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…
Digital Arithmetic: Division Algorithms
DEFF Research Database (Denmark)
Montuschi, Paolo; Nannarelli, Alberto
2017-01-01
implement it in hardware to not compromise the overall computation performances. This entry explains the basic algorithms, suitable for hardware and software, to implement division in computer systems. Two classes of algorithms implement division or square root: digit-recurrence and multiplicative (e.......g., Newton–Raphson) algorithms. The first class of algorithms, the digit-recurrence type, is particularly suitable for hardware implementation as it requires modest resources and provides good performance on contemporary technology. The second class of algorithms, the multiplicative type, requires...
Fuchs, Lynn S.; Fuchs, Douglas; Compton, Donald L.; Powell, Sarah R.; Seethaler, Pamela M.; Capizzi, Andrea M.; Schatschneider, Christopher; Fletcher, Jack M.
2006-01-01
The purpose of this study was to examine the cognitive correlates of RD-grade skill in arithmetic, algorithmic computation, and arithmetic word problems. Third graders (N = 312) were measured on language, nonverbal problem solving, concept formation, processing speed, long-term memory, working memory, phonological decoding, and sight word…
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
Effective arithmetic in finite fields based on Chudnovsky's multiplication algorithm
Atighehchi , Kévin; Ballet , Stéphane; Bonnecaze , Alexis; Rolland , Robert
2016-01-01
International audience; Thanks to a new construction of the Chudnovsky and Chudnovsky multiplication algorithm, we design efficient algorithms for both the exponentiation and the multiplication in finite fields. They are tailored to hardware implementation and they allow computations to be parallelized, while maintaining a low number of bilinear multiplications.À partir d'une nouvelle construction de l'algorithme de multiplication de Chudnovsky et Chudnovsky, nous concevons des algorithmes ef...
On Chudnovsky-Based Arithmetic Algorithms in Finite Fields
Atighehchi, Kevin; Ballet, Stéphane; Bonnecaze, Alexis; Rolland, Robert
2015-01-01
Thanks to a new construction of the so-called Chudnovsky-Chudnovsky multiplication algorithm, we design efficient algorithms for both the exponentiation and the multiplication in finite fields. They are tailored to hardware implementation and they allow computations to be parallelized while maintaining a low number of bilinear multiplications. We give an example with the finite field ${\\mathbb F}_{16^{13}}$.
A software framework for pipelined arithmetic algorithms in field programmable gate arrays
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.
Algorithmic solution of arithmetic problems and operands-answer associations in long-term memory.
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.
Directory of Open Access Journals (Sweden)
Hatim Zaini
2004-12-01
Full Text Available paper introduces a novel method for complex number representation. The proposed Redundant Complex Binary Number System (RCBNS is developed by combining a Redundant Binary Number and a complex number in base (-1+j. Donald [1] and Walter Penny [2,3] represented complex numbers using base –j and (-1+j in the classified algorithmic models. A Redundant Complex Binary Number System consists of both real and imaginary-radix number systems that form a redundant integer digit set. This system is formed by using complex radix of (-1+j and a digit set of á= 3, where á assumes a value of -3, -2, -1, 0, 1, 2, 3. The arithmetic operations of complex numbers with this system treat the real and imaginary parts as one unit. The carry-free addition has the advantage of Redundancy in number representation in the arithmetic operations. Results of the arithmetic operations are in the RCBNS form. The two methods for conversion from the RCBNS form to the standard binary number form have been presented. In this paper the RCBNS reduces the number of steps required to perform complex number arithmetic operations, thus enhancing the speed.
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.
Indian Academy of Sciences (India)
Keywords. Number theory; arithmetic; cryptography; RSA; public key cryptosystem; prime numbers; factorization; algorithms; residue class ring; theoretical computer science; internet security; information theory; trapdoor oneway function.
Designing and implementing of improved cryptographic algorithm using modular arithmetic theory
Directory of Open Access Journals (Sweden)
Maryam Kamarzarrin
2015-05-01
Full Text Available Maintaining the privacy and security of people information are two most important principles of electronic health plan. One of the methods of creating privacy and securing of information is using Public key cryptography system. In this paper, we compare two algorithms, Common And Fast Exponentiation algorithms, for enhancing the efficiency of public key cryptography. We express that a designed system by Fast Exponentiation Algorithm has high speed and performance but low power consumption and space occupied compared with Common Exponentiation algorithm. Although designed systems by Common Exponentiation algorithm have slower speed and lower performance, designing by this algorithm has less complexity, and easier designing compared with Fast Exponentiation algorithm. In this paper, we will try to examine and compare two different methods of exponentiation, also observe performance Impact of these two approaches in the form of hardware with VHDL language on FPGA.
Development of arithmetical abilities
Directory of Open Access Journals (Sweden)
Tatjana Levstek
2014-02-01
Full Text Available Arithmetic (from the word 'arithmos' which means 'numbers' is an elementary branch of mathematics. Numeracy is essential for understanding mathematics, so the development of arithmetic abilities has been an area of scientific research for a long time. Recent research has shown that the development of arithmetic abilities is not based only on gaining experience and learning. Some arithmetic abilities, especially the sense of quantity, are innate. Even babies are able to distinguish between groups with different number of elements and they perceive numeracy amodally. Six-month-olds distinguish between two groups with the numeracy ratio of 1 : 2. With age this ratio improves rapidly. Five-year-old children already distinguish between groups with the number ratio 7 : 8. The ability to compare two quantities begins to develop after 15 months of age and children learn how to count spontaneously, together with the acquisition of language. Speech enables children to understand number in its abstract, symbolic sense, thus opening the way to symbolic arithmetic. During the preschool period children use intuition when doing calculations, but in school the arithmetic is based on the knowledge of arithmetical algorithms. So, in order to acquire mathematical knowledge, it is necessary to incorporate memory and automate arithmetical processes, without the use of intuition. However, research has shown that intuition is very important and is even a predictive factor for the development of mathematical abilities throughout the schooling process.
PDES, Fips Standard Data Encryption Algorithm
International Nuclear Information System (INIS)
Nessett, D.N.
1991-01-01
Description of program or function: PDES performs the National Bureau of Standards FIPS Pub. 46 data encryption/decryption algorithm used for the cryptographic protection of computer data. The DES algorithm is designed to encipher and decipher blocks of data consisting of 64 bits under control of a 64-bit key. The key is generated in such a way that each of the 56 bits used directly by the algorithm are random and the remaining 8 error-detecting bits are set to make the parity of each 8-bit byte of the key odd, i. e. there is an odd number of '1' bits in each 8-bit byte. Each member of a group of authorized users of encrypted computer data must have the key that was used to encipher the data in order to use it. Data can be recovered from cipher only by using exactly the same key used to encipher it, but with the schedule of addressing the key bits altered so that the deciphering process is the reverse of the enciphering process. A block of data to be enciphered is subjected to an initial permutation, then to a complex key-dependent computation, and finally to a permutation which is the inverse of the initial permutation. Two PDES routines are included; both perform the same calculation. One, identified as FDES.MAR, is designed to achieve speed in execution, while the other identified as PDES.MAR, presents a clearer view of how the algorithm is executed
DEFF Research Database (Denmark)
Edjabou, Maklawe Essonanawe; Martín-Fernández, Josep Antoni; Scheutz, Charlotte
2017-01-01
Data for fractional solid waste composition provide relative magnitudes of individual waste fractions, the percentages of which always sum to 100, thereby connecting them intrinsically. Due to this sum constraint, waste composition data represent closed data, and their interpretation and analysis......, have the potential to generate spurious or misleading results. Therefore, ¨compositional data should be transformed adequately prior to any statistical analysis, such as computing mean, standard deviation and correlation coefficients....... require statistical methods, other than classical statistics that are suitable only for non-constrained data such as absolute values. However, the closed characteristics of waste composition data are often ignored when analysed. The results of this study showed, for example, that unavoidable animal...... and plastic packaging. However, correlation tests applied to waste fraction compositions (percentage values) showed a negative association in this regard, thus demonstrating that statistical analyses applied to compositional waste fraction data, without addressing the closed characteristics of these data...
Edjabou, Maklawe Essonanawe; Martín-Fernández, Josep Antoni; Scheutz, Charlotte; Astrup, Thomas Fruergaard
2017-11-01
Data for fractional solid waste composition provide relative magnitudes of individual waste fractions, the percentages of which always sum to 100, thereby connecting them intrinsically. Due to this sum constraint, waste composition data represent closed data, and their interpretation and analysis require statistical methods, other than classical statistics that are suitable only for non-constrained data such as absolute values. However, the closed characteristics of waste composition data are often ignored when analysed. The results of this study showed, for example, that unavoidable animal-derived food waste amounted to 2.21±3.12% with a confidence interval of (-4.03; 8.45), which highlights the problem of the biased negative proportions. A Pearson's correlation test, applied to waste fraction generation (kg mass), indicated a positive correlation between avoidable vegetable food waste and plastic packaging. However, correlation tests applied to waste fraction compositions (percentage values) showed a negative association in this regard, thus demonstrating that statistical analyses applied to compositional waste fraction data, without addressing the closed characteristics of these data, have the potential to generate spurious or misleading results. Therefore, ¨compositional data should be transformed adequately prior to any statistical analysis, such as computing mean, standard deviation and correlation coefficients. Copyright © 2017 Elsevier Ltd. All rights reserved.
Indian Academy of Sciences (India)
algorithms built into the computer corresponding to the logic- circuit rules that are used to .... For the purpose of carrying ou t ari thmetic or logical operations the memory is organized in terms .... In fixed point representation, one essentially uses integer arithmetic operators assuming the binary point to be at some point other ...
Arithmetic processor design for the T9000 transputer
Knowles, Simon C.
1991-12-01
This paper describes aspects of the arithmetic algorithms, architecture, and VLSI engineering of the 64-bit floating-point unit of the T9000 Transputer. The unit is fully conformant to the IEEE-754 floating-point arithmetic standard, and has been implemented in a 1 micrometers , triple- metal CMOS technology. The 160,000 transistor design performs addition in 40 ns, double precision multiplication in 60 ns, and double-precision division or square root in 300 ns. It will sustain 17 MFlops on the Linpac benchmark, yet occupies less than 15 mm2 of silicon--about 8.5% of the die area of T9000.
Bell, Eric T
1927-01-01
The central topic of this book is the presentation of the author's principle of arithmetical paraphrases, which won him the BÃ´cher Prize in 1924. This general principle served to unify and extend many isolated results in the theory of numbers. The author successfully provides a systematic attempt to find a unified theory for each of various classes of related important problems in the theory of numbers, including its interrelations with algebra and analysis. This book will be of interest to advanced students in various branches of mathematics, including number theory, abstract algebra, ellipti
Fried, Michael D
2006-01-01
Field Arithmetic explores Diophantine fields through their absolute Galois groups. This largely self-contained treatment starts with techniques from algebraic geometry, number theory, and profinite groups. Graduate students can effectively learn generalizations of finite field ideas. We use Haar measure on the absolute Galois group to replace counting arguments. New Chebotarev density variants interpret diophantine properties. Here we have the only complete treatment of Galois stratifications, used by Denef and Loeser, et al, to study Chow motives of Diophantine statements.Progress from the fi
Arithmetic the foundation of mathematics
2015-01-01
Arithmetic factors into our lives on a daily basis, so it's hard to imagine a world without the six basic operations: addition, subtraction, multiplication, division, raising to powers, and finding roots. Readers will get a solid overview of arithmetic, while offering useful examples of how they are used in routine activities, such as social media applications. It reinforces Common Core math standards, including understanding basic math concepts and how they apply to students' daily lives and challenges. A history of arithmetic helps provide a contextual framework for the course of its develop
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...... as possible. The use of diﬀerent approaches such as neural networks and machine learning can lead to fast and eﬃcient solutions however, these solutions are expensive in terms of hardware resources and power consumption. A possible solution to this problem can be use of approximate arithmetic. In many image...... 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....
Water cycle algorithm: A detailed standard code
Sadollah, Ali; Eskandar, Hadi; Lee, Ho Min; Yoo, Do Guen; Kim, Joong Hoon
Inspired by the observation of the water cycle process and movements of rivers and streams toward the sea, a population-based metaheuristic algorithm, the water cycle algorithm (WCA) has recently been proposed. Lately, an increasing number of WCA applications have appeared and the WCA has been utilized in different optimization fields. This paper provides detailed open source code for the WCA, of which the performance and efficiency has been demonstrated for solving optimization problems. The WCA has an interesting and simple concept and this paper aims to use its source code to provide a step-by-step explanation of the process it follows.
DEFF Research Database (Denmark)
Gil, J. I. Burgos; Feliu, Elisenda
2012-01-01
We give a new construction of higher arithmetic Chow groups for quasi-projective arithmetic varieties over a field. Our definition agrees with the higher arithmetic Chow groups defined by Goncharov for projective arithmetic varieties over a field. These groups are the analogue, in the Arakelov co...
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!!!
Arithmetic Progressions on Conics
Ciss, Abdoul Aziz; Moody, Dustin
2016-01-01
In this paper, we look at long arithmetic progressions on conics. By an arithmetic progression on a curve, we mean the existence of rational points on the curve whose x-coordinates are in arithmetic progression. We revisit arithmetic progressions on the unit circle, constructing 3-term progressions of points in the first quadrant containing an arbitrary rational point on the unit circle. We also provide infinite families of three term progressions on the unit hyperbola, as well as conics ax2 ...
No Arithmetic Cyclic Quadrilaterals
Beauregard, Raymond A.
2006-01-01
A quadrilateral is arithmetic if its area is an integer and its sides are integers in an arithmetic progression, and it is cyclic if it can be inscribed in a circle. The author shows that no quadrilateral is both arithmetic and cyclic.
[Acquisition of arithmetic knowledge].
Fayol, Michel
2008-01-01
The focus of this paper is on contemporary research on the number counting and arithmetical competencies that emerge during infancy, the preschool years, and the elementary school. I provide a brief overview of the evolution of children's conceptual knowledge of arithmetic knowledge, the acquisition and use of counting and how they solve simple arithmetic problems (e.g. 4 + 3).
Comparing Mental Arithmetic Modes of Presentation in Elementary School Mathematics
Schall, William E.
1973-01-01
Mental arithmetic problems were presented in one of five modes to 14 fifth-grade classrooms. Results showed no significant gains in ability to use mental arithmetic or in performance on a standardized arithmetic achievement test, but gains on a problem-solving retention test and in positive attitudes. (DT)
Arithmetic Progressions on Conics.
Ciss, Abdoul Aziz; Moody, Dustin
2017-01-01
In this paper, we look at long arithmetic progressions on conics. By an arithmetic progression on a curve, we mean the existence of rational points on the curve whose x -coordinates are in arithmetic progression. We revisit arithmetic progressions on the unit circle, constructing 3-term progressions of points in the first quadrant containing an arbitrary rational point on the unit circle. We also provide infinite families of three term progressions on the unit hyperbola, as well as conics ax 2 + cy 2 = 1 containing arithmetic progressions as long as 8 terms.
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.
Alignment of Custom Standards by Machine Learning Algorithms
Directory of Open Access Journals (Sweden)
Adela Sirbu
2010-09-01
Full Text Available Building an efficient model for automatic alignment of terminologies would bring a significant improvement to the information retrieval process. We have developed and compared two machine learning based algorithms whose aim is to align 2 custom standards built on a 3 level taxonomy, using kNN and SVM classifiers that work on a vector representation consisting of several similarity measures. The weights utilized by the kNN were optimized with an evolutionary algorithm, while the SVM classifier's hyper-parameters were optimized with a grid search algorithm. The database used for train was semi automatically obtained by using the Coma++ tool. The performance of our aligners is shown by the results obtained on the test set.
[Standard algorithm of molecular typing of Yersinia pestis strains].
Eroshenko, G A; Odinokov, G N; Kukleva, L M; Pavlova, A I; Krasnov, Ia M; Shavina, N Iu; Guseva, N P; Vinogradova, N A; Kutyrev, V V
2012-01-01
Development of the standard algorithm of molecular typing of Yersinia pestis that ensures establishing of subspecies, biovar and focus membership of the studied isolate. Determination of the characteristic strain genotypes of plague infectious agent of main and nonmain subspecies from various natural foci of plague of the Russian Federation and the near abroad. Genotyping of 192 natural Y. pestis strains of main and nonmain subspecies was performed by using PCR methods, multilocus sequencing and multilocus analysis of variable tandem repeat number. A standard algorithm of molecular typing of plague infectious agent including several stages of Yersinia pestis differentiation by membership: in main and nonmain subspecies, various biovars of the main subspecies, specific subspecies; natural foci and geographic territories was developed. The algorithm is based on 3 typing methods--PCR, multilocus sequence typing and multilocus analysis of variable tandem repeat number using standard DNA targets--life support genes (terC, ilvN, inv, glpD, napA, rhaS and araC) and 7 loci of variable tandem repeats (ms01, ms04, ms06, ms07, ms46, ms62, ms70). The effectiveness of the developed algorithm is shown on the large number of natural Y. pestis strains. Characteristic sequence types of Y. pestis strains of various subspecies and biovars as well as MLVA7 genotypes of strains from natural foci of plague of the Russian Federation and the near abroad were established. The application of the developed algorithm will increase the effectiveness of epidemiologic monitoring of plague infectious agent, and analysis of epidemics and outbreaks of plague with establishing the source of origin of the strain and routes of introduction of the infection.
Plain Polynomial Arithmetic on GPU
International Nuclear Information System (INIS)
Haque, Sardar Anisul; Maza, Marc Moreno
2012-01-01
As for serial code on CPUs, parallel code on GPUs for dense polynomial arithmetic relies on a combination of asymptotically fast and plain algorithms. Those are employed for data of large and small size, respectively. Parallelizing both types of algorithms is required in order to achieve peak performances. In this paper, we show that the plain dense polynomial multiplication can be efficiently parallelized on GPUs. Remarkably, it outperforms (highly optimized) FFT-based multiplication up to degree 2 12 while on CPU the same threshold is usually at 2 6 . We also report on a GPU implementation of the Euclidean Algorithm which is both work-efficient and runs in linear time for input polynomials up to degree 2 18 thus showing the performance of the GCD algorithm based on systolic arrays.
Monkeys display classic signatures of human symbolic arithmetic.
Cantlon, Jessica F; Merritt, Dustin J; Brannon, Elizabeth M
2016-03-01
Non-human primates compare quantities in a crude manner, by approximating their values. Less is known about the mental transformations that non-humans can perform over approximate quantities, such as arithmetic transformations. There is evidence that human symbolic arithmetic has a deep psychological connection with the primitive, approximate forms of quantification of non-human animals. Here, we ask whether the subtle performance signatures that humans exhibit during symbolic arithmetic also bear a connection to primitive arithmetic. Specifically, we examined the problem size effect, the tie effect, and the practice effect-effects which are commonly observed in children's math performance in school. We show that, like humans, monkeys exhibited the problem size and tie effects, indicating commonalities in arithmetic algorithms with humans. Unlike humans, however, monkeys did not exhibit a practice effect. Together, these findings provide new evidence for a cognitive relation between non-symbolic and symbolic arithmetic.
A review of lossless audio compression standards and algorithms
Muin, Fathiah Abdul; Gunawan, Teddy Surya; Kartiwi, Mira; Elsheikh, Elsheikh M. A.
2017-09-01
Over the years, lossless audio compression has gained popularity as researchers and businesses has become more aware of the need for better quality and higher storage demand. This paper will analyse various lossless audio coding algorithm and standards that are used and available in the market focusing on Linear Predictive Coding (LPC) specifically due to its popularity and robustness in audio compression, nevertheless other prediction methods are compared to verify this. Advanced representation of LPC such as LSP decomposition techniques are also discussed within this paper.
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
Standard Sine Fitting Algorithms Applied To Blade Tip Timing Data
Directory of Open Access Journals (Sweden)
Kaźmierczak Krzysztof
2014-12-01
Full Text Available Blade Tip Timing (BTT is a non-intrusive method to measure blade vibration in turbomachinery. Time of Arrival (TOA is recorded when a blade is passing a stationary sensor. The measurement data, in form of undersampled (aliased tip-deflection signal, are difficult to analyze with standard signal processing methods like digital filters or Fourier Transform. Several indirect methods are applied to process TOA sequences, such as reconstruction of aliased spectrum and Least-Squares Fitting to harmonic oscillator model. We used standard sine fitting algorithms provided by IEEE-STD-1057 to estimate blade vibration parameters. Blade-tip displacement was simulated in time domain using SDOF model, sampled by stationary sensors and then processed by the sinefit.m toolkit. We evaluated several configurations of different sensor placement, noise level and number of data. Results of the linear sine fitting, performed with the frequency known a priori, were compared with the non-linear ones. Some of non-linear iterations were not convergent. The algorithms and testing results are aimed to be used in analysis of asynchronous blade vibration.
Price, Gavin R; Mazzocco, Michèle M M; Ansari, Daniel
2013-01-02
Do individual differences in the brain mechanisms for arithmetic underlie variability in high school mathematical competence? Using functional magnetic resonance imaging, we correlated brain responses to single digit calculation with standard scores on the Preliminary Scholastic Aptitude Test (PSAT) math subtest in high school seniors. PSAT math scores, while controlling for PSAT Critical Reading scores, correlated positively with calculation activation in the left supramarginal gyrus and bilateral anterior cingulate cortex, brain regions known to be engaged during arithmetic fact retrieval. At the same time, greater activation in the right intraparietal sulcus during calculation, a region established to be involved in numerical quantity processing, was related to lower PSAT math scores. These data reveal that the relative engagement of brain mechanisms associated with procedural versus memory-based calculation of single-digit arithmetic problems is related to high school level mathematical competence, highlighting the fundamental role that mental arithmetic fluency plays in the acquisition of higher-level mathematical competence.
Foundation of Basic Arithmetic
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 11; Issue 2. Foundation of Basic Arithmetic. Jasbir S Chahal. General Article Volume 11 Issue 2 February 2006 pp 6-16. Fulltext. Click here to view fulltext PDF. Permanent link: http://www.ias.ac.in/article/fulltext/reso/011/02/0006-0016. Keywords. Different ...
A functional interpretation for nonstandard arithmetic
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
A library for prototyping the computer arithmetic level in elliptic curve cryptography
Imbert, Laurent; Peirera, Agostinho; Tisserand, Arnaud
2007-09-01
This paper presents the first version of a software library called PACE ("Prototyping Arithmetic in Cryptography Easily"). This is a C++ library under LGPL license. It provides number systems and algorithms for prototyping the arithmetic layer in cryptographic applications. The first version of PACE includes basic support of prime finite fields and ECC (Elliptic Curve Cryptography) basic algorithms for software implementations.
Algebra, Arithmetic, and Geometry
Tschinkel, Yuri
2009-01-01
The two volumes of "Algebra, Arithmetic, and Geometry: In Honor of Y.I. Manin" are composed of invited expository articles and extensions detailing Manin's contributions to the subjects, and are in celebration of his 70th birthday. The well-respected and distinguished contributors include: Behrend, Berkovich, Bost, Bressler, Calaque, Carlson, Chambert-Loir, Colombo, Connes, Consani, Dabrowski, Deninger, Dolgachev, Donaldson, Ekedahl, Elsenhans, Enriques, Etingof, Fock, Friedlander, Geemen, Getzler, Goncharov, Harris, Iskovskikh, Jahnel, Kaledin, Kapranov, Katz, Kaufmann, Kollar, Kont
Arithmetic of Complex Manifolds
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.
Towards an arithmetical logic the arithmetical foundations of logic
Gauthier, Yvon
2015-01-01
This book offers an original contribution to the foundations of logic and mathematics, and focuses on the internal logic of mathematical theories, from arithmetic or number theory to algebraic geometry. Arithmetical logic is the term used to refer to the internal logic of classical arithmetic, here called Fermat-Kronecker arithmetic, and combines Fermat’s method of infinite descent with Kronecker’s general arithmetic of homogeneous polynomials. The book also includes a treatment of theories in physics and mathematical physics to underscore the role of arithmetic from a constructivist viewpoint. The scope of the work intertwines historical, mathematical, logical and philosophical dimensions in a unified critical perspective; as such, it will appeal to a broad readership from mathematicians to logicians, to philosophers interested in foundational questions. Researchers and graduate students in the fields of philosophy and mathematics will benefit from the author’s critical approach to the foundations of l...
Mental Computation or Standard Algorithm? Children's Strategy Choices on Multi-Digit Subtractions
Torbeyns, Joke; Verschaffel, Lieven
2016-01-01
This study analyzed children's use of mental computation strategies and the standard algorithm on multi-digit subtractions. Fifty-eight Flemish 4th graders of varying mathematical achievement level were individually offered subtractions that either stimulated the use of mental computation strategies or the standard algorithm in one choice and two…
Energy efficient data sorting using standard sorting algorithms
Bunse, Christian
2011-01-01
Protecting the environment by saving energy and thus reducing carbon dioxide emissions is one of todays hottest and most challenging topics. Although the perspective for reducing energy consumption, from ecological and business perspectives is clear, from a technological point of view, the realization especially for mobile systems still falls behind expectations. Novel strategies that allow (software) systems to dynamically adapt themselves at runtime can be effectively used to reduce energy consumption. This paper presents a case study that examines the impact of using an energy management component that dynamically selects and applies the "optimal" sorting algorithm, from an energy perspective, during multi-party mobile communication. Interestingly, the results indicate that algorithmic performance is not key and that dynamically switching algorithms at runtime does have a significant impact on energy consumption. © Springer-Verlag Berlin Heidelberg 2011.
Arithmetic circuits for DSP applications
Stouraitis, Thanos
2017-01-01
Arithmetic Circuits for DSP Applications is a complete resource on arithmetic circuits for digital signal processing (DSP). It covers the key concepts, designs and developments of different types of arithmetic circuits, which can be used for improving the efficiency of implementation of a multitude of DSP applications. Each chapter includes various applications of the respective class of arithmetic circuits along with information on the future scope of research. Written for students, engineers, and researchers in electrical and computer engineering, this comprehensive text offers a clear understanding of different types of arithmetic circuits used for digital signal processing applications. The text includes contributions from noted researchers on a wide range of topics, including a review o circuits used in implementing basic operations like additions and multiplications; distributed arithmetic as a technique for the multiplier-less implementation of inner products for DSP applications; discussions on look ...
Hybrid content addressable memory MSD arithmetic
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.
Introduction to cardinal arithmetic
Holz, M; Weitz, E
1999-01-01
This book is an introduction into modern cardinal arithmetic in the frame of the axioms of Zermelo-Fraenkel set theory together with the axiom of choice (ZFC). A first part describes the classical theory developed by Bernstein, Cantor, Hausdorff, König and Tarski between 1870 and 1930. Next, the development in the 1970s led by Galvin, Hajnal and Silver is characterized. The third part presents the fundamental investigations in pcf theory which have been worked out by Shelah to answer the questions left open in the 1970s.Reviews:'The authors aim their text at beginners in set theory. They start
Conceptual Knowledge of Fraction Arithmetic
Siegler, Robert S.; Lortie-Forgues, Hugues
2015-01-01
Understanding an arithmetic operation implies, at minimum, knowing the direction of effects that the operation produces. However, many children and adults, even those who execute arithmetic procedures correctly, may lack this knowledge on some operations and types of numbers. To test this hypothesis, we presented preservice teachers (Study 1),…
Conceptual Knowledge of Decimal Arithmetic
Lortie-Forgues, Hugues; Siegler, Robert S.
2017-01-01
In 2 studies (Ns = 55 and 54), the authors examined a basic form of conceptual understanding of rational number arithmetic, the direction of effect of decimal arithmetic operations, at a level of detail useful for informing instruction. Middle school students were presented tasks examining knowledge of the direction of effects (e.g., "True or…
A parallel row-based algorithm for standard cell placement with integrated error control
Sargent, Jeff S.; Banerjee, Prith
1989-01-01
A new row-based parallel algorithm for standard-cell placement targeted for execution on a hypercube multiprocessor is presented. Key features of this implementation include a dynamic simulated-annealing schedule, row-partitioning of the VLSI chip image, and two novel approaches to control error in parallel cell-placement algorithms: (1) Heuristic Cell-Coloring; (2) Adaptive Sequence Length Control.
Arithmetic functions in torus and tree networks
Bhanot, Gyan; Blumrich, Matthias A.; Chen, Dong; Gara, Alan G.; Giampapa, Mark E.; Heidelberger, Philip; Steinmacher-Burow, Burkhard D.; Vranas, Pavlos M.
2007-12-25
Methods and systems for performing arithmetic functions. In accordance with a first aspect of the invention, methods and apparatus are provided, working in conjunction of software algorithms and hardware implementation of class network routing, to achieve a very significant reduction in the time required for global arithmetic operation on the torus. Therefore, it leads to greater scalability of applications running on large parallel machines. The invention involves three steps in improving the efficiency and accuracy of global operations: (1) Ensuring, when necessary, that all the nodes do the global operation on the data in the same order and so obtain a unique answer, independent of roundoff error; (2) Using the topology of the torus to minimize the number of hops and the bidirectional capabilities of the network to reduce the number of time steps in the data transfer operation to an absolute minimum; and (3) Using class function routing to reduce latency in the data transfer. With the method of this invention, every single element is injected into the network only once and it will be stored and forwarded without any further software overhead. In accordance with a second aspect of the invention, methods and systems are provided to efficiently implement global arithmetic operations on a network that supports the global combining operations. The latency of doing such global operations are greatly reduced by using these methods.
Directory of Open Access Journals (Sweden)
A. S. Poljakov
2014-01-01
Full Text Available The data on the characteristics of international standard algorithms «lightweight cryptography» while application in hardware implementation based on microchips of FPGA are provided. A compari-son of the characteristics of these algorithms with the characteristics of several widely-used standard encryption algorithms is made and possibilities of lightweight cryptography algorithms are evaluated.
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.
Glatard, T; Pennec, X
2006-01-01
Medical image registration is pre-processing needed for many medical image analysis procedures. A very large number of registration algorithms are available today, but their performance is often not known and very difficult to assess due to the lack of gold standard. The Bronze Standard algorithm is a very data and compute intensive statistical approach for quantifying registration algorithms accuracy. In this paper, we describe the Bronze Standard application and we discuss the need for grids to tackle such computations on medical image databases. We demonstrate MOTEUR, a service-based workflow engine optimized for dealing with data intensive applications. MOTEUR eases the enactment of the Bronze Standard and similar applications on the EGEE production grid infrastructure. It is a generic workflow engine, based on current standards and freely available, that can be used to instrument legacy application code at low cost.
Guest Editors' Introduction: Special Section on Computer Arithmetic
DEFF Research Database (Denmark)
Nannarelli, Alberto; Seidel, Peter-Michael; Tang, Ping Tak Peter
2014-01-01
The articles in this special issue focus on current trends and developments in the field of computer arithmetic. This is a field that encompasses the definition and standardization of arithmetic system for computers. The field also deals with issues of hardware and software implementations...... and 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...... engineering. Advances in this field span from being highly theoretical (for instance, new exotic number systems) to being highly practical (for instance, new floating-point units for microprocessors)....
Directory of Open Access Journals (Sweden)
Waqas Javaid
2014-09-01
Full Text Available Though there are a number of benefits associated with cellular manufacturing systems, its implementation (identification of part families and corresponding machine groups for real life problems is still a challenging task. To handle the complexity of optimizing multiple objectives and larger size of the problem, most of the researchers in the past two decades or so have focused on developing genetic algorithm (GA based techniques. Recently this trend has shifted from standard GA to hybrid GA (HGA based approaches in the quest for greater effectiveness as far as convergence on to the optimum solution is concerned. In order to prove the point, that HGAs possess better convergence abilities than standard GAs, a methodology, initially based on standard GA and later on hybridized with a local search heuristic (LSH, has been developed during this research. Computational experience shows that HGA maintains its accuracy level with increase in problem size, whereas standard GA looses its effectiveness as the problem size grows.
Nanna, Robert J.
2016-01-01
Algorithms and representations have been an important aspect of the work of mathematics, especially for understanding concepts and communicating ideas about concepts and mathematical relationships. They have played a key role in various mathematics standards documents, including the Common Core State Standards for Mathematics. However, there have…
Arithmetic Abilities in Children With Developmental Dyslexia: Performance on French ZAREKI-R Test.
De Clercq-Quaegebeur, Maryse; Casalis, Séverine; Vilette, Bruno; Lemaitre, Marie-Pierre; Vallée, Louis
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 Number Processing Assessment Battery for Children; von Aster & Dellatolas, 2006), we analyzed the arithmetic abilities of 47 French children with dyslexia attending 3rd, 4th, and 5th grade. Of them, 40% displayed arithmetic deficits, mostly with regard to number transcoding and mental calculation. Their individual profiles of performance accounted for varying strengths and weaknesses in arithmetic abilities. Our findings showed the pathway for the development of arithmetic abilities in children with dyslexia is not unique. Our study contrasts with the hypotheses suggesting the mutual exclusiveness of the phonological representation deficit and the core number module deficit.
Error adaptation in mental arithmetic.
Desmet, Charlotte; Imbo, Ineke; De Brauwer, Jolien; Brass, Marcel; Fias, Wim; Notebaert, Wim
2012-01-01
Until now, error and conflict adaptation have been studied extensively using simple laboratory tasks. A common finding is that responses slow down after errors. According to the conflict monitoring theory, performance should also improve after an error. However, this is usually not observed. In this study, we investigated whether the characteristics of the experimental paradigms normally used could explain this absence. More precisely, these paradigms have in common that behavioural adaptation has little room to be expressed. We therefore studied error and conflict adaptation effects in a task that encounters the richness of everyday life's behavioural adaptation--namely, mental arithmetic, where multiple solution strategies are available. In accordance with our hypothesis, we observed that post-error accuracy increases after errors in mental arithmetic. No support for conflict adaptation in mental arithmetic was found. Implications for current theories of conflict and error monitoring are discussed.
Short Note: Every Large Set of Integers Contains a Three Term Arithmetic Progression
Korvin, Gabor
2014-01-01
I show that a trivial modification of a standard proof of the Roth's Theorem on triples in arithmetic progression would lead to the following Theorem: If A is a "large set" that is its elements are monotone increasing integers and the sum of reciprocals of its elements diverges then the sequence contains an arithmetic progression of length three.
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
Arithmetic learning in advanced age
Kremser, Christian; Pertl, Marie-Theres; Gizewski, Elke; Benke, Thomas; Delazer, Margarete
2018-01-01
Acquisition of numerical knowledge and understanding of numerical information are crucial for coping with the changing demands of our digital society. In this study, we assessed arithmetic learning in older and younger individuals in a training experiment including brain imaging. In particular, we assessed age-related effects of training intensity, prior arithmetic competence, and neuropsychological variables on the acquisition of new arithmetic knowledge and on the transfer to new, unknown problems. Effects were assessed immediately after training and after 3 months. Behavioural results showed higher training effects for younger individuals than for older individuals and significantly better performance after 90 problem repetitions than after 30 repetitions in both age groups. A correlation analysis indicated that older adults with lower memory and executive functions at baseline could profit more from intensive training. Similarly, training effects in the younger group were higher for those individuals who had lower arithmetic competence and executive functions prior to intervention. In younger adults, successful transfer was associated with higher executive functions. Memory and set-shifting emerged as significant predictors of training effects in the older group. For the younger group, prior arithmetic competence was a significant predictor of training effects, while cognitive flexibility was a predictor of transfer effects. After training, a subgroup of participants underwent an MRI assessment. A voxel-based morphometry analysis showed a significant interaction between training effects and grey matter volume of the right middle temporal gyrus extending to the angular gyrus for the younger group relative to the older group. The reverse contrast (older group vs. younger group) did not yield any significant results. These results suggest that improvements in arithmetic competence are supported by temporo-parietal areas in the right hemisphere in younger
An algorithm for compression of bilevel images.
Reavy, M D; Boncelet, C G
2001-01-01
This paper presents the block arithmetic coding for image compression (BACIC) algorithm: a new method for lossless bilevel image compression which can replace JBIG, the current standard for bilevel image compression. BACIC uses the block arithmetic coder (BAC): a simple, efficient, easy-to-implement, variable-to-fixed arithmetic coder, to encode images. BACIC models its probability estimates adaptively based on a 12-bit context of previous pixel values; the 12-bit context serves as an index into a probability table whose entries are used to compute p(1) (the probability of a bit equaling one), the probability measure BAC needs to compute a codeword. In contrast, the Joint Bilevel Image Experts Group (JBIG) uses a patented arithmetic coder, the IBM QM-coder, to compress image data and a predetermined probability table to estimate its probability measures. JBIG, though, has not get been commercially implemented; instead, JBIG's predecessor, the Group 3 fax (G3), continues to be used. BACIC achieves compression ratios comparable to JBIG's and is introduced as an alternative to the JBIG and G3 algorithms. BACIC's overall compression ratio is 19.0 for the eight CCITT test images (compared to JBIG's 19.6 and G3's 7.7), is 16.0 for 20 additional business-type documents (compared to JBIG's 16.0 and G3's 6.74), and is 3.07 for halftone images (compared to JBIG's 2.75 and G3's 0.50).
Predicting Arithmetic Abilities: The Role of Preparatory Arithmetic Markers and Intelligence
Stock, Pieter; Desoete, Annemie; Roeyers, Herbert
2009-01-01
Arithmetic abilities acquired in kindergarten are found to be strong predictors for later deficient arithmetic abilities. This longitudinal study (N = 684) was designed to examine if it was possible to predict the level of children's arithmetic abilities in first and second grade from their performance on preparatory arithmetic abilities in…
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
Machine Arithmetic in Residual Classes,
1981-04-03
rsmainder/residue, as this ascape /-nsues from thp determination of system. It can be. zaalizpd ;n the presence of th- arithmetic urit, which wor~s in thz sys...modules Nj. Page 417. Proof. Proof ascaps /ensues directly from the theorem of Gauss. Actually/really, since according to condition (py, qj)-=-. then
Equations for arithmetic pointed tori
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.
Squares in arithmetic progression over cubic fields
Bremner, Andrew; Siksek, Samir
2015-01-01
Euler showed that there can be no more than three integer squares in arithmetic progression. In quadratic number fields, Xarles has shown that there can be arithmetic progressions of five squares, but not of six. Here, we prove that there are no cubic number fields which contain five squares in arithmetic progression.
Computer arithmetic and validity theory, implementation, and applications
Kulisch, Ulrich
2013-01-01
This is the revised and extended second edition of the successful basic book on computer arithmetic. It is consistent with the newest recent standard developments in the field. The book shows how the arithmetic capability of the computer can be enhanced. The work is motivated by the desire and the need to improve the accuracy of numerical computing and to control the quality of the computed results (validity). The accuracy requirements for the elementary floating-point operations are extended to the customary product spaces of computations including interval spaces. The mathematical properties
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.
DEFF Research Database (Denmark)
Bron, Esther E.; Smits, Marion; van der Flier, Wiesje M.
