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.

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)

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

Reading Aloud and Solving Simple Arithmetic Calculation Intervention (Learning Therapy) Improves Inhibition, Verbal Episodic Memory, Focus Attention and Processing Speed in Healthy Elderly People: Evidence from a Randomized Controlled Trial

PubMed Central

Nouchi, Rui; Taki, Yasuyuki; Takeuchi, Hikaru; Nozawa, Takayuki; Sekiguchi, Atsushi; Kawashima, Ryuta

2016-01-01

Background: Previous reports have described that simple cognitive training using reading aloud and solving simple arithmetic calculations, so-called “learning therapy”, can improve executive functions and processing speed in the older adults. Nevertheless, it is not well-known whether learning therapy improve a wide range of cognitive functions or not. We investigated the beneficial effects of learning therapy on various cognitive functions in healthy older adults. Methods: We used a single-blinded intervention with two groups (learning therapy group: LT and waiting list control group: WL). Sixty-four elderly were randomly assigned to LT or WL. In LT, participants performed reading Japanese aloud and solving simple calculations training tasks for 6 months. WL did not participate in the intervention. We measured several cognitive functions before and after 6 months intervention periods. Results: Compared to WL, results revealed that LT improved inhibition performance in executive functions (Stroop: LT (Mean = 3.88) vs. WL (Mean = 1.22), adjusted p = 0.013 and reverse Stroop LT (Mean = 3.22) vs. WL (Mean = 1.59), adjusted p = 0.015), verbal episodic memory (Logical Memory (LM): LT (Mean = 4.59) vs. WL (Mean = 2.47), adjusted p = 0.015), focus attention (D-CAT: LT (Mean = 2.09) vs. WL (Mean = −0.59), adjusted p = 0.010) and processing speed compared to the WL control group (digit symbol coding: LT (Mean = 5.00) vs. WL (Mean = 1.13), adjusted p = 0.015 and Symbol Search (SS): LT (Mean = 3.47) vs. WL (Mean = 1.81), adjusted p = 0.014). Discussion: This randomized controlled trial (RCT) can be showed the benefit of LT on inhibition of executive functions, verbal episodic memory, focus attention and processing speed in healthy elderly people. Our results were discussed under overlapping hypothesis. PMID:27242481

Reading Aloud and Solving Simple Arithmetic Calculation Intervention (Learning Therapy) Improves Inhibition, Verbal Episodic Memory, Focus Attention and Processing Speed in Healthy Elderly People: Evidence from a Randomized Controlled Trial.

PubMed

Nouchi, Rui; Taki, Yasuyuki; Takeuchi, Hikaru; Nozawa, Takayuki; Sekiguchi, Atsushi; Kawashima, Ryuta

2016-01-01

Previous reports have described that simple cognitive training using reading aloud and solving simple arithmetic calculations, so-called "learning therapy", can improve executive functions and processing speed in the older adults. Nevertheless, it is not well-known whether learning therapy improve a wide range of cognitive functions or not. We investigated the beneficial effects of learning therapy on various cognitive functions in healthy older adults. We used a single-blinded intervention with two groups (learning therapy group: LT and waiting list control group: WL). Sixty-four elderly were randomly assigned to LT or WL. In LT, participants performed reading Japanese aloud and solving simple calculations training tasks for 6 months. WL did not participate in the intervention. We measured several cognitive functions before and after 6 months intervention periods. Compared to WL, results revealed that LT improved inhibition performance in executive functions (Stroop: LT (Mean = 3.88) vs. WL (Mean = 1.22), adjusted p = 0.013 and reverse Stroop LT (Mean = 3.22) vs. WL (Mean = 1.59), adjusted p = 0.015), verbal episodic memory (Logical Memory (LM): LT (Mean = 4.59) vs. WL (Mean = 2.47), adjusted p = 0.015), focus attention (D-CAT: LT (Mean = 2.09) vs. WL (Mean = -0.59), adjusted p = 0.010) and processing speed compared to the WL control group (digit symbol coding: LT (Mean = 5.00) vs. WL (Mean = 1.13), adjusted p = 0.015 and Symbol Search (SS): LT (Mean = 3.47) vs. WL (Mean = 1.81), adjusted p = 0.014). This randomized controlled trial (RCT) can be showed the benefit of LT on inhibition of executive functions, verbal episodic memory, focus attention and processing speed in healthy elderly people. Our results were discussed under overlapping hypothesis.

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)

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…

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.

Undergraduate paramedic students cannot do drug calculations.

PubMed

Eastwood, Kathryn; Boyle, Malcolm J; Williams, Brett

2012-01-01

Previous investigation of drug calculation skills of qualified paramedics has highlighted poor mathematical ability with no published studies having been undertaken on undergraduate paramedics. There are three major error classifications. Conceptual errors involve an inability to formulate an equation from information given, arithmetical errors involve an inability to operate a given equation, and finally computation errors are simple errors of addition, subtraction, division and multiplication. The objective of this study was to determine if undergraduate paramedics at a large Australia university could accurately perform common drug calculations and basic mathematical equations normally required in the workplace. A cross-sectional study methodology using a paper-based questionnaire was administered to undergraduate paramedic students to collect demographical data, student attitudes regarding their drug calculation performance, and answers to a series of basic mathematical and drug calculation questions. Ethics approval was granted. The mean score of correct answers was 39.5% with one student scoring 100%, 3.3% of students (n=3) scoring greater than 90%, and 63% (n=58) scoring 50% or less, despite 62% (n=57) of the students stating they 'did not have any drug calculations issues'. On average those who completed a minimum of year 12 Specialist Maths achieved scores over 50%. Conceptual errors made up 48.5%, arithmetical 31.1% and computational 17.4%. This study suggests undergraduate paramedics have deficiencies in performing accurate calculations, with conceptual errors indicating a fundamental lack of mathematical understanding. The results suggest an unacceptable level of mathematical competence to practice safely in the unpredictable prehospital environment.

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.

Simple formula for the surface area of the body and a simple model for anthropometry.

PubMed

Reading, Bruce D; Freeman, Brian

2005-03-01

The body surface area (BSA) of any adult, when derived from the arithmetic mean of the different values calculated from four independent accepted formulae, can be expressed accurately in Systeme International d'Unites (SI) units by the simple equation BSA = 1/6(WH)0.5, where W is body weight in kg, H is body height in m, and BSA is in m2. This formula, which is derived in part by modeling the body as a simple solid of revolution or a prolate spheroid (i.e., a stretched ellipsoid of revolution) gives students, teachers, and clinicians a simple rule for the rapid estimation of surface area using rational units. The formula was tested independently for human subjects by using it to predict body volume and then comparing this prediction against the actual volume measured by Archimedes' principle. Copyright 2005 Wiley-Liss, Inc.

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

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.

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.

Introducing Calculators to Learners Early in Their Schooling: The Effect on Long-Term Arithmetic Proficiency

ERIC Educational Resources Information Center

Mogari, David; Faleye, Sunday

2012-01-01

There are opposing views about calculator use in school mathematics. This paper reports on a study that investigated the arithmetic proficiency of mathematics 1 university students and the effects of calculator usage at school level on their proficiency. The study followed a descriptive survey design involving the use of questionnaire and data…

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…

A Study of Arithmetical Problem Solving Abilities of Young Children through the Use of Calculators.

ERIC Educational Resources Information Center

McNicol, Shirley; And Others

A study was conducted to: (1) observe through a case study approach the exploratory behavior exhibited by 8-year-old boys and girls when calculators were made available in problem-solving situations; (2) investigate changes that occur in the kinds of arithmetical problems children construct following the introduction of calculators; and (3)…

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…

Undergraduate paramedic students cannot do drug calculations

PubMed Central

Eastwood, Kathryn; Boyle, Malcolm J; Williams, Brett

2012-01-01

BACKGROUND: Previous investigation of drug calculation skills of qualified paramedics has highlighted poor mathematical ability with no published studies having been undertaken on undergraduate paramedics. There are three major error classifications. Conceptual errors involve an inability to formulate an equation from information given, arithmetical errors involve an inability to operate a given equation, and finally computation errors are simple errors of addition, subtraction, division and multiplication. The objective of this study was to determine if undergraduate paramedics at a large Australia university could accurately perform common drug calculations and basic mathematical equations normally required in the workplace. METHODS: A cross-sectional study methodology using a paper-based questionnaire was administered to undergraduate paramedic students to collect demographical data, student attitudes regarding their drug calculation performance, and answers to a series of basic mathematical and drug calculation questions. Ethics approval was granted. RESULTS: The mean score of correct answers was 39.5% with one student scoring 100%, 3.3% of students (n=3) scoring greater than 90%, and 63% (n=58) scoring 50% or less, despite 62% (n=57) of the students stating they ‘did not have any drug calculations issues’. On average those who completed a minimum of year 12 Specialist Maths achieved scores over 50%. Conceptual errors made up 48.5%, arithmetical 31.1% and computational 17.4%. CONCLUSIONS: This study suggests undergraduate paramedics have deficiencies in performing accurate calculations, with conceptual errors indicating a fundamental lack of mathematical understanding. The results suggest an unacceptable level of mathematical competence to practice safely in the unpredictable prehospital environment. PMID:25215067

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

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…

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…

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.

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

ERIC Educational Resources Information Center

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

2018-01-01

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

Individual Differences in Mathematical Competence Modulate Brain Responses to Arithmetic Errors: An fMRI Study

ERIC Educational Resources Information Center

Ansari, Daniel; Grabner, Roland H.; Koschutnig, Karl; Reishofer, Gernot; Ebner, Franz

2011-01-01

Data from both neuropsychological and neuroimaging studies have implicated the left inferior parietal cortex in calculation. Comparatively less attention has been paid to the neural responses associated with the commission of calculation errors and how the processing of arithmetic errors is modulated by individual differences in mathematical…

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.

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.

Genetic fidelity and variability of micropropagated cassava plants (Manihot esculenta Crantz) evaluated using ISSR markers.

PubMed

Vidal, Á M; Vieira, L J; Ferreira, C F; Souza, F V D; Souza, A S; Ledo, C A S

2015-07-14

Molecular markers are efficient for assessing the genetic fidelity of various species of plants after in vitro culture. In this study, we evaluated the genetic fidelity and variability of micropropagated cassava plants (Manihot esculenta Crantz) using inter-simple sequence repeat markers. Twenty-two cassava accessions from the Embrapa Cassava & Fruits Germplasm Bank were used. For each accession, DNA was extracted from a plant maintained in the field and from 3 plants grown in vitro. For DNA amplification, 27 inter-simple sequence repeat primers were used, of which 24 generated 175 bands; 100 of those bands were polymorphic and were used to study genetic variability among accessions of cassava plants maintained in the field. Based on the genetic distance matrix calculated using the arithmetic complement of the Jaccard's index, genotypes were clustered using the unweighted pair group method using arithmetic averages. The number of bands per primer was 2-13, with an average of 7.3. For most micropropagated accessions, the fidelity study showed no genetic variation between plants of the same accessions maintained in the field and those maintained in vitro, confirming the high genetic fidelity of the micropropagated plants. However, genetic variability was observed among different accessions grown in the field, and clustering based on the dissimilarity matrix revealed 7 groups. Inter-simple sequence repeat markers were efficient for detecting the genetic homogeneity of cassava plants derived from meristem culture, demonstrating the reliability of this propagation system.

Cross-Cultural Investigation into Cognitive Underpinnings of Individual Differences in Early Arithmetic

ERIC Educational Resources Information Center

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…

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…

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.

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.

A Single-Boundary Accumulator Model of Response Times in an Addition Verification Task

PubMed Central

Faulkenberry, Thomas J.

2017-01-01

Current theories of mathematical cognition offer competing accounts of the interplay between encoding and calculation in mental arithmetic. Additive models propose that manipulations of problem format do not interact with the cognitive processes used in calculation. Alternatively, interactive models suppose that format manipulations have a direct effect on calculation processes. In the present study, we tested these competing models by fitting participants' RT distributions in an arithmetic verification task with a single-boundary accumulator model (the shifted Wald distribution). We found that in addition to providing a more complete description of RT distributions, the accumulator model afforded a potentially more sensitive test of format effects. Specifically, we found that format affected drift rate, which implies that problem format has a direct impact on calculation processes. These data give further support for an interactive model of mental arithmetic. PMID:28769853

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.

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.

Do calendrical savants use calculation to answer date questions? A functional magnetic resonance imaging study

PubMed Central

Cowan, Richard; Frith, Chris

2009-01-01

Calendrical savants can name the weekdays for dates from different years with remarkable speed and accuracy. Whether calculation rather than just memory is involved is disputed. Grounds for doubting whether they can calculate are reviewed and criteria for attributing date calculation skills to them are discussed. At least some calendrical savants possess date calculation skills. A behavioural characteristic observed in many calendrical savants is increased response time for questions about more remote years. This may be because more remote years require more calculation or because closer years are more practised. An experiment is reported that used functional magnetic resonance imaging to attempt to discriminate between these explanations. Only two savants could be scanned and excessive head movement corrupted one savant's mental arithmetic data. Nevertheless, there was increased parietal activation during both mental arithmetic and date questions and this region showed increased activity with more remote dates. These results suggest that the calendrical skills observed in savants result from intensive practice with calculations used in solving mental arithmetic problems. The mystery is not how they solve these problems, but why. PMID:19528025

Research on Process Models of Basic Arithmetic Skills, Technical Report No. 303. Psychology and Education Series - Final Report.

ERIC Educational Resources Information Center

Suppes, Patrick; And Others

This report presents a theory of eye movement that accounts for main features of the stochastic behavior of eye-fixation durations and direction of movement of saccades in the process of solving arithmetic exercises of addition and subtraction. The best-fitting distribution of fixation durations with a relatively simple theoretical justification…

Beneficial effects of reading aloud and solving simple arithmetic calculations (learning therapy) on a wide range of cognitive functions in the healthy elderly: study protocol for a randomized controlled trial

PubMed Central

2012-01-01

Background Almost all cognitive functions decline with age. Results of previous studies have shown that cognitive training related to everyday life (reading aloud and solving simple arithmetic calculations), namely learning therapy, can improve two cognitive function (executive functions and processing speed) in elderly people. However, it remains unclear whether learning therapy engenders improvement of various cognitive functions or not. We investigate the impact of learning therapy on various cognitive functions (executive functions, episodic memory, short-term memory, working memory, attention, reading ability, and processing speed) in healthy older adults. Methods We use a single-blinded intervention with two parallel groups (a learning therapy group and a waiting list control group). Testers are blind to the study hypothesis and the group membership of participants. Through an advertisement in local newspaper, 64 healthy older adults are recruited. They will be assigned randomly to a learning therapy group or a waiting list control group. In the learning therapy group, participants are required to perform two cognitive tasks for 6 months: reading Japanese aloud and solving simple calculations. The waiting list group does not participate in the intervention. The primary outcome measure is the Stroop test score: a measure of executive function. Secondary outcome measures are assessments including the following: verbal fluency task, logical memory, first and second names, digit span forward, digit span backward, Japanese reading test, digit cancellation task, digit symbol coding, and symbol search. We assess these outcome measures before and after the intervention. Discussion This report is the first study which investigates the beneficial effects of learning therapy on a wide range of cognitive functions of elderly people. Our study provides sufficient evidence of learning therapy effectiveness. Most cognitive functions, which are correlated strongly with daily life activities, decrease with age. These study results can elucidate effects of cognitive training on elderly people. Trial registration This trial was registered in The University Hospital Medical Information Network Clinical Trials Registry (No. UMIN000006998). PMID:22483196

Beneficial effects of reading aloud and solving simple arithmetic calculations (learning therapy) on a wide range of cognitive functions in the healthy elderly: study protocol for a randomized controlled trial.

PubMed

Nouchi, Rui; Taki, Yasuyuki; Takeuchi, Hikaru; Hashizume, Hiroshi; Nozawa, Takayuki; Sekiguchi, Atsushi; Nouchi, Haruka; Kawashima, Ryuta

2012-04-06

Almost all cognitive functions decline with age. Results of previous studies have shown that cognitive training related to everyday life (reading aloud and solving simple arithmetic calculations), namely learning therapy, can improve two cognitive function (executive functions and processing speed) in elderly people. However, it remains unclear whether learning therapy engenders improvement of various cognitive functions or not. We investigate the impact of learning therapy on various cognitive functions (executive functions, episodic memory, short-term memory, working memory, attention, reading ability, and processing speed) in healthy older adults. We use a single-blinded intervention with two parallel groups (a learning therapy group and a waiting list control group). Testers are blind to the study hypothesis and the group membership of participants. Through an advertisement in local newspaper, 64 healthy older adults are recruited. They will be assigned randomly to a learning therapy group or a waiting list control group. In the learning therapy group, participants are required to perform two cognitive tasks for 6 months: reading Japanese aloud and solving simple calculations. The waiting list group does not participate in the intervention. The primary outcome measure is the Stroop test score: a measure of executive function. Secondary outcome measures are assessments including the following: verbal fluency task, logical memory, first and second names, digit span forward, digit span backward, Japanese reading test, digit cancellation task, digit symbol coding, and symbol search. We assess these outcome measures before and after the intervention. This report is the first study which investigates the beneficial effects of learning therapy on a wide range of cognitive functions of elderly people. Our study provides sufficient evidence of learning therapy effectiveness. Most cognitive functions, which are correlated strongly with daily life activities, decrease with age. These study results can elucidate effects of cognitive training on elderly people. This trial was registered in The University Hospital Medical Information Network Clinical Trials Registry (No. UMIN000006998).

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.

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.

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.

The beneficial effects of cognitive training with simple calculation and reading aloud in an elderly postsurgical population: study protocol for a randomized controlled trial.

PubMed

Kulason, Kay; Nouchi, Rui; Hoshikawa, Yasushi; Noda, Masafumi; Okada, Yoshinori; Kawashima, Ryuta

2016-07-22

This project proposes a pilot study to investigate the positive healing effects of cognitive training with simple arithmetic and reading aloud on elderly postsurgical patients. Elderly patients undergoing surgery have an increased risk of Postoperative Cognitive Decline (POCD), a condition in which learning, memory, and processing speed is greatly reduced after surgery. Since elderly patients are more likely to exhibit symptoms of POCD, the incidence is increasing as the population receiving surgery has aged. Little effort has been expended, however, to find treatments for POCD. Learning therapy, which consists of a combination of reading aloud and solving simple arithmetic problems, was developed in Japan as a treatment for Alzheimer's Disease to improve cognitive functions. Because patients with Alzheimer's Disease experience similar issues as those with POCD in learning, memory, and processing speed, a cognitive intervention based on the learning-therapy treatments used for Alzheimer's Disease could show advantageous outcomes for those at risk of POCD. Cognitive function will be measured before and after surgery using three different tests (Mini-Mental Status Exam, Frontal Assessment Battery, and Cogstate computerized tests). Subjects will be randomly divided into two groups-one that receives a Simple Calculation and Reading Aloud intervention (SCRA) and a waitlisted control group that does not receive SCRA. To measure cognition before and after the intervention, the previously mentioned three tests will be used. The obtained data will be analyzed using statistical tests such as ANCOVA to indicate whether the cognitive intervention group has made improvements in their cognitive functions. In addition, questionnaires will also be administered to collect data on mental and emotional statuses. This report will be the first pilot study to investigate the beneficial effects of SCRA on elderly surgical patients. Previous studies have shown sufficient evidence on the effectiveness of learning therapy in healthy elderly people and in those with Dementia. Therefore, this study will clarify whether SCRA can improve cognitive function in the more specialized group of elderly surgical patients. University Hospital Medical Information Network Clinical Trial Registry, UMIN000019832 . Registered on 18 November 2015.

Comorbidity of Arithmetic and Reading Disorder: Basic Number Processing and Calculation in Children with Learning Impairments

ERIC Educational Resources Information Center

Raddatz, Julia; Kuhn, Jörg-Tobias; Holling, Heinz; Moll, Kristina; Dobel, Christian

2017-01-01

The aim of the present study was to investigate the cognitive profiles of primary school children (age 82-133 months) on a battery of basic number processing and calculation tasks. The sample consisted of four groups matched for age and IQ: arithmetic disorder only (AD; n = 20), reading disorder only (RD; n = 40), a comorbid group (n = 27), and an…

Brain Activation during Addition and Subtraction Tasks In-Noise and In-Quiet

PubMed Central

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

2011-01-01

Background: In spite of extensive research conducted to study how human brain works, little is known about a special function of the brain that stores and manipulates information—the working memory—and how noise influences this special ability. In this study, Functional magnetic resonance imaging (fMRI) was used to investigate brain responses to arithmetic problems solved in noisy and quiet backgrounds. Methods: Eighteen healthy young males performed simple arithmetic operations of addition and subtraction with in-quiet and in-noise backgrounds. The MATLAB-based Statistical Parametric Mapping (SPM8) was implemented on the fMRI datasets to generate and analyse the activated brain regions. Results: Group results showed that addition and subtraction operations evoked extended activation in the left inferior parietal lobe, left precentral gyrus, left superior parietal lobe, left supramarginal gyrus, and left middle temporal gyrus. This supported the hypothesis that the human brain relatively activates its left hemisphere more compared with the right hemisphere when solving arithmetic problems. The insula, middle cingulate cortex, and middle frontal gyrus, however, showed more extended right hemispheric activation, potentially due to the involvement of attention, executive processes, and working memory. For addition operations, there was extensive left hemispheric activation in the superior temporal gyrus, inferior frontal gyrus, and thalamus. In contrast, subtraction tasks evoked a greater activation of similar brain structures in the right hemisphere. For both addition and subtraction operations, the total number of activated voxels was higher for in-noise than in-quiet conditions. Conclusion: These findings suggest that when arithmetic operations were delivered auditorily, the auditory, attention, and working memory functions were required to accomplish the executive processing of the mathematical calculation. The respective brain activation patterns appear to be modulated by the noisy background condition. PMID:22135581

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.

Network-Physics (NP) BEC DIGITAL(#)-VULNERABILITY; ``Q-Computing"=Simple-Arithmetic;Modular-Congruences=SignalXNoise PRODUCTS=Clock-model;BEC-Factorization;RANDOM-# Definition;P=/=NP TRIVIAL Proof!!!

NASA Astrophysics Data System (ADS)

Pi, E. I.; Siegel, E.

2010-03-01

Siegel[AMS Natl.Mtg.(2002)-Abs.973-60-124] digits logarithmic- law inversion to ONLY BEQS BEC:Quanta/Bosons=#: EMP-like SEVERE VULNERABILITY of ONLY #-networks(VS.ANALOG INvulnerability) via Barabasi NP(VS.dynamics[Not.AMS(5/2009)] critique);(so called)``quantum-computing''(QC) = simple-arithmetic (sansdivision);algorithmiccomplexities:INtractibility/UNdecidabi lity/INefficiency/NONcomputability/HARDNESS(so MIScalled) ``noise''-induced-phase-transition(NIT)ACCELERATION:Cook-Levin theorem Reducibility = RG fixed-points; #-Randomness DEFINITION via WHAT? Query(VS. Goldreich[Not.AMS(2002)] How? mea culpa)= ONLY MBCS hot-plasma v #-clumping NON-random BEC; Modular-Arithmetic Congruences = Signal x Noise PRODUCTS = clock-model; NON-Shor[Physica A,341,586(04)]BEC logarithmic-law inversion factorization: Watkins #-theory U statistical- physics); P=/=NP C-S TRIVIAL Proof: Euclid!!! [(So Miscalled) computational-complexity J-O obviation(3 millennia AGO geometry: NO:CC,``CS'';``Feet of Clay!!!'']; Query WHAT?:Definition: (so MIScalled)``complexity''=UTTER-SIMPLICITY!! v COMPLICATEDNESS MEASURE(S).

Group differences in adult simple arithmetic: good retrievers, not-so-good retrievers, and perfectionists.

PubMed

Hecht, Steven A

2006-01-01

We used the choice/no-choice methodology in two experiments to examine patterns of strategy selection and execution in groups of undergraduates. Comparisons between choice and no-choice trials revealed three groups. Some participants good retrievers) were consistently able to use retrieval to solve almost all arithmetic problems. Other participants (perfectionists) successfully used retrieval substantially less often in choice-allowed trials than when strategy choices were prohibited. Not-so-good retrievers retrieved correct answers less often than the other participants in both the choice-allowed and no-choice conditions. No group differences emerged with respect to time needed to search and access answers from long-term memory; however, not-so-good retrievers were consistently slower than the other subgroups at executing fact-retrieval processes that are peripheral to memory search and access. Theoretical models of simple arithmetic, such as the Strategy Choice and Discovery Simulation (Shrager & Siegler, 1998), should be updated to include the existence of both perfectionist and not-so-good retriever adults.

Approaches in highly parameterized inversion: TSPROC, a general time-series processor to assist in model calibration and result summarization

USGS Publications Warehouse

Westenbroek, Stephen M.; Doherty, John; Walker, John F.; Kelson, Victor A.; Hunt, Randall J.; Cera, Timothy B.

2012-01-01

The TSPROC (Time Series PROCessor) computer software uses a simple scripting language to process and analyze time series. It was developed primarily to assist in the calibration of environmental models. The software is designed to perform calculations on time-series data commonly associated with surface-water models, including calculation of flow volumes, transformation by means of basic arithmetic operations, and generation of seasonal and annual statistics and hydrologic indices. TSPROC can also be used to generate some of the key input files required to perform parameter optimization by means of the PEST (Parameter ESTimation) computer software. Through the use of TSPROC, the objective function for use in the model-calibration process can be focused on specific components of a hydrograph.

Inexact hardware for modelling weather & climate

NASA Astrophysics Data System (ADS)

Düben, Peter D.; McNamara, Hugh; Palmer, Tim

2014-05-01

The use of stochastic processing hardware and low precision arithmetic in atmospheric models is investigated. Stochastic processors allow hardware-induced faults in calculations, sacrificing exact calculations in exchange for improvements in performance and potentially accuracy and a reduction in power consumption. A similar trade-off is achieved using low precision arithmetic, with improvements in computation and communication speed and savings in storage and memory requirements. As high-performance computing becomes more massively parallel and power intensive, these two approaches may be important stepping stones in the pursuit of global cloud resolving atmospheric modelling. The impact of both, hardware induced faults and low precision arithmetic is tested in the dynamical core of a global atmosphere model. Our simulations show that both approaches to inexact calculations do not substantially affect the quality of the model simulations, provided they are restricted to act only on smaller scales. This suggests that inexact calculations at the small scale could reduce computation and power costs without adversely affecting the quality of the simulations.

Students who developed logical reasoning skills reported improved confidence in drug dose calculation: Feedback from remedial maths classes.

PubMed

Shelton, Chris

2016-06-01

The safe administration of drugs is a focus of attention in healthcare. It is regarded as acceptable that a formula card or mnemonic can be used to find the correct dose and fill a prescription even though this removes any requirement for performing the underlying computation. Feedback and discussion in class reveal that confidence in arithmetic skills can be low even when students are able to pass the end of semester drug calculation exam. To see if confidence in the understanding and performance of arithmetic for drug calculations can be increased by emphasising student's innate powers of logical reasoning after reflection. Remedial classes offered for students who have declared a dislike or lack of confidence in arithmetic have been developed from student feedback adopting a reasoning by logical step methodology. Students who gave up two hours of their free learning time were observed to engage seriously with the learning methods, focussing on the innate ability to perform logical reasoning necessary for drug calculation problems. Working in small groups allowed some discussion of the route to the answer and this was followed by class discussion and reflection. The results were recorded as weekly self-assessment scores for confidence in calculation. A self-selecting group who successfully completed the end of semester drug calculation exam reported low to moderate confidence in arithmetic. After four weeks focussing on logical skills a significant increase in self-belief was measured. This continued to rise in students who remained in the classes. Many students hold a negative belief regarding their own mathematical abilities. This restricts the learning of arithmetic skills making alternate routes using mnemonics and memorised steps an attractive alternative. Practising stepwise logical reasoning skills consolidated by personal reflection has been effective in developing student's confidence and awareness of their innate powers of deduction supporting an increase in competence in drug administration. Copyright © 2016 Elsevier Ltd. All rights reserved.

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,…

No Generalization of Practice for Nonzero Simple Addition

ERIC Educational Resources Information Center

Campbell, Jamie I. D.; Beech, Leah C.

2014-01-01

Several types of converging evidence have suggested recently that skilled adults solve very simple addition problems (e.g., 2 + 1, 4 + 2) using a fast, unconscious counting algorithm. These results stand in opposition to the long-held assumption in the cognitive arithmetic literature that such simple addition problems normally are solved by fact…

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.

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…

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.

The use of imprecise processing to improve accuracy in weather & climate prediction

NASA Astrophysics Data System (ADS)

Düben, Peter D.; McNamara, Hugh; Palmer, T. N.

2014-08-01

The use of stochastic processing hardware and low precision arithmetic in atmospheric models is investigated. Stochastic processors allow hardware-induced faults in calculations, sacrificing bit-reproducibility and precision in exchange for improvements in performance and potentially accuracy of forecasts, due to a reduction in power consumption that could allow higher resolution. A similar trade-off is achieved using low precision arithmetic, with improvements in computation and communication speed and savings in storage and memory requirements. As high-performance computing becomes more massively parallel and power intensive, these two approaches may be important stepping stones in the pursuit of global cloud-resolving atmospheric modelling. The impact of both hardware induced faults and low precision arithmetic is tested using the Lorenz '96 model and the dynamical core of a global atmosphere model. In the Lorenz '96 model there is a natural scale separation; the spectral discretisation used in the dynamical core also allows large and small scale dynamics to be treated separately within the code. Such scale separation allows the impact of lower-accuracy arithmetic to be restricted to components close to the truncation scales and hence close to the necessarily inexact parametrised representations of unresolved processes. By contrast, the larger scales are calculated using high precision deterministic arithmetic. Hardware faults from stochastic processors are emulated using a bit-flip model with different fault rates. Our simulations show that both approaches to inexact calculations do not substantially affect the large scale behaviour, provided they are restricted to act only on smaller scales. By contrast, results from the Lorenz '96 simulations are superior when small scales are calculated on an emulated stochastic processor than when those small scales are parametrised. This suggests that inexact calculations at the small scale could reduce computation and power costs without adversely affecting the quality of the simulations. This would allow higher resolution models to be run at the same computational cost.

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…

Age difference in numeral recognition and calculation: an event-related potential study.

PubMed

Xuan, Dong; Wang, Suhong; Yang, Yilin; Meng, Ping; Xu, Feng; Yang, Wen; Sheng, Wei; Yang, Yuxia

2007-01-01

In this study, we investigated the age difference in numeral recognition and calculation in one group of school-aged children (n = 38) and one of undergraduate students (n = 26) using the event-related potential (ERP) methods. Consistent with previous reports, the age difference was significant in behavioral results. Both numeral recognition and calculation elicited a negativity peaking at about 170-280 ms (N2) and a positivity peaking at 200-470 ms (pSW) in raw ERPs, and a difference potential (dN3) between 360 and 450 ms. The difference between the two age groups indicated that more attention resources were devoted to arithmetical tasks in school-aged children, and that school-aged children and undergraduate students appear to use different strategies to solve arithmetical problems. The analysis of frontal negativity suggested that numeral recognition and mental calculation impose greater load on working memory and executive function in schoolchildren than in undergraduate students. The topography data determined that the parietal regions were responsible for arithmetical function in humans, and there was an age-related difference in the area of cerebral activation.

Dissociation between exact and approximate addition in developmental dyslexia.

PubMed

Yang, Xiujie; Meng, Xiangzhi

2016-09-01

Previous research has suggested that number sense and language are involved in number representation and calculation, in which number sense supports approximate arithmetic, and language permits exact enumeration and calculation. Meanwhile, individuals with dyslexia have a core deficit in phonological processing. Based on these findings, we thus hypothesized that children with dyslexia may exhibit exact calculation impairment while doing mental arithmetic. The reaction time and accuracy while doing exact and approximate addition with symbolic Arabic digits and non-symbolic visual arrays of dots were compared between typically developing children and children with dyslexia. Reaction time analyses did not reveal any differences across two groups of children, the accuracies, interestingly, revealed a distinction of approximation and exact addition across two groups of children. Specifically, two groups of children had no differences in approximation. Children with dyslexia, however, had significantly lower accuracy in exact addition in both symbolic and non-symbolic tasks than that of typically developing children. Moreover, linguistic performances were selectively associated with exact calculation across individuals. These results suggested that children with dyslexia have a mental arithmetic deficit specifically in the realm of exact calculation, while their approximation ability is relatively intact. Copyright © 2016 Elsevier Ltd. All rights reserved.

Individual differences in solving arithmetic word problems

PubMed Central

2013-01-01

Background With the present functional magnetic resonance imaging (fMRI) study at 3 T, we investigated the neural correlates of visualization and verbalization during arithmetic word problem solving. In the domain of arithmetic, visualization might mean to visualize numbers and (intermediate) results while calculating, and verbalization might mean that numbers and (intermediate) results are verbally repeated during calculation. If the brain areas involved in number processing are domain-specific as assumed, that is, that the left angular gyrus (AG) shows an affinity to the verbal domain, and that the left and right intraparietal sulcus (IPS) shows an affinity to the visual domain, the activation of these areas should show a dependency on an individual’s cognitive style. Methods 36 healthy young adults participated in the fMRI study. The participants habitual use of visualization and verbalization during solving arithmetic word problems was assessed with a short self-report assessment. During the fMRI measurement, arithmetic word problems that had to be solved by the participants were presented in an event-related design. Results We found that visualizers showed greater brain activation in brain areas involved in visual processing, and that verbalizers showed greater brain activation within the left angular gyrus. Conclusions Our results indicate that cognitive styles or preferences play an important role in understanding brain activation. Our results confirm, that strong visualizers use mental imagery more strongly than weak visualizers during calculation. Moreover, our results suggest that the left AG shows a specific affinity to the verbal domain and subserves number processing in a modality-specific way. PMID:23883107

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.

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

The Ability of Conceptual Monitoring and the Quality of Working Memory at Children With Calculation Difficulties

ERIC Educational Resources Information Center

Arsic, Sladjana; Eminovic, Fadilj; Stankovic, Ivona

2011-01-01

Calculia is considered to be the ability of performing arithmetic operations, the preconditions for the development of mathematical skills in the complex functioning of psychological functions represented in neuro-anatomical systems, as well in the interaction with the environment. Problems in acquiring arithmetic skills can be described as…

[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.

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.

Fast Fuzzy Arithmetic Operations

NASA Technical Reports Server (NTRS)

Hampton, Michael; Kosheleva, Olga

1997-01-01

In engineering applications of fuzzy logic, the main goal is not to simulate the way the experts really think, but to come up with a good engineering solution that would (ideally) be better than the expert's control, In such applications, it makes perfect sense to restrict ourselves to simplified approximate expressions for membership functions. If we need to perform arithmetic operations with the resulting fuzzy numbers, then we can use simple and fast algorithms that are known for operations with simple membership functions. In other applications, especially the ones that are related to humanities, simulating experts is one of the main goals. In such applications, we must use membership functions that capture every nuance of the expert's opinion; these functions are therefore complicated, and fuzzy arithmetic operations with the corresponding fuzzy numbers become a computational problem. In this paper, we design a new algorithm for performing such operations. This algorithm is applicable in the case when negative logarithms - log(u(x)) of membership functions u(x) are convex, and reduces computation time from O(n(exp 2))to O(n log(n)) (where n is the number of points x at which we know the membership functions u(x)).

40 CFR 60.2943 - How do I convert my 1-hour arithmetic averages into the appropriate averaging times and units?

Code of Federal Regulations, 2010 CFR

2010-07-01

... averages into the appropriate averaging times and units? 60.2943 Section 60.2943 Protection of Environment... SOURCES Operator Training and Qualification Monitoring § 60.2943 How do I convert my 1-hour arithmetic averages into the appropriate averaging times and units? (a) Use Equation 1 in § 60.2975 to calculate...

40 CFR 60.2943 - How do I convert my 1-hour arithmetic averages into the appropriate averaging times and units?

Code of Federal Regulations, 2012 CFR

2012-07-01

... averages into the appropriate averaging times and units? 60.2943 Section 60.2943 Protection of Environment... SOURCES Operator Training and Qualification Monitoring § 60.2943 How do I convert my 1-hour arithmetic averages into the appropriate averaging times and units? (a) Use Equation 1 in § 60.2975 to calculate...

40 CFR 60.2943 - How do I convert my 1-hour arithmetic averages into the appropriate averaging times and units?

Code of Federal Regulations, 2011 CFR

2011-07-01

... averages into the appropriate averaging times and units? 60.2943 Section 60.2943 Protection of Environment... SOURCES Operator Training and Qualification Monitoring § 60.2943 How do I convert my 1-hour arithmetic averages into the appropriate averaging times and units? (a) Use Equation 1 in § 60.2975 to calculate...

Influence of the large-small split effect on strategy choice in complex subtraction.

PubMed

Xiang, Yan Hui; Wu, Hao; Shang, Rui Hong; Chao, Xiaomei; Ren, Ting Ting; Zheng, Li Ling; Mo, Lei

2018-04-01

Two main theories have been used to explain the arithmetic split effect: decision-making process theory and strategy choice theory. Using the inequality paradigm, previous studies have confirmed that individuals tend to adopt a plausibility-checking strategy and a whole-calculation strategy to solve large and small split problems in complex addition arithmetic, respectively. This supports strategy choice theory, but it is unknown whether this theory also explains performance in solving different split problems in complex subtraction arithmetic. This study used small, intermediate and large split sizes, with each split condition being further divided into problems requiring and not requiring borrowing. The reaction times (RTs) for large and intermediate splits were significantly shorter than those for small splits, while accuracy was significantly higher for large and middle splits than for small splits, reflecting no speed-accuracy trade-off. Further, RTs and accuracy differed significantly between the borrow and no-borrow conditions only for small splits. This study indicates that strategy choice theory is suitable to explain the split effect in complex subtraction arithmetic. That is, individuals tend to choose the plausibility-checking strategy or the whole-calculation strategy according to the split size. © 2016 International Union of Psychological Science.

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.

Does Calculation or Word-Problem Instruction Provide A Stronger Route to Pre-Algebraic Knowledge?

PubMed Central

Fuchs, Lynn S.; Powell, Sarah R.; Cirino, Paul T.; Schumacher, Robin F.; Marrin, Sarah; Hamlett, Carol L.; Fuchs, Douglas; Compton, Donald L.; Changas, Paul C.

2014-01-01

The focus of this study was connections among 3 aspects of mathematical cognition at 2nd grade: calculations, word problems, and pre-algebraic knowledge. We extended the literature, which is dominated by correlational work, by examining whether intervention conducted on calculations or word problems contributes to improved performance in the other domain and whether intervention in either or both domains contributes to pre-algebraic knowledge. Participants were 1102 children in 127 2nd-grade classrooms in 25 schools. Teachers were randomly assigned to 3 conditions: calculation intervention, word-problem intervention, and business-as-usual control. Intervention, which lasted 17 weeks, was designed to provide research-based linkages between arithmetic calculations or arithmetic word problems (depending on condition) to pre-algebraic knowledge. Multilevel modeling suggested calculation intervention improved calculation but not word-problem outcomes; word-problem intervention enhanced word-problem but not calculation outcomes; and word-problem intervention provided a stronger route than calculation intervention to pre-algebraic knowledge. PMID:25541565

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.

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.

The generative basis of natural number concepts.

PubMed

Leslie, Alan M; Gelman, Rochel; Gallistel, C R

2008-06-01

Number concepts must support arithmetic inference. Using this principle, it can be argued that the integer concept of exactly ONE is a necessary part of the psychological foundations of number, as is the notion of the exact equality - that is, perfect substitutability. The inability to support reasoning involving exact equality is a shortcoming in current theories about the development of numerical reasoning. A simple innate basis for the natural number concepts can be proposed that embodies the arithmetic principle, supports exact equality and also enables computational compatibility with real- or rational-valued mental magnitudes.

Architecture and data processing alternatives for the TSE computer. Volume 2: Extraction of topological information from an image by the Tse computer

NASA Technical Reports Server (NTRS)

Jones, J. R.; Bodenheimer, R. E.

1976-01-01

A simple programmable Tse processor organization and arithmetic operations necessary for extraction of the desired topological information are described. Hardware additions to this organization are discussed along with trade-offs peculiar to the tse computing concept. An improved organization is presented along with the complementary software for the various arithmetic operations. The performance of the two organizations is compared in terms of speed, power, and cost. Software routines developed to extract the desired information from an image are included.

Effects of alcohol on complex performance.

DOT National Transportation Integrated Search

1969-08-01

Nine subjects were tested on a battery of tasks involving monitoring (simple reaction time, choice reaction time, and meter monitoring), two-dimensional compensatory tracking, and mental arithmetic. Three workloads were presented--monitoring plus tra...

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.

Beyond hemispheric dominance: brain regions underlying the joint lateralization of language and arithmetic to the left hemisphere.

PubMed

Pinel, Philippe; Dehaene, Stanislas

2010-01-01

Language and arithmetic are both lateralized to the left hemisphere in the majority of right-handed adults. Yet, does this similar lateralization reflect a single overall constraint of brain organization, such an overall "dominance" of the left hemisphere for all linguistic and symbolic operations? Is it related to the lateralization of specific cerebral subregions? Or is it merely coincidental? To shed light on this issue, we performed a "colateralization analysis" over 209 healthy subjects: We investigated whether normal variations in the degree of left hemispheric asymmetry in areas involved in sentence listening and reading are mirrored in the asymmetry of areas involved in mental arithmetic. Within the language network, a region-of-interest analysis disclosed partially dissociated patterns of lateralization, inconsistent with an overