysteresis loops. Linearity function and logarithm function are both adopted to code the five parameters of JA model. Roulette wheel selection is used and the selection pressure is adjusted adaptively by deducting a proportional which depends on current generation common value. The Crossover operator is established by combining arithmetic crossover and multipoint crossover. Nonuniform mutation is improved by adjusting the mutation ratio adaptively. The algorithm is used to estimate the parameters of one kind of silicon-steel sheet’s hysteresis loops, and the results are in good agreement with published data. - Highlights: • We present a method to find JA parameters for both major and minor loops. • Fitness function is based on distances between key points of normalized loops. • The selection pressure is adjusted adaptively based on generations

  15. How are things adding up? Neural differences between arithmetic operations are due to general problem solving strategies.

    Science.gov (United States)

    Tschentscher, Nadja; Hauk, Olaf

    2014-05-15

    A number of previous studies have interpreted differences in brain activation between arithmetic operation types (e.g. addition and multiplication) as evidence in favor of distinct cortical representations, processes or neural systems. It is still not clear how differences in general task complexity contribute to these neural differences. Here, we used a mental arithmetic paradigm to disentangle brain areas related to general problem solving from those involved in operation type specific processes (addition versus multiplication). We orthogonally varied operation type and complexity. Importantly, complexity was defined not only based on surface criteria (for example number size), but also on the basis of individual participants' strategy ratings, which were validated in a detailed behavioral analysis. We replicated previously reported operation type effects in our analyses based on surface criteria. However, these effects vanished when controlling for individual strategies. Instead, procedural strategies contrasted with memory retrieval reliably activated fronto-parietal and motor regions, while retrieval strategies activated parietal cortices. This challenges views that operation types rely on partially different neural systems, and suggests that previously reported differences between operation types may have emerged due to invalid measures of complexity. We conclude that mental arithmetic is a powerful paradigm to study brain networks of abstract problem solving, as long as individual participants' strategies are taken into account. Copyright © 2014 Elsevier Inc. All rights reserved.

  16. Deficits in working memory, reading comprehension and arithmetic skills in children with mouth breathing syndrome: analytical cross-sectional study

    Directory of Open Access Journals (Sweden)

    Rita Cristina Sadako Kuroishi

    Full Text Available CONTEXT AND OBJECTIVE: Mouth breathing syndrome is very common among school-age children, and it is possibly related to learning difficulties and low academic achievement. In this study, we investigated working memory, reading comprehension and arithmetic skills in children with nasal and mouth breathing. DESIGN AND SETTING: Analytical cross-sectional study with control group conducted in a public university hospital. METHODS: 42 children (mean age = 8.7 years who had been identified as mouth breathers were compared with a control group (mean age = 8.4 years matched for age and schooling. All the participants underwent a clinical interview, tone audiometry, otorhinolaryngological evaluation and cognitive assessment of phonological working memory (numbers and pseudowords, reading comprehension and arithmetic skills. RESULTS: Children with mouth breathing had poorer performance than controls, regarding reading comprehension (P = 0.006, arithmetic (P = 0.025 and working memory for pseudowords (P = 0.002, but not for numbers (P = 0.76. CONCLUSION: Children with mouth breathing have low academic achievement and poorer phonological working memory than controls. Teachers and healthcare professionals should be aware of the association of mouth breathing with children's physical and cognitive health.

  17. New Hybrid Algorithms for Estimating Tree Stem Diameters at Breast Height Using a Two Dimensional Terrestrial Laser Scanner

    Directory of Open Access Journals (Sweden)

    Jianlei Kong

    2015-07-01

    Full Text Available In this paper, a new algorithm to improve the accuracy of estimating diameter at breast height (DBH for tree trunks in forest areas is proposed. First, the information is collected by a two-dimensional terrestrial laser scanner (2DTLS, which emits laser pulses to generate a point cloud. After extraction and filtration, the laser point clusters of the trunks are obtained, which are optimized by an arithmetic means method. Then, an algebraic circle fitting algorithm in polar form is non-linearly optimized by the Levenberg-Marquardt method to form a new hybrid algorithm, which is used to acquire the diameters and positions of the trees. Compared with previous works, this proposed method improves the accuracy of diameter estimation of trees significantly and effectively reduces the calculation time. Moreover, the experimental results indicate that this method is stable and suitable for the most challenging conditions, which has practical significance in improving the operating efficiency of forest harvester and reducing the risk of causing accidents.

  18. Identifying Strategies in Arithmetic with the Operand Recognition Paradigm: A Matter of Switch Cost?

    Science.gov (United States)

    Thevenot, Catherine; Castel, Caroline; Danjon, Juliette; Fayol, Michel

    2015-01-01

    Determining adults' and children's strategies in mental arithmetic constitutes a central issue in the domain of numerical cognition. However, despite the considerable amount of research on this topic, the conclusions in the literature are not always coherent. Therefore, there is a need to carry on the investigation, and this is the reason why we…

  19. A New Modified Firefly Algorithm

    Directory of Open Access Journals (Sweden)

    Medha Gupta

    2016-07-01

    Full Text Available Nature inspired meta-heuristic algorithms studies the emergent collective intelligence of groups of simple agents. Firefly Algorithm is one of the new such swarm-based metaheuristic algorithm inspired by the flashing behavior of fireflies. The algorithm was first proposed in 2008 and since then has been successfully used for solving various optimization problems. In this work, we intend to propose a new modified version of Firefly algorithm (MoFA and later its performance is compared with the standard firefly algorithm along with various other meta-heuristic algorithms. Numerical studies and results demonstrate that the proposed algorithm is superior to existing algorithms.

  20. Age-Related Differences of Individuals' Arithmetic Strategy Utilization with Different Level of Math Anxiety.

    Science.gov (United States)

    Si, Jiwei; Li, Hongxia; Sun, Yan; Xu, Yanli; Sun, Yu

    2016-01-01

    The present study used the choice/no-choice method to investigate the effect of math anxiety on the strategy used in computational estimation and mental arithmetic tasks and to examine age-related differences in this regard. Fifty-seven fourth graders, 56 sixth graders, and 60 adults were randomly selected to participate in the experiment. Results showed the following: (1) High-anxious individuals were more likely to use a rounding-down strategy in the computational estimation task under the best-choice condition. Additionally, sixth-grade students and adults performed faster than fourth-grade students on the strategy execution parameter. Math anxiety affected response times (RTs) and the accuracy with which strategies were executed. (2) The execution of the partial-decomposition strategy was superior to that of the full-decomposition strategy on the mental arithmetic task. Low-math-anxious persons provided more accurate answers than did high-math-anxious participants under the no-choice condition. This difference was significant for sixth graders. With regard to the strategy selection parameter, the RTs for strategy selection varied with age.

  1. Age-Related Differences of Individuals’ Arithmetic Strategy Utilization with Different Level of Math Anxiety

    Science.gov (United States)

    Si, Jiwei; Li, Hongxia; Sun, Yan; Xu, Yanli; Sun, Yu

    2016-01-01

    The present study used the choice/no-choice method to investigate the effect of math anxiety on the strategy used in computational estimation and mental arithmetic tasks and to examine age-related differences in this regard. Fifty-seven fourth graders, 56 sixth graders, and 60 adults were randomly selected to participate in the experiment. Results showed the following: (1) High-anxious individuals were more likely to use a rounding-down strategy in the computational estimation task under the best-choice condition. Additionally, sixth-grade students and adults performed faster than fourth-grade students on the strategy execution parameter. Math anxiety affected response times (RTs) and the accuracy with which strategies were executed. (2) The execution of the partial-decomposition strategy was superior to that of the full-decomposition strategy on the mental arithmetic task. Low-math-anxious persons provided more accurate answers than did high-math-anxious participants under the no-choice condition. This difference was significant for sixth graders. With regard to the strategy selection parameter, the RTs for strategy selection varied with age. PMID:27803685

  2. Age-related Differences of Individuals’ Arithmetic Strategy Utilization with Different Level of Math Anxiety

    Directory of Open Access Journals (Sweden)

    Jiwei Si

    2016-10-01

    Full Text Available The present study used the choice/no-choice method to investigate the effect of math anxiety on the strategy used in computational estimation and mental arithmetic tasks and to examine age-related differences in this regard. 57 fourth graders, 56 sixth graders, and 60 adults were randomly selected to participate in the experiment. Results showed the following: (1 High-anxious individuals were more likely to use a rounding-down strategy in the computational estimation task under the best-choice condition. Additionally, sixth-grade students and adults performed faster than fourth-grade students on the strategy execution parameter. Math anxiety affected response times (RTs and the accuracy with which strategies were executed. (2 The execution of the partial-decomposition strategy was superior to that of the full-decomposition strategy on the mental arithmetic task. Low-math-anxious persons provided more accurate answers than did high-math-anxious participants under the no-choice condition. This difference was significant for sixth graders. With regard to the strategy selection parameter, the RTs for strategy selection varied with age.