2015-01-01
Abstract Algorithms for computer-aided diagnosis of dementia based on structural MRI have demonstrated high performance in the literature, but are difficult to compare as different data sets and methodology were used for evaluation. In addition, it is unclear how the algorithms would perform...... on previously unseen data, and thus, how they would perform in clinical practice when there is no real opportunity to adapt the algorithm to the data at hand. To address these comparability, generalizability and clinical applicability issues, we organized a grand challenge that aimed to objectively compare......, patients with mild cognitive impairment and healthy controls. The diagnosis based on clinical criteria was used as reference standard, as it was the best available reference despite its known limitations. For evaluation, a previously unseen test set was used consisting of 354 T1-weighted MRI scans...
Indian Academy of Sciences (India)
C. S. Rajan
2006-11-11
Nov 11, 2006 ... If the manifold is sitting inside n-dimensional space, then we get for free a Riemannian metric, by restricting the standard quadratic form given by taking squares of lengths. But it is useful to take a more abstract viewpoint. Examples: linear subspaces and circles (flat geometry), spheres. (positively curved or ...
Van Rooijen, M; Verhoeven, L; 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 numeracy in children with CP over a two year period and studied which cognitive factors were predictive of arithmetic performance. A longitudinal study with three measurement waves separated by one year was conducted. 56 children participated (37 boys, M=6.0 years, SD=.58). Standardized tasks were used to assess verbal- and visual-spatial working memory, executive functioning, fine motor skills and early numeracy performance. In addition, experimental tasks were developed to measure counting and arithmetic. The results showed that early numeracy performance of children with CP increased between 6 and 8 years of age. Structural equation modelling showed that early numeracy was strongly related to arithmetic performance at the consecutive year. Working memory, counting and fine motor skills were all positively related to early numeracy performance a year later. Furthermore, working memory and fine motor skills were precursors of the development of early numeracy. Considering the importance of numeracy and arithmetic in daily life and in academic and work success, children with CP could substantially benefit from intervention programs aimed at increasing working memory and early numeracy performance. Copyright © 2015 Elsevier Ltd. All rights reserved.
Indian Academy of Sciences (India)
have been found in Vedic Mathematics which are dated much before Euclid's algorithm. A programming language Is used to describe an algorithm for execution on a computer. An algorithm expressed using a programming language Is called a program. From activities 1-3, we can observe that: • Each activity is a command.
Performance evaluation of grid-enabled registration algorithms using bronze-standards
Glatard, T; Montagnat, J
2006-01-01
Evaluating registration algorithms is difficult due to the lack of gold standard in most clinical procedures. The bronze standard is a real-data based statistical method providing an alternative registration reference through a computationally intensive image database registration procedure. We propose in this paper an efficient implementation of this method through a grid-interfaced workflow enactor enabling the concurrent processing of hundreds of image registrations in a couple of hours only. The performances of two different grid infrastructures were compared. We computed the accuracy of 4 different rigid registration algorithms on longitudinal MRI images of brain tumors. Results showed an average subvoxel accuracy of 0.4 mm and 0.15 degrees in rotation.
Patel, Sanjay R; Weng, Jia; Rueschman, Michael; Dudley, Katherine A; Loredo, Jose S; Mossavar-Rahmani, Yasmin; Ramirez, Maricelle; Ramos, Alberto R; Reid, Kathryn; Seiger, Ashley N; Sotres-Alvarez, Daniela; Zee, Phyllis C; Wang, Rui
2015-09-01
While actigraphy is considered objective, the process of setting rest intervals to calculate sleep variables is subjective. We sought to evaluate the reproducibility of actigraphy-derived measures of sleep using a standardized algorithm for setting rest intervals. Observational study. Community-based. A random sample of 50 adults aged 18-64 years free of severe sleep apnea participating in the Sueño sleep ancillary study to the Hispanic Community Health Study/Study of Latinos. N/A. Participants underwent 7 days of continuous wrist actigraphy and completed daily sleep diaries. Studies were scored twice by each of two scorers. Rest intervals were set using a standardized hierarchical approach based on event marker, diary, light, and activity data. Sleep/wake status was then determined for each 30-sec epoch using a validated algorithm, and this was used to generate 11 variables: mean nightly sleep duration, nap duration, 24-h sleep duration, sleep latency, sleep maintenance efficiency, sleep fragmentation index, sleep onset time, sleep offset time, sleep midpoint time, standard deviation of sleep duration, and standard deviation of sleep midpoint. Intra-scorer intraclass correlation coefficients (ICCs) were high, ranging from 0.911 to 0.995 across all 11 variables. Similarly, inter-scorer ICCs were high, also ranging from 0.911 to 0.995, and mean inter-scorer differences were small. Bland-Altman plots did not reveal any systematic disagreement in scoring. With use of a standardized algorithm to set rest intervals, scoring of actigraphy for the purpose of generating a wide array of sleep variables is highly reproducible. © 2015 Associated Professional Sleep Societies, LLC.
Indian Academy of Sciences (India)
algorithms such as synthetic (polynomial) division have been found in Vedic Mathematics which are dated much before Euclid's algorithm. A programming language ... ·1 x:=sln(theta) x : = sm(theta) 1. ~. Idl d.t Read A.B,C. ~ lei ~ Print x.y.z. L;;;J. Figure 2 Symbols used In flowchart language to rep- resent Assignment, Read.
Indian Academy of Sciences (India)
In the previous articles, we have discussed various common data-structures such as arrays, lists, queues and trees and illustrated the widely used algorithm design paradigm referred to as 'divide-and-conquer'. Although there has been a large effort in realizing efficient algorithms, there are not many universally accepted ...
Linden, Michael; Muschalla, Beate
2012-09-01
There is a general consensus that diagnoses for mental disorders should be based on criteria and algorithms as given in ICD or DSM. Standardized clinical interviews are recommended as diagnostic methods. In ICD and DSM, much emphasis is put on algorithms, while the underlying criteria get much less attention. The question is how valid are the criteria that are collected by structured diagnostic interviews. 209 patients from a cardiology inpatient unit were interviewed with the Mini International Neuropsychiatric Interview (MINI). 32 (15.3%) were diagnosed as suffering from a major depressive episode or dysthymia. Additionally, a thorough clinical examination was done by a psychiatric expert in 15 patients. The standardized diagnosis of present major depression was reaffirmed in one. In total, four patients were suffering from some kind of depressive disorder presently or life time. Two patients were suffering from anxiety disorders, two from adjustment disorders, and four from different types of organic brain disorders. Most important, there are 3 out of 15 who are not mentally ill. Our observations show that standardized diagnostic interviews cannot be used to make specific differential diagnoses, but rather catch unspecific syndromes. This is partly due to the fact that the wording, definition, and understanding of the underlying criteria is rather vague. This is an even greater problem if there is any somatic comorbidity. In the revision of ICD and DSM, a glossary of psychopathological terms and guidelines for the training of clinicians should be included.
Real-time mental arithmetic task recognition from EEG signals.
Wang, Qiang; Sourina, Olga
2013-03-01
Electroencephalography (EEG)-based monitoring the state of the user's brain functioning and giving her/him the visual/audio/tactile feedback is called neurofeedback technique, and it could allow the user to train the corresponding brain functions. It could provide an alternative way of treatment for some psychological disorders such as attention deficit hyperactivity disorder (ADHD), where concentration function deficit exists, autism spectrum disorder (ASD), or dyscalculia where the difficulty in learning and comprehending the arithmetic exists. In this paper, a novel method for multifractal analysis of EEG signals named generalized Higuchi fractal dimension spectrum (GHFDS) was proposed and applied in mental arithmetic task recognition from EEG signals. Other features such as power spectrum density (PSD), autoregressive model (AR), and statistical features were analyzed as well. The usage of the proposed fractal dimension spectrum of EEG signal in combination with other features improved the mental arithmetic task recognition accuracy in both multi-channel and one-channel subject-dependent algorithms up to 97.87% and 84.15% correspondingly. Based on the channel ranking, four channels were chosen which gave the accuracy up to 97.11%. Reliable real-time neurofeedback system could be implemented based on the algorithms proposed in this paper.
Arithmetic knowledge in early semantic dementia.
Luzzi, Simona; Cafazzo, Viviana; Silvestrini, Mauro; Provinciali, Leandro
2013-09-01
The issue of whether arithmetic knowledge is invariably spared or impaired in semantic dementia is still under debate. The corpus of data mainly relies on single case-report descriptions. Relative to this issue, only one paper, by Julien et al. (Neuropsychologia 44(10): 2732-2744, 2008) explored in a systematic way arithmetic knowledge in an SD patient group. The present study is aimed to explore calculation in a group of eight patients affected by early semantic dementia (SD) using a neuropsychological battery devised to examine arithmetic knowledge (arithmetic signs recognition, arithmetic facts and written and mental calculation). These SD patients showed problems in recognition of arithmetic signs, difficulty in arithmetic facts and procedural errors in calculation. Still, the pattern of answers that the SD patients showed was not completely homogeneous and some individual variations were present. In contrast with most literature, the present study provides evidence for impairment of arithmetic knowledge in patients with early semantic dementia and contributes to the recent evidence that arithmetic knowledge cannot be considered an independent domain within the semantic system.
Scalable Normal Basis Arithmetic Unit for Elliptic Curve Cryptography
Directory of Open Access Journals (Sweden)
J. Schmidt
2005-01-01
Full Text Available The design of a scalable arithmetic unit for operations over elements of GF(2m represented in normal basis is presented. The unit is applicable in public-key cryptography. It comprises a pipelined Massey-Omura multiplier and a shifter. We equipped the multiplier with additional data paths to enable easy implementation of both multiplication and inversion in a single arithmetic unit. We discuss optimum design of the shifter with respect to the inversion algorithm and multiplier performance. The functionality of the multiplier/inverter has been tested by simulation and implemented in Xilinx Virtex FPGA.We present implementation data for various digit widths which exhibit a time minimum for digit width D = 15.
Jha, Abhinav K; Kupinski, Matthew A; Rodríguez, Jeffrey J; Stephen, Renu M; Stopeck, Alison T
2012-07-07
In many studies, the estimation of the apparent diffusion coefficient (ADC) of lesions in visceral organs in diffusion-weighted (DW) magnetic resonance images requires an accurate lesion-segmentation algorithm. To evaluate these lesion-segmentation algorithms, region-overlap measures are used currently. However, the end task from the DW images is accurate ADC estimation, and the region-overlap measures do not evaluate the segmentation algorithms on this task. Moreover, these measures rely on the existence of gold-standard segmentation of the lesion, which is typically unavailable. In this paper, we study the problem of task-based evaluation of segmentation algorithms in DW imaging in the absence of a gold standard. We first show that using manual segmentations instead of gold-standard segmentations for this task-based evaluation is unreliable. We then propose a method to compare the segmentation algorithms that does not require gold-standard or manual segmentation results. The no-gold-standard method estimates the bias and the variance of the error between the true ADC values and the ADC values estimated using the automated segmentation algorithm. The method can be used to rank the segmentation algorithms on the basis of both the ensemble mean square error and precision. We also propose consistency checks for this evaluation technique.
Scatter-Reducing Sounding Filtration Using a Genetic Algorithm and Mean Monthly Standard Deviation
Mandrake, Lukas
2013-01-01
Retrieval algorithms like that used by the Orbiting Carbon Observatory (OCO)-2 mission generate massive quantities of data of varying quality and reliability. A computationally efficient, simple method of labeling problematic datapoints or predicting soundings that will fail is required for basic operation, given that only 6% of the retrieved data may be operationally processed. This method automatically obtains a filter designed to reduce scatter based on a small number of input features. Most machine-learning filter construction algorithms attempt to predict error in the CO2 value. By using a surrogate goal of Mean Monthly STDEV, the goal is to reduce the retrieved CO2 scatter rather than solving the harder problem of reducing CO2 error. This lends itself to improved interpretability and performance. This software reduces the scatter of retrieved CO2 values globally based on a minimum number of input features. It can be used as a prefilter to reduce the number of soundings requested, or as a post-filter to label data quality. The use of the MMS (Mean Monthly Standard deviation) provides a much cleaner, clearer filter than the standard ABS(CO2-truth) metrics previously employed by competitor methods. The software's main strength lies in a clearer (i.e., fewer features required) filter that more efficiently reduces scatter in retrieved CO2 rather than focusing on the more complex (and easily removed) bias issues.
Fokkinga, M.M.
1992-01-01
An algorithm is the input-output effect of a computer program; mathematically, the notion of algorithm comes close to the notion of function. Just as arithmetic is the theory and practice of calculating with numbers, so is ALGORITHMICS the theory and practice of calculating with algorithms. Just as
Memory Updating and Mental Arithmetic.
Han, Cheng-Ching; Yang, Tsung-Han; Lin, Chia-Yuan; Yen, Nai-Shing
2016-01-01
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.
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.
Characterization and Comparison of the 10-2 SITA-Standard and Fast Algorithms
Directory of Open Access Journals (Sweden)
Yaniv Barkana
2012-01-01
Full Text Available Purpose: To compare the 10-2 SITA-standard and SITA-fast visual field programs in patients with glaucoma. Methods: We enrolled 26 patients with open angle glaucoma with involvement of at least one paracentral location on 24-2 SITA-standard field test. Each subject performed 10-2 SITA-standard and SITA-fast tests. Within 2 months this sequence of tests was repeated. Results: SITA-fast was 30% shorter than SITA-standard (5.5±1.1 vs 7.9±1.1 minutes, <0.001. Mean MD was statistically significantly higher for SITA-standard compared with SITA-fast at first visit (Δ=0.3 dB, =0.017 but not second visit. Inter-visit difference in MD or in number of depressed points was not significant for both programs. Bland-Altman analysis showed that clinically significant variations can exist in individual instances between the 2 programs and between repeat tests with the same program. Conclusions: The 10-2 SITA-fast algorithm is significantly shorter than SITA-standard. The two programs have similar long-term variability. Average same-visit between-program and same-program between-visit sensitivity results were similar for the study population, but clinically significant variability was observed for some individual test pairs. Group inter- and intra-program test results may be comparable, but in the management of the individual patient field change should be verified by repeat testing.
Indian Academy of Sciences (India)
In the program shown in Figure 1, we have repeated the algorithm. M times and we can make the following observations. Each block is essentially a different instance of "code"; that is, the objects differ by the value to which N is initialized before the execution of the. "code" block. Thus, we can now avoid the repetition of the ...
An Examination of Four Arithmetic Attitude Scales.
Mastantuono, Albert Kenneth; Anttonen, Ralph George
This study examines at the elementary school level four different types of instruments in order to assess their capability to measure the attitudes toward arithmetic of third and fifth grade children. The four arithmetic attitude instruments were administered using a Latin Square model and included: the Dutton-Thurstone Scale, the Dutton-Likert…
Numerical Magnitude Representations Influence Arithmetic Learning
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
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…
ASIC For Complex Fixed-Point Arithmetic
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.
Basri, M.; Mawengkang, H.; Zamzami, E. M.
2018-03-01
Limitations of storage sources is one option to switch to cloud storage. Confidentiality and security of data stored on the cloud is very important. To keep up the confidentiality and security of such data can be done one of them by using cryptography techniques. Data Encryption Standard (DES) is one of the block cipher algorithms used as standard symmetric encryption algorithm. This DES will produce 8 blocks of ciphers combined into one ciphertext, but the ciphertext are weak against brute force attacks. Therefore, the last 8 block cipher will be converted into 8 random images using Least Significant Bit (LSB) algorithm which later draws the result of cipher of DES algorithm to be merged into one.
Computer arithmetic and verilog HDL fundamentals
Cavanagh, Joseph
2009-01-01
Verilog Hardware Description Language (HDL) is the state-of-the-art method for designing digital and computer systems. Ideally suited to describe both combinational and clocked sequential arithmetic circuits, Verilog facilitates a clear relationship between the language syntax and the physical hardware. It provides a very easy-to-learn and practical means to model a digital system at many levels of abstraction. Computer Arithmetic and Verilog HDL Fundamentals details the steps needed to master computer arithmetic for fixed-point, decimal, and floating-point number representations for all prima
Assessing operating characteristics of CAD algorithms in the absence of a gold standard
International Nuclear Information System (INIS)
Roy Choudhury, Kingshuk; Paik, David S.; Yi, Chin A.; Napel, Sandy; Roos, Justus; Rubin, Geoffrey D.
2010-01-01
Purpose: The authors examine potential bias when using a reference reader panel as ''gold standard'' for estimating operating characteristics of CAD algorithms for detecting lesions. As an alternative, the authors propose latent class analysis (LCA), which does not require an external gold standard to evaluate diagnostic accuracy. Methods: A binomial model for multiple reader detections using different diagnostic protocols was constructed, assuming conditional independence of readings given true lesion status. Operating characteristics of all protocols were estimated by maximum likelihood LCA. Reader panel and LCA based estimates were compared using data simulated from the binomial model for a range of operating characteristics. LCA was applied to 36 thin section thoracic computed tomography data sets from the Lung Image Database Consortium (LIDC): Free search markings of four radiologists were compared to markings from four different CAD assisted radiologists. For real data, bootstrap-based resampling methods, which accommodate dependence in reader detections, are proposed to test of hypotheses of differences between detection protocols. Results: In simulation studies, reader panel based sensitivity estimates had an average relative bias (ARB) of -23% to -27%, significantly higher (p-value <0.0001) than LCA (ARB -2% to -6%). Specificity was well estimated by both reader panel (ARB -0.6% to -0.5%) and LCA (ARB 1.4%-0.5%). Among 1145 lesion candidates LIDC considered, LCA estimated sensitivity of reference readers (55%) was significantly lower (p-value 0.006) than CAD assisted readers' (68%). Average false positives per patient for reference readers (0.95) was not significantly lower (p-value 0.28) than CAD assisted readers' (1.27). Conclusions: Whereas a gold standard based on a consensus of readers may substantially bias sensitivity estimates, LCA may be a significantly more accurate and consistent means for evaluating diagnostic accuracy.
Specificity and Overlap in Skills Underpinning Reading and Arithmetical Fluency
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…
Quality of Arithmetic Education for Children with Cerebral Palsy
Jenks, Kathleen M.; de Moor, Jan; van Lieshout, Ernest C. D. M.; Withagen, Floortje
2010-01-01
The aim of this exploratory study was to investigate the quality of arithmetic education for children with cerebral palsy. The use of individual educational plans, amount of arithmetic instruction time, arithmetic instructional grouping, and type of arithmetic teaching method were explored in three groups: children with cerebral palsy (CP) in…
DEFF Research Database (Denmark)
Nica, Florin Valentin Traian; Ritchie, Ewen; Leban, Krisztina Monika
2013-01-01
, genetic algorithm and particle swarm are shortly presented in this paper. These two algorithms are tested to determine their performance on five different benchmark test functions. The algorithms are tested based on three requirements: precision of the result, number of iterations and calculation time...
Visuospatial and verbal memory in mental arithmetic.
Clearman, Jack; Klinger, Vojtěch; Szűcs, Dénes
2017-09-01
Working memory allows complex information to be remembered and manipulated over short periods of time. Correlations between working memory and mathematics achievement have been shown across the lifespan. However, only a few studies have examined the potentially distinct contributions of domain-specific visuospatial and verbal working memory resources in mental arithmetic computation. Here we aimed to fill this gap in a series of six experiments pairing addition and subtraction tasks with verbal and visuospatial working memory and interference tasks. In general, we found higher levels of interference between mental arithmetic and visuospatial working memory tasks than between mental arithmetic and verbal working memory tasks. Additionally, we found that interference that matched the working memory domain of the task (e.g., verbal task with verbal interference) lowered working memory performance more than mismatched interference (verbal task with visuospatial interference). Findings suggest that mental arithmetic relies on domain-specific working memory resources.
How to be Brilliant at Mental Arithmetic
Webber, Beryl
2010-01-01
How to be Brilliant at Mental Arithmetic addresses the twin pillars of mental arithmetic - mental recall and mental agility. Mental recall depends on familiarity with number bonds and plenty of opportunity to practise. Mental agility depends more on confidence with the number system and the four operations. Using the worksheets in this book, students will learn about: tens and units; addition, subtraction, multiplication and division; addition shortcuts; product squares; quick recall; number se
Foundations of arithmetic differential geometry
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.
Directory of Open Access Journals (Sweden)
Robert D Moore
2014-05-01
Full Text Available The current study investigated the influence of cardiorespiratory fitness on arithmetic cognition in forty 9-10 year old children. Measures included a standardized mathematics achievement test to assess conceptual and computational knowledge, self-reported strategy selection, and an experimental arithmetic verification task (including small and large addition problems, which afforded the measurement of event-related brain potentials (ERPs. No differences in math achievement were observed as a function of fitness level, but all children performed better on math concepts relative to math computation. Higher fit children reported using retrieval more often to solve large arithmetic problems, relative to lower fit children. During the arithmetic verification task, higher fit children exhibited superior performance for large problems, as evidenced by greater d’ scores, while all children exhibited decreased accuracy and longer reaction time for large relative to small problems, and incorrect relative to correct solutions. On the electrophysiological level, modulations of early (P1, N170 and late ERP components (P3, N400 were observed as a function of problem size and solution correctness. Higher fit children exhibited selective modulations for N170, P3 and N400 amplitude relative to lower fit children, suggesting that fitness influences symbolic encoding, attentional resource allocation and semantic processing during arithmetic tasks. The current study contributes to the fitness-cognition literature by demonstrating that the benefits of cardiorespiratory fitness extend to arithmetic cognition, which has important implications for the educational environment and the context of learning.
Cognitive precursors of arithmetic development in primary school children with cerebral palsy.
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.
Elementary functions algorithms and implementation
Muller, Jean-Michel
2016-01-01
This textbook presents the concepts and tools necessary to understand, build, and implement algorithms for computing elementary functions (e.g., logarithms, exponentials, and the trigonometric functions). Both hardware- and software-oriented algorithms are included, along with issues related to accurate floating-point implementation. This third edition has been updated and expanded to incorporate the most recent advances in the field, new elementary function algorithms, and function software. After a preliminary chapter that briefly introduces some fundamental concepts of computer arithmetic, such as floating-point arithmetic and redundant number systems, the text is divided into three main parts. Part I considers the computation of elementary functions using algorithms based on polynomial or rational approximations and using table-based methods; the final chapter in this section deals with basic principles of multiple-precision arithmetic. Part II is devoted to a presentation of “shift-and-add” algorithm...
A Quantification of the 3D Modeling Capabilities of the Kinectfusion Algorithm
2014-03-27
algorithm. This allows the three-dimensional points to be converted to a single global coordinate system, which allows the third stage to progress . In... arithmetic mean, standard deviation, maximum, minimum, median, range, third quartile, first quartile, and IQR were calculated. Along with the statistics...registration of 3-d shapes. In Robotics -DL tentative, pages 586–606. International Society for Optics and Photonics, 1992. [9] J. F. Blinn and M. E
Aubin, S; Beaulieu, L; Pouliot, S; Pouliot, J; Roy, R; Girouard, L M; Martel-Brisson, N; Vigneault, E; Laverdière, J
2003-07-01
An algorithm for the daily localization of the prostate using implanted markers and a standard video-based electronic portal imaging device (V-EPID) has been tested. Prior to planning, three gold markers were implanted in the prostate of seven patients. The clinical images were acquired with a BeamViewPlus 2.1 V-EPID for each field during the normal course radiotherapy treatment and are used off-line to determine the ability of the automatic marker detection algorithm to adequately and consistently detect the markers. Clinical images were obtained with various dose levels from ranging 2.5 to 75 MU. The algorithm is based on marker attenuation characterization in the portal image and spatial distribution. A total of 1182 clinical images were taken. The results show an average efficiency of 93% for the markers detected individually and 85% for the group of markers. This algorithm accomplishes the detection and validation in 0.20-0.40 s. When the center of mass of the group of implanted markers is used, then all displacements can be corrected to within 1.0 mm in 84% of the cases and within 1.5 mm in 97% of cases. The standard video-based EPID tested provides excellent marker detection capability even with low dose levels. The V-EPID can be used successfully with radiopaque markers and the automatic detection algorithm to track and correct the daily setup deviations due to organ motions.
DEFF Research Database (Denmark)
Walden, K; Bélanger, L M; Biering-Sørensen, F
2016-01-01
STUDY DESIGN: Validation study. OBJECTIVES: To describe the development and validation of a computerized application of the international standards for neurological classification of spinal cord injury (ISNCSCI). SETTING: Data from acute and rehabilitation care. METHODS: The Rick Hansen Institute......-ISNCSCI Algorithm (RHI-ISNCSCI Algorithm) was developed based on the 2011 version of the ISNCSCI and the 2013 version of the worksheet. International experts developed the design and logic with a focus on usability and features to standardize the correct classification of challenging cases. A five-phased process...... a standardized method to accurately derive the level and severity of SCI from the raw data of the ISNCSCI examination. The web interface assists in maximizing usability while minimizing the impact of human error in classifying SCI. SPONSORSHIP: This study is sponsored by the Rick Hansen Institute and supported...
Dynamic mental number line in simple arithmetic.
Yu, Xiaodan; Liu, Jie; Li, Dawei; Liu, Hang; Cui, Jiaxin; Zhou, Xinlin
2016-05-01
Studies have found that spatial-numerical associations could extend to arithmetic. Addition leads to rightward shift in spatial attention while subtraction leads to leftward shift (e.g., Knops et al. 2009; McCrink et al. 2007; Pinhas & Fischer 2008), which is consistent with the hypothesis of static mental number line (MNL) for arithmetic. The current investigation tested the hypothesis of dynamic mental number line which was shaped by the relative magnitudes of two operands in simple arithmetic. Horizontal and vertical electrooculograms (HEOG and VEOG) during simple arithmetic were recorded. Results showed that the direction of eye movements was dependent on the relative magnitudes of two operands. Subtraction was associated with larger rightward eye movements than addition (Experiment 1), and smaller-operand-first addition (e.g., 2+9) was associated with larger rightward eye movement than larger-operand-first addition (e.g., 9+2) only when the difference of two operands was large (Experiment 2). The results suggest that the direction of the mental number line could be dynamic during simple arithmetic, and that the eyes move along the dynamic mental number line to search for solutions.
Glatthorn, Jonas; Beckschäfer, Philip
2014-01-01
Hemispherical photography is a well-established method to optically assess ecological parameters related to plant canopies; e.g. ground-level light regimes and the distribution of foliage within the crown space. Interpreting hemispherical photographs involves classifying pixels as either sky or vegetation. A wide range of automatic thresholding or binarization algorithms exists to classify the photographs. The variety in methodology hampers ability to compare results across studies. To identify an optimal threshold selection method, this study assessed the accuracy of seven binarization methods implemented in software currently available for the processing of hemispherical photographs. Therefore, binarizations obtained by the algorithms were compared to reference data generated through a manual binarization of a stratified random selection of pixels. This approach was adopted from the accuracy assessment of map classifications known from remote sensing studies. Percentage correct (Pc) and kappa-statistics (K) were calculated. The accuracy of the algorithms was assessed for photographs taken with automatic exposure settings (auto-exposure) and photographs taken with settings which avoid overexposure (histogram-exposure). In addition, gap fraction values derived from hemispherical photographs were compared with estimates derived from the manually classified reference pixels. All tested algorithms were shown to be sensitive to overexposure. Three of the algorithms showed an accuracy which was high enough to be recommended for the processing of histogram-exposed hemispherical photographs: "Minimum" (Pc 98.8%; K 0.952), "Edge Detection" (Pc 98.1%; K 0.950), and "Minimum Histogram" (Pc 98.1%; K 0.947). The Minimum algorithm overestimated gap fraction least of all (11%). The overestimation by the algorithms Edge Detection (63%) and Minimum Histogram (67%) were considerably larger. For the remaining four evaluated algorithms (IsoData, Maximum Entropy, MinError, and Otsu
Arithmetic geometry over global function fields
Longhi, Ignazio; Trihan, Fabien
2014-01-01
This volume collects the texts of five courses given in the Arithmetic Geometry Research Programme 2009–2010 at the CRM Barcelona. All of them deal with characteristic p global fields; the common theme around which they are centered is the arithmetic of L-functions (and other special functions), investigated in various aspects. Three courses examine some of the most important recent ideas in the positive characteristic theory discovered by Goss (a field in tumultuous development, which is seeing a number of spectacular advances): they cover respectively crystals over function fields (with a number of applications to L-functions of t-motives), gamma and zeta functions in characteristic p, and the binomial theorem. The other two are focused on topics closer to the classical theory of abelian varieties over number fields: they give respectively a thorough introduction to the arithmetic of Jacobians over function fields (including the current status of the BSD conjecture and its geometric analogues, and the con...
Impact of optokinetic stimulation on mental arithmetic.
Masson, Nicolas; Pesenti, Mauro; Dormal, Valérie
2017-07-01
Solving arithmetic problems has been shown to induce shifts of spatial attention, subtraction problems orienting attention to the left side, and addition problems to the right side of space. At the neurofunctional level, the activations elicited by the solving of arithmetical problems resemble those elicited by horizontal eye movements. Whether overt orientation of attention (i.e., eye movements) can be linked to the solving procedure is, however, still under debate. In the present study, we used optokinetic stimulation (OKS) to trigger automatic eye movements to orient participants' overt attention to the right or to the left of their visual field while they were solving addition or subtraction problems. The results show that, in comparison to leftward OKS and a control condition, rightward OKS facilitates the solving of addition problems that necessitate a carrying procedure. Subtraction solving was unaffected by leftward or rightward OKS. These results converge with previous findings to show that attentional shifts are functionally related to mental arithmetic processing.
A parallel simulated annealing algorithm for standard cell placement on a hypercube computer
Jones, Mark Howard
1987-01-01
A parallel version of a simulated annealing algorithm is presented which is targeted to run on a hypercube computer. A strategy for mapping the cells in a two dimensional area of a chip onto processors in an n-dimensional hypercube is proposed such that both small and large distance moves can be applied. Two types of moves are allowed: cell exchanges and cell displacements. The computation of the cost function in parallel among all the processors in the hypercube is described along with a distributed data structure that needs to be stored in the hypercube to support parallel cost evaluation. A novel tree broadcasting strategy is used extensively in the algorithm for updating cell locations in the parallel environment. Studies on the performance of the algorithm on example industrial circuits show that it is faster and gives better final placement results than the uniprocessor simulated annealing algorithms. An improved uniprocessor algorithm is proposed which is based on the improved results obtained from parallelization of the simulated annealing algorithm.
Mikhaylova, E.; Kolstein, M.; De Lorenzo, G.; Chmeissani, M.
2014-01-01
A novel positron emission tomography (PET) scanner design based on a room-temperature pixelated CdTe solid-state detector is being developed within the framework of the Voxel Imaging PET (VIP) Pathfinder project [1]. The simulation results show a great potential of the VIP to produce high-resolution images even in extremely challenging conditions such as the screening of a human head [2]. With unprecedented high channel density (450 channels/cm3) image reconstruction is a challenge. Therefore optimization is needed to find the best algorithm in order to exploit correctly the promising detector potential. The following reconstruction algorithms are evaluated: 2-D Filtered Backprojection (FBP), Ordered Subset Expectation Maximization (OSEM), List-Mode OSEM (LM-OSEM), and the Origin Ensemble (OE) algorithm. The evaluation is based on the comparison of a true image phantom with a set of reconstructed images obtained by each algorithm. This is achieved by calculation of image quality merit parameters such as the bias, the variance and the mean square error (MSE). A systematic optimization of each algorithm is performed by varying the reconstruction parameters, such as the cutoff frequency of the noise filters and the number of iterations. The region of interest (ROI) analysis of the reconstructed phantom is also performed for each algorithm and the results are compared. Additionally, the performance of the image reconstruction methods is compared by calculating the modulation transfer function (MTF). The reconstruction time is also taken into account to choose the optimal algorithm. The analysis is based on GAMOS [3] simulation including the expected CdTe and electronic specifics. PMID:25018777
Basile, Vito; Guadagno, Gianluca; Ferrario, Maddalena; Fassi, Irene
2018-03-01
In this paper a parametric, modular and scalable algorithm allowing a fully automated assembly of a backplane fiber-optic interconnection circuit is presented. This approach guarantees the optimization of the optical fiber routing inside the backplane with respect to specific criteria (i.e. bending power losses), addressing both transmission performance and overall costs issues. Graph theory has been exploited to simplify the complexity of the NxN full-mesh backplane interconnection topology, firstly, into N independent sub-circuits and then, recursively, into a limited number of loops easier to be generated. Afterwards, the proposed algorithm selects a set of geometrical and architectural parameters whose optimization allows to identify the optimal fiber optic routing for each sub-circuit of the backplane. The topological and numerical information provided by the algorithm are then exploited to control a robot which performs the automated assembly of the backplane sub-circuits. The proposed routing algorithm can be extended to any array architecture and number of connections thanks to its modularity and scalability. Finally, the algorithm has been exploited for the automated assembly of an 8x8 optical backplane realized with standard multimode (MM) 12-fiber ribbons.
Training of Attention in Children With Low Arithmetical Achievement.
Guarnera, M; D'Amico, A
2014-01-01
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 Disabil...
A computational model of fraction arithmetic.
Braithwaite, David W; Pyke, Aryn A; Siegler, Robert S
2017-10-01
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 with the problems from a widely used textbook series. The simulation generated many phenomena of children's fraction arithmetic performance through a small number of common learning mechanisms operating on a biased input set. The biases were not unique to this textbook series-they were present in 2 other textbook series as well-nor were the phenomena unique to a particular sample of children-they were present in another sample as well. Among other phenomena, the model predicted the high difficulty of fraction division, variable strategy use by individual children and on individual problems, relative frequencies of different types of strategy errors on different types of problems, and variable effects of denominator equality on the four arithmetic operations. The model also generated nonintuitive predictions regarding the relative difficulties of several types of problems and the potential effectiveness of a novel instructional approach. Perhaps the most general lesson of the findings is that the statistical distribution of problems that learners encounter can influence mathematics learning in powerful and nonintuitive ways. (PsycINFO Database Record (c) 2017 APA, all rights reserved).
Historical Analysis of "The Arithmetic Teacher."
Dwyer, Evelyn M.
Articles published in the journal "The Arithmetic Teacher" in 1954-55, 1969, and 1986-88 were analyzed to assess the development of the journal. Note is made of such factors as size, cost, and appearance. Of greater concern is the focus. In the 1954-55 issues, a pragmatic philosophy of education, with emphasis on the usefulness of mathematics and…
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
Generalized Euler constants for arithmetical progressions
Dilcher, Karl
1992-07-01
The work of Lehmer and Briggs on Euler constants in arithmetical progressions is extended to the generalized Euler constants that arise in the Laurent expansion of ζ(s) about s = 1 . The results are applied to the summation of several classes of slowly converging series. A table of the constants is provided.
A geometric characterization of arithmetic varieties
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
The main result is the characterization of arithmetically defined divisors in the plane as geometrically rigid divisors in the plane. Keywords. Equisingular; geometrically rigid. 1. Introduction. This paper is an attempt to generalize a result of Belyi (see [1]). Theorem (Belyi). Let C be a smooth projective curve over an algebraic ...
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...
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/
Self-reference in Arithmetic I
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
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
On Arithmetic-Geometric-Mean Polynomials
Griffiths, Martin; MacHale, Des
2017-01-01
We study here an aspect of an infinite set "P" of multivariate polynomials, the elements of which are associated with the arithmetic-geometric-mean inequality. In particular, we show in this article that there exist infinite subsets of probability "P" for which every element may be expressed as a finite sum of squares of real…
Specificity and overlap in skills underpinning reading and arithmetical fluency
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,
Personal Experience and Arithmetic Meaning in Semantic Dementia
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…
The influence of implicit hand-based representations on mental arithmetic.
Klein, Elise; Moeller, Korbinian; Willmes, Klaus; Nuerk, Hans-Christoph; Domahs, Frank
2011-01-01
Recently, a strong functional relationship between finger counting and number processing has been suggested. It has been argued that bodily experiences such as finger counting may influence the structure of the basic mental representations of numbers even in adults. However, to date it remains unclear whether the structure of finger counting systems also influences educated adults' performance in mental arithmetic. In the present study, we pursued this question by examining finger-based sub-base-five effects in an addition production task. With the standard effect of a carry operation (i.e., base-10 crossing) being replicated, we observed an additional sub-base-five effect such that crossing a sub-base-five boundary led to a relative response time increase. For the case of mental arithmetic sub-base-five effects have previously been reported only in children. However, it remains unclear whether finger-based numerical effects in mental arithmetic reflect an important but transitory step in the development of arithmetical skills. The current findings suggest that even in adults embodied representations such as finger counting patterns modulate arithmetic performance. Thus, they support the general idea that even seemingly abstract cognition in adults may at least partly be rooted in our bodily experiences.
The influence of implicit hand-based representations on mental arithmetic
Directory of Open Access Journals (Sweden)
Elise eKlein
2011-09-01
Full Text Available Recently, a strong functional relationship between finger counting and number processing has been suggested. It has been argued that bodily experiences such as finger counting may influence the structure of the basic mental representations of numbers even in adults. However, to date it remains unclear whether the structure of finger counting systems also influences educated adults’ performance in mental arithmetic.In the present study, we pursued this question by examining finger-based sub-base-five effects in an addition production task. With the standard effect of a carry operation (i.e., base 10 crossing being replicated, we observed an additional sub-base-five effect such that crossing a sub-base 5 boundary led to a relative response time increase. For the case of mental arithmetic sub-base-five effects have previously been reported only in children. However, it remains unclear whether finger-based numerical effects in mental arithmetic reflect an important but transitory step in the development of arithmetical skills. The current findings suggest that even in adults embodied representations such as finger counting patterns modulate arithmetic performance. Thus, they support the general idea that even seemingly abstract cognition in adults may at least partly be rooted in our bodily experiences.
DEFF Research Database (Denmark)
Cook, Gerald; Lin, Ching-Fang
1980-01-01
The local linearization algorithm is presented as a possible numerical integration scheme to be used in real-time simulation. A second-order nonlinear example problem is solved using different methods. The local linearization approach is shown to require less computing time and give significant...... improvement in accuracy over the classical second-order integration methods....
Energy Technology Data Exchange (ETDEWEB)
Kamph, Jerome Henri; Robinson, Darren; Wetter, Michael
2009-09-01
There is an increasing interest in the use of computer algorithms to identify combinations of parameters which optimise the energy performance of buildings. For such problems, the objective function can be multi-modal and needs to be approximated numerically using building energy simulation programs. As these programs contain iterative solution algorithms, they introduce discontinuities in the numerical approximation to the objective function. Metaheuristics often work well for such problems, but their convergence to a global optimum cannot be established formally. Moreover, different algorithms tend to be suited to particular classes of optimization problems. To shed light on this issue we compared the performance of two metaheuristics, the hybrid CMA-ES/HDE and the hybrid PSO/HJ, in minimizing standard benchmark functions and real-world building energy optimization problems of varying complexity. From this we find that the CMA-ES/HDE performs well on more complex objective functions, but that the PSO/HJ more consistently identifies the global minimum for simpler objective functions. Both identified similar values in the objective functions arising from energy simulations, but with different combinations of model parameters. This may suggest that the objective function is multi-modal. The algorithms also correctly identified some non-intuitive parameter combinations that were caused by a simplified control sequence of the building energy system that does not represent actual practice, further reinforcing their utility.
