Personal Experience and Arithmetic Meaning in Semantic Dementia

Science.gov (United States)

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

2010-01-01

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

Guest Editors' Introduction: Special Section on Computer Arithmetic

DEFF Research Database (Denmark)

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

2014-01-01

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

Numerical Magnitude Representations Influence Arithmetic Learning

Science.gov (United States)

Booth, Julie L.; Siegler, Robert S.

2008-01-01

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

A Computational Model of Fraction Arithmetic

Science.gov (United States)

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

2017-01-01

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

Specificity and Overlap in Skills Underpinning Reading and Arithmetical Fluency

Science.gov (United States)

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

2013-01-01

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

ASIC For Complex Fixed-Point Arithmetic

Science.gov (United States)

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

1995-01-01

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

Arithmetic groups and their generalizations what, why, and how

CERN Document Server

Ji, Lizhen

2010-01-01

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

New technological design of arithmetics

International Nuclear Information System (INIS)

Hanitriarivo, R.

2008-01-01

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

Perceiving fingers in single-digit arithmetic problems.

Science.gov (United States)

Berteletti, Ilaria; Booth, James R

2015-01-01

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

Baby Arithmetic: One Object Plus One Tone

Science.gov (United States)

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

2004-01-01

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

Trace formulae for arithmetical systems

International Nuclear Information System (INIS)

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

1992-09-01

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

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.

Face Recognition using Approximate Arithmetic

DEFF Research Database (Denmark)

Marso, Karol

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

Specificity and overlap in skills underpinning reading and arithmetical fluency

NARCIS (Netherlands)

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

2013-01-01

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

If Gravity is Geometry, is Dark Energy just Arithmetic?

Science.gov (United States)

Czachor, Marek

2017-04-01

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

Arithmetic geometry over global function fields

CERN Document Server

Longhi, Ignazio; Trihan, Fabien

2014-01-01

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

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.

Approximate Arithmetic Training Improves Informal Math Performance in Low Achieving Preschoolers

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Emily Szkudlarek

2018-05-01

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

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

Science.gov (United States)

Szkudlarek, Emily; Brannon, Elizabeth M

2018-01-01

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

Arithmetical meadows

OpenAIRE

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

2009-01-01

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

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

OpenAIRE

Buium, Alexandru; Dupuy, Taylor

2013-01-01

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

Interactive Realizability and the elimination of Skolem functions in Peano Arithmetic

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Federico Aschieri

2012-10-01

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

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

Science.gov (United States)

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

2018-03-01

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

Studi Kompresi Data dengan Metode Arithmetic Coding

OpenAIRE

Santoso, Petrus

2001-01-01

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

Operator Arithmetic-Harmonic Mean Inequality on Krein Spaces

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M. Dehghani

2014-03-01

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

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

International Nuclear Information System (INIS)

Zhang Wansheng; Wang Yonggang

2005-01-01

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

Matrix inequalities for the difference between arithmetic mean and harmonic mean

OpenAIRE

Liao, Wenshi; Wu, Junliang

2015-01-01

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

Some studies on arithmetical chaos in classical and quantum mechanics

International Nuclear Information System (INIS)

Bolte, J.

1993-04-01

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

How to be Brilliant at Mental Arithmetic

CERN Document Server

Webber, Beryl

2010-01-01

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

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

Science.gov (United States)

Gilmore, Camilla K; Bryant, Peter

2006-06-01

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

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

Science.gov (United States)

Huber, Maria; Kipman, Ulrike; Pletzer, Belinda

2014-07-01

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

Learning, Realizability and Games in Classical Arithmetic

Science.gov (United States)

Aschieri, Federico

2010-12-01

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

Frege, Dedekind, and Peano on the foundations of arithmetic

CERN Document Server

Gillies, Donald

2013-01-01

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

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

Science.gov (United States)

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

2009-11-01

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

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

Science.gov (United States)

Cherri, Abdallah K.

1998-08-01

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

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.

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

Science.gov (United States)

Prather, Richard; Alibali, Martha W.

2011-01-01

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

Bit-wise arithmetic coding for data compression

Science.gov (United States)

Kiely, A. B.

1994-01-01

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

Optimized 4-bit Quantum Reversible Arithmetic Logic Unit

Science.gov (United States)

Ayyoub, Slimani; Achour, Benslama

2017-08-01

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

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

Science.gov (United States)

Berg, Derek H.; Hutchinson, Nancy L.

2010-01-01

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

Hybrid content addressable memory MSD arithmetic

Science.gov (United States)

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

1990-07-01

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

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

Science.gov (United States)

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

2016-10-01

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

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

Science.gov (United States)

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

2018-04-01

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

Rewrite systems for integer arithmetic

NARCIS (Netherlands)

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

1995-01-01

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

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.

Investigation of an American Arithmetic Text Book (I)

OpenAIRE

植村, 憲治; UEMURA, Kenji

2006-01-01

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

Higher arithmetic an algorithmic introduction to number theory

CERN Document Server

Edwards, Harold M

2008-01-01

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

A novel chaotic encryption scheme based on arithmetic coding

International Nuclear Information System (INIS)

Mi Bo; Liao Xiaofeng; Chen Yong

2008-01-01

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

Relating arithmetical techniques of proportion to geometry

DEFF Research Database (Denmark)

Wijayanti, Dyana

2015-01-01

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

Rewrite systems for integer arithmetic

NARCIS (Netherlands)

Walters, H.R.; Zantema, H.

1994-01-01

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

RSFQ logic arithmetic

International Nuclear Information System (INIS)

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

1989-01-01

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

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

Science.gov (United States)

Fayol, Michel; Barrouillet, Pierre; Marinthe, Catherine

1998-01-01

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

PandA : pairings and arithmetic

NARCIS (Netherlands)

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

2014-01-01

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

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

Science.gov (United States)

Braithwaite, David W; Siegler, Robert S

2018-04-26

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

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

Science.gov (United States)

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

2014-04-01

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

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

Science.gov (United States)

Rinne, Luke F; Mazzocco, Michèle M M

2014-01-01

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

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

Science.gov (United States)

Guthrie, Lisa G; Vallée-Tourangeau, Frédéric

2018-02-03

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

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

Directory of Open Access Journals (Sweden)

Weiping Li

2016-03-01

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

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

Science.gov (United States)

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

2017-02-01

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

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.

Torsionfree Sheaves over a Nodal Curve of Arithmetic Genus One

Indian Academy of Sciences (India)

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

Computer arithmetic and validity theory, implementation, and applications

CERN Document Server

Kulisch, Ulrich

2013-01-01

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

Groups and fields in arithmetic

NARCIS (Netherlands)

Kosters, Michiel F.

2014-01-01

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

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

Science.gov (United States)

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

2015-07-01

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

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

OpenAIRE

Pongyupinpanich, Surapong

2012-01-01

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

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

NARCIS (Netherlands)

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

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

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

Science.gov (United States)

Wong, Terry Tin-Yau

2017-12-01

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

Dictionary of algebra, arithmetic, and trigonometry

CERN Document Server

Krantz, Steven G

2000-01-01

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

Self-reference in Arithmetic I

NARCIS (Netherlands)

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

2014-01-01

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

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

Directory of Open Access Journals (Sweden)

Yongxin eLi

2013-12-01

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

Equations for arithmetic pointed tori

NARCIS (Netherlands)

Sijsling, J.R.

2010-01-01

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

Solutions to Arithmetic Convolution Equations

Czech Academy of Sciences Publication Activity Database

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

2007-01-01

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

Memory updating and mental arithmetic

Directory of Open Access Journals (Sweden)

Cheng-Ching eHan

2016-02-01

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

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

Science.gov (United States)

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

2016-04-01

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

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

Science.gov (United States)

Wang, Li-Qun; Saito, Masao

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

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

Science.gov (United States)

Fehr, Thorsten; Code, Chris; Herrmann, Manfred

2007-10-03

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

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

Science.gov (United States)

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

2005-01-01

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

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.

Some arithmetically symmetrical bandpass filters

Science.gov (United States)

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

1981-01-01

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

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

NARCIS (Netherlands)

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

2009-01-01

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

Domain-General Factors Influencing Numerical and Arithmetic Processing

Directory of Open Access Journals (Sweden)

André Knops

2017-12-01

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

A functional interpretation for nonstandard arithmetic

NARCIS (Netherlands)

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

2012-01-01

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

Lattice for FPGAs using logarithmic arithmetic

Czech Academy of Sciences Publication Activity Database

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

2002-01-01

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

Non-commutative arithmetic circuits with division

Czech Academy of Sciences Publication Activity Database

Hrubeš, Pavel; Wigderson, A.

2015-01-01

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

Relational thinking: The bridge between arithmetic and algebra

Directory of Open Access Journals (Sweden)

Ayhan Kızıltoprak

2017-09-01

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

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

Directory of Open Access Journals (Sweden)

Shirley Rapoport

2016-10-01

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

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

Science.gov (United States)

Rapoport, Shirley; Rubinsten, Orly; Katzir, Tami

2016-01-01

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

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

Science.gov (United States)

Rapoport, Shirley; Rubinsten, Orly; Katzir, Tami

2016-01-01

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

Arithmetic functions in torus and tree networks

Science.gov (United States)

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

2007-12-25

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

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

Science.gov (United States)

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

2008-08-01

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

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

Science.gov (United States)

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

2017-12-01

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

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

Science.gov (United States)

Braithwaite, David W.; Siegler, Robert S.

2018-01-01

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

Arithmetic of Complex Manifolds

CERN Document Server

Lange, Herbert

1989-01-01

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

Should we naturalize mind, or should we arithmetize matter?

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Marchal Bruno

2017-12-01

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

Trinary signed-digit arithmetic using an efficient encoding scheme

Science.gov (United States)

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

2000-09-01

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

Circuit lower bounds in bounded arithmetics

Czech Academy of Sciences Publication Activity Database

Pich, Ján

2015-01-01

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

Fuzzy Logic and Arithmetical Hierarchy III

Czech Academy of Sciences Publication Activity Database

Hájek, Petr

2001-01-01

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

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

Science.gov (United States)

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

2004-01-01

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

A Non-Arithmetical Gödel Logic

Czech Academy of Sciences Publication Activity Database

Hájek, Petr

2005-01-01

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

Quantile arithmetic methodology for uncertainty propagation in fault trees

International Nuclear Information System (INIS)

Abdelhai, M.; Ragheb, M.

1986-01-01

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

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

Science.gov (United States)

Glaser, Anton

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

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

Science.gov (United States)

Hinault, T; Lemaire, P

2016-01-01

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

An efficient adaptive arithmetic coding image compression technology

International Nuclear Information System (INIS)

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

2011-01-01

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

Nonverbal arithmetic in humans: light from noise.

Science.gov (United States)

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

2007-10-01

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

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

OpenAIRE

Zhao, Yufei

2013-01-01

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

Digital Arithmetic: Division Algorithms

DEFF Research Database (Denmark)

Montuschi, Paolo; Nannarelli, Alberto

2017-01-01

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

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

NARCIS (Netherlands)

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

2009-01-01

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

A Unified Formal Description of Arithmetic and Set Theoretical Data Types

OpenAIRE

Tarau, Paul

2010-01-01

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

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

Science.gov (United States)

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

2009-07-01

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

Secret Codes, Remainder Arithmetic, and Matrices.

Science.gov (United States)

Peck, Lyman C.

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

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

Science.gov (United States)

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

2018-01-01

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

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

Science.gov (United States)

Education Development Center, Inc., Newton, MA.

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

Segment LLL Reduction of Lattice Bases Using Modular Arithmetic

Directory of Open Access Journals (Sweden)

Sanjay Mehrotra

2010-07-01

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

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

Science.gov (United States)

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

2017-06-13

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

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

Directory of Open Access Journals (Sweden)

Bruno Rütsche

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

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

Science.gov (United States)

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

2015-01-01

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

Introduction to cardinal arithmetic

CERN Document Server

Holz, M; Weitz, E

1999-01-01

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

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

Science.gov (United States)

Zevenbergen, Robyn; Hyde, Merv; Power, Des

2001-12-01

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

Arithmetic of quantum entropy function

International Nuclear Information System (INIS)

Sen, Ashoke

2009-01-01

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

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.

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

Science.gov (United States)

Thevenot, Catherine; Fanget, Muriel; Fayol, Michel

2007-09-01

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

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

Science.gov (United States)

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

2002-01-01

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

Arithmetic convergent sequence space defined by modulus function

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Taja Yaying

2019-10-01

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

A sorting network in bounded arithmetic

Czech Academy of Sciences Publication Activity Database

Jeřábek, Emil

2011-01-01

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

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

CERN Document Server

Husserl, Edmund

2003-01-01

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

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

NARCIS (Netherlands)

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

2015-01-01

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

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

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Kiran Vanbinst

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

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

Science.gov (United States)

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

2000-11-01

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

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

NARCIS (Netherlands)

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

2009-01-01

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

File compression and encryption based on LLS and arithmetic coding

Science.gov (United States)

Yu, Changzhi; Li, Hengjian; Wang, Xiyu

2018-03-01

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

Partial sums of arithmetical functions with absolutely convergent ...

Indian Academy of Sciences (India)

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

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

Science.gov (United States)

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

2017-01-01

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

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

NARCIS (Netherlands)

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

2009-01-01

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

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

Directory of Open Access Journals (Sweden)

Amandine eVan Rinsveld

2015-03-01

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

Quantum arithmetic with the Quantum Fourier Transform

OpenAIRE

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

2014-01-01

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

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

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Stephan E. Vogel

2017-12-01

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

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

Science.gov (United States)

De Visscher, Alice; Noël, Marie-Pascale

2013-01-01

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

The Duality Principle in Teaching Arithmetic and Geometric Series

Science.gov (United States)

Yeshurun, Shraga

1978-01-01

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

Verification of Linear (In)Dependence in Finite Precision Arithmetic

Czech Academy of Sciences Publication Activity Database

Rohn, Jiří

2014-01-01

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

Coherent states, pseudodifferential analysis and arithmetic

Science.gov (United States)

Unterberger, André

2012-06-01

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

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

Science.gov (United States)

Lynn, Richard; Irwing, Paul

2008-01-01

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

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

KAUST Repository

Lin, Sian-Jheng

2016-12-24

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

Heuristics and representational change in two-move matchstick arithmetic tasks

Directory of Open Access Journals (Sweden)

Michael Öllinger

2006-01-01

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

Model Theory in Algebra, Analysis and Arithmetic

CERN Document Server

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

2014-01-01

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

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

CERN Document Server

Palchaudhuri, Ayan

2016-01-01

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

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

OpenAIRE

Kalan, Marko

2015-01-01

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

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

Science.gov (United States)

Taani, Osama

2014-01-01

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

Bi-amalgamations subject to the arithmetical property

OpenAIRE

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

2016-01-01

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

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

Science.gov (United States)

Singer, Vivian; Strasser, Kathernie

2017-12-01

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

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

Science.gov (United States)

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

2013-01-01

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

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

Science.gov (United States)

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

2012-02-15

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

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

Science.gov (United States)

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

1996-05-01

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

Arithmetic learning with the use of graphic organiser

Science.gov (United States)

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

2018-01-01

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

Multistate Memristive Tantalum Oxide Devices for Ternary Arithmetic

Science.gov (United States)

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

2016-11-01

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

Simplification of integrity constraints with aggregates and arithmetic built-ins

DEFF Research Database (Denmark)

Martinenghi, Davide

2004-01-01

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

Bit-Wise Arithmetic Coding For Compression Of Data

Science.gov (United States)

Kiely, Aaron

1996-01-01

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

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

Science.gov (United States)

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

2013-10-01

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

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

Science.gov (United States)

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

2017-08-01

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

Non-Archimedean L-functions and arithmetical Siegel modular forms

CERN Document Server

1991-01-01

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

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

Science.gov (United States)

Shaki, Samuel; Fischer, Martin H

2017-01-01

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

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.

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

KAUST Repository

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

2016-01-01

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

Why Is Learning Fraction and Decimal Arithmetic so Difficult?

Science.gov (United States)

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

2015-01-01

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

A wild model of linear arithmetic and discretely ordered modules

Czech Academy of Sciences Publication Activity Database

Glivický, Petr; Pudlák, Pavel

2017-01-01

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

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

NARCIS (Netherlands)

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

2013-01-01

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

The arithmetic of supersymmetric vacua

Energy Technology Data Exchange (ETDEWEB)

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

2016-07-07

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

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

Indian Academy of Sciences (India)

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

Numeral words and arithmetic operations in the Alor-Pantar languages

NARCIS (Netherlands)

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

2014-01-01

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

A Learning Trajectory for Teaching Social Arithmetic using RME Approach

Science.gov (United States)

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

2018-04-01

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

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

Science.gov (United States)

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

2014-01-01

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

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

Science.gov (United States)

Heikalabad, Saeed Rasouli; Gadim, Mahya Rahimpour

2018-06-01

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

Decidable and undecidable arithmetic functions in actin filament networks

Science.gov (United States)

Schumann, Andrew

2018-01-01

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

Brauer groups and obstruction problems moduli spaces and arithmetic

CERN Document Server

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

2017-01-01

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

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

Science.gov (United States)

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

2015-08-01

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

Alternating minima and maxima, Nash equilibria and bounded arithmetic

Czech Academy of Sciences Publication Activity Database

Pudlák, Pavel; Thapen, Neil

2012-01-01

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

The Lanczos and Conjugate Gradient Algorithms in Finite Precision Arithmetic

Czech Academy of Sciences Publication Activity Database

Meurant, G.; Strakoš, Zdeněk

2006-01-01

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

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

Science.gov (United States)

Buelow, Melissa T; Frakey, Laura L

2013-06-01

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

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

Science.gov (United States)

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

2018-04-01

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

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

Directory of Open Access Journals (Sweden)

Adeneye O. A. Awofala

2014-07-01

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

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

Science.gov (United States)

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

2013-09-01

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

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

OpenAIRE

NAIKA, MEGADAHALLI SIDDA MAHADEVA; SHIVASHANKAR, CHANDRAPPA

2017-01-01

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

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

International Nuclear Information System (INIS)

Aerts, Diederik; Czachor, Marek; Kuna, Maciej

2016-01-01

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

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

International Nuclear Information System (INIS)

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

2013-01-01

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

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

Science.gov (United States)

Marshall, Sandra P.

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

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

International Nuclear Information System (INIS)

Wang Xing-Yuan; Xie Yi-Xin

2011-01-01

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

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

CERN Document Server

Yong, Lam Lay

2004-01-01

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

On the arithmetic of fractal dimension using hyperhelices

International Nuclear Information System (INIS)

Toledo-Suarez, Carlos D.

2009-01-01

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

An algorithm for the arithmetic classification of multilattices.

Science.gov (United States)

Indelicato, Giuliana

2013-01-01

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

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

Directory of Open Access Journals (Sweden)

Tobias U. Hauser

2013-06-01

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

Alternative proposal of arithmetic and image operations in optical parallel computation

Science.gov (United States)

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

2001-10-01

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

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

Science.gov (United States)

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

2015-01-01

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

Relational Thinking: Learning Arithmetic in Order to Promote Algebraic Thinking

Science.gov (United States)

Napaphun, Vishnu

2012-01-01

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

Algebra 1 groups, rings, fields and arithmetic

CERN Document Server

Lal, Ramji

2017-01-01

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

Arithmetic fundamental groups and moduli of curves

International Nuclear Information System (INIS)

Makoto Matsumoto

2000-01-01

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

The Structure of Models of Peano Arithmetic

CERN Document Server

Kossak, Roman

2006-01-01

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

Optical modular arithmetic

Science.gov (United States)

Pavlichin, Dmitri S.; Mabuchi, Hideo

2014-06-01

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

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

Science.gov (United States)

Macdonald, R I

1987-10-01

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

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

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

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

2017-01-01

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

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

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Véronique Cornu

2017-12-01

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

Automatically Proving Termination and Memory Safety for Programs with Pointer Arithmetic

DEFF Research Database (Denmark)

Ströder, Thomas; Giesl, Jürgen; Brockschmidt, Marc

2017-01-01

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

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

Science.gov (United States)

De Visscher, Alice; Noël, Marie-Pascale

2014-01-01

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

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

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Barrouillet, Pierre; Poirier, Louise

1997-01-01

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

Design of arithmetic circuits in quantum dot cellular automata nanotechnology

CERN Document Server

Sridharan, K

2015-01-01

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

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

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

2017-01-01

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

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

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

2018-05-01

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

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

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Otsuka, Yuki; Osaka, Naoyuki

2015-01-01

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

The geometric and arithmetic volume of Shimura varieties of orthogonal type

CERN Document Server

Hörmann, Fritz

2015-01-01

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

The Arithmetic of Elliptic Fibrations in Gauge Theories on a Circle

CERN Document Server

Grimm, Thomas W.; Klevers, Denis

2016-01-01

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

General Dirichlet Series, Arithmetic Convolution Equations and Laplace Transforms

Czech Academy of Sciences Publication Activity Database

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

2009-01-01

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

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

International Nuclear Information System (INIS)

Arnold, V.

2008-01-01

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

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.

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

Science.gov (United States)

Persky, Ronald L.

2003-01-01

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

Abelian groups and quadratic residues in weak arithmetic

Czech Academy of Sciences Publication Activity Database

Jeřábek, Emil

2010-01-01

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

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

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Caroline Hornung

2017-10-01

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

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

Science.gov (United States)

Hornung, Caroline; Martin, Romain; Fayol, Michel

2017-01-01

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

Gaussian width bounds with applications to arithmetic progressions in random settings

NARCIS (Netherlands)

J. Briët (Jop); S. Gopi (Sivakanth)

2017-01-01

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

The arithmetic basis of special relativity

International Nuclear Information System (INIS)

Greenspan, D.

1976-01-01

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

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

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.

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

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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.

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

CERN Document Server

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

2018-01-01

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

Using fuzzy arithmetic in containment event trees

International Nuclear Information System (INIS)

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

2000-01-01

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

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

Science.gov (United States)

Oyama, Katsunori; Sakatani, Kaoru

2016-01-01

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

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

NARCIS (Netherlands)

Top, Jaap

1993-01-01

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

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

Science.gov (United States)

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

2013-02-01

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

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

Science.gov (United States)

Galli, Reto; Tenca, Alexandre F.

2001-11-01

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

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

Czech Academy of Sciences Publication Activity Database

Tichý, Milan; Schier, Jan; Gregg, D.