  3. A comparison of global optimization algorithms with standard benchmark functions and real-world applications using Energy Plus

    Energy Technology Data Exchange (ETDEWEB)

    Kamph, Jerome Henri; Robinson, Darren; Wetter, Michael

    2009-09-01

    There is an increasing interest in the use of computer algorithms to identify combinations of parameters which optimise the energy performance of buildings. For such problems, the objective function can be multi-modal and needs to be approximated numerically using building energy simulation programs. As these programs contain iterative solution algorithms, they introduce discontinuities in the numerical approximation to the objective function. Metaheuristics often work well for such problems, but their convergence to a global optimum cannot be established formally. Moreover, different algorithms tend to be suited to particular classes of optimization problems. To shed light on this issue we compared the performance of two metaheuristics, the hybrid CMA-ES/HDE and the hybrid PSO/HJ, in minimizing standard benchmark functions and real-world building energy optimization problems of varying complexity. From this we find that the CMA-ES/HDE performs well on more complex objective functions, but that the PSO/HJ more consistently identifies the global minimum for simpler objective functions. Both identified similar values in the objective functions arising from energy simulations, but with different combinations of model parameters. This may suggest that the objective function is multi-modal. The algorithms also correctly identified some non-intuitive parameter combinations that were caused by a simplified control sequence of the building energy system that does not represent actual practice, further reinforcing their utility.

  4. Hybrid Cryptosystem Using Tiny Encryption Algorithm and LUC Algorithm

    Science.gov (United States)

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

    2018-01-01

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

  5. CMIS arithmetic and multiwire news for QCD on the connection machine

    International Nuclear Information System (INIS)

    Brickner, R.G.

    1991-01-01

    Our collaboration has been running Wilson fermion QCD simulations on various Connection Machines for over a year and a half. During this time, we have continually optimized our code for operations found in the fermion matrix inversion. Our current version of the matrix inversion is written almost entirely in CMIS (Connection Machine Instruction Set), and utilizes both high-speed arithmetic and multiwire 'news' (nearest-neighbor communications). We present details of how these and other features of our code are implemented on the CM-2. (orig.)

  6. A new frequency-domain criterion for elimination of limit cycles in fixed-point state-space digital filters using saturation arithmetic

    International Nuclear Information System (INIS)

    Singh, Vimal

    2007-01-01

    In [Singh V. Elimination of overflow oscillations in fixed-point state-space digital filters using saturation arithmetic. IEEE Trans Circ Syst 1990;37(6):814-8], a frequency-domain criterion for the suppression of limit cycles in fixed-point state-space digital filters using saturation overflow arithmetic was presented. The passivity property owing to the presence of multiple saturation nonlinearities was exploited therein. In the present paper, a new notion of passivity, namely, that involving the state variables is considered, thereby arriving at an entirely new frequency-domain criterion for the suppression of limit cycles in such filters

  7. The Cognitive Foundations of Reading and Arithmetic Skills in 7- to 10-Year-Olds

    Science.gov (United States)

    Durand, Marianne; Hulme, Charles; Larkin, Rebecca; Snowling, Margaret

    2005-01-01

    A range of possible predictors of arithmetic and reading were assessed in a large sample (N=162) of children between ages 7 years 5 months and 10 years 4 months. A confirmatory factor analysis of the predictors revealed a good fit to a model consisting of four latent variables (verbal ability, nonverbal ability, search speed, and phonological…

  8. 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, ...

  9. Using Mouse and Keyboard Dynamics to Detect Cognitive Stress During Mental Arithmetic

    OpenAIRE

    Ayesh, Aladdin, 1972-; Stacey, Martin; Lim, Yee Mei

    2015-01-01

    To build a personalized e-learning system that can deliver adaptive learning content based on student’s cognitive effort and efficiency, it is important to develop a construct that can help measuring perceived mental state, such as stress and cognitive load. The construct must be able to be quantified, computerized and automated. Our research investigates how mouse and keyboard dynamics analyses could be used to detect cognitive stress, which is induced by high mental arithmetic demand with t...

  10. Engineering a Cache-Oblivious Sorting Algorithm

    DEFF Research Database (Denmark)

    Brodal, Gerth Stølting; Fagerberg, Rolf; Vinther, Kristoffer

    2007-01-01

    This paper is an algorithmic engineering study of cache-oblivious sorting. We investigate by empirical methods a number of implementation issues and parameter choices for the cache-oblivious sorting algorithm Lazy Funnelsort, and compare the final algorithm with Quicksort, the established standard...

  11. Implications of an arithmetical symmetry of the commutant for modular invariants

    International Nuclear Information System (INIS)

    Ruelle, P.; Thiran, E.; Weyers, J.

    1993-01-01

    We point out the existence of an arithmetical symmetry for the commutant of the modular matrices S and T. This symmetry holds for all affine simple Lie algebras at all levels and implies the equality of certain coefficients in any modular invariant. Particularizing to SU(3) k , we classify the modular invariant partition functions when k+3 is an integer coprime with 6 and when it is a power of either 2 or 3. Our results imply that no detailed knowledge of the commutant is needed to undertake a classification of all modular invariants. (orig.)

  12. Vector-matrix-quaternion, array and arithmetic packages: All HAL/S functions implemented in Ada

    Science.gov (United States)

    Klumpp, Allan R.; Kwong, David D.

    1986-01-01

    The HAL/S avionics programmers have enjoyed a variety of tools built into a language tailored to their special requirements. Ada is designed for a broader group of applications. Rather than providing built-in tools, Ada provides the elements with which users can build their own. Standard avionic packages remain to be developed. These must enable programmers to code in Ada as they have coded in HAL/S. The packages under development at JPL will provide all of the vector-matrix, array, and arithmetic functions described in the HAL/S manuals. In addition, the linear algebra package will provide all of the quaternion functions used in Shuttle steering and Galileo attitude control. Furthermore, using Ada's extensibility, many quaternion functions are being implemented as infix operations; equivalent capabilities were never implemented in HAL/S because doing so would entail modifying the compiler and expanding the language. With these packages, many HAL/S expressions will compile and execute in Ada, unchanged. Others can be converted simply by replacing the implicit HAL/S multiply operator with the Ada *. Errors will be trapped and identified. Input/output will be convenient and readable.

  13. Mathematical learning disabilities and attention deficit and/or hyperactivity disorder: A study of the cognitive processes involved in arithmetic problem solving.

    Science.gov (United States)

    Iglesias-Sarmiento, Valentín; Deaño, Manuel; Alfonso, Sonia; Conde, Ángeles

    2017-02-01

    The purpose of this study was to examine the contribution of cognitive functioning to arithmetic problem solving and to explore the cognitive profiles of children with attention deficit and/or hyperactivity disorder (ADHD) and with mathematical learning disabilities (MLD). The sample was made up of a total of 90 students of 4th, 5th, and 6th grade organized in three: ADHD (n=30), MLD (n=30) and typically achieving control (TA; n=30) group. Assessment was conducted in two sessions in which the PASS processes and arithmetic problem solving were evaluated. The ADHD group's performance in planning and attention was worse than that of the control group. Children with MLD obtained poorer results than the control group in planning and simultaneous and successive processing. Executive processes predicted arithmetic problem solving in the ADHD group whereas simultaneous processing was the unique predictor in the MLD sample. Children with ADHD and with MLD showed characteristic cognitive profiles. Groups' problem-solving performance can be predicted from their cognitive functioning. Copyright © 2016 Elsevier Ltd. All rights reserved.