Directory of Open Access Journals (Sweden)
Ari Shawakat Tahir
2015-12-01
Full Text Available The Steganography is an art and science of hiding information by embedding messages within other, seemingly harmless messages and lots of researches are working in it. Proposed system is using AES Algorithm and Lossy technique to overcome the limitation of previous work and increasing the process’s speed. The sender uses AES Algorithm to encrypt message and image, then using LSB technique to hide encrypted data in encrypted message. The receive get the original data using the keys that had been used in encryption process. The proposed system has been implemented in NetBeans 7.3 software uses image and data in different size to find the system’s speed.
Kim, Seonah; Orendt, Anita M; Ferraro, Marta B; Facelli, Julio C
2009-10-01
This article describes the application of our distributed computing framework for crystal structure prediction (CSP) the modified genetic algorithms for crystal and cluster prediction (MGAC), to predict the crystal structure of flexible molecules using the general Amber force field (GAFF) and the CHARMM program. The MGAC distributed computing framework includes a series of tightly integrated computer programs for generating the molecule's force field, sampling crystal structures using a distributed parallel genetic algorithm and local energy minimization of the structures followed by the classifying, sorting, and archiving of the most relevant structures. Our results indicate that the method can consistently find the experimentally known crystal structures of flexible molecules, but the number of missing structures and poor ranking observed in some crystals show the need for further improvement of the potential. Copyright 2009 Wiley Periodicals, Inc.
Studies on Design Automation and Arithmetic Circuit Design for Single-Flux-Quantum Digital Circuits
小畑, 幸嗣; Obata, Koji
2008-01-01
Superconductive single-flux-quantum (SFQ) circuit technology attracts attention as a nextgeneration technology of integrated circuits because of its ultra-fast computation speedand low power consumption. In SFQ digital circuits, unlike CMOS digital circuits, apulse is used as a carrier of information and the representation of the logic values isdifferent from that in CMOS digital circuits. Therefore, design automation algorithms andstructure of arithmetic circuits suitable for SFQ digital cir...
Implementing arithmetic and other analytic operations by transcriptional regulation.
Directory of Open Access Journals (Sweden)
Sean M Cory
2008-04-01
Full Text Available The transcriptional regulatory machinery of a gene can be viewed as a computational device, with transcription factor concentrations as inputs and expression level as the output. This view begs the question: what kinds of computations are possible? We show that different parameterizations of a simple chemical kinetic model of transcriptional regulation are able to approximate all four standard arithmetic operations: addition, subtraction, multiplication, and division, as well as various equality and inequality operations. This contrasts with other studies that emphasize logical or digital notions of computation in biological networks. We analyze the accuracy and precision of these approximations, showing that they depend on different sets of parameters, and are thus independently tunable. We demonstrate that networks of these "arithmetic" genes can be combined to accomplish yet more complicated computations by designing and simulating a network that detects statistically significant elevations in a time-varying signal. We also consider the much more general problem of approximating analytic functions, showing that this can be achieved by allowing multiple transcription factor binding sites on the promoter. These observations are important for the interpretation of naturally occurring networks and imply new possibilities for the design of synthetic networks.
Hierarchical clustering using the arithmetic-harmonic cut: complexity and experiments.
Directory of Open Access Journals (Sweden)
Romeo Rizzi
Full Text Available Clustering, particularly hierarchical clustering, is an important method for understanding and analysing data across a wide variety of knowledge domains with notable utility in systems where the data can be classified in an evolutionary context. This paper introduces a new hierarchical clustering problem defined by a novel objective function we call the arithmetic-harmonic cut. We show that the problem of finding such a cut is NP-hard and APX-hard but is fixed-parameter tractable, which indicates that although the problem is unlikely to have a polynomial time algorithm (even for approximation, exact parameterized and local search based techniques may produce workable algorithms. To this end, we implement a memetic algorithm for the problem and demonstrate the effectiveness of the arithmetic-harmonic cut on a number of datasets including a cancer type dataset and a corona virus dataset. We show favorable performance compared to currently used hierarchical clustering techniques such as k-Means, Graclus and Normalized-Cut. The arithmetic-harmonic cut metric overcoming difficulties other hierarchical methods have in representing both intercluster differences and intracluster similarities.
Ahmed, J U; Awwal, A A
1992-09-10
A memory-efficient dual cell and a multioutput parallel arithmetic logic unit are designed by using a polarization-encoded optical shadow-casting scheme. The design algorithms for identifying the source patterns, input encoding, and output mask are also presented.
Nonverbal arithmetic in humans: light from noise.
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.
Dictionary of algebra, arithmetic, and trigonometry
Krantz, Steven G
2000-01-01
Clear, rigorous definitions of mathematical terms are crucial to good scientific and technical writing-and to understanding the writings of others. Scientists, engineers, mathematicians, economists, technical writers, computer programmers, along with teachers, professors, and students, all have the need for comprehensible, working definitions of mathematical expressions. To meet that need, CRC Press proudly introduces its Dictionary of Algebra, Arithmetic, and Trigonometry- the second published volume in the CRC Comprehensive Dictionary of Mathematics. More than three years in development, top academics and professionals from prestigious institutions around the world bring you more than 2,800 detailed definitions, written in a clear, readable style, complete with alternative meanings, and related references.From Abelian cohomology to zero ring and from the very basic to the highly advanced, this unique lexicon includes terms associated with arithmetic, algebra, and trigonometry, with natural overlap into geom...
An efficient algorithm for generating random number pairs drawn from a bivariate normal distribution
Campbell, C. W.
1983-01-01
An efficient algorithm for generating random number pairs from a bivariate normal distribution was developed. Any desired value of the two means, two standard deviations, and correlation coefficient can be selected. Theoretically the technique is exact and in practice its accuracy is limited only by the quality of the uniform distribution random number generator, inaccuracies in computer function evaluation, and arithmetic. A FORTRAN routine was written to check the algorithm and good accuracy was obtained. Some small errors in the correlation coefficient were observed to vary in a surprisingly regular manner. A simple model was developed which explained the qualities aspects of the errors.
Coherent states, pseudodifferential analysis and arithmetic
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’.
Real closures of models of weak arithmetic
Czech Academy of Sciences Publication Activity Database
Jeřábek, Emil; Kolodziejczyk, L. A.
2013-01-01
Roč. 52, 1-2 (2013), s. 143-157 ISSN 0933-5846 R&D Projects: GA AV ČR IAA100190902; GA MŠk(CZ) 1M0545 Institutional support: RVO:67985840 Keywords : bounded arithmetic * real-closed field * recursive saturation Subject RIV: BA - General Mathematics http://link.springer.com/article/10.1007%2Fs00153-012-0311-x
Individual differences in solving arithmetic word problems
2013-01-01
Background With the present functional magnetic resonance imaging (fMRI) study at 3 T, we investigated the neural correlates of visualization and verbalization during arithmetic word problem solving. In the domain of arithmetic, visualization might mean to visualize numbers and (intermediate) results while calculating, and verbalization might mean that numbers and (intermediate) results are verbally repeated during calculation. If the brain areas involved in number processing are domain-specific as assumed, that is, that the left angular gyrus (AG) shows an affinity to the verbal domain, and that the left and right intraparietal sulcus (IPS) shows an affinity to the visual domain, the activation of these areas should show a dependency on an individual’s cognitive style. Methods 36 healthy young adults participated in the fMRI study. The participants habitual use of visualization and verbalization during solving arithmetic word problems was assessed with a short self-report assessment. During the fMRI measurement, arithmetic word problems that had to be solved by the participants were presented in an event-related design. Results We found that visualizers showed greater brain activation in brain areas involved in visual processing, and that verbalizers showed greater brain activation within the left angular gyrus. Conclusions Our results indicate that cognitive styles or preferences play an important role in understanding brain activation. Our results confirm, that strong visualizers use mental imagery more strongly than weak visualizers during calculation. Moreover, our results suggest that the left AG shows a specific affinity to the verbal domain and subserves number processing in a modality-specific way. PMID:23883107
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
Number sense in teaching and learning arithmetic
DEFF Research Database (Denmark)
Rezat, Sebastian; Ejersbo, Lisser Rye
2018-01-01
From the beginning of CERME conferences, the concept of number sense and its relation to the teaching and learning arithmetic and number systems has been a central theme. However, different meanings of the term have been used, and it has not always been clear which meaning is referred to. Depending......? Second, what can be done to foster the development of number sense? Third, what is the scope of number sense in terms of different number domains including fractions and negative numbers?...
Marghetis, Tyler; Núñez, Rafael; Bergen, Benjamin K
2014-01-01
Mathematics requires precise inferences about abstract objects inaccessible to perception. How is this possible? One proposal is that mathematical reasoning, while concerned with entirely abstract objects, nevertheless relies on neural resources specialized for interacting with the world-in other words, mathematics may be grounded in spatial or sensorimotor systems. Mental arithmetic, for instance, could involve shifts in spatial attention along a mental "number-line", the product of cultural artefacts and practices that systematically spatialize number and arithmetic. Here, we investigate this hypothesized spatial processing during exact, symbolic arithmetic (e.g., 4 + 3 = 7). Participants added and subtracted single-digit numbers and selected the exact solution from responses in the top corners of a computer monitor. While they made their selections using a computer mouse, we recorded the movement of their hand as indexed by the streaming x, y coordinates of the computer mouse cursor. As predicted, hand movements during addition and subtraction were systematically deflected toward the right and the left, respectively, as if calculation involved simultaneously simulating motion along a left-to-right mental number-line. This spatial-arithmetical bias, moreover, was distinct from-but correlated with-individuals' spatial-numerical biases (i.e., spatial-numerical association of response codes, SNARC, effect). These results are the first evidence that exact, symbolic arithmetic prompts systematic spatial processing associated with mental calculation. We discuss the possibility that mathematical calculation relies, in part, on an integrated system of spatial processes.
Sargent, Jeff Scott
1988-01-01
A new row-based parallel algorithm for standard-cell placement targeted for execution on a hypercube multiprocessor is presented. Key features of this implementation include a dynamic simulated-annealing schedule, row-partitioning of the VLSI chip image, and two novel new approaches to controlling error in parallel cell-placement algorithms; Heuristic Cell-Coloring and Adaptive (Parallel Move) Sequence Control. Heuristic Cell-Coloring identifies sets of noninteracting cells that can be moved repeatedly, and in parallel, with no buildup of error in the placement cost. Adaptive Sequence Control allows multiple parallel cell moves to take place between global cell-position updates. This feedback mechanism is based on an error bound derived analytically from the traditional annealing move-acceptance profile. Placement results are presented for real industry circuits and the performance is summarized of an implementation on the Intel iPSC/2 Hypercube. The runtime of this algorithm is 5 to 16 times faster than a previous program developed for the Hypercube, while producing equivalent quality placement. An integrated place and route program for the Intel iPSC/2 Hypercube is currently being developed.
Is an interval the right result of arithmetic operations on intervals?
Piegat Andrzej; Landowski Marek
2017-01-01
For many scientists interval arithmetic (IA, I arithmetic) seems to be easy and simple. However, this is not true. Interval arithmetic is complicated. This is confirmed by the fact that, for years, new, alternative versions of this arithmetic have been created and published. These new versions tried to remove shortcomings and weaknesses of previously proposed options of the arithmetic, which decreased the prestige not only of interval arithmetic itself, but also of fuzzy arithmetic, which, to...
Image and video compression for multimedia engineering fundamentals, algorithms, and standards
Shi, Yun Q
2008-01-01
Part I: Fundamentals Introduction Quantization Differential Coding Transform Coding Variable-Length Coding: Information Theory Results (II) Run-Length and Dictionary Coding: Information Theory Results (III) Part II: Still Image Compression Still Image Coding: Standard JPEG Wavelet Transform for Image Coding: JPEG2000 Nonstandard Still Image Coding Part III: Motion Estimation and Compensation Motion Analysis and Motion Compensation Block Matching Pel-Recursive Technique Optical Flow Further Discussion and Summary on 2-D Motion Estimation Part IV: Video Compression Fundam
Directory of Open Access Journals (Sweden)
Ari Muzakir
2017-05-01
Full Text Available Ease of deployment of digital image through the internet has positive and negative sides, especially for owners of the original digital image. The positive side of the ease of rapid deployment is the owner of that image deploys digital image files to various sites in the world address. While the downside is that if there is no copyright that serves as protector of the image it will be very easily recognized ownership by other parties. Watermarking is one solution to protect the copyright and know the results of the digital image. With Digital Image Watermarking, copyright resulting digital image will be protected through the insertion of additional information such as owner information and the authenticity of the digital image. The least significant bit (LSB is one of the algorithm is simple and easy to understand. The results of the simulations carried out using android smartphone shows that the LSB watermarking technique is not able to be seen by naked human eye, meaning there is no significant difference in the image of the original files with images that have been inserted watermarking. The resulting image has dimensions of 640x480 with a bit depth of 32 bits. In addition, to determine the function of the ability of the device (smartphone in processing the image using this application used black box testing.
Directory of Open Access Journals (Sweden)
T. Schrader
2003-01-01
Full Text Available A new coaxial device with 7-mm-N-connector was developed providing calculable complex reflection coefficients for traceable calibration of vector network analyzers (VNA. It was specifically designed to fill the gap between 0 Hz (DC, direct current and 250MHz, though the device was tested up to 10GHz. The frequency dependent reflection coefficient of this device can be described by a model, which is characterized by traceable measurements. It is therefore regarded as a “traceable model". The new idea of using such models for traceability has been verified, found to be valid and was used for these investigations. The DC resistance value was extracted from RF measurements up to 10 GHz by means of Genetic Algorithms (GA. The GA was used to obtain the elements of the model describing the reflection coefficient Γ of a network of SMD resistors. The DC values determined with the GA from RF measurements match the traceable value at DC within 3·10-3, which is in good agreement with measurements using reference air lines at GHz frequencies.
International Nuclear Information System (INIS)
Kainberger, Franz; Pokieser, Peter; Imhof, Herwig; Czembirek, Heinrich; Fruehwald, Franz
2002-01-01
Guidelines can be regarded as special forms of algorithms and have been shown to be useful tools for supporting medical decision making. With the Council Directive 97/43/Euratom recommendations concerning referral criteria for medical exposure have to be implemented into national law of all EU member states. The time- and cost-consuming efforts of developing, implementing, and updating such guidelines are balanced by the acceptance in clinical practice and eventual better health outcomes. Clearly defined objectives with special attention drawn on national and regional differences among potential users, support from organisations with expertise in evidence-based medicine, separated development of the evidence component and the recommendations component, and large-scale strategies for distribution and implementation are necessary. Editors as well as users of guidelines for referral criteria have to be aware which expectations can be met and which cannot be fulfilled with this instrument; thus, dealing with guidelines requires a new form of ''diagnostic reasoning'' based on medical ethics. (orig.)
The Time Course of Spatial Attention Shifts in Elementary Arithmetic.
Liu, Dixiu; Cai, Danni; Verguts, Tom; Chen, Qi
2017-04-19
It has been proposed that elementary arithmetic induces spatial shifts of attention. However, the timing of this arithmetic-space association remains unknown. Here we investigate this issue with a target detection paradigm. Detecting targets in the right visual field was faster than in the left visual field when preceded by an addition operation, while detecting targets in the left visual field was faster than in the right visual field when preceded by a subtraction operation. The arithmetic-space association was found both at the end of the arithmetic operation and during calculation. In contrast, the processing of operators themselves did not induce spatial biases. Our results suggest that the arithmetic-space association resides in the mental arithmetic operation rather than in the individual numbers or the operators. Moreover, the temporal course of this effect was different in addition and subtraction.
A Note on Arithmetic Progressions on Quartic Elliptic Curves
Ulas, Maciej
2005-05-01
G. Campbell described a technique for producing infinite families of quartic elliptic curves containing a length-9 arithmetic progression. He also gave an example of a quartic elliptic curve containing a length-12 arithmetic progression. In this note we give a construction of an infinite family of quartics on which there is an arithmetic progression of length 10. Then we show that there exists an infinite family of quartics containing a sequence of length 12.
Alexia for arithmetical signs. A cause of disturbed calculation.
Ferro, J M; Silveira Botelho, M A
1980-03-01
Asymbolic acalculia is a variety of acalculia characterized by a failure to differentiate the arithmetical symbols. Two patients presenting this disturbance as the only source of their calculating errors are reported. Neither aphasia nor visuo-verbal disconnection could explain the failure to identify the arithmetical signs. This defect is interpreted as an alexia for this particular semiotic system, the arithmetical signs being stripped of their names and of the corresponding computational rules.
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)
Algebra 1 groups, rings, fields and arithmetic
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.
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)
Simmons, Fiona R.; Singleton, Chris
2008-01-01
We review significant empirical studies of the arithmetic abilities of children with dyslexia. These studies suggest that the academic impairments of children with dyslexia are not limited to reading and spelling, but also include aspects of mathematics. A consistent finding across a number of studies is that children with dyslexia have difficulty…
Arithmetic after School: How Do Adults' Mental Arithmetic Abilities Evolve with Age?
Charron, Camilo; Fischer, Jean-Paul; Meljac, Claire
2008-01-01
To date, few studies have investigated the evolution of problem solving and general numeracy abilities during adulthood: skills that have obvious social importance. In this research, evolutions in adults' mental arithmetic skills were investigated using data from the IVQ 2004 French national survey, which tested 9,185 adults aged between 18 and…
Wiemers, Michael; Bekkering, Harold; Lindemann, Oliver
2014-01-01
Recent research on spatial number representations suggests that the number space is not necessarily horizontally organized and might also be affected by acquired associations between magnitude and sensory experiences in vertical space. Evidence for this claim is, however, controversial. The present study now aims to compare vertical and horizontal spatial associations in mental arithmetic. In Experiment 1, participants solved addition and subtraction problems and indicated the result verbally while moving their outstretched right arm continuously left-, right-, up-, or downwards. The analysis of the problem-solving performances revealed a motion-arithmetic compatibility effect for spatial actions along both the horizontal and the vertical axes. Performances in additions was impaired while making downward compared to upward movements as well as when moving left compared to right and vice versa in subtractions. In Experiment 2, instead of being instructed to perform active body movements, participants calculated while the problems moved in one of the four relative directions on the screen. For visual motions, only the motion-arithmetic compatibility effect for the vertical dimension could be replicated. Taken together, our findings provide first evidence for an impact of spatial processing on mental arithmetic. Moreover, the stronger effect of the vertical dimension supports the idea that mental calculations operate on representations of numerical magnitude that are grounded in a vertically organized mental number space.
DEFF Research Database (Denmark)
Kowalska, Justyna D; Mocroft, Amanda; Ledergerber, Bruno
2011-01-01
cohort classification (LCC) as reported by the site investigator, and 4 algorithms (ALG) created based on survival times after specific AIDS events. Results: A total of 2,783 deaths occurred, 540 CoDe forms were collected, and 488 were used to evaluate agreements. The agreement between CC and LCC...... are a natural consequence of an increased awareness and knowledge in the field. To monitor and analyze changes in mortality over time, we have explored this issue within the EuroSIDA study and propose a standardized protocol unifying data collected and allowing for classification of all deaths as AIDS or non-AIDS...... related, including events with missing cause of death. Methods: Several classifications of the underlying cause of death as AIDS or non-AIDS related within the EuroSIDA study were compared: central classification (CC-reference group) based on an externally standardised method (the CoDe procedures), local...
Transfer of training in alphabet arithmetic.
Campbell, Jamie I D; Chen, Yalin; Allen, Kurtis; Beech, Leah
2016-11-01
In recent years, several researchers have proposed that skilled adults may solve single-digit addition problems (e.g., 3 + 1 = 4, 4 + 3 = 7) using a fast counting procedure. Practicing a procedure, however, often leads to transfer of learning to unpracticed items; consequently, the fast counting theory was potentially challenged by subsequent studies that found no generalization of practice for simple addition. In two experiments reported here (Ns = 48), we examined generalization in an alphabet arithmetic task (e.g., B + 5 = C D E F G) to determine that counting-based procedures do produce generalization. Both experiments showed robust generalization (i.e., faster response times relative to control problems) when a test problem's letter augend and answer letter sequence overlapped with practiced problems (e.g., practice B + 5 = C D E F G, test B + 3 = C D E ). In Experiment 2, test items with an unpracticed letter but whose answer was in a practiced letter sequence (e.g., practice C + 3 = DEF, test D + 2 = E F) also displayed generalization. Reanalysis of previously published addition generalization experiments (combined n = 172) found no evidence of facilitation when problems were preceded by problems with a matching augend and counting sequence. The clear presence of generalization in counting-based alphabet arithmetic, and the absence of generalization of practice effects in genuine addition, represent a challenge to fast counting theories of skilled adults' simple addition.
Arithmetic Training Does Not Improve Approximate Number System Acuity
Directory of Open Access Journals (Sweden)
Marcus Lindskog
2016-10-01
Full Text Available The Approximate Number System (ANS is thought to support non-symbolic representations of numerical magnitudes in humans. Recently much debate has focused on the causal direction for an observed relation between ANS acuity and arithmetic fluency. Here we investigate if arithmetic training can improve ANS acuity. We show with an experimental training study consisting of six 45-minute training sessions that although feedback during arithmetic training improves arithmetic performance substantially, it does not influence ANS acuity. Hence, we find no support for a causal link where symbolic arithmetic training influences the ANS acuity. Further, although short-term number memory is likely involved in arithmetic tasks we did not find that short-term memory capacity for numbers, measured by a digit-span test, was effected by arithmetic training. This suggests that the improvement in arithmetic fluency may have occurred independent of short-term memory efficiency, but rather due to long-term memory processes and/or mental calculation strategy development. The theoretical implications of these findings are discussed.
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 ...
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
On the order of magnitude of some arithmetical functions under ...
Indian Academy of Sciences (India)
Let ≥ 2 be an integer and let () denote the sum of the digits in base of the positive integer . We look for an estimate of the average of some multiplicative arithmetical functions under constraints on the arithmetical congruence of the integers and the sum of their digits.
Covering an arithmetic progression with geometric progressions and vice versa
Sanna, Carlo
2013-01-01
We show that there exists a positive constant C such that the following holds: Given an infinite arithmetic progression A of real numbers and a sufficiently large integer n (depending on A), there needs at least Cn geometric progressions to cover the first n terms of A. A similar result is presented, with the role of arithmetic and geometric progressions reversed.
Szemerédi's theorem and problems on arithmetic progressions
Shkredov, I. D.
2006-12-01
Szemerédi's famous theorem on arithmetic progressions asserts that every subset of integers of positive asymptotic density contains arithmetic progressions of arbitrary length. His remarkable theorem has been developed into a major new area of combinatorial number theory. This is the topic of the present survey.
Derivations and generating degrees in the ring of arithmetical ...
Indian Academy of Sciences (India)
In this paper we study a family of derivations in the ring of arithmetical functions of several variables over an integral domain, and compute the generating degrees of the ring of arithmetical functions over the kernel of these derivations. Author Affiliations. Alexandru Zaharescu1 Mohammad Zaki1. Department of Mathematics ...
Numeral Writing Skill and Elementary Arithmetic Mental Calculations
Johansson, Bo S.
2005-01-01
The paper reports three studies addressing the role of numeral writing for arithmetic performance. About 650 children in the age range 5-7 years participated in the studies. The results demonstrate a positive correlation between number of digits correctly written and number of arithmetic problems solved. The correlations between number of reversed…
Arithmetic Training Does Not Improve Approximate Number System Acuity.
Lindskog, Marcus; Winman, Anders; Poom, Leo
2016-01-01
The approximate number system (ANS) is thought to support non-symbolic representations of numerical magnitudes in humans. Recently much debate has focused on the causal direction for an observed relation between ANS acuity and arithmetic fluency. Here we investigate if arithmetic training can improve ANS acuity. We show with an experimental training study consisting of six 45-min training sessions that although feedback during arithmetic training improves arithmetic performance substantially, it does not influence ANS acuity. Hence, we find no support for a causal link where symbolic arithmetic training influences ANS acuity. Further, although short-term number memory is likely involved in arithmetic tasks we did not find that short-term memory capacity for numbers, measured by a digit-span test, was effected by arithmetic training. This suggests that the improvement in arithmetic fluency may have occurred independent of short-term memory efficiency, but rather due to long-term memory processes and/or mental calculation strategy development. The theoretical implications of these findings are discussed.
COGNITIVE ARITHMETIC: Mental Processing of Addition and Multiplication
Sugiyanto, -
2016-01-01
In contrast to the many studies of languages processing, there have been relatively few studies of arithmetic processing in cognitive psychology. Author of textbooks for university students, such as Solso (1991), do not appear to feel a need to address cognitive arithmetic issues in their books.
Genetic Programming with Smooth Operators for Arithmetic Expressions
DEFF Research Database (Denmark)
Ursem, Rasmus Kjær; Krink, Thiemo
2002-01-01
This paper introduces the smooth operators for arithmetic expressions as an approach to smoothening the search space in Genetic Programming (GP). Smooth operator GP interpolates between arithmetic operators such as * and /, thereby allowing a gradual adaptation to the problem. The suggested appro...
On the order of magnitude of some arithmetical functions under ...
Indian Academy of Sciences (India)
Let q ≥ 2 be an integer and let Sq(n) denote the sum of the digits in base q of the positive integer n. We look for an estimate of the average of some multiplicative arithmetical functions under constraints on the arithmetical congruence of the integers and the sum of their digits. Keywords. Sum of digits function; multiplicative ...
Balzi, Daniela; Barchielli, Alessandro; Battistella, Giuseppe; Gnavi, Roberto; Inio, Andrea; Tessari, Roberta; Picariello, Roberta; Canova, Cristina; Simonato, Lorenzo
2008-01-01
to define an algorithm to estimate prevalence of ischemic heart disease from health administrative datasets. four Italian areas: Venezia, Treviso, Torino, Firenze. resident population in the four areas in the period 2002-2004 (only 2003 for Firenze) for a total of 2,350,000 inhabitants in 2003. annual crude and standardized prevalence rate (x100 inhabitants), 95% confidence intervals by area. Quality (comparability and coherence) indicators are also reported the algorithm is based on record linkage of hospital discharges (SDO), pharmacological prescriptions (PF), exemptions from health-tax exemptions (ET) and causes of mortality (CM). From SDO we extracted discharges for ICD9-CM codes 410*-414* in all diagnoses in the estimation year and during the four years immediately preceding. We selected from PF subjects with at least two prescriptions of organic nitrates (ATC = C01DA*) in the estimation year. From ET subjects with a new exemption for ischemic heart disease (002.414) or who obtained exemption in the three years preceding, were selected. We also considered all deaths in the year for ischemic heart disease (ICD9 CM 410-414). Cases were defined as ischemic heart disease prevalent cases if they were extracted at least once from one of the datasets and if they were alive on January 1 of the estimation year. estimated crude prevalence ranges from 2.5 to 4%. The standardized prevalence led to a narrower range of values (2.8-3.3%). Venezia and Firenze show a higher standardized prevalence in both sexes (men 4.7% and 4.4%; women 2.3% and 2.2% respectively); Treviso and Torino present a lower standardized prevalence (men: 3.9%; women: 1.9%). The hospital discharges are the main source to identify prevalent subjects (34-48% of subjects are solely identified by SDO), pharmacological prescriptions are a relevant source in Firenze and Torino (27-28%), while they are less relevant in Venezia and Treviso (13-15%). ET shows a different contribution to prevalent case
Arithmetic groups and their generalizations what, why, and how
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.
Advanced topics in the arithmetic of elliptic curves
Silverman, Joseph H
1994-01-01
In the introduction to the first volume of The Arithmetic of Elliptic Curves (Springer-Verlag, 1986), I observed that "the theory of elliptic curves is rich, varied, and amazingly vast," and as a consequence, "many important topics had to be omitted." I included a brief introduction to ten additional topics as an appendix to the first volume, with the tacit understanding that eventually there might be a second volume containing the details. You are now holding that second volume. it turned out that even those ten topics would not fit Unfortunately, into a single book, so I was forced to make some choices. The following material is covered in this book: I. Elliptic and modular functions for the full modular group. II. Elliptic curves with complex multiplication. III. Elliptic surfaces and specialization theorems. IV. Neron models, Kodaira-Neron classification of special fibers, Tate's algorithm, and Ogg's conductor-discriminant formula. V. Tate's theory of q-curves over p-adic fields. VI. Neron's theory of can...
Distraction of Mental Arithmetic by Background Speech.
Perham, Nick; Marsh, John E; Clarkson, Martin; Lawrence, Rosie; Sörqvist, Patrik
2016-06-01
When solving mental arithmetic problems, one can easily be distracted by someone speaking in the background and this distraction is greater if the speech comprises numbers. We explored the basis of this disruption by asking participants to solve mental addition problems (e.g., "45 + 17 = ?") in three different conditions: background speech comprising numbers in ascending order (e.g., "61, 62, 63, 64, 65"), background speech comprising numbers in descending order (e.g., "65, 64, 63, 62, 61"), and quiet. Performance was best in quiet, worse in the descending numbers condition, and poorest in the ascending numbers condition. In view of these findings, we suggest that disruption arises as a by-product of preventing the primed, but inaccurate, candidate responses from assuming the control of action. Alternative explanations are also discussed.
PaCAL: A Python Package for Arithmetic Computations with Random Variables
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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.
Arithmetic coding with adaptive context-tree weighting for the H.264 video coders
Hong, Danny; van der Schaar, Mihaela; Pesquet-Popescu, Beatrice
2004-01-01
We propose applying an adaptive context-tree weighting (CTW) method in the H.264 video coders. We first investigate two different ways to incorporating the CTW method into an H.264 coder and compare the coding effectiveness of using the method with that of using the context models specified in the H.264 standard. We then describe a novel approach for automatically adapting the CTW method based on the syntactic element to be coded and the encoding parameters. We show that our CTW-based arithmetic coding method yields similar or better compression results compared with the context-based adaptive arithmetic coding method used in H.264, without having to specify so many context models.
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...... it to automatically construct a symbolic execution graph that over-approximates all possible runs of a program and that can be used to prove memory safety. This graph is then transformed into an integer transition system, whose termination can be proved by standard techniques. We implemented this approach...... in the automated termination prover AProVE and demonstrate its capability of analyzing C programs with pointer arithmetic that existing tools cannot handle....
Frege, Dedekind, and Peano on the foundations of arithmetic
Gillies, Donald
2013-01-01
First published in 1982, this reissue contains a critical exposition of the views of Frege, Dedekind and Peano on the foundations of arithmetic. The last quarter of the 19th century witnessed a remarkable growth of interest in the foundations of arithmetic. This work analyses both the reasons for this growth of interest within both mathematics and philosophy and the ways in which this study of the foundations of arithmetic led to new insights in philosophy and striking advances in logic. This historical-critical study provides an excellent introduction to the problems of the philosop
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
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
Asymptotic formulas for sequence factorial of arithmetic progression
Aṣiru, Muniru A.
2014-08-01
This note provides asymptotic formulas for approximating the sequence factorial of members of a finite arithmetic progression by using Stirling, Burnside and other more accurate asymptotic formulas for large factorials that have appeared in the literature.
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.
Muluh, E T; Vaughan, C L; John, L R
2011-03-01
Early, late and slow waves of event-related potentials (erps) appearing around 0-300 ms, 300-500 ms and after 500 ms respectively post-question presentation have been differentially associated to mental arithmetic processing (MAP). We hypothesized that arithmetic-operation effect (AOE) will show greater modulation of early components (P100, P200) in high-frequency erps; late components (P300, N300) and slow waves in low-frequency ERP when large-size problems are employed. Fourteen normal human subjects mentally processed large- and small-size addition, division, multiplication and subtraction problems. Spatiotemporal differences between these arithmetic-operations were studied by way of comparing amplitudes and latencies of early, late and slow waves. All components were modulated by AOE. Modulated was observed as early as 100 ms post-question presentation (in high-frequency ERP components). AOE was very pronounced in large-size problems (in low-frequency ERP components). Results suggest that modulation by AOE of ERP components is improved when large-size problems and low-frequency ERP components are employed. Thus, differentiation of neuropsychological processes manifested by amplitude and latency of ERP components may be best studied by first separating components into high- and low-frequency erps. Findings raise the potential of obtaining ERP indices that may improve findings about the degree (and time) of engagement of cognitive processes (e.g. Strategy employed in MAP). Copyright © 2010 International Federation of Clinical Neurophysiology. Published by Elsevier Ireland Ltd. All rights reserved.
The effect of cognitive, personality, and background factors on the WAIS-III Arithmetic subtest.
Karzmark, Peter
2009-01-01
In the Wechsler system the Arithmetic subtest has been viewed as a measure of concentration, working memory, or freedom from distractibility. However, a wide range of other influences on Arithmetic performance has been proposed. The current study was intended to examine these to further characterize what is measured by the Arithmetic subtest. Participants were 118 adults referred for neuropsychological assessment. The results indicate a strong association between WAIS-III Arithmetic and the other WMI (Working Memory Index) subtests. Arithmetic also showed a high association with Arithmetic skill and verbal memory. Moderate contributions to Arithmetic performance were found for most other cognitive measures. Measures of anxiety and of background factors, such as perceived difficulty learning Arithmetic, were weakly related to Arithmetic scores. These results suggest that although Arithmetic may be considered a measure of concentration or working memory, many other factors influence it and its specificity as a concentration measure is limited.
On the second moment for primes in an arithmetic progression
Goldston, D. A.; Yildirim, C. Y.
Assuming the Generalized Riemann Hypothesis, we obtain a lower bound within a constant factor of the conjectured asymptotic result for the second moment for primes in an individual arithmetic progression in short intervals. Previous results were averaged over all progression of a given modulus. The method uses a short divisor sum approximation for the von Mangoldt function, together with some new results for binary correlations of this divisor sum approximation in arithmetic progressions.
Frontal midline theta oscillations during mental arithmetic: effects of stress
Gärtner, Matti; Grimm, Simone; Bajbouj, Malek
2015-01-01
Complex cognitive tasks such as mental arithmetic heavily rely on intact, well-coordinated prefrontal cortex (PFC) function. Converging evidence suggests that frontal midline theta (FMT) oscillations play an important role during the execution of such PFC-dependent tasks. Additionally, it is well-established that acute stress impairs PFC function, and recent evidence suggests that FMT is decreased under stress. In this EEG study, we investigated FMT oscillations during a mental arithmetic tas...
Arithmetical aspects of the large sieve inequality
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...
Conference on Number Theory and Arithmetic Geometry
Silverman, Joseph; Stevens, Glenn; Modular forms and Fermat’s last theorem
1997-01-01
This volume contains expanded versions of lectures given at an instructional conference on number theory and arithmetic geometry held August 9 through 18, 1995 at Boston University. Contributor's includeThe purpose of the conference, and of this book, is to introduce and explain the many ideas and techniques used by Wiles in his proof that every (semi-stable) elliptic curve over Q is modular, and to explain how Wiles' result can be combined with Ribet's theorem and ideas of Frey and Serre to show, at long last, that Fermat's Last Theorem is true. The book begins with an overview of the complete proof, followed by several introductory chapters surveying the basic theory of elliptic curves, modular functions, modular curves, Galois cohomology, and finite group schemes. Representation theory, which lies at the core of Wiles' proof, is dealt with in a chapter on automorphic representations and the Langlands-Tunnell theorem, and this is followed by in-depth discussions of Serre's conjectures, Galois deformations, ...
Adams operations on higher arithmetic K-theory
DEFF Research Database (Denmark)
Feliu, Elisenda
2010-01-01
We construct Adams operations on the rational higher arithmetic K-groups of a proper arithmetic variety. The de¿nition applies to the higher arithmetic K-groups given by Takeda as well as to the groups suggested by Deligne and Soulé, by means of the homotopy groups of the homotopy ¿ber of the reg......We construct Adams operations on the rational higher arithmetic K-groups of a proper arithmetic variety. The de¿nition applies to the higher arithmetic K-groups given by Takeda as well as to the groups suggested by Deligne and Soulé, by means of the homotopy groups of the homotopy ¿ber...... of the regulator map. They are compatible with the Adams operations on algebraic K-theory. The de¿nition relies on the chain morphism representing Adams operations in higher algebraic K-theory given previously by the author. It is shown that this chain morphism commutes strictly with the representative...
Mental arithmetic in the bilingual brain: Language matters.
Van Rinsveld, Amandine; Dricot, Laurence; Guillaume, Mathieu; Rossion, Bruno; Schiltz, Christine
2017-07-01
How do bilinguals solve arithmetic problems in each of their languages? We investigated this question by exploring the neural substrates of mental arithmetic in bilinguals. Critically, our population was composed of a homogeneous group of adults who were fluent in both of their instruction languages (i.e., German as first instruction language and French as second instruction language). Twenty bilinguals were scanned with fMRI (3T) while performing mental arithmetic. Both simple and complex problems were presented to disentangle memory retrieval occuring in very simple problems from arithmetic computation occuring in more complex problems. In simple additions, the left temporal regions were more activated in German than in French, whereas no brain regions showed additional activity in the reverse constrast. Complex additions revealed the reverse pattern, since the activations of regions for French surpassed the same computations in German and the extra regions were located predominantly in occipital regions. Our results thus highlight that highly proficient bilinguals rely on differential activation patterns to solve simple and complex additions in each of their languages, suggesting different solving procedures. The present study confirms the critical role of language in arithmetic problem solving and provides novel insights into how highly proficient bilinguals solve arithmetic problems. Copyright © 2017 Elsevier Ltd. All rights reserved.
Assessing Adult Learner’s Numeracy as Related to Gender and Performance in Arithmetic
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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.
Alpert, Bruce S
2011-04-01
We evaluated two new Welch Allyn automated blood pressure (BP) algorithms. The first, SureBP, estimates BP during cuff inflation; the second, StepBP, does so during deflation. We followed the American National Standards Institute/Association for the Advancement of Medical Instrumentation SP10:2006 standard for testing and data analysis. The data were also analyzed using the British Hypertension Society analysis strategy. We tested children, adolescents, and adults. The requirements of the American National Standards Institute/Association for the Advancement of Medical Instrumentation SP10:2006 standard were fulfilled with respect to BP levels, arm sizes, and ages. Association for the Advancement of Medical Instrumentation SP10 Method 1 data analysis was used. The mean±standard deviation for the device readings compared with auscultation by paired, trained, blinded observers in the SureBP mode were -2.14±7.44 mmHg for systolic BP (SBP) and -0.55±5.98 mmHg for diastolic BP (DBP). In the StepBP mode, the differences were -3.61±6.30 mmHg for SBP and -2.03±5.30 mmHg for DBP. Both algorithms achieved an A grade for both SBP and DBP by British Hypertension Society analysis. The SureBP inflation-based algorithm will be available in many new-generation Welch Allyn monitors. Its use will reduce the time it takes to estimate BP in critical patient care circumstances. The device will not need to inflate to excessive suprasystolic BPs to obtain the SBP values. Deflation is rapid once SBP has been determined, thus reducing the total time of cuff inflation and reducing patient discomfort. If the SureBP fails to obtain a BP value, the StepBP algorithm is activated to estimate BP by traditional deflation methodology.
Carver, Robert L; Sprunger, Conrad P; Hogstrom, Kenneth R; Popple, Richard A; Antolak, John A
2016-05-08
The purpose of this study was to evaluate the accuracy and calculation speed of electron dose distributions calculated by the Eclipse electron Monte Carlo (eMC) algorithm for use with bolus electron conformal therapy (ECT). The recent com-mercial availability of bolus ECT technology requires further validation of the eMC dose calculation algorithm. eMC-calculated electron dose distributions for bolus ECT have been compared to previously measured TLD-dose points throughout patient-based cylindrical phantoms (retromolar trigone and nose), whose axial cross sections were based on the mid-PTV (planning treatment volume) CT anatomy. The phantoms consisted of SR4 muscle substitute, SR4 bone substitute, and air. The treatment plans were imported into the Eclipse treatment planning system, and electron dose distributions calculated using 1% and pencil beam algorithm (PBA). The eMC has comparable accuracy to the pencil beam redefinition algorithm (PBRA) used for bolus ECT planning and has acceptably low dose calculation times. The eMC accuracy decreased when smoothing was used in high-gradient dose regions. The eMC accuracy was consistent with that previously reported for accuracy of the eMC electron dose algorithm and shows that the algorithm is suitable for clinical implementation of bolus ECT.
Interstructure Lattices and Types of Peano Arithmetic
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?
Directory of Open Access Journals (Sweden)
Li Liu
2015-06-01
Full Text Available Background To accelerate progress toward the Millennium Development Goal 4, reliable information on causes of child mortality is critical. With more national verbal autopsy (VA studies becoming available, how to improve consistency of national VA derived child causes of death should be considered for the purpose of global comparison. We aimed to adapt a standardized computer algorithm to re–analyze national child VA studies conducted in Uganda, Rwanda and Ghana recently, and compare our results with those derived from physician review to explore issues surrounding the application of the standardized algorithm in place of physician review. Methods and Findings We adapted the standardized computer algorithm considering the disease profile in Uganda, Rwanda and Ghana. We then derived cause–specific mortality fractions applying the adapted algorithm and compared the results with those ascertained by physician review by examining the individual– and population–level agreement. Our results showed that the leading causes of child mortality in Uganda, Rwanda and Ghana were pneumonia (16.5–21.1% and malaria (16.8–25.6% among children below five years and intrapartum–related complications (6.4–10.7% and preterm birth complications (4.5–6.3% among neonates. The individual level agreement was poor to substantial across causes (kappa statistics: –0.03 to 0.83, with moderate to substantial agreement observed for injury, congenital malformation, preterm birth complications, malaria and measles. At the population level, despite fairly different cause–specific mortality fractions, the ranking of the leading causes was largely similar. Conclusions The standardized computer algorithm produced internally consistent distribution of causes of child mortality. The results were also qualitatively comparable to those based on physician review from the perspective of public health policy. The standardized computer algorithm has the advantage of
Guide to FPGA Implementation of Arithmetic Functions
Deschamps, Jean-Pierre; Cantó, Enrique
2012-01-01
This book is designed both for FPGA users interested in developing new, specific components - generally for reducing execution times –and IP core designers interested in extending their catalog of specific components. The main focus is circuit synthesis and the discussion shows, for example, how a given algorithm executing some complex function can be translated to a synthesizable circuit description, as well as which are the best choices the designer can make to reduce the circuit cost, latency, or power consumption. This is not a book on algorithms. It is a book that shows how to translate efficiently an algorithm to a circuit, using techniques such as parallelism, pipeline, loop unrolling, and others. Numerous examples of FPGA implementation are described throughout this book and the circuits are modeled in VHDL. Complete and synthesizable source files are available for download.
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Hunt Anthony
2005-09-01
Full Text Available Abstract Background Accurate measurement of the QT interval is very important from a clinical and pharmaceutical drug safety screening perspective. Expert manual measurement is both imprecise and imperfectly reproducible, yet it is used as the reference standard to assess the accuracy of current automatic computer algorithms, which thus produce reproducible but incorrect measurements of the QT interval. There is a scientific imperative to evaluate the most commonly used algorithms with an accurate and objective 'gold standard' and investigate novel automatic algorithms if the commonly used algorithms are found to be deficient. Methods This study uses a validated computer simulation of 8 different noise contaminated ECG waveforms (with known QT intervals of 461 and 495 ms, generated from a cell array using Luo-Rudy membrane kinetics and the Crank-Nicholson method, as a reference standard to assess the accuracy of commonly used QT measurement algorithms. Each ECG contaminated with 39 mixtures of noise at 3 levels of intensity was first filtered then subjected to three threshold methods (T1, T2, T3, two T wave slope methods (S1, S2 and a Novel method. The reproducibility and accuracy of each algorithm was compared for each ECG. Results The coefficient of variation for methods T1, T2, T3, S1, S2 and Novel were 0.36, 0.23, 1.9, 0.93, 0.92 and 0.62 respectively. For ECGs of real QT interval 461 ms the methods T1, T2, T3, S1, S2 and Novel calculated the mean QT intervals(standard deviations to be 379.4(1.29, 368.5(0.8, 401.3(8.4, 358.9(4.8, 381.5(4.6 and 464(4.9 ms respectively. For ECGs of real QT interval 495 ms the methods T1, T2, T3, S1, S2 and Novel calculated the mean QT intervals(standard deviations to be 396.9(1.7, 387.2(0.97, 424.9(8.7, 386.7(2.2, 396.8(2.8 and 493(0.97 ms respectively. These results showed significant differences between means at >95% confidence level. Shifting ECG baselines caused large errors of QT interval with T1 and T2
Poletti, Pierre-Alexandre; Platon, Alexandra; De Perrot, Thomas; Sarasin, Francois; Andereggen, Elisabeth; Rutschmann, Olivier; Dupuis-Lozeron, Elise; Perneger, Thomas; Gervaz, Pascal; Becker, Christoph D
2011-12-01
To evaluate an algorithm integrating ultrasound and low-dose unenhanced CT with oral contrast medium (LDCT) in the assessment of acute appendicitis, to reduce the need of conventional CT. Ultrasound was performed upon admission in 183 consecutive adult patients (111 women, 72 men, mean age 32) with suspicion of acute appendicitis and a BMI between 18.5 and 30 (step 1). No further examination was recommended when ultrasound was positive for appendicitis, negative with low clinical suspicion, or demonstrated an alternative diagnosis. All other patients underwent LDCT (30 mAs) (step 2). Standard intravenously enhanced CT (180 mAs) was performed after indeterminate LDCT (step 3). No further imaging was recommended after ultrasound in 84 (46%) patients; LDCT was obtained in 99 (54%). LDCT was positive or negative for appendicitis in 81 (82%) of these 99 patients, indeterminate in 18 (18%) who underwent standard CT. Eighty-six (47%) of the 183 patients had a surgically proven appendicitis. The sensitivity and specificity of the algorithm were 98.8% and 96.9%. The proposed algorithm achieved high sensitivity and specificity for detection of acute appendicitis, while reducing the need for standard CT and thus limiting exposition to radiation and to intravenous contrast media.
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Poletti, Pierre-Alexandre; Platon, Alexandra [University Hospital of Geneva, Department of Radiology, Geneva (Switzerland); University Hospital of Geneva, Emergency Center, Geneva (Switzerland); Perrot, Thomas de; Becker, Christoph D. [University Hospital of Geneva, Department of Radiology, Geneva (Switzerland); Sarasin, Francois; Rutschmann, Olivier [University Hospital of Geneva, Emergency Center, Geneva (Switzerland); Andereggen, Elisabeth [University Hospital of Geneva, Emergency Center, Geneva (Switzerland); University Hospital of Geneva, Department of Surgery, Geneva (Switzerland); Dupuis-Lozeron, Elise; Perneger, Thomas [University Hospital of Geneva, Division of Clinical Epidemiology, Geneva (Switzerland); Gervaz, Pascal [University Hospital of Geneva, Department of Surgery, Geneva (Switzerland)
2011-12-15
To evaluate an algorithm integrating ultrasound and low-dose unenhanced CT with oral contrast medium (LDCT) in the assessment of acute appendicitis, to reduce the need of conventional CT. Ultrasound was performed upon admission in 183 consecutive adult patients (111 women, 72 men, mean age 32) with suspicion of acute appendicitis and a BMI between 18.5 and 30 (step 1). No further examination was recommended when ultrasound was positive for appendicitis, negative with low clinical suspicion, or demonstrated an alternative diagnosis. All other patients underwent LDCT (30 mAs) (step 2). Standard intravenously enhanced CT (180 mAs) was performed after indeterminate LDCT (step 3). No further imaging was recommended after ultrasound in 84 (46%) patients; LDCT was obtained in 99 (54%). LDCT was positive or negative for appendicitis in 81 (82%) of these 99 patients, indeterminate in 18 (18%) who underwent standard CT. Eighty-six (47%) of the 183 patients had a surgically proven appendicitis. The sensitivity and specificity of the algorithm were 98.8% and 96.9%. The proposed algorithm achieved high sensitivity and specificity for detection of acute appendicitis, while reducing the need for standard CT and thus limiting exposition to radiation and to intravenous contrast media. (orig.)
Castro, Mariana N; Vigo, Daniel E; Chu, Elvina M; Fahrer, Rodolfo D; de Achával, Delfina; Costanzo, Elsa Y; Leiguarda, Ramón C; Nogués, Martín; Cardinali, Daniel P; Guinjoan, Salvador M
2009-04-01
Schizophrenia patients exhibit an abnormal autonomic response to mental stress. We sought to determine the cardiac autonomic response to mental arithmetic stress in their unaffected first-degree relatives. Heart rate variability (HRV) analysis was performed on recordings obtained before, during, and after a standard mental arithmetic task to induce mental stress. 22 unaffected first-degree relatives of patients meeting DSM-IV criteria for schizophrenia (R) and 22 healthy individuals (C) were included in this study. Patients' relatives (R) had a normal response to the mental arithmetic stress test, showing an increased heart rate compared with controls. They also displayed the characteristic pattern of relative contributions of HRV components that consists of increased low-frequency (LF) HRV and decreased high-frequency (HF) HRV. Recovery of the resting pattern of HRV immediately after stress termination was observed in healthy subjects (LF 62+/-16% vs. 74+/-10% , HF 37+/-16% vs. 25+/-10%, F=9.616, p=0.004), but not in patients' relatives (LF 60+/-19% vs. 70+/-13%, HF 40+/-19% vs. 29+/-13%, F=8.4, p=0.056). First-degree relatives of schizophrenia patients exhibit an abnormal pattern of protracted response to mental arithmetic stress, though less intense than that observed in patients in a previous study. This suggests that a pattern of autonomic response to stress may therefore be familial and heritable.
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.
Relation between arithmetic performance and phonological working memory in children.
Silva, Kelly da; Zuanetti, Patrícia Aparecida; Borcat, Vanessa Trombini Ribeiro; Guedes-Granzotti, Raphaela Barroso; Kuroishi, Rita Cristina Sadako; Domenis, Daniele Ramos; Fukuda, Marisa Tomoe Hebihara
2017-08-17
To compare the results of Loop Phonological Working Memory (LPWM) in children without global learning alterations, with lower and average/higher arithmetic performance. The study was conducted with 30 children, between the ages of seven and nine years old, who attended the second or third grade of elementary school in the public network. Exclusion criteria were children with suggestive signs of hearing loss, neurological disorders, poor performance in the reading comprehension test or in speech therapy. The children included in the study were submitted to the subtest of arithmetic of Academic Achievement Test for division into two groups (G1 and G2). The G1 was composed of children with low performance in arithmetic and G2 for children with average/higher performance in arithmetic. All children were submitted to PWM assessment through the repetition of pseudowords test. Statistical analysis was performed using the Mann-Whitney test and a p-value memory are related to difficulties in arithmetic tests.
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.
Number processing and arithmetic skills in children with cochlear implants
Pixner, Silvia; Leyrer, Martin; Moeller, Korbinian
2014-01-01
Though previous findings report that hearing impaired children exhibit impaired language and arithmetic skills, our current understanding of how hearing and the associated language impairments may influence the development of arithmetic skills is still limited. In the current study numerical/arithmetic performance of 45 children with a cochlea implant were compared to that of controls matched for hearing age, intelligence and sex. Our main results were twofold disclosing that children with CI show general as well as specific numerical/arithmetic impairments. On the one hand, we found an increased percentage of children with CI with an indication of dyscalculia symptoms, a general slowing in multiplication and subtraction as well as less accurate number line estimations. On the other hand, however, children with CI exhibited very circumscribed difficulties associated with place-value processing. Performance declined specifically when subtraction required a borrow procedure and number line estimation required the integration of units, tens, and hundreds instead of only units and tens. Thus, it seems that despite initially atypical language development, children with CI are able to acquire arithmetic skills in a qualitatively similar fashion as their normal hearing peers. Nonetheless, when demands on place-value understanding, which has only recently been proposed to be language mediated, hearing impaired children experience specific difficulties. PMID:25566152
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.
On Goncharov's regulator and higher arithmetic Chow groups
DEFF Research Database (Denmark)
Gil, J. I. Burgos; Feliu, Elisenda; Takeda, Y.
2011-01-01
In this paper, we show that the regulator defined by Goncharov in [10] from higher algebraic Chow groups to Deligne–Beilinson cohomology agrees with Beilinson’s regulator. We give a direct comparison of Goncharov’s regulator to the construction given by Burgos Gil and Feliu in [5]. As a consequen......, we show that the higher arithmetic Chow groups defined by Goncharov agree, for all projective arithmetic varieties over an arithmetic field, with the ones defined by Burgos Gil and Feliu.......In this paper, we show that the regulator defined by Goncharov in [10] from higher algebraic Chow groups to Deligne–Beilinson cohomology agrees with Beilinson’s regulator. We give a direct comparison of Goncharov’s regulator to the construction given by Burgos Gil and Feliu in [5]. As a consequence...
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.
File compression and encryption based on LLS and arithmetic coding
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.
A Note on Arithmetic Progressions on Elliptic Curves
Campbell, Garikai
2003-02-01
Andrew Bremner (Experiment. Math. 8 (1999), 409-413) has described a technique for producing infinite families of elliptic curves containing length 7 and length 8 arithmetic progressions. This note describes another way to produce infinite families of elliptic curves containing length 7 and length 8 arithmetic progressions. We illustrate how the technique articulated here gives an easy way to produce an elliptic curve containing a length 12 progression and an infinite family of elliptic curves containing a length 9 progression, with the caveat that these curves are not in Weierstrass form.
Lakhani, Gopal
2013-04-01
This article presents four modifications to the JPEG arithmetic coding (JAC) algorithm, a topic not studied well before. It then compares the compression performance of the modified JPEG with JPEG XR, the latest block-based image coding standard. We first show that the bulk of inter/intra-block redundancy, caused due to the use of the block-based approach by JPEG, can be captured by applying efficient prediction coding. We propose the following modifications to JAC to take advantages of our prediction approach. 1) We code a totally different DC difference. 2) JAC tests a DCT coefficient by considering its bits in the increasing order of significance for coding the most significant bit position. It causes plenty of redundancy because JAC always begins with the zeroth bit. We modify this coding order and propose alternations to the JPEG coding procedures. 3) We predict the sign of significant DCT coefficients, a problem is not addressed from the perspective of the JPEG decoder before. 4) We reduce the number of binary tests that JAC codes to mark end-of-block. We provide experimental results for two sets of eight-bit gray images. The first set consists of nine classical test images mostly of size 512 × 512 pixels. The second set consists of 13 images of size 2000 × 3000 pixels or more. Our modifications to JAC obtain extra-ordinary amount of code reduction without adding any kind of losses. More specifically, when we quantize the images using the default quantizers, our modifications reduce the total JAC code size of the images of these two sets by about 8.9 and 10.6%, and the JPEG Huffman code size by about 16.3 and 23.4%, respectively, on the average. Gains are even higher for coarsely quantized images. Finally, we compare the modified JAC with two settings of JPEG XR, one with no block overlapping and the other with the default transform (we denote them by JXR0 and JXR1, respectively). Our results show that for the finest quality rate image coding, the modified
A CABAC codec of H.264AVC with secure arithmetic coding
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.
Transcranial random noise stimulation mitigates increased difficulty in an arithmetic learning task.
Popescu, Tudor; Krause, Beatrix; Terhune, Devin B; Twose, Olivia; Page, Thomas; Humphreys, Glyn; Cohen Kadosh, Roi
2016-01-29
Proficiency in arithmetic learning can be achieved by using a multitude of strategies, the most salient of which are procedural learning (applying a certain set of computations) and rote learning (direct retrieval from long-term memory). Here we investigated the effect of transcranial random noise stimulation (tRNS), a non-invasive brain stimulation method previously shown to enhance cognitive training, on both types of learning in a 5-day sham-controlled training study, under two conditions of task difficulty, defined in terms of item repetition. On the basis of previous research implicating the prefrontal and posterior parietal cortex in early and late stages of arithmetic learning, respectively, sham-controlled tRNS was applied to bilateral prefrontal cortex for the first 3 days and to the posterior parietal cortex for the last 2 days of a 5-day training phase. The training involved learning to solve arithmetic problems by applying a calculation algorithm; both trained and untrained problems were used in a brief testing phase at the end of the training phase. Task difficulty was manipulated between subjects by using either a large ("easy" condition) or a small ("difficult" condition) number of repetition of problems during training. Measures of attention and working memory were acquired before and after the training phase. As compared to sham, participants in the tRNS condition displayed faster reaction times and increased learning rate during the training phase; as well as faster reaction times for both trained and untrained (new) problems, which indicated a transfer effect after the end of training. All stimulation effects reached significance only in the "difficult" condition when number of repetition was lower. There were no transfer effects of tRNS on attention or working memory. The results support the view that tRNS can produce specific facilitative effects on numerical cognition--specifically, on arithmetic learning. They also highlight the importance of
Interactive Realizability and the elimination of Skolem functions in Peano Arithmetic
Directory of Open Access Journals (Sweden)
Federico Aschieri
2012-10-01
Full Text Available We present a new syntactical proof that first-order Peano Arithmetic with Skolem axioms is conservative over Peano Arithmetic alone for arithmetical formulas. This result – which shows that the Excluded Middle principle can be used to eliminate Skolem functions – has been previously proved by other techniques, among them the epsilon substitution method and forcing. In our proof, we employ Interactive Realizability, a computational semantics for Peano Arithmetic which extends Kreisel's modified realizability to the classical case.
Directory of Open Access Journals (Sweden)
E. Bakumenko
2009-06-01
Full Text Available In the article is examined accordance of the integrated environment of study course «Foundations of algoritmization and programming» with the requirements of international standards of quality IMS and SCORM for distance learning systems.
Frontal Midline Theta Oscillations during Mental Arithmetic: Effects of Stress
Directory of Open Access Journals (Sweden)
Matti eGärtner
2015-04-01
Full Text Available Complex cognitive tasks such as mental arithmetic heavily rely on intact, well-coordinated prefrontal cortex (PFC function. Converging evidence suggests that frontal midline theta (FMT oscillations play an important role during the execution of such PFC-dependent tasks. Additionally, it is well-established that acute stress impairs PFC function, and recent evidence suggests that FMT is decreased under stress. In this EEG study, we investigated FMT oscillations during a mental arithmetic task that was carried out in a stressful and a neutral control condition. Our results show late-onset, sustained FMT increases during mental arithmetic. In the neutral condition FMT started to increase earlier than in the stress condition. Direct comparison of the conditions quantified this difference by showing stronger FMT increases in the neutral condition in an early time window. Between-subject correlation analysis showed that attenuated FMT under stress was related to slowed reaction times. Our results suggest that FMT is associated with stimulus independent mental processes during the natural and complex PFC-dependent task of mental arithmetic, and is a possible marker for intact PFC function that is disrupted under stress.
On Some Conjectures on the Monotonicity of Some Arithmetical Sequences
2012-01-01
visit of P. S. to the Centro de Ciencias Matemáticas de la UNAM in Morelia in August 2012. During the preparation of this paper, F. L. was supported in...THE MONOTONICITY OF SOME ARITHMETICAL SEQUENCES ∗ Florian Luca † Centro de Ciencias Matemáticas, Universidad Nacional Autonoma de México, C.P. 58089
Single-Digit Arithmetic in Children with Dyslexia
Boets, Bart; De Smedt, Bert
2010-01-01
It has been suggested that individuals with dyslexia show poorer performance on those aspects of arithmetic that involve the manipulation of verbal representations, such as the use of fact retrieval strategies. The present study examined this in 13 children with dyslexia who showed normal general mathematics achievement and 16 matched controls.…
Bit-Wise Arithmetic Coding For Compression Of Data
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.
Arithmetically Related Ideal Topologies and the Infinitude of Primes ...
African Journals Online (AJOL)
The late J. Knopfmacher and the author [12] have studied some ties between arithmetic properties of the multiplicative structure of commutative rings with identity and the topologies induced by some coset classes. In the present communication it is shown that the ideas used there are capable of a further extension. Namely ...
Arithmetical Strategies of a Student with Down Syndrome
Rumiati, Rumi
2014-01-01
Kayla was a 15 years old girl with Down syndrome attending a special education school in Indonesia. A modification of Wright et al.'s (2006) approach to assessment documented her number knowledge and arithmetical strategies. This paper discusses the assessment process and the results focusing on her ability to solve number problems. Results show…
Relational Thinking: Learning Arithmetic in Order to Promote Algebraic Thinking
Napaphun, Vishnu
2012-01-01
Trends in the curriculum reform propose that algebra should be taught throughout the grades, starting in elementary school. The aim should be to decrease the discontinuity between the arithmetic in elementary school and the algebra in upper grades. This study was conducted to investigate and characterise upper elementary school students…
Why Is Learning Fraction and Decimal Arithmetic so Difficult?
Lortie-Forgues, Hugues; Tian, Jing; Siegler, Robert S.
2015-01-01
Fraction and decimal arithmetic are crucial for later mathematics achievement and for ability to succeed in many professions. Unfortunately, these capabilities pose large difficulties for many children and adults, and students' proficiency in them has shown little sign of improvement over the past three decades. To summarize what is known about…
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.
Towards Metamathematics of Weak Arithmetics over Fuzzy Logic
Czech Academy of Sciences Publication Activity Database
Hájek, Petr
2011-01-01
Roč. 19, č. 3 (2011), s. 467-475 ISSN 1367-0751 R&D Projects: GA AV ČR IAA100300503 Institutional research plan: CEZ:AV0Z10300504 Keywords : weak arithmetics * mathematical fuzzy logic * Gödel’s theorem * essential undecidability Subject RIV: BA - General Mathematics Impact factor: 0.913, year: 2011
Frontal midline theta oscillations during mental arithmetic: effects of stress.
Gärtner, Matti; Grimm, Simone; Bajbouj, Malek
2015-01-01
Complex cognitive tasks such as mental arithmetic heavily rely on intact, well-coordinated prefrontal cortex (PFC) function. Converging evidence suggests that frontal midline theta (FMT) oscillations play an important role during the execution of such PFC-dependent tasks. Additionally, it is well-established that acute stress impairs PFC function, and recent evidence suggests that FMT is decreased under stress. In this EEG study, we investigated FMT oscillations during a mental arithmetic task that was carried out in a stressful and a neutral control condition. Our results show late-onset, sustained FMT increases during mental arithmetic. In the neutral condition FMT started to increase earlier than in the stress condition. Direct comparison of the conditions quantified this difference by showing stronger FMT increases in the neutral condition in an early time window. Between-subject correlation analysis showed that attenuated FMT under stress was related to slowed reaction times. Our results suggest that FMT is associated with stimulus independent mental processes during the natural and complex PFC-dependent task of mental arithmetic, and is a possible marker for intact PFC function that is disrupted under stress.
Young Children's Mental Arithmetic Errors: A Working-Memory Analysis.
Brainerd, Charles J.
1983-01-01
Presents a stochastic model for distinguishing mental arithmetic errors according to causes of failure. A series of experiments (1) studied questions of goodness of fit and model validity among four and five year olds and (2) used the model to measure the relative contributions of developmental improvements in short-term memory and arithmetical…
Arithmetic Word Problem Solving: A Situation Strategy First Framework
Brissiaud, Remi; Sander, Emmanuel
2010-01-01
Before instruction, children solve many arithmetic word problems with informal strategies based on the situation described in the problem. A Situation Strategy First framework is introduced that posits that initial representation of the problem activates a situation-based strategy even after instruction: only when it is not efficient for providing…
Sex Differences in Arithmetical Performance Scores: Central Tendency and Variability
Martens, R.; Hurks, P. P. M.; Meijs, C.; Wassenberg, R.; Jolles, J.
2011-01-01
The present study aimed to analyze sex differences in arithmetical performance in a large-scale sample of 390 children (193 boys) frequenting grades 1-9. Past research in this field has focused primarily on average performance, implicitly assuming homogeneity of variance, for which support is scarce. This article examined sex differences in…
Simple arithmetic: not so simple for highly math anxious individuals
Sprute, Lisa; Maloney, Erin A; Beilock, Sian L; Berman, Marc G
2017-01-01
Abstract 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. PMID:29140499
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
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
Optimal combinations bounds of root-square and arithmetic means ...
Indian Academy of Sciences (India)
Optimal combinations bounds of root-square and arithmetic means for Toader mean. YU-MING CHU1,∗. , MIAO-KUN WANG2 and SONG-LIANG QIU3. 1Department of Mathematics and Computing Science, Hunan City University,. Yiyang 413000, China. 2Department of Mathematics, Huzhou Teachers College, Huzhou ...
Numbers in action: individual differences and interactivity in mental arithmetic.
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.
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.
A note on conservativity relations among bounded arithmetic theories
Czech Academy of Sciences Publication Activity Database
Krajíček, Jan; Impagliazzo, R.
2002-01-01
Roč. 48, č. 3 (2002), s. 375-377 ISSN 0942-5616 R&D Projects: GA AV ČR IAA1019901; GA MŠk LN00A056 Keywords : bounded arithmetic%constant depth Frege systems Subject RIV: BA - General Mathematics Impact factor: 0.365, year: 2002
Partial sums of arithmetical functions with absolutely convergent ...
Indian Academy of Sciences (India)
, Chennai 600 113, India. E-mail: biswajyoti@imsc.res.in. MS received 9 May 2015; revised 9 July 2015. Abstract. For an arithmetical function f with absolutely convergent Ramanujan expansion, we derive an asymptotic formula for the sum. ∑.
DEFF Research Database (Denmark)
Jensen, Søren Tapdrup
2014-01-01
ISO 12647-2 specifies CIELAB values for primary and secondary colors, but only tolerances for the primary solid colors. Press operators in lithography still favor density measurements for process control to assure quality and reproducibility during a production run. Since there is no direct...... that the algorithm has high degree of accuracy in predicting the ink layer thickness that conforms to ISO 12647-2 aim point, but errors in the prediction occur when the measured sum of the secondary colors have a low ∆Eab to the standard....
Directory of Open Access Journals (Sweden)
Wilke MH
2011-12-01
Full Text Available Abstract Introduction The management of bloodstream infections especially sepsis is a difficult task. An optimal antibiotic therapy (ABX is paramount for success. Procalcitonin (PCT is a well investigated biomarker that allows close monitoring of the infection and management of ABX. It has proven to be a cost-efficient diagnostic tool. In Diagnoses Related Groups (DRG based reimbursement systems, hospitals get only a fixed amount of money for certain treatments. Thus it's very important to obtain an optimal balance of clinical treatment and resource consumption namely the length of stay in hospital and especially in the Intensive Care Unit (ICU. We investigated which economic effects an optimized PCT-based algorithm for antibiotic management could have. Materials and methods We collected inpatient episode data from 16 hospitals. These data contain administrative and clinical information such as length of stay, days in the ICU or diagnoses and procedures. From various RCTs and reviews there are different algorithms for the use of PCT to manage ABX published. Moreover RCTs and meta-analyses have proven possible savings in days of ABX (ABD and length of stay in ICU (ICUD. As the meta-analyses use studies on different patient populations (pneumonia, sepsis, other bacterial infections, we undertook a short meta-analyses of 6 relevant studies investigating in sepsis or ventilator associated pneumonia (VAP. From this analyses we obtained savings in ABD and ICUD by calculating the weighted mean differences. Then we designed a new PCT-based algorithm using results from two very recent reviews. The algorithm contains evidence from several studies. From the patient data we calculated cost estimates using German National standard costing information for the German G-DRG system. We developed a simulation model where the possible savings and the extra costs for (in average 8 PCT tests due to our algorithm were brought into equation. Results We calculated ABD
Brain systems involved in arithmetic with positive versus negative numbers.
Gullick, Margaret M; Wolford, George
2014-02-01
Positive number arithmetic is based on combining and separating sets of items, with systematic differences in brain activity in specific regions depending on operation. In contrast, arithmetic with negative numbers involves manipulating abstract values worth less than zero, possibly involving different operation-activity relationships in these regions. Use of procedural arithmetic knowledge, including transformative rules like "minus a negative is plus a positive," may also differ by operand sign. Here, we examined whether the activity evoked in negative number arithmetic was similar to that seen in positive problems, using region of interest analyses (ROIs) to examine a specific set of brain regions. Negative-operand problems demonstrated a positive-like effect of operation in the inferior parietal lobule with more activity for subtraction than addition, as well as increased activity across operation. Interestingly, while positive-operand problems demonstrated the expected addition > subtraction activity difference in the angular gyrus, negative problems showed a reversed effect, with relatively more activity for subtraction than addition. Negative subtraction problems may be understood after translation to addition via rule, thereby invoking more addition-like activity. Whole-brain analyses showed increased right caudate activity for negative-operand problems across operation, indicating a possible overall increase in usage of procedural rules. Arithmetic with negative numbers may thus shows some operation-activity relationships similar to positive numbers, but may also be affected by strategy. This study examines the flexibility of the mental number system by exploring to what degree the processing of an applied usage of a difficult, abstract mathematical concept is similar to that for positive numbers. Copyright © 2012 Wiley Periodicals, Inc.
Interactivity, efficiency, and individual differences in mental arithmetic.
Vallée-Tourangeau, Frédéric
2013-01-01
Thinking efficiency was examined in mental arithmetic as a function of the degree of interactivity afforded by the task. Participants carried out single-digit additions, involving either 7 or 11 numbers, as fast and as accurately as possible. They completed the sums in blocks, five from the short 7-number set first, and five from the longer 11-number set second. These sets were interpolated among a series of other tasks that measured numeracy and arithmetic skills, working memory capacity, visuo-spatial processing speed, and attention switching, in such a way as to permit the presentation of the sets twice, once with each of the sums presented on a piece of paper and participants placing their hands flat on the table and once with the sums presented as a set of manipulable tokens. Efficiency was measured as the ratio of performance over time invested. A significant interaction between condition and set size was observed: Efficiency was slightly better in the static condition for short sums but declined substantially relative to the interactive condition for long sums. Twenty-two percent of the variance in efficiency for hard sums in the static condition was explained by arithmetic skills and working memory capacity, whereas 45% of this variance was explained by arithmetic skills, working memory capacity, and attention switching skills in the interactive condition. A separate sample of 17 participants who provided concurrent verbal protocols as they solved the problems revealed that paths to solution and arithmetic strategies were substantially transformed by the opportunity to manipulate tokens.
Synthesis Optimization on Galois-Field Based Arithmetic Operators for Rijndael Cipher
Directory of Open Access Journals (Sweden)
Petrus Mursanto
2011-08-01
Full Text Available A series of experiments has been conducted to show that FPGA synthesis of Galois-Field (GF based arithmetic operators can be optimized automatically to improve Rijndael Cipher throughput. Moreover, it has been demonstrated that efficiency improvement in GF operators does not directly correspond to the system performance at application level. The experiments were motivated by so many research works that focused on improving performance of GF operators. Each of the variants has the most efficient form in either time (fastest or space (smallest occupied area when implemented in FPGA chips. In fact, GF operators are not utilized individually, but rather integrated one to the others to implement algorithms. Contribution of this paper is to raise issue on GF-based application performance and suggest alternative aspects that potentially affect it. Instead of focusing on GF operator efficiency, system characteristics are worth considered in optimizing application performance.
Uncertainty analysis for dynamic properties of MEMS resonator supported by fuzzy arithmetics
Directory of Open Access Journals (Sweden)
A Martowicz
2016-04-01
Full Text Available In the paper the application of uncertainty analysis performed formicroelectromechanical resonator is presented. Main objective ofundertaken analysis is to assess the propagation of considered uncertaintiesin the variation of chosen dynamic characteristics of Finite Element model ofmicroresonator. Many different model parameters have been assumed tobe uncertain: geometry and material properties. Apart from total uncertaintypropagation, sensitivity analysis has been carried out to study separateinfluences of all input uncertain characteristics. Uncertainty analysis has beenperformed by means of fuzzy arithmetics in which alpha-cut strategy hasbeen applied to assemble output fuzzy number. Monte Carlo Simulation andGenetic Algorithms have been employed to calculate intervals connectedwith each alpha-cut of searched fuzzy number. Elaborated model ofmicroresonator has taken into account in a simplified way the presence ofsurrounding air and constant electrostatic field.
DEFF Research Database (Denmark)
Dung, Phan Anh; Hansen, Michael Reichhardt
2015-01-01
into account negative factors such as cache misses, garbage collection and overhead due to task creations, because such factors may introduce sequential bottlenecks with severe consequences for the parallel efficiency. The experiments were conducted using the functional programming language F# and .NET......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...... implementations in a functional programming language. Thereafter, the parallelism inherent in the decision procedures is analyzed using the Directed Acyclic Graph (DAG) model of multicore parallelism. In the step from a DAG model to a parallel implementation, the parallel implementation is optimized taking...
The impact of arithmetic representation on implementing MLP-BP on FPGAs: a study.
Savich, Antony W; Moussa, Medhat; Areibi, Shawki
2007-01-01
In this paper, arithmetic representations for implementing multilayer perceptrons trained using the error backpropagation algorithm (MLP-BP) neural networks on field-programmable gate arrays (FPGAs) are examined in detail. Both floating-point (FLP) and fixed-point (FXP) formats are studied and the effect of precision of representation and FPGA area requirements are considered. A generic very high-speed integrated circuit hardware description language (VHDL) program was developed to help experiment with a large number of formats and designs. The results show that an MLP-BP network uses less clock cycles and consumes less real estate when compiled in an FXP format, compared with a larger and slower functioning compilation in an FLP format with similar data representation width, in bits, or a similar precision and range.
Guimaraes, Carolina V; Grzeszczuk, Robert; Bisset, George S; Donnelly, Lane F
2018-03-01
When implementing or monitoring department-sanctioned standardized radiology reports, feedback about individual faculty performance has been shown to be a useful driver of faculty compliance. Most commonly, these data are derived from manual audit, which can be both time-consuming and subject to sampling error. The purpose of this study was to evaluate whether a software program using natural language processing and machine learning could accurately audit radiologist compliance with the use of standardized reports compared with performed manual audits. Radiology reports from a 1-month period were loaded into such a software program, and faculty compliance with use of standardized reports was calculated. For that same period, manual audits were performed (25 reports audited for each of 42 faculty members). The mean compliance rates calculated by automated auditing were then compared with the confidence interval of the mean rate by manual audit. The mean compliance rate for use of standardized reports as determined by manual audit was 91.2% with a confidence interval between 89.3% and 92.8%. The mean compliance rate calculated by automated auditing was 92.0%, within that confidence interval. This study shows that by use of natural language processing and machine learning algorithms, an automated analysis can accurately define whether reports are compliant with use of standardized report templates and language, compared with manual audits. This may avoid significant labor costs related to conducting the manual auditing process. Copyright © 2017 American College of Radiology. Published by Elsevier Inc. All rights reserved.
Counting and Arithmetic of the Inca
Directory of Open Access Journals (Sweden)
Ximena Catepillán
2012-08-01
Full Text Available The Inca Empire - the greatest pre-Columbian empire on the American continent - extended from Ecuador to central Chile for more than five thousand miles. Its capital was Cuzco established in the high Peruvian Andes. This highly advanced civilization developed a counting system used to run the empire - in particular, to build the 14,000 mile road structure and monumental architecture. Some of the algorithms believed to be used by the Inca to do computations using a yupana, an ancient calculating device, will be presented, as well as classroom activities for the course “Mathematics in Non-European Cultures” for non Mathematics and Science majors offered at Millersville University of Pennsylvania.
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
Visualizing the Arithmetic of Complex Numbers
Soto-Johnson, Hortensia
2014-01-01
The Common Core State Standards Initiative stresses the importance of developing a geometric and algebraic understanding of complex numbers in their different forms (i.e., Cartesian, polar and exponential). Unfortunately, most high school textbooks do not offer such explanations much less exercises that encourage students to bridge geometric and…
JavaGenes and Condor: Cycle-Scavenging Genetic Algorithms
Globus, Al; Langhirt, Eric; Livny, Miron; Ramamurthy, Ravishankar; Soloman, Marvin; Traugott, Steve
2000-01-01
A genetic algorithm code, JavaGenes, was written in Java and used to evolve pharmaceutical drug molecules and digital circuits. JavaGenes was run under the Condor cycle-scavenging batch system managing 100-170 desktop SGI workstations. Genetic algorithms mimic biological evolution by evolving solutions to problems using crossover and mutation. While most genetic algorithms evolve strings or trees, JavaGenes evolves graphs representing (currently) molecules and circuits. Java was chosen as the implementation language because the genetic algorithm requires random splitting and recombining of graphs, a complex data structure manipulation with ample opportunities for memory leaks, loose pointers, out-of-bound indices, and other hard to find bugs. Java garbage-collection memory management, lack of pointer arithmetic, and array-bounds index checking prevents these bugs from occurring, substantially reducing development time. While a run-time performance penalty must be paid, the only unacceptable performance we encountered was using standard Java serialization to checkpoint and restart the code. This was fixed by a two-day implementation of custom checkpointing. JavaGenes is minimally integrated with Condor; in other words, JavaGenes must do its own checkpointing and I/O redirection. A prototype Java-aware version of Condor was developed using standard Java serialization for checkpointing. For the prototype to be useful, standard Java serialization must be significantly optimized. JavaGenes is approximately 8700 lines of code and a few thousand JavaGenes jobs have been run. Most jobs ran for a few days. Results include proof that genetic algorithms can evolve directed and undirected graphs, development of a novel crossover operator for graphs, a paper in the journal Nanotechnology, and another paper in preparation.
Paris, Yvonne; Toro?Salazar, Olga H.; Gauthier, Naomi S.; Rotondo, Kathleen M.; Arnold, Lucy; Hamershock, Rose; Saudek, David E.; Fulton, David R.; Renaud, Ashley; Alexander, Mark E.