2010-01-01

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

Foundations of arithmetic differential geometry

CERN Document Server

Buium, Alexandru

2017-01-01

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

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

Czech Academy of Sciences Publication Activity Database

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

2007-01-01

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

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

OpenAIRE

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

2013-01-01

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

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

Science.gov (United States)

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

2014-01-01

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

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

NARCIS (Netherlands)

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

2007-01-01

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

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

Science.gov (United States)

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

2017-12-01

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

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

Science.gov (United States)

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

2007-01-01

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

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

CSIR Research Space (South Africa)

Butgereit, L

2009-01-01

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

A practical approach to model checking Duration Calculus using Presburger Arithmetic

DEFF Research Database (Denmark)

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

2014-01-01

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

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.

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

NARCIS (Netherlands)

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

2009-01-01

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

The arithmetic of elliptic fibrations in gauge theories on a circle

Energy Technology Data Exchange (ETDEWEB)

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

2016-06-20

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

The arithmetic of elliptic fibrations in gauge theories on a circle

Science.gov (United States)

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

2016-06-01

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

The arithmetic of elliptic fibrations in gauge theories on a circle

International Nuclear Information System (INIS)

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

2016-01-01

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

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

Science.gov (United States)

Cipora, Krzysztof; Nuerk, Hans-Christoph

2013-01-01

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

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

Directory of Open Access Journals (Sweden)

Humberto Muñoz

2009-06-01

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

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

Science.gov (United States)

Daches Cohen, Lital; Rubinsten, Orly

2017-01-01

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

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

Science.gov (United States)

Kidd, Teresa A.; Saudargas, Richard A.

1988-01-01

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

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

Science.gov (United States)

Desoete, Annemie

2008-01-01

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

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

Directory of Open Access Journals (Sweden)

Megremi Athanasia

2015-01-01

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

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

Science.gov (United States)

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

2009-12-01

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

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

Science.gov (United States)

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

2018-05-15

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

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

Directory of Open Access Journals (Sweden)

Ailsa Humphries

2018-01-01

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

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

Science.gov (United States)

Humphries, Ailsa; Chen, Zhe; Neumann, Ewald

2017-01-01

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

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

Science.gov (United States)

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

2002-01-01

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

Hard Lessons: Why Rational Number Arithmetic Is so Difficult for so Many People

Science.gov (United States)

Siegler, Robert S.; Lortie-Forgues, Hugues

2017-01-01

Fraction and decimal arithmetic pose large difficulties for many children and adults. This is a serious problem, because proficiency with these skills is crucial for learning more advanced mathematics and science and for success in many occupations. This review identifies two main classes of difficulties that underlie poor understanding of…

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...

Naming Speed and Effortful and Automatic Inhibition in Children with Arithmetic Learning Disabilities

Science.gov (United States)

D'Amico, Antonella; Passolunghi, Maria Chiara

2009-01-01

We report a two-year longitudinal study aimed at investigating the rate of access to numerical and non-numerical information in long-term memory and the functioning of automatic and effortful cognitive inhibition processes in children with arithmetical learning disabilities (ALDs). Twelve children with ALDs, of age 9.3 years, and twelve…

Enhancing Arithmetic and Word-Problem Solving Skills Efficiently by Individualized Computer-Assisted Practice

Science.gov (United States)

Schoppek, Wolfgang; Tulis, Maria

2010-01-01

The fluency of basic arithmetical operations is a precondition for mathematical problem solving. However, the training of skills plays a minor role in contemporary mathematics instruction. The authors proposed individualization of practice as a means to improve its efficiency, so that the time spent with the training of skills is minimized. As a…

THE EFFECT OF PLAYING SNAKE AND LADDER TOWARD THE RESULT STUDY OF ARITHMETIC ADDITION FOR STUDENT WITH MENTALLY RETARDED STUDENT

Directory of Open Access Journals (Sweden)

Arianti Iman Sari

2016-12-01

Full Text Available The purpose of this research were to describe: (1 the study result of arithmetic addition operation for fourth grade student with mentally retarded in SDLB before playing the Snake and Ladder activity (2 the study result of arithmetic addition operation for fourth grade student with mentally retarded in SDLB after playing the Snake and Ladder activity (3 the effect of Snake and Ladder playing toward the result study of arithmetic addition for fourth grade student with mentally retarded SDLB. This research used SSR (Single Subject Research with A-B-A design. Collecting the data was done by using assessment instrument, tests and observations. The result of this research showed that playing Snake and Ladder affected the study result of arithmetic addition operation for fourth-grade children with mentally retarded student in SDLB. Tujuan penelitian ini adalah mendeskripsikan (1 Hasil belajar penjumlahan siswa kelas 4 SDLB sebelum melakukan kegiatan bermain Ular Tangga (2 Hasil belajar penjumlahan siswa kelas 4 SDLB sesudah melakukan kegiatan bermain Ular Tangga (3 Pengaruh bermain Ular Tangga terhadap hasil belajar penjumlahan siswa kelas 4 SDLB. Penelitian ini menggunakan rancangan penelitian SSR (Single Subject Research dengan desain A-B-A. Pengumpulan data menggunakan instrumen assesmen, tes dan observasi. Hasil penelitian menunjukkan bermain ular tangga berpengaruh terhadap hasil belajar penjumlahan siswa tunagrahita kelas 4 SDLB.

On the form of the forgetting function: the effects of arithmetic and logarithmic distributions of delays.

Science.gov (United States)

Sargisson, Rebecca J; White, K Geoffrey

2003-11-01

Forgetting functions with 18 delay intervals were generated for delayed matching-to-sample performance in pigeons. Delay interval variation was achieved by arranging five different sets of five delays across daily sessions. In different conditions, the delays were distributed in arithmetic or logarithmic series. There was no convincing evidence for different effects on discriminability of the distributions of different delays. The mean data were better fitted by some mathematical functions than by others, but the best-fitting functions depended on the distribution of delays. In further conditions with a fixed set of five delays, discriminability was higher with a logarithmic distribution of delays than with an arithmetic distribution. This result is consistent with the treatment of the forgetting function in terms of generalization decrement.

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

Science.gov (United States)

Daches Cohen, Lital; Rubinsten, Orly

2017-01-01

Math anxiety is influenced by environmental, cognitive, and personal factors. Yet, the concurrent relationships between these factors have not been examined. To this end, the current study investigated how the math anxiety of 30 sixth graders is affected by: (a) mother’s math anxiety and maternal behaviors (environmental factors); (b) children’s arithmetic skills (cognitive factors); and (c) intrinsic math motivation (personal factor). A rigorous assessment of children’s math anxiety was made by using both explicit and implicit measures. The results indicated that accessible self-representations of math anxiety, as reflected by the explicit self-report questionnaire, were strongly affected by arithmetic skills. However, unconscious cognitive constructs of math anxiety, as reflected by the numerical dot-probe task, were strongly affected by environmental factors, such as maternal behaviors and mothers’ attitudes toward math. Furthermore, the present study provided preliminary evidence of intergenerational transmission of math anxiety. The conclusions are that in order to better understand the etiology of math anxiety, multiple facets of parenting and children’s skills should be taken into consideration. Implications for researchers, parents, and educators are discussed. PMID:29180973

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

Directory of Open Access Journals (Sweden)

Lital Daches Cohen

2017-11-01

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

The Arithmetical Machine Zero + 1 in Mathematics Laboratory: Instrumental Genesis and Semiotic Mediation

Science.gov (United States)

Maschietto, Michela

2015-01-01

This paper presents the analysis of two teaching experiments carried out in the context of the mathematics laboratory in a primary school (grades 3 and 4) with the use of the pascaline Zero + 1, an arithmetical machine. The teaching experiments are analysed by coordinating two theoretical frameworks, i.e. the instrumental approach and the Theory…

Solution Strategies and Achievement in Dutch Complex Arithmetic: Latent Variable Modeling of Change

Science.gov (United States)

Hickendorff, Marian; Heiser, Willem J.; van Putten, Cornelis M.; Verhelst, Norman D.

2009-01-01

In the Netherlands, national assessments at the end of primary school (Grade 6) show a decline of achievement on problems of complex or written arithmetic over the last two decades. The present study aims at contributing to an explanation of the large achievement decrease on complex division, by investigating the strategies students used in…

Development of Working Memory and Performance in Arithmetic: A Longitudinal Study with Children

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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…

Instrument for bone mineral measurement using a microprocessor as the control and arithmetic element

International Nuclear Information System (INIS)

Alberi, J.L.; Hardy, W.H. II.

1975-11-01

A self-contained instrument for the determination of bone mineral content by photon absorptometry is described. A high-resolution detection system allows measurements to be made at up to 16 photon energies. Control and arithmetic functions are performed by a microprocessor. Analysis capability and limitations are discussed

Realization of two-dimensional transformations by the arithmetical module of an intelligent graphics terminal

International Nuclear Information System (INIS)

Leich, A.; Polyntsev, A.D.

1982-01-01

The structure and software of the arithmetical module for the multi-microprocessor intelligent graphics terminal designed for realization of the world coordinate two-dimensional transformation are described. The module performs the operations like coordinate system displacement, scaling and rotation as well as transformations for window/viewport separation

Metacognition for strategy selection during arithmetic problem-solving in young and older adults.

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Geurten, Marie; Lemaire, Patrick

2018-04-19

We examined participants' strategy choices and metacognitive judgments during arithmetic problem-solving. Metacognitive judgments were collected either prospectively or retrospectively. We tested whether metacognitive judgments are related to strategy choices on the current problems and on the immediately following problems, and age-related differences in relations between metacognition and strategy choices. Data showed that both young and older adults were able to make accurate retrospective, but not prospective, judgments. Moreover, the accuracy of retrospective judgments was comparable in young and older adults when participants had to select and execute the better strategy. Metacognitive accuracy was even higher in older adults when participants had to only select the better strategy. Finally, low-confidence judgments on current items were more frequently followed by better strategy selection on immediately succeeding items than high-confidence judgments in both young and older adults. Implications of these findings to further our understanding of age-related differences and similarities in adults' metacognitive monitoring and metacognitive regulation for strategy selection in the context of arithmetic problem solving are discussed.

Modified LMI condition for the realization of limit cycle-free digital filters using saturation arithmetic

International Nuclear Information System (INIS)

Singh, Vimal

2007-01-01

A criterion in the form of linear matrix inequality for the elimination of limit cycles in a class of state-space digital filters using saturation arithmetic is presented. The criterion is a modified form of a previously reported criterion

Age-related differences in strategic monitoring during arithmetic problem solving.

Science.gov (United States)

Geurten, Marie; Lemaire, Patrick

2017-10-01

We examined the role of metacognitive monitoring in strategic behavior during arithmetic problem solving, a process that is expected to shed light on age-related differences in strategy selection. Young and older adults accomplished better strategy-judgment, better strategy-selection, and strategy-execution tasks. Data showed that participants made better strategy judgments when problems were problems with homogeneous unit digits (i.e., problems with both unit digits smaller or larger than 5; 31×62) relative to problems with heterogeneous unit digits (i.e., problems with one unit digit smaller or larger than 5; 31×67) and when the better strategy was cued on rounding-up problems (e.g., 68×23) compared to rounding-down problems (e.g., 36×53). Results also indicated higher rates of better strategy judgment in young than in older adults. These aging effects differed across problem types. Older adults made more accurate judgments on rounding-up problems than on rounding-down problems when the cued strategy was rounding-up, while young adults did not show such problem-related differences. Moreover, strategy selection correlated with strategy judgment, and even more so in older adults than in young adults. To discuss the implications of these findings, we propose a theoretical framework of how strategy judgments occur in young and older adults and discuss how this framework enables to understand relationships between metacognitive monitoring and strategic behaviors when participants solve arithmetic problems. Copyright © 2017 Elsevier B.V. All rights reserved.

Deficits in working memory, reading comprehension and arithmetic skills in children with mouth breathing syndrome: analytical cross-sectional study.

Science.gov (United States)

Kuroishi, Rita Cristina Sadako; Garcia, Ricardo Basso; Valera, Fabiana Cardoso Pereira; Anselmo-Lima, Wilma Terezinha; Fukuda, Marisa Tomoe Hebihara

2015-01-01

Mouth breathing syndrome is very common among school-age children, and it is possibly related to learning difficulties and low academic achievement. In this study, we investigated working memory, reading comprehension and arithmetic skills in children with nasal and mouth breathing. Analytical cross-sectional study with control group conducted in a public university hospital. 42 children (mean age = 8.7 years) who had been identified as mouth breathers were compared with a control group (mean age = 8.4 years) matched for age and schooling. All the participants underwent a clinical interview, tone audiometry, otorhinolaryngological evaluation and cognitive assessment of phonological working memory (numbers and pseudowords), reading comprehension and arithmetic skills. Children with mouth breathing had poorer performance than controls, regarding reading comprehension (P = 0.006), arithmetic (P = 0.025) and working memory for pseudowords (P = 0.002), but not for numbers (P = 0.76). Children with mouth breathing have low academic achievement and poorer phonological working memory than controls. Teachers and healthcare professionals should be aware of the association of mouth breathing with children's physical and cognitive health.

Short-term memory impairment and arithmetical ability.

Science.gov (United States)

Butterworth, B; Cipolotti, L; Warrington, E K

1996-02-01

We document the dissociation of preserved calculation skills in a patient with impaired auditory short-term memory. The patient (MRF) had a memory span of three digits. Furthermore, he showed rapid decrement in performance of single digits and letters with both auditory and visual presentation in the Brown-Peterson forgetting task. Analysis of his calculation skills revealed a normal ability to solve auditorily presented multidigit addition and subtraction problems such as 173 + 68 and to execute the Paced Auditory Serial Addition Task (Sampson, 1956, 1958; Gronwall, 1977). In addition, his performance on other tests, including arithmetic manipulation of natural numbers, decimals and fractions, approximation, magnitude, ratio, and percentage, appeared to be normal (Hitch, 1978b). It is argued that these findings require a revision of Baddeley and Hitch's (1974) concept of the function of working memory.

Neurocognitive Effects of Transcranial Direct Current Stimulation in Arithmetic Learning and Performance: A Simultaneous tDCS-fMRI Study.

Science.gov (United States)

Hauser, Tobias U; Rütsche, Bruno; Wurmitzer, Karoline; Brem, Silvia; Ruff, Christian C; Grabner, Roland H

A small but increasing number of studies suggest that non-invasive brain stimulation by means of transcranial direct current stimulation (tDCS) can modulate arithmetic processes that are essential for higher-order mathematical skills and that are impaired in dyscalculic individuals. However, little is known about the neural mechanisms underlying such stimulation effects, and whether they are specific to cognitive processes involved in different arithmetic tasks. We addressed these questions by applying tDCS during simultaneous functional magnetic resonance imaging (fMRI) while participants were solving two types of complex subtraction problems: repeated problems, relying on arithmetic fact learning and problem-solving by fact retrieval, and novel problems, requiring calculation procedures. Twenty participants receiving left parietal anodal plus right frontal cathodal stimulation were compared with 20 participants in a sham condition. We found a strong cognitive and neural dissociation between repeated and novel problems. Repeated problems were solved more accurately and elicited increased activity in the bilateral angular gyri and medial plus lateral prefrontal cortices. Solving novel problems, in contrast, was accompanied by stronger activation in the bilateral intraparietal sulci and the dorsomedial prefrontal cortex. Most importantly, tDCS decreased the activation of the right inferior frontal cortex while solving novel (compared to repeated) problems, suggesting that the cathodal stimulation rendered this region unable to respond to the task-specific cognitive demand. The present study revealed that tDCS during arithmetic problem-solving can modulate the neural activity in proximity to the electrodes specifically when the current demands lead to an engagement of this area. Copyright © 2016 Elsevier Inc. All rights reserved.

A Teachable Agent Game Engaging Primary School Children to Learn Arithmetic Concepts and Reasoning

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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…

Syntactic Awareness and Arithmetic Word Problem Solving in Children with and without Learning Disabilities

Science.gov (United States)

Peake, Christian; Jiménez, Juan E.; Rodríguez, Cristina; Bisschop, Elaine; Villarroel, Rebeca

2015-01-01

Arithmetic word problem (AWP) solving is a highly demanding task for children with learning disabilities (LD) since verbal and mathematical information have to be integrated. This study examines specifically how syntactic awareness (SA), the ability to manage the grammatical structures of language, affects AWP solving. Three groups of children in…

Brain potentials during mental arithmetic: effects of extensive practice and problem difficulty

OpenAIRE

Pauli, Paul; Lutzenberger, W.; Rau, H.; Birbaumer, N.; Rickard, T. C.; Yaroush, R. A.; Bourne, L. E. J.

2011-01-01

Recent behavioral investigations indicate that the processes underlying mental arithmetic change systematically with practice from deliberate, conscious calculation to automatic, direct retrieval of answers from memory [Bourne, L.E.Jr. and Rickard, T.C., Mental calculation: The development of a cognitive skill, Paper presented at the Interamerican Congress of Psychology, San Jose, Costa Rica, 1991; Psychol. Rev., 95 (1988) 492-527]. Results reviewed by Moscovitch and Winocur [In: The handbook...

Assessing flood forecast uncertainty with fuzzy arithmetic

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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

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

NARCIS (Netherlands)

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

2009-01-01

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

Learning Arithmetic Outdoors in Junior High School--Influence on Performance and Self-Regulating Skills

Science.gov (United States)

Fägerstam, Emilia; Samuelsson, Joakim

2014-01-01

This study aims to explore the influence of outdoor teaching among students, aged 13, on arithmetic performance and self-regulation skills as previous research concerning outdoor mathematics learning is limited. This study had a quasi-experimental design. An outdoor and a traditional group answered a test and a self-regulation skills questionnaire…

How are things adding up? Neural differences between arithmetic operations are due to general problem solving strategies.

Science.gov (United States)

Tschentscher, Nadja; Hauk, Olaf

2014-05-15

A number of previous studies have interpreted differences in brain activation between arithmetic operation types (e.g. addition and multiplication) as evidence in favor of distinct cortical representations, processes or neural systems. It is still not clear how differences in general task complexity contribute to these neural differences. Here, we used a mental arithmetic paradigm to disentangle brain areas related to general problem solving from those involved in operation type specific processes (addition versus multiplication). We orthogonally varied operation type and complexity. Importantly, complexity was defined not only based on surface criteria (for example number size), but also on the basis of individual participants' strategy ratings, which were validated in a detailed behavioral analysis. We replicated previously reported operation type effects in our analyses based on surface criteria. However, these effects vanished when controlling for individual strategies. Instead, procedural strategies contrasted with memory retrieval reliably activated fronto-parietal and motor regions, while retrieval strategies activated parietal cortices. This challenges views that operation types rely on partially different neural systems, and suggests that previously reported differences between operation types may have emerged due to invalid measures of complexity. We conclude that mental arithmetic is a powerful paradigm to study brain networks of abstract problem solving, as long as individual participants' strategies are taken into account. Copyright © 2014 Elsevier Inc. All rights reserved.

Deficits in working memory, reading comprehension and arithmetic skills in children with mouth breathing syndrome: analytical cross-sectional study

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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.

Identifying Strategies in Arithmetic with the Operand Recognition Paradigm: A Matter of Switch Cost?

Science.gov (United States)

Thevenot, Catherine; Castel, Caroline; Danjon, Juliette; Fayol, Michel

2015-01-01

Determining adults' and children's strategies in mental arithmetic constitutes a central issue in the domain of numerical cognition. However, despite the considerable amount of research on this topic, the conclusions in the literature are not always coherent. Therefore, there is a need to carry on the investigation, and this is the reason why we…

Age-Related Differences of Individuals' Arithmetic Strategy Utilization with Different Level of Math Anxiety.

Science.gov (United States)

Si, Jiwei; Li, Hongxia; Sun, Yan; Xu, Yanli; Sun, Yu

2016-01-01

The present study used the choice/no-choice method to investigate the effect of math anxiety on the strategy used in computational estimation and mental arithmetic tasks and to examine age-related differences in this regard. Fifty-seven fourth graders, 56 sixth graders, and 60 adults were randomly selected to participate in the experiment. Results showed the following: (1) High-anxious individuals were more likely to use a rounding-down strategy in the computational estimation task under the best-choice condition. Additionally, sixth-grade students and adults performed faster than fourth-grade students on the strategy execution parameter. Math anxiety affected response times (RTs) and the accuracy with which strategies were executed. (2) The execution of the partial-decomposition strategy was superior to that of the full-decomposition strategy on the mental arithmetic task. Low-math-anxious persons provided more accurate answers than did high-math-anxious participants under the no-choice condition. This difference was significant for sixth graders. With regard to the strategy selection parameter, the RTs for strategy selection varied with age.

Age-Related Differences of Individuals’ Arithmetic Strategy Utilization with Different Level of Math Anxiety

Science.gov (United States)

Si, Jiwei; Li, Hongxia; Sun, Yan; Xu, Yanli; Sun, Yu

2016-01-01

The present study used the choice/no-choice method to investigate the effect of math anxiety on the strategy used in computational estimation and mental arithmetic tasks and to examine age-related differences in this regard. Fifty-seven fourth graders, 56 sixth graders, and 60 adults were randomly selected to participate in the experiment. Results showed the following: (1) High-anxious individuals were more likely to use a rounding-down strategy in the computational estimation task under the best-choice condition. Additionally, sixth-grade students and adults performed faster than fourth-grade students on the strategy execution parameter. Math anxiety affected response times (RTs) and the accuracy with which strategies were executed. (2) The execution of the partial-decomposition strategy was superior to that of the full-decomposition strategy on the mental arithmetic task. Low-math-anxious persons provided more accurate answers than did high-math-anxious participants under the no-choice condition. This difference was significant for sixth graders. With regard to the strategy selection parameter, the RTs for strategy selection varied with age. PMID:27803685

Age-related Differences of Individuals’ Arithmetic Strategy Utilization with Different Level of Math Anxiety

Directory of Open Access Journals (Sweden)

Jiwei Si

2016-10-01

Full Text Available The present study used the choice/no-choice method to investigate the effect of math anxiety on the strategy used in computational estimation and mental arithmetic tasks and to examine age-related differences in this regard. 57 fourth graders, 56 sixth graders, and 60 adults were randomly selected to participate in the experiment. Results showed the following: (1 High-anxious individuals were more likely to use a rounding-down strategy in the computational estimation task under the best-choice condition. Additionally, sixth-grade students and adults performed faster than fourth-grade students on the strategy execution parameter. Math anxiety affected response times (RTs and the accuracy with which strategies were executed. (2 The execution of the partial-decomposition strategy was superior to that of the full-decomposition strategy on the mental arithmetic task. Low-math-anxious persons provided more accurate answers than did high-math-anxious participants under the no-choice condition. This difference was significant for sixth graders. With regard to the strategy selection parameter, the RTs for strategy selection varied with age.

