Multiprocessing system for performing floating point arithmetic operations
Energy Technology Data Exchange (ETDEWEB)
Nguyenphu, M.; Thatcher, L.E.
1990-10-02
This patent describes a data processing system. It comprises: a fixed point arithmetic processor means for performing fixed point arithmetic operations and including control means for decoding a floating point arithmetic instruction specifying a floating point arithmetic operation, and an addressing means for computing addresses for floating point data for the floating point operation from a memory means. The memory means for storing data and including means for receiving the addresses from the fixed point arithmetic processor means and providing the floating point data to a floating point arithmetic processor means; and the floating point arithmetic processor means for performing floating point arithmetic operations and including control means for decoding the floating point instruction and performing the specified floating point arithmetic operation upon the floating point data from the memory means.
Adams operations on higher arithmetic K-theory
DEFF Research Database (Denmark)
Feliu, Elisenda
2010-01-01
We construct Adams operations on the rational higher arithmetic K-groups of a proper arithmetic variety. The de¿nition applies to the higher arithmetic K-groups given by Takeda as well as to the groups suggested by Deligne and Soulé, by means of the homotopy groups of the homotopy ¿ber of the reg......We construct Adams operations on the rational higher arithmetic K-groups of a proper arithmetic variety. The de¿nition applies to the higher arithmetic K-groups given by Takeda as well as to the groups suggested by Deligne and Soulé, by means of the homotopy groups of the homotopy ¿ber...... of the regulator map. They are compatible with the Adams operations on algebraic K-theory. The de¿nition relies on the chain morphism representing Adams operations in higher algebraic K-theory given previously by the author. It is shown that this chain morphism commutes strictly with the representative...
Arithmetic Operations Beyond Floating Point Number Precision
Wang, Chih-Yueh; Chen, Hong-Yu; Chen, Yung-Ko
2010-01-01
In basic computational physics classes, students often raise the question of how to compute a number that exceeds the numerical limit of the machine. While technique of avoiding overflow/underflow has practical application in the electrical and electronics engineering industries, it is not commonly utilized in scientific computing, because scientific notation is adequate in most cases. We present an undergraduate project that deals with such calculations beyond a machine's numerical limit, known as arbitrary precision arithmetic. The assignment asks students to investigate the validity of floating point number precision and the approach of calculating the exact value of a large number, using the basic scientific programming language Fortran. Examples of the successive multiplication of even number and the multiplication and division of two overflowing floats are presented. The application of the scheme to hardware and firmware design which requires the allocation of finite memory, as in a digital signal proce...
Independence of basic arithmetic operations: evidence from cognitive neuropsychology
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María P. Salguero-Alcañiz
2013-10-01
Full Text Available The cases described in literature evidence that arithmetical operations can function independently, which allows to infer that the cognitive processes involved in the different operations might be different. Objective of that work is to determine the different processes involved in the resolution of arithmetical operations: addition, subtraction and multiplication. Method: Instrument: Assesment of Numeric Processing and Calculation Battery (Salguero & Alameda, 2007, 2011. Subjects. Patients of acquired cerebral injury. Results and conclusions: The patient MNL preserves the addition and the multiplication but he presents altered the subtraction. On the contrary, the patient PP shows alterations in addition and multiplication but he conserves the skills for the subtraction. ISR presents a selective deficit for multiplication with intact addition and substraction. Finally, ACH preserves the addition but presents deficit for substraction and multiplication. This double dissociation confirms the postulates of the anatomical functional model of Dehaene and Cohen (1995, 1997 that consider a double route for the resolution of arithmetical simple operations: linguistic route, for numerical information learned automatically (of memory and would be used for the operations of addition and multiplication, on the other hand the semantic elaboration would be for substraction.
Interval arithmetic operations for uncertainty analysis with correlated interval variables
Institute of Scientific and Technical Information of China (English)
Chao Jiang; Chun-Ming Fu; Bing-Yu Ni; Xu Han
2016-01-01
A new interval arithmetic method is proposed to solve interval functions with correlated intervals through which the overestimation problem existing in interval analy-sis could be significantly alleviated. The correlation between interval parameters is defined by the multidimensional par-allelepiped model which is convenient to describe the correlative and independent interval variables in a unified framework. The original interval variables with correlation are transformed into the standard space without correlation, and then the relationship between the original variables and the standard interval variables is obtained. The expressions of four basic interval arithmetic operations, namely addi-tion, subtraction, multiplication, and division, are given in the standard space. Finally, several numerical examples and a two-step bar are used to demonstrate the effectiveness of the proposed method.
Interval arithmetic operations for uncertainty analysis with correlated interval variables
Jiang, Chao; Fu, Chun-Ming; Ni, Bing-Yu; Han, Xu
2016-08-01
A new interval arithmetic method is proposed to solve interval functions with correlated intervals through which the overestimation problem existing in interval analysis could be significantly alleviated. The correlation between interval parameters is defined by the multidimensional parallelepiped model which is convenient to describe the correlative and independent interval variables in a unified framework. The original interval variables with correlation are transformed into the standard space without correlation, and then the relationship between the original variables and the standard interval variables is obtained. The expressions of four basic interval arithmetic operations, namely addition, subtraction, multiplication, and division, are given in the standard space. Finally, several numerical examples and a two-step bar are used to demonstrate the effectiveness of the proposed method.
Implementing arithmetic and other analytic operations by transcriptional regulation.
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Sean M Cory
2008-04-01
Full Text Available The transcriptional regulatory machinery of a gene can be viewed as a computational device, with transcription factor concentrations as inputs and expression level as the output. This view begs the question: what kinds of computations are possible? We show that different parameterizations of a simple chemical kinetic model of transcriptional regulation are able to approximate all four standard arithmetic operations: addition, subtraction, multiplication, and division, as well as various equality and inequality operations. This contrasts with other studies that emphasize logical or digital notions of computation in biological networks. We analyze the accuracy and precision of these approximations, showing that they depend on different sets of parameters, and are thus independently tunable. We demonstrate that networks of these "arithmetic" genes can be combined to accomplish yet more complicated computations by designing and simulating a network that detects statistically significant elevations in a time-varying signal. We also consider the much more general problem of approximating analytic functions, showing that this can be achieved by allowing multiple transcription factor binding sites on the promoter. These observations are important for the interpretation of naturally occurring networks and imply new possibilities for the design of synthetic networks.
Understanding and Using Principles of Arithmetic: Operations Involving Negative Numbers
Prather, Richard W.; Alibali, Martha W.
2008-01-01
Previous work has investigated adults' knowledge of principles for arithmetic with positive numbers (Dixon, Deets, & Bangert, 2001). The current study extends this past work to address adults' knowledge of principles of arithmetic with a negative number, and also investigates links between knowledge of principles and problem representation.…
Data Encryption and Decryption Algorithm Using Hamming Code and Arithmetic Operations
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Kurapati Sundar Teja
2015-08-01
Full Text Available This paper explains the implementation of data encryption and decryption algorithm using hamming code and arithmetic operations with the help of Verilog HDL. As the days are passing the old algorithms are not remained so strong cryptanalyst are familiar with them. Hamming code is one of forward error correcting code which has got many applications. In this paper hamming code algorithm was discussed and the implementation of it was done with arithmetic operations. For high security some arithmetic operations are added with hamming code process. A 3-bit data will be encrypted as 14-bit and using decryption process again we will receives 3-bit original data. The implemented design was tested on Spartan3A FPGA kit.
Differences between Flemish and Chinese Primary Students' Mastery of Basic Arithmetic Operations
Zhao, Ningning; Valcke, Martin; Desoete, Annemie; Burny, Elise; Imbo, Ineke
2014-01-01
The present paper investigates differences in the process of mastering the four basic arithmetic operations (addition, subtraction, multiplication and division) between Flemish and Chinese children from Grade 3 till Grade 6 (i.e. from 8 to 11 years old). The results showed, firstly, that Chinese students outperformed Flemish students in each grade…
Synthesis Optimization on Galois-Field Based Arithmetic Operators for Rijndael Cipher
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Petrus Mursanto
2011-08-01
Full Text Available A series of experiments has been conducted to show that FPGA synthesis of Galois-Field (GF based arithmetic operators can be optimized automatically to improve Rijndael Cipher throughput. Moreover, it has been demonstrated that efficiency improvement in GF operators does not directly correspond to the system performance at application level. The experiments were motivated by so many research works that focused on improving performance of GF operators. Each of the variants has the most efficient form in either time (fastest or space (smallest occupied area when implemented in FPGA chips. In fact, GF operators are not utilized individually, but rather integrated one to the others to implement algorithms. Contribution of this paper is to raise issue on GF-based application performance and suggest alternative aspects that potentially affect it. Instead of focusing on GF operator efficiency, system characteristics are worth considered in optimizing application performance.
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…
Designing reversible arithmetic, logic circuit to implement micro-operation in quantum computation
Kalita, Gunajit; Saikia, Navajit
2016-10-01
The futuristic computing is desired to be more power full with low-power consumption. That is why quantum computing has been a key area of research for quite some time and is getting more and more attention. Quantum logic being reversible, a significant amount of contributions has been reported on reversible logic in recent times. Reversible circuits are essential parts of quantum computers, and hence their designs are of great importance. In this paper, designs of reversible circuits are proposed using a recently proposed reversible gate for arithmetic and logic operations to implement various micro-operations (simple add and subtract, add with carry, subtract with borrow, transfer, incrementing, decrementing etc., and logic operations like XOR, XNOR, complementing etc.) in a reversible computer like quantum computer. The two new reversible designs proposed here for half adder and full adders are also used in the presented reversible circuits to implement various microoperations. The quantum costs of these designs are comparable. Many of the implemented micro-operations are not seen in previous literatures. The performances of the proposed circuits are compared with existing designs wherever available.
Arithmetic partial differential equations
Buium, Alexandru; Simanca, Santiago R.
2006-01-01
We develop an arithmetic analogue of linear partial differential equations in two independent ``space-time'' variables. The spatial derivative is a Fermat quotient operator, while the time derivative is the usual derivation. This allows us to ``flow'' integers or, more generally, points on algebraic groups with coordinates in rings with arithmetic flavor. In particular, we show that elliptic curves have certain canonical ``flows'' on them that are the arithmetic analogues of the heat and wave...
Interval arithmetic in calculations
Bairbekova, Gaziza; Mazakov, Talgat; Djomartova, Sholpan; Nugmanova, Salima
2016-10-01
Interval arithmetic is the mathematical structure, which for real intervals defines operations analogous to ordinary arithmetic ones. This field of mathematics is also called interval analysis or interval calculations. The given math model is convenient for investigating various applied objects: the quantities, the approximate values of which are known; the quantities obtained during calculations, the values of which are not exact because of rounding errors; random quantities. As a whole, the idea of interval calculations is the use of intervals as basic data objects. In this paper, we considered the definition of interval mathematics, investigated its properties, proved a theorem, and showed the efficiency of the new interval arithmetic. Besides, we briefly reviewed the works devoted to interval analysis and observed basic tendencies of development of integral analysis and interval calculations.
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S.G.Srikantaswamy
2011-12-01
Full Text Available The process of exchanging information is called Communication. The basic Communication system involvestransmitter, receiver and the channel. The data transmitted by the sender reaches receiver through thechannel. The unauthorized parties (cracker,hacker, eavesdropper, or attacker should not be able to access the information at the channel. Therefore transmitting data securely from the sender to the receiver is a very important aspect. A cryptographic system is unconditionally secure if the cipher text produced by the system does not contain enough information to determine uniquely the corresponding plaintext, no matter how much cipher text is available. A cryptographic system is said to be computationally secure if the cost of breaking the cipher exceeds the value of the encrypted information and the time required to break the cipher exceeds the useful lifetime of the content. One time pad system can be called as unconditionally secure algorithm, if the keys (pad usedare truly random in nature. In this paper, we are demonstrating that one-time pad can be used as an efficient encryption scheme by involving arithmetic and logical operations. Here we proposed a new key generation technique, to generate a key of any length just by providing a seed value, to encrypt the message. The problem generating key value has been solved by the use of key generation algorithm.
Type-IV DCT, DST, and MDCT algorithms with reduced numbers of arithmetic operations
Shao, Xuancheng
2007-01-01
We present algorithms for the type-IV discrete cosine transform (DCT-IV) and discrete sine transform (DST-IV), as well as for the modified discrete cosine transform (MDCT) and its inverse, that achieve a lower count of real multiplications and additions than previously published algorithms, without sacrificing numerical accuracy. Asymptotically, the operation count is reduced from ~2NlogN to ~(17/9)NlogN for a power-of-two transform size N. These results are derived by considering the DCT to be a special case of a DFT of length 8N, with certain symmetries, and then pruning redundant operations from a recent improved fast Fourier transform algorithm (based on a recursive rescaling of the conjugate-pair split radix algorithm). The improved algorithms for DST-IV and MDCT follow immediately from the improved count for the DCT-IV.
Type-II/III DCT/DST algorithms with reduced number of arithmetic operations
Shao, Xuancheng
2007-01-01
We present algorithms for the discrete cosine transform (DCT) and discrete sine transform (DST), of types II and III, that achieve a lower count of real multiplications and additions than previously published algorithms, without sacrificing numerical accuracy. Asymptotically, the operation count is reduced from ~ 2N log_2 N to ~ (17/9) N log_2 N for a power-of-two transform size N. Furthermore, we show that a further N multiplications may be saved by a certain rescaling of the inputs or outputs, generalizing a well-known technique for N=8 by Arai et al. These results are derived by considering the DCT to be a special case of a DFT of length 4N, with certain symmetries, and then pruning redundant operations from a recent improved fast Fourier transform algorithm (based on a recursive rescaling of the conjugate-pair split radix algorithm). The improved algorithms for DCT-III, DST-II, and DST-III follow immediately from the improved count for the DCT-II.
Fried, Michael D
2006-01-01
Field Arithmetic explores Diophantine fields through their absolute Galois groups. This largely self-contained treatment starts with techniques from algebraic geometry, number theory, and profinite groups. Graduate students can effectively learn generalizations of finite field ideas. We use Haar measure on the absolute Galois group to replace counting arguments. New Chebotarev density variants interpret diophantine properties. Here we have the only complete treatment of Galois stratifications, used by Denef and Loeser, et al, to study Chow motives of Diophantine statements.Progress from the fi
Arithmetic the foundation of mathematics
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
Individual differences in cognitive arithmetic.
Geary, D C; Widaman, K F
1987-06-01
Unities in the processes involved in solving arithmetic problems of varying operations have been suggested by studies that have used both factor-analytic and information-processing methods. We designed the present study to investigate the convergence of mental processes assessed by paper-and-pencil measures defining the Numerical Facility factor and component processes for cognitive arithmetic identified by using chronometric techniques. A sample of 100 undergraduate students responded to 320 arithmetic problems in a true-false reaction-time (RT) verification paradigm and were administered a battery of ability measures spanning Numerical Facility, Perceptual Speed, and Spatial Relations factors. The 320 cognitive arithmetic problems comprised 80 problems of each of four types: simple addition, complex addition, simple multiplication, and complex multiplication. The information-processing results indicated that regression models that included a structural variable consistent with memory network retrieval of arithmetic facts were the best predictors of RT to each of the four types of arithmetic problems. The results also verified the effects of other elementary processes that are involved in the mental solving of arithmetic problems, including encoding of single digits and carrying to the next column for complex problems. The relation between process components and ability measures was examined by means of structural equation modeling. The final structural model revealed a strong direct relation between a factor subsuming efficiency of retrieval of arithmetic facts and of executing the carry operation and the traditional Numerical Facility factor. Furthermore, a moderate direct relation between a factor subsuming speed of encoding digits and decision and response times and the traditional Perceptual Speed factor was also found. No relation between structural variables representing cognitive arithmetic component processes and ability measures spanning the Spatial
DEFF Research Database (Denmark)
Gil, J. I. Burgos; Feliu, Elisenda
2012-01-01
We give a new construction of higher arithmetic Chow groups for quasi-projective arithmetic varieties over a field. Our definition agrees with the higher arithmetic Chow groups defined by Goncharov for projective arithmetic varieties over a field. These groups are the analogue, in the Arakelov co...
Prabhakaran, V; Rypma, B; Gabrieli, J D
2001-01-01
Brain activation was examined using functional magnetic resonance imaging during mathematical problem solving in 7 young healthy participants. Problems were selected from the Necessary Arithmetic Operations Test (NAOT; R. B. Ekstrom, J. W. French, H. H. Harman, & D. Dermen, 1976). Participants solved 3 types of problems: 2-operation problems requiring mathematical reasoning and text processing, 1-operation problems requiring text processing but minimal mathematical reasoning, and 0-operation problems requiring minimal text processing and controlling sensorimotor demands of the NAOT problems. Two-operation problems yielded major activations in bilateral frontal regions similar to those found in other problem-solving tasks, indicating that the processes mediated by these regions subserve many forms of reasoning. Findings suggest a dissociation in mathematical problem solving between reasoning, mediated by frontal cortex, and text processing, mediated by temporal cortex.
J.A. Bergstra; C.A. Middelburg
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
Kessel, Cathy
This paper illustrates a different conception of arithmetic, an arithmetic with reasons as well as rules. This arithmetic includes making connections between different representations and making sense of rules as well as using them. It provides a foundation for "Algebra the Web of Knowledge and Skill" in the sense that algebra can be…
Gil, J I Burgos
2009-01-01
We give a new construction of higher arithmetic Chow groups for quasi-projective arithmetic varieties over a field. Our definition agrees with the higher arithmetic Chow groups defined by Goncharov for projective arithmetic varieties over a field. These groups are the analogue, in the Arakelov context, of the higher algebraic Chow groups defined by Bloch. The degree zero group agrees with the arithmetic Chow groups of Burgos. Our new construction is shown to be a contravariant functor and is endowed with a product structure, which is commutative and associative.
Dynamically Reconfigurable Processor for Floating Point Arithmetic
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S. Anbumani,
2014-01-01
Full Text Available Recently, development of embedded processors is toward miniaturization and energy saving for ecology. On the other hand, high performance arithmetic circuits are required in a lot of application in science and technology. Dynamically reconfigurable processors have been developed to meet these requests. They can change circuit configuration according to instructions in program instantly during operations.This paper describes, a dynamically reconfigurable circuit for floating-point arithmetic is proposed. The arithmetic circuit consists of two single precision floating-point arithmetic circuits. It performs double precision floating-point arithmetic by reconfiguration. Dynamic reconfiguration changes circuit construction at one clock cycle during operation without stopping circuits. It enables reconfiguration of circuits in a few nano seconds. The proposed circuit is reconfigured in two modes. In first mode it performs one double precision floating-point arithmetic or else the circuit will perform two parallel operations of single precision floating-point arithmetic. The new system design reduces implementation area by reconfiguring common parts of each operation. It also increases the processing speed with a very little number of clocks.
Encoding of multi-alphabet sources by binary arithmetic coding
Guo, Muling; Oka, Takahumi; Kato, Shigeo; Kajiwara, Hiroshi; Kawamura, Naoto
1998-12-01
In case of encoding a multi-alphabet source, the multi- alphabet symbol sequence can be encoded directly by a multi- alphabet arithmetic encoder, or the sequence can be first converted into several binary sequences and then each binary sequence is encoded by binary arithmetic encoder, such as the L-R arithmetic coder. Arithmetic coding, however, requires arithmetic operations for each symbol and is computationally heavy. In this paper, a binary representation method using Huffman tree is introduced to reduce the number of arithmetic operations, and a new probability approximation for L-R arithmetic coding is further proposed to improve the coding efficiency when the probability of LPS (Least Probable Symbol) is near 0.5. Simulation results show that our proposed scheme has high coding efficacy and can reduce the number of coding symbols.
Development of arithmetical abilities
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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.
How to be Brilliant at Mental Arithmetic
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
Robertson, Jane I.
1979-01-01
Three types of arithmetic algorithms are discussed and compared. These are algorithms designed to get the right answer, computer algorithms, and algorithms designed to get the right answer and understand why. (MP)
Design of optimized Interval Arithmetic Multiplier
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Rajashekar B.Shettar
2011-07-01
Full Text Available Many DSP and Control applications that require the user to know how various numericalerrors(uncertainty affect the result. This uncertainty is eliminated by replacing non-interval values withintervals. Since most DSPs operate in real time environments, fast processors are required to implementinterval arithmetic. The goal is to develop a platform in which Interval Arithmetic operations areperformed at the same computational speed as present day signal processors. So we have proposed thedesign and implementation of Interval Arithmetic multiplier, which operates with IEEE 754 numbers. Theproposed unit consists of a floating point CSD multiplier, Interval operation selector. This architectureimplements an algorithm which is faster than conventional algorithm of Interval multiplier . The costoverhead of the proposed unit is 30% with respect to a conventional floating point multiplier. Theperformance of proposed architecture is better than that of a conventional CSD floating-point multiplier,as it can perform both interval multiplication and floating-point multiplication as well as Intervalcomparisons
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.
Implementing decimal floating-point arithmetic through binary: some suggestions
Brisebarre, Nicolas; Ercegovac, Milos; Louvet, Nicolas; Martin-Dorel, Erik; Muller, Jean-Michel; Panhaleux, Adrien
2010-01-01
International audience; We propose several algorithms and provide some related results that make it possible to implement decimal floating-point arithmetic on a processor that does not have decimal operators, using the available binary floating-point functions. In this preliminary study, we focus on round-to-nearest mode only. We show that several functions in decimal32 and decimal64 arithmetic can be implemented using binary64 and binary128 floating-point arithmetic, respectively. Specifical...
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K. Anup Kumar
2012-07-01
Full Text Available In this investigation, we have modified the Feistel cipher by taking the plaintext in the form of a pair of square matrices. Here we have introduced the operation multiplication with the key matrices and the modular arithmetic addition in encryption. The modular arithmetic inverse of the key matrix is introduced in decryption. The cryptanalysis carried out in this paper clearly indicate that this cipher cannot be broken by the brute force attack and the known plaintext attack.
Cardinal arithmetic for skeptics
Shelah, Saharon
2008-01-01
We present a survey of some results of the pcf-theory and their applications to cardinal arithmetic. We review basics notions (in section 1), briefly look at history in section 2 (and some personal history in section 3). We present main results on pcf in section 5 and describe applications to cardinal arithmetic in section 6. The limitations on independence proofs are discussed in section 7, and in section 8 we discuss the status of two axioms that arise in the new setting. Applications to other areas are found in section 9.
Arithmetic Circuit Verification Based on Word-Level Decision Diagrams
1998-05-01
the addition of *BMDs may have exponential operations in the worst case. Arditi [3] used *BMDs for verification of arithmetic assembly instructions...pp. 6:509-516. [3] ARDITI , L. *BMDS can delay the use of theorem proving for verifying arithmetic as- sembly instructions. In Proceedings of the
A curious arithmetic of fractal dimension for polyadic Cantor sets
Villatoro, Francisco R
2009-01-01
Fractal sets, by definition, are non-differentiable, however their dimension can be continuous, differentiable, and arithmetically manipulable as function of their construction parameters. A new arithmetic for fractal dimension of polyadic Cantor sets is introduced by means of properly defining operators for the addition, subtraction, multiplication, and division. The new operators have the usual properties of the corresponding operations with real numbers. The combination of an infinitesimal change of fractal dimension with these arithmetic operators allows the manipulation of fractal dimension with the tools of calculus.
Connecting Arithmetic to Algebra
Darley, Joy W.; Leapard, Barbara B.
2010-01-01
Algebraic thinking is a top priority in mathematics classrooms today. Because elementary school teachers lay the groundwork to develop students' capacity to think algebraically, it is crucial for teachers to have a conceptual understanding of the connections between arithmetic and algebra and be confident in communicating these connections. Many…
Brumer, Armand
2011-01-01
We study the arithmetic of division fields of semistable abelian varieties A over the rationals. The Galois group of the 2-division field of A is analyzed when the conductor is odd and squarefree. The irreducible semistable mod 2 representations of small conductor are determined under GRH. These results are used in "Paramodular abelian varieties of odd conductor," arXiv:1004.4699.
FPGA Based Quadruple Precision Floating Point Arithmetic for Scientific Computations
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Mamidi Nagaraju
2012-09-01
Full Text Available In this project we explore the capability and flexibility of FPGA solutions in a sense to accelerate scientific computing applications which require very high precision arithmetic, based on IEEE 754 standard 128-bit floating-point number representations. Field Programmable Gate Arrays (FPGA is increasingly being used to design high end computationally intense microprocessors capable of handling floating point mathematical operations. Quadruple Precision Floating-Point Arithmetic is important in computational fluid dynamics and physical modelling, which require accurate numerical computations. However, modern computers perform binary arithmetic, which has flaws in representing and rounding the numbers. As the demand for quadruple precision floating point arithmetic is predicted to grow, the IEEE 754 Standard for Floating-Point Arithmetic includes specifications for quadruple precision floating point arithmetic. We implement quadruple precision floating point arithmetic unit for all the common operations, i.e. addition, subtraction, multiplication and division. While previous work has considered circuits for low precision floating-point formats, we consider the implementation of 128-bit quadruple precision circuits. The project will provide arithmetic operation, simulation result, hardware design, Input via PS/2 Keyboard interface and results displayed on LCD using Xilinx virtex5 (XC5VLX110TFF1136 FPGA device.
Single electron tunneling based arithmetic computation
Lageweg, C.R.
2004-01-01
In this dissertation we investigate the implementation of computer arithmetic operations with Single Electron Tunneling (SET) technology based circuits. In our research we focus on the effective utilization of the SET technologys specific characteristic, i.e., the ability to control the transport of
Memory updating and mental arithmetic
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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.
Marklof, J
2005-01-01
The central objective in the study of quantum chaos is to characterize universal properties of quantum systems that reflect the regular or chaotic features of the underlying classical dynamics. Most developments of the past 25 years have been influenced by the pioneering models on statistical properties of eigenstates (Berry 1977) and energy levels (Berry and Tabor 1977; Bohigas, Giannoni and Schmit 1984). Arithmetic quantum chaos (AQC) refers to the investigation of quantum system with additional arithmetic structures that allow a significantly more extensive analysis than is generally possible. On the other hand, the special number-theoretic features also render these systems non-generic, and thus some of the expected universal phenomena fail to emerge. Important examples of such systems include the modular surface and linear automorphisms of tori (`cat maps') which will be described below.
Algebra, Arithmetic, and Geometry
Tschinkel, Yuri
2009-01-01
The two volumes of "Algebra, Arithmetic, and Geometry: In Honor of Y.I. Manin" are composed of invited expository articles and extensions detailing Manin's contributions to the subjects, and are in celebration of his 70th birthday. The well-respected and distinguished contributors include: Behrend, Berkovich, Bost, Bressler, Calaque, Carlson, Chambert-Loir, Colombo, Connes, Consani, Dabrowski, Deninger, Dolgachev, Donaldson, Ekedahl, Elsenhans, Enriques, Etingof, Fock, Friedlander, Geemen, Getzler, Goncharov, Harris, Iskovskikh, Jahnel, Kaledin, Kapranov, Katz, Kaufmann, Kollar, Kont
Towards an arithmetical logic the arithmetical foundations of logic
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...
Arithmetic functions in torus and tree networks
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.
Directory of Open Access Journals (Sweden)
Filiz VAROL
2012-01-01
Full Text Available The main purpose of this literature review is to investigate common arithmetic difficulties experienced by students in mathematicswhile solving mathematics problems that require arithmetic operations. There are many reasons why children engage arithmetic error, such as carelessness, lack of knowledge, and misconceptions. If errors continue even after many years, this means that these errors are not random errors and need attention. In this review, first, main reasons that cause students to experience difficulties in arithmetic operations were investigated and then they were explained with examples. This study will be an important resource for people who focus on teaching and learning mathematics, especially in elementary education. Bu alan yazın taramasının temel amacı öğrencilerin matematikte dört işlem konusunda yaşadıkları yaygın aritmetik güçlükleri ortaya çıkartmaktır. Çocukların aritmetikte hata yapmalarının birçok nedeni vardır: Dikkatsizlik, bilgi eksikliği, kavram yanılgıları gibi. Çocukların yapmış oldukları hatalar süreklilik arz edip yıllar sonra bile benzerlik gösteriyorsa bu hatalar rastgele hatalar değildir ve dikkate değerdir. Bu çalışmada da ilk önce öğrencilerin aritmetik işlemlerde neden güçlük yaşadıkları araştırılmış, daha sonra da en yaygın yaşanan güçlükler örneklerle açıklanmaya çalışılmıştır. Bu alan yazın taramasının matematik eğitimi ve öğretimi alanında çalışmalar yapan araştırmacılar için önemli bir kaynak olacağı düşünülmektedir.
Introduction to cardinal arithmetic
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
Arithmetic soft-core accelerators
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 operat
Binary Tree Arithmetic with Generalized Constructors
Tarau, Paul
2013-01-01
We describe arithmetic computations in terms of operations on some well known free algebras (S1S, S2S and ordered rooted binary trees) while emphasizing the common structure present in all them when seen as isomorphic with the set of natural numbers. Constructors and deconstructors seen through an initial algebra semantics are generalized to recursively defined functions obeying similar laws. Implementation using Scala's apply and unapply are discussed together with an application to a realis...
Valuations on arithmetic surfaces
Institute of Scientific and Technical Information of China (English)
XU Ning
2009-01-01
In this paper,we give the definition of the height of a valuation and the definition of the big field Cp,G,where p is a prime and G R is an additive subgroup containing 1.We conclude that Cp,G is a field and Cp,G is algebraically closed.Based on this the author obtains the complete classification of valuations on arithmetic surfaces.Furthermore,for any m ≤ n ∈ Z,let Vm,n be an R-vector space of dimension n - m + 1,whose coordinates are indexed from rn to n.We generalize the definition of Cp,G,where p is a prime and G C Vm,n is an additive subgroup containing 1.We also conclude that Cp,G is a field if m ≤ 0 ≤ n.
Valuations on arithmetic surfaces
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
In this paper, we give the definition of the height of a valuation and the definition of the big field Cp,G, where p is a prime and GR is an additive subgroup containing 1. We conclude that Cp,G is a field and Cp,G is algebraically closed. Based on this the author obtains the complete classification of valuations on arithmetic surfaces. Furthermore, for any m ≤n∈ Z, let Vm,n be an R-vector space of dimension n-m + 1, whose coordinates are indexed from m to n. We generalize the definition of Cp,G, where p is a prime and GVm,n is an additive subgroup containing 1. We also conclude that Cp,G is a field if m ≤0 ≤n.
Blueprints - towards absolute arithmetic?
Lorscheid, Oliver
2012-01-01
One of the driving motivations to develop $\\F_1$-geometry is the hope to translate Weil's proof of the Riemann hypothesis from positive characteristics to number fields, which might result in a proof of the classical Riemann hypothesis. The underlying idea is that the spectrum of $\\Z$ should find an interpretation as a curve over $\\F_1$, which has a completion $\\bar{\\Spec\\Z}$ analogous to a curve over a finite field. The hope is that intersection theory for divisors on the arithmetic surface $\\bar{\\Spec\\Z} \\times \\bar{\\Spec\\Z}$ will allow to mimic Weil's proof. It turns out that it is possible to define an object $\\bar{\\Spec\\Z}$ from the viewpoint of blueprints that has certain properties, which come close to the properties of its analogs in positive characteristic. This shall be explained in the following note, which is a summary of a talk given at the Max Planck Institute in March, 2012.
If Gravity is Geometry, is Dark Energy just Arithmetic?
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.
If Gravity is Geometry, is Dark Energy just Arithmetic?
Czachor, Marek
2017-02-01
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.
The stochastic properties of input spike trains control neuronal arithmetic.
Bures, Zbynek
2012-02-01
In the nervous system, the representation of signals is based predominantly on the rate and timing of neuronal discharges. In most everyday tasks, the brain has to carry out a variety of mathematical operations on the discharge patterns. Recent findings show that even single neurons are capable of performing basic arithmetic on the sequences of spikes. However, the interaction of the two spike trains, and thus the resulting arithmetic operation may be influenced by the stochastic properties of the interacting spike trains. If we represent the individual discharges as events of a random point process, then an arithmetical operation is given by the interaction of two point processes. Employing a probabilistic model based on detection of coincidence of random events and complementary computer simulations, we show that the point process statistics control the arithmetical operation being performed and, particularly, that it is possible to switch from subtraction to division solely by changing the distribution of the inter-event intervals of the processes. Consequences of the model for evaluation of binaural information in the auditory brainstem are demonstrated. The results accentuate the importance of the stochastic properties of neuronal discharge patterns for information processing in the brain; further studies related to neuronal arithmetic should therefore consider the statistics of the interacting spike trains.
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...
Vamvakoussi, Xenia; Van Dooren, Wim; Verschaffel, Lieven
2013-01-01
This study tested the hypothesis that intuitions about the effect of operations, e.g., "addition makes bigger" and "division makes smaller", are still present in educated adults, even after years of instruction. To establish the intuitive character, we applied a reaction time methodology, grounded in dual process theories of reasoning. Educated…
Hildebrandt, K Jannis; Benda, Jan; Hennig, R Matthias
2011-10-01
Sensory pathways process behaviorally relevant signals in various contexts and therefore have to adapt to differing background conditions. Depending on changes in signal statistics, this adjustment might be a combination of two fundamental computational operations: subtractive adaptation shifting a neuron's threshold and divisive gain control scaling its sensitivity. The cricket auditory system has to deal with highly stereotyped conspecific songs at low carrier frequencies, and likely much more variable predator signals at high frequencies. We proposed that due to the differences between the two signal classes, the operation that is implemented by adaptation depends on the carrier frequency. We aimed to identify the biophysical basis underlying the basic computational operations of subtraction and division. We performed in vivo intracellular and extracellular recordings in a first-order auditory interneuron (AN2) that is active in both mate recognition and predator avoidance. We demonstrated subtractive shifts at the carrier frequency of conspecific songs and division at the predator-like carrier frequency. Combined application of current injection and acoustic stimuli for each cell allowed us to demonstrate the subtractive effect of cell-intrinsic adaptation currents. Pharmacological manipulation enabled us to demonstrate that presynaptic inhibition is most likely the source of divisive gain control. We showed that adjustment to the sensory context can depend on the class of signals that are relevant to the animal. We further revealed that presynaptic inhibition is a simple mechanism for divisive operations. Unlike other proposed mechanisms, it is widely available in the sensory periphery of both vertebrates and invertebrates.
The Development of Arithmetical Abilities
Butterworth, Brian
2005-01-01
Background: Arithmetical skills are essential to the effective exercise of citizenship in a numerate society. How these skills are acquired, or fail to be acquired, is of great importance not only to individual children but to the organisation of formal education and its role in society. Method: The evidence on the normal and abnormal…
Groups and fields in arithmetic
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
On Architectural Practice and Arithmetic Abilities in Renaissance Italy
Directory of Open Access Journals (Sweden)
Giulia Ceriani Sebregondi
2015-06-01
Full Text Available The article examines the figure of the architect at work in Renaissance Italy, when a major change occurred in the practice of design with the spread of arithmetic. This deep scientific, technical, methodological, and cultural shift involved the image of the architect and his profession, his relationship with the patron, as well as the cultural conception of architecture. The essay, crossing disciplinary boundaries, analyses some technical aspects of architectural design in early modern Italy only marginally investigated. If proportional systems and architecture’s theoretical questions have been amply studied, the practical culture, the daily professional practice and its working tools, such as the operative arithmetic actually known to architects, have been only sporadically analysed. During the Renaissance, especially in Italy, an important development of mathematics occurred and arithmetic was clarified and simplified so to allow its diffusion, but at the same time those disciplines remained essentially despised by aristocratic and intellectual elites. What was the architects’ role in this moment of deep change? Which was the arithmetic usually employed by them in the design process? When did Hindu-Arabic numbers and fractions became familiar in the field of architecture? In the secular battle between geometry and arithmetic, which system was used in what professional cases? The essay illustrates how architects with different backgrounds responded to this change, through a comparative analysis of all the architectural drawings containing numbers and calculations made by Michelangelo Buonarroti (1475–1564, Baldassarre Peruzzi (1481–1536, and Antonio da Sangallo the Younger (1484–1546.
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.
Computer arithmetic and validity theory, implementation, and applications
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
Brain systems involved in arithmetic with positive versus negative numbers.
Gullick, Margaret M; Wolford, George
2014-02-01
Positive number arithmetic is based on combining and separating sets of items, with systematic differences in brain activity in specific regions depending on operation. In contrast, arithmetic with negative numbers involves manipulating abstract values worth less than zero, possibly involving different operation-activity relationships in these regions. Use of procedural arithmetic knowledge, including transformative rules like "minus a negative is plus a positive," may also differ by operand sign. Here, we examined whether the activity evoked in negative number arithmetic was similar to that seen in positive problems, using region of interest analyses (ROIs) to examine a specific set of brain regions. Negative-operand problems demonstrated a positive-like effect of operation in the inferior parietal lobule with more activity for subtraction than addition, as well as increased activity across operation. Interestingly, while positive-operand problems demonstrated the expected addition > subtraction activity difference in the angular gyrus, negative problems showed a reversed effect, with relatively more activity for subtraction than addition. Negative subtraction problems may be understood after translation to addition via rule, thereby invoking more addition-like activity. Whole-brain analyses showed increased right caudate activity for negative-operand problems across operation, indicating a possible overall increase in usage of procedural rules. Arithmetic with negative numbers may thus shows some operation-activity relationships similar to positive numbers, but may also be affected by strategy. This study examines the flexibility of the mental number system by exploring to what degree the processing of an applied usage of a difficult, abstract mathematical concept is similar to that for positive numbers.
The retrieval and selection of arithmetic facts in oral arithmetic.
Megías, Patricia; Macizo, Pedro
2016-10-01
We examined the co-activation and the selection of arithmetic facts in oral arithmetic. In two experiments, participants had to verify whether simple additions were correct or not. In Experiment 1, additions were presented in the auditory-verbal format; in Experiment 2, additions were presented in the digit format but simulating the temporal sequence of auditory problems of Experiment 1. Results were similar in both experiments. Firstly, participants took the same time to respond when an addition was incorrect but the result was that of multiplying the operands (e.g., 2+4=8) relative to a control addition with unrelated result. Secondly, participants took more time to respond when the result of multiplying the operands of the first trial was presented again in a correct addition problem (e.g., 2+6=8) relative to a control addition. This pattern of results is discussed in terms of the temporal resolution to which auditory problems are resolved and the role of an inhibitory mechanism involved in the selection of arithmetic facts.
Rodionov, Anatoly
2007-01-01
A new incremental algorithm for data compression is presented. For a sequence of input symbols algorithm incrementally constructs a p-adic integer number as an output. Decoding process starts with less significant part of a p-adic integer and incrementally reconstructs a sequence of input symbols. Algorithm is based on certain features of p-adic numbers and p-adic norm. p-adic coding algorithm may be considered as of generalization a popular compression technique - arithmetic coding algorithms. It is shown that for p = 2 the algorithm works as integer variant of arithmetic coding; for a special class of models it gives exactly the same codes as Huffman's algorithm, for another special model and a specific alphabet it gives Golomb-Rice codes.
The neural circuits for arithmetic principles.