2016-01-01
Background: Pediatric syncope is common. Cardiac causes are rarely found. We describe and assess a pragmatic approach to these patients first seen by a pediatric cardiologist in the New England region, using Standardized Clinical Assessment and Management Plans (SCAMPs). Methods and Results: Ambulatory patients aged 7 to 21 years initially seen for syncope at participating New England Congenital Cardiology Association practices over a 2.5‐year period were evaluated using a SCAMP. Findings wer...
Park, Joonkoo; Brannon, Elizabeth M
2014-10-01
A nonverbal primitive number sense allows approximate estimation and mental manipulations on numerical quantities without the use of numerical symbols. In a recent randomized controlled intervention study in adults, we demonstrated that repeated training on a non-symbolic approximate arithmetic task resulted in improved exact symbolic arithmetic performance, suggesting a causal relationship between the primitive number sense and arithmetic competence. Here, we investigate the potential mechanisms underlying this causal relationship. We constructed multiple training conditions designed to isolate distinct cognitive components of the approximate arithmetic task. We then assessed the effectiveness of these training conditions in improving exact symbolic arithmetic in adults. We found that training on approximate arithmetic, but not on numerical comparison, numerical matching, or visuo-spatial short-term memory, improves symbolic arithmetic performance. In addition, a second experiment revealed that our approximate arithmetic task does not require verbal encoding of number, ruling out an alternative explanation that participants use exact symbolic strategies during approximate arithmetic training. Based on these results, we propose that nonverbal numerical quantity manipulation is one key factor that drives the link between the primitive number sense and symbolic arithmetic competence. Future work should investigate whether training young children on approximate arithmetic tasks even before they solidify their symbolic number understanding is fruitful for improving readiness for math education. Copyright © 2014 Elsevier B.V. All rights reserved.
Dimitriadis, Stavros; Sun, Yu; Laskaris, Nikolaos; Thakor, Nitish; Bezerianos, Anastasios
2016-10-01
Working memory (WM) is a distributed cognitive process that employs communication between prefrontal cortex and posterior brain regions in the form of cross-frequency coupling between theta ( θ) and high-alpha ( α2) brain waves. A novel method for deriving causal interactions between brain waves of different frequencies is essential for a better understanding of the neural dynamics of such complex cognitive process. Here, we proposed a novel method to estimate transfer entropy ( TE) through a symbolization scheme, which is based on neural-gas algorithm (NG) and encodes a bivariate time series in the form of two symbolic sequences. Given the symbolic sequences, the delay symbolic transfer entropy ( dSTE NG ) is defined. Our approach is akin to standard symbolic transfer entropy ( STE) that incorporates the ordinal pattern (OP) symbolization technique. We assessed the proposed method in a WM-invoked paradigm that included a mental arithmetic task at various levels of difficulty. Effective interactions between Frontal θ ( F θ ) and [Formula: see text] ( PO α2 ) brain waves were detected in multichannel EEG recordings from 16 subjects. Compared with conventional methods, our technique was less sensitive to noise and demonstrated improved computational efficiency in quantifying the dominating direction of effective connectivity between brain waves of different spectral content. Moreover, we discovered an efferent F θ connectivity pattern and an afferent PO α2 one, in all the levels of the task. Further statistical analysis revealed an increasing dSTE NG strength following the task's difficulty.
International Nuclear Information System (INIS)
Suter, Basil; Testa, Enrique; Stämpfli, Patrick; Konala, Praveen; Rasch, Helmut; Friederich, Niklaus F; Hirschmann, Michael T
2015-01-01
The introduction of a standardized SPECT/CT algorithm including a localization scheme, which allows accurate identification of specific patterns and thresholds of SPECT/CT tracer uptake, could lead to a better understanding of the bone remodeling and specific failure modes of unicondylar knee arthroplasty (UKA). The purpose of the present study was to introduce a novel standardized SPECT/CT algorithm for patients after UKA and evaluate its clinical applicability, usefulness and inter- and intra-observer reliability. Tc-HDP-SPECT/CT images of consecutive patients (median age 65, range 48–84 years) with 21 knees after UKA were prospectively evaluated. The tracer activity on SPECT/CT was localized using a specific standardized UKA localization scheme. For tracer uptake analysis (intensity and anatomical distribution pattern) a 3D volumetric quantification method was used. The maximum intensity values were recorded for each anatomical area. In addition, ratios between the respective value in the measured area and the background tracer activity were calculated. The femoral and tibial component position (varus-valgus, flexion-extension, internal and external rotation) was determined in 3D-CT. The inter- and intraobserver reliability of the localization scheme, grading of the tracer activity and component measurements were determined by calculating the intraclass correlation coefficients (ICC). The localization scheme, grading of the tracer activity and component measurements showed high inter- and intra-observer reliabilities for all regions (tibia, femur and patella). For measurement of component position there was strong agreement between the readings of the two observers; the ICC for the orientation of the femoral component was 0.73-1.00 (intra-observer reliability) and 0.91-1.00 (inter-observer reliability). The ICC for the orientation of the tibial component was 0.75-1.00 (intra-observer reliability) and 0.77-1.00 (inter-observer reliability). The SPECT
Suter, Basil; Testa, Enrique; Stämpfli, Patrick; Konala, Praveen; Rasch, Helmut; Friederich, Niklaus F; Hirschmann, Michael T
2015-03-20
The introduction of a standardized SPECT/CT algorithm including a localization scheme, which allows accurate identification of specific patterns and thresholds of SPECT/CT tracer uptake, could lead to a better understanding of the bone remodeling and specific failure modes of unicondylar knee arthroplasty (UKA). The purpose of the present study was to introduce a novel standardized SPECT/CT algorithm for patients after UKA and evaluate its clinical applicability, usefulness and inter- and intra-observer reliability. Tc-HDP-SPECT/CT images of consecutive patients (median age 65, range 48-84 years) with 21 knees after UKA were prospectively evaluated. The tracer activity on SPECT/CT was localized using a specific standardized UKA localization scheme. For tracer uptake analysis (intensity and anatomical distribution pattern) a 3D volumetric quantification method was used. The maximum intensity values were recorded for each anatomical area. In addition, ratios between the respective value in the measured area and the background tracer activity were calculated. The femoral and tibial component position (varus-valgus, flexion-extension, internal and external rotation) was determined in 3D-CT. The inter- and intraobserver reliability of the localization scheme, grading of the tracer activity and component measurements were determined by calculating the intraclass correlation coefficients (ICC). The localization scheme, grading of the tracer activity and component measurements showed high inter- and intra-observer reliabilities for all regions (tibia, femur and patella). For measurement of component position there was strong agreement between the readings of the two observers; the ICC for the orientation of the femoral component was 0.73-1.00 (intra-observer reliability) and 0.91-1.00 (inter-observer reliability). The ICC for the orientation of the tibial component was 0.75-1.00 (intra-observer reliability) and 0.77-1.00 (inter-observer reliability). The SPECT/CT algorithm
International Nuclear Information System (INIS)
Beaulieu, Luc; Girouard, Louis-Martin; Aubin, Sylviane; Aubry, Jean-Francois; Brouard, Lucie; Roy-Lacroix, Lise; Dumont, Jean; Tremblay, Daniel; Laverdiere, Jacques; Vigneault, Eric
2004-01-01
Online prostate positioning using gold markers and a standard video-based electronic portal imaging device is reported. The average systematic (random) errors have been reduced from 2.1 mm (2.7 mm) to 0.5 mm (1.5 mm) in AP direction, 1.1 mm (1.7 mm) to 0.7 mm (1.2 mm) SI and 1.2 mm (1.7 mm) to 0.6 mm (1.3 mm) LR
Balbin, Jessie R.; Fausto, Janette C.; Janabajab, John Michael M.; Malicdem, Daryl James L.; Marcelo, Reginald N.; Santos, Jan Jeffrey Z.
2017-06-01
Mango production is highly vital in the Philippines. It is very essential in the food industry as it is being used in markets and restaurants daily. The quality of mangoes can affect the income of a mango farmer, thus incorrect time of harvesting will result to loss of quality mangoes and income. Scientific farming is much needed nowadays together with new gadgets because wastage of mangoes increase annually due to uncouth quality. This research paper focuses on profiling and sorting of Mangifera Indica using image processing techniques and pattern recognition. The image of a mango is captured on a weekly basis from its early stage. In this study, the researchers monitor the growth and color transition of a mango for profiling purposes. Actual dimensions of the mango are determined through image conversion and determination of pixel and RGB values covered through MATLAB. A program is developed to determine the range of the maximum size of a standard ripe mango. Hue, light, saturation (HSL) correction is used in the filtering process to assure the exactness of RGB values of a mango subject. By pattern recognition technique, the program can determine if a mango is standard and ready to be exported.
To what extent are arithmetic progressions of fractional parts stochastic?
Arnol'd, V. I.
2008-04-01
For the sequence of residues of division of n members of an arithmetic progression by a real number N, it is proved that the Kolmogorov stochasticity parameter \\lambda_n tends to 0 as n tends to infinity when the progression step is commensurable with N. In contrast, for the case when the step is incommensurable with N, examples are given in which the stochasticity parameter \\lambda_n not only does not tend to 0, but even takes some arbitrary large values (infrequently). Too small and too large values of the stochasticity parameter both indicate a small probability that the corresponding sequence is random. Thus, long arithmetic progressions of fractional parts are apparently much less stochastic than for geometric progressions (which provide moderate values of the stochasticity parameter, similar to its values for genuinely random sequences).
Cardiorespiratory Information Dynamics during Mental Arithmetic and Sustained Attention.
Widjaja, Devy; Montalto, Alessandro; Vlemincx, Elke; Marinazzo, Daniele; Van Huffel, Sabine; Faes, Luca
2015-01-01
An analysis of cardiorespiratory dynamics during mental arithmetic, which induces stress, and sustained attention was conducted using information theory. The information storage and internal information of heart rate variability (HRV) were determined respectively as the self-entropy of the tachogram, and the self-entropy of the tachogram conditioned to the knowledge of respiration. The information transfer and cross information from respiration to HRV were assessed as the transfer and cross-entropy, both measures of cardiorespiratory coupling. These information-theoretic measures identified significant nonlinearities in the cardiorespiratory time series. Additionally, it was shown that, although mental stress is related to a reduction in vagal activity, no difference in cardiorespiratory coupling was found when several mental states (rest, mental stress, sustained attention) are compared. However, the self-entropy of HRV conditioned to respiration was very informative to study the predictability of RR interval series during mental tasks, and showed higher predictability during mental arithmetic compared to sustained attention or rest.
Single-digit arithmetic in children with dyslexia
Boets, Bart; De Smedt, Bert
2010-01-01
It has been suggested that individuals with dyslexia show poorer performance on those aspects of arithmetic that involve the manipulation of verbal representations, such as the use of fact retrieval strategies. The present study examined this in 13 children with dyslexia who showed normal general mathematics achievement and 16 matched controls. All children completed a multiplication and a subtraction task, which were specifically designed to elicit the use of retrieval and procedural strateg...
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
Topological Aspects of Infinitude of Primes in Arithmetic Progressions
Czech Academy of Sciences Publication Activity Database
Marko, F.; Porubský, Štefan
2015-01-01
Roč. 140, č. 2 (2015), s. 221-237 ISSN 0010-1354 R&D Projects: GA ČR(CZ) GAP201/12/2351 Institutional support: RVO:67985807 Keywords : coset topology * topological semigroup * topological density * Dirichlet theorem on primes * arithmetical progression * maximal ideal * ring of finite character * residually finite ring * infinitude of primes * pseudoprime Subject RIV: BA - General Mathematics Impact factor: 0.333, year: 2015
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
When listening to rain sounds boosts arithmetic ability.
Proverbio, Alice Mado; De Benedetto, Francesco; Ferrari, Maria Vittoria; Ferrarini, Giorgia
2018-01-01
Studies in the literature have provided conflicting evidence about the effects of background noise or music on concurrent cognitive tasks. Some studies have shown a detrimental effect, while others have shown a beneficial effect of background auditory stimuli. The aim of this study was to investigate the influence of agitating, happy or touching music, as opposed to environmental sounds or silence, on the ability of non-musician subjects to perform arithmetic operations. Fifty university students (25 women and 25 men, 25 introverts and 25 extroverts) volunteered for the study. The participants were administered 180 easy or difficult arithmetic operations (division, multiplication, subtraction and addition) while listening to heavy rain sounds, silence or classical music. Silence was detrimental when participants were faced with difficult arithmetic operations, as it was associated with significantly worse accuracy and slower RTs than music or rain sound conditions. This finding suggests that the benefit of background stimulation was not music-specific but possibly due to an enhanced cerebral alertness level induced by the auditory stimulation. Introverts were always faster than extroverts in solving mathematical problems, except when the latter performed calculations accompanied by the sound of heavy rain, a condition that made them as fast as introverts. While the background auditory stimuli had no effect on the arithmetic ability of either group in the easy condition, it strongly affected extroverts in the difficult condition, with RTs being faster during agitating or joyful music as well as rain sounds, compared to the silent condition. For introverts, agitating music was associated with faster response times than the silent condition. This group difference may be explained on the basis of the notion that introverts have a generally higher arousal level compared to extroverts and would therefore benefit less from the background auditory stimuli.
Torsionfree sheaves over a nodal curve of arithmetic genus one
Indian Academy of Sciences (India)
(n, d) is empty. Let X be a geometrically irreducible nodal curve of arithmetic genus one defined over R. We assume that X does not have any other real points apart from the node. Let UX(n, d) denote the moduli space of semistable torsionfree sheaves of rank n and degree d on X, and let U. X. (n, d) ⊂ UX(n, d) be the open ...
When listening to rain sounds boosts arithmetic ability.
Directory of Open Access Journals (Sweden)
Alice Mado Proverbio
Full Text Available Studies in the literature have provided conflicting evidence about the effects of background noise or music on concurrent cognitive tasks. Some studies have shown a detrimental effect, while others have shown a beneficial effect of background auditory stimuli. The aim of this study was to investigate the influence of agitating, happy or touching music, as opposed to environmental sounds or silence, on the ability of non-musician subjects to perform arithmetic operations. Fifty university students (25 women and 25 men, 25 introverts and 25 extroverts volunteered for the study. The participants were administered 180 easy or difficult arithmetic operations (division, multiplication, subtraction and addition while listening to heavy rain sounds, silence or classical music. Silence was detrimental when participants were faced with difficult arithmetic operations, as it was associated with significantly worse accuracy and slower RTs than music or rain sound conditions. This finding suggests that the benefit of background stimulation was not music-specific but possibly due to an enhanced cerebral alertness level induced by the auditory stimulation. Introverts were always faster than extroverts in solving mathematical problems, except when the latter performed calculations accompanied by the sound of heavy rain, a condition that made them as fast as introverts. While the background auditory stimuli had no effect on the arithmetic ability of either group in the easy condition, it strongly affected extroverts in the difficult condition, with RTs being faster during agitating or joyful music as well as rain sounds, compared to the silent condition. For introverts, agitating music was associated with faster response times than the silent condition. This group difference may be explained on the basis of the notion that introverts have a generally higher arousal level compared to extroverts and would therefore benefit less from the background auditory stimuli.
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.
On theories of bounded arithmetic for NC1
Czech Academy of Sciences Publication Activity Database
Jeřábek, Emil
2011-01-01
Roč. 162, č. 4 (2011), s. 322-340 ISSN 0168-0072 R&D Projects: GA AV ČR IAA1019401; GA MŠk(CZ) 1M0545 Institutional research plan: CEZ:AV0Z10190503 Keywords : bounded arithmetic * circuit complexity * propositional translation Subject RIV: BA - General Mathematics Impact factor: 0.450, year: 2011 http://www.sciencedirect.com/science/article/pii/S0168007210001260
A novel algorithm combining oversampling and digital lock-in amplifier of high speed and precision.
Li, Gang; Zhou, Mei; He, Feng; Lin, Ling
2011-09-01
Because of a large amount of arithmetic in the standard digital lock-in detection, a high performance processor is needed to implement the algorithm in real time. This paper presents a novel algorithm that integrates oversampling and high-speed lock-in detection. The algorithm sets the sampling frequency as a whole-number multiple of four of the input signal frequency, and then uses the common downsampling technology to lower the sampling frequency to four times of the input signal frequency. It could effectively remove the noise interference and improve the detection accuracy. After that the phase sensitive detector is implemented. It simply does the addition and subtraction on four points in the period of same phase and replaces almost all the multiplication operations to speed up digital lock-in detection calculation substantially. Furthermore, the correction factor is introduced to improve the calculation accuracy of the amplitude, and an error caused by the algorithm in theory can be eliminated completely. The results of the simulation and actual experiments show that the novel algorithm combining digital lock-in detection and oversampling not only has the high precision, but also has the unprecedented speed. In our work, the new algorithm is suitable for the real-time weak signal detection in the general microprocessor not just digital signal processor. © 2011 American Institute of Physics
Single-digit arithmetic in children with dyslexia.
Boets, Bart; De Smedt, Bert
2010-05-01
It has been suggested that individuals with dyslexia show poorer performance on those aspects of arithmetic that involve the manipulation of verbal representations, such as the use of fact retrieval strategies. The present study examined this in 13 children with dyslexia who showed normal general mathematics achievement and 16 matched controls. All children completed a multiplication and a subtraction task, which were specifically designed to elicit the use of retrieval and procedural strategies, respectively. Our findings revealed that despite normal mathematics achievement, children with dyslexia were less accurate and slower in single-digit arithmetic, particularly in multiplication. The reaction time data revealed an interesting group by operation interaction. Control children were significantly faster in multiplication than in subtraction, whereas no such operation effect was found in children with dyslexia. This suggests that in multiplication children with dyslexia used less retrieval or less efficient retrieval (or both). This is in line with the hypothesis that children with dyslexia may have difficulties with the verbal aspects of number and arithmetic, as retrieval strategies depend upon phonological representations in long-term memory. Copyright 2010 John Wiley & Sons, Ltd.
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.
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
Endocrine and haemodynamic stress responses to an arithmetic cognitive challenge.
Trico, Domenico; Fanfani, Alberto; Varocchi, Francesca; Bernini, Giampaolo
2017-07-01
We aimed at developing and validating a simple, highly repeatable computer-based tool, which could be employed to simulate the effects of an acute mental stress on endocrine and haemodynamic stress responses. Fifteen subjects underwent a mental cognitive challenge, employing an ad hoc designed web tool (available at http://bagame.altervista.org) that proposed a series of random arithmetic operations (addictions or subtractions) between one- to three-digit numbers for 10 minutes. We measured plasma epinephrine, norepinephrine, cortisol, and ACTH, in addition to heart rate (HR), systolic (SBP) and diastolic (DBP) blood pressure throughout the test. The arithmetic mental challenge promptly activated the sympatho-adrenomedullary axis (epinephrine +112±24%, pmental arithmetic ability. We developed and validated a computer-based tool that is effective for simulating endocrine and haemodynamic responses to an acute mental stress. This novel tool is easy-to-use, freely-accessible, and it can be employed to further investigate stress-related pathophysiological mechanisms and their role in cardiovascular diseases.
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 +…
Satoh, Hiroyasu
1994-01-01
Effects of caffeine on arithmetic performance were investigated with 217 university students. A double-blind study for arithmetic skill test and hemodynamic effects was carried out after drinking caffeine-free or caffeine-containing (100, 180 and 250 mg) coffee. Eleven rounds of the arithmetic tests were performed ; first four rounds before, and subsequently seven rounds after coffee break. Each round consisted of three 1-min arithmetic tests. The arithmetic skill for each round was averaged....
Is an interval the right result of arithmetic operations on intervals?
Directory of Open Access Journals (Sweden)
Piegat Andrzej
2017-09-01
Full Text Available For many scientists interval arithmetic (IA, I arithmetic seems to be easy and simple. However, this is not true. Interval arithmetic is complicated. This is confirmed by the fact that, for years, new, alternative versions of this arithmetic have been created and published. These new versions tried to remove shortcomings and weaknesses of previously proposed options of the arithmetic, which decreased the prestige not only of interval arithmetic itself, but also of fuzzy arithmetic, which, to a great extent, is based on it. In our opinion, the main reason for the observed shortcomings of the present IA is the assumption that the direct result of arithmetic operations on intervals is also an interval. However, the interval is not a direct result but only a simplified representative (indicator of the result. This hypothesis seems surprising, but investigations prove that it is true. The paper shows what conditions should be satisfied by the result of interval arithmetic operations to call it a “result”, how great its dimensionality is, how to perform arithmetic operations and solve equations. Examples illustrate the proposed method of interval computations.
Directory of Open Access Journals (Sweden)
S Kaennakham
2016-09-01
Full Text Available The interaction between discretization error and modeling error has led to some doubts in adopting Solution Adaptive Grid (SAG strategies with LES. Existing SAG approaches contain undesired aspects making the use of one complicated and less convenient to apply to real engineering applications. In this work, a new refinement algorithm is proposed aiming to enhance the efficiency of SAG methodology in terms of simplicity in defining, less user's judgment, designed especially for standard Smagorinsky LES and computational affordability. The construction of a new refinement variable as a function of the Taylor scale, corresponding to the kinetic energy balance requirement of the Smagorinsky SGS model is presented. The numerical study has been tested out with a turbulent plane jet in two dimensions. It is found that the result quality can be effectively improved as well as a significant reduction in CPU time compared to fixed grid cases.
Schämann, M.; Bücker, M.; Hessel, S.; Langmann, U.
2008-05-01
High data rates combined with high mobility represent a challenge for the design of cellular devices. Advanced algorithms are required which result in higher complexity, more chip area and increased power consumption. However, this contrasts to the limited power supply of mobile devices. This presentation discusses the application of an HSDPA receiver which has been optimized regarding power consumption with the focus on the algorithmic and architectural level. On algorithmic level the Rake combiner, Prefilter-Rake equalizer and MMSE equalizer are compared regarding their BER performance. Both equalizer approaches provide a significant increase of performance for high data rates compared to the Rake combiner which is commonly used for lower data rates. For both equalizer approaches several adaptive algorithms are available which differ in complexity and convergence properties. To identify the algorithm which achieves the required performance with the lowest power consumption the algorithms have been investigated using SystemC models regarding their performance and arithmetic complexity. Additionally, for the Prefilter Rake equalizer the power estimations of a modified Griffith (LMS) and a Levinson (RLS) algorithm have been compared with the tool ORINOCO supplied by ChipVision. The accuracy of this tool has been verified with a scalable architecture of the UMTS channel estimation described both in SystemC and VHDL targeting a 130 nm CMOS standard cell library. An architecture combining all three approaches combined with an adaptive control unit is presented. The control unit monitors the current condition of the propagation channel and adjusts parameters for the receiver like filter size and oversampling ratio to minimize the power consumption while maintaining the required performance. The optimization strategies result in a reduction of the number of arithmetic operations up to 70% for single components which leads to an estimated power reduction of up to 40
Directory of Open Access Journals (Sweden)
M. Schämann
2008-05-01
Full Text Available High data rates combined with high mobility represent a challenge for the design of cellular devices. Advanced algorithms are required which result in higher complexity, more chip area and increased power consumption. However, this contrasts to the limited power supply of mobile devices.
This presentation discusses the application of an HSDPA receiver which has been optimized regarding power consumption with the focus on the algorithmic and architectural level. On algorithmic level the Rake combiner, Prefilter-Rake equalizer and MMSE equalizer are compared regarding their BER performance. Both equalizer approaches provide a significant increase of performance for high data rates compared to the Rake combiner which is commonly used for lower data rates. For both equalizer approaches several adaptive algorithms are available which differ in complexity and convergence properties. To identify the algorithm which achieves the required performance with the lowest power consumption the algorithms have been investigated using SystemC models regarding their performance and arithmetic complexity. Additionally, for the Prefilter Rake equalizer the power estimations of a modified Griffith (LMS and a Levinson (RLS algorithm have been compared with the tool ORINOCO supplied by ChipVision. The accuracy of this tool has been verified with a scalable architecture of the UMTS channel estimation described both in SystemC and VHDL targeting a 130 nm CMOS standard cell library.
An architecture combining all three approaches combined with an adaptive control unit is presented. The control unit monitors the current condition of the propagation channel and adjusts parameters for the receiver like filter size and oversampling ratio to minimize the power consumption while maintaining the required performance. The optimization strategies result in a reduction of the number of arithmetic operations up to 70% for single components which leads to an
Paris, Yvonne; Toro-Salazar, Olga H; Gauthier, Naomi S; Rotondo, Kathleen M; Arnold, Lucy; Hamershock, Rose; Saudek, David E; Fulton, David R; Renaud, Ashley; Alexander, Mark E
2016-02-19
Pediatric syncope is common. Cardiac causes are rarely found. We describe and assess a pragmatic approach to these patients first seen by a pediatric cardiologist in the New England region, using Standardized Clinical Assessment and Management Plans (SCAMPs). Ambulatory patients aged 7 to 21 years initially seen for syncope at participating New England Congenital Cardiology Association practices over a 2.5-year period were evaluated using a SCAMP. Findings were iteratively analyzed and the care pathway was revised. The vast majority (85%) of the 1254 patients had typical syncope. A minority had exercise-related or more problematic symptoms. Guideline-defined testing identified one patient with cardiac syncope. Syncope Severity Scores correlated well between physician and patient perceived symptoms. Orthostatic vital signs were of limited use. Largely incidental findings were seen in 10% of ECGs and 11% of echocardiograms. The 10% returning for follow-up, by design, reported more significant symptoms, but did not have newly recognized cardiac disease. Iterative analysis helped refine the approach. SCAMP methodology confirmed that the vast majority of children referred to the outpatient pediatric cardiology setting had typical low-severity neurally mediated syncope that could be effectively evaluated in a single visit using minimal resources. A simple scoring system can help triage patients into treatment categories. Prespecified criteria permitted the effective diagnosis of the single patient with a clear cardiac etiology. Patients with higher syncope scores still have a very low risk of cardiac disease, but may warrant attention. © 2016 The Authors. Published on behalf of the American Heart Association, Inc., by Wiley Blackwell.
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.
Directory of Open Access Journals (Sweden)
Luke F Rinne
Full Text Available Does knowing when mental arithmetic judgments are right--and when they are wrong--lead to more accurate judgments over time? We hypothesize that the successful detection of errors (and avoidance of false alarms may contribute to the development of mental arithmetic performance. Insight into error detection abilities can be gained by examining the "calibration" of mental arithmetic judgments-that is, the alignment between confidence in judgments and the accuracy of those judgments. Calibration may be viewed as a measure of metacognitive monitoring ability. We conducted a developmental longitudinal investigation of the relationship between the calibration of children's mental arithmetic judgments and their performance on a mental arithmetic task. Annually between Grades 5 and 8, children completed a problem verification task in which they rapidly judged the accuracy of arithmetic expressions (e.g., 25 + 50 = 75 and rated their confidence in each judgment. Results showed that calibration was strongly related to concurrent mental arithmetic performance, that calibration continued to develop even as mental arithmetic accuracy approached ceiling, that poor calibration distinguished children with mathematics learning disability from both low and typically achieving children, and that better calibration in Grade 5 predicted larger gains in mental arithmetic accuracy between Grades 5 and 8. We propose that good calibration supports the implementation of cognitive control, leading to long-term improvement in mental arithmetic accuracy. Because mental arithmetic "fluency" is critical for higher-level mathematics competence, calibration of confidence in mental arithmetic judgments may represent a novel and important developmental predictor of future mathematics performance.
The neural correlates of mental arithmetic in adolescents: a longitudinal fNIRS study.
Artemenko, Christina; Soltanlou, Mojtaba; Ehlis, Ann-Christine; Nuerk, Hans-Christoph; Dresler, Thomas
2018-03-10
Arithmetic processing in adults is known to rely on a frontal-parietal network. However, neurocognitive research focusing on the neural and behavioral correlates of arithmetic development has been scarce, even though the acquisition of arithmetic skills is accompanied by changes within the fronto-parietal network of the developing brain. Furthermore, experimental procedures are typically adjusted to constraints of functional magnetic resonance imaging, which may not reflect natural settings in which children and adolescents actually perform arithmetic. Therefore, we investigated the longitudinal neurocognitive development of processes involved in performing the four basic arithmetic operations in 19 adolescents. By using functional near-infrared spectroscopy, we were able to use an ecologically valid task, i.e., a written production paradigm. A common pattern of activation in the bilateral fronto-parietal network for arithmetic processing was found for all basic arithmetic operations. Moreover, evidence was obtained for decreasing activation during subtraction over the course of 1 year in middle and inferior frontal gyri, and increased activation during addition and multiplication in angular and middle temporal gyri. In the self-paced block design, parietal activation in multiplication and left angular and temporal activation in addition were observed to be higher for simple than for complex blocks, reflecting an inverse effect of arithmetic complexity. In general, the findings suggest that the brain network for arithmetic processing is already established in 12-14 year-old adolescents, but still undergoes developmental changes.
Foley, Alana E; Vasilyeva, Marina; Laski, Elida V
2017-06-01
This study examined the mediating role of children's use of decomposition strategies in the relation between visuospatial memory (VSM) and arithmetic accuracy. Children (N = 78; Age M = 9.36) completed assessments of VSM, arithmetic strategies, and arithmetic accuracy. Consistent with previous findings, VSM predicted arithmetic accuracy in children. Extending previous findings, the current study showed that the relation between VSM and arithmetic performance was mediated by the frequency of children's use of decomposition strategies. Identifying the role of arithmetic strategies in this relation has implications for increasing the math performance of children with lower VSM. Statement of contribution What is already known on this subject? The link between children's visuospatial working memory and arithmetic accuracy is well documented. Frequency of decomposition strategy use is positively related to children's arithmetic accuracy. Children's spatial skill positively predicts the frequency with which they use decomposition. What does this study add? Short-term visuospatial memory (VSM) positively relates to the frequency of children's decomposition use. Decomposition use mediates the relation between short-term VSM and arithmetic accuracy. Children with limited short-term VSM may struggle to use decomposition, decreasing accuracy. © 2016 The British Psychological Society.
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.
Information Theory, Inference and Learning Algorithms
Mackay, David J. C.
2003-10-01
Information theory and inference, often taught separately, are here united in one entertaining textbook. These topics lie at the heart of many exciting areas of contemporary science and engineering - communication, signal processing, data mining, machine learning, pattern recognition, computational neuroscience, bioinformatics, and cryptography. This textbook introduces theory in tandem with applications. Information theory is taught alongside practical communication systems, such as arithmetic coding for data compression and sparse-graph codes for error-correction. A toolbox of inference techniques, including message-passing algorithms, Monte Carlo methods, and variational approximations, are developed alongside applications of these tools to clustering, convolutional codes, independent component analysis, and neural networks. The final part of the book describes the state of the art in error-correcting codes, including low-density parity-check codes, turbo codes, and digital fountain codes -- the twenty-first century standards for satellite communications, disk drives, and data broadcast. Richly illustrated, filled with worked examples and over 400 exercises, some with detailed solutions, David MacKay's groundbreaking book is ideal for self-learning and for undergraduate or graduate courses. Interludes on crosswords, evolution, and sex provide entertainment along the way. In sum, this is a textbook on information, communication, and coding for a new generation of students, and an unparalleled entry point into these subjects for professionals in areas as diverse as computational biology, financial engineering, and machine learning.
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.
Oscillatory EEG Correlates of Arithmetic Strategies: A Training Study
Grabner, Roland H.; De Smedt, Bert
2012-01-01
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 parietooccipital 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 sensitive to fact retrieval not only in mental arithmetic but also in other domains. PMID:23162495
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.
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...
VLSI processor for high-performance arithmetic computations
McQuillan, S. E.; McCanny, J. V.
1991-12-01
A high performance VLSI architecture to perform combined multiply-accumulate, divide, and square root operations is proposed. The circuit is highly regular, requires only minimal control, and can be pipelined right down to the bit level. The system can also be reconfigured on every cycle to perform one or more of these operations. The throughput rate for each operation is the same and is wordlength independent. This is achieved using redundant arithmetic. With current CMOS technology, throughput rates in excess of 80 million operations per second are expected.
14-term Arithmetic Progressions on Quartic Elliptic Curves
MacLeod, Allan J.
2006-01-01
Let P_4(x) be a rational quartic polynomial which is not the square of a quadratic. Both Campbell and Ulas considered the problem of finding an rational arithmetic progression x_1,x_2,...,x_n, with P_4(x_i) a rational square for 1<=i<=n. They found examples with n=10 and n=12. By simplifying Ulas' approach, we can derive more general parametric solutions for n=10, which give a large number of examples with n=12 and a few with n=14.
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
CIMPA Summer School on Arithmetic and Geometry Around Hypergeometric Functions
Uludağ, A; Yoshida, Masaaki; Arithmetic and Geometry Around Hypergeometric Functions
2007-01-01
This volume comprises the Lecture Notes of the CIMPA Summer School "Arithmetic and Geometry around Hypergeometric Functions" held at Galatasaray University, Istanbul in 2005. It contains lecture notes, a survey article, research articles, and the results of a problem session. Key topics are moduli spaces of points on P1 and Picard-Terada-Deligne-Mostow theory, moduli spaces of K3 surfaces, complex hyperbolic geometry, ball quotients, GKZ hypergeometric structures, Hilbert and Picard modular surfaces, uniformizations of complex orbifolds, algebraicity of values of Schwartz triangle functions, and Thakur's hypergeometric function. The book provides a background, gives detailed expositions and indicates new research directions. It is directed to postgraduate students and researchers.
Energy Technology Data Exchange (ETDEWEB)
Demmel, James W. [Univ. of California, Berkeley, CA (United States)
2017-09-14
This project addresses both communication-avoiding algorithms, and reproducible floating-point computation. Communication, i.e. moving data, either between levels of memory or processors over a network, is much more expensive per operation than arithmetic (measured in time or energy), so we seek algorithms that greatly reduce communication. We developed many new algorithms for both dense and sparse, and both direct and iterative linear algebra, attaining new communication lower bounds, and getting large speedups in many cases. We also extended this work in several ways: (1) We minimize writes separately from reads, since writes may be much more expensive than reads on emerging memory technologies, like Flash, sometimes doing asymptotically fewer writes than reads. (2) We extend the lower bounds and optimal algorithms to arbitrary algorithms that may be expressed as perfectly nested loops accessing arrays, where the array subscripts may be arbitrary affine functions of the loop indices (eg A(i), B(i,j+k, k+3*m-7, …) etc.). (3) We extend our communication-avoiding approach to some machine learning algorithms, such as support vector machines. This work has won a number of awards. We also address reproducible floating-point computation. We define reproducibility to mean getting bitwise identical results from multiple runs of the same program, perhaps with different hardware resources or other changes that should ideally not change the answer. Many users depend on reproducibility for debugging or correctness. However, dynamic scheduling of parallel computing resources, combined with nonassociativity of floating point addition, makes attaining reproducibility a challenge even for simple operations like summing a vector of numbers, or more complicated operations like the Basic Linear Algebra Subprograms (BLAS). We describe an algorithm that computes a reproducible sum of floating point numbers, independent of the order of summation. The algorithm depends only on a
Algorithms for worst-case tolerance optimization
DEFF Research Database (Denmark)
Schjær-Jacobsen, Hans; Madsen, Kaj
1979-01-01
New algorithms are presented for the solution of optimum tolerance assignment problems. The problems considered are defined mathematically as a worst-case problem (WCP), a fixed tolerance problem (FTP), and a variable tolerance problem (VTP). The basic optimization problem without tolerances...... is denoted the zero tolerance problem (ZTP). For solution of the WCP we suggest application of interval arithmetic and also alternative methods. For solution of the FTP an algorithm is suggested which is conceptually similar to algorithms previously developed by the authors for the ZTP. Finally, the VTP...... is solved by a double-iterative algorithm in which the inner iteration is performed by the FTP- algorithm. The application of the algorithm is demonstrated by means of relatively simple numerical examples. Basic properties, such as convergence properties, are displayed based on the examples....
General Purpose Convolution Algorithm in S4 Classes by Means of FFT
Directory of Open Access Journals (Sweden)
Peter Ruckdeschel
2014-08-01
By means of object orientation this default algorithm is overloaded by more specific algorithms where possible, in particular where explicit convolution formulae are available. Our focus is on R package distr which implements this approach, overloading operator + for convolution; based on this convolution, we define a whole arithmetics of mathematical operations acting on distribution objects, comprising operators +, -, *, /, and ^.
Design of arithmetic circuits in quantum dot cellular automata nanotechnology
Sridharan, K
2015-01-01
This research monograph focuses on the design of arithmetic circuits in Quantum Dot Cellular Automata (QCA). Using the fact that the 3-input majority gate is a primitive in QCA, the book sets out to discover hitherto unknown properties of majority logic in the context of arithmetic circuit designs. The pursuit for efficient adders in QCA takes two forms. One involves application of the new results in majority logic to existing adders. The second involves development of a custom adder for QCA technology. A QCA adder named as hybrid adder is proposed and it is shown that it outperforms existing multi-bit adders with respect to area and delay. The work is extended to the design of a low-complexity multiplier for signed numbers in QCA. Furthermore the book explores two aspects unique to QCA technology, namely thermal robustness and the role of interconnects. In addition, the book introduces the reader to QCA layout design and simulation using QCADesigner. Features & Benefits: This research-based book: · �...
Semiotic mediation: from multiplication properties to arithmetical expressions
Directory of Open Access Journals (Sweden)
Andrea Maffia
2016-04-01
Full Text Available Multiplication is introduced early in primary school, but its properties are usually introduced after the rote memorization of multiplicative facts. In this paper we present a teaching experiment aimed to early introducing arithmetical properties of multiplication. It is realized through an artefact built on the rectangle model for multiplication. Children activity is designed and analyzed using Theory of Semiotic Mediation. The development of the relational meaning of arithmetical expressions is shown through the enchaining of representations from signs related to the activity with the artefact to mathematical ones. In particular, the role of the teacher in the process of semiotic mediation results as crucial. Mediazione semiotica: dalle proprietà della moltiplicazione alle espressioni aritmeticheLa moltiplicazione viene presentata presto nella scuola primaria, ma le sue proprietà sono introdotte solo dopo che le cosiddette tabelline sono state memorizzate. Nell’articolo si presenta un teaching experiment volto a introdurre precocemente le proprietà della moltiplicazione per facilitare la memorizzazione di fatti moltiplicativi. L’esperimento è centrato sull’uso di un artefatto costruito sul modello rettangolare della moltiplicazione. L’attività degli studenti è progettata e analizzata nel quadro della Teoria della Mediazione Semiotica (TMS. Lo sviluppo del significato relazionale delle espressioni aritmetiche viene mostrato attraverso la concatenazione di rappresentazioni che vanno da segni strettamente legati all’attività con l’artefatto fino a segni matematici. In particolare, si evidenzia il ruolo dell’insegnante nello sviluppo del processo di mediazione semiotica.