  14. Multiple Skills Underlie Arithmetic Performance: A Large-Scale Structural Equation Modeling Analysis

    Directory of Open Access Journals (Sweden)

    Sarit Ashkenazi

    2017-12-01

    Full Text Available Current theoretical approaches point to the importance of several cognitive skills not specific to mathematics for the etiology of mathematics disorders (MD. In the current study, we examined the role of many of these skills, specifically: rapid automatized naming, attention, reading, and visual perception, on mathematics performance among a large group of college students (N = 1,322 with a wide range of arithmetic proficiency. Using factor analysis, we discovered that our data clustered to four latent variables 1 mathematics, 2 perception speed, 3 attention and 4 reading. In subsequent structural equation modeling, we found that the latent variable perception speed had a strong and meaningful effect on mathematics performance. Moreover, sustained attention, independent from the effect of the latent variable perception speed, had a meaningful, direct effect on arithmetic fact retrieval and procedural knowledge. The latent variable reading had a modest effect on mathematics performance. Specifically, reading comprehension, independent from the effect of the latent variable reading, had a meaningful direct effect on mathematics, and particularly on number line knowledge. Attention, tested by the attention network test, had no effect on mathematics, reading or perception speed. These results indicate that multiple factors can affect mathematics performance supporting a heterogeneous approach to mathematics. These results have meaningful implications for the diagnosis and intervention of pure and comorbid learning disorders.

  15. The arithmetic problem size effect in children: an event-related potential study

    Directory of Open Access Journals (Sweden)

    Leen eVan Beek

    2014-09-01

    Full Text Available This study used for the first time event-related potentials (ERPs to examine the well-known arithmetic problem size effect in children. The electrophysiological correlates of this problem size effect have been well documented in adults, but such information in children is lacking. In the present study, 22 typically developing 12-year-olds were asked to solve single-digit addition problems of small (sum ≤ 10 and large problem size (sum > 10 and to speak the solution into a voice key while ERPs were recorded. Children displayed similar early and late components compared to previous adult studies on the problem size effect. There was no effect of problem size on the early components P1, N1 and P2. The peak amplitude of the N2 component showed more negative potentials on left and right anterior electrodes for large additions compared to small additions, which might reflect differences in attentional and working memory resources between large and small problems. The mean amplitude of the late positivity component (LPC, which follows the N2, was significantly larger for large than for small additions at right parieto-occipital electrodes, in line with previous adult data. The ERPs of the problem size effect during arithmetic might be a useful neural marker for future studies on fact retrieval impairments in children with mathematical difficulties.

  16. Novel search algorithms for a mid-infrared spectral library of cotton contaminants.

    Science.gov (United States)

    Loudermilk, J Brian; Himmelsbach, David S; Barton, Franklin E; de Haseth, James A

    2008-06-01

    During harvest, a variety of plant based contaminants are collected along with cotton lint. The USDA previously created a mid-infrared, attenuated total reflection (ATR), Fourier transform infrared (FT-IR) spectral library of cotton contaminants for contaminant identification as the contaminants have negative impacts on yarn quality. This library has shown impressive identification rates for extremely similar cellulose based contaminants in cases where the library was representative of the samples searched. When spectra of contaminant samples from crops grown in different geographic locations, seasons, and conditions and measured with a different spectrometer and accessories were searched, identification rates for standard search algorithms decreased significantly. Six standard algorithms were examined: dot product, correlation, sum of absolute values of differences, sum of the square root of the absolute values of differences, sum of absolute values of differences of derivatives, and sum of squared differences of derivatives. Four categories of contaminants derived from cotton plants were considered: leaf, stem, seed coat, and hull. Experiments revealed that the performance of the standard search algorithms depended upon the category of sample being searched and that different algorithms provided complementary information about sample identity. These results indicated that choosing a single standard algorithm to search the library was not possible. Three voting scheme algorithms based on result frequency, result rank, category frequency, or a combination of these factors for the results returned by the standard algorithms were developed and tested for their capability to overcome the unpredictability of the standard algorithms' performances. The group voting scheme search was based on the number of spectra from each category of samples represented in the library returned in the top ten results of the standard algorithms. This group algorithm was able to identify

  17. CIMPA Summer School on Arithmetic and Geometry Around Hypergeometric Functions

    CERN Document Server

    Uludağ, A; Yoshida, Masaaki; Arithmetic and Geometry Around Hypergeometric Functions

    2007-01-01

    This volume comprises the Lecture Notes of the CIMPA Summer School "Arithmetic and Geometry around Hypergeometric Functions" held at Galatasaray University, Istanbul in 2005. It contains lecture notes, a survey article, research articles, and the results of a problem session. Key topics are moduli spaces of points on P1 and Picard-Terada-Deligne-Mostow theory, moduli spaces of K3 surfaces, complex hyperbolic geometry, ball quotients, GKZ hypergeometric structures, Hilbert and Picard modular surfaces, uniformizations of complex orbifolds, algebraicity of values of Schwartz triangle functions, and Thakur's hypergeometric function. The book provides a background, gives detailed expositions and indicates new research directions. It is directed to postgraduate students and researchers.

  18. Desynchronization of Theta-Phase Gamma-Amplitude Coupling during a Mental Arithmetic Task in Children with Attention Deficit/Hyperactivity Disorder.

    Directory of Open Access Journals (Sweden)

    Jun Won Kim

    Full Text Available Theta-phase gamma-amplitude coupling (TGC measurement has recently received attention as a feasible method of assessing brain functions such as neuronal interactions. The purpose of this electroencephalographic (EEG study is to understand the mechanisms underlying the deficits in attentional control in children with attention deficit/hyperactivity disorder (ADHD by comparing the power spectra and TGC at rest and during a mental arithmetic task.Nineteen-channel EEGs were recorded from 97 volunteers (including 53 subjects with ADHD from a camp for hyperactive children under two conditions (rest and task performance. The EEG power spectra and the TGC data were analyzed. Correlation analyses between the Intermediate Visual and Auditory (IVA continuous performance test (CPT scores and EEG parameters were performed.No significant difference in the power spectra was detected between the groups at rest and during task performance. However, TGC was reduced during the arithmetic task in the ADHD group compared with the normal group (F = 16.70, p < 0.001. The TGC values positively correlated with the IVA CPT scores but negatively correlated with theta power.Our findings suggest that desynchronization of TGC occurred during the arithmetic task in ADHD children. TGC in ADHD children is expected to serve as a promising neurophysiological marker of network deactivation during attention-demanding tasks.

  19. The "Parrot Math" Attack on Memorization

    Directory of Open Access Journals (Sweden)

    Bill Quirk

    2013-01-01

    Full Text Available Constructivist math educators regularly cite Parrot Math by Thomas C. O'Brien. Although this paper promotes constructivist "activity-based" learning over direct instruction, it's primary claim to fame is the open hostility to memorization. Professor O'Brien rejects "memorization and parrot-like drill " in favor of "children's invented strategies." He references a paper by Kamii and Dominick as evidence of "considerable research" showing that mastery of the standard algorithms of arithmetic is harmful for children. [See The Bogus Research in Kamii and Dominick's Harmful Algorithms Papers

  20. Parallel Construction of Irreducible Polynomials

    DEFF Research Database (Denmark)

    Frandsen, Gudmund Skovbjerg

    Let arithmetic pseudo-NC^k denote the problems that can be solved by log space uniform arithmetic circuits over the finite prime field GF(p) of depth O(log^k (n + p)) and size polynomial in (n + p). We show that the problem of constructing an irreducible polynomial of specified degree over GF(p) ...... of polynomials is in arithmetic NC^3. Our algorithm works over any field and compared to other known algorithms it does not assume the ability to take p'th roots when the field has characteristic p....

  1. 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.)

  2. CompGC: Efficient Offline/Online Semi-Honest Two-Party Computation

    Science.gov (United States)

    2017-02-03

    modular way. Just as a programmer writes code for a complex function by using existing simpler functions, the circuits for these functions use...We observe that real-world functions are generally constructed in a modular way, comprising many standard components for common tasks like arithmetic...overall garbled circuit computation; see Section 6 for details. More technically , a component-based garbling scheme is a triple of algorithms (GARBLE

  3. Spatial complexity of character based writing systems and arithmetic in primary school: a longitudinal study

    Directory of Open Access Journals (Sweden)

    Maja eRodic

    2015-03-01

    Full Text Available Previous research has consistently found an association between spatial and mathematical abilities. We hypothesised that this link may partially explain the consistently observed advantage in mathematics demonstrated by Asian children. Spatial complexity of the character-based writing systems may reflect or lead to a cognitive advantage relevant to mathematics. 721 6-9 -year old children from the UK and Russia were assessed on a battery of cognitive skills and arithmetic. The Russian children were recruited from specialist linguistic schools and divided into 4 different language groups, based on the second language they were learning (i.e. English, Spanish, Chinese and Japanese. The UK children attended regular schools and were not learning any second language. The testing took place twice across the school year, once at the beginning, before the start of the second language acquisition, and once at the end of the year. The study had two aims: (1 to test whether spatial ability predicts mathematical ability in 7-9 year old children across the samples; (2 to test whether acquisition and usage of a character-based writing system leads to an advantage in performance in arithmetic and related cognitive tasks. The longitudinal link from spatial ability to mathematics was found only in the Russian sample. The effect of second language acquisition on mathematics or other cognitive skills was negligible, although some effect of Chinese language on mathematical reasoning was suggested. Overall, the findings suggest that although spatial ability is related to mathematics at this age, one academic year of exposure to spatially complex writing systems is not enough to provide a mathematical advantage. Other educational and socio-cultural factors might play a greater role in explaining individual and cross-cultural differences in arithmetic at this age.

  4. Spatial complexity of character-based writing systems and arithmetic in primary school: a longitudinal study.

    Science.gov (United States)

    Rodic, Maja; Tikhomirova, Tatiana; Kolienko, Tatiana; Malykh, Sergey; Bogdanova, Olga; Zueva, Dina Y; Gynku, Elena I; Wan, Sirui; Zhou, Xinlin; Kovas, Yulia

    2015-01-01

    Previous research has consistently found an association between spatial and mathematical abilities. We hypothesized that this link may partially explain the consistently observed advantage in mathematics demonstrated by East Asian children. Spatial complexity of the character-based writing systems may reflect or lead to a cognitive advantage relevant to mathematics. Seven hundered and twenty one 6-9-year old children from the UK and Russia were assessed on a battery of cognitive skills and arithmetic. The Russian children were recruited from specialist linguistic schools and divided into four different language groups, based on the second language they were learning (i.e., English, Spanish, Chinese, and Japanese). The UK children attended regular schools and were not learning any second language. The testing took place twice across the school year, once at the beginning, before the start of the second language acquisition, and once at the end of the year. The study had two aims: (1) to test whether spatial ability predicts mathematical ability in 7-9 year-old children across the samples; (2) to test whether acquisition and usage of a character-based writing system leads to an advantage in performance in arithmetic and related cognitive tasks. The longitudinal link from spatial ability to mathematics was found only in the Russian sample. The effect of second language acquisition on mathematics or other cognitive skills was negligible, although some effect of Chinese language on mathematical reasoning was suggested. Overall, the findings suggest that although spatial ability is related to mathematics at this age, one academic year of exposure to spatially complex writing systems is not enough to provide a mathematical advantage. Other educational and socio-cultural factors might play a greater role in explaining individual and cross-cultural differences in arithmetic at this age.

  5. Spatial complexity of character-based writing systems and arithmetic in primary school: a longitudinal study

    Science.gov (United States)

    Rodic, Maja; Tikhomirova, Tatiana; Kolienko, Tatiana; Malykh, Sergey; Bogdanova, Olga; Zueva, Dina Y.; Gynku, Elena I.; Wan, Sirui; Zhou, Xinlin; Kovas, Yulia

    2015-01-01

    Previous research has consistently found an association between spatial and mathematical abilities. We hypothesized that this link may partially explain the consistently observed advantage in mathematics demonstrated by East Asian children. Spatial complexity of the character-based writing systems may reflect or lead to a cognitive advantage relevant to mathematics. Seven hundered and twenty one 6–9-year old children from the UK and Russia were assessed on a battery of cognitive skills and arithmetic. The Russian children were recruited from specialist linguistic schools and divided into four different language groups, based on the second language they were learning (i.e., English, Spanish, Chinese, and Japanese). The UK children attended regular schools and were not learning any second language. The testing took place twice across the school year, once at the beginning, before the start of the second language acquisition, and once at the end of the year. The study had two aims: (1) to test whether spatial ability predicts mathematical ability in 7–9 year-old children across the samples; (2) to test whether acquisition and usage of a character-based writing system leads to an advantage in performance in arithmetic and related cognitive tasks. The longitudinal link from spatial ability to mathematics was found only in the Russian sample. The effect of second language acquisition on mathematics or other cognitive skills was negligible, although some effect of Chinese language on mathematical reasoning was suggested. Overall, the findings suggest that although spatial ability is related to mathematics at this age, one academic year of exposure to spatially complex writing systems is not enough to provide a mathematical advantage. Other educational and socio-cultural factors might play a greater role in explaining individual and cross-cultural differences in arithmetic at this age. PMID:25859235

  6. Analysis of ANSI N13.11: the performance algorithm

    International Nuclear Information System (INIS)

    Roberson, P.L.; Hadley, R.T.; Thorson, M.R.

    1982-06-01

    The method of performance testing for personnel dosimeters specified in draft ANSI N13.11, Criteria for Testing Personnel Dosimetry Performance is evaluated. Points addressed are: (1) operational behavior of the performance algorithm; (2) dependence on the number of test dosimeters; (3) basis for choosing an algorithm; and (4) other possible algorithms. The performance algorithm evaluated for each test category is formed by adding the calibration bias and its standard deviation. This algorithm is not optimal due to a high dependence on the standard deviation. The dependence of the calibration bias on the standard deviation is significant because of the low number of dosimeters (15) evaluated per category. For categories with large standard deviations the uncertainty in determining the performance criterion is large. To have a reasonable chance of passing all categories in one test, we required a 95% probability of passing each category. Then, the maximum permissible standard deviation is 30% even with a zero bias. For test categories with standard deviations <10%, the bias can be as high as 35%. For intermediate standard deviations, the chance of passing a category is improved by using a 5 to 10% negative bias. Most multipurpose personnel dosimetry systems will probably require detailed calibration adjustments to pass all categories within two rounds of testing

  7. A Hypergraph and Arithmetic Residue-based Probabilistic Neural Network for classification in Intrusion Detection Systems.

    Science.gov (United States)

    Raman, M R Gauthama; Somu, Nivethitha; Kirthivasan, Kannan; Sriram, V S Shankar

    2017-08-01

    Over the past few decades, the design of an intelligent Intrusion Detection System (IDS) remains an open challenge to the research community. Continuous efforts by the researchers have resulted in the development of several learning models based on Artificial Neural Network (ANN) to improve the performance of the IDSs. However, there exists a tradeoff with respect to the stability of ANN architecture and the detection rate for less frequent attacks. This paper presents a novel approach based on Helly property of Hypergraph and Arithmetic Residue-based Probabilistic Neural Network (HG AR-PNN) to address the classification problem in IDS. The Helly property of Hypergraph was exploited for the identification of the optimal feature subset and the arithmetic residue of the optimal feature subset was used to train the PNN. The performance of HG AR-PNN was evaluated using KDD CUP 1999 intrusion dataset. Experimental results prove the dominance of HG AR-PNN classifier over the existing classifiers with respect to the stability and improved detection rate for less frequent attacks. Copyright © 2017 Elsevier Ltd. All rights reserved.

  8. AES ALGORITHM IMPLEMENTATION IN PROGRAMMING LANGUAGES

    Directory of Open Access Journals (Sweden)

    Luminiţa DEFTA

    2010-12-01

    Full Text Available Information encryption represents the usage of an algorithm to convert an unknown message into an encrypted one. It is used to protect the data against unauthorized access. Protected data can be stored on a media device or can be transmitted through the network. In this paper we describe a concrete implementation of the AES algorithm in the Java programming language (available from Java Development Kit 6 libraries and C (using the OpenSSL library. AES (Advanced Encryption Standard is an asymmetric key encryption algorithm formally adopted by the U.S. government and was elected after a long process of standardization.

  9. Practical considerations for the implantation of a fuzzy control algorithm in a DSP; Consideraciones practicas para la implantacion de un algoritmo de control difuso en un DSP

    Energy Technology Data Exchange (ETDEWEB)

    Perez C, B.; Benitez R, J.S.; Pacheco S, J.O. [ININ, 52045 Ocoyoacac, Estado de Mexico (Mexico)

    2003-07-01

    The development of a digital system based on a DSP to implant a Mamdani type algorithm of fuzzy control whose objective is to regulate the neutron power in a nuclear research reactor Type TRIGA Mark III is presented. Its are simultaneously carried out the aggregation des fuzzy stages discreeting the universe of the output variable. The format MPF for the handling of the floating point in the arithmetic operations is used. (Author)

  10. Deaf and Hard of Hearing Students' Problem-Solving Strategies with Signed Arithmetic Story Problems

    Science.gov (United States)

    Pagliaro, Claudia M.; Ansell, Ellen

    2011-01-01

    The use of problem-solving strategies by 59 deaf and hard of hearing children, grades K-3, was investigated. The children were asked to solve 9 arithmetic story problems presented to them in American Sign Language. The researchers found that while the children used the same general types of strategies that are used by hearing children (i.e.,…

  11. Modified Firefly Algorithm

    Directory of Open Access Journals (Sweden)

    Surafel Luleseged Tilahun

    2012-01-01

    Full Text Available Firefly algorithm is one of the new metaheuristic algorithms for optimization problems. The algorithm is inspired by the flashing behavior of fireflies. In the algorithm, randomly generated solutions will be considered as fireflies, and brightness is assigned depending on their performance on the objective function. One of the rules used to construct the algorithm is, a firefly will be attracted to a brighter firefly, and if there is no brighter firefly, it will move randomly. In this paper we modify this random movement of the brighter firefly by generating random directions in order to determine the best direction in which the brightness increases. If such a direction is not generated, it will remain in its current position. Furthermore the assignment of attractiveness is modified in such a way that the effect of the objective function is magnified. From the simulation result it is shown that the modified firefly algorithm performs better than the standard one in finding the best solution with smaller CPU time.

  12. Development and Application of Milk-Run Distribution Systems in the Express Industry Based on Saving Algorithm

    Directory of Open Access Journals (Sweden)

    Zhenlai You

    2014-01-01

    Full Text Available This paper introduces the milk-run schema into the express distribution logistics through the feasibility analysis of application of cyclic goods-taking schema in the express industry. In order to reach fully loaded as far as possible in distribution, the article improves the traditional model, adopting multi-objective decision and conforming constraint conditions to Milk-run schema, even approximating the practical truth solves model through the C-W saving algorithm. It can effectively shorten the distance and Lower costs by means of reasonable route planning. Finally, the paper has verified the model and its effectiveness of arithmetic application by means of cases analysis.

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

    Science.gov (United States)

    Regier, Michael D; Moodie, Erica E M

    2016-05-01

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

  14. Real time equilibrium reconstruction algorithm in EAST tokamak

    International Nuclear Information System (INIS)

    Wang Huazhong; Luo Jiarong; Huang Qinchao

    2004-01-01

    The EAST (HT-7U) superconducting tokamak is a national project of China on fusion research, with a capability of long-pulse (∼1000 s) operation. In order to realize a long-duration steady-state operation of EAST, some significant capability of real-time control is required. It would be very crucial to obtain the current profile parameters and the plasma shapes in real time by a flexible control system. As those discharge parameters cannot be directly measured, so a current profile consistent with the magnetohydrodynamic equilibrium should be evaluated from external magnetic measurements, based on a linearized iterative least square method, which can meet the requirements of the measurements. The arithmetic that the EFIT (equilibrium fitting code) is used for reference will be given in this paper and the computational efforts are reduced by parameterizing the current profile linearly in terms of a number of physical parameters. In order to introduce this reconstruction algorithm clearly, the main hardware design will be listed also. (authors)

  15. Arithmetical aspects of the large sieve inequality

    CERN Document Server

    2009-01-01

    This book is an elaboration of a series of lectures given at the Harish-Chandra Research Institute. The reader will be taken through a journey on the arithmetical sides of the large sieve inequality when applied to the Farey dissection. This will reveal connections between this inequality, the Selberg sieve and other less used notions like pseudo-characters and the $\\Lambda_Q$-function, as well as extend these theories. One of the leading themes of these notes is the notion of so-called\\emph{local models} that throws a unifying light on the subject. As examples and applications, the authors present, among other things, an extension of the Brun-Tichmarsh Theorem, a new proof of Linnik's Theorem on quadratic residues and an equally novel one of the Vinogradov three primes Theorem; the authors also consider the problem of small prime gaps, of sums of two squarefree numbers and several other ones, some of them being new, like a sharp upper bound for the number of twin primes $p$ that are such that $p+1$ is square...

  16. Modeling Brain Responses in an Arithmetic Working Memory Task

    Science.gov (United States)

    Hamid, Aini Ismafairus Abd; Yusoff, Ahmad Nazlim; Mukari, Siti Zamratol-Mai Sarah; Mohamad, Mazlyfarina; Manan, Hanani Abdul; Hamid, Khairiah Abdul

    2010-07-01

    Functional magnetic resonance imaging (fMRI) was used to investigate brain responses due to arithmetic working memory. Nine healthy young male subjects were given simple addition and subtraction instructions in noise and in quiet. The general linear model (GLM) and random field theory (RFT) were implemented in modelling the activation. The results showed that addition and subtraction evoked bilateral activation in Heschl's gyrus (HG), superior temporal gyrus (STG), inferior frontal gyrus (IFG), supramarginal gyrus (SG) and precentral gyrus (PCG). The HG, STG, SG and PCG activate higher number of voxels in noise as compared to in quiet for addition and subtraction except for IFG that showed otherwise. The percentage of signal change (PSC) in all areas is higher in quiet as compared to in noise. Surprisingly addition (not subtraction) exhibits stronger activation.

  17. DEBT AMORTIZATION AND SIMPLE INTEREST: THE CASE OF PAYMENTS IN AN ARITHMETIC PROGRESSION

    OpenAIRE

    Clovis José Daudt Lyra Darrigue Faro

    2014-01-01

    With the argument that, necessarily, compound interest implies anatocism, the Brazilian Judiciary has been determining that, specially for the case of  debt amortization in accordance with the so called Tabela Price, when we have constant payments, the use of simple interest. With the same determination occurring in the case of the Constant Amortization Scheme, when the payments follow arithmetic progressions.  However, as simple interest lacks the property of time subdivision, it is shown th...