Liu, Jie; Zhang, Han; Chen, Chuansheng; Chen, Hui; Cui, Jiaxin; Zhou, Xinlin
2017-02-15
Arithmetic principles are the regularities underlying arithmetic computation. Little is known about how the brain supports the processing of arithmetic principles. The current fMRI study examined neural activation and functional connectivity during the processing of verbalized arithmetic principles, as compared to numerical computation and general language processing. As expected, arithmetic principles elicited stronger activation in bilateral horizontal intraparietal sulcus and right supramarginal gyrus than did language processing, and stronger activation in left middle temporal lobe and left orbital part of inferior frontal gyrus than did computation. In contrast, computation elicited greater activation in bilateral horizontal intraparietal sulcus (extending to posterior superior parietal lobule) than did either arithmetic principles or language processing. Functional connectivity analysis with the psychophysiological interaction approach (PPI) showed that left temporal-parietal (MTG-HIPS) connectivity was stronger during the processing of arithmetic principle and language than during computation, whereas parietal-occipital connectivities were stronger during computation than during the processing of arithmetic principles and language. Additionally, the left fronto-parietal (orbital IFG-HIPS) connectivity was stronger during the processing of arithmetic principles than during computation. The results suggest that verbalized arithmetic principles engage a neural network that overlaps but is distinct from the networks for computation and language processing.
Arithmetic Operations on Trapezoidal Fuzzy Numbers
Directory of Open Access Journals (Sweden)
J. Vahidi
2013-10-01
Full Text Available In this paper, several new algebraic mathematics for positive fuzzy numbers of type $(\\overline{a}, \\overline{\\overline{a}}, \\overline{\\overline{\\overline{a}}}, \\overline{\\overline{\\overline{\\overline{a}}}}$ are devised and do not need the computation of $\\alpha$-cut of the fuzzy number. Direct mathematical expressions to evaluate exponential, square root, logarithms, inverse exponential etc. of positive fuzzy numbers of type $(\\overline{a}, \\overline{\\overline{a}}, \\overline{\\overline{\\overline{a}}}, \\overline{\\overline{\\overline{\\overline{a}}}}$ are obtained using the basic analytical principles of algebraic mathematics and Taylor series expansion. At the end, Various numerical examples are also solved to demonstrate the use of contrived expressions.
Arithmetic Operations Beyond Floating Point Number Precision
Wang, Chih-Yueh; Yin, Chen-Yang; Chen, Hong-Yu; Chen, Yung-Ko
2010-01-01
In basic computational physics classes, students often raise the question of how to compute a number that exceeds the numerical limit of the machine. While technique of avoiding overflow/underflow has practical application in the electrical and electronics engineering industries, it is not commonly utilized in scientific computing, because scientific notation is adequate in most cases. We present an undergraduate project that deals with such calculations beyond a machine's numerical limit, kn...
脉冲神经膜系统实现有符号整数的算术运算%Spiking Neural P Systems for Performing Signed Integer Arithmetic Operations
Institute of Scientific and Technical Information of China (English)
彭献武; 樊晓平; 刘建勋; 文宏
2013-01-01
Spiking neural P systems are a new class of bio-inspired computing devices incorporating the ideas of spiking neural networks into P systems, and have powerful computational capability and potential capability in solving computationally hard problems. In this paper, we consider spiking neural P systems as devices which can be used to perform some basic arithmetic operations, namely two's complement, addition/subtraction on signed integers, and multiplication on two arbitrary natural numbers. The inputs and outputs of those systems are indicated by binary form and encoded as corresponding spike trains. This paper provides an answer to an open problem about multiplication operation of two arbitrary natural numbers formulated by Gutiérrez-Naranjo MA. And Leporati A. The present work maybe considered as the basis for more complex applications, and maybe for designing of a CPU based on spiking neural P systems.%脉冲神经膜系统是一种结合脉冲神经网络和膜系统特点的新型生物计算装置,具有强大的计算能力和解决计算难问题的潜力.本文考虑在脉冲神经膜系统这种装置上处理一些简单的算术运算问题,包括二进制补码转换、有符号整数的加、减运算和任意两个自然数的乘法运算,这些系统的输入、输出数均采用二进制方式,编码采用合适的脉冲序列.本文较好地解决了Gutiérrez-Naranjo MA.和Leporati A.提出的关于如何实现两个任意自然数乘法运算的公开问题.当前工作可以作为解决更加复杂问题的基础,也有助于设计基于脉冲神经膜系统的生物型CPU.
Some results on uniform arithmetic circuit complexity
DEFF Research Database (Denmark)
Frandsen, Gudmund Skovbjerg; Valence, Mark; Barrington, David A. Mix
1994-01-01
We introduce a natural set of arithmetic expressions and define the complexity class AE to consist of all those arithmetic functions (over the fieldsF 2n) that are described by these expressions. We show that AE coincides with the class of functions that are computable with constant depth...... that if some such representation is X-uniform (where X is P or DLOGTIME), then the arithmetic complexity of a function (measured with X-uniform unbounded fan-in arithmetic circuits) is identical to the Boolean complexity of this function (measured with X-uniform threshold circuits). We show the existence...... and polynomial-size unbounded fan-in arithmetic circuits satisfying a natural uniformity constraint (DLOGTIME-uniformity). A 1-input and 1-output arithmetic function over the fieldsF2n may be identified with ann-input andn-output Boolean function when field elements are represented as bit strings. We prove...
Coinductive Formal Reasoning in Exact Real Arithmetic
Niqui, Milad
2008-01-01
In this article we present a method for formally proving the correctness of the lazy algorithms for computing homographic and quadratic transformations -- of which field operations are special cases-- on a representation of real numbers by coinductive streams. The algorithms work on coinductive stream of M\\"obius maps and form the basis of the Edalat--Potts exact real arithmetic. We use the machinery of the Coq proof assistant for the coinductive types to present the formalisation. The formalised algorithms are only partially productive, i.e., they do not output provably infinite streams for all possible inputs. We show how to deal with this partiality in the presence of syntactic restrictions posed by the constructive type theory of Coq. Furthermore we show that the type theoretic techniques that we develop are compatible with the semantics of the algorithms as continuous maps on real numbers. The resulting Coq formalisation is available for public download.
Interval Arithmetic for Nonlinear Problem Solving
2013-01-01
Implementation of interval arithmetic in complex problems has been hampered by the tedious programming exercise needed to develop a particular implementation. In order to improve productivity, the use of interval mathematics is demonstrated using the computing platform INTLAB that allows for the development of interval-arithmetic-based programs more efficiently than with previous interval-arithmetic libraries. An interval-Newton Generalized-Bisection (IN/GB) method is developed in this platfo...
Joint source channel coding using arithmetic codes
Bi, Dongsheng
2009-01-01
Based on the encoding process, arithmetic codes can be viewed as tree codes and current proposals for decoding arithmetic codes with forbidden symbols belong to sequential decoding algorithms and their variants. In this monograph, we propose a new way of looking at arithmetic codes with forbidden symbols. If a limit is imposed on the maximum value of a key parameter in the encoder, this modified arithmetic encoder can also be modeled as a finite state machine and the code generated can be treated as a variable-length trellis code. The number of states used can be reduced and techniques used fo
Dark energy as a manifestation of nontrivial arithmetic
Czachor, Marek
2016-01-01
Arithmetic operations (addition, subtraction, multiplication, division), as well as the calculus they imply, are non-unique. The examples of four-dimensional spaces, $\\mathbb{R}_+^4$ 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 e...
Arithmetic for First Graders Lacking Number Concepts
Kamii, Constance; Rummelsburg, Judith
2008-01-01
To build cognitive foundation for number, twenty-six low-performing, low-SES first graders did mathematical physical-knowledge activities, such as "bowling," during the first half of the year. As their arithmetic readiness developed, they tried more word problems and games. At the end of the year, these children did better in mental arithmetic and…
Level statistics in arithmetical and pseudo-arithmetical chaos
Energy Technology Data Exchange (ETDEWEB)
Braun, Petr; Haake, Fritz, E-mail: Petr.Braun@uni-due.d [Fachbereich Physik, Universitaet Duisburg-Essen, 47048 Duisburg (Germany)
2010-07-02
We investigate a long-standing riddle in quantum chaos, posed by certain fully chaotic billiards with constant negative curvature whose periodic orbits are highly degenerate in length. Depending on the boundary conditions for the quantum wavefunctions, the energy spectra either have uncorrelated levels usually associated with classical integrability or conform to the 'universal' Wigner-Dyson type although the classical dynamics in both cases is the same. The resolution turns out surprisingly simple. The Maslov indices of orbits within multiplets of degenerate length either yield equal phases for the respective Feynman amplitudes (and thus Poissonian level statistics) or give rise to amplitudes with uncorrelated phases (leading to Wigner-Dyson level correlations). The recent semiclassical explanation of spectral universality in quantum chaos is thus extended to the latter case of 'pseudo-arithmetical' chaos. (fast track communication)
Secure Arithmetic Computation with No Honest Majority
Ishai, Yuval; Sahai, Amit
2008-01-01
We study the complexity of securely evaluating arithmetic circuits over finite rings. This question is motivated by natural secure computation tasks. Focusing mainly on the case of two-party protocols with security against malicious parties, our main goals are to: (1) only make black-box calls to the ring operations and standard cryptographic primitives, and (2) minimize the number of such black-box calls as well as the communication overhead. We present several solutions which differ in their efficiency, generality, and underlying intractability assumptions. These include: 1. An unconditionally secure protocol in the OT-hybrid model which makes a black-box use of an arbitrary ring $R$, but where the number of ring operations grows linearly with (an upper bound on) $\\log|R|$. 2. Computationally secure protocols in the OT-hybrid model which make a black-box use of an underlying ring, and in which the number of ring operations does not grow with the ring size. These results extend a previous approach of Naor an...
Arithmetical Chaos and Quantum Cosmology
Forte, Luca Antonio
2008-01-01
In this note, we present the formalism to start a quantum analysis for the recent billiard representation introduced by Damour, Henneaux and Nicolai in the study of the cosmological singularity. In particular we use the theory of Maass automorphic forms and recent mathematical results about arithmetical dynamical systems. The predictions of the billiard model give precise automorphic properties for the wave function (Maass-Hecke eigenform), the asymptotic number of quantum states (Selberg asymptotics for PSL(2,Z)), the distribution for the level spacing statistics (the Poissonian one) and the absence of scarred states. The most interesting implication of this model is perhaps that the discrete spectrum is fully embedded in the continuous one.
Plain Polynomial Arithmetic on GPU
Anisul Haque, Sardar; Moreno Maza, Marc
2012-10-01
As for serial code on CPUs, parallel code on GPUs for dense polynomial arithmetic relies on a combination of asymptotically fast and plain algorithms. Those are employed for data of large and small size, respectively. Parallelizing both types of algorithms is required in order to achieve peak performances. In this paper, we show that the plain dense polynomial multiplication can be efficiently parallelized on GPUs. Remarkably, it outperforms (highly optimized) FFT-based multiplication up to degree 212 while on CPU the same threshold is usually at 26. We also report on a GPU implementation of the Euclidean Algorithm which is both work-efficient and runs in linear time for input polynomials up to degree 218 thus showing the performance of the GCD algorithm based on systolic arrays.
Negative numbers in simple arithmetic.
Das, Runa; LeFevre, Jo-Anne; Penner-Wilger, Marcie
2010-10-01
Are negative numbers processed differently from positive numbers in arithmetic problems? In two experiments, adults (N = 66) solved standard addition and subtraction problems such as 3 + 4 and 7 - 4 and recasted versions that included explicit negative signs-that is, 3 - (-4), 7 + (-4), and (-4) + 7. Solution times on the recasted problems were slower than those on standard problems, but the effect was much larger for addition than subtraction. The negative sign may prime subtraction in both kinds of recasted problem. Problem size effects were the same or smaller in recasted than in standard problems, suggesting that the recasted formats did not interfere with mental calculation. These results suggest that the underlying conceptual structure of the problem (i.e., addition vs. subtraction) is more important for solution processes than the presence of negative numbers.
Critical Path Reduction of Distributed Arithmetic Based FIR Filter
Directory of Open Access Journals (Sweden)
Sunita Badave
2016-03-01
Full Text Available Operating speed, which is reciprocal of critical path computation time, is one of the prominent design matrices of finite impulse response (FIR filters. It is largely affected by both, system architecture as well as technique used to design arithmetic modules. A large computation time of multipliers in conventionally designed multipliers, limits the speed of system architecture. Distributed arithmetic is one of the techniques, used to provide multiplier-free multiplication in the implementation of FIR filter. However suffers from a sever limitation of exponential growth of look up table (LUT with order of filter. An improved distributed arithmetic technique is addressed here to design for system architecture of FIR filter. In proposed technique, a single large LUT of conventional DA is replaced by number of smaller indexed LUT pages to restrict exponential growth and to reduce system access time. It also eliminates the use of adders. Selection module selects the desired value from desired page, which leads to reduce computational time of critical path. Trade off between access times of LUT pages and selection module helps to achieve minimum critical path so as to maximize the operating speed. Implementations are targeted to Xilinx ISE, Virtex IV devices. FIR filter with 8 bit data width of input sample results are presented here. It is observed that, proposed design perform significantly faster as compared to the conventional DA and existing DA based designs.
Single-digit arithmetic in children with dyslexia.
Boets, Bart; De Smedt, Bert
2010-05-01
It has been suggested that individuals with dyslexia show poorer performance on those aspects of arithmetic that involve the manipulation of verbal representations, such as the use of fact retrieval strategies. The present study examined this in 13 children with dyslexia who showed normal general mathematics achievement and 16 matched controls. All children completed a multiplication and a subtraction task, which were specifically designed to elicit the use of retrieval and procedural strategies, respectively. Our findings revealed that despite normal mathematics achievement, children with dyslexia were less accurate and slower in single-digit arithmetic, particularly in multiplication. The reaction time data revealed an interesting group by operation interaction. Control children were significantly faster in multiplication than in subtraction, whereas no such operation effect was found in children with dyslexia. This suggests that in multiplication children with dyslexia used less retrieval or less efficient retrieval (or both). This is in line with the hypothesis that children with dyslexia may have difficulties with the verbal aspects of number and arithmetic, as retrieval strategies depend upon phonological representations in long-term memory.
Directory of Open Access Journals (Sweden)
Urszula eMihulowicz
2014-05-01
Full Text Available Different specific mechanisms have been suggested for solving single-digit arithmetic operations. However, the neural correlates underlying basic arithmetic (multiplication, addition, subtraction are still under debate. In the present study, we systematically assessed single-digit arithmetic in a group of acute stroke patients (n=45 with circumscribed left- or right-hemispheric brain lesions. Lesion sites significantly related to impaired performance were found only in the left-hemisphere damaged group. Deficits in multiplication and addition were related to subcortical/white matter brain regions differing from those for subtraction tasks, corroborating the notion of distinct processing pathways for different arithmetic tasks. Additionally, our results further point to the importance of investigating fiber pathways in numerical cognition.
Computer arithmetic and verilog HDL fundamentals
Cavanagh, Joseph
2009-01-01
Verilog Hardware Description Language (HDL) is the state-of-the-art method for designing digital and computer systems. Ideally suited to describe both combinational and clocked sequential arithmetic circuits, Verilog facilitates a clear relationship between the language syntax and the physical hardware. It provides a very easy-to-learn and practical means to model a digital system at many levels of abstraction. Computer Arithmetic and Verilog HDL Fundamentals details the steps needed to master computer arithmetic for fixed-point, decimal, and floating-point number representations for all prima
Quality of Arithmetic Education for Children with Cerebral Palsy
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…
Visuospatial and verbal memory in mental arithmetic.
Clearman, Jack; Klinger, Vojtěch; Szűcs, Dénes
2016-08-01
Working memory allows complex information to be remembered and manipulated over short periods of time. Correlations between working memory and mathematics achievement have been shown across the lifespan. However, only a few studies have examined the potentially distinct contributions of domain-specific visuospatial and verbal working memory resources in mental arithmetic computation. Here we aimed to fill this gap in a series of six experiments pairing addition and subtraction tasks with verbal and visuospatial working memory and interference tasks. In general, we found higher levels of interference between mental arithmetic and visuospatial working memory tasks than between mental arithmetic and verbal working memory tasks. Additionally, we found that interference that matched the working memory domain of the task (e.g., verbal task with verbal interference) lowered working memory performance more than mismatched interference (verbal task with visuospatial interference). Findings suggest that mental arithmetic relies on domain-specific working memory resources.
ERROR CORRECTION IN HIGH SPEED ARITHMETIC,
The errors due to a faulty high speed multiplier are shown to be iterative in nature. These errors are analyzed in various aspects. The arithmetic coding technique is suggested for the improvement of high speed multiplier reliability. Through a number theoretic investigation, a large class of arithmetic codes for single iterative error correction are developed. The codes are shown to have near-optimal rates and to render a simple decoding method. The implementation of these codes seems highly practical. (Author)
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.
A Novel Block-Based Scheme for Arithmetic Coding
Directory of Open Access Journals (Sweden)
Qi-Bin Hou
2014-06-01
Full Text Available It is well-known that for a given sequence, its optimal codeword length is fixed. Many coding schemes have been proposed to make the codeword length as close to the optimal value as possible. In this paper, a new block-based coding scheme operating on the subsequences of a source sequence is proposed. It is proved that the optimal codeword lengths of the subsequences are not larger than that of the given sequence. Experimental results using arithmetic coding will be presented.
Arithmetic geometry over global function fields
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...
Learning, Realizability and Games in Classical Arithmetic
Aschieri, Federico
2010-01-01
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...
Design of Parity Preserving Logic Based Fault Tolerant Reversible Arithmetic Logic Unit
Directory of Open Access Journals (Sweden)
Rakshith Saligram1
2013-06-01
Full Text Available Reversible Logic is gaining significant consideration as the potential logic design style for implementation in modern nanotechnology and quantum computing with minimal impact on physical entropy .Fault Tolerant reversible logic is one class of reversible logic that maintain the parity of the input and the outputs. Significant contributions have been made in the literature towards the design of fault tolerant reversible logic gate structures and arithmetic units, however, there are not many efforts directed towards the design of fault tolerant reversible ALUs. Arithmetic Logic Unit (ALU is the prime performing unit in any computing device and it has to be made fault tolerant. In this paper we aim to design one such fault tolerant reversible ALU that is constructed using parity preserving reversible logic gates. The designed ALU can generate up to seven Arithmetic operations and four logical operations
Design of Parity Preserving Logic Based Fault Tolerant Reversible Arithmetic Logic Unit
Directory of Open Access Journals (Sweden)
Rakshith Saligram
2013-07-01
Full Text Available Reversible Logic is gaining significant consideration as the potential logic design style for implementationin modern nanotechnology and quantum computing with minimal impact on physical entropy .FaultTolerant reversible logic is one class of reversible logic that maintain the parity of the input and theoutputs. Significant contributions have been made in the literature towards the design of fault tolerantreversible logic gate structures and arithmetic units, however, there are not many efforts directed towardsthe design of fault tolerant reversible ALUs. Arithmetic Logic Unit (ALU is the prime performing unit inany computing device and it has to be made fault tolerant. In this paper we aim to design one such faulttolerant reversible ALU that is constructed using parity preserving reversible logic gates. The designedALU can generate up to seven Arithmetic operations and four logical operations.
Multistate Memristive Tantalum Oxide Devices for Ternary Arithmetic
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.
Multistate Memristive Tantalum Oxide Devices for Ternary Arithmetic
Kim, Wonjoo; Chattopadhyay, Anupam; Siemon, Anne; Linn, Eike; Waser, Rainer; Rana, Vikas
2016-01-01
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. PMID:27834352
The interpretability logic of all reasonable arithmetical theories
Joosten, J.J.; Visser, A.
2008-01-01
This paper is a presentation of a status quæstionis, to wit of the problem of the interpretability logic of all reasonable arithmetical theories. We present both the arithmetical side and the modal side of the question.
Derivations and Generating Degrees in the Ring of Arithmetical Functions
Indian Academy of Sciences (India)
Alexandru Zaharescu; Mohammad Zaki
2007-05-01
In this paper we study a family of derivations in the ring of arithmetical functions of several variables over an integral domain, and compute the generating degrees of the ring of arithmetical functions over the kernel of these derivations.
Some questions on spectrum and arithmetic of locally symmetric spaces
Rajan, C S
2010-01-01
We consider the question that the spectrum and arithmetic of locally symmetric spaces defined by congruent arithmetical lattices should mutually determine each other. We frame these questions in the context of automorphic representations.
Set Theory and Arithmetic in Fuzzy Logic
Běhounek, L. (Libor); Haniková, Z. (Zuzana)
2015-01-01
This chapter offers a review of Petr Hájek’s contributions to first-order axiomatic theories in fuzzy logic (in particular, ZF-style fuzzy set theories, arithmetic with a fuzzy truth predicate, and fuzzy set theory with unrestricted comprehension schema). Generalizations of Hájek’s results in these areas to MTL as the background logic are presented and discussed.
Model Theory in Algebra, Analysis and Arithmetic
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.
Relating arithmetical techniques of proportion to geometry
DEFF Research Database (Denmark)
Wijayanti, Dyana
2015-01-01
. 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...... results show that the explanation in two domains has different approach, but basically they are mathematically related....
Arithmetic and Cognitive Contributions to Algebra
Cirino, Paul T.; Tolar, Tammy D.; Fuchs, Lynn S.
2013-01-01
Algebra is a prerequisite for access to STEM careers and occupational success (NMAP, 2008a), yet algebra is difficult for students through high school (US DOE, 2008). Growth in children's conceptual and procedural arithmetical knowledge is reciprocal, although conceptual knowledge has more impact on procedural knowledge than the reverse…
A study of a curious arithmetic function
Farhi, Bakir
2010-01-01
In this note, we study the arithmetic function $f : \\mathbb{Z}_+^* \\to \\mathbb{Q}_+^*$ defined by $f(2^k \\ell) = \\ell^{1 - k}$ ($\\forall k, \\ell \\in \\mathbb{N}$, $\\ell$ odd). We show several important properties about that function and then we use them to obtain some curious results involving the 2-adic valuation.
Retrieval-Induced Forgetting of Arithmetic Facts
Campbell, Jamie I. D.; Thompson, Valerie A.
2012-01-01
Retrieval-induced forgetting (RIF) is a widely studied phenomenon of human memory, but RIF of arithmetic facts remains relatively unexplored. In 2 experiments, we investigated RIF of simple addition facts (2 + 3 = 5) from practice of their multiplication counterparts (2 x 3 = 6). In both experiments, robust RIF expressed in response times occurred…
Secret Codes, Remainder Arithmetic, and Matrices.
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.…
Towards sensible floating-point arithmetic
Energy Technology Data Exchange (ETDEWEB)
Cody, W.J.
1980-01-01
Efforts to promote the development of high-quality transportable numerical software show that few, if any, of the floating-point arithmetic systems in existing computers are completely satisfactory for serious numerical computation. Examination of the defects in these systems leads to specifications for a sensible floating-point system from a numerical analyst's viewpoint. 1 table.
The functional anatomy of single-digit arithmetic in children with developmental dyslexia.
Evans, Tanya M; Flowers, D Lynn; Napoliello, Eileen M; Olulade, Olumide A; Eden, Guinevere F
2014-11-01
Some arithmetic procedures, such as addition of small numbers, rely on fact retrieval mechanisms supported by left hemisphere perisylvian language areas, while others, such as subtraction, rely on procedural-based mechanisms subserved by bilateral parietal cortices. Previous work suggests that developmental dyslexia, a reading disability, is accompanied by subtle deficits in retrieval-based arithmetic, possibly because of compromised left hemisphere function. To test this prediction, we compared brain activity underlying arithmetic problem solving in children with and without dyslexia during addition and subtraction operations using a factorial design. The main effect of arithmetic operation (addition versus subtraction) for both groups combined revealed activity during addition in the left superior temporal gyrus and activity during subtraction in the bilateral intraparietal sulcus, the right supramarginal gyrus and the anterior cingulate, consistent with prior studies. For the main effect of diagnostic group (dyslexics versus controls), we found less activity in dyslexic children in the left supramarginal gyrus. Finally, the interaction analysis revealed that while the control group showed a strong response in the right supramarginal gyrus for subtraction but not for addition, the dyslexic group engaged this region for both operations. This provides physiological evidence in support of the theory that children with dyslexia, because of disruption to left hemisphere language areas, use a less optimal route for retrieval-based arithmetic, engaging right hemisphere parietal regions typically used by good readers for procedural-based arithmetic. Our results highlight the importance of language processing for mathematical processing and illustrate that children with dyslexia have impairments that extend beyond reading.
Specificity and overlap in skills underpinning reading and arithmetical fluency
V. van Daal; A. van der Leij; H. Adèr
2012-01-01
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, arith
Language-specific memory for everyday arithmetic facts in Chinese-English bilinguals.
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.
Benavides-Varela, S; Piva, D; Burgio, F; Passarini, L; Rolma, G; Meneghello, F; Semenza, C
2017-03-01
Arithmetical deficits in right-hemisphere damaged patients have been traditionally considered secondary to visuo-spatial impairments, although the exact relationship between the two deficits has rarely been assessed. The present study implemented a voxelwise lesion analysis among 30 right-hemisphere damaged patients and a controlled, matched-sample, cross-sectional analysis with 35 cognitively normal controls regressing three composite cognitive measures on standardized numerical measures. The results showed that patients and controls significantly differ in Number comprehension, Transcoding, and Written operations, particularly subtractions and multiplications. The percentage of patients performing below the cutoffs ranged between 27% and 47% across these tasks. Spatial errors were associated with extensive lesions in fronto-temporo-parietal regions -which frequently lead to neglect- whereas pure arithmetical errors appeared related to more confined lesions in the right angular gyrus and its proximity. Stepwise regression models consistently revealed that spatial errors were primarily predicted by composite measures of visuo-spatial attention/neglect and representational abilities. Conversely, specific errors of arithmetic nature linked to representational abilities only. Crucially, the proportion of arithmetical errors (ranging from 65% to 100% across tasks) was higher than that of spatial ones. These findings thus suggest that unilateral right hemisphere lesions can directly affect core numerical/arithmetical processes, and that right-hemisphere acalculia is not only ascribable to visuo-spatial deficits as traditionally thought.
GDI based full adders for energy efficient arithmetic applications
Directory of Open Access Journals (Sweden)
Mohan Shoba
2016-03-01
Full Text Available Addition is a vital arithmetic operation and acts as a building block for synthesizing all other operations. A high-performance adder is one of the key components in the design of application specific integrated circuits. In this paper, three low power full adders are designed with full swing AND, OR and XOR gates to alleviate threshold voltage problem which is commonly encountered in Gate Diffusion Input (GDI logic. This problem usually does not allow the full adder circuits to operate without additional inverters. However, the three full adders are successfully realized using full swing gates with the significant improvement in their performance. The performance of the proposed designs is compared with the other full adder designs, namely CMOS, CPL, hybrid and GDI through SPICE simulations using 45 nm technology models. Simulation results reveal that proposed designs have lower energy consumption among all the conventional designs taken for comparison.
Interval Semantics for Standard Floating-Point Arithmetic
Edmonson, W W
2008-01-01
If the non-zero finite floating-point numbers are interpreted as point intervals, then the effect of rounding can be interpreted as computing one of the bounds of the result according to interval arithmetic. We give an interval interpretation for the signed zeros and infinities, so that the undefined operations 0*inf, inf - inf, inf/inf, and 0/0 become defined. In this way no operation remains that gives rise to an error condition. Mathematically questionable features of the floating-point standard become well-defined sets of reals. Interval semantics provides a basis for the verification of numerical algorithms. We derive the results of the newly defined operations and consider the implications for hardware implementation.
On automatic differentiation of codes with COMPLEX arithmetic with respect to real variables
Energy Technology Data Exchange (ETDEWEB)
Pusch, G.D.; Bischof, C. [Argonne National Lab., IL (United States); Carle, A. [Rice Univ., St. Houston, TX (United States)
1995-06-01
We explore what it means to apply automatic differentiation with respect to a set of real variables to codes containing complex arithmetic. That is, both dependent and independent variables with respect to differentiation are real variables, but in order to exploit features of complex mathematics, part of the code is expressed by employing complex arithmetic. We investigate how one can apply automatic differentiation to complex variables if one exploits the homomorphism of the complex numbers C onto R{sup 2}. It turns out that, by and large, the usual rules of differentiation apply, but subtle differences in special cases arise for sqrt (), abs (), and the power operator.
Arithmetic Practice Can Be Modified to Promote Understanding of Mathematical Equivalence
McNeil, Nicole M.; Fyfe, Emily R.; Dunwiddie, April E.
2015-01-01
This experiment tested if a modified version of arithmetic practice facilitates understanding of math equivalence. Children within 2nd-grade classrooms (N = 166) were randomly assigned to practice single-digit addition facts using 1 of 2 workbooks. In the control workbook, problems were presented in the traditional "operations = answer"…
The Duality of Zero in the Transition from Arithmetic to Algebra
Gallardo, Aurora; Hernandez, Abraham
2005-01-01
This article shows that the recognition of the dualities in equality (operator-equivalent) of the minus sign (unary-binary) and the zero (nullity-totality) during the transitional process from arithmetic to algebra by 12-13 year-old students constitutes a possible way to achieve the extension of the natural number domain to the integers. (Contains…
A Maximum Time Difference Pipelined Arithmetic Unit Based on CMOS Gate Array
Institute of Scientific and Technical Information of China (English)
唐志敏; 夏培肃
1995-01-01
This paper describes a maximum time difference pipelined arithmetic chip,the 36-bit adder and subtractor based on 1.5μm CMOS gate array.The chip can operate at 60MHz,and consumes less than 0.5Watt.The results are also studied,and a more precise model of delay time difference is proposed.
The Performance of Chinese Primary School Students on Realistic Arithmetic Word Problems
Xin, Ziqiang; Lin, Chongde; Zhang, Li; Yan, Rong
2007-01-01
Compared with standard arithmetic word problems demanding only the direct use of number operations and computations, realistic problems are harder to solve because children need to incorporate "real-world" knowledge into their solutions. Using the realistic word problem testing materials developed by Verschaffel, De Corte, and Lasure…
Floating-point arithmetic unit for pro-log based control systems
Energy Technology Data Exchange (ETDEWEB)
Macmillan, D.C.
1978-01-01
A floating-point unit was designed for use with control systems based on Pro-Log four-bit or eight-bit microprocessors. The unit consists of a single board which can be pin-connected into existing control systems. It provides the capability for floating-point arithmetic computations, including operations with transcendental and exponential functions. 9 figures, 2 tables.
Spatial ability explains the male advantage in approximate arithmetic
Directory of Open Access Journals (Sweden)
Wei eWei
2016-03-01
Full Text Available Previous research has shown that females consistently outperform males in exact arithmetic, perhaps due to the former’s advantage in language processing. Much less is known about gender difference in approximate arithmetic. Given that approximate arithmetic is highly associated with visuospatial processing and there is a male advantage in visuospatial processing, we hypothesized that males would perform better than females in approximate arithmetic. In two experiments (496 children in Experiment 1 and 554 college students in Experiment 2, we found that males showed better performance in approximate arithmetic. Furthermore, gender differences in approximate were accounted for by gender differences in spatial ability.
HIGH SPEED POINT ARITHMETIC ARCHITECTURE FOR ECC ON FPGA
Directory of Open Access Journals (Sweden)
Rahila Bilal,
2010-09-01
Full Text Available Elliptic curve cryptography plays a crucial role in networking and communication security. ECC have evolved in the recent past as an important alternative to established systems like RSA. This paper describes the implementation of an elliptic curve coprocessor based on the FPGA , which can provide a significant speedup for these cryptosystems. The FPGA configuration file is synthesized from VHDL code applying different hardware synthesis products. The implementation of ECC lies in three levels: scalar multiplication, point addition/doubling and finite field modular arithmetic. In this paper, we present a novel fast architecture for the point addition/doubling level in the projective coordinate. The proposed Architecture is based on Binary Field. The Design performs multiplication using Polynomial Basis. Analysis shows that, with reasonable hardware overhead, our architecture can achieve a high speedup for the point addition operation and point Doubling operation.Furthermore, the architecture is parameterized for different data widths to evaluate the optimal resource utilization.
Floating-Point Arithmetic on Round-to-Nearest Representations
Kornerup, Peter; Panhaleux, Adrien
2012-01-01
Recently we introduced a class of number representations denoted RN-representations, allowing an un-biased rounding-to-nearest to take place by a simple truncation. In this paper we briefly review the binary fixed-point representation in an encoding which is essentially an ordinary 2's complement representation with an appended round-bit. Not only is this rounding a constant time operation, so is also sign inversion, both of which are at best log-time operations on ordinary 2's complement representations. Addition, multiplication and division is defined in such a way that rounding information can be carried along in a meaningful way, at minimal cost. Based on the fixed-point encoding we here define a floating point representation, and describe to some detail a possible implementation of a floating point arithmetic unit employing this representation, including also the directed roundings.
Recursive double-size fixed precision arithmetic
Chabot, Christophe; Fousse, Laurent; Giorgi, Pascal
2011-01-01
This work is a part of the SHIVA (Secured Hardware Immune Versatile Architecture) project whose purpose is to provide a programmable and reconfigurable hardware module with high level of security. We propose a recursive double-size fixed precision arithmetic called RecInt. Our work can be split in two parts. First we developped a C++ software library with performances comparable to GMP ones. Secondly our simple representation of the integers allows an implementation on FPGA. Our idea is to consider sizes that are a power of 2 and to apply doubling techniques to implement them efficiently: we design a recursive data structure where integers of size 2^k, for k>k0 can be stored as two integers of size 2^{k-1}. Obviously for k<=k0 we use machine arithmetic instead (k0 depending on the architecture).
Dictionary of algebra, arithmetic, and trigonometry
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...
Arithmetic Properties of the Ramanujan Function
Indian Academy of Sciences (India)
Florian Luca; Igor E Shparlinski
2006-02-01
We study some arithmetic properties of the Ramanujan function (), such as the largest prime divisor ( ()) and the number of distinct prime divisors (()) of () for various sequences of . In particular, we show that ( ()) ≥ $(\\log n)^{33/31+(1)}$ for infinitely many , and $$P((p)(p^2)(p^3))>(1+(1))\\frac{\\log\\log p\\log\\log\\log p}{\\log\\log\\log\\log p}$$ for every prime with $(p)≠ 0$.
Arithmetic Algorithms for Hereditarily Binary Natural Numbers
Tarau, Paul
2013-01-01
We study some essential arithmetic properties of a new tree-based number representation, {\\em hereditarily binary numbers}, defined by applying recursively run-length encoding of bijective base-2 digits. Our representation expresses giant numbers like the largest known prime number and its related perfect number as well as the largest known Woodall, Cullen, Proth, Sophie Germain and twin primes as trees of small sizes. More importantly, our number representation supports novel algorithms that...
Arithmetic expressions optimisation using dual polarity property
Moraga Claudio; Stanković Radomir S.; Janković Dragan
2003-01-01
A method for optimisation of fixed polarity arithmetic expressions (FPAEs) based on dual polarity is proposed. The method exploits a simple relationship between two FPAEs for dual polarities. It starts from the zero polarity FPAE of the given function and calculates all FPAEs using the dual polarity route. Using one-bit check carries out conversion from one FPAE to another. Each term in an FPAE is processed by the proposed processing rule. Terms, which differ in a single position, can be subs...
Embedded systems design with special arithmetic and number systems
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.
Beyond-Binary Arithmetic: Algorithms and VLSI Implementations
Aoki, Takafumi; Higuchi, Tatsuo
2000-01-01
Beyond-binary arithmetic algorithms are defined as a new class of computer arithmetic algorithms which employ non-binary data representations to achieve higher performances beyond those of conventional binary algorithms. This paper presents prominent examples of beyond-binary arithmetic algorithms: examples include (i) a high-radix redundant division algorithm without using lookup tables, (ii) a high-radix redundant CORDIC algorithm for fast vector rotation, and (iii) redundant complex arithm...
A Geometric Characterization of Arithmetic Varieties
Indian Academy of Sciences (India)
Kapil Hari Paranjape
2002-08-01
A result of Belyi can be stated as follows. Every curve defined over a number field can be expressed as a cover of the projective line with branch locus contained in a rigid divisor. We define the notion of geometrically rigid divisors in surfaces and then show that every surface defined over a number field can be expressed as a cover of the projective plane with branch locus contained in a geometrically rigid divisor in the plane. The main result is the characterization of arithmetically defined divisors in the plane as geometrically rigid divisors in the plane.
Floating point arithmetic in future supercomputers
Bailey, David H.; Barton, John T.; Simon, Horst D.; Fouts, Martin J.
1989-01-01
Considerations in the floating-point design of a supercomputer are discussed. Particular attention is given to word size, hardware support for extended precision, format, and accuracy characteristics. These issues are discussed from the perspective of the Numerical Aerodynamic Simulation Systems Division at NASA Ames. The features believed to be most important for a future supercomputer floating-point design include: (1) a 64-bit IEEE floating-point format with 11 exponent bits, 52 mantissa bits, and one sign bit and (2) hardware support for reasonably fast double-precision arithmetic.
L Functions and arithmetic : L Functions and arithmetic at Harvard, June 2016
Ruíz Duarte, Eduardo
2016-01-01
This is a document which has the notes from my favourite talks at the congress L-Functions and arithmetic, at Harvard on June 9-13, 2016. The information of this document was made with all the pictures of slides I took and notes from the blackboard according to my understanding, and my questions to
Arithmetic after School: How Do Adults' Mental Arithmetic Abilities Evolve with Age?
Charron, Camilo; Fischer, Jean-Paul; Meljac, Claire
2008-01-01
To date, few studies have investigated the evolution of problem solving and general numeracy abilities during adulthood: skills that have obvious social importance. In this research, evolutions in adults' mental arithmetic skills were investigated using data from the IVQ 2004 French national survey, which tested 9,185 adults aged between 18 and…
On the Formalist Theory of Arithmetic
Boyce, Stephen
2010-01-01
This paper presents evidence that the metatheory of the (formalist) first order theory of arithmetic is subject to paradox. For the proof of this claim I exhibit a classical first-order number theory S' that results from modifications of Mendelson's S such that: the consistency of S implies that S' is consistent and yet S' is inconsistent. S' results from Mendelson's S when: 'a2' is added to the primitive symbols (and formation rules appropriately modified); the notion of an 'interpretation' is modified so that 'a2' is informally, an arbitrary numeral; every formula that is an instance of the following schema is added as a proper axiom: B[a2] => (x)B[x] (where B[a2] is the result of substituting 'a2' for every free occurrence of x in B[x]). Since S' contains Peano arithmetic and is recursively axiomatised we can modify G\\"odel's technique to define a G\\"odel sentence for S', say (x)R[x]. S' may be shown to be inconsistent since(x)R[x] must be an S' theorem. The result is difficult to square with the accepted ...
Masson, Nicolas; Pesenti, Mauro
2016-07-01
Solving arithmetic problems has been shown to induce shifts of spatial attention in simple probe-detection tasks, subtractions orienting attention to the left side and additions to the right side of space. Whether these attentional shifts constitute epiphenomena or are critically linked to the calculation process is still unknown. In the present study, we investigate participants' performance on addition and subtraction solving while they have to detect central or lateralized targets. The results show that lateralized distractors presented in the hemifield congruent to the operation to be solved interfere with arithmetical solving: participants are slower to solve subtractions or additions when distractors are located on the left or on the right, respectively. These results converge with previous data to show that attentional shifts underlie not only number processing but also mental arithmetic. They extend them as they reveal the reverse effect of the one previously reported by showing that inducing attention shifts interferes with the solving of arithmetic problems. They also demonstrate that spatial attentional shifts are part of the calculation procedure of solving mentally arithmetic problems. Their functional role is to access, from the first operand, the representation of the result in a direction congruent to the operation.
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.
Transfer Effects in Children's Recall of Arithmetic Facts
van Galen, Mirte S.; Reitsma, Pieter
2011-01-01
Predictions of the Identical Elements (IE) model of arithmetic fact representation (Rickard, 2005; Rickard & Bourne, 1996) about transfer between arithmetic facts were tested in primary school children. The aim of the study was to test whether the IE model, constructed to explain adult performance, also applies to children. The IE model…
A novel chaotic encryption scheme based on arithmetic coding
Energy Technology Data Exchange (ETDEWEB)
Mi Bo [Department of Computer Science and Engineering, Chongqing University, Chongqing 400044 (China)], E-mail: mi_bo@163.com; Liao Xiaofeng; Chen Yong [Department of Computer Science and Engineering, Chongqing University, Chongqing 400044 (China)
2008-12-15
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.
Typing a Core Binary Field Arithmetic in a Light Logic
Cesena, Emanuele; Pedicini, Marco; Roversi, Luca
2011-01-01
We design a library for binary field arithmetic and we supply a core API which is completely developed in DLAL, extended with a fix point formula. Since DLAL is a restriction of linear logic where only functional programs with polynomial evaluation cost can be typed, we obtain the core of a functional programming setting for binary field arithmetic with built-in polynomial complexity.
Conceptual knowledge of arithmetic for Chinese- and Canadian-educated adults.
Robinson, Katherine M; Beatch, Jacqueline-Ann
2016-12-01
This study investigated whether Canadian- and Chinese-educated adults differ in their understanding of simple arithmetic concepts. Participants (n = 21 per group) solved 3-term addition and subtraction (e.g., 5 + 22 - 22 and 3 + 24 - 26) and multiplication and division (e.g., 2 × 28 ÷ 28 and 4 × 39 ÷ 13) problems. All problems could be solved more easily if conceptual knowledge of the relationship between the 2 operations in each problem was understood and applied. Accuracy, solution time, and immediately retrospective self-reports of problem-solving strategy data were collected. Participants also completed a timed arithmetic fluency task. Chinese-educated participants demonstrated stronger conceptual understanding of arithmetic on all problems and outperformed Canadian-educated participants on the fluency task. A cluster analysis revealed 4 groups of individuals: weak concept users, who rarely used conceptual knowledge to aid their problem solving; strong concept users, who almost exclusively used their conceptual knowledge to facilitate problem solving; addition and subtraction concept users, who frequently used conceptual knowledge except on difficult multiplication and division problems; and multiplication and division concept users, who frequently used conceptual knowledge except on difficult addition and subtraction problems. Chinese-educated participants were more likely to be in the strong concept clusters, and none were in the weak concept cluster, providing further evidence of stronger conceptual knowledge of arithmetic. These results demonstrate for the 1st time that there are strong cross-cultural differences in conceptual knowledge of simple arithmetic, even in adulthood. (PsycINFO Database Record
Computer Arithmetic Algorithms for Mega-Digit Floating Point Numbers' Precision
Directory of Open Access Journals (Sweden)
Musbah J. Aqel
2007-01-01
Full Text Available IEEE standard 754 floating point is the most common representation used for floating point numbers, and many computer arithmetic algorithms are developed for basic operations on this standard. In this study, new computer algorithms are proposed to increase the precision range and to solve some problems that are available while using these algorithms. However, these algorithms provide an optional range of required accuracy (Mega-Digit precision to meet new computer's applications.
Directory of Open Access Journals (Sweden)
Lucimar M.F. de Carvalho
2008-06-01
Full Text Available OBJECTIVE: To investigate different fuzzy arithmetical operations to support in the diagnostic of epileptic events and non epileptic events. METHOD: A neuro-fuzzy system was developed using the NEFCLASS (NEuro Fuzzy CLASSIfication architecture and an artificial neural network with backpropagation learning algorithm (ANNB. RESULTS: The study was composed by 244 patients with a bigger frequency of the feminine sex. The number of right decisions at the test phase, obtained by the NEFCLASS and ANNB was 83.60% and 90.16%, respectively. The best sensibility result was attained by NEFCLASS (84.90%; the best specificity result were attained by ANNB with 95.65%. CONCLUSION: The proposed neuro-fuzzy system combined the artificial neural network capabilities in the pattern classifications together with the fuzzy logic qualitative approach, leading to a bigger rate of system success.OBJETIVO: Investigar diferentes operações aritméticas difusas para auxíliar no diagnóstico de eventos epilépticos e eventos não-epilépticos. MÉTODO: Um sistema neuro-difuso foi desenvolvido utilizando a arquitetura NEFCLASS (NEuro Fuzzy CLASSIfication e uma rede neural artificial com o algoritmo de aprendizagem backpropagation (RNAB. RESULTADOS: A amostra estudada foi de 244 pacientes com maior freqüência no sexo feminino. O número de decisões corretas na fase de teste, obtidas através do NEFCLASS e RNAB foi de 83,60% e 90,16%, respectivamente. O melhor resultado de sensibilidade foi obtido com o NEFCLASS (84,90%; o melhor resultado de especificidade foi obtido com a RNAB (95,65%. CONCLUSÃO: O sistema neuro-difuso proposto combinou a capacidade das redes neurais artificiais na classificação de padrões juntamente com a abordagem qualitativa da logica difusa, levando a maior taxa de acertos do sistema.
On the pullback of an arithmetic theta function
Kudla, Stephen
2011-01-01
In this paper, we consider the relation between the simplest types of arithmetic theta series, those associated to the cycles on the moduli space $\\Cal C$ of elliptic curves with CM by the ring of integers $\\OK$ in an imaginary quadratic field $\\kay$, on the one hand, and those associated to cycles on the arithmetic surface $\\M$ parametrizing 2-dimensional abelian varieties with an action of the maximal order $O_B$ in an indefinite quaternion algebra $B$ over $\\Q$, on the other. We show that the arithmetic degree of the pullback to $Cal C$ of the arithmetic theta function of weight 3/2 valued in $\\hat CH^1(\\M)$ can be expressed as a linear combination of arithmetic theta functions of weight 1 for $\\Cal C$ and unary theta series. This identity can be viewed as an arithmetic seesaw identity. In addition, we show that the arithmetic theta series of weight 1 coincide with the central derivative of certain incoherent Eisenstein series for SL(2)/Q, generalizing earlier joint work with M. Rapoport for the case of a ...
Software implementation of floating-Point arithmetic on a reduced-Instruction-set processor
Energy Technology Data Exchange (ETDEWEB)
Gross, T.
1985-11-01
Current single chip implementations of reduced-instruction-set processors do not support hardware floating-point operations. Instead, floating-point operations have to be provided either by a coprocessor or by software. This paper discusses issues arising from a software implementation of floating-point arithmetic for the MIPS processor, an experimental VLSI architecture. Measurements indicate that an acceptable level of performance is achieved, but this approach is no substitute for a hardware accelerator if higher-precision results are required. This paper includes instruction profiles for the basic floating-point operations and evaluates the usefulness of some aspects of the instruction set.
Similarity interference in learning and retrieving arithmetic facts.
De Visscher, A; Noël, M-P
2016-01-01
Storing the solution of simple calculations in long-term memory is an important learning in primary school that is subsequently essential in adult daily living. While most children succeed in storing arithmetic facts to which they have been trained at school, huge individual differences are reported, particularly in children with developmental dyscalculia, who show a severe and persistent deficit in arithmetic facts learning. This chapter reports important advances in the understanding of the development of an arithmetic facts network and focuses on the detrimental effect of similarity interference. First, at the retrieval stage, connectionist models highlighted that the similarity of the neighbor problems in the arithmetic facts network creates interference. More recently, the similarity interference during the learning stage was pointed out in arithmetic facts learning. The interference parameter, that captures the proactive interference that a problem receives from previously learned problems, was shown as a substantial determinant of the performance across multiplication problems. This proactive interference was found both in children and adults and showed that when a problem is highly similar to previously learned ones, it is more difficult to remember it. Furthermore, the sensitivity to this similarity interference determined individual differences in the learning and retrieving of arithmetic facts, giving new insights for interindividual differences. Regarding the atypical development, hypersensitivity-to-interference in memory was related to arithmetic facts deficit in a single case of developmental dyscalculia and in a group of fourth-grade children with low arithmetic facts knowledge. In sum, the impact of similarity interference is shown in the learning stage of arithmetic facts and concerns the typical and atypical development.
An Efficient Adaptive Binary Arithmetic Coder Based on Logarithmic Domain.
Yu, Quanhe; Yu, Wei; Yang, Ping; Zheng, Jianhua; Zheng, Xiaozhen; He, Yun
2015-11-01
This paper proposes an efficient adaptive binary arithmetic coder based on a logarithmic domain (LBAC) and a probability estimation based on the LBAC (P-LBAC). Both the LBAC and the P-LBAC achieve a high data-compression ratio with low complexity and a hardware-efficient structure. They introduce a mapping mechanism between the logarithmic domain and the original domain for both the coding process and the probability estimation. The proposed schemes have high accuracy and constitute an efficient BAC. The proposed LBAC and P-LBAC do not use either multiplication and division operations or lookup tables, and only addition and shifting operations are required. The proposed LBAC is designed to favor the coding of multiple symbols and has high throughput. The proposed P-LBAC achieves a good tradeoff between accuracy and speed in probability estimation through a single parameter. When the proposed algorithms are implemented on H.265/HEVC platforms, and they achieve a compression efficiency equivalent to that of CABAC.
Fleeting footsteps tracing the conception of arithmetic and algebra in ancient China
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.
A Novel Three-Moduli Set and its Associated Arithmetic Residue to Binary Converter
Directory of Open Access Journals (Sweden)
Mohammad Mehdi Lotfinejad
2016-05-01
Full Text Available Residue number system (RNS is a non-weighted and carry-free number system which is suitable for high speed and parallel arithmetic operations. The complexity and efficiency of RNS arithmetic hardware design are highly influenced by two critical issues including ithe selected moduli set and iithe residue to binary conversion algorithm. In this paper we propose a new three-moduli set {22n-1, 2n+1, 2n-1} and then introduce a cost-efficient and a speed-efficient residue to binary converters for the proposed moduli set. The proposed moduli set consists of pair wise relatively prime and balanced moduli, which can offer fast internal RNS processing and efficient implementation of the residue to binary converter. The proposed residue to binary converters are memory less and consist of adders. In comparison with other residue to binary converters for a three-moduli set, the proposed converters have better area-time complexity.
Frege, Dedekind, and Peano on the foundations of arithmetic
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
Pricing Arithmetic Asian Options under the CEV Process
Directory of Open Access Journals (Sweden)
Bin Peng
2010-12-01
Full Text Available This paper discusses the pricing of arithmetic Asian options when the underlying stock follows the constant elasticity of variance (CEV process. We build a binomial tree method to estimate the CEV process and use it to price arithmetic Asian options. We find that the binomial tree method for the lognormal case can effectively solve the computational problems arising from the inherent complexities of arithmetic Asian options when the stock price follows CEV process. We present numerical results to demonstrate the validity and the convergence of the approach for the different parameter values set in CEV process.
On interpretations of bounded arithmetic and bounded set theory
Pettigrew, Richard
2008-01-01
In a recent paper, Kaye and Wong proved the following result, which they considered to belong to the folklore of mathematical logic. THEOREM: The first-order theories of Peano arithmetic and ZF with the axiom of infinity negated are mutually interpretable with interpretations that are inverse to each other. In this note, I describe a theory of sets that stands in the same relation to the bounded arithmetic IDelta0 + exp. Because of the weakness of this theory of sets, I cannot straightforwardly adapt Kaye and Wong's interpretation of the arithmetic in the set theory. Instead, I am forced to produce a different interpretation.
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
Evaluation of Huffman and Arithmetic Algorithms for Multimedia Compression Standards
Shahbahrami, Asadollah; Rostami, Mobin Sabbaghi; Mobarhan, Mostafa Ayoubi
2011-01-01
Compression is a technique to reduce the quantity of data without excessively reducing the quality of the multimedia data. The transition and storing of compressed multimedia data is much faster and more efficient than original uncompressed multimedia data. There are various techniques and standards for multimedia data compression, especially for image compression such as the JPEG and JPEG2000 standards. These standards consist of different functions such as color space conversion and entropy coding. Arithmetic and Huffman coding are normally used in the entropy coding phase. In this paper we try to answer the following question. Which entropy coding, arithmetic or Huffman, is more suitable compared to other from the compression ratio, performance, and implementation points of view? We have implemented and tested Huffman and arithmetic algorithms. Our implemented results show that compression ratio of arithmetic coding is better than Huffman coding, while the performance of the Huffman coding is higher than A...
Distributed Arithmetic Coding for the Asymmetric Slepian-Wolf problem
Grangetto, M; Olmo, G
2007-01-01
Distributed source coding schemes are typically based on the use of channels codes as source codes. In this paper we propose a new paradigm, termed "distributed arithmetic coding", which exploits the fact that arithmetic codes are good source as well as channel codes. In particular, we propose a distributed binary arithmetic coder for Slepian-Wolf coding with decoder side information, along with a soft joint decoder. The proposed scheme provides several advantages over existing Slepian-Wolf coders, especially its good performance at small block lengths, and the ability to incorporate arbitrary source models in the encoding process, e.g. context-based statistical models. We have compared the performance of distributed arithmetic coding with turbo codes and low-density parity-check codes, and found that the proposed approach has very competitive performance.
Finite Field Arithmetic Architecture Based on Cellular Array
Directory of Open Access Journals (Sweden)
Kee-Won Kim
2015-05-01
Full Text Available Recently, various finite field arithmetic structures are introduced for VLSI circuit implementation on cryptosystems and error correcting codes. In this study, we present an efficient finite field arithmetic architecture based on cellular semi-systolic array for Montgomery multiplication by choosing a proper Montgomery factor which is highly suitable for the design on parallel structures. Therefore, our architecture has reduced a time complexity by 50% compared to typical architecture.
Guest Editors' Introduction: Special Section on Computer Arithmetic
DEFF Research Database (Denmark)
Nannarelli, Alberto; Seidel, Peter-Michael; Tang, Ping Tak Peter
2014-01-01
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 and th...... engineering. Advances in this field span from being highly theoretical (for instance, new exotic number systems) to being highly practical (for instance, new floating-point units for microprocessors)....
Torsionfree Sheaves over a Nodal Curve of Arithmetic Genus One
Indian Academy of Sciences (India)
Usha N Bhosle; Indranil Biswas
2008-02-01
We classify all isomorphism classes of stable torsionfree sheaves on an irreducible nodal curve of arithmetic genus one defined over $\\mathbb{C}$. Let be a nodal curve of arithmetic genus one defined over $\\mathbb{R}$, with exactly one node, such that does not have any real points apart from the node. We classify all isomorphism classes of stable real algebraic torsionfree sheaves over of even rank. We also classify all isomorphism classes of real algebraic torsionfree sheaves over of rank one.
A Computational Interpretation of the Axiom of Determinacy in Arithmetic
Hida, Takanori
2012-01-01
We investigate the computational content of the axiom of determinacy (AD) in the setting of classical arithmetic in all finite types with the principle of dependent choices (DC). By employing the notion of realizability interpretation for arithmetic given by Berardi, Bezem and Coquand (1998), we interpret the negative translation of AD. Consequently, the combination of the negative translation with this realizability semantics can be seen as a model of DC, AD and the negation of the axiom of ...
Unseen But not Unsolved: Doing Arithmetic Non-Consciously
Sklar, Asael Y.; Hassin, Ran R.
2011-01-01
The modal view in the cognitive sciences holds that consciousness is necessary for abstract, symbolic and rule-following computations. Hence, mathematical thinking in general, and doing arithmetic more specifically, are widely believed to require consciousness. In the current paper we use continuous flash suppression to expose participants to extremely long-duration (up to 2000 milliseconds) subliminal arithmetic equations. The results of three experiments show that the equations were solved ...
Lossless compression catalyst based on binary allocation via modular arithmetic
Mastriani, Mario
2014-01-01
A new binary (bit-level) lossless compression catalyst method based on a modular arithmetic, called Binary Allocation via Modular Arithmetic (BAMA), has been introduced in this paper. In other words, BAMA is for storage and transmission of binary sequences, digital signal, images and video, also streaming and all kinds of digital transmission. As we said, our method does not compress, but facilitates the action of the real compressor, in our case, any lossless compression algorithm (Run Lengt...
Finite and Infinite Arithmetic Progressions Related to Beta-Expansion
Directory of Open Access Journals (Sweden)
Bing Li
2014-01-01
Full Text Available Let 1<β<2 and ε(x,β be the β-expansion of x∈[0,1. Denote by Aβ(x the set of positions where the digit 1 appears in ε(x,β. We consider the sets of points x such that Aβ(x contains arbitrarily long arithmetic progressions and includes infinite arithmetic progressions, respectively. Their sizes are investigated from the topological, metric, and dimensional viewpoints.
Conference on Number Theory and Arithmetic Geometry
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, ...
A pipelined 50-MHz CMOS 64-bit floating-point arithmetic processor
Energy Technology Data Exchange (ETDEWEB)
Benschneider, B.J.; Bowhill, W.J.; Cooper, E.M.; Gronowski, P.E.; Peng, V.; Pickholtz, J.D.; Samudrala, S. (Digital Equipment Corp., Hudson, MA (US)); Gavrielov, M.N. (LSI Logic Corp., Milpitas, CA (US)); Maheshwari, V.K. (AT and T Bell Labs., Allentown, PA (US))
1989-10-01
A 135 K transistor, uniformly pipelined 50-MHz CMOS 64-bit floating-point arithmetic processor chip is described. The execution unit is capable of sustaining pipelined performance of one 32-bit or 64-bit result every 20 ns for all operations except double-precision multiply (40 ns) and divide. The chip employs an exponent difference prediction scheme and a unified leading-one and sticky-bit computation logic for the addition (ADD) and subtraction (SUB) operations. A hardware multiplier using a radix-8 modified Booth algorithm and a divider using a radix-2 SRT algorithm ar used.
Zou, Tiefang; Peng, Haitao; Cai, Ming; Wu, Hequan; Hu, Lin
2016-09-01
In order to analyze the uncertainty of a reconstructed result, the Interval Algorithm (IA), the Affine Arithmetic (AA) and the Modified Affine Arithmetic (MAA) were introduced firstly, and then a Taylor-Affine Arithmetic (TAA) was proposed based on the MAA and Taylor series. Steps of the TAA, especially in analyzing uncertainty of a simulation result were given. Through the preceding five numerical cases, its application was demonstrated and its feasibility was validated. Results showed that no matter other methods (The IA, AA, the Upper and Lower bound Method, the Finite Difference Method) work well or bad, the TAA work well, even under the condition that the MAA cannot work in some cases because of the division/root operation in these models. Furthermore, in order to make sure that the result obtained from the TAA can be very close to the accurate interval, a simple algorithm was proposed based on the sub-interval technique, its feasibility was validated by two other numerical cases. Finally, a vehicle-pedestrian test was given to demonstrate the application of the TAA in practice. In the vehicle-pedestrian test, the interval [35.5, 39.1]km/h of the impact velocity can be calculated according to steps of the TAA, such interval information will be more useful in accident responsibility identification than a single number. This study will provide a new alternative method for uncertainty analysis in accident reconstruction.
Dumas, Jean-Guillaume
2007-01-01
We present an algorithm to perform arithmetic operations over small extension field via numerical routines. The idea is to convert the $X$-adic representation of modular polynomials, with $X$ an indeterminate, to a $q$-adic representation where $q$ is a prime power larger than the field characteristic. With some control on the different involved sizes it is then possible to perform some of the $q$-adic arithmetic directly with floating point operators. Depending also on the number of performed numerical operations one can then convert back to the $q$-adic or $X$-adic representation and eventually mod out high residues. In this note we present a new version of both conversions: more tabulations and a way to reduce the number of divisions involved in the process are presented.
Reading, arithmetic, and task orientation--how are they related?
Lundberg, Ingvar; Sterner, Görel
2006-12-01
A sample of 60 children in Grade 3 was followed over one year. In the first year, an extensive battery of assessments was used including aspects of reading, arithmetic, and working memory. Teachers rated the children on 7-point scales on various motivational dimensions summarized to a total score tentatively called task orientation. In the follow-up assessment one year later, the testing and teacher ratings were repeated. The cross-sectional correlations between reading, arithmetic, and task orientation were all high (about +.70). The high correlation between reading and arithmetic decreased significantly when task orientation was partialed out, and it was further reduced when working memory as assessed by backward digit span was added to the controlling factors. Also, teacher ratings of cognitive ability and language development accounted for some of the common variance between reading and arithmetic. The correlation between task orientation and school achievement cannot be causally interpreted in cross-sectional designs. Some support for a "causal" hypothesis, however, was obtained in crosslagged correlation analyses indicating that task orientation in Grade 3 may have a causal impact on the level of performance in reading, and in arithmetic in Grade 4. Most likely, however, there is also a reciprocal relationship.
Number processing and arithmetic skills in children with cochlear implants
Pixner, Silvia; Leyrer, Martin; Moeller, Korbinian
2014-01-01
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. PMID:25566152
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.
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.
Institute of Scientific and Technical Information of China (English)
Prabhu E; Mangalam H; Karthick S
2016-01-01
In this work, power efficient butterfly unit based FFT architecture is presented. The butterfly unit is designed using floating-point fused arithmetic units. The fused arithmetic units include two-term dot product unit and add-subtract unit. In these arithmetic units, operations are performed over complex data values. A modified fused floating-point two-term dot product and an enhanced model for the Radix-4 FFT butterfly unit are proposed. The modified fused two-term dot product is designed using Radix-16 booth multiplier. Radix-16 booth multiplier will reduce the switching activities compared to Radix-8 booth multiplier in existing system and also will reduce the area required. The proposed architecture is implemented efficiently for Radix-4 decimation in time (DIT) FFT butterfly with the two floating-point fused arithmetic units. The proposed enhanced architecture is synthesized, implemented, placed and routed on a FPGA device using Xilinx ISE tool. It is observed that the Radix-4 DIT fused floating-point FFT butterfly requires 50.17% less space and 12.16% reduced power compared to the existing methods and the proposed enhanced model requires 49.82% less space on the FPGA device compared to the proposed design. Also, reduced power consumption is addressed by utilizing the reusability technique, which results in 11.42% of power reduction of the enhanced model compared to the proposed design.
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.
Design and Implementation of Fixed Point Arithmetic Unit
Directory of Open Access Journals (Sweden)
S Ramanathan
2016-06-01
Full Text Available This paper aims at Implementation of Fixed Point Arithmetic Unit. The real number is represented in Qn.m format where n is the number of bits to the left of the binary point and m is the number of bits to the right of the binary point. The Fixed Point Arithmetic Unit was designed using Verilog HDL. The Fixed Point Arithmetic Unit incorporates adder, multiplier and subtractor. We carried out the simulations in ModelSim and Cadence IUS, used Cadence RTL Compiler for synthesis and used Cadence SoC Encounter for physical design and targeted 180 nm Technology for ASIC implementation. From the synthesis result it is found that our design consumes 1.524 mW of power and requires area 20823.26 μm2 .
Image compression with QM-AYA adaptive binary arithmetic coder
Cheng, Joe-Ming; Langdon, Glen G., Jr.
1993-01-01
The Q-coder has been reported in the literature, and is a renorm-driven binary adaptive arithmetic coder. A similar renorm-driven coder, the QM coder, uses the same approach with an initial attack to more rapidly estimate the statistics in the beginning, and with a different state table. The QM coder is the adaptive binary arithmetic coder employed in the JBIG and JPEG image compression algorithms. The QM-AYA arithmetic coder is similar to the QM coder, with a different state table, that offers balanced improvements to the QM probability estimation for the less skewed distributions. The QM-AYA performs better when the probability estimate is near 0.5 for each binary symbol. An approach for constructing effective index change tables for Q-coder type adaptation is discussed.
Age-related differences in arithmetic strategy sequential effects.
Lemaire, Patrick
2016-03-01
In this article, I review a series of new findings concerning how age-related changes in strategic variations are modulated by sequential effects. Sequential effects refer to how strategy selection and strategy execution on current problems are influenced by which strategy is used on immediately preceding problems. Two sequential effects during strategy selection (i.e., strategy revisions and strategy perseverations) and during strategy execution (i.e., strategy switch costs and modulations of poorer strategy effects) are presented. I also discuss how these effects change with age during adulthood. These phenomena are important, as they shed light on arithmetic processes and how these processes change with age during adulthood. In particular, they speak to the role of executive control while participants select and execute arithmetic strategies. Finally, I discuss the implications of sequential effects for theories of strategies and of arithmetic.
Grounding Concepts An Empirical Basis for Arithmetical Knowledge
Jenkins, C S
2008-01-01
Grounding Concepts tackles the issue of arithmetical knowledge, developing a new position which respects three intuitions which have appeared impossible to satisfy simultaneously: a priorism, mind-independence realism, and empiricism.Drawing on a wide range of philosophical influences, but avoiding unnecessary technicality, a view is developed whereby arithmetic can be known through the examination of empirically grounded concepts. These are concepts which, owing to their relationship to sensory input, are non-accidentally accurate representations of the mind-independent world. Examination of
An efficient adaptive arithmetic coding image compression technology
Institute of Scientific and Technical Information of China (English)
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.
Reason's Nearest Kin Philosophies of Arithmetic from Kant to Carnap
Potter, Michael
2000-01-01
How do we account for the truth of arithmetic? And if it does not depend for its truth on the way the world is, what constrains the world to conform to arithmetic? Reason's Nearest Kin is a critical examination of the astonishing progress made towards answering these questions from the late nineteenth to the mid-twentieth century. In the space of fifty years Frege, Dedekind, Russell, Wittgenstein, Ramsey, Hilbert, and Carnap developed accounts of the content of arithmeticthat were brilliantly original both technically and philosophically. Michael Potter's innovative study presents them all as
The identities of additive binary arithmetics
Klyachko, Anton A
2011-01-01
Operations of arbitrary arity expressible via addition modulo 2^n and bitwise addition modulo 2 admit a simple description. The identities connecting these two additions have finite basis. Moreover, the universal algebra with these two operations is rationally equivalent to a nilpotent ring and, therefore, generates a Specht variety.
On Arithmetic Progressions in Recurrences - A new characterization of the Fibonacci sequence
Pinter, Akos
2010-01-01
We show that essentially the Fibonacci sequence is the unique binary recurrence which contains infinitely many three-term arithmetic progressions. A criterion for general linear recurrences having infinitely many three-term arithmetic progressions is also given.
Directory of Open Access Journals (Sweden)
Naresh Grover
2014-02-01
Full Text Available Most of the algorithms implemented in FPGAs used to be fixed-point. Floating-point operations are useful for computations involving large dynamic range, but they require significantly more resources than integer operations. With the current trends in system requirements and available FPGAs, floating-point implementations are becoming more common and designers are increasingly taking advantage of FPGAs as a platform for floating-point implementations. The rapid advance in Field-Programmable Gate Array (FPGA technology makes such devices increasingly attractive for implementing floating-point arithmetic. Compared to Application Specific Integrated Circuits, FPGAs offer reduced development time and costs. Moreover, their flexibility enables field upgrade and adaptation of hardware to run-time conditions. A 32 bit floating point arithmetic unit with IEEE 754 Standard has been designed using VHDL code and all operations of addition, subtraction, multiplication and division are tested on Xilinx. Thereafter, Simulink model in MAT lab has been created for verification of VHDL code of that Floating Point Arithmetic Unit in Modelsim.
Relational Thinking: Learning Arithmetic in Order to Promote Algebraic Thinking
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…
Motivating children to learn arithmetic with an adaptive robot game
Janssen, J.B.; Wal, C.C. van der; Neerincx, M.A.; Looije, R.
2011-01-01
Based on a ‘learning by playing’ concept, a basic arithmetic learning task was extended with an engaging game to achieve long-term educational interaction for children. Personalization was added to this learning task, to further support the child’s motivation and success in learning. In an experimen
Beginners' Progress in Early Arithmetic in the Swedish Compulsory School
Eriksson, Gota
2008-01-01
This article focuses on spontaneous knowledge-building in the field of "the arithmetic "of" the child." The aim is to investigate the conceptual progress of fifteen children during their early school years in the compulsory school. The study is based on the epistemology of radical constructivism and the methodology of "multiple clinical…
Toward a Student-Centred Process of Teaching Arithmetic
Eriksson, Gota
2011-01-01
This article describes a way toward a student-centred process of teaching arithmetic, where the content is harmonized with the students' conceptual levels. At school start, one classroom teacher is guided in recurrent teaching development meetings in order to develop teaching based on the students' prerequisites and to successively learn the…
A TRANSLATION OF RUSSIAN FIRST-GRADE ARITHMETIC.
CALANDRA, ALEXANDER
THIS IS AN ENGLISH TRANSLATION OF A RUSSIAN TEXTBOOK ON FIRST-GRADE ARITHMETIC COMPLETE WITH GRAPHS, PICTURES, PROBLEMS, AND LESSONS. ADDITION, SUBTRACTION, MULTIPLICATION, AND DIVISION APPEAR IN 892 PROBLEMS. THE THREE SECTIONS ARE ENTITLED "THE FIRST TEN,""THE SECOND TEN," AND "THE FIRST HUNDRED." THIS TRANSLATION…
Partial sums of arithmetical functions with absolutely convergent Ramanujan expansions
Indian Academy of Sciences (India)
BISWAJYOTI SAHA
2016-08-01
For an arithmetical function $f$ with absolutely convergent Ramanujan expansion, we derive an asymptotic formula for the $\\sum_{n\\leq N}$ f(n)$ with explicit error term. As a corollary we obtain new results about sum-of-divisors functions and Jordan’s totient functions.
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.
Introducing Number and Arithmetic Concepts with Number Sticks.
Baroody, Arthur J.
1993-01-01
This article compares the relative merits of using Cuisenaire rods (unsegmented, unnumbered, and representing continuous quantities) and number sticks (segmented, numbered, and representing discrete quantities) to introduce number and arithmetic concepts to beginning students or students with learning difficulties or mental disabilities. (DB)
24 CFR Appendix E to Part 3500 - Arithmetic Steps
2010-04-01
... 24 Housing and Urban Development 5 2010-04-01 2010-04-01 false Arithmetic Steps E Appendix E to Part 3500 Housing and Urban Development Regulations Relating to Housing and Urban Development (Continued) OFFICE OF ASSISTANT SECRETARY FOR HOUSING-FEDERAL HOUSING COMMISSIONER, DEPARTMENT OF HOUSING...
Arithmetical Strategies of a Student with Down Syndrome
Rumiati, Rumi
2014-01-01
Kayla was a 15 years old girl with Down syndrome attending a special education school in Indonesia. A modification of Wright et al.'s (2006) approach to assessment documented her number knowledge and arithmetical strategies. This paper discusses the assessment process and the results focusing on her ability to solve number problems. Results show…
Sex Differences in Arithmetical Performance Scores: Central Tendency and Variability
Martens, R.; Hurks, P. P. M.; Meijs, C.; Wassenberg, R.; Jolles, J.
2011-01-01
The present study aimed to analyze sex differences in arithmetical performance in a large-scale sample of 390 children (193 boys) frequenting grades 1-9. Past research in this field has focused primarily on average performance, implicitly assuming homogeneity of variance, for which support is scarce. This article examined sex differences in…
Effects of Numerical Surface Form in Arithmetic Word Problems
Orrantia, Josetxu; Múñez, David; San Romualdo, Sara; Verschaffel, Lieven
2015-01-01
Adults' simple arithmetic performance is more efficient when operands are presented in Arabic digit (3 + 5) than in number word (three + five) formats. An explanation provided is that visual familiarity with digits is higher respect to number words. However, most studies have been limited to single-digit addition and multiplication problems. In…
Why Is Learning Fraction and Decimal Arithmetic so Difficult?
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…
Degrading Precision Arithmetics for Low-power FIR Implementation
DEFF Research Database (Denmark)
Albicocco, Pietro; Cardarilli, Gian Carlo; Nannarelli, Alberto
2011-01-01
dissipation is mandatory. After a review of the possible "standard" optimization techniques, the paper addresses aggressive methodologies where power and area savings are obtained by introducing the concept of "Degrading Precision Arithmetic" (DPA). Three different approaches are discussed: DPA-I, based...
Embedding adaptive arithmetic coder in chaos-based cryptography
Li, Heng-Jian; Zhang, Jia-Shu
2010-05-01
In this study an adaptive arithmetic coder is embedded in the Baptista-type chaotic cryptosystem for implementing secure data compression. To build the multiple lookup tables of secure data compression, the phase space of chaos map with a uniform distribution in the search mode is divided non-uniformly according to the dynamic probability estimation of plaintext symbols. As a result, more probable symbols are selected according to the local statistical characters of plaintext and the required number of iterations is small since the more probable symbols have a higher chance to be visited by the chaotic search trajectory. By exploiting non-uniformity in the probabilities under which a number of iteration to be coded takes on its possible values, the compression capability is achieved by adaptive arithmetic code. Therefore, the system offers both compression and security. Compared with original arithmetic coding, simulation results on Calgary Corpus files show that the proposed scheme suffers from a reduction in compression performance less than 12% and is not susceptible to previously carried out attacks on arithmetic coding algorithms.
Thinking Mathematically: Integrating Arithmetic and Algebra in Elementary School.
Carpenter, Thomas P.; Franke, Megan Loef; Levi, Linda
This book is designed to help teachers understand children's intuitive problem solving and computational processes and to figure out how to use that knowledge to enhance students' understanding of arithmetic. This book provides numerous examples of classroom dialogues that indicate how algebraic ideas emerge in children's thinking and what…
Arithmetic Word-Problem-Solving in Huntington's Disease
Allain, P.; Verny, C.; Aubin, G.; Pinon, K.; Bonneau, D.; Dubas, F.; Gall, D.L.
2005-01-01
The purpose of this study was to examine executive functioning in patients with Huntington's disease using an arithmetic word-problem-solving task including eight solvable problems of increasing complexity and four aberrant problems. Ten patients with Huntington's disease and 12 normal control subjects matched by age and education were tested.…
The Impact of Arithmetic Skills on Mastery of Quantitative Analysis
Directory of Open Access Journals (Sweden)
Bruce K. Blaylock
2012-01-01
Full Text Available Over the past several years math education has moved from a period where all math calculations were done by hand to an era where most calculations are done using a calculator or computer. There are certainly benefits to this approach, but when one concomitantly recognizes the declining scores on national standardized mathematics exams, it raises the question, “Could the lack of technology-assisted arithmetic manipulation skills have a carryover to understanding higher-level mathematical concepts or is it just a spurious correlation?” Eighty-seven students were tested for their ability to do simple arithmetic and algebra by hand. These scores were then regressed on three important areas of quantitative analysis: recognizing the appropriate tool to use in an analysis, creating a model to carry out the analysis, and interpreting the results of the analysis. The study revealed a significant relationship between the ability to accurately do arithmetic calculations and the ability to recognize the appropriate tool and creating a model. It found no significant relationship between results interpretation and arithmetic skills.
Probability Quantization for Multiplication-Free Binary Arithmetic Coding
Cheung, K. -M.
1995-01-01
A method has been developed to improve on Witten's binary arithmetic coding procedure of tracking a high value and a low value. The new method approximates the probability of the less probable symbol, which improves the worst-case coding efficiency.
A Stock Pricing Model Based on Arithmetic Brown Motion
Institute of Scientific and Technical Information of China (English)
YAN Yong-xin; HAN Wen-xiu
2001-01-01
This paper presents a new stock pricing model based on arithmetic Brown motion. The model overcomes the shortcomings of Gordon model completely. With the model investors can estimate the stock value of surplus companies, deficit companies, zero increase companies and bankrupt companies in long term investment or in short term investment.
Non-Archimedean L-functions and arithmetical Siegel modular forms
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: ...
Vectors a Fortran 90 module for 3-dimensional vector and dyadic arithmetic
Energy Technology Data Exchange (ETDEWEB)
Brock, B.C.
1998-02-01
A major advance contained in the new Fortran 90 language standard is the ability to define new data types and the operators associated with them. Writing computer code to implement computations with real and complex three-dimensional vectors and dyadics is greatly simplified if the equations can be implemented directly, without the need to code the vector arithmetic explicitly. The Fortran 90 module described here defines new data types for real and complex 3-dimensional vectors and dyadics, along with the common operations needed to work with these objects. Routines to allow convenient initialization and output of the new types are also included. In keeping with the philosophy of data abstraction, the details of the implementation of the data types are maintained private, and the functions and operators are made generic to simplify the combining of real, complex, single- and double-precision vectors and dyadics.
Imprecise Arithmetic for Low Power Image Processing
DEFF Research Database (Denmark)
Albicocco, Pietro; Cardarilli, Gian Carlo; Nannarelli, Alberto
2012-01-01
Sometimes reducing the precision of a numerical processor, by introducing errors, can lead to significant performance (delay, area and power dissipation) improvements without compromising the overall quality of the processing. In this work, we show how to perform the two basic operations, additio...... and multiplication, in an imprecise manner by simplifying the hardware implementation. With the proposed ”sloppy” operations, we obtain a reduction in delay, area and power dissipation, and the error introduced is still acceptable for applications such as image processing.......Sometimes reducing the precision of a numerical processor, by introducing errors, can lead to significant performance (delay, area and power dissipation) improvements without compromising the overall quality of the processing. In this work, we show how to perform the two basic operations, addition...
Pang, Yuye; Sun, Jun; Wang, Jia; Wang, Peng
In this paper, the statistical characteristic of the Error Detection Delay (EDD) of Finite Precision Binary Arithmetic Codes (FPBAC) is discussed. It is observed that, apart from the probability of the Forbidden Symbol (FS) inserted into the list of the source symbols, the probability of the source sequence and the operation precision as well as the position of the FS in the coding interval can affect the statistical characteristic of the EDD. Experiments demonstrate that the actual distribution of the EDD of FPBAC is quite different from the geometric distribution of infinite precision arithmetic codes. This phenomenon is researched deeply, and a new statistical model (gamma distribution) of the actual distribution of the EDD is proposed, which can make a more precise prediction of the EDD. Finally, the relation expressions between the parameters of gamma distribution and the related factors affecting the distribution are given.
Park, Joonkoo; Brannon, Elizabeth M
2014-10-01
A nonverbal primitive number sense allows approximate estimation and mental manipulations on numerical quantities without the use of numerical symbols. In a recent randomized controlled intervention study in adults, we demonstrated that repeated training on a non-symbolic approximate arithmetic task resulted in improved exact symbolic arithmetic performance, suggesting a causal relationship between the primitive number sense and arithmetic competence. Here, we investigate the potential mechanisms underlying this causal relationship. We constructed multiple training conditions designed to isolate distinct cognitive components of the approximate arithmetic task. We then assessed the effectiveness of these training conditions in improving exact symbolic arithmetic in adults. We found that training on approximate arithmetic, but not on numerical comparison, numerical matching, or visuo-spatial short-term memory, improves symbolic arithmetic performance. In addition, a second experiment revealed that our approximate arithmetic task does not require verbal encoding of number, ruling out an alternative explanation that participants use exact symbolic strategies during approximate arithmetic training. Based on these results, we propose that nonverbal numerical quantity manipulation is one key factor that drives the link between the primitive number sense and symbolic arithmetic competence. Future work should investigate whether training young children on approximate arithmetic tasks even before they solidify their symbolic number understanding is fruitful for improving readiness for math education.
Arithmetic computation using self-assembly of DNA tiles:subtraction and division
Institute of Scientific and Technical Information of China (English)
Xuncai Zhang; Yanfeng Wang; Zhihua Chen; Jin Xu; Guangzhao Cui
2009-01-01
Recently,experiments have demonstrated that simple binary arithmetic and logical operations can be computed by the process of selfassembly of DNA tiles.In this paper,we show how the tile assembly process can be used for subtraction and division.In order to achieve this aim,four systems,including the comparator system,the duplicator system,the subtraction system,and the division system,are proposed to compute the difference and quotient of two input numbers using the tile assembly model.This work indicates that these systems can be carried out in polynomial time with optimal O(1)distinct tile types in parallel and at very low cost.Furthermore,we provide a scheme to factor the product of two prime numbers,and it is a breakthrough in basic biological operations using a molecular computer by self-assembly.
Heights of varieties in multiprojective spaces and arithmetic Nullstellensatze
D'Andrea, Carlos; Sombra, Martin
2011-01-01
We present bounds for the degree and the height of the polynomials arising in some central problems in effective algebraic geometry including the implicitation of rational maps and the effective Nullstellensatz over a variety. Our treatment is based on arithmetic intersection theory in products of projective spaces and extends to the arithmetic setting constructions and results due to Jelonek. A key role is played by the notion of canonical mixed heights of multiprojective varieties. We study this notion from the point of view of resultant theory and establish some of its basic properties, including its behavior with respect to intersections, projections and products. We obtain analogous results for the function field case, including a parametric Nullstellensatz.
Cardiorespiratory Information Dynamics during Mental Arithmetic and Sustained Attention.
Widjaja, Devy; Montalto, Alessandro; Vlemincx, Elke; Marinazzo, Daniele; Van Huffel, Sabine; Faes, Luca
2015-01-01
An analysis of cardiorespiratory dynamics during mental arithmetic, which induces stress, and sustained attention was conducted using information theory. The information storage and internal information of heart rate variability (HRV) were determined respectively as the self-entropy of the tachogram, and the self-entropy of the tachogram conditioned to the knowledge of respiration. The information transfer and cross information from respiration to HRV were assessed as the transfer and cross-entropy, both measures of cardiorespiratory coupling. These information-theoretic measures identified significant nonlinearities in the cardiorespiratory time series. Additionally, it was shown that, although mental stress is related to a reduction in vagal activity, no difference in cardiorespiratory coupling was found when several mental states (rest, mental stress, sustained attention) are compared. However, the self-entropy of HRV conditioned to respiration was very informative to study the predictability of RR interval series during mental tasks, and showed higher predictability during mental arithmetic compared to sustained attention or rest.
Well-rounded zeta-function of planar arithmetic lattices
Fukshansky, Lenny
2012-01-01
We investigate the properties of the zeta-function of well-rounded sublattices of a fixed arithmetic lattice in the plane. In particular, we show that this function has abscissa of convergence at $s=1$ with a real pole of order 2, improving upon a recent result of S. Kuehnlein. We use this result to show that the number of well-rounded sublattices of a planar arithmetic lattice of index less or equal $N$ is $O(N \\log N)$ as $N \\to \\infty$. To obtain these results, we produce a description of integral well-rounded sublattices of a fixed planar integral well-rounded lattice and investigate convergence properties of a zeta-function of similarity classes of such lattices, building on some previous results of the author.
An algorithm for redundant binary bit-pipelined rational arithmetic
Energy Technology Data Exchange (ETDEWEB)
Kornerup, P. (Dept. of Mathematics and Computer Science, Odense Universitet, Odense (DK)); Matula, D.W. (Dept. of Computer Science and Engineering, Southern Methodist Univ., Dallas, TX (US))
1990-08-01
The authors introduce a redundant binary representation of the rationals and an associated algorithm for computing the sum, difference, product, quotient, and other useful functions of two rational operands, employing our representation. The authors' algorithm extends Gosper's partial quotient arithmetic algorithm and allows the design of an on-line arithmetic unit with computations granularized at the signed bit level. Each input or output port can independently be set to receive/produce operands/result in either binary radix or our binary rational representation. The authors investigate by simulation the interconnection of several such units for the parallel computation of more complicated expressions in a tree-pipelined manner, with particular regards to measuring individual and compound on-line delays.
INTERVAL ARITHMETIC AND STATIC INTERVAL FINITE ELEMENT METHOD
Institute of Scientific and Technical Information of China (English)
郭书祥; 吕震宙
2001-01-01
When the uncertainties of structures may be bounded in intervals, through some suitable discretization, interval finite element method can be constructed by combining the interval analysis with the traditional finite element method(FEM). The two parameters,median and deviation, were used to represent the uncertainties of interval variables. Based on the arithmetic rules of intervals, some properties and arithmetic rules of interval variables were demonstrated. Combining the procedure of interval analysis with FEM, a static linear interval finite element method was presented to solve the non-random uncertain structures. The solving of the characteristic parameters of n-freedom uncertain displacement field of the static governing equation was transformed into 2 n-order linear equations. It is shown by a numerical example that the proposed method is practical and effective.
Measuring the Invisible: A Process among Arithmetic, Geometry and Music
Saito, Fumikazu; PEPG em Educação Matemática/HEEMa/PUCSP PEPG em História da Ciência/CESIMA/PUCSP; Bromberg,Carla
2015-01-01
Abstract: The parallel between music and mathematics abounded in sixteenth-century studies. Referring to the concept of proportions, it was then assumed that theorists considered audible and visible proportions to be analogous. However, when approaching the treatises and focusing on how those processes of mensuration took place, we realise that there were differences concerning the very notion of quantifying. In this paper, we would like to identify the roles played by arithmetic and geometry...
Computing Integer Powers in Floating-Point Arithmetic
Kornerup, Peter; Muller, Jean-Michel
2007-01-01
We introduce two algorithms for accurately evaluating powers to a positive integer in floating-point arithmetic, assuming a fused multiply-add (fma) instruction is available. We show that our log-time algorithm always produce faithfully-rounded results, discuss the possibility of getting correctly rounded results, and show that results correctly rounded in double precision can be obtained if extended-precision is available with the possibility to round into double precision (with a single rounding).
Computing Integer Powers in Floating-Point Arithmetic
Kornerup, Peter; Lefèvre, Vincent; Muller, Jean-Michel
2007-01-01
We introduce two algorithms for accurately evaluating powers to a positive integer in floating-point arithmetic, assuming a fused multiply-add (fma) instruction is available. We show that our log-time algorithm always produce faithfully-rounded results, discuss the possibility of getting correctly rounded results, and show that results correctly rounded in double precision can be obtained if extended-precision is available with the possibility to round into double precision (with a single rou...
Real-time mental arithmetic task recognition from EEG signals.
Wang, Qiang; Sourina, Olga
2013-03-01
Electroencephalography (EEG)-based monitoring the state of the user's brain functioning and giving her/him the visual/audio/tactile feedback is called neurofeedback technique, and it could allow the user to train the corresponding brain functions. It could provide an alternative way of treatment for some psychological disorders such as attention deficit hyperactivity disorder (ADHD), where concentration function deficit exists, autism spectrum disorder (ASD), or dyscalculia where the difficulty in learning and comprehending the arithmetic exists. In this paper, a novel method for multifractal analysis of EEG signals named generalized Higuchi fractal dimension spectrum (GHFDS) was proposed and applied in mental arithmetic task recognition from EEG signals. Other features such as power spectrum density (PSD), autoregressive model (AR), and statistical features were analyzed as well. The usage of the proposed fractal dimension spectrum of EEG signal in combination with other features improved the mental arithmetic task recognition accuracy in both multi-channel and one-channel subject-dependent algorithms up to 97.87% and 84.15% correspondingly. Based on the channel ranking, four channels were chosen which gave the accuracy up to 97.11%. Reliable real-time neurofeedback system could be implemented based on the algorithms proposed in this paper.
From functional programming to multicore parallelism: A case study based on Presburger Arithmetic
DEFF Research Database (Denmark)
Dung, Phan Anh; Hansen, Michael Reichhardt
2011-01-01
The overall goal of this work is studying parallelization of functional programs with the specific case study of decision procedures for Presburger Arithmetic (PA). PA is a first order theory of integers accepting addition as its only operation. Whereas it has wide applications in different areas......, we are interested in using PA in connection with the Duration Calculus Model Checker (DCMC) [5]. There are effective decision procedures for PA including Cooper’s algorithm and the Omega Test; however, their complexity is extremely high with doubly exponential lower bound and triply exponential upper...... in the SMT-solver Z3 [8] which has the capability of solving Presburger formulas. Functional programming is well-suited for the domain of decision procedures, and its immutability feature helps to reduce parallelization effort. While Haskell has progressed with a lot of parallelismrelated research [6], we...
Lieu, Richard
2016-01-01
A hierarchy of statistics of increasing sophistication and accuracy is proposed, to exploit an interesting and fundamental arithmetic structure in the photon bunching noise of incoherent light of large photon occupation number, with the purpose of suppressing the noise and rendering a more reliable and unbiased measurement of the light intensity. The method does not require any new hardware, rather it operates at the software level, with the help of high precision computers, to reprocess the intensity time series of the incident light to create a new series with smaller bunching noise coherence length. The ultimate accuracy improvement of this method of flux measurement is limited by the timing resolution of the detector, the precision of the computer in manipulating numbers, and the photon occupation number of the beam (the higher the photon number the better the performance). The principal application is sensitivity enhancement of radio astronomical observations.
A novel VLSI architecture of arithmetic encoder with reduced memory in SPIHT
Liu, Kai; Li, YunSong; Belyaev, Eugeniy
2010-08-01
The paper presents a context-based arithmetic coder's VLSI architecture used in SPIHT with reduced memory, which is used for high speed real-time applications. For hardware implementation, a dedicated context model is proposed for the coder. Each context can be processed in parallel and high speed operators are used for interval calculations. An embedded register array is used for cumulative frequency update. As a result, the coder can consume one symbol at each clock cycle. After FPGA synthesis and simulation, the throughput of our coder is comparable with those of similar hardware architectures used in ASIC technology. Especially, the memory capacity of the coder is smaller than those of corresponding systems.
Directory of Open Access Journals (Sweden)
Luke F Rinne
Full Text Available 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.
Su, Yan; Jun, Xie Cheng
2006-08-01
An algorithm of combining LZC and arithmetic coding algorithm for image compression is presented and both theory deduction and simulation result prove the correctness and feasibility of the algorithm. According to the characteristic of context-based adaptive binary arithmetic coding and entropy, LZC was modified to cooperate the optimized piecewise arithmetic coding, this algorithm improved the compression ratio without any additional time consumption compared to traditional method.
A optimized context-based adaptive binary arithmetic coding algorithm in progressive H.264 encoder
Xiao, Guang; Shi, Xu-li; An, Ping; Zhang, Zhao-yang; Gao, Ge; Teng, Guo-wei
2006-05-01
Context-based Adaptive Binary Arithmetic Coding (CABAC) is a new entropy coding method presented in H.264/AVC that is highly efficient in video coding. In the method, the probability of current symbol is estimated by using the wisely designed context model, which is adaptive and can approach to the statistic characteristic. Then an arithmetic coding mechanism largely reduces the redundancy in inter-symbol. Compared with UVLC method in the prior standard, CABAC is complicated but efficiently reduce the bit rate. Based on thorough analysis of coding and decoding methods of CABAC, This paper proposed two methods, sub-table method and stream-reuse methods, to improve the encoding efficiency implemented in H.264 JM code. In JM, the CABAC function produces bits one by one of every syntactic element. Multiplication operating times after times in the CABAC function lead to it inefficient.The proposed algorithm creates tables beforehand and then produce every bits of syntactic element. In JM, intra-prediction and inter-prediction mode selection algorithm with different criterion is based on RDO(rate distortion optimization) model. One of the parameter of the RDO model is bit rate that is produced by CABAC operator. After intra-prediction or inter-prediction mode selection, the CABAC stream is discard and is recalculated to output stream. The proposed Stream-reuse algorithm puts the stream in memory that is created in mode selection algorithm and reuses it in encoding function. Experiment results show that our proposed algorithm can averagely speed up 17 to 78 MSEL higher speed for QCIF and CIF sequences individually compared with the original algorithm of JM at the cost of only a little memory space. The CABAC was realized in our progressive h.264 encoder.
Foley, Alana E; Vasilyeva, Marina; Laski, Elida V
2016-12-14
This study examined the mediating role of children's use of decomposition strategies in the relation between visuospatial memory (VSM) and arithmetic accuracy. Children (N = 78; Age M = 9.36) completed assessments of VSM, arithmetic strategies, and arithmetic accuracy. Consistent with previous findings, VSM predicted arithmetic accuracy in children. Extending previous findings, the current study showed that the relation between VSM and arithmetic performance was mediated by the frequency of children's use of decomposition strategies. Identifying the role of arithmetic strategies in this relation has implications for increasing the math performance of children with lower VSM. Statement of contribution What is already known on this subject? The link between children's visuospatial working memory and arithmetic accuracy is well documented. Frequency of decomposition strategy use is positively related to children's arithmetic accuracy. Children's spatial skill positively predicts the frequency with which they use decomposition. What does this study add? Short-term visuospatial memory (VSM) positively relates to the frequency of children's decomposition use. Decomposition use mediates the relation between short-term VSM and arithmetic accuracy. Children with limited short-term VSM may struggle to use decomposition, decreasing accuracy.
LOGIC DEVICES, *OPTICAL CIRCUITS, *OPTICAL SWITCHING, HETEROJUNCTIONS, PHOTOTRANSISTORS, ELECTROOPTICS, LASER CAVITIES, OPTICAL PROCESSING, PARALLEL PROCESSING, BISTABLE DEVICES, GATES(CIRCUITS), VOLTAGE, BINARY ARITHMETIC .
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.
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.
Vedas and the Development of Arithmetic and Algebra
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Gurudeo A. Tularam
2010-01-01
Full Text Available Problem statement: Algebra developed in three stages: rhetorical or prose algebra, syncopated or abbreviated algebra and symbolic algebra-known as school algebra. School algebra developed rather early in India and the literature now suggests that the first civilization to develop symbolic algebra was the Vedic Indians. Approach: Philosophical ideas of the time influenced the development of the decimal system and arithmetic and that in turn led to algebra. Indeed, symbolic algebraic ideas are deep rooted in Vedic philosophy. The Vedic arithmetic and mathematics were of a high level at an early period and the Hindus used algebraic ideas to generate formulas simplifying calculations. Results: In the main, they developed formulas to understand the physical world satisfying the needs of religion (apara and para vidya. While geometrical focus, logic and proof type are features of Greek mathematics, boldness of conception, abstraction, symbolism are essentially in Indian mathematics. From such a history study, a number of implications can be drawn regarding the learning of algebra. Real life, imaginative and creative problems that encourage risk should be the focus in student learning; allowing students freely move between numbers, magnitudes and symbols rather than taking separate static or unchanging view. A move from concrete to pictorial to symbolic modes was present in ancient learning. Real life practical needs motivated the progress to symbolic algebra. The use of rich context based problems that stimulate and motivate students to raise levels higher to transfer knowledge should be the focus of learning. Conclusion/Recommendations: The progress from arithmetic to algebra in India was achieved through different modes of learning, risk taking, problem solving and higher order thinking all in line with current emphasis in mathematics education but at rather early stage in human history.
On Some Conjectures on the Monotonicity of Some Arithmetical Sequences
2012-01-01
THE MONOTONICITY OF SOME ARITHMETICAL SEQUENCES ∗ Florian Luca † Centro de Ciencias Matemáticas, Universidad Nacional Autonoma de México, C.P. 58089...visit of P. S. to the Centro de Ciencias Matemáticas de la UNAM in Morelia in August 2012. During the preparation of this paper, F. L. was supported in...n+ k k )2 = dn for all n ≥ 0, (3.22) is the central Delannoy number. When r = (2, 2), we get that S(2,2)(n) = n∑ k=0 ( n k )2(n+ k k )2 = An for all n
Strategy-Enhanced Interactive Proving and Arithmetic Simplification for PVS
diVito, Ben L.
2003-01-01
We describe an approach to strategy-based proving for improved interactive deduction in specialized domains. An experimental package of strategies (tactics) and support functions called Manip has been developed for PVS to reduce the tedium of arithmetic manipulation. Included are strategies aimed at algebraic simplification of real-valued expressions. A general deduction architecture is described in which domain-specific strategies, such as those for algebraic manipulation, are supported by more generic features, such as term-access techniques applicable in arbitrary settings. An extended expression language provides access to subterms within a sequent.
A Fast π/4-DQPSK Demodulation Arithmetic and Realization
Institute of Scientific and Technical Information of China (English)
ZHOU Guo-yong; ZHONG Hong-sheng; WANG Jun-mei
2004-01-01
The modulated signals of π /4-DQPSK can be demodulated with the differenced method,and the technology has been used in the communication. The traditional demodulated method needs a lot of calculation. In this paper, a new method based on fast arithmetic digital demodulation of DQPSK is presented. The new method only uses the sign of the modulated signal instead of digital signal through the A/D in the traditional method. With the new method, the system has higher speed, and can save some hardware in the FPGA. An experiment of the new method with the DQPSK is given in this paper.
Quantum error correcting codes and 4-dimensional arithmetic hyperbolic manifolds
Guth, Larry; Lubotzky, Alexander
2014-08-01
Using 4-dimensional arithmetic hyperbolic manifolds, we construct some new homological quantum error correcting codes. They are low density parity check codes with linear rate and distance nɛ. Their rate is evaluated via Euler characteristic arguments and their distance using {Z}_2-systolic geometry. This construction answers a question of Zémor ["On Cayley graphs, surface codes, and the limits of homological coding for quantum error correction," in Proceedings of Second International Workshop on Coding and Cryptology (IWCC), Lecture Notes in Computer Science Vol. 5557 (2009), pp. 259-273], who asked whether homological codes with such parameters could exist at all.
On consistency of the weighted arithmetical mean complex judgement matrix
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
The weighted arithmetical mean complex judgement matrix(WAMCJM)is the most common method for aggregating group opinions,but it has a shortcoming,namely the WAMCJM of the perfectly consistent judgement matrices given by experts canot guarantee its perfect consistency.An upper bound of the WAMCJM's consistency is presented.Simultaneously,a compatibility index of judging the aggregating extent of group opinions is also introduced.The WAMCJM is of acceptable consistency and is proved provided the compatibilities of all judgement matrices given by experts are smaller than the threshold value of acceptable consistency.These conclusions are important to group decision making.
A VLSI architecture for simplified arithmetic Fourier transform algorithm
Reed, Irving S.; Shih, Ming-Tang; Truong, T. K.; Hendon, E.; Tufts, D. W.
1992-01-01
The arithmetic Fourier transform (AFT) is a number-theoretic approach to Fourier analysis which has been shown to perform competitively with the classical FFT in terms of accuracy, complexity, and speed. Theorems developed in a previous paper for the AFT algorithm are used here to derive the original AFT algorithm which Bruns found in 1903. This is shown to yield an algorithm of less complexity and of improved performance over certain recent AFT algorithms. A VLSI architecture is suggested for this simplified AFT algorithm. This architecture uses a butterfly structure which reduces the number of additions by 25 percent of that used in the direct method.
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...
CIMPA Summer School on Arithmetic and Geometry Around Hypergeometric Functions
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.
Pricing Arithmetic Asian Options under Hybrid Stochastic and Local Volatility
Directory of Open Access Journals (Sweden)
Min-Ku Lee
2014-01-01
Full Text Available Recently, hybrid stochastic and local volatility models have become an industry standard for the pricing of derivatives and other problems in finance. In this study, we use a multiscale stochastic volatility model incorporated by the constant elasticity of variance to understand the price structure of continuous arithmetic average Asian options. The multiscale partial differential equation for the option price is approximated by a couple of single scale partial differential equations. In terms of the elasticity parameter governing the leverage effect, a correction to the stochastic volatility model is made for more efficient pricing and hedging of Asian options.
Arithmetic progressions in Salem-type subsets of the integers
Potgieter, Paul
2010-01-01
Given a subset of the integers of zero density, we define the weaker notion of fractional density of such a set. It is shown how this notion corresponds to that of the Hausdorff dimension of a compact subset of the reals. We then show that a version of a theorem of {\\L}aba and Pramanik on 3-term arithmetic progressions in subsets of the unit interval also holds for subsets of the integers with fractional density and satisfying certain Fourier-decay conditions.
Operator theory, operator algebras and applications
Lebre, Amarino; Samko, Stefan; Spitkovsky, Ilya
2014-01-01
This book consists of research papers that cover the scientific areas of the International Workshop on Operator Theory, Operator Algebras and Applications, held in Lisbon in September 2012. The volume particularly focuses on (i) operator theory and harmonic analysis (singular integral operators with shifts; pseudodifferential operators, factorization of almost periodic matrix functions; inequalities; Cauchy type integrals; maximal and singular operators on generalized Orlicz-Morrey spaces; the Riesz potential operator; modification of Hadamard fractional integro-differentiation), (ii) operator algebras (invertibility in groupoid C*-algebras; inner endomorphisms of some semi group, crossed products; C*-algebras generated by mappings which have finite orbits; Folner sequences in operator algebras; arithmetic aspect of C*_r SL(2); C*-algebras of singular integral operators; algebras of operator sequences) and (iii) mathematical physics (operator approach to diffraction from polygonal-conical screens; Poisson geo...
An Efficient Image Compression Technique Based on Arithmetic Coding
Directory of Open Access Journals (Sweden)
Prof. Rajendra Kumar Patel
2012-12-01
Full Text Available The rapid growth of digital imaging applications, including desktop publishing, multimedia, teleconferencing, and high visual definition has increased the need for effective and standardized image compression techniques. Digital Images play a very important role for describing the detailed information. The key obstacle for many applications is the vast amount of data required to represent a digital image directly. The various processes of digitizing the images to obtain it in the best quality for the more clear and accurate information leads to the requirement of more storage space and better storage and accessing mechanism in the form of hardware or software. In this paper we concentrate mainly on the above flaw so that we reduce the space with best quality image compression. State-ofthe-art techniques can compress typical images from 1/10 to 1/50 their uncompressed size without visibly affecting image quality. From our study I observe that there is a need of good image compression technique which provides better reduction technique in terms of storage and quality. Arithmetic coding is the best way to reducing encoding data. So in this paper we propose arithmetic coding with walsh transformation based image compression technique which is an efficient way of reduction
Cardiorespiratory Information Dynamics during Mental Arithmetic and Sustained Attention.
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Devy Widjaja
Full Text Available An analysis of cardiorespiratory dynamics during mental arithmetic, which induces stress, and sustained attention was conducted using information theory. The information storage and internal information of heart rate variability (HRV were determined respectively as the self-entropy of the tachogram, and the self-entropy of the tachogram conditioned to the knowledge of respiration. The information transfer and cross information from respiration to HRV were assessed as the transfer and cross-entropy, both measures of cardiorespiratory coupling. These information-theoretic measures identified significant nonlinearities in the cardiorespiratory time series. Additionally, it was shown that, although mental stress is related to a reduction in vagal activity, no difference in cardiorespiratory coupling was found when several mental states (rest, mental stress, sustained attention are compared. However, the self-entropy of HRV conditioned to respiration was very informative to study the predictability of RR interval series during mental tasks, and showed higher predictability during mental arithmetic compared to sustained attention or rest.
Design of arithmetic circuits in quantum dot cellular automata nanotechnology
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: · �...
Semiotic mediation: from multiplication properties to arithmetical expressions
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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.
Brauer groups and obstruction problems moduli spaces and arithmetic
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...
Efficient Interpolant Generation in Satisfiability Modulo Linear Integer Arithmetic
Griggio, Alberto; Sebastiani, Roberto
2010-01-01
The problem of computing Craig interpolants in SAT and SMT has recently received a lot of interest, mainly for its applications in formal verification. Efficient algorithms for interpolant generation have been presented for some theories of interest ---including that of equality and uninterpreted functions, linear arithmetic over the rationals, and their combination--- and they are successfully used within model checking tools. For the theory of linear arithmetic over the integers (LA(Z)), however, the problem of finding an interpolant is more challenging, and the task of developing efficient interpolant generators for the full theory LA(Z) is still the objective of ongoing research. In this paper we try to close this gap. We build on previous work and present a novel interpolation algorithm for SMT(LA(Z)), which exploits the full power of current state-of-the-art SMT(LA(Z)) solvers. We demonstrate the potential of our approach with an extensive experimental evaluation of our implementation of the proposed al...
Number word structure in first and second language influences arithmetic skills
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Anat ePrior
2015-03-01
Full Text Available Languages differ in how they represent numerical information, and specifically whether the verbal notation of numbers follows the same order as the symbolic notation (in non-inverted languages, e.g. Hebrew, 25, twenty-five or whether the two notations diverge (in inverted languages, e.g. Arabic, 25, five-and-twenty. We examined how the structure of number-words affects how arithmetic operations are processed by bilingual speakers of an inverted and a non-inverted language. We examined Arabic-Hebrew bilinguals' performance in the first language, L1 (inverted and in the second language, L2 (non-inverted. Their performance was compared to that of Hebrew L1 speakers, who do not speak an inverted language. Participants judged the accuracy of addition problems presented aurally in L1, aurally in L2 or in visual symbolic notation. Problems were presented such that they matched or did not match the structure of number words in the language. Arabic-Hebrew bilinguals demonstrated both flexibility in processing and adaptation to the language of aural-verbal presentation – they were more accurate for the inverted order of presentation in Arabic, but more accurate for non-inverted order of presentation in Hebrew, thus exhibiting the same pattern found for native Hebrew speakers. In addition, whereas native Hebrew speakers preferred the non-inverted order in visual symbolic presentation as well, the Arabic-Hebrew bilinguals showed enhanced flexibility, without a significant preference for one order over the other, in either speed or accuracy. These findings suggest that arithmetic processing is sensitive to the linguistic representations of number words. Moreover, bilinguals exposed to inverted and non-inverted languages showed influence of both systems, and enhanced flexibility in processing. Thus, the L1 does not seem to have exclusive power in shaping numerical mental representations, but rather the system remains open to influences from a later learned
On the order of magnitude of some arithmetical functions under digital constraint I
Indian Academy of Sciences (India)
Karam Aloui
2015-11-01
Let ≥ 2 be an integer and let () denote the sum of the digits in base of the positive integer . We look for an estimate of the average of some multiplicative arithmetical functions under constraints on the arithmetical congruence of the integers and the sum of their digits.
Early Number and Arithmetic Performance of Ecuadorian 4-5-Year-Olds
Bojorque, Gina; Torbeyns, Joke; Moscoso, Jheni; Van Nijlen, Daniël; Verschaffel, Lieven
2015-01-01
This study aimed at (a) constructing a reliable and valid test to assess Ecuadorian 4-5-year olds' number and arithmetic skills; (b) providing empirical data on Ecuadorian 4-5-year olds' number and arithmetic skills; and (c) confronting these children's actual performances with the performances expected by national experts in this domain. We…
Jenks, Kathleen M.; de Moor, Jan; van Lieshout, Ernest 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 = 41) and mainstream education (n = 16) and…
Sex Differences in Mental Arithmetic, Digit Span, and "g" Defined as Working Memory Capacity
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…
Sabrewing: a lightweight architecture for combined floating-point and integer arithmetic
Bruintjes, Tom M.; Walters, Karel H.G.; Gerez, Sabih H.; Molenkamp, Bert; Smit, Gerard J.M.
2012-01-01
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 contemporar
Relationship of Bender Memory to Achievement in Arithmetic by First Graders.
Snyder, Robert T.; And Others
1980-01-01
Arithmetic and reading achievement scores of 84 children were correlated with power and precision of Bender Memory using the Bender Visual Memory Technique (BVMT). Of the 20 correlations, 16 were significant. Support for recommended use of the BVMT as a screening instrument for early assessment of arithmetic skill is provided. (Author/SJL)
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
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 (n
Binary Arithmetic From Hariot (CA, 1600 A.D.) to the Computer Age.
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,…
Affine arithmetic in matrix form for polynomial evaluation and algebraic curve drawing
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
This paper shows how tight bounds for the range of a bivariate polynomial can be found using a matrix method based on affine arithmetic. Then, this method is applied to drawing an algebraic curve with a hierarchical algorithm, which demonstrates that more accurate answers can be obtained more rapidly than using conventional interval arithmetic.
Weinstein, Lawrence; Laverghetta, Antonio
2009-01-01
Undergraduate and graduate students at Cameron University (N = 158) were given the D'Amore Test of Elementary Arithmetic to test whether or not experience in college mathematics courses might be associated with a relative increase in arithmetic performance compared to those students who had not taken college mathematics courses. We found that only…
Salillas, Elena; Wicha, Nicole Y Y
2012-07-01
Language and math are intertwined during children's learning of arithmetic concepts, but the importance of language in adult arithmetic processing is less clear. To determine whether early learning plays a critical role in the math-language connection in adults, we tested retrieval of simple multiplication in adult bilinguals who learned arithmetic in only one language. We measured electrophysiological and behavioral responses during correctness judgments for problems presented as digits or as number words in Spanish or English. Problems presented in the language in which participants learned arithmetic elicited larger, more graded, and qualitatively different brain responses than did problems presented in participants' other language, and these responses more closely resembled responses for digits, even when participants' other language was more dominant. These findings suggest that the memory networks for simple multiplication are established when arithmetic concepts are first learned and are independent of language dominance in adulthood.
Teachers’ Beliefs and Practices Regarding the Role of Executive Functions in Reading and Arithmetic
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
Square lattice Ising model {chi}-tilde{sup (5)} ODE in exact arithmetic
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Nickel, B [Department of Physics, University of Guelph, Guelph, Ontario N1G 2W1 (Canada); Jensen, I; Guttmann, A J [ARC Centre of Excellence for Mathematics and Statistics of Complex Systems, Department of Mathematics and Statistics, The University of Melbourne, Victoria 3010 (Australia); Boukraa, S [LPTHIRM and Departement d' Aeronautique, Universite de Blida, Blida (Algeria); Hassani, S; Zenine, N [Centre de Recherche Nucleaire d' Alger, 2 Bd. Frantz Fanon, BP 399, 16000 Alger (Algeria); Maillard, J-M, E-mail: bgn@physics.uoguelph.c, E-mail: I.Jensen@ms.unimelb.edu.a, E-mail: boukraa@mail.univ-blida.d, E-mail: tonyg@ms.unimelb.edu.a, E-mail: maillard@lptmc.jussieu.f, E-mail: njzenine@yahoo.co [LPTMC, UMR 7600 CNRS, Universite de Paris, Tour 24, 4eme etage, case 121, 4 Place Jussieu, 75252 Paris Cedex 05 (France)
2010-05-14
We obtain in exact arithmetic the order 24 linear differential operator L{sub 24} and the right-hand side E{sup (5)} of the inhomogeneous equation L{sub 24}({Phi}{sup (5)}) = E{sup (5)}, where {Phi}{sup (5)}={chi}-tilde{sup (5)}-{chi}-tilde{sup (3)}/2+{chi}-tilde{sup (1)}/120 is a linear combination of n-particle contributions to the susceptibility of the square lattice Ising model. In Bostan et al (2009 J. Phys. A: Math. Theor. 42 275209), the operator L{sub 24} (modulo a prime) was shown to factorize into L{sub 12}{sup (left){center_dot}}L{sub 12}{sup (right)}; here we prove that no further factorization of the order 12 operator L{sub 12}{sup (left)} is possible. We use the exact ODE to obtain the behaviour of {chi}-tilde{sup (5)} at the ferromagnetic critical point and to obtain a limited number of analytic continuations of {chi}-tilde{sup (5)} beyond the principal disc defined by its high temperature series. Contrary to a speculation in Boukraa et al (2008 J. Phys. A: Math. Theor. 41 455202), we find that {chi}-tilde{sup (5)} is singular at w = 1/2 on an infinite number of branches.
Conference on Arithmetic and Ideal Theory of Rings and Semigroups
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.
On quaternions and octonions their geometry, arithmetic, and symmetry
AUTHOR|(CDS)2067326
2003-01-01
This book investigates the geometry of quaternion and octonion algebras. Following a comprehensive historical introduction, the book illuminates the special properties of 3- and 4-dimensional Euclidean spaces using quaternions, leading to enumerations of the corresponding finite groups of symmetries. The second half of the book discusses the less familiar octonion algebra, concentrating on its remarkable "triality symmetry" after an appropriate study of Moufang loops. The authors also describe the arithmetics of the quaternions and octonions. The book concludes with a new theory of octonion factorization. Topics covered include the geometry of complex numbers, quaternions and 3-dimensional groups, quaternions and 4-dimensional groups, Hurwitz integral quaternions, composition algebras, Moufang loops, octonions and 8-dimensional geometry, integral octonions, and the octonion projective plane.
Task difficulty in mental arithmetic affects microsaccadic rates and magnitudes.
Siegenthaler, Eva; Costela, Francisco M; McCamy, Michael B; Di Stasi, Leandro L; Otero-Millan, Jorge; Sonderegger, Andreas; Groner, Rudolf; Macknik, Stephen; Martinez-Conde, Susana
2014-01-01
Microsaccades are involuntary, small-magnitude saccadic eye movements that occur during attempted visual fixation. Recent research has found that attention can modulate microsaccade dynamics, but few studies have addressed the effects of task difficulty on microsaccade parameters, and those have obtained contradictory results. Further, no study to date has investigated the influence of task difficulty on microsaccade production during the performance of non-visual tasks. Thus, the effects of task difficulty on microsaccades, isolated from sensory modality, remain unclear. Here we investigated the effects of task difficulty on microsaccades during the performance of a non-visual, mental arithmetic task with two levels of complexity. We found that microsaccade rates decreased and microsaccade magnitudes increased with increased task difficulty. We propose that changes in microsaccade rates and magnitudes with task difficulty are mediated by the effects of varying attentional inputs on the rostral superior colliculus activity map.
An algorithm for the arithmetic classification of multilattices
Indelicato, Giuliana
2009-01-01
A procedure for the construction and the classification of multilattices in arbitrary dimension is proposed. The algorithm allows to determine explicitly the location of the points of a multilattice given its space group, and to determine whether two multilattices are arithmetically equivalent. The algorithm is based on ideas from integer matrix theory, in particular the reduction to the Smith normal form. Among the applications of this procedure is a software package that allows the classification of complex crystalline structures and the determination of their space groups. Also, it can be used to determine the symmetry of regular systems of points in high dimension, with applications to the study of quasicrystals and sets of points with noncrystallographic symmetry in low dimension, such as viral capsid structures.
International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics
DEVELOPMENTS IN RELIABLE COMPUTING
1999-01-01
The SCAN conference, the International Symposium on Scientific Com puting, Computer Arithmetic and Validated Numerics, takes place bian nually under the joint auspices of GAMM (Gesellschaft fiir Angewandte Mathematik und Mechanik) and IMACS (International Association for Mathematics and Computers in Simulation). SCAN-98 attracted more than 100 participants from 21 countries all over the world. During the four days from September 22 to 25, nine highlighted, plenary lectures and over 70 contributed talks were given. These figures indicate a large participation, which was partly caused by the attraction of the organizing country, Hungary, but also the effec tive support system have contributed to the success. The conference was substantially supported by the Hungarian Research Fund OTKA, GAMM, the National Technology Development Board OMFB and by the J6zsef Attila University. Due to this funding, it was possible to subsidize the participation of over 20 scientists, mainly from Eastern European countries. I...
Development of ferrite logic devices for an arithmetic processor
Heckler, C. H., Jr.
1972-01-01
A number of fundamentally ultra-reliable, all-magnetic logic circuits are developed using as a basis a single element ferrite structure wired as a logic delay element. By making minor additions or changes to the basic wiring pattern of the delay element other logic functions such as OR, AND, NEGATION, MAJORITY, EXCLUSIVE-OR, and FAN-OUT are developed. These logic functions are then used in the design of a full-adder, a set/reset flip-flop, and an edge detector. As a demonstration of the utility of all the developed devices, an 8-bit, all-magnetic, logic arithmetic unit capable of controlled addition, subtraction, and multiplication is designed. A new basic ferrite logic element and associated complementary logic scheme with the potential of improved performance is also described. Finally, an improved batch process for fabricating joint-free power drive and logic interconnect conductors for this basic class of all-magnetic logic is presented.
Arithmetic and local circuitry underlying dopamine prediction errors.
Eshel, Neir; Bukwich, Michael; Rao, Vinod; Hemmelder, Vivian; Tian, Ju; Uchida, Naoshige
2015-09-10
Dopamine neurons are thought to facilitate learning by comparing actual and expected reward. Despite two decades of investigation, little is known about how this comparison is made. To determine how dopamine neurons calculate prediction error, we combined optogenetic manipulations with extracellular recordings in the ventral tegmental area while mice engaged in classical conditioning. Here we demonstrate, by manipulating the temporal expectation of reward, that dopamine neurons perform subtraction, a computation that is ideal for reinforcement learning but rarely observed in the brain. Furthermore, selectively exciting and inhibiting neighbouring GABA (γ-aminobutyric acid) neurons in the ventral tegmental area reveals that these neurons are a source of subtraction: they inhibit dopamine neurons when reward is expected, causally contributing to prediction-error calculations. Finally, bilaterally stimulating ventral tegmental area GABA neurons dramatically reduces anticipatory licking to conditioned odours, consistent with an important role for these neurons in reinforcement learning. Together, our results uncover the arithmetic and local circuitry underlying dopamine prediction errors.
Neighborhood consistency in mental arithmetic: Behavioral and ERP evidence
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Verguts Tom
2007-12-01
Full Text Available Abstract Background Recent cognitive and computational models (e.g. the Interacting Neighbors Model state that in simple multiplication decade and unit digits of the candidate answers (including the correct result are represented separately. Thus, these models challenge holistic views of number representation as well as traditional accounts of the classical problem size effect in simple arithmetic (i.e. the finding that large problems are answered slower and less accurate than small problems. Empirical data supporting this view are still scarce. Methods Data of 24 participants who performed a multiplication verification task with Arabic digits (e.g. 8 × 4 = 36 - true or false? are reported. Behavioral (i.e. RT and errors and EEG (i.e. ERP measures were recorded in parallel. Results We provide evidence for neighborhood-consistency effects in the verification of simple multiplication problems (e.g. 8 × 4. Behaviorally, we find that decade-consistent lures, which share their decade digit with the correct result (e.g. 36, are harder to reject than matched inconsistent lures, which differ in both digits from the correct result (e.g. 28. This neighborhood consistency effect in product verification is similar to recent observations in the production of multiplication results. With respect to event-related potentials we find significant differences for consistent compared to inconsistent lures in the N400 (increased negativity and Late Positive Component (reduced positivity. In this respect consistency effects in our paradigm resemble lexico-semantic effects earlier found in simple arithmetic and in orthographic input processing. Conclusion Our data suggest that neighborhood consistency effects in simple multiplication stem at least partly from central (lexico-semantic' stages of processing. These results are compatible with current models on the representation of simple multiplication facts – in particular with the Interacting Neighbors Model
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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.
Generic construction of efficient matrix product operators
Hubig, C.; McCulloch, I. P.; Schollwöck, U.
2017-01-01
Matrix product operators (MPOs) are at the heart of the second-generation density matrix renormalization group (DMRG) algorithm formulated in matrix product state language. We first summarize the widely known facts on MPO arithmetic and representations of single-site operators. Second, we introduce three compression methods (rescaled SVD, deparallelization, and delinearization) for MPOs and show that it is possible to construct efficient representations of arbitrary operators using MPO arithmetic and compression. As examples, we construct powers of a short-ranged spin-chain Hamiltonian, a complicated Hamiltonian of a two-dimensional system and, as proof of principle, the long-range four-body Hamiltonian from quantum chemistry.
Children's Use of Arithmetic Shortcuts: The Role of Attitudes in Strategy Choice
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Katherine M. Robinson
2012-01-01
Full Text Available Current models of strategy choice do not account for children's attitudes towards different problem solving strategies. Grade 2, 3, and 4 students solved three sets of three-term addition problems. On inversion problems (e.g., 4 + 8 − 8, if children understand the inverse relation between the operations, no calculations are required. On associativity problems (e.g., 5 + 27 − 23, if children understand the associative relation between the operations, problem solving can be facilitated by performing subtraction before addition. A brief intervention involving demonstrations of different problem solving strategies followed the first problem set. Shortcut use increased after the intervention, particularly for students who preferred shortcuts to the left-to-right algorithm. In the third set, children were given transfer problems (e.g., 8 + 4 − 8, 4 − 8 + 8, 27 + 5 − 23. Shortcut use was similar to first set suggesting that transfer did occur. That shortcut use increased the most for students who had positive attitudes about the shortcuts suggests that attitudes have important implications for subsequent arithmetic performance.
2014-01-01
of arithmetic circuits such as adders and multipliers, the arithmetic transform is often used due to its compact- ness [1, 3, 15, 21, 23]. However, for...ai in the spectrum is called an arithmetic coefficient. 332i-MVLSC˙V2 5 6 SHINOBU NAGAYAMA et al. Example 2. Consider the 1-bit adder function f (x1...expressions can be directly realized without any rounding error using only AND gates and adders [16, 20]. Since rounding error is caused only when a given
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Fazal NOORBASHA
2012-08-01
Full Text Available In this present study includes the Very Large Scale Integration (VLSI system implementation of 200MHz, 8-bit, 90nm Complementary Metal Oxide Semiconductor (CMOS Arithmetic and Logic Unit (ALU processor control with logic gate design style and 0.12µm six metal 90nm CMOS fabrication technology. The system blocks and the behaviour are defined and the logical design is implemented in gate level in the design phase. Then, the logic circuits are simulated and the subunits are converted in to 90nm CMOS layout. Finally, in order to construct the VLSI system these units are placed in the floor plan and simulated with analog and digital, logic and switch level simulators. The results of the simulations indicates that the VLSI system can control different instructions which can divided into sub groups: transfer instructions, arithmetic and logic instructions, rotate and shift instructions, branch instructions, input/output instructions, control instructions. The data bus of the system is 16-bit. It runs at 200MHz, and operating power is 1.2V. In this paper, the parametric analysis of the system, the design steps and obtained results are explained.
Wei, Wei; Lu, Hao; Zhao, Hui; Chen, Chuansheng; Dong, Qi; Zhou, Xinlin
2012-03-01
Studies have shown that female children, on average, consistently outperform male children in arithmetic. In the research reported here, 1,556 pupils (8 to 11 years of age) from urban and rural regions in the greater Beijing area completed 10 cognitive tasks. Results showed that girls outperformed boys in arithmetic tasks (i.e., simple subtraction, complex multiplication), as well as in numerosity-comparison, number-comparison, number-series-completion, choice reaction time, and word-rhyming tasks. Boys outperformed girls in a mental rotation task. Controlling for scores on the word-rhyming task eliminated gender differences in arithmetic, whereas controlling for scores on numerical-processing tasks (number comparison, numerosity estimation, numerosity comparison, and number-series completion) and general cognitive tasks (choice reaction time, Raven's Progressive Matrices, and mental rotation) did not. These results suggest that girls' advantage in arithmetic is likely due to their advantage in language processing.
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.
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...
Chiu, Ming Ming
2001-01-01
Novices and experts used the same metaphors to understand and solve problems with negative numbers. Results suggest that the metaphors used by both the children and the adults are central to understanding arithmetic. (Author/MM)
Linguistic and spatial skills predict early arithmetic development via counting sequence knowledge.
Zhang, Xiao; Koponen, Tuire; Räsänen, Pekka; Aunola, Kaisa; Lerkkanen, Marja-Kristiina; Nurmi, Jari-Erik
2014-01-01
Utilizing a longitudinal sample of Finnish children (ages 6-10), two studies examined how early linguistic (spoken vs. written) and spatial skills predict later development of arithmetic, and whether counting sequence knowledge mediates these associations. In Study 1 (N = 1,880), letter knowledge and spatial visualization, measured in kindergarten, predicted the level of arithmetic in first grade, and later growth through third grade. Study 2 (n = 378) further showed that these associations were mediated by counting sequence knowledge measured in first grade. These studies add to the literature by demonstrating the importance of written language for arithmetic development. The findings are consistent with the hypothesis that linguistic and spatial skills can improve arithmetic development by enhancing children's number-related knowledge.
Proposed radix- and word-length-independent standard for floating-point arithmetic
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Cody, W.J.; Coonen, J.T.; Gay, D.M.; Hanson, K.; Hough, D.; Kahan, W.; Karpinski, R.; Palmer, J.; Ris, F.N.; Stevenson, D.
1984-01-01
The Microprocessor Standards Committee of the IEEE Computer Society sponsors two groups drafting proposed standards for floating-point arithmetic. The first, Task P754, reported Draft 10.0 of a Proposed Standard for Binary Floating-point Arithmetic out of committee in December, 1982. The document is now a de facto standard and is progressing slowly through the approval process within the IEEE Computer Society. In August 1983, the second group, Task P854, completed Draft 1.0 of a Proposed Radix- and Word-length independent Standard for Floating-point Arithmetic that generalizes and is upward compatible with the IEEE Proposed Standard for Binary Floating-point Arithmetic. This article places their contents before the public for the first time. 10 references, 3 tables.
Does an Arithmetic Coding Followed by Run-length Coding Enhance the Compression Ratio?
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Mohammed Otair
2015-07-01
Full Text Available Compression is a technique to minimize the quantity of image without excessively decreasing the quality of the image. Then, the translating of compressed image is much more efficient and rapidly than original image. Arithmetic and Huffman coding are mostly used techniques in the entropy coding. This study tries to prove that RLC may be added after Arithmetic coding as an extra processing step which may therefore be coded efficiently without any further degradation of the image quality. So, the main purpose of this study is to answer the following question "Which entropy coding, arithmetic with RLC or Huffman with RLC, is more suitable from the compression ratio perspective?" Finally, experimental results show that an Arithmetic followed by RLC coding yields better compression performance than Huffman with RLC coding.
User interfaces and data entry with real time inverse arithmetic coding
Kaifosh, Patrick
2010-01-01
This paper introduces real time inverse arithmetic coding and user interfaces based thereupon. The main idea is that information-efficient data entry can be achieved by ensuring that each input's associated display space and ease of selection are at all times related to the input's probability of being selected. As with data entry based on inverse arithmetic coding, the layout initially depends on the probabilities of the possible inputs; however, real time inverse arithmetic coding differs in that the user's actions are interpreted not to navigate this probability distribution but rather to modify it according to a learned update rule, which approximates the conditioning of the probability distribution on the user's actions. Potential applications of real time inverse arithmetic coding include text entry, file browsing, integrated multi-program user interfaces, assistive technologies for users with movement disabilities, and ergonomic input methods.
Wei, W; Lu, H.; Zhao, H.; Chen, C.; Dong, Q.; Zhou, X.
2012-01-01
Studies have shown that female children, on average, consistently outperform male children in arithmetic. In the research reported here, 1,556 pupils (8 to 11 years of age) from urban and rural regions in the greater Beijing area completed 10 cognitive tasks. Results showed that girls outperformed boys in arithmetic tasks (i.e., simple subtraction, complex multiplication), as well as in numerosity-comparison, number-comparison, number-series-completion, choice reaction time, and word-rhyming ...
Algorithm XXX : functions to support the IEEE standard for binary floating-point arithmetic.
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Cody, W. J.; Mathematics and Computer Science
1993-12-01
This paper describes C programs for the support functions copysign(x,y), logb(x), scalb(x,n), nextafter(x,y), finite(x), and isnan(x) recommended in the Appendix to the IEEE Standard for Binary Floating-Point Arithmetic. In the case of logb, the modified definition given in the later IEEE Standard for Radix-Independent Floating-Point Arithmetic is followed. These programs should run without modification on most systems conforming to the binary standard.
Advanced topics in the arithmetic of elliptic curves
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...
Signatures of arithmetic simplicity in metabolic network architecture.
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William J Riehl
2010-04-01
Full Text Available Metabolic networks perform some of the most fundamental functions in living cells, including energy transduction and building block biosynthesis. While these are the best characterized networks in living systems, understanding their evolutionary history and complex wiring constitutes one of the most fascinating open questions in biology, intimately related to the enigma of life's origin itself. Is the evolution of metabolism subject to general principles, beyond the unpredictable accumulation of multiple historical accidents? Here we search for such principles by applying to an artificial chemical universe some of the methodologies developed for the study of genome scale models of cellular metabolism. In particular, we use metabolic flux constraint-based models to exhaustively search for artificial chemistry pathways that can optimally perform an array of elementary metabolic functions. Despite the simplicity of the model employed, we find that the ensuing pathways display a surprisingly rich set of properties, including the existence of autocatalytic cycles and hierarchical modules, the appearance of universally preferable metabolites and reactions, and a logarithmic trend of pathway length as a function of input/output molecule size. Some of these properties can be derived analytically, borrowing methods previously used in cryptography. In addition, by mapping biochemical networks onto a simplified carbon atom reaction backbone, we find that properties similar to those predicted for the artificial chemistry hold also for real metabolic networks. These findings suggest that optimality principles and arithmetic simplicity might lie beneath some aspects of biochemical complexity.
Modulation of human motoneuron activity by a mental arithmetic task.
Bensoussan, Laurent; Duclos, Yann; Rossi-Durand, Christiane
2012-10-01
This study aimed to determine whether the performance of a mental task affects motoneuron activity. To this end, the tonic discharge pattern of wrist extensor motor units was analyzed in healthy subjects while they were required to maintain a steady wrist extension force and to concurrently perform a mental arithmetic (MA) task. A shortening of the mean inter-spike interval (ISI) and a decrease in ISI variability occurred when MA task was superimposed to the motor task. Aloud and silent MA affected equally the rate and variability of motoneuron discharge. Increases in surface EMG activity and force level were consistent with the modulation of the motor unit discharge rate. Trial-by-trial analysis of the characteristics of motor unit firing revealed that performing MA increases activation of wrist extensor SMU. It is suggested that increase in muscle spindle afferent activity, resulting from fusimotor drive activation by MA, may have contributed to the increase in synaptic inputs to motoneurons during the mental task performance, likely together with enhancement in the descending drive. The finding that a mental task affects motoneuron activity could have consequences in assessment of motor disabilities and in rehabilitation in motor pathologies.
Circular Interval Arithmetic Applied on LDMT for Linear Interval System
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Stephen Ehidiamhen Uwamusi
2014-07-01
Full Text Available The paper considers the LDMT Factorization of a general nxn matrix arising from system of interval linear equations. We paid special emphasis on Interval Cholesky Factorization. The basic computational tool used is the square root method of circular interval arithmetic in a sense analogous to Gargantini and Henrici as well as the generalized square root method due to Petkovic which enables the construction of the square root of the resulting diagonal matrix. We also made use of Rump’s method for multiplying two intervals expressed in the form of midpoint-radius respectively. Numerical example of matrix factorization in this regard is given which forms the basis of discussion. It is shown that LDMT even though is a numerically stable method for any diagonally dominant matrix it also can lead to excess width of the solution set. It is also pointed out that in spite of the above mentioned objection to interval LDMT it has in addition , the advantage that in the presence of several solution sets sharing the same interval matrix the LDMT Factorization requires to be computed only once which helps in saving substantial computational time. This may be found applicable in the development of military hard ware which requires shooting at a single point but produces multiple broadcast at all other points
Context adaptive binary arithmetic decoding on transport triggered architectures
Rouvinen, Joona; Jääskeläinen, Pekka; Rintaluoma, Tero; Silvén, Olli; Takala, Jarmo
2008-02-01
Video coding standards, such as MPEG-4, H.264, and VC1, define hybrid transform based block motion compensated techniques that employ almost the same coding tools. This observation has been a foundation for defining the MPEG Reconfigurable Multimedia Coding framework that targets to facilitate multi-format codec design. The idea is to send a description of the codec with the bit stream, and to reconfigure the coding tools accordingly on-the-fly. This kind of approach favors software solutions, and is a substantial challenge for the implementers of mobile multimedia devices that aim at high energy efficiency. In particularly as high definition formats are about to be required from mobile multimedia devices, variable length decoders are becoming a serious bottleneck. Even at current moderate mobile video bitrates software based variable length decoders swallow a major portion of the resources of a mobile processor. In this paper we present a Transport Triggered Architecture (TTA) based programmable implementation for Context Adaptive Binary Arithmetic de-Coding (CABAC) that is used e.g. in the main profile of H.264 and in JPEG2000. The solution can be used even for other variable length codes.
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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.
Soft and Joint Source-Channel Decoding of Quasi-Arithmetic Codes
Guionnet, Thomas; Guillemot, Christine
2004-12-01
The issue of robust and joint source-channel decoding of quasi-arithmetic codes is addressed. Quasi-arithmetic coding is a reduced precision and complexity implementation of arithmetic coding. This amounts to approximating the distribution of the source. The approximation of the source distribution leads to the introduction of redundancy that can be exploited for robust decoding in presence of transmission errors. Hence, this approximation controls both the trade-off between compression efficiency and complexity and at the same time the redundancy ( excess rate) introduced by this suboptimality. This paper provides first a state model of a quasi-arithmetic coder and decoder for binary and[InlineEquation not available: see fulltext.]-ary sources. The design of an error-resilient soft decoding algorithm follows quite naturally. The compression efficiency of quasi-arithmetic codes allows to add extra redundancy in the form of markers designed specifically to prevent desynchronization. The algorithm is directly amenable for iterative source-channel decoding in the spirit of serial turbo codes. The coding and decoding algorithms have been tested for a wide range of channel signal-to-noise ratios (SNRs). Experimental results reveal improved symbol error rate (SER) and SNR performances against Huffman and optimal arithmetic codes.
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Robert D Moore
2014-05-01
Full Text Available The current study investigated the influence of cardiorespiratory fitness on arithmetic cognition in forty 9-10 year old children. Measures included a standardized mathematics achievement test to assess conceptual and computational knowledge, self-reported strategy selection, and an experimental arithmetic verification task (including small and large addition problems, which afforded the measurement of event-related brain potentials (ERPs. No differences in math achievement were observed as a function of fitness level, but all children performed better on math concepts relative to math computation. Higher fit children reported using retrieval more often to solve large arithmetic problems, relative to lower fit children. During the arithmetic verification task, higher fit children exhibited superior performance for large problems, as evidenced by greater d’ scores, while all children exhibited decreased accuracy and longer reaction time for large relative to small problems, and incorrect relative to correct solutions. On the electrophysiological level, modulations of early (P1, N170 and late ERP components (P3, N400 were observed as a function of problem size and solution correctness. Higher fit children exhibited selective modulations for N170, P3 and N400 amplitude relative to lower fit children, suggesting that fitness influences symbolic encoding, attentional resource allocation and semantic processing during arithmetic tasks. The current study contributes to the fitness-cognition literature by demonstrating that the benefits of cardiorespiratory fitness extend to arithmetic cognition, which has important implications for the educational environment and the context of learning.
An Eﬃcient Approach for Solving Optimization over Linear Arithmetic Constraints
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Li Chen; Jing-Zheng Wu; Yin-Run Lv; Yong-Ji Wang
2016-01-01
Satisfiability Modulo Theories (SMT) have been widely investigated over the last decade. Recently researchers have extended SMT to the optimization problem over linear arithmetic constraints. To the best of our knowledge, Symba and OPT-MathSAT are two most eﬃcient solvers available for this problem. The key algorithms used by Symba and OPT-MathSAT consist of the loop of two procedures: 1) critical finding for detecting a critical point, which is very likely to be globally optimal, and 2) global checking for confirming the critical point is really globally optimal. In this paper, we propose a new approach based on the Simplex method widely used in operation research. Our fundamental idea is to find several critical points by constructing and solving a series of linear problems with the Simplex method. Our approach replaces the algorithms of critical finding in Symba and OPT-MathSAT, and reduces the runtime of critical finding and decreases the number of executions of global checking. The correctness of our approach is proved. The experiment evaluates our implementation against Symba and OPT-MathSAT on a critical class of problems in real-time systems. Our approach outperforms Symba on 99.6% of benchmarks and is superior to OPT-MathSAT in large-scale cases where the number of tasks is more than 24. The experimental results demonstrate that our approach has great potential and competitiveness for the optimization problem.
A case study of arithmetic facts dyscalculia caused by a hypersensitivity-to-interference in memory.
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.
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.
Ultraspectral sounder data compression using a novel marker-based error-resilient arithmetic coder
Huang, Bormin; Sriraja, Y.; Wei, Shih-Chieh
2006-08-01
Entropy coding techniques aim to achieve the entropy of the source data by assigning variable-length codewords to symbols with the code lengths linked to the corresponding symbol probabilities. Entropy coders (e.g. Huffman coding, arithmetic coding), in one form or the other, are commonly used as the last stage in various compression schemes. While these variable-length coders provide better compression than fixed-length coders, they are vulnerable to transmission errors. Even a single bit error in the transmission process can cause havoc in the subsequent decoded stream. To cope with it, this research proposes a marker-based sentinel mechanism in entropy coding for error detection and recovery. We use arithmetic coding as an example to demonstrate this error-resilient technique for entropy coding. Experimental results on ultraspectral sounder data indicate that the marker-based error-resilient arithmetic coder provides remarkable robustness to correct transmission errors without significantly compromising the compression gains.
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...
A VHDL Implementation of Direct, Pipelined and Distributed Arithmetic FIR Filters
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Sucharitha. L
2013-03-01
Full Text Available Digital filters are typically used to modify or alter the attributes of a signal in the time or frequency domain. In this project, various FIR filter structures will be studied and implemented in VHDL. Basic arithmetic blocks to carry out DSP on FPGAs will be discussed. The very popular LUT based approach for arithmetic circuit implementation will be presented. The conventional PDSP MAC and Distributed arithmetic MAC units will be implemented and their performance will be compared. Usage of Pipelining in multipliers for improving the speed will also be discussed. The ModelSim XE simulator will be used to simulate the design at various stages. Xilinx synthesis tool (XST will be used to synthesize the design for spartan3E family FPGA (XC3S500E. Xilinx Placement {&} Routing tools will be used for backend, design optimization and I/O routing
FUZZY ARITHMETIC AND SOLVING OF THE STATIC GOVERNING EQUATIONS OF FUZZY FINITE ELEMENT METHOD
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郭书祥; 吕震宙; 冯立富
2002-01-01
The key component of finite element analysis of structures with fuzzy parameters,which is associated with handling of some fuzzy information and arithmetic relation of fuzzy variables, was the solving of the governing equations of fuzzy finite element method. Based on a given interval representation of fuzzy numbers, some arithmetic rules of fuzzy numbers and fuzzy variables were developed in terms of the properties of interval arithmetic.According to the rules and by the theory of interval finite element method, procedures for solving the static governing equations of fuzzy finite element method of structures were presented. By the proposed procedure, the possibility distributions of responses of fuzzy structures can be generated in terms of the membership functions of the input fuzzy numbers.It is shown by a numerical example that the computational burden of the presented procedures is low and easy to implement. The effectiveness and usefulness of the presented procedures are also illustrated.
Dehaene, S; Cohen, L
1997-06-01
We describe two acalculic patients, one with a left subcortical lesion and the other with a right inferior parietal lesion and Gerstmann's syndrome. Both suffered from "pure anarithmetia": they could read arabic numerals and write them to dictation, but experienced a pronounced calculation deficit. On closer analysis, however, distinct deficits were found. The subcortical case suffered from a selective deficit of rote verbal knowledge, including but not limited to arithmetic tables, while her semantic knowledge of numerical quantities was intact. Conversely the inferior parietal case suffered from a category-specific impairment of quantitative numerical knowledge, particularly salient in subtraction and number bissection tasks, with preserved knowledge of rote arithmetic facts. This double dissociation suggests that numerical knowledge is processed in different formats within distinct cerebral pathways. We suggest that a left subcortical network contributes to the storage and retrieval of rote verbal arithmetic facts, while a bilateral inferior parietal network is dedicated to the mental manipulation of numerical quantities.
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Verônica Bender Haydu
2006-01-01
Full Text Available The equivalence paradigm has been applied to the development of a variety of procedures applied to teach reading, writing and arithmetic. This work aimed to investigate the effect of teaching stimulus equivalence relations between three different forms of arithmetic sum problems on problem-solving behavior. Seven first grade students of Fundamental Schooling (=Elementary Schooling were submitted to a pre-test, and a post-test with sum problems printed in the form of slave (A, operations (B and word problems (C. The conditional discrimination procedure established relations between A-B and A-C. Six of seven participants responded accordingly to the established classes. The performance of the participants in the post-test was higher than in the pre-test. It was concluded that the establishment of equivalence relations between arithmetic sum problems in the form of slave, operations, and word problems enhanced the performance of the resolution of those types of problems.
Van Rinsveld, Amandine; Brunner, Martin; Landerl, Karin; Schiltz, Christine; Ugen, Sonja
2015-01-01
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.
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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.
Ultrafast all-optical arithmetic logic based on hydrogenated amorphous silicon microring resonators
Gostimirovic, Dusan; Ye, Winnie N.
2016-03-01
For decades, the semiconductor industry has been steadily shrinking transistor sizes to fit more performance into a single silicon-based integrated chip. This technology has become the driving force for advances in education, transportation, and health, among others. However, transistor sizes are quickly approaching their physical limits (channel lengths are now only a few silicon atoms in length), and Moore's law will likely soon be brought to a stand-still despite many unique attempts to keep it going (FinFETs, high-k dielectrics, etc.). This technology must then be pushed further by exploring (almost) entirely new methodologies. Given the explosive growth of optical-based long-haul telecommunications, we look to apply the use of high-speed optics as a substitute to the digital model; where slow, lossy, and noisy metal interconnections act as a major bottleneck to performance. We combine the (nonlinear) optical Kerr effect with a single add-drop microring resonator to perform the fundamental AND-XOR logical operations of a half adder, by all-optical means. This process is also applied to subtraction, higher-order addition, and the realization of an all-optical arithmetic logic unit (ALU). The rings use hydrogenated amorphous silicon as a material with superior nonlinear properties to crystalline silicon, while still maintaining CMOS-compatibility and the many benefits that come with it (low cost, ease of fabrication, etc.). Our method allows for multi-gigabit-per-second data rates while maintaining simplicity and spatial minimalism in design for high-capacity manufacturing potential.
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.
Systems chemistry: logic gates, arithmetic units, and network motifs in small networks.
Wagner, Nathaniel; Ashkenasy, Gonen
2009-01-01
A mixture of molecules can be regarded as a network if all the molecular components participate in some kind of interaction with other molecules--either physical or functional interactions. Template-assisted ligation reactions that direct replication processes can serve as the functional elements that connect two members of a chemical network. In such a process, the template does not necessarily catalyze its own formation, but rather the formation of another molecule, which in turn can operate as a template for reactions within the network medium. It was postulated that even networks made up of small numbers of molecules possess a wealth of molecular information sufficient to perform rather complex behavior. To probe this assumption, we have constructed virtual arrays consisting of three replicating molecules, in which dimer templates are capable of catalyzing reactants to form additional templates. By using realistic parameters from peptides or DNA replication experiments, we simulate the construction of various functional motifs within the networks. Specifically, we have designed and implemented each of the three-element Boolean logic gates, and show how these networks are assembled from four basic "building blocks". We also show how the catalytic pathways can be wired together to perform more complex arithmetic units and network motifs, such as the half adder and half subtractor computational modules, and the coherent feed-forward loop network motifs under different sets of parameters. As in previous studies of chemical networks, some of the systems described display behavior that would be difficult to predict without the numerical simulations. Furthermore, the simulations reveal trends and characteristics that should be useful as "recipes" for future design of experimental functional motifs and for potential integration into modular circuits and molecular computation devices.
On the torsion in the cohomology of arithmetic hyperbolic 3-manifolds
Marshall, Simon
2011-01-01
In this paper we consider the cohomology of a closed arithmetic hyperbolic 3-manifold with coefficients in the local system defined by the even symmetric powers of the standard representation of SL(2,C). The cohomology is defined over the integers and is a finite abelian group. We show that the order of the 2nd cohomology grows exponentially as the local system grows. We also consider the twisted Ruelle zeta function of a closed arithmetic hyperbolic 3-manifold and we express the leading coefficient of its Laurent expansion at the origin in terms of the orders of the torsion subgroups of the cohomology.
The geometric and arithmetic volume of Shimura varieties of orthogonal type
Hörmann, Fritz
2011-01-01
We apply the theory of Borcherds products to calculate arithmetic volumes (heights) of Shimura varieties of orthogonal type up to contributions from very bad primes. The approach is analogous to the well-known computation of their geometric volume by induction, using special cycles. A functorial theory of integral models of toroidal compactifications of those varieties and a theory of arithmetic Chern classes of integral automorphic vector bundles with singular metrics are used. We obtain some evidence in the direction of Kudla's conjectures on relations of heights of special cycles on these varieties to special derivatives of Eisenstein series.
The B-coder: an improved binary arithmetic coder and probability estimator
Kelly, Benjamin G.; Brailsford, David F.
2006-01-01
In this paper we present the B-coder, an efficient binary arithmetic coder that performs extremely well on a wide range of data. The B-coder should be classed as an `approximate’ arithmetic coder, because of its use of an approximation to multiplication. We show that the approximation used in the B-coder has an efficiency cost of 0.003 compared to Shannon entropy. At the heart of the B-coder is an efficient state machine that adapts rapidly to the data to be coded. The adaptation is achieved ...
Applications of interval arithmetic in solving polynomial equations by Wu's elimination method
Institute of Scientific and Technical Information of China (English)
CHEN; Falai; YANG; Wu
2005-01-01
Wu's elimination method is an important method for solving multivariate polynomial equations. In this paper, we apply interval arithmetic to Wu's method and convert the problem of solving polynomial equations into that of solving interval polynomial equations. Parallel results such as zero-decomposition theorem are obtained for interval polynomial equations. The advantages of the new approach are two-folds: First, the problem of the numerical instability arisen from floating-point arithmetic is largely overcome. Second,the low efficiency of the algorithm caused by large intermediate coefficients introduced by exact compaction is dramatically improved. Some examples are provided to illustrate the effectiveness of the proposed algorithm.
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Ashkan Emami Ale Agha
2013-06-01
Full Text Available One of the most important concepts in multi programming Operating Systems is scheduling. It helps in choosing the processes for execution. Round robin method is one of the most important algorithms in scheduling. It is the most popular algorithm due to its fairness and starvation free nature towards the processes, which is achieved by using proper quantum time. The main challenge in this algorithm is selection of quantum time. This parameter affects on average Waiting Time and average Turnaround Time in execution queue. As the quantum time is static, it causes less context switching in case of high quantum time and high context switching in case of less quantum time. Increasing context switch leads to high average waiting time, high average turnaround time which is an overhead and degrades the system performance. With respect to these points, the algorithms should calculate proper value for the quantum time. Two main classes of algorithms that are proposed to calculate the quantum time include static and dynamic methods. In static methods quantum time is fixed during the scheduling. Dynamic algorithms are one of these methods that change the value of quantum time in each cycle. For example in one method the value of quantum time in each cycle is equal to the median of burst times of processes in ready queue and for another method this value is equal to arithmetic mean of burst times of ready processes.In this paper we proposed a new method to obtaining quantum time in each cycle based on arithmetic-harmonic mean (HARM. Harmonic mean is calculated by dividing the number of observations by the reciprocal of each number in the series. With examples we show that in some cases it can provides better scheduling criteria and improves the average Turnaround Time and average Waiting Time.
Alcoholado, Cristián; Diaz, Anita; Tagle, Arturo; Nussbaum, Miguel; Infante, Cristián
2016-01-01
This study aims to understand the differences in student learning outcomes and classroom behaviour when using the interpersonal computer, personal computer and pen-and-paper to solve arithmetic exercises. In this multi-session experiment, third grade students working on arithmetic exercises from various curricular units were divided into three…
Algebraic functions of complexity one, a Weierstrass theorem, and three arithmetic operations
Beloshapka, V. K.
2016-07-01
The Weierstrass theorem concerning functions admitting an algebraic addition theorem enables us to give an explicit description of algebraic functions of two variables of analytical complexity one. Their description is divided into three cases: the general case, which is elliptic, and two special ones, a multiplicative and an additive one. All cases have a unified description; they are the orbits of an action of the gauge pseudogroup. The first case is a 1-parameter family of orbits of "elliptic addition," the second is the orbit of multiplication, and the third of addition. Here the multiplication and addition can be derived from the "elliptic addition" by passages to a limit. On the other hand, the elliptic orbits correspond to complex structures on the torus, the multiplicative orbit corresponds to the complex structure on the cylinder, and the additive one to that on the complex plane. This work was financially supported by the Russian Foundation for Basic Research under grants nos. 14-00709-a and 13-01-12417-ofi-m2.
Guthormsen, Amy M.; Fisher, Kristie J.; Bassok, Miriam; Osterhout, Lee; DeWolf, Melissa; Holyoak, Keith J.
2016-01-01
Research on language processing has shown that the disruption of conceptual integration gives rise to specific patterns of event-related brain potentials (ERPs)--N400 and P600 effects. Here, we report similar ERP effects when adults performed cross-domain conceptual integration of analogous semantic and mathematical relations. In a problem-solving…
Formulae for Arithmetic on Genus 2 Hyperelliptic Curves
DEFF Research Database (Denmark)
Lange, Tanja
2005-01-01
The ideal class group of hyperelliptic curves can be used in cryptosystems based on the discrete logarithm problem. In this article we present explicit formulae to perform the group operations for genus 2 curves. The formulae are completely general but to achieve the lowest number of operations w...
Deaño, Manuel Deaño; Alfonso, Sonia; Das, Jagannath Prasad
2015-03-01
This study reports the cognitive and arithmetic improvement of a mathematical model based on the program PASS Remedial Program (PREP), which aims to improve specific cognitive processes underlying academic skills such as arithmetic. For this purpose, a group of 20 students from the last four grades of Primary Education was divided into two groups. One group (n=10) received training in the program and the other served as control. Students were assessed at pre and post intervention in the PASS cognitive processes (planning, attention, simultaneous and successive processing), general level of intelligence, and arithmetic performance in calculus and solving problems. Performance of children from the experimental group was significantly higher than that of the control group in cognitive process and arithmetic. This joint enhancement of cognitive and arithmetic processes was a result of the operationalization of training that promotes the encoding task, attention and planning, and learning by induction, mediation and verbalization. The implications of this are discussed.
Institute of Scientific and Technical Information of China (English)
袁利国; 傅新楚; 余荣忠
2005-01-01
In this paper, we discuss a class of piecewise linear hyperbolic maps on the 2-torus. These maps arise in the second-order digital filter with two's complement arithmetic. By introducing codings underlying the map operations, we give some admissibility conditions for symbolic sequences and find some periodic properties of these symbolic sequences. Then we use these conditions to check the admissibility of periodic symbol sequences.
Arithmetic memory networks established in childhood are changed by experience in adulthood.
Martinez-Lincoln, Amanda; Cortinas, Christina; Wicha, Nicole Y Y
2015-01-01
Adult bilinguals show stronger access to multiplication tables when using the language in which they learned arithmetic during childhood (LA+) than the other language (LA-), implying language-specific encoding of math facts. However, most bilinguals use LA+ throughout their life, confounding the impact of encoding and use. We tested if using arithmetic facts in LA- could reduce this LA- disadvantage. We measured event related brain potentials while bilingual teachers judged the correctness of multiplication problems in each of their languages. Critically, each teacher taught arithmetic in either LA+ or LA-. Earlier N400 peak latency was observed in both groups for the teaching than non-teaching language, showing more efficient access to these facts with use. LA+ teachers maintained an LA+ advantage, while LA- teachers showed equivalent N400 congruency effects (for incorrect versus correct solutions) in both languages. LA- teachers also showed a late positive component that may reflect conflict monitoring between their LA+ and a strong LA-. Thus, the LA- disadvantage for exact arithmetic established in early bilingual education can be mitigated by later use of LA-.
Viljaranta, Jaana; Lerkkanen, Marja-Kristiina; Poikkeus, Anna-Maija; Aunola, Kaisa; Nurmi, Jari-Erik
2009-01-01
To examine the cross-lagged relationships between children's task motivation in mathematics and literacy, and their related performance, 139 children aged 5-6 years were examined twice during their kindergarten year. The results showed that only math-related task motivation and arithmetic performance showed cross-lagged relationship: the higher…
Arithmetical Thinking in Children Attending Special Schools for the Intellectually Disabled
Eriksson, Gota
2008-01-01
This article focuses on spontaneous and progressive knowledge building in ''the arithmetic of the child.'' The aim is to investigate variations in the behavior patterns of eight pupils attending a school for the intellectually disabled. The study is based on the epistemology of radical constructivism and the methodology of multiple clinical…
Supervision of Teachers Based on Adjusted Arithmetic Learning in Special Education
Eriksson, Gota
2008-01-01
This article reports on 20 children's learning in arithmetic after teaching was adjusted to their conceptual development. The report covers periods from three months up to three terms in an ongoing intervention study of teachers and children in schools for the intellectually disabled and of remedial teaching in regular schools. The researcher…
Eye Gaze Reveals a Fast, Parallel Extraction of the Syntax of Arithmetic Formulas
Schneider, Elisa; Maruyama, Masaki; Dehaene, Stanislas; Sigman, Mariano
2012-01-01
Mathematics shares with language an essential reliance on the human capacity for recursion, permitting the generation of an infinite range of embedded expressions from a finite set of symbols. We studied the role of syntax in arithmetic thinking, a neglected component of numerical cognition, by examining eye movement sequences during the…
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...
The Design and Testing of Multimedia for Teaching Arithmetic to Deaf Learners
Techaraungrong, Piyaporn; Suksakulchai, Surachai; Kaewprapan, Wacheerapan; Murphy, Elizabeth
2017-01-01
The purpose of the study reported on in this paper was to design and test multimedia for deaf and hard of hearing (DHH) learners. The study focused on counting, addition and subtraction with grade one (age 7) DHH learners in Thailand. The multimedia created for the study was informed by design considerations for DHH learners of arithmetic and…
Hubber, Paula J; Gilmore, Camilla; Cragg, Lucy
2014-05-01
Previous research has demonstrated that working memory plays an important role in arithmetic. Different arithmetical strategies rely on working memory to different extents-for example, verbal working memory has been found to be more important for procedural strategies, such as counting and decomposition, than for retrieval strategies. Surprisingly, given the close connection between spatial and mathematical skills, the role of visuospatial working memory has received less attention and is poorly understood. This study used a dual-task methodology to investigate the impact of a dynamic spatial n-back task (Experiment 1) and tasks loading the visuospatial sketchpad and central executive (Experiment 2) on adults' use of counting, decomposition, and direct retrieval strategies for addition. While Experiment 1 suggested that visuospatial working memory plays an important role in arithmetic, especially when counting, the results of Experiment 2 suggested this was primarily due to the domain-general executive demands of the n-back task. Taken together, these results suggest that maintaining visuospatial information in mind is required when adults solve addition arithmetic problems by any strategy but the role of domain-general executive resources is much greater than that of the visuospatial sketchpad.
Spontaneous Focusing on Numerosity as a Domain-Specific Predictor of Arithmetical Skills
Hannula, Minna M.; Lepola, Janne; Lehtinen, Erno
2010-01-01
The aim of this 2 year longitudinal study was to explore whether children's individual differences in spontaneous focusing on numerosity (SFON) in kindergarten predict arithmetical and reading skills 2 years later in school. Moreover, we investigated whether the positive relationship between SFON and mathematical skills is explained by children's…
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…
Kamii, Constance
This book describes and develops an innovative program of teaching arithmetic in the early elementary grades. The educational strategies employed are based on Jean Piaget's constructivist scientific ideas of how children develop logico-mathematical thinking. The book is written in collaboration with a classroom teacher and premised on the…
Dairy, Lorna
This study is the final report of a three year project to find out if the use of Cuisenaire rods in kindergarten, first, and second grades upgrades arithmetic achievement. Both experimental and control schools enrolled children with average ability who came from lower middle class homes. Children in the experimental kindergarten classes were…
The Arithmetic Mean - Geometric Mean - Harmonic Mean: Inequalities and a Spectrum of Applications
Indian Academy of Sciences (India)
Prithwijit De
2016-12-01
The Arithmetic Mean – Geometric Mean – Harmonic Meaninequality, AM–GM–HM inequality in short, is one of thefundamental inequalities in Algebra, and it is used extensivelyin olympiad mathematics to solve many problems. Theaim of this article is to acquaint students with the inequality,its proof and various applications.
The foundations of arithmetic a logico-mathematical enquiry into the concept of number
Frege, Gottlob
1986-01-01
The Foundations of Arithmetic is undoubtedly the best introduction to Frege's thought; it is here that Frege expounds the central notions of his philosophy, subjecting the views of his predecessors and contemporaries to devastating analysis. The book represents the first philosophically sound discussion of the concept of number in Western civilization. It profoundly influenced developments in the philosophy of mathematics, general ontology, and mathematics.
Hardware realizations of arithmetic with complex integer numbers on PLD-base
Directory of Open Access Journals (Sweden)
Opanasenko V. N.
2008-10-01
Full Text Available Hardware realizations of arithmetic with complex integer numbers were proposed. The generators of sine and cosine with different frequency were used to make behavior stand. Real verification was made by block Spartan–3–400 Evaluation Kit, which connect up PCI of personal computer.
Evaluation of AnimalWatch: An Intelligent Tutoring System for Arithmetic and Fractions
Beal, Carole R.; Arroyo, Ivon M.; Cohen, Paul R.; Woolf, Beverly P.
2010-01-01
Three studies were conducted with middle school students to evaluate a web-based intelligent tutoring system (ITS) for arithmetic and fractions. The studies involved pre and post test comparisons, as well as group comparisons to assess the impact of the ITS on students' math problem solving. Results indicated that students improved from pre to…
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…
Partial sums of the M\\"obius function in arithmetic progressions assuming GRH
Halupczok, Karin
2011-01-01
We consider Mertens' function M(x,q,a) in arithmetic progression, Assuming the generalized Riemann hypothesis (GRH), we show an upper bound that is uniform for all moduli which are not too large. For the proof, a former method of K. Soundararajan is extended to L-series.
A Teachable Agent Game Engaging Primary School Children to Learn Arithmetic Concepts and Reasoning
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…
Joint source/channel iterative arithmetic decoding with JPEG 2000 image transmission application
Zaibi, Sonia; Zribi, Amin; Pyndiah, Ramesh; Aloui, Nadia
2012-12-01
Motivated by recent results in Joint Source/Channel coding and decoding, we consider the decoding problem of Arithmetic Codes (AC). In fact, in this article we provide different approaches which allow one to unify the arithmetic decoding and error correction tasks. A novel length-constrained arithmetic decoding algorithm based on Maximum A Posteriori sequence estimation is proposed. The latter is based on soft-input decoding using a priori knowledge of the source-symbol sequence and the compressed bit-stream lengths. Performance in the case of transmission over an Additive White Gaussian Noise channel is evaluated in terms of Packet Error Rate. Simulation results show that the proposed decoding algorithm leads to significant performance gain while exhibiting very low complexity. The proposed soft input arithmetic decoder can also generate additional information regarding the reliability of the compressed bit-stream components. We consider the serial concatenation of the AC with a Recursive Systematic Convolutional Code, and perform iterative decoding. We show that, compared to tandem and to trellis-based Soft-Input Soft-Output decoding schemes, the proposed decoder exhibits the best performance/complexity tradeoff. Finally, the practical relevance of the presented iterative decoding system is validated under an image transmission scheme based on the JPEG 2000 standard and excellent results in terms of decoded image quality are obtained.
On the history of van der Waerden's theorem on arithmetic progressions
Directory of Open Access Journals (Sweden)
Tom C. Brown
2001-12-01
Full Text Available In this expository note, we discuss the celebrated theorem known as ``van der Waerden's theorem on arithmetic progressions", the history of work on upper and lower bounds for the function associated with this theorem, a number of generalizations, and some open problems.
Development of Working Memory and Performance in Arithmetic: A Longitudinal Study with Children
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…
Arithmetic Facts Storage Deficit: The Hypersensitivity-to-Interference in Memory Hypothesis
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…
A High-Throughput Binary Arithmetic Coding Architecture for H.264/AVC CABAC
Liu, Yizhong; Song, Tian; Shimamoto, Takashi
In this paper, we propose a high-throughput binary arithmetic coding architecture for CABAC (Context Adaptive Binary Arithmetic Coding) which is one of the entropy coding tools used in the H.264/AVC main and high profiles. The full CABAC encoding functions, including binarization, context model selection, arithmetic encoding and bits generation, are implemented in this proposal. The binarization and context model selection are implemented in a proposed binarizer, in which a FIFO is used to pack the binarization results and output 4 bins in one clock. The arithmetic encoding and bits generation are implemented in a four-stage pipeline with the encoding ability of 4 bins/clock. In order to improve the processing speed, the context variables access and update for 4 bins are paralleled and the pipeline path is balanced. Also, because of the outstanding bits issue, a bits packing and generation strategy for 4 bins paralleled processing is proposed. After implemented in verilog-HDL and synthesized with Synopsys Design Compiler using 90nm libraries, this proposal can work at the clock frequency of 250MHz and takes up about 58K standard cells, 3.2Kbits register files and 27.6K bits ROM. The throughput of processing 1000M bins per second can be achieved in this proposal for the HDTV applications.
Linguistic and Spatial Skills Predict Early Arithmetic Development via Counting Sequence Knowledge
Zhang, Xiao; Koponen, Tuire; Räsänen, Pekka; Aunola, Kaisa; Lerkkanen, Marja-Kristiina; Nurmi, Jari-Erik
2014-01-01
Utilizing a longitudinal sample of Finnish children (ages 6-10), two studies examined how early linguistic (spoken vs. written) and spatial skills predict later development of arithmetic, and whether counting sequence knowledge mediates these associations. In Study 1 (N = 1,880), letter knowledge and spatial visualization, measured in…
Sigal's Ineffective Computer-Based Practice of Arithmetic: A Case Study.
Hativa, Nira
1988-01-01
A student was observed practicing arithmetic with a computer-assisted instruction (CAI) system. She enjoyed practice and believed that it helped. However, she consistently failed to solve problems on the computer that she could do with pencil and paper. This paper suggests reasons for her problems and draws implications for CAI. (Author/PK)
Hativa, Nira
1992-01-01
Examined the problem-solving strategies of above average students (n=42) in grades 2-4 on problems involving forgotten or new material while practicing arithmetic with a computer. Identified the different problem-solving strategies used, sorted them into categories, and illustrated them with examples from students' protocols. Made suggestions for…
Identifying Strategies in Arithmetic with the Operand Recognition Paradigm: A Matter of Switch Cost?
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…
An Arithmetical Hierarchy of the Law of Excluded Middle and Related Principles
DEFF Research Database (Denmark)
Akama, Yohji; Berardi, Stefano; Hayashi, Susumu;
2004-01-01
The topic of this paper is Relative Constructivism. We are concerned with classifying non-constructive principles from the constructive viewpoint.We compare, up to provability in Intuitionistic Arithmetic, sub-classical principles like Markov's Principle, (a function-free version of) Weak König...
Reinvention of early algebra : developmental research on the transition from arithmetic to algebra
Amerom, B.A. van
2002-01-01
In chapter 1 we give our reasons for carrying out this developmental research project on the transition from arithmetic to algebra, which includes the design of an experimental learning strand on solving equations. Chapter 2 describes the theoretical background of the book: current views on the teac
Bragman, Ruth; Hardy, Robert C.
1982-01-01
Results from testing 20 first graders in a remedial class in Maryland indicated that: same pattern recognition was significantly higher than reverse pattern recognition; identical pattern recognition did not affect performance on reading and arithmetic achievement; reverse pattern recognition significantly affected performance on reading and…
The effects of eating or skipping breakfast on ERP correlates of mental arithmetic were studied in preadolescents differing in experience (age) and mathematical skills. Participants, randomly assigned to treatment [eat (B) or skip (SB) breakfast (each, n = 41)], were sub-grouped by age [8.8 yrs (B: ...
Children's Understanding of the Arithmetic Concepts of Inversion and Associativity
Robinson, Katherine M.; Ninowski, Jerilyn E.; Gray, Melissa L.
2006-01-01
Previous studies have shown that even preschoolers can solve inversion problems of the form a + b - b by using the knowledge that addition and subtraction are inverse operations. In this study, a new type of inversion problem of the form d x e [divided by] e was also examined. Grade 6 and 8 students solved inversion problems of both types as well…
RAID-6 reed-solomon codes with asymptotically optimal arithmetic complexities
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.
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.
A New Arithmetic Coding System Combining Source Channel Coding and MAP Decoding
Institute of Scientific and Technical Information of China (English)
PANG Yu-ye; SUN Jun; WANG Jia
2007-01-01
A new arithmetic coding system combining source channel coding and maximum a posteriori decoding were proposed.It combines source coding and error correction tasks into one unified process by introducing an adaptive forbidden symbol.The proposed system achieves fixed length code words by adaptively adjusting the probability of the forbidden symbol and adding tail digits of variable length.The corresponding improved MAP decoding metric was derived.The proposed system can improve the performance.Simulations were performed on AWGN channels with various noise levels by using both hard and soft decision with BPSK modulation.The results show its performance is slightly better than that of our adaptive arithmetic error correcting coding system using a forbidden symbol.
Lightweight Floating-Point Arithmetic: Case Study of Inverse Discrete Cosine Transform
Fang, Fang; Chen, Tsuhan; Rutenbar, Rob A.
2002-12-01
To enable floating-point (FP) signal processing applications in low-power mobile devices, we propose lightweight floating-point arithmetic. It offers a wider range of precision/power/speed/area trade-offs, but is wrapped in forms that hide the complexity of the underlying implementations from both multimedia software designers and hardware designers. Libraries implemented in C++ and Verilog provide flexible and robust floating-point units with variable bit-width formats, multiple rounding modes and other features. This solution bridges the design gap between software and hardware, and accelerates the design cycle from algorithm to chip by avoiding the translation to fixed-point arithmetic. We demonstrate the effectiveness of the proposed scheme using the inverse discrete cosine transform (IDCT), in the context of video coding, as an example. Further, we implement lightweight floating-point IDCT into hardware and demonstrate the power and area reduction.
Directory of Open Access Journals (Sweden)
Erich Selder
2015-01-01
Full Text Available The correspondence between right triangles with rational sides, triplets of rational squares in arithmetic succession and integral solutions of certain quadratic forms is well-known. We show how this correspondence can be extended to the generalized notions of rational θ-triangles, rational squares occurring in arithmetic progressions and concordant forms. In our approach we establish one-to-one mappings to rational points on certain elliptic curves and examine in detail the role of solutions of the θ-congruent number problem and the concordant form problem associated with nontrivial torsion points on the corresponding elliptic curves. This approach allows us to combine and extend some disjoint results obtained by a number of authors, to clarify some statements in the literature and to answer some hitherto open questions.
Boulgouris, N V; Tzovaras, D; Strintzis, M G
2001-01-01
The optimal predictors of a lifting scheme in the general n-dimensional case are obtained and applied for the lossless compression of still images using first quincunx sampling and then simple row-column sampling. In each case, the efficiency of the linear predictors is enhanced nonlinearly. Directional postprocessing is used in the quincunx case, and adaptive-length postprocessing in the row-column case. Both methods are seen to perform well. The resulting nonlinear interpolation schemes achieve extremely efficient image decorrelation. We further investigate context modeling and adaptive arithmetic coding of wavelet coefficients in a lossless compression framework. Special attention is given to the modeling contexts and the adaptation of the arithmetic coder to the actual data. Experimental evaluation shows that the best of the resulting coders produces better results than other known algorithms for multiresolution-based lossless image coding.
Nested arithmetic progressions of oscillatory phases in Olsen's enzyme reaction model.
Gallas, Marcia R; Gallas, Jason A C
2015-06-01
We report some regular organizations of stability phases discovered among self-sustained oscillations of a biochemical oscillator. The signature of such organizations is a nested arithmetic progression in the number of spikes of consecutive windows of periodic oscillations. In one of them, there is a main progression of windows whose consecutive number of spikes differs by one unit. Such windows are separated by a secondary progression of smaller windows whose number of spikes differs by two units. Another more complex progression involves a fan-like nested alternation of stability phases whose number of spikes seems to grow indefinitely and to accumulate methodically in cycles. Arithmetic progressions exist abundantly in several control parameter planes and can be observed by tuning just one among several possible rate constants governing the enzyme reaction.
Arithmetic Accuracy in Children From High- and Low-Income Schools
Directory of Open Access Journals (Sweden)
Elida V. Laski
2016-04-01
Full Text Available This study investigated income group differences in kindergartners’ and first graders’ (N = 161 arithmetic by examining the link between accuracy and strategy use on simple and complex addition problems. Low-income children were substantially less accurate than high-income children, in terms of both percentage of correctly solved problems and the magnitude of errors, with low-income first graders being less accurate than high-income kindergartners. Higher-income children were more likely to use sophisticated mental strategies than their lower-income peers, who used predominantly inefficient counting or inappropriate strategies. Importantly, this difference in strategies mediated the relation between income group and addition. Examining underlying strategies has implications for understanding income group differences in arithmetic and potential means of remedying it via instruction.
Math anxiety differentially affects WAIS-IV arithmetic performance in undergraduates.
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.
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.
Low Complexity DCT-based DSC approach forHyperspectral Image Compression with Arithmetic Code
Directory of Open Access Journals (Sweden)
Meena Babu Vallakati
2012-09-01
Full Text Available This paper proposes low complexity codec for lossy compression on a sample hyperspectral image. These images have two kinds of redundancies: 1 spatial; and 2 spectral. A discrete cosine transform (DCT- based Distributed Source Coding(DSC paradigm with Arithmetic code for low complexity is introduced. Here, Set-partitioning based approach is applied to reorganize DCT coefficients into wavelet like tree structure as Setpartitioning works on wavelet transform, and extract the sign, refinement, and significance bitplanes. The extracted refinement bits are Arithmetic encoded, then by applying low density parity check based (LDPC-based Slepian-Wolf coder is implement to our DSC strategy. Experimental results for SAMSON (Spectroscopic Aerial Mapping System with Onboard Navigation data show that proposed scheme achieve peak signal to noise ratio and compression to a very good extent for water cube compared to building, land or forest cube.
Cryptanalysis of a chaos-based cryptosystem with an embedded adaptive arithmetic coder
Institute of Scientific and Technical Information of China (English)
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 19050508).Although thisnew 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.
Lightweight Floating-Point Arithmetic: Case Study of Inverse Discrete Cosine Transform
Directory of Open Access Journals (Sweden)
Fang Fang
2002-09-01
Full Text Available To enable floating-point (FP signal processing applications in low-power mobile devices, we propose lightweight floating-point arithmetic. It offers a wider range of precision/power/speed/area trade-offs, but is wrapped in forms that hide the complexity of the underlying implementations from both multimedia software designers and hardware designers. Libraries implemented in C++ and Verilog provide flexible and robust floating-point units with variable bit-width formats, multiple rounding modes and other features. This solution bridges the design gap between software and hardware, and accelerates the design cycle from algorithm to chip by avoiding the translation to fixed-point arithmetic. We demonstrate the effectiveness of the proposed scheme using the inverse discrete cosine transform (IDCT, in the context of video coding, as an example. Further, we implement lightweight floating-point IDCT into hardware and demonstrate the power and area reduction.
Arithmetic of automatically forming meridian tire tread pattern on basis of unigraphics
Institute of Scientific and Technical Information of China (English)
Xiuting WEI; Ping ZHANG; Xiaoning SU
2009-01-01
Tire tread pattern affects the performance of motor vehicles and traffic safety; therefore, designing it accurately is very important. This paper mainly discusses the arithmetic that can form tire tread patterns automati-cally and rapidly. The algorithm flow is given. Then, the principle of planar picture creating three-dimensional patterns concretely is analyzed. The experimental results of the meridian tire pattern based on the UG API function prove the feasibility and excellence of the proposed method.
Separators of Arithmetically Cohen-Macaulay fat points in P^1 x P^1
Guardo, Elena
2010-01-01
Let Z be a set of fat points in P^1 x P^1 that is also arithmetically Cohen-Macaulay (ACM). We describe how to compute the degree of a separator of a fat point of multiplicity m for each point in the support of Z using only a numerical description of Z. Our formula extends the case of reduced points which was previously known.
Institute of Scientific and Technical Information of China (English)
ZHANG Yun-ting; ZHANG Quan; ZHANG Jing; LI Wei
2005-01-01
Background Asymmetry of bilateral cerebral function, i.e. laterality, is an important phenomenon in many brain actions: arithmetic calculation may be one of these phenomena. In this study, first, laterality of brain areas associated with arithmetic calculations was revealed by functional magnetic resonance imaging (fMRI). Second, the relationship among laterality, handedness, and types of arithmetic task was assessed. Third, we postulate possible reasons for laterality.Methods Using a block-designed experiment, twenty-five right-handed and seven left-handed healthy volunteers carried out simple calculations, complex calculations and proximity judgments. T1WI and GRE-EPI fMRI were performed with a GE 1.5T whole body MRI scanner. Statistical parametric mapping (SPM99) was used to process data and localize functional areas. Numbers of activated voxels were recorded to calculate laterality index for evaluating the laterality of functional brain areas.Results For both groups, the activation of functional areas in the frontal lobe showed a tendency towards the nonpredominant hand side, but the functional areas in the inferior parietal lobule had left laterality. During simple and complex calculations, the laterality indices of the prefrontal cortex and premotor area were higher in the right-handed group than that in the left-handed group, whereas the laterality of the inferior parietal lobule had no such significant difference. In both groups, when the difficulty of the task increased, the laterality of the prefrontal cortex, premotor area, and inferior parietal lobule decreased, but the laterality of posterior part of the inferior frontal gyrus increased.Conclusions The laterality of the functional brain areas associated with arithmetic calculations can be detected with fMRI. The laterality of the functional areas was related to handedness and task difficulty.
Generalization of the proposed IEEE standard for floating-point arithmetic
Energy Technology Data Exchange (ETDEWEB)
Cody, W.J.
1982-12-10
Several years ago the Microprocessor Standards Committee of the IEEE Computer Society established a Floating-Point Working Group to draft a standard binary floating-point arithmetic on 32-bit microprocessors. As that task neared completion, a second working group was established to generalize the proposed binary standard for other radices and wordlengths. We discuss the emerging generalization, its influence on final deliberations on the proposed binary standard, and the implications for numerical computation.
Manos, P.; Turner, L. R.
1972-01-01
Approximations which can be evaluated with precision using floating-point arithmetic are presented. The particular set of approximations thus far developed are for the function TAN and the functions of USASI FORTRAN excepting SQRT and EXPONENTIATION. These approximations are, furthermore, specialized to particular forms which are especially suited to a computer with a small memory, in that all of the approximations can share one general purpose subroutine for the evaluation of a polynomial in the square of the working argument.
Cheng, Julian; Olbright, G. R.; Bryan, R. P.
1991-10-01
The architecture described in the paper supports binary addition by means of optical logic gates and symbolic substitution utilizing heterojunction phototransistors and lasers. The high-speed optical switches are compatible with surface-normal architecture, require low-input optical energies, and afford high optical gain. A highly compact binary half-adder is described to demonstrate the implementation of the binary arithmetic with heterojunction-phototransistor optical logic gates and surface emitting lasers.
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
一个改进的算术编码算法%An Improved Arithmetic Coding Algorithm
Institute of Scientific and Technical Information of China (English)
海梅; 张建军; 倪兴芳
2004-01-01
Arithmetic coding is the most powerful technique for statiscal lossless encoding that has attracted much attention in recent years. In this paper, we presents a new implementation of bit-level arithmetic coding by use of integer additions and shifts. The new algorithm has less computation complexity and is more flexible to use, and thus is very suitable for software and hardware design. We also discuss the application of the algorithm to the data encryption.
The Effect Of Peer Collaboration On Children’s Arithmetic And Self-Regulated Learning Skills
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Joakim Samuelsson
2010-12-01
Full Text Available The present study examines the effect of peer collaboration, teaching children arithmetic in the beginning of 7th grade, age 13 years. Peer collaboration groups are compared to two different structured teaching methods, traditional and independent teaching. Progress made by these students are related to measures of their arithmetic ability, calculation and quantitative concept, as well as their self-regulated learning skills in mathematics, characterised as internal and instrumental motivation, self-concept and anxiety. The results will be discussed with reference to Piaget´s theory of the relation between social interaction and cognitive development. This study has a split-plot factorial design with time as within-subject and type of intervention as a between-subject factor. Students’ progress in quantitative concepts is significantly better if teachers teach traditionally or with peer collaboration. The results show that there are no significant differences between teaching methods when assessing arithmetic in total and calculation. Peer collaboration is more effective than traditional and independent work for students’ internal motivation. Traditional work and peer collaboration are more effective than independent work for students’ self-concept.
Heuristics and representational change in two-move matchstick arithmetic tasks
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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.
Zhang, Yushu; Xiao, Di; Wen, Wenying; Nan, Hai; Su, Moting
2015-10-01
In this paper, we propose a novel secure arithmetic coding based on digitalized modified logistic map (DMLM) and linear feedback shift register (LFSR). An input binary sequence is first mapped into a table, which is then scrambled by two cyclic shift steps driven by the keys resulting from DMLM-LFSR. Next, each column is encoded using traditional arithmetic coding (TAC) and randomized arithmetic coding (RAC). During the RAC process, the exchange of two intervals is controlled by the keystream generated from the DMLM. At the same time, a few bits of the present column sequence are extracted to interfere the generation of new keystream used for the next column. The final ciphertext sequence is obtained by XORing the compressed sequence and the keystream generated by the LFSR. Results show the compression ratio of our scheme is slightly higher than that of TAC, but the security is improved due to the architecture of shift-perturbance. DMLM and LFSR theories also ensure high sensitivity and strong randomness. The appended complexity is only O (N) , where N is the number of the input symbols.
Potential Infinity, Abstraction Principles and Arithmetic (Leśniewski Style
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Rafal Urbaniak
2016-06-01
Full Text Available This paper starts with an explanation of how the logicist research program can be approached within the framework of Leśniewski’s systems. One nice feature of the system is that Hume’s Principle is derivable in it from an explicit definition of natural numbers. I generalize this result to show that all predicative abstraction principles corresponding to second-level relations, which are provably equivalence relations, are provable. However, the system fails, despite being much neater than the construction of Principia Mathematica (PM. One of the key reasons is that, just as in the case of the system of PM, without the assumption that infinitely many objects exist, (renderings of most of the standard axioms of Peano Arithmetic are not derivable in the system. I prove that introducing modal quantifiers meant to capture the intuitions behind potential infinity results in the (renderings of axioms of Peano Arithmetic (PA being valid in all relational models (i.e. Kripke-style models, to be defined later on of the extended language. The second, historical part of the paper contains a user-friendly description of Leśniewski’s own arithmetic and a brief investigation into its properties.
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Stavros I Dimitriadis
2016-09-01
Full Text Available Many neuroimaging studies have demonstrated the different functional contribution of spatial distinct anatomical brain areas to working memory (WM subsystems in various cognitive tasks that demand both local information processing and a coordinated mechanism between them. In WM cognitive tasks using electroencephalography (EEG, brain rhythms, such as θ and α, have been linked to a specific functional role located over a brain area but their functional coupling has not been yet studied extensively. In the present study, analyzing an arithmetic task designed with five cognitive workload levels (CWLs, we demonstrated the functional/effective coupling between the two subsystems of the WM, the central executive located over frontal (F brain areas that oscillates on the dominant θ rhythm (Frontalθ/Fθ and the storage buffer located over parieto-occipital (PO brain areas that operates on the α2 dominant brain rhythm (Parieto-Occipitalα2 / POα2. Our analysis focused on demonstrating important differences between and within WM subsystems in relation to behavioral performance. Attempting to uncover the distinct role of amplitude, phase within and between frequencies and also the hierarchical role of functionally specialized brain areas related to the task, we employed a repertoire of brain connectivity estimators. Specifically, for each CWL, we conducted a a conventional signal power analysis within both frequency bands at Fθ and POα2 ,b the intra and inter-frequency phase interactions between Fθ and POα2 and c their causal phase and amplitude relationship. We found no significant statistical difference of signal power and of phase interactions between correct and wrong answers. Interestingly, the study of causal interactions between Fθ and POα2 revealed frontal brain region(s as the leader, while the strength was able to differentiate correct from wrong responses, in every CWL with absolute accuracy. Additionally, zero time-lag between
Gated Clock Implementation of Arithmetic Logic Unit (ALU
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Dr. Neelam R. Prakash
2013-05-01
Full Text Available Low power design has emerged as one of the challenging area in today’s ASIC (Application specific integrated circuit design. With continuous decrease in transistor size, power density is increasing and there is an urgent need for reduction in total power consumption. Clock gating is one most effective technique for low power synchronous circuit design. Clock gating technique in low power design is used to reduce the dynamic power consumption. Clock signal in a synchronous circuit is used for synchronization only and hence does not carry any important information. Since clock is applied to each block of a synchronous circuit, and clock switches for every cycle, clock power is the major part of dynamic power consumption in synchronous circuits. Clock gating is a well known technique to reduce clock power. In clock gating clock to an idle block is disabled. Thus significant amount of power consumption is reduced by employing clock gating. In this paper an ALU design is proposed employing Gated clock for its operation. Design simulation has been performed on Xilinx ISE design suite, and power calculation is done by Xilinx Xpower analyzer. Results show that approximately 17% of total clock power consumption is reduced by gated clock implementation.
An Optimised Distributed Arithmetic Architecture for 8×8 DTT
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Ranjan K. Senapati
2015-08-01
Full Text Available Discrete Tchebichef Transform (DTT is an orthogonal transform and is used in many applications like image and video compression, feature extraction, artefact analysis, blind integrity verification and pattern recognition. In comparison with DCT, DTT has better image reconstruction quality for certain class of images. Direct implementation of DTT requires large number of multiplications, which are time-consuming and expensive in a simple processor. To perform in real time, these large number of operations can be completely avoided in our proposed architecture. The proposed architecture uses distributed (DA based technique which offers high speed and small area. The basic architecture consists of one dimensional (1D row DTT followed by a transpose register array and another 1D column DTT. The 1D DTT structure only requires 15 adders to build a compressed adder matrix and is also ROM free. Compared with DCT architecture, the proposed architecture shows an improvement in speed and reduction in area by 5% on a Xilinx vertex-4 FPGA platform.
Power, Sarah D.; Kushki, Azadeh; Chau, Tom
2011-10-01
Near-infrared spectroscopy (NIRS) has recently been investigated as a non-invasive brain-computer interface (BCI) for individuals with severe motor impairments. For the most part, previous research has investigated the development of NIRS-BCIs operating under synchronous control paradigms, which require the user to exert conscious control over their mental activity whenever the system is vigilant. Though functional, this is mentally demanding and an unnatural way to communicate. An attractive alternative to the synchronous control paradigm is system-paced control, in which users are required to consciously modify their brain activity only when they wish to affect the BCI output, and can remain in a more natural, 'no-control' state at all other times. In this study, we investigated the feasibility of a system-paced NIRS-BCI with one intentional control (IC) state corresponding to the performance of either mental arithmetic or mental singing. In particular, this involved determining if these tasks could be distinguished, individually, from the unconstrained 'no-control' state. Deploying a dual-wavelength frequency domain near-infrared spectrometer, we interrogated nine sites around the frontopolar locations (International 10-20 System) while eight able-bodied adults performed mental arithmetic and mental singing to answer multiple-choice questions within a system-paced paradigm. With a linear classifier trained on a six-dimensional feature set, an overall classification accuracy of 71.2% across participants was achieved for the mental arithmetic versus no-control classification problem. While the mental singing versus no-control classification was less successful across participants (62.7% on average), four participants did attain accuracies well in excess of chance, three of which were above 70%. Analyses were performed offline. Collectively, these results are encouraging, and demonstrate the potential of a system-paced NIRS-BCI with one IC state corresponding to
On Generalized Carleson Operators of Periodic Wavelet Packet Expansions
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Shyam Lal
2013-01-01
Full Text Available Three new theorems based on the generalized Carleson operators for the periodic Walsh-type wavelet packets have been established. An application of these theorems as convergence a.e. for the periodic Walsh-type wavelet packet expansion of block function with the help of summation by arithmetic means has been studied.
Natural Number Bias in Operations with Missing Numbers
Christou, Konstantinos P.
2015-01-01
This study investigates the hypothesis that there is a natural number bias that influences how students understand the effects of arithmetical operations involving both Arabic numerals and numbers that are represented by symbols for missing numbers. It also investigates whether this bias correlates with other aspects of students' understanding of…
Johansson, H T
2015-01-01
We present an efficient implementation for the evaluation of Wigner 3j, 6j, and 9j symbols. These represent numerical transformation coefficients that are used in the quantum theory of angular momentum. They can be expressed as sums and square roots of ratios of integers. The integers can be very large due to factorials. We avoid numerical precision loss due to cancellation through the use of multi-word integer arithmetic for exact accumulation of all sums. A fixed relative accuracy is maintained as the limited number of floating-point operations in the final step only incur rounding errors in the least significant bits. Time spent to evaluate large multi-word integers is in turn reduced by using explicit prime factorisation of the ingoing factorials, thereby improving execution speed. Comparison with existing routines shows the efficiency of our approach and we therefore provide a computer code based on this work.
Switching Arithmetic for DC to DC Converters Using Delta Sigma Modulator Based Control Circuit
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K.Diwakar
2016-02-01
Full Text Available In the proposed arithmetic unit for dc to dc converters using delta sigma modulator, a new technique is proposed for addition and multiplication of sampled analog signals. The output is in digital form to drive the converters. The conventional method has input signal limitation whereas in the proposed method the inputs can vary to full-scale. The addition of two discrete signals is done by sampling the two signals at a period called update period and feeding each signal to the input of signal dependant delta sigma modulator for half of the update period and combining the outputs for the update period. The extension of three discrete data addition can be carried out by using the same technique. For the multiplication of two discrete signals different method is adopted. One analog signal is fed to the input of first delta-sigma modulator (DSM1 after sampling. The sampled output of the second analog signal is negated or not negated depending on the bit state at the output of DSM1 and is fed to the input of second DSM(DSM2. The resulting bit stream at the output of DSM2 is the digital representation of the product of the sampled data of the two analog signals. In order to multiply three discrete data, the sampled output of third data is negated or not negated depending on the bit state at the output of DSM2 and is fed to the input of third DSM(DSM3. The resulting bit stream at the output of DSM3 is the digital representation of the product of the sampled data of the three analog signals. Using the proposed adder and multiplier circuits any expressions can be evaluated such that the average value of the digital output of the arithmetic unit over the update period gives the value of expressions during that period. The digital output of the arithmetic unit is used to drive the dc-dc converters.
Lógica y Pensamiento Aritmético (Logic and Arithmetic Thinking
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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.
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.
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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.
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.
Watermarking Capable of Identifying Embedding Order Based on an Arithmetic Mechanism
Institute of Scientific and Technical Information of China (English)
张新鹏; 王朔中; 张开文
2003-01-01
A digital watermark as a means for copyright protection may be crippled when a fake mark is embedded on top of it since both watermarks are detectable. In dealing with this problem, a watermarking scheme that does not satisfy the law of commutation is proposed. In this scheme, an order function based on an arithmetic mechanism is employed to identify the embedding order without affecting detection of the regular watermark. An earlier watermark corresponds to a larger value of the order function. In this way, the embedding order or watermarks can be identified according to the order function.
Paranoia.Ada: A diagnostic program to evaluate Ada floating-point arithmetic
Hjermstad, Chris
1986-01-01
Many essential software functions in the mission critical computer resource application domain depend on floating point arithmetic. Numerically intensive functions associated with the Space Station project, such as emphemeris generation or the implementation of Kalman filters, are likely to employ the floating point facilities of Ada. Paranoia.Ada appears to be a valuabe program to insure that Ada environments and their underlying hardware exhibit the precision and correctness required to satisfy mission computational requirements. As a diagnostic tool, Paranoia.Ada reveals many essential characteristics of an Ada floating point implementation. Equipped with such knowledge, programmers need not tremble before the complex task of floating point computation.
A Pixel Domain Video Coding based on Turbo code and Arithmetic code
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Cyrine Lahsini
2012-05-01
Full Text Available In recent years, with emerging applications such as multimedia sensors networks, wirelesslow-power surveillance and mobile camera phones, the traditional video coding architecture in beingchallenged. In fact, these applications have different requirements than those of the broadcast videodelivery systems: a low power consumption at the encoder side is essential.In this context, we propose a pixel-domain video coding scheme which fits well in these senarios.In this system, both the arithmetic and turbo codes are used to encode the video sequence's frames.Simulations results show significant gains over Pixel-domain Wyner-Ziv video codeingr.
Saniga, M
2001-01-01
It is shown that the two sequences of characteristic dimensions of transfinite heterotic string space-time found by El Naschie can be remarkably well accounted for in terms of the arithmetic of self-conjugate homaloidal nets of plane algebraic curves of orders 3 to 20. A firm algebraic geometrical justification is thus given not only for all the relevant dimensions of the classical theory, but also for other two dimensions proposed by El Naschie, viz. the inverse of quantum gravity coupling constant (~42.36067977) and that of (one half of) fine structure constant (~68.54101967). A non-trivial coupling between the two El Naschie sequences is also revealed.
The Influence of verbalization on the pattern of cortical activation during mental arithmetic
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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
A formalized proof of Dirichlet's theorem on primes in arithmetic progression
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John Harrison
2009-01-01
Full Text Available We describe the formalization using the HOL Light theorem prover of Dirichlet's theorem on primes in arithmetic progression. The proof turned out to be more straightforward than expected, but this depended on a careful choice of an informal proof to use as a starting-point. The goal of this paper iis twofold. First we describe a simple and efficient proof of the theorem informally, which iis otherwise difficult to find in one self-contained place at an elementary level. We also describe its, largely routine, HOL Light formalization, a task that took only a few days.
A motif extraction algorithm based on hashing and modulo-4 arithmetic.
Sheng, Huitao; Mehrotra, Kishan; Mohan, Chilukuri; Raina, Ramesh
2008-01-01
We develop an algorithm to identify cis-elements in promoter regions of coregulated genes. This algorithm searches for subsequences of desired length whose frequency of occurrence is relatively high, while accounting for slightly perturbed variants using hash table and modulo arithmetic. Motifs are evaluated using profile matrices and higher-order Markov background model. Simulation results show that our algorithm discovers more motifs present in the test sequences, when compared with two well-known motif-discovery tools (MDScan and AlignACE). The algorithm produces very promising results on real data set; the output of the algorithm contained many known motifs.
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.
Klein, Elise; Suchan, Julia; Moeller, Korbinian; Karnath, Hans-Otto; Knops, André; Wood, Guilherme; Nuerk, Hans-Christoph; Willmes, Klaus
2016-03-01
The current study provides a generalizable account of the anatomo-functional associations as well as the connectivity of representational codes underlying numerical processing as suggested by the triple code model (TCM) of numerical cognition. By evaluating the neural networks subserving numerical cognition in two specific and substantially different numerical tasks with regard to both grey matter localizations as well as white matter tracts we (1) considered the possibility of additional memory-related cortex areas crucial for arithmetic fact retrieval (e.g., the hippocampus); (2) specified the functional involvement of prefrontal areas in number magnitude processing, and, finally; (3) identified the connections between these anatomo-functional instantiations of the representations involved in number magnitude processing and arithmetic fact retrieval employing probabilistic fiber tracking. The resulting amendments to the TCM are summarized in a schematic update, and ideas concerning the possible functional interplay between number magnitude processing and arithmetic fact retrieval are discussed.
Connecting Gr\\"obner Bases Programs with Coq to do Proofs in Algebra, Geometry and Arithmetics
Pottier, Loïc
2010-01-01
We describe how we connected three programs that compute Groebner bases to Coq, to do automated proofs on algebraic, geometrical and arithmetical expressions. The result is a set of Coq tactics and a certificate mechanism (downloadable at http://www-sop.inria.fr/marelle/Loic.Pottier/gb-keappa.tgz). The programs are: F4, GB \\, and gbcoq. F4 and GB are the fastest (up to our knowledge) available programs that compute Groebner bases. Gbcoq is slow in general but is proved to be correct (in Coq), and we adapted it to our specific problem to be efficient. The automated proofs concern equalities and non-equalities on polynomials with coefficients and indeterminates in R or Z, and are done by reducing to Groebner computation, via Hilbert's Nullstellensatz. We adapted also the results of Harrison, to allow to prove some theorems about modular arithmetics. The connection between Coq and the programs that compute Groebner bases is done using the "external" tactic of Coq that allows to call arbitrary programs accepting ...
The arithmetic problem size effect in children: an event-related potential study
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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.
Implementation of an Arithmetic Logic Using Area Efficient Carry Lookahead Adder
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Navneet Dubey
2014-12-01
Full Text Available An arithmetic logic unit acts as the basic building blocks or cell of a central processing unit of a c omputer. And it is a digital circuit comprised of the basic electronics components, which is used to perform va rious function of arithmetic and logic and integral opera tions further the purpose of this work is to propos e the design of an 8-bit ALU which supports 4-bit multipl ication. Thus, the functionalities of the ALU in th is study consist of following main functions like addi tion also subtraction, increment, decrement, AND, O R, NOT, XOR, NOR also two complement generation Multip lication. And the functions with the adder in the airthemetic logic unit are implemented using a Carr y Look Ahead adder joined by a ripple carry approac h. The design of the following multiplier is achieved using the Booths Algorithm therefore the proposed A LU can be designed by using verilog or VHDL and can al so be designed on Cadence Virtuoso platform
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Karin eLanderl
2013-07-01
Full Text Available Numerical processing has been demonstrated to be closely associated with arithmetic skills, however, our knowledge on the development of the relevant cognitive mechanisms is limited. The present longitudinal study investigated the developmental trajectories of numerical processing in 42 children with age-adequate arithmetic development and 41 children with dyscalculia over a two-year period from beginning of Grade 2, when children were 7;6 years old, to beginning of Grade 4. A battery of numerical processing tasks (dot enumeration, non-symbolic and symbolic comparison of one- and two-digit numbers, physical comparison, number line estimation was given five times during the study (beginning and middle of each school year. Efficiency of numerical processing was a very good indicator of development in numerical processing while within-task effects remained largely constant and showed low long-term stability before middle of Grade 3. Children with dyscalculia showed less efficient numerical processing reflected in specifically prolonged response times. Importantly, they showed consistently larger slopes for dot enumeration in the subitizing range, an untypically large compatibility effect when processing two-digit numbers, and they were consistently less accurate in placing numbers on a number line. Thus, we were able to identify parameters that can be used in future research to characterize numerical processing in typical and dyscalculic development. These parameters can also be helpful for identification of children who struggle in their numerical development.
Non-formal mechanisms in mathematical cognitive development: The case of arithmetic.
Braithwaite, David W; Goldstone, Robert L; van der Maas, Han L J; Landy, David H
2016-04-01
The idea that cognitive development involves a shift towards abstraction has a long history in psychology. One incarnation of this idea holds that development in the domain of mathematics involves a shift from non-formal mechanisms to formal rules and axioms. Contrary to this view, the present study provides evidence that reliance on non-formal mechanisms may actually increase with age. Participants - Dutch primary school children - evaluated three-term arithmetic expressions in which violation of formally correct order of evaluation led to errors, termed foil errors. Participants solved the problems as part of their regular mathematics practice through an online study platform, and data were collected from over 50,000 children representing approximately 10% of all primary schools in the Netherlands, suggesting that the results have high external validity. Foil errors were more common for problems in which formally lower-priority sub-expressions were spaced close together, and also for problems in which such sub-expressions were relatively easy to calculate. We interpret these effects as resulting from reliance on two non-formal mechanisms, perceptual grouping and opportunistic selection, to determine order of evaluation. Critically, these effects reliably increased with participants' grade level, suggesting that these mechanisms are not phased out but actually become more important over development, even when they cause systematic violations of formal rules. This conclusion presents a challenge for the shift towards abstraction view as a description of cognitive development in arithmetic. Implications of this result for educational practice are discussed.
The Arithmetic of Elliptic Fibrations in Gauge Theories on a Circle
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 ...
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.
Guberman, Raisa
2016-01-01
One of the key courses in the mathematics teacher education program in Israel is arithmetic, which engages in contents which these pre-service mathematics teachers (PMTs) will later teach at school. Teaching arithmetic involves knowledge about the essence of the concept of "number" and the development thereof, calculation methods and…
Dearing, Eric; Casey, Beth M.; Ganley, Colleen M.; Tillinger, Miriam; Laski, Elida; Montecillo, Christine
2012-01-01
The present study addressed girls' (N=127) early numerical and spatial reasoning skills, within the context of a critical environment in which these cognitive skills develop, namely their homes. Specifically, proximal links between distal family socioeconomic conditions and first-grade girls' arithmetic and spatial skills were examined (mean…
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.
2008-01-01
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) an
Egeland, Jens; Bosnes, Ole; Johansen, Hans
2009-01-01
Confirmatory Factor Analyses (CFA) of the Wechsler Adult Intelligence Scale-III (WAIS-III) lend partial support to the four-factor model proposed in the test manual. However, the Arithmetic subtest has been especially difficult to allocate to one factor. Using the new Norwegian WAIS-III version, we tested factor models differing in the number of…
Gallardo, Aurora
2002-01-01
Analyzes from an historical perspective the extension of the natural-number domain to integers in students' transition from arithmetic to algebra in the context of word problems. Extracts four levels of acceptance of these numbers--subtrahend, relative number, isolated number and formal negative number--from historical texts. The first three…
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.
The Power of 2: How an Apparently Irregular Numeration System Facilitates Mental Arithmetic.
Bender, Andrea; Beller, Sieghard
2017-01-01
Mangarevan traditionally contained two numeration systems: a general one, which was highly regular, decimal, and extraordinarily extensive; and a specific one, which was restricted to specific objects, based on diverging counting units, and interspersed with binary steps. While most of these characteristics are shared by numeration systems in related languages in Oceania, the binary steps are unique. To account for these characteristics, this article draws on-and tries to integrate-insights from anthropology, archeology, linguistics, psychology, and cognitive science more generally. The analysis of mental arithmetic with these systems reveals that both types of systems entailed cognitive advantages and served important functions in the cultural context of their application. How these findings speak to more general questions revolving around the theoretical models and evolutionary trajectory of numerical cognition will be discussed in the .
Schütt, Matthias; Yui, Noriko
2015-01-01
This volume presents a lively introduction to the rapidly developing and vast research areas surrounding Calabi–Yau varieties and string theory. With its coverage of the various perspectives of a wide area of topics such as Hodge theory, Gross–Siebert program, moduli problems, toric approach, and arithmetic aspects, the book gives a comprehensive overview of the current streams of mathematical research in the area. The contributions in this book are based on lectures that took place during workshops with the following thematic titles: “Modular Forms Around String Theory,” “Enumerative Geometry and Calabi–Yau Varieties,” “Physics Around Mirror Symmetry,” “Hodge Theory in String Theory.” The book is ideal for graduate students and researchers learning about Calabi–Yau varieties as well as physics students and string theorists who wish to learn the mathematics behind these varieties.
Modeling and Implementation of Reliable Ternary Arithmetic and Logic Unit Design Using Vhdl
Directory of Open Access Journals (Sweden)
Meruva Kumar Raja
2014-06-01
Full Text Available Multivalve logic is a reliable method for defining, analyzing, testing and implementing the basic combinational circuitry with VHDL simulator. It offers better utilization of transmission channels because of its high speed for higher information carried out and it gives more efficient performance. One of the main realizing of the MVL (ternary logic is that reduces the number of required computation steps, simplicity and energy efficiency in digital logic design. This paper using reliable method is brought out for implementing the basic combinational, sequential and TALU (Ternary Arithmetic and Logic Unit circuitry with minimum number of ternary switching circuits (Multiplexers. In this the potential of VHDL modelling and simulation that can be applied to ternary switching circuits to verify its functionality and timing specifications. An intention is to show how proposed simulator can be used to simulate MVL circuits and to evaluate system performance.
An Adaptive Joint Source/Channel Coding Using Error Correcting Arithmetic Codes
Institute of Scientific and Technical Information of China (English)
LIU Jun-qing; PANG Yu-ye; SUN Jun
2007-01-01
An approximately optimal adaptive arithmetic coding (AC) system using a forbidden symbol (FS) over noisy channels was proposed which allows one to jointly and adaptively design the source decoding and channel correcting in a single process, with superior performance compared with traditional separated techniques.The concept of adaptiveness is applied not only to the source model but also to the amount of coding redundancy.In addition,an improved branch metric computing algorithm and a faster sequential searching algorithm compared with the system proposed by Grangetto were proposed.The proposed system is tested in the case of image transmission over the AWGN channel, and compared with traditional separated system in terms of packet error rate and complexity.Both hard and soft decoding were taken into account.
de Zeeuw, Eveline L.; van Beijsterveldt, Catharina E.M.; Glasner, Tina J.; de Geus, Eco J.C.; Boomsma, Dorret I.
2016-01-01
Even children attending the same primary school and taught by the same teacher differ greatly in their performance. In the Netherlands, performance at the end of primary school determines the enrollment in a particular level of secondary education. Identifying the impact of genes and the environment on individual differences in educational achievement between children is important. The Netherlands Twin Register has collected data on scores of tests used in primary school (ages 6 to 12) to monitor a child’s educational progress in four domains, i.e. arithmetic, word reading, reading comprehension and spelling (1058 MZ and 1734 DZ twin pairs), and of a final test (2451 MZ and 4569 DZ twin pairs) in a large Dutch cohort. In general, individual differences in educational achievement were to a large extent due to genes and the influence of the family environment was negligible. Moreover, there is no evidence for gender differences in the underlying etiology. PMID:27182184
Context-Adaptive Arithmetic Coding Scheme for Lossless Bit Rate Reduction of MPEG Surround in USAC
Yoon, Sungyong; Pang, Hee-Suk; Sung, Koeng-Mo
We propose a new coding scheme for lossless bit rate reduction of the MPEG Surround module in unified speech and audio coding (USAC). The proposed scheme is based on context-adaptive arithmetic coding for efficient bit stream composition of spatial parameters. Experiments show that it achieves the significant lossless bit reduction of 9.93% to 12.14% for spatial parameters and 8.64% to 8.96% for the overall MPEG Surround bit streams compared to the original scheme. The proposed scheme, which is not currently included in USAC, can be used for the improved coding efficiency of MPEG Surround in USAC, where the saved bits can be utilized by the other modules in USAC.
Ntsama, Eloundou Pascal; Colince, Welba; Ele, Pierre
2016-01-01
In this article, we make a comparative study for a new approach compression between discrete cosine transform (DCT) and discrete wavelet transform (DWT). We seek the transform proper to vector quantization to compress the EMG signals. To do this, we initially associated vector quantization and DCT, then vector quantization and DWT. The coding phase is made by the SPIHT coding (set partitioning in hierarchical trees coding) associated with the arithmetic coding. The method is demonstrated and evaluated on actual EMG data. Objective performance evaluations metrics are presented: compression factor, percentage root mean square difference and signal to noise ratio. The results show that method based on the DWT is more efficient than the method based on the DCT.
Daud, Shahidah Md; Ramli, Razamin; Kasim, Maznah Mat; Kayat, Kalsom; Razak, Rafidah Abd
2015-12-01
Malaysian Homestay is very unique. It is classified as Community Based Tourism (CBT). Homestay Programme which is a community events where a tourist stays together with a host family for a period of time and enjoying cultural exchange besides having new experiences. Homestay programme has booming the tourism industry since there is over 100 Homestay Programme currently being registered with the Ministry of Culture and Tourism Malaysia. However, only few Homestay Programme enjoying the benefits of success Homestay Programme. Hence, this article seeks to identify the critical success factors for a Homestay Programme in Malaysia. An Arithmetic Average method is utilized to further evaluate the identified success factors in a more meaningful way. The findings will help Homestay Programme function as a community development tool that manages tourism resources. Thus, help the community in improving local economy and creating job opportunities.
High-Precision Floating-Point Arithmetic in ScientificComputation
Energy Technology Data Exchange (ETDEWEB)
Bailey, David H.
2004-12-31
At the present time, IEEE 64-bit floating-point arithmetic is sufficiently accurate for most scientific applications. However, for a rapidly growing body of important scientific computing applications, a higher level of numeric precision is required: some of these applications require roughly twice this level; others require four times; while still others require hundreds or more digits to obtain numerically meaningful results. Such calculations have been facilitated by new high-precision software packages that include high-level language translation modules to minimize the conversion effort. These activities have yielded a number of interesting new scientific results in fields as diverse as quantum theory, climate modeling and experimental mathematics, a few of which are described in this article. Such developments suggest that in the future, the numeric precision used for a scientific computation may be as important to the program design as are the algorithms and data structures.
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.
A hardware architecture for a context-adaptive binary arithmetic coder
Sudharsanan, Subramania; Cohen, Adam
2005-03-01
The H.264 video compression standard uses a context-adaptive binary arithmetic coder (CABAC) as an entropy coding mechanism. While the coder provides excellent compression efficiency, it is computationally demanding. On typical general-purpose processors, it can take up to hundreds of cycles to encode a single bit. In this paper, we propose an architecture for a CABAC encoder that can easily be incorporated into system-on-chip designs for H.264 compression. The CABAC is inherently serial and we divide the problem into several stages to derive a design that can provide a throughput of two cycles per encoded bit. The engine proposed is capable of handling binarization of the syntactical elements and provides the coded bit-stream via a first-in first-out buffer. The design is implemented on an Altera FPGA platform that can run at 50 MHz enabling a 25 Mbps encoding rate.
Optimal Combinations Bounds of Root-Square and Arithmetic Means for Toader Mean
Indian Academy of Sciences (India)
Yu-Ming Chu; Miao-Kun Wang; Song-Liang Qiu
2012-02-01
We find the greatest values 1 and 2, and the least values 1 and 2, such that the double inequalities $_1S(a,b)+(1-_1)A(a,b) < T(a,b) < _1S(a,b)+(1-_1)A(a,b)$ and $S^{_2}(a,b)A^{1-_2}(a,b) < T(a,b) < S^{_2}(a,b)A^{1-_2}(a,b)$ hold for all ,>0 with ≠ . As applications, we get two new bounds for the complete elliptic integral of the second kind in terms of elementary functions. Here, $S(a,b)=[(a^2+b^2)/2]^{1/2},A(a,b)=(a+b)/2$, and $T(a,b)=\\frac{2}{}\\int^{/2}_{0}\\sqrt{a^2\\cos^2+b^2\\sin^2}d$ denote the root-square, arithmetic, and Toader means of two positive numbers and , respectively.
Analysis and compensation of the effects of analog VLSI arithmetic on the LMS algorithm.
Carvajal, Gonzalo; Figueroa, Miguel; Sbarbaro, Daniel; Valenzuela, Waldo
2011-07-01
Analog very large scale integration implementations of neural networks can compute using a fraction of the size and power required by their digital counterparts. However, intrinsic limitations of analog hardware, such as device mismatch, charge leakage, and noise, reduce the accuracy of analog arithmetic circuits, degrading the performance of large-scale adaptive systems. In this paper, we present a detailed mathematical analysis that relates different parameters of the hardware limitations to specific effects on the convergence properties of linear perceptrons trained with the least-mean-square (LMS) algorithm. Using this analysis, we derive design guidelines and introduce simple on-chip calibration techniques to improve the accuracy of analog neural networks with a small cost in die area and power dissipation. We validate our analysis by evaluating the performance of a mixed-signal complementary metal-oxide-semiconductor implementation of a 32-input perceptron trained with LMS.
Dix, Annika; van der Meer, Elke
2015-04-01
This study investigates cognitive resource allocation dependent on fluid and numerical intelligence in arithmetic/algebraic tasks varying in difficulty. Sixty-six 11th grade students participated in a mathematical verification paradigm, while pupil dilation as a measure of resource allocation was collected. Students with high fluid intelligence solved the tasks faster and more accurately than those with average fluid intelligence, as did students with high compared to average numerical intelligence. However, fluid intelligence sped up response times only in students with average but not high numerical intelligence. Further, high fluid but not numerical intelligence led to greater task-related pupil dilation. We assume that fluid intelligence serves as a domain-general resource that helps to tackle problems for which domain-specific knowledge (numerical intelligence) is missing. The allocation of this resource can be measured by pupil dilation.
Power system transient stability simulation under uncertainty based on Taylor model arithmetic
Institute of Scientific and Technical Information of China (English)
Shouxiang WANG; Zhijie ZHENG; Chengshan WANG
2009-01-01
The Taylor model arithmetic is introduced to deal with uncertainty. The uncertainty of model parameters is described by Taylor models and each variable in functions is replaced with the Taylor model (TM). Thus,time domain simulation under uncertainty is transformed to the integration of TM-based differential equations. In this paper, the Taylor series method is employed to compute differential equations; moreover, power system time domain simulation under uncertainty based on Taylor model method is presented. This method allows a rigorous estimation of the influence of either form of uncertainty and only needs one simulation. It is computationally fast compared with the Monte Carlo method, which is another technique for uncertainty analysis. The proposed method has been tested on the 39-bus New England system. The test results illustrate the effectiveness and practical value of the approach by comparing with the results of Monte Carlo simulation and traditional time domain simulation.
Localized Model and Arithmetic System Based on Two Image Sensors Under Complex Circumstance
Institute of Scientific and Technical Information of China (English)
HE Guang-lin; YUAN Ben-sheng
2009-01-01
Two image sensors simulate directly the way of disposing images with the human's two eyes,so it has important value to apply in many domains,such as object identification,small unmaned aerial vehicle (UAV),workpiece localization,robot navigation and so on.The object localization based on two image sensors is studied in this paper.It concentrates on how to apply two charge coupled device (CCD) image sensors to object localization of sphere in complex environments.At first a space model of the two image sensors is set up,then Hough transformation is adopted to get localizated model and arithmetic system.An experiment platform is built in order to prove the correctness and feasibility of that localization algorithm.
The Integration of Arithmetic Knowledge and Semantic Knowledge in Addition Facts%加法运算中数学知识和语义知识的整合
Institute of Scientific and Technical Information of China (English)
陈栩茜; 何本炫; 张积家
2012-01-01
which influenced semantic processing could influence the arithmetical cognition processing? Four experiments were engaged in the present study by using the revised version of semantic priming number matching task (Experiment 1 and 2) and the original semantic priming number matching task used by Bassok et al. (Experiment 3 and 4), in which the addition operation and categorical semantic relation were taken as objects, and the sum effect was taken as index. The findings were mainly consistent with the study of Bassok et al. (2008). It suggested that the integrating process of the two kinds of knowledge is cultural universal. In addition, the categorical concept as well as the symmetry of the addition operation and categorical relation could influence the processing of addition operation. Moreover, it should be noted that Sura effect affected mainly by restraint of the neutral numbers in Experiment 1 and 2, whereas by activity of the sum numbers in Experiment 4. Therefore, the essence of Sum Effects was also discussed according to the recent results. Activity of the sum numbers can be considered as failure of restraint. Thus, the essence of Sum Effects was failure of restraint: although people tried to restrain two kinds of numbers, they can only restrain one of those (fail). These failures of restraint were mainly influenced by the pattern of the task. And the Sum effects can be representated by either of these failures. In short, results suggested a strong influence of semantic relation on arithmetical cognitive processing. The factors which could influence categorical processing could also influence addition operation processing.
Directory of Open Access Journals (Sweden)
Zu-Jun Ma
2013-01-01
Full Text Available We propose the interval grey uncertain linguistic correlated ordered arithmetic averaging (IGULCOA operator and the induced interval grey uncertain linguistic correlated ordered arithmetic averaging (I-IGULCOA operator based on the correlation properties of the Choquet integral and the interval grey uncertain linguistic variables to investigate the multiple attribute group decision making (MAGDM problems, in which both the attribute weights and the expert weights are correlative. Firstly, the relative concepts of interval grey uncertain linguistic variables are defined and the operation rules between the two interval grey uncertain linguistic variables are established. Then, two new aggregation operators: the interval grey uncertain linguistic correlated ordered arithmetic averaging (IGULCOA operator and the induced interval grey uncertain linguistic correlated ordered arithmetic averaging (I-IGULCOA operator are developed and some desirable properties of the I-IGULCOA operator are studied, such as commutativity, idempotency, monotonicity, and boundness. Furthermore, the IGULCOA and I-IGULCOA operators based approach is developed to solve the MAGDM problems, in which both the attribute weights and the expert weights are correlative and the attribute values take the form of the interval grey uncertain linguistic variables. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness.
Rosenberg-Lee, Miriam; Ashkenazi, Sarit; Chen, Tianwen; Young, Christina B; Geary, David C; Menon, Vinod
2015-05-01
Developmental dyscalculia (DD) is marked by specific deficits in processing numerical and mathematical information despite normal intelligence (IQ) and reading ability. We examined how brain circuits used by young children with DD to solve simple addition and subtraction problems differ from those used by typically developing (TD) children who were matched on age, IQ, reading ability, and working memory. Children with DD were slower and less accurate during problem solving than TD children, and were especially impaired on their ability to solve subtraction problems. Children with DD showed significantly greater activity in multiple parietal, occipito-temporal and prefrontal cortex regions while solving addition and subtraction problems. Despite poorer performance during subtraction, children with DD showed greater activity in multiple intra-parietal sulcus (IPS) and superior parietal lobule subdivisions in the dorsal posterior parietal cortex as well as fusiform gyrus in the ventral occipito-temporal cortex. Critically, effective connectivity analyses revealed hyper-connectivity, rather than reduced connectivity, between the IPS and multiple brain systems including the lateral fronto-parietal and default mode networks in children with DD during both addition and subtraction. These findings suggest the IPS and its functional circuits are a major locus of dysfunction during both addition and subtraction problem solving in DD, and that inappropriate task modulation and hyper-connectivity, rather than under-engagement and under-connectivity, are the neural mechanisms underlying problem solving difficulties in children with DD. We discuss our findings in the broader context of multiple levels of analysis and performance issues inherent in neuroimaging studies of typical and atypical development.
Motoki, Shinji; Nakasato, Naohito; Ishikawa, Tadashi; Yuasa, Fukuko; Fukushige, Toshiyuki; Kawai, Atsushi; Makino, Junichiro
2014-01-01
Higher order corrections in perturbative quantum field theory are required for precise theoretical analysis to investigate new physics beyond the Standard Model. This indicates that we need to evaluate Feynman loop diagram with multi-loop integral which may require multi-precision calculation. We developed a dedicated accelerator system for multi-precision calculation (GRAPE9-MPX). We present performance results of our system for the case of Feynman two-loop box and three-loop selfenergy diagrams with multi-precision.
Rosenberg-Lee, Miriam; Ashkenazi, Sarit; Chen, Tianwen; Young, Christina B.; Geary, David C.; Menon, Vinod
2015-01-01
Developmental dyscalculia (DD) is marked by specific deficits in processing numerical and mathematical information despite normal intelligence (IQ) and reading ability. We examined how brain circuits used by young children with DD to solve simple addition and subtraction problems differ from those used by typically developing (TD) children who…
Algebra Structure of RSA Arithmetic%RSA算法中的代数结构
Institute of Scientific and Technical Information of China (English)
司光东; 杨加喜; 谭示崇; 肖国镇
2011-01-01
本文首次应用二次剩余理论对RSA中的代数结构进行了研究.计算出了Zn中模n的二次剩余和二次非剩余的个数,对它们之间的关系进行了分析,并用所有二次剩余构成的群对Zn进行了分割,证明了所有陪集构成的商群是一个Klein四元群.对强RSA的结构进行了研究,证明了强RSA中存在阶为φ(n)/2的元素,并且强RSA中Zn可由三个二次非剩余的元素生成.确定了Zn中任意元素的阶,证明了Zn中所有元素阶的最大值是lcm(p-1,q-1),并且给出了如何寻找Zn中最大阶元素方法.从而解决了RSA中的代数结构.%Based on the theory of quadratic residues, the algebra structure of RSA arithmetic is researched in this paper. This work calculates numbers of quadratic residues and non-residues in the group Zn* and investigates their relationship. Z*n is divided up by the group made up with all quadratic residues in Z*n and all cosets form a quotient group of order 4 which is a Klein group.Studyed the structure of strong RSA further,it shows that the element of order φ( n)/2 exists and the group Z*n can be generated by three elements of quadratic non-residues. Let the facterization n = p · q, the order of each element can be calculated, and the biggest order of all element is lcn ( p - 1, q - 1 ) in Z*n. It also shows how to find the element of the biggest order. So the algebra structure of RSA arithmetic is solved.
Oppel, S.; Federer, R.N.; O'Brien, D. M.; Powell, A.N.; Hollmén, Tuula E.
2010-01-01
Many studies of nutrient allocation to egg production in birds use stable isotope ratios of egg yolk to identify the origin of nutrients. Dry egg yolk contains >50% lipids, which are known to be depleted in 13C. Currently, researchers remove lipids from egg yolk using a chemical lipid-extraction procedure before analyzing the isotopic composition of protein in egg yolk. We examined the effects of chemical lipid extraction on ??13C, ??15N, and ??34S of avian egg yolk and explored the utility of an arithmetic lipid correction model to adjust whole yolk ??13C for lipid content. We analyzed the dried yolk of 15 captive Spectacled Eider (Somateriafischeri) and 20 wild King Eider (S. spectabilis) eggs, both as whole yolk and after lipid extraction with a 2:1 chloroform:methanol solution. We found that chemical lipid extraction leads to an increase of (mean ?? SD) 3.3 ?? 1.1% in ??13C, 1.1 ?? 0.5% in ??15N, and 2.3 ?? 1.1% in ??34S. Arithmetic lipid correction provided accurate values for lipid-extracted S13C in captive Spectacled Eiders fed on a homogeneous high-quality diet. However, arithmetic lipid correction was unreliable for wild King Eiders, likely because of their differential incorporation of macronutrients from isotopically distinct environments during migration. For that reason, we caution against applying arithmetic lipid correction to the whole yolk ??13C of migratory birds, because these methods assume that all egg macronutrients are derived from the same dietary sources. ?? 2010 The American Ornithologists' Union.
Roy, Sukhdev; Topolancik, Juraj; Vollmer, Frank
2010-01-01
We present designs of all-optical computing circuits, namely, half-full adder/subtractor, de-multiplexer, multiplexer, and an arithmetic unit, based on bacteriorhodopsin (BR) protein coated microcavity switch in a tree architecture. The basic all-optical switch consists of an input infrared (IR) laser beam at 1310 nm in a single mode fiber (SMF-28) switched by a control pulsed laser beam at 532 nm, which triggers the change in the resonance condition on a silica bead coated with BR between two tapered fibers. We show that fast switching of 50 us can be achieved by injecting a blue laser beam at 410 nm that helps in truncating the BR photocycle at the M intermediate state. Realization of all-optical switch with BR coated microcavity switch has been done experimentally. Based on this basic switch configuration, designs of all-optical higher computing circuits have been presented. The design requires 2n-1 switches to realize n bit computation. The proposed designs require less number of switches than terahertz o...
A comparison of the effects of preferred music, arithmetic and humour on cold pressor pain.
Mitchell, Laura A; MacDonald, Raymond A R; Brodie, Eric E
2006-05-01
Research studies of 'audioanalgesia', the ability of music to affect pain perception, have significantly increased in number during the past two decades. Listening to preferred music in particular may provide an emotionally engaging distraction capable of reducing both the sensation of pain itself and the accompanying negative affective experience. The current study uses experimentally induced cold pressor pain to compare the effects of preferred music to two types of distracting stimuli found effective within the previous studies; mental arithmetic, a cognitive distraction, and humour, which may emotionally engage us in a similar manner to music. Forty-four participants (24 females, 20 males) underwent three cold pressor trials in counterbalanced order. The Paced Auditory Serial Addition Task provided the cognitive distraction and a choice was given from three types of audiotaped stand-up comedy. Participants provided their own preferred music. A circulating and cooling water bath administered cold pressor stimulation. Tolerance time, pain intensity on visual analogue scale and the pain rating index and perceived control were measured. Preferred music listening was found to significantly increase tolerance in comparison to the cognitive task, and significantly increase perceived control in comparison to humour. Ratings of pain intensity did not significantly differ. The results suggest preferred music listening to offer effective distraction and enhancement of control as a pain intervention under controlled laboratory conditions.
Multiple gcd-closed sets and determinants of matrices associated with arithmetic functions
Directory of Open Access Journals (Sweden)
Hong Siao
2016-03-01
Full Text Available Let f be an arithmetic function and S = {x1, …, xn} be a set of n distinct positive integers. By (f(xi, xj (resp. (f[xi, xj] we denote the n × n matrix having f evaluated at the greatest common divisor (xi, xj (resp. the least common multiple [xi, xj] of x, and xj as its (i, j-entry, respectively. The set S is said to be gcd closed if (xi, xj ∈ S for 1 ≤ i, j ≤ n. In this paper, we give formulas for the determinants of the matrices (f(xi, xj and (f[xi, xj] if S consists of multiple coprime gcd-closed sets (i.e., S equals the union of S1, …, Sk with k ≥ 1 being an integer and S1, …, Sk being gcd-closed sets such that (lcm(Si, lcm(Sj = 1 for all 1 ≤ i ≠ j ≤ k. This extends the Bourque-Ligh, Hong’s and the Hong-Loewy formulas obtained in 1993, 2002 and 2011, respectively. It also generalizes the famous Smith’s determinant.
Hinault, Thomas; Lemaire, Patrick; Phillips, Natalie
2016-01-01
This study investigated age-related differences in electrophysiological signatures of sequential modulations of poorer strategy effects. Sequential modulations of poorer strategy effects refer to decreased poorer strategy effects (i.e., poorer performance when the cued strategy is not the best) on current problem following poorer strategy problems compared to after better strategy problems. Analyses on electrophysiological (EEG) data revealed important age-related changes in time, frequency, and coherence of brain activities underlying sequential modulations of poorer strategy effects. More specifically, sequential modulations of poorer strategy effects were associated with earlier and later time windows (i.e., between 200- and 550 ms and between 850- and 1250 ms). Event-related potentials (ERPs) also revealed an earlier onset in older adults, together with more anterior and less lateralized activations. Furthermore, sequential modulations of poorer strategy effects were associated with theta and alpha frequencies in young adults while these modulations were found in delta frequency and theta inter-hemispheric coherence in older adults, consistent with qualitatively distinct patterns of brain activity. These findings have important implications to further our understanding of age-related differences and similarities in sequential modulations of cognitive control processes during arithmetic strategy execution.
DEFF Research Database (Denmark)
Høyrup, Jens
. Next it goes on with complicated cases where the arithmetical series is not proportional to 1 – 2 – 3 ..., and the fraction is not an aliquot part. Fibonacci gives an algebraic solution to one variant and also general formulae for all variants – but these do not come from his algebra, and he thus...... cannot have derived them himself. A complete survey of occurrences once again points to al-Andalus. 3. Chapter 15 Section 1 of Fibonacci’s Liber abbaci mainly deals with the ancient theory of means though not telling so. If M is one such mean between A and B, it is shown systematically how each...... of these three numbers can be found if the other two are given – once more by means of algebra, Elements II.5–6, and proportion techniques. The lettering shows that Fibonacci uses an Arabic or Greek source, but no known Arabic or Greek work contains anything similar. However, the structural affinity suggests...
Error Recovery Properties and Soft Decoding of Quasi-Arithmetic Codes
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Christine Guillemot
2007-08-01
Full Text Available This paper first introduces a new set of aggregated state models for soft-input decoding of quasi arithmetic (QA codes with a termination constraint. The decoding complexity with these models is linear with the sequence length. The aggregation parameter controls the tradeoff between decoding performance and complexity. It is shown that close-to-optimal decoding performance can be obtained with low values of the aggregation parameter, that is, with a complexity which is significantly reduced with respect to optimal QA bit/symbol models. The choice of the aggregation parameter depends on the synchronization recovery properties of the QA codes. This paper thus describes a method to estimate the probability mass function (PMF of the gain/loss of symbols following a single bit error (i.e., of the difference between the number of encoded and decoded symbols. The entropy of the gain/loss turns out to be the average amount of information conveyed by a length constraint on both the optimal and aggregated state models. This quantity allows us to choose the value of the aggregation parameter that will lead to close-to-optimal decoding performance. It is shown that the optimum position for the length constraint is not the last time instant of the decoding process. This observation leads to the introduction of a new technique for robust decoding of QA codes with redundancy which turns out to outperform techniques based on the concept of forbidden symbol.
Monochromatic 4-term arithmetic progressions in 2-colorings of $\\mathbb Z_n$
Lu, Linyuan
2011-01-01
This paper is motivated by a recent result of Wolf \\cite{wolf} on the minimum number of monochromatic 4-term arithmetic progressions(4-APs, for short) in $\\Z_p$, where $p$ is a prime number. Wolf proved that there is a 2-coloring of $\\Z_p$ with 0.000386% fewer monochromatic 4-APs than random 2-colorings; the proof is probabilistic and non-constructive. In this paper, we present an explicit and simple construction of a 2-coloring with 9.3% fewer monochromatic 4-APs than random 2-colorings. This problem leads us to consider the minimum number of monochromatic 4-APs in $\\Z_n$ for general $n$. We obtain both lower bound and upper bound on the minimum number of monochromatic 4-APs in all 2-colorings of $\\Z_n$. Wolf proved that any 2-coloring of $\\Z_p$ has at least $(1/16+o(1))p^2$ monochromatic 4-APs. We improve this lower bound into $(7/96+o(1))p^2$. Our results on $\\Z_n$ naturally apply to the similar problem on $[n]$ (i.e., $\\{1,2,..., n\\}$). In 2008, Parillo, Robertson, and Saracino \\cite{prs} constructed a 2-...
Energy Technology Data Exchange (ETDEWEB)
Drmac, Z. [Univ. of Colorado, Boulder, CO (United States). Dept. of Computer Science
1997-07-01
In this paper the author considers how to compute the singular value decomposition (SVD) A = U{Sigma}V{sup {tau}} of A = [a{sub 1}, a{sub 2}] {element_of} R{sup mx2} accurately in floating point arithmetic. It is shown how to compute the Jacobi rotation V (the right singular vector matrix) and how to compute AV = U{Sigma} even if the floating point representation of V is the identity matrix. In the case (norm of (a{sub 1})){sub 2} {much_gt} (norm of (a{sub 2})){sub 2}, underflow can produce the identity matrix as the floating point value of V, even for a{sub 1}, a{sub 2} that are far from being mutually orthogonal. This can cause loss of accuracy and failure of convergence of the floating point implementation of the Jacobi method for computing the SVD. The modified Jacobi method recommended in this paper can be implemented as a reliable and highly accurate procedure for computing the SVD of general real matrices whenever the exact singular values do not exceed the underflow or overflow limits.
Complexity modeling for context-based adaptive binary arithmetic coding (CABAC) in H.264/AVC decoder
Lee, Szu-Wei; Kuo, C.-C. Jay
2007-09-01
One way to save the power consumption in the H.264 decoder is for the H.264 encoder to generate decoderfriendly bit streams. By following this idea, a decoding complexity model of context-based adaptive binary arithmetic coding (CABAC) for H.264/AVC is investigated in this research. Since different coding modes will have an impact on the number of quantized transformed coeffcients (QTCs) and motion vectors (MVs) and, consequently, the complexity of entropy decoding, the encoder with a complexity model can estimate the complexity of entropy decoding and choose the best coding mode to yield the best tradeoff between the rate, distortion and decoding complexity performance. The complexity model consists of two parts: one for source data (i.e. QTCs) and the other for header data (i.e. the macro-block (MB) type and MVs). Thus, the proposed CABAC decoding complexity model of a MB is a function of QTCs and associated MVs, which is verified experimentally. The proposed CABAC decoding complexity model can provide good estimation results for variant bit streams. Practical applications of this complexity model will also be discussed.
Context adaptive binary arithmetic coding-based data hiding in partially encrypted H.264/AVC videos
Xu, Dawen; Wang, Rangding
2015-05-01
A scheme of data hiding directly in a partially encrypted version of H.264/AVC videos is proposed which includes three parts, i.e., selective encryption, data embedding and data extraction. Selective encryption is performed on context adaptive binary arithmetic coding (CABAC) bin-strings via stream ciphers. By careful selection of CABAC entropy coder syntax elements for selective encryption, the encrypted bitstream is format-compliant and has exactly the same bit rate. Then a data-hider embeds the additional data into partially encrypted H.264/AVC videos using a CABAC bin-string substitution technique without accessing the plaintext of the video content. Since bin-string substitution is carried out on those residual coefficients with approximately the same magnitude, the quality of the decrypted video is satisfactory. Video file size is strictly preserved even after data embedding. In order to adapt to different application scenarios, data extraction can be done either in the encrypted domain or in the decrypted domain. Experimental results have demonstrated the feasibility and efficiency of the proposed scheme.
Arithmetically Cohen-Macaulay sets of points in P^1 x P^1
Guardo, Elena
2015-01-01
This brief presents a solution to the interpolation problem for arithmetically Cohen-Macaulay (ACM) sets of points in the multiprojective space P^1 x P^1. It collects the various current threads in the literature on this topic with the aim of providing a self-contained, unified introduction while also advancing some new ideas. The relevant constructions related to multiprojective spaces are reviewed first, followed by the basic properties of points in P^1 x P^1, the bigraded Hilbert function, and ACM sets of points. The authors then show how, using a combinatorial description of ACM points in P^1 x P^1, the bigraded Hilbert function can be computed and, as a result, solve the interpolation problem. In subsequent chapters, they consider fat points and double points in P^1 x P^1 and demonstrate how to use their results to answer questions and problems of interest in commutative algebra. Throughout the book, chapters end with a brief historical overview, citations of related results, and, where relevan...
Suárez-Pellicioni, M; Núñez-Peña, M I; Colomé, A
2013-12-01
This study uses event-related brain potentials to investigate the difficulties that high math anxious individuals face when processing dramatically incorrect solutions to simple arithmetical problems. To this end, thirteen high math-anxious (HMA) and thirteen low math-anxious (LMA) individuals were presented with simple addition problems in a verification task. The proposed solution could be correct, incorrect but very close to the correct one (small-split), or dramatically incorrect (large-split). The two groups did not differ in mathematical ability or trait anxiety. We reproduced previous results for flawed scores suggesting HMA difficulties in processing large-split solutions. Moreover, large-split solutions elicited a late positive component (P600/P3b) which was more enhanced and delayed in the HMA group. Our study proposes that the pattern of flawed scores found by previous studies (and that we replicate) has to do with HMA individuals'difficulties in inhibiting an extended processing of irrelevant information (large-split solutions).
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.
Cameron, Kristie E; Clarke, Katrina H; Bizo, Lewis A; Starkey, Nicola J
2016-05-01
The aim of this study was to compare the demand for food under concurrent progressive- and fixed-ratio schedules. Twelve brushtail possums participated in 16 conditions where schedule, progression and food type were varied. An incrementing schedule increased the fixed-ratio requirement within and across sessions and was arranged as either a geometric sequence (base 2), or an arithmetic sequence (step 5). Two foods were tested: a flaked barley and coco-pop(®) mix versus rolled oats. Overall, performance was similar for most possums in the within- and across-session incrementing schedules. An analysis of the estimates of essential value and break point produced the same account of demand for foods under the geometric or arithmetic progressions and within- and across-session procedures for 8 of 12 possums. Six possums showed higher demand for rolled oats compared to flaked barley, and two possums showed higher demand for flaked barley compared to rolled oats. Incrementing ratios within, rather than between sessions using an arithmetic progression was demonstrated to be a time efficient procedure for investigating demand for different food types without affecting conclusions about the relative demand for those foods.
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Sayaka Tsutsumi
2011-01-01
Full Text Available Arithmetic-like reasoning has been demonstrated in various animals in captive and seminatural environments, but it is unclear whether such competence is practiced in the wild. Using a hypothetical foraging paradigm, we demonstrate that wild vervet monkeys spontaneously adjust their “foraging behavior” deploying arithmetic-like reasoning. Presented with arithmetic-like problems in artificially controlled feeding conditions, all the monkeys tested attempted to retrieve “artificial prey” according to the quantity of the remainder when the task involved one subtraction only (i.e., “2−1”, while one monkey out of four did so when it was sequentially subtracted twice (i.e., “2−1−1”. This monkey also adjusted his “foraging behavior” according to the quantity of the reminder for a task requiring stepwise mental manipulation (i.e., “(2−1−1”, though the results became less evident. This suggests that vervet monkeys are capable of spontaneously deploying mental manipulations of numerosity for cost-benefit calculation of foraging but that the extent of such capacity varies among individuals. Different foraging strategies might be deployed according to different levels of mental manipulation capacity in each individual in a given population. In addition to providing empirical data, the current study provides an easily adaptable field technique that would allow comparison across taxa and habitat using a uniform method.
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.
Age-related differences in children's strategy repetition: A study in arithmetic.
Lemaire, Patrick; Brun, Fleur
2016-10-01
Third and fifth graders (Experiment 1) and fifth and seventh graders (Experiment 2) accomplished computational estimation tasks in which they provided estimates to two-digit arithmetic problems (e.g., 34+68). Participants saw trials, each including three consecutive problems. Each trial was separated by a letter judgment task (i.e., participants needed to say whether a series of four letters included only vowels, only consonants, or both types of letters). On each problem, children were asked to select the better of the following strategies: rounding down (i.e., rounding both operands down to the nearest decades; e.g., 30+60=90) or rounding up (rounding both operands up to the nearest decades; e.g., 40+70=110). Half of the trials were repeated strategy trials (i.e., the better strategy was the same for the first two prime problems and the last target problem) and half were unrepeated strategy trials (i.e., the better strategy was different for prime and target problems). We found that (a) children repeated the same strategy over successive problems, even when they should change strategies to obtain better performance, (b) strategy repetitions decreased with age, (c) repeating the same strategy gave children performance benefits, and (d) these strategy repetition benefits were similar across grades. These effects of strategy repetition during strategy selection and strategy execution have important empirical and theoretical implications regarding how children choose among strategies, how children execute selected strategies on each problem, and how strategic variations change with age.
NIOS Custom Instruction on Floating-Point Arithmetic%NIOS浮点运算定制指令的实现
Institute of Scientific and Technical Information of China (English)
陈鹏; 蔡雪梅
2011-01-01
To improve the efficiency of floating-point arithmetic on NIOS system, a module of using Verilog to implement singleprecision floating-point addition. subtraction and multiplication is proposed, and its function in Quartus is verified through waveform simulation. According to the custom instruction feature of NIOS ii, adding this module to SOPC Builder, expanding a new hardwarebased floating-point arithmetic instruction, which can be applied in NIOS IDE. Comparing the output and calculating time between NIOS ii software arithmetic and the new hardware floating-point instructions, the supenority of the hardware instruction computation is verified, and a more efficient choice is provided for NIOS in floating-point arirhmetic.%为提高NIOS系统的浮点计算效率,使用Verilog语言实现了单精度浮点数加减及乘法运算的功能模块,并通过波形验证其功能,依据NIOSⅡ定制指令的制定规范,将这一功能添加到SOPC Builder中,扩展出新的基于硬件电路的浮点运算指令,使之在NIOS软件环境中得到应用.通过NIOSⅡ本身软件浮点计算和新增硬件指令进行运算结果和时间上的对比,证实硬件指令计算的优越性,为NIOS下的浮点运算提供了更有效率的选择.
Vanbinst, Kiran; Ghesquière, Pol; De Smedt, Bert
2014-11-01
Deficits in arithmetic fact retrieval constitute the hallmark of children with mathematical learning difficulties (MLD). It remains, however, unclear which cognitive deficits underpin these difficulties in arithmetic fact retrieval. Many prior studies defined MLD by considering low achievement criteria and not by additionally taking the persistence of the MLD into account. Therefore, the present longitudinal study contrasted children with persistent MLD (MLD-p; mean age: 9 years 2 months) and typically developing (TD) children (mean age: 9 years 6 months) at three time points, to explore whether differences in arithmetic strategy development were associated with differences in numerical magnitude processing, working memory and phonological processing. Our longitudinal data revealed that children with MLD-p had persistent arithmetic fact retrieval deficits at each time point. Children with MLD-p showed persistent impairments in symbolic, but not in nonsymbolic, magnitude processing at each time point. The two groups differed in phonological processing, but not in working memory. Our data indicate that both domain-specific and domain-general cognitive abilities contribute to individual differences in children's arithmetic strategy development, and that the symbolic processing of numerical magnitudes might be a particular risk factor for children with MLD-p.
On Statistics of Log-Ratio of Arithmetic Mean to Geometric Mean for Nakagami-m Fading Power
Wang, Ning; Cheng, Julian; Tellambura, Chintha
To assess the performance of maximum-likelihood (ML) based Nakagami m parameter estimators, current methods rely on Monte Carlo simulation. In order to enable the analytical performance evaluation of ML-based m parameter estimators, we study the statistical properties of a parameter Δ, which is defined as the log-ratio of the arithmetic mean to the geometric mean for Nakagami-m fading power. Closed-form expressions are derived for the probability density function (PDF) of Δ. It is found that for large sample size, the PDF of Δ can be well approximated by a two-parameter Gamma PDF.
Bounds for the Arithmetic Mean in Terms of the Neuman-Sándor and Other Bivariate Means
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Fan Zhang
2013-01-01
Full Text Available We present the largest values α1, α2, and α3 and the smallest values β1, β2, and β3 such that the double inequalities α1M(a,b+(1-α1H(a,b0 with a≠b, where M(a,b, A(a,b, He(a,b, H(a,b and H-(a,b denote the Neuman-Sándor, arithmetic, Heronian, harmonic, and harmonic root-square means of a and b, respectively.
2012-01-01
In this present study includes the Very Large Scale Integration (VLSI) system implementation of 200MHz, 8-bit, 90nm Complementary Metal Oxide Semiconductor (CMOS) Arithmetic and Logic Unit (ALU) processor control with logic gate design style and 0.12µm six metal 90nm CMOS fabrication technology. The system blocks and the behaviour are defined and the logical design is implemented in gate level in the design phase. Then, the logic circuits are simulated and the subunits are converted in to 90n...
Effects of cognitive appraisal and mental workload factors on performance in an arithmetic task.
Galy, Edith; Mélan, Claudine
2015-12-01
We showed in a previous study an additive interaction between intrinsic and extraneous cognitive loads and of participants' alertness in an 1-back working memory task. The interaction between intrinsic and extraneous cognitive loads was only observed when participants' alertness was low (i.e. in the morning). As alertness is known to reflect an individual's general functional state, we suggested that the working memory capacity available for germane cognitive load depends on a participant's functional state, in addition to intrinsic and extraneous loads induced by the task and task conditions. The relationships between the different load types and their assessment by specific load measures gave rise to a modified cognitive load model. The aim of the present study was to complete the model by determining to what extent and at what processing level an individual's characteristics intervene in order to implement efficient strategies in a working memory task. Therefore, the study explored participants' cognitive appraisal of the situation in addition to the load factors considered previously-task difficulty, time pressure and alertness. Each participant performed a mental arithmetic task in four different cognitive load conditions (crossover of two task difficulty conditions and of two time pressure conditions), both while their alertness was low (9 a.m.) and high (4 p.m.). Results confirmed an additive effect of task difficulty and time pressure, previously reported in the 1-back memory task, thereby lending further support to the modified cognitive load model. Further, in the high intrinsic and extraneous load condition, performance was reduced on the morning session (i.e. when alertness was low) on one hand, and in those participants' having a threat appraisal of the situation on the other hand. When these factors were included into the analysis, a performance drop occurred in the morning irrespective of cognitive appraisal, and with threat appraisal in the
Lakhani, Gopal
2013-04-01
This article presents four modifications to the JPEG arithmetic coding (JAC) algorithm, a topic not studied well before. It then compares the compression performance of the modified JPEG with JPEG XR, the latest block-based image coding standard. We first show that the bulk of inter/intra-block redundancy, caused due to the use of the block-based approach by JPEG, can be captured by applying efficient prediction coding. We propose the following modifications to JAC to take advantages of our prediction approach. 1) We code a totally different DC difference. 2) JAC tests a DCT coefficient by considering its bits in the increasing order of significance for coding the most significant bit position. It causes plenty of redundancy because JAC always begins with the zeroth bit. We modify this coding order and propose alternations to the JPEG coding procedures. 3) We predict the sign of significant DCT coefficients, a problem is not addressed from the perspective of the JPEG decoder before. 4) We reduce the number of binary tests that JAC codes to mark end-of-block. We provide experimental results for two sets of eight-bit gray images. The first set consists of nine classical test images mostly of size 512 × 512 pixels. The second set consists of 13 images of size 2000 × 3000 pixels or more. Our modifications to JAC obtain extra-ordinary amount of code reduction without adding any kind of losses. More specifically, when we quantize the images using the default quantizers, our modifications reduce the total JAC code size of the images of these two sets by about 8.9 and 10.6%, and the JPEG Huffman code size by about 16.3 and 23.4%, respectively, on the average. Gains are even higher for coarsely quantized images. Finally, we compare the modified JAC with two settings of JPEG XR, one with no block overlapping and the other with the default transform (we denote them by JXR0 and JXR1, respectively). Our results show that for the finest quality rate image coding, the modified
Realization of the Arithmetic Logic Unit Based on QuartusII%基于QuartusⅡ的ALU的实现
Institute of Scientific and Technical Information of China (English)
陈辉; 周自立
2012-01-01
Being the experiment of the arithmetic device parts which belongs to Principle of Computer Organization-ALU, it is teaching point to calculator professional teacher, is also the knowledge of the difficuh comprehension that the majority of students reflects. Quite a few students are unable to complete this experiment nicely. Being a kind of EDA design software, QuartuslI provide many platens integrity design environment. To help the students solve the problem, by introducing two methods about the realization of the arithmetic unit and carrying out a simple ALU, the two methods of the specific implementation are proposed.%计算机组成原理运算器部件ALU实验,一直是计算机专业老师的教学重点,也是多数学生反映的学习难点之一,相当一部分学生不能很好地完成这个实验。QuartusⅡ作为一种EDA设计软件,提供了完整的多平台设计环境。为了帮助学生更好地完成ALU实验,介绍了实现ALU的两种方法,并以实现简单的ALU为例,详细介绍这两种方法的具体实现。
Friedrich, Björn; Heil, Peter
2017-01-01
Onsets of acoustic stimuli are salient transients and are relevant in humans for the perception of music and speech. Previous studies of onset-duration discrimination and matching focused on whether onsets are perceived categorically. In this study, we address two issues. First, we revisit onset-duration matching and measure, for 79 conditions, how accurately and precisely human listeners can adjust the onset duration of a comparison stimulus to subjectively match that of a standard stimulus. Second, we explore measures for quantifying performance in this and other matching tasks. The conventional measures of accuracy and precision are defined by arithmetic descriptive statistics and the Euclidean distance function on the real numbers. We propose novel measures based on geometric descriptive statistics and the log-ratio distance function, the Euclidean distance function on the positive-real numbers. Only these properly account for the fact that the magnitude of onset durations, like the magnitudes of most physical quantities, can attain only positive real values. The conventional (arithmetic) measures possess a convexity bias that yields errors that grow with the width of the distribution of matches. This convexity bias leads to misrepresentations of the constant error and could even imply the existence of perceptual illusions where none exist. This is not so for the proposed (geometric) measures. We collected up to 68 matches from a given listener for each condition (about 34,000 matches in total) and examined inter-listener variability and the effects of onset duration, plateau duration, sound level, carrier, and restriction of the range of adjustable comparison stimuli on measures of accuracy and precision. Results obtained with the conventional measures generally agree with those reported in the literature. The variance across listeners is highly heterogeneous for the conventional measures but is homogeneous for the proposed measures. Furthermore, the proposed
Lepola, Janne; Niemi, Pekka; Kuikka, Mira; Hannula, Minna M.
2005-01-01
This 3-year longitudinal study examined how motivational tendencies, that is, task orientation and social dependence orientation, as well as cognitive-linguistic prerequisites of reading and math skills (i.e., phonological awareness, rapid naming, oral language comprehension skills, number sequence and basic arithmetic skills) measured in…
Directory of Open Access Journals (Sweden)
Malcus Cassiano Kuhn
2016-12-01
Full Text Available The article discusses the geometry in the arithmetic of the Order and Progress series and of the Concordia series, edited by the Evangelical Lutheran Church of Brazil for their parochial schools of the 20th century, in Rio Grande do Sul. The Missouri Synod, today Evangelical Lutheran Church of Brazil, began mission in the gaucho German colonies in 1900, founding religious congregations and parochial schools. These schools were inserted in a missionary and community project that sought to teach the mother tongue, mathematics, cultural, social, and mainly, religious values. Basing on cultural history, analyzed two arithmetic of the Order and Progress series and four arithmetic of the Concordia series, edited by the Lutheran Church for their schools. It has been found that the geometric knowledges were related to geometric shapes, scale drawings, length measures, surface measures, volume measures and the old measures Brazilian. The authors of the arithmetic used the strategy of presenting teaching proposals of the geometry of practical form and associated with real situations so that students of the gaucho Lutheran parochial schools appropriating these mathematical knowledges, and in future, to make the correct administration of your family budget and the management of your rural property.
An Analysis of the Contents and Pedagogy of Al-Kashi's 1427 "Key to Arithmetic" (Miftah Al-Hisab)
Ta'ani, Osama Hekmat
2011-01-01
Al-Kashi's 1427 "Key to Arithmetic" had important use over several hundred years in mathematics teaching in Medieval Islam throughout the time of the Ottoman Empire. Its pedagogical features have never been studied before. In this dissertation I have made a close pedagogical analysis of these features and discovered several teaching…
Hativa, Nira
This report summarizes the results of studies of four computer-assisted integrated learning systems (ILS) designed to teach students arithmetic: two in Israel (TOAM--distributed in the United States as DEGEM and SEMEL) and two in the United States (CCC and WICAT). The qualitative and quantitative studies identified cognitive, sociological, and…
Otisk, Marek
This paper deals with comments and glosses to the first chapter of the second book of Boethius's Introduction to Arithmetic from the last quarter of the 10th century. Those texts were written by Gerbert of Aurillac (Scholium ad Boethii Arithmeticam Institutionem l. II, c. 1), Abbo of Fleury (commentary on the Calculus by Victorius of Aquitaine, the so-called De numero, mensura et pondere), Notker of Liège (De superparticularibus) and by the anonymous author (De arithmetica Boetii). The main aim of this paper is to show that Boethius's statements about the converting numerical sequences to equality from this work could be interpreted minimally in two different ways. This paper discussed also the application of this topic in other liberal arts (like astronomy, music, grammar etc.) and in playing game called rithmomachia, the medieval philosophers' game.
Karwowski, Damian; Domański, Marek
2016-01-01
An improved context-based adaptive binary arithmetic coding (CABAC) is presented. The idea for the improvement is to use a more accurate mechanism for estimation of symbol probabilities in the standard CABAC algorithm. The authors' proposal of such a mechanism is based on the context-tree weighting technique. In the framework of a high-efficiency video coding (HEVC) video encoder, the improved CABAC allows 0.7% to 4.5% bitrate saving compared to the original CABAC algorithm. The application of the proposed algorithm marginally affects the complexity of HEVC video encoder, but the complexity of video decoder increases by 32% to 38%. In order to decrease the complexity of video decoding, a new tool has been proposed for the improved CABAC that enables scaling of the decoder complexity. Experiments show that this tool gives 5% to 7.5% reduction of the decoding time while still maintaining high efficiency in the data compression.
Institute of Scientific and Technical Information of China (English)
吴修广; 沈永明; 郑永红
2004-01-01
A numerical model for shallow water flow has been developed based on the unsteady Reynolds-averaged NavierStokes equations with the hydrodynamic pressure instead of hydrostatic pressure assumption. The equations are transformed into the σ-coordinate system and the eddy viscosity is calculated with the standard k - e turbulence model. The control volume method is used to discrete the equations, and the boundary conditions at the bed for shallow water models only include vertical diffusion terms expressed with wall functions. And the semi-implicit method for pressure linked equation arithmetic is adopted to solve the equations. The model is applied to the 2D vertical plane flow of a curent over two steep-sided trenches for which experiment data are available for comparison and good agreement is obtained. And the model is used to predicting the flow in a channel with a steep-sided submerged breakwater at the bottom, and the streamline is drawn.
Duality theories for Boolean algebras with operators
Givant, Steven
2014-01-01
In this new text, Steven Givant—the author of several acclaimed books, including works co-authored with Paul Halmos and Alfred Tarski—develops three theories of duality for Boolean algebras with operators. Givant addresses the two most recognized dualities (one algebraic and the other topological) and introduces a third duality, best understood as a hybrid of the first two. This text will be of interest to graduate students and researchers in the fields of mathematics, computer science, logic, and philosophy who are interested in exploring special or general classes of Boolean algebras with operators. Readers should be familiar with the basic arithmetic and theory of Boolean algebras, as well as the fundamentals of point-set topology.
Green, Michael; Piel, John A.; Flowers, Claudia
2008-01-01
The authors examined the impact of manipulative-based instruction on 2 independent cohorts of preservice elementary teachers. In Study 1, 50 participants engaged in problem solving with operations on whole numbers and fractions using concrete and representational manipulatives over 5 classes. Pre- to posttest performance on a mathematics survey…
Diagonalization of the symmetrized discrete i th right shift operator
Fuentes, Marc
2007-01-01
In this paper, we consider the symmetric part of the so-called ith right shift operator. We determine its eigenvalues as also the associated eigenvectors in a complete and closed form. The proposed proof is elementary, using only basical skills such as Trigonometry, Arithmetic and Linear algebra. The first section is devoted to the introduction of the tackled problem. Second and third parts contain almost all the ?technical? stuff of the proofE Afterwards, we continue with the end of the proof, provide a graphical illustration of the results, as well as an application on the polyhedral ?sandwiching? of a special compact of arising in Signal theory.
Reversible arithmetic logic unit for quantum arithmetic
DEFF Research Database (Denmark)
Thomsen, Michael Kirkedal; Glück, Robert; Axelsen, Holger Bock
2010-01-01
-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...
NAND flash error correction arithmetic based on ECC embedded BCH code%ECC嵌入BCH码的NAND闪存纠错算法
Institute of Scientific and Technical Information of China (English)
李进; 金龙旭; 李国宁; 张珂; 傅瑶; 朱鹏
2012-01-01
针对现有闪存基于硬件ECC纠错算法的纠错能力差,而基于RS码和BCH码纠错算法的译码耗时长的问题,提出一种适于空间应用的硬件ECC嵌入BCH码的闪存纠错算法.分析了闪存内部组织结构特点及闪存硬件ECC纠错原理,提出了一种嵌入BCH(2084,2048,3)码的闪存纠错算法.采用一种蝶形阵列处理机制来迭代计算BCH校验码.使用地面检测设备对闪存纠错算法进行了试验验证.结果表明,纠错算法能快速稳定、可靠地工作,在Flash单页2 kB/页下,可以纠正24b错误.该纠错提高了空间相机图像存储系统的可靠性.%In order to resolve the problem of the low error correcting capability of hardware ECC and the being time-consuming of decoder based on RS code or BCH code, a NAND flash error correction algorithm based on hardware ECC embedded BCH code for space application was proposed in this paper. First, this paper presents the structural characteristic of flash. Then the principle of data flash hardware ECC was analyzed. An embedded BCH code error correction arithmetic was put fonvard. Then the check code of BCH encoder was calculated by an 8-bit parallel butterfly array processing mechanism. Finally, the verification experiments to NAND controller in the prototype machine of XX-X space multi-spectral camera were carried out. The experiments results showed that the proposed error correction algorithms can operate fast, efficiently, reliably, and stably. The algorithm is able to correct 24b errors in 2 kB/page. The algorithm can improve the reliability of the space camera data storage.
The Tie Effect in Mental Arithmetic%心算加工中tie effect的加工机制
Institute of Scientific and Technical Information of China (English)
田花; 刘昌
2011-01-01
This article is to review the tie effect in simple arithmetic. Tie effect means that simple arithmetic problems with repeated operands （i. e., ties such as 3 ＋ 3,4×4） are solved more quickly and accurately than similar nontie problems （e. g., 3 ＋ 4,4 × 5）. Furthermore, problem size and tie effect so interact that latencies on both ties and nonties increase with the problem size, but the increase is much greater in nonties than in ties. There are two possible explanations for the tie effect, i.e., encoding-based and access- based accounts. Encoding-based accounts propose that the tie advantage occurs because repetition of the same physical stimulus results in faster encoding of ties than of nonties. Alternatively, access-based accounts propose that ties may be easier to solve than nonties because of differences in accessibility in memory or differences in the solution processes. Access-based accounts fall into three categories： familiarity, interference, variability in solution approaches. According to familiarity explanations, acee~ibility so varies with practice that the tie effect is related to the frequency with which problems are encountered. Ties receive more practice and the connections between operands and answers in memory are greater. So ties are solved more quickly. According to interference explanations, ties and nonties are defined as separate categories of problems and the interference is greater within categories than between category. Thus, because the tie category includes relatively few problems, ties received less inhibitory input than nonties. According to solution approach explanations, even simple arithmetic is solved not only by direct retrieval from memory but by nov_retrieval procedures. Ties are solved by direct retrieval procedures and nonties are solved by nonretrieval procedures which are slower than direct retrieval. The encoding-account can＇ t provide reasonable explanations for the tie ~ size interaction. Aceess
Licensed operating reactors: Status summary report, data as of December 31, 1995. Volume 20
Energy Technology Data Exchange (ETDEWEB)
NONE
1996-06-01
The US Nuclear Regulatory Commission`s monthly summary of licensed nuclear power reactor data is based primarily on the operating data report submitted by licensees for each unit. This report is divided into two sections: the first contains summary highlights and the second contains data on each individual unit in commercial operation. Section 1 availability factors, capacity factors, and forced outage rates are simple arithmetic averages. Section 2 items in the cumulative column are generally as reported by the licensees and notes to the use of weighted averages and starting dates other than commercial operation are provided.
Directory of Open Access Journals (Sweden)
Nadia Nosworthy
Full Text Available Recently, there has been a growing emphasis on basic number processing competencies (such as the ability to judge which of two numbers is larger and their role in predicting individual differences in school-relevant math achievement. Children's ability to compare both symbolic (e.g. Arabic numerals and nonsymbolic (e.g. dot arrays magnitudes has been found to correlate with their math achievement. The available evidence, however, has focused on computerized paradigms, which may not always be suitable for universal, quick application in the classroom. Furthermore, it is currently unclear whether both symbolic and nonsymbolic magnitude comparison are related to children's performance on tests of arithmetic competence and whether either of these factors relate to arithmetic achievement over and above other factors such as working memory and reading ability. In order to address these outstanding issues, we designed a quick (2 minute paper-and-pencil tool to assess children's ability to compare symbolic and nonsymbolic numerical magnitudes and assessed the degree to which performance on this measure explains individual differences in achievement. Children were required to cross out the larger of two, single-digit numerical magnitudes under time constraints. Results from a group of 160 children from grades 1-3 revealed that both symbolic and nonsymbolic number comparison accuracy were related to individual differences in arithmetic achievement. However, only symbolic number comparison performance accounted for unique variance in arithmetic achievement. The theoretical and practical implications of these findings are discussed which include the use of this measure as a possible tool for identifying students at risk for future difficulties in mathematics.
The Design of CABAC Arithmetic Encoder Based on FPGA%基于 FPGA的 CABAC算术编码器设计
Institute of Scientific and Technical Information of China (English)
王震; 张延军
2015-01-01
A highly active arithmetic coder of the adaptive binary arithmetic entropy coding algorithm( CABCA) is given out ,which is based on context .CABAC is the entropy coding method adopted in the new H .264/AVC .As the development of ultra high definition video , a more harsher requiment of arithmetic encoder is proposed in compression .However ,the CABAC is very complex so that it is very hard to be implemented by hardware .To meet the requiment ,a high‐speed arithmetic encoder structure is proposed according to double‐path context storage and pipeline design ,which can eliminate the data dependence and get high throughput with very little cost .%提出一种高效率的基于上下文的自适应二进制算术熵编码（CABAC ）的算术编码架构．CABAC是新型 H ．264／AVC 视频压缩标准采用的熵编码机制．当代超高清视频技术的发展，对算术编码的压缩效率提出了越来越苛刻的要求．但CABAC算法复杂度高，硬件实现难度大．为了满足CABAC的性能要求，提出一种快速高效的算术编码硬件加速器，通过采用双路径存储上下文和多级流水线设计，消除了数据依赖，用很小的代价获得了较高的吞吐率．
Guo, Hua; Zheng, Yandong; Zhang, Xiyong; Li, Zhoujun
2016-04-28
In resource-constrained wireless networks, resources such as storage space and communication bandwidth are limited. To guarantee secure communication in resource-constrained wireless networks, group keys should be distributed to users. The self-healing group key distribution (SGKD) scheme is a promising cryptographic tool, which can be used to distribute and update the group key for the secure group communication over unreliable wireless networks. Among all known SGKD schemes, exponential arithmetic based SGKD (E-SGKD) schemes reduce the storage overhead to constant, thus is suitable for the the resource-constrained wireless networks. In this paper, we provide a new mechanism to achieve E-SGKD schemes with backward secrecy. We first propose a basic E-SGKD scheme based on a known polynomial-based SGKD, where it has optimal storage overhead while having no backward secrecy. To obtain the backward secrecy and reduce the communication overhead, we introduce a novel approach for message broadcasting and self-healing. Compared with other E-SGKD schemes, our new E-SGKD scheme has the optimal storage overhead, high communication efficiency and satisfactory security. The simulation results in Zigbee-based networks show that the proposed scheme is suitable for the resource-restrained wireless networks. Finally, we show the application of our proposed scheme.
Directory of Open Access Journals (Sweden)
Hua Guo
2016-04-01
Full Text Available In resource-constrained wireless networks, resources such as storage space and communication bandwidth are limited. To guarantee secure communication in resource-constrained wireless networks, group keys should be distributed to users. The self-healing group key distribution (SGKD scheme is a promising cryptographic tool, which can be used to distribute and update the group key for the secure group communication over unreliable wireless networks. Among all known SGKD schemes, exponential arithmetic based SGKD (E-SGKD schemes reduce the storage overhead to constant, thus is suitable for the the resource-constrained wireless networks. In this paper, we provide a new mechanism to achieve E-SGKD schemes with backward secrecy. We first propose a basic E-SGKD scheme based on a known polynomial-based SGKD, where it has optimal storage overhead while having no backward secrecy. To obtain the backward secrecy and reduce the communication overhead, we introduce a novel approach for message broadcasting and self-healing. Compared with other E-SGKD schemes, our new E-SGKD scheme has the optimal storage overhead, high communication efficiency and satisfactory security. The simulation results in Zigbee-based networks show that the proposed scheme is suitable for the resource-restrained wireless networks. Finally, we show the application of our proposed scheme.
Deferne, J L; Leeds, A R
1996-08-01
The objective of this study was to test the effect of a supplement of blackcurrant seed oil (BSO), a rich source of gamma-linolenic acid (C18:3n-6) on the resting blood pressure (BP) and cardiovascular reactivity to a psychological stress in borderline hypertensive individuals. Twenty-seven male volunteers found to have a BP lying persistently within the borderline range, were allocated randomly to one of two groups at the end of a 4-week baseline period. The first group received a daily supplement of 6 g safflower oil for the consecutive 8 weeks while the second the same dose of blackcurrant seed oil. In addition to weekly measurements of resting BP, BP and heart rate reactivity to a standardised 5-min test of mental arithmetic were recorded before, and at the end of the supplementation period. BSO inhibited BP reactivity by over 40% (ANOVA for repeated measures diastolic (D) BP P = 0.026, systolic (S) BP P = 0.021). The decrease in DBP for the subjects on BSO was significantly different from the slight changes observed in the safflower group (ANOVA for repeated measures P = 0.018 for time-treatment interaction). We conclude that gamma-linolenic-rich fatty acid preparations are likely to influence cardiovascular control, by mechanisms yet to be clarified.
Ultra-Low-Voltage Self-Body Biasing Scheme and Its Application to Basic Arithmetic Circuits
Directory of Open Access Journals (Sweden)
Ramiro Taco
2015-01-01
Full Text Available The gate level body biasing (GLBB is assessed in the context of ultra-low-voltage logic designs. To this purpose, a GLBB mirror full adder is implemented by using a commercial 45 nm bulk CMOS triple-well technology and compared to equivalent conventional zero body-biased CMOS and dynamic threshold voltage MOSFET (DTMOS circuits under different running conditions. Postlayout simulations demonstrate that, at the parity of leakage power consumption, the GLBB technique exhibits a significant concurrent reduction of the energy per operation and the delay in comparison to the conventional CMOS and DTMOS approaches. The silicon area required by the GLBB full adder is halved with respect to the equivalent DTMOS implementation, but it is higher in comparison to conventional CMOS design. Performed analysis also proves that the GLBB solution exhibits a high level of robustness against temperature fluctuations and process variations.
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.
Directory of Open Access Journals (Sweden)
Antonio Frías
2007-09-01
Full Text Available En este trabajo identificamos una variable lingüística en los problemas aritméticos verbales de dos pasos, que denominamos “nodo”. Describimos una experiencia con estudiantes de 5º y 6º de primaria (10 y 12 años cuyo fin fue observar si esta variable lingüística tiene o no influencia significativa en la elección de las operaciones necesarias para solucionar este tipo de problemas. Los resultados obtenidos muestran que el número de nodos en un problema de dos pasos tiene efecto significativo en el proceso de resolución. Esta influencia no se ve alterada por otros factores considerados en este estudio. In this work we identify a new factor in two-steps arithmetic word problems, which we denominate "node” factor. We describe an experience with 5th and 6th grade primary students (11 and 12-year-old pupils whose purpose was to observe if this factor has or has not significant influence in the election of the necessary operations to solve this type of problems. The obtained results show that the number of nodes in a problem of two steps has significant effect in the resolution process. This significant influence is not altered by other factors considered in this study.
Dostal, Jiri
1993-01-01
This book provides the reader with the practical knowledge necessary to select and use operational amplifier devices. It presents an extensive treatment of applications and a practically oriented, unified theory of operational circuits.Provides the reader with practical knowledge necessary to select and use operational amplifier devices. Presents an extensive treatment of applications and a practically oriented, unified theory of operational circuits
Pathak, Rohit; Joshi, Satyadhar
Within a span of over a decade, India has become one of the most favored destinations across the world for Business Process Outsourcing (BPO) operations. India has rapidly achieved the status of being the most preferred destination for BPO for companies located in the US and Europe. Security and privacy are the two major issues needed to be addressed by the Indian software industry to have an increased and long-term outsourcing contract from the US. Another important issue is about sharing employee’s information to ensure that data and vital information of an outsourcing company is secured and protected. To ensure that the confidentiality of a client’s information is maintained, BPOs need to implement some data security measures. In this paper, we propose a new protocol for specifically for BPO Secure Multi-Party Computation (SMC). As there are many computations and surveys which involve confidential data from many parties or organizations and the concerned data is property of the organization, preservation and security of this data is of prime importance for such type of computations. Although the computation requires data from all the parties, but none of the associated parties would want to reveal their data to the other parties. We have proposed a new efficient and scalable protocol to perform computation on encrypted information. The information is encrypted in a manner that it does not affect the result of the computation. It uses modifier tokens which are distributed among virtual parties, and finally used in the computation. The computation function uses the acquired data and modifier tokens to compute right result from the encrypted data. Thus without revealing the data, right result can be computed and privacy of the parties is maintained. We have given a probabilistic security analysis of hacking the protocol and shown how zero hacking security can be achieved. Also we have analyzed the specific case of Indian BPO.
全定制CORDIC运算器设计%Full Custom CORDIC Arithmetic Unit Design
Institute of Scientific and Technical Information of China (English)
毕卓; 戴益君
2011-01-01
浮点三角函数计算是导航系统、三维图像处理、雷达信号预处理等领域的基本运算.本文采用CORDIC算法及全定制集成电路设计方法实现了一种浮点三角函数计算电路,其输出数据兼容IEEE-754单精度浮点数标准.本文首先介绍了CORDIC算法的原理,并根据性能优先的原则采用了流水线结构；然后给出了基于SMIC O.13μm 1P8M CMOS工艺下的静态电路结构及版图设计.全定制CORDIC运算器的面积为605 284μm2,最长路径延时(SS条件下)为3.013ns.%Floating-point trigonometric computing is a fundamental operation in navigation systems, 3D image processing, radar signal preprocessing and so on. This paper presents a floating point trigonometric computing circuit using a CORDIC algorithm and a full custom layout method, and the output data are compatible with the IEEE-754 signal precision floating-point standard. It describes the CORDIC algorithm principle and chooses a pipeline structure based on the principle of priority on performance. A static circuit structure and a full custom layout are given in the SIMC 0.13μm 1P8M CMOS process. The silicon area of data path is 605 284/W and the critical path delay is 3.013ns in the SS (Slow-Slow) corners.
Directory of Open Access Journals (Sweden)
Verônica Bender Haydu
2006-01-01
Full Text Available O paradigma da equivalência de estímulos tem sido usado para o desenvolvimento de diversos procedimentos aplicáveis ao ensino de leitura, escrita e aritmética. O objetivo do presente estudo foi o de investigar o efeito do ensino de relações de equivalência entre três formas de apresentação de problemas aritméticos de adição sobre o comportamento de resolver problemas. Sete alunos da 1ª série do ensino fundamental foram submetidos a um pré-teste e pós-teste com problemas de adição impressos nas formas de balança (A, operação (B e sentença lingüística (C. O treino de equivalência de estímulos estabeleceu relações entre A-B e A-C. Seis dos sete participantes responderam de acordo com as classes estabelecidas. O desempenho dos participantes no pós-teste foi superior ao apresentado no pré-teste. Conclui-se que o estabelecimento de relações de equivalência entre problemas aritméticos de adição em forma de balança, operação e sentença lingüística melhorou o desempenho na resolução problemas desses tipos.The equivalence paradigm has been applied to the development of a variety of procedures applied to teach reading, writing and arithmetic. This work aimed to investigate the effect of teaching stimulus equivalence relations between three different forms of arithmetic sum problems on problem-solving behavior. Seven first grade students of Fundamental Schooling (=Elementary Schooling were submitted to a pre-test, and a post-test with sum problems printed in the form of slave (A, operations (B and word problems (C. The conditional discrimination procedure established relations between A-B and A-C. Six of seven participants responded accordingly to the established classes. The performance of the participants in the post-test was higher than in the pre-test. It was concluded that the establishment of equivalence relations between arithmetic sum problems in the form of slave, operations, and word problems enhanced
Reproducibility of neuroimaging analyses across operating systems.
Glatard, Tristan; Lewis, Lindsay B; Ferreira da Silva, Rafael; Adalat, Reza; Beck, Natacha; Lepage, Claude; Rioux, Pierre; Rousseau, Marc-Etienne; Sherif, Tarek; Deelman, Ewa; Khalili-Mahani, Najmeh; Evans, Alan C
2015-01-01
Neuroimaging pipelines are known to generate different results depending on the computing platform where they are compiled and executed. We quantify these differences for brain tissue classification, fMRI analysis, and cortical thickness (CT) extraction, using three of the main neuroimaging packages (FSL, Freesurfer and CIVET) and different versions of GNU/Linux. We also identify some causes of these differences using library and system call interception. We find that these packages use mathematical functions based on single-precision floating-point arithmetic whose implementations in operating systems continue to evolve. While these differences have little or no impact on simple analysis pipelines such as brain extraction and cortical tissue classification, their accumulation creates important differences in longer pipelines such as subcortical tissue classification, fMRI analysis, and cortical thickness extraction. With FSL, most Dice coefficients between subcortical classifications obtained on different operating systems remain above 0.9, but values as low as 0.59 are observed. Independent component analyses (ICA) of fMRI data differ between operating systems in one third of the tested subjects, due to differences in motion correction. With Freesurfer and CIVET, in some brain regions we find an effect of build or operating system on cortical thickness. A first step to correct these reproducibility issues would be to use more precise representations of floating-point numbers in the critical sections of the pipelines. The numerical stability of pipelines should also be reviewed.
Arnau, David; Arevalillo-Herraez, Miguel; Puig, Luis; Gonzalez-Calero, Jose Antonio
2013-01-01
Designers of interactive learning environments with a focus on word problem solving usually have to compromise between the amount of resolution paths that a user is allowed to follow and the quality of the feedback provided. We have built an intelligent tutoring system (ITS) that is able to both track the user's actions and provide adequate…
Tsichritzis, Dionysios C; Rheinboldt, Werner
1974-01-01
Operating Systems deals with the fundamental concepts and principles that govern the behavior of operating systems. Many issues regarding the structure of operating systems, including the problems of managing processes, processors, and memory, are examined. Various aspects of operating systems are also discussed, from input-output and files to security, protection, reliability, design methods, performance evaluation, and implementation methods.Comprised of 10 chapters, this volume begins with an overview of what constitutes an operating system, followed by a discussion on the definition and pr
Boehme, Thomas K
1987-01-01
Operational Calculus, Volume II is a methodical presentation of operational calculus. An outline of the general theory of linear differential equations with constant coefficients is presented. Integral operational calculus and advanced topics in operational calculus, including locally integrable functions and convergence in the space of operators, are also discussed. Formulas and tables are included.Comprised of four sections, this volume begins with a discussion on the general theory of linear differential equations with constant coefficients, focusing on such topics as homogeneous and non-ho
Directory of Open Access Journals (Sweden)
Power Sarah D
2012-03-01
Full Text Available Abstract Background Near-infrared spectroscopy (NIRS is an optical imaging technology that has recently been investigated for use in a safe, non-invasive brain-computer interface (BCI for individuals with severe motor impairments. To date, most NIRS-BCI studies have attempted to discriminate two mental states (e.g., a mental task and rest, which could potentially lead to a two-choice BCI system. In this study, we attempted to automatically differentiate three mental states - specifically, intentional activity due to 1 a mental arithmetic (MA task and 2 a mental singing (MS task, and 3 an unconstrained, "no-control (NC" state - to investigate the feasibility of a three-choice system-paced NIRS-BCI. Results Deploying a dual-wavelength frequency domain near-infrared spectrometer, we interrogated nine sites around the frontopolar locations while 7 able-bodied adults performed mental arithmetic and mental singing to answer multiple-choice questions within a system-paced paradigm. With a linear classifier trained on a ten-dimensional feature set, an overall classification accuracy of 56.2% was achieved for the MA vs. MS vs. NC classification problem and all individual participant accuracies significantly exceeded chance (i.e., 33%. However, as anticipated based on results of previous work, the three-class discrimination was unsuccessful for three participants due to the ineffectiveness of the mental singing task. Excluding these three participants increases the accuracy rate to 62.5%. Even without training, three of the remaining four participants achieved accuracies approaching 70%, the value often cited as being necessary for effective BCI communication. Conclusions These results are encouraging and demonstrate the potential of a three-state system-paced NIRS-BCI with two intentional control states corresponding to mental arithmetic and mental singing.
Keyl, M.; Kiukas, J.; Werner, R. F.
2016-05-01
In this paper, we introduce Schwartz operators as a non-commutative analog of Schwartz functions and provide a detailed discussion of their properties. We equip them, in particular, with a number of different (but equivalent) families of seminorms which turns the space of Schwartz operators into a Fréchet space. The study of the topological dual leads to non-commutative tempered distributions which are discussed in detail as well. We show, in particular, that the latter can be identified with a certain class of quadratic forms, therefore making operations like products with bounded (and also some unbounded) operators and quantum harmonic analysis available to objects which are otherwise too singular for being a Hilbert space operator. Finally, we show how the new methods can be applied by studying operator moment problems and convergence properties of fluctuation operators.
Alcock-Zeilinger, Judith
2016-01-01
In this paper, we give a generic algorithm of the transition operators between Hermitian Young projection operators corresponding to equivalent irreducible representations of SU(N), using the compact expressions of Hermitian Young projection operators derived in a companion paper. We show that the Hermitian Young projection operators together with their transition operators constitute a fully orthogonal basis for the algebra of invariants of $V^{\\otimes m}$ that exhibits a systematically simplified multiplication table. We discuss the full algebra of invariants over $V^{\\otimes 3}$ and $V^{\\otimes 4}$ as explicit examples. In our presentation we make use of various standard concepts such as Young projection operators, Clebsch-Gordan operators, and invariants (in birdtrack notation). We tie these perspectives together and use them to shed light on each other.
Institute of Scientific and Technical Information of China (English)
郑雪静
2013-01-01
Arithmetic thinking and algebraic thinking are the two basic forms of students' mathematical think-ing, for the normal school students whose the future career will be engaged in primary school mathematics ed-ucation, this paper proposes the use of algebraic thinking explained arithmetic thinking, in-depth study materi-als to seize the connection point with algebraic thinking and arithmetic thinking, standing on the high point from algebraic thinking in arithmetic thinking, which will effectively cultivate their abilities from algebraic thinking regression arithmetic thinking.%算术思维和代数思维是学生数学思维的两种基本形态，对于未来将要从事小学数学教育工作的师范生，用代数思维解释算术思维、深入钻研教材抓住代数思维与算术思维的联结点、站在高观点从代数思维反观算术思维，这些将有效培养学生从代数思维回归算术思维的能力。
Institute of Scientific and Technical Information of China (English)
张新鹏; 王朔中; 张开文
2003-01-01
A digital watermark as a means for copyright protection may be crippled when a fake mark is embedded on top of it since both watermarks are detectable. In dealing with this problem, a watermarking scheme that does not satisfy the law of commutation is proposed. In this scheme, an order function based on an arithmetic mechanism is employed to identify the embedding order without affecting detection of the regular watermark. An earlier watermark corresponds to a larger value of the order function. In this way, the embedding order or watermarks can be identified according to the order function.
Directory of Open Access Journals (Sweden)
V. U.K.. Sastry
2006-01-01
Full Text Available In this paper, we have developed a block cipher by applying an iterative method. In the process of encryption, we have used a key matrix (K in which all the elements are binary bits. In the process of decryption, we have utilized the modular arithmetic inverse (K-1. In the process of encryption, the elements of the plaintext and the elements of the key are thoroughly mixed so that the strength of the algorithm increases remarkably. In this we have obtained the ciphertext for large blocks of plaintext.
Institute of Scientific and Technical Information of China (English)
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2010-01-01
This is the note for a series of lectures that the author gave at the Centre de Recerca Matemtica (CRM), Bellaterra, Barcelona, Spain on October 19–24, 2009. The aim is to give a comprehensive description of some recent work of the author and his students on generalisations of the Gross-Zagier formula, Euler systems on Shimura curves, and rational points on elliptic curves.
Arithmetic Shifting Considered Harmful,
1976-09-01
Processor Handbook . ( 1915), p. 4— 13. (25] Dumpty, Humpty. Quoted in Carroll, Lewis, Through the Looking Glass , — Chapter VI. ~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ •~~~~~~~~~ •. ~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Mieczkowski, Edward
2012-01-01
The set of segments, each of the next is n times bigger than the first one is a simple geometric interpretation of the set $\\mathbb{N}$ of natural numbers. In this paper we investigate the opposite situation. We construct an algebraic structure similar to the set $\\mathbb{N}$ which describes the set of congruent triangles, each of the next has the sides n times bigger than the first one. Later we do the same with the set of congruent tetrahedrons, and finally with a set of simplices of any dimension.
Visser, Albert
2014-01-01
In this paper we study a new relation between sentences: the jump relation. The idea of the jump relation is based on an analysis of Feferman's Theorem that the inconsistency of a theory U is interpretable over U. The jump relation is based on a converse of Feferman's Theorem: if a sentence is inter
Visser, A.|info:eu-repo/dai/nl/068579985
2015-01-01
In this paper we study a new relation between sentences: transducibility. The idea of transducibility is based on an analysis of Feferman's Theorem that the inconsistency of a theory U is interpretable over U. Transducibility is based on a converse of Feferman's Theorem: if a sentence is interpretab
Sellmaier, Florian; Schmidhuber, Michael
2015-01-01
The book describes the basic concepts of spaceflight operations, for both, human and unmanned missions. The basic subsystems of a space vehicle are explained in dedicated chapters, the relationship of spacecraft design and the very unique space environment are laid out. Flight dynamics are taught as well as ground segment requirements. Mission operations are divided into preparation including management aspects, execution and planning. Deep space missions and space robotic operations are included as special cases. The book is based on a course held at the German Space Operation Center (GSOC).
He, Yunfeng; Zhou, Xinlin; Shi, Dexin; Song, Hairong; Zhang, Hui; Shi, Jiannong
2016-01-01
Approximate number system (ANS) acuity and mathematical ability have been found to be closely associated in recent studies. However, whether and how these two measures are causally related still remain less addressed. There are two hypotheses about the possible causal relationship: ANS acuity influences mathematical performances, or access to math education sharpens ANS acuity. Evidences in support of both hypotheses have been reported, but these two hypotheses have never been tested simultaneously. Therefore, questions still remain whether only one-direction or reciprocal causal relationships existed in the association. In this work, we provided a new evidence on the causal relationship between ANS acuity and arithmetic ability. ANS acuity and mathematical ability of elementary-school students were measured sequentially at three time points within one year, and all possible causal directions were evaluated simultaneously using cross-lagged regression analysis. The results show that ANS acuity influences later arithmetic ability while the reverse causal direction was not supported. Our finding adds a strong evidence to the causal association between ANS acuity and mathematical ability, and also has important implications for educational intervention designed to train ANS acuity and thereby promote mathematical ability.