Cohomological dimension and arithmetical rank of some determinantal ideals
Directory of Open Access Journals (Sweden)
Davide Bolognini
2015-05-01
Full Text Available Let M be a (2 × n non-generic matrix of linear forms in a polynomial ring. For large classes of such matrices, we compute the cohomological dimension (cd and the arithmetical rank (ara of the ideal I_2(M generated by the 2-minors of M. Over an algebraically closed field, any (2×n-matrix of linear forms can be written in the Kronecker-Weierstrass normal form, as a concatenation of scroll, Jordan and nilpotent blocks. Badescu and Valla computed ara(I_2 (M when M is a concatenation of scroll blocks. In this case we compute cd(I2 (M and extend these results to concatenations of Jordan blocks. Eventually we compute ara(I_2(M and cd(I_2 (M in an interesting mixed case, when M contains both Jordan and scroll blocks. In all cases we show that ara(I_2(M is less than the arithmetical rank of the determinantal ideal of a generic matrix.
Cardiorespiratory Information Dynamics during Mental Arithmetic and Sustained Attention.
Directory of Open Access Journals (Sweden)
Devy Widjaja
Full Text Available An analysis of cardiorespiratory dynamics during mental arithmetic, which induces stress, and sustained attention was conducted using information theory. The information storage and internal information of heart rate variability (HRV were determined respectively as the self-entropy of the tachogram, and the self-entropy of the tachogram conditioned to the knowledge of respiration. The information transfer and cross information from respiration to HRV were assessed as the transfer and cross-entropy, both measures of cardiorespiratory coupling. These information-theoretic measures identified significant nonlinearities in the cardiorespiratory time series. Additionally, it was shown that, although mental stress is related to a reduction in vagal activity, no difference in cardiorespiratory coupling was found when several mental states (rest, mental stress, sustained attention are compared. However, the self-entropy of HRV conditioned to respiration was very informative to study the predictability of RR interval series during mental tasks, and showed higher predictability during mental arithmetic compared to sustained attention or rest.
Arithmetic learning with the use of graphic organiser
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.
Brauer groups and obstruction problems moduli spaces and arithmetic
Hassett, Brendan; Várilly-Alvarado, Anthony; Viray, Bianca
2017-01-01
The contributions in this book explore various contexts in which the derived category of coherent sheaves on a variety determines some of its arithmetic. This setting provides new geometric tools for interpreting elements of the Brauer group. With a view towards future arithmetic applications, the book extends a number of powerful tools for analyzing rational points on elliptic curves, e.g., isogenies among curves, torsion points, modular curves, and the resulting descent techniques, as well as higher-dimensional varieties like K3 surfaces. Inspired by the rapid recent advances in our understanding of K3 surfaces, the book is intended to foster cross-pollination between the fields of complex algebraic geometry and number theory. Contributors: · Nicolas Addington · Benjamin Antieau · Kenneth Ascher · Asher Auel · Fedor Bogomolov · Jean-Louis Colliot-Thélène · Krishna Dasaratha · Brendan Hassett · Colin Ingalls · Martí Lahoz · Emanuele Macrì · Kelly McKinnie · Andrew Obus · Ekin Ozman · Raman...
Multistate Memristive Tantalum Oxide Devices for Ternary Arithmetic
Kim, Wonjoo; Chattopadhyay, Anupam; Siemon, Anne; Linn, Eike; Waser, Rainer; Rana, Vikas
2016-11-01
Redox-based resistive switching random access memory (ReRAM) offers excellent properties to implement future non-volatile memory arrays. Recently, the capability of two-state ReRAMs to implement Boolean logic functionality gained wide interest. Here, we report on seven-states Tantalum Oxide Devices, which enable the realization of an intrinsic modular arithmetic using a ternary number system. Modular arithmetic, a fundamental system for operating on numbers within the limit of a modulus, is known to mathematicians since the days of Euclid and finds applications in diverse areas ranging from e-commerce to musical notations. We demonstrate that multistate devices not only reduce the storage area consumption drastically, but also enable novel in-memory operations, such as computing using high-radix number systems, which could not be implemented using two-state devices. The use of high radix number system reduces the computational complexity by reducing the number of needed digits. Thus the number of calculation operations in an addition and the number of logic devices can be reduced.
Decidable and undecidable arithmetic functions in actin filament networks
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.
DEFF Research Database (Denmark)
Mahnke, Martina; Uprichard, Emma
2014-01-01
changes: it’s not the ocean, it’s the internet we’re talking about, and it’s not a TV show producer, but algorithms that constitute a sort of invisible wall. Building on this assumption, most research is trying to ‘tame the algorithmic tiger’. While this is a valuable and often inspiring approach, we...
A New Modified Firefly Algorithm
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Medha Gupta
2016-07-01
Full Text Available Nature inspired meta-heuristic algorithms studies the emergent collective intelligence of groups of simple agents. Firefly Algorithm is one of the new such swarm-based metaheuristic algorithm inspired by the flashing behavior of fireflies. The algorithm was first proposed in 2008 and since then has been successfully used for solving various optimization problems. In this work, we intend to propose a new modified version of Firefly algorithm (MoFA and later its performance is compared with the standard firefly algorithm along with various other meta-heuristic algorithms. Numerical studies and results demonstrate that the proposed algorithm is superior to existing algorithms.
Suzuki, Shigeru; Machida, Haruhiko; Tanaka, Isao; Ueno, Eiko
2013-03-01
The purpose of this study was to evaluate the performance of model-based iterative reconstruction (MBIR) in measurement of the inner diameter of models of blood vessels and compare performance between MBIR and a standard filtered back projection (FBP) algorithm. Vascular models with wall thicknesses of 0.5, 1.0, and 1.5 mm were scanned with a 64-MDCT unit and densities of contrast material yielding 275, 396, and 542 HU. Images were reconstructed images by MBIR and FBP, and the mean diameter of each model vessel was measured by software automation. Twenty separate measurements were repeated for each vessel, and variance among the repeated measures was analyzed for determination of measurement error. For all nine model vessels, CT attenuation profiles were compared along a line passing through the luminal center on axial images reconstructed with FBP and MBIR, and the 10-90% edge rise distances at the boundary between the vascular wall and the lumen were evaluated. For images reconstructed with FBP, measurement errors were smallest for models with 1.5-mm wall thickness, except those filled with 275-HU contrast material, and errors grew as the density of the contrast material decreased. Measurement errors with MBIR were comparable to or less than those with FBP. In CT attenuation profiles of images reconstructed with MBIR, the 10-90% edge rise distances at the boundary between the lumen and vascular wall were relatively short for each vascular model compared with those of the profile curves of FBP images. MBIR is better than standard FBP for reducing reconstruction blur and improving the accuracy of diameter measurement at CT angiography.
Fuzzy Nonlinier Mix-Integer Goal Programming with Genetic Algorithms
Samsuryadi, Samsuryadi
2003-01-01
System's reability optimization problems are modeled using fuzzy nonlinier mix-integer goal programming problems, involving imprecise nonlinier mix-integer information. Furthermore, fuzzy nonlinier mix-integer goal programming is transformed into nonlinier mix-integer programming problem and the problem i solved using genetic algorithms by means of Matlab 5.3 software. The results or genetic algorithms with operator arithmetic crossover are the large of initial population number does not give...
Sex Differences in Mental Arithmetic, Digit Span, and "g" Defined as Working Memory Capacity
Lynn, Richard; Irwing, Paul
2008-01-01
Meta-analyses are presented of sex differences in (1) the (mental) arithmetic subtest of the Wechsler intelligence tests for children and adolescents (the WISC and WPPSI tests), showing that boys obtained a mean advantage of 0.11d; (2) the (mental) arithmetic subtest of the Wechsler intelligence tests for adults (the WAIS tests) showing a mean…
Binary Arithmetic From Hariot (CA, 1600 A.D.) to the Computer Age.
Glaser, Anton
This history of binary arithmetic begins with details of Thomas Hariot's contribution and includes specific references to Hariot's manuscripts kept at the British Museum. A binary code developed by Sir Francis Bacon is discussed. Briefly mentioned are contributions to binary arithmetic made by Leibniz, Fontenelle, Gauss, Euler, Benzout, Barlow,…
Sabrewing: A lightweight architecture for combined floating-point and integer arithmetic
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
Partition of a Set Which Contains an Infinite Arithmetic (Respectively Geometric) Progression
Smarandache, Florentin
2009-01-01
We prove that for any partition of a set which contains an infinite arithmetic (respectively geometric) progression into two disjoint subsets, at least one of these subsets contains an infinite number of triplets such that each triplet is an arithmetic (respectively geometric) progression.
Children Learn Spurious Associations in Their Math Textbooks: Examples from Fraction Arithmetic
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…
Predicting Arithmetical Achievement from Neuro-Psychological Performance: A Longitudinal Study.
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)
Inhibition and Shifting in Children with Learning Deficits in Arithmetic and Reading
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…
Working Memory in Dutch Children with Reading- and Arithmetic-Related LD
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),…
Executive function in relation to arithmetic development in children with cerebral palsy
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
Jenks, Kathleen M.; de Moor, Jan; van Lieshout, Ernest C. D. M.
2009-01-01
Background: Although it is believed that children with cerebral palsy are at high risk for learning difficulties and arithmetic difficulties in particular, few studies have investigated this issue. Methods: Arithmetic ability was longitudinally assessed in children with cerebral palsy in special (n = 41) and mainstream education (n = 16) and…
Arithmetic Achievement in Children with Cerebral Palsy or Spina Bifida Meningomyelocele
Jenks, Kathleen M.; van Lieshout, Ernest C. D. M.; de Moor, Jan
2009-01-01
The aim of this study was to establish whether children with a physical disability resulting from central nervous system disorders (CNSd) show a level of arithmetic achievement lower than that of non-CNSd children and whether this is related to poor automaticity of number facts or reduced arithmetic instruction time. Twenty-two children with CNSd…
Accelerating scientific computations with mixed precision algorithms
Baboulin, Marc; Buttari, Alfredo; Dongarra, Jack; Kurzak, Jakub; Langou, Julie; Langou, Julien; Luszczek, Piotr; Tomov, Stanimire
2009-12-01
On modern architectures, the performance of 32-bit operations is often at least twice as fast as the performance of 64-bit operations. By using a combination of 32-bit and 64-bit floating point arithmetic, the performance of many dense and sparse linear algebra algorithms can be significantly enhanced while maintaining the 64-bit accuracy of the resulting solution. The approach presented here can apply not only to conventional processors but also to other technologies such as Field Programmable Gate Arrays (FPGA), Graphical Processing Units (GPU), and the STI Cell BE processor. Results on modern processor architectures and the STI Cell BE are presented. Program summaryProgram title: ITER-REF Catalogue identifier: AECO_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AECO_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 7211 No. of bytes in distributed program, including test data, etc.: 41 862 Distribution format: tar.gz Programming language: FORTRAN 77 Computer: desktop, server Operating system: Unix/Linux RAM: 512 Mbytes Classification: 4.8 External routines: BLAS (optional) Nature of problem: On modern architectures, the performance of 32-bit operations is often at least twice as fast as the performance of 64-bit operations. By using a combination of 32-bit and 64-bit floating point arithmetic, the performance of many dense and sparse linear algebra algorithms can be significantly enhanced while maintaining the 64-bit accuracy of the resulting solution. Solution method: Mixed precision algorithms stem from the observation that, in many cases, a single precision solution of a problem can be refined to the point where double precision accuracy is achieved. A common approach to the solution of linear systems, either dense or sparse, is to perform the LU
Fofonoff, N. P.; Millard, R. C., Jr.
Algorithms for computation of fundamental properties of seawater, based on the practicality salinity scale (PSS-78) and the international equation of state for seawater (EOS-80), are compiled in the present report for implementing and standardizing computer programs for oceanographic data processing. Sample FORTRAN subprograms and tables are given…
Hardware realization of an SVM algorithm implemented in FPGAs
Wiśniewski, Remigiusz; Bazydło, Grzegorz; Szcześniak, Paweł
2017-08-01
The paper proposes a technique of hardware realization of a space vector modulation (SVM) of state function switching in matrix converter (MC), oriented on the implementation in a single field programmable gate array (FPGA). In MC the SVM method is based on the instantaneous space-vector representation of input currents and output voltages. The traditional computation algorithms usually involve digital signal processors (DSPs) which consumes the large number of power transistors (18 transistors and 18 independent PWM outputs) and "non-standard positions of control pulses" during the switching sequence. Recently, hardware implementations become popular since computed operations may be executed much faster and efficient due to nature of the digital devices (especially concurrency). In the paper, we propose a hardware algorithm of SVM computation. In opposite to the existing techniques, the presented solution applies COordinate Rotation DIgital Computer (CORDIC) method to solve the trigonometric operations. Furthermore, adequate arithmetic modules (that is, sub-devices) used for intermediate calculations, such as code converters or proper sectors selectors (for output voltages and input current) are presented in detail. The proposed technique has been implemented as a design described with the use of Verilog hardware description language. The preliminary results of logic implementation oriented on the Xilinx FPGA (particularly, low-cost device from Artix-7 family from Xilinx was used) are also presented.
MM Algorithms for Geometric and Signomial Programming.
Lange, Kenneth; Zhou, Hua
2014-02-01
This paper derives new algorithms for signomial programming, a generalization of geometric programming. The algorithms are based on a generic principle for optimization called the MM algorithm. In this setting, one can apply the geometric-arithmetic mean inequality and a supporting hyperplane inequality to create a surrogate function with parameters separated. Thus, unconstrained signomial programming reduces to a sequence of one-dimensional minimization problems. Simple examples demonstrate that the MM algorithm derived can converge to a boundary point or to one point of a continuum of minimum points. Conditions under which the minimum point is unique or occurs in the interior of parameter space are proved for geometric programming. Convergence to an interior point occurs at a linear rate. Finally, the MM framework easily accommodates equality and inequality constraints of signomial type. For the most important special case, constrained quadratic programming, the MM algorithm involves very simple updates.
Gas Source Localization via Behaviour Based Mobile Robot and Weighted Arithmetic Mean
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.
Digital image processing an algorithmic approach with Matlab
Qidwai, Uvais
2009-01-01
Introduction to Image Processing and the MATLAB EnvironmentIntroduction Digital Image Definitions: Theoretical Account Image Properties MATLAB Algorithmic Account MATLAB CodeImage Acquisition, Types, and File I/OImage Acquisition Image Types and File I/O Basics of Color Images Other Color Spaces Algorithmic Account MATLAB CodeImage ArithmeticIntroduction Operator Basics Theoretical TreatmentAlgorithmic Treatment Coding ExamplesAffine and Logical Operations, Distortions, and Noise in ImagesIntroduction Affine Operations Logical Operators Noise in Images Distortions in ImagesAlgorithmic Account
Embedded systems design with special arithmetic and number systems
Sousa, Leonel; Chang, Chip-Hong
2017-01-01
This book introduces readers to alternative approaches to designing efficient embedded systems using unconventional number systems. The authors describe various systems that can be used for designing efficient embedded and application-specific processors, such as Residue Number System, Logarithmic Number System, Redundant Binary Number System Double-Base Number System, Decimal Floating Point Number System and Continuous Valued Number System. Readers will learn the strategies and trade-offs of using unconventional number systems in application-specific processors and be able to apply and design appropriate arithmetic operations from these number systems to boost the performance of digital systems. • Serves as a single-source reference to designing embedded systems with unconventional number systems • Covers theory as well as implementation on application-specific processors • Explains mathematical concepts in a manner accessible to readers with diverse backgrounds.
GDI based full adders for energy efficient arithmetic applications
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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.
Can business and economics students perform elementary arithmetic?
Standing, Lionel G; Sproule, Robert A; Leung, Ambrose
2006-04-01
Business and economics majors (N=146) were tested on the D'Amore Test of Elementary Arithmetic, which employs third-grade test items from 1932. Only 40% of the subjects passed the test by answering 10 out of 10 items correctly. Self-predicted scores were a good predictor of actual scores, but performance was not associated with demographic variables, grades in calculus courses, liking for science or computers, or mathematics anxiety. Scores decreased over the subjects' initial years on campus. The hardest test item, with an error rate of 23%, required the subject to evaluate (36 x 7) + (33 x 7). The results are similar to those of Standing in 2006, despite methodological changes intended to maximize performance.
On quaternions and octonions their geometry, arithmetic, and symmetry
AUTHOR|(CDS)2067326
2003-01-01
This book investigates the geometry of quaternion and octonion algebras. Following a comprehensive historical introduction, the book illuminates the special properties of 3- and 4-dimensional Euclidean spaces using quaternions, leading to enumerations of the corresponding finite groups of symmetries. The second half of the book discusses the less familiar octonion algebra, concentrating on its remarkable "triality symmetry" after an appropriate study of Moufang loops. The authors also describe the arithmetics of the quaternions and octonions. The book concludes with a new theory of octonion factorization. Topics covered include the geometry of complex numbers, quaternions and 3-dimensional groups, quaternions and 4-dimensional groups, Hurwitz integral quaternions, composition algebras, Moufang loops, octonions and 8-dimensional geometry, integral octonions, and the octonion projective plane.
International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics
DEVELOPMENTS IN RELIABLE COMPUTING
1999-01-01
The SCAN conference, the International Symposium on Scientific Com puting, Computer Arithmetic and Validated Numerics, takes place bian nually under the joint auspices of GAMM (Gesellschaft fiir Angewandte Mathematik und Mechanik) and IMACS (International Association for Mathematics and Computers in Simulation). SCAN-98 attracted more than 100 participants from 21 countries all over the world. During the four days from September 22 to 25, nine highlighted, plenary lectures and over 70 contributed talks were given. These figures indicate a large participation, which was partly caused by the attraction of the organizing country, Hungary, but also the effec tive support system have contributed to the success. The conference was substantially supported by the Hungarian Research Fund OTKA, GAMM, the National Technology Development Board OMFB and by the J6zsef Attila University. Due to this funding, it was possible to subsidize the participation of over 20 scientists, mainly from Eastern European countries. I...
Modeling Brain Responses in an Arithmetic Working Memory Task
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.
Conference on Arithmetic and Ideal Theory of Rings and Semigroups
Fontana, Marco; Geroldinger, Alfred; Olberding, Bruce
2016-01-01
This book consists of both expository and research articles solicited from speakers at the conference entitled "Arithmetic and Ideal Theory of Rings and Semigroups," held September 22–26, 2014 at the University of Graz, Graz, Austria. It reflects recent trends in multiplicative ideal theory and factorization theory, and brings together for the first time in one volume both commutative and non-commutative perspectives on these areas, which have their roots in number theory, commutative algebra, and algebraic geometry. Topics discussed include topological aspects in ring theory, Prüfer domains of integer-valued polynomials and their monadic submonoids, and semigroup algebras. It will be of interest to practitioners of mathematics and computer science, and researchers in multiplicative ideal theory, factorization theory, number theory, and algebraic geometry.
Neighborhood consistency in mental arithmetic: Behavioral and ERP evidence
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Verguts Tom
2007-12-01
Full Text Available Abstract Background Recent cognitive and computational models (e.g. the Interacting Neighbors Model state that in simple multiplication decade and unit digits of the candidate answers (including the correct result are represented separately. Thus, these models challenge holistic views of number representation as well as traditional accounts of the classical problem size effect in simple arithmetic (i.e. the finding that large problems are answered slower and less accurate than small problems. Empirical data supporting this view are still scarce. Methods Data of 24 participants who performed a multiplication verification task with Arabic digits (e.g. 8 × 4 = 36 - true or false? are reported. Behavioral (i.e. RT and errors and EEG (i.e. ERP measures were recorded in parallel. Results We provide evidence for neighborhood-consistency effects in the verification of simple multiplication problems (e.g. 8 × 4. Behaviorally, we find that decade-consistent lures, which share their decade digit with the correct result (e.g. 36, are harder to reject than matched inconsistent lures, which differ in both digits from the correct result (e.g. 28. This neighborhood consistency effect in product verification is similar to recent observations in the production of multiplication results. With respect to event-related potentials we find significant differences for consistent compared to inconsistent lures in the N400 (increased negativity and Late Positive Component (reduced positivity. In this respect consistency effects in our paradigm resemble lexico-semantic effects earlier found in simple arithmetic and in orthographic input processing. Conclusion Our data suggest that neighborhood consistency effects in simple multiplication stem at least partly from central (lexico-semantic' stages of processing. These results are compatible with current models on the representation of simple multiplication facts – in particular with the Interacting Neighbors Model
Avancini, Chiara; Galfano, Giovanni; Szűcs, Dénes
2014-12-01
Event-related potential (ERP) studies have detected several characteristic consecutive amplitude modulations in both implicit and explicit mental arithmetic tasks. Implicit tasks typically focused on the arithmetic relatedness effect (in which performance is affected by semantic associations between numbers) while explicit tasks focused on the distance effect (in which performance is affected by the numerical difference of to-be-compared numbers). Both task types elicit morphologically similar ERP waves which were explained in functionally similar terms. However, to date, the relationship between these tasks has not been investigated explicitly and systematically. In order to fill this gap, here we examined whether ERP effects and their underlying cognitive processes in implicit and explicit mental arithmetic tasks differ from each other. The same group of participants performed both an implicit number-matching task (in which arithmetic knowledge is task-irrelevant) and an explicit arithmetic-verification task (in which arithmetic knowledge is task-relevant). 129-channel ERP data differed substantially between tasks. In the number-matching task, the arithmetic relatedness effect appeared as a negativity over left-frontal electrodes whereas the distance effect was more prominent over right centro-parietal electrodes. In the verification task, all probe types elicited similar N2b waves over right fronto-central electrodes and typical centro-parietal N400 effects over central electrodes. The distance effect appeared as an early-rising, long-lasting left parietal negativity. We suggest that ERP effects in the implicit task reflect access to semantic memory networks and to magnitude discrimination, respectively. In contrast, effects of expectation violation are more prominent in explicit tasks and may mask more delicate cognitive processes. Copyright © 2014 The Authors. Published by Elsevier B.V. All rights reserved.
Fabbri, Marco
2011-01-01
It is known that number and space representations are connected to one another in numerical and arithmetic abilities. Numbers are represented using the metaphor of a mental number line, oriented along horizontal and vertical space. This number line also seems to be linked to mental arithmetic, which is based partly on arithmetic fact retrieval. It seems that number representation and mental arithmetic are linked together. The present study tested the effect of spatial contextual congruency between stimulus presentation and response key arrangements in arithmetic fact retrieval, using number-matching and addition verification tasks. For both tasks in Experiment 1, a contextual congruency effect was present horizontally (i.e., horizontal presentation of stimuli and horizontal response key alignments) but not vertically (i.e., vertical presentation of stimuli but horizontal response key alignments). In Experiment 2, both tasks showed a contextual congruency effect for both spatial conditions. Experiment 1 showed that the interference and distance effects were found in the horizontal condition, probably because of the spatial congruency between stimulus presentation and response key arrangements. This spatial congruency could be related to the activation of the horizontal number line. Experiment 2 showed similar interference and distance effects for both spatial conditions, suggesting that the congruency between stimulus presentation and response alignment could facilitate the retrieval of arithmetic facts. This facilitation could be related to the activation of both horizontal and vertical number lines. The results are discussed in light of the possible role of a mental number line in arithmetic fact retrieval.
Improved FHT Algorithms for Fast Computation of the Discrete Hartley Transform
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M. T. Hamood
2013-05-01
Full Text Available In this paper, by using the symmetrical properties of the discrete Hartley transform (DHT, an improved radix-2 fast Hartley transform (FHT algorithm with arithmetic complexity comparable to that of the real-valued fast Fourier transform (RFFT is developed. It has a simple and regular butterfly structure and possesses the in-place computation property. Furthermore, using the same principles, the development can be extended to more efficient radix-based FHT algorithms. An example for the improved radix-4 FHT algorithm is given to show the validity of the presented method. The arithmetic complexity for the new algorithms are computed and then compared with the existing FHT algorithms. The results of these comparisons have shown that the developed algorithms reduce the number of multiplications and additions considerably.
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.
Mental arithmetic and non-speech office noise: an exploration of interference-by-content.
Perham, Nick; Hodgetts, Helen; Banbury, Simon
2013-01-01
An interference-by-content account of auditory distraction - in which the impairment to task performance derives from the similarity of what is being recalled and what is being ignored - was explored concerning mental arithmetic performance. Participants completed both a serial recall and a mental arithmetic task in the presence of quiet, office noise with speech (OS) and office noise without speech (ONS). Both tasks revealed that the two office noise condition's significantly impaired performance. That the ONS produced this deficit suggests that an interference-by-content account cannot explain impairment to mental arithmetic performance by background sound.
Zhou, Xinlin; Chen, Chuansheng; Qiao, Sibing; Chen, Chunhui; Chen, Lan; Lu, Na; Dong, Qi
2009-12-11
To test whether the retrieval of arithmetic facts is independent of numerical notations, this study investigated the event-related potentials elicited by single-digit addition and multiplication problems in Arabic digits and Chinese number words. The results showed that, in comparison with addition, multiplication elicited a greater N300-like component at the left anterior electrodes and greater late positive potentials at the right posterior electrodes, regardless of numerical notations. The operation effects lasted from 250 to 900 ms for Arabic digits, but from 250 to 1400 ms for Chinese number words when participants were asked to respond only to false arithmetic equations (experiment one), and lasted from 350 to 1400 ms for Arabic digits and Chinese number words when participants were asked to respond to both true and false arithmetic equations (experiment two). The consistency in the operation effects in ERPs (i.e., a dissociation of brain organization for different arithmetic operations) for different number notations suggests that mental representation and retrieval of arithmetic facts may be relatively independent of numerical notations.
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.
Directory of Open Access Journals (Sweden)
Kiran Vanbinst
Full Text Available In this article, we tested, using a 1-year longitudinal design, whether symbolic numerical magnitude processing or children's numerical representation of Arabic digits, is as important to arithmetic as phonological awareness is to reading. Children completed measures of symbolic comparison, phonological awareness, arithmetic, reading at the start of third grade and the latter two were retested at the start of fourth grade. Cross-sectional and longitudinal correlations indicated that symbolic comparison was a powerful domain-specific predictor of arithmetic and that phonological awareness was a unique predictor of reading. Crucially, the strength of these independent associations was not significantly different. This indicates that symbolic numerical magnitude processing is as important to arithmetic development as phonological awareness is to reading and suggests that symbolic numerical magnitude processing is a good candidate for screening children at risk for developing mathematical difficulties.
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.
On the constant in the Mertens product for arithmetic progressions. II
Languasco, A.; Zaccagnini, A.
2009-03-01
We give explicit numerical values with 100 decimal digits for the constant in the Mertens product over primes in the arithmetic progressions a operatorname{mod} q , for q in \\{3 , ..., 100\\} and (a, q) = 1 .
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...
Signatures of arithmetic simplicity in metabolic network architecture.
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William J Riehl
2010-04-01
Full Text Available Metabolic networks perform some of the most fundamental functions in living cells, including energy transduction and building block biosynthesis. While these are the best characterized networks in living systems, understanding their evolutionary history and complex wiring constitutes one of the most fascinating open questions in biology, intimately related to the enigma of life's origin itself. Is the evolution of metabolism subject to general principles, beyond the unpredictable accumulation of multiple historical accidents? Here we search for such principles by applying to an artificial chemical universe some of the methodologies developed for the study of genome scale models of cellular metabolism. In particular, we use metabolic flux constraint-based models to exhaustively search for artificial chemistry pathways that can optimally perform an array of elementary metabolic functions. Despite the simplicity of the model employed, we find that the ensuing pathways display a surprisingly rich set of properties, including the existence of autocatalytic cycles and hierarchical modules, the appearance of universally preferable metabolites and reactions, and a logarithmic trend of pathway length as a function of input/output molecule size. Some of these properties can be derived analytically, borrowing methods previously used in cryptography. In addition, by mapping biochemical networks onto a simplified carbon atom reaction backbone, we find that properties similar to those predicted for the artificial chemistry hold also for real metabolic networks. These findings suggest that optimality principles and arithmetic simplicity might lie beneath some aspects of biochemical complexity.
Modulation of human motoneuron activity by a mental arithmetic task.
Bensoussan, Laurent; Duclos, Yann; Rossi-Durand, Christiane
2012-10-01
This study aimed to determine whether the performance of a mental task affects motoneuron activity. To this end, the tonic discharge pattern of wrist extensor motor units was analyzed in healthy subjects while they were required to maintain a steady wrist extension force and to concurrently perform a mental arithmetic (MA) task. A shortening of the mean inter-spike interval (ISI) and a decrease in ISI variability occurred when MA task was superimposed to the motor task. Aloud and silent MA affected equally the rate and variability of motoneuron discharge. Increases in surface EMG activity and force level were consistent with the modulation of the motor unit discharge rate. Trial-by-trial analysis of the characteristics of motor unit firing revealed that performing MA increases activation of wrist extensor SMU. It is suggested that increase in muscle spindle afferent activity, resulting from fusimotor drive activation by MA, may have contributed to the increase in synaptic inputs to motoneurons during the mental task performance, likely together with enhancement in the descending drive. The finding that a mental task affects motoneuron activity could have consequences in assessment of motor disabilities and in rehabilitation in motor pathologies. Copyright © 2012 Elsevier B.V. All rights reserved.
Dumontheil, Iroise; Klingberg, Torkel
2012-05-01
Visuospatial working memory (WM) capacity is highly correlated with mathematical reasoning abilities and can predict future development of arithmetical performance. Activity in the intraparietal sulcus (IPS) during visuospatial WM tasks correlates with interindividual differences in WM capacity. This region has also been implicated in numerical representation, and its structure and activity reflect arithmetical performance impairments (e.g., dyscalculia). We collected behavioral (N = 246) and neuroimaging data (N = 46) in a longitudinal sample to test whether IPS activity during a visuospatial WM task could provide more information than psychological testing alone and predict arithmetical performance 2 years later in healthy participants aged 6-16 years. Nonverbal reasoning and verbal and visuospatial WM measures were found to be independent predictors of arithmetical outcome. In addition, WM activation in the left IPS predicted arithmetical outcome independently of behavioral measures. A logistic model including both behavioral and imaging data showed improved sensitivity by correctly classifying more than twice as many children as poor arithmetical performers after 2 years than a model with behavioral measures only. These results demonstrate that neuroimaging data can provide useful information in addition to behavioral assessments and be used to improve the identification of individuals at risk of future low academic performance.
Common substrate for mental arithmetic and finger representation in the parietal cortex.
Andres, Michael; Michaux, Nicolas; Pesenti, Mauro
2012-09-01
The history of mathematics provides several examples of the use of fingers to count or calculate. These observations converge with developmental data showing that fingers play a critical role in the acquisition of arithmetic knowledge. Further studies evidenced specific interference of finger movements with arithmetic problem solving in adults, raising the question of whether or not finger and number manipulations rely on common brain areas. In the present study, functional magnetic resonance imaging (fMRI) was used to investigate the possible overlap between the brain areas involved in mental arithmetic and those involved in finger discrimination. Solving subtraction and multiplication problems was found to increase cerebral activation bilaterally in the horizontal part of the intraparietal sulcus (hIPS) and in the posterior part of the superior parietal lobule (PSPL). Finger discrimination was associated with increased activity in a bilateral occipito-parieto-precentral network extending from the extrastriate body area to the primary somatosensory and motor cortices. A conjunction analysis showed common areas for mental arithmetic and finger representation in the hIPS and PSPL bilaterally. Voxelwise correlations further showed that finger discrimination and mental arithmetic induced a similar pattern of activity within the parietal areas only. Pattern similarity was more important for the left than for the right hIPS and for subtraction than for multiplication. These findings provide the first evidence that the brain circuits involved in finger representation also underlie arithmetic operations in adults. Copyright © 2012 Elsevier Inc. All rights reserved.
Separating stages of arithmetic verification: An ERP study with a novel paradigm.
Avancini, Chiara; Soltész, Fruzsina; Szűcs, Dénes
2015-08-01
In studies of arithmetic verification, participants typically encounter two operands and they carry out an operation on these (e.g. adding them). Operands are followed by a proposed answer and participants decide whether this answer is correct or incorrect. However, interpretation of results is difficult because multiple parallel, temporally overlapping numerical and non-numerical processes of the human brain may contribute to task execution. In order to overcome this problem here we used a novel paradigm specifically designed to tease apart the overlapping cognitive processes active during arithmetic verification. Specifically, we aimed to separate effects related to detection of arithmetic correctness, detection of the violation of strategic expectations, detection of physical stimulus properties mismatch and numerical magnitude comparison (numerical distance effects). Arithmetic correctness, physical stimulus properties and magnitude information were not task-relevant properties of the stimuli. We distinguished between a series of temporally highly overlapping cognitive processes which in turn elicited overlapping ERP effects with distinct scalp topographies. We suggest that arithmetic verification relies on two major temporal phases which include parallel running processes. Our paradigm offers a new method for investigating specific arithmetic verification processes in detail. Copyright © 2015 Elsevier Ltd. All rights reserved.
Directory of Open Access Journals (Sweden)
M. Balasubbareddy
2015-12-01
Full Text Available A novel optimization algorithm is proposed to solve single and multi-objective optimization problems with generation fuel cost, emission, and total power losses as objectives. The proposed method is a hybridization of the conventional cuckoo search algorithm and arithmetic crossover operations. Thus, the non-linear, non-convex objective function can be solved under practical constraints. The effectiveness of the proposed algorithm is analyzed for various cases to illustrate the effect of practical constraints on the objectives' optimization. Two and three objective multi-objective optimization problems are formulated and solved using the proposed non-dominated sorting-based hybrid cuckoo search algorithm. The effectiveness of the proposed method in confining the Pareto front solutions in the solution region is analyzed. The results for single and multi-objective optimization problems are physically interpreted on standard test functions as well as the IEEE-30 bus test system with supporting numerical and graphical results and also validated against existing methods.
Identification procedure for epistemic uncertainties using inverse fuzzy arithmetic
Haag, T.; Herrmann, J.; Hanss, M.
2010-10-01
For the mathematical representation of systems with epistemic uncertainties, arising, for example, from simplifications in the modeling procedure, models with fuzzy-valued parameters prove to be a suitable and promising approach. In practice, however, the determination of these parameters turns out to be a non-trivial problem. The identification procedure to appropriately update these parameters on the basis of a reference output (measurement or output of an advanced model) requires the solution of an inverse problem. Against this background, an inverse method for the computation of the fuzzy-valued parameters of a model with epistemic uncertainties is presented. This method stands out due to the fact that it only uses feedforward simulations of the model, based on the transformation method of fuzzy arithmetic, along with the reference output. An inversion of the system equations is not necessary. The advancement of the method presented in this paper consists of the identification of multiple input parameters based on a single reference output or measurement. An optimization is used to solve the resulting underdetermined problems by minimizing the uncertainty of the identified parameters. Regions where the identification procedure is reliable are determined by the computation of a feasibility criterion which is also based on the output data of the transformation method only. For a frequency response function of a mechanical system, this criterion allows a restriction of the identification process to some special range of frequency where its solution can be guaranteed. Finally, the practicability of the method is demonstrated by covering the measured output of a fluid-filled piping system by the corresponding uncertain FE model in a conservative way.
Processes in arithmetic strategy selection: a fMRI study.
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.
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.
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Walker Neff
2011-08-01
Full Text Available Abstract Background Trends in the causes of child mortality serve as important global health information to guide efforts to improve child survival. With child mortality declining in Bangladesh, the distribution of causes of death also changes. The three verbal autopsy (VA studies conducted with the Bangladesh Demographic and Health Surveys provide a unique opportunity to study these changes in child causes of death. Methods To ensure comparability of these trends, we developed a standardized algorithm to assign causes of death using symptoms collected through the VA studies. The original algorithms applied were systematically reviewed and key differences in cause categorization, hierarchy, case definition, and the amount of data collected were compared to inform the development of the standardized algorithm. Based primarily on the 2004 cause categorization and hierarchy, the standardized algorithm guarantees comparability of the trends by only including symptom data commonly available across all three studies. Results Between 1993 and 2004, pneumonia remained the leading cause of death in Bangladesh, contributing to 24% to 33% of deaths among children under 5. The proportion of neonatal mortality increased significantly from 36% (uncertainty range [UR]: 31%-41% to 56% (49%-62% during the same period. The cause-specific mortality fractions due to birth asphyxia/birth injury and prematurity/low birth weight (LBW increased steadily, with both rising from 3% (2%-5% to 13% (10%-17% and 10% (7%-15%, respectively. The cause-specific mortality rates decreased significantly due to neonatal tetanus and several postneonatal causes (tetanus: from 7 [4-11] to 2 [0.4-4] per 1,000 live births (LB; pneumonia: from 26 [20-33] to 15 [11-20] per 1,000 LB; diarrhea: from 12 [8-17] to 4 [2-7] per 1,000 LB; measles: from 5 [2-8] to 0.2 [0-0.7] per 1,000 LB; injury: from 11 [7-17] to 3 [1-5] per 1,000 LB; and malnutrition: from 9 [6-13] to 5 [2-7]. Conclusions
Canonical algorithms for numerical integration of charged particle motion equations
Efimov, I. N.; Morozov, E. A.; Morozova, A. R.
2017-02-01
A technique for numerically integrating the equation of charged particle motion in a magnetic field is considered. It is based on the canonical transformations of the phase space in Hamiltonian mechanics. The canonical transformations make the integration process stable against counting error accumulation. The integration algorithms contain a minimum possible amount of arithmetics and can be used to design accelerators and devices of electron and ion optics.
SSTL I/O Standard Based Arithmetic Circuits Design on FPGA
DEFF Research Database (Denmark)
Goswami, Kavita; Pandey, Bishwajeet; Hussain, Dil muhammed Akbar
2016-01-01
-Tiryagbhyam”. SSTL135_R is minimum I/O power consumer. SSTL135_DCI is maximum power consumer. When we use SSTL135_R in place of SSTL12, SSTL12_DCI, SSTL15, and SSTL135_DCI, there is 42.5%, 82.7%, 28.12%, and 72.9% reduction in I/O power at 21oC, 40oC, 53.5oC and 56.7oC. This design is implemented on Artix-7 FPGA...
Joux, Antoine
2009-01-01
Illustrating the power of algorithms, Algorithmic Cryptanalysis describes algorithmic methods with cryptographically relevant examples. Focusing on both private- and public-key cryptographic algorithms, it presents each algorithm either as a textual description, in pseudo-code, or in a C code program.Divided into three parts, the book begins with a short introduction to cryptography and a background chapter on elementary number theory and algebra. It then moves on to algorithms, with each chapter in this section dedicated to a single topic and often illustrated with simple cryptographic applic
Hougardy, Stefan
2016-01-01
Algorithms play an increasingly important role in nearly all fields of mathematics. This book allows readers to develop basic mathematical abilities, in particular those concerning the design and analysis of algorithms as well as their implementation. It presents not only fundamental algorithms like the sieve of Eratosthenes, the Euclidean algorithm, sorting algorithms, algorithms on graphs, and Gaussian elimination, but also discusses elementary data structures, basic graph theory, and numerical questions. In addition, it provides an introduction to programming and demonstrates in detail how to implement algorithms in C++. This textbook is suitable for students who are new to the subject and covers a basic mathematical lecture course, complementing traditional courses on analysis and linear algebra. Both authors have given this "Algorithmic Mathematics" course at the University of Bonn several times in recent years.