  18. Growing the Character Values to Students Through Application of Realistic Mathematics Education (RME in the Social Arithmetic Learning

    Directory of Open Access Journals (Sweden)

    Amin Suyitno

    2015-06-01

    Full Text Available AbstractEducating students at the Basic Education level is not only demanded that the students are clever, but there are also other demand which no less important that is to educate so that students have a good character value. Educating  the students to have a good character value is started from home, school, and community. In school, educating character to students is not only the duty of teachers of Religion or Civics class, but also the duty of all teachers, including the teachers in Mathematics. Math teacher does not need to hold special time for educating of character, but it can be integrated into any material taught, and also in different application of learning models. This paper examines how the efforts of mathematics teacher in educating of character to the students of Basic Education, especially in Junior High School through the application of Realistic Mathematics Education (RME on the material of Social Arithmetic. Through presenting of the material of Social Arithmetic by RME learning model, students can be given a character education through the attitude of honesty, tolerance, discipline, cooperation, creative, independent, democratic, curiosity, love of peace, social care, responsibility, and so on. In conclusion, educational character values to students can be done by mathematics teacher through a variety of materials.  One of them  through presenting of the material of Social Arithmetic by RME learning model.

  19. Trinary arithmetic and logic unit (TALU) using savart plate and spatial light modulator (SLM) suitable for optical computation in multivalued logic

    Science.gov (United States)

    Ghosh, Amal K.; Bhattacharya, Animesh; Raul, Moumita; Basuray, Amitabha

    2012-07-01

    Arithmetic logic unit (ALU) is the most important unit in any computing system. Optical computing is becoming popular day-by-day because of its ultrahigh processing speed and huge data handling capability. Obviously for the fast processing we need the optical TALU compatible with the multivalued logic. In this regard we are communicating the trinary arithmetic and logic unit (TALU) in modified trinary number (MTN) system, which is suitable for the optical computation and other applications in multivalued logic system. Here the savart plate and spatial light modulator (SLM) based optoelectronic circuits have been used to exploit the optical tree architecture (OTA) in optical interconnection network.

  20. A pilot study of a new method of cognitive stimulation using abacus arithmetic in healthy and cognitively impaired elderly subjects.

    Science.gov (United States)

    Matías-Guiu, J A; Pérez-Martínez, D A; Matías-Guiu, J

    2016-06-01

    This study explores the applicability of a cognitive stimulation method based on abacus arithmetic in elderly people with and without cognitive impairment. This observational and prospective pilot study was performed in 2 hospitals. The study assessed the applicability of a programme of arithmetic training developed for use in the elderly population. The primary endpoint was an evaluation of the stimulation programme, in terms of usability, satisfaction, and participation, in healthy elderly controls and elderly patients with mild cognitive impairment or Alzheimer disease. Secondary endpoints were family satisfaction, caregiver burden, and the behaviour and cognition of patients. Usability, satisfaction, and degree of participation were high. The Mini-Mental State Examination showed significant changes (23.1±4.8 before the intervention vs 24.9±4.2 afterwards, P=.002); there were no changes on the Trail Making Test parts A and B, Yesavage Geriatric Depression scale, and Zarit caregiver burden scale. The study suggests that cognitive stimulation with abacus arithmetic may be used in elderly people with and without cognitive impairment. Further studies will be needed to evaluate the efficacy of this kind of programmes. Copyright © 2014 Sociedad Española de Neurología. Published by Elsevier España, S.L.U. All rights reserved.

  1. Process-based Assignment-Setting Change for Support of Overcoming Bottlenecks in Learning by Problem-Posing in Arithmetic Word Problems

    Science.gov (United States)

    Supianto, A. A.; Hayashi, Y.; Hirashima, T.

    2017-02-01

    Problem-posing is well known as an effective activity to learn problem-solving methods. Monsakun is an interactive problem-posing learning environment to facilitate arithmetic word problems learning for one operation of addition and subtraction. The characteristic of Monsakun is problem-posing as sentence-integration that lets learners make a problem of three sentences. Monsakun provides learners with five or six sentences including dummies, which are designed through careful considerations by an expert teacher as a meaningful distraction to the learners in order to learn the structure of arithmetic word problems. The results of the practical use of Monsakun in elementary schools show that many learners have difficulties in arranging the proper answer at the high level of assignments. The analysis of the problem-posing process of such learners found that their misconception of arithmetic word problems causes impasses in their thinking and mislead them to use dummies. This study proposes a method of changing assignments as a support for overcoming bottlenecks of thinking. In Monsakun, the bottlenecks are often detected as a frequently repeated use of a specific dummy. If such dummy can be detected, it is the key factor to support learners to overcome their difficulty. This paper discusses how to detect the bottlenecks and to realize such support in learning by problem-posing.

  2. A Novel 2D Image Compression Algorithm Based on Two Levels DWT and DCT Transforms with Enhanced Minimize-Matrix-Size Algorithm for High Resolution Structured Light 3D Surface Reconstruction

    Science.gov (United States)

    Siddeq, M. M.; Rodrigues, M. A.

    2015-09-01

    Image compression techniques are widely used on 2D image 2D video 3D images and 3D video. There are many types of compression techniques and among the most popular are JPEG and JPEG2000. In this research, we introduce a new compression method based on applying a two level discrete cosine transform (DCT) and a two level discrete wavelet transform (DWT) in connection with novel compression steps for high-resolution images. The proposed image compression algorithm consists of four steps. (1) Transform an image by a two level DWT followed by a DCT to produce two matrices: DC- and AC-Matrix, or low and high frequency matrix, respectively, (2) apply a second level DCT on the DC-Matrix to generate two arrays, namely nonzero-array and zero-array, (3) apply the Minimize-Matrix-Size algorithm to the AC-Matrix and to the other high-frequencies generated by the second level DWT, (4) apply arithmetic coding to the output of previous steps. A novel decompression algorithm, Fast-Match-Search algorithm (FMS), is used to reconstruct all high-frequency matrices. The FMS-algorithm computes all compressed data probabilities by using a table of data, and then using a binary search algorithm for finding decompressed data inside the table. Thereafter, all decoded DC-values with the decoded AC-coefficients are combined in one matrix followed by inverse two levels DCT with two levels DWT. The technique is tested by compression and reconstruction of 3D surface patches. Additionally, this technique is compared with JPEG and JPEG2000 algorithm through 2D and 3D root-mean-square-error following reconstruction. The results demonstrate that the proposed compression method has better visual properties than JPEG and JPEG2000 and is able to more accurately reconstruct surface patches in 3D.

  3. NEUTRON ALGORITHM VERIFICATION TESTING

    International Nuclear Information System (INIS)

    COWGILL, M.; MOSBY, W.; ARGONNE NATIONAL LABORATORY-WEST

    2000-01-01

    Active well coincidence counter assays have been performed on uranium metal highly enriched in 235 U. The data obtained in the present program, together with highly enriched uranium (HEU) metal data obtained in other programs, have been analyzed using two approaches, the standard approach and an alternative approach developed at BNL. Analysis of the data with the standard approach revealed that the form of the relationship between the measured reals and the 235 U mass varied, being sometimes linear and sometimes a second-order polynomial. In contrast, application of the BNL algorithm, which takes into consideration the totals, consistently yielded linear relationships between the totals-corrected reals and the 235 U mass. The constants in these linear relationships varied with geometric configuration and level of enrichment. This indicates that, when the BNL algorithm is used, calibration curves can be established with fewer data points and with more certainty than if a standard algorithm is used. However, this potential advantage has only been established for assays of HEU metal. In addition, the method is sensitive to the stability of natural background in the measurement facility

  4. Improved Bat Algorithm Applied to Multilevel Image Thresholding

    Directory of Open Access Journals (Sweden)

    Adis Alihodzic

    2014-01-01

    Full Text Available Multilevel image thresholding is a very important image processing technique that is used as a basis for image segmentation and further higher level processing. However, the required computational time for exhaustive search grows exponentially with the number of desired thresholds. Swarm intelligence metaheuristics are well known as successful and efficient optimization methods for intractable problems. In this paper, we adjusted one of the latest swarm intelligence algorithms, the bat algorithm, for the multilevel image thresholding problem. The results of testing on standard benchmark images show that the bat algorithm is comparable with other state-of-the-art algorithms. We improved standard bat algorithm, where our modifications add some elements from the differential evolution and from the artificial bee colony algorithm. Our new proposed improved bat algorithm proved to be better than five other state-of-the-art algorithms, improving quality of results in all cases and significantly improving convergence speed.

  5. Content validation of a standardized algorithm for ostomy care.

    Science.gov (United States)

    Beitz, Janice; Gerlach, Mary; Ginsburg, Pat; Ho, Marianne; McCann, Eileen; Schafer, Vickie; Scott, Vera; Stallings, Bobbie; Turnbull, Gwen

    2010-10-01

    The number of ostomy care clinician experts is limited and the majority of ostomy care is provided by non-specialized clinicians or unskilled caregivers and family. The purpose of this study was to obtain content validation data for a new standardized algorithm for ostomy care developed by expert wound ostomy continence nurse (WOCN) clinicians. After face validity was established using overall review and suggestions from WOCN experts, 166 WOCNs self-identified as having expertise in ostomy care were surveyed online for 6 weeks in 2009. Using a cross-sectional, mixed methods study design and a 30-item instrument with a 4-point Likert-type scale, the participants were asked to quantify the degree of validity of the Ostomy Algorithm's decisions and components. Participants' open-ended comments also were thematically analyzed. Using a scale of 1 to 4, the mean score of the entire algorithm was 3.8 (4 = relevant/very relevant). The algorithm's content validity index (CVI) was 0.95 (out of 1.0). Individual component mean scores ranged from 3.59 to 3.91. Individual CVIs ranged from 0.90 to 0.98. Qualitative data analysis revealed themes of difficulty associated with algorithm formatting, especially orientation and use of the Studio Alterazioni Cutanee Stomali (Study on Peristomal Skin Lesions [SACS™ Instrument]) and the inability of algorithms to capture all individual patient attributes affecting ostomy care. Positive themes included content thoroughness and the helpful clinical photos. Suggestions were offered for algorithm improvement. Study results support the strong content validity of the algorithm and research to ascertain its construct validity and effect on care outcomes is warranted.

  6. Heart rate variability response to mental arithmetic stress in patients with schizophrenia Autonomic response to stress in schizophrenia

    NARCIS (Netherlands)

    Castro, Mariana N.; Vigo, Daniel E.; Weidema, Hylke; Fahrer, Rodolfo D.; Chu, Elvina M.; De Achaval, Delfina; Nogues, Martin; Leiguarda, Ramon C.; Cardinali, Daniel P.; Guinjoan, Salvador N.

    Background: The vulnerability-stress hypothesis is an established model of schizophrenia symptom formation. We sought to characterise the pattern of the cardiac autonomic response to mental arithmetic stress in patients with stable schizophrenia. Methods: We performed heart rate variability (HRV)

  7. A Modular Approach to Arithmetic and Logic Unit Design on a Reconfigurable Hardware Platform for Educational Purpose

    Science.gov (United States)

    Oztekin, Halit; Temurtas, Feyzullah; Gulbag, Ali

    The Arithmetic and Logic Unit (ALU) design is one of the important topics in Computer Architecture and Organization course in Computer and Electrical Engineering departments. There are ALU designs that have non-modular nature to be used as an educational tool. As the programmable logic technology has developed rapidly, it is feasible that ALU design based on Field Programmable Gate Array (FPGA) is implemented in this course. In this paper, we have adopted the modular approach to ALU design based on FPGA. All the modules in the ALU design are realized using schematic structure on Altera's Cyclone II Development board. Under this model, the ALU content is divided into four distinct modules. These are arithmetic unit except for multiplication and division operations, logic unit, multiplication unit and division unit. User can easily design any size of ALU unit since this approach has the modular nature. Then, this approach was applied to microcomputer architecture design named BZK.SAU.FPGA10.0 instead of the current ALU unit.

  8. Low Cost Design of an Advanced Encryption Standard (AES) Processor Using a New Common-Subexpression-Elimination Algorithm

    Science.gov (United States)

    Chen, Ming-Chih; Hsiao, Shen-Fu

    In this paper, we propose an area-efficient design of Advanced Encryption Standard (AES) processor by applying a new common-expression-elimination (CSE) method to the sub-functions of various transformations required in AES. The proposed method reduces the area cost of realizing the sub-functions by extracting the common factors in the bit-level XOR/AND-based sum-of-product expressions of these sub-functions using a new CSE algorithm. Cell-based implementation results show that the AES processor with our proposed CSE method has significant area improvement compared with previous designs.

  9. Magnitude Representation and Working Memory Updating in Children With Arithmetic and Reading Comprehension Disabilities.

    Science.gov (United States)

    Pelegrina, Santiago; Capodieci, Agnese; Carretti, Barbara; Cornoldi, Cesare

    2015-01-01

    It has been argued that children with learning disabilities (LD) encounter severe problems in working memory (WM) tasks, especially when they need to update information stored in their WM. It is not clear, however, to what extent this is due to a generally poor updating ability or to a difficulty specific to the domain to be processed. To examine this issue, two groups of children with arithmetic or reading comprehension LD and a group of typically developing children (9 to 10 years old) were assessed using two updating tasks requiring to select the smallest numbers or objects presented. The results showed that children with an arithmetic disability failed in a number updating task, but not in the object updating task. The opposite was true for the group with poor reading comprehension, whose performance was worse in the object than in the number updating task. It may be concluded that the problem of WM updating in children with LD is also due to a poor representation of the material to be updated. In addition, our findings suggest that the mental representation of the size of objects relates to the semantic representation of the objects' properties and differs from the quantitative representation of numbers. © Hammill Institute on Disabilities 2014.

  10. Opposition-Based Adaptive Fireworks Algorithm

    Directory of Open Access Journals (Sweden)

    Chibing Gong

    2016-07-01

    Full Text Available A fireworks algorithm (FWA is a recent swarm intelligence algorithm that is inspired by observing fireworks explosions. An adaptive fireworks algorithm (AFWA proposes additional adaptive amplitudes to improve the performance of the enhanced fireworks algorithm (EFWA. The purpose of this paper is to add opposition-based learning (OBL to AFWA with the goal of further boosting performance and achieving global optimization. Twelve benchmark functions are tested in use of an opposition-based adaptive fireworks algorithm (OAFWA. The final results conclude that OAFWA significantly outperformed EFWA and AFWA in terms of solution accuracy. Additionally, OAFWA was compared with a bat algorithm (BA, differential evolution (DE, self-adapting control parameters in differential evolution (jDE, a firefly algorithm (FA, and a standard particle swarm optimization 2011 (SPSO2011 algorithm. The research results indicate that OAFWA ranks the highest of the six algorithms for both solution accuracy and runtime cost.

  11. Optimal Fungal Space Searching Algorithms.

    Science.gov (United States)

    Asenova, Elitsa; Lin, Hsin-Yu; Fu, Eileen; Nicolau, Dan V; Nicolau, Dan V

    2016-10-01

    Previous experiments have shown that fungi use an efficient natural algorithm for searching the space available for their growth in micro-confined networks, e.g., mazes. This natural "master" algorithm, which comprises two "slave" sub-algorithms, i.e., collision-induced branching and directional memory, has been shown to be more efficient than alternatives, with one, or the other, or both sub-algorithms turned off. In contrast, the present contribution compares the performance of the fungal natural algorithm against several standard artificial homologues. It was found that the space-searching fungal algorithm consistently outperforms uninformed algorithms, such as Depth-First-Search (DFS). Furthermore, while the natural algorithm is inferior to informed ones, such as A*, this under-performance does not importantly increase with the increase of the size of the maze. These findings suggest that a systematic effort of harvesting the natural space searching algorithms used by microorganisms is warranted and possibly overdue. These natural algorithms, if efficient, can be reverse-engineered for graph and tree search strategies.

  12. Group leaders optimization algorithm

    Science.gov (United States)

    Daskin, Anmer; Kais, Sabre

    2011-03-01

    We present a new global optimization algorithm in which the influence of the leaders in social groups is used as an inspiration for the evolutionary technique which is designed into a group architecture. To demonstrate the efficiency of the method, a standard suite of single and multi-dimensional optimization functions along with the energies and the geometric structures of Lennard-Jones clusters are given as well as the application of the algorithm on quantum circuit design problems. We show that as an improvement over previous methods, the algorithm scales as N 2.5 for the Lennard-Jones clusters of N-particles. In addition, an efficient circuit design is shown for a two-qubit Grover search algorithm which is a quantum algorithm providing quadratic speedup over the classical counterpart.

  13. Embedded systems design with special arithmetic and number systems

    CERN Document Server

    Sousa, Leonel; Chang, Chip-Hong

    2017-01-01

    This book introduces readers to alternative approaches to designing efficient embedded systems using unconventional number systems. The authors describe various systems that can be used for designing efficient embedded and application-specific processors, such as Residue Number System, Logarithmic Number System, Redundant Binary Number System Double-Base Number System, Decimal Floating Point Number System and Continuous Valued Number System. Readers will learn the strategies and trade-offs of using unconventional number systems in application-specific processors and be able to apply and design appropriate arithmetic operations from these number systems to boost the performance of digital systems. • Serves as a single-source reference to designing embedded systems with unconventional number systems • Covers theory as well as implementation on application-specific processors • Explains mathematical concepts in a manner accessible to readers with diverse backgrounds.

  14. Conference on Arithmetic and Ideal Theory of Rings and Semigroups

    CERN Document Server

    Fontana, Marco; Geroldinger, Alfred; Olberding, Bruce

    2016-01-01

    This book consists of both expository and research articles solicited from speakers at the conference entitled "Arithmetic and Ideal Theory of Rings and Semigroups," held September 22–26, 2014 at the University of Graz, Graz, Austria. It reflects recent trends in multiplicative ideal theory and factorization theory, and brings together for the first time in one volume both commutative and non-commutative perspectives on these areas, which have their roots in number theory, commutative algebra, and algebraic geometry. Topics discussed include topological aspects in ring theory, Prüfer domains of integer-valued polynomials and their monadic submonoids, and semigroup algebras. It will be of interest to practitioners of mathematics and computer science, and researchers in multiplicative ideal theory, factorization theory, number theory, and algebraic geometry.

  15. Brain potentials during mental arithmetic: effects of extensive practice and problem difficulty.

    Science.gov (United States)

    Pauli, P; Lutzenberger, W; Rau, H; Birbaumer, N; Rickard, T C; Yaroush, R A; Bourne, L E

    1994-07-01

    Recent behavioral investigations indicate that the processes underlying mental arithmetic change systematically with practice from deliberate, conscious calculation to automatic, direct retrieval of answers from memory [Bourne, L.E.Jr. and Rickard, T.C., Mental calculation: The development of a cognitive skill, Paper presented at the Interamerican Congress of Psychology, San Jose, Costa Rica, 1991: Psychol. Rev., 95 (1988) 492-527]. Results reviewed by Moscovitch and Winocur [In: The handbook of aging and cognition, Erlbaum, Hillsdale, NJ, 1992, pp. 315-372] suggest that consciously controlled processes are more dependent on frontal lobe function than are automatic processes. It is appropriate, therefore to determine whether transitions in the locus of primary brain activity occur with practice on mental calculation. In this experiment, we examine the relationship between characteristics of event-related brain potentials (ERPs) and mental arithmetic. Single-digit mental multiplication problems varying in difficulty (problem size) were used, and subjects were trained on these problems for four sessions. Problem-size and practice effects were reliably found in behavioral measures (RT). The ERP was characterized by a pronounced late positivity after task presentation followed by a slow wave, and a negativity during response indication. These components responded differentially to the practice and problem-size manipulations. Practice mainly affected topography of the amplitude of positivity and offset latency of slow wave, and problem-size mainly offset latency of slow wave and pre-response negativity. Fronto-central positivity diminished from session to session, and the focus of positivity centered finally at centro-parietal regions.(ABSTRACT TRUNCATED AT 250 WORDS)

  16. A parallel simulated annealing algorithm for standard cell placement on a hypercube computer

    Science.gov (United States)

    Jones, Mark Howard

    1987-01-01

    A parallel version of a simulated annealing algorithm is presented which is targeted to run on a hypercube computer. A strategy for mapping the cells in a two dimensional area of a chip onto processors in an n-dimensional hypercube is proposed such that both small and large distance moves can be applied. Two types of moves are allowed: cell exchanges and cell displacements. The computation of the cost function in parallel among all the processors in the hypercube is described along with a distributed data structure that needs to be stored in the hypercube to support parallel cost evaluation. A novel tree broadcasting strategy is used extensively in the algorithm for updating cell locations in the parallel environment. Studies on the performance of the algorithm on example industrial circuits show that it is faster and gives better final placement results than the uniprocessor simulated annealing algorithms. An improved uniprocessor algorithm is proposed which is based on the improved results obtained from parallelization of the simulated annealing algorithm.

  17. Research on fast Fourier transforms algorithm of huge remote sensing image technology with GPU and partitioning technology.

    Science.gov (United States)

    Yang, Xue; Li, Xue-You; Li, Jia-Guo; Ma, Jun; Zhang, Li; Yang, Jan; Du, Quan-Ye

    2014-02-01

    Fast Fourier transforms (FFT) is a basic approach to remote sensing image processing. With the improvement of capacity of remote sensing image capture with the features of hyperspectrum, high spatial resolution and high temporal resolution, how to use FFT technology to efficiently process huge remote sensing image becomes the critical step and research hot spot of current image processing technology. FFT algorithm, one of the basic algorithms of image processing, can be used for stripe noise removal, image compression, image registration, etc. in processing remote sensing image. CUFFT function library is the FFT algorithm library based on CPU and FFTW. FFTW is a FFT algorithm developed based on CPU in PC platform, and is currently the fastest CPU based FFT algorithm function library. However there is a common problem that once the available memory or memory is less than the capacity of image, there will be out of memory or memory overflow when using the above two methods to realize image FFT arithmetic. To address this problem, a CPU and partitioning technology based Huge Remote Fast Fourier Transform (HRFFT) algorithm is proposed in this paper. By improving the FFT algorithm in CUFFT function library, the problem of out of memory and memory overflow is solved. Moreover, this method is proved rational by experiment combined with the CCD image of HJ-1A satellite. When applied to practical image processing, it improves effect of the image processing, speeds up the processing, which saves the time of computation and achieves sound result.

  18. Algorithmic complexity of quantum capacity

    Science.gov (United States)

    Oskouei, Samad Khabbazi; Mancini, Stefano

    2018-04-01

    We analyze the notion of quantum capacity from the perspective of algorithmic (descriptive) complexity. To this end, we resort to the concept of semi-computability in order to describe quantum states and quantum channel maps. We introduce algorithmic entropies (like algorithmic quantum coherent information) and derive relevant properties for them. Then we show that quantum capacity based on semi-computable concept equals the entropy rate of algorithmic coherent information, which in turn equals the standard quantum capacity. Thanks to this, we finally prove that the quantum capacity, for a given semi-computable channel, is limit computable.

  19. Higher-order force gradient symplectic algorithms

    Science.gov (United States)

    Chin, Siu A.; Kidwell, Donald W.

    2000-12-01

    We show that a recently discovered fourth order symplectic algorithm, which requires one evaluation of force gradient in addition to three evaluations of the force, when iterated to higher order, yielded algorithms that are far superior to similarly iterated higher order algorithms based on the standard Forest-Ruth algorithm. We gauge the accuracy of each algorithm by comparing the step-size independent error functions associated with energy conservation and the rotation of the Laplace-Runge-Lenz vector when solving a highly eccentric Kepler problem. For orders 6, 8, 10, and 12, the new algorithms are approximately a factor of 103, 104, 104, and 105 better.

  20. The Interpretations and Applications of Boethius's Introduction to the Arithmetic II, 1 at the End of the 10th Century

    Czech Academy of Sciences Publication Activity Database

    Otisk, Marek

    2014-01-01

    Roč. 5, - (2014), s. 33-56 ISSN 2038-3657 Institutional support: RVO:67985955 Keywords : Boethius * arithmetic * Gerbert of Aurillac * Abbo of Fleury * Notker of Liège Subject RIV: AA - Philosophy ; Religion