CMIS arithmetic and multiwire news for QCD on the connection machine

International Nuclear Information System (INIS)

Brickner, R.G.

1991-01-01

Our collaboration has been running Wilson fermion QCD simulations on various Connection Machines for over a year and a half. During this time, we have continually optimized our code for operations found in the fermion matrix inversion. Our current version of the matrix inversion is written almost entirely in CMIS (Connection Machine Instruction Set), and utilizes both high-speed arithmetic and multiwire 'news' (nearest-neighbor communications). We present details of how these and other features of our code are implemented on the CM-2. (orig.)

A new frequency-domain criterion for elimination of limit cycles in fixed-point state-space digital filters using saturation arithmetic

International Nuclear Information System (INIS)

Singh, Vimal

2007-01-01

In [Singh V. Elimination of overflow oscillations in fixed-point state-space digital filters using saturation arithmetic. IEEE Trans Circ Syst 1990;37(6):814-8], a frequency-domain criterion for the suppression of limit cycles in fixed-point state-space digital filters using saturation overflow arithmetic was presented. The passivity property owing to the presence of multiple saturation nonlinearities was exploited therein. In the present paper, a new notion of passivity, namely, that involving the state variables is considered, thereby arriving at an entirely new frequency-domain criterion for the suppression of limit cycles in such filters

The Cognitive Foundations of Reading and Arithmetic Skills in 7- to 10-Year-Olds

Science.gov (United States)

Durand, Marianne; Hulme, Charles; Larkin, Rebecca; Snowling, Margaret

2005-01-01

A range of possible predictors of arithmetic and reading were assessed in a large sample (N=162) of children between ages 7 years 5 months and 10 years 4 months. A confirmatory factor analysis of the predictors revealed a good fit to a model consisting of four latent variables (verbal ability, nonverbal ability, search speed, and phonological…

Conference on Number Theory and Arithmetic Geometry

CERN Document Server

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

1997-01-01

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

Using Mouse and Keyboard Dynamics to Detect Cognitive Stress During Mental Arithmetic

OpenAIRE

Ayesh, Aladdin, 1972-; Stacey, Martin; Lim, Yee Mei

2015-01-01

To build a personalized e-learning system that can deliver adaptive learning content based on student’s cognitive effort and efficiency, it is important to develop a construct that can help measuring perceived mental state, such as stress and cognitive load. The construct must be able to be quantified, computerized and automated. Our research investigates how mouse and keyboard dynamics analyses could be used to detect cognitive stress, which is induced by high mental arithmetic demand with t...

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

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J. Michal

2003-09-01

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

Implications of an arithmetical symmetry of the commutant for modular invariants

International Nuclear Information System (INIS)

Ruelle, P.; Thiran, E.; Weyers, J.

1993-01-01

We point out the existence of an arithmetical symmetry for the commutant of the modular matrices S and T. This symmetry holds for all affine simple Lie algebras at all levels and implies the equality of certain coefficients in any modular invariant. Particularizing to SU(3) k , we classify the modular invariant partition functions when k+3 is an integer coprime with 6 and when it is a power of either 2 or 3. Our results imply that no detailed knowledge of the commutant is needed to undertake a classification of all modular invariants. (orig.)

Mathematical learning disabilities and attention deficit and/or hyperactivity disorder: A study of the cognitive processes involved in arithmetic problem solving.

Science.gov (United States)

Iglesias-Sarmiento, Valentín; Deaño, Manuel; Alfonso, Sonia; Conde, Ángeles

2017-02-01

The purpose of this study was to examine the contribution of cognitive functioning to arithmetic problem solving and to explore the cognitive profiles of children with attention deficit and/or hyperactivity disorder (ADHD) and with mathematical learning disabilities (MLD). The sample was made up of a total of 90 students of 4th, 5th, and 6th grade organized in three: ADHD (n=30), MLD (n=30) and typically achieving control (TA; n=30) group. Assessment was conducted in two sessions in which the PASS processes and arithmetic problem solving were evaluated. The ADHD group's performance in planning and attention was worse than that of the control group. Children with MLD obtained poorer results than the control group in planning and simultaneous and successive processing. Executive processes predicted arithmetic problem solving in the ADHD group whereas simultaneous processing was the unique predictor in the MLD sample. Children with ADHD and with MLD showed characteristic cognitive profiles. Groups' problem-solving performance can be predicted from their cognitive functioning. Copyright © 2016 Elsevier Ltd. All rights reserved.

Multiple Skills Underlie Arithmetic Performance: A Large-Scale Structural Equation Modeling Analysis

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Sarit Ashkenazi

2017-12-01

Full Text Available Current theoretical approaches point to the importance of several cognitive skills not specific to mathematics for the etiology of mathematics disorders (MD. In the current study, we examined the role of many of these skills, specifically: rapid automatized naming, attention, reading, and visual perception, on mathematics performance among a large group of college students (N = 1,322 with a wide range of arithmetic proficiency. Using factor analysis, we discovered that our data clustered to four latent variables 1 mathematics, 2 perception speed, 3 attention and 4 reading. In subsequent structural equation modeling, we found that the latent variable perception speed had a strong and meaningful effect on mathematics performance. Moreover, sustained attention, independent from the effect of the latent variable perception speed, had a meaningful, direct effect on arithmetic fact retrieval and procedural knowledge. The latent variable reading had a modest effect on mathematics performance. Specifically, reading comprehension, independent from the effect of the latent variable reading, had a meaningful direct effect on mathematics, and particularly on number line knowledge. Attention, tested by the attention network test, had no effect on mathematics, reading or perception speed. These results indicate that multiple factors can affect mathematics performance supporting a heterogeneous approach to mathematics. These results have meaningful implications for the diagnosis and intervention of pure and comorbid learning disorders.

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.

CIMPA Summer School on Arithmetic and Geometry Around Hypergeometric Functions

CERN Document Server

Uludağ, A; Yoshida, Masaaki; Arithmetic and Geometry Around Hypergeometric Functions

2007-01-01

This volume comprises the Lecture Notes of the CIMPA Summer School "Arithmetic and Geometry around Hypergeometric Functions" held at Galatasaray University, Istanbul in 2005. It contains lecture notes, a survey article, research articles, and the results of a problem session. Key topics are moduli spaces of points on P1 and Picard-Terada-Deligne-Mostow theory, moduli spaces of K3 surfaces, complex hyperbolic geometry, ball quotients, GKZ hypergeometric structures, Hilbert and Picard modular surfaces, uniformizations of complex orbifolds, algebraicity of values of Schwartz triangle functions, and Thakur's hypergeometric function. The book provides a background, gives detailed expositions and indicates new research directions. It is directed to postgraduate students and researchers.

Desynchronization of Theta-Phase Gamma-Amplitude Coupling during a Mental Arithmetic Task in Children with Attention Deficit/Hyperactivity Disorder.

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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.

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

Science.gov (United States)

Barrouillet, P; Fayol, M

1998-03-01

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

Spatial complexity of character based writing systems and arithmetic in primary school: a longitudinal study

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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.

Spatial complexity of character-based writing systems and arithmetic in primary school: a longitudinal study.

Science.gov (United States)

Rodic, Maja; Tikhomirova, Tatiana; Kolienko, Tatiana; Malykh, Sergey; Bogdanova, Olga; Zueva, Dina Y; Gynku, Elena I; Wan, Sirui; Zhou, Xinlin; Kovas, Yulia

2015-01-01

Previous research has consistently found an association between spatial and mathematical abilities. We hypothesized that this link may partially explain the consistently observed advantage in mathematics demonstrated by East Asian children. Spatial complexity of the character-based writing systems may reflect or lead to a cognitive advantage relevant to mathematics. Seven hundered and twenty one 6-9-year old children from the UK and Russia were assessed on a battery of cognitive skills and arithmetic. The Russian children were recruited from specialist linguistic schools and divided into four different language groups, based on the second language they were learning (i.e., English, Spanish, Chinese, and Japanese). The UK children attended regular schools and were not learning any second language. The testing took place twice across the school year, once at the beginning, before the start of the second language acquisition, and once at the end of the year. The study had two aims: (1) to test whether spatial ability predicts mathematical ability in 7-9 year-old children across the samples; (2) to test whether acquisition and usage of a character-based writing system leads to an advantage in performance in arithmetic and related cognitive tasks. The longitudinal link from spatial ability to mathematics was found only in the Russian sample. The effect of second language acquisition on mathematics or other cognitive skills was negligible, although some effect of Chinese language on mathematical reasoning was suggested. Overall, the findings suggest that although spatial ability is related to mathematics at this age, one academic year of exposure to spatially complex writing systems is not enough to provide a mathematical advantage. Other educational and socio-cultural factors might play a greater role in explaining individual and cross-cultural differences in arithmetic at this age.

Spatial complexity of character-based writing systems and arithmetic in primary school: a longitudinal study

Science.gov (United States)

Rodic, Maja; Tikhomirova, Tatiana; Kolienko, Tatiana; Malykh, Sergey; Bogdanova, Olga; Zueva, Dina Y.; Gynku, Elena I.; Wan, Sirui; Zhou, Xinlin; Kovas, Yulia

2015-01-01

Previous research has consistently found an association between spatial and mathematical abilities. We hypothesized that this link may partially explain the consistently observed advantage in mathematics demonstrated by East Asian children. Spatial complexity of the character-based writing systems may reflect or lead to a cognitive advantage relevant to mathematics. Seven hundered and twenty one 6–9-year old children from the UK and Russia were assessed on a battery of cognitive skills and arithmetic. The Russian children were recruited from specialist linguistic schools and divided into four different language groups, based on the second language they were learning (i.e., English, Spanish, Chinese, and Japanese). The UK children attended regular schools and were not learning any second language. The testing took place twice across the school year, once at the beginning, before the start of the second language acquisition, and once at the end of the year. The study had two aims: (1) to test whether spatial ability predicts mathematical ability in 7–9 year-old children across the samples; (2) to test whether acquisition and usage of a character-based writing system leads to an advantage in performance in arithmetic and related cognitive tasks. The longitudinal link from spatial ability to mathematics was found only in the Russian sample. The effect of second language acquisition on mathematics or other cognitive skills was negligible, although some effect of Chinese language on mathematical reasoning was suggested. Overall, the findings suggest that although spatial ability is related to mathematics at this age, one academic year of exposure to spatially complex writing systems is not enough to provide a mathematical advantage. Other educational and socio-cultural factors might play a greater role in explaining individual and cross-cultural differences in arithmetic at this age. PMID:25859235

A Hypergraph and Arithmetic Residue-based Probabilistic Neural Network for classification in Intrusion Detection Systems.

Science.gov (United States)

Raman, M R Gauthama; Somu, Nivethitha; Kirthivasan, Kannan; Sriram, V S Shankar

2017-08-01

Over the past few decades, the design of an intelligent Intrusion Detection System (IDS) remains an open challenge to the research community. Continuous efforts by the researchers have resulted in the development of several learning models based on Artificial Neural Network (ANN) to improve the performance of the IDSs. However, there exists a tradeoff with respect to the stability of ANN architecture and the detection rate for less frequent attacks. This paper presents a novel approach based on Helly property of Hypergraph and Arithmetic Residue-based Probabilistic Neural Network (HG AR-PNN) to address the classification problem in IDS. The Helly property of Hypergraph was exploited for the identification of the optimal feature subset and the arithmetic residue of the optimal feature subset was used to train the PNN. The performance of HG AR-PNN was evaluated using KDD CUP 1999 intrusion dataset. Experimental results prove the dominance of HG AR-PNN classifier over the existing classifiers with respect to the stability and improved detection rate for less frequent attacks. Copyright © 2017 Elsevier Ltd. All rights reserved.

Deaf and Hard of Hearing Students' Problem-Solving Strategies with Signed Arithmetic Story Problems

Science.gov (United States)

Pagliaro, Claudia M.; Ansell, Ellen

2011-01-01

The use of problem-solving strategies by 59 deaf and hard of hearing children, grades K-3, was investigated. The children were asked to solve 9 arithmetic story problems presented to them in American Sign Language. The researchers found that while the children used the same general types of strategies that are used by hearing children (i.e.,…

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

Science.gov (United States)

Kim, J. B.; Won, E.

2018-03-01

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

Arithmetical aspects of the large sieve inequality

CERN Document Server

2009-01-01

This book is an elaboration of a series of lectures given at the Harish-Chandra Research Institute. The reader will be taken through a journey on the arithmetical sides of the large sieve inequality when applied to the Farey dissection. This will reveal connections between this inequality, the Selberg sieve and other less used notions like pseudo-characters and the $\\Lambda_Q$-function, as well as extend these theories. One of the leading themes of these notes is the notion of so-called\\emph{local models} that throws a unifying light on the subject. As examples and applications, the authors present, among other things, an extension of the Brun-Tichmarsh Theorem, a new proof of Linnik's Theorem on quadratic residues and an equally novel one of the Vinogradov three primes Theorem; the authors also consider the problem of small prime gaps, of sums of two squarefree numbers and several other ones, some of them being new, like a sharp upper bound for the number of twin primes $p$ that are such that $p+1$ is square...

Modeling Brain Responses in an Arithmetic Working Memory Task

Science.gov (United States)

Hamid, Aini Ismafairus Abd; Yusoff, Ahmad Nazlim; Mukari, Siti Zamratol-Mai Sarah; Mohamad, Mazlyfarina; Manan, Hanani Abdul; Hamid, Khairiah Abdul

2010-07-01

Functional magnetic resonance imaging (fMRI) was used to investigate brain responses due to arithmetic working memory. Nine healthy young male subjects were given simple addition and subtraction instructions in noise and in quiet. The general linear model (GLM) and random field theory (RFT) were implemented in modelling the activation. The results showed that addition and subtraction evoked bilateral activation in Heschl's gyrus (HG), superior temporal gyrus (STG), inferior frontal gyrus (IFG), supramarginal gyrus (SG) and precentral gyrus (PCG). The HG, STG, SG and PCG activate higher number of voxels in noise as compared to in quiet for addition and subtraction except for IFG that showed otherwise. The percentage of signal change (PSC) in all areas is higher in quiet as compared to in noise. Surprisingly addition (not subtraction) exhibits stronger activation.

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

OpenAIRE

Clovis José Daudt Lyra Darrigue Faro

2014-01-01

With the argument that, necessarily, compound interest implies anatocism, the Brazilian Judiciary has been determining that, specially for the case of  debt amortization in accordance with the so called Tabela Price, when we have constant payments, the use of simple interest. With the same determination occurring in the case of the Constant Amortization Scheme, when the payments follow arithmetic progressions.  However, as simple interest lacks the property of time subdivision, it is shown th...

Growing the Character Values to Students Through Application of Realistic Mathematics Education (RME in the Social Arithmetic Learning

Directory of Open Access Journals (Sweden)

Amin Suyitno

2015-06-01

Full Text Available AbstractEducating students at the Basic Education level is not only demanded that the students are clever, but there are also other demand which no less important that is to educate so that students have a good character value. Educating  the students to have a good character value is started from home, school, and community. In school, educating character to students is not only the duty of teachers of Religion or Civics class, but also the duty of all teachers, including the teachers in Mathematics. Math teacher does not need to hold special time for educating of character, but it can be integrated into any material taught, and also in different application of learning models. This paper examines how the efforts of mathematics teacher in educating of character to the students of Basic Education, especially in Junior High School through the application of Realistic Mathematics Education (RME on the material of Social Arithmetic. Through presenting of the material of Social Arithmetic by RME learning model, students can be given a character education through the attitude of honesty, tolerance, discipline, cooperation, creative, independent, democratic, curiosity, love of peace, social care, responsibility, and so on. In conclusion, educational character values to students can be done by mathematics teacher through a variety of materials.  One of them  through presenting of the material of Social Arithmetic by RME learning model.

Trinary arithmetic and logic unit (TALU) using savart plate and spatial light modulator (SLM) suitable for optical computation in multivalued logic

Science.gov (United States)

Ghosh, Amal K.; Bhattacharya, Animesh; Raul, Moumita; Basuray, Amitabha

2012-07-01

Arithmetic logic unit (ALU) is the most important unit in any computing system. Optical computing is becoming popular day-by-day because of its ultrahigh processing speed and huge data handling capability. Obviously for the fast processing we need the optical TALU compatible with the multivalued logic. In this regard we are communicating the trinary arithmetic and logic unit (TALU) in modified trinary number (MTN) system, which is suitable for the optical computation and other applications in multivalued logic system. Here the savart plate and spatial light modulator (SLM) based optoelectronic circuits have been used to exploit the optical tree architecture (OTA) in optical interconnection network.

A pilot study of a new method of cognitive stimulation using abacus arithmetic in healthy and cognitively impaired elderly subjects.

Science.gov (United States)

Matías-Guiu, J A; Pérez-Martínez, D A; Matías-Guiu, J

2016-06-01

This study explores the applicability of a cognitive stimulation method based on abacus arithmetic in elderly people with and without cognitive impairment. This observational and prospective pilot study was performed in 2 hospitals. The study assessed the applicability of a programme of arithmetic training developed for use in the elderly population. The primary endpoint was an evaluation of the stimulation programme, in terms of usability, satisfaction, and participation, in healthy elderly controls and elderly patients with mild cognitive impairment or Alzheimer disease. Secondary endpoints were family satisfaction, caregiver burden, and the behaviour and cognition of patients. Usability, satisfaction, and degree of participation were high. The Mini-Mental State Examination showed significant changes (23.1±4.8 before the intervention vs 24.9±4.2 afterwards, P=.002); there were no changes on the Trail Making Test parts A and B, Yesavage Geriatric Depression scale, and Zarit caregiver burden scale. The study suggests that cognitive stimulation with abacus arithmetic may be used in elderly people with and without cognitive impairment. Further studies will be needed to evaluate the efficacy of this kind of programmes. Copyright © 2014 Sociedad Española de Neurología. Published by Elsevier España, S.L.U. All rights reserved.

Process-based Assignment-Setting Change for Support of Overcoming Bottlenecks in Learning by Problem-Posing in Arithmetic Word Problems

Science.gov (United States)

Supianto, A. A.; Hayashi, Y.; Hirashima, T.

2017-02-01

Problem-posing is well known as an effective activity to learn problem-solving methods. Monsakun is an interactive problem-posing learning environment to facilitate arithmetic word problems learning for one operation of addition and subtraction. The characteristic of Monsakun is problem-posing as sentence-integration that lets learners make a problem of three sentences. Monsakun provides learners with five or six sentences including dummies, which are designed through careful considerations by an expert teacher as a meaningful distraction to the learners in order to learn the structure of arithmetic word problems. The results of the practical use of Monsakun in elementary schools show that many learners have difficulties in arranging the proper answer at the high level of assignments. The analysis of the problem-posing process of such learners found that their misconception of arithmetic word problems causes impasses in their thinking and mislead them to use dummies. This study proposes a method of changing assignments as a support for overcoming bottlenecks of thinking. In Monsakun, the bottlenecks are often detected as a frequently repeated use of a specific dummy. If such dummy can be detected, it is the key factor to support learners to overcome their difficulty. This paper discusses how to detect the bottlenecks and to realize such support in learning by problem-posing.

Heart rate variability response to mental arithmetic stress in patients with schizophrenia Autonomic response to stress in schizophrenia

NARCIS (Netherlands)

Castro, Mariana N.; Vigo, Daniel E.; Weidema, Hylke; Fahrer, Rodolfo D.; Chu, Elvina M.; De Achaval, Delfina; Nogues, Martin; Leiguarda, Ramon C.; Cardinali, Daniel P.; Guinjoan, Salvador N.

Background: The vulnerability-stress hypothesis is an established model of schizophrenia symptom formation. We sought to characterise the pattern of the cardiac autonomic response to mental arithmetic stress in patients with stable schizophrenia. Methods: We performed heart rate variability (HRV)

A Modular Approach to Arithmetic and Logic Unit Design on a Reconfigurable Hardware Platform for Educational Purpose

Science.gov (United States)

Oztekin, Halit; Temurtas, Feyzullah; Gulbag, Ali

The Arithmetic and Logic Unit (ALU) design is one of the important topics in Computer Architecture and Organization course in Computer and Electrical Engineering departments. There are ALU designs that have non-modular nature to be used as an educational tool. As the programmable logic technology has developed rapidly, it is feasible that ALU design based on Field Programmable Gate Array (FPGA) is implemented in this course. In this paper, we have adopted the modular approach to ALU design based on FPGA. All the modules in the ALU design are realized using schematic structure on Altera's Cyclone II Development board. Under this model, the ALU content is divided into four distinct modules. These are arithmetic unit except for multiplication and division operations, logic unit, multiplication unit and division unit. User can easily design any size of ALU unit since this approach has the modular nature. Then, this approach was applied to microcomputer architecture design named BZK.SAU.FPGA10.0 instead of the current ALU unit.

Advanced topics in the arithmetic of elliptic curves

CERN Document Server

Silverman, Joseph H

1994-01-01

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

Magnitude Representation and Working Memory Updating in Children With Arithmetic and Reading Comprehension Disabilities.

Science.gov (United States)

Pelegrina, Santiago; Capodieci, Agnese; Carretti, Barbara; Cornoldi, Cesare

2015-01-01

It has been argued that children with learning disabilities (LD) encounter severe problems in working memory (WM) tasks, especially when they need to update information stored in their WM. It is not clear, however, to what extent this is due to a generally poor updating ability or to a difficulty specific to the domain to be processed. To examine this issue, two groups of children with arithmetic or reading comprehension LD and a group of typically developing children (9 to 10 years old) were assessed using two updating tasks requiring to select the smallest numbers or objects presented. The results showed that children with an arithmetic disability failed in a number updating task, but not in the object updating task. The opposite was true for the group with poor reading comprehension, whose performance was worse in the object than in the number updating task. It may be concluded that the problem of WM updating in children with LD is also due to a poor representation of the material to be updated. In addition, our findings suggest that the mental representation of the size of objects relates to the semantic representation of the objects' properties and differs from the quantitative representation of numbers. © Hammill Institute on Disabilities 2014.

Embedded systems design with special arithmetic and number systems

CERN Document Server

Sousa, Leonel; Chang, Chip-Hong

2017-01-01

This book introduces readers to alternative approaches to designing efficient embedded systems using unconventional number systems. The authors describe various systems that can be used for designing efficient embedded and application-specific processors, such as Residue Number System, Logarithmic Number System, Redundant Binary Number System Double-Base Number System, Decimal Floating Point Number System and Continuous Valued Number System. Readers will learn the strategies and trade-offs of using unconventional number systems in application-specific processors and be able to apply and design appropriate arithmetic operations from these number systems to boost the performance of digital systems. • Serves as a single-source reference to designing embedded systems with unconventional number systems • Covers theory as well as implementation on application-specific processors • Explains mathematical concepts in a manner accessible to readers with diverse backgrounds.

Conference on Arithmetic and Ideal Theory of Rings and Semigroups

CERN Document Server

Fontana, Marco; Geroldinger, Alfred; Olberding, Bruce

2016-01-01

This book consists of both expository and research articles solicited from speakers at the conference entitled "Arithmetic and Ideal Theory of Rings and Semigroups," held September 22–26, 2014 at the University of Graz, Graz, Austria. It reflects recent trends in multiplicative ideal theory and factorization theory, and brings together for the first time in one volume both commutative and non-commutative perspectives on these areas, which have their roots in number theory, commutative algebra, and algebraic geometry. Topics discussed include topological aspects in ring theory, Prüfer domains of integer-valued polynomials and their monadic submonoids, and semigroup algebras. It will be of interest to practitioners of mathematics and computer science, and researchers in multiplicative ideal theory, factorization theory, number theory, and algebraic geometry.

Brain potentials during mental arithmetic: effects of extensive practice and problem difficulty.

Science.gov (United States)

Pauli, P; Lutzenberger, W; Rau, H; Birbaumer, N; Rickard, T C; Yaroush, R A; Bourne, L E

1994-07-01

Recent behavioral investigations indicate that the processes underlying mental arithmetic change systematically with practice from deliberate, conscious calculation to automatic, direct retrieval of answers from memory [Bourne, L.E.Jr. and Rickard, T.C., Mental calculation: The development of a cognitive skill, Paper presented at the Interamerican Congress of Psychology, San Jose, Costa Rica, 1991: Psychol. Rev., 95 (1988) 492-527]. Results reviewed by Moscovitch and Winocur [In: The handbook of aging and cognition, Erlbaum, Hillsdale, NJ, 1992, pp. 315-372] suggest that consciously controlled processes are more dependent on frontal lobe function than are automatic processes. It is appropriate, therefore to determine whether transitions in the locus of primary brain activity occur with practice on mental calculation. In this experiment, we examine the relationship between characteristics of event-related brain potentials (ERPs) and mental arithmetic. Single-digit mental multiplication problems varying in difficulty (problem size) were used, and subjects were trained on these problems for four sessions. Problem-size and practice effects were reliably found in behavioral measures (RT). The ERP was characterized by a pronounced late positivity after task presentation followed by a slow wave, and a negativity during response indication. These components responded differentially to the practice and problem-size manipulations. Practice mainly affected topography of the amplitude of positivity and offset latency of slow wave, and problem-size mainly offset latency of slow wave and pre-response negativity. Fronto-central positivity diminished from session to session, and the focus of positivity centered finally at centro-parietal regions.(ABSTRACT TRUNCATED AT 250 WORDS)

The Interpretations and Applications of Boethius's Introduction to the Arithmetic II, 1 at the End of the 10th Century

Czech Academy of Sciences Publication Activity Database

Otisk, Marek

2014-01-01

Roč. 5, - (2014), s. 33-56 ISSN 2038-3657 Institutional support: RVO:67985955 Keywords : Boethius * arithmetic * Gerbert of Aurillac * Abbo of Fleury * Notker of Liège Subject RIV: AA - Philosophy ; Religion

Beyond Hemispheric Dominance: Brain Regions Underlying the Joint Lateralization of Language and Arithmetic to the Left Hemisphere

Science.gov (United States)

Pinel, Philippe; Dehaene, Stanislas

2010-01-01

Language and arithmetic are both lateralized to the left hemisphere in the majority of right-handed adults. Yet, does this similar lateralization reflect a single overall constraint of brain organization, such an overall "dominance" of the left hemisphere for all linguistic and symbolic operations? Is it related to the lateralization of specific…

Sensory trigeminal ULF-TENS stimulation reduces HRV response to experimentally induced arithmetic stress: A randomized clinical trial.

Science.gov (United States)

Monaco, Annalisa; Cattaneo, Ruggero; Ortu, Eleonora; Constantinescu, Marian Vladimir; Pietropaoli, Davide

2017-05-01

Ultra Low Frequency Transcutaneous Electric Nervous Stimulation (ULF-TENS) is extensively used for pain relief and for the diagnosis and treatment of temporomandibular disorders (TMD). In addition to its local effects, ULF-TENS acts on the autonomic nervous system (ANS), with particular reference to the periaqueductal gray (PAG), promoting the release of endogenous opioids and modulating descending pain systems. It has been suggested that the PAG participates in the coupling between the emotional stimulus and the appropriate behavioral autonomic response. This function is successfully investigated by HRV. Therefore, our goal is to investigate the effects of trigeminal ULF-TENS stimulation on autonomic behavior in terms of HRV and respiratory parameters during an experimentally-induced arithmetic stress test in healthy subjects. Thirty healthy women between 25 and 35years of age were enrolled and randomly assigned to either the control (TENS stimulation off) or test group (TENS stimulation on). Heart (HR, LF, HF, LF/HF ratio, DET, RMSSD, PNN50, RR) and respiratory (BR) rate were evaluated under basal, T1 (TENS off/on), and stress (mathematical task) conditions. Results showed that HRV parameters and BR significantly changed during the arithmetic stress paradigm (pTENS and control group could be discriminated only by non-linear HRV data, namely RR and DET (p=0.038 and p=0.027, respectively). During the arithmetic task, LF/HF ratio was the most sensitive parameter to discriminate between groups (p=0.019). Our data suggest that trigeminal sensory ULF-TENS reduces the autonomic response in terms of HRV and BR during acute mental stress in healthy subjects. Future directions of our work aim at applying the HRV and BR analysis, with and without TENS stimulation, to individuals with dysfunctional ANS among those with TMD. Copyright © 2017 Elsevier Inc. All rights reserved.

Implementation of a digital optical matrix-vector multiplier using a holographic look-up table and residue arithmetic

Science.gov (United States)

Habiby, Sarry F.

1987-01-01

The design and implementation of a digital (numerical) optical matrix-vector multiplier are presented. The objective is to demonstrate the operation of an optical processor designed to minimize computation time in performing a practical computing application. This is done by using the large array of processing elements in a Hughes liquid crystal light valve, and relying on the residue arithmetic representation, a holographic optical memory, and position coded optical look-up tables. In the design, all operations are performed in effectively one light valve response time regardless of matrix size. The features of the design allowing fast computation include the residue arithmetic representation, the mapping approach to computation, and the holographic memory. In addition, other features of the work include a practical light valve configuration for efficient polarization control, a model for recording multiple exposures in silver halides with equal reconstruction efficiency, and using light from an optical fiber for a reference beam source in constructing the hologram. The design can be extended to implement larger matrix arrays without increasing computation time.

Adaptivna digitalna sita v strukturi porazdeljene aritmetike: Adaptive digital filter implementation with distributed arithmetic structure:

OpenAIRE

Babič, Rudolf; Horvat, Bogomir; Osebik, Davorin

2001-01-01

Adaptive digital filters have a wide range of applications in the area of signal processing where only minimum a priori knowledge of signal characteristics is available. In this article the adaptive FIR digital filter implementation based on the distributed arithmetic technique is described. The major problem with conventional adaptive digital filter is the need for fast multipliers. When using a hardware implementation. These multipliers take up the disproportional amount of the overall cost...

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.

A cognitive stressor for event-related potential studies: the Portland arithmetic stress task.

Science.gov (United States)

Atchley, Rachel; Ellingson, Roger; Klee, Daniel; Memmott, Tabatha; Oken, Barry

2017-05-01

In this experiment, we developed and evaluated the Portland Arithmetic Stress Task (PAST) as a cognitive stressor to evaluate acute and sustained stress reactivity for event-related potential (ERP) studies. The PAST is a titrated arithmetic task adapted from the Montreal Imaging Stress Task (MIST), with added experimental control over presentation parameters, improved and synchronized acoustic feedback and generation of timing markers needed for physiological analyzes of real-time brain activity. Thirty-one older adults (M = 60 years) completed the PAST. EEG was recorded to assess feedback-related negativity (FRN) and the magnitude of the stress response through autonomic nervous system activity and salivary cortisol. Physiological measures other than EEG included heart rate, respiration rate, heart rate variability, blood pressure and salivary cortisol. These measures were collected at several time points throughout the task. Feedback-related negativity evoked-potential responses were elicited and they significantly differed depending on whether positive or negative feedback was received. The PAST also increased systolic blood pressure, heart rate variability and respiration rates compared to a control condition attentional task. These preliminary results suggest that the PAST is an effective cognitive stressor. Successful measurement of the feedback-related negativity suggests that the PAST is conducive to EEG and time-sensitive ERP experiments. Moreover, the physiological findings support the PAST as a potent method for inducing stress in older adult participants. Further research is needed to confirm these results, but the PAST shows promise as a tool for cognitive stress induction for time-locked event-related potential experiments.

Sound arithmetic: auditory cues in the rehabilitation of impaired fact retrieval.

Science.gov (United States)

Domahs, Frank; Zamarian, Laura; Delazer, Margarete

2008-04-01

The present single case study describes the rehabilitation of an acquired impairment of multiplication fact retrieval. In addition to a conventional drill approach, one set of problems was preceded by auditory cues while the other half was not. After extensive repetition, non-specific improvements could be observed for all trained problems (e.g., 3 * 7) as well as for their non-trained complementary problems (e.g., 7 * 3). Beyond this general improvement, specific therapy effects were found for problems trained with auditory cues. These specific effects were attributed to an involvement of implicit memory systems and/or attentional processes during training. Thus, the present results demonstrate that cues in the training of arithmetic facts do not have to be visual to be effective.

Desynchronization of Theta-Phase Gamma-Amplitude Coupling during a Mental Arithmetic Task in Children with Attention Deficit/Hyperactivity Disorder.

Science.gov (United States)

Kim, Jun Won; Kim, Bung-Nyun; Lee, Jaewon; Na, Chul; Kee, Baik Seok; Min, Kyung Joon; Han, Doug Hyun; Kim, Johanna Inhyang; Lee, Young Sik

2016-01-01

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 attention-demanding tasks.

Implementation of a fast digital optical matrix-vector multiplier using a holographic look-up table and residue arithmetic

Science.gov (United States)

Habiby, Sarry F.; Collins, Stuart A., Jr.

1987-01-01

The design and implementation of a digital (numerical) optical matrix-vector multiplier are presented. A Hughes liquid crystal light valve, the residue arithmetic representation, and a holographic optical memory are used to construct position coded optical look-up tables. All operations are performed in effectively one light valve response time with a potential for a high information density.

Number word structure in first and second language influences arithmetic skills

Directory of Open Access Journals (Sweden)

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

Lossless Authentication Watermarking Based on Adaptive Modular Arithmetic

Directory of Open Access Journals (Sweden)

H. Yang

2010-04-01

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

An Analysis of the Contents and Pedagogy of Al-Kashi's 1427 "Key to Arithmetic" (Miftah Al-Hisab)

Science.gov (United States)

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…

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

Science.gov (United States)

Thevenot, C; Barrouillet, P; Fayol, M

2001-05-01

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

Tensor Arithmetic, Geometric and Mathematic Principles of Fluid Mechanics in Implementation of Direct Computational Experiments

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Bogdanov Alexander

2016-01-01

Full Text Available The architecture of a digital computing system determines the technical foundation of a unified mathematical language for exact arithmetic-logical description of phenomena and laws of continuum mechanics for applications in fluid mechanics and theoretical physics. The deep parallelization of the computing processes results in functional programming at a new technological level, providing traceability of the computing processes with automatic application of multiscale hybrid circuits and adaptive mathematical models for the true reproduction of the fundamental laws of physics and continuum mechanics.

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

Science.gov (United States)

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

2016-01-01

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

Development of numerical processing in children with typical and dyscalculic arithmetic skills—a longitudinal study

Science.gov (United States)

Landerl, Karin

2013-01-01

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 2-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. PMID:23898310

VLSI System Implementation of 200 MHz, 8-bit, 90nm CMOS Arithmetic and Logic Unit (ALU Processor Controller

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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.

International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics

CERN Document Server

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...

Spontaneous Meta-Arithmetic as the First Step Toward School Algebra (La meta-aritmética espontánea como el primer paso hacia el álgebra escolar

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Shai Caspi

2012-01-01

Full Text Available Taking as a point of departure the vision of school algebra as a formalized meta-discourse of arithmetic, we have been following six pairs of 7th-grade students (12-13 years old as they gradually modify their spontaneous meta-arithmetic toward the “official” algebraic form of talk. In this paper we take a look at the very beginning of this process. Preliminary analyses of data have shown, unsurprisingly, that while reflecting on arithmetic processes and relations, the uninitiated 7th graders were employing colloquial means, which could not protect them against occasional ambiguities. More unexpectedly, this spontaneous meta-arithmetic, although not supported by any previous algebraic schooling, displayed some algebra-like features, not to be normally found in everyday discourses.Tomando como punto de partida la visión del álgebra escolar como un meta-discurso formalizado de la aritmética, hemos estado siguiendo a seis pares de estudiantes de 7º curso (12-13 años cuando modifican gradualmente su meta-aritmética espontánea hacia la forma algebraica “oficial” de hablar. En este artículo miramos el principio de este proceso. Los análisis preliminares de los datos han mostrado, como era de esperar, que mientras reflexionaban sobre los procesos y relaciones aritméticas, los alumnos no iniciados emplearon medios coloquiales que no evitaban las ambigüedades ocasionales. Más inesperadamente, esta meta-aritmética espontánea, a pesar de no apoyarse en ninguna enseñanza algebraica previa, desplegó algunas características similares al álgebra que no se encuentran normalmente en los discursos diarios.

Supertracker: A Programmable Parallel Pipeline Arithmetic Processor For Auto-Cueing Target Processing

Science.gov (United States)

Mack, Harold; Reddi, S. S.

1980-04-01

Supertracker represents a programmable parallel pipeline computer architecture that has been designed to meet the real time image processing requirements of auto-cueing target data processing. The prototype bread-board currently under development will be designed to perform input video preprocessing and processing for 525-line and 875-line TV formats FLIR video, automatic display gain and contrast control, and automatic target cueing, classification, and tracking. The video preprocessor is capable of performing operations full frames of video data in real time, e.g., frame integration, storage, 3 x 3 convolution, and neighborhood processing. The processor architecture is being implemented using bit-slice microprogrammable arithmetic processors, operating in parallel. Each processor is capable of up to 20 million operations per second. Multiple frame memories are used for additional flexibility.

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

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A Martowicz

2016-04-01

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

Performance analysis of Arithmetic Mean method in determining peak junction temperature of semiconductor device

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Mohana Sundaram Muthuvalu

2015-12-01

Full Text Available High reliability users of microelectronic devices have been derating junction temperature and other critical stress parameters to improve device reliability and extend operating life. The reliability of a semiconductor is determined by junction temperature. This paper gives a useful analysis on mathematical approach which can be implemented to predict temperature of a silicon die. The problem could be modeled as heat conduction equation. In this study, numerical approach based on implicit scheme and Arithmetic Mean (AM iterative method will be applied to solve the governing heat conduction equation. Numerical results are also included in order to assert the effectiveness of the proposed technique.

Coping Strategies Applied to Comprehend Multistep Arithmetic Word Problems by Students with Above-Average Numeracy Skills and Below-Average Reading Skills

Science.gov (United States)

Nortvedt, Guri A.

2011-01-01

This article discusses how 13-year-old students with above-average numeracy skills and below-average reading skills cope with comprehending word problems. Compared to other students who are proficient in numeracy and are skilled readers, these students are more disadvantaged when solving single-step and multistep arithmetic word problems. The…

Development of numerical processing in children with typical and dyscalculic arithmetic skills – a longitudinal study

Directory of Open Access Journals (Sweden)

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.

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

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Hai Zhu

2018-01-01

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

Deaf and hard of hearing students' problem-solving strategies with signed arithmetic story problems.

Science.gov (United States)

Pagliaro, Claudia M; Ansell, Ellen

2012-01-01

The use of problem-solving strategies by 59 deaf and hard of hearing children, grades K-3, was investigated. The children were asked to solve 9 arithmetic story problems presented to them in American Sign Language. The researchers found that while the children used the same general types of strategies that are used by hearing children (i.e., modeling, counting, and fact-based strategies), they showed an overwhelming use of counting strategies for all types of problems and at all ages. This difference may have its roots in language or instruction (or in both), and calls attention to the need for conceptual rather than procedural mathematics instruction for deaf and hard of hearing students.

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

Science.gov (United States)

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

1986-01-01

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

Energy-Efficient Wide Datapath Integer Arithmetic Logic Units Using Superconductor Logic

Science.gov (United States)

Ayala, Christopher Lawrence

Complementary Metal-Oxide-Semiconductor (CMOS) technology is currently the most widely used integrated circuit technology today. As CMOS approaches the physical limitations of scaling, it is unclear whether or not it can provide long-term support for niche areas such as high-performance computing and telecommunication infrastructure, particularly with the emergence of cloud computing. Alternatively, superconductor technologies based on Josephson junction (JJ) switching elements such as Rapid Single Flux Quantum (RSFQ) logic and especially its new variant, Energy-Efficient Rapid Single Flux Quantum (ERSFQ) logic have the capability to provide an ultra-high-speed, low power platform for digital systems. The objective of this research is to design and evaluate energy-efficient, high-speed 32-bit integer Arithmetic Logic Units (ALUs) implemented using RSFQ and ERSFQ logic as the first steps towards achieving practical Very-Large-Scale-Integration (VLSI) complexity in digital superconductor electronics. First, a tunable VHDL superconductor cell library is created to provide a mechanism to conduct design exploration and evaluation of superconductor digital circuits from the perspectives of functionality, complexity, performance, and energy-efficiency. Second, hybrid wave-pipelining techniques developed earlier for wide datapath RSFQ designs have been used for efficient arithmetic and logic circuit implementations. To develop the core foundation of the ALU, the ripple-carry adder and the Kogge-Stone parallel prefix carry look-ahead adder are studied as representative candidates on opposite ends of the design spectrum. By combining the high-performance features of the Kogge-Stone structure and the low complexity of the ripple-carry adder, a 32-bit asynchronous wave-pipelined hybrid sparse-tree ALU has been designed and evaluated using the VHDL cell library tuned to HYPRES' gate-level characteristics. The designs and techniques from this research have been implemented using

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.

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

OpenAIRE

Caroline Hornung; Romain Martin; Michel Fayol; Michel Fayol

2017-01-01

In the present study, we opted for a longitudinal design and examined rapid automatized naming (RAN) performance from two perspectives. In a first step, we examined the structure of RAN performance from a general cognitive perspective. We investigated whether rapid naming measures (e.g., digit RAN and color RAN) reflect a mainly domain-general factor or domain-specific factors. In a second step, we examined how the best fitting RAN model was related to reading and arithmetic outcomes, assesse...

Calabi-Yau varieties: arithmetic, geometry and physics lecture notes on concentrated graduate courses

CERN Document Server

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.

An innovation on high-grade CNC machines tools for B-spline curve method of high-speed interpolation arithmetic

Science.gov (United States)

Zhang, Wanjun; Gao, Shanping; Cheng, Xiyan; Zhang, Feng

2017-04-01

A novel on high-grade CNC machines tools for B Spline curve method of High-speed interpolation arithmetic is introduced. In the high-grade CNC machines tools CNC system existed the type value points is more trouble, the control precision is not strong and so on, In order to solve this problem. Through specific examples in matlab7.0 simulation result showed that that the interpolation error significantly reduced, the control precision is improved markedly, and satisfy the real-time interpolation of high speed, high accuracy requirements.

The impact of finger counting habits on arithmetic in adults and children.

Science.gov (United States)

Newman, Sharlene D; Soylu, Firat

2014-07-01

Here, we explored the impact of finger counting habits on arithmetic in both adults and children. Two groups of participants were examined, those that begin counting with their left hand (left-starters) and those that begin counting with their right hand (right-starters). For the adults, performance on an addition task in which participants added 2 two-digit numbers was compared. The results revealed that left-starters were slower than right-starters when adding and they had lower forward and backward digit-span scores. The children (aged 5-12) showed similar results on a single-digit timed addition task-right-starters outperformed left-starters. However, the children did not reveal differences in working memory or verbal and non-verbal intelligence as a function of finger counting habit. We argue that the motor act of finger counting influences how number is represented and suggest that left-starters may have a more bilateral representation that accounts for the slower processing.

A pedagogical example of second-order arithmetic sequences applied to the construction of computer passwords by upper elementary grade students

Science.gov (United States)

Coggins, Porter E.

2015-04-01

The purpose of this paper is (1) to present how general education elementary school age students constructed computer passwords using digital root sums and second-order arithmetic sequences, (2) argue that computer password construction can be used as an engaging introduction to generate interest in elementary school students to study mathematics related to computer science, and (3) share additional mathematical ideas accessible to elementary school students that can be used to create computer passwords. This paper serves to fill a current gap in the literature regarding the integration of mathematical content accessible to upper elementary school students and aspects of computer science in general, and computer password construction in particular. In addition, the protocols presented here can serve as a hook to generate further interest in mathematics and computer science. Students learned to create a random-looking computer password by using biometric measurements of their shoe size, height, and age in months and to create a second-order arithmetic sequence, then converted the resulting numbers into characters that become their computer passwords. This password protocol can be used to introduce students to good computer password habits that can serve a foundation for a life-long awareness of data security. A refinement of the password protocol is also presented.

On the validity of the arithmetic-geometric mean method to locate the optimal solution in a supply chain system

Science.gov (United States)

Chung, Kun-Jen

2012-08-01

Cardenas-Barron [Cardenas-Barron, L.E. (2010) 'A Simple Method to Compute Economic order Quantities: Some Observations', Applied Mathematical Modelling, 34, 1684-1688] indicates that there are several functions in which the arithmetic-geometric mean method (AGM) does not give the minimum. This article presents another situation to reveal that the AGM inequality to locate the optimal solution may be invalid for Teng, Chen, and Goyal [Teng, J.T., Chen, J., and Goyal S.K. (2009), 'A Comprehensive Note on: An Inventory Model under Two Levels of Trade Credit and Limited Storage Space Derived without Derivatives', Applied Mathematical Modelling, 33, 4388-4396], Teng and Goyal [Teng, J.T., and Goyal S.K. (2009), 'Comment on 'Optimal Inventory Replenishment Policy for the EPQ Model under Trade Credit Derived without Derivatives', International Journal of Systems Science, 40, 1095-1098] and Hsieh, Chang, Weng, and Dye [Hsieh, T.P., Chang, H.J., Weng, M.W., and Dye, C.Y. (2008), 'A Simple Approach to an Integrated Single-vendor Single-buyer Inventory System with Shortage', Production Planning and Control, 19, 601-604]. So, the main purpose of this article is to adopt the calculus approach not only to overcome shortcomings of the arithmetic-geometric mean method of Teng et al. (2009), Teng and Goyal (2009) and Hsieh et al. (2008), but also to develop the complete solution procedures for them.

