Basic mathematical function libraries for scientific computation

NASA Technical Reports Server (NTRS)

Galant, David C.

1989-01-01

Ada packages implementing selected mathematical functions for the support of scientific and engineering applications were written. The packages provide the Ada programmer with the mathematical function support found in the languages Pascal and FORTRAN as well as an extended precision arithmetic and a complete complex arithmetic. The algorithms used are fully described and analyzed. Implementation assumes that the Ada type FLOAT objects fully conform to the IEEE 754-1985 standard for single binary floating-point arithmetic, and that INTEGER objects are 32-bit entities. Codes for the Ada packages are included as appendixes.

The neural correlates of mental arithmetic in adolescents: a longitudinal fNIRS study.

PubMed

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.

The role of physical digit representation and numerical magnitude representation in children's multiplication fact retrieval.

PubMed

De Visscher, Alice; Noël, Marie-Pascale; De Smedt, Bert

2016-12-01

Arithmetic facts, in particular multiplication tables, are thought to be stored in long-term memory and to be interference prone. At least two representations underpinning these arithmetic facts have been suggested: a physical representation of the digits and a numerical magnitude representation. We hypothesized that both representations are possible sources of interference that could explain individual differences in multiplication fact performance and/or in strategy use. We investigated the specificity of these interferences on arithmetic fact retrieval and explored the relation between interference and performance on the different arithmetic operations and on general mathematics achievement. Participants were 79 fourth-grade children (M age =9.6 years) who completed a products comparison and a multiplication production task with verbal strategy reports. Performances on a speeded calculation test including the four operations and on a general mathematics achievement test were also collected. Only the interference coming from physical representations was a significant predictor of the performance across multiplications. However, both the magnitude and physical representations were unique predictors of individual differences in multiplication. The frequency of the retrieval strategy across multiplication problems and across individuals was determined only by the physical representation, which therefore is suggested as being responsible for memory storage issues. Interestingly, this impact of physical representation was not observed when predicting performance on subtraction or on general mathematical achievement. In contrast, the impact of the numerical magnitude representation was more general in that it was observed across all arithmetic operations and in general mathematics achievement. Copyright © 2016 Elsevier Inc. All rights reserved.

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

PubMed

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.

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

PubMed

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

2018-05-15

In the development of math ability, a large variability of performance in solving simple arithmetic problems is observed and has not found a compelling explanation yet. One robust effect in simple multiplication facts is the problem size effect, indicating better performance for small problems compared to large ones. Recently, behavioral studies brought to light another effect in multiplication facts, the interference effect. That is, high interfering problems (receiving more proactive interference from previously learned problems) are more difficult to retrieve than low interfering problems (in terms of physical feature overlap, namely the digits, De Visscher and Noël, 2014). At the behavioral level, the sensitivity to the interference effect is shown to explain individual differences in the performance of solving multiplications in children as well as in adults. The aim of the present study was to investigate the individual differences in multiplication ability in relation to the neural interference effect and the neural problem size effect. To that end, we used a paradigm developed by De Visscher, Berens, et al. (2015) that contrasts the interference effect and the problem size effect in a multiplication verification task, during functional magnetic resonance imaging (fMRI) acquisition. Forty-two healthy adults, who showed high variability in an arithmetic fluency test, participated in our fMRI study. In order to control for the general reasoning level, the IQ was taken into account in the individual differences analyses. Our findings revealed a neural interference effect linked to individual differences in multiplication in the left inferior frontal gyrus, while controlling for the IQ. This interference effect in the left inferior frontal gyrus showed a negative relation with individual differences in arithmetic fluency, indicating a higher interference effect for low performers compared to high performers. This region is suggested in the literature to be involved in resolution of proactive interference. Besides, no correlation between the neural problem size effect and multiplication performance was found. This study supports the idea that the interference due to similarities/overlap of physical traits (the digits) is crucial in memorizing arithmetic facts and in determining individual differences in arithmetic. Copyright © 2018 Elsevier Inc. All rights reserved.

What basic number processing measures in kindergarten explain unique variability in first-grade arithmetic proficiency?

PubMed

Bartelet, Dimona; Vaessen, Anniek; Blomert, Leo; Ansari, Daniel

2014-01-01

Relations between children's mathematics achievement and their basic number processing skills have been reported in both cross-sectional and longitudinal studies. Yet, some key questions are currently unresolved, including which kindergarten skills uniquely predict children's arithmetic fluency during the first year of formal schooling and the degree to which predictors are contingent on children's level of arithmetic proficiency. The current study assessed kindergarteners' non-symbolic and symbolic number processing efficiency. In addition, the contribution of children's underlying magnitude representations to differences in arithmetic achievement was assessed. Subsequently, in January of Grade 1, their arithmetic proficiency was assessed. Hierarchical regression analysis revealed that children's efficiency to compare digits, count, and estimate numerosities uniquely predicted arithmetic differences above and beyond the non-numerical factors included. Moreover, quantile regression analysis indicated that symbolic number processing efficiency was consistently a significant predictor of arithmetic achievement scores regardless of children's level of arithmetic proficiency, whereas their non-symbolic number processing efficiency was not. Finally, none of the task-specific effects indexing children's representational precision was significantly associated with arithmetic fluency. The implications of the results are 2-fold. First, the findings indicate that children's efficiency to process symbols is important for the development of their arithmetic fluency in Grade 1 above and beyond the influence of non-numerical factors. Second, the impact of children's non-symbolic number processing skills does not depend on their arithmetic achievement level given that they are selected from a nonclinical population. Copyright © 2013 Elsevier Inc. All rights reserved.

The Differential Role of Verbal and Spatial Working Memory in the Neural Basis of Arithmetic

PubMed Central

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

Digital Ratiometer

NASA Technical Reports Server (NTRS)

Beer, R.

1985-01-01

Small, low-cost comparator with 24-bit-precision yields ratio signal from pair of analog or digital input signals. Arithmetic logic chips (bit-slice) sample two 24-bit analog-to-digital converters approximately once every millisecond and accumulate them in two 24-bit registers. Approach readily modified to arbitrary precision.

Specific arithmetic calculation deficits in children with Turner syndrome.

PubMed

Rovet, J; Szekely, C; Hockenberry, M N

1994-12-01

Study 1 compared arithmetic processing skills on the WRAT-R in 45 girls with Turner syndrome (TS) and 92 age-matched female controls. Results revealed significant underachievement by subjects with TS, which reflected their poorer performance on problems requiring the retrieval of addition and multiplication facts and procedural knowledge for addition and division operations. TS subjects did not differ qualitatively from controls in type of procedural error committed. Study 2, which compared the performance of 10 subjects with TS and 31 controls on the Keymath Diagnostic Arithmetic Test, showed that the TS group had less adequate knowledge of arithmetic, subtraction, and multiplication procedures but did not differ from controls on Fact items. Error analyses revealed that TS subjects were more likely to confuse component steps or fail to separate intermediate steps or to complete problems. TS subjects relied to a greater degree on verbal than visual-spatial abilities in arithmetic processing while their visual-spatial abilities were associated with retrieval of simple multidigit addition facts and knowledge of subtraction, multiplication, and division procedures. Differences between the TS and control groups increased with age for Keymath, but not WRAT-R, procedures. Discrepant findings are related to the different task constraints (timed vs. untimed, single vs. alternate versions, size of item pool) and the use of different strategies (counting vs. fact retrieval). It is concluded that arithmetic difficulties in females with TS are due to less adequate procedural skills, combined with poorer fact retrieval in timed testing situations, rather than to inadequate visual-spatial abilities.

Design and implementation of the modified signed digit multiplication routine on a ternary optical computer.

PubMed

Xu, Qun; Wang, Xianchao; Xu, Chao

2017-06-01

Multiplication with traditional electronic computers is faced with a low calculating accuracy and a long computation time delay. To overcome these problems, the modified signed digit (MSD) multiplication routine is established based on the MSD system and the carry-free adder. Also, its parallel algorithm and optimization techniques are studied in detail. With the help of a ternary optical computer's characteristics, the structured data processor is designed especially for the multiplication routine. Several ternary optical operators are constructed to perform M transformations and summations in parallel, which has accelerated the iterative process of multiplication. In particular, the routine allocates data bits of the ternary optical processor based on digits of multiplication input, so the accuracy of the calculation results can always satisfy the users. Finally, the routine is verified by simulation experiments, and the results are in full compliance with the expectations. Compared with an electronic computer, the MSD multiplication routine is not only good at dealing with large-value data and high-precision arithmetic, but also maintains lower power consumption and fewer calculating delays.

Exploring Hill Ciphers with Graphing Calculators.

ERIC Educational Resources Information Center

St. John, Dennis

1998-01-01

Explains how to code and decode messages using Hill ciphers which combine matrix multiplication and modular arithmetic. Discusses how a graphing calculator can facilitate the matrix and modular arithmetic used in the coding and decoding procedures. (ASK)

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

PubMed

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

2016-10-01

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

Optical computation using residue arithmetic.

PubMed

Huang, A; Tsunoda, Y; Goodman, J W; Ishihara, S

1979-01-15

Using residue arithmetic it is possible to perform additions, subtractions, multiplications, and polynomial evaluation without the necessity for carry operations. Calculations can, therefore, be performed in a fully parallel manner. Several different optical methods for performing residue arithmetic operations are described. A possible combination of such methods to form a matrix vector multiplier is considered. The potential advantages of optics in performing these kinds of operations are discussed.

An Elementary Algorithm to Evaluate Trigonometric Functions to High Precision

ERIC Educational Resources Information Center

Johansson, B. Tomas

2018-01-01

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

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

ERIC Educational Resources Information Center

Taani, Osama

2014-01-01

In this paper, I discuss one of the most distinguishing features of Jamshid al-Kashi's pedagogy from his "Key to Arithmetic", a well-known Arabic mathematics textbook from the fifteenth century. This feature is the multiple paths that he includes to find a desired result. In the first section light is shed on al-Kashi's life…

Arithmetic memory networks established in childhood are changed by experience in adulthood

PubMed Central

Martinez-Lincoln, Amanda; Cortinas, Christina; Wicha, Nicole Y. Y.

2014-01-01

Adult bilinguals show stronger access to multiplication tables when using the language in which they learned arithmetic during childhood (LA+) than the other language (LA−), implying language-specific encoding of math facts. However, most bilinguals use LA+ throughout their life, confounding the impact of encoding and use. We tested if using arithmetic facts in LA− could reduce this LA− disadvantage. We measured event related brain potentials while bilingual teachers judged the correctness of multiplication problems in each of their languages. Critically, each teacher taught arithmetic in either LA+ or LA−. Earlier N400 peak latency was observed in both groups for the teaching than non-teaching language, showing more efficient access to these facts with use. LA+ teachers maintained an LA+ advantage, while LA− teachers showed equivalent N400 congruency effects (for incorrect versus correct solutions) in both languages. LA− teachers also showed a late positive component that may reflect conflict monitoring between their LA+ and a strong LA−. Thus, the LA− disadvantage for exact arithmetic established in early bilingual education can be mitigated by later use of LA−. PMID:25445361

Assessing hemispheric specialization for processing arithmetic skills in adults: A functional transcranial doppler ultrasonography (fTCD) study.

PubMed

Connaughton, Veronica M; Amiruddin, Azhani; Clunies-Ross, Karen L; French, Noel; Fox, Allison M

2017-05-01

A major model of the cerebral circuits that underpin arithmetic calculation is the triple-code model of numerical processing. This model proposes that the lateralization of mathematical operations is organized across three circuits: a left-hemispheric dominant verbal code; a bilateral magnitude representation of numbers and a bilateral Arabic number code. This study simultaneously measured the blood flow of both middle cerebral arteries using functional transcranial Doppler ultrasonography to assess hemispheric specialization during the performance of both language and arithmetic tasks. The propositions of the triple-code model were assessed in a non-clinical adult group by measuring cerebral blood flow during the performance of multiplication and subtraction problems. Participants were 17 adults aged between 18-27 years. We obtained laterality indices for each type of mathematical operation and compared these in participants with left-hemispheric language dominance. It was hypothesized that blood flow would lateralize to the left hemisphere during the performance of multiplication operations, but would not lateralize during the performance of subtraction operations. Hemispheric blood flow was significantly left lateralized during the multiplication task, but was not lateralized during the subtraction task. Compared to high spatial resolution neuroimaging techniques previously used to measure cerebral lateralization, functional transcranial Doppler ultrasonography is a cost-effective measure that provides a superior temporal representation of arithmetic cognition. These results provide support for the triple-code model of arithmetic processing and offer complementary evidence that multiplication operations are processed differently in the adult brain compared to subtraction operations. Copyright © 2017 Elsevier B.V. All rights reserved.

Probability Quantization for Multiplication-Free Binary Arithmetic Coding

NASA Technical Reports Server (NTRS)

Cheung, K. -M.

1995-01-01

A method has been developed to improve on Witten's binary arithmetic coding procedure of tracking a high value and a low value. The new method approximates the probability of the less probable symbol, which improves the worst-case coding efficiency.

Exploiting the chaotic behaviour of atmospheric models with reconfigurable architectures

NASA Astrophysics Data System (ADS)

Russell, Francis P.; Düben, Peter D.; Niu, Xinyu; Luk, Wayne; Palmer, T. N.

2017-12-01

Reconfigurable architectures are becoming mainstream: Amazon, Microsoft and IBM are supporting such architectures in their data centres. The computationally intensive nature of atmospheric modelling is an attractive target for hardware acceleration using reconfigurable computing. Performance of hardware designs can be improved through the use of reduced-precision arithmetic, but maintaining appropriate accuracy is essential. We explore reduced-precision optimisation for simulating chaotic systems, targeting atmospheric modelling, in which even minor changes in arithmetic behaviour will cause simulations to diverge quickly. The possibility of equally valid simulations having differing outcomes means that standard techniques for comparing numerical accuracy are inappropriate. We use the Hellinger distance to compare statistical behaviour between reduced-precision CPU implementations to guide reconfigurable designs of a chaotic system, then analyse accuracy, performance and power efficiency of the resulting implementations. Our results show that with only a limited loss in accuracy corresponding to less than 10% uncertainty in input parameters, the throughput and energy efficiency of a single-precision chaotic system implemented on a Xilinx Virtex-6 SX475T Field Programmable Gate Array (FPGA) can be more than doubled.

Constrained Chebyshev approximations to some elementary functions suitable for evaluation with floating point arithmetic

NASA Technical Reports Server (NTRS)

Manos, P.; Turner, L. R.

1972-01-01

Approximations which can be evaluated with precision using floating-point arithmetic are presented. The particular set of approximations thus far developed are for the function TAN and the functions of USASI FORTRAN excepting SQRT and EXPONENTIATION. These approximations are, furthermore, specialized to particular forms which are especially suited to a computer with a small memory, in that all of the approximations can share one general purpose subroutine for the evaluation of a polynomial in the square of the working argument.

Functional dissociations between four basic arithmetic operations in the human posterior parietal cortex: A cytoarchitectonic mapping study

PubMed Central

Rosenberg-Lee, Miriam; Chang, Ting Ting; Young, Christina B; Wu, Sarah; Menon, Vinod

2011-01-01

Although lesion studies over the past several decades have focused on functional dissociations in posterior parietal cortex (PPC) during arithmetic, no consistent view has emerged of its differential involvement in addition, subtraction, multiplication, and division. To circumvent problems with poor anatomical localization, we examined functional overlap and dissociations in cytoarchitectonically-defined subdivisions of the intraparietal sulcus (IPS), superior parietal lobule (SPL) and angular gyrus (AG), across these four operations. Compared to a number identification control task, all operations except addition, showed a consistent profile of left posterior IPS activation and deactivation in the right posterior AG. Multiplication and subtraction differed significantly in right, but not left, IPS and AG activity, challenging the view that the left AG differentially subserves retrieval during multiplication. Although addition and multiplication both rely on retrieval, multiplication evoked significantly greater activation in right posterior IPS, as well as the prefrontal cortex, lingual and fusiform gyri, demonstrating that addition and multiplication engage different brain processes. Comparison of PPC responses to the two pairs of inverse operations: division vs. multiplication and subtraction vs. addition revealed greater activation of left lateral SPL during division, suggesting that processing inverse relations is operation specific. Our findings demonstrate that individual IPS, SPL and AG subdivisions are differentially modulated by the four arithmetic operations and they point to significant functional heterogeneity and individual differences in activation and deactivation within the PPC. Critically, these effects are related to retrieval, calculation and inversion, the three key cognitive processes that are differentially engaged by arithmetic operations. Our findings point to distributed representation of these processes in the human PPC and also help explain why lesion and previous imaging studies have yielded inconsistent findings. PMID:21616086

Functional dissociations between four basic arithmetic operations in the human posterior parietal cortex: a cytoarchitectonic mapping study.

PubMed

Rosenberg-Lee, Miriam; Chang, Ting Ting; Young, Christina B; Wu, Sarah; Menon, Vinod

2011-07-01

Although lesion studies over the past several decades have focused on functional dissociations in posterior parietal cortex (PPC) during arithmetic, no consistent view has emerged of its differential involvement in addition, subtraction, multiplication, and division. To circumvent problems with poor anatomical localization, we examined functional overlap and dissociations in cytoarchitectonically defined subdivisions of the intraparietal sulcus (IPS), superior parietal lobule (SPL) and angular gyrus (AG), across these four operations. Compared to a number identification control task, all operations except addition, showed a consistent profile of left posterior IPS activation and deactivation in the right posterior AG. Multiplication and subtraction differed significantly in right, but not left, IPS and AG activity, challenging the view that the left AG differentially subserves retrieval during multiplication. Although addition and multiplication both rely on retrieval, multiplication evoked significantly greater activation in right posterior IPS, as well as the prefrontal cortex, lingual and fusiform gyri, demonstrating that addition and multiplication engage different brain processes. Comparison of PPC responses to the two pairs of inverse operations: division versus multiplication and subtraction versus addition revealed greater activation of left lateral SPL during division, suggesting that processing inverse relations is operation specific. Our findings demonstrate that individual IPS, SPL and AG subdivisions are differentially modulated by the four arithmetic operations and they point to significant functional heterogeneity and individual differences in activation and deactivation within the PPC. Critically, these effects are related to retrieval, calculation and inversion, the three key cognitive processes that are differentially engaged by arithmetic operations. Our findings point to distribute representation of these processes in the human PPC and also help explain why lesion and previous imaging studies have yielded inconsistent findings. Copyright © 2011 Elsevier Ltd. All rights reserved.

Arabidopsis plants perform arithmetic division to prevent starvation at night

PubMed Central

Scialdone, Antonio; Mugford, Sam T; Feike, Doreen; Skeffington, Alastair; Borrill, Philippa; Graf, Alexander; Smith, Alison M; Howard, Martin

2013-01-01

Photosynthetic starch reserves that accumulate in Arabidopsis leaves during the day decrease approximately linearly with time at night to support metabolism and growth. We find that the rate of decrease is adjusted to accommodate variation in the time of onset of darkness and starch content, such that reserves last almost precisely until dawn. Generation of these dynamics therefore requires an arithmetic division computation between the starch content and expected time to dawn. We introduce two novel chemical kinetic models capable of implementing analog arithmetic division. Predictions from the models are successfully tested in plants perturbed by a night-time light period or by mutations in starch degradation pathways. Our experiments indicate which components of the starch degradation apparatus may be important for appropriate arithmetic division. Our results are potentially relevant for any biological system dependent on a food reserve for survival over a predictable time period. DOI: http://dx.doi.org/10.7554/eLife.00669.001 PMID:23805380

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

PubMed

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

2017-02-01

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

Retrieval-Induced Forgetting of Arithmetic Facts

ERIC Educational Resources Information Center

Campbell, Jamie I. D.; Thompson, Valerie A.

2012-01-01

Retrieval-induced forgetting (RIF) is a widely studied phenomenon of human memory, but RIF of arithmetic facts remains relatively unexplored. In 2 experiments, we investigated RIF of simple addition facts (2 + 3 = 5) from practice of their multiplication counterparts (2 x 3 = 6). In both experiments, robust RIF expressed in response times occurred…

Basic Mathematics Operations--A Math Practice Booklet.

ERIC Educational Resources Information Center

Herr, Nicholas K.

Intended for use in vocational high schools, the workbook is designed to help the student understand and develop skill in performing the four basic arithmetical operations: addition, subtraction, multiplication, and division. Also stressed is the correct reading and writing of numbers. The booklet consists of explanatory text, arithmetic problems,…

Technology Performance Level (TPL) Scoring Tool

DOE Office of Scientific and Technical Information (OSTI.GOV)

Weber, Jochem; Roberts, Jesse D.; Costello, Ronan

2016-09-01

Three different ways of combining scores are used in the revised formulation. These are arithmetic mean, geometric mean and multiplication with normalisation. Arithmetic mean is used when combining scores that measure similar attributes, e.g. used for combining costs. The arithmetic mean has the property that it is similar to a logical OR, e.g. when combining costs it does not matter what the individual costs are only what the combined cost is. Geometric mean and Multiplication are used when combining scores that measure disparate attributes. Multiplication is similar to a logical AND, it is used to combine ‘must haves.’ As amore » result, this method is more punitive than the geometric mean; to get a good score in the combined result it is necessary to have a good score in ALL of the inputs. e.g. the different types of survivability are ‘must haves.’ On balance, the revised TPL is probably less punitive than the previous spreadsheet, multiplication is used sparingly as a method of combining scores. This is in line with the feedback of the Wave Energy Prize judges.« less

Developmental dissociation in the neural responses to simple multiplication and subtraction problems

PubMed Central

Prado, Jérôme; Mutreja, Rachna; Booth, James R.

2014-01-01

Mastering single-digit arithmetic during school years is commonly thought to depend upon an increasing reliance on verbally memorized facts. An alternative model, however, posits that fluency in single-digit arithmetic might also be achieved via the increasing use of efficient calculation procedures. To test between these hypotheses, we used a cross-sectional design to measure the neural activity associated with single-digit subtraction and multiplication in 34 children from 2nd to 7th grade. The neural correlates of language and numerical processing were also identified in each child via localizer scans. Although multiplication and subtraction were undistinguishable in terms of behavior, we found a striking developmental dissociation in their neural correlates. First, we observed grade-related increases of activity for multiplication, but not for subtraction, in a language-related region of the left temporal cortex. Second, we found grade-related increases of activity for subtraction, but not for multiplication, in a region of the right parietal cortex involved in the procedural manipulation of numerical quantities. The present results suggest that fluency in simple arithmetic in children may be achieved by both increasing reliance on verbal retrieval and by greater use of efficient quantity-based procedures, depending on the operation. PMID:25089323

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

PubMed

Fehr, Thorsten; Code, Chris; Herrmann, Manfred

2007-10-03

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

Developmental Dissociation in the Neural Responses to Simple Multiplication and Subtraction Problems

ERIC Educational Resources Information Center

Prado, Jérôme; Mutreja, Rachna; Booth, James R.

2014-01-01

Mastering single-digit arithmetic during school years is commonly thought to depend upon an increasing reliance on verbally memorized facts. An alternative model, however, posits that fluency in single-digit arithmetic might also be achieved via the increasing use of efficient calculation procedures. To test between these hypotheses, we used a…

Measuring Middle Grades Teachers' Understanding of Rational Numbers with the Mixture Rasch Model

ERIC Educational Resources Information Center

Izsak, Andrew; Orrill, Chandra Hawley; Cohen, Allan S.; Brown, Rachael Eriksen

2010-01-01

We report the development of a multiple-choice instrument that measures the mathematical knowledge needed for teaching arithmetic with fractions, decimals, and proportions. In particular, the instrument emphasizes the knowledge needed to reason about such arithmetic when numbers are embedded in problem situations. We administered our instrument to…

Effects of Numerical Surface Form in Arithmetic Word Problems

ERIC Educational Resources Information Center

Orrantia, Josetxu; Múñez, David; San Romualdo, Sara; Verschaffel, Lieven

2015-01-01

Adults' simple arithmetic performance is more efficient when operands are presented in Arabic digit (3 + 5) than in number word (three + five) formats. An explanation provided is that visual familiarity with digits is higher respect to number words. However, most studies have been limited to single-digit addition and multiplication problems. In…

Redundant binary number representation for an inherently parallel arithmetic on optical computers.

PubMed

De Biase, G A; Massini, A

1993-02-10

A simple redundant binary number representation suitable for digital-optical computers is presented. By means of this representation it is possible to build an arithmetic with carry-free parallel algebraic sums carried out in constant time and parallel multiplication in log N time. This redundant number representation naturally fits the 2's complement binary number system and permits the construction of inherently parallel arithmetic units that are used in various optical technologies. Some properties of this number representation and several examples of computation are presented.

Theoretical lower bounds for parallel pipelined shift-and-add constant multiplications with n-input arithmetic operators

NASA Astrophysics Data System (ADS)

Cruz Jiménez, Miriam Guadalupe; Meyer Baese, Uwe; Jovanovic Dolecek, Gordana

2017-12-01

New theoretical lower bounds for the number of operators needed in fixed-point constant multiplication blocks are presented. The multipliers are constructed with the shift-and-add approach, where every arithmetic operation is pipelined, and with the generalization that n-input pipelined additions/subtractions are allowed, along with pure pipelining registers. These lower bounds, tighter than the state-of-the-art theoretical limits, are particularly useful in early design stages for a quick assessment in the hardware utilization of low-cost constant multiplication blocks implemented in the newest families of field programmable gate array (FPGA) integrated circuits.

Moving along the number line: operational momentum in nonsymbolic arithmetic.

PubMed

McCrink, Koleen; Dehaene, Stanislas; Dehaene-Lambertz, Ghislaine

2007-11-01

Can human adults perform arithmetic operations with large approximate numbers, and what effect, if any, does an internal spatial-numerical representation of numerical magnitude have on their responses? We conducted a psychophysical study in which subjects viewed several hundred short videos of sets of objects being added or subtracted from one another and judged whether the final numerosity was correct or incorrect. Over a wide range of possible outcomes, the subjects' responses peaked at the approximate location of the true numerical outcome and gradually tapered off as a function of the ratio of the true and proposed outcomes (Weber's law). Furthermore, an operational momentum effect was observed, whereby addition problems were overestimated and subtraction problems were underestimated. The results show that approximate arithmetic operates according to precise quantitative rules, perhaps analogous to those characterizing movement on an internal continuum.

Separating stages of arithmetic verification: An ERP study with a novel paradigm.

PubMed

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.

Solving Ordinary Differential Equations

NASA Technical Reports Server (NTRS)

Krogh, F. T.

1987-01-01

Initial-value ordinary differential equation solution via variable order Adams method (SIVA/DIVA) package is collection of subroutines for solution of nonstiff ordinary differential equations. There are versions for single-precision and double-precision arithmetic. Requires fewer evaluations of derivatives than other variable-order Adams predictor/ corrector methods. Option for direct integration of second-order equations makes integration of trajectory problems significantly more efficient. Written in FORTRAN 77.

Efficient Boundary Extraction of BSP Solids Based on Clipping Operations.

PubMed

Wang, Charlie C L; Manocha, Dinesh

2013-01-01

We present an efficient algorithm to extract the manifold surface that approximates the boundary of a solid represented by a Binary Space Partition (BSP) tree. Our polygonization algorithm repeatedly performs clipping operations on volumetric cells that correspond to a spatial convex partition and computes the boundary by traversing the connected cells. We use point-based representations along with finite-precision arithmetic to improve the efficiency and generate the B-rep approximation of a BSP solid. The core of our polygonization method is a novel clipping algorithm that uses a set of logical operations to make it resistant to degeneracies resulting from limited precision of floating-point arithmetic. The overall BSP to B-rep conversion algorithm can accurately generate boundaries with sharp and small features, and is faster than prior methods. At the end of this paper, we use this algorithm for a few geometric processing applications including Boolean operations, model repair, and mesh reconstruction.

Multiplier Architecture for Coding Circuits

NASA Technical Reports Server (NTRS)

Wang, C. C.; Truong, T. K.; Shao, H. M.; Deutsch, L. J.

1986-01-01

Multipliers based on new algorithm for Galois-field (GF) arithmetic regular and expandable. Pipeline structures used for computing both multiplications and inverses. Designs suitable for implementation in very-large-scale integrated (VLSI) circuits. This general type of inverter and multiplier architecture especially useful in performing finite-field arithmetic of Reed-Solomon error-correcting codes and of some cryptographic algorithms.

Cool's Clams Casino

ERIC Educational Resources Information Center

Cobey, Paul; Williams, David E.

1977-01-01

A mathematical game that reinforces basic multiplication facts, strengthens concepts of factors and multiples, and also provides arithmetic drill is described. Four variations of the game are also provided. (JT)

Distinct representations of subtraction and multiplication in the neural systems for numerosity and language

PubMed Central

Prado, Jérôme; Mutreja, Rachna; Zhang, Hongchuan; Mehta, Rucha; Desroches, Amy S.; Minas, Jennifer E.; Booth, James R.

2010-01-01

It has been proposed that recent cultural inventions such as symbolic arithmetic recycle evolutionary older neural mechanisms. A central assumption of this hypothesis is that the degree to which a pre-existing mechanism is recycled depends upon the degree of similarity between its initial function and the novel task. To test this assumption, we investigated whether the brain region involved in magnitude comparison in the intraparietal sulcus (IPS), localized by a numerosity comparison task, is recruited to a greater degree by arithmetic problems that involve number comparison (single-digit subtractions) than by problems that involve retrieving facts from memory (single-digit multiplications). Our results confirmed that subtractions are associated with greater activity in the IPS than multiplications, whereas multiplications elicit greater activity than subtractions in regions involved in verbal processing including the middle temporal gyrus and inferior frontal gyrus that were localized by a phonological processing task. Pattern analyses further indicated that the neural mechanisms more active for subtraction than multiplication in the IPS overlap with those involved in numerosity comparison, and that the strength of this overlap predicts inter-individual performance in the subtraction task. These findings provide novel evidence that elementary arithmetic relies on the co-option of evolutionary older neural circuits. PMID:21246667

A new numerically stable implementation of the T-matrix method for electromagnetic scattering by spheroidal particles

NASA Astrophysics Data System (ADS)

Somerville, W. R. C.; Auguié, B.; Le Ru, E. C.

2013-07-01

We propose, describe, and demonstrate a new numerically stable implementation of the extended boundary-condition method (EBCM) to compute the T-matrix for electromagnetic scattering by spheroidal particles. Our approach relies on the fact that for many of the EBCM integrals in the special case of spheroids, a leading part of the integrand integrates exactly to zero, which causes catastrophic loss of precision in numerical computations. This feature was in fact first pointed out by Waterman in the context of acoustic scattering and electromagnetic scattering by infinite cylinders. We have recently studied it in detail in the case of electromagnetic scattering by particles. Based on this study, the principle of our new implementation is therefore to compute all the integrands without the problematic part to avoid the primary cause of loss of precision. Particular attention is also given to choosing the algorithms that minimise loss of precision in every step of the method, without compromising on speed. We show that the resulting implementation can efficiently compute in double precision arithmetic the T-matrix and therefore optical properties of spheroidal particles to a high precision, often down to a remarkable accuracy (10-10 relative error), over a wide range of parameters that are typically considered problematic. We discuss examples such as high-aspect ratio metallic nanorods and large size parameter (≈35) dielectric particles, which had been previously modelled only using quadruple-precision arithmetic codes.

Concurrent error detecting codes for arithmetic processors

NASA Technical Reports Server (NTRS)

Lim, R. S.

1979-01-01

A method of concurrent error detection for arithmetic processors is described. Low-cost residue codes with check-length l and checkbase m = 2 to the l power - 1 are described for checking arithmetic operations of addition, subtraction, multiplication, division complement, shift, and rotate. Of the three number representations, the signed-magnitude representation is preferred for residue checking. Two methods of residue generation are described: the standard method of using modulo m adders and the method of using a self-testing residue tree. A simple single-bit parity-check code is described for checking the logical operations of XOR, OR, and AND, and also the arithmetic operations of complement, shift, and rotate. For checking complement, shift, and rotate, the single-bit parity-check code is simpler to implement than the residue codes.

Desirable floating-point arithmetic and elementary functions for numerical computation

NASA Technical Reports Server (NTRS)

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.

On the design of a radix-10 online floating-point multiplier

NASA Astrophysics Data System (ADS)

McIlhenny, Robert D.; Ercegovac, Milos D.

2009-08-01

This paper describes an approach to design and implement a radix-10 online floating-point multiplier. An online approach is considered because it offers computational flexibility not available with conventional arithmetic. The design was coded in VHDL and compiled, synthesized, and mapped onto a Virtex 5 FPGA to measure cost in terms of LUTs (look-up-tables) as well as the cycle time and total latency. The routing delay which was not optimized is the major component in the cycle time. For a rough estimate of the cost/latency characteristics, our design was compared to a standard radix-2 floating-point multiplier of equivalent precision. The results demonstrate that even an unoptimized radix-10 online design is an attractive implementation alternative for FPGA floating-point multiplication.

Computationally efficient method for optical simulation of solar cells and their applications

NASA Astrophysics Data System (ADS)

Semenikhin, I.; Zanuccoli, M.; Fiegna, C.; Vyurkov, V.; Sangiorgi, E.

2013-01-01

This paper presents two novel implementations of the Differential method to solve the Maxwell equations in nanostructured optoelectronic solid state devices. The first proposed implementation is based on an improved and computationally efficient T-matrix formulation that adopts multiple-precision arithmetic to tackle the numerical instability problem which arises due to evanescent modes. The second implementation adopts the iterative approach that allows to achieve low computational complexity O(N logN) or better. The proposed algorithms may work with structures with arbitrary spatial variation of the permittivity. The developed two-dimensional numerical simulator is applied to analyze the dependence of the absorption characteristics of a thin silicon slab on the morphology of the front interface and on the angle of incidence of the radiation with respect to the device surface.

If Gravity is Geometry, is Dark Energy just Arithmetic?

NASA Astrophysics Data System (ADS)

Czachor, Marek

2017-04-01

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

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

PubMed

Braithwaite, David W; Siegler, Robert S

2018-04-26

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

FAST TRACK COMMUNICATION: Reversible arithmetic logic unit for quantum arithmetic

NASA Astrophysics Data System (ADS)

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

2010-09-01

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

Numerical Development

ERIC Educational Resources Information Center

Siegler, Robert S.; Braithwaite, David W.

2016-01-01

In this review, we attempt to integrate two crucial aspects of numerical development: learning the magnitudes of individual numbers and learning arithmetic. Numerical magnitude development involves gaining increasingly precise knowledge of increasing ranges and types of numbers: from non-symbolic to small symbolic numbers, from smaller to larger…

Mathematical abilities in dyslexic children: a diffusion tensor imaging study.

PubMed

Koerte, Inga K; Willems, Anna; Muehlmann, Marc; Moll, Kristina; Cornell, Sonia; Pixner, Silvia; Steffinger, Denise; Keeser, Daniel; Heinen, Florian; Kubicki, Marek; Shenton, Martha E; Ertl-Wagner, Birgit; Schulte-Körne, Gerd

2016-09-01

Dyslexia is characterized by a deficit in language processing which mainly affects word decoding and spelling skills. In addition, children with dyslexia also show problems in mathematics. However, for the latter, the underlying structural correlates have not been investigated. Sixteen children with dyslexia (mean age 9.8 years [0.39]) and 24 typically developing children (mean age 9.9 years [0.29]) group matched for age, gender, IQ, and handedness underwent 3 T MR diffusion tensor imaging as well as cognitive testing. Tract-Based Spatial Statistics were performed to correlate behavioral data with diffusion data. Children with dyslexia performed worse than controls in standardized verbal number tasks, such as arithmetic efficiency tests (addition, subtraction, multiplication, division). In contrast, the two groups did not differ in the nonverbal number line task. Arithmetic efficiency, representing the total score of the four arithmetic tasks, multiplication, and division, correlated with diffusion measures in widespread areas of the white matter, including bilateral superior and inferior longitudinal fasciculi in children with dyslexia compared to controls. Children with dyslexia demonstrated lower performance in verbal number tasks but performed similarly to controls in a nonverbal number task. Further, an association between verbal arithmetic efficiency and diffusion measures was demonstrated in widespread areas of the white matter suggesting compensatory mechanisms in children with dyslexia compared to controls. Taken together, poor fact retrieval in children with dyslexia is likely a consequence of deficits in the language system, which not only affects literacy skills but also impacts on arithmetic skills.

Paranoia.Ada: A diagnostic program to evaluate Ada floating-point arithmetic

NASA Technical Reports Server (NTRS)

Hjermstad, Chris

1986-01-01

Many essential software functions in the mission critical computer resource application domain depend on floating point arithmetic. Numerically intensive functions associated with the Space Station project, such as emphemeris generation or the implementation of Kalman filters, are likely to employ the floating point facilities of Ada. Paranoia.Ada appears to be a valuabe program to insure that Ada environments and their underlying hardware exhibit the precision and correctness required to satisfy mission computational requirements. As a diagnostic tool, Paranoia.Ada reveals many essential characteristics of an Ada floating point implementation. Equipped with such knowledge, programmers need not tremble before the complex task of floating point computation.

Right-Brain/Left-Brain Integrated Associative Processor Employing Convertible Multiple-Instruction-Stream Multiple-Data-Stream Elements

NASA Astrophysics Data System (ADS)

Hayakawa, Hitoshi; Ogawa, Makoto; Shibata, Tadashi

2005-04-01

A very large scale integrated circuit (VLSI) architecture for a multiple-instruction-stream multiple-data-stream (MIMD) associative processor has been proposed. The processor employs an architecture that enables seamless switching from associative operations to arithmetic operations. The MIMD element is convertible to a regular central processing unit (CPU) while maintaining its high performance as an associative processor. Therefore, the MIMD associative processor can perform not only on-chip perception, i.e., searching for the vector most similar to an input vector throughout the on-chip cache memory, but also arithmetic and logic operations similar to those in ordinary CPUs, both simultaneously in parallel processing. Three key technologies have been developed to generate the MIMD element: associative-operation-and-arithmetic-operation switchable calculation units, a versatile register control scheme within the MIMD element for flexible operations, and a short instruction set for minimizing the memory size for program storage. Key circuit blocks were designed and fabricated using 0.18 μm complementary metal-oxide-semiconductor (CMOS) technology. As a result, the full-featured MIMD element is estimated to be 3 mm2, showing the feasibility of an 8-parallel-MIMD-element associative processor in a single chip of 5 mm× 5 mm.

Individual strategy ratings improve the control for task difficulty effects in arithmetic problem solving paradigms.

PubMed

Tschentscher, Nadja; Hauk, Olaf

2015-01-01

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.

Individual strategy ratings improve the control for task difficulty effects in arithmetic problem solving paradigms

PubMed Central

Tschentscher, Nadja; Hauk, Olaf

2015-01-01

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. PMID:26321997

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

NASA Astrophysics Data System (ADS)

Oztekin, Halit; Temurtas, Feyzullah; Gulbag, Ali

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

MGUPGMA: A Fast UPGMA Algorithm With Multiple Graphics Processing Units Using NCCL

PubMed Central

Hua, Guan-Jie; Hung, Che-Lun; Lin, Chun-Yuan; Wu, Fu-Che; Chan, Yu-Wei; Tang, Chuan Yi

2017-01-01

A phylogenetic tree is a visual diagram of the relationship between a set of biological species. The scientists usually use it to analyze many characteristics of the species. The distance-matrix methods, such as Unweighted Pair Group Method with Arithmetic Mean and Neighbor Joining, construct a phylogenetic tree by calculating pairwise genetic distances between taxa. These methods have the computational performance issue. Although several new methods with high-performance hardware and frameworks have been proposed, the issue still exists. In this work, a novel parallel Unweighted Pair Group Method with Arithmetic Mean approach on multiple Graphics Processing Units is proposed to construct a phylogenetic tree from extremely large set of sequences. The experimental results present that the proposed approach on a DGX-1 server with 8 NVIDIA P100 graphic cards achieves approximately 3-fold to 7-fold speedup over the implementation of Unweighted Pair Group Method with Arithmetic Mean on a modern CPU and a single GPU, respectively. PMID:29051701

MGUPGMA: A Fast UPGMA Algorithm With Multiple Graphics Processing Units Using NCCL.

PubMed

Hua, Guan-Jie; Hung, Che-Lun; Lin, Chun-Yuan; Wu, Fu-Che; Chan, Yu-Wei; Tang, Chuan Yi

2017-01-01

A phylogenetic tree is a visual diagram of the relationship between a set of biological species. The scientists usually use it to analyze many characteristics of the species. The distance-matrix methods, such as Unweighted Pair Group Method with Arithmetic Mean and Neighbor Joining, construct a phylogenetic tree by calculating pairwise genetic distances between taxa. These methods have the computational performance issue. Although several new methods with high-performance hardware and frameworks have been proposed, the issue still exists. In this work, a novel parallel Unweighted Pair Group Method with Arithmetic Mean approach on multiple Graphics Processing Units is proposed to construct a phylogenetic tree from extremely large set of sequences. The experimental results present that the proposed approach on a DGX-1 server with 8 NVIDIA P100 graphic cards achieves approximately 3-fold to 7-fold speedup over the implementation of Unweighted Pair Group Method with Arithmetic Mean on a modern CPU and a single GPU, respectively.

Multiplication Fact Fluency Using Doubles

ERIC Educational Resources Information Center

Flowers, Judith M.; Rubenstein, Rheta N.

2010-01-01

Not knowing multiplication facts creates a gap in a student's mathematics development and undermines confidence and disposition toward further mathematical learning. Learning multiplication facts is a first step in proportional reasoning, "the capstone of elementary arithmetic and the gateway to higher mathematics" (NRC 2001, p. 242). Proportional…

Stabilizing canonical-ensemble calculations in the auxiliary-field Monte Carlo method

NASA Astrophysics Data System (ADS)

Gilbreth, C. N.; Alhassid, Y.

2015-03-01

Quantum Monte Carlo methods are powerful techniques for studying strongly interacting Fermi systems. However, implementing these methods on computers with finite-precision arithmetic requires careful attention to numerical stability. In the auxiliary-field Monte Carlo (AFMC) method, low-temperature or large-model-space calculations require numerically stabilized matrix multiplication. When adapting methods used in the grand-canonical ensemble to the canonical ensemble of fixed particle number, the numerical stabilization increases the number of required floating-point operations for computing observables by a factor of the size of the single-particle model space, and thus can greatly limit the systems that can be studied. We describe an improved method for stabilizing canonical-ensemble calculations in AFMC that exhibits better scaling, and present numerical tests that demonstrate the accuracy and improved performance of the method.

Supercomputing on massively parallel bit-serial architectures

NASA Technical Reports Server (NTRS)

Iobst, Ken

1985-01-01

Research on the Goodyear Massively Parallel Processor (MPP) suggests that high-level parallel languages are practical and can be designed with powerful new semantics that allow algorithms to be efficiently mapped to the real machines. For the MPP these semantics include parallel/associative array selection for both dense and sparse matrices, variable precision arithmetic to trade accuracy for speed, micro-pipelined train broadcast, and conditional branching at the processing element (PE) control unit level. The preliminary design of a FORTRAN-like parallel language for the MPP has been completed and is being used to write programs to perform sparse matrix array selection, min/max search, matrix multiplication, Gaussian elimination on single bit arrays and other generic algorithms. A description is given of the MPP design. Features of the system and its operation are illustrated in the form of charts and diagrams.

Perceiving fingers in single-digit arithmetic problems.

PubMed

Berteletti, Ilaria; Booth, James R

2015-01-01

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

Perceiving fingers in single-digit arithmetic problems

PubMed Central

Berteletti, Ilaria; Booth, James R.

2015-01-01

In this study, we investigate in children the neural underpinnings of finger representation and finger movement involved in single-digit arithmetic problems. Evidence suggests that finger representation and finger-based strategies play an important role in learning and understanding arithmetic. Because different operations rely on different networks, we compared activation for subtraction and multiplication problems in independently localized finger somatosensory and motor areas and tested whether activation was related to skill. Brain activations from children between 8 and 13 years of age revealed that only subtraction problems significantly activated finger motor areas, suggesting reliance on finger-based strategies. In addition, larger subtraction problems yielded greater somatosensory activation than smaller problems, suggesting a greater reliance on finger representation for larger numerical values. Interestingly, better performance in subtraction problems was associated with lower activation in the finger somatosensory area. Our results support the importance of fine-grained finger representation in arithmetical skill and are the first neurological evidence for a functional role of the somatosensory finger area in proficient arithmetical problem solving, in particular for those problems requiring quantity manipulation. From an educational perspective, these results encourage investigating whether different finger-based strategies facilitate arithmetical understanding and encourage educational practices aiming at integrating finger representation and finger-based strategies as a tool for instilling stronger numerical sense. PMID:25852582

Corporate Consolidation: An Event Study of Historic Stock Prices in the Defense Aerospace Industry

DTIC Science & Technology

2009-12-01

1994 Raytheon Xyplex Inc 1/3/1995 Boeing Precision Gear 4/3/1995 Raytheon Raytheon E-Systems Inc 6/30/1995 Raytheon Litwin Engineers & Construction...Acquirer 6/30/1995 Litwin Engineers & Construction Raytheon Arithmetic Return Logarithmic Return Note: * is significant at the 5% level 90

Calculating with light using a chip-scale all-optical abacus.

PubMed

Feldmann, J; Stegmaier, M; Gruhler, N; Ríos, C; Bhaskaran, H; Wright, C D; Pernice, W H P

2017-11-02

Machines that simultaneously process and store multistate data at one and the same location can provide a new class of fast, powerful and efficient general-purpose computers. We demonstrate the central element of an all-optical calculator, a photonic abacus, which provides multistate compute-and-store operation by integrating functional phase-change materials with nanophotonic chips. With picosecond optical pulses we perform the fundamental arithmetic operations of addition, subtraction, multiplication, and division, including a carryover into multiple cells. This basic processing unit is embedded into a scalable phase-change photonic network and addressed optically through a two-pulse random access scheme. Our framework provides first steps towards light-based non-von Neumann arithmetic.

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

PubMed

Tschentscher, Nadja; Hauk, Olaf

2014-05-15

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

A 640-MHz 32-megachannel real-time polyphase-FFT spectrum analyzer

NASA Technical Reports Server (NTRS)

Zimmerman, G. A.; Garyantes, M. F.; Grimm, M. J.; Charny, B.

1991-01-01

A polyphase fast Fourier transform (FFT) spectrum analyzer being designed for NASA's Search for Extraterrestrial Intelligence (SETI) Sky Survey at the Jet Propulsion Laboratory is described. By replacing the time domain multiplicative window preprocessing with polyphase filter processing, much of the processing loss of windowed FFTs can be eliminated. Polyphase coefficient memory costs are minimized by effective use of run length compression. Finite word length effects are analyzed, producing a balanced system with 8 bit inputs, 16 bit fixed point polyphase arithmetic, and 24 bit fixed point FFT arithmetic. Fixed point renormalization midway through the computation is seen to be naturally accommodated by the matrix FFT algorithm proposed. Simulation results validate the finite word length arithmetic analysis and the renormalization technique.

Multiple task performance as a predictor of the potential of air traffic controller trainees.

DOT National Transportation Integrated Search

1972-01-01

Two hundred and twenty-nine air traffic controller trainees were tested on the CAMI Multiple Task Performance Battery. The battery provides objective measures of monitoring, arithmetical skills, visual discrimination, and group problem solving. The c...

A parallel algorithm for computing the eigenvalues of a symmetric tridiagonal matrix

NASA Technical Reports Server (NTRS)

Swarztrauber, Paul N.

1993-01-01

A parallel algorithm, called polysection, is presented for computing the eigenvalues of a symmetric tridiagonal matrix. The method is based on a quadratic recurrence in which the characteristic polynomial is constructed on a binary tree from polynomials whose degree doubles at each level. Intervals that contain exactly one zero are determined by the zeros of polynomials at the previous level which ensures that different processors compute different zeros. The signs of the polynomials at the interval endpoints are determined a priori and used to guarantee that all zeros are found. The use of finite-precision arithmetic may result in multiple zeros; however, in this case, the intervals coalesce and their number determines exactly the multiplicity of the zero. For an N x N matrix the eigenvalues can be determined in O(log-squared N) time with N-squared processors and O(N) time with N processors. The method is compared with a parallel variant of bisection that requires O(N-squared) time on a single processor, O(N) time with N processors, and O(log N) time with N-squared processors.

Re-assessing acalculia: Distinguishing spatial and purely arithmetical deficits in right-hemisphere damaged patients.

PubMed

Benavides-Varela, S; Piva, D; Burgio, F; Passarini, L; Rolma, G; Meneghello, F; Semenza, C

2017-03-01

Arithmetical deficits in right-hemisphere damaged patients have been traditionally considered secondary to visuo-spatial impairments, although the exact relationship between the two deficits has rarely been assessed. The present study implemented a voxelwise lesion analysis among 30 right-hemisphere damaged patients and a controlled, matched-sample, cross-sectional analysis with 35 cognitively normal controls regressing three composite cognitive measures on standardized numerical measures. The results showed that patients and controls significantly differ in Number comprehension, Transcoding, and Written operations, particularly subtractions and multiplications. The percentage of patients performing below the cutoffs ranged between 27% and 47% across these tasks. Spatial errors were associated with extensive lesions in fronto-temporo-parietal regions -which frequently lead to neglect- whereas pure arithmetical errors appeared related to more confined lesions in the right angular gyrus and its proximity. Stepwise regression models consistently revealed that spatial errors were primarily predicted by composite measures of visuo-spatial attention/neglect and representational abilities. Conversely, specific errors of arithmetic nature linked to representational abilities only. Crucially, the proportion of arithmetical errors (ranging from 65% to 100% across tasks) was higher than that of spatial ones. These findings thus suggest that unilateral right hemisphere lesions can directly affect core numerical/arithmetical processes, and that right-hemisphere acalculia is not only ascribable to visuo-spatial deficits as traditionally thought. Copyright © 2017 Elsevier Ltd. All rights reserved.

Phonology and arithmetic in the language-calculation network.

PubMed

Andin, Josefine; Fransson, Peter; Rönnberg, Jerker; Rudner, Mary

2015-04-01

Arithmetic and language processing involve similar neural networks, but the relative engagement remains unclear. In the present study we used fMRI to compare activation for phonological, multiplication and subtraction tasks, keeping the stimulus material constant, within a predefined language-calculation network including left inferior frontal gyrus and angular gyrus (AG) as well as superior parietal lobule and the intraparietal sulcus bilaterally. Results revealed a generally left lateralized activation pattern within the language-calculation network for phonology and a bilateral activation pattern for arithmetic, and suggested regional differences between tasks. In particular, we found a more prominent role for phonology than arithmetic in pars opercularis of the left inferior frontal gyrus but domain generality in pars triangularis. Parietal activation patterns demonstrated greater engagement of the visual and quantity systems for calculation than language. This set of findings supports the notion of a common, but regionally differentiated, language-calculation network. Copyright © 2015 The Authors. Published by Elsevier Inc. All rights reserved.

Identifying Blocks Formed by Curbed Fractures Using Exact Arithmetic

NASA Astrophysics Data System (ADS)

Zheng, Y.; Xia, L.; Yu, Q.; Zhang, X.

2015-12-01

Identifying blocks formed by fractures is important in rock engineering. Most studies assume the fractures to be perfect planar whereas curved fractures are rarely considered. However, large fractures observed in the field are often curved. This paper presents a new method for identifying rock blocks formed by both curved and planar fractures based on the element-block-assembling approach. The curved and planar fractures are represented as triangle meshes and planar discs, respectively. In the beginning of the identification method, the intersection segments between different triangle meshes are calculated and the intersected triangles are re-meshed to construct a piecewise linear complex (PLC). Then, the modeling domain is divided into tetrahedral subdomains under the constraint of the PLC and these subdomains are further decomposed into element blocks by extended planar fractures. Finally, the element blocks are combined and the subdomains are assembled to form complex blocks. The combination of two subdomains is skipped if and only if the common facet lies on a curved fracture. In this study, the exact arithmetic is used to handle the computational errors, which may threat the robustness of the block identification program when the degenerated cases are encountered. Specifically, a real number is represented as the ratio between two integers and the basic arithmetic such as addition, subtraction, multiplication and division between different real numbers can be performed exactly if an arbitrary precision integer package is used. In this way, the exact construction of blocks can be achieved without introducing computational errors. Several analytical examples are given in this paper and the results show effectiveness of this method in handling arbitrary shaped blocks. Moreover, there is no limitation on the number of blocks in a block system. The results also show (suggest) that the degenerated cases can be handled without affecting the robustness of the identification program.

Differential recruitment of brain networks in single-digit addition and multiplication: Evidence from EEG oscillations in theta and lower alpha bands.

PubMed

Wang, Lihan; Gan, John Q; Zhang, Li; Wang, Haixian

2018-06-01

Previous neuroimaging research investigating dissociation between single-digit addition and multiplication has suggested that the former placed more reliance on the visuo-spatial processing whereas the latter on the verbal processing. However, there has been little exploration into the disassociation in spatio-temporal dynamics of the oscillatory brain activity in specific frequency bands during the two arithmetic operations. To address this issue, the electroencephalogram (EEG) data were recorded from 19 participants engaged in a delayed verification arithmetic task. By analyzing oscillatory EEG activity in theta (5-7 Hz) and lower alpha frequency (9-10 Hz) bands, we found different patterns of oscillatory brain activity between single-digit addition and multiplication during the early processing stage (0-400 ms post-operand onset). Experiment results in this study showed a larger phasic increase of theta-band power for addition than for multiplication in the midline and the right frontal and central regions during the operator and operands presentation intervals, which was extended to the right parietal and the right occipito-temporal regions during the interval immediately after the operands presentation. In contrast, during multiplication higher phase-locking in lower alpha band was evident in the centro-parietal regions during the operator presentation, which was extended to the left fronto-central and anterior regions during the operands presentation. Besides, we found stronger theta phase synchrony between the parietal areas and the right occipital areas for single-digit addition than for multiplication during operands encoding. These findings of oscillatory brain activity extend the previous observations on functional dissociation between the two arithmetic operations. Copyright © 2018 Elsevier B.V. All rights reserved.

Neural computation of arithmetic functions

NASA Technical Reports Server (NTRS)

Siu, Kai-Yeung; Bruck, Jehoshua

1990-01-01

An area of application of neural networks is considered. A neuron is modeled as a linear threshold gate, and the network architecture considered is the layered feedforward network. It is shown how common arithmetic functions such as multiplication and sorting can be efficiently computed in a shallow neural network. Some known results are improved by showing that the product of two n-bit numbers and sorting of n n-bit numbers can be computed by a polynomial-size neural network using only four and five unit delays, respectively. Moreover, the weights of each threshold element in the neural networks require O(log n)-bit (instead of n-bit) accuracy. These results can be extended to more complicated functions such as multiple products, division, rational functions, and approximation of analytic functions.

Multiple task performance as a predictor of the potential of air traffic controller trainees : a followup study.

DOT National Transportation Integrated Search

1974-11-01

Two hundred and twenty-nine air traffic controller trainees were tested on the CAMI Multiple Task Performance Battery. The battery provides objective measures of monitoring, arithmetical skills, visual discrimination, and group problem solving. The c...

Neurocognitive accounts of developmental dyscalculia and its remediation.

PubMed

Iuculano, T

2016-01-01

Numbers are one of the most pervasive stimulus categories in our environment and an integral foundation of modern society. Yet, up to 20% of individuals fail to understand, represent, and manipulate numbers and form the basis of arithmetic, a condition termed developmental dyscalculia (DD). Multiple cognitive and neural systems including those that serve numerical, mnemonic, visuospatial, and cognitive control functions have independently been implicated in the etiology of DD, yet most studies have not taken a comprehensive or dynamic view of the disorder. This chapter supports the view of DD as a multifaceted neurodevelopmental disorder that is the result of multiple aberrancies at one or multiple levels of the information processing hierarchy, which supports successful arithmetic learning, and suggests that interventions should target all these systems to achieve successful outcomes, at the behavioral and neural levels. © 2016 Elsevier B.V. All rights reserved.

Symptoms of anxiety and depression are related to cardiovascular responses to active, but not passive, coping tasks.

PubMed

Yuenyongchaiwat, Kornanong; Baker, Ian S; Sheffield, David

2017-01-01

Anxiety and depression have been linked to blunted blood pressure (BP) and heart rate (HR) reactions to mental stress tests; however, most studies have not included indices of underlying hemodynamics nor multiple stress tasks. This study sought to examine the relationships of anxiety and depression with hemodynamic responses to acute active and passive coping tasks. A total of 104 participants completed the Hospital Anxiety and Depression Scales and mental arithmetic, speech, and cold pressor tasks while BP, HR, total peripheral resistance, and cardiac output (CO) were assessed. After adjustment for traditional risk factors and baseline cardiovascular activity, depression scores were negatively associated with systolic BP, HR, and CO responses to the mental arithmetic task, while anxiety scores were inversely related to the systolic BP response to mental arithmetic. High anxiety or depression scores appear to be associated with blunted cardiac reactions to mental arithmetic (an active coping task), but not to the cold pressor test or speech tasks. Future research should further examine potential mechanisms and longitudinal pathways relating depression and anxiety to cardiovascular reactivity. TCTR20160208004.

Neurocognitive predictors of financial capacity in traumatic brain injury.

PubMed

Martin, Roy C; Triebel, Kristen; Dreer, Laura E; Novack, Thomas A; Turner, Crystal; Marson, Daniel C

2012-01-01

To develop cognitive models of financial capacity (FC) in patients with traumatic brain injury (TBI). Longitudinal design. Inpatient brain injury rehabilitation unit. Twenty healthy controls, and 24 adults with moderate-to-severe TBI were assessed at baseline (30 days postinjury) and 6 months postinjury. The FC instrument (FCI) and a neuropsychological test battery. Univariate correlation and multiple regression procedures were employed to develop cognitive models of FCI performance in the TBI group, at baseline and 6-month time follow-up. Three cognitive predictor models of FC were developed. At baseline, measures of mental arithmetic/working memory and immediate verbal memory predicted baseline FCI performance (R = 0.72). At 6-month follow-up, measures of executive function and mental arithmetic/working memory predicted 6-month FCI performance (R = 0.79), and a third model found that these 2 measures at baseline predicted 6-month FCI performance (R = 0.71). Multiple cognitive functions are associated with initial impairment and partial recovery of FC in moderate-to-severe TBI patients. In particular, arithmetic, working memory, and executive function skills appear critical to recovery of FC in TBI. The study results represent an initial step toward developing a neurocognitive model of FC in patients with TBI.

Bit-parallel arithmetic in a massively-parallel associative processor

NASA Technical Reports Server (NTRS)

Scherson, Isaac D.; Kramer, David A.; Alleyne, Brian D.

1992-01-01

A simple but powerful new architecture based on a classical associative processor model is presented. Algorithms for performing the four basic arithmetic operations both for integer and floating point operands are described. For m-bit operands, the proposed architecture makes it possible to execute complex operations in O(m) cycles as opposed to O(m exp 2) for bit-serial machines. A word-parallel, bit-parallel, massively-parallel computing system can be constructed using this architecture with VLSI technology. The operation of this system is demonstrated for the fast Fourier transform and matrix multiplication.

Reduced Precision Redundancy Applied to Arithmetic Operations in Field Programmable Gate Arrays for Satellite Control and Sensor Systems

DTIC Science & Technology

2008-12-01

Figure 2. Definition of Attitude Angles and Torque Components in Spacecraft Reference Frame...Figure 5. PD controller in ideal three-axis-stabilized spacecraft ADCS. ................................16 Figure 6. Extract Position Angles function in...performance of spacecraft systems. Two categories of system architectures are discussed: recursive data management, found in feedback control systems; and

Enhanced Graphics for Extended Scale Range

NASA Technical Reports Server (NTRS)

Hanson, Andrew J.; Chi-Wing Fu, Philip

2012-01-01

Enhanced Graphics for Extended Scale Range is a computer program for rendering fly-through views of scene models that include visible objects differing in size by large orders of magnitude. An example would be a scene showing a person in a park at night with the moon, stars, and galaxies in the background sky. Prior graphical computer programs exhibit arithmetic and other anomalies when rendering scenes containing objects that differ enormously in scale and distance from the viewer. The present program dynamically repartitions distance scales of objects in a scene during rendering to eliminate almost all such anomalies in a way compatible with implementation in other software and in hardware accelerators. By assigning depth ranges correspond ing to rendering precision requirements, either automatically or under program control, this program spaces out object scales to match the precision requirements of the rendering arithmetic. This action includes an intelligent partition of the depth buffer ranges to avoid known anomalies from this source. The program is written in C++, using OpenGL, GLUT, and GLUI standard libraries, and nVidia GEForce Vertex Shader extensions. The program has been shown to work on several computers running UNIX and Windows operating systems.

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

PubMed Central

2012-01-01

Background The aim of the present functional magnetic resonance imaging (fMRI) study at 3 T was to investigate the influence of the verbal-visual cognitive style on cerebral activation patterns during mental arithmetic. In the domain of arithmetic, a visual style might for example mean to visualize numbers and (intermediate) results, and a verbal style might mean, that numbers and (intermediate) results are verbally repeated. In this study, we investigated, first, whether verbalizers show activations in areas for language processing, and whether visualizers show activations in areas for visual processing during mental arithmetic. Some researchers have proposed that the left and right intraparietal sulcus (IPS), and the left angular gyrus (AG), two areas involved in number processing, show some domain or modality specificity. That is, verbal for the left AG, and visual for the left and right IPS. We investigated, second, whether the activation in these areas implied in number processing depended on an individual's cognitive style. Methods 42 young healthy adults participated in the fMRI study. The study comprised two functional sessions. In the first session, subtraction and multiplication problems were presented in an event-related design, and in the second functional session, multiplications were presented in two formats, as Arabic numerals and as written number words, in an event-related design. The individual's habitual use of visualization and verbalization during mental arithmetic was assessed by a short self-report assessment. Results We observed in both functional sessions that the use of verbalization predicts activation in brain areas associated with language (supramarginal gyrus) and auditory processing (Heschl's gyrus, Rolandic operculum). However, we found no modulation of activation in the left AG as a function of verbalization. Conclusions Our results confirm that strong verbalizers use mental speech as a form of mental imagination more strongly than weak verbalizers. Moreover, our results suggest that the left AG has no specific affinity to the verbal domain and subserves number processing in a modality-general way. PMID:22404872

92 Years of the Ising Model: A High Resolution Monte Carlo Study

NASA Astrophysics Data System (ADS)

Xu, Jiahao; Ferrenberg, Alan M.; Landau, David P.

2018-04-01

Using extensive Monte Carlo simulations that employ the Wolff cluster flipping and data analysis with histogram reweighting and quadruple precision arithmetic, we have investigated the critical behavior of the simple cubic Ising model with lattice sizes ranging from 163 to 10243. By analyzing data with cross correlations between various thermodynamic quantities obtained from the same data pool, we obtained the critical inverse temperature K c = 0.221 654 626(5) and the critical exponent of the correlation length ν = 0.629 912(86) with precision that improves upon previous Monte Carlo estimates.

Arithmetic on Your Phone: A Large Scale Investigation of Simple Additions and Multiplications.

PubMed

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.

Arithmetic on Your Phone: A Large Scale Investigation of Simple Additions and Multiplications

PubMed Central

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

Operator Priming and Generalization of Practice in Adults' Simple Arithmetic

ERIC Educational Resources Information Center

Chen, Yalin; Campbell, Jamie I. D.

2016-01-01

There is a renewed debate about whether educated adults solve simple addition problems (e.g., 2 + 3) by direct fact retrieval or by fast, automatic counting-based procedures. Recent research testing adults' simple addition and multiplication showed that a 150-ms preview of the operator (+ or ×) facilitated addition, but not multiplication,…

Number Theoretic Background

NASA Astrophysics Data System (ADS)

Rudnick, Z.

Contents: 1. Introduction 2. Divisibility 2.1. Basics on Divisibility 2.2. The Greatest Common Divisor 2.3. The Euclidean Algorithm 2.4. The Diophantine Equation ax+by=c 3. Prime Numbers 3.1. The Fundamental Theorem of Arithmetic 3.2. There Are Infinitely Many Primes 3.3. The Density of Primes 3.4. Primes in Arithmetic Progressions 4. Continued Fractions 5. Modular Arithmetic 5.1. Congruences 5.2. Modular Inverses 5.3. The Chinese Remainder Theorem 5.4. The Structure of the Multiplicative Group (Z/NZ)^* 5.5. Primitive Roots 6. Quadratic Congruences 6.1. Euler's Criterion 6.2. The Legendre Symbol and Quadratic Reciprocity 7. Pell's Equation 7.1. The Group Law 7.2. Integer Solutions 7.3. Finding the Fundamental Solution 8. The Riemann Zeta Function 8.1 Analytic Continuation and Functinal Equation of ζ(s) 8.2 Connecting the Primes and the Zeros of ζ(s) 8.3 The Riemann Hypothesis References

Estimating cognitive workload using wavelet entropy-based features during an arithmetic task.

PubMed

Zarjam, Pega; Epps, Julien; Chen, Fang; Lovell, Nigel H

2013-12-01

Electroencephalography (EEG) has shown promise as an indicator of cognitive workload; however, precise workload estimation is an ongoing research challenge. In this investigation, seven levels of workload were induced using an arithmetic task, and the entropy of wavelet coefficients extracted from EEG signals is shown to distinguish all seven levels. For a subject-independent multi-channel classification scheme, the entropy features achieved high accuracy, up to 98% for channels from the frontal lobes, in the delta frequency band. This suggests that a smaller number of EEG channels in only one frequency band can be deployed for an effective EEG-based workload classification system. Together with analysis based on phase locking between channels, these results consistently suggest increased synchronization of neural responses for higher load levels. Copyright © 2013 Elsevier Ltd. All rights reserved.

Solving lattice QCD systems of equations using mixed precision solvers on GPUs

NASA Astrophysics Data System (ADS)

Clark, M. A.; Babich, R.; Barros, K.; Brower, R. C.; Rebbi, C.

2010-09-01

Modern graphics hardware is designed for highly parallel numerical tasks and promises significant cost and performance benefits for many scientific applications. One such application is lattice quantum chromodynamics (lattice QCD), where the main computational challenge is to efficiently solve the discretized Dirac equation in the presence of an SU(3) gauge field. Using NVIDIA's CUDA platform we have implemented a Wilson-Dirac sparse matrix-vector product that performs at up to 40, 135 and 212 Gflops for double, single and half precision respectively on NVIDIA's GeForce GTX 280 GPU. We have developed a new mixed precision approach for Krylov solvers using reliable updates which allows for full double precision accuracy while using only single or half precision arithmetic for the bulk of the computation. The resulting BiCGstab and CG solvers run in excess of 100 Gflops and, in terms of iterations until convergence, perform better than the usual defect-correction approach for mixed precision.

Nonsymbolic number and cumulative area representations contribute shared and unique variance to symbolic math competence

PubMed Central

Lourenco, Stella F.; Bonny, Justin W.; Fernandez, Edmund P.; Rao, Sonia

2012-01-01

Humans and nonhuman animals share the capacity to estimate, without counting, the number of objects in a set by relying on an approximate number system (ANS). Only humans, however, learn the concepts and operations of symbolic mathematics. Despite vast differences between these two systems of quantification, neural and behavioral findings suggest functional connections. Another line of research suggests that the ANS is part of a larger, more general system of magnitude representation. Reports of cognitive interactions and common neural coding for number and other magnitudes such as spatial extent led us to ask whether, and how, nonnumerical magnitude interfaces with mathematical competence. On two magnitude comparison tasks, college students estimated (without counting or explicit calculation) which of two arrays was greater in number or cumulative area. They also completed a battery of standardized math tests. Individual differences in both number and cumulative area precision (measured by accuracy on the magnitude comparison tasks) correlated with interindividual variability in math competence, particularly advanced arithmetic and geometry, even after accounting for general aspects of intelligence. Moreover, analyses revealed that whereas number precision contributed unique variance to advanced arithmetic, cumulative area precision contributed unique variance to geometry. Taken together, these results provide evidence for shared and unique contributions of nonsymbolic number and cumulative area representations to formally taught mathematics. More broadly, they suggest that uniquely human branches of mathematics interface with an evolutionarily primitive general magnitude system, which includes partially overlapping representations of numerical and nonnumerical magnitude. PMID:23091023

Modified signed-digit arithmetic based on redundant bit representation.

PubMed

Huang, H; Itoh, M; Yatagai, T

1994-09-10

Fully parallel modified signed-digit arithmetic operations are realized based on redundant bit representation of the digits proposed. A new truth-table minimizing technique is presented based on redundant-bitrepresentation coding. It is shown that only 34 minterms are enough for implementing one-step modified signed-digit addition and subtraction with this new representation. Two optical implementation schemes, correlation and matrix multiplication, are described. Experimental demonstrations of the correlation architecture are presented. Both architectures use fixed minterm masks for arbitrary-length operands, taking full advantage of the parallelism of the modified signed-digit number system and optics.

Individual differences in mathematical competence predict parietal brain activation during mental calculation.

PubMed

Grabner, Roland H; Ansari, Daniel; Reishofer, Gernot; Stern, Elsbeth; Ebner, Franz; Neuper, Christa

2007-11-01

Functional neuroimaging studies have revealed that parietal brain circuits subserve arithmetic problem solving and that their recruitment dynamically changes as a function of training and development. The present study investigated whether the brain activation during mental calculation is also modulated by individual differences in mathematical competence. Twenty-five adult students were selected from a larger pool based on their performance on standardized tests of intelligence and arithmetic and divided into groups of individuals with relatively lower and higher mathematical competence. These groups did not differ in their non-numerical intelligence or age. In an fMRI block-design, participants had to verify the correctness of single-digit and multi-digit multiplication problems. Analyses revealed that the individuals with higher mathematical competence displayed stronger activation of the left angular gyrus while solving both types of arithmetic problems. Additional correlational analyses corroborated the association between individual differences in mathematical competence and angular gyrus activation, even when variability in task performance was controlled for. These findings demonstrate that the recruitment of the left angular gyrus during arithmetic problem solving underlies individual differences in mathematical ability and suggests a stronger reliance on automatic, language-mediated processes in more competent individuals.

Designed cell consortia as fragrance-programmable analog-to-digital converters.

PubMed

Müller, Marius; Ausländer, Simon; Spinnler, Andrea; Ausländer, David; Sikorski, Julian; Folcher, Marc; Fussenegger, Martin

2017-03-01

Synthetic biology advances the rational engineering of mammalian cells to achieve cell-based therapy goals. Synthetic gene networks have nearly reached the complexity of digital electronic circuits and enable single cells to perform programmable arithmetic calculations or to provide dynamic remote control of transgenes through electromagnetic waves. We designed a synthetic multilayered gaseous-fragrance-programmable analog-to-digital converter (ADC) allowing for remote control of digital gene expression with 2-bit AND-, OR- and NOR-gate logic in synchronized cell consortia. The ADC consists of multiple sampling-and-quantization modules sensing analog gaseous fragrance inputs; a gas-to-liquid transducer converting fragrance intensity into diffusible cell-to-cell signaling compounds; a digitization unit with a genetic amplifier circuit to improve the signal-to-noise ratio; and recombinase-based digital expression switches enabling 2-bit processing of logic gates. Synthetic ADCs that can remotely control cellular activities with digital precision may enable the development of novel biosensors and may provide bioelectronic interfaces synchronizing analog metabolic pathways with digital electronics.

On the Rapid Computation of Various Polylogarithmic Constants

NASA Technical Reports Server (NTRS)

Bailey, David H.; Borwein, Peter; Plouffe, Simon

1996-01-01

We give algorithms for the computation of the d-th digit of certain transcendental numbers in various bases. These algorithms can be easily implemented (multiple precision arithmetic is not needed), require virtually no memory, and feature run times that scale nearly linearly with the order of the digit desired. They make it feasible to compute, for example, the billionth binary digit of log(2) or pi on a modest workstation in a few hours run time. We demonstrate this technique by computing the ten billionth hexadecimal digit of pi, the billionth hexadecimal digits of pi-squared, log(2) and log-squared(2), and the ten billionth decimal digit of log(9/10). These calculations rest on the observation that very special types of identities exist for certain numbers like pi, pi-squared, log(2) and log-squared(2). These are essentially polylogarithmic ladders in an integer base. A number of these identities that we derive in this work appear to be new, for example a critical identity for pi.

The bilinear complexity and practical algorithms for matrix multiplication

NASA Astrophysics Data System (ADS)

Smirnov, A. V.

2013-12-01

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

Student Strategies Suggesting Emergence of Mental Structures Supporting Logical and Abstract Thinking: Multiplicative Reasoning

ERIC Educational Resources Information Center

Carrier, Jim

2014-01-01

For many students, developing mathematical reasoning can prove to be challenging. Such difficulty may be explained by a deficit in the core understanding of many arithmetical concepts taught in early school years. Multiplicative reasoning is one such concept that produces an essential foundation upon which higher-level mathematical thinking skills…

Technical and Practical Issues in the Structure and Clinical Invariance of the Wechsler Scales: A Rejoinder to Commentaries

ERIC Educational Resources Information Center

Weiss, Lawrence G.; Keith, Timothy Z.; Zhu, Jianjun; Chen, Hsinyi

2013-01-01

This discussion article addresses issues related to expansion of the Wechsler model from four to five factors; multiple broad CHC abilities measured by the Arithmetic subtest; advantages and disadvantages of including complex tasks requiring integration of multiple broad abilities when measuring intelligence; limitations of factor analysis, which…

Efficient Probabilistic Diagnostics for Electrical Power Systems

NASA Technical Reports Server (NTRS)

Mengshoel, Ole J.; Chavira, Mark; Cascio, Keith; Poll, Scott; Darwiche, Adnan; Uckun, Serdar

2008-01-01

We consider in this work the probabilistic approach to model-based diagnosis when applied to electrical power systems (EPSs). Our probabilistic approach is formally well-founded, as it based on Bayesian networks and arithmetic circuits. We investigate the diagnostic task known as fault isolation, and pay special attention to meeting two of the main challenges . model development and real-time reasoning . often associated with real-world application of model-based diagnosis technologies. To address the challenge of model development, we develop a systematic approach to representing electrical power systems as Bayesian networks, supported by an easy-to-use speci.cation language. To address the real-time reasoning challenge, we compile Bayesian networks into arithmetic circuits. Arithmetic circuit evaluation supports real-time diagnosis by being predictable and fast. In essence, we introduce a high-level EPS speci.cation language from which Bayesian networks that can diagnose multiple simultaneous failures are auto-generated, and we illustrate the feasibility of using arithmetic circuits, compiled from Bayesian networks, for real-time diagnosis on real-world EPSs of interest to NASA. The experimental system is a real-world EPS, namely the Advanced Diagnostic and Prognostic Testbed (ADAPT) located at the NASA Ames Research Center. In experiments with the ADAPT Bayesian network, which currently contains 503 discrete nodes and 579 edges, we .nd high diagnostic accuracy in scenarios where one to three faults, both in components and sensors, were inserted. The time taken to compute the most probable explanation using arithmetic circuits has a small mean of 0.2625 milliseconds and standard deviation of 0.2028 milliseconds. In experiments with data from ADAPT we also show that arithmetic circuit evaluation substantially outperforms joint tree propagation and variable elimination, two alternative algorithms for diagnosis using Bayesian network inference.

BASIC2 INTERPRETER; minimal basic language. [MCS-80,8080-based microcomputers; 8080 Assembly language

DOE Office of Scientific and Technical Information (OSTI.GOV)

McGoldrick, P.R.; Allison, T.G.

The BASIC2 INTERPRETER was developed to provide a high-level easy-to-use language for performing both control and computational functions in the MCS-80. The package is supplied as two alternative implementations, hardware and software. The ''software'' implementation provides the following capabilities: entry and editing of BASIC programs, device-independent I/O, special functions to allow access from BASIC to any I/O port, formatted printing, special INPUT/OUTPUT-and-proceed statements to allow I/O without interrupting BASIC program execution, full arithmetic expressions, limited string manipulation (10 or fewer characters), shorthand forms for common BASIC keywords, immediate mode BASIC statement execution, and capability of running a BASIC program thatmore » is stored in PROM. The allowed arithmetic operations are addition, subtraction, multiplication, division, and raising a number to a positive integral power. In the second, or ''hardware'', implementation of BASIC2 requiring an Am9511 Arithmetic Processing Unit (APU) interfaced to the 8080 microprocessor, arithmetic operations are performed by the APU. The following additional built-in functions are available in this implementation: square root, sine, cosine, tangent, arcsine, arccosine, arctangent, exponential, logarithm base e, and logarithm base 10. MCS-80,8080-based microcomputers; 8080 Assembly language; Approximately 8K bytes of RAM to store the assembled interpreter, additional user program space, and necessary peripheral devices. The hardware implementation requires an Am9511 Arithmetic Processing Unit and an interface board (reference 2).« less

Vectors a Fortran 90 module for 3-dimensional vector and dyadic arithmetic

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brock, B.C.

1998-02-01

A major advance contained in the new Fortran 90 language standard is the ability to define new data types and the operators associated with them. Writing computer code to implement computations with real and complex three-dimensional vectors and dyadics is greatly simplified if the equations can be implemented directly, without the need to code the vector arithmetic explicitly. The Fortran 90 module described here defines new data types for real and complex 3-dimensional vectors and dyadics, along with the common operations needed to work with these objects. Routines to allow convenient initialization and output of the new types are alsomore » included. In keeping with the philosophy of data abstraction, the details of the implementation of the data types are maintained private, and the functions and operators are made generic to simplify the combining of real, complex, single- and double-precision vectors and dyadics.« less

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

NASA Astrophysics Data System (ADS)

Lieu, Richard

2018-01-01

A hierarchy of statistics of increasing sophistication and accuracy is proposed, to exploit an interesting and fundamental arithmetic structure in the photon bunching noise of incoherent light of large photon occupation number, with the purpose of suppressing the noise and rendering a more reliable and unbiased measurement of the light intensity. The method does not require any new hardware, rather it operates at the software level, with the help of high precision computers, to reprocess the intensity time series of the incident light to create a new series with smaller bunching noise coherence length. The ultimate accuracy improvement of this method of flux measurement is limited by the timing resolution of the detector and the photon occupation number of the beam (the higher the photon number the better the performance). The principal application is accuracy improvement in the bolometric flux measurement of a radio source.

What Kinds of Numbers Do Students Assign to Literal Symbols? Aspects of the Transition from Arithmetic to Algebra

ERIC Educational Resources Information Center

Christou, Konstantinos P.; Vosniadou, Stella

2012-01-01

Three experiments used multiple methods--open-ended assessments, multiple-choice questionnaires, and interviews--to investigate the hypothesis that the development of students' understanding of the concept of real variable in algebra may be influenced in fundamental ways by their initial concept of number, which seems to be organized around the…

A VLSI architecture for performing finite field arithmetic with reduced table look-up

NASA Technical Reports Server (NTRS)

Hsu, I. S.; Truong, T. K.; Reed, I. S.

1986-01-01

A new table look-up method for finding the log and antilog of finite field elements has been developed by N. Glover. In his method, the log and antilog of a field element is found by the use of several smaller tables. The method is based on a use of the Chinese Remainder Theorem. The technique often results in a significant reduction in the memory requirements of the problem. A VLSI architecture is developed for a special case of this new algorithm to perform finite field arithmetic including multiplication, division, and the finding of an inverse element in the finite field.

Memory Updating and Mental Arithmetic

PubMed Central

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. PMID:26869971

Neural correlates of mathematical problem solving.

PubMed

Lin, Chun-Ling; Jung, Melody; Wu, Ying Choon; She, Hsiao-Ching; Jung, Tzyy-Ping

2015-03-01

This study explores electroencephalography (EEG) brain dynamics associated with mathematical problem solving. EEG and solution latencies (SLs) were recorded as 11 neurologically healthy volunteers worked on intellectually challenging math puzzles that involved combining four single-digit numbers through basic arithmetic operators (addition, subtraction, division, multiplication) to create an arithmetic expression equaling 24. Estimates of EEG spectral power were computed in three frequency bands - θ (4-7 Hz), α (8-13 Hz) and β (14-30 Hz) - over a widely distributed montage of scalp electrode sites. The magnitude of power estimates was found to change in a linear fashion with SLs - that is, relative to a base of power spectrum, theta power increased with longer SLs, while alpha and beta power tended to decrease. Further, the topographic distribution of spectral fluctuations was characterized by more pronounced asymmetries along the left-right and anterior-posterior axes for solutions that involved a longer search phase. These findings reveal for the first time the topography and dynamics of EEG spectral activities important for sustained solution search during arithmetical problem solving.

On the interrelation of multiplication and division in secondary school children.

PubMed

Huber, Stefan; Fischer, Ursula; Moeller, Korbinian; Nuerk, Hans-Christoph

2013-01-01

Each division problem can be transformed into as a multiplication problem and vice versa. Recent research has indicated strong developmental parallels between multiplication and division in primary school children. In this study, we were interested in (i) whether these developmental parallels persist into secondary school, (ii) whether similar developmental parallels can be observed for simple and complex problems, (iii) whether skill level modulates this relationship, and (iv) whether the correlations are specific and not driven by general cognitive or arithmetic abilities. Therefore, we assessed performance of 5th and 6th graders attending two secondary school types of the German educational system in simple and complex multiplication as well as division while controlling for non-verbal intelligence, short-term memory, and other arithmetic abilities. Accordingly, we collected data from students differing in skills levels due to either age (5th < 6th grade) or school type (general < intermediate secondary school). We observed moderate to strong bivariate and partial correlations between multiplication and division with correlations being higher for simple tasks but nevertheless reliable for complex tasks. Moreover, the association between simple multiplication and division depended on students' skill levels as reflected by school types, but not by age. Partial correlations were higher for intermediate than for general secondary school children. In sum, these findings emphasize the importance of the inverse relationship between multiplication and division which persists into later developmental stages. However, evidence for skill-related differences in the relationship between multiplication and division was restricted to the differences for school types.

A Potpourri of Math Ideas.

ERIC Educational Resources Information Center

Weisberg, Phyllis G.

1987-01-01

The article offers practical games and "tricks" to help remediate deficits in arithmetic and mathematics at the elementary school level. Games include using the fingers to calculate, lattice multiplication, dividing paper into equal columns, square games, code cracking games, and fraction dominoes. (Author/DB)

How Children Choose among Serial Recall Strategies.

ERIC Educational Resources Information Center

McGilly, Kate; Siegler, Robert S.

1989-01-01

Investigated the serial recall strategies of 96 children aged 5-8 years by applying a theoretical and methodological approach originally developed to investigate preschoolers' arithmetic strategies. Results indicated the use of multiple approaches for serial recall and adaptive strategy choices. (RJC)

An interval precise integration method for transient unbalance response analysis of rotor system with uncertainty

NASA Astrophysics Data System (ADS)

Fu, Chao; Ren, Xingmin; Yang, Yongfeng; Xia, Yebao; Deng, Wangqun

2018-07-01

A non-intrusive interval precise integration method (IPIM) is proposed in this paper to analyze the transient unbalance response of uncertain rotor systems. The transfer matrix method (TMM) is used to derive the deterministic equations of motion of a hollow-shaft overhung rotor. The uncertain transient dynamic problem is solved by combing the Chebyshev approximation theory with the modified precise integration method (PIM). Transient response bounds are calculated by interval arithmetic of the expansion coefficients. Theoretical error analysis of the proposed method is provided briefly, and its accuracy is further validated by comparing with the scanning method in simulations. Numerical results show that the IPIM can keep good accuracy in vibration prediction of the start-up transient process. Furthermore, the proposed method can also provide theoretical guidance to other transient dynamic mechanical systems with uncertainties.

The contribution of general cognitive abilities and number abilities to different aspects of mathematics in children.

PubMed

Träff, Ulf

2013-10-01

This study examined the relative contributions of general cognitive abilities and number abilities to word problem solving, calculation, and arithmetic fact retrieval in a sample of 134 children aged 10 to 13 years. The following tasks were administered: listening span, visual matrix span, verbal fluency, color naming, Raven's Progressive Matrices, enumeration, number line estimation, and digit comparison. Hierarchical multiple regressions demonstrated that number abilities provided an independent contribution to fact retrieval and word problem solving. General cognitive abilities contributed to problem solving and calculation. All three number tasks accounted for a similar amount of variance in fact retrieval, whereas only the number line estimation task contributed unique variance in word problem solving. Verbal fluency and Raven's matrices accounted for an equal amount of variance in problem solving and calculation. The current findings demonstrate, in accordance with Fuchs and colleagues' developmental model of mathematical learning (Developmental Psychology, 2010, Vol. 46, pp. 1731-1746), that both number abilities and general cognitive abilities underlie 10- to 13-year-olds' proficiency in problem solving, whereas only number abilities underlie arithmetic fact retrieval. Thus, the amount and type of cognitive contribution to arithmetic proficiency varies between the different aspects of arithmetic. Furthermore, how closely linked a specific aspect of arithmetic is to the whole number representation systems is not the only factor determining the amount and type of cognitive contribution in 10- to 13-year-olds. In addition, the mathematical complexity of the task appears to influence the amount and type of cognitive support. Copyright © 2013 Elsevier Inc. All rights reserved.

On the interrelation of multiplication and division in secondary school children

PubMed Central

Huber, Stefan; Fischer, Ursula; Moeller, Korbinian; Nuerk, Hans-Christoph

2013-01-01

Multiplication and division are conceptually inversely related: Each division problem can be transformed into as a multiplication problem and vice versa. Recent research has indicated strong developmental parallels between multiplication and division in primary school children. In this study, we were interested in (i) whether these developmental parallels persist into secondary school, (ii) whether similar developmental parallels can be observed for simple and complex problems, (iii) whether skill level modulates this relationship, and (iv) whether the correlations are specific and not driven by general cognitive or arithmetic abilities. Therefore, we assessed performance of 5th and 6th graders attending two secondary school types of the German educational system in simple and complex multiplication as well as division while controlling for non-verbal intelligence, short-term memory, and other arithmetic abilities. Accordingly, we collected data from students differing in skills levels due to either age (5th < 6th grade) or school type (general < intermediate secondary school). We observed moderate to strong bivariate and partial correlations between multiplication and division with correlations being higher for simple tasks but nevertheless reliable for complex tasks. Moreover, the association between simple multiplication and division depended on students' skill levels as reflected by school types, but not by age. Partial correlations were higher for intermediate than for general secondary school children. In sum, these findings emphasize the importance of the inverse relationship between multiplication and division which persists into later developmental stages. However, evidence for skill-related differences in the relationship between multiplication and division was restricted to the differences for school types. PMID:24133476

Design and algorithm research of high precision airborne infrared touch screen

NASA Astrophysics Data System (ADS)

Zhang, Xiao-Bing; Wang, Shuang-Jie; Fu, Yan; Chen, Zhao-Quan

2016-10-01

There are shortcomings of low precision, touch shaking, and sharp decrease of touch precision when emitting and receiving tubes are failure in the infrared touch screen. A high precision positioning algorithm based on extended axis is proposed to solve these problems. First, the unimpeded state of the beam between emitting and receiving tubes is recorded as 0, while the impeded state is recorded as 1. Then, the method of oblique scan is used, in which the light of one emitting tube is used for five receiving tubes. The impeded information of all emitting and receiving tubes is collected as matrix. Finally, according to the method of arithmetic average, the position of the touch object is calculated. The extended axis positioning algorithm is characteristic of high precision in case of failure of individual infrared tube and affects slightly the precision. The experimental result shows that the 90% display area of the touch error is less than 0.25D, where D is the distance between adjacent emitting tubes. The conclusion is gained that the algorithm based on extended axis has advantages of high precision, little impact when individual infrared tube is failure, and using easily.

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

PubMed

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

2018-02-01

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

The Truth about PEDMAS

ERIC Educational Resources Information Center

Ameis, Jerry A.

2011-01-01

When learning the order of operations, students are instructed to adhere to a directive when determining the numerical value of an arithmetic expression. A more typical approach is the use of a popular mnemonic called PEDMAS (parentheses, exponents, division, multiplication, addition, subtraction). The literature is scant on conceptual approaches…

Signed-negabinary-arithmetic-based optical computing by use of a single liquid-crystal-display panel.

PubMed

Datta, Asit K; Munshi, Soumika

2002-03-10

Based on the negabinary number representation, parallel one-step arithmetic operations (that is, addition and subtraction), logical operations, and matrix-vector multiplication on data have been optically implemented, by use of a two-dimensional spatial-encoding technique. For addition and subtraction, one of the operands in decimal form is converted into the unsigned negabinary form, whereas the other decimal number is represented in the signed negabinary form. The result of operation is obtained in the mixed negabinary form and is converted back into decimal. Matrix-vector multiplication for unsigned negabinary numbers is achieved through the convolution technique. Both of the operands for logical operation are converted to their signed negabinary forms. All operations are implemented by use of a unique optical architecture. The use of a single liquid-crystal-display panel to spatially encode the input data, operational kernels, and decoding masks have simplified the architecture as well as reduced the cost and complexity.

lsjk—a C++ library for arbitrary-precision numeric evaluation of the generalized log-sine functions

NASA Astrophysics Data System (ADS)

Kalmykov, M. Yu.; Sheplyakov, A.

2005-10-01

Generalized log-sine functions Lsj(k)(θ) appear in higher order ɛ-expansion of different Feynman diagrams. We present an algorithm for the numerical evaluation of these functions for real arguments. This algorithm is implemented as a C++ library with arbitrary-precision arithmetics for integer 0⩽k⩽9 and j⩾2. Some new relations and representations of the generalized log-sine functions are given. Program summaryTitle of program:lsjk Catalogue number:ADVS Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADVS Program obtained from: CPC Program Library, Queen's University of Belfast, N. Ireland Licensing terms: GNU General Public License Computers:all Operating systems:POSIX Programming language:C++ Memory required to execute:Depending on the complexity of the problem, at least 32 MB RAM recommended No. of lines in distributed program, including testing data, etc.:41 975 No. of bytes in distributed program, including testing data, etc.:309 156 Distribution format:tar.gz Other programs called:The CLN library for arbitrary-precision arithmetics is required at version 1.1.5 or greater External files needed:none Nature of the physical problem:Numerical evaluation of the generalized log-sine functions for real argument in the region 0<θ<π. These functions appear in Feynman integrals Method of solution:Series representation for the real argument in the region 0<θ<π Restriction on the complexity of the problem:Limited up to Lsj(9)(θ), and j is an arbitrary integer number. Thus, all function up to the weight 12 in the region 0<θ<π can be evaluated. The algorithm can be extended up to higher values of k(k>9) without modification Typical running time:Depending on the complexity of problem. See text below.

Segmentation quality evaluation using region-based precision and recall measures for remote sensing images

NASA Astrophysics Data System (ADS)

Zhang, Xueliang; Feng, Xuezhi; Xiao, Pengfeng; He, Guangjun; Zhu, Liujun

2015-04-01

Segmentation of remote sensing images is a critical step in geographic object-based image analysis. Evaluating the performance of segmentation algorithms is essential to identify effective segmentation methods and optimize their parameters. In this study, we propose region-based precision and recall measures and use them to compare two image partitions for the purpose of evaluating segmentation quality. The two measures are calculated based on region overlapping and presented as a point or a curve in a precision-recall space, which can indicate segmentation quality in both geometric and arithmetic respects. Furthermore, the precision and recall measures are combined by using four different methods. We examine and compare the effectiveness of the combined indicators through geometric illustration, in an effort to reveal segmentation quality clearly and capture the trade-off between the two measures. In the experiments, we adopted the multiresolution segmentation (MRS) method for evaluation. The proposed measures are compared with four existing discrepancy measures to further confirm their capabilities. Finally, we suggest using a combination of the region-based precision-recall curve and the F-measure for supervised segmentation evaluation.

[A case of pure anarithmetia associated with disability in processing of abstract spatial relationship].

PubMed

Hirayama, Kazumi; Taguchi, Yuzuru; Tsukamoto, Tetsuro

2002-10-01

A 35-year-old right handed man developed pure anarithmetia after an left parieto-occipital subcortical hemorrhage. His intelligence, memory, language, and construction ability were all within normal limits. No hemispatial neglect, agraphia, finger agnosia, or right-left disorientation were noted. He showed no impairments in reading numbers aloud, pointing to written numbers, writing numbers to dictation, decomposition of numbers, estimation of numbers of dots, reading and writing of arithmetic signs, comprehension of arithmetic signs, appreciation of number values, appreciation of dots' number, counting aloud, alignment numbers, comprehension of the commulative law and the distributive law, retrieval of the table value (ku-ku), immediate memory for arithmetic problems, and use of electric calculator. He showed, however, remarkable difficulty even in addition and subtraction between one figure digits, and used counting on his fingers or intuitive strategy to solve the problems even when he could solve them. He could not execute multiplication and division, if the problems required other than the table value (ku-ku). Thus, he seemed to have difficulties in both of elemental arithmetic facts and calculating procedures. In addition, his backward digit span and reading of analogue clocks were deteriorated, and he showed logico-grammatical disorder of Luria. Our case supports the notion that there is a neural system which was shared in part between processing of abstract spatial relationship and calculation.

Magnitude knowledge: the common core of numerical development.

PubMed

Siegler, Robert S

2016-05-01

The integrated theory of numerical development posits that a central theme of numerical development from infancy to adulthood is progressive broadening of the types and ranges of numbers whose magnitudes are accurately represented. The process includes four overlapping trends: (1) representing increasingly precisely the magnitudes of non-symbolic numbers, (2) connecting small symbolic numbers to their non-symbolic referents, (3) extending understanding from smaller to larger whole numbers, and (4) accurately representing the magnitudes of rational numbers. The present review identifies substantial commonalities, as well as differences, in these four aspects of numerical development. With both whole and rational numbers, numerical magnitude knowledge is concurrently correlated with, longitudinally predictive of, and causally related to multiple aspects of mathematical understanding, including arithmetic and overall math achievement. Moreover, interventions focused on increasing numerical magnitude knowledge often generalize to other aspects of mathematics. The cognitive processes of association and analogy seem to play especially large roles in this development. Thus, acquisition of numerical magnitude knowledge can be seen as the common core of numerical development. © 2016 John Wiley & Sons Ltd.

Using femtosecond laser to fabricate highly precise interior three-dimensional microstructures in polymeric flow chip

PubMed Central

Lee, Chia-Yu; Chang, Ting-Chou; Wang, Shau-Chun; Chien, Chih-Wei; Cheng, Chung-Wei

2010-01-01

This paper reports using femtosecond laser marker to fabricate the three-dimensional interior microstructures in one closed flow channel of plastic substrate. Strip-like slots in the dimensions of 800 μm×400 μm×65 μm were ablated with pulse Ti:sapphire laser at 800 nm (pulse duration of ∼120 fs with 1 kHz repetition rate) on acrylic slide. After ablation, defocused beams were used to finish the surface of microstructures. Having finally polished with sonication, the laser fabricated structures are highly precise with the arithmetic roughness of 1.5 and 4.5 nm. Fabricating such highly precise microstructures cannot be accomplished with nanosecond laser marking or other mechanical drilling methods. In addition, since laser ablation can directly engrave interior microstructures in one closed chip, glue smearing problems to damage molded microstructures possibly to occur during the chip sealing procedures can be avoided too. PMID:21079695

Using femtosecond laser to fabricate highly precise interior three-dimensional microstructures in polymeric flow chip.

PubMed

Lee, Chia-Yu; Chang, Ting-Chou; Wang, Shau-Chun; Chien, Chih-Wei; Cheng, Chung-Wei

2010-10-18

This paper reports using femtosecond laser marker to fabricate the three-dimensional interior microstructures in one closed flow channel of plastic substrate. Strip-like slots in the dimensions of 800 μm×400 μm×65 μm were ablated with pulse Ti:sapphire laser at 800 nm (pulse duration of ∼120 fs with 1 kHz repetition rate) on acrylic slide. After ablation, defocused beams were used to finish the surface of microstructures. Having finally polished with sonication, the laser fabricated structures are highly precise with the arithmetic roughness of 1.5 and 4.5 nm. Fabricating such highly precise microstructures cannot be accomplished with nanosecond laser marking or other mechanical drilling methods. In addition, since laser ablation can directly engrave interior microstructures in one closed chip, glue smearing problems to damage molded microstructures possibly to occur during the chip sealing procedures can be avoided too.

Pushing the limits of Monte Carlo simulations for the three-dimensional Ising model

NASA Astrophysics Data System (ADS)

Ferrenberg, Alan M.; Xu, Jiahao; Landau, David P.

2018-04-01

While the three-dimensional Ising model has defied analytic solution, various numerical methods like Monte Carlo, Monte Carlo renormalization group, and series expansion have provided precise information about the phase transition. Using Monte Carlo simulation that employs the Wolff cluster flipping algorithm with both 32-bit and 53-bit random number generators and data analysis with histogram reweighting and quadruple precision arithmetic, we have investigated the critical behavior of the simple cubic Ising Model, with lattice sizes ranging from 163 to 10243. By analyzing data with cross correlations between various thermodynamic quantities obtained from the same data pool, e.g., logarithmic derivatives of magnetization and derivatives of magnetization cumulants, we have obtained the critical inverse temperature Kc=0.221 654 626 (5 ) and the critical exponent of the correlation length ν =0.629 912 (86 ) with precision that exceeds all previous Monte Carlo estimates.

When listening to rain sounds boosts arithmetic ability

PubMed Central

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. PMID:29466472

When listening to rain sounds boosts arithmetic ability.

PubMed

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.

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lieu, Richard

A hierarchy of statistics of increasing sophistication and accuracy is proposed to exploit an interesting and fundamental arithmetic structure in the photon bunching noise of incoherent light of large photon occupation number, with the purpose of suppressing the noise and rendering a more reliable and unbiased measurement of the light intensity. The method does not require any new hardware, rather it operates at the software level with the help of high-precision computers to reprocess the intensity time series of the incident light to create a new series with smaller bunching noise coherence length. The ultimate accuracy improvement of this methodmore » of flux measurement is limited by the timing resolution of the detector and the photon occupation number of the beam (the higher the photon number the better the performance). The principal application is accuracy improvement in the signal-limited bolometric flux measurement of a radio source.« less

Strategy over operation: neural activation in subtraction and multiplication during fact retrieval and procedural strategy use in children.

PubMed

Polspoel, Brecht; Peters, Lien; Vandermosten, Maaike; De Smedt, Bert

2017-09-01

Arithmetic development is characterized by strategy shifts between procedural strategy use and fact retrieval. This study is the first to explicitly investigate children's neural activation associated with the use of these different strategies. Participants were 26 typically developing 4th graders (9- to 10-year-olds), who, in a behavioral session, were asked to verbally report on a trial-by-trial basis how they had solved 100 subtraction and multiplication items. These items were subsequently presented during functional magnetic resonance imaging. An event-related design allowed us to analyze the brain responses during retrieval and procedural trials, based on the children's verbal reports. During procedural strategy use, and more specifically for the decomposition of operands strategy, activation increases were observed in the inferior and superior parietal lobes (intraparietal sulci), inferior to superior frontal gyri, bilateral areas in the occipital lobe, and insular cortex. For retrieval, in comparison to procedural strategy use, we observed increased activity in the bilateral angular and supramarginal gyri, left middle to inferior temporal gyrus, right superior temporal gyrus, and superior medial frontal gyrus. No neural differences were found between the two operations under study. These results are the first in children to provide direct evidence for alternate neural activation when different arithmetic strategies are used and further unravel that previously found effects of operation on brain activity reflect differences in arithmetic strategy use. Hum Brain Mapp 38:4657-4670, 2017. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.

Percolation on shopping and cashback electronic commerce networks

NASA Astrophysics Data System (ADS)

Fu, Tao; Chen, Yini; Qin, Zhen; Guo, Liping

2013-06-01

Many realistic networks live in the form of multiple networks, including interacting networks and interdependent networks. Here we study percolation properties of a special kind of interacting networks, namely Shopping and Cashback Electronic Commerce Networks (SCECNs). We investigate two actual SCECNs to extract their structural properties, and develop a mathematical framework based on generating functions for analyzing directed interacting networks. Then we derive the necessary and sufficient condition for the absence of the system-wide giant in- and out- component, and propose arithmetic to calculate the corresponding structural measures in the sub-critical and supercritical regimes. We apply our mathematical framework and arithmetic to those two actual SCECNs to observe its accuracy, and give some explanations on the discrepancies. We show those structural measures based on our mathematical framework and arithmetic are useful to appraise the status of SCECNs. We also find that the supercritical regime of the whole network is maintained mainly by hyperlinks between different kinds of websites, while those hyperlinks between the same kinds of websites can only enlarge the sizes of in-components and out-components.

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

PubMed Central

Daches Cohen, Lital; Rubinsten, Orly

2017-01-01

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

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

NASA Technical Reports Server (NTRS)

Habiby, Sarry F.

1987-01-01

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

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

PubMed

Daches Cohen, Lital; Rubinsten, Orly

2017-01-01

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

Study on Dynamic Alignment Technology of COIL Resonator

NASA Astrophysics Data System (ADS)

Xiong, M. D.; Zou, X. J.; Guo, J. H.; Jia, S. N.; Zhang2, Z. B.

2006-10-01

The performance of great power chemical oxygen-iodine laser (COIL) beam is decided mostly by resonator mirror maladjustment and environment vibration. To improve the performance of light beam, an auto-alignment device is used in COIL resonator, the device can keep COIL resonator collimating by adjusting the optical components of resonator. So the coupling model of COIL resonator is present. The multivariable self study fuzzy uncoupling arithmetic and six-dimensional micro drive technology are used to design a six-input-three-output uncoupling controller, resulting in the realization of the high precision dynamic alignment. The experiments indicate that the collimating range of this system is 8 mrad, precision is 5 urad and frequency response is 20Hz, which meet the demand of resonator alignment system.

Triangle Geometry Processing for Surface Modeling and Cartesian Grid Generation

NASA Technical Reports Server (NTRS)

Aftosmis, Michael J. (Inventor); Melton, John E. (Inventor); Berger, Marsha J. (Inventor)

2002-01-01

Cartesian mesh generation is accomplished for component based geometries, by intersecting components subject to mesh generation to extract wetted surfaces with a geometry engine using adaptive precision arithmetic in a system which automatically breaks ties with respect to geometric degeneracies. During volume mesh generation, intersected surface triangulations are received to enable mesh generation with cell division of an initially coarse grid. The hexagonal cells are resolved, preserving the ability to directionally divide cells which are locally well aligned.

Triangle geometry processing for surface modeling and cartesian grid generation

DOEpatents

Aftosmis, Michael J [San Mateo, CA; Melton, John E [Hollister, CA; Berger, Marsha J [New York, NY

2002-09-03

Cartesian mesh generation is accomplished for component based geometries, by intersecting components subject to mesh generation to extract wetted surfaces with a geometry engine using adaptive precision arithmetic in a system which automatically breaks ties with respect to geometric degeneracies. During volume mesh generation, intersected surface triangulations are received to enable mesh generation with cell division of an initially coarse grid. The hexagonal cells are resolved, preserving the ability to directionally divide cells which are locally well aligned.

Implementation details of the coupled QMR algorithm

NASA Technical Reports Server (NTRS)

Freund, Roland W.; Nachtigal, Noel M.

1992-01-01

The original quasi-minimal residual method (QMR) relies on the three-term look-ahead Lanczos process, to generate basis vectors for the underlying Krylov subspaces. However, empirical observations indicate that, in finite precision arithmetic, three-term vector recurrences are less robust than mathematically equivalent coupled two-term recurrences. Therefore, we recently proposed a new implementation of the QMR method based on a coupled two-term look-ahead Lanczos procedure. In this paper, we describe implementation details of this coupled QMR algorithm, and we present results of numerical experiments.

The most precise computations using Euler's method in standard floating-point arithmetic applied to modelling of biological systems.

PubMed

Kalinina, Elizabeth A

2013-08-01

The explicit Euler's method is known to be very easy and effective in implementation for many applications. This article extends results previously obtained for the systems of linear differential equations with constant coefficients to arbitrary systems of ordinary differential equations. Optimal (providing minimum total error) step size is calculated at each step of Euler's method. Several examples of solving stiff systems are included. Copyright © 2013 Elsevier Ireland Ltd. All rights reserved.

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

PubMed

Domahs, Frank; Zamarian, Laura; Delazer, Margarete

2008-04-01

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

40 CFR 98.243 - Calculating GHG emissions.

Code of Federal Regulations, 2014 CFR

2014-07-01

...(b)(1) through (3). (c) Mass balance for each petrochemical process unit. Calculate the emissions of... determine the carbon content of each sample according to the procedures of § 98.244(b)(4). If multiple valid carbon content measurements are made during the monthly measurement period, average them arithmetically...

Can Dyscalculics Estimate the Results of Arithmetic Problems?

ERIC Educational Resources Information Center

Ganor-Stern, Dana

2017-01-01

The present study is the first to examine the computation estimation skills of dyscalculics versus controls using the estimation comparison task. In this task, participants judged whether an estimated answer to a multidigit multiplication problem was larger or smaller than a given reference number. While dyscalculics were less accurate than…

Predicting Arithmetic Abilities: The Role of Preparatory Arithmetic Markers and Intelligence

ERIC Educational Resources Information Center

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…

Effects of using multi-vide ruler kit in the acquisition of numeracy skills among PROTIM students

NASA Astrophysics Data System (ADS)

Arumugan, Hemalatha A./P.; Obeng, Sharifah Nasriah Wan; Talib, Corrienna Abdul; Bunyamin, Muhammad Abdul Hadi; Ali, Marlina; Ibrahim, Norhasniza; Zawadzki, Rainer

2017-08-01

One effective way to teach arithmetic more interestingly and make it easier to learn is through the use of instructional materials. These can help students master certain mathematical skills, particularly multiplication and division, often considered difficult amongst primary school pupils. Nevertheless, the insufficiency of appropriate instructional materials causes difficulty in understanding how to use the proper technique or apply the concept, especially in multiplication. With this in mind, this study investigated whether the innovative and creative instructional material designed to assist and enhance numeracy skills, namely the Multi-vide Ruler kit, could increase students' ability in solving multiplication and division questions and whether it affected their interest in solving numeracy problems. Participants in this study included ten PROTIM (Program Tiga M [Three M Program] - membaca [reading], menulis [writing] dan mengira [calculate]) students, 9-10 years old, who had difficulties in reading, writing and arithmetic. In order to get appropriate support for qualitative research, a pre and post-test containing ten basic mathematical operations, was implemented together with the Multi-vide Ruler Kit. The findings of the qualitative case study, with the pre and post-tests, showed significant differences in their achievement and interest in two-digit multiplication and division operations. The results suggest that this approach could improve PROTIM student's ability to solve basic mathematical operations. What was most encouraging was the increase in students' interest in solving numeracy problems.

The high accuracy data processing system of laser interferometry signals based on MSP430

NASA Astrophysics Data System (ADS)

Qi, Yong-yue; Lin, Yu-chi; Zhao, Mei-rong

2009-07-01

Generally speaking there are two orthogonal signals used in single-frequency laser interferometer for differentiating direction and electronic subdivision. However there usually exist three errors with the interferential signals: zero offsets error, unequal amplitude error and quadrature phase shift error. These three errors have a serious impact on subdivision precision. Based on Heydemann error compensation algorithm, it is proposed to achieve compensation of the three errors. Due to complicated operation of the Heydemann mode, a improved arithmetic is advanced to decrease the calculating time effectively in accordance with the special characteristic that only one item of data will be changed in each fitting algorithm operation. Then a real-time and dynamic compensatory circuit is designed. Taking microchip MSP430 as the core of hardware system, two input signals with the three errors are turned into digital quantity by the AD7862. After data processing in line with improved arithmetic, two ideal signals without errors are output by the AD7225. At the same time two original signals are turned into relevant square wave and imported to the differentiating direction circuit. The impulse exported from the distinguishing direction circuit is counted by the timer of the microchip. According to the number of the pulse and the soft subdivision the final result is showed by LED. The arithmetic and the circuit are adopted to test the capability of a laser interferometer with 8 times optical path difference and the measuring accuracy of 12-14nm is achieved.

Procedural and Conceptual Changes in Young Children's Problem Solving

ERIC Educational Resources Information Center

Voutsina, Chronoula

2012-01-01

This study analysed the different types of arithmetic knowledge that young children utilise when solving a multiple-step addition task. The focus of the research was on the procedural and conceptual changes that occur as children develop their overall problem solving approach. Combining qualitative case study with a micro-genetic approach,…

Transitions in Learning: Evidence for Simultaneously Activated Strategies.

ERIC Educational Resources Information Center

Goldin-Meadow, Susan; And Others

Children rarely cite more than one strategy when asked to explain how they solved a particular arithmetic problem, hence their verbal explanations will not necessarily reveal whether they have considered multiple strategies on that problem. However, previous work has shown that, when asked to explain their performance on a task, children often use…

Tic Tac Toe Math. Instructional Guide.

ERIC Educational Resources Information Center

Cooper, Richard

This instructional guide and set of three companion workbooks are intended for use in an arithmetic course based on the Tic Tac Toe method of addition and multiplication, which is an alternative means of learning to add and multiply that was developed for students whose learning disabilities (including difficulty in distinguishing left from right…

Stages in Constructing and Coordinating Units Additively and Multiplicatively (Part 2)

ERIC Educational Resources Information Center

Ulrich, Catherine

2016-01-01

This is the second of a two-part article that presents a theory of unit construction and coordination that underlies radical constructivist empirical studies of student learning ranging from young students' counting strategies to high school students' algebraic reasoning. In Part I, I discussed the formation of arithmetical units and composite…

Stages in Constructing and Coordinating Units Additively and Multiplicatively (Part 1)

ERIC Educational Resources Information Center

Ulrich, Catherine

2015-01-01

This is the first of a two-part article that presents a theory of unit construction and coordination that underlies radical constructivist empirical studies of student learning ranging from young students' counting strategies to high school students' algebraic reasoning. My explanation starts with the formation of arithmetical units, which presage…

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

PubMed

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

2015-12-01

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

A method for deriving lower bounds for the complexity of monotone arithmetic circuits computing real polynomials

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gashkov, Sergey B; Sergeev, Igor' S

2012-10-31

This work suggests a method for deriving lower bounds for the complexity of polynomials with positive real coefficients implemented by circuits of functional elements over the monotone arithmetic basis {l_brace}x+y, x {center_dot} y{r_brace} Union {l_brace}a {center_dot} x | a Element-Of R{sub +}{r_brace}. Using this method, several new results are obtained. In particular, we construct examples of polynomials of degree m-1 in each of the n variables with coefficients 0 and 1 having additive monotone complexity m{sup (1-o(1))n} and multiplicative monotone complexity m{sup (1/2-o(1))n} as m{sup n}{yields}{infinity}. In this form, the lower bounds derived here are sharp. Bibliography: 72 titles.

Multiple advanced logic gates made of DNA-Ag nanocluster and the application for intelligent detection of pathogenic bacterial genes.

PubMed

Lin, Xiaodong; Liu, Yaqing; Deng, Jiankang; Lyu, Yanlong; Qian, Pengcheng; Li, Yunfei; Wang, Shuo

2018-02-21

The integration of multiple DNA logic gates on a universal platform to implement advance logic functions is a critical challenge for DNA computing. Herein, a straightforward and powerful strategy in which a guanine-rich DNA sequence lighting up a silver nanocluster and fluorophore was developed to construct a library of logic gates on a simple DNA-templated silver nanoclusters (DNA-AgNCs) platform. This library included basic logic gates, YES, AND, OR, INHIBIT, and XOR, which were further integrated into complex logic circuits to implement diverse advanced arithmetic/non-arithmetic functions including half-adder, half-subtractor, multiplexer, and demultiplexer. Under UV irradiation, all the logic functions could be instantly visualized, confirming an excellent repeatability. The logic operations were entirely based on DNA hybridization in an enzyme-free and label-free condition, avoiding waste accumulation and reducing cost consumption. Interestingly, a DNA-AgNCs-based multiplexer was, for the first time, used as an intelligent biosensor to identify pathogenic genes, E. coli and S. aureus genes, with a high sensitivity. The investigation provides a prototype for the wireless integration of multiple devices on even the simplest single-strand DNA platform to perform diverse complex functions in a straightforward and cost-effective way.

Quality of Arithmetic Education for Children with Cerebral Palsy

ERIC Educational Resources Information Center

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…

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

PubMed

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

2018-03-01

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

Abacus in the brain: a longitudinal functional MRI study of a skilled abacus user with a right hemispheric lesion.

PubMed

Tanaka, Satoshi; Seki, Keiko; Hanakawa, Takashi; Harada, Madoka; Sugawara, Sho K; Sadato, Norihiro; Watanabe, Katsumi; Honda, Manabu

2012-01-01

The abacus, a traditional physical calculation device, is still widely used in Asian countries. Previous behavioral work has shown that skilled abacus users perform rapid and precise mental arithmetic by manipulating a mental representation of an abacus, which is based on visual imagery. However, its neurophysiological basis remains unclear. Here, we report the case of a patient who was a good abacus user, but transiently lost her "mental abacus" and superior arithmetic performance after a stroke owing to a right hemispheric lesion including the dorsal premotor cortex (PMd) and inferior parietal lobule (IPL). Functional magnetic resonance imaging experiments were conducted 6 and 13 months after her stroke. In the mental calculation task, her brain activity was shifted from the language-related areas, including Broca's area and the left dorsolateral prefrontal and IPLs, to the visuospatial-related brain areas including the left superior parietal lobule (SPL), according to the recovery of her arithmetic abilities. In the digit memory task, activities in the bilateral SPL, and right visual association cortex were also observed after recovery. The shift of brain activities was consistent with her subjective report that she was able to shift the calculation strategy from linguistic to visuospatial as her mental abacus became stable again. In a behavioral experiment using an interference paradigm, a visual presentation of an abacus picture, but not a human face picture, interfered with the performance of her digit memory, confirming her use of the mental abacus after recovery. This is the first case report on the impairment of the mental abacus by a brain lesion and on recovery-related brain activity. We named this rare case "abacus-based acalculia." Together with previous neuroimaging studies, the present result suggests an important role for the PMd and parietal cortex in the superior arithmetic ability of abacus users.

Fish tissue lipid-C:N relationships for correcting δ(13) C values and estimating lipid content in aquatic food-web studies.

PubMed

Hoffman, Joel C; Sierszen, Michael E; Cotter, Anne M

2015-11-15

Normalizing δ(13) C values of animal tissue for lipid content is necessary to accurately interpret food-web relationships from stable isotope analysis. To reduce the effort and expense associated with chemical extraction of lipids, various studies have tested arithmetic mass balance to mathematically normalize δ(13) C values for lipid content; however, the approach assumes that lipid content is related to the tissue C:N ratio. We evaluated two commonly used models for estimating tissue lipid content based on C:N ratio (a mass balance model and a stoichiometric model) by comparing model predictions to measure the lipid content of white muscle tissue. We then determined the effect of lipid model choice on δ(13) C values normalized using arithmetic mass balance. To do so, we used a collection of fish from Lake Superior spanning a wide range in lipid content (5% to 73% lipid). We found that the lipid content was positively related to the bulk muscle tissue C:N ratio. The two different lipid models produced similar estimates of lipid content based on tissue C:N, within 6% for tissue C:N values <7. Normalizing δ(13) C values using an arithmetic mass-balance equation based on either model yielded similar results, with a small bias (<1‰) compared with results based on chemical extraction. Among-species consistency in the relationship between fish muscle tissue C:N ratio and lipid content supports the application of arithmetic mass balance to normalize δ(13) C values for lipid content. The uncertainty associated with both lipid extraction quality and choice of model parameters constrains the achievable precision of normalized δ(13) C values to about ±1.0‰. Published in 2015. This article is a U.S. Government work and is in the public domain in the U.S.A.

Implicit Learning of Arithmetic Regularities Is Facilitated by Proximal Contrast

PubMed Central

Prather, Richard W.

2012-01-01

Natural number arithmetic is a simple, powerful and important symbolic system. Despite intense focus on learning in cognitive development and educational research many adults have weak knowledge of the system. In current study participants learn arithmetic principles via an implicit learning paradigm. Participants learn not by solving arithmetic equations, but through viewing and evaluating example equations, similar to the implicit learning of artificial grammars. We expand this to the symbolic arithmetic system. Specifically we find that exposure to principle-inconsistent examples facilitates the acquisition of arithmetic principle knowledge if the equations are presented to the learning in a temporally proximate fashion. The results expand on research of the implicit learning of regularities and suggest that contrasting cases, show to facilitate explicit arithmetic learning, is also relevant to implicit learning of arithmetic. PMID:23119101

Arithmetic Circuit Verification Based on Symbolic Computer Algebra

NASA Astrophysics Data System (ADS)

Watanabe, Yuki; Homma, Naofumi; Aoki, Takafumi; Higuchi, Tatsuo

This paper presents a formal approach to verify arithmetic circuits using symbolic computer algebra. Our method describes arithmetic circuits directly with high-level mathematical objects based on weighted number systems and arithmetic formulae. Such circuit description can be effectively verified by polynomial reduction techniques using Gröbner Bases. In this paper, we describe how the symbolic computer algebra can be used to describe and verify arithmetic circuits. The advantageous effects of the proposed approach are demonstrated through experimental verification of some arithmetic circuits such as multiply-accumulator and FIR filter. The result shows that the proposed approach has a definite possibility of verifying practical arithmetic circuits.

Cognitive Analysis of Educational Games: The Number Game.

PubMed

van der Maas, Han L J; Nyamsuren, Enkhbold

2017-04-01

We analyze the cognitive strategies underlying performance in the Number task, a Math game that requires both arithmetic fluency and mathematical creativity. In this game all elements in a set of numbers (for instance, 2, 5, 9) have to be used precisely once to create a target number (for instance, 27) with basic arithmetic operations (solution: [5-2] × 9). We argue that some instances of this game are NP complete, by showing its relation to the well-known Partition problem. We propose heuristics based on the distinction in forward and backward reasoning. The Number Game is part of Math Garden, a popular online educational platform for practicing and monitoring math skills using innovations in computerized adaptive testing. These educational games generate enormous amounts of rich data on children's cognitive development. We found converging evidence for the use of forward proximity heuristics in the data of Math Garden, consisting of more than 20 million answers to 1,700 items. Item difficulties and the structure of correct answers were analyzed. Copyright © 2016 Cognitive Science Society, Inc.

The neural circuits for arithmetic principles.

PubMed

Liu, Jie; Zhang, Han; Chen, Chuansheng; Chen, Hui; Cui, Jiaxin; Zhou, Xinlin

2017-02-15

Arithmetic principles are the regularities underlying arithmetic computation. Little is known about how the brain supports the processing of arithmetic principles. The current fMRI study examined neural activation and functional connectivity during the processing of verbalized arithmetic principles, as compared to numerical computation and general language processing. As expected, arithmetic principles elicited stronger activation in bilateral horizontal intraparietal sulcus and right supramarginal gyrus than did language processing, and stronger activation in left middle temporal lobe and left orbital part of inferior frontal gyrus than did computation. In contrast, computation elicited greater activation in bilateral horizontal intraparietal sulcus (extending to posterior superior parietal lobule) than did either arithmetic principles or language processing. Functional connectivity analysis with the psychophysiological interaction approach (PPI) showed that left temporal-parietal (MTG-HIPS) connectivity was stronger during the processing of arithmetic principle and language than during computation, whereas parietal-occipital connectivities were stronger during computation than during the processing of arithmetic principles and language. Additionally, the left fronto-parietal (orbital IFG-HIPS) connectivity was stronger during the processing of arithmetic principles than during computation. The results suggest that verbalized arithmetic principles engage a neural network that overlaps but is distinct from the networks for computation and language processing. Copyright © 2016 Elsevier Inc. All rights reserved.

Towards a system-paced near-infrared spectroscopy brain-computer interface: differentiating prefrontal activity due to mental arithmetic and mental singing from the no-control state.

PubMed

Power, Sarah D; Kushki, Azadeh; Chau, Tom

2011-12-01

Near-infrared spectroscopy (NIRS) has recently been investigated as a non-invasive brain-computer interface (BCI) for individuals with severe motor impairments. For the most part, previous research has investigated the development of NIRS-BCIs operating under synchronous control paradigms, which require the user to exert conscious control over their mental activity whenever the system is vigilant. Though functional, this is mentally demanding and an unnatural way to communicate. An attractive alternative to the synchronous control paradigm is system-paced control, in which users are required to consciously modify their brain activity only when they wish to affect the BCI output, and can remain in a more natural, 'no-control' state at all other times. In this study, we investigated the feasibility of a system-paced NIRS-BCI with one intentional control (IC) state corresponding to the performance of either mental arithmetic or mental singing. In particular, this involved determining if these tasks could be distinguished, individually, from the unconstrained 'no-control' state. Deploying a dual-wavelength frequency domain near-infrared spectrometer, we interrogated nine sites around the frontopolar locations (International 10-20 System) while eight able-bodied adults performed mental arithmetic and mental singing to answer multiple-choice questions within a system-paced paradigm. With a linear classifier trained on a six-dimensional feature set, an overall classification accuracy of 71.2% across participants was achieved for the mental arithmetic versus no-control classification problem. While the mental singing versus no-control classification was less successful across participants (62.7% on average), four participants did attain accuracies well in excess of chance, three of which were above 70%. Analyses were performed offline. Collectively, these results are encouraging, and demonstrate the potential of a system-paced NIRS-BCI with one IC state corresponding to either mental arithmetic or mental singing.

Towards a system-paced near-infrared spectroscopy brain-computer interface: differentiating prefrontal activity due to mental arithmetic and mental singing from the no-control state

NASA Astrophysics Data System (ADS)

Power, Sarah D.; Kushki, Azadeh; Chau, Tom

2011-10-01

Near-infrared spectroscopy (NIRS) has recently been investigated as a non-invasive brain-computer interface (BCI) for individuals with severe motor impairments. For the most part, previous research has investigated the development of NIRS-BCIs operating under synchronous control paradigms, which require the user to exert conscious control over their mental activity whenever the system is vigilant. Though functional, this is mentally demanding and an unnatural way to communicate. An attractive alternative to the synchronous control paradigm is system-paced control, in which users are required to consciously modify their brain activity only when they wish to affect the BCI output, and can remain in a more natural, 'no-control' state at all other times. In this study, we investigated the feasibility of a system-paced NIRS-BCI with one intentional control (IC) state corresponding to the performance of either mental arithmetic or mental singing. In particular, this involved determining if these tasks could be distinguished, individually, from the unconstrained 'no-control' state. Deploying a dual-wavelength frequency domain near-infrared spectrometer, we interrogated nine sites around the frontopolar locations (International 10-20 System) while eight able-bodied adults performed mental arithmetic and mental singing to answer multiple-choice questions within a system-paced paradigm. With a linear classifier trained on a six-dimensional feature set, an overall classification accuracy of 71.2% across participants was achieved for the mental arithmetic versus no-control classification problem. While the mental singing versus no-control classification was less successful across participants (62.7% on average), four participants did attain accuracies well in excess of chance, three of which were above 70%. Analyses were performed offline. Collectively, these results are encouraging, and demonstrate the potential of a system-paced NIRS-BCI with one IC state corresponding to either mental arithmetic or mental singing.

Specificity and Overlap in Skills Underpinning Reading and Arithmetical Fluency

ERIC Educational Resources Information Center

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…

Obtaining identical results with double precision global accuracy on different numbers of processors in parallel particle Monte Carlo simulations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cleveland, Mathew A., E-mail: cleveland7@llnl.gov; Brunner, Thomas A.; Gentile, Nicholas A.

2013-10-15

We describe and compare different approaches for achieving numerical reproducibility in photon Monte Carlo simulations. Reproducibility is desirable for code verification, testing, and debugging. Parallelism creates a unique problem for achieving reproducibility in Monte Carlo simulations because it changes the order in which values are summed. This is a numerical problem because double precision arithmetic is not associative. Parallel Monte Carlo, both domain replicated and decomposed simulations, will run their particles in a different order during different runs of the same simulation because the non-reproducibility of communication between processors. In addition, runs of the same simulation using different domain decompositionsmore » will also result in particles being simulated in a different order. In [1], a way of eliminating non-associative accumulations using integer tallies was described. This approach successfully achieves reproducibility at the cost of lost accuracy by rounding double precision numbers to fewer significant digits. This integer approach, and other extended and reduced precision reproducibility techniques, are described and compared in this work. Increased precision alone is not enough to ensure reproducibility of photon Monte Carlo simulations. Non-arbitrary precision approaches require a varying degree of rounding to achieve reproducibility. For the problems investigated in this work double precision global accuracy was achievable by using 100 bits of precision or greater on all unordered sums which where subsequently rounded to double precision at the end of every time-step.« less

Foundation Mathematics for the Physical Sciences

NASA Astrophysics Data System (ADS)

Riley, K. F.; Hobson, M. P.

2011-03-01

1. Arithmetic and geometry; 2. Preliminary algebra; 3. Differential calculus; 4. Integral calculus; 5. Complex numbers and hyperbolic functions; 6. Series and limits; 7. Partial differentiation; 8. Multiple integrals; 9. Vector algebra; 10. Matrices and vector spaces; 11. Vector calculus; 12. Line, surface and volume integrals; 13. Laplace transforms; 14. Ordinary differential equations; 15. Elementary probability; Appendices; Index.

Student Solution Manual for Foundation Mathematics for the Physical Sciences

NASA Astrophysics Data System (ADS)

Riley, K. F.; Hobson, M. P.

2011-03-01

1. Arithmetic and geometry; 2. Preliminary algebra; 3. Differential calculus; 4. Integral calculus; 5. Complex numbers and hyperbolic functions; 6. Series and limits; 7. Partial differentiation; 8. Multiple integrals; 9. Vector algebra; 10. Matrices and vector spaces; 11. Vector calculus; 12. Line, surface and volume integrals; 13. Laplace transforms; 14. Ordinary differential equations; 15. Elementary probability; Appendix.

Sex and Personality Differences in Performance on Number Computation in 11-Year-Old Children.

ERIC Educational Resources Information Center

Riding, R. J.; Borg, M. G.

1987-01-01

Eighty-four 11-year-olds were grouped in three levels of extraversion on the basis of their Junior Eysenck Personality Inventory score. They were then given an arithmetic test consisting of addition, subtraction, division, and multiplication. A significant interaction between extraversion, sex, and type of operation was found. (Author/CH)

Examining Gender DIF on a Multiple-Choice Test of Mathematics: A Confirmatory Approach.

ERIC Educational Resources Information Center

Ryan, Katherine E.; Fan, Meichu

1996-01-01

Results for 3,244 female and 3,033 male junior high school students from the Second International Mathematics Study show that applied items in algebra, geometry, and computation were easier for males but arithmetic items were differentially easier for females. Implications of these findings for assessment and instruction are discussed. (SLD)

Commentary: Decaying Numerical Skills. "I Can't Divide by 60 in My Head!"

ERIC Educational Resources Information Center

Parslow, Graham R.

2010-01-01

As an undergraduate in the 1960s, the author mostly used a slide rule for calculations and a Marchant-brand motor-operated mechanical calculator for statistics. This was after an elementary education replete with learning multiplication tables and taking speed and accuracy tests in arithmetic. Times have changed and assuming even basic calculation…

Strategy Repetition in Young and Older Adults: A Study in Arithmetic

ERIC Educational Resources Information Center

Lemaire, Patrick; Leclère, Mariel

2014-01-01

We investigated a new phenomenon that sheds light on age-related differences in strategy selection: the strategy repetition phenomenon (i.e., tendency to repeat the same strategy over consecutive items). Young and older adults had to provide the best estimates of multiplication problems like 47 × 86. They had to select the best of 2 rounding…

The Inequality of Arithmetic and Geometric Means from Multiple Perspectives

ERIC Educational Resources Information Center

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…

Children's use of decomposition strategies mediates the visuospatial memory and arithmetic accuracy relation.

PubMed

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.

Exploring the Feasibility of a DNA Computer: Design of an ALU Using Sticker-Based DNA Model.

PubMed

Sarkar, Mayukh; Ghosal, Prasun; Mohanty, Saraju P

2017-09-01

Since its inception, DNA computing has advanced to offer an extremely powerful, energy-efficient emerging technology for solving hard computational problems with its inherent massive parallelism and extremely high data density. This would be much more powerful and general purpose when combined with other existing well-known algorithmic solutions that exist for conventional computing architectures using a suitable ALU. Thus, a specifically designed DNA Arithmetic and Logic Unit (ALU) that can address operations suitable for both domains can mitigate the gap between these two. An ALU must be able to perform all possible logic operations, including NOT, OR, AND, XOR, NOR, NAND, and XNOR; compare, shift etc., integer and floating point arithmetic operations (addition, subtraction, multiplication, and division). In this paper, design of an ALU has been proposed using sticker-based DNA model with experimental feasibility analysis. Novelties of this paper may be in manifold. First, the integer arithmetic operations performed here are 2s complement arithmetic, and the floating point operations follow the IEEE 754 floating point format, resembling closely to a conventional ALU. Also, the output of each operation can be reused for any next operation. So any algorithm or program logic that users can think of can be implemented directly on the DNA computer without any modification. Second, once the basic operations of sticker model can be automated, the implementations proposed in this paper become highly suitable to design a fully automated ALU. Third, proposed approaches are easy to implement. Finally, these approaches can work on sufficiently large binary numbers.

Frontal and Parietal Cortices Show Different Spatiotemporal Dynamics across Problem-solving Stages.

PubMed

Tschentscher, Nadja; Hauk, Olaf

2016-08-01

Arithmetic problem-solving can be conceptualized as a multistage process ranging from task encoding over rule and strategy selection to step-wise task execution. Previous fMRI research suggested a frontal-parietal network involved in the execution of complex numerical and nonnumerical tasks, but evidence is lacking on the particular contributions of frontal and parietal cortices across time. In an arithmetic task paradigm, we evaluated individual participants' "retrieval" and "multistep procedural" strategies on a trial-by-trial basis and contrasted those in time-resolved analyses using combined EEG and MEG. Retrieval strategies relied on direct retrieval of arithmetic facts (e.g., 2 + 3 = 5). Procedural strategies required multiple solution steps (e.g., 12 + 23 = 12 + 20 + 3 or 23 + 10 + 2). Evoked source analyses revealed independent activation dynamics within the first second of problem-solving in brain areas previously described as one network, such as the frontal-parietal cognitive control network: The right frontal cortex showed earliest effects of strategy selection for multistep procedural strategies around 300 msec, before parietal cortex activated around 700 msec. In time-frequency source power analyses, memory retrieval and multistep procedural strategies were differentially reflected in theta, alpha, and beta frequencies: Stronger beta and alpha desynchronizations emerged for procedural strategies in right frontal, parietal, and temporal regions as function of executive demands. Arithmetic fact retrieval was reflected in right prefrontal increases in theta power. Our results demonstrate differential brain dynamics within frontal-parietal networks across the time course of a problem-solving process, and analyses of different frequency bands allowed us to disentangle cortical regions supporting the underlying memory and executive functions.

Neurocognitive Predictors of Mathematical Processing in School-Aged Children with Spina Bifida and Their Typically Developing Peers: Attention, Working Memory, and Fine Motor Skills

PubMed Central

Raghubar, Kimberly P.; Barnes, Marcia A.; Dennis, Maureen; Cirino, Paul T.; Taylor, Heather; Landry, Susan

2015-01-01

Objective Math and attention are related in neurobiological and behavioral models of mathematical cognition. This study employed model-driven assessments of attention and math in children with spina bifida myelomeningocele (SBM), who have known math difficulties and specific attentional deficits, to more directly examine putative relations between attention and mathematical processing. The relation of other domain general abilities and math was also investigated. Method Participants were 9.5-year-old children with SBM (N = 44) and typically developing children (N = 50). Participants were administered experimental exact and approximate arithmetic tasks, and standardized measures of math fluency and calculation. Cognitive measures included the Attention Network Test (ANT), and standardized measures of fine motor skills, verbal working memory (WM), and visual-spatial WM. Results Children with SBM performed similarly to peers on exact arithmetic but more poorly on approximate and standardized arithmetic measures. On the ANT, children with SBM differed from controls on orienting attention but not alerting and executive attention. Multiple mediation models showed that: fine motor skills and verbal WM mediated the relation of group to approximate arithmetic; fine motor skills and visual-spatial WM mediated the relation of group to math fluency; and verbal and visual-spatial WM mediated the relation of group to math calculation. Attention was not a significant mediator of the effects of group for any aspect of math in this study. Conclusions Results are discussed with reference to models of attention, WM, and mathematical cognition. PMID:26011113

Visual perception can account for the close relation between numerosity processing and computational fluency.

PubMed

Zhou, Xinlin; Wei, Wei; Zhang, Yiyun; Cui, Jiaxin; Chen, Chuansheng

2015-01-01

Studies have shown that numerosity processing (e.g., comparison of numbers of dots in two dot arrays) is significantly correlated with arithmetic performance. Researchers have attributed this association to the fact that both tasks share magnitude processing. The current investigation tested an alternative hypothesis, which states that visual perceptual ability (as measured by a figure-matching task) can account for the close relation between numerosity processing and arithmetic performance (computational fluency). Four hundred and twenty four third- to fifth-grade children (220 boys and 204 girls, 8.0-11.0 years old; 120 third graders, 146 fourth graders, and 158 fifth graders) were recruited from two schools (one urban and one suburban) in Beijing, China. Six classes were randomly selected from each school, and all students in each selected class participated in the study. All children were given a series of cognitive and mathematical tests, including numerosity comparison, figure matching, forward verbal working memory, visual tracing, non-verbal matrices reasoning, mental rotation, choice reaction time, arithmetic tests and curriculum-based mathematical achievement test. Results showed that figure-matching ability had higher correlations with numerosity processing and computational fluency than did other cognitive factors (e.g., forward verbal working memory, visual tracing, non-verbal matrix reasoning, mental rotation, and choice reaction time). More important, hierarchical multiple regression showed that figure matching ability accounted for the well-established association between numerosity processing and computational fluency. In support of the visual perception hypothesis, the results suggest that visual perceptual ability, rather than magnitude processing, may be the shared component of numerosity processing and arithmetic performance.

Visual perception can account for the close relation between numerosity processing and computational fluency

PubMed Central

Zhou, Xinlin; Wei, Wei; Zhang, Yiyun; Cui, Jiaxin; Chen, Chuansheng

2015-01-01

Studies have shown that numerosity processing (e.g., comparison of numbers of dots in two dot arrays) is significantly correlated with arithmetic performance. Researchers have attributed this association to the fact that both tasks share magnitude processing. The current investigation tested an alternative hypothesis, which states that visual perceptual ability (as measured by a figure-matching task) can account for the close relation between numerosity processing and arithmetic performance (computational fluency). Four hundred and twenty four third- to fifth-grade children (220 boys and 204 girls, 8.0–11.0 years old; 120 third graders, 146 fourth graders, and 158 fifth graders) were recruited from two schools (one urban and one suburban) in Beijing, China. Six classes were randomly selected from each school, and all students in each selected class participated in the study. All children were given a series of cognitive and mathematical tests, including numerosity comparison, figure matching, forward verbal working memory, visual tracing, non-verbal matrices reasoning, mental rotation, choice reaction time, arithmetic tests and curriculum-based mathematical achievement test. Results showed that figure-matching ability had higher correlations with numerosity processing and computational fluency than did other cognitive factors (e.g., forward verbal working memory, visual tracing, non-verbal matrix reasoning, mental rotation, and choice reaction time). More important, hierarchical multiple regression showed that figure matching ability accounted for the well-established association between numerosity processing and computational fluency. In support of the visual perception hypothesis, the results suggest that visual perceptual ability, rather than magnitude processing, may be the shared component of numerosity processing and arithmetic performance. PMID:26441740

Neurocognitive predictors of mathematical processing in school-aged children with spina bifida and their typically developing peers: Attention, working memory, and fine motor skills.

PubMed

Raghubar, Kimberly P; Barnes, Marcia A; Dennis, Maureen; Cirino, Paul T; Taylor, Heather; Landry, Susan

2015-11-01

Math and attention are related in neurobiological and behavioral models of mathematical cognition. This study employed model-driven assessments of attention and math in children with spina bifida myelomeningocele (SBM), who have known math difficulties and specific attentional deficits, to more directly examine putative relations between attention and mathematical processing. The relation of other domain general abilities and math was also investigated. Participants were 9.5-year-old children with SBM (n = 44) and typically developing children (n = 50). Participants were administered experimental exact and approximate arithmetic tasks, and standardized measures of math fluency and calculation. Cognitive measures included the Attention Network Test (ANT), and standardized measures of fine motor skills, verbal working memory (WM), and visual-spatial WM. Children with SBM performed similarly to peers on exact arithmetic, but more poorly on approximate and standardized arithmetic measures. On the ANT, children with SBM differed from controls on orienting attention, but not on alerting and executive attention. Multiple mediation models showed that fine motor skills and verbal WM mediated the relation of group to approximate arithmetic; fine motor skills and visual-spatial WM mediated the relation of group to math fluency; and verbal and visual-spatial WM mediated the relation of group to math calculation. Attention was not a significant mediator of the effects of group for any aspect of math in this study. Results are discussed with reference to models of attention, WM, and mathematical cognition. (c) 2015 APA, all rights reserved).

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

PubMed

Huber, Maria; Kipman, Ulrike; Pletzer, Belinda

2014-07-01

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

A finite difference Hartree-Fock program for atoms and diatomic molecules

NASA Astrophysics Data System (ADS)

Kobus, Jacek

2013-03-01

The newest version of the two-dimensional finite difference Hartree-Fock program for atoms and diatomic molecules is presented. This is an updated and extended version of the program published in this journal in 1996. It can be used to obtain reference, Hartree-Fock limit values of total energies and multipole moments for a wide range of diatomic molecules and their ions in order to calibrate existing and develop new basis sets, calculate (hyper)polarizabilities (αzz, βzzz, γzzzz, Az,zz, Bzz,zz) of atoms, homonuclear and heteronuclear diatomic molecules and their ions via the finite field method, perform DFT-type calculations using LDA or B88 exchange functionals and LYP or VWN correlations ones or the self-consistent multiplicative constant method, perform one-particle calculations with (smooth) Coulomb and Krammers-Henneberger potentials and take account of finite nucleus models. The program is easy to install and compile (tarball+configure+make) and can be used to perform calculations within double- or quadruple-precision arithmetic. Catalogue identifier: ADEB_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADEB_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License version 2 No. of lines in distributed program, including test data, etc.: 171196 No. of bytes in distributed program, including test data, etc.: 9481802 Distribution format: tar.gz Programming language: Fortran 77, C. Computer: any 32- or 64-bit platform. Operating system: Unix/Linux. RAM: Case dependent, from few MB to many GB Classification: 16.1. Catalogue identifier of previous version: ADEB_v1_0 Journal reference of previous version: Comput. Phys. Comm. 98(1996)346 Does the new version supersede the previous version?: Yes Nature of problem: The program finds virtually exact solutions of the Hartree-Fock and density functional theory type equations for atoms, diatomic molecules and their ions. The lowest energy eigenstates of a given irreducible representation and spin can be obtained. The program can be used to perform one-particle calculations with (smooth) Coulomb and Krammers-Henneberger potentials and also DFT-type calculations using LDA or B88 exchange functionals and LYP or VWN correlations ones or the self-consistent multiplicative constant method. Solution method: Single-particle two-dimensional numerical functions (orbitals) are used to construct an antisymmetric many-electron wave function of the restricted open-shell Hartree-Fock model. The orbitals are obtained by solving the Hartree-Fock equations as coupled two-dimensional second-order (elliptic) partial differential equations (PDEs). The Coulomb and exchange potentials are obtained as solutions of the corresponding Poisson equations. The PDEs are discretized by the eighth-order central difference stencil on a two-dimensional single grid, and the resulting large and sparse system of linear equations is solved by the (multicolour) successive overrelaxation ((MC)SOR) method. The self-consistent-field iterations are interwoven with the (MC)SOR ones and orbital energies and normalization factors are used to monitor the convergence. The accuracy of solutions depends mainly on the grid and the system under consideration, which means that within double precision arithmetic one can obtain orbitals and energies having up to 12 significant figures. If more accurate results are needed, quadruple-precision floating-point arithmetic can be used. Reasons for new version: Additional features, many modifications and corrections, improved convergence rate, overhauled code and documentation. Summary of revisions: see ChangeLog found in tar.gz archive Restrictions: The present version of the program is restricted to 60 orbitals. The maximum grid size is determined at compilation time. Unusual features: The program uses two C routines for allocating and deallocating memory. Several BLAS (Basic Linear Algebra System) routines are emulated by the program. When possible they should be replaced by their library equivalents. Additional comments: automake and autoconf tools are required to build and compile the program; checked with f77, gfortran and ifort compilers Running time: Very case dependent - from a few CPU seconds for the H2 defined on a small grid up to several weeks for the Hartree-Fock-limit calculations for 40-50 electron molecules.

On the convergence and accuracy of the FDTD method for nanoplasmonics.

PubMed

Lesina, Antonino Calà; Vaccari, Alessandro; Berini, Pierre; Ramunno, Lora

2015-04-20

Use of the Finite-Difference Time-Domain (FDTD) method to model nanoplasmonic structures continues to rise - more than 2700 papers have been published in 2014 on FDTD simulations of surface plasmons. However, a comprehensive study on the convergence and accuracy of the method for nanoplasmonic structures has yet to be reported. Although the method may be well-established in other areas of electromagnetics, the peculiarities of nanoplasmonic problems are such that a targeted study on convergence and accuracy is required. The availability of a high-performance computing system (a massively parallel IBM Blue Gene/Q) allows us to do this for the first time. We consider gold and silver at optical wavelengths along with three "standard" nanoplasmonic structures: a metal sphere, a metal dipole antenna and a metal bowtie antenna - for the first structure comparisons with the analytical extinction, scattering, and absorption coefficients based on Mie theory are possible. We consider different ways to set-up the simulation domain, we vary the mesh size to very small dimensions, we compare the simple Drude model with the Drude model augmented with two critical points correction, we compare single-precision to double-precision arithmetic, and we compare two staircase meshing techniques, per-component and uniform. We find that the Drude model with two critical points correction (at least) must be used in general. Double-precision arithmetic is needed to avoid round-off errors if highly converged results are sought. Per-component meshing increases the accuracy when complex geometries are modeled, but the uniform mesh works better for structures completely fillable by the Yee cell (e.g., rectangular structures). Generally, a mesh size of 0.25 nm is required to achieve convergence of results to ∼ 1%. We determine how to optimally setup the simulation domain, and in so doing we find that performing scattering calculations within the near-field does not necessarily produces large errors but reduces the computational resources required.

Study on digital closed-loop system of silicon resonant micro-sensor

NASA Astrophysics Data System (ADS)

Xu, Yefeng; He, Mengke

2008-10-01

Designing a micro, high reliability weak signal extracting system is a critical problem need to be solved in the application of silicon resonant micro-sensor. The closed-loop testing system based on FPGA uses software to replace hardware circuit which dramatically decrease the system's mass and power consumption and make the system more compact, both correlation theory and frequency scanning scheme are used in extracting weak signal, the adaptive frequency scanning arithmetic ensures the system real-time. The error model was analyzed to show the solution to enhance the system's measurement precision. The experiment results show that the closed-loop testing system based on FPGA has the personality of low power consumption, high precision, high-speed, real-time etc, and also the system is suitable for different kinds of Silicon Resonant Micro-sensor.

A numerical comparison of discrete Kalman filtering algorithms: An orbit determination case study

NASA Technical Reports Server (NTRS)

Thornton, C. L.; Bierman, G. J.

1976-01-01

The numerical stability and accuracy of various Kalman filter algorithms are thoroughly studied. Numerical results and conclusions are based on a realistic planetary approach orbit determination study. The case study results of this report highlight the numerical instability of the conventional and stabilized Kalman algorithms. Numerical errors associated with these algorithms can be so large as to obscure important mismodeling effects and thus give misleading estimates of filter accuracy. The positive result of this study is that the Bierman-Thornton U-D covariance factorization algorithm is computationally efficient, with CPU costs that differ negligibly from the conventional Kalman costs. In addition, accuracy of the U-D filter using single-precision arithmetic consistently matches the double-precision reference results. Numerical stability of the U-D filter is further demonstrated by its insensitivity of variations in the a priori statistics.

Working memory and arithmetic calculation in children: the contributory roles of processing speed, short-term memory, and reading.

PubMed

Berg, Derek H

2008-04-01

The cognitive underpinnings of arithmetic calculation in children are noted to involve working memory; however, cognitive processes related to arithmetic calculation and working memory suggest that this relationship is more complex than stated previously. The purpose of this investigation was to examine the relative contributions of processing speed, short-term memory, working memory, and reading to arithmetic calculation in children. Results suggested four important findings. First, processing speed emerged as a significant contributor of arithmetic calculation only in relation to age-related differences in the general sample. Second, processing speed and short-term memory did not eliminate the contribution of working memory to arithmetic calculation. Third, individual working memory components--verbal working memory and visual-spatial working memory--each contributed unique variance to arithmetic calculation in the presence of all other variables. Fourth, a full model indicated that chronological age remained a significant contributor to arithmetic calculation in the presence of significant contributions from all other variables. Results are discussed in terms of directions for future research on working memory in arithmetic calculation.

Solving Math Problems Approximately: A Developmental Perspective

PubMed Central

Ganor-Stern, Dana

2016-01-01

Although solving arithmetic problems approximately is an important skill in everyday life, little is known about the development of this skill. Past research has shown that when children are asked to solve multi-digit multiplication problems approximately, they provide estimates that are often very far from the exact answer. This is unfortunate as computation estimation is needed in many circumstances in daily life. The present study examined 4th graders, 6th graders and adults’ ability to estimate the results of arithmetic problems relative to a reference number. A developmental pattern was observed in accuracy, speed and strategy use. With age there was a general increase in speed, and an increase in accuracy mainly for trials in which the reference number was close to the exact answer. The children tended to use the sense of magnitude strategy, which does not involve any calculation but relies mainly on an intuitive coarse sense of magnitude, while the adults used the approximated calculation strategy which involves rounding and multiplication procedures, and relies to a greater extent on calculation skills and working memory resources. Importantly, the children were less accurate than the adults, but were well above chance level. In all age groups performance was enhanced when the reference number was smaller (vs. larger) than the exact answer and when it was far (vs. close) from it, suggesting the involvement of an approximate number system. The results suggest the existence of an intuitive sense of magnitude for the results of arithmetic problems that might help children and even adults with difficulties in math. The present findings are discussed in the context of past research reporting poor estimation skills among children, and the conditions that might allow using children estimation skills in an effective manner. PMID:27171224

Routine Microsecond Molecular Dynamics Simulations with AMBER on GPUs. 1. Generalized Born

PubMed Central

2012-01-01

We present an implementation of generalized Born implicit solvent all-atom classical molecular dynamics (MD) within the AMBER program package that runs entirely on CUDA enabled NVIDIA graphics processing units (GPUs). We discuss the algorithms that are used to exploit the processing power of the GPUs and show the performance that can be achieved in comparison to simulations on conventional CPU clusters. The implementation supports three different precision models in which the contributions to the forces are calculated in single precision floating point arithmetic but accumulated in double precision (SPDP), or everything is computed in single precision (SPSP) or double precision (DPDP). In addition to performance, we have focused on understanding the implications of the different precision models on the outcome of implicit solvent MD simulations. We show results for a range of tests including the accuracy of single point force evaluations and energy conservation as well as structural properties pertainining to protein dynamics. The numerical noise due to rounding errors within the SPSP precision model is sufficiently large to lead to an accumulation of errors which can result in unphysical trajectories for long time scale simulations. We recommend the use of the mixed-precision SPDP model since the numerical results obtained are comparable with those of the full double precision DPDP model and the reference double precision CPU implementation but at significantly reduced computational cost. Our implementation provides performance for GB simulations on a single desktop that is on par with, and in some cases exceeds, that of traditional supercomputers. PMID:22582031

Comparison of missing value imputation methods in time series: the case of Turkish meteorological data

NASA Astrophysics Data System (ADS)

Yozgatligil, Ceylan; Aslan, Sipan; Iyigun, Cem; Batmaz, Inci

2013-04-01

This study aims to compare several imputation methods to complete the missing values of spatio-temporal meteorological time series. To this end, six imputation methods are assessed with respect to various criteria including accuracy, robustness, precision, and efficiency for artificially created missing data in monthly total precipitation and mean temperature series obtained from the Turkish State Meteorological Service. Of these methods, simple arithmetic average, normal ratio (NR), and NR weighted with correlations comprise the simple ones, whereas multilayer perceptron type neural network and multiple imputation strategy adopted by Monte Carlo Markov Chain based on expectation-maximization (EM-MCMC) are computationally intensive ones. In addition, we propose a modification on the EM-MCMC method. Besides using a conventional accuracy measure based on squared errors, we also suggest the correlation dimension (CD) technique of nonlinear dynamic time series analysis which takes spatio-temporal dependencies into account for evaluating imputation performances. Depending on the detailed graphical and quantitative analysis, it can be said that although computational methods, particularly EM-MCMC method, are computationally inefficient, they seem favorable for imputation of meteorological time series with respect to different missingness periods considering both measures and both series studied. To conclude, using the EM-MCMC algorithm for imputing missing values before conducting any statistical analyses of meteorological data will definitely decrease the amount of uncertainty and give more robust results. Moreover, the CD measure can be suggested for the performance evaluation of missing data imputation particularly with computational methods since it gives more precise results in meteorological time series.

78 FR 27898 - Approval and Promulgation of State Implementation Plan Revisions; Infrastructure Requirements for...

Federal Register 2010, 2011, 2012, 2013, 2014

2013-05-13

... arithmetic mean PM 2.5 concentration from single or multiple community- oriented monitors, and 65 [mu]g/m\\3...-oriented monitor within an area. In addition, the 24-hour PM 10 standard was revised to be based on the...): Stationary source monitoring and reporting. 110(a)(2)(G): Emergency powers. 110(a)(2)(H): Future SIP...

One Mouse per Child: Interpersonal Computer for Individual Arithmetic Practice

ERIC Educational Resources Information Center

Alcoholado, C.; Nussbaum, M.; Tagle, A.; Gomez, F.; Denardin, F.; Susaeta, H.; Villalta, M.; Toyama, K.

2012-01-01

Single Display Groupware (SDG) allows multiple people in the same physical space to interact simultaneously over a single communal display through individual input devices that work on the same machine. The aim of this paper is to show how SDG can be used to improve the way resources are used in schools, allowing students to work simultaneously on…

Programmed First Course in Algebra, Revised Form H, Student's Text, Part I, Unit 60.

ERIC Educational Resources Information Center

Buck, R. Creighton; And Others

This is part one of a two-part SMSG Programed Algebra Text for high school students. The general plan of the course is to build upon the student's experience with arithmetic. The student is initially led to extract from his or her experience the fundamental properties of addition and multiplication. The text then introduces negative real numbers…

Grade 9 Pilot Test. Mathematics. June 1988 = 9e Annee Test Pilote. Mathematiques. Juin 1988.

ERIC Educational Resources Information Center

Alberta Dept. of Education, Edmonton.

This pilot test for ninth grade mathematics is written in both French and English. The test consists of 75 multiple-choice items. Students are given 90 minutes to complete the examination and the use of a calculator is highly recommended. The test content covers a wide range of mathematical topics including: decimals; exponents; arithmetic word…

Inconsistencies in Numerical Simulations of Dynamical Systems Using Interval Arithmetic

NASA Astrophysics Data System (ADS)

Nepomuceno, Erivelton G.; Peixoto, Márcia L. C.; Martins, Samir A. M.; Rodrigues, Heitor M.; Perc, Matjaž

Over the past few decades, interval arithmetic has been attracting widespread interest from the scientific community. With the expansion of computing power, scientific computing is encountering a noteworthy shift from floating-point arithmetic toward increased use of interval arithmetic. Notwithstanding the significant reliability of interval arithmetic, this paper presents a theoretical inconsistency in a simulation of dynamical systems using a well-known implementation of arithmetic interval. We have observed that two natural interval extensions present an empty intersection during a finite time range, which is contrary to the fundamental theorem of interval analysis. We have proposed a procedure to at least partially overcome this problem, based on the union of the two generated pseudo-orbits. This paper also shows a successful case of interval arithmetic application in the reduction of interval width size on the simulation of discrete map. The implications of our findings on the reliability of scientific computing using interval arithmetic have been properly addressed using two numerical examples.

Mathematics anxiety in children with developmental dyscalculia.

PubMed

Rubinsten, Orly; Tannock, Rosemary

2010-07-15

Math anxiety, defined as a negative affective response to mathematics, is known to have deleterious effects on math performance in the general population. However, the assumption that math anxiety is directly related to math performance, has not yet been validated. Thus, our primary objective was to investigate the effects of math anxiety on numerical processing in children with specific deficits in the acquisition of math skills (Developmental Dyscalculia; DD) by using a novel affective priming task as an indirect measure. Participants (12 children with DD and 11 typically-developing peers) completed a novel priming task in which an arithmetic equation was preceded by one of four types of priming words (positive, neutral, negative or related to mathematics). Children were required to indicate whether the equation (simple math facts based on addition, subtraction, multiplication or division) was true or false. Typically, people respond to target stimuli more quickly after presentation of an affectively-related prime than after one that is unrelated affectively. Participants with DD responded faster to targets that were preceded by both negative primes and math-related primes. A reversed pattern was present in the control group. These results reveal a direct link between emotions, arithmetic and low achievement in math. It is also suggested that arithmetic-affective priming might be used as an indirect measure of math anxiety.

A parallel solver for huge dense linear systems

NASA Astrophysics Data System (ADS)

Badia, J. M.; Movilla, J. L.; Climente, J. I.; Castillo, M.; Marqués, M.; Mayo, R.; Quintana-Ortí, E. S.; Planelles, J.

2011-11-01

HDSS (Huge Dense Linear System Solver) is a Fortran Application Programming Interface (API) to facilitate the parallel solution of very large dense systems to scientists and engineers. The API makes use of parallelism to yield an efficient solution of the systems on a wide range of parallel platforms, from clusters of processors to massively parallel multiprocessors. It exploits out-of-core strategies to leverage the secondary memory in order to solve huge linear systems O(100.000). The API is based on the parallel linear algebra library PLAPACK, and on its Out-Of-Core (OOC) extension POOCLAPACK. Both PLAPACK and POOCLAPACK use the Message Passing Interface (MPI) as the communication layer and BLAS to perform the local matrix operations. The API provides a friendly interface to the users, hiding almost all the technical aspects related to the parallel execution of the code and the use of the secondary memory to solve the systems. In particular, the API can automatically select the best way to store and solve the systems, depending of the dimension of the system, the number of processes and the main memory of the platform. Experimental results on several parallel platforms report high performance, reaching more than 1 TFLOP with 64 cores to solve a system with more than 200 000 equations and more than 10 000 right-hand side vectors. New version program summaryProgram title: Huge Dense System Solver (HDSS) Catalogue identifier: AEHU_v1_1 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEHU_v1_1.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.: 87 062 No. of bytes in distributed program, including test data, etc.: 1 069 110 Distribution format: tar.gz Programming language: Fortran90, C Computer: Parallel architectures: multiprocessors, computer clusters Operating system: Linux/Unix Has the code been vectorized or parallelized?: Yes, includes MPI primitives. RAM: Tested for up to 190 GB Classification: 6.5 External routines: MPI ( http://www.mpi-forum.org/), BLAS ( http://www.netlib.org/blas/), PLAPACK ( http://www.cs.utexas.edu/~plapack/), POOCLAPACK ( ftp://ftp.cs.utexas.edu/pub/rvdg/PLAPACK/pooclapack.ps) (code for PLAPACK and POOCLAPACK is included in the distribution). Catalogue identifier of previous version: AEHU_v1_0 Journal reference of previous version: Comput. Phys. Comm. 182 (2011) 533 Does the new version supersede the previous version?: Yes Nature of problem: Huge scale dense systems of linear equations, Ax=B, beyond standard LAPACK capabilities. Solution method: The linear systems are solved by means of parallelized routines based on the LU factorization, using efficient secondary storage algorithms when the available main memory is insufficient. Reasons for new version: In many applications we need to guarantee a high accuracy in the solution of very large linear systems and we can do it by using double-precision arithmetic. Summary of revisions: Version 1.1 Can be used to solve linear systems using double-precision arithmetic. New version of the initialization routine. The user can choose the kind of arithmetic and the values of several parameters of the environment. Running time: About 5 hours to solve a system with more than 200 000 equations and more than 10 000 right-hand side vectors using double-precision arithmetic on an eight-node commodity cluster with a total of 64 Intel cores.

Differences in Arithmetic Performance between Chinese and German Children Are Accompanied by Differences in Processing of Symbolic Numerical Magnitude

PubMed Central

Lonnemann, Jan; Linkersdörfer, Janosch; Hasselhorn, Marcus; Lindberg, Sven

2016-01-01

Symbolic numerical magnitude processing skills are assumed to be fundamental to arithmetic learning. It is, however, still an open question whether better arithmetic skills are reflected in symbolic numerical magnitude processing skills. To address this issue, Chinese and German third graders were compared regarding their performance in arithmetic tasks and in a symbolic numerical magnitude comparison task. Chinese children performed better in the arithmetic tasks and were faster in deciding which one of two Arabic numbers was numerically larger. The group difference in symbolic numerical magnitude processing was fully mediated by the performance in arithmetic tasks. We assume that a higher degree of familiarity with arithmetic in Chinese compared to German children leads to a higher speed of retrieving symbolic numerical magnitude knowledge. PMID:27630606

Measuring Arithmetic: A Psychometric Approach to Understanding Formatting Effects and Domain Specificity

ERIC Educational Resources Information Center

Rhodes, Katherine T.; Branum-Martin, Lee; Washington, Julie A.; Fuchs, Lynn S.

2017-01-01

Using multitrait, multimethod data, and confirmatory factor analysis, the current study examined the effects of arithmetic item formatting and the possibility that across formats, abilities other than arithmetic may contribute to children's answers. Measurement hypotheses were guided by several leading theories of arithmetic cognition. With a…

Personal Experience and Arithmetic Meaning in Semantic Dementia

ERIC Educational Resources Information Center

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…

Numerical determination of partial spectrum of Hermitian matrices using a Lánczos method with selective reorthogonalization

NASA Astrophysics Data System (ADS)

Johnson, Chris; Kennedy, A. D.

2013-03-01

We introduce a new algorithm for finding the eigenvalues and eigenvectors of Hermitian matrices within a specified region, based upon the LANSO algorithm of Parlett and Scott. It uses selective reorthogonalization to avoid the duplication of eigenpairs in finite-precision arithmetic, but uses a new bound to decide when such reorthogonalization is required, and only reorthogonalizes with respect to eigenpairs within the region of interest. We investigate its performance for the Hermitian Wilson-Dirac operator γ5D in lattice quantum chromodynamics, and compare it with previous methods.

On the Floating Point Performance of the i860 Microprocessor

NASA Technical Reports Server (NTRS)

Lee, King; Kutler, Paul (Technical Monitor)

1997-01-01

The i860 microprocessor is a pipelined processor that can deliver two double precision floating point results every clock. It is being used in the Touchstone project to develop a teraflop computer by the year 2000. With such high computational capabilities it was expected that memory bandwidth would limit performance on many kernels. Measured performance of three kernels showed performance is less than what memory bandwidth limitations would predict. This paper develops a model that explains the discrepancy in terms of memory latencies and points to some problems involved in moving data from memory to the arithmetic pipelines.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bailey, David

In the January 2002 edition of SIAM News, Nick Trefethen announced the '$100, 100-Digit Challenge'. In this note he presented ten easy-to-state but hard-to-solve problems of numerical analysis, and challenged readers to find each answer to ten-digit accuracy. Trefethen closed with the enticing comment: 'Hint: They're hard! If anyone gets 50 digits in total, I will be impressed.' This challenge obviously struck a chord in hundreds of numerical mathematicians worldwide, as 94 teams from 25 nations later submitted entries. Many of these submissions exceeded the target of 50 correct digits; in fact, 20 teams achieved a perfect score of 100more » correct digits. Trefethen had offered $100 for the best submission. Given the overwhelming response, a generous donor (William Browning, founder of Applied Mathematics, Inc.) provided additional funds to provide a $100 award to each of the 20 winning teams. Soon after the results were out, four participants, each from a winning team, got together and agreed to write a book about the problems and their solutions. The team is truly international: Bornemann is from Germany, Laurie is from South Africa, Wagon is from the USA, and Waldvogel is from Switzerland. This book provides some mathematical background for each problem, and then shows in detail how each of them can be solved. In fact, multiple solution techniques are mentioned in each case. The book describes how to extend these solutions to much larger problems and much higher numeric precision (hundreds or thousands of digit accuracy). The authors also show how to compute error bounds for the results, so that one can say with confidence that one's results are accurate to the level stated. Numerous numerical software tools are demonstrated in the process, including the commercial products Mathematica, Maple and Matlab. Computer programs that perform many of the algorithms mentioned in the book are provided, both in an appendix to the book and on a website. In the process, the authors take the reader on a wide-ranging tour of modern numerical mathematics, with enough background material so that even readers with little or no training in numerical analysis can follow. Here is a list of just a few of the topics visited: numerical quadrature (i.e., numerical integration), series summation, sequence extrapolation, contour integration, Fourier integrals, high-precision arithmetic, interval arithmetic, symbolic computing, numerical linear algebra, perturbation theory, Euler-Maclaurin summation, global minimization, eigenvalue methods, evolutionary algorithms, matrix preconditioning, random walks, special functions, elliptic functions, Monte-Carlo methods, and numerical differentiation.« less

Anatomically ordered tapping interferes more with one-digit addition than two-digit addition: a dual-task fMRI study.

PubMed

Soylu, Firat; Newman, Sharlene D

2016-02-01

Fingers are used as canonical representations for numbers across cultures. In previous imaging studies, it was shown that arithmetic processing activates neural resources that are known to participate in finger movements. Additionally, in one dual-task study, it was shown that anatomically ordered finger tapping disrupts addition and subtraction more than multiplication, possibly due to a long-lasting effect of early finger counting experiences on the neural correlates and organization of addition and subtraction processes. How arithmetic task difficulty and tapping complexity affect the concurrent performance is still unclear. If early finger counting experiences have bearing on the neural correlates of arithmetic in adults, then one would expect anatomically and non-anatomically ordered tapping to have different interference effects, given that finger counting is usually anatomically ordered. To unravel these issues, we studied how (1) arithmetic task difficulty and (2) the complexity of the finger tapping sequence (anatomical vs. non-anatomical ordering) affect concurrent performance and use of key neural circuits using a mixed block/event-related dual-task fMRI design with adult participants. The results suggest that complexity of the tapping sequence modulates interference on addition, and that one-digit addition (fact retrieval), compared to two-digit addition (calculation), is more affected from anatomically ordered tapping. The region-of-interest analysis showed higher left angular gyrus BOLD response for one-digit compared to two-digit addition, and in no-tapping conditions than dual tapping conditions. The results support a specific association between addition fact retrieval and anatomically ordered finger movements in adults, possibly due to finger counting strategies that deploy anatomically ordered finger movements early in the development.

[Event-related potentials in Chinese characters semantic priming and arithmetic tasks: comparative study between healthy children and children with cognitive disorder].

PubMed

Dong, Xuan; Wang, Su-hong; Yang, Yi-lin; Ren, Yan-ling; Meng, Ping; Yang, Yu-xia

2007-10-30

To explore the cognitive psychological process of healthy children and children with cognitive disorder. Single Chinese character semantic priming and arithmetic tasks were delivered to 20 8-year-old healthy children, and 20 11-year-old healthy children, and 30 children with attention deficit hyperactivity disorder, 23 children with epilepsy, and 22 age-matched normal children as controls. Electroencephalography was used. Event-related potential was distilled by BESA software. (1) During the Chinese character semantic priming, the amplitudes of N2 toward the non-related words and pseudo-words in the 8-year-old group were 12.1 microV and 11.7 microV respectively, both significantly larger than those of the 11-year-old group (3.7 microV and 4.8 microV, respectively, both P<0.05). The amplitudes of N2 and P2 toward the non-related words and pseudo-words among the children with attention deficit hyperactivity disorder were both significantly lower than those in the healthy children (both P<0.05). (2) During the arithmetic task, the latency values of P2 and P3 of addition, subtraction, and multiplication in the 8-year-old group of healthy children were all significantly longer than those of the 11-year-old group of healthy children (all P<0.05). The P3 latency of the children with epilepsy was significantly longer than that of the healthy children (P<0.05). Chinese character and arithmetic cognitive waves are steady. ERP can be used to estimate the healthy children's personality index. Quantitative indicators are helpful in diagnosis and treatment of cognitive and learning disorders.

Mathematical modelling of Bit-Level Architecture using Reciprocal Quantum Logic

NASA Astrophysics Data System (ADS)

Narendran, S.; Selvakumar, J.

2018-04-01

Efficiency of high-performance computing is on high demand with both speed and energy efficiency. Reciprocal Quantum Logic (RQL) is one of the technology which will produce high speed and zero static power dissipation. RQL uses AC power supply as input rather than DC input. RQL has three set of basic gates. Series of reciprocal transmission lines are placed in between each gate to avoid loss of power and to achieve high speed. Analytical model of Bit-Level Architecture are done through RQL. Major drawback of reciprocal Quantum Logic is area, because of lack in proper power supply. To achieve proper power supply we need to use splitters which will occupy large area. Distributed arithmetic uses vector- vector multiplication one is constant and other is signed variable and each word performs as a binary number, they rearranged and mixed to form distributed system. Distributed arithmetic is widely used in convolution and high performance computational devices.

Synesthesia affects verification of simple arithmetic equations.

PubMed

Ghirardelli, Thomas G; Mills, Carol Bergfeld; Zilioli, Monica K C; Bailey, Leah P; Kretschmar, Paige K

2010-01-01

To investigate the effects of color-digit synesthesia on numerical representation, we presented a synesthete, called SE, in the present study, and controls with mathematical equations for verification. In Experiment 1, SE verified addition equations made up of digits that either matched or mismatched her color-digit photisms or were in black. In Experiment 2A, the addends were presented in the different color conditions and the solution was presented in black, whereas in Experiment 2B the addends were presented in black and the solutions were presented in the different color conditions. In Experiment 3, multiplication and division equations were presented in the same color conditions as in Experiment 1. SE responded significantly faster to equations that matched her photisms than to those that did not; controls did not show this effect. These results suggest that photisms influence the processing of digits in arithmetic verification, replicating and extending previous findings.

The cognitive foundations of early arithmetic skills: It is counting and number judgment, but not finger gnosis, that count.

PubMed

Long, Imogen; Malone, Stephanie A; Tolan, Anne; Burgoyne, Kelly; Heron-Delaney, Michelle; Witteveen, Kate; Hulme, Charles

2016-12-01

Following on from ideas developed by Gerstmann, a body of work has suggested that impairments in finger gnosis may be causally related to children's difficulties in learning arithmetic. We report a study with a large sample of typically developing children (N=197) in which we assessed finger gnosis and arithmetic along with a range of other relevant cognitive predictors of arithmetic skills (vocabulary, counting, and symbolic and nonsymbolic magnitude judgments). Contrary to some earlier claims, we found no meaningful association between finger gnosis and arithmetic skills. Counting and symbolic magnitude comparison were, however, powerful predictors of arithmetic skills, replicating a number of earlier findings. Our findings seriously question theories that posit either a simple association or a causal connection between finger gnosis and the development of arithmetic skills. Crown Copyright © 2016. Published by Elsevier Inc. All rights reserved.

[Acquisition of arithmetic knowledge].

PubMed

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).

The Development of Arithmetic Principle Knowledge: How Do We Know What Learners Know?

ERIC Educational Resources Information Center

Prather, Richard W.; Alibali, Martha W.

2009-01-01

This paper reviews research on learners' knowledge of three arithmetic principles: "Commutativity", "Relation to Operands", and "Inversion." Studies of arithmetic principle knowledge vary along several dimensions, including the age of the participants, the context in which the arithmetic is presented, and most importantly, the type of knowledge…

How to interpret cognitive training studies: A reply to Lindskog & Winman

PubMed Central

Park, Joonkoo; Brannon, Elizabeth M.

2017-01-01

In our previous studies, we demonstrated that repeated training on an approximate arithmetic task selectively improves symbolic arithmetic performance (Park & Brannon, 2013, 2014). We proposed that mental manipulation of quantity is the common cognitive component between approximate arithmetic and symbolic arithmetic, driving the causal relationship between the two. In a commentary to our work, Lindskog and Winman argue that there is no evidence of performance improvement during approximate arithmetic training and that this challenges the proposed causal relationship between approximate arithmetic and symbolic arithmetic. Here, we argue that causality in cognitive training experiments is interpreted from the selectivity of transfer effects and does not hinge upon improved performance in the training task. This is because changes in the unobservable cognitive elements underlying the transfer effect may not be observable from performance measures in the training task. We also question the validity of Lindskog and Winman’s simulation approach for testing for a training effect, given that simulations require a valid and sufficient model of a decision process, which is often difficult to achieve. Finally we provide an empirical approach to testing the training effects in adaptive training. Our analysis reveals new evidence that approximate arithmetic performance improved over the course of training in Park and Brannon (2014). We maintain that our data supports the conclusion that approximate arithmetic training leads to improvement in symbolic arithmetic driven by the common cognitive component of mental quantity manipulation. PMID:26972469

The fault-tree compiler

NASA Technical Reports Server (NTRS)

Martensen, Anna L.; Butler, Ricky W.

1987-01-01

The Fault Tree Compiler Program is a new reliability tool used to predict the top event probability for a fault tree. Five different gate types are allowed in the fault tree: AND, OR, EXCLUSIVE OR, INVERT, and M OF N gates. The high level input language is easy to understand and use when describing the system tree. In addition, the use of the hierarchical fault tree capability can simplify the tree description and decrease program execution time. The current solution technique provides an answer precise (within the limits of double precision floating point arithmetic) to the five digits in the answer. The user may vary one failure rate or failure probability over a range of values and plot the results for sensitivity analyses. The solution technique is implemented in FORTRAN; the remaining program code is implemented in Pascal. The program is written to run on a Digital Corporation VAX with the VMS operation system.

Fiber optic combiner and duplicator

NASA Technical Reports Server (NTRS)

1979-01-01

The investigation of the possible development of two optical devices, one to take two images as inputs and to present their arithmetic sum as a single output, the other to take one image as input and present two identical images as outputs is described. Significant engineering time was invested in establishing precision fiber optics drawing capabilities, real time monitoring of the fiber size and exact measuring of fiber optics ribbons. Various assembly procedures and tooling designs were investigated and prototype models were built and evaluated that established technical assurance that the device was feasible and could be fabricated. Although the interleaver specification in its entirety was not achieved, the techniques developed in the course of the program improved the quality of images transmitted by fiber optic arrays by at least an order of magnitude. These techniques are already being applied to the manufacture of precise fiber optic components.

The Fault Tree Compiler (FTC): Program and mathematics

NASA Technical Reports Server (NTRS)

Butler, Ricky W.; Martensen, Anna L.

1989-01-01

The Fault Tree Compiler Program is a new reliability tool used to predict the top-event probability for a fault tree. Five different gate types are allowed in the fault tree: AND, OR, EXCLUSIVE OR, INVERT, AND m OF n gates. The high-level input language is easy to understand and use when describing the system tree. In addition, the use of the hierarchical fault tree capability can simplify the tree description and decrease program execution time. The current solution technique provides an answer precisely (within the limits of double precision floating point arithmetic) within a user specified number of digits accuracy. The user may vary one failure rate or failure probability over a range of values and plot the results for sensitivity analyses. The solution technique is implemented in FORTRAN; the remaining program code is implemented in Pascal. The program is written to run on a Digital Equipment Corporation (DEC) VAX computer with the VMS operation system.

Approximate Arithmetic Training Improves Informal Math Performance in Low Achieving Preschoolers

PubMed Central

Szkudlarek, Emily; Brannon, Elizabeth M.

2018-01-01

Recent studies suggest that practice with approximate and non-symbolic arithmetic problems improves the math performance of adults, school aged children, and preschoolers. However, the relative effectiveness of approximate arithmetic training compared to available educational games, and the type of math skills that approximate arithmetic targets are unknown. The present study was designed to (1) compare the effectiveness of approximate arithmetic training to two commercially available numeral and letter identification tablet applications and (2) to examine the specific type of math skills that benefit from approximate arithmetic training. Preschool children (n = 158) were pseudo-randomly assigned to one of three conditions: approximate arithmetic, letter identification, or numeral identification. All children were trained for 10 short sessions and given pre and post tests of informal and formal math, executive function, short term memory, vocabulary, alphabet knowledge, and number word knowledge. We found a significant interaction between initial math performance and training condition, such that children with low pretest math performance benefited from approximate arithmetic training, and children with high pretest math performance benefited from symbol identification training. This effect was restricted to informal, and not formal, math problems. There were also effects of gender, socio-economic status, and age on post-test informal math score after intervention. A median split on pretest math ability indicated that children in the low half of math scores in the approximate arithmetic training condition performed significantly better than children in the letter identification training condition on post-test informal math problems when controlling for pretest, age, gender, and socio-economic status. Our results support the conclusion that approximate arithmetic training may be especially effective for children with low math skills, and that approximate arithmetic training improves early informal, but not formal, math skills. PMID:29867624

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

PubMed

Szkudlarek, Emily; Brannon, Elizabeth M

2018-01-01

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

Selections from 2017: Image Processing with AstroImageJ

NASA Astrophysics Data System (ADS)

Kohler, Susanna

2017-12-01

Editors note:In these last two weeks of 2017, well be looking at a few selections that we havent yet discussed on AAS Nova from among the most-downloaded paperspublished in AAS journals this year. The usual posting schedule will resume in January.AstroImageJ: Image Processing and Photometric Extraction for Ultra-Precise Astronomical Light CurvesPublished January2017The AIJ image display. A wide range of astronomy specific image display options and image analysis tools are available from the menus, quick access icons, and interactive histogram. [Collins et al. 2017]Main takeaway:AstroImageJ is a new integrated software package presented in a publication led byKaren Collins(Vanderbilt University,Fisk University, andUniversity of Louisville). Itenables new users even at the level of undergraduate student, high school student, or amateur astronomer to quickly start processing, modeling, and plotting astronomical image data.Why its interesting:Science doesnt just happen the momenta telescope captures a picture of a distantobject. Instead, astronomical images must firstbe carefully processed to clean up thedata, and this data must then be systematically analyzed to learn about the objects within it. AstroImageJ as a GUI-driven, easily installed, public-domain tool is a uniquelyaccessible tool for thisprocessing and analysis, allowing even non-specialist users to explore and visualizeastronomical data.Some features ofAstroImageJ:(as reported by Astrobites)Image calibration:generate master flat, dark, and bias framesImage arithmetic:combineimages viasubtraction, addition, division, multiplication, etc.Stack editing:easily perform operations on a series of imagesImage stabilization and image alignment featuresPrecise coordinate converters:calculate Heliocentric and Barycentric Julian DatesWCS coordinates:determine precisely where atelescope was pointed for an image by PlateSolving using Astronomy.netMacro and plugin support:write your own macrosMulti-aperture photometry with interactive light curve fitting:plot light curves of a star in real timeCitationKaren A. Collins et al 2017 AJ 153 77. doi:10.3847/1538-3881/153/2/77

Proceedings of the Conference of the International Group for the Psychology of Mathematics Education (22nd, Stellenbosch, South Africa, July 12-17, 1998). Volume 2.

ERIC Educational Resources Information Center

Olivier, Alwyn, Ed.; Newstead, Karen, Ed.

The second volume of this proceedings contains the first portion of the research reports. Papers include: (1) "Learning Algebraic Strategies Using a Computerized Balance Model" (James Aczel); (2) "Children's Perception of Multiplicative Structure in Diagrams" (Bjornar Alseth); (3) "A Discussion of Different Approaches to Arithmetic Teaching"…

How Do We Choose among Strategies to Accomplish Cognitive Tasks? Evidence from Behavioral and Event-Related Potential Data in Arithmetic Problem Solving

ERIC Educational Resources Information Center

Taillan, Julien; Dufau, Stéphane; Lemaire, Patrick

2015-01-01

We used event-related potentials (ERPs) to determine the time course of mechanisms underlying strategy selection. Participants had to select the better strategy on multiplication problems (i.e., 51 × 27) to find approximate products. They could choose between rounding up and rounding down both operands to their nearest decades. Two types of…

Effects of Finger Counting on Numerical Development – The Opposing Views of Neurocognition and Mathematics Education

PubMed Central

Moeller, Korbinian; Martignon, Laura; Wessolowski, Silvia; Engel, Joachim; Nuerk, Hans-Christoph

2011-01-01

Children typically learn basic numerical and arithmetic principles using finger-based representations. However, whether or not reliance on finger-based representations is beneficial or detrimental is the subject of an ongoing debate between researchers in neurocognition and mathematics education. From the neurocognitive perspective, finger counting provides multisensory input, which conveys both cardinal and ordinal aspects of numbers. Recent data indicate that children with good finger-based numerical representations show better arithmetic skills and that training finger gnosis, or “finger sense,” enhances mathematical skills. Therefore neurocognitive researchers conclude that elaborate finger-based numerical representations are beneficial for later numerical development. However, research in mathematics education recommends fostering mentally based numerical representations so as to induce children to abandon finger counting. More precisely, mathematics education recommends first using finger counting, then concrete structured representations and, finally, mental representations of numbers to perform numerical operations. Taken together, these results reveal an important debate between neurocognitive and mathematics education research concerning the benefits and detriments of finger-based strategies for numerical development. In the present review, the rationale of both lines of evidence will be discussed. PMID:22144969

Compensation for the signal processing characteristics of ultrasound B-mode scanners in adaptive speckle reduction.

PubMed

Crawford, D C; Bell, D S; Bamber, J C

1993-01-01

A systematic method to compensate for nonlinear amplification of individual ultrasound B-scanners has been investigated in order to optimise performance of an adaptive speckle reduction (ASR) filter for a wide range of clinical ultrasonic imaging equipment. Three potential methods have been investigated: (1) a method involving an appropriate selection of the speckle recognition feature was successful when the scanner signal processing executes simple logarithmic compressions; (2) an inverse transform (decompression) of the B-mode image was effective in correcting for the measured characteristics of image data compression when the algorithm was implemented in full floating point arithmetic; (3) characterising the behaviour of the statistical speckle recognition feature under conditions of speckle noise was found to be the method of choice for implementation of the adaptive speckle reduction algorithm in limited precision integer arithmetic. In this example, the statistical features of variance and mean were investigated. The third method may be implemented on commercially available fast image processing hardware and is also better suited for transfer into dedicated hardware to facilitate real-time adaptive speckle reduction. A systematic method is described for obtaining ASR calibration data from B-mode images of a speckle producing phantom.

Parsimonious estimation of the Wechsler Memory Scale, Fourth Edition demographically adjusted index scores: immediate and delayed memory.

PubMed

Miller, Justin B; Axelrod, Bradley N; Schutte, Christian

2012-01-01

The recent release of the Wechsler Memory Scale Fourth Edition contains many improvements from a theoretical and administration perspective, including demographic corrections using the Advanced Clinical Solutions. Although the administration time has been reduced from previous versions, a shortened version may be desirable in certain situations given practical time limitations in clinical practice. The current study evaluated two- and three-subtest estimations of demographically corrected Immediate and Delayed Memory index scores using both simple arithmetic prorating and regression models. All estimated values were significantly associated with observed index scores. Use of Lin's Concordance Correlation Coefficient as a measure of agreement showed a high degree of precision and virtually zero bias in the models, although the regression models showed a stronger association than prorated models. Regression-based models proved to be more accurate than prorated estimates with less dispersion around observed values, particularly when using three subtest regression models. Overall, the present research shows strong support for estimating demographically corrected index scores on the WMS-IV in clinical practice with an adequate performance using arithmetically prorated models and a stronger performance using regression models to predict index scores.

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

ERIC Educational Resources Information Center

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

2016-01-01

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

Non-symbolic arithmetic in adults and young children.

PubMed

Barth, Hilary; La Mont, Kristen; Lipton, Jennifer; Dehaene, Stanislas; Kanwisher, Nancy; Spelke, Elizabeth

2006-01-01

Five experiments investigated whether adults and preschool children can perform simple arithmetic calculations on non-symbolic numerosities. Previous research has demonstrated that human adults, human infants, and non-human animals can process numerical quantities through approximate representations of their magnitudes. Here we consider whether these non-symbolic numerical representations might serve as a building block of uniquely human, learned mathematics. Both adults and children with no training in arithmetic successfully performed approximate arithmetic on large sets of elements. Success at these tasks did not depend on non-numerical continuous quantities, modality-specific quantity information, the adoption of alternative non-arithmetic strategies, or learned symbolic arithmetic knowledge. Abstract numerical quantity representations therefore are computationally functional and may provide a foundation for formal mathematics.

Multiple solution of linear algebraic systems by an iterative method with recomputed preconditioner in the analysis of microstrip structures

NASA Astrophysics Data System (ADS)

Ahunov, Roman R.; Kuksenko, Sergey P.; Gazizov, Talgat R.

2016-06-01

A multiple solution of linear algebraic systems with dense matrix by iterative methods is considered. To accelerate the process, the recomputing of the preconditioning matrix is used. A priory condition of the recomputing based on change of the arithmetic mean of the current solution time during the multiple solution is proposed. To confirm the effectiveness of the proposed approach, the numerical experiments using iterative methods BiCGStab and CGS for four different sets of matrices on two examples of microstrip structures are carried out. For solution of 100 linear systems the acceleration up to 1.6 times, compared to the approach without recomputing, is obtained.

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

PubMed

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

2006-06-01

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

Effect of Numerical Error on Gravity Field Estimation for GRACE and Future Gravity Missions

NASA Astrophysics Data System (ADS)

McCullough, Christopher; Bettadpur, Srinivas

2015-04-01

In recent decades, gravity field determination from low Earth orbiting satellites, such as the Gravity Recovery and Climate Experiment (GRACE), has become increasingly more effective due to the incorporation of high accuracy measurement devices. Since instrumentation quality will only increase in the near future and the gravity field determination process is computationally and numerically intensive, numerical error from the use of double precision arithmetic will eventually become a prominent error source. While using double-extended or quadruple precision arithmetic will reduce these errors, the numerical limitations of current orbit determination algorithms and processes must be accurately identified and quantified in order to adequately inform the science data processing techniques of future gravity missions. The most obvious numerical limitation in the orbit determination process is evident in the comparison of measured observables with computed values, derived from mathematical models relating the satellites' numerically integrated state to the observable. Significant error in the computed trajectory will corrupt this comparison and induce error in the least squares solution of the gravitational field. In addition, errors in the numerically computed trajectory propagate into the evaluation of the mathematical measurement model's partial derivatives. These errors amalgamate in turn with numerical error from the computation of the state transition matrix, computed using the variational equations of motion, in the least squares mapping matrix. Finally, the solution of the linearized least squares system, computed using a QR factorization, is also susceptible to numerical error. Certain interesting combinations of each of these numerical errors are examined in the framework of GRACE gravity field determination to analyze and quantify their effects on gravity field recovery.

Multiple advanced logic gates made of DNA-Ag nanocluster and the application for intelligent detection of pathogenic bacterial genes† †Electronic supplementary information (ESI) available: Chemicals, materials and DNA sequences used in the investigation, the construction of YES, AND, OR, XOR and INH logic gates, CD and PAGE experimental results. See DOI: 10.1039/c7sc05246d

PubMed Central

Lin, Xiaodong; Deng, Jiankang; Lyu, Yanlong; Qian, Pengcheng; Li, Yunfei

2018-01-01

The integration of multiple DNA logic gates on a universal platform to implement advance logic functions is a critical challenge for DNA computing. Herein, a straightforward and powerful strategy in which a guanine-rich DNA sequence lighting up a silver nanocluster and fluorophore was developed to construct a library of logic gates on a simple DNA-templated silver nanoclusters (DNA-AgNCs) platform. This library included basic logic gates, YES, AND, OR, INHIBIT, and XOR, which were further integrated into complex logic circuits to implement diverse advanced arithmetic/non-arithmetic functions including half-adder, half-subtractor, multiplexer, and demultiplexer. Under UV irradiation, all the logic functions could be instantly visualized, confirming an excellent repeatability. The logic operations were entirely based on DNA hybridization in an enzyme-free and label-free condition, avoiding waste accumulation and reducing cost consumption. Interestingly, a DNA-AgNCs-based multiplexer was, for the first time, used as an intelligent biosensor to identify pathogenic genes, E. coli and S. aureus genes, with a high sensitivity. The investigation provides a prototype for the wireless integration of multiple devices on even the simplest single-strand DNA platform to perform diverse complex functions in a straightforward and cost-effective way. PMID:29675221

Mathematics anxiety in children with developmental dyscalculia

PubMed Central

2010-01-01

Background Math anxiety, defined as a negative affective response to mathematics, is known to have deleterious effects on math performance in the general population. However, the assumption that math anxiety is directly related to math performance, has not yet been validated. Thus, our primary objective was to investigate the effects of math anxiety on numerical processing in children with specific deficits in the acquisition of math skills (Developmental Dyscalculia; DD) by using a novel affective priming task as an indirect measure. Methods Participants (12 children with DD and 11 typically-developing peers) completed a novel priming task in which an arithmetic equation was preceded by one of four types of priming words (positive, neutral, negative or related to mathematics). Children were required to indicate whether the equation (simple math facts based on addition, subtraction, multiplication or division) was true or false. Typically, people respond to target stimuli more quickly after presentation of an affectively-related prime than after one that is unrelated affectively. Result Participants with DD responded faster to targets that were preceded by both negative primes and math-related primes. A reversed pattern was present in the control group. Conclusion These results reveal a direct link between emotions, arithmetic and low achievement in math. It is also suggested that arithmetic-affective priming might be used as an indirect measure of math anxiety. PMID:20633269

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

PubMed Central

Li, Yongxin; Hu, Yuzheng; Wang, Yunqi; Weng, Jian; Chen, Feiyan

2013-01-01

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 gray 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. PMID:24367320

Lithium Niobate Arithmetic Logic Unit

DTIC Science & Technology

1991-03-01

Boot51] A.D. Booth, "A Signed Binary Multiplication Technique," Quarterly Journal of Mechanics and Applied Mathematics , Vol. IV Part 2, 1951. [ChWi79...Trans. Computers, Vol. C-26, No. 7, July 1977, pp. 681-687. [Wake8 I] John F. Wakerly , "Miocrocomputer Architecture and Programming," John Wiley and...different division methods and discusses their applicability to simple bit serial implementation. Several different designs are then presented and

All for one but not one for all: how multiple number representations are recruited in one numerical task.

PubMed

Wood, Guilherme; Nuerk, Hans-Christoph; Moeller, Korbinian; Geppert, Barbara; Schnitker, Ralph; Weber, Jochen; Willmes, Klaus

2008-01-02

Number processing recruits a complex network of multiple numerical representations. Usually the components of this network are examined in a between-task approach with the disadvantage of relying upon different instructions, tasks, and inhomogeneous stimulus sets across different studies. A within-task approach may avoid these disadvantages and access involved numerical representations more specifically. In the present study we employed a within-task approach to investigate numerical representations activated in the number bisection task (NBT) using parametric rapid event-related fMRI. Participants were to judge whether the central number of a triplet was also its arithmetic mean (e.g. 23_26_29) or not (e.g. 23_25_29). Activation in the left inferior parietal cortex was associated with the deployment of arithmetic fact knowledge, while activation of the intraparietal cortex indicated more intense magnitude processing, instrumental aspects of calculation and integration of the base-10 structure of two-digit numbers. These results replicate evidence from the literature. Furthermore, activation in the dorsolateral and ventrolateral prefrontal cortex revealed mechanisms of feature monitoring and inhibition as well as allocation of cognitive resources recruited to solve a specific triplet. We conclude that the network of numerical representations should rather be studied in a within-task approach than in varying between-task approaches.

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

PubMed

Hinault, T; Lemaire, P

2016-01-01

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

Reconfigurable data path processor

NASA Technical Reports Server (NTRS)

Donohoe, Gregory (Inventor)

2005-01-01

A reconfigurable data path processor comprises a plurality of independent processing elements. Each of the processing elements advantageously comprising an identical architecture. Each processing element comprises a plurality of data processing means for generating a potential output. Each processor is also capable of through-putting an input as a potential output with little or no processing. Each processing element comprises a conditional multiplexer having a first conditional multiplexer input, a second conditional multiplexer input and a conditional multiplexer output. A first potential output value is transmitted to the first conditional multiplexer input, and a second potential output value is transmitted to the second conditional multiplexer output. The conditional multiplexer couples either the first conditional multiplexer input or the second conditional multiplexer input to the conditional multiplexer output, according to an output control command. The output control command is generated by processing a set of arithmetic status-bits through a logical mask. The conditional multiplexer output is coupled to a first processing element output. A first set of arithmetic bits are generated according to the processing of the first processable value. A second set of arithmetic bits may be generated from a second processing operation. The selection of the arithmetic status-bits is performed by an arithmetic-status bit multiplexer selects the desired set of arithmetic status bits from among the first and second set of arithmetic status bits. The conditional multiplexer evaluates the select arithmetic status bits according to logical mask defining an algorithm for evaluating the arithmetic status bits.

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

ERIC Educational Resources Information Center

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 +…

On Kedlaya-type inequalities for weighted means.

PubMed

Páles, Zsolt; Pasteczka, Paweł

2018-01-01

In 2016 we proved that for every symmetric, repetition invariant and Jensen concave mean [Formula: see text] the Kedlaya-type inequality [Formula: see text] holds for an arbitrary [Formula: see text] ([Formula: see text] stands for the arithmetic mean). We are going to prove the weighted counterpart of this inequality. More precisely, if [Formula: see text] is a vector with corresponding (non-normalized) weights [Formula: see text] and [Formula: see text] denotes the weighted mean then, under analogous conditions on [Formula: see text], the inequality [Formula: see text] holds for every [Formula: see text] and [Formula: see text] such that the sequence [Formula: see text] is decreasing.

Boundary implications for frequency response of interval FIR and IIR filters

NASA Technical Reports Server (NTRS)

Bose, N. K.; Kim, K. D.

1991-01-01

It is shown that vertex implication results in parameter space apply to interval trigonometric polynomials. Subsequently, it is shown that the frequency responses of both interval FIR and IIR filters are bounded by the frequency responses of certain extreme filters. The results apply directly in the evaluation of properties of designed filters, especially because it is more realistic to bound the filter coefficients from above and below instead of determining those with infinite precision because of finite arithmetic effects. Illustrative examples are provided to show how the extreme filters might be easily derived in any specific interval FIR or IIR filter design problem.

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

PubMed Central

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

2015-01-01

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

Intersession consistency of single-trial classification of the prefrontal response to mental arithmetic and the no-control state by NIRS.

PubMed

Power, Sarah D; Kushki, Azadeh; Chau, Tom

2012-01-01

Near-infrared spectroscopy (NIRS) has been recently investigated for use in noninvasive brain-computer interface (BCI) technologies. Previous studies have demonstrated the ability to classify patterns of neural activation associated with different mental tasks (e.g., mental arithmetic) using NIRS signals. Though these studies represent an important step towards the realization of an NIRS-BCI, there is a paucity of literature regarding the consistency of these responses, and the ability to classify them on a single-trial basis, over multiple sessions. This is important when moving out of an experimental context toward a practical system, where performance must be maintained over longer periods. When considering response consistency across sessions, two questions arise: 1) can the hemodynamic response to the activation task be distinguished from a baseline (or other task) condition, consistently across sessions, and if so, 2) are the spatiotemporal characteristics of the response which best distinguish it from the baseline (or other task) condition consistent across sessions. The answers will have implications for the viability of an NIRS-BCI system, and the design strategies (especially in terms of classifier training protocols) adopted. In this study, we investigated the consistency of classification of a mental arithmetic task and a no-control condition over five experimental sessions. Mixed model linear regression on intrasession classification accuracies indicate that the task and baseline states remain differentiable across multiple sessions, with no significant decrease in accuracy (p = 0.67). Intersession analysis, however, revealed inconsistencies in spatiotemporal response characteristics. Based on these results, we investigated several different practical classifier training protocols, including scenarios in which the training and test data come from 1) different sessions, 2) the same session, and 3) a combination of both. Results indicate that when selecting optimal classifier training protocols for NIRS-BCI, a compromise between accuracy and convenience (e.g., in terms of duration/frequency of training data collection) must be considered.

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

PubMed Central

Rapoport, Shirley; Rubinsten, Orly; Katzir, Tami

2016-01-01

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

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

PubMed

Rapoport, Shirley; Rubinsten, Orly; Katzir, Tami

2016-01-01

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

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

PubMed

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

2018-04-01

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

Number line estimation and complex mental calculation: Is there a shared cognitive process driving the two tasks?

PubMed

Montefinese, Maria; Semenza, Carlo

2018-05-17

It is widely accepted that different number-related tasks, including solving simple addition and subtraction, may induce attentional shifts on the so-called mental number line, which represents larger numbers on the right and smaller numbers on the left. Recently, it has been shown that different number-related tasks also employ spatial attention shifts along with general cognitive processes. Here we investigated for the first time whether number line estimation and complex mental arithmetic recruit a common mechanism in healthy adults. Participants' performance in two-digit mental additions and subtractions using visual stimuli was compared with their performance in a mental bisection task using auditory numerical intervals. Results showed significant correlations between participants' performance in number line bisection and that in two-digit mental arithmetic operations, especially in additions, providing a first proof of a shared cognitive mechanism (or multiple shared cognitive mechanisms) between auditory number bisection and complex mental calculation.

Situational Context Affects Definiteness Preferences: Accommodation of Presuppositions

PubMed Central

Clifton, Charles

2013-01-01

Four experiments used self-paced reading and eyetracking to demonstrate that readers are, under some conditions, sensitive to the presuppositions of definite vs. indefinite DPs (determiner phrases). Reading was faster when the context stereotypically provided a single possible referent for a definite DP or multiple possible referents for an indefinite DP than when context and DP definiteness were mismatched. This finding goes beyond previous evidence that definite DPs are processed more rapidly than indefinite DPs when there is a unique or familiar referent in the context, showing that readers are sensitive to the semantics and pragmatics of (in)definiteness. However, the finding was obtained only when readers had to perform a simple arithmetic task between reading a sentence and seeing a question about it. The intervening task may have encouraged them to process the sentence more deeply in order to form a representation that would persist while doing the arithmetic. The methodological implications of this observation are discussed. PMID:22732029

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

PubMed

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

2017-12-01

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

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

PubMed

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.

Aggregation operators of neutrosophic linguistic numbers for multiple attribute group decision making.

PubMed

Ye, Jun

2016-01-01

Based on the concept of neutrosophic linguistic numbers (NLNs) in symbolic neutrosophic theory presented by Smarandache in 2015, the paper firstly proposes basic operational laws of NLNs and the expected value of a NLN to rank NLNs. Then, we propose the NLN weighted arithmetic average (NLNWAA) and NLN weighted geometric average (NLNWGA) operators and discuss their properties. Further, we establish a multiple attribute group decision-making (MAGDM) method by using the NLNWAA and NLNWGA operators under NLN environment. Finally, an illustrative example on a decision-making problem of manufacturing alternatives in the flexible manufacturing system is given to show the application of the proposed MAGDM method.

Do Children Understand Fraction Addition?

ERIC Educational Resources Information Center

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

2017-01-01

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

Dissociation between arithmetic relatedness and distance effects is modulated by task properties: an ERP study comparing explicit vs. implicit arithmetic processing.

PubMed

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.

Dissociation between arithmetic relatedness and distance effects is modulated by task properties: An ERP study comparing explicit vs. implicit arithmetic processing

PubMed Central

Avancini, Chiara; Galfano, Giovanni; Szűcs, Dénes

2014-01-01

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. PMID:25450162

Exploring the relationship between math anxiety and gender through implicit measurement

PubMed Central

Rubinsten, Orly; Bialik, Noam; Solar, Yael

2012-01-01

Math anxiety, defined as a negative affective response to mathematics, is suggested as a strong antecedent for the low visibility of women in the science and engineering workforce. However, the assumption of gender differences in math anxiety is still being studied and results are inconclusive, probably due to the use of explicit measures such as direct questionnaires. Thus, our primary objective was to investigate the effects of math anxiety on numerical processing in males and females by using a novel affective priming task as an indirect measure. Specifically, university students (23 males and 30 females) completed a priming task in which an arithmetic equation was preceded by one of four types of priming words (positive, neutral, negative, or related to mathematics). Participants were required to indicate whether the equation (simple math facts based on addition, subtraction, multiplication, or division) was true or false. People are typically found to respond to target stimuli more rapidly after presentation of an affectively related prime than after an affectively unrelated one. In the current study, shorter response latencies for positive as compared to negative affective primes were found in the male group. An affective priming effect was found in the female group as well, but with a reversed pattern. That is, significantly shorter response latencies were observed in the female group for negative as compared to positive targets. That is, for females, negative affective primes act as affectively related to simple arithmetic problems. In contrast, males associated positive affect with simple arithmetic. In addition, only females with lower or insignificant negative affect toward arithmetic study at faculties of mathematics and science. We discuss the advantages of examining pure anxiety factors with implicit measures which are free of response factors. In addition it is suggested that environmental factors may enhance the association between math achievements and math anxiety in females. PMID:23087633

Exploring the relationship between math anxiety and gender through implicit measurement.

PubMed

Rubinsten, Orly; Bialik, Noam; Solar, Yael

2012-01-01

Math anxiety, defined as a negative affective response to mathematics, is suggested as a strong antecedent for the low visibility of women in the science and engineering workforce. However, the assumption of gender differences in math anxiety is still being studied and results are inconclusive, probably due to the use of explicit measures such as direct questionnaires. Thus, our primary objective was to investigate the effects of math anxiety on numerical processing in males and females by using a novel affective priming task as an indirect measure. Specifically, university students (23 males and 30 females) completed a priming task in which an arithmetic equation was preceded by one of four types of priming words (positive, neutral, negative, or related to mathematics). Participants were required to indicate whether the equation (simple math facts based on addition, subtraction, multiplication, or division) was true or false. People are typically found to respond to target stimuli more rapidly after presentation of an affectively related prime than after an affectively unrelated one. In the current study, shorter response latencies for positive as compared to negative affective primes were found in the male group. An affective priming effect was found in the female group as well, but with a reversed pattern. That is, significantly shorter response latencies were observed in the female group for negative as compared to positive targets. That is, for females, negative affective primes act as affectively related to simple arithmetic problems. In contrast, males associated positive affect with simple arithmetic. In addition, only females with lower or insignificant negative affect toward arithmetic study at faculties of mathematics and science. We discuss the advantages of examining pure anxiety factors with implicit measures which are free of response factors. In addition it is suggested that environmental factors may enhance the association between math achievements and math anxiety in females.

Aztec arithmetic revisited: land-area algorithms and Acolhua congruence arithmetic.

PubMed

Williams, Barbara J; Jorge y Jorge, María del Carmen

2008-04-04

Acolhua-Aztec land records depicting areas and side dimensions of agricultural fields provide insight into Aztec arithmetic. Hypothesizing that recorded areas resulted from indigenous calculation, in a study of sample quadrilateral fields we found that 60% of the area values could be reproduced exactly by computation. In remaining cases, discrepancies between computed and recorded areas were consistently small, suggesting use of an unknown indigenous arithmetic. In revisiting the research, we discovered evidence for the use of congruence principles, based on proportions between the standard linear Acolhua measure and their units of shorter length. This procedure substitutes for computation with fractions and is labeled "Acolhua congruence arithmetic." The findings also clarify variance between Acolhua and Tenochca linear units, long an issue in understanding Aztec metrology.

Reconfigurable pipelined processor

DOE Office of Scientific and Technical Information (OSTI.GOV)

Saccardi, R.J.

1989-09-19

This patent describes a reconfigurable pipelined processor for processing data. It comprises: a plurality of memory devices for storing bits of data; a plurality of arithmetic units for performing arithmetic functions with the data; cross bar means for connecting the memory devices with the arithmetic units for transferring data therebetween; at least one counter connected with the cross bar means for providing a source of addresses to the memory devices; at least one variable tick delay device connected with each of the memory devices and arithmetic units; and means for providing control bits to the variable tick delay device formore » variably controlling the input and output operations thereof to selectively delay the memory devices and arithmetic units to align the data for processing in a selected sequence.« less

Program of arithmetic improvement by means of cognitive enhancement: an intervention in children with special educational needs.

PubMed

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.

Contributions of Domain-General Cognitive Resources and Different Forms of Arithmetic Development to Pre-Algebraic Knowledge

PubMed Central

Fuchs, Lynn S.; Compton, Donald L.; Fuchs, Douglas; Powell, Sarah R.; Schumacher, Robin F.; Hamlett, Carol L.; Vernier, Emily; Namkung, Jessica M.; Vukovic, Rose K.

2012-01-01

The purpose of this study was to investigate the contributions of domain-general cognitive resources and different forms of arithmetic development to individual differences in pre-algebraic knowledge. Children (n=279; mean age=7.59 yrs) were assessed on 7 domain-general cognitive resources as well as arithmetic calculations and word problems at start of 2nd grade and on calculations, word problems, and pre-algebraic knowledge at end of 3rd grade. Multilevel path analysis, controlling for instructional effects associated with the sequence of classrooms in which students were nested across grades 2–3, indicated arithmetic calculations and word problems are foundational to pre-algebraic knowledge. Also, results revealed direct contributions of nonverbal reasoning and oral language to pre-algebraic knowledge, beyond indirect effects that are mediated via arithmetic calculations and word problems. By contrast, attentive behavior, phonological processing, and processing speed contributed to pre-algebraic knowledge only indirectly via arithmetic calculations and word problems. PMID:22409764

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

PubMed

Lambert, Kevin

2013-06-01

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

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

PubMed

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

2009-07-01

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

A Pacific Ocean general circulation model for satellite data assimilation

NASA Technical Reports Server (NTRS)

Chao, Y.; Halpern, D.; Mechoso, C. R.

1991-01-01

A tropical Pacific Ocean General Circulation Model (OGCM) to be used in satellite data assimilation studies is described. The transfer of the OGCM from a CYBER-205 at NOAA's Geophysical Fluid Dynamics Laboratory to a CRAY-2 at NASA's Ames Research Center is documented. Two 3-year model integrations from identical initial conditions but performed on those two computers are compared. The model simulations are very similar to each other, as expected, but the simulations performed with the higher-precision CRAY-2 is smoother than that with the lower-precision CYBER-205. The CYBER-205 and CRAY-2 use 32 and 64-bit mantissa arithmetic, respectively. The major features of the oceanic circulation in the tropical Pacific, namely the North Equatorial Current, the North Equatorial Countercurrent, the South Equatorial Current, and the Equatorial Undercurrent, are realistically produced and their seasonal cycles are described. The OGCM provides a powerful tool for study of tropical oceans and for the assimilation of satellite altimetry data.

Conceptual Knowledge of Fraction Arithmetic

ERIC Educational Resources Information Center

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),…

Disabilities of Arithmetic and Mathematical Reasoning: Perspectives from Neurology and Neuropsychology.

ERIC Educational Resources Information Center

Rourke, Byron P.; Conway, James A.

1997-01-01

Reviews current research on brain-behavior relationships in disabilities of arithmetic and mathematical reasoning from both a neurological and a neuropsychological perspective. Defines developmental dyscalculia and the developmental importance of right versus left hemisphere integrity for the mediation of arithmetic learning and explores…

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

ERIC Educational Resources Information Center

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…

A Computational Model of Fraction Arithmetic

ERIC Educational Resources Information Center

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…

Arithmetic 400. A Computer Educational Program.

ERIC Educational Resources Information Center

Firestein, Laurie

"ARITHMETIC 400" is the first of the next generation of educational programs designed to encourage thinking about arithmetic problems. Presented in video game format, performance is a measure of correctness, speed, accuracy, and fortune as well. Play presents a challenge to individuals at various skill levels. The program, run on an Apple…

Simulating Network Retrieval of Arithmetic Facts.

ERIC Educational Resources Information Center

Ashcraft, Mark H.

This report describes a simulation of adults' retrieval of arithmetic facts from a network-based memory representation. The goals of the simulation project are to: demonstrate in specific form the nature of a spreading activation model of mental arithmetic; account for three important reaction time effects observed in laboratory investigations;…

Individual Differences in Children's Understanding of Inversion and Arithmetical Skill

ERIC Educational Resources Information Center

Gilmore, Camilla K.; Bryant, Peter

2006-01-01

Background and aims: In order to develop arithmetic expertise, children must understand arithmetic principles, such as the inverse relationship between addition and subtraction, in addition to learning calculation skills. We report two experiments that investigate children's understanding of the principle of inversion and the relationship between…

The Practice of Arithmetic in Liberian Schools.

ERIC Educational Resources Information Center

Brenner, Mary E.

1985-01-01

Describes a study of Liberian schools in which students of the Vai tribe are instructed in Western mathematical practices which differ from those of the students' home culture. Reports that the Vai children employed syncretic arithmetic practices, combining two distinct systems of arithmetic in a classroom environment that tacitly facilitated the…

From Arithmetic Sequences to Linear Equations

ERIC Educational Resources Information Center

Matsuura, Ryota; Harless, Patrick

2012-01-01

The first part of the article focuses on deriving the essential properties of arithmetic sequences by appealing to students' sense making and reasoning. The second part describes how to guide students to translate their knowledge of arithmetic sequences into an understanding of linear equations. Ryota Matsuura originally wrote these lessons for…

Baby Arithmetic: One Object Plus One Tone

ERIC Educational Resources Information Center

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

2004-01-01

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

Conceptual Knowledge of Decimal Arithmetic

ERIC Educational Resources Information Center

Lortie-Forgues, Hugues; Siegler, Robert S.

2016-01-01

In two studies (N's = 55 and 54), we 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…

IBM system/360 assembly language interval arithmetic software

NASA Technical Reports Server (NTRS)

Phillips, E. J.

1972-01-01

Computer software designed to perform interval arithmetic is described. An interval is defined as the set of all real numbers between two given numbers including or excluding one or both endpoints. Interval arithmetic consists of the various elementary arithmetic operations defined on the set of all intervals, such as interval addition, subtraction, union, etc. One of the main applications of interval arithmetic is in the area of error analysis of computer calculations. For example, it has been used sucessfully to compute bounds on sounding errors in the solution of linear algebraic systems, error bounds in numerical solutions of ordinary differential equations, as well as integral equations and boundary value problems. The described software enables users to implement algorithms of the type described in references efficiently on the IBM 360 system.

Factor structure of the Norwegian version of the WAIS-III in a clinical sample: the arithmetic problem.

PubMed

Egeland, Jens; Bosnes, Ole; Johansen, Hans

2009-09-01

Confirmatory Factor Analyses (CFA) of the Wechsler Adult Intelligence Scale-III (WAIS-III) lend partial support to the four-factor model proposed in the test manual. However, the Arithmetic subtest has been especially difficult to allocate to one factor. Using the new Norwegian WAIS-III version, we tested factor models differing in the number of factors and in the placement of the Arithmetic subtest in a mixed clinical sample (n = 272). Only the four-factor solutions had adequate goodness-of-fit values. Allowing Arithmetic to load on both the Verbal Comprehension and Working Memory factors provided a more parsimonious solution compared to considering the subtest only as a measure of Working Memory. Effects of education were particularly high for both the Verbal Comprehension tests and Arithmetic.

Evaluation of the Triple Code Model of numerical processing-Reviewing past neuroimaging and clinical findings.

PubMed

Siemann, Julia; Petermann, Franz

2018-01-01

This review reconciles past findings on numerical processing with key assumptions of the most predominant model of arithmetic in the literature, the Triple Code Model (TCM). This is implemented by reporting diverse findings in the literature ranging from behavioral studies on basic arithmetic operations over neuroimaging studies on numerical processing to developmental studies concerned with arithmetic acquisition, with a special focus on developmental dyscalculia (DD). We evaluate whether these studies corroborate the model and discuss possible reasons for contradictory findings. A separate section is dedicated to the transfer of TCM to arithmetic development and to alternative accounts focusing on developmental questions of numerical processing. We conclude with recommendations for future directions of arithmetic research, raising questions that require answers in models of healthy as well as abnormal mathematical development. This review assesses the leading model in the field of arithmetic processing (Triple Code Model) by presenting knowledge from interdisciplinary research. It assesses the observed contradictory findings and integrates the resulting opposing viewpoints. The focus is on the development of arithmetic expertise as well as abnormal mathematical development. The original aspect of this article is that it points to a gap in research on these topics and provides possible solutions for future models. Copyright © 2017 Elsevier Ltd. All rights reserved.

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

PubMed

Cipora, Krzysztof; Nuerk, Hans-Christoph

2013-01-01

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

Microarray-based Resequencing of Multiple Bacillus anthracis Isolates

DTIC Science & Technology

2004-12-17

generated an Unweighted Pair Group Method Arithmetic Mean ( UPGMA ) tree (see methods [56]; Figure 3). The strains group together in a manner broadly similar...was created using DNADIST, plotted as a UPGMA tree using NEIGHBOR and the tree plotted using DRAWGRAM [56]. The B1 strain A0465 was used as an...distance matrix was created using DNADIST, plotted as a UPGMA tree using NEIGHBOR and the tree plotted using DRAWGRAM [57]. Additional data files The

Study on initiative vibration absorbing technology of optics in strong disturbed environment

NASA Astrophysics Data System (ADS)

Jia, Si-nan; Xiong, Mu-di; Zou, Xiao-jie

2007-12-01

Strong disturbed environment is apt to cause irregular vibration, which seriously affects optical collimation. To improve the performance of laser beam, three-point dynamic vibration absorbing method is proposed, and laser beam initiative vibration absorbing system is designed. The maladjustment signal is detected by position sensitive device (PSD), three groups of PZT are driven to adjust optical element in real-time, so the performance of output-beam is improved. The coupling model of the system is presented. Multivariable adaptive closed-loop decoupling arithmetic is used to design three-input-three-output decoupling controller, so that high precision dynamic adjusting is realized. Experiments indicate that the system has good shock absorbing efficiency.

An O(log sup 2 N) parallel algorithm for computing the eigenvalues of a symmetric tridiagonal matrix

NASA Technical Reports Server (NTRS)

Swarztrauber, Paul N.

1989-01-01

An O(log sup 2 N) parallel algorithm is presented for computing the eigenvalues of a symmetric tridiagonal matrix using a parallel algorithm for computing the zeros of the characteristic polynomial. The method is based on a quadratic recurrence in which the characteristic polynomial is constructed on a binary tree from polynomials whose degree doubles at each level. Intervals that contain exactly one zero are determined by the zeros of polynomials at the previous level which ensures that different processors compute different zeros. The exact behavior of the polynomials at the interval endpoints is used to eliminate the usual problems induced by finite precision arithmetic.

VLSI architectures for computing multiplications and inverses in GF(2m)

NASA Technical Reports Server (NTRS)

Wang, C. C.; Truong, T. K.; Shao, H. M.; Deutsch, L. J.; Omura, J. K.

1985-01-01

Finite field arithmetic logic is central in the implementation of Reed-Solomon coders and in some cryptographic algorithms. There is a need for good multiplication and inversion algorithms that are easily realized on VLSI chips. Massey and Omura recently developed a new multiplication algorithm for Galois fields based on a normal basis representation. A pipeline structure is developed to realize the Massey-Omura multiplier in the finite field GF(2m). With the simple squaring property of the normal-basis representation used together with this multiplier, a pipeline architecture is also developed for computing inverse elements in GF(2m). The designs developed for the Massey-Omura multiplier and the computation of inverse elements are regular, simple, expandable and, therefore, naturally suitable for VLSI implementation.

VLSI architectures for computing multiplications and inverses in GF(2-m)

NASA Technical Reports Server (NTRS)

Wang, C. C.; Truong, T. K.; Shao, H. M.; Deutsch, L. J.; Omura, J. K.; Reed, I. S.

1983-01-01

Finite field arithmetic logic is central in the implementation of Reed-Solomon coders and in some cryptographic algorithms. There is a need for good multiplication and inversion algorithms that are easily realized on VLSI chips. Massey and Omura recently developed a new multiplication algorithm for Galois fields based on a normal basis representation. A pipeline structure is developed to realize the Massey-Omura multiplier in the finite field GF(2m). With the simple squaring property of the normal-basis representation used together with this multiplier, a pipeline architecture is also developed for computing inverse elements in GF(2m). The designs developed for the Massey-Omura multiplier and the computation of inverse elements are regular, simple, expandable and, therefore, naturally suitable for VLSI implementation.

VLSI architectures for computing multiplications and inverses in GF(2m).

PubMed

Wang, C C; Truong, T K; Shao, H M; Deutsch, L J; Omura, J K; Reed, I S

1985-08-01

Finite field arithmetic logic is central in the implementation of Reed-Solomon coders and in some cryptographic algorithms. There is a need for good multiplication and inversion algorithms that can be easily realized on VLSI chips. Massey and Omura recently developed a new multiplication algorithm for Galois fields based on a normal basis representation. In this paper, a pipeline structure is developed to realize the Massey-Omura multiplier in the finite field GF(2m). With the simple squaring property of the normal basis representation used together with this multiplier, a pipeline architecture is developed for computing inverse elements in GF(2m). The designs developed for the Massey-Omura multiplier and the computation of inverse elements are regular, simple, expandable, and therefore, naturally suitable for VLSI implementation.

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

PubMed

Gilmore, Camilla K; Bryant, Peter

2006-06-01

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

Fabrication of an infrared Shack-Hartmann sensor by combining high-speed single-point diamond milling and precision compression molding processes.

PubMed

Zhang, Lin; Zhou, Wenchen; Naples, Neil J; Yi, Allen Y

2018-05-01

A novel fabrication method by combining high-speed single-point diamond milling and precision compression molding processes for fabrication of discontinuous freeform microlens arrays was proposed. Compared with slow tool servo diamond broaching, high-speed single-point diamond milling was selected for its flexibility in the fabrication of true 3D optical surfaces with discontinuous features. The advantage of single-point diamond milling is that the surface features can be constructed sequentially by spacing the axes of a virtual spindle at arbitrary positions based on the combination of rotational and translational motions of both the high-speed spindle and linear slides. By employing this method, each micro-lenslet was regarded as a microstructure cell by passing the axis of the virtual spindle through the vertex of each cell. An optimization arithmetic based on minimum-area fabrication was introduced to the machining process to further increase the machining efficiency. After the mold insert was machined, it was employed to replicate the microlens array onto chalcogenide glass. In the ensuing optical measurement, the self-built Shack-Hartmann wavefront sensor was proven to be accurate in detecting an infrared wavefront by both experiments and numerical simulation. The combined results showed that precision compression molding of chalcogenide glasses could be an economic and precision optical fabrication technology for high-volume production of infrared optics.

A Substituting Meaning for the Equals Sign in Arithmetic Notating Tasks

ERIC Educational Resources Information Center

Jones, Ian; Pratt, Dave

2012-01-01

Three studies explore arithmetic tasks that support both substitutive and basic relational meanings for the equals sign. The duality of meanings enabled children to engage meaningfully and purposefully with the structural properties of arithmetic statements in novel ways. Some, but not all, children were successful at the adapted task and were…

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

ERIC Educational Resources Information Center

Prather, Richard; Alibali, Martha W.

2011-01-01

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

Identifying Simple Numerical Stimuli: Processing Inefficiencies Exhibited by Arithmetic Learning Disabled Children.

ERIC Educational Resources Information Center

Koontz, Kristine L.; Berch, Daniel B.

1996-01-01

Children with arithmetic learning disabilities (n=16) and normally achieving controls (n=16) in grades 3-5 were administered a battery of computerized tasks. Memory spans for both letters and digits were found to be smaller among the arithmetic learning disabled children. Implications for teaching are discussed. (Author/CMS)

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

ERIC Educational Resources Information Center

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,…

ASIC For Complex Fixed-Point Arithmetic

NASA Technical Reports Server (NTRS)

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

1995-01-01

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

Arithmetic Performance of Children with Cerebral Palsy: The Influence of Cognitive and Motor Factors

ERIC Educational Resources Information Center

van Rooijen, Maaike; Verhoeven, Ludo; Smits, Dirk-Wouter; Ketelaar, Marjolijn; Becher, Jules G.; Steenbergen, Bert

2012-01-01

Children diagnosed with cerebral palsy (CP) often show difficulties in arithmetic compared to their typically developing peers. The present study explores whether cognitive and motor variables are related to arithmetic performance of a large group of primary school children with CP. More specifically, the relative influence of non-verbal…

Cognitive Arithmetic: Evidence for the Development of Automaticity.

ERIC Educational Resources Information Center

LeFevre, Jo-Anne; Bisanz, Jeffrey

To determine whether children's knowledge of arithmetic facts becomes increasingly "automatic" with age, 7-year-olds, 11-year-olds, and adults were given a number-matching task for which mental arithmetic should have been irrelevant. Specifically, students were required to verify the presence of a probe number in a previously presented pair (e.g.,…

Continuity in Representation between Children and Adults: Arithmetic Knowledge Hinders Undergraduates' Algebraic Problem Solving

ERIC Educational Resources Information Center

McNeil, Nicole M.; Rittle-Johnson, Bethany; Hattikudur, Shanta; Petersen, Lori A.

2010-01-01

This study examined if solving arithmetic problems hinders undergraduates' accuracy on algebra problems. The hypothesis was that solving arithmetic problems would hinder accuracy because it activates an operational view of equations, even in educated adults who have years of experience with algebra. In three experiments, undergraduates (N = 184)…

Fostering Formal Commutativity Knowledge with Approximate Arithmetic

PubMed Central

Hansen, Sonja Maria; Haider, Hilde; Eichler, Alexandra; Godau, Claudia; Frensch, Peter A.; Gaschler, Robert

2015-01-01

How can we enhance the understanding of abstract mathematical principles in elementary school? Different studies found out that nonsymbolic estimation could foster subsequent exact number processing and simple arithmetic. Taking the commutativity principle as a test case, we investigated if the approximate calculation of symbolic commutative quantities can also alter the access to procedural and conceptual knowledge of a more abstract arithmetic principle. Experiment 1 tested first graders who had not been instructed about commutativity in school yet. Approximate calculation with symbolic quantities positively influenced the use of commutativity-based shortcuts in formal arithmetic. We replicated this finding with older first graders (Experiment 2) and third graders (Experiment 3). Despite the positive effect of approximation on the spontaneous application of commutativity-based shortcuts in arithmetic problems, we found no comparable impact on the application of conceptual knowledge of the commutativity principle. Overall, our results show that the usage of a specific arithmetic principle can benefit from approximation. However, the findings also suggest that the correct use of certain procedures does not always imply conceptual understanding. Rather, the conceptual understanding of commutativity seems to lag behind procedural proficiency during elementary school. PMID:26560311

Frontoparietal white matter diffusion properties predict mental arithmetic skills in children

PubMed Central

Tsang, Jessica M.; Dougherty, Robert F.; Deutsch, Gayle K.; Wandell, Brian A.; Ben-Shachar, Michal

2009-01-01

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. PMID:19948963

Recoded and nonrecoded trinary signed-digit adders and multipliers with redundant-bit representations

NASA Astrophysics Data System (ADS)

Cherri, Abdallah K.; Alam, Mohammed S.

1998-07-01

Highly-efficient two-step recoded and one-step nonrecoded trinary signed-digit (TSD) carry-free adders subtracters are presented on the basis of redundant-bit representation for the operands digits. It has been shown that only 24 (30) minterms are needed to implement the two-step recoded (the one-step nonrecoded) TSD addition for any operand length. Optical implementation of the proposed arithmetic can be carried out by use of correlation- or matrix-multiplication-based schemes, saving 50% of the system memory. Furthermore, we present four different multiplication designs based on our proposed recoded and nonrecoded TSD adders. Our multiplication designs require a small number of reduced minterms to generate the multiplication partial products. Finally, a recently proposed pipelined iterative-tree algorithm can be used in the TSD adders multipliers; consequently, efficient use of all available adders can be made.

Recoded and nonrecoded trinary signed-digit adders and multipliers with redundant-bit representations.

PubMed

Cherri, A K; Alam, M S

1998-07-10

Highly-efficient two-step recoded and one-step nonrecoded trinary signed-digit (TSD) carry-free adders-subtracters are presented on the basis of redundant-bit representation for the operands' digits. It has been shown that only 24 (30) minterms are needed to implement the two-step recoded (the one-step nonrecoded) TSD addition for any operand length. Optical implementation of the proposed arithmetic can be carried out by use of correlation- or matrix-multiplication-based schemes, saving 50% of the system memory. Furthermore, we present four different multiplication designs based on our proposed recoded and nonrecoded TSD adders. Our multiplication designs require a small number of reduced minterms to generate the multiplication partial products. Finally, a recently proposed pipelined iterative-tree algorithm can be used in the TSD adders-multipliers; consequently, efficient use of all available adders can be made.

Computing the Density Matrix in Electronic Structure Theory on Graphics Processing Units.

PubMed

Cawkwell, M J; Sanville, E J; Mniszewski, S M; Niklasson, Anders M N

2012-11-13

The self-consistent solution of a Schrödinger-like equation for the density matrix is a critical and computationally demanding step in quantum-based models of interatomic bonding. This step was tackled historically via the diagonalization of the Hamiltonian. We have investigated the performance and accuracy of the second-order spectral projection (SP2) algorithm for the computation of the density matrix via a recursive expansion of the Fermi operator in a series of generalized matrix-matrix multiplications. We demonstrate that owing to its simplicity, the SP2 algorithm [Niklasson, A. M. N. Phys. Rev. B2002, 66, 155115] is exceptionally well suited to implementation on graphics processing units (GPUs). The performance in double and single precision arithmetic of a hybrid GPU/central processing unit (CPU) and full GPU implementation of the SP2 algorithm exceed those of a CPU-only implementation of the SP2 algorithm and traditional matrix diagonalization when the dimensions of the matrices exceed about 2000 × 2000. Padding schemes for arrays allocated in the GPU memory that optimize the performance of the CUBLAS implementations of the level 3 BLAS DGEMM and SGEMM subroutines for generalized matrix-matrix multiplications are described in detail. The analysis of the relative performance of the hybrid CPU/GPU and full GPU implementations indicate that the transfer of arrays between the GPU and CPU constitutes only a small fraction of the total computation time. The errors measured in the self-consistent density matrices computed using the SP2 algorithm are generally smaller than those measured in matrices computed via diagonalization. Furthermore, the errors in the density matrices computed using the SP2 algorithm do not exhibit any dependence of system size, whereas the errors increase linearly with the number of orbitals when diagonalization is employed.

Optical computing using optical flip-flops in Fourier processors: use in matrix multiplication and discrete linear transforms.

PubMed

Ando, S; Sekine, S; Mita, M; Katsuo, S

1989-12-15

An architecture and the algorithms for matrix multiplication using optical flip-flops (OFFs) in optical processors are proposed based on residue arithmetic. The proposed system is capable of processing all elements of matrices in parallel utilizing the information retrieving ability of optical Fourier processors. The employment of OFFs enables bidirectional data flow leading to a simpler architecture and the burden of residue-to-decimal (or residue-to-binary) conversion to operation time can be largely reduced by processing all elements in parallel. The calculated characteristics of operation time suggest a promising use of the system in a real time 2-D linear transform.

Finding New Math Identities by Computer

NASA Technical Reports Server (NTRS)

Bailey, David H.; Chancellor, Marisa K. (Technical Monitor)

1996-01-01

Recently a number of interesting new mathematical identities have been discovered by means of numerical searches on high performance computers, using some newly discovered algorithms. These include the following: pi = ((sup oo)(sub k=0))(Sigma) (1 / 16) (sup k) ((4 / 8k+1) - (2 / 8k+4) - (1 / 8k+5) - (1 / 8k+6)) and ((17 pi(exp 4)) / 360) = ((sup oo)(sub k=1))(Sigma) (1 + (1/2) + (1/3) + ... + (1/k))(exp 2) k(exp -2), zeta(3, 1, 3, 1, ..., 3, 1) = (2 pi(exp 4m) / (4m+2)! where m = number of (3,1) pairs. and where zeta(n1,n2,...,nr) = (sub k1 (is greater than) k2 (is greater than) ... (is greater than) kr)(Sigma) (1 / (k1 (sup n1) k2 (sup n2) ... kr (sup nr). The first identity is remarkable in that it permits one to compute the n-th binary or hexadecimal digit of pu directly, without computing any of the previous digits, and without using multiple precision arithmetic. Recently the ten billionth hexadecimal digit of pi was computed using this formula. The third identity has connections to quantum field theory. (The first and second of these been formally established; the third is affirmed by numerical evidence only.) The background and results of this work will be described, including an overview of the algorithms and computer techniques used in these studies.

Economical Implementation of a Filter Engine in an FPGA

NASA Technical Reports Server (NTRS)

Kowalski, James E.

2009-01-01

A logic design has been conceived for a field-programmable gate array (FPGA) that would implement a complex system of multiple digital state-space filters. The main innovative aspect of this design lies in providing for reuse of parts of the FPGA hardware to perform different parts of the filter computations at different times, in such a manner as to enable the timely performance of all required computations in the face of limitations on available FPGA hardware resources. The implementation of the digital state-space filter involves matrix vector multiplications, which, in the absence of the present innovation, would ordinarily necessitate some multiplexing of vector elements and/or routing of data flows along multiple paths. The design concept calls for implementing vector registers as shift registers to simplify operand access to multipliers and accumulators, obviating both multiplexing and routing of data along multiple paths. Each vector register would be reused for different parts of a calculation. Outputs would always be drawn from the same register, and inputs would always be loaded into the same register. A simple state machine would control each filter. The output of a given filter would be passed to the next filter, accompanied by a "valid" signal, which would start the state machine of the next filter. Multiple filter modules would share a multiplication/accumulation arithmetic unit. The filter computations would be timed by use of a clock having a frequency high enough, relative to the input and output data rate, to provide enough cycles for matrix and vector arithmetic operations. This design concept could prove beneficial in numerous applications in which digital filters are used and/or vectors are multiplied by coefficient matrices. Examples of such applications include general signal processing, filtering of signals in control systems, processing of geophysical measurements, and medical imaging. For these and other applications, it could be advantageous to combine compact FPGA digital filter implementations with other application-specific logic implementations on single integrated-circuit chips. An FPGA could readily be tailored to implement a variety of filters because the filter coefficients would be loaded into memory at startup.

Working Memory and Arithmetic Calculation in Children: The Contributory Roles of Processing Speed, Short-Term Memory, and Reading

ERIC Educational Resources Information Center

Berg, Derek H.

2008-01-01

The cognitive underpinnings of arithmetic calculation in children are noted to involve working memory; however, cognitive processes related to arithmetic calculation and working memory suggest that this relationship is more complex than stated previously. The purpose of this investigation was to examine the relative contributions of processing…

Arithmetic Achievement in Children with Cerebral Palsy or Spina Bifida Meningomyelocele

ERIC Educational Resources Information Center

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…

The Association between Arithmetic and Reading Performance in School: A Meta-Analytic Study

ERIC Educational Resources Information Center

Singer, Vivian; Strasser, Kathernie

2017-01-01

Many studies of school achievement find a significant association between reading and arithmetic achievement. The magnitude of the association varies widely across the studies, but the sources of this variation have not been identified. The purpose of this paper is to examine the magnitude and determinants of the relation between arithmetic and…

24 CFR Appendix E to Part 3500 - Arithmetic Steps

Code of Federal Regulations, 2010 CFR

2010-04-01

... 24 Housing and Urban Development 5 2010-04-01 2010-04-01 false Arithmetic Steps E Appendix E to...—Arithmetic Steps I. Example Illustrating Aggregate Analysis: ASSUMPTIONS: Disbursements: $360 for school... Payment: July 1 Step 1—Initial Trial Balance Aggregate pmt disb bal Jun 0 0 0 Jul 130 500 −370 Aug 130 0...

Computational Fluency and Strategy Choice Predict Individual and Cross-National Differences in Complex Arithmetic

ERIC Educational Resources Information Center

Vasilyeva, Marina; Laski, Elida V.; Shen, Chen

2015-01-01

The present study tested the hypothesis that children's fluency with basic number facts and knowledge of computational strategies, derived from early arithmetic experience, predicts their performance on complex arithmetic problems. First-grade students from United States and Taiwan (N = 152, mean age: 7.3 years) were presented with problems that…

Arithmetic Difficulties in Children with Cerebral Palsy Are Related to Executive Function and Working Memory

ERIC Educational Resources Information Center

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…

Cognitive Impairments of Children with Severe Arithmetic Difficulties: Cognitive Deficit or Developmental Lag?

ERIC Educational Resources Information Center

Berg, Derek H.

2008-01-01

An age-matched/achievement-matched design was utilized to examine the cognitive functioning of children with severe arithmetic difficulties. A battery of cognitive tasks was administered to three groups of elementary aged children: 20 children with severe arithmetic difficulties (SAD), 20 children matched in age (CAM) to the children with SAD, and…

A Cross-Cultural Investigation into the Development of Place-Value Concepts of Children in Taiwan and the United States.

ERIC Educational Resources Information Center

Yang, Ma Tzu-Lin; Cobb, Paul

1995-01-01

Compares mathematics achievement of children in Taiwan and the United States by analyzing the arithmetical learning contexts of each. Interviews with parents and teachers identify cultural beliefs about learning arithmetic; interviews with students identify level of sophistication of arithmetical concepts. Found greater understanding by Chinese…

Comparing the Use of the Interpersonal Computer, Personal Computer and Pen-and-Paper When Solving Arithmetic Exercises

ERIC Educational Resources Information Center

Alcoholado, Cristián; Diaz, Anita; Tagle, Arturo; Nussbaum, Miguel; Infante, Cristián

2016-01-01

This study aims to understand the differences in student learning outcomes and classroom behaviour when using the interpersonal computer, personal computer and pen-and-paper to solve arithmetic exercises. In this multi-session experiment, third grade students working on arithmetic exercises from various curricular units were divided into three…

Changes of brain response induced by simulated weightlessness

NASA Astrophysics Data System (ADS)

Wei, Jinhe; Yan, Gongdong; Guan, Zhiqiang

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

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

PubMed

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

2009-05-01

Arithmetic ability was tested in children with cerebral palsy without severe intellectual impairment (verbal IQ >or= 70) attending special (n = 41) or mainstream education (n = 16) as well as control children in mainstream education (n = 16) throughout first and second grade. Children with cerebral palsy in special education did not appear to have fully automatized arithmetic facts by the end of second grade. Their lower accuracy and consistently slower (verbal) response times raise important concerns for their future arithmetic development. Differences in arithmetic performance between children with cerebral palsy in special or mainstream education were not related to localization of cerebral palsy or to gross motor impairment. Rather, lower accuracy and slower verbal responses were related to differences in nonverbal intelligence and the presence of epilepsy. Left-hand impairment was related to slower verbal responses but not to lower accuracy.

Computational fluency and strategy choice predict individual and cross-national differences in complex arithmetic.

PubMed

Vasilyeva, Marina; Laski, Elida V; Shen, Chen

2015-10-01

The present study tested the hypothesis that children's fluency with basic number facts and knowledge of computational strategies, derived from early arithmetic experience, predicts their performance on complex arithmetic problems. First-grade students from United States and Taiwan (N = 152, mean age: 7.3 years) were presented with problems that differed in difficulty: single-, mixed-, and double-digit addition. Children's strategy use varied as a function of problem difficulty, consistent with Siegler's theory of strategy choice. The use of decomposition strategy interacted with computational fluency in predicting the accuracy of double-digit addition. Further, the frequency of decomposition and computational fluency fully mediated cross-national differences in accuracy on these complex arithmetic problems. The results indicate the importance of both fluency with basic number facts and the decomposition strategy for later arithmetic performance. (c) 2015 APA, all rights reserved).

The MasPar MP-1 As a Computer Arithmetic Laboratory

PubMed Central

Anuta, Michael A.; Lozier, Daniel W.; Turner, Peter R.

1996-01-01

This paper is a blueprint for the use of a massively parallel SIMD computer architecture for the simulation of various forms of computer arithmetic. The particular system used is a DEC/MasPar MP-1 with 4096 processors in a square array. This architecture has many advantages for such simulations due largely to the simplicity of the individual processors. Arithmetic operations can be spread across the processor array to simulate a hardware chip. Alternatively they may be performed on individual processors to allow simulation of a massively parallel implementation of the arithmetic. Compromises between these extremes permit speed-area tradeoffs to be examined. The paper includes a description of the architecture and its features. It then summarizes some of the arithmetic systems which have been, or are to be, implemented. The implementation of the level-index and symmetric level-index, LI and SLI, systems is described in some detail. An extensive bibliography is included. PMID:27805123

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

PubMed Central

Vanbinst, Kiran; Ansari, Daniel; Ghesquière, Pol; De Smedt, Bert

2016-01-01

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. PMID:26942935

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

NASA Astrophysics Data System (ADS)

Cherri, Abdallah K.

1998-08-01

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

Visuospatial and verbal memory in mental arithmetic.

PubMed

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.

The semantic system is involved in mathematical problem solving.

PubMed

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

2018-02-01

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

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

ERIC Educational Resources Information Center

Education Development Center, Inc., Newton, MA.

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

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

ERIC Educational Resources Information Center

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…

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

ERIC Educational Resources Information Center

Barrouillet, Pierre; Poirier, Louise

1997-01-01

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

Working Memory as a Predictor of Written Arithmetical Skills in Children: The Importance of Central Executive Functions

ERIC Educational Resources Information Center

Andersson, Ulf

2008-01-01

Background: The study was conducted in an attempt to further our understanding of how working memory contributes to written arithmetical skills in children. Aim: The aim was to pinpoint the contribution of different central executive functions and to examine the contribution of the two subcomponents of children's written arithmetical skills.…

Contributions of Domain-General Cognitive Resources and Different Forms of Arithmetic Development to Pre-Algebraic Knowledge

ERIC Educational Resources Information Center

Fuchs, Lynn S.; Compton, Donald L.; Fuchs, Douglas; Powell, Sarah R.; Schumacher, Robin F.; Hamlett, Carol L.; Vernier, Emily; Namkung, Jessica M.; Vukovic, Rose K.

2012-01-01

The purpose of this study was to investigate the contributions of domain-general cognitive resources and different forms of arithmetic development to individual differences in pre-algebraic knowledge. Children (n = 279, mean age = 7.59 years) were assessed on 7 domain-general cognitive resources as well as arithmetic calculations and word problems…

Error-correcting codes in computer arithmetic.

NASA Technical Reports Server (NTRS)

Massey, J. L.; Garcia, O. N.

1972-01-01

Summary of the most important results so far obtained in the theory of coding for the correction and detection of errors in computer arithmetic. Attempts to satisfy the stringent reliability demands upon the arithmetic unit are considered, and special attention is given to attempts to incorporate redundancy into the numbers themselves which are being processed so that erroneous results can be detected and corrected.

Limitations to Teaching Children 2 + 2 = 4: Typical Arithmetic Problems Can Hinder Learning of Mathematical Equivalence

ERIC Educational Resources Information Center

McNeil, Nicole M.

2008-01-01

Do typical arithmetic problems hinder learning of mathematical equivalence? Second and third graders (7-9 years old; N= 80) received lessons on mathematical equivalence either with or without typical arithmetic problems (e.g., 15 + 13 = 28 vs. 28 = 28, respectively). Children then solved math equivalence problems (e.g., 3 + 9 + 5 = 6 + __),…

Arithmetic Data Cube as a Data Intensive Benchmark

NASA Technical Reports Server (NTRS)

Frumkin, Michael A.; Shabano, Leonid

2003-01-01

Data movement across computational grids and across memory hierarchy of individual grid machines is known to be a limiting factor for application involving large data sets. In this paper we introduce the Data Cube Operator on an Arithmetic Data Set which we call Arithmetic Data Cube (ADC). We propose to use the ADC to benchmark grid capabilities to handle large distributed data sets. The ADC stresses all levels of grid memory by producing 2d views of an Arithmetic Data Set of d-tuples described by a small number of parameters. We control data intensity of the ADC by controlling the sizes of the views through choice of the tuple parameters.

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

PubMed

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

2009-11-01

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

Quantum mechanics problems in observer's mathematics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Khots, Boris; Khots, Dmitriy; iMath Consulting LLC, Omaha, Nebraska

2012-11-06

This work considers the ontology, guiding equation, Schrodinger's equation, relation to the Born Rule, the conditional wave function of a subsystem in a setting of arithmetic, algebra and topology provided by Observer's Mathematics (see www.mathrelativity.com). Observer's Mathematics creates new arithmetic, algebra, geometry, topology, analysis and logic which do not contain the concept of continuum, but locally coincide with the standard fields. Certain results and communications pertaining to solutions of these problems are provided. In particular, we prove the following theorems: Theorem I (Two-slit interference). Let {Psi}{sub 1} be a wave from slit 1, {Psi}{sub 2} - from slit 2, andmore » {Psi} = {Psi}{sub 1}+{Psi}{sub 2}. Then the probability of {Psi} being a wave equals to 0.5. Theorem II (k-bodies solution). For W{sub n} from m-observer point of view with m>log{sub 10}((2 Multiplication-Sign 10{sup 2n}-1){sup 2k}+1), the probability of standard expression of Hamiltonian variation is less than 1 and depends on n,m,k.« less

Text-interpreter language for flexible generation of patient notes and instructions.

PubMed

Forker, T S

1992-01-01

An interpreted computer language has been developed along with a windowed user interface and multi-printer-support formatter to allow preparation of documentation of patient visits, including progress notes, prescriptions, excuses for work/school, outpatient laboratory requisitions, and patient instructions. Input is by trackball or mouse with little or no keyboard skill required. For clinical problems with specific protocols, the clinician can be prompted with problem-specific items of history, exam, and lab data to be gathered and documented. The language implements a number of text-related commands as well as branching logic and arithmetic commands. In addition to generating text, it is simple to implement arithmetic calculations such as weight-specific drug dosages; multiple branching decision-support protocols for paramedical personnel (or physicians); and calculation of clinical scores (e.g., coma or trauma scores) while simultaneously documenting the status of each component of the score. ASCII text files produced by the interpreter are available for computerized quality audit. Interpreter instructions are contained in text files users can customize with any text editor.

Low numeracy predicts reduced accuracy of retrospective reports of frequency of sexual behavior.

PubMed

McAuliffe, Timothy L; DiFranceisco, Wayne; Reed, Barbara R

2010-12-01

Assessment of the frequency of sexual behavior relies on participants' ability to arithmetically aggregate information over time and across partners. This study examines the effect of numeracy (arithmetic skills) on the accuracy of retrospective reports of sexual behavior. For 91 days, the participants completed daily reports about their sexual activity. Participants then completed a survey on sexual behavior over the same period. The discrepancies between the survey-based and the diary-based measures of frequency of vaginal and anal intercourse were evaluated. Multiple regression analysis showed that the discrepancy between retrospective and diary measurements of sexual intercourse increased with lower numeracy (P = 0.026), lower education (P = 0.001), aggregate question format compared to partner-by-partner format (P = 0.031) and higher frequency of intercourse occasions (P < 0.001). Lower numeracy led to a 1.5-fold increase (adjusted mean = 14.1-20.9) in the discrepancy for those using the aggregate question format and a 2.0-fold increase (adjusted mean = 3.7-7.6) for those using the partner-by-partner format.

Adolescents’ Functional Numeracy Is Predicted by Their School Entry Number System Knowledge

PubMed Central

Geary, David C.; Hoard, Mary K.; Nugent, Lara; Bailey, Drew H.

2013-01-01

One in five adults in the United States is functionally innumerate; they do not possess the mathematical competencies needed for many modern jobs. We administered functional numeracy measures used in studies of young adults’ employability and wages to 180 thirteen-year-olds. The adolescents began the study in kindergarten and participated in multiple assessments of intelligence, working memory, mathematical cognition, achievement, and in-class attentive behavior. Their number system knowledge at the beginning of first grade was defined by measures that assessed knowledge of the systematic relations among Arabic numerals and skill at using this knowledge to solve arithmetic problems. Early number system knowledge predicted functional numeracy more than six years later (ß = 0.195, p = .0014) controlling for intelligence, working memory, in-class attentive behavior, mathematical achievement, demographic and other factors, but skill at using counting procedures to solve arithmetic problems did not. In all, we identified specific beginning of schooling numerical knowledge that contributes to individual differences in adolescents’ functional numeracy and demonstrated that performance on mathematical achievement tests underestimates the importance of this early knowledge. PMID:23382934

A cognitive characterization of dyscalculia in Turner syndrome.

PubMed

Bruandet, Marie; Molko, Nicolas; Cohen, Laurent; Dehaene, Stanislas

2004-01-01

Current theories of number processing postulate that the human abilities for arithmetic are based on cerebral circuits that are partially laid down under genetic control and later modified by schooling and education. This view predicts the existence of genetic diseases that interfere specifically with components of the number system. Here, we investigate whether Turner syndrome (TS) corresponds to this definition. TS is a genetic disorder which affects one woman in 2500 and is characterized by partial or complete absence of one X chromosome. In addition to well-characterized physical and hormonal dysfunction, TS patients exhibit cognitive deficits including dyscalculia. We tested 12 women with Turner syndrome and 13 control subjects on a cognitive battery including arithmetical tests (addition, subtraction, multiplication, division) as well as tests of the understanding of numerosity and quantity (cognitive estimation, estimation, comparison, bisection, subitizing/counting). Impairments were observed in cognitive estimation, subitizing, and calculation. We examine whether these deficits can be attributed to a single source, and discuss the possible implications of hormonal and genetic factors in the neuropsychological profile of TS patients.

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

PubMed

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

1994-07-01

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

Academic skills in the long term after epilepsy surgery in childhood.

PubMed

Puka, Klajdi; Smith, Mary Lou

2016-09-01

We evaluated the progression of academic skills in a cohort of patients who underwent, or were considered for, epilepsy surgery in childhood, four to eleven years before. The few existing studies that have evaluated cognitive function in the long term after surgery have examined intelligence and memory. Participants were 97 patients with childhood-onset intractable epilepsy; 61 had undergone resective epilepsy surgery. Participants completed standardized tests of reading, spelling, arithmetic, and intelligence at baseline and, on average, 7years after. Surgical patients were additionally assessed one year postsurgery. At baseline and long-term follow-up, 61% and 69% of patients, respectively, scored at least one standard deviation below normative data in at least one academic domain. Evaluation of change over time while controlling for IQ showed that arithmetic scores were lower at long-term follow-up in comparison with those at baseline among all patient groups, whereas reading and spelling scores remained unchanged. Few advantages were associated with seizure control. Multiple regression analyses found that older age at surgery, cessation of antiepileptic medications, improved IQ, and low baseline scores were independently associated with improvement in some academic domains among all patient groups. We found that arithmetic scores were lower at long-term follow-up, suggesting a lack of ongoing development or deterioration in skills. Reading and spelling scores remained stable suggesting that patients made gains in abilities at a rate expected for their increase in age; this finding contrasts with recent short-term outcome studies identifying significantly lower scores over time in these areas. Copyright © 2016 Elsevier Inc. All rights reserved.

Interoperation transfer in Chinese-English bilinguals' arithmetic.

PubMed

Campbell, Jamie I D; Dowd, Roxanne R

2012-10-01

We examined interoperation transfer of practice in adult Chinese-English bilinguals' memory for simple multiplication (6 × 8 = 48) and addition (6 + 8 = 14) facts. The purpose was to determine whether they possessed distinct number-fact representations in both Chinese (L1) and English (L2). Participants repeatedly practiced multiplication problems (e.g., 4 × 5 = ?), answering a subset in L1 and another subset in L2. Then separate groups answered corresponding addition problems (4 + 5 = ?) and control addition problems in either L1 (N = 24) or L2 (N = 24). The results demonstrated language-specific negative transfer of multiplication practice to corresponding addition problems. Specifically, large simple addition problems (sum > 10) presented a significant response time cost (i.e., retrieval-induced forgetting) after their multiplication counterparts were practiced in the same language, relative to practice in the other language. The results indicate that our Chinese-English bilinguals had multiplication and addition facts represented in distinct language-specific memory stores.

Improving Weather Forecasts Through Reduced Precision Data Assimilation

NASA Astrophysics Data System (ADS)

Hatfield, Samuel; Düben, Peter; Palmer, Tim

2017-04-01

We present a new approach for improving the efficiency of data assimilation, by trading numerical precision for computational speed. Future supercomputers will allow a greater choice of precision, so that models can use a level of precision that is commensurate with the model uncertainty. Previous studies have already indicated that the quality of climate and weather forecasts is not significantly degraded when using a precision less than double precision [1,2], but so far these studies have not considered data assimilation. Data assimilation is inherently uncertain due to the use of relatively long assimilation windows, noisy observations and imperfect models. Thus, the larger rounding errors incurred from reducing precision may be within the tolerance of the system. Lower precision arithmetic is cheaper, and so by reducing precision in ensemble data assimilation, we can redistribute computational resources towards, for example, a larger ensemble size. Because larger ensembles provide a better estimate of the underlying distribution and are less reliant on covariance inflation and localisation, lowering precision could actually allow us to improve the accuracy of weather forecasts. We will present results on how lowering numerical precision affects the performance of an ensemble data assimilation system, consisting of the Lorenz '96 toy atmospheric model and the ensemble square root filter. We run the system at half precision (using an emulation tool), and compare the results with simulations at single and double precision. We estimate that half precision assimilation with a larger ensemble can reduce assimilation error by 30%, with respect to double precision assimilation with a smaller ensemble, for no extra computational cost. This results in around half a day extra of skillful weather forecasts, if the error-doubling characteristics of the Lorenz '96 model are mapped to those of the real atmosphere. Additionally, we investigate the sensitivity of these results to observational error and assimilation window length. Half precision hardware will become available very shortly, with the introduction of Nvidia's Pascal GPU architecture and the Intel Knights Mill coprocessor. We hope that the results presented here will encourage the uptake of this hardware. References [1] Peter D. Düben and T. N. Palmer, 2014: Benchmark Tests for Numerical Weather Forecasts on Inexact Hardware, Mon. Weather Rev., 142, 3809-3829 [2] Peter D. Düben, Hugh McNamara and T. N. Palmer, 2014: The use of imprecise processing to improve accuracy in weather & climate prediction, J. Comput. Phys., 271, 2-18

The influence of cardiorespiratory fitness on strategic, behavioral, and electrophysiological indices of arithmetic cognition in preadolescent children

PubMed Central

Moore, R. Davis; Drollette, Eric S.; Scudder, Mark R.; Bharij, Aashiv; Hillman, Charles H.

2014-01-01

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. PMID:24829556

Inversion of Density Interfaces Using the Pseudo-Backpropagation Neural Network Method

NASA Astrophysics Data System (ADS)

Chen, Xiaohong; Du, Yukun; Liu, Zhan; Zhao, Wenju; Chen, Xiaocheng

2018-05-01

This paper presents a new pseudo-backpropagation (BP) neural network method that can invert multi-density interfaces at one time. The new method is based on the conventional forward modeling and inverse modeling theories in addition to conventional pseudo-BP neural network arithmetic. A 3D inversion model for gravity anomalies of multi-density interfaces using the pseudo-BP neural network method is constructed after analyzing the structure and function of the artificial neural network. The corresponding iterative inverse formula of the space field is presented at the same time. Based on trials of gravity anomalies and density noise, the influence of the two kinds of noise on the inverse result is discussed and the scale of noise requested for the stability of the arithmetic is analyzed. The effects of the initial model on the reduction of the ambiguity of the result and improvement of the precision of inversion are discussed. The correctness and validity of the method were verified by the 3D model of the three interfaces. 3D inversion was performed on the observed gravity anomaly data of the Okinawa trough using the program presented herein. The Tertiary basement and Moho depth were obtained from the inversion results, which also testify the adaptability of the method. This study has made a useful attempt for the inversion of gravity density interfaces.

The NASA Reanalysis Ensemble Service - Advanced Capabilities for Integrated Reanalysis Access and Intercomparison

NASA Astrophysics Data System (ADS)

Tamkin, G.; Schnase, J. L.; Duffy, D.; Li, J.; Strong, S.; Thompson, J. H.

2017-12-01

NASA's efforts to advance climate analytics-as-a-service are making new capabilities available to the research community: (1) A full-featured Reanalysis Ensemble Service (RES) comprising monthly means data from multiple reanalysis data sets, accessible through an enhanced set of extraction, analytic, arithmetic, and intercomparison operations. The operations are made accessible through NASA's climate data analytics Web services and our client-side Climate Data Services Python library, CDSlib; (2) A cloud-based, high-performance Virtual Real-Time Analytics Testbed supporting a select set of climate variables. This near real-time capability enables advanced technologies like Spark and Hadoop-based MapReduce analytics over native NetCDF files; and (3) A WPS-compliant Web service interface to our climate data analytics service that will enable greater interoperability with next-generation systems such as ESGF. The Reanalysis Ensemble Service includes the following: - New API that supports full temporal, spatial, and grid-based resolution services with sample queries - A Docker-ready RES application to deploy across platforms - Extended capabilities that enable single- and multiple reanalysis area average, vertical average, re-gridding, standard deviation, and ensemble averages - Convenient, one-stop shopping for commonly used data products from multiple reanalyses including basic sub-setting and arithmetic operations (e.g., avg, sum, max, min, var, count, anomaly) - Full support for the MERRA-2 reanalysis dataset in addition to, ECMWF ERA-Interim, NCEP CFSR, JMA JRA-55 and NOAA/ESRL 20CR… - A Jupyter notebook-based distribution mechanism designed for client use cases that combines CDSlib documentation with interactive scenarios and personalized project management - Supporting analytic services for NASA GMAO Forward Processing datasets - Basic uncertainty quantification services that combine heterogeneous ensemble products with comparative observational products (e.g., reanalysis, observational, visualization) - The ability to compute and visualize multiple reanalysis for ease of inter-comparisons - Automated tools to retrieve and prepare data collections for analytic processing

MRI-based treatment planning with pseudo CT generated through atlas registration.

PubMed

Uh, Jinsoo; Merchant, Thomas E; Li, Yimei; Li, Xingyu; Hua, Chiaho

2014-05-01

To evaluate the feasibility and accuracy of magnetic resonance imaging (MRI)-based treatment planning using pseudo CTs generated through atlas registration. A pseudo CT, providing electron density information for dose calculation, was generated by deforming atlas CT images previously acquired on other patients. The authors tested 4 schemes of synthesizing a pseudo CT from single or multiple deformed atlas images: use of a single arbitrarily selected atlas, arithmetic mean process using 6 atlases, and pattern recognition with Gaussian process (PRGP) using 6 or 12 atlases. The required deformation for atlas CT images was derived from a nonlinear registration of conjugated atlas MR images to that of the patient of interest. The contrasts of atlas MR images were adjusted by histogram matching to reduce the effect of different sets of acquisition parameters. For comparison, the authors also tested a simple scheme assigning the Hounsfield unit of water to the entire patient volume. All pseudo CT generating schemes were applied to 14 patients with common pediatric brain tumors. The image similarity of real patient-specific CT and pseudo CTs constructed by different schemes was compared. Differences in computation times were also calculated. The real CT in the treatment planning system was replaced with the pseudo CT, and the dose distribution was recalculated to determine the difference. The atlas approach generally performed better than assigning a bulk CT number to the entire patient volume. Comparing atlas-based schemes, those using multiple atlases outperformed the single atlas scheme. For multiple atlas schemes, the pseudo CTs were similar to the real CTs (correlation coefficient, 0.787-0.819). The calculated dose distribution was in close agreement with the original dose. Nearly the entire patient volume (98.3%-98.7%) satisfied the criteria of chi-evaluation (<2% maximum dose and 2 mm range). The dose to 95% of the volume and the percentage of volume receiving at least 95% of the prescription dose in the planning target volume differed from the original values by less than 2% of the prescription dose (root-mean-square, RMS < 1%). The PRGP scheme did not perform better than the arithmetic mean process with the same number of atlases. Increasing the number of atlases from 6 to 12 often resulted in improvements, but statistical significance was not always found. MRI-based treatment planning with pseudo CTs generated through atlas registration is feasible for pediatric brain tumor patients. The doses calculated from pseudo CTs agreed well with those from real CTs, showing dosimetric accuracy within 2% for the PTV when multiple atlases were used. The arithmetic mean process may be a reasonable choice over PRGP for the synthesis scheme considering performance and computational costs.

MRI-based treatment planning with pseudo CT generated through atlas registration

DOE Office of Scientific and Technical Information (OSTI.GOV)

Uh, Jinsoo, E-mail: jinsoo.uh@stjude.org; Merchant, Thomas E.; Hua, Chiaho

2014-05-15

Purpose: To evaluate the feasibility and accuracy of magnetic resonance imaging (MRI)-based treatment planning using pseudo CTs generated through atlas registration. Methods: A pseudo CT, providing electron density information for dose calculation, was generated by deforming atlas CT images previously acquired on other patients. The authors tested 4 schemes of synthesizing a pseudo CT from single or multiple deformed atlas images: use of a single arbitrarily selected atlas, arithmetic mean process using 6 atlases, and pattern recognition with Gaussian process (PRGP) using 6 or 12 atlases. The required deformation for atlas CT images was derived from a nonlinear registration ofmore » conjugated atlas MR images to that of the patient of interest. The contrasts of atlas MR images were adjusted by histogram matching to reduce the effect of different sets of acquisition parameters. For comparison, the authors also tested a simple scheme assigning the Hounsfield unit of water to the entire patient volume. All pseudo CT generating schemes were applied to 14 patients with common pediatric brain tumors. The image similarity of real patient-specific CT and pseudo CTs constructed by different schemes was compared. Differences in computation times were also calculated. The real CT in the treatment planning system was replaced with the pseudo CT, and the dose distribution was recalculated to determine the difference. Results: The atlas approach generally performed better than assigning a bulk CT number to the entire patient volume. Comparing atlas-based schemes, those using multiple atlases outperformed the single atlas scheme. For multiple atlas schemes, the pseudo CTs were similar to the real CTs (correlation coefficient, 0.787–0.819). The calculated dose distribution was in close agreement with the original dose. Nearly the entire patient volume (98.3%–98.7%) satisfied the criteria of chi-evaluation (<2% maximum dose and 2 mm range). The dose to 95% of the volume and the percentage of volume receiving at least 95% of the prescription dose in the planning target volume differed from the original values by less than 2% of the prescription dose (root-mean-square, RMS < 1%). The PRGP scheme did not perform better than the arithmetic mean process with the same number of atlases. Increasing the number of atlases from 6 to 12 often resulted in improvements, but statistical significance was not always found. Conclusions: MRI-based treatment planning with pseudo CTs generated through atlas registration is feasible for pediatric brain tumor patients. The doses calculated from pseudo CTs agreed well with those from real CTs, showing dosimetric accuracy within 2% for the PTV when multiple atlases were used. The arithmetic mean process may be a reasonable choice over PRGP for the synthesis scheme considering performance and computational costs.« less

MRI-based treatment planning with pseudo CT generated through atlas registration

PubMed Central

Uh, Jinsoo; Merchant, Thomas E.; Li, Yimei; Li, Xingyu; Hua, Chiaho

2014-01-01

Purpose: To evaluate the feasibility and accuracy of magnetic resonance imaging (MRI)-based treatment planning using pseudo CTs generated through atlas registration. Methods: A pseudo CT, providing electron density information for dose calculation, was generated by deforming atlas CT images previously acquired on other patients. The authors tested 4 schemes of synthesizing a pseudo CT from single or multiple deformed atlas images: use of a single arbitrarily selected atlas, arithmetic mean process using 6 atlases, and pattern recognition with Gaussian process (PRGP) using 6 or 12 atlases. The required deformation for atlas CT images was derived from a nonlinear registration of conjugated atlas MR images to that of the patient of interest. The contrasts of atlas MR images were adjusted by histogram matching to reduce the effect of different sets of acquisition parameters. For comparison, the authors also tested a simple scheme assigning the Hounsfield unit of water to the entire patient volume. All pseudo CT generating schemes were applied to 14 patients with common pediatric brain tumors. The image similarity of real patient-specific CT and pseudo CTs constructed by different schemes was compared. Differences in computation times were also calculated. The real CT in the treatment planning system was replaced with the pseudo CT, and the dose distribution was recalculated to determine the difference. Results: The atlas approach generally performed better than assigning a bulk CT number to the entire patient volume. Comparing atlas-based schemes, those using multiple atlases outperformed the single atlas scheme. For multiple atlas schemes, the pseudo CTs were similar to the real CTs (correlation coefficient, 0.787–0.819). The calculated dose distribution was in close agreement with the original dose. Nearly the entire patient volume (98.3%–98.7%) satisfied the criteria of chi-evaluation (<2% maximum dose and 2 mm range). The dose to 95% of the volume and the percentage of volume receiving at least 95% of the prescription dose in the planning target volume differed from the original values by less than 2% of the prescription dose (root-mean-square, RMS < 1%). The PRGP scheme did not perform better than the arithmetic mean process with the same number of atlases. Increasing the number of atlases from 6 to 12 often resulted in improvements, but statistical significance was not always found. Conclusions: MRI-based treatment planning with pseudo CTs generated through atlas registration is feasible for pediatric brain tumor patients. The doses calculated from pseudo CTs agreed well with those from real CTs, showing dosimetric accuracy within 2% for the PTV when multiple atlases were used. The arithmetic mean process may be a reasonable choice over PRGP for the synthesis scheme considering performance and computational costs. PMID:24784377

Design of a self-adaptive fuzzy PID controller for piezoelectric ceramics micro-displacement system

NASA Astrophysics Data System (ADS)

Zhang, Shuang; Zhong, Yuning; Xu, Zhongbao

2008-12-01

In order to improve control precision of the piezoelectric ceramics (PZT) micro-displacement system, a self-adaptive fuzzy Proportional Integration Differential (PID) controller is designed based on the traditional digital PID controller combining with fuzzy control. The arithmetic gives a fuzzy control rule table with the fuzzy control rule and fuzzy reasoning, through this table, the PID parameters can be adjusted online in real time control. Furthermore, the automatic selective control is achieved according to the change of the error. The controller combines the good dynamic capability of the fuzzy control and the high stable precision of the PID control, adopts the method of using fuzzy control and PID control in different segments of time. In the initial and middle stage of the transition process of system, that is, when the error is larger than the value, fuzzy control is used to adjust control variable. It makes full use of the fast response of the fuzzy control. And when the error is smaller than the value, the system is about to be in the steady state, PID control is adopted to eliminate static error. The problems of PZT existing in the field of precise positioning are overcome. The results of the experiments prove that the project is correct and practicable.

Scale and the evolutionarily based approximate number system: an exploratory study

NASA Astrophysics Data System (ADS)

Delgado, Cesar; Jones, M. Gail; You, Hye Sun; Robertson, Laura; Chesnutt, Katherine; Halberda, Justin

2017-05-01

Crosscutting concepts such as scale, proportion, and quantity are recognised by U.S. science standards as a potential vehicle for students to integrate their scientific and mathematical knowledge; yet, U.S. students and adults trail their international peers in scale and measurement estimation. Culturally based knowledge of scale such as measurement units may be built on evolutionarily-based systems of number such as the approximate number system (ANS), which processes approximate representations of numerical magnitude. ANS is related to mathematical achievement in pre-school and early elementary students, but there is little research on ANS among older students or in science-related areas such as scale. Here, we investigate the relationship between ANS precision in public school U.S. seventh graders and their accuracy estimating the length of standard units of measurement in SI and U.S. customary units. We also explored the relationship between ANS and science and mathematics achievement. Accuracy estimating the metre was positively and significantly related to ANS precision. Mathematics achievement, science achievement, and accuracy estimating other units were not significantly related to ANS. We thus suggest that ANS precision may be related to mathematics understanding beyond arithmetic, beyond the early school years, and to the crosscutting concepts of scale, proportion, and quantity.

What difference does a year of schooling make?: Maturation of brain response and connectivity between 2nd and 3rd grades during arithmetic problem solving

PubMed Central

Rosenberg-Lee, Miriam; Barth, Maria; Menon, Vinod

2011-01-01

Early elementary schooling in 2nd and 3rd grades (ages 7-9) is an important period for the acquisition and mastery of basic mathematical skills. Yet, we know very little about neurodevelopmental changes that might occur over a year of schooling. Here we examine behavioral and neurodevelopmental changes underlying arithmetic problem solving in a well-matched group of 2nd (n = 45) and 3rd (n = 45) grade children. Although 2nd and 3rd graders did not differ on IQ or grade- and age-normed measures of math, reading and working memory, 3rd graders had higher raw math scores (effect sizes = 1.46-1.49) and were more accurate than 2nd graders in an fMRI task involving verification of simple and complex two-operand addition problems (effect size = 0.43). In both 2nd and 3rd graders, arithmetic complexity was associated with increased responses in right inferior frontal sulcus and anterior insula, regions implicated in domain-general cognitive control, and in left intraparietal sulcus (IPS) and superior parietal lobule (SPL) regions important for numerical and arithmetic processing. Compared to 2nd graders, 3rd graders showed greater activity in dorsal stream parietal areas right SPL, IPS and angular gyrus (AG) as well as ventral visual stream areas bilateral lingual gyrus (LG), right lateral occipital cortex (LOC) and right parahippocampal gyrus (PHG). Significant differences were also observed in the prefrontal cortex (PFC), with 3rd graders showing greater activation in left dorsal lateral PFC (dlPFC) and greater deactivation in the ventral medial PFC (vmPFC). Third graders also showed greater functional connectivity between the left dlPFC and multiple posterior brain areas, with larger differences in dorsal stream parietal areas SPL and AG, compared to ventral stream visual areas LG, LOC and PHG. No such between-grade differences were observed in functional connectivity between the vmPFC and posterior brain regions. These results suggest that even the narrow one-year interval spanning grades 2 and 3 is characterized by significant arithmetic task-related changes in brain response and connectivity, and argue that pooling data across wide age ranges and grades can miss important neurodevelopmental changes. Our findings have important implications for understanding brain mechanisms mediating early maturation of mathematical skills and, more generally, for educational neuroscience. PMID:21620984

Arithmetic learning in advanced age.

PubMed

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

2018-01-01

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

Arithmetic learning in advanced age

PubMed Central

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 participants, while learning in older people might be more widespread. Overall, our study indicates that arithmetic learning depends on the training intensity as well as on person-related factors including individual age, arithmetic competence before training, memory, and executive functions. In conclusion, we suggest that major progress can be also achieved by older participants, but that interventions have to take into account individual variables in order to provide maximal benefit. PMID:29489905

One way Doppler Extractor. Volume 2: Digital VCO technique

NASA Technical Reports Server (NTRS)

Nossen, E. J.; Starner, E. R.

1974-01-01

A feasibility analysis and trade-offs for a one-way Doppler extractor using digital VCO techniques is presented. The method of Doppler measurement involves the use of a digital phase lock loop; once this loop is locked to the incoming signal, the precise frequency and hence the Doppler component can be determined directly from the contents of the digital control register. The only serious error source is due to internally generated noise. Techniques are presented for minimizing this error source and achieving an accuracy of 0.01 Hz in a one second averaging period. A number of digitally controlled oscillators were analyzed from a performance and complexity point of view. The most promising technique uses an arithmetic synthesizer as a digital waveform generator.

Processes in arithmetic strategy selection: a fMRI study.

PubMed

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.

Cognitive predictors of children's development in mathematics achievement: A latent growth modeling approach.

PubMed

Xenidou-Dervou, Iro; Van Luit, Johannes E H; Kroesbergen, Evelyn H; Friso-van den Bos, Ilona; Jonkman, Lisa M; van der Schoot, Menno; van Lieshout, Ernest C D M

2018-04-24

Research has identified various domain-general and domain-specific cognitive abilities as predictors of children's individual differences in mathematics achievement. However, research into the predictors of children's individual growth rates, namely between-person differences in within-person change in mathematics achievement is scarce. We assessed 334 children's domain-general and mathematics-specific early cognitive abilities and their general mathematics achievement longitudinally across four time-points within the first and second grades of primary school. As expected, a constellation of multiple cognitive abilities contributed to the children's starting level of mathematical success. Specifically, latent growth modeling revealed that WM abilities, IQ, counting skills, nonsymbolic and symbolic approximate arithmetic and comparison skills explained individual differences in the children's initial status on a curriculum-based general mathematics achievement test. Surprisingly, however, only one out of all the assessed cognitive abilities was a unique predictor of the children's individual growth rates in mathematics achievement: their performance in the symbolic approximate addition task. In this task, children were asked to estimate the sum of two large numbers and decide if this estimated sum was smaller or larger compared to a third number. Our findings demonstrate the importance of multiple domain-general and mathematics-specific cognitive skills for identifying children at risk of struggling with mathematics and highlight the significance of early approximate arithmetic skills for the development of one's mathematical success. We argue the need for more research focus on explaining children's individual growth rates in mathematics achievement. © 2018 John Wiley & Sons Ltd.

Software Aspects of IEEE Floating-Point Computations for Numerical Applications in High Energy Physics

ScienceCinema

Arnold, Jeffrey

2018-05-14

Floating-point computations are at the heart of much of the computing done in high energy physics. The correctness, speed and accuracy of these computations are of paramount importance. The lack of any of these characteristics can mean the difference between new, exciting physics and an embarrassing correction. This talk will examine practical aspects of IEEE 754-2008 floating-point arithmetic as encountered in HEP applications. After describing the basic features of IEEE floating-point arithmetic, the presentation will cover: common hardware implementations (SSE, x87) techniques for improving the accuracy of summation, multiplication and data interchange compiler options for gcc and icc affecting floating-point operations hazards to be avoided. About the speaker: Jeffrey M Arnold is a Senior Software Engineer in the Intel Compiler and Languages group at Intel Corporation. He has been part of the Digital->Compaq->Intel compiler organization for nearly 20 years; part of that time, he worked on both low- and high-level math libraries. Prior to that, he was in the VMS Engineering organization at Digital Equipment Corporation. In the late 1980s, Jeff spent 2½ years at CERN as part of the CERN/Digital Joint Project. In 2008, he returned to CERN to spent 10 weeks working with CERN/openlab. Since that time, he has returned to CERN multiple times to teach at openlab workshops and consult with various LHC experiments. Jeff received his Ph.D. in physics from Case Western Reserve University.

Processes in arithmetic strategy selection: a fMRI study

PubMed Central

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. PMID:25698995

Dynamic topographical pattern classification of multichannel prefrontal NIRS signals: II. Online differentiation of mental arithmetic and rest

NASA Astrophysics Data System (ADS)

Schudlo, Larissa C.; Chau, Tom

2014-02-01

Objective. Near-infrared spectroscopy (NIRS) has recently gained attention as a modality for brain-computer interfaces (BCIs), which may serve as an alternative access pathway for individuals with severe motor impairments. For NIRS-BCIs to be used as a real communication pathway, reliable online operation must be achieved. Yet, only a limited number of studies have been conducted online to date. These few studies were carried out under a synchronous paradigm and did not accommodate an unconstrained resting state, precluding their practical clinical implication. Furthermore, the potentially discriminative power of spatiotemporal characteristics of activation has yet to be considered in an online NIRS system. Approach. In this study, we developed and evaluated an online system-paced NIRS-BCI which was driven by a mental arithmetic activation task and accommodated an unconstrained rest state. With a dual-wavelength, frequency domain near-infrared spectrometer, measurements were acquired over nine sites of the prefrontal cortex, while ten able-bodied participants selected letters from an on-screen scanning keyboard via intentionally controlled brain activity (using mental arithmetic). Participants were provided dynamic NIR topograms as continuous visual feedback of their brain activity as well as binary feedback of the BCI's decision (i.e. if the letter was selected or not). To classify the hemodynamic activity, temporal features extracted from the NIRS signals and spatiotemporal features extracted from the dynamic NIR topograms were used in a majority vote combination of multiple linear classifiers. Main results. An overall online classification accuracy of 77.4 ± 10.5% was achieved across all participants. The binary feedback was found to be very useful during BCI use, while not all participants found value in the continuous feedback provided. Significance. These results demonstrate that mental arithmetic is a potent mental task for driving an online system-paced NIRS-BCI. BCI feedback that reflects the classifier's decision has the potential to improve user performance. The proposed system can provide a framework for future online NIRS-BCI development and testing.

Numerical predictors of arithmetic success in grades 1-6.

PubMed

Lyons, Ian M; Price, Gavin R; Vaessen, Anniek; Blomert, Leo; Ansari, Daniel

2014-09-01

Math relies on mastery and integration of a wide range of simpler numerical processes and concepts. Recent work has identified several numerical competencies that predict variation in math ability. We examined the unique relations between eight basic numerical skills and early arithmetic ability in a large sample (N = 1391) of children across grades 1-6. In grades 1-2, children's ability to judge the relative magnitude of numerical symbols was most predictive of early arithmetic skills. The unique contribution of children's ability to assess ordinality in numerical symbols steadily increased across grades, overtaking all other predictors by grade 6. We found no evidence that children's ability to judge the relative magnitude of approximate, nonsymbolic numbers was uniquely predictive of arithmetic ability at any grade. Overall, symbolic number processing was more predictive of arithmetic ability than nonsymbolic number processing, though the relative importance of symbolic number ability appears to shift from cardinal to ordinal processing. © 2014 John Wiley & Sons Ltd.

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

PubMed

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.

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

PubMed

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.

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

ERIC Educational Resources Information Center

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

2002-01-01

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

Gauss Elimination: Workhorse of Linear Algebra.

DTIC Science & Technology

1995-08-05

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

Comparison of the arithmetic and geometric means in estimating crown diameter and crown cross-sectional area

Treesearch

KaDonna Randolph

2010-01-01

The use of the geometric and arithmetic means for estimating tree crown diameter and crown cross-sectional area were examined for trees with crown width measurements taken at the widest point of the crown and perpendicular to the widest point of the crown. The average difference between the geometric and arithmetic mean crown diameters was less than 0.2 ft in absolute...

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

PubMed

De Visscher, Alice; Noël, Marie-Pascale

2013-01-01

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

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

PubMed Central

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

2015-01-01

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. PMID:22682904

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

PubMed Central

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

2013-01-01

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

Developmental changes in mental arithmetic: evidence for increased functional specialization in the left inferior parietal cortex.

PubMed

Rivera, S M; Reiss, A L; Eckert, M A; Menon, V

2005-11-01

Arithmetic reasoning is arguably one of the most important cognitive skills a child must master. Here we examine neurodevelopmental changes in mental arithmetic. Subjects (ages 8-19 years) viewed arithmetic equations and were asked to judge whether the results were correct or incorrect. During two-operand addition or subtraction trials, for which accuracy was comparable across age, older subjects showed greater activation in the left parietal cortex, along the supramarginal gyrus and adjoining anterior intra-parietal sulcus as well as the left lateral occipital temporal cortex. These age-related changes were not associated with alterations in gray matter density, and provide novel evidence for increased functional maturation with age. By contrast, younger subjects showed greater activation in the prefrontal cortex, including the dorsolateral and ventrolateral prefrontal cortex and the anterior cingulate cortex, suggesting that they require comparatively more working memory and attentional resources to achieve similar levels of mental arithmetic performance. Younger subjects also showed greater activation of the hippocampus and dorsal basal ganglia, reflecting the greater demands placed on both declarative and procedural memory systems. Our findings provide evidence for a process of increased functional specialization of the left inferior parietal cortex in mental arithmetic, a process that is accompanied by decreased dependence on memory and attentional resources with development.

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

PubMed

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.

Arithmetic strategy development and its domain-specific and domain-general cognitive correlates: a longitudinal study in children with persistent mathematical learning difficulties.

PubMed

Vanbinst, Kiran; Ghesquière, Pol; De Smedt, Bert

2014-11-01

Deficits in arithmetic fact retrieval constitute the hallmark of children with mathematical learning difficulties (MLD). It remains, however, unclear which cognitive deficits underpin these difficulties in arithmetic fact retrieval. Many prior studies defined MLD by considering low achievement criteria and not by additionally taking the persistence of the MLD into account. Therefore, the present longitudinal study contrasted children with persistent MLD (MLD-p; mean age: 9 years 2 months) and typically developing (TD) children (mean age: 9 years 6 months) at three time points, to explore whether differences in arithmetic strategy development were associated with differences in numerical magnitude processing, working memory and phonological processing. Our longitudinal data revealed that children with MLD-p had persistent arithmetic fact retrieval deficits at each time point. Children with MLD-p showed persistent impairments in symbolic, but not in nonsymbolic, magnitude processing at each time point. The two groups differed in phonological processing, but not in working memory. Our data indicate that both domain-specific and domain-general cognitive abilities contribute to individual differences in children's arithmetic strategy development, and that the symbolic processing of numerical magnitudes might be a particular risk factor for children with MLD-p. Copyright © 2014 Elsevier Ltd. All rights reserved.

Link between cognitive neuroscience and education: the case of clinical assessment of developmental dyscalculia.

PubMed

Rubinsten, Orly

2015-01-01

In recent years, cognitive neuroscience research has identified several biological and cognitive features of number processing deficits that may now make it possible to diagnose mental or educational impairments in arithmetic, even earlier and more precisely than is possible using traditional assessment tools. We provide two sets of recommendations for improving cognitive assessment tools, using the important case of mathematics as an example. (1) neurocognitive tests would benefit substantially from incorporating assessments (based on findings from cognitive neuroscience) that entail systematic manipulation of fundamental aspects of number processing. Tests that focus on evaluating networks of core neurocognitive deficits have considerable potential to lead to more precise diagnosis and to provide the basis for designing specific intervention programs tailored to the deficits exhibited by the individual child. (2) implicit knowledge, derived from inspection of variables that are irrelevant to the task at hand, can also provide a useful assessment tool. Implicit knowledge is powerful and plays an important role in human development, especially in cases of psychiatric or neurological deficiencies (such as math learning disabilities or math anxiety).

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

PubMed Central

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

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

PubMed Central

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

2014-01-01

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

The functional anatomy of single-digit arithmetic in children with developmental dyslexia.

PubMed

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.

Specific Learning Disorder: Prevalence and Gender Differences

PubMed Central

Moll, Kristina; Kunze, Sarah; Neuhoff, Nina; Bruder, Jennifer; Schulte-Körne, Gerd

2014-01-01

Comprehensive models of learning disorders have to consider both isolated learning disorders that affect one learning domain only, as well as comorbidity between learning disorders. However, empirical evidence on comorbidity rates including all three learning disorders as defined by DSM-5 (deficits in reading, writing, and mathematics) is scarce. The current study assessed prevalence rates and gender ratios for isolated as well as comorbid learning disorders in a representative sample of 1633 German speaking children in 3rd and 4th Grade. Prevalence rates were analysed for isolated as well as combined learning disorders and for different deficit criteria, including a criterion for normal performance. Comorbid learning disorders occurred as frequently as isolated learning disorders, even when stricter cutoff criteria were applied. The relative proportion of isolated and combined disorders did not change when including a criterion for normal performance. Reading and spelling deficits differed with respect to their association with arithmetic problems: Deficits in arithmetic co-occurred more often with deficits in spelling than with deficits in reading. In addition, comorbidity rates for arithmetic and reading decreased when applying stricter deficit criteria, but stayed high for arithmetic and spelling irrespective of the chosen deficit criterion. These findings suggest that the processes underlying the relationship between arithmetic and reading might differ from those underlying the relationship between arithmetic and spelling. With respect to gender ratios, more boys than girls showed spelling deficits, while more girls were impaired in arithmetic. No gender differences were observed for isolated reading problems and for the combination of all three learning disorders. Implications of these findings for assessment and intervention of learning disorders are discussed. PMID:25072465

Specific learning disorder: prevalence and gender differences.

PubMed

Moll, Kristina; Kunze, Sarah; Neuhoff, Nina; Bruder, Jennifer; Schulte-Körne, Gerd

2014-01-01

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

The Functional Anatomy of Single-Digit Arithmetic in Children with Developmental Dyslexia

PubMed Central

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

Accelerating scientific computations with mixed precision algorithms

NASA Astrophysics Data System (ADS)

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 factorization of the coefficient matrix using Gaussian elimination. First, the coefficient matrix A is factored into the product of a lower triangular matrix L and an upper triangular matrix U. Partial row pivoting is in general used to improve numerical stability resulting in a factorization PA=LU, where P is a permutation matrix. The solution for the system is achieved by first solving Ly=Pb (forward substitution) and then solving Ux=y (backward substitution). Due to round-off errors, the computed solution, x, carries a numerical error magnified by the condition number of the coefficient matrix A. In order to improve the computed solution, an iterative process can be applied, which produces a correction to the computed solution at each iteration, which then yields the method that is commonly known as the iterative refinement algorithm. Provided that the system is not too ill-conditioned, the algorithm produces a solution correct to the working precision. Running time: seconds/minutes

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

NASA Astrophysics Data System (ADS)

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.

Language and arithmetic--a study using the intracarotid amobarbital procedure.

PubMed

Delazer, Margarete; Karner, Elfriede; Unterberger, Iris; Walser, Gerald; Waldenberger, Peter; Trinka, Eugen; Benke, Thomas

2005-08-22

The intracarotid amobarbital procedure is used as a standard procedure in presurgical evaluation to assess hemispheric lateralization of language and memory, but has not been applied to investigate numerical processing. Patients with medically intractable epilepsy (n=20) were consecutively recruited during a presurgical evaluation programme. All 14 patients with left-lateralized language showed better arithmetic performance with the left hemisphere (intracarotid amobarbital procedure right), while five out of six patients with bilateral or right-hemispheric language representation showed better performance with the right hemisphere (intracarotid amobarbital procedure left). Furthermore, in patients with left-lateralized language, an interaction between intracarotid amobarbital procedure and type of arithmetic operation was found. The study suggests a close association between language lateralization and hemispheric specialization for arithmetic processing.

Algoritmi matematici nelle lettere di Gerbert

NASA Astrophysics Data System (ADS)

Rossi, P.

The content of Gerbert's "scientific" letters is analyzed in detail, with special emphasis on arithmetical and geometrical issues, such as multiplication and division rules related to the use of abacus, superparticular numbers and evaluation of the area of an equilateral triangle. It is shown that Gerbert's area formula, albeit based on rational fractions, could hardly be conceived without knowledge of Pythagoras' theorem. This fact casts a light also on the astronomical tools created by Gerbert, where the didactical aspect cannot be separated from the accuracy of the demonstrations and of the measurements.

Multiple-Baseline Detection of a Geostationary Satellite with the Navy Precision Optical Interferometer

DTIC Science & Technology

2015-01-01

Multiple-baseline detection of a geostationary satellite with the Navy Precision Optical Interferometer J. Thomas Armstronga, Ellyn K. Bainesa...observations of a geostationary satellite using the Navy Precision Optical Inter- ferometer (NPOI) during the glint season of March 2015. We succeeded in...the second night. These baseline lengths correspond to a resolution of ∼4 m at geostationary altitude. This is the first multiple-baseline

Physical activity and sedentary time in relation to academic achievement in children.

PubMed

Haapala, Eero A; Väistö, Juuso; Lintu, Niina; Westgate, Kate; Ekelund, Ulf; Poikkeus, Anna-Maija; Brage, Soren; Lakka, Timo A

2017-06-01

To investigate the independent and combined associations of objectively measured moderate-to-vigorous physical activity (MVPA) and sedentary time (ST) with reading and arithmetic skills. Cross-sectional/prospective. Participants were 89 boys and 69 girls aged 6-8 years. MVPA and ST were measured using a combined heart rate and movement sensor and body fat percentage by dual-energy X-ray absorptiometry in Grade 1. Reading fluency, reading comprehension, and arithmetic skills were assessed using standardized tests in Grades 1-3. The data were analyzed using linear regression analyses and analyses of covariance with repeated measures. In boys, MVPA was directly and ST inversely associated with reading fluency in Grades 1-3 and arithmetic skills in Grade 1 (P<0.05). Higher levels of MVPA were also related to better reading comprehension in Grade 1 (P<0.05). Most of the associations of MVPA and ST with reading and arithmetic skills attenuated after mutual adjustment for MVPA or ST. Furthermore, boys with a combination of lower levels of MVPA and higher levels of ST had consistently poorer reading fluency (P=0.002) and reading comprehension (P=0.027) across Grades 1-3 than other boys. In girls, ST was directly associated with arithmetic skills in Grade 2 (P<0.05). However, this relationship of ST with arithmetic skills was no longer significant after adjustment for body fat percentage. Lower levels of MVPA and higher levels of ST and particularly their combination were related to poorer reading skills in boys. In girls, higher levels of ST were related to better arithmetic skills. Copyright © 2016 Sports Medicine Australia. Published by Elsevier Ltd. All rights reserved.

Algorithm XXX : functions to support the IEEE standard for binary floating-point arithmetic.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cody, W. J.; Mathematics and Computer Science

1993-12-01

This paper describes C programs for the support functions copysign(x,y), logb(x), scalb(x,n), nextafter(x,y), finite(x), and isnan(x) recommended in the Appendix to the IEEE Standard for Binary Floating-Point Arithmetic. In the case of logb, the modified definition given in the later IEEE Standard for Radix-Independent Floating-Point Arithmetic is followed. These programs should run without modification on most systems conforming to the binary standard.

Relation between arithmetic performance and phonological working memory in children.

PubMed

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 <0.05 was considered significant. The study included 20 girls and 10 boys, mean age 8.7 years. The G1 was composed of 17 children and G2 of 13 children. There was a statistically significant difference between the groups studied for the repetition of pseudowords with three and four syllables. The results of this study provide support for the hypothesis that changes in phonological working memory are related to difficulties in arithmetic tests.

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

PubMed

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.

Neurofunctional Differences Associated with Arithmetic Processing in Turner Syndrome

PubMed Central

Kesler, Shelli R.; Menon, Vinod; Reiss, Allan L.

2011-01-01

Turner syndrome (TS) is a neurogenetic disorder characterized by the absence of one X chromosome in a phenotypic female. Individuals with TS are at risk for impairments in mathematics. We investigated the neural mechanisms underlying arithmetic processing in TS. Fifteen subjects with TS and 15 age-matched typically developing controls were scanned using functional MRI while they performed easy (two-operand) and difficult (three-operand) versions of an arithmetic processing task. Both groups activated fronto-parietal regions involved in arithmetic processing during the math tasks. Compared with controls, the TS group recruited additional neural resources in frontal and parietal regions during the easier, two-operand math task. During the more difficult three-operand task, individuals with TS demonstrated significantly less activation in frontal, parietal and subcortical regions than controls. However, the TS group’s performance on both math tasks was comparable to controls. Individuals with TS demonstrate activation differences in fronto-parietal areas during arithmetic tasks compared with controls. They must recruit additional brain regions during a relatively easy task and demonstrate a potentially inefficient response to increased task difficulty compared with controls. PMID:16135780

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

PubMed

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

2017-01-01

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

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

PubMed

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

2015-01-01

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

Computations of Eisenstein series on Fuchsian groups

NASA Astrophysics Data System (ADS)

Avelin, Helen

2008-09-01

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

Particle size analysis of some water/oil/water multiple emulsions.

PubMed

Ursica, L; Tita, D; Palici, I; Tita, B; Vlaia, V

2005-04-29

Particle size analysis gives useful information about the structure and stability of multiple emulsions, which are important characteristics of these systems. It also enables the observation of the growth process of particles dispersed in multiple emulsions, accordingly, the evolution of their dimension in time. The size of multiple particles in the seven water/oil/water (W/O/W) emulsions was determined by measuring the particles size observed during the microscopic examination. In order to describe the distribution of the size of multiple particles, the value of two parameters that define the particle size was calculated: the arithmetical mean diameter and the median diameter. The results of the particle size analysis in the seven multiple emulsions W/O/W studied are presented as histograms of the distribution density immediately, 1 and 3 months after the preparation of each emulsion, as well as by establishing the mean and the median diameter of particles. The comparative study of the distribution histograms and of the mean and median diameters of W/O/W multiple particles indicates that the prepared emulsions are fine and very fine dispersions, stable, and presenting a growth of the abovementioned diameters during the study.

Compositional Verification with Abstraction, Learning, and SAT Solving

DTIC Science & Technology

2015-05-01

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

Quantum simulation of an ultrathin body field-effect transistor with channel imperfections

NASA Astrophysics Data System (ADS)

Vyurkov, V.; Semenikhin, I.; Filippov, S.; Orlikovsky, A.

2012-04-01

An efficient program for the all-quantum simulation of nanometer field-effect transistors is elaborated. The model is based on the Landauer-Buttiker approach. Our calculation of transmission coefficients employs a transfer-matrix technique involving the arbitrary precision (multiprecision) arithmetic to cope with evanescent modes. Modified in such way, the transfer-matrix technique turns out to be much faster in practical simulations than that of scattering-matrix. Results of the simulation demonstrate the impact of realistic channel imperfections (random charged centers and wall roughness) on transistor characteristics. The Landauer-Buttiker approach is developed to incorporate calculation of the noise at an arbitrary temperature. We also validate the ballistic Landauer-Buttiker approach for the usual situation when heavily doped contacts are indispensably included into the simulation region.

Changing computing paradigms towards power efficiency

PubMed Central

Klavík, Pavel; Malossi, A. Cristiano I.; Bekas, Costas; Curioni, Alessandro

2014-01-01

Power awareness is fast becoming immensely important in computing, ranging from the traditional high-performance computing applications to the new generation of data centric workloads. In this work, we describe our efforts towards a power-efficient computing paradigm that combines low- and high-precision arithmetic. We showcase our ideas for the widely used kernel of solving systems of linear equations that finds numerous applications in scientific and engineering disciplines as well as in large-scale data analytics, statistics and machine learning. Towards this goal, we developed tools for the seamless power profiling of applications at a fine-grain level. In addition, we verify here previous work on post-FLOPS/W metrics and show that these can shed much more light in the power/energy profile of important applications. PMID:24842033

Compression of 3D Point Clouds Using a Region-Adaptive Hierarchical Transform.

PubMed

De Queiroz, Ricardo; Chou, Philip A

2016-06-01

In free-viewpoint video, there is a recent trend to represent scene objects as solids rather than using multiple depth maps. Point clouds have been used in computer graphics for a long time and with the recent possibility of real time capturing and rendering, point clouds have been favored over meshes in order to save computation. Each point in the cloud is associated with its 3D position and its color. We devise a method to compress the colors in point clouds which is based on a hierarchical transform and arithmetic coding. The transform is a hierarchical sub-band transform that resembles an adaptive variation of a Haar wavelet. The arithmetic encoding of the coefficients assumes Laplace distributions, one per sub-band. The Laplace parameter for each distribution is transmitted to the decoder using a custom method. The geometry of the point cloud is encoded using the well-established octtree scanning. Results show that the proposed solution performs comparably to the current state-of-the-art, in many occasions outperforming it, while being much more computationally efficient. We believe this work represents the state-of-the-art in intra-frame compression of point clouds for real-time 3D video.

Spatial and temporal heterogeneity of neural responses in human posteromedial cortex.

PubMed

Daitch, Amy L; Parvizi, Josef

2018-05-01

Neuroimaging evidence supports a role of the default mode network (DMN) in spontaneous thought and goal-driven internally oriented processes, such as recalling an autobiographical event, and has demonstrated its deactivation during focused, externally oriented attention. Recent work suggests that the DMN is not a homogeneous network but rather is composed of at least several subnetworks, which are engaged in distinct functions; however, it is still unclear if these different functions rely on the same neuronal populations. In this study, we used intracranial EEG to record from the posteromedial cortex (PMC), a core hub of the DMN, in 13 human subjects, during autobiographical memory retrieval (internally oriented), arithmetic processing (externally oriented), and cued rest (spontaneous thought), allowing us to measure activity from anatomically precise PMC sites with high temporal resolution. We observed a heterogeneous, yet spatially organized, pattern of activity across tasks. Many sites, primarily in the more ventral portion of PMC, were engaged during autobiographical recall and suppressed during arithmetic processing. Other more dorsal PMC sites were engaged during the cued-rest condition. Of these rest-active sites, some exhibited variable temporal dynamics across trials, possibly reflecting various forms of spontaneous thought, while others showed only transient activity at the beginning of cued-rest trials (i.e., after a switch from a task to cued rest), possibly involved in shifting the brain from a more focused to a more exploratory attentional state. These results suggest heterogeneity of function even within an individual node of the DMN.

A generalized algorithm to design finite field normal basis multipliers

NASA Technical Reports Server (NTRS)

Wang, C. C.

1986-01-01

Finite field arithmetic logic is central in the implementation of some error-correcting coders and some cryptographic devices. There is a need for good multiplication algorithms which can be easily realized. Massey and Omura recently developed a new multiplication algorithm for finite fields based on a normal basis representation. Using the normal basis representation, the design of the finite field multiplier is simple and regular. The fundamental design of the Massey-Omura multiplier is based on a design of a product function. In this article, a generalized algorithm to locate a normal basis in a field is first presented. Using this normal basis, an algorithm to construct the product function is then developed. This design does not depend on particular characteristics of the generator polynomial of the field.

Stochastic control system parameter identifiability

NASA Technical Reports Server (NTRS)

Lee, C. H.; Herget, C. J.

1975-01-01

The parameter identification problem of general discrete time, nonlinear, multiple input/multiple output dynamic systems with Gaussian white distributed measurement errors is considered. The knowledge of the system parameterization was assumed to be known. Concepts of local parameter identifiability and local constrained maximum likelihood parameter identifiability were established. A set of sufficient conditions for the existence of a region of parameter identifiability was derived. A computation procedure employing interval arithmetic was provided for finding the regions of parameter identifiability. If the vector of the true parameters is locally constrained maximum likelihood (CML) identifiable, then with probability one, the vector of true parameters is a unique maximal point of the maximum likelihood function in the region of parameter identifiability and the constrained maximum likelihood estimation sequence will converge to the vector of true parameters.

Numerical Demons in Monte Carlo Estimation of Bayesian Model Evidence with Application to Soil Respiration Models

NASA Astrophysics Data System (ADS)

Elshall, A. S.; Ye, M.; Niu, G. Y.; Barron-Gafford, G.

2016-12-01

Bayesian multimodel inference is increasingly being used in hydrology. Estimating Bayesian model evidence (BME) is of central importance in many Bayesian multimodel analysis such as Bayesian model averaging and model selection. BME is the overall probability of the model in reproducing the data, accounting for the trade-off between the goodness-of-fit and the model complexity. Yet estimating BME is challenging, especially for high dimensional problems with complex sampling space. Estimating BME using the Monte Carlo numerical methods is preferred, as the methods yield higher accuracy than semi-analytical solutions (e.g. Laplace approximations, BIC, KIC, etc.). However, numerical methods are prone the numerical demons arising from underflow of round off errors. Although few studies alluded to this issue, to our knowledge this is the first study that illustrates these numerical demons. We show that the precision arithmetic can become a threshold on likelihood values and Metropolis acceptance ratio, which results in trimming parameter regions (when likelihood function is less than the smallest floating point number that a computer can represent) and corrupting of the empirical measures of the random states of the MCMC sampler (when using log-likelihood function). We consider two of the most powerful numerical estimators of BME that are the path sampling method of thermodynamic integration (TI) and the importance sampling method of steppingstone sampling (SS). We also consider the two most widely used numerical estimators, which are the prior sampling arithmetic mean (AS) and posterior sampling harmonic mean (HM). We investigate the vulnerability of these four estimators to the numerical demons. Interesting, the most biased estimator, namely the HM, turned out to be the least vulnerable. While it is generally assumed that AM is a bias-free estimator that will always approximate the true BME by investing in computational effort, we show that arithmetic underflow can hamper AM resulting in severe underestimation of BME. TI turned out to be the most vulnerable, resulting in BME overestimation. Finally, we show how SS can be largely invariant to rounding errors, yielding the most accurate and computational efficient results. These research results are useful for MC simulations to estimate Bayesian model evidence.

40 CFR 60.58b - Compliance and performance testing.

Code of Federal Regulations, 2010 CFR

2010-07-01

... demonstrated municipal waste combustor unit load shall be the highest 4-hour arithmetic average load achieved... shall be the highest 4-hour arithmetic average temperature achieved at the particulate matter control...

The effect of cerebral palsy on arithmetic accuracy is mediated by working memory, intelligence, early numeracy, and instruction time.

PubMed

Jenks, Kathleen M; de Moor, Jan; van Lieshout, Ernest C D M; Maathuis, Karel G B; Keus, Inge; Gorter, Jan Willem

2007-01-01

The development of addition and subtraction accuracy was assessed in first graders with cerebral palsy (CP) in both mainstream (16) and special education (41) and a control group of first graders in mainstream education (16). The control group out-performed the CP groups in addition and subtraction accuracy and this difference could not be fully explained by differences in intelligence. Both CP groups showed evidence of working memory deficits. The three groups exhibited different developmental patterns in the area of early numeracy skills. Children with CP in special education were found to receive less arithmetic instruction and instruction time was positively related to arithmetic accuracy. Structural equation modeling revealed that the effect of CP on arithmetic accuracy is mediated by intelligence, working memory, early numeracy, and instruction time.

Optimized 4-bit Quantum Reversible Arithmetic Logic Unit

NASA Astrophysics Data System (ADS)

Ayyoub, Slimani; Achour, Benslama

2017-08-01

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

Representation of natural numbers in quantum mechanics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Benioff, Paul

2001-03-01

This paper represents one approach to making explicit some of the assumptions and conditions implied in the widespread representation of numbers by composite quantum systems. Any nonempty set and associated operations is a set of natural numbers or a model of arithmetic if the set and operations satisfy the axioms of number theory or arithmetic. This paper is limited to k-ary representations of length L and to the axioms for arithmetic modulo k{sup L}. A model of the axioms is described based on an abstract L-fold tensor product Hilbert space H{sup arith}. Unitary maps of this space onto a physicalmore » parameter based product space H{sup phy} are then described. Each of these maps makes states in H{sup phy}, and the induced operators, a model of the axioms. Consequences of the existence of many of these maps are discussed along with the dependence of Grover's and Shor's algorithms on these maps. The importance of the main physical requirement, that the basic arithmetic operations are efficiently implementable, is discussed. This condition states that there exist physically realizable Hamiltonians that can implement the basic arithmetic operations and that the space-time and thermodynamic resources required are polynomial in L.« less

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

PubMed

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

2017-12-01

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

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

PubMed Central

Richardson, Sophie; Hubber, Paula J.; Keeble, Sarah; Gilmore, Camilla

2017-01-01

Our ability to perform arithmetic relies heavily on working memory, the manipulation and maintenance of information in mind. Previous research has found that in adults, procedural strategies, particularly counting, rely on working memory to a greater extent than retrieval strategies. During childhood there are changes in the types of strategies employed, as well as an increase in the accuracy and efficiency of strategy execution. As such it seems likely that the role of working memory in arithmetic may also change, however children and adults have never been directly compared. This study used traditional dual-task methodology, with the addition of a control load condition, to investigate the extent to which working memory requirements for different arithmetic strategies change with age between 9–11 years, 12–14 years and young adulthood. We showed that both children and adults employ working memory when solving arithmetic problems, no matter what strategy they choose. This study highlights the importance of considering working memory in understanding the difficulties that some children and adults have with mathematics, as well as the need to include working memory in theoretical models of mathematical cognition. PMID:29228008

Simple arithmetic: not so simple for highly math anxious individuals

PubMed Central

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

Marijuana Primes, Marijuana Expectancies, and Arithmetic Efficiency*

PubMed Central

Hicks, Joshua A.; Pedersen, Sarah L.; McCarthy, Denis M.; Friedman, Ronald S.

2009-01-01

Objective: Previous research has shown that primes associated with alcohol influence behavior consistent with specific alcohol expectancies. The present study examined whether exposure to marijuana-related primes and marijuana expectancies interact to produce similar effects. Specifically, the present study examined whether marijuana primes and marijuana expectancies regarding cognitive and behavioral impairment interact to influence performance on an arithmetic task. Method: Two independent samples (N = 260) of undergraduate students (both marijuana users and nonusers) first completed measures of marijuana-outcome expectancies associated with cognitive and behavioral impairment and with general negative effects (Sample 2). Later in the semester, participants were exposed to marijuana-related (or neutral) primes and then completed an arithmetic task. Results: Results from Sample 1 indicated that participants who were exposed to marijuana-themed magazine covers performed more poorly on the arithmetic task if they expected that marijuana would lead to cognitive and behavioral impairment. Results from Sample 2 indicated that, for marijuana users, cognitive and behavioral impairment expectancies, but not expectancies regarding general negative effects, similarly moderated arithmetic performance for participants exposed to marijuana-related words. Conclusions: Results support the hypothesis that the implicit activation of specific marijuana-outcome expectancies can influence cognitive processes. Implications for research on marijuana are discussed. PMID:19371490

DNS of incompressible turbulence in a periodic box with up to 4096^3 grid points

NASA Astrophysics Data System (ADS)

Kaneda, Yukio

2007-11-01

Turbulence of incompressible fluid obeying the Navier-Stokes (NS) equations under periodic boundary conditions is one of the simplest dynamical systems keeping the essence of turbulence dynamics, and suitable for the study of high Reynolds number (Re) turbulence by direct numerical simulation (DNS). This talk presents a review on DNS of such a system with the number N^3 of the grid points up to 4096^3, performed on the Earth Simulator (ES). The ES consists of 640 processor nodes (=5120 arithmetic processors) with 10TB of main memory and the peak performance of 40 Tflops. The DNSs are based on a spectral method free from alias error. The convolution sums in the wave vector space were evaluated by radix-4 Fast Fourier Transforms with double precision arithmetic. Sustained performance of 16.4 Tflops was achieved on the 2048^3 DNS by using 512 processor nodes of the ES. The DNSs consist of two series; one is with kmax η1 (Series 1) and the other with kmax η2 (Series 2), where kmax is the highest wavenumber in each simulation, and η is the Kolmogorov length scale. In the 4096^3 DNS, the Taylor-scale Reynolds number Rλ1130 (675) and the ratio L/η of the integral length scale L to η is approximately 2133(1040), in Series 1 (Series 2). Such DNS data are expected to shed some light on the basic questions in turbulence research, including those on (i) the normalized mean rate of energy dissipation in the high Re limit, (ii) the universality of energy spectrum at small scale, (iii) scale- and Re- dependences of the statistics, and (iv) intermittency. We have constructed a database consisting of (a) animations and figures of turbulent fields (b) statistics including those associated with (i)-(iv) noted above, (c) snapshot data of the velocity fields. The data size of (c) can be very large for large N. For example, one snapshot of single precision data of the velocity vector field of the 4096^3 DNS requires approximately 0.8 TB.

Trinary signed-digit arithmetic using an efficient encoding scheme

NASA Astrophysics Data System (ADS)

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

2000-09-01

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

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

NASA Astrophysics Data System (ADS)

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

2000-11-01

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

Bit-wise arithmetic coding for data compression

NASA Technical Reports Server (NTRS)

Kiely, A. B.

1994-01-01

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

The Duality Principle in Teaching Arithmetic and Geometric Series

ERIC Educational Resources Information Center

Yeshurun, Shraga

1978-01-01

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

Modified-Signed-Digit Optical Computing Using Fan-Out

NASA Technical Reports Server (NTRS)

Liu, Hua-Kuang; Zhou, Shaomin; Yeh, Pochi

1996-01-01

Experimental optical computing system containing optical fan-out elements implements modified signed-digit (MSD) arithmetic and logic. In comparison with previous optical implementations of MSD arithmetic, this one characterized by larger throughput, greater flexibility, and simpler optics.

Association between Abacus Training and Improvement in Response Inhibition: A Case-control Study

PubMed Central

Na, Kyoung-Sae; Lee, Soyoung Irene; Park, Jun-Ho; Jung, Han-Yong; Ryu, Jung-Hee

2015-01-01

Objective The abacus, first used in Asian countries more than 800 years ago, enables efficient arithmetic calculation via visuo-spatial configuration. We investigated whether abacus-trained children performed better on cognitive tasks and demonstrated higher levels of arithmetic abilities compared to those without such training. Methods We recruited 75 elementary school children (43 abacus-trained and 32 not so trained). Attention, memory, and arithmetic abilities were measured, and we compared the abacus with the control group. Results Children who had learned to use an abacus committed fewer commission errors and showed better arithmetic ability than did controls. We found no significant differences between children with and without abacus training in other areas of attention. Conclusion We speculate that abacus training improves response inhibition via neuroanatomical alterations of the areas that regulate such functions. Further studies are needed to confirm the association between abacus training and better response inhibition. PMID:26243843

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

PubMed

Singer, Vivian; Strasser, Kathernie

2017-12-01

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

Adults' Arithmetic Builds on Fast and Automatic Processing of Arabic Digits: Evidence from an Audiovisual Matching Paradigm

PubMed Central

Sasanguie, Delphine; Reynvoet, Bert

2014-01-01

Several studies have shown that performance on symbolic number tasks is related to individual differences in arithmetic. However, it is not clear which process is responsible for this association, i.e. fast, automatic processing of symbols per se or access to the underlying non-symbolic representation of the symbols. To dissociate between both options, adult participants performed an audiovisual matching paradigm. Auditory presented number words needed to be matched with either Arabic digits or dot patterns. The results revealed that a distance effect was present in the dots-number word matching task and absent in the digit-number word matching task. Crucially, only performance in the digit task contributed to the variance in arithmetical abilities. This led us to conclude that adults' arithmetic builds on the ability to quickly and automatically process Arabic digits, without the underlying non-symbolic magnitude representation being activated. PMID:24505308

The cognitive foundations of reading and arithmetic skills in 7- to 10-year-olds.

PubMed

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

2005-06-01

A range of possible predictors of arithmetic and reading were assessed in a large sample (N=162) of children between ages 7 years 5 months and 10 years 4 months. A confirmatory factor analysis of the predictors revealed a good fit to a model consisting of four latent variables (verbal ability, nonverbal ability, search speed, and phonological memory) and two manifest variables (digit comparison and phoneme deletion). A path analysis showed that digit comparison and verbal ability were unique predictors of variations in arithmetic skills, whereas phoneme deletion and verbal ability were unique predictors of variations in reading skills. These results confirm earlier findings that phoneme deletion ability appears to be a critical foundation for learning to read (decode). In addition, variations in the speed of accessing numerical quantity information appear to be a critical foundation for the development of arithmetic skills.

Predicting course performance in freshman and sophomore physics courses: Women are more predictable than men

NASA Astrophysics Data System (ADS)

McCammon, Susan; Golden, Jeannie; Wuensch, Karl L.

This study investigated the extent to which thinking skills and mathematical competency would predict the course performance of freshman and sophomore science majors enrolled in physics courses. Multiple-regression equations revealed that algebra and critical thinking skills were the best overall predictors across several physics courses. Although arithmetic skills, math anxiety, and primary mental abilities scores also correlated with performance, they were redundant with the algebra and critical thinking. The most surprising finding of the study was the differential validity by sex; predictor variables were successful in predicting course performance for women but not for men.

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

NASA Astrophysics Data System (ADS)

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

2017-11-01

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

Peer-to-peer Monte Carlo simulation of photon migration in topical applications of biomedical optics

NASA Astrophysics Data System (ADS)

Doronin, Alexander; Meglinski, Igor

2012-09-01

In the framework of further development of the unified approach of photon migration in complex turbid media, such as biological tissues we present a peer-to-peer (P2P) Monte Carlo (MC) code. The object-oriented programming is used for generalization of MC model for multipurpose use in various applications of biomedical optics. The online user interface providing multiuser access is developed using modern web technologies, such as Microsoft Silverlight, ASP.NET. The emerging P2P network utilizing computers with different types of compute unified device architecture-capable graphics processing units (GPUs) is applied for acceleration and to overcome the limitations, imposed by multiuser access in the online MC computational tool. The developed P2P MC was validated by comparing the results of simulation of diffuse reflectance and fluence rate distribution for semi-infinite scattering medium with known analytical results, results of adding-doubling method, and with other GPU-based MC techniques developed in the past. The best speedup of processing multiuser requests in a range of 4 to 35 s was achieved using single-precision computing, and the double-precision computing for floating-point arithmetic operations provides higher accuracy.

Peer-to-peer Monte Carlo simulation of photon migration in topical applications of biomedical optics.

PubMed

Doronin, Alexander; Meglinski, Igor

2012-09-01

In the framework of further development of the unified approach of photon migration in complex turbid media, such as biological tissues we present a peer-to-peer (P2P) Monte Carlo (MC) code. The object-oriented programming is used for generalization of MC model for multipurpose use in various applications of biomedical optics. The online user interface providing multiuser access is developed using modern web technologies, such as Microsoft Silverlight, ASP.NET. The emerging P2P network utilizing computers with different types of compute unified device architecture-capable graphics processing units (GPUs) is applied for acceleration and to overcome the limitations, imposed by multiuser access in the online MC computational tool. The developed P2P MC was validated by comparing the results of simulation of diffuse reflectance and fluence rate distribution for semi-infinite scattering medium with known analytical results, results of adding-doubling method, and with other GPU-based MC techniques developed in the past. The best speedup of processing multiuser requests in a range of 4 to 35 s was achieved using single-precision computing, and the double-precision computing for floating-point arithmetic operations provides higher accuracy.

Programmable single-cell mammalian biocomputers.

PubMed

Ausländer, Simon; Ausländer, David; Müller, Marius; Wieland, Markus; Fussenegger, Martin

2012-07-05

Synthetic biology has advanced the design of standardized control devices that program cellular functions and metabolic activities in living organisms. Rational interconnection of these synthetic switches resulted in increasingly complex designer networks that execute input-triggered genetic instructions with precision, robustness and computational logic reminiscent of electronic circuits. Using trigger-controlled transcription factors, which independently control gene expression, and RNA-binding proteins that inhibit the translation of transcripts harbouring specific RNA target motifs, we have designed a set of synthetic transcription–translation control devices that could be rewired in a plug-and-play manner. Here we show that these combinatorial circuits integrated a two-molecule input and performed digital computations with NOT, AND, NAND and N-IMPLY expression logic in single mammalian cells. Functional interconnection of two N-IMPLY variants resulted in bitwise intracellular XOR operations, and a combinatorial arrangement of three logic gates enabled independent cells to perform programmable half-subtractor and half-adder calculations. Individual mammalian cells capable of executing basic molecular arithmetic functions isolated or coordinated to metabolic activities in a predictable, precise and robust manner may provide new treatment strategies and bio-electronic interfaces in future gene-based and cell-based therapies.

Cognition, emotion, and arithmetic in primary school: A cross-cultural investigation.

PubMed

Rodic, Maja; Cui, Jiaxin; Malykh, Sergey; Zhou, Xinlin; Gynku, Elena I; Bogdanova, Elena L; Zueva, Dina Y; Y Bogdanova, Olga; Kovas, Yulia

2018-06-01

The study investigated cross-cultural differences in variability and average performance in arithmetic, mathematical reasoning, symbolic and non-symbolic magnitude processing, intelligence, spatial ability, and mathematical anxiety in 890 6- to 9-year-old children from the United Kingdom, Russia, and China. Cross-cultural differences explained 28% of the variance in arithmetic and 17.3% of the variance in mathematical reasoning, with Chinese children outperforming the other two groups. No cross-cultural differences were observed for spatial ability and mathematical anxiety. In all samples, symbolic magnitude processing and mathematical reasoning were independently related to early arithmetic. Other factors, such as non-symbolic magnitude processing, mental rotation, intelligence, and mathematical anxiety, produced differential patterns across the populations. The results are discussed in relation to potential influences of parental practice, school readiness, and linguistic factors on individual differences in early mathematics. Statement of contribution What is already known on this subject? Cross-cultural differences in mathematical ability are present in preschool children. Similar mechanisms of mathematical development operate in preschool children from the United Kingdom, Russia, and China. Tasks that require understanding of numbers are best predictors of arithmetic in preschool children. What does this study add? Cross-cultural differences in mathematical ability become greater with age/years of formal education. Similar mechanisms of mathematical development operate in early primary school children from the United Kingdom, Russia, and China. Symbolic number magnitude and mathematical reasoning are the main predictors of arithmetic in all three populations. © 2018 The Authors British Journal of Developmental Psychology published by John Wiley & Sons Ltd on behalf of British Psychological Society.

The relative importance of two different mathematical abilities to mathematical achievement.

PubMed

Nunes, Terezinha; Bryant, Peter; Barros, Rossana; Sylva, Kathy

2012-03-01

Two distinct abilities, mathematical reasoning and arithmetic skill, might make separate and specific contributions to mathematical achievement. However, there is little evidence to inform theory and educational practice on this matter. The aims of this study were (1) to assess whether mathematical reasoning and arithmetic make independent contributions to the longitudinal prediction of mathematical achievement over 5 years and (2) to test the specificity of this prediction. Data from Avon Longitudinal Study of Parents and Children (ALSPAC) were available on 2,579 participants for analyses of KS2 achievement and on 1,680 for the analyses of KS3 achievement. Hierarchical regression analyses were used to assess the independence and specificity of the contribution of mathematical reasoning and arithmetic skill to the prediction of achievement in KS2 and KS3 mathematics, science, and English. Age, intelligence, and working memory (WM) were controls in these analyses. Mathematical reasoning and arithmetic did make independent contributions to the prediction of mathematical achievement; mathematical reasoning was by far the stronger predictor of the two. These predictions were specific in so far as these measures were more strongly related to mathematics than to science or English. Intelligence and WM were non-specific predictors; intelligence contributed more to the prediction of science than of maths, and WM predicted maths and English equally well. There is clear justification for making a distinction between mathematical reasoning and arithmetic skills. The implication is that schools must plan explicitly to improve mathematical reasoning as well as arithmetic skills. ©2011 The British Psychological Society.

Brain Correlates of Mathematical Competence in Processing Mathematical Representations

PubMed Central

Grabner, Roland H.; Reishofer, Gernot; Koschutnig, Karl; Ebner, Franz

2011-01-01

The ability to extract numerical information from different representation formats (e.g., equations, tables, or diagrams) is a key component of mathematical competence but little is known about its neural correlate. Previous studies comparing mathematically less and more competent adults have focused on mental arithmetic and reported differences in left angular gyrus (AG) activity which were interpreted to reflect differential reliance on arithmetic fact retrieval during problem solving. The aim of the present functional magnetic resonance imaging study was to investigate the brain correlates of mathematical competence in a task requiring the processing of typical mathematical representations. Twenty-eight adults of lower and higher mathematical competence worked on a representation matching task in which they had to evaluate whether the numerical information of a symbolic equation matches that of a bar chart. Two task conditions without and one condition with arithmetic demands were administered. Both competence groups performed equally well in the non-arithmetic conditions and only differed in accuracy in the condition requiring calculation. Activation contrasts between the groups revealed consistently stronger left AG activation in the more competent individuals across all three task conditions. The finding of competence-related activation differences independently of arithmetic demands suggests that more and less competent individuals differ in a cognitive process other than arithmetic fact retrieval. Specifically, it is argued that the stronger left AG activity in the more competent adults may reflect their higher proficiency in processing mathematical symbols. Moreover, the study demonstrates competence-related parietal activation differences that were not accompanied by differential experimental performance. PMID:22069387

Activities for Students: Averaging Rates--Deciding when to Use the Harmonic or Arithmetic Mean

ERIC Educational Resources Information Center

Brown, S. L.; Rizzardi, M. A.

2005-01-01

The article describes the harmonic mean and explores situations for using it. Activities that involve hands-on practice for students are provided. Students learn to recognize which mean, harmonic or arithmetic, is appropriate.

Changing computing paradigms towards power efficiency.

PubMed

Klavík, Pavel; Malossi, A Cristiano I; Bekas, Costas; Curioni, Alessandro

2014-06-28

Power awareness is fast becoming immensely important in computing, ranging from the traditional high-performance computing applications to the new generation of data centric workloads. In this work, we describe our efforts towards a power-efficient computing paradigm that combines low- and high-precision arithmetic. We showcase our ideas for the widely used kernel of solving systems of linear equations that finds numerous applications in scientific and engineering disciplines as well as in large-scale data analytics, statistics and machine learning. Towards this goal, we developed tools for the seamless power profiling of applications at a fine-grain level. In addition, we verify here previous work on post-FLOPS/W metrics and show that these can shed much more light in the power/energy profile of important applications. © 2014 The Author(s) Published by the Royal Society. All rights reserved.

BIREFRINGENT FILTER MODEL

NASA Technical Reports Server (NTRS)

Cross, P. L.

1994-01-01

Birefringent filters are often used as line-narrowing components in solid state lasers. The Birefringent Filter Model program generates a stand-alone model of a birefringent filter for use in designing and analyzing a birefringent filter. It was originally developed to aid in the design of solid state lasers to be used on aircraft or spacecraft to perform remote sensing of the atmosphere. The model is general enough to allow the user to address problems such as temperature stability requirements, manufacturing tolerances, and alignment tolerances. The input parameters for the program are divided into 7 groups: 1) general parameters which refer to all elements of the filter; 2) wavelength related parameters; 3) filter, coating and orientation parameters; 4) input ray parameters; 5) output device specifications; 6) component related parameters; and 7) transmission profile parameters. The program can analyze a birefringent filter with up to 12 different components, and can calculate the transmission and summary parameters for multiple passes as well as a single pass through the filter. The Jones matrix, which is calculated from the input parameters of Groups 1 through 4, is used to calculate the transmission. Output files containing the calculated transmission or the calculated Jones' matrix as a function of wavelength can be created. These output files can then be used as inputs for user written programs. For example, to plot the transmission or to calculate the eigen-transmittances and the corresponding eigen-polarizations for the Jones' matrix, write the appropriate data to a file. The Birefringent Filter Model is written in Microsoft FORTRAN 2.0. The program format is interactive. It was developed on an IBM PC XT equipped with an 8087 math coprocessor, and has a central memory requirement of approximately 154K. Since Microsoft FORTRAN 2.0 does not support complex arithmetic, matrix routines for addition, subtraction, and multiplication of complex, double precision variables are included. The Birefringent Filter Model was written in 1987.

Genetic Parallel Programming: design and implementation.

PubMed

Cheang, Sin Man; Leung, Kwong Sak; Lee, Kin Hong

2006-01-01

This paper presents a novel Genetic Parallel Programming (GPP) paradigm for evolving parallel programs running on a Multi-Arithmetic-Logic-Unit (Multi-ALU) Processor (MAP). The MAP is a Multiple Instruction-streams, Multiple Data-streams (MIMD), general-purpose register machine that can be implemented on modern Very Large-Scale Integrated Circuits (VLSIs) in order to evaluate genetic programs at high speed. For human programmers, writing parallel programs is more difficult than writing sequential programs. However, experimental results show that GPP evolves parallel programs with less computational effort than that of their sequential counterparts. It creates a new approach to evolving a feasible problem solution in parallel program form and then serializes it into a sequential program if required. The effectiveness and efficiency of GPP are investigated using a suite of 14 well-studied benchmark problems. Experimental results show that GPP speeds up evolution substantially.

Effective implementation of wavelet Galerkin method

NASA Astrophysics Data System (ADS)

Finěk, Václav; Šimunková, Martina

2012-11-01

It was proved by W. Dahmen et al. that an adaptive wavelet scheme is asymptotically optimal for a wide class of elliptic equations. This scheme approximates the solution u by a linear combination of N wavelets and a benchmark for its performance is the best N-term approximation, which is obtained by retaining the N largest wavelet coefficients of the unknown solution. Moreover, the number of arithmetic operations needed to compute the approximate solution is proportional to N. The most time consuming part of this scheme is the approximate matrix-vector multiplication. In this contribution, we will introduce our implementation of wavelet Galerkin method for Poisson equation -Δu = f on hypercube with homogeneous Dirichlet boundary conditions. In our implementation, we identified nonzero elements of stiffness matrix corresponding to the above problem and we perform matrix-vector multiplication only with these nonzero elements.

On the structure of arithmetic sums of Cantor sets with constant ratios of dissection

NASA Astrophysics Data System (ADS)

Anisca, Razvan; Chlebovec, Christopher

2009-09-01

We investigate conditions which imply that the topological structure of the arithmetic sum of two Cantor sets with constant ratios of dissection at each step is either: a Cantor set, a finite union of closed intervals, or three mixed models (L, R and M-Cantorval). We obtain general results that apply in particular for the case of homogeneous Cantor sets, thus generalizing the results of Mendes and Oliveira. The method used here is new in this context. We also produce results regarding the arithmetic sum of two affine Cantor sets of a special kind.

Fast reversible wavelet image compressor

NASA Astrophysics Data System (ADS)

Kim, HyungJun; Li, Ching-Chung

1996-10-01

We present a unified image compressor with spline biorthogonal wavelets and dyadic rational filter coefficients which gives high computational speed and excellent compression performance. Convolutions with these filters can be preformed by using only arithmetic shifting and addition operations. Wavelet coefficients can be encoded with an arithmetic coder which also uses arithmetic shifting and addition operations. Therefore, from the beginning to the end, the while encoding/decoding process can be done within a short period of time. The proposed method naturally extends form the lossless compression to the lossy but high compression range and can be easily adapted to the progressive reconstruction.

Fault tolerant computing: A preamble for assuring viability of large computer systems

NASA Technical Reports Server (NTRS)

Lim, R. S.

1977-01-01

The need for fault-tolerant computing is addressed from the viewpoints of (1) why it is needed, (2) how to apply it in the current state of technology, and (3) what it means in the context of the Phoenix computer system and other related systems. To this end, the value of concurrent error detection and correction is described. User protection, program retry, and repair are among the factors considered. The technology of algebraic codes to protect memory systems and arithmetic codes to protect memory systems and arithmetic codes to protect arithmetic operations is discussed.

An Input Routine Using Arithmetic Statements for the IBM 704 Digital Computer

NASA Technical Reports Server (NTRS)

Turner, Don N.; Huff, Vearl N.

1961-01-01

An input routine has been designed for use with FORTRAN or SAP coded programs which are to be executed on an IBM 704 digital computer. All input to be processed by the routine is punched on IBM cards as declarative statements of the arithmetic type resembling the FORTRAN language. The routine is 850 words in length. It is capable of loading fixed- or floating-point numbers, octal numbers, and alphabetic words, and of performing simple arithmetic as indicated on input cards. Provisions have been made for rapid loading of arrays of numbers in consecutive memory locations.

The neural bases of the multiplication problem-size effect across countries

PubMed Central

Prado, Jérôme; Lu, Jiayan; Liu, Li; Dong, Qi; Zhou, Xinlin; Booth, James R.

2013-01-01

Multiplication problems involving large numbers (e.g., 9 × 8) are more difficult to solve than problems involving small numbers (e.g., 2 × 3). Behavioral research indicates that this problem-size effect might be due to different factors across countries and educational systems. However, there is no neuroimaging evidence supporting this hypothesis. Here, we compared the neural correlates of the multiplication problem-size effect in adults educated in China and the United States. We found a greater neural problem-size effect in Chinese than American participants in bilateral superior temporal regions associated with phonological processing. However, we found a greater neural problem-size effect in American than Chinese participants in right intra-parietal sulcus (IPS) associated with calculation procedures. Therefore, while the multiplication problem-size effect might be a verbal retrieval effect in Chinese as compared to American participants, it may instead stem from the use of calculation procedures in American as compared to Chinese participants. Our results indicate that differences in educational practices might affect the neural bases of symbolic arithmetic. PMID:23717274

Multiple autoclave cycles affect the surface of rotary nickel-titanium files: an atomic force microscopy study.

PubMed

Valois, Caroline R A; Silva, Luciano P; Azevedo, Ricardo B

2008-07-01

The purpose of this study was to evaluate the surface of rotary nickel-titanium (Ni-Ti) files after multiple autoclave cycles. Two different types of rotary Ni-Ti (Greater Taper and ProFile) were attached to a glass base. After 1, 5, and 10 autoclave cycles the files were positioned in the atomic force microscope. The analyses were performed on 15 different points. The same files were used as control before any autoclave cycle. The following vertical topographic parameters were measured: arithmetic mean roughness, maximum height, and root mean square. The differences were tested by analysis of variance with Tukey test. All topographic parameters were higher for both Greater Taper and ProFile after 10 cycles compared with the control (P < .05). ProFile also showed higher topographic parameters after 5 cycles compared with the control (P < .05). The results indicated that multiple autoclave cycles increase the depth of surface irregularities located on rotary Ni-Ti files.

Redesigning Arithmetic for Student Success: Supporting Faculty to Teach in New Ways

ERIC Educational Resources Information Center

Bickerstaff, Susan; Lontz, Barbara; Cormier, Maria Scott; Xu, Di

2014-01-01

This chapter describes a promising new approach to teaching developmental arithmetic and prealgebra, and presents research findings that demonstrate how a faculty support network helped instructors adopt new teaching strategies and gain confidence in teaching the reformed course.

Versatile analog pulse height computer performs real-time arithmetic operations

NASA Technical Reports Server (NTRS)

Brenner, R.; Strauss, M. G.

1967-01-01

Multipurpose analog pulse height computer performs real-time arithmetic operations on relatively fast pulses. This computer can be used for identification of charged particles, pulse shape discrimination, division of signals from position sensitive detectors, and other on-line data reduction techniques.

Pre-schoolers Learn at Home.

ERIC Educational Resources Information Center

Smith, Penny

1985-01-01

Reviews: "ArithMagic (Counting, Addition, Subtraction)" which uses graphics to illustrate/review basic arithmetic concepts; "The Sweet Shop" which uses graphics (and a character called Mr. Jellybean) to teach arithmetic concepts; and "Math Magic," a monster-filled arcade game that teaches addition and subtraction.…

Efficacy of a single dose of milbemycin oxime/praziquantel combination tablets, Milpro(®), against adult Echinococcus multilocularis in dogs and both adult and immature E. multilocularis in young cats.

PubMed

Cvejic, Dejan; Schneider, Claudia; Fourie, Josephus; de Vos, Christa; Bonneau, Stephane; Bernachon, Natalia; Hellmann, Klaus

2016-03-01

Two single-site, laboratory, negatively controlled, masked, randomised dose confirmation studies were performed: one in dogs, the other in cats. After a period of acclimatisation, both the dogs and cats were orally infected with Echinococcus multilocularis protoscoleces. In the dog study, 10 dogs received a single dose of Milpro® tablets at a minimum dose of 0.5 mg/kg milbemycin oxime and 5 mg/kg praziquantel 18 days post-infection and 10 dogs received no treatment. In the cat study, 10 cats received a single dose of Milpro® tablets at a minimum dose of 2 mg/kg milbemycin oxime and 5 mg/kg praziquantel 7 days post-infection, 10 cats received a single dose of the treatment 18 days post-infection and 10 cats remained untreated. In both studies, intestinal worm counts were performed 23 days post-infection at necropsy. No worms were retrieved from any of the 30 treated animals. Nine of 10 control dogs had multiple worms (geometric mean 91, arithmetic mean 304) and all 10 control cats had multiple worms (geometric mean 216, arithmetic mean 481). The difference in worm counts between all three treated groups and their controls was highly significant (ANOVA p values of log transformed data <0.0001). Efficacy of 100 % was demonstrated for the elimination of adult E. multilocularis in dogs and cats as well as for elimination of immature E. multilocularis in cats as evidenced by the effectiveness of treatment 7 days post-infection. The treatments were well accepted and tolerated, and there were no adverse drug reactions observed.

Learning, Realizability and Games in Classical Arithmetic

NASA Astrophysics Data System (ADS)

Aschieri, Federico

2010-12-01

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

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

NASA Astrophysics Data System (ADS)

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

2008-08-01

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

Validation of a particle tracking analysis method for the size determination of nano- and microparticles

NASA Astrophysics Data System (ADS)

Kestens, Vikram; Bozatzidis, Vassili; De Temmerman, Pieter-Jan; Ramaye, Yannic; Roebben, Gert

2017-08-01

Particle tracking analysis (PTA) is an emerging technique suitable for size analysis of particles with external dimensions in the nano- and sub-micrometre scale range. Only limited attempts have so far been made to investigate and quantify the performance of the PTA method for particle size analysis. This article presents the results of a validation study during which selected colloidal silica and polystyrene latex reference materials with particle sizes in the range of 20 nm to 200 nm were analysed with NS500 and LM10-HSBF NanoSight instruments and video analysis software NTA 2.3 and NTA 3.0. Key performance characteristics such as working range, linearity, limit of detection, limit of quantification, sensitivity, robustness, precision and trueness were examined according to recommendations proposed by EURACHEM. A model for measurement uncertainty estimation following the principles described in ISO/IEC Guide 98-3 was used for quantifying random and systematic variations. For nominal 50 nm and 100 nm polystyrene and a nominal 80 nm silica reference materials, the relative expanded measurement uncertainties for the three measurands of interest, being the mode, median and arithmetic mean of the number-weighted particle size distribution, varied from about 10% to 12%. For the nominal 50 nm polystyrene material, the relative expanded uncertainty of the arithmetic mean of the particle size distributions increased up to 18% which was due to the presence of agglomerates. Data analysis was performed with software NTA 2.3 and NTA 3.0. The latter showed to be superior in terms of sensitivity and resolution.

Effect of Mental Arithmetic on heart rate responses during Parabolic Flights: the Barcelona Zero-G Challenge

NASA Astrophysics Data System (ADS)

Osborne, Jeffrey R.; Alonsopérez Lanza, María Victoria; Desclaux, David Ferrer; Goswami, Nandu; González Alonso, Daniel Ventura; Moser, Maximilian; Grote, Vincent; Garcia-Cuadrado, Gloria; Perez-Poch, Antoni

2014-07-01

When an astronaut transitions from a low to high gravitational environment, fluid shifts from the head towards the feet resulting in orthostatic intolerance and syncope. Ground based experiments have shown that by stimulating the cardiovascular system via simple mental stressors, syncope can be delayed, potentially enabling astronauts to reach assistance before loss of consciousness. However, the effect of mental stressors on the stimulation of the cardiovascular system in gravitational environments different than that of Earth's is unknown. As such, this paper investigates the effects that mental stressors under various gravitational environments. To do this, a pilot study was performed in which two participants were flown on two separate parabolic flights that simulated hyper and hypogravity conditions. The plane used was an Aerobatic Single-Engine Cap-10B plane (twin seater), and each participant executed 11 parabolas. The participants were the winners of the Barcelona Zero-G Challenge 2011 organized by UPC Universitat Politècnica de Catalunya-BarcelonaTech and Aeroclub Barcelona-Sabadell. Measurements were made of the participants' hemodynamic and autonomic response throughout the parabolas, using a Chronocord: high precision HRV monitor. Comparisons of the baseline response without mental stressors, and the response with mental stressors during different gravitational loading conditions were made. It was observed that there is an increase in cardiovascular activity during hypo- and hyper-gravity when performing mental arithmetic. Our results show that the twin seater aerobatic single engine CAP-10B aicraft can provide changing gravitational loading conditions for enough periods to study changes in physiological systems.

Non-symbolic approximate arithmetic training improves math performance in preschoolers.

PubMed

Park, Joonkoo; Bermudez, Vanessa; Roberts, Rachel C; Brannon, Elizabeth M

2016-12-01

Math proficiency at early school age is an important predictor of later academic achievement. Thus, an important goal for society should be to improve math readiness in preschool-age children, especially in low-income children who typically arrive in kindergarten with less mathematical competency than their higher income peers. The majority of existing research-based math intervention programs target symbolic verbal number concepts in young children. However, very little attention has been paid to the preverbal intuitive ability to approximately represent numerical quantity, which is hypothesized to be an important foundation for full-fledged mathematical thinking. Here, we tested the hypothesis that repeated engagement of non-symbolic approximate addition and subtraction of large arrays of items results in improved math skills in very young children, an idea that stems from our previous studies in adults. In the current study, 3- to 5-year-olds showed selective improvements in math skills after multiple days of playing a tablet-based non-symbolic approximate arithmetic game compared with children who played a memory game. These findings, collectively with our previous reports, suggest that mental manipulation of approximate numerosities provides an important tool for improving math readiness, even in preschoolers who have yet to master the meaning of number words. Copyright © 2016 Elsevier Inc. All rights reserved.

Non-symbolic approximate arithmetic training improves math performance in preschoolers

PubMed Central

Park, Joonkoo; Bermudez, Vanessa; Roberts, Rachel C.; Brannon, Elizabeth M.

2016-01-01

Math proficiency in early school age is an important predictor of later academic achievement. Thus, an important goal for society should be to improve math readiness in pre-school age children, especially in low-income children who typically arrive in kindergarten with less mathematical competency than their higher-income peers. The majority of existing research-based math intervention programs target symbolic, verbal number concepts in young children. However, very little attention has been paid to the preverbal, intuitive ability to approximately represent numerical quantity, which is hypothesized to be an important foundation for full-fledged mathematical thinking. Here, we test the hypothesis that repeated engagement of non-symbolic approximate addition and subtraction of large array of items results in improved math skills in very young children, an idea that stems from our previous studies in adults. Three to five year-old children showed selective improvements in math skills after multiple days of playing a tablet-based non-symbolic approximate arithmetic game compared to children who played a memory game. These findings, collectively with our previous reports, suggest that mental manipulation of approximate numerosities provides an important tool for improving math readiness, even in preschoolers who have yet to master the meaning of number words. PMID:27596808

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

ERIC Educational Resources Information Center

Persky, Ronald L.

2003-01-01

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

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

PubMed

Macdonald, R I

1987-10-01

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

Instabilities caused by floating-point arithmetic quantization.

NASA Technical Reports Server (NTRS)

Phillips, C. L.

1972-01-01

It is shown that an otherwise stable digital control system can be made unstable by signal quantization when the controller operates on floating-point arithmetic. Sufficient conditions of instability are determined, and an example of loss of stability is treated when only one quantizer is operated.

Babies and Math: A Meta-Analysis of Infants' Simple Arithmetic Competence

ERIC Educational Resources Information Center

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

2017-01-01

Wynn's (1992) seminal research reported that infants looked longer at stimuli representing "incorrect" versus "correct" solutions of basic addition and subtraction problems and concluded that infants have innate arithmetical abilities. Since then, infancy researchers have attempted to replicate this effect, yielding mixed…

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

PubMed

Oyama, Katsunori; Sakatani, Kaoru

2016-01-01

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

Developmental and Individual Differences in Understanding of Fractions

PubMed Central

Siegler, Robert S.; Pyke, Aryn A.

2014-01-01

We examined developmental and individual differences in 6th and 8th graders’ fraction arithmetic and overall mathematics achievement and related them to differences in understanding of fraction magnitudes, whole number division, executive functioning, and metacognitive judgments within a cross sectional design. Results indicated that the difference between low achieving and higher achieving children’s fraction arithmetic knowledge, already substantial in 6th grade, was much greater in 8th grade. The fraction arithmetic knowledge of low achieving children was similar in the two grades, whereas higher achieving children showed much greater knowledge in 8th than 6th grade, despite both groups having been in the same classrooms, using the same textbooks, and having the same teachers and classmates. Individual differences in both fraction arithmetic and mathematics achievement test scores were predicted by differences in fraction magnitude knowledge and whole number division, even after the contributions of reading achievement and executive functioning were statistically controlled. Instructional implications of the findings are discussed. PMID:23244401

Syntactic Awareness and Arithmetic Word Problem Solving in Children With and Without Learning Disabilities.

PubMed

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.

Arithmetic of five-part of leukocytes based on image process

NASA Astrophysics Data System (ADS)

Li, Yian; Wang, Guoyou; Liu, Jianguo

2007-12-01

This paper apply computer image processing and pattern recognizition methods to solve the problem of auto classification and counting of leukocytes (white blood cell) in peripheral blood. In this paper a new leukocyte arithmetic of five-part based on image process and pattern recognizition is presented, which relized auto classify of leukocyte. The first aim is detect the leukocytes . A major requirement of the whole system is to classify these leukocytes to 5 classes. This arithmetic bases on notability mechanism of eyes, process image by sequence, divides up leukocytes and pick up characters. Using the prior kwonledge of cells and image shape information, this arithmetic divides up the probable shape of Leukocyte first by a new method based on Chamfer and then gets the detail characters. It can reduce the mistake judge rate and the calculation greatly. It also has the learning fuction. This paper also presented a new measurement of karyon's shape which can provide more accurate information. This algorithm has great application value in clinical blood test .

Multilevel Analysis of Multiple-Baseline Data Evaluating Precision Teaching as an Intervention for Improving Fluency in Foundational Reading Skills for at Risk Readers

ERIC Educational Resources Information Center

Brosnan, Julie; Moeyaert, Mariola; Brooks Newsome, Kendra; Healy, Olive; Heyvaert, Mieke; Onghena, Patrick; Van den Noortgate, Wim

2018-01-01

In this article, multiple-baseline across participants designs were used to evaluate the impact of a precision teaching (PT) program, within a Tier 2 Response to Intervention framework, targeting fluency in foundational reading skills with at risk kindergarten readers. Thirteen multiple-baseline design experiments that included participation from…

File compression and encryption based on LLS and arithmetic coding

NASA Astrophysics Data System (ADS)

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.

Developing an effective multimedia in education for special education (MESE): An introduction to arithmetic

NASA Astrophysics Data System (ADS)

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 ALARM Experiment

ERIC Educational Resources Information Center

Gerhardt, Ira

2015-01-01

An experiment was conducted over three recent semesters of an introductory calculus course to test whether it was possible to quantify the effect that difficulty with basic algebraic and arithmetic computation had on individual performance. Points lost during the term were classified as being due to either algebraic and arithmetic mistakes…

Updating Working Memory and Arithmetical Attainment in School

ERIC Educational Resources Information Center

Iuculano, Teresa; Moro, Raffaella; Butterworth, Brian

2011-01-01

Here we wished to determine how the sub-components of Working Memory (Phonological-Loop and Central Executive) influence children's arithmetical development. Specifically, we aimed at distinguishing between Working Memory inhibition and updating processes within the Central Executive, and the domain-specificity (words and numbers) of both…

Does Your Graphing Software Real-ly Work?

ERIC Educational Resources Information Center

Marchand, R. J.; McDevitt, T. J.; Bosse, Michael J.; Nandakumar, N. R.

2007-01-01

Many popular mathematical software products including Maple, Mathematica, Derive, Mathcad, Matlab, and some of the TI calculators produce incorrect graphs because they use complex arithmetic instead of "real" arithmetic. This article expounds on this issue, provides possible remedies for instructors to share with their students, and demonstrates…

Using Self-Generated Drawings to Solve Arithmetic Word Problems.

ERIC Educational Resources Information Center

Van Essen, Gerard; Hamaker, Christiaan

1990-01-01

Results are presented from two intervention studies which investigate whether encouraging elementary students to generate drawings of arithmetic word problems facilitates problem-solving performance. Findings indicate that fifth graders (N=50) generated many drawings of word problems and improved problem solutions after the intervention, whereas…

Attentional bias induced by solving simple and complex addition and subtraction problems.

PubMed

Masson, Nicolas; Pesenti, Mauro

2014-01-01

The processing of numbers has been shown to induce shifts of spatial attention in simple probe detection tasks, with small numbers orienting attention to the left and large numbers to the right side of space. Recently, the investigation of this spatial-numerical association has been extended to mental arithmetic with the hypothesis that solving addition or subtraction problems may induce attentional displacements (to the right and to the left, respectively) along a mental number line onto which the magnitude of the numbers would range from left to right, from small to large numbers. Here we investigated such attentional shifts using a target detection task primed by arithmetic problems in healthy participants. The constituents of the addition and subtraction problems (first operand; operator; second operand) were flashed sequentially in the centre of a screen, then followed by a target on the left or the right side of the screen, which the participants had to detect. This paradigm was employed with arithmetic facts (Experiment 1) and with more complex arithmetic problems (Experiment 2) in order to assess the effects of the operation, the magnitude of the operands, the magnitude of the results, and the presence or absence of a requirement for the participants to carry or borrow numbers. The results showed that arithmetic operations induce some spatial shifts of attention, possibly through a semantic link between the operation and space.

Faster fourier transformation: The algorithm of S. Winograd

NASA Technical Reports Server (NTRS)

Zohar, S.

1979-01-01

The new DFT algorithm of S. Winograd is developed and presented in detail. This is an algorithm which uses about 1/5 of the number of multiplications used by the Cooley-Tukey algorithm and is applicable to any order which is a product of relatively prime factors from the following list: 2,3,4,5,7,8,9,16. The algorithm is presented in terms of a series of tableaus which are convenient, compact, graphical representations of the sequence of arithmetic operations in the corresponding parts of the algorithm. Using these in conjunction with included Tables makes it relatively easy to apply the algorithm and evaluate its performance.

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

ERIC Educational Resources Information Center

Marshall, Sandra P.

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

The Performance of Chinese Primary School Students on Realistic Arithmetic Word Problems

ERIC Educational Resources Information Center

Xin, Ziqiang; Lin, Chongde; Zhang, Li; Yan, Rong

2007-01-01

Compared with standard arithmetic word problems demanding only the direct use of number operations and computations, realistic problems are harder to solve because children need to incorporate "real-world" knowledge into their solutions. Using the realistic word problem testing materials developed by Verschaffel, De Corte, and Lasure…

Counting and RAN: Predictors of Arithmetic Calculation and Reading Fluency

ERIC Educational Resources Information Center

Koponen, Tuire; Salmi, Paula; Eklund, Kenneth; Aro, Tuija

2013-01-01

This study examined whether counting and rapid automatized naming (RAN) could operate as significant predictors of both later arithmetic calculation and reading fluency. The authors also took an important step to clarify the cognitive mechanisms underlying these predictive relationships by controlling for the effect of phonological awareness and…

The Development of Arithmetical Abilities

ERIC Educational Resources Information Center

Butterworth, Brian

2005-01-01

Background: Arithmetical skills are essential to the effective exercise of citizenship in a numerate society. How these skills are acquired, or fail to be acquired, is of great importance not only to individual children but to the organisation of formal education and its role in society. Method: The evidence on the normal and abnormal…

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

ERIC Educational Resources Information Center

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…

Arithmetic Word-Problem-Solving in Huntington's Disease

ERIC Educational Resources Information Center

Allain, P.; Verny, C.; Aubin, G.; Pinon, K.; Bonneau, D.; Dubas, F.; Gall, D.L.

2005-01-01

The purpose of this study was to examine executive functioning in patients with Huntington's disease using an arithmetic word-problem-solving task including eight solvable problems of increasing complexity and four aberrant problems. Ten patients with Huntington's disease and 12 normal control subjects matched by age and education were tested.…

Numerical Processing Efficiency Improved in Experienced Mental Abacus Children

ERIC Educational Resources Information Center

Wang, Yunqi; Geng, Fengji; Hu, Yuzheng; Du, Fenglei; Chen, Feiyan

2013-01-01

Experienced mental abacus (MA) users are able to perform mental arithmetic calculations with unusual speed and accuracy. However, it remains unclear whether their extraordinary gains in mental arithmetic ability are accompanied by an improvement in numerical processing efficiency. To address this question, the present study, using a numerical…

40 CFR 133.101 - Definitions.

Code of Federal Regulations, 2010 CFR

2010-07-01

... arithmetic mean of pollutant parameter values for samples collected in a period of 7 consecutive days. (b) 30-day average. The arithmetic mean of pollutant parameter values of samples collected in a period of 30... percentile value for the 30-day average effluent quality achieved by a treatment works in a period of at...

Computer-Based Arithmetic Test Generation

ERIC Educational Resources Information Center

Trocchi, Robert F.

1973-01-01

The computer can be a welcome partner in the instructional process, but only if there is man-machine interaction. Man should not compromise system design because of available hardware; the computer must fit the system design for the result to represent an acceptable solution to instructional technology. The Arithmetic Test Generator system fits…

Teaching Linear Algebra: Proceeding More Efficiently by Staying Comfortably within Z

ERIC Educational Resources Information Center

Beaver, Scott

2015-01-01

For efficiency in a linear algebra course the instructor may wish to avoid the undue arithmetical distractions of rational arithmetic. In this paper we explore how to write fraction-free problems of various types including elimination, matrix inverses, orthogonality, and the (non-normalizing) Gram-Schmidt process.

The Codevelopment of Children's Fraction Arithmetic Skill and Fraction Magnitude Understanding

ERIC Educational Resources Information Center

Bailey, Drew H.; Hansen, Nicole; Jordan, Nancy C.

2017-01-01

The importance of fraction knowledge to later mathematics achievement, along with U.S. students' poor knowledge of fraction concepts and procedures, has prompted research on the development of fraction learning. In the present study, participants' (N = 536) development of fraction magnitude understanding and fraction arithmetic skills was assessed…

Mathematics: Essential to Marketing. Student's Manual and Teacher's Guide.

ERIC Educational Resources Information Center

Helton, Betty G.; Griffin, Jennie

This document contains both a student's manual and a teacher's guide for high school mathematics essential to marketing. The student's manual contains 34 assignments within the following 11 units: (1) arithmetic fundamentals; (2) application of arithmetic fundamentals; (3) cashiering; (4) inventory procedures; (5) invoices; (6) computing employee…

Teacher Actions to Facilitate Early Algebraic Reasoning

ERIC Educational Resources Information Center

Hunter, Jodie

2015-01-01

In recent years there has been an increased emphasis on integrating the teaching of arithmetic and algebra in primary school classrooms. This requires teachers to develop links between arithmetic and algebra and use pedagogical actions that facilitate algebraic reasoning. Drawing on findings from a classroom-based study, this paper provides an…

SMP That Help Foster Algebraic Thinking

ERIC Educational Resources Information Center

Billings, Esther M. H.

2017-01-01

Arithmetic is a major mathematical focus in elementary school curriculum, and researchers such as Mason (2008) claim that "algebraic thinking is required in order to make sense of arithmetic" (p. 58). When adding, subtracting, multiplying, and dividing, learners must rely on a small set of fundamental properties also important for the…

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

ERIC Educational Resources Information Center

Kidd, Teresa A.; Saudargas, Richard A.

1988-01-01

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

Idempotents a la mod

ERIC Educational Resources Information Center

Sibley, Thomas Q.

2012-01-01

An idempotent satisfies the equation x[superscript 2] = x. In ordinary arithmetic, this is so easy to solve it's boring. We delight the mathematical palette here, topping idempotents off with modular arithmetic and a series of exercises determining for which n there are more than two idempotents (mod n) and exactly how many there are.

Early Numeracy in Cerebral Palsy: Review and Future Research

ERIC Educational Resources Information Center

van Rooijen, Maaike; Verhoeven, Ludo; Steenbergen, Bert

2011-01-01

Children with cerebral palsy (CP) often have problems with arithmetic, but the development of numerical abilities in these children has received only minor attention. In comparison, detailed accounts have been written on the arithmetic abilities of typically developing children, but a theoretical framework is still lacking. A promising perspective…

Remedial Instruction to Enhance Mathematical Ability of Dyscalculics

ERIC Educational Resources Information Center

Kumar, S. Praveen; Raja, B. William Dharma

2012-01-01

The ability to do arithmetic calculations is essential to school-based learning and skill development in an information rich society. Arithmetic is a basic academic skill that is needed for learning which includes the skills such as counting, calculating, reasoning etc. that are used for performing mathematical calculations. Unfortunately, many…

SAR processing on the MPP

NASA Technical Reports Server (NTRS)

Batcher, K. E.; Eddey, E. E.; Faiss, R. O.; Gilmore, P. A.

1981-01-01

The processing of synthetic aperture radar (SAR) signals using the massively parallel processor (MPP) is discussed. The fast Fourier transform convolution procedures employed in the algorithms are described. The MPP architecture comprises an array unit (ARU) which processes arrays of data; an array control unit which controls the operation of the ARU and performs scalar arithmetic; a program and data management unit which controls the flow of data; and a unique staging memory (SM) which buffers and permutes data. The ARU contains a 128 by 128 array of bit-serial processing elements (PE). Two-by-four surarrays of PE's are packaged in a custom VLSI HCMOS chip. The staging memory is a large multidimensional-access memory which buffers and permutes data flowing with the system. Efficient SAR processing is achieved via ARU communication paths and SM data manipulation. Real time processing capability can be realized via a multiple ARU, multiple SM configuration.

Properties of the internal clock.

PubMed

Church, R M

1984-01-01

Evidence has been cited for the following properties of the parts of the psychological process used for timing intervals: The pacemaker has a mean rate that can be varied by drugs, diet, and stress. The switch has a latency to operate and it can be operated in various modes, such as run, stop, and reset. The accumulator times up, in absolute, arithmetic units. Working memory can be reset on command or, after lesions have been created in the fimbria fornix, when there is a gap in a signal. The transformation from the accumulator to reference memory is done with a multiplicative constant that is affected by drugs, lesions, and individual differences. The comparator uses a ratio between the value in the accumulator (or working memory) and reference memory. Finally, there must be multiple switch-accumulator modules to handle simultaneous temporal processing; and the psychological timing process may be used on some occasions and not on others.

Using a Cray Y-MP as an array processor for a RISC Workstation

NASA Technical Reports Server (NTRS)

Lamaster, Hugh; Rogallo, Sarah J.

1992-01-01

As microprocessors increase in power, the economics of centralized computing has changed dramatically. At the beginning of the 1980's, mainframes and super computers were often considered to be cost-effective machines for scalar computing. Today, microprocessor-based RISC (reduced-instruction-set computer) systems have displaced many uses of mainframes and supercomputers. Supercomputers are still cost competitive when processing jobs that require both large memory size and high memory bandwidth. One such application is array processing. Certain numerical operations are appropriate to use in a Remote Procedure Call (RPC)-based environment. Matrix multiplication is an example of an operation that can have a sufficient number of arithmetic operations to amortize the cost of an RPC call. An experiment which demonstrates that matrix multiplication can be executed remotely on a large system to speed the execution over that experienced on a workstation is described.

An effective method on pornographic images realtime recognition

NASA Astrophysics Data System (ADS)

Wang, Baosong; Lv, Xueqiang; Wang, Tao; Wang, Chengrui

2013-03-01

In this paper, skin detection, texture filtering and face detection are used to extract feature on an image library, training them with the decision tree arithmetic to create some rules as a decision tree classifier to distinguish an unknown image. Experiment based on more than twenty thousand images, the precision rate can get 76.21% when testing on 13025 pornographic images and elapsed time is less than 0.2s. This experiment shows it has a good popularity. Among the steps mentioned above, proposing a new skin detection model which called irregular polygon region skin detection model based on YCbCr color space. This skin detection model can lower the false detection rate on skin detection. A new method called sequence region labeling on binary connected area can calculate features on connected area, it is faster and needs less memory than other recursive methods.

Numerical ‘health check’ for scientific codes: the CADNA approach

NASA Astrophysics Data System (ADS)

Scott, N. S.; Jézéquel, F.; Denis, C.; Chesneaux, J.-M.

2007-04-01

Scientific computation has unavoidable approximations built into its very fabric. One important source of error that is difficult to detect and control is round-off error propagation which originates from the use of finite precision arithmetic. We propose that there is a need to perform regular numerical 'health checks' on scientific codes in order to detect the cancerous effect of round-off error propagation. This is particularly important in scientific codes that are built on legacy software. We advocate the use of the CADNA library as a suitable numerical screening tool. We present a case study to illustrate the practical use of CADNA in scientific codes that are of interest to the Computer Physics Communications readership. In doing so we hope to stimulate a greater awareness of round-off error propagation and present a practical means by which it can be analyzed and managed.

Detection of the Haemophilus somnus antibodies in the bulls' reproductive tract fluids using the ELISA. I. Elaboration of the ELISA for the detection of the specific antibodies in the IgG, IgM and IgA classes.

PubMed

Stefaniak, T

1993-01-01

The conditions of the ELISA for detecting the Haemophilus somnus antibodies in IgG, IgM and IgA classes were elaborated. The test was adapted for examining the seminal plasma, preputial washings and blood serum samples of bulls. In order to obtain the more precise evaluation of results, the tests were made for two different dilutions of the examined material. The arising out of this method difficulty in the evaluation of the intensity of reaction was solved by introducing the specific, semi-quantitative method of classification, using the eleven-degree scale. The mean arithmetic classificational values calculated from absorbance readings were called "absorbance index". The introduced parameter proved to be especially useful while comparing the reaction of antibodies in reproductive tract fluids samples.

[Haptic tracking control for minimally invasive robotic surgery].

PubMed

Xu, Zhaohong; Song, Chengli; Wu, Wenwu

2012-06-01

Haptic feedback plays a significant role in minimally invasive robotic surgery (MIRS). A major deficiency of the current MIRS is the lack of haptic perception for the surgeon, including the commercially available robot da Vinci surgical system. In this paper, a dynamics model of a haptic robot is established based on Newton-Euler method. Because it took some period of time in exact dynamics solution, we used a digital PID arithmetic dependent on robot dynamics to ensure real-time bilateral control, and it could improve tracking precision and real-time control efficiency. To prove the proposed method, an experimental system in which two Novint Falcon haptic devices acting as master-slave system has been developed. Simulations and experiments showed proposed methods could give instrument force feedbacks to operator, and bilateral control strategy is an effective method to master-slave MIRS. The proposed methods could be used to tele-robotic system.

Representing exact number visually using mental abacus.

PubMed

Frank, Michael C; Barner, David

2012-02-01

Mental abacus (MA) is a system for performing rapid and precise arithmetic by manipulating a mental representation of an abacus, a physical calculation device. Previous work has speculated that MA is based on visual imagery, suggesting that it might be a method of representing exact number nonlinguistically, but given the limitations on visual working memory, it is unknown how MA structures could be stored. We investigated the structure of the representations underlying MA in a group of children in India. Our results suggest that MA is represented in visual working memory by splitting the abacus into a series of columns, each of which is independently stored as a unit with its own detailed substructure. In addition, we show that the computations of practiced MA users (but not those of control participants) are relatively insensitive to verbal interference, consistent with the hypothesis that MA is a nonlinguistic format for exact numerical computation.

[Mathematical cognitive function in children with attention deficit hyperactivity disorder: a behavior and event-related potential study].

PubMed

Wang, Dan-dan; Dong, Xuan; Ren, Yan-ling; Wang, Su-hong; Yang, Shuo; Tu, Wen-juan; Huang, Jin-zhong; Shen, Hui-juan; Yi, Yang; Jiang, Kai-hua

2013-05-28

To explore the mathematics cognitive function of children with attention deficit hyperactivity disorder and explore neural mechanisms with event-related potential(ERP) and behaviors. Behavior data and ERP elicited by performing mental calculation tasks were recorded in 27 children with ADHD and 29 normal controls from July to October 2012 at Third Affiliated Hospital of Soochow University.The differences of behaviors and N2 component of ERP were compared and analyzed. The reaction time of the children with ADHD were longer than the control group in addition, subtraction and multiplication ((949 ± 144) vs (829 ± 166) ms, (981 ± 129) vs (856 ± 170) ms, (944 ± 136) vs (825 ± 172) ms, all P < 0.05). While the correct rate were less than normal control in all three arithmetic operations (0.80% (0.72%, 0.88%) vs 0.90% (0.85%,0.96%), 0.78% (0.64%,0.85%) vs 0.90% (0.84%,0.93%), 0.86% (0.74%,0.92%) vs 0.93%(0.90%,0.98%), all P < 0.05). N2 component could be elicited by all subjects in forehead. The amplitude of N2 of children with ADHD were significantly lower than control group in all three arithmetic operations at left frontal (F3: (-3.5 ± 5.2) vs (-6.7 ± 3.5)µV, (-3.8 ± 4.0) vs (-7.4 ± 4.5)µV, -5.8 (-7.6,1.6) vs -6.4(-10.3, -4.9) µV, all P < 0.05) and Fz ((-4.3 ± 6.4) vs ( -7.4 ± 4.2) µV, (-5.0 ± 5.4) vs (-7.9 ± 4.6)µV, -5.2(-9.7, -0.6) vs -7.9 (-10.5, -5.1)µV, all P < 0.05), the latency of ADHD group were prolonger than controls in subtraction operations at right and left frontal ((328 ± 36) vs (307 ± 27)ms, 325 (307,354)vs 309 (280, 330)ms) and frontal electrodes ((331 ± 35) vs (311 ± 30) ms, all P < 0.05). In addition and multiplication operations, there was no significant difference in latency (all P > 0.05). The children with ADHD have weak capacities of inhibition irrelevant information and paying attention to control. Their deficits in mental arithmetics may be due to the difficulties of selecting the best strategy during cognitive tasks.

Fpga based L-band pulse doppler radar design and implementation

NASA Astrophysics Data System (ADS)

Savci, Kubilay

As its name implies RADAR (Radio Detection and Ranging) is an electromagnetic sensor used for detection and locating targets from their return signals. Radar systems propagate electromagnetic energy, from the antenna which is in part intercepted by an object. Objects reradiate a portion of energy which is captured by the radar receiver. The received signal is then processed for information extraction. Radar systems are widely used for surveillance, air security, navigation, weather hazard detection, as well as remote sensing applications. In this work, an FPGA based L-band Pulse Doppler radar prototype, which is used for target detection, localization and velocity calculation has been built and a general-purpose Pulse Doppler radar processor has been developed. This radar is a ground based stationary monopulse radar, which transmits a short pulse with a certain pulse repetition frequency (PRF). Return signals from the target are processed and information about their location and velocity is extracted. Discrete components are used for the transmitter and receiver chain. The hardware solution is based on Xilinx Virtex-6 ML605 FPGA board, responsible for the control of the radar system and the digital signal processing of the received signal, which involves Constant False Alarm Rate (CFAR) detection and Pulse Doppler processing. The algorithm is implemented in MATLAB/SIMULINK using the Xilinx System Generator for DSP tool. The field programmable gate arrays (FPGA) implementation of the radar system provides the flexibility of changing parameters such as the PRF and pulse length therefore it can be used with different radar configurations as well. A VHDL design has been developed for 1Gbit Ethernet connection to transfer digitized return signal and detection results to PC. An A-Scope software has been developed with C# programming language to display time domain radar signals and detection results on PC. Data are processed both in FPGA chip and on PC. FPGA uses fixed point arithmetic operations as it is fast and facilitates source requirement as it consumes less hardware than floating point arithmetic operations. The software uses floating point arithmetic operations, which ensure precision in processing at the expense of speed. The functionality of the radar system has been tested for experimental validation in the field with a moving car and the validation of submodules are tested with synthetic data simulated on MATLAB.

Discrete mathematical physics and particle modeling

NASA Astrophysics Data System (ADS)

Greenspan, D.

The theory and application of the arithmetic approach to the foundations of both Newtonian and special relativistic mechanics are explored. Using only arithmetic, a reformulation of the Newtonian approach is given for: gravity; particle modeling of solids, liquids, and gases; conservative modeling of laminar and turbulent fluid flow, heat conduction, and elastic vibration; and nonconservative modeling of heat convection, shock-wave generation, the liquid drop problem, porous flow, the interface motion of a melting solid, soap films, string vibrations, and solitons. An arithmetic reformulation of special relativistic mechanics is given for theory in one space dimension, relativistic harmonic oscillation, and theory in three space dimensions. A speculative quantum mechanical model of vibrations in the water molecule is also discussed.

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

NASA Astrophysics Data System (ADS)

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

2012-07-01

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

Developing an Energy Policy for the United States

ERIC Educational Resources Information Center

Keefe, Pat

2014-01-01

Al Bartlett's video "Arithmetic, Population, and Energy" spells out many of the complex issues related to energy use in our society. Bartlett makes the point that basic arithmetic is the fundamental obstacle preventing us from being able to grasp the relationships between energy consumption, population, and lifestyles. In an earlier…