Karabağ Aydin, Arzu; Dinç, Leyla
2017-05-01
Drug dosage calculation skill is critical for all nursing students to ensure patient safety, particularly during clinical practice. The study purpose was to evaluate the effectiveness of Web-based instruction on improving nursing students' arithmetical and drug dosage calculation skills using a pretest-posttest design. A total of 63 nursing students participated. Data were collected through the Demographic Information Form, and the Arithmetic Skill Test and Drug Dosage Calculation Skill Test were used as pre and posttests. The pretest was conducted in the classroom. A Web site was then constructed, which included audio presentations of lectures, quizzes, and online posttests. Students had Web-based training for 8 weeks and then they completed the posttest. Pretest and posttest scores were compared using the Wilcoxon test and correlation coefficients were used to identify the relationship between arithmetic and calculation skills scores. The results demonstrated that Web-based teaching improves students' arithmetic and drug dosage calculation skills. There was a positive correlation between the arithmetic skill and drug dosage calculation skill scores of students. Web-based teaching programs can be used to improve knowledge and skills at a cognitive level in nursing students.
Language-specific memory for everyday arithmetic facts in Chinese-English bilinguals.
Chen, Yalin; Yanke, Jill; Campbell, Jamie I D
2016-04-01
The role of language in memory for arithmetic facts remains controversial. Here, we examined transfer of memory training for evidence that bilinguals may acquire language-specific memory stores for everyday arithmetic facts. Chinese-English bilingual adults (n = 32) were trained on different subsets of simple addition and multiplication problems. Each operation was trained in one language or the other. The subsequent test phase included all problems with addition and multiplication alternating across trials in two blocks, one in each language. Averaging over training language, the response time (RT) gains for trained problems relative to untrained problems were greater in the trained language than in the untrained language. Subsequent analysis showed that English training produced larger RT gains for trained problems relative to untrained problems in English at test relative to the untrained Chinese language. In contrast, there was no evidence with Chinese training that problem-specific RT gains differed between Chinese and the untrained English language. We propose that training in Chinese promoted a translation strategy for English arithmetic (particularly multiplication) that produced strong cross-language generalization of practice, whereas training in English strengthened relatively weak, English-language arithmetic memories and produced little generalization to Chinese (i.e., English training did not induce an English translation strategy for Chinese language trials). The results support the existence of language-specific strengthening of memory for everyday arithmetic facts.
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.
Spatial working memory and arithmetic deficits in children with nonverbal learning difficulties.
Mammarella, Irene Cristina; Lucangeli, Daniela; Cornoldi, Cesare
2010-01-01
Visuospatial working memory and its involvement in arithmetic were examined in two groups of 7- to 11-year-olds: one comprising children described by teachers as displaying symptoms of nonverbal learning difficulties (N = 21), the other a control group without learning disabilities (N = 21). The two groups were matched for verbal abilities, age, gender, and sociocultural level. The children were presented with a visuospatial working memory battery of recognition tests involving visual, spatial-sequential and spatial-simultaneous processes, and two arithmetic tasks (number ordering and written calculations). The two groups were found to differ on some spatial tasks but not in the visual working memory tasks. On the arithmetic tasks, the children with nonverbal learning difficulties made more errors than controls in calculation and were slower in number ordering. A discriminant function analysis confirmed the crucial role of spatial-sequential working memory in distinguishing between the two groups. Results are discussed with reference to spatial working memory and arithmetic difficulties in nonverbal learning disabilities. Implications for the relationship between visuospatial working memory and arithmetic are also considered.
Frontoparietal white matter diffusion properties predict mental arithmetic skills in children.
Tsang, Jessica M; Dougherty, Robert F; Deutsch, Gayle K; Wandell, Brian A; Ben-Shachar, Michal
2009-12-29
Functional MRI studies of mental arithmetic consistently report blood oxygen level-dependent signals in the parietal and frontal regions. We tested whether white matter pathways connecting these regions are related to mental arithmetic ability by using diffusion tensor imaging (DTI) to measure these pathways in 28 children (age 10-15 years, 14 girls) and assessing their mental arithmetic skills. For each child, we identified anatomically the anterior portion of the superior longitudinal fasciculus (aSLF), a pathway connecting parietal and frontal cortex. We measured fractional anisotropy in a core region centered along the length of the aSLF. Fractional anisotropy in the left aSLF positively correlates with arithmetic approximation skill, as measured by a mental addition task with approximate answer choices. The correlation is stable in adjacent core aSLF regions but lower toward the pathway endpoints. The correlation is not explained by shared variance with other cognitive abilities and did not pass significance in the right aSLF. These measurements used DTI, a structural method, to test a specific functional model of mental arithmetic.
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.
Tel, G.
We define the notion of total algorithms for networks of processes. A total algorithm enforces that a "decision" is taken by a subset of the processes, and that participation of all processes is required to reach this decision. Total algorithms are an important building block in the design of
Group leaders optimization algorithm
Daskin, Anmer; Kais, Sabre
2011-03-01
We present a new global optimization algorithm in which the influence of the leaders in social groups is used as an inspiration for the evolutionary technique which is designed into a group architecture. To demonstrate the efficiency of the method, a standard suite of single and multi-dimensional optimization functions along with the energies and the geometric structures of Lennard-Jones clusters are given as well as the application of the algorithm on quantum circuit design problems. We show that as an improvement over previous methods, the algorithm scales as N 2.5 for the Lennard-Jones clusters of N-particles. In addition, an efficient circuit design is shown for a two-qubit Grover search algorithm which is a quantum algorithm providing quadratic speedup over the classical counterpart.
International Nuclear Information System (INIS)
Larcos, G.; Chi, K.K.G.; Berry, G.; Westmead Hospital, Sydney, NSW; Shiell, A.
2000-01-01
There is a controversy regarding the investigation of patients with suspected acute pulmonary embolism (PE). To compare the cost-effectiveness of alternative methods of diagnosing acute PE, chest helical computed tomography (CT) alone and in combination with venous ultrasound (US) of legs and pulmonary angiography (PA) were compared to a conventional algorithm using ventilation-perfusion (V/Q) scintigraphy supplemented in selected cases by US and PA. A decision-analytical model was constructed to model the costs and effects of the three diagnostic strategies in a hypothetical cohort of 1000 patients each. Transition probabilities were based on published data. Life years gained by each strategy were estimated from published mortality rates. Schedule fees were used to estimate costs. The V/Q protocol is both more expensive and more effective than CT alone resulting in 20.1 additional lives saved at a (discounted) cost of $940 per life year gained. An additional 2.5 lives can be saved if CT replaces V/Q scintigraphy in the diagnostic algorithm but at a cost of $23,905 per life year saved. It resulted that the more effective diagnostic strategies are also more expensive. In patients with suspected PE, the incremental cost-effectiveness of the V/Q based strategy over CT alone is reasonable in comparison with other health interventions. The cost-effectiveness of the supplemented CT strategy is more questionable. Copyright (2000) The Australasian College of Physicians
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 elementary education were formed: children with arithmetic learning disabilities (ALD), children with reading learning disabilities (RLD), and children with comorbid arithmetic and reading learning disabilities (ARLD). Mediation analysis confirmed that SA was a mediator variable for both groups of children with reading disabilities when solving AWPs, but not for children in the ALD group. All groups performed below the control group in the problem solving task. When SA was controlled for, semantic structure and position of the unknown set were variables that affected both groups with ALD. Specifically, children with ALD only were more affected by the place of the unknown set. © Hammill Institute on Disabilities 2014.
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...
Retrieval or nonretrieval strategies in mental arithmetic? An operand recognition paradigm.
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.
Language, arithmetic word problems, and deaf students: Linguistic strategies used to solve tasks
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.
Tower of London test performance in children with poor arithmetic skills.
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.
Directory of Open Access Journals (Sweden)
Hans Schonemann
1996-12-01
Full Text Available Some algorithms for singularity theory and algebraic geometry The use of Grobner basis computations for treating systems of polynomial equations has become an important tool in many areas. This paper introduces of the concept of standard bases (a generalization of Grobner bases and the application to some problems from algebraic geometry. The examples are presented as SINGULAR commands. A general introduction to Grobner bases can be found in the textbook [CLO], an introduction to syzygies in [E] and [St1]. SINGULAR is a computer algebra system for computing information about singularities, for use in algebraic geometry. The basic algorithms in SINGULAR are several variants of a general standard basis algorithm for general monomial orderings (see [GG]. This includes wellorderings (Buchberger algorithm ([B1], [B2] and tangent cone orderings (Mora algorithm ([M1], [MPT] as special cases: It is able to work with non-homogeneous and homogeneous input and also to compute in the localization of the polynomial ring in 0. Recent versions include algorithms to factorize polynomials and a factorizing Grobner basis algorithm. For a complete description of SINGULAR see [Si].
The functional anatomy of single-digit arithmetic in children with developmental dyslexia.
Evans, Tanya M; Flowers, D Lynn; Napoliello, Eileen M; Olulade, Olumide A; Eden, Guinevere F
2014-11-01
Some arithmetic procedures, such as addition of small numbers, rely on fact retrieval mechanisms supported by left hemisphere perisylvian language areas, while others, such as subtraction, rely on procedural-based mechanisms subserved by bilateral parietal cortices. Previous work suggests that developmental dyslexia, a reading disability, is accompanied by subtle deficits in retrieval-based arithmetic, possibly because of compromised left hemisphere function. To test this prediction, we compared brain activity underlying arithmetic problem solving in children with and without dyslexia during addition and subtraction operations using a factorial design. The main effect of arithmetic operation (addition versus subtraction) for both groups combined revealed activity during addition in the left superior temporal gyrus and activity during subtraction in the bilateral intraparietal sulcus, the right supramarginal gyrus and the anterior cingulate, consistent with prior studies. For the main effect of diagnostic group (dyslexics versus controls), we found less activity in dyslexic children in the left supramarginal gyrus. Finally, the interaction analysis revealed that while the control group showed a strong response in the right supramarginal gyrus for subtraction but not for addition, the dyslexic group engaged this region for both operations. This provides physiological evidence in support of the theory that children with dyslexia, because of disruption to left hemisphere language areas, use a less optimal route for retrieval-based arithmetic, engaging right hemisphere parietal regions typically used by good readers for procedural-based arithmetic. Our results highlight the importance of language processing for mathematical processing and illustrate that children with dyslexia have impairments that extend beyond reading. Copyright © 2014 Elsevier Inc. All rights reserved.
The Functional Anatomy of Single-Digit Arithmetic in Children with Developmental Dyslexia
Evans, Tanya M.; Flowers, D. Lynn; Napoliello, Eileen M.; Olulade, Olumide A.; Eden, Guinevere F.
2014-01-01
Some arithmetic procedures, such as addition of small numbers, rely on fact retrieval mechanisms supported by left hemisphere perisylvian language areas, while others, such as subtraction, rely on procedural-based mechanisms subserved by bilateral parietal cortices. Previous work suggests that developmental dyslexia, a reading disability, is accompanied by subtle deficits in retrieval-based arithmetic, possibly because of compromised left hemisphere function. To test this prediction, we compared brain activity underlying arithmetic problem solving in children with and without dyslexia during addition and subtraction operations using a factorial design. The main effect of arithmetic operation (addition versus subtraction) for both groups combined revealed activity during addition in the left superior temporal gyrus and activity during subtraction in bilateral intraparietal sulcus, right supramarginal gyrus and the anterior cingulate, consistent with prior studies. For the main effect of diagnostic group (dyslexics versus controls), we found less activity in dyslexic children in the left supramarginal gyrus. Finally, the interaction analysis revealed that while the control group showed a strong response in right supramarginal gyrus for subtraction but not for addition, the dyslexic group engaged this region for both operations. This provides physiological evidence in support of the theory that children with dyslexia, because of disruption to left hemisphere language areas, use a less optimal route for retrieval-based arithmetic, engaging right hemisphere parietal regions typically used by good readers for procedural-based arithmetic. Our results highlight the importance of language processing for mathematical processing and illustrate that children with dyslexia have impairments that extend beyond reading. PMID:25067820
Van Rinsveld, Amandine; Brunner, Martin; Landerl, Karin; Schiltz, Christine; Ugen, Sonja
2015-01-01
Solving arithmetic problems is a cognitive task that heavily relies on language processing. One might thus wonder whether this language-reliance leads to qualitative differences (e.g., greater difficulties, error types, etc.) in arithmetic for bilingual individuals who frequently have to solve arithmetic problems in more than one language. The present study investigated how proficiency in two languages interacts with arithmetic problem solving throughout language acquisition in adolescents and young adults. Additionally, we examined whether the number word structure that is specific to a given language plays a role in number processing over and above bilingual proficiency. We addressed these issues in a German–French educational bilingual setting, where there is a progressive transition from German to French as teaching language. Importantly, German and French number naming structures differ clearly, as two-digit number names follow a unit-ten order in German, but a ten-unit order in French. We implemented a transversal developmental design in which bilingual pupils from grades 7, 8, 10, 11, and young adults were asked to solve simple and complex additions in both languages. The results confirmed that language proficiency is crucial especially for complex addition computation. Simple additions in contrast can be retrieved equally well in both languages after extended language practice. Additional analyses revealed that over and above language proficiency, language-specific number word structures (e.g., unit-ten vs. ten-unit) also induced significant modulations of bilinguals' arithmetic performances. Taken together, these findings support the view of a strong relation between language and arithmetic in bilinguals. PMID:25821442
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.
Flexible transfer of knowledge in mental arithmetic--an fMRI study.
Ischebeck, Anja; Zamarian, Laura; Schocke, Michael; Delazer, Margarete
2009-02-01
Recent imaging studies could show that fact acquisition in arithmetic is associated with decreasing activation in several frontal and parietal areas, and relatively increasing activation within the angular gyrus, indicating a switch from direct calculation to retrieval of a learned fact from memory. So far, however, little is known about the transfer of learned facts between arithmetic operations. The aim of the present fMRI study was to investigate whether and how newly acquired arithmetic knowledge might transfer from trained multiplication problems to related division problems. On the day before scanning, ten complex multiplication problems were trained. Within the scanner, trained multiplication problems were compared with untrained multiplication problems, and division problems related to multiplication (transfer condition) were compared with unrelated division problems (no-transfer condition). Replicating earlier results, untrained multiplication problems activated several frontal and parietal brain areas more strongly than trained multiplication problems, while trained multiplication problems showed relatively stronger activation in the left angular gyrus than untrained multiplication problems. Concerning division, an ROI analysis indicated that activation in the left angular gyrus was relatively stronger for the transfer condition than for the no-transfer condition. We also observed distinct inter-individual differences with regard to transfer that modulated activation within the left angular gyrus. Activation within the left angular gyrus was generally higher for participants who showed a transfer effect for division problems. In conclusion, the present study yielded some evidence that successful transfer of knowledge between arithmetic operations is accompanied by modifications of brain activation patterns. The left angular gyrus seems not only to be involved in the retrieval of stored arithmetic facts, but also in the transfer between arithmetic
Giordano, Pablo C; Beccaria, Alejandro J; Goicoechea, Héctor C
2011-11-01
A comparison between the classic Plackett-Burman design (PB) ANOVA analysis and a genetic algorithm (GA) approach to identify significant factors have been carried out. This comparison was made by applying both analyses to data obtained from the experimental results when optimizing both chemical and enzymatic hydrolysis of three lignocellulosic feedstocks (corn and wheat bran, and pine sawdust) by a PB experimental design. Depending on the kind of biomass and the hydrolysis being considered, different results were obtained. Interestingly, some interactions were found to be significant by the GA approach and allowed to identify significant factors, that otherwise, based only in the classic PB analysis, would have not been taken into account in a further optimization step. Improvements in the fitting of c.a. 80% were obtained when comparing the coefficient of determination (R2) computed for both methods. Copyright © 2011 Elsevier Ltd. All rights reserved.
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....
Munir, Kusnendar, Jajang; Rahmadhani
2016-02-01
This research aims to develop and test the effectiveness of multimedia in education for special education (MESE) of students with cognitive disabilities in introducing Arithmetic. Students with cognitive disabilities are those who have a level of intelligence under the normal ones. They think concretely and tend to have a very limited memory, switched concentration and forgot easily. The mastery of words is minimal, and also requires a long time to learn. These limitations will interfere in introduction learning to Arithmetic, with the material of numbers 1 to 10. The study resulted that MESE is worth to be used and enhanced the ability of the students.
The Differential Role of Verbal and Spatial Working Memory in the Neural Basis of Arithmetic
Demir, Özlem Ece; Prado, Jérôme; Booth, James R.
2014-01-01
We examine the relations of verbal and spatial WM ability to the neural bases of arithmetic in school-age children. We independently localize brain regions subserving verbal versus spatial representations. For multiplication, higher verbal WM ability is associated with greater recruitment of the left temporal cortex, identified by the verbal localizer. For multiplication and subtraction, higher spatial WM ability is associated with greater recruitment of right parietal cortex, identified by the spatial localizer. Depending on their WM ability, children engage different neural systems that manipulate different representations to solve arithmetic problems. PMID:25144257
Competing Biases in Mental Arithmetic: When Division Is More and Multiplication Is Less.
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.
Gilmore, Camilla K.; Bryant, Peter
2008-01-01
Understanding conceptual relationships is an important aspect of learning arithmetic. Most studies of arithmetic, however, do not distinguish between children's understanding of a concept and their ability to identify situations in which it might be relevant. We compared 8- to 9-year-old children's use of a computational shortcut based on the…
Control part design : application to FELIN arithmetic coprocesso
Zysman, Eytan
1988-01-01
Ce travail présente la conception de la partie contrôle du coprocesseur arithmétique Felin ( fonctions élémentaires intégrées). La démarche suivie repose sur des techniques garantissant les performances du circuit et menant à une génération automatique du dessin des masques. Une description structurée des algorithmes de Felin a permis de maitriser leur complexité. Cette structuration se traduit par une décomposition de la partie contrôlé en trois niveaux d'interprétation. Les trois niveaux so...
Children, algorithm and the decimal numeral system
Directory of Open Access Journals (Sweden)
Clélia Maria Ignatius Nogueira
2010-08-01
Full Text Available A large number of studies in Mathematics Education approach some possible problems in the study of algorithms in the early school years of arithmetic teaching. However, this discussion is not exhausted. In this feature, this article presents the results of a research which proposed to investigate if the arithmetic’s teaching, with emphasis in the fundamental operation’s algorithm, cooperate to build the mathematics knowledge, specifically of the Decimal Numeral System. In order to achieve this purpose, we interviewed, using the Piaget Critique Clinical Method, twenty students from a public school. The result’s analysis indicates that they mechanically reproduce the regular algorithm’s techniques without notice the relations between the techniques and the principle and the Decimal Numeral System’s properties.
Algorithms for Monte Carlo calculations with fermions
International Nuclear Information System (INIS)
Weingarten, D.
1985-01-01
We describe a fermion Monte Carlo algorithm due to Petcher and the present author and another due to Fucito, Marinari, Parisi and Rebbi. For the first algorithm we estimate the number of arithmetic operations required to evaluate a vacuum expectation value grows as N 11 /msub(q) on an N 4 lattice with fixed periodicity in physical units and renormalized quark mass msub(q). For the second algorithm the rate of growth is estimated to be N 8 /msub(q) 2 . Numerical experiments are presented comparing the two algorithms on a lattice of size 2 4 . With a hopping constant K of 0.15 and β of 4.0 we find the number of operations for the second algorithm is about 2.7 times larger than for the first and about 13 000 times larger than for corresponding Monte Carlo calculations with a pure gauge theory. An estimate is given for the number of operations required for more realistic calculations by each algorithm on a larger lattice. (orig.)
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
Do Birth Order, Family Size and Gender Affect Arithmetic Achievement in Elementary School?
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…
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…
Arithmetic Facts Storage Deficit: The Hypersensitivity-to-Interference in Memory Hypothesis
De Visscher, Alice; Noël, Marie-Pascale
2014-01-01
Dyscalculia, or mathematics learning disorders, is currently known to be heterogeneous (Wilson & Dehaene, 2007). While various profiles of dyscalculia coexist, a general and persistent hallmark of this math learning disability is the difficulty in memorizing arithmetic facts (Geary, Hoard & Hamson, 1999; Jordan & Montani, 1997; Slade…
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....
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…
Architectures and Arithmetic for Low Static Power Consumption in Nanoscale CMOS
Directory of Open Access Journals (Sweden)
Peter Nilsson
2009-01-01
Full Text Available This paper focuses on leakage reduction at architecture and arithmetic level. A methodology for considerable reduction of the static power consumption is shown. Simulations are done in a typical 130 nm CMOS technology. Based on the simulation results, the static power consumption is estimated and compared for different filter architectures. Substantial power reductions are shown in both FIR-filters and IIR-filters. Three different types of architectures, namely, bit-parallel, digit-serial, and bit-serial structures are used to demonstrate the methodology. The paper also shows that the relative power ratio is strongly dependent on the used word length; that is, the gain in power ratio is larger for longer word lengths. A static power ratio at 0.48 is shown for the bit-serial FIR-filter and a power ratio at 0.11 is shown in the arithmetic part of the FIR-filter. The static power ratio in the IIR-filter is 0.36 in the bit-serial filter and 0.06 in the arithmetic part of the filter. It is also shown that the use of storage, such as registers, relatively the arithmetic part, affects the power ratio. The relatively lower power consumption in the IIR-filter compared to the FIR-filter is due to the lower use of registers.
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
Simple arithmetic versus intuitive understanding: the case of the impact factor
Rousseau, R.; Leydesdorff, L.
2011-01-01
We discuss the "rate of averages" versus the "average of rates" in the case of the impact factor. Synchronous as well as diachronous journal impact factors are sensitive to adding non-cited articles (to the denominator). This is a consequence of basic properties of elementary arithmetic. Our
Finding the General Term for an Arithmetic Progression: Alternatives to the Formula
Yeo, Joseph B. W.
2010-01-01
Secondary school students in Singapore are expected to find an expression for the general or "nth" term of an arithmetic progression (AP) without using the AP formula T[subscript n] = a + (n-1)d, where "a" is the first term, "n" is the number of terms and "d" is the common difference between successive…
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…
Hard Lessons: Why Rational Number Arithmetic Is so Difficult for so Many People
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…
Identifying Strategies in Arithmetic with the Operand Recognition Paradigm: A Matter of Switch Cost?
Thevenot, Catherine; Castel, Caroline; Danjon, Juliette; Fayol, Michel
2015-01-01
Determining adults' and children's strategies in mental arithmetic constitutes a central issue in the domain of numerical cognition. However, despite the considerable amount of research on this topic, the conclusions in the literature are not always coherent. Therefore, there is a need to carry on the investigation, and this is the reason why we…
Alternative proposal of arithmetic and image operations in optical parallel computation
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.
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
Hardware realizations of arithmetic with complex integer numbers on PLD-base
Directory of Open Access Journals (Sweden)
Opanasenko V. N.
2008-10-01
Full Text Available Hardware realizations of arithmetic with complex integer numbers were proposed. The generators of sine and cosine with different frequency were used to make behavior stand. Real verification was made by block Spartan–3–400 Evaluation Kit, which connect up PCI of personal computer.
Spatial Working Memory and Arithmetic Deficits in Children with Nonverbal Learning Difficulties
Mammarella, Irene Cristina; Lucangeli, Daniela; Cornoldi, Cesare
2010-01-01
Visuospatial working memory and its involvement in arithmetic were examined in two groups of 7- to 11-year-olds: one comprising children described by teachers as displaying symptoms of nonverbal learning difficulties (N = 21), the other a control group without learning disabilities (N = 21). The two groups were matched for verbal abilities, age,…
Differences between Flemish and Chinese Primary Students' Mastery of Basic Arithmetic Operations
Zhao, Ningning; Valcke, Martin; Desoete, Annemie; Burny, Elise; Imbo, Ineke
2014-01-01
The present paper investigates differences in the process of mastering the four basic arithmetic operations (addition, subtraction, multiplication and division) between Flemish and Chinese children from Grade 3 till Grade 6 (i.e. from 8 to 11 years old). The results showed, firstly, that Chinese students outperformed Flemish students in each grade…
Development of Working Memory and Performance in Arithmetic: A Longitudinal Study with Children
López, Magdalena
2014-01-01
Introduction: This study has aimed to investigate the relationship between the development of working memory and performance on arithmetic activities. Method: We conducted a 3-year longitudinal study of a sample of 90 children, that was followed during the first, second and third year of primary school. All children were tested on measures of WM…
Executive Functioning in Children, and Its Relations with Reasoning, Reading, and Arithmetic
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…
Mental Arithmetic and Strategy Use with Indirect Number Problems up to One Hundred.
Beishuizen, M.; And Others
1997-01-01
Mental arithmetic strategies were studied with 91 Dutch third graders who computed by splitting off 10s and units in both numbers or counting by 10s up or down from the first unsplit number. Results reveal flexibility in changing between and within strategy use. Implications for instruction are discussed. (SLD)
Spatial Biases During Mental Arithmetic: Evidence from Eye Movements on a Blank Screen
Directory of Open Access Journals (Sweden)
Matthias eHartmann
2015-01-01
Full Text Available While the influence of spatial-numerical associations in number categorization tasks has been well established, their role in mental arithmetic is less clear. It has been hypothesized that mental addition leads to rightward and upward shifts of spatial attention (along the mental number line, whereas subtraction leads to leftward and downward shifts. We addressed this hypothesis by analyzing spontaneous eye movements during mental arithmetic. Participants solved verbally presented arithmetic problems (e.g., 2+7, 8-3 aloud while looking at a blank screen. We found that eye movements reflected spatial biases in the ongoing mental operation: Gaze position shifted more upward when participants solved addition compared to subtraction problems, and the horizontal gaze position was partly determined by the magnitude of the operands. Interestingly, the difference between addition and subtraction trials was driven by the operator (plus vs. minus but was not influenced by the computational process. Thus, our results do not support the idea of a mental movement toward the solution during arithmetic but indicate a semantic association between operation and space.
The Role of Short-term Working Memory in Mental Arithmetic
Hitch, Graham J.
1978-01-01
Two simple quantitative models were derived from a series of experiments which explored the role of information storage in working memory when performing mental arithmetic. The decay model is a tractable analysis of a complex task which assumes a decay process in working storage. Similar analyses are recommended for problem solving activities…
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 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.
Hubber, Paula J; Gilmore, Camilla; Cragg, Lucy
2014-05-01
Previous research has demonstrated that working memory plays an important role in arithmetic. Different arithmetical strategies rely on working memory to different extents-for example, verbal working memory has been found to be more important for procedural strategies, such as counting and decomposition, than for retrieval strategies. Surprisingly, given the close connection between spatial and mathematical skills, the role of visuospatial working memory has received less attention and is poorly understood. This study used a dual-task methodology to investigate the impact of a dynamic spatial n-back task (Experiment 1) and tasks loading the visuospatial sketchpad and central executive (Experiment 2) on adults' use of counting, decomposition, and direct retrieval strategies for addition. While Experiment 1 suggested that visuospatial working memory plays an important role in arithmetic, especially when counting, the results of Experiment 2 suggested this was primarily due to the domain-general executive demands of the n-back task. Taken together, these results suggest that maintaining visuospatial information in mind is required when adults solve addition arithmetic problems by any strategy but the role of domain-general executive resources is much greater than that of the visuospatial sketchpad.
On the relation between the mental number line and arithmetic competencies.
Link, Tanja; Nuerk, Hans-Christoph; Moeller, Korbinian
2014-01-01
In this study, we aimed at investigating whether it is indeed the spatial magnitude representation that links number line estimation performance to other basic numerical and arithmetic competencies. Therefore, estimations of 45 fourth-graders in both a bounded and a new unbounded number line estimation task (with only a start-point and a unit given) were correlated with their performance in a variety of tasks including addition, subtraction, and number magnitude comparison. Assuming that both number line tasks assess the same underlying mental number line representation, unbounded number line estimation should also be associated with other basic numerical and arithmetic competencies. However, results indicated that children's estimation performance in the bounded but not the unbounded number line estimation task was correlated significantly with numerical and arithmetic competencies. We conclude that unbounded and bounded number line estimation tasks do not assess the same underlying spatial-numerical representation. Rather, the observed association between bounded number line estimation and numerical/arithmetic competencies may be driven by additional numerical processes (e.g., proportion judgement, addition/subtraction) recruited to solve the task.
Spatial biases during mental arithmetic: evidence from eye movements on a blank screen.
Hartmann, Matthias; Mast, Fred W; Fischer, Martin H
2015-01-01
While the influence of spatial-numerical associations in number categorization tasks has been well established, their role in mental arithmetic is less clear. It has been hypothesized that mental addition leads to rightward and upward shifts of spatial attention (along the "mental number line"), whereas subtraction leads to leftward and downward shifts. We addressed this hypothesis by analyzing spontaneous eye movements during mental arithmetic. Participants solved verbally presented arithmetic problems (e.g., 2 + 7, 8-3) aloud while looking at a blank screen. We found that eye movements reflected spatial biases in the ongoing mental operation: Gaze position shifted more upward when participants solved addition compared to subtraction problems, and the horizontal gaze position was partly determined by the magnitude of the operands. Interestingly, the difference between addition and subtraction trials was driven by the operator (plus vs. minus) but was not influenced by the computational process. Thus, our results do not support the idea of a mental movement toward the solution during arithmetic but indicate a semantic association between operation and space.
Spatial Skills as a Predictor of First Grade Girls' Use of Higher Level Arithmetic Strategies
Laski, Elida V.; Casey, Beth M.; Yu, Qingyi; Dulaney, Alana; Heyman, Miriam; Dearing, Eric
2013-01-01
Girls are more likely than boys to use counting strategies rather than higher-level mental strategies to solve arithmetic problems. Prior research suggests that dependence on counting strategies may have negative implications for girls' later math achievement. We investigated the relation between first-grade girls' verbal and spatial skills and…
[ELECTROPHYSIOLOGIC ANALYSIS OF MENTAL ARITHMETIC TASK BY THE "MINIMUM SPANNING TREE" METHOD].
Boha, Roland; Tóth Brigitta; Kardos, Zsófia; Bálint, File; Gaál, Zsófia Anna; Molnár, Márk
2016-03-30
In the present study basic arithmetic induced rearrangements in functional connections of the brain were investigated by using graph theoretical analysis what becomes increasingly important both in theoretical neuroscience and also in clinical investigations. During mental arithmetic operations (working) memory plays an important role, but there are only a few studies in which an attempt was made to separate this effect from the process of arithmetic operations themselves. The goal of our study was to separate the neural networks involved in cognitive functions. As an attempt to clarify this issue the graph-theoretical "minimal spanning tree" method was used for the analysis of EEG recorded during task performance. The effects of passive viewing, number recognition and mental arithmetic on PLI based minimal spanning trees (MST) were investigated on the EEG in young adults (adding task: 17 subjects; passive viewing and number recognition: 16 subjects) in the θ (4-8 Hz) frequency band. Occipital task relevant synchronization was found by using the different methods, probably related to the effect of visual stimulation. With respect to diameter, eccentricity and fraction of leafs different task-related changes were found. It was shown that the task related changes of various graph indices are capable to identify networks behind the various relevant dominant functions. Thus the "minimal spanning tree" method is suitable for the analysis of the reorganization of the brain with respect to cognitive functions.
The effects of eating or skipping breakfast on ERP correlates of mental arithmetic were studied in preadolescents differing in experience (age) and mathematical skills. Participants, randomly assigned to treatment [eat (B) or skip (SB) breakfast (each, n = 41)], were sub-grouped by age [8.8 yrs (B: ...
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...
Fehr, Thorsten; Weber, Jochen; Willmes, Klaus; Herrmann, Manfred
2010-01-01
Prodigies are individuals with exceptional mental abilities. How is it possible that some of these people mentally calculate exponentiations with high accuracy and speed? We examined CP, a mental calculation prodigy, and a control group of 11 normal calculators for moderate mental arithmetic tasks. CP has additionally been tested for exceptionally…
Evaluation of AnimalWatch: An Intelligent Tutoring System for Arithmetic and Fractions
Beal, Carole R.; Arroyo, Ivon M.; Cohen, Paul R.; Woolf, Beverly P.
2010-01-01
Three studies were conducted with middle school students to evaluate a web-based intelligent tutoring system (ITS) for arithmetic and fractions. The studies involved pre and post test comparisons, as well as group comparisons to assess the impact of the ITS on students' math problem solving. Results indicated that students improved from pre to…
Logical strength of complexity theory and a formalization of the PCP theorem in bounded arithmetic
Pich, Ján
2014-01-01
We present several known formalizations of theorems from computational complexity in bounded arithmetic and formalize the PCP theorem in the theory PV1 (no formalization of this theorem was known). This includes a formalization of the existence and of some properties of the (n,d,{\\lambda})-graphs in PV1.
The foundations of arithmetic a logico-mathematical enquiry into the concept of number
Frege, Gottlob
1986-01-01
The Foundations of Arithmetic is undoubtedly the best introduction to Frege's thought; it is here that Frege expounds the central notions of his philosophy, subjecting the views of his predecessors and contemporaries to devastating analysis. The book represents the first philosophically sound discussion of the concept of number in Western civilization. It profoundly influenced developments in the philosophy of mathematics, general ontology, and mathematics.
Aging, rule-violation checking strategies, and strategy combination: An EEG study in arithmetic.
Hinault, Thomas; Lemaire, Patrick
2017-10-01
In arithmetic, rule-violation checking strategies are used while participants solve problems that violate arithmetic rules, like the five rule (i.e., products of problems including five as an operand end with either five or zero; e.g., 5×14=70) or the parity rule (i.e., when at least one of the two operands is even, the product is also even; otherwise the product is odd; e.g., 4×13=52). When problems violate both rules, participants use strategy combination and have better performance on both-rule than on one-rule violation problems (i.e., five or parity rule). Aging studies found that older adults efficiently use one-rule violation checking strategies but have difficulties to combine two strategies. To better understand these aging effects, we used EEG and found important age-related changes while participants used rule-violation checking strategies. We compared participants' performance while they verified arithmetic problems that differ in number and type of violated rule. More specifically, both-rule violation problems elicited larger negativity than one-rule violation problems between 600 and 800ms. Five-rule violation problems differed from parity-rule violation problems between 1100 and 1200ms. Moreover, rule-violation checking strategies and strategy combination involved delta, theta, and lower alpha frequencies. Age-related changes in ERPs and frequency were associated with less efficient strategy combination. Moreover, efficient use of one-rule violation checking strategies in older adults was associated with changes in ERPs and frequency. These findings contribute to further our understanding of age-related changes and invariance in arithmetic strategies, and in combination of arithmetic strategies. Copyright © 2017 Elsevier B.V. All rights reserved.
Tsugayasu, Rie; Handa, Toshiyuki; Kaneko, Yuzuru; Ichinohe, Tatsuya
2010-03-01
The aim of the present study was to examine the effect of intravenous midazolam and propofol sedation on autonomic nervous activities during psychological stress, and whether these results are associated with changes in subjective stress feelings. Seven healthy male volunteers were included in a randomized crossover manner. The heart rate (HR), HR variability, arterial oxygen saturation, and bispectral index value were continuously monitored. A mental arithmetic task for 7 minutes was given with or without intravenous sedation with midazolam or propofol. A bispectral index value of 75 to 85 and an Observer's Assessment of Alertness/Sedation score of 4 were the targeted sedation level in both groups. HR variability was assessed using the power spectral analysis (low-frequency [LF] and high-frequency [HF] components and LF/HF ratio). The faces anxiety scale was used to grade their stress feelings after each mental arithmetic task. During the mental arithmetic task with intravenous sedation, no differences were found in the bispectral index values, arterial oxygen saturation, or the results of the mental arithmetic task between the 2 groups. The HR, LF/HF ratio, and normalized unit LF increased, and the normalized unit HF decreased in both groups. However, the percentage of changes in LF/HF ratio, normalized unit LF, and normalized unit HF were smaller in the midazolam group. In addition, the reduction in faces anxiety scale was greater in the midazolam group. These results suggest that midazolam more effectively suppresses sympathetic nervous activation and reduces subjective stress feelings during a mental arithmetic task than propofol. Copyright (c) 2010 American Association of Oral and Maxillofacial Surgeons. Published by Elsevier Inc. All rights reserved.
Grabner, Roland H; Ansari, Daniel; Koschutnig, Karl; Reishofer, Gernot; Ebner, Franz
2013-05-01
While the left angular gyrus (lAG) has been repeatedly implicated in mental arithmetic, its precise functional role has not been established. On the one hand, it has been speculated that the lAG is involved in task-specific processes. On the other hand, the observation of relative deactivation during arithmetic has led to the contention that differential lAG activation reflects task-unrelated difficulty effects associated with the default mode network (DMN). Using functional magnetic resonance imaging, we investigated the neural correlates of the associative confusion effect that allowed us to dissociate effects of task difficulty and task-related arithmetic processes on lAG activation. The associative confusion effect is characterized by poorer performance while verifying addition and multiplication equations whose solutions are associated with the other operation (confusion equations: e.g., "9 × 6 = 15") compared with solutions unrelated to both operations (non-confusion equations: e.g., "9 × 6 = 52"). Comparing these two conditions revealed higher activation of the anterior lAG (areas PGa, PFm, and PF) and the left dorsolateral prefrontal cortex for the confusion problems. This effect displayed only slight anatomical overlap with the well-established reverse problem-size effect (small minus large problems) and task-related deactivation in the parietal cortex. The finding of greater lAG activity (less deactivation) in the more difficult task condition is inconsistent with the hypothesis that lAG activation during mental arithmetic reflects task difficulty related modulations of the DMN. Instead, the present findings provide further support for the symbol-referent mapping hypothesis, suggesting that the lAG mediates the automatic mapping of arithmetic problems onto solutions stored in memory. Copyright © 2011 Wiley Periodicals, Inc.
The Inequality of Arithmetic and Geometric Means from Multiple Perspectives
Askey, Richard; Matsuura, Ryota; Sword, Sarah
2015-01-01
NCTM's Connections Standard recommends that students in grades 9-12 "develop an increased capacity to link mathematical ideas and a deeper understanding of how more than one approach to the same problem can lead to equivalent results, even though the approaches might look quite different" (NCTM 2000, p. 354). In this article, the authors…
Numerical Algorithm for Delta of Asian Option
Directory of Open Access Journals (Sweden)
Boxiang Zhang
2015-01-01
Full Text Available We study the numerical solution of the Greeks of Asian options. In particular, we derive a close form solution of Δ of Asian geometric option and use this analytical form as a control to numerically calculate Δ of Asian arithmetic option, which is known to have no explicit close form solution. We implement our proposed numerical method and compare the standard error with other classical variance reduction methods. Our method provides an efficient solution to the hedging strategy with Asian options.
Fixed-point error analysis of Winograd Fourier transform algorithms
Patterson, R. W.; Mcclellan, J. H.
1978-01-01
The quantization error introduced by the Winograd Fourier transform algorithm (WFTA) when implemented in fixed-point arithmetic is studied and compared with that of the fast Fourier transform (FFT). The effect of ordering the computational modules and the relative contributions of data quantization error and coefficient quantization error are determined. In addition, the quantization error introduced by the Good-Winograd (GW) algorithm, which uses Good's prime-factor decomposition for the discrete Fourier transform (DFT) together with Winograd's short length DFT algorithms, is studied. Error introduced by the WFTA is, in all cases, worse than that of the FFT. In general, the WFTA requires one or two more bits for data representation to give an error similar to that of the FFT. Error introduced by the GW algorithm is approximately the same as that of the FFT.
Directory of Open Access Journals (Sweden)
Wang Zi Min
2016-01-01
Full Text Available With the development of social services, people’s living standards improve further requirements, there is an urgent need for a way to adapt to the complex situation of the new positioning technology. In recent years, RFID technology have a wide range of applications in all aspects of life and production, such as logistics tracking, car alarm, security and other items. The use of RFID technology to locate, it is a new direction in the eyes of the various research institutions and scholars. RFID positioning technology system stability, the error is small and low-cost advantages of its location algorithm is the focus of this study.This article analyzes the layers of RFID technology targeting methods and algorithms. First, RFID common several basic methods are introduced; Secondly, higher accuracy to political network location method; Finally, LANDMARC algorithm will be described. Through this it can be seen that advanced and efficient algorithms play an important role in increasing RFID positioning accuracy aspects.Finally, the algorithm of RFID location technology are summarized, pointing out the deficiencies in the algorithm, and put forward a follow-up study of the requirements, the vision of a better future RFID positioning technology.
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Rushan Ziatdinov
2012-07-01
Full Text Available In this paper, we describe the possibilities of using a rapid mental computation system in elementary education. The system consists of a number of readily memorized operations that allow one to perform arithmetic computations very quickly. These operations are actually simple algorithms which can develop or improve the algorithmic thinking of pupils. Using a rapid mental computation system allows forming the basis for the study of computer science in secondary school.
Algorithmic complexity of quantum capacity
Oskouei, Samad Khabbazi; Mancini, Stefano
2018-04-01
We analyze the notion of quantum capacity from the perspective of algorithmic (descriptive) complexity. To this end, we resort to the concept of semi-computability in order to describe quantum states and quantum channel maps. We introduce algorithmic entropies (like algorithmic quantum coherent information) and derive relevant properties for them. Then we show that quantum capacity based on semi-computable concept equals the entropy rate of algorithmic coherent information, which in turn equals the standard quantum capacity. Thanks to this, we finally prove that the quantum capacity, for a given semi-computable channel, is limit computable.
Fleeting footsteps tracing the conception of arithmetic and algebra in ancient China
Yong, Lam Lay
2004-01-01
The Hindu-Arabic numeral system (1, 2, 3,...) is one of mankind''sgreatest achievements and one of its most commonly usedinventions. How did it originate? Those who have written about thenumeral system have hypothesized that it originated in India; however,there is little evidence to support this claim. This book provides considerable evidence to show that theHindu-Arabic numeral system, despite its commonly accepted name,has its origins in the Chinese rod numeral system. This system waswidely used in China from antiquity till the 16th century. It was usedby officials, astronomers, traders and others to perform addition,subtraction, multiplication, division and other arithmetic operations,and also used by mathematicians to develop arithmetic andalgebra. Based on this system, numerous mathematical treatises werewritten.
Math anxiety differentially affects WAIS-IV arithmetic performance in undergraduates.
Buelow, Melissa T; Frakey, Laura L
2013-06-01
Previous research has shown that math anxiety can influence the math performance level; however, to date, it is unknown whether math anxiety influences performance on working memory tasks during neuropsychological evaluation. In the present study, 172 undergraduate students completed measures of math achievement (the Math Computation subtest from the Wide Range Achievement Test-IV), math anxiety (the Math Anxiety Rating Scale-Revised), general test anxiety (from the Adult Manifest Anxiety Scale-College version), and the three Working Memory Index tasks from the Wechsler Adult Intelligence Scale-IV Edition (WAIS-IV; Digit Span [DS], Arithmetic, Letter-Number Sequencing [LNS]). Results indicated that math anxiety predicted performance on Arithmetic, but not DS or LNS, above and beyond the effects of gender, general test anxiety, and math performance level. Our findings suggest that math anxiety can negatively influence WAIS-IV working memory subtest scores. Implications for clinical practice include the utilization of LNS in individuals expressing high math anxiety.
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)
Design of Improved Arithmetic Logic Unit in Quantum-Dot Cellular Automata
Heikalabad, Saeed Rasouli; Gadim, Mahya Rahimpour
2018-03-01
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.
Nested arithmetic progressions of oscillatory phases in Olsen's enzyme reaction model
Gallas, Marcia R.; Gallas, Jason A. C.
2015-06-01
We report some regular organizations of stability phases discovered among self-sustained oscillations of a biochemical oscillator. The signature of such organizations is a nested arithmetic progression in the number of spikes of consecutive windows of periodic oscillations. In one of them, there is a main progression of windows whose consecutive number of spikes differs by one unit. Such windows are separated by a secondary progression of smaller windows whose number of spikes differs by two units. Another more complex progression involves a fan-like nested alternation of stability phases whose number of spikes seems to grow indefinitely and to accumulate methodically in cycles. Arithmetic progressions exist abundantly in several control parameter planes and can be observed by tuning just one among several possible rate constants governing the enzyme reaction.
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.
Attention Contributes to Arithmetic Deficits in New-Onset Childhood Absence Epilepsy
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Dazhi Cheng
2017-09-01
Full Text Available 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.
Desirable floating-point arithmetic and elementary functions for numerical computation
Hull, T. E.
1978-01-01
The topics considered are: (1) the base of the number system, (2) precision control, (3) number representation, (4) arithmetic operations, (5) other basic operations, (6) elementary functions, and (7) exception handling. The possibility of doing without fixed-point arithmetic is also mentioned. The specifications are intended to be entirely at the level of a programming language such as FORTRAN. The emphasis is on convenience and simplicity from the user's point of view. Conforming to such specifications would have obvious beneficial implications for the portability of numerical software, and for proving programs correct, as well as attempting to provide facilities which are most suitable for the user. The specifications are not complete in every detail, but it is intended that they be complete in spirit - some further details, especially syntatic details, would have to be provided, but the proposals are otherwise relatively complete.
Effects of cold-pressor and mental arithmetic on pupillary light reflex.
Davis, B C; Daluwatte, C; Colona, N C; Yao, D G
2013-08-01
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.
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...
RAID-6 reed-solomon codes with asymptotically optimal arithmetic complexities
Lin, Sian-Jheng
2016-12-24
In computer storage, RAID 6 is a level of RAID that can tolerate two failed drives. When RAID-6 is implemented by Reed-Solomon (RS) codes, the penalty of the writing performance is on the field multiplications in the second parity. In this paper, we present a configuration of the factors of the second-parity formula, such that the arithmetic complexity can reach the optimal complexity bound when the code length approaches infinity. In the proposed approach, the intermediate data used for the first parity is also utilized to calculate the second parity. To the best of our knowledge, this is the first approach supporting the RAID-6 RS codes to approach the optimal arithmetic complexity.
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
International Nuclear Information System (INIS)
Burkitt, A.N.; Irving, A.C.
1988-01-01
Two of the methods that are widely used in lattice gauge theory calculations requiring inversion of the fermion matrix are the Lanczos and the conjugate gradient algorithms. Those algorithms are already known to be closely related. In fact for matrix inversion, in exact arithmetic, they give identical results at each iteration and are just alternative formulations of a single algorithm. This equivalence survives rounding errors. We give the identities between the coefficients of the two formulations, enabling many of the best features of them to be combined. (orig.)
International Nuclear Information System (INIS)
Vignes, J.
1986-01-01
Any result of algorithms provided by a computer always contains an error resulting from floating-point arithmetic round-off error propagation. Furthermore signal processing algorithms are also generally performed with data containing errors. The permutation-perturbation method, also known under the name CESTAC (controle et estimation stochastique d'arrondi de calcul) is a very efficient practical method for evaluating these errors and consequently for estimating the exact significant decimal figures of any result of algorithms performed on a computer. The stochastic approach of this method, its probabilistic proof, and the perfect agreement between the theoretical and practical aspects are described in this paper [fr
Mohit Tyagi,; Kavita Khare
2011-01-01
This paper provides the details for novel adder/subtractor arithmetic unit that combines Binary, Binary Code Decimal (BCD) and single precision Binary floating point operations in a single structure. The unit is able to perform effective addition-subtraction operations on unsigned, sign-magnitude, and various complement representations. The design is runtime reconfigurable or can be implemented in ASIC as a runtime configurable unit and maximum utilization of hardware resource are the feature...
Optimal inequalities for bounding Toader mean by arithmetic and quadratic means.
Zhao, Tie-Hong; Chu, Yu-Ming; Zhang, Wen
2017-01-01
In this paper, we present the best possible parameters [Formula: see text] and [Formula: see text] such that the double inequality [Formula: see text] holds for all [Formula: see text] and [Formula: see text] with [Formula: see text], and we provide new bounds for the complete elliptic integral [Formula: see text] [Formula: see text] of the second kind, where [Formula: see text], [Formula: see text] and [Formula: see text] are the Toader, arithmetic, and quadratic means of a and b , respectively.
Short effective intervals containing primes in arithmetic progressions and the seven cubes problem
Kadiri, H.
2008-09-01
For any epsilon>0 and any non-exceptional modulus qge3 , we prove that, for x large enough ( xge alpha_{epsilon}log^2 q ), the interval left[ e^x,e^{x+epsilon }right] contains a prime p in any of the arithmetic progressions modulo q . We apply this result to establish that every integer n larger than exp(71 000) is a sum of seven cubes.
The Didactic Contract from the implementation of a didactic sequence to teach Arithmetic Progression
Souza, Carla Maria Pinto; Lima, Anna Paula de Avellar Brito
2014-01-01
This paper results from a research that aimed to investigate the dealings between teacher and students in application of a didactic sequence previously established for the teaching of Arithmetic Progression (AP). The survey was conducted in four stages: preparation of the didactic sequence, preliminary analysis of the proposal to the teacher, implementation of the sequence. The didactic sequence sought to accommodate the elaborate steps proposed by Brousseau, the typology of Didactic Situatio...
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
Arithmetic properties of the first secant variety to a projective variety
Vermeire, Peter
2010-01-01
Under an explicit positivity condition, we show the first secant variety of a linearly normal smooth variety is projectively normal, give results on the regularity of the ideal of the secant variety, and give conditions on the variety that are equivalent to the secant variety being arithmetically Cohen-Macaulay. Under this same condition, we then show that if $X$ satisfies $N_{p+2\\dim(X)}$, then the secant variety satisfies $N_{3,p}$.
The Influence of verbalization on the pattern of cortical activation during mental arithmetic.
Zarnhofer, Sabrina; Braunstein, Verena; Ebner, Franz; Koschutnig, Karl; Neuper, Christa; Reishofer, Gernot; Ischebeck, Anja
2012-03-12
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. 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. 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. Our results confirm that strong verbalizers use mental speech as a form of mental imagination more strongly than weak verbalizers. Moreover, our results
Competing Biases in Mental Arithmetic: When Division Is More and Multiplication Is Less
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 (...
Bit-systolic arithmetic arrays using dynamic differential gallium arsenide circuits
Beagles, Grant; Winters, Kel; Eldin, A. G.
1992-01-01
A new family of gallium arsenide circuits for fine grained bit-systolic arithmetic arrays is introduced. This scheme combines features of two recent techniques of dynamic gallium arsenide FET logic and differential dynamic single-clock CMOS logic. The resulting circuits are fast and compact, with tightly constrained series FET propagation paths, low fanout, no dc power dissipation, and depletion FET implementation without level shifting diodes.
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
Directory of Open Access Journals (Sweden)
Nadja eTschentscher
2015-08-01
Full Text Available Mental arithmetic is a powerful paradigm to study problem solving using neuroimaging methods. However, the evaluation of task complexity varies significantly across neuroimaging studies. Most studies have parameterized task complexity by objective features such as the number size. Only a few studies used subjective rating procedures. In fMRI, we provided evidence that strategy self-reports control better for task complexity across arithmetic conditions than objective features (Tschentscher and Hauk, 2014. Here, we analyzed the relative predictive value of self-reported strategies and objective features for performance in addition and multiplication tasks, by using a paradigm designed for neuroimaging research. We found a superiority of strategy ratings as predictor of performance above objective features. In a Principal Component Analysis on reaction times, the first component explained over 90 percent of variance and factor loadings reflected percentages of self-reported strategies well. In multiple regression analyses on reaction times, self-reported strategies performed equally well or better than objective features, depending on the operation type. A Receiver Operating Characteristic (ROC analysis confirmed this result. Reaction times classified task complexity better when defined by individual ratings. This suggests that participants’ strategy ratings are reliable predictors of arithmetic complexity and should be taken into account in neuroimaging research.
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.
Heuristics and representational change in two-move matchstick arithmetic tasks
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Michael Öllinger
2006-01-01
Full Text Available Insight problems are problems where the problem solver struggles to find a solution until * aha! * the solution suddenly appears. Two contemporary theories suggest that insight problems are difficult either because problem solvers begin with an incorrect representation of the problem, or that problem solvers apply inappropriate heuristics to the problem. The relative contributions of representational change and inappropriate heuristics on the process of insight problem solving was studied with a task that required the problem solver to move two matchsticks in order to transform an incorrect arithmetic statement into a correct one. Problem solvers (N = 120 worked on two different types of two-move matchstick arithmetic problems that both varied with respect to the effectiveness of heuristics and to the degree of a necessary representational change of the problem representation. A strong influence of representational change on solution rates was found whereas the influence of heuristics hadminimal effects on solution rates. That is, the difficulty of insight problems within the two-move matchstick arithmetic domain is governed by the degree of representational change required. A model is presented that details representational change as the necessary condition for ensuring that appropriate heuristics can be applied on the proper problem representation.
Dormal, Valérie; Schuller, Anne-Marie; Nihoul, Julie; Pesenti, Mauro; Andres, Michael
2014-07-01
Recent behavioural and brain imaging studies have provided evidence for rightward and leftward attention shifts while solving addition and subtraction problems respectively, suggesting that mental arithmetic makes use of mechanisms akin to those underlying spatial attention. However, this hypothesis mainly relies on correlative data and the causal relevance of spatial attention for mental arithmetic remains unclear. In order to test whether the mechanisms underlying spatial attention are necessary to perform arithmetic operations, we compared the performance of right brain-lesioned patients, with and without left unilateral neglect, and healthy controls in addition and subtraction of two-digit numbers. We predicted that patients with left unilateral neglect would be selectively impaired in the subtraction task while being unimpaired in the addition task. The results showed that neglect patients made more errors than the two other groups to subtract large numbers, whereas they were still able to solve large addition problems matched for difficulty and magnitude of the answer. This finding demonstrates a causal relationship between the ability to attend the left side of space and the solving of large subtraction problems. A plausible account is that attention shifts help localizing the position of the answer on a spatial continuum while subtracting large numbers. Copyright © 2014 Elsevier Ltd. All rights reserved.
Prolonged reaction to mental arithmetic stress in first-degree relatives of schizophrenia patients.
Abhishekh, Hulegar A; Kumar, Naveen C; Thirthalli, Jagadisha; Chandrashekar, H; Gangadhar, Bangalore N; Sathyaprabha, Talakad N
2014-10-01
Several studies have reported abnormal heart rate variability (HRV) in schizophrenia patients, suggesting a pathophysiological link between central autonomic dysfunction and symptoms of schizophrenia and that these could be heritable. This study aimed at evaluating cardiac autonomic response to mental arithmetic stress in first-degree relatives of schizophrenia patients (FDRS) employing HRV analysis. HRV measures were computed for 25 healthy FDRS and 25 age- and gender-matched controls during rest, mental arithmetic stress task and recovery period. Subtracting serial sevens from 700 for five minutes formed the stress task. Recovery period lasted five minutes starting from the termination of the stress task. Both groups showed similar alterations during the stress task. After stress termination, recovery to the basal values was observed in controls but not in patients' relatives, maintaining a pattern similar to that during the stress task. Poor recovery from cardiac autonomic functions (CAF) alterations induced by arithmetic stress may be a heritable trait marker of schizophrenia. Our report supports endophenotypic potential of HRV in schizophrenia research.
Neurophysiological evidence for the validity of verbal strategy reports in mental arithmetic.
Grabner, Roland H; De Smedt, Bert
2011-04-01
Behavioral research has shown that arithmetic problems (e.g., 6+2=) are solved with various strategies, which can be inferred from the size of the presented problems or from trial-by-trial verbal strategy reports. The validity of these verbal strategy reports, however, has been repeatedly questioned. In the present electroencephalography study, we compared the association of both approaches with the oscillatory brain responses during arithmetic problem solving. Nineteen adults solved small and large addition and subtraction problems and indicated the applied strategy (fact retrieval vs. procedure use) on a trial-by-trial basis by means of verbal strategy reports. Analysis of event-related (de-)synchronization (ERS/ERD) in theta and alpha frequencies revealed a general convergence of verbal strategy reports and the problem size approach, with fact retrieval being accompanied by higher left-hemispheric theta ERS, and procedural strategies being reflected in higher widespread ERD in the lower alpha band and bilateral parietooccipital ERD in the upper alpha band. A direct comparison of the neurophysiological data from both approaches suggests a higher sensitivity of verbal strategy reports to problem solving strategies applied in mental arithmetic, particularly for large problems. Taken together, the current data provide the first neurophysiological evidence for the validity of verbal strategy reports. Copyright © 2011 Elsevier B.V. All rights reserved.
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.
Unpacking symbolic number comparison and its relation with arithmetic in adults.
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.
Hu, T C
2002-01-01
Newly enlarged, updated second edition of a valuable text presents algorithms for shortest paths, maximum flows, dynamic programming and backtracking. Also discusses binary trees, heuristic and near optimums, matrix multiplication, and NP-complete problems. 153 black-and-white illus. 23 tables.Newly enlarged, updated second edition of a valuable, widely used text presents algorithms for shortest paths, maximum flows, dynamic programming and backtracking. Also discussed are binary trees, heuristic and near optimums, matrix multiplication, and NP-complete problems. New to this edition: Chapter 9
Hybrid Cryptosystem Using Tiny Encryption Algorithm and LUC Algorithm
Rachmawati, Dian; Sharif, Amer; Jaysilen; Andri Budiman, Mohammad
2018-01-01
Security becomes a very important issue in data transmission and there are so many methods to make files more secure. One of that method is cryptography. Cryptography is a method to secure file by writing the hidden code to cover the original file. Therefore, if the people do not involve in cryptography, they cannot decrypt the hidden code to read the original file. There are many methods are used in cryptography, one of that method is hybrid cryptosystem. A hybrid cryptosystem is a method that uses a symmetric algorithm to secure the file and use an asymmetric algorithm to secure the symmetric algorithm key. In this research, TEA algorithm is used as symmetric algorithm and LUC algorithm is used as an asymmetric algorithm. The system is tested by encrypting and decrypting the file by using TEA algorithm and using LUC algorithm to encrypt and decrypt the TEA key. The result of this research is by using TEA Algorithm to encrypt the file, the cipher text form is the character from ASCII (American Standard for Information Interchange) table in the form of hexadecimal numbers and the cipher text size increase by sixteen bytes as the plaintext length is increased by eight characters.
Modular Regularization Algorithms
DEFF Research Database (Denmark)
Jacobsen, Michael
2004-01-01
The class of linear ill-posed problems is introduced along with a range of standard numerical tools and basic concepts from linear algebra, statistics and optimization. Known algorithms for solving linear inverse ill-posed problems are analyzed to determine how they can be decomposed into indepen......The class of linear ill-posed problems is introduced along with a range of standard numerical tools and basic concepts from linear algebra, statistics and optimization. Known algorithms for solving linear inverse ill-posed problems are analyzed to determine how they can be decomposed...... into independent modules. These modules are then combined to form new regularization algorithms with other properties than those we started out with. Several variations are tested using the Matlab toolbox MOORe Tools created in connection with this thesis. Object oriented programming techniques are explained...... and used to set up the illposed problems in the toolbox. Hereby, we are able to write regularization algorithms that automatically exploit structure in the ill-posed problem without being rewritten explicitly. We explain how to implement a stopping criteria for a parameter choice method based upon...
DEFF Research Database (Denmark)
Markham, Annette
layered set of accounts to help build our understanding of how individuals relate to their devices, search systems, and social network sites. This work extends critical analyses of the power of algorithms in implicating the social self by offering narrative accounts from multiple perspectives. It also...
Directory of Open Access Journals (Sweden)
Anna Bourmistrova
2011-02-01
Full Text Available The autodriver algorithm is an intelligent method to eliminate the need of steering by a driver on a well-defined road. The proposed method performs best on a four-wheel steering (4WS vehicle, though it is also applicable to two-wheel-steering (TWS vehicles. The algorithm is based on coinciding the actual vehicle center of rotation and road center of curvature, by adjusting the kinematic center of rotation. The road center of curvature is assumed prior information for a given road, while the dynamic center of rotation is the output of dynamic equations of motion of the vehicle using steering angle and velocity measurements as inputs. We use kinematic condition of steering to set the steering angles in such a way that the kinematic center of rotation of the vehicle sits at a desired point. At low speeds the ideal and actual paths of the vehicle are very close. With increase of forward speed the road and tire characteristics, along with the motion dynamics of the vehicle cause the vehicle to turn about time-varying points. By adjusting the steering angles, our algorithm controls the dynamic turning center of the vehicle so that it coincides with the road curvature center, hence keeping the vehicle on a given road autonomously. The position and orientation errors are used as feedback signals in a closed loop control to adjust the steering angles. The application of the presented autodriver algorithm demonstrates reliable performance under different driving conditions.
Energy Technology Data Exchange (ETDEWEB)
Grefenstette, J.J.
1994-12-31
Genetic algorithms solve problems by using principles inspired by natural population genetics: They maintain a population of knowledge structures that represent candidate solutions, and then let that population evolve over time through competition and controlled variation. GAs are being applied to a wide range of optimization and learning problems in many domains.
TEXT COMPRESSION ALGORITHMS - A COMPARATIVE STUDY
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S. Senthil
2011-12-01
Full Text Available Data Compression may be defined as the science and art of the representation of information in a crisply condensed form. For decades, Data compression has been one of the critical enabling technologies for the ongoing digital multimedia revolution. There are a lot of data compression algorithms which are available to compress files of different formats. This paper provides a survey of different basic lossless data compression algorithms. Experimental results and comparisons of the lossless compression algorithms using Statistical compression techniques and Dictionary based compression techniques were performed on text data. Among the Statistical coding techniques, the algorithms such as Shannon-Fano Coding, Huffman coding, Adaptive Huffman coding, Run Length Encoding and Arithmetic coding are considered. Lempel Ziv scheme which is a dictionary based technique is divided into two families: one derived from LZ77 (LZ77, LZSS, LZH, LZB and LZR and the other derived from LZ78 (LZ78, LZW, LZFG, LZC and LZT. A set of interesting conclusions are derived on this basis.
Optimal Fungal Space Searching Algorithms.
Asenova, Elitsa; Lin, Hsin-Yu; Fu, Eileen; Nicolau, Dan V; Nicolau, Dan V
2016-10-01
Previous experiments have shown that fungi use an efficient natural algorithm for searching the space available for their growth in micro-confined networks, e.g., mazes. This natural "master" algorithm, which comprises two "slave" sub-algorithms, i.e., collision-induced branching and directional memory, has been shown to be more efficient than alternatives, with one, or the other, or both sub-algorithms turned off. In contrast, the present contribution compares the performance of the fungal natural algorithm against several standard artificial homologues. It was found that the space-searching fungal algorithm consistently outperforms uninformed algorithms, such as Depth-First-Search (DFS). Furthermore, while the natural algorithm is inferior to informed ones, such as A*, this under-performance does not importantly increase with the increase of the size of the maze. These findings suggest that a systematic effort of harvesting the natural space searching algorithms used by microorganisms is warranted and possibly overdue. These natural algorithms, if efficient, can be reverse-engineered for graph and tree search strategies.
Engineering a cache-oblivious sorting algorithm
DEFF Research Database (Denmark)
Brodal, Gerth Stølting; Fagerberg, Rolf; Vinther, Kristoffer
2007-01-01
This paper is an algorithmic engineering study of cache-oblivious sorting. We investigate by empirical methods a number of implementation issues and parameter choices for the cache-oblivious sorting algorithm Lazy Funnelsort, and compare the final algorithm with Quicksort, the established standard...
NEUTRON ALGORITHM VERIFICATION TESTING
Energy Technology Data Exchange (ETDEWEB)
COWGILL,M.; MOSBY,W.; ARGONNE NATIONAL LABORATORY-WEST
2000-07-19
Active well coincidence counter assays have been performed on uranium metal highly enriched in {sup 235}U. The data obtained in the present program, together with highly enriched uranium (HEU) metal data obtained in other programs, have been analyzed using two approaches, the standard approach and an alternative approach developed at BNL. Analysis of the data with the standard approach revealed that the form of the relationship between the measured reals and the {sup 235}U mass varied, being sometimes linear and sometimes a second-order polynomial. In contrast, application of the BNL algorithm, which takes into consideration the totals, consistently yielded linear relationships between the totals-corrected reals and the {sup 235}U mass. The constants in these linear relationships varied with geometric configuration and level of enrichment. This indicates that, when the BNL algorithm is used, calibration curves can be established with fewer data points and with more certainty than if a standard algorithm is used. However, this potential advantage has only been established for assays of HEU metal. In addition, the method is sensitive to the stability of natural background in the measurement facility.
Complex Binary Number System Algorithms and Circuits
Jamil, Tariq
2013-01-01
This book is a compilation of the entire research work on the topic of Complex Binary Number System (CBNS) carried out by the author as the principal investigator and members of his research groups at various universities during the years 1992-2012. Pursuant to these efforts spanning several years, the realization of CBNS as a viable alternative to represent complex numbers in an 'all-in-one' binary number format has become possible and efforts are underway to build computer hardware based on this unique number system. It is hoped that this work will be of interest to anyone involved in computer arithmetic and digital logic design and kindle renewed enthusiasm among the engineers working in the areas of digital signal and image processing for developing newer and efficient algorithms and techniques incorporating CBNS.
Practical considerations for the implantation of a fuzzy control algorithm in a DSP
International Nuclear Information System (INIS)
Perez C, B.; Benitez R, J.S.; Pacheco S, J.O.
2003-01-01
The development of a digital system based on a DSP to implant a Mamdani type algorithm of fuzzy control whose objective is to regulate the neutron power in a nuclear research reactor Type TRIGA Mark III is presented. Its are simultaneously carried out the aggregation des fuzzy stages discreeting the universe of the output variable. The format MPF for the handling of the floating point in the arithmetic operations is used. (Author)
An image encryption algorithm utilizing julia sets and hilbert curves.
Directory of Open Access Journals (Sweden)
Yuanyuan Sun
Full Text Available Image encryption is an important and effective technique to protect image security. In this paper, a novel image encryption algorithm combining Julia sets and Hilbert curves is proposed. The algorithm utilizes Julia sets' parameters to generate a random sequence as the initial keys and gets the final encryption keys by scrambling the initial keys through the Hilbert curve. The final cipher image is obtained by modulo arithmetic and diffuse operation. In this method, it needs only a few parameters for the key generation, which greatly reduces the storage space. Moreover, because of the Julia sets' properties, such as infiniteness and chaotic characteristics, the keys have high sensitivity even to a tiny perturbation. The experimental results indicate that the algorithm has large key space, good statistical property, high sensitivity for the keys, and effective resistance to the chosen-plaintext attack.
An image encryption algorithm utilizing julia sets and hilbert curves.
Sun, Yuanyuan; Chen, Lina; Xu, Rudan; Kong, Ruiqing
2014-01-01
Image encryption is an important and effective technique to protect image security. In this paper, a novel image encryption algorithm combining Julia sets and Hilbert curves is proposed. The algorithm utilizes Julia sets' parameters to generate a random sequence as the initial keys and gets the final encryption keys by scrambling the initial keys through the Hilbert curve. The final cipher image is obtained by modulo arithmetic and diffuse operation. In this method, it needs only a few parameters for the key generation, which greatly reduces the storage space. Moreover, because of the Julia sets' properties, such as infiniteness and chaotic characteristics, the keys have high sensitivity even to a tiny perturbation. The experimental results indicate that the algorithm has large key space, good statistical property, high sensitivity for the keys, and effective resistance to the chosen-plaintext attack.
Some uses of the symmetric Lanczos algorithm - and why it works!
Energy Technology Data Exchange (ETDEWEB)
Druskin, V.L. [Schlumberger-Doll Research, Ridgefield, CT (United States); Greenbaum, A. [Courant Institute of Mathematical Sciences, New York, NY (United States); Knizhnerman, L.A. [Central Geophysical Expedition, Moscow (Russian Federation)
1996-12-31
The Lanczos algorithm uses a three-term recurrence to construct an orthonormal basis for the Krylov space corresponding to a symmetric matrix A and a starting vector q{sub 1}. The vectors and recurrence coefficients produced by this algorithm can be used for a number of purposes, including solving linear systems Au = {var_phi} and computing the matrix exponential e{sup -tA}{var_phi}. Although the vectors produced in finite precision arithmetic are not orthogonal, we show why they can still be used effectively for these purposes. The reason is that the 2-norm of the residual is essentially determined by the tridiagonal matrix and the next recurrence coefficient produced by the finite precision Lanczos computation. It follows that if the same tridiagonal matrix and recurrence coefficient are produced by the exact Lanczos algorithm applied to some other problem, then exact arithmetic bounds on the residual for that problem will hold for the finite precision computation. In order to establish exact arithmetic bounds for the different problem, it is necessary to have some information about the eigenvalues of the new coefficient matrix. Here we make use of information already established in the literature, and we also prove a new result for indefinite matrices.
Masson, Nicolas; Pesenti, Mauro; Coyette, Françoise; Andres, Michael; Dormal, Valérie
2017-10-01
Recent findings suggest that mental arithmetic involves shifting attention on a mental continuum in which numbers would be ordered from left to right, from small to large numbers, with addition and subtraction causing rightward or leftward shifts, respectively. Neuropsychological data showing that brain-damaged patients with left neglect experience difficulties in solving subtraction but not addition problems support this hypothesis. However, the reverse dissociation is needed to establish the causal role of spatial attention in mental arithmetic. R.H., a 65-year-old left-brain-damaged patient exhibiting right unilateral visuospatial and representational neglect, was tested with various numerical tasks including numerical comparison, arithmetic problem-solving, and numerical interval bisection. In numerical comparison, R.H. showed a selective response latency increase when judging numbers larger than the references whereas his performance was normal for numbers smaller than the references. In the arithmetic task, R.H. was impaired in solving addition but not subtraction problems. In contrast, performance in number bisection shows a deviation toward larger numbers. These results establish a double dissociation between subtraction and addition solving in patients with left versus right neglect and demonstrate clear evidence that attentional mechanisms are crucial for mental arithmetic. We suggest that attention shifts are involved whenever a number is represented relative to another on a mental continuum, be it during numerical comparison or arithmetic problem-solving. R.H.'s performance in numerical interval bisection indicates that this task involves processes that are distinct from those involved in number comparison and mental arithmetic. (PsycINFO Database Record (c) 2017 APA, all rights reserved).
Opposition-Based Adaptive Fireworks Algorithm
Directory of Open Access Journals (Sweden)
Chibing Gong
2016-07-01
Full Text Available A fireworks algorithm (FWA is a recent swarm intelligence algorithm that is inspired by observing fireworks explosions. An adaptive fireworks algorithm (AFWA proposes additional adaptive amplitudes to improve the performance of the enhanced fireworks algorithm (EFWA. The purpose of this paper is to add opposition-based learning (OBL to AFWA with the goal of further boosting performance and achieving global optimization. Twelve benchmark functions are tested in use of an opposition-based adaptive fireworks algorithm (OAFWA. The final results conclude that OAFWA significantly outperformed EFWA and AFWA in terms of solution accuracy. Additionally, OAFWA was compared with a bat algorithm (BA, differential evolution (DE, self-adapting control parameters in differential evolution (jDE, a firefly algorithm (FA, and a standard particle swarm optimization 2011 (SPSO2011 algorithm. The research results indicate that OAFWA ranks the highest of the six algorithms for both solution accuracy and runtime cost.
Directory of Open Access Journals (Sweden)
Maja eRodic
2015-03-01
Full Text Available Previous research has consistently found an association between spatial and mathematical abilities. We hypothesised that this link may partially explain the consistently observed advantage in mathematics demonstrated by Asian children. Spatial complexity of the character-based writing systems may reflect or lead to a cognitive advantage relevant to mathematics. 721 6-9 -year old children from the UK and Russia were assessed on a battery of cognitive skills and arithmetic. The Russian children were recruited from specialist linguistic schools and divided into 4 different language groups, based on the second language they were learning (i.e. English, Spanish, Chinese and Japanese. The UK children attended regular schools and were not learning any second language. The testing took place twice across the school year, once at the beginning, before the start of the second language acquisition, and once at the end of the year. The study had two aims: (1 to test whether spatial ability predicts mathematical ability in 7-9 year old children across the samples; (2 to test whether acquisition and usage of a character-based writing system leads to an advantage in performance in arithmetic and related cognitive tasks. The longitudinal link from spatial ability to mathematics was found only in the Russian sample. The effect of second language acquisition on mathematics or other cognitive skills was negligible, although some effect of Chinese language on mathematical reasoning was suggested. Overall, the findings suggest that although spatial ability is related to mathematics at this age, one academic year of exposure to spatially complex writing systems is not enough to provide a mathematical advantage. Other educational and socio-cultural factors might play a greater role in explaining individual and cross-cultural differences in arithmetic at this age.
Arithmetic on Your Phone: A Large Scale Investigation of Simple Additions and Multiplications
Zimmerman, Federico; Shalom, Diego; Gonzalez, Pablo A.; Garrido, Juan Manuel; Alvarez Heduan, Facundo; Dehaene, Stanislas; Sigman, Mariano; Rieznik, Andres
2016-01-01
We present the results of a gamified mobile device arithmetic application which allowed us to collect vast amount of data in simple arithmetic operations. Our results confirm and replicate, on a large sample, six of the main principles derived in a long tradition of investigation: size effect, tie effect, size-tie interaction effect, five-effect, RTs and error rates correlation effect, and most common error effect. Our dataset allowed us to perform a robust analysis of order effects for each individual problem, for which there is controversy both in experimental findings and in the predictions of theoretical models. For addition problems, the order effect was dominated by a max-then-min structure (i.e 7+4 is easier than 4+7). This result is predicted by models in which additions are performed as a translation starting from the first addend, with a distance given by the second addend. In multiplication, we observed a dominance of two effects: (1) a max-then-min pattern that can be accounted by the fact that it is easier to perform fewer additions of the largest number (i.e. 8x3 is easier to compute as 8+8+8 than as 3+3+…+3) and (2) a phonological effect by which problems for which there is a rhyme (i.e. "seis por cuatro es veinticuatro") are performed faster. Above and beyond these results, our study bares an important practical conclusion, as proof of concept, that participants can be motivated to perform substantial arithmetic training simply by presenting it in a gamified format. PMID:28033357
Deaño, Manuel Deaño; Alfonso, Sonia; Das, Jagannath Prasad
2015-03-01
This study reports the cognitive and arithmetic improvement of a mathematical model based on the program PASS Remedial Program (PREP), which aims to improve specific cognitive processes underlying academic skills such as arithmetic. For this purpose, a group of 20 students from the last four grades of Primary Education was divided into two groups. One group (n=10) received training in the program and the other served as control. Students were assessed at pre and post intervention in the PASS cognitive processes (planning, attention, simultaneous and successive processing), general level of intelligence, and arithmetic performance in calculus and solving problems. Performance of children from the experimental group was significantly higher than that of the control group in cognitive process and arithmetic. This joint enhancement of cognitive and arithmetic processes was a result of the operationalization of training that promotes the encoding task, attention and planning, and learning by induction, mediation and verbalization. The implications of this are discussed. Copyright © 2014 Elsevier Ltd. All rights reserved.
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.
Masson, Nicolas; Pesenti, Mauro
2016-07-01
Solving arithmetic problems has been shown to induce shifts of spatial attention in simple probe-detection tasks, subtractions orienting attention to the left side and additions to the right side of space. Whether these attentional shifts constitute epiphenomena or are critically linked to the calculation process is still unknown. In the present study, we investigate participants' performance on addition and subtraction solving while they have to detect central or lateralized targets. The results show that lateralized distractors presented in the hemifield congruent to the operation to be solved interfere with arithmetical solving: participants are slower to solve subtractions or additions when distractors are located on the left or on the right, respectively. These results converge with previous data to show that attentional shifts underlie not only number processing but also mental arithmetic. They extend them as they reveal the reverse effect of the one previously reported by showing that inducing attention shifts interferes with the solving of arithmetic problems. They also demonstrate that spatial attentional shifts are part of the calculation procedure of solving mentally arithmetic problems. Their functional role is to access, from the first operand, the representation of the result in a direction congruent to the operation.
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.
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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.
Constant-coefficient FIR filters based on residue number system arithmetic
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Stamenković Negovan
2012-01-01
Full Text Available In this paper, the design of a Finite Impulse Response (FIR filter based on the residue number system (RNS is presented. We chose to implement it in the (RNS, because the RNS offers high speed and low power dissipation. This architecture is based on the single RNS multiplier-accumulator (MAC unit. The three moduli set {2n+1,2n,2n-1}, which avoids 2n+1 modulus, is used to design FIR filter. A numerical example illustrates the principles of residue encoding, residue arithmetic, and residue decoding for FIR filters.
A formalized proof of Dirichlet's theorem on primes in arithmetic progression
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John Harrison
2009-01-01
Full Text Available We describe the formalization using the HOL Light theorem prover of Dirichlet's theorem on primes in arithmetic progression. The proof turned out to be more straightforward than expected, but this depended on a careful choice of an informal proof to use as a starting-point. The goal of this paper iis twofold. First we describe a simple and efficient proof of the theorem informally, which iis otherwise difficult to find in one self-contained place at an elementary level. We also describe its, largely routine, HOL Light formalization, a task that took only a few days.
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U. A. Sychou
2014-01-01
Full Text Available In this article, the problem of the practical realization of nonlinear systems with chaotic dynam-ics for targeted generation of chaotic sequences in digital devices is considered. The possible applica-tion in this task with using fixed-point arithmetic to ensure the identity of the obtained results on dif-ferent hardware and software platforms is studied. The implementation of logistic mapping is described; carry out the analysis of the results. This article proposes using the obtained results for the various tasks of the field of mobile robotics.
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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.