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

Science.gov (United States)

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

2016-06-01

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

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

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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.

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

International Nuclear Information System (INIS)

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

2003-01-01

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

The use of arithmetic average method in identifying critical success criteria for Homestay Programmes

Science.gov (United States)

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.

Arithmetically Cohen-Macaulay sets of points in P^1 x P^1

CERN Document Server

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...

Black tea aroma inhibited increase of salivary chromogranin-A after arithmetic tasks.

Science.gov (United States)

Yoto, Ai; Fukui, Natsuki; Kaneda, Chisa; Torita, Shoko; Goto, Keiichi; Nanjo, Fumio; Yokogoshi, Hidehiko

2018-01-24

Growing attention has been paid to the effects of food flavor components on alleviating negative brain functions caused by stressful lifestyles. In this study, we investigated the alleviating effect of two kinds of black tea aromas on physical and psychological stress induced by the Uchida-Kraepelin test, based on salivary chromogranin-A (CgA) levels as a stress marker and subjective evaluations (Profile of Mood States). Compared with the water exposure control, inhaling black tea aroma (Darjeeling and Assam in this study) induced lower salivary CgA concentration levels after 30 min of mental stress load tasks. This anti-stress effect of black tea aroma did not differ between the two tea types even though the concentration of the anti-stress components in the Darjeeling tea aroma was higher than that in the Assam aroma. However, Darjeeling tea aroma tended to decrease the tension and/or anxiety score immediately after the first exposure. Inhaling black tea aroma may diminish stress levels caused by arithmetic mental stress tasks, and Darjeeling tea aroma tended to improve mood before mental stress load.

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

Directory of Open Access Journals (Sweden)

Grégoire Waelchli

2010-01-01

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

Interstructure Lattices and Types of Peano Arithmetic

Science.gov (United States)

Abdul-Quader, Athar

The collection of elementary substructures of a model of PA forms a lattice, and is referred to as the substructure lattice of the model. In this thesis, we study substructure and interstructure lattices of models of PA. We apply techniques used in studying these lattices to other problems in the model theory of PA. In Chapter 2, we study a problem that had its origin in Simpson ([Sim74]), who used arithmetic forcing to show that every countable model of PA has an expansion to PA* that is pointwise definable. Enayat ([Ena88]) later showed that there are 2N0 models with the property that every expansion to PA* is pointwise definable. In this Chapter, we use techniques involved in representations of lattices to show that there is a model of PA with this property which contains an infinite descending chain of elementary cuts. In Chapter 3, we study the question of when subsets can be coded in elementary end extensions with prescribed interstructure lattices. This problem originated in Gaifman [Gai76], who showed that every model of PA has a conservative, minimal elementary end extension. That is, every model of PA has a minimal elementary end extension which codes only definable sets. Kossak and Paris [KP92] showed that if a model is countable and a subset X can be coded in any elementary end extension, then it can be coded in a minimal extension. Schmerl ([Sch14] and [Sch15]) extended this work by considering which collections of sets can be the sets coded in a minimal elementary end extension. In this Chapter, we extend this work to other lattices. We study two questions: given a countable model M, which sets can be coded in an elementary end extension such that the interstructure lattice is some prescribed finite distributive lattice; and, given an arbitrary model M, which sets can be coded in an elementary end extension whose interstructure lattice is a finite Boolean algebra?

Processes in arithmetic strategy selection: A fMRI study.

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Julien eTaillan

2015-02-01

Full Text Available This neuroimaging (fMRI study investigated neural correlates of strategy selection. Young adults performed an arithmetic task in two different conditions. In both conditions, participants had to provide estimates of two-digit multiplication problems like 54 x 78. In the choice condition, participants had to select the better of two available rounding strategies, rounding-up strategy (RU (i.e., doing 60x80 = 4,800 or rounding-down strategy (RD (i.e., doing 50x70=3,500 to estimate product of 54x78. In the no-choice condition, participants did not have to select strategy on each problem but were told which strategy to use; they executed RU and RD strategies each on a series of problems. Participants also had a control task (i.e., providing correct products of multiplication problems like 40x50. Brain activations and performance were analyzed as a function of these conditions. Participants were able to frequently choose the better strategy in the choice condition; they were also slower when they executed the difficult RU than the easier RD. Neuroimaging data showed greater brain activations in right anterior cingulate cortex (ACC, dorso-lateral prefrontal cortex (DLPFC, and angular gyrus (ANG, when selecting (relative to executing the better strategy on each problem. Moreover, RU was associated with more parietal cortex activation than RD. These results suggest an important role of fronto-parietal network in strategy selection and have important implications for our further understanding and modelling cognitive processes underlying strategy selection.

Processes in arithmetic strategy selection: a fMRI study.

Science.gov (United States)

Taillan, Julien; Ardiale, Eléonore; Anton, Jean-Luc; Nazarian, Bruno; Félician, Olivier; Lemaire, Patrick

2015-01-01

This neuroimaging (functional magnetic resonance imaging) study investigated neural correlates of strategy selection. Young adults performed an arithmetic task in two different conditions. In both conditions, participants had to provide estimates of two-digit multiplication problems like 54 × 78. In the choice condition, participants had to select the better of two available rounding strategies, rounding-up (RU) strategy (i.e., doing 60 × 80 = 4,800) or rounding-down (RD) strategy (i.e., doing 50 × 70 = 3,500 to estimate product of 54 × 78). In the no-choice condition, participants did not have to select strategy on each problem but were told which strategy to use; they executed RU and RD strategies each on a series of problems. Participants also had a control task (i.e., providing correct products of multiplication problems like 40 × 50). Brain activations and performance were analyzed as a function of these conditions. Participants were able to frequently choose the better strategy in the choice condition; they were also slower when they executed the difficult RU than the easier RD. Neuroimaging data showed greater brain activations in right anterior cingulate cortex (ACC), dorso-lateral prefrontal cortex (DLPFC), and angular gyrus (ANG), when selecting (relative to executing) the better strategy on each problem. Moreover, RU was associated with more parietal cortex activation than RD. These results suggest an important role of fronto-parietal network in strategy selection and have important implications for our further understanding and modeling cognitive processes underlying strategy selection.

Measuring acetabular cup orientation on antero-posterior radiographs of the hip after total hip arthroplasty with a vector arithmetic radiological method. Is it valid and verified for daily clinical practice?

Energy Technology Data Exchange (ETDEWEB)

Craiovan, B.; Weber, M.; Worlicek, M.; Schneider, M.; Springorum, H.R.; Grifka, J.; Renkawitz, T. [University Medical Center Regensburg, Bad Abbach/Regensburg (Germany). Orthopedic Surgery; Zeman, F. [University Medical Center Regensburg, Bad Abbach/Regensburg (Germany). Center for Clinical Studies

2016-06-15

The aim of this prospective study is to validate a vector arithmetic method for measuring acetabular cup orientation after total hip arthroplasty (THA) and to verify the clinical practice. We measured cup anteversion and inclination of 123 patients after cementless primary THA twice by two examiners on AP pelvic radiographs with a vector arithmetic method and compared with a 3D-CT based reconstruction model within the same radiographic coronal plane. The mean difference between the radiographic and the 3D-CT measurements was -1.4 ±3.9 for inclination and 0.8 ±7.9 for anteversion with excellent correlation for inclination (r=0.81, p < 0.001) and moderate correlation for anteversion (r=0.65, p < 0.001). The intraclass correlation coefficient for measurements on radiographs ranged from 0.98 (95%-CI: 0.98; 0.99) for the first observer to 0.94 (95%-CI: 0.92; 0.96) for the second observer. The interrater reliability was 0.96 (95%-CI: 0.93; 0.98) for inclination and 0.93 (95%-CI: 0.85; 0.96) for anteversion. The largest errors in measurements were associated with an extraordinary pelvic tilt. In order to get a valuable measurement for measuring cup position after THA on pelvic radiographs by this vector arithmetic method, there is a need for a correct postoperative ap view, with special regards to the pelvic tilt for the future.

Babies and math: A meta-analysis of infants' simple arithmetic competence.

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Christodoulou, Joan; Lac, Andrew; Moore, David S

2017-08-01

Wynn's (1992) seminal research reported that infants looked longer at stimuli representing "incorrect" versus "correct" solutions of basic addition and subtraction problems and concluded that infants have innate arithmetical abilities. Since then, infancy researchers have attempted to replicate this effect, yielding mixed findings. The present meta-analysis aimed to systematically compile and synthesize all of the primary replications and extensions of Wynn (1992) that have been conducted to date. The synthesis included 12 studies consisting of 26 independent samples and 550 unique infants. The summary effect, computed using a random-effects model, was statistically significant, d = +0.34, p < .001, suggesting that the phenomenon Wynn originally reported is reliable. Five different tests of publication bias yielded mixed results, suggesting that while a moderate level of publication bias is probable, the summary effect would be positive even after accounting for this issue. Out of the 10 metamoderators tested, none were found to be significant, but most of the moderator subgroups were significantly different from a null effect. Although this meta-analysis provides support for Wynn's original findings, further research is warranted to understand the underlying mechanisms responsible for infants' visual preferences for "mathematically incorrect" test stimuli. (PsycINFO Database Record (c) 2017 APA, all rights reserved).

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

DEFF Research Database (Denmark)

Dung, Phan Anh; Hansen, Michael Reichhardt

2015-01-01

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

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

Science.gov (United States)

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

2018-03-01

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

Designing reversible arithmetic, logic circuit to implement micro-operation in quantum computation

International Nuclear Information System (INIS)

Kalita, Gunajit; Saikia, Navajit

2016-01-01

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. (paper)

Multiple gcd-closed sets and determinants of matrices associated with arithmetic functions

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Hong Siao

2016-01-01

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.

Advanced Arithmetic from Twelfth-Century Al-Andalus, Surviving Only (and anonymously) in Latin Translation?

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...

Arithmetic problem-solving: effect of equivalence relations between three different forms of presenting problems / Resolução de problemas aritméticos: efeito de relações de equivalência entre três diferentes formas de apresentação dos problemas

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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.

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.

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

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Tooraj Nikoubin

2010-01-01

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

Arithmetic and algebraic problem solving and resource allocation: the distinct impact of fluid and numerical intelligence.

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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. Copyright © 2014 Society for Psychophysiological Research.

A structural equation modeling of executive functions, IQ and mathematical skills in primary students: Differential effects on number production, mental calculus and arithmetical problems.

Science.gov (United States)

Arán Filippetti, Vanessa; Richaud, María Cristina

2017-10-01

Though the relationship between executive functions (EFs) and mathematical skills has been well documented, little is known about how both EFs and IQ differentially support diverse math domains in primary students. Inconsistency of results may be due to the statistical techniques employed, specifically, if the analysis is conducted with observed variables, i.e., regression analysis, or at the latent level, i.e., structural equation modeling (SEM). The current study explores the contribution of both EFs and IQ in mathematics through an SEM approach. A total of 118 8- to 12-year-olds were administered measures of EFs, crystallized (Gc) and fluid (Gf) intelligence, and math abilities (i.e., number production, mental calculus and arithmetical problem-solving). Confirmatory factor analysis (CFA) offered support for the three-factor solution of EFs: (1) working memory (WM), (2) shifting, and (3) inhibition. Regarding the relationship among EFs, IQ and math abilities, the results of the SEM analysis showed that (i) WM and age predict number production and mental calculus, and (ii) shifting and sex predict arithmetical problem-solving. In all of the SEM models, EFs partially or totally mediated the relationship between IQ, age and math achievement. These results suggest that EFs differentially supports math abilities in primary-school children and is a more significant predictor of math achievement than IQ level.

Application of Interval Arithmetic in the Evaluation of Transfer Capabilities by Considering the Sources of Uncertainty

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Prabha Umapathy

2009-01-01

Full Text Available Total transfer capability (TTC is an important index in a power system with large volume of inter-area power exchanges. This paper proposes a novel technique to determine the TTC and its confidence intervals in the system by considering the uncertainties in the load and line parameters. The optimal power flow (OPF method is used to obtain the TTC. Variations in the load and line parameters are incorporated using the interval arithmetic (IA method. The IEEE 30 bus test system is used to illustrate the proposed methodology. Various uncertainties in the line, load and both line and load are incorporated in the evaluation of total transfer capability. From the results, it is observed that the solutions obtained through the proposed method provide much wider information in terms of closed interval form which is more useful in ensuring secured operation of the interconnected system in the presence of uncertainties in load and line parameters.

Why does placing the question before an arithmetic word problem improve performance? A situation model account.

Science.gov (United States)

Thevenot, Catherine; Devidal, Michel; Barrouillet, Pierre; Fayol, Michel

2007-01-01

The aim of this paper is to investigate the controversial issue of the nature of the representation constructed by individuals to solve arithmetic word problems. More precisely, we consider the relevance of two different theories: the situation or mental model theory (Johnson-Laird, 1983; Reusser, 1989) and the schema theory (Kintsch & Greeno, 1985; Riley, Greeno, & Heller, 1983). Fourth-graders who differed in their mathematical skills were presented with problems that varied in difficulty and with the question either before or after the text. We obtained the classic effect of the position of the question, with better performance when the question was presented prior to the text. In addition, this effect was more marked in the case of children who had poorer mathematical skills and in the case of more difficult problems. We argue that this pattern of results is compatible only with the situation or mental model theory, and not with the schema theory.

Probabilistic and Fuzzy Arithmetic Approaches for the Treatment of Uncertainties in the Installation of Torpedo Piles

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Denise Margareth Kazue Nishimura Kunitaki

2008-01-01

Full Text Available The “torpedo” pile is a foundation system that has been recently considered to anchor mooring lines and risers of floating production systems for offshore oil exploitation. The pile is installed in a free fall operation from a vessel. However, the soil parameters involved in the penetration model of the torpedo pile contain uncertainties that can affect the precision of analysis methods to evaluate its final penetration depth. Therefore, this paper deals with methodologies for the assessment of the sensitivity of the response to the variation of the uncertain parameters and mainly to incorporate into the analysis method techniques for the formal treatment of the uncertainties. Probabilistic and “possibilistic” approaches are considered, involving, respectively, the Monte Carlo method (MC and concepts of fuzzy arithmetic (FA. The results and performance of both approaches are compared, stressing the ability of the latter approach to efficiently deal with the uncertainties of the model, with outstanding computational efficiency, and therefore, to comprise an effective design tool.

Evidence of Mixed-mode oscillations and Farey arithmetic in double plasma system in presence of fireball

Science.gov (United States)

Mitra, Vramori; Sarma, Bornali; Sarma, Arun

2017-10-01

Plasma fireballs are luminous glowing region formed around a positively biased electrode. The present work reports the observation of mix mode oscillation (MMO) in the dynamics of plasma oscillations that are excited in the presence of fireball in a double plasma device. Source voltage and applied electrode voltage are considered as the controlling parameters for the experiment. Many sequences of distinct multi peaked periodic states reflects the presence of MMO with the variation of control parameter. The sequences of states with two patterns are characterized well by Farey arithmetic, which provides rational approximations of irrational numbers. These states can be characterized by a firing number, the ratio of the number of small amplitude oscillations to the total number of oscillations per period. The dynamical transition in plasma fireball is also demonstrated by spectral analysis, recurrence quantification analysis (RQA) and by statistical measures viz., skewness and kurtosis. The mix mode phenomenon observed in the experiment is consistent with a model that describes the dynamics of ionization instabilities.

Impact of ageing on problem size and proactive interference in arithmetic facts solving.

Science.gov (United States)

Archambeau, Kim; De Visscher, Alice; Noël, Marie-Pascale; Gevers, Wim

2018-02-01

Arithmetic facts (AFs) are required when solving problems such as "3 × 4" and refer to calculations for which the correct answer is retrieved from memory. Currently, two important effects that modulate the performance in AFs have been highlighted: the problem size effect and the proactive interference effect. The aim of this study is to investigate possible age-related changes of the problem size effect and the proactive interference effect in AF solving. To this end, the performance of young and older adults was compared in a multiplication production task. Furthermore, an independent measure of proactive interference was assessed to further define the architecture underlying this effect in multiplication solving. The results indicate that both young and older adults were sensitive to the effects of interference and of the problem size. That is, both interference and problem size affected performance negatively: the time needed to solve a multiplication problem increases as the level of interference and the size of the problem increase. Regarding the effect of ageing, the problem size effect remains constant with age, indicating a preserved AF network in older adults. Interestingly, sensitivity to proactive interference in multiplication solving was less pronounced in older than in younger adults suggesting that part of the proactive interference has been overcome with age.

Context adaptive binary arithmetic coding-based data hiding in partially encrypted H.264/AVC videos

Science.gov (United States)

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.

Modelling uncertainties in the diffusion-advection equation for radon transport in soil using interval arithmetic.

Science.gov (United States)

Chakraverty, S; Sahoo, B K; Rao, T D; Karunakar, P; Sapra, B K

2018-02-01

Modelling radon transport in the earth crust is a useful tool to investigate the changes in the geo-physical processes prior to earthquake event. Radon transport is modeled generally through the deterministic advection-diffusion equation. However, in order to determine the magnitudes of parameters governing these processes from experimental measurements, it is necessary to investigate the role of uncertainties in these parameters. Present paper investigates this aspect by combining the concept of interval uncertainties in transport parameters such as soil diffusivity, advection velocity etc, occurring in the radon transport equation as applied to soil matrix. The predictions made with interval arithmetic have been compared and discussed with the results of classical deterministic model. The practical applicability of the model is demonstrated through a case study involving radon flux measurements at the soil surface with an accumulator deployed in steady-state mode. It is possible to detect the presence of very low levels of advection processes by applying uncertainty bounds on the variations in the observed concentration data in the accumulator. The results are further discussed. Copyright © 2017 Elsevier Ltd. All rights reserved.

Vector-matrix-quaternion, array and arithmetic packages: All HAL/S functions implemented in Ada

Science.gov (United States)

Klumpp, Allan R.; Kwong, David D.

1986-01-01

The HAL/S avionics programmers have enjoyed a variety of tools built into a language tailored to their special requirements. Ada is designed for a broader group of applications. Rather than providing built-in tools, Ada provides the elements with which users can build their own. Standard avionic packages remain to be developed. These must enable programmers to code in Ada as they have coded in HAL/S. The packages under development at JPL will provide all of the vector-matrix, array, and arithmetic functions described in the HAL/S manuals. In addition, the linear algebra package will provide all of the quaternion functions used in Shuttle steering and Galileo attitude control. Furthermore, using Ada's extensibility, many quaternion functions are being implemented as infix operations; equivalent capabilities were never implemented in HAL/S because doing so would entail modifying the compiler and expanding the language. With these packages, many HAL/S expressions will compile and execute in Ada, unchanged. Others can be converted simply by replacing the implicit HAL/S multiply operator with the Ada *. Errors will be trapped and identified. Input/output will be convenient and readable.

等差级数与等比级数乘积项级数的判敛与求和浅析%Convergence and Summation of Arithmetical Series and Geometric Series Product Series

Institute of Scientific and Technical Information of China (English)

石会萍

2012-01-01

在级数理论中,一般来说,判断级数的敛散性是比较困难的,有时尽管能判断其收敛,但要求其和却是十分困难的。文中根据等差级数和等比级数的特点,给出了一类基于等差级数和等比级数乘积项的无穷级数的判敛与求和方法。%In series theory, generally, it is difficult to determine the convergence and divergence of se- ries. Though sometimes the convergence can be determined, it is very difficult to determine the summa- tion. Based on the characteristics of the arithmetical and geometric series, a method of summation and con- vergence is put forward, based on arithmetical series and assessment of product of the geometric series of infinite series.

Redundant Radix-4 Representation With High Speed Arithmetic Coprocessor Using Carry Save And Redundant Signed Digit Technique

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Ashish Manoharrao Ingale

2015-08-01

Full Text Available Division is the inverse of multiplication so basic division consist of a sequence of subtraction which are just additions of the negations of the subtrahends Therefore CS addition can be used in the arithmetic for division as well. Division is however more complicated than multiplication in that subtrahend multiple of divisor chosen at any steps depends on the magnitude result of the preceding subtraction and that magnitude is not readily available with CS representation. Assuming twos complement representation subtraction with carry save representation is carried out in usual manner of the farming the ones complement of the subtrahend and then adding that with a 1 also added into the least significant bit position subtraction is performed by adding the negation of the subtrahend which twos complement representation consist of the ones complement addition of 1 in the least significant bit position.

A novel reversible logic gate and its systematic approach to implement cost-efficient arithmetic logic circuits using QCA.

Science.gov (United States)

Ahmad, Peer Zahoor; Quadri, S M K; Ahmad, Firdous; Bahar, Ali Newaz; Wani, Ghulam Mohammad; Tantary, Shafiq Maqbool

2017-12-01

Quantum-dot cellular automata, is an extremely small size and a powerless nanotechnology. It is the possible alternative to current CMOS technology. Reversible QCA logic is the most important issue at present time to reduce power losses. This paper presents a novel reversible logic gate called the F-Gate. It is simplest in design and a powerful technique to implement reversible logic. A systematic approach has been used to implement a novel single layer reversible Full-Adder, Full-Subtractor and a Full Adder-Subtractor using the F-Gate. The proposed Full Adder-Subtractor has achieved significant improvements in terms of overall circuit parameters among the most previously cost-efficient designs that exploit the inevitable nano-level issues to perform arithmetic computing. The proposed designs have been authenticated and simulated using QCADesigner tool ver. 2.0.3.

Ultrafast all-optical arithmetic logic based on hydrogenated amorphous silicon microring resonators

Science.gov (United States)

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.

Rational and systematic teaching in Colombia: the case of arithmetic in the textbooks of G.M. Bruño (1900-1930

Directory of Open Access Journals (Sweden)

Fernando Romero Loaiza

2015-06-01

Full Text Available The arrival to Colombia of the Order of Brothers from the Christian Schools of La Salle took place in the context of the conservative influence and hegemony of the catholic Church in the education field. This process influenced the form of teaching in diferents scientific disciplines, as: grammar, math, calculus, geometry, biology, zoology, among others. Here will be treated the case of the Lasalian pedagogy, which illustrates the “systematic” and “Rational” way of teaching within methodical basis. To demonstrate those mentioned aspects, a ‘corpus’ of eighteen (18 arithmetic books by G.M. Bruño, which were published between 1900-1930, have been selected and subudued to a content analysis.

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.

Improvement in the Accuracy of Flux Measurement of Radio Sources by Exploiting an Arithmetic Pattern in Photon Bunching Noise

Energy Technology Data Exchange (ETDEWEB)

Lieu, Richard [Department of Physics, University of Alabama, Huntsville, AL 35899 (United States)

2017-07-20

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 and the photon occupation number of the beam (the higher the photon number the better the performance). The principal application is accuracy improvement in the signal-limited bolometric flux measurement of a radio source.

Improvement in the accuracy of flux measurement of radio sources by exploiting an arithmetic pattern in photon bunching noise

Science.gov (United States)

Lieu, Richard

2018-01-01

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 and the photon occupation number of the beam (the higher the photon number the better the performance). The principal application is accuracy improvement in the bolometric flux measurement of a radio source.

The Interpretations and Applications of Boethius's Introduction to the Arithmetic II,1 at the End of the 10th Century

Science.gov (United States)

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.

A binary-decision-diagram-based two-bit arithmetic logic unit on a GaAs-based regular nanowire network with hexagonal topology

International Nuclear Information System (INIS)

Zhao Hongquan; Kasai, Seiya; Shiratori, Yuta; Hashizume, Tamotsu

2009-01-01

A two-bit arithmetic logic unit (ALU) was successfully fabricated on a GaAs-based regular nanowire network with hexagonal topology. This fundamental building block of central processing units can be implemented on a regular nanowire network structure with simple circuit architecture based on graphical representation of logic functions using a binary decision diagram and topology control of the graph. The four-instruction ALU was designed by integrating subgraphs representing each instruction, and the circuitry was implemented by transferring the logical graph structure to a GaAs-based nanowire network formed by electron beam lithography and wet chemical etching. A path switching function was implemented in nodes by Schottky wrap gate control of nanowires. The fabricated circuit integrating 32 node devices exhibits the correct output waveforms at room temperature allowing for threshold voltage variation.

Influence of mental abacus calculation practice on mental arithmetic in children: a fMRI study

International Nuclear Information System (INIS)

Long Jinfeng; Zhao Kunyuan; Wang Bin; Li Lixin; Shen Xiaojun

2009-01-01

Objective: To investigate the influence of mental abacus calculation practice on mental arithmetic in children with functional magnetic resonance imaging (fMRI). Methods: Twelve children who had practiced mental abacus calculation for 3 years and 12 untrained children (The two groups were matched in terms of age, handedness and education) underwent fMRI during mental calculation tasks. The related behavior data were recorded at the same time. All data were analyzed with statistical parametric mapping 2. Results: The calculation accuracy was significantly higher [(95.00±7.16)% vs.(74.26±16.07)%. t=-4.084, P<0.01]; and the reaction time was significantly shorter [(597.91±124.05) ms vs. (770.07± 148.54) ms, t=3.082, P<0.01] in trained group than untrained group. The extent and magnitude of the activated areas were significantly increased in the untrained group compared with the trained group. The activated areas mainly localized in the frontal and parietal lobes in untrained group, while the brain activated areas were few and mainly localized in occipital and parietal lobes in the trained group. Conclusion: Mental abacus calculation can enhance the information processing m some brain areas, and improve the utilization efficiency of neural resources. (authors)

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

Science.gov (United States)

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

2018-04-01

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

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

Institute of Scientific and Technical Information of China (English)

周明; 冯民富

2012-01-01

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

Rational Arithmetic Mathematica Functions to Evaluate the Two-Sided One Sample K-S Cumulative Sampling Distribution

Directory of Open Access Journals (Sweden)

J. Randall Brown

2007-06-01

Full Text Available One of the most widely used goodness-of-fit tests is the two-sided one sample Kolmogorov-Smirnov (K-S test which has been implemented by many computer statistical software packages. To calculate a two-sided p value (evaluate the cumulative sampling distribution, these packages use various methods including recursion formulae, limiting distributions, and approximations of unknown accuracy developed over thirty years ago. Based on an extensive literature search for the two-sided one sample K-S test, this paper identifies an exact formula for sample sizes up to 31, six recursion formulae, and one matrix formula that can be used to calculate a p value. To ensure accurate calculation by avoiding catastrophic cancelation and eliminating rounding error, each of these formulae is implemented in rational arithmetic. For the six recursion formulae and the matrix formula, computational experience for sample sizes up to 500 shows that computational times are increasing functions of both the sample size and the number of digits in the numerator and denominator integers of the rational number test statistic. The computational times of the seven formulae vary immensely but the Durbin recursion formula is almost always the fastest. Linear search is used to calculate the inverse of the cumulative sampling distribution (find the confidence interval half-width and tables of calculated half-widths are presented for sample sizes up to 500. Using calculated half-widths as input, computational times for the fastest formula, the Durbin recursion formula, are given for sample sizes up to two thousand.

EEG correlates of a mental arithmetic task in patients with first episode schizophrenia and schizoaffective disorder.

Science.gov (United States)

Garakh, Zhanna; Zaytseva, Yuliya; Kapranova, Alexandra; Fiala, Ondrej; Horacek, Jiri; Shmukler, Alexander; Gurovich, Isaac Ya; Strelets, Valeria B

2015-11-01

To evaluate the spectral power of the cortical bands in patients with first episode schizophrenia and schizoaffective disorder at rest and during the performance of a mental arithmetic task. We analyzed EEG spectral power (SP) in the resting state and subsequently while counting down from 200 in steps of 7, in 32 first episode schizophrenia patients (SZ), 32 patients with first episode schizoaffective disorder (SA) and healthy controls (HC, n=40). Behavioral parameters such as accuracy and counting speed were also evaluated. Both SZ and SA patients were slower in counting than HC, no difference was obtained in the accuracy and counting speed in the patient groups. In the resting state patients showed elevated midline theta power, off-midline anterior beta 2 power and decreased central/posterior alpha power. The SA group occupied an intermediate position between the schizophrenia patients and controls. In task performance patients lacked a typical increase of midline theta, left anterior beta 2, and anterior gamma power; however, schizoaffective patients demonstrated a growing trend of power in the gamma band in left anterior off-midline sites similar to HC. Moreover, alpha power was less inhibited in schizoaffective patients and more pronounced in schizophrenia patients indicating distinct inhibitory mechanisms in these psychotic disorders. Patients with SA demonstrate less alteration in the spectral power of bands at rest than SZ, and present spectral power changes during cognitive task performance close to the controls. Our study contributes to the present evidence on the neurophysiological distinction between schizophrenia and schizoaffective disorder. Copyright © 2015 International Federation of Clinical Neurophysiology. Published by Elsevier Ireland Ltd. All rights reserved.

Striving for Excellence Sometimes Hinders High Achievers: Performance-Approach Goals Deplete Arithmetical Performance in Students with High Working Memory Capacity

Science.gov (United States)

Crouzevialle, Marie; Smeding, Annique; Butera, Fabrizio

2015-01-01

We tested whether the goal to attain normative superiority over other students, referred to as performance-approach goals, is particularly distractive for high-Working Memory Capacity (WMC) students—that is, those who are used to being high achievers. Indeed, WMC is positively related to high-order cognitive performance and academic success, a record of success that confers benefits on high-WMC as compared to low-WMC students. We tested whether such benefits may turn out to be a burden under performance-approach goal pursuit. Indeed, for high achievers, aiming to rise above others may represent an opportunity to reaffirm their positive status—a stake susceptible to trigger disruptive outcome concerns that interfere with task processing. Results revealed that with performance-approach goals—as compared to goals with no emphasis on social comparison—the higher the students’ WMC, the lower their performance at a complex arithmetic task (Experiment 1). Crucially, this pattern appeared to be driven by uncertainty regarding the chances to outclass others (Experiment 2). Moreover, an accessibility measure suggested the mediational role played by status-related concerns in the observed disruption of performance. We discuss why high-stake situations can paradoxically lead high-achievers to sub-optimally perform when high-order cognitive performance is at play. PMID:26407097

Some basic theorems on the cross-sums of certain class of numbers (M-1) when the operations are done with different bases M of the arithmetic

International Nuclear Information System (INIS)

Ozoemena, P.C.; Onwumechili, C.A.

1988-11-01

Some new theorems have been propounded for the numbers (M-1), as they relate to other numerals, through the basic arithmetical operations, at different bases M. For some reason, we give the proof of the theorems for the case M=10 using mathematical induction, and by Peano's fifth axiom make our generalizations. Comments are made in respect of the numbers (M-1), (in this case 9). Apart from our theorems facilitating mathematical operations, evidences have also been given, from different sources of the interesting properties of this class of numbers, represented in our own case by the numeral 9. The theorems neither violate the divisibility rule for 9 nor are they a consequence of it. From symmetry, a suggestion is made in respect of the possible origin of the numeration in base 10, and the case of a ten dimensional Universe reconsidered. (author). 18 refs, 1 fig., 4 tabs

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

Science.gov (United States)

Siegel, J.; Siegel, Edward Carl-Ludwig

2011-03-01

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

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

Science.gov (United States)

Carvajal, Gonzalo; Figueroa, Miguel

2014-07-01

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

Resolução de problemas aritméticos: efeito de relações de equivalência entre três diferentes formas de apresentação dos problemas Arithmetic problem-solving: effect of equivalence relations between three different forms of presenting problems

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

Effects of cognitive appraisal and mental workload factors on performance in an arithmetic task.

Science.gov (United States)

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

Mapping of arithmetic processing by navigated repetitive transcranial magnetic stimulation in patients with parietal brain tumors and correlation with postoperative outcome.

Science.gov (United States)

Ille, Sebastian; Drummer, Katharina; Giglhuber, Katrin; Conway, Neal; Maurer, Stefanie; Meyer, Bernhard; Krieg, Sandro M

2018-03-26

Preserving functionality is of significant importance during neurosurgical resection of brain tumors. Specialized centers also map further brain functions apart from motor and language functions, such as arithmetic processing (AP). The mapping of AP by navigated repetitive transcranial magnetic stimulation (nrTMS) in healthy volunteers has been demonstrated. The present study aimed to correlate the results of mapping AP with functional patient outcomes. We included 26 patients with parietal brain tumors. Due to preoperative impairment of AP, mapping was not possible in 8 patients (31%). We stimulated 52 cortical sites by nrTMS while patients performed a calculation task. Pre- and postoperatively, patients underwent a standardized number-processing and calculation test (NPCT). Tumor resection was blinded to nrTMS results, and the change in NPCT performance was correlated to resected AP-positive spots as identified by nrTMS. The resection of AP-positive sites correlated with a worsening of the postoperative NPCT result in 12 cases. In 3 cases, no AP-positive sites were resected and the postoperative NPCT result was similar to or better than preoperatively. Also, in 3 cases, the postoperative NPCT result was better than preoperatively, although AP-positive sites were resected. Despite only presenting a low number of cases, nrTMS might be a useful tool for preoperative mapping of AP. However, the reliability of the present results has to be evaluated in a larger series and by intraoperative mapping data. Copyright © 2018 Elsevier Inc. All rights reserved.

Optimizing occupational exposure measurement strategies when estimating the log-scale arithmetic mean value--an example from the reinforced plastics industry.

Science.gov (United States)

Lampa, Erik G; Nilsson, Leif; Liljelind, Ingrid E; Bergdahl, Ingvar A

2006-06-01

When assessing occupational exposures, repeated measurements are in most cases required. Repeated measurements are more resource intensive than a single measurement, so careful planning of the measurement strategy is necessary to assure that resources are spent wisely. The optimal strategy depends on the objectives of the measurements. Here, two different models of random effects analysis of variance (ANOVA) are proposed for the optimization of measurement strategies by the minimization of the variance of the estimated log-transformed arithmetic mean value of a worker group, i.e. the strategies are optimized for precise estimation of that value. The first model is a one-way random effects ANOVA model. For that model it is shown that the best precision in the estimated mean value is always obtained by including as many workers as possible in the sample while restricting the number of replicates to two or at most three regardless of the size of the variance components. The second model introduces the 'shared temporal variation' which accounts for those random temporal fluctuations of the exposure that the workers have in common. It is shown for that model that the optimal sample allocation depends on the relative sizes of the between-worker component and the shared temporal component, so that if the between-worker component is larger than the shared temporal component more workers should be included in the sample and vice versa. The results are illustrated graphically with an example from the reinforced plastics industry. If there exists a shared temporal variation at a workplace, that variability needs to be accounted for in the sampling design and the more complex model is recommended.

The Situation Model and Problem Model in Arithmetic Problem Solving%论数学问题解决中情境模型与问题模型的关系

Institute of Scientific and Technical Information of China (English)

和美君; 刘儒德

2012-01-01

情境模型与问题模型是数学问题解决研究中的两个重要概念，前者是对问题所述情境的日常化的定性表征，后者是基于图式知识对问题关键变量的数量关系表征。本文介绍了两种模型的发展历史以及目前存在的争议，并提出未来研究需要解决的问题。%Situation model and problem model are two important concepts in arithmetic problem solving and representation. However, researchers have different opinions about their definitions, roles and relationships in the process of problem solving. Therefore, our aim is to talk about their development history, discriminate the concepts, and reveal the controversies and future study direction. On the basis of general text comprehension theory （Van Dijk ＆ Kintsch, 1983）, Kintsch and Greeno （1985）first proposed the construction of problem models in arithmetic problem solving research field. They argued that problem solvers would construct textbase and problem model, and the latter one was the only high-level representation problem solvers constructed. This left other researchers unsatisfied, and many began to express their own opinions and propose the concept of the situation model. Nathan, Kintsch, and Young （1992） argued that while Kintsch and Greeno（1985） placed too much emphasis on schemata and problem models, the situation model was very important for it could make explicit the implicit conditions in the problem, and could also monitor and even correct possible mistakes in problem models. Then, Moreau and Coquin-Viennot（2003）studied the nature of representation problem solvers constructed through the information types they chose when doing different tasks, and proved that when solving problems, students would construct different representations according to different task requirements, and meanwhile, the mathematical ability of students had a great impact on the their capability of choosing relevant information to construct

Do Children Understand Fraction Addition?

Science.gov (United States)

Braithwaite, David W.; Tian, Jing; Siegler, Robert S.

2017-01-01

Many children fail to master fraction arithmetic even after years of instruction. A recent theory of fraction arithmetic (Braithwaite, Pyke, & Siegler, in press) hypothesized that this poor learning of fraction arithmetic procedures reflects poor conceptual understanding of them. To test this hypothesis, we performed three experiments…

A natural history of mathematics: George Peacock and the making of English algebra.

Science.gov (United States)

Lambert, Kevin

2013-06-01

In a series of papers read to the Cambridge Philosophical Society through the 1820s, the Cambridge mathematician George Peacock laid the foundation for a natural history of arithmetic that would tell a story of human progress from counting to modern arithmetic. The trajectory of that history, Peacock argued, established algebraic analysis as a form of universal reasoning that used empirically warranted operations of mind to think with symbols on paper. The science of counting would suggest arithmetic, arithmetic would suggest arithmetical algebra, and, finally, arithmetical algebra would suggest symbolic algebra. This philosophy of suggestion provided the foundation for Peacock's "principle of equivalent forms," which justified the practice of nineteenth-century English symbolic algebra. Peacock's philosophy of suggestion owed a considerable debt to the early Cambridge Philosophical Society culture of natural history. The aim of this essay is to show how that culture of natural history was constitutively significant to the practice of nineteenth-century English algebra.

Jumping in Arithmetic

NARCIS (Netherlands)

Visser, Albert

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

Jumping in Arithmetic

NARCIS (Netherlands)

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

Radicals in arithmetic

NARCIS (Netherlands)

W.J. Palenstijn (Willem Jan)

2014-01-01

htmlabstractLet K be a field. A radical is an element of the algebraic closure of K of which a power is contained in K. In this thesis we develop a method for determining what we call entanglement. This describes unexpected additive relations between radicals, and is encoded in an entanglement

Radicals in arithmetic

NARCIS (Netherlands)

Palenstijn, Willem Jan

2014-01-01

Let K be a field. A radical is an element of the algebraic closure of K of which a power is contained in K. In this thesis we develop a method for determining what we call entanglement. This describes unexpected additive relations between radicals, and is encoded in an entanglement group. We give

Modelling arithmetic operations

Energy Technology Data Exchange (ETDEWEB)

Shabanov-kushnarenk, Yu P

1981-01-01

The possibility of modelling finite alphabetic operators using formal intelligence theory, is explored, with the setting up of models of a 3-digit adder and a multidigit subtractor, as examples. 2 references.

Transductions in Arithmetic

NARCIS (Netherlands)

Visser, A.

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

Lourenço Filho e o moderno ensino de aritmética: produção e circulação de um modelo pedagógico - Lourenço Filho and modern teaching arithmetic: production and circulation of a model educational

Directory of Open Access Journals (Sweden)

Wagner Rodrigues Valente, Brasil

2014-09-01

Full Text Available O texto analisa a produção e a circulação de material utilizado para o ensino de Aritmética que ficou conhecido com o nome de Cartas, Mapas ou Quadros de Parker. O material teve circulação durante toda a primeira metade do século 20. A análise realizada mostra o papel de Lourenço Filho na longa permanência deste dispositivo de ensino, transformado em ícone da pedagogia moderna da matemática na escola primária.Palavras-chave: história da educação matemática, pedagogia intuitiva da aritmética, Lourenço Filho, Cartas de Parker. LOURENÇO FILHO AND MODERN TEACHING ARITHMETIC: PRODUCTION AND CIRCULATION OF A MODEL EDUCATIONALAbstractThe text examines the production and circulation of material used for teaching arithmetic which became known by the name of Tables, Maps and Charts Parker. The material was outstanding during the entire first half of the twentieth century. The analysis shows the role of Lourenço Filho long stay in this teaching device, transformed into an icon of modern pedagogy of mathematics in primary school.Key-words: history of mathematics education, object lessons of arithmetic, Lourenço Filho, Tables Parker.LOURENÇO FILHO Y LA FORMA MODERNA DE LA ENSEÑANZA DE ARITMÉTICA: PRODUCCIÓN Y DISTRIBUCIÓN DE UN MODELO EDUCATIVO ResumenEl texto tiene como objetivo analizar la producción y circulación de material utilizado para la enseñanza de la aritmética que se conoció con el nombre de tablas, mapas y gráficos Parker. El material fue excelente durante toda la primera mitad del siglo 20. El análisis pone de manifiesto el papel de Lourenço Filho como responsable de la larga persistencia de este dispositivo de enseñanza, convertido en un icono de la pedagogía moderna de las matemáticas en la escuela primaria.Palabras-clave: historia de la enseñanza de las matemáticas, pedagogía aritmética intuitiva, Lourenço Filho, Tablas Parker. LOURENÇO FILHO ET L'ENSEIGNEMENT MODERNE DU CALCUL: PRODUCTION ET

Changes of brain response induced by simulated weightlessness

Science.gov (United States)

Wei, Jinhe; Yan, Gongdong; Guan, Zhiqiang

The characteristics change of brain response was studied during 15° head-down tilt (HDT) comparing with 45° head-up tilt (HUT). The brain responses evaluated included the EEG power spectra change at rest and during mental arithmetic, and the event-related potentials (ERPs) of somatosensory, selective attention and mental arithmetic activities. The prominent feature of brain response change during HDT revealed that the brain function was inhibited to some extent. Such inhibition included that the significant increment of "40Hz" activity during HUT arithmetic almost disappeared during HDT arithmetic, and that the positive-potential effect induced by HDT presented in all kinds of ERPs measured, but the slow negative wave reflecting mental arithmetic and memory process was elongated. These data suggest that the brain function be affected profoundly by the simulated weightlessness, therefore, the brain function change during space flight should be studied systematically.

The semantic system is involved in mathematical problem solving.

Science.gov (United States)

Zhou, Xinlin; Li, Mengyi; Li, Leinian; Zhang, Yiyun; Cui, Jiaxin; Liu, Jie; Chen, Chuansheng

2018-02-01

Numerous studies have shown that the brain regions around bilateral intraparietal cortex are critical for number processing and arithmetical computation. However, the neural circuits for more advanced mathematics such as mathematical problem solving (with little routine arithmetical computation) remain unclear. Using functional magnetic resonance imaging (fMRI), this study (N = 24 undergraduate students) compared neural bases of mathematical problem solving (i.e., number series completion, mathematical word problem solving, and geometric problem solving) and arithmetical computation. Direct subject- and item-wise comparisons revealed that mathematical problem solving typically had greater activation than arithmetical computation in all 7 regions of the semantic system (which was based on a meta-analysis of 120 functional neuroimaging studies on semantic processing). Arithmetical computation typically had greater activation in the supplementary motor area and left precentral gyrus. The results suggest that the semantic system in the brain supports mathematical problem solving. Copyright © 2017 Elsevier Inc. All rights reserved.

The spectrum of hyperbolic surfaces

CERN Document Server

Bergeron, Nicolas

2016-01-01

This text is an introduction to the spectral theory of the Laplacian on compact or finite area hyperbolic surfaces. For some of these surfaces, called “arithmetic hyperbolic surfaces”, the eigenfunctions are of arithmetic nature, and one may use analytic tools as well as powerful methods in number theory to study them. After an introduction to the hyperbolic geometry of surfaces, with a special emphasis on those of arithmetic type, and then an introduction to spectral analytic methods on the Laplace operator on these surfaces, the author develops the analogy between geometry (closed geodesics) and arithmetic (prime numbers) in proving the Selberg trace formula. Along with important number theoretic applications, the author exhibits applications of these tools to the spectral statistics of the Laplacian and the quantum unique ergodicity property. The latter refers to the arithmetic quantum unique ergodicity theorem, recently proved by Elon Lindenstrauss. The fruit of several graduate level courses at Orsay...

Gauss Elimination: Workhorse of Linear Algebra.

Science.gov (United States)

1995-08-05

linear algebra computation for solving systems, computing determinants and determining the rank of matrix. All of these are discussed in varying contexts. These include different arithmetic or algebraic setting such as integer arithmetic or polynomial rings as well as conventional real (floating-point) arithmetic. These have effects on both accuracy and complexity analyses of the algorithm. These, too, are covered here. The impact of modern parallel computer architecture on GE is also

EEG Correlates of the Flow State: A Combination of Increased Frontal Theta and Moderate Frontocentral Alpha Rhythm in the Mental Arithmetic Task

Directory of Open Access Journals (Sweden)

Kenji Katahira

2018-03-01

Full Text Available Flow experience is a subjective state experienced during holistic involvement in a certain activity, which has been reported to function as a factor promoting motivation, skill development, and better performance in the activity. To verify the positive effects of flow and develop a method to utilize it, the establishment of a reliable measurement of the flow state is essential. The present study utilized an electroencephalogram (EEG during an experimentally evoked flow state and examined the possibility of objective measurement of immediate flow. A total of 16 participants (10 males, 6 females participated in the experiment that employed a mental arithmetic task developed in a previous study. Post-trial self-report of the flow state and EEG during task execution were measured and compared among three conditions (Boredom, Flow, and Overload that had different levels of task difficulty. Furthermore, the correlations between subjective flow items and EEG activity were examined. As expected, the ratings on the subjective evaluation items representing the flow state were the highest in the Flow condition. Regarding the EEG data, theta activities in the frontal areas were higher in the Flow and the Overload conditions than in the Boredom condition, and alpha activity in the frontal areas and the right central area gradually increased depending on the task difficulty. These EEG activities correlated with self-reported flow experience, especially items related to the concentration on the task and task difficulty. From the results, the flow state was characterized by increased theta activities in the frontal areas and moderate alpha activities in the frontal and central areas. The former may be related to a high level of cognitive control and immersion in task, and the latter suggests that the load on the working memory was not excessive. The findings of this study suggest the possibility of distinguishing the flow state from other states using multiple

EEG Correlates of the Flow State: A Combination of Increased Frontal Theta and Moderate Frontocentral Alpha Rhythm in the Mental Arithmetic Task.

Science.gov (United States)

Katahira, Kenji; Yamazaki, Yoichi; Yamaoka, Chiaki; Ozaki, Hiroaki; Nakagawa, Sayaka; Nagata, Noriko

2018-01-01

Flow experience is a subjective state experienced during holistic involvement in a certain activity, which has been reported to function as a factor promoting motivation, skill development, and better performance in the activity. To verify the positive effects of flow and develop a method to utilize it, the establishment of a reliable measurement of the flow state is essential. The present study utilized an electroencephalogram (EEG) during an experimentally evoked flow state and examined the possibility of objective measurement of immediate flow. A total of 16 participants (10 males, 6 females) participated in the experiment that employed a mental arithmetic task developed in a previous study. Post-trial self-report of the flow state and EEG during task execution were measured and compared among three conditions (Boredom, Flow, and Overload) that had different levels of task difficulty. Furthermore, the correlations between subjective flow items and EEG activity were examined. As expected, the ratings on the subjective evaluation items representing the flow state were the highest in the Flow condition. Regarding the EEG data, theta activities in the frontal areas were higher in the Flow and the Overload conditions than in the Boredom condition, and alpha activity in the frontal areas and the right central area gradually increased depending on the task difficulty. These EEG activities correlated with self-reported flow experience, especially items related to the concentration on the task and task difficulty. From the results, the flow state was characterized by increased theta activities in the frontal areas and moderate alpha activities in the frontal and central areas. The former may be related to a high level of cognitive control and immersion in task, and the latter suggests that the load on the working memory was not excessive. The findings of this study suggest the possibility of distinguishing the flow state from other states using multiple EEG activities

Specific learning disorder: prevalence and gender differences.

Directory of Open Access Journals (Sweden)

Kristina Moll

Full Text Available Comprehensive models of learning disorders have to consider both isolated learning disorders that affect one learning domain only, as well as comorbidity between learning disorders. However, empirical evidence on comorbidity rates including all three learning disorders as defined by DSM-5 (deficits in reading, writing, and mathematics is scarce. The current study assessed prevalence rates and gender ratios for isolated as well as comorbid learning disorders in a representative sample of 1633 German speaking children in 3rd and 4th Grade. Prevalence rates were analysed for isolated as well as combined learning disorders and for different deficit criteria, including a criterion for normal performance. Comorbid learning disorders occurred as frequently as isolated learning disorders, even when stricter cutoff criteria were applied. The relative proportion of isolated and combined disorders did not change when including a criterion for normal performance. Reading and spelling deficits differed with respect to their association with arithmetic problems: Deficits in arithmetic co-occurred more often with deficits in spelling than with deficits in reading. In addition, comorbidity rates for arithmetic and reading decreased when applying stricter deficit criteria, but stayed high for arithmetic and spelling irrespective of the chosen deficit criterion. These findings suggest that the processes underlying the relationship between arithmetic and reading might differ from those underlying the relationship between arithmetic and spelling. With respect to gender ratios, more boys than girls showed spelling deficits, while more girls were impaired in arithmetic. No gender differences were observed for isolated reading problems and for the combination of all three learning disorders. Implications of these findings for assessment and intervention of learning disorders are discussed.

The arithmetic of strings

International Nuclear Information System (INIS)

Freund, P.G.O.

1988-01-01

According to the author nobody has succeeded as yet in extracting any new numbers from string theory. This paper discusses how if one cannot get new numbers from string theory, maybe one can get new strings out of number theory. Number theory is generally regarded as the purest form of mathematics. So how can it conceivably make contact with physics which aims at describing nature? The author discusses how the connecting link of these two disciplines is provided by the compact Riemann surfaces. These appear as world sheets of interacting strings. For instance, string-string scattering at the three-loop level involves the four external strings attaching themselves to a genus three compact surface

On Spectrum and Arithmetic

Indian Academy of Sciences (India)

C. S. Rajan

2006-11-11

Nov 11, 2006 ... In other words, knowing the sounds that emanate from the drum can you figure out the shape of the drum? ... other words it is the lift of the metric to a natural second order differential operator. self-adjoint. ... It is expected in some fundamental sense that these spaces are universal for the class of algebraic ...

Topics in arithmetic combinatorics

OpenAIRE

Sanders, Tom

2007-01-01

E-thesis pagination differs from approved hard bound copy, Cambridge University Library classmark: PhD.30726 This thesis is chiefly concerned with a classical conjecture of Littlewood's regarding the L^1-norm of the Fourier transform, and the closely related idempotent theorem. The vast majority of the results regarding these problems are, in some sense, qualitative or at the very least infinitary and it has become increasingly apparent that a quantitative state of affairs is desirable. ...

Foundation of Basic Arithmetic

Indian Academy of Sciences (India)

with carpenters and farmers. When the count is large, it is .... the most profound ideas in the history of mathematics. Because of its simplicity it ... civilized people. However, the archaeological discoveries .... men produced by antiquity. Figure 7.

Supergeometry and arithmetic geometry

International Nuclear Information System (INIS)

Schwarz, A.; Shapiro, I.

2006-01-01

We define a superspace over a ring R as a functor on a subcategory of the category of supercommutative R-algebras. As an application the notion of a p-adic superspace is introduced and used to give a transparent construction of the Frobenius map on p-adic cohomology of a smooth projective variety over Z p (the ring of p-adic integers)

Compositional Verification with Abstraction, Learning, and SAT Solving

Science.gov (United States)

2015-05-01

arithmetic, and bit-vectors (currently, via bit-blasting). The front-end is based on an existing tool called UFO [8] which converts C programs to the Horn...supports propositional logic, linear arithmetic, and bit-vectors (via bit-blasting). The front-end is based on the tool UFO [8]. It encodes safety of...tool UFO [8]. The encoding in Horn-SMT only uses the theory of Linear Rational Arithmetic. All experiments were carried out on an Intel R© CoreTM2 Quad

Computations of Eisenstein series on Fuchsian groups

Science.gov (United States)

Avelin, Helen

2008-09-01

We present numerical investigations of the value distribution and distribution of Fourier coefficients of the Eisenstein series E(z;s) on arithmetic and non-arithmetic Fuchsian groups. Our numerics indicate a Gaussian limit value distribution for a real-valued rotation of E(z;s) as operatorname{Re} sD1/2 , operatorname{Im} sto infty and also, on non-arithmetic groups, a complex Gaussian limit distribution for E(z;s) when operatorname{Re} s>1/2 near 1/2 and operatorname{Im} sto infty , at least if we allow operatorname{Re} sto 1/2 at some rate. Furthermore, on non-arithmetic groups and for fixed s with operatorname{Re} s ge 1/2 near 1/2 , our numerics indicate a Gaussian limit distribution for the appropriately normalized Fourier coefficients.

Pascal-SC a computer language for scientific computation

CERN Document Server

Bohlender, Gerd; von Gudenberg, Jürgen Wolff; Rheinboldt, Werner; Siewiorek, Daniel

1987-01-01

Perspectives in Computing, Vol. 17: Pascal-SC: A Computer Language for Scientific Computation focuses on the application of Pascal-SC, a programming language developed as an extension of standard Pascal, in scientific computation. The publication first elaborates on the introduction to Pascal-SC, a review of standard Pascal, and real floating-point arithmetic. Discussions focus on optimal scalar product, standard functions, real expressions, program structure, simple extensions, real floating-point arithmetic, vector and matrix arithmetic, and dynamic arrays. The text then examines functions a

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

International Nuclear Information System (INIS)

Wang Jihong; Wang Lianghou; Fang Zongliang

2011-01-01

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

Ratio of geometric means to analyze continuous outcomes in meta-analysis: comparison to mean differences and ratio of arithmetic means using empiric data and simulation.

Science.gov (United States)

Friedrich, Jan O; Adhikari, Neill K J; Beyene, Joseph

2012-07-30

Meta-analyses pooling continuous outcomes can use mean differences (MD), standardized MD (MD in pooled standard deviation units, SMD), or ratio of arithmetic means (RoM). Recently, ratio of geometric means using ad hoc (RoGM (ad hoc) ) or Taylor series (RoGM (Taylor) ) methods for estimating variances have been proposed as alternative effect measures for skewed continuous data. Skewed data are suggested for summary measures of clinical parameters restricted to positive values which have large coefficients of variation (CV). Our objective was to compare performance characteristics of RoGM (ad hoc) and RoGM (Taylor) to MD, SMD, and RoM. We used empiric data from systematic reviews reporting continuous outcomes and selected from each the meta-analysis with the most and at least 5 trials (Cochrane Database [2008, Issue 1]). We supplemented this with simulations conducted with representative parameters. Pooled results were calculated using each effect measure. Of the reviews, 232/5053 met the inclusion criteria. Empiric data and simulation showed that RoGM (ad hoc) exhibits more extreme treatment effects and greater heterogeneity than all other effect measures. Compared with MD, SMD, and RoM, RoGM (Taylor) exhibits similar treatment effects, more heterogeneity when CV ≤0.7, and less heterogeneity when CV > 0.7. In conclusion, RoGM (Taylor) may be considered for pooling continuous outcomes in meta-analysis when data are skewed, but RoGM (ad hoc) should not be used. However, clinicians' lack of familiarity with geometric means combined with acceptable performance characteristics of RoM in most situations suggests that RoM may be the preferable ratio method for pooling continuous outcomes in meta-analysis. Copyright © 2012 John Wiley & Sons, Ltd.

A Ternary Hybrid EEG-NIRS Brain-Computer Interface for the Classification of Brain Activation Patterns during Mental Arithmetic, Motor Imagery, and Idle State.

Science.gov (United States)

Shin, Jaeyoung; Kwon, Jinuk; Im, Chang-Hwan

2018-01-01

The performance of a brain-computer interface (BCI) can be enhanced by simultaneously using two or more modalities to record brain activity, which is generally referred to as a hybrid BCI. To date, many BCI researchers have tried to implement a hybrid BCI system by combining electroencephalography (EEG) and functional near-infrared spectroscopy (NIRS) to improve the overall accuracy of binary classification. However, since hybrid EEG-NIRS BCI, which will be denoted by hBCI in this paper, has not been applied to ternary classification problems, paradigms and classification strategies appropriate for ternary classification using hBCI are not well investigated. Here we propose the use of an hBCI for the classification of three brain activation patterns elicited by mental arithmetic, motor imagery, and idle state, with the aim to elevate the information transfer rate (ITR) of hBCI by increasing the number of classes while minimizing the loss of accuracy. EEG electrodes were placed over the prefrontal cortex and the central cortex, and NIRS optodes were placed only on the forehead. The ternary classification problem was decomposed into three binary classification problems using the "one-versus-one" (OVO) classification strategy to apply the filter-bank common spatial patterns filter to EEG data. A 10 × 10-fold cross validation was performed using shrinkage linear discriminant analysis (sLDA) to evaluate the average classification accuracies for EEG-BCI, NIRS-BCI, and hBCI when the meta-classification method was adopted to enhance classification accuracy. The ternary classification accuracies for EEG-BCI, NIRS-BCI, and hBCI were 76.1 ± 12.8, 64.1 ± 9.7, and 82.2 ± 10.2%, respectively. The classification accuracy of the proposed hBCI was thus significantly higher than those of the other BCIs ( p < 0.005). The average ITR for the proposed hBCI was calculated to be 4.70 ± 1.92 bits/minute, which was 34.3% higher than that reported for a previous binary hBCI study.

On formally undecidable propositions of Principia mathematica and related systems

CERN Document Server

Gödel, Kurt

1962-01-01

In 1931, a young Austrian mathematician published an epoch-making paper containing one of the most revolutionary ideas in logic since Aristotle. Kurt Giidel maintained, and offered detailed proof, that in any arithmetic system, even in elementary parts of arithmetic, there are propositions which cannot be proved or disproved within the system. It is thus uncertain that the basic axioms of arithmetic will not give rise to contradictions. The repercussions of this discovery are still being felt and debated in 20th-century mathematics.The present volume reprints the first English translation of

Parallel Construction of Irreducible Polynomials

DEFF Research Database (Denmark)

Frandsen, Gudmund Skovbjerg

Let arithmetic pseudo-NC^k denote the problems that can be solved by log space uniform arithmetic circuits over the finite prime field GF(p) of depth O(log^k (n + p)) and size polynomial in (n + p). We show that the problem of constructing an irreducible polynomial of specified degree over GF(p) ...... of polynomials is in arithmetic NC^3. Our algorithm works over any field and compared to other known algorithms it does not assume the ability to take p'th roots when the field has characteristic p....

O caderno de uma professora-aluna e as propostas para o ensino da aritmética na escola ativa (Minas Gerais, década de 1930 - A teacher’s notebook and the proposals for teaching arithmetic in active school (Minas Gerais, 1930

Directory of Open Access Journals (Sweden)

Diogo Alves de Faria Reis

2014-01-01

Full Text Available O artigo versa sobre o caderno de Metodologia da Aritmética de Imene Guimarães, aluna da professora Alda Lodi (1898-2002 na segunda turma da Escola de Aperfeiçoamento de Minas Gerais. Alda Lodi participou do grupo de docentes enviadas pelo governo mineiro ao Teacher’s College, nos Estados Unidos, para se prepararem para atuar na formação de professoras primárias em exercício no contexto das reformas educacionais de 1927-1928. Considerando a relevância, as potencialidades e os limites dos cadernos escolares como fonte, os registros desse caderno de 1932 são estudados e cotejados com outros materiais, em busca de uma compreensão inicial dos modos de apropriação das propostas para o ensino da aritmética no momento da adesão ao ideário da escola ativaem Minas Gerais.Palavras-chave: cadernos escolares, metodologia da aritmética, Escola de Aperfeiçoamento de Minas Gerais, Alda Lodi, história da educação matemática brasileira.A TEACHER’S NOTEBOOK AND THE PROPOSALS FOR TEACHING ARITHMETIC IN ACTIVE SCHOOL (MINAS GERAIS, 1930AbstractThe article focuses on a notebook which belonged to Imene Guimarães, a student of professor Alda Lodi (1898-2002 in Escola de Aperfeiçoamento, an institution of continuing education for teachers created by educational reforms promoted by the government of the state of Minas Gerais in 1927-1928. Alda Lodi taught Methodology of Arithmetic in this institution. Considering the relevance, potentialities and limitations of school notebooks as a source for the history of education, the records of this notebook of 1932 are studied and compared with other materials for the purpose of an initial understanding of the modes of appropriation of proposals for renovating the teaching of arithmetic according to the ideas associated to active school in Minas Gerais.Keywords: school notebooks, methodology of arithmetic, Escola de Aperfeiçoamento de Minas Gerais, Alda Lodi, history of mathematics education in

Context adaptive coding of bi-level images

DEFF Research Database (Denmark)

Forchhammer, Søren

2008-01-01

With the advent of sequential arithmetic coding, the focus of highly efficient lossless data compression is placed on modelling the data. Rissanen's Algorithm Context provided an elegant solution to universal coding with optimal convergence rate. Context based arithmetic coding laid the grounds f...

A condition for the overflow stability of second-order digital filters that is satisfied by all scaled state-space structures using saturation

NARCIS (Netherlands)

Ritzerfeld, J.H.F.

1989-01-01

A set of conditions is derived that ensures overflow stability of second-order digital filters for different classes of overflow arithmetics, involving only the elements of the state-transition matrix. The well-known arithmetic saturation, zeroing, and two's-complement lead to different stability

The "Number Crunch" Game: A Simple Vehicle for Building Algebraic Reasoning Skills

Science.gov (United States)

Sugden, Steve

2012-01-01

A newspaper numbers game based on simple arithmetic relationships is discussed. Its potential to give students of elementary algebra practice in semi-"ad hoc" reasoning and to build general arithmetic reasoning skills is explored. (Contains 3 figures, 7 tables and 3 notes.)

Brain correlates of mathematical competence in processing mathematical representations

Directory of Open Access Journals (Sweden)

Roland H. Grabner

2011-11-01

Full Text Available The ability to extract numerical information from different representation formats (e.g., equations, tables, or diagrams is a key component of mathematical competence but little is known about its neural correlate. Previous studies comparing mathematically less and more competent adults have focused on mental arithmetic and reported differences in left angular gyrus activity which were interpreted to reflect differential reliance on arithmetic fact retrieval during problem solving. The aim of the present functional magnetic resonance imaging (fMRI study was to investigate the brain correlates of mathematical competence in a task requiring the processing of typical mathematical representations. Twenty-eight adults of lower and higher mathematical competence worked on a representation matching task in which they had to evaluate whether the numerical information of a symbolic equation matches that of a bar chart. Two task conditions without and one condition with arithmetic demands were administered. Both competence groups performed equally well in the non-arithmetic conditions and only differed in accuracy in the condition requiring calculation. Activation contrasts between the groups revealed consistently stronger left angular gyrus activation in the more competent individuals across all three task conditions. The finding of competence-related activation differences independently of arithmetic demands suggests that more and less competent individuals differ in a cognitive process other than arithmetic fact retrieval. Specifically, it is argued that the stronger left angular gyrus activity in the more competent adults may reflect their higher proficiency in processing mathematical symbols. Moreover, the study demonstrates competence-related parietal activation differences that were not accompanied by differential experimental performance.

Pre-schoolers Learn at Home.

Science.gov (United States)

Smith, Penny

1985-01-01

Reviews: "ArithMagic (Counting, Addition, Subtraction)" which uses graphics to illustrate/review basic arithmetic concepts; "The Sweet Shop" which uses graphics (and a character called Mr. Jellybean) to teach arithmetic concepts; and "Math Magic," a monster-filled arcade game that teaches addition and subtraction.…

Modular forms and special cycles on Shimura curves (AM-161)

CERN Document Server

Kudla, Stephen S; Yang, Tonghai

2006-01-01

Modular Forms and Special Cycles on Shimura Curves is a thorough study of the generating functions constructed from special cycles, both divisors and zero-cycles, on the arithmetic surface ""M"" attached to a Shimura curve ""M"" over the field of rational numbers. These generating functions are shown to be the q-expansions of modular forms and Siegel modular forms of genus two respectively, valued in the Gillet-Soulé arithmetic Chow groups of ""M"". The two types of generating functions are related via an arithmetic inner product formula. In addition, an analogue of the classical Siegel-Weil

Fast reversible wavelet image compressor

Science.gov (United States)

Kim, HyungJun; Li, Ching-Chung

1996-10-01

We present a unified image compressor with spline biorthogonal wavelets and dyadic rational filter coefficients which gives high computational speed and excellent compression performance. Convolutions with these filters can be preformed by using only arithmetic shifting and addition operations. Wavelet coefficients can be encoded with an arithmetic coder which also uses arithmetic shifting and addition operations. Therefore, from the beginning to the end, the while encoding/decoding process can be done within a short period of time. The proposed method naturally extends form the lossless compression to the lossy but high compression range and can be easily adapted to the progressive reconstruction.

Teaching Linear Algebra: Proceeding More Efficiently by Staying Comfortably within Z

Science.gov (United States)

Beaver, Scott

2015-01-01

For efficiency in a linear algebra course the instructor may wish to avoid the undue arithmetical distractions of rational arithmetic. In this paper we explore how to write fraction-free problems of various types including elimination, matrix inverses, orthogonality, and the (non-normalizing) Gram-Schmidt process.

Hybridized centroid technique for 3D Molodensky-Badekas ...

African Journals Online (AJOL)

In view of this, the present study developed and tested two new hybrid centroid techniques known as the harmonic-quadratic mean and arithmetic-quadratic mean centroids. The proposed hybrid approaches were compared with the geometric mean, harmonic mean, median, quadratic mean and arithmetic mean. In addition ...

A quasi-spectral method for Cauchy problem of 2/D Laplace equation on an annulus

Science.gov (United States)

Saito, Katsuyoshi; Nakada, Manabu; Iijima, Kentaro; Onishi, Kazuei

2005-01-01

Real numbers are usually represented in the computer as a finite number of digits hexa-decimal floating point numbers. Accordingly the numerical analysis is often suffered from rounding errors. The rounding errors particularly deteriorate the precision of numerical solution in inverse and ill-posed problems. We attempt to use a multi-precision arithmetic for reducing the rounding error evil. The use of the multi-precision arithmetic system is by the courtesy of Dr Fujiwara of Kyoto University. In this paper we try to show effectiveness of the multi-precision arithmetic by taking two typical examples; the Cauchy problem of the Laplace equation in two dimensions and the shape identification problem by inverse scattering in three dimensions. It is concluded from a few numerical examples that the multi-precision arithmetic works well on the resolution of those numerical solutions, as it is combined with the high order finite difference method for the Cauchy problem and with the eigenfunction expansion method for the inverse scattering problem.

Non-unique factorizations algebraic, combinatorial and analytic theory

CERN Document Server

Geroldinger, Alfred

2006-01-01

From its origins in algebraic number theory, the theory of non-unique factorizations has emerged as an independent branch of algebra and number theory. Focused efforts over the past few decades have wrought a great number and variety of results. However, these remain dispersed throughout the vast literature. For the first time, Non-Unique Factorizations: Algebraic, Combinatorial, and Analytic Theory offers a look at the present state of the theory in a single, unified resource.Taking a broad look at the algebraic, combinatorial, and analytic fundamentals, this book derives factorization results and applies them in concrete arithmetical situations using appropriate transfer principles. It begins with a basic introduction that can be understood with knowledge of standard basic algebra. The authors then move to the algebraic theory of monoids, arithmetic theory of monoids, the structure of sets of lengths, additive group theory, arithmetical invariants, and the arithmetic of Krull monoids. They also provide a s...

A quasi-spectral method for Cauchy problem of 2/D Laplace equation on an annulus

International Nuclear Information System (INIS)

Saito, Katsuyoshi; Nakada, Manabu; Iijima, Kentaro; Onishi, Kazuei

2005-01-01

Real numbers are usually represented in the computer as a finite number of digits hexa-decimal floating point numbers. Accordingly the numerical analysis is often suffered from rounding errors. The rounding errors particularly deteriorate the precision of numerical solution in inverse and ill-posed problems. We attempt to use a multi-precision arithmetic for reducing the rounding error evil. The use of the multi-precision arithmetic system is by the courtesy of Dr Fujiwara of Kyoto University. In this paper we try to show effectiveness of the multi-precision arithmetic by taking two typical examples; the Cauchy problem of the Laplace equation in two dimensions and the shape identification problem by inverse scattering in three dimensions. It is concluded from a few numerical examples that the multi-precision arithmetic works well on the resolution of those numerical solutions, as it is combined with the high order finite difference method for the Cauchy problem and with the eigenfunction expansion method for the inverse scattering problem

Determination of serum IgD radioimmunoassay

Energy Technology Data Exchange (ETDEWEB)

Fayol, V.; Hartmann, D.J.; Sabbagh, I.; Ville, G.

1986-01-01

We describe a sensitive liquid phase radioimmunoassay for serum IgD. Extreme values obtained from 85 control patients sera are 0.2 and 121 mg/l with an arithmetic mean of 25 mg/l. In atopic patients (with high serum IgE levels), arithmetic mean is 47 mg/l.

Software For Computing Selected Functions

Science.gov (United States)

Grant, David C.

1992-01-01

Technical memorandum presents collection of software packages in Ada implementing mathematical functions used in science and engineering. Provides programmer with function support in Pascal and FORTRAN, plus support for extended-precision arithmetic and complex arithmetic. Valuable for testing new computers, writing computer code, or developing new computer integrated circuits.

The Developmental Onset of Symbolic Approximation: Beyond Nonsymbolic Representations, The Language of Numbers Matters

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Iro eXenidou-Dervou

2015-04-01

Full Text Available Symbolic (i.e., with Arabic numerals approximate arithmetic with large numerosities is an important predictor of mathematics. It was previously evidenced to onset before formal schooling at the kindergarten age (Gilmore et al., 2007 and was assumed to map onto pre-existing nonsymbolic (i.e., abstract magnitudes representations. With a longitudinal study (Experiment 1, we show, for the first time, that nonsymbolic and symbolic arithmetic demonstrate different developmental trajectories. In contrast to Gilmore et al.’s (2007 findings, Experiment 1 showed that symbolic arithmetic onsets in grade 1, with the start of formal schooling, not earlier. Gilmore et al. (2007 had examined English-speaking children, whereas we assessed a large Dutch-speaking sample. The Dutch language for numbers can be cognitively more demanding, for example, due to the inversion property in numbers above twenty. Thus, for instance, the number 48 is named in Dutch achtenveertig (eight and forty instead of forty eight. To examine the effect of the language of numbers, we conducted a cross-cultural study with English- and Dutch-speaking children that had similar SES and math achievement skills (Experiment 2. Results demonstrated that Dutch-speaking kindergarteners lagged behind English-speaking children in symbolic arithmetic, not nonsymbolic and demonstrated a WM overload in symbolic arithmetic, not nonsymbolic. Also, we show for the first time that the ability to name two-digit numbers highly correlates with symbolic approximate arithmetic not nonsymbolic. Our experiments empirically demonstrate that the symbolic number system is modulated more by development and education than the nonsymbolic system. Also, in contrast to the nonsymbolic system, the symbolic system is modulated by language.

Teacher Actions to Facilitate Early Algebraic Reasoning

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Hunter, Jodie

2015-01-01

In recent years there has been an increased emphasis on integrating the teaching of arithmetic and algebra in primary school classrooms. This requires teachers to develop links between arithmetic and algebra and use pedagogical actions that facilitate algebraic reasoning. Drawing on findings from a classroom-based study, this paper provides an…

Determination of serum IgD radioimmunoassay

International Nuclear Information System (INIS)

Fayol, V.; Hartmann, D.J.; Sabbagh, I.; Ville, G.

1986-01-01

We describe a sensitive liquid phase radioimmunoassay for serum IgD. Extreme values obtained from 85 control patients sera are 0.2 and 121 mg/l with an arithmetic mean of 25 mg/l. In atopic patients (with high serum IgE levels), arithmetic mean is 47 mg/l [fr

Remedial Instruction to Enhance Mathematical Ability of Dyscalculics

Science.gov (United States)

Kumar, S. Praveen; Raja, B. William Dharma

2012-01-01

The ability to do arithmetic calculations is essential to school-based learning and skill development in an information rich society. Arithmetic is a basic academic skill that is needed for learning which includes the skills such as counting, calculating, reasoning etc. that are used for performing mathematical calculations. Unfortunately, many…

The Teachers' Views on Soroban Abacus Training

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Altiparmak, Kemal

2016-01-01

Soroban abacus training is called as mental arithmetic training in our country. It is known for mental arithmetic to increase the ability of four mode operations. Besides this, how is the situation for the students which are having Soroban abacus training in the terms of problem solving abilities, creativity, development of concepts, attraction…

Sign Language for K-8 Mathematics by 3D Interactive Animation

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Adamo-Villani, Nicoletta; Doublestein, John; Martin, Zachary

2005-01-01

We present a new highly interactive computer animation tool to increase the mathematical skills of deaf children. We aim at increasing the effectiveness of (hearing) parents in teaching arithmetic to their deaf children, and the opportunity of deaf children to learn arithmetic via interactive media. Using state-of-the-art computer animation…

Early Integration of Tutorial Support in Beginning Algebra

Science.gov (United States)

Copus, Colleen; McKinney, Betsy

2016-01-01

Anecdotal observations reveal that most students with strong arithmetic skills will succeed in the Beginning Algebra course even if they have no previous experience with algebra. In trying to quantify this with an initial teacher-created survey of arithmetic skills, it was observed, for three consecutive semesters, that students who scored in the…

Managing Your Mathematics Program: A Total System. A Guide to the U-SAIL Basic Mathematics System.

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Hales, Carma M.; Jones, Maurine E.

The Utah System Approach to Individual Learning (U-SAIL) Mathematics System was developed to make it possible for teachers to provide excellence in arithmetic instruction. It is based on the premise that in order to teach arithmetic well, teachers must accurately assess, teach directly, provide students with focused practice, corrective feedback,…

Developing an Energy Policy for the United States

Science.gov (United States)

Keefe, Pat

2014-01-01

Al Bartlett's video "Arithmetic, Population, and Energy" spells out many of the complex issues related to energy use in our society. Bartlett makes the point that basic arithmetic is the fundamental obstacle preventing us from being able to grasp the relationships between energy consumption, population, and lifestyles. In an earlier…

Fulltext PDF

Indian Academy of Sciences (India)

The Arithmetic Mean – Geometric Mean – Harmonic. Mean: Inequalities and a Spectrum of Applications. The Arithmetic Mean – Geometric Mean – Harmonic Mean inequality, AM–GM–HM inequality in short, is one of the fundamental inequalities in Algebra, and it is used exten- sively in olympiad mathematics to solve many ...

Arithmetics, geometry and conformal fields

CERN Document Server

Itzykson, Claude

1992-03-17

The last few years have witnessed a remarkeble conjunction of methods in such diverse domains as strings and topological field theory, two dimensional statistical physics, classical and quantum integrable systems. The lectures will aim to present some of the underlying mathematics at an elementary and pedagogical level, for their intrinsic value.

Cubic forms algebra, geometry, arithmetic

CERN Document Server

Manin, Yu I

1986-01-01

Since this book was first published in English, there has been important progress in a number of related topics. The class of algebraic varieties close to the rational ones has crystallized as a natural domain for the methods developed and expounded in this volume. For this revised edition, the original text has been left intact (except for a few corrections) and has been brought up to date by the addition of an Appendix and recent references.The Appendix sketches some of the most essential new results, constructions and ideas, including the solutions of the Luroth and Zariski problems, the th

Cardinal arithmetic in weak theories

NARCIS (Netherlands)

Visser, A.

In this paper we develop the theory of cardinals in the theory COPY. This is the theory of two total, jointly injective binary predicates in a second order version, where we may quantify over binary relations. The only second order axioms of the theory are the axiom asserting the existence of an

Efficient Probabilistic Diagnostics for Electrical Power Systems

Science.gov (United States)

Mengshoel, Ole J.; Chavira, Mark; Cascio, Keith; Poll, Scott; Darwiche, Adnan; Uckun, Serdar

2008-01-01

We consider in this work the probabilistic approach to model-based diagnosis when applied to electrical power systems (EPSs). Our probabilistic approach is formally well-founded, as it based on Bayesian networks and arithmetic circuits. We investigate the diagnostic task known as fault isolation, and pay special attention to meeting two of the main challenges . model development and real-time reasoning . often associated with real-world application of model-based diagnosis technologies. To address the challenge of model development, we develop a systematic approach to representing electrical power systems as Bayesian networks, supported by an easy-to-use speci.cation language. To address the real-time reasoning challenge, we compile Bayesian networks into arithmetic circuits. Arithmetic circuit evaluation supports real-time diagnosis by being predictable and fast. In essence, we introduce a high-level EPS speci.cation language from which Bayesian networks that can diagnose multiple simultaneous failures are auto-generated, and we illustrate the feasibility of using arithmetic circuits, compiled from Bayesian networks, for real-time diagnosis on real-world EPSs of interest to NASA. The experimental system is a real-world EPS, namely the Advanced Diagnostic and Prognostic Testbed (ADAPT) located at the NASA Ames Research Center. In experiments with the ADAPT Bayesian network, which currently contains 503 discrete nodes and 579 edges, we .nd high diagnostic accuracy in scenarios where one to three faults, both in components and sensors, were inserted. The time taken to compute the most probable explanation using arithmetic circuits has a small mean of 0.2625 milliseconds and standard deviation of 0.2028 milliseconds. In experiments with data from ADAPT we also show that arithmetic circuit evaluation substantially outperforms joint tree propagation and variable elimination, two alternative algorithms for diagnosis using Bayesian network inference.

Computing GA_{5} index of armchair polyhex nanotube

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Mohammad Reza Farahani

2014-10-01

Full Text Available The fifth geometric-arithmetic index of a graph $G$ is defined to be GA_5(G. This index was introduced by  A. Graovac et al.  in 2011. In this paper, we give explicit formulas for the fifth geometric-arithmetic index of a family of Hexagonal Nanotubes namely: Armchair Polyhex Nanotubes.

The Effectiveness of Korean Number Naming on Insight into Numbers in Dutch Students with Mild Intellectual Disabilities

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Van Luit, Johannes E. H.; Van der Molen, Mariet J.

2011-01-01

Background: Children from Asian countries score higher on early years' arithmetic tests than children from Europe or the United States of America. An explanation for these differences may be the way numbers are named. A clear ten-structure like in the Korean language method leads to a better insight into numbers and arithmetic skills. This…

Comments on Beckmann's Uniform Reducts

OpenAIRE

Cook, Stephen

2006-01-01

Arnold Beckmann defined the uniform reduct of a propositional proof system f to be the set of those bounded arithmetical formulas whose propositional translations have polynomial size f-proofs. We prove that the uniform reduct of f + Extended Frege consists of all true bounded arithmetical formulas iff f + Extended Frege simulates every proof system.

Cued Recall from Image and Sentence Memory: A Shift from Episodic to Identical Elements Representation

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Rickard, Timothy C.; Bajic, Daniel

2006-01-01

The applicability of the identical elements (IE) model of arithmetic fact retrieval (T. C. Rickard, A. F. Healy, & L. E. Bourne, 1994) to cued recall from episodic (image and sentence) memory was explored in 3 transfer experiments. In agreement with results from arithmetic, speedup following even minimal practice recalling a missing word from an…

Basic Numerical Capacities and Prevalence of Developmental Dyscalculia: The Havana Survey

Science.gov (United States)

Reigosa-Crespo, Vivian; Valdes-Sosa, Mitchell; Butterworth, Brian; Estevez, Nancy; Rodriguez, Marisol; Santos, Elsa; Torres, Paul; Suarez, Ramon; Lage, Agustin

2012-01-01

The association of enumeration and number comparison capacities with arithmetical competence was examined in a large sample of children from 2nd to 9th grades. It was found that efficiency on numerical capacities predicted separately more than 25% of the variance in the individual differences on a timed arithmetical test, and this occurred for…

The Relationship Between Problem Size and Fixation Patterns During Addition, Subtraction, Multiplication, and Division

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Evan T. Curtis

2016-08-01

Full Text Available Eye-tracking methods have only rarely been used to examine the online cognitive processing that occurs during mental arithmetic on simple arithmetic problems, that is, addition and multiplication problems with single-digit operands (e.g., operands 2 through 9; 2 + 3, 6 x 8 and the inverse subtraction and division problems (e.g., 5 – 3; 48 ÷ 6. Participants (N = 109 solved arithmetic problems from one of the four operations while their eye movements were recorded. We found three unique fixation patterns. During addition and multiplication, participants allocated half of their fixations to the operator and one-quarter to each operand, independent of problem size. The pattern was similar on small subtraction and division problems. However, on large subtraction problems, fixations were distributed approximately evenly across the three stimulus components. On large division problems, over half of the fixations occurred on the left operand, with the rest distributed between the operation sign and the right operand. We discuss the relations between these eye tracking patterns and other research on the differences in processing across arithmetic operations.

Addition and Subtraction but Not Multiplication and Division Cause Shifts of Spatial Attention

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Mengjin Li

2018-05-01

Full Text Available Many studies have shown that solving addition and subtraction problems can induce overt shifts of spatial attention. In particular, right-side targets are detected faster than left-side targets when preceded by an addition operation, while left-side targets are detected faster than right-side targets when preceded by a subtraction operation. However, the interaction between space and arithmetic in multiplication or division is hardly studied and remains controversial. In order to make a strong case for the interaction between space and mental arithmetic, we attempted to replicate the spatial-arithmetic association in addition and subtraction (Experiment 1, and at the same time investigated whether shift of spatial attention would also be induced by multiplication or division operations (Experiment 2. We found that solving addition problems facilitated the detection of right-side targets, whereas left-side targets were detected faster after solving subtraction problems. However, no interaction between space and arithmetic operation was observed in multiplication or division. The implication of these findings is discussed.

Water pressure control device for control rod drive

International Nuclear Information System (INIS)

Sato, Hideyuki.

1981-01-01

Purpose: To minimize the fluctuations in the reactor water level upon occurrence of abnormality by inputting the level signal of the reactor to an arithmetic unit for controlling the pressure of control rod drive water to thereby enable effective reactor level control. Constitution: Signal from a flow rate transmitter is inputted into an arithmetic unit to perform constant flow rate control upon normal operation. While on the other hand, if abnormality occurs such as feedwater pump trips, the arithmetic unit is switched from the constant flow rate control to the reactor water level control. Reactor water level signal is inputted into the arithmetic unit and the control valve is most suitably controlled, whereby water is fed from CST to the reactor by way of control rod drive water system to secure the reactor water level if feedwater to the reactor is interrupted by loss of coolants on the feedwater system. Since this enables to minimize the fluctuations in the reactor water level upon abnormality, the reactor water level can be controlled most suitably by the reactor water level signal. (Moriyama, K.)

Symptoms of anxiety and depression are related to cardiovascular responses to active, but not passive, coping tasks.

Science.gov (United States)

Yuenyongchaiwat, Kornanong; Baker, Ian S; Sheffield, David

2017-01-01

Anxiety and depression have been linked to blunted blood pressure (BP) and heart rate (HR) reactions to mental stress tests; however, most studies have not included indices of underlying hemodynamics nor multiple stress tasks. This study sought to examine the relationships of anxiety and depression with hemodynamic responses to acute active and passive coping tasks. A total of 104 participants completed the Hospital Anxiety and Depression Scales and mental arithmetic, speech, and cold pressor tasks while BP, HR, total peripheral resistance, and cardiac output (CO) were assessed. After adjustment for traditional risk factors and baseline cardiovascular activity, depression scores were negatively associated with systolic BP, HR, and CO responses to the mental arithmetic task, while anxiety scores were inversely related to the systolic BP response to mental arithmetic. High anxiety or depression scores appear to be associated with blunted cardiac reactions to mental arithmetic (an active coping task), but not to the cold pressor test or speech tasks. Future research should further examine potential mechanisms and longitudinal pathways relating depression and anxiety to cardiovascular reactivity. TCTR20160208004.

Algebraic groups and their birational invariants

CERN Document Server

Voskresenskiĭ, V E

2011-01-01

Since the late 1960s, methods of birational geometry have been used successfully in the theory of linear algebraic groups, especially in arithmetic problems. This book--which can be viewed as a significant revision of the author's book, Algebraic Tori (Nauka, Moscow, 1977)--studies birational properties of linear algebraic groups focusing on arithmetic applications. The main topics are forms and Galois cohomology, the Picard group and the Brauer group, birational geometry of algebraic tori, arithmetic of algebraic groups, Tamagawa numbers, R-equivalence, projective toric varieties, invariants of finite transformation groups, and index-formulas. Results and applications are recent. There is an extensive bibliography with additional comments that can serve as a guide for further reading.

Spin the Wheels

Science.gov (United States)

Critchett, John

2011-01-01

The Fibonacci series has been studied since it was first described by Leonardo of Pisa--Fibonacci--in 1202. It begins with the sequence 1, 1, 2, 3, 5, 8... Each succeeding number is the sum of the previous two. In number theory courses, students are introduced to the concept of modulo arithmetic, sometimes called "clock" arithmetic. In modulo…

Environmental Gradient Analysis, Ordination, and Classification in Environmental Impact Assessments.

Science.gov (United States)

1987-09-01

agglomerative clustering algorithms for mainframe computers: (1) the unweighted pair-group method that V uses arithmetic averages ( UPGMA ), (2) the...hierarchical agglomerative unweighted pair-group method using arithmetic averages ( UPGMA ), which is also called average linkage clustering. This method was...dendrograms produced by weighted clustering (93). Sneath and Sokal (94), Romesburg (84), and Seber• (90) also strongly recommend the UPGMA . A dendrogram

Comparative study on preliminary breakdown pulse trains observed in Johor, Malaysia and Florida, USA

Science.gov (United States)

Baharudin, Z. A.; Ahmad, Noor Azlinda; Fernando, M.; Cooray, V.; Mäkelä, J. S.

2012-11-01

In this paper, the preliminary breakdown (PB) pulse train preceding the negative first return stroke (RS) is recorded using a broad band antenna system. These analyses were carried out in Johor Bahru, Malaysia and Florida, United States. This is a novel initiative at examining and identifying the characteristics of the PB pulse trains in the negative cloud-to-ground flashes observed in Malaysia. The arithmetic mean of the total pulse train duration is 12.3 ms and the weighted arithmetic mean of the pulse durations and interpulse intervals are 11 μs and 152 μs, respectively. The arithmetic mean ratio between the maximum peak amplitude of the PB pulse and the peak RS electric field was 27.8%, and the corresponding value in Florida was 29.4%. The arithmetic mean of the time duration between the most active part of the pulse train, and the RS was 57.6 ms in Malaysia and 22 ms in Florida. A qualitative comparison of our results with those obtained earlier in Sri Lanka, Sweden and Finland supports the hypothesis that the PBP/RS ratio is higher in the northern regions compared to the tropical regions.

A componential model of human interaction with graphs: 1. Linear regression modeling

Science.gov (United States)

Gillan, Douglas J.; Lewis, Robert

1994-01-01

Task analyses served as the basis for developing the Mixed Arithmetic-Perceptual (MA-P) model, which proposes (1) that people interacting with common graphs to answer common questions apply a set of component processes-searching for indicators, encoding the value of indicators, performing arithmetic operations on the values, making spatial comparisons among indicators, and repsonding; and (2) that the type of graph and user's task determine the combination and order of the components applied (i.e., the processing steps). Two experiments investigated the prediction that response time will be linearly related to the number of processing steps according to the MA-P model. Subjects used line graphs, scatter plots, and stacked bar graphs to answer comparison questions and questions requiring arithmetic calculations. A one-parameter version of the model (with equal weights for all components) and a two-parameter version (with different weights for arithmetic and nonarithmetic processes) accounted for 76%-85% of individual subjects' variance in response time and 61%-68% of the variance taken across all subjects. The discussion addresses possible modifications in the MA-P model, alternative models, and design implications from the MA-P model.

El inductismo aritmético y su influencia en la enseñanza del número

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Alfonso ORTIZ COMAS

2009-11-01

Full Text Available RESUMEN: En este artículo presentamos las características de una corriente epistemológica y matemática que hemos denominado inductivismo aritmético. Exponemos dos hechos fundamentales para la Educación Matemática, como son la confirmación de la influencia del inductivismo en los manuales de aritmética publicados en España desde el siglo XVI y su repercusión en la enseñanza de la aritmética del número natural. Además, exponemos algunas consideraciones inductivistas sobre las series y sucesiones de números naturales.ABSTRACT: Arithmetic Inductivism is an epistemological approach to Arithmetic with specific characteristics which are analysed in the present paper. Additionally, the two following fundamental facts for Mathematics Education are also explained: Firstly, the influence of inductivism trend on arithmetical concepts as it can be appreciated by examinning the books published in Spain since the XVIth century to now; secondly, its influence on teaching and learning natural numbers and school arithmetic. Finally, some remarks about inductive reasoning related to natural numbers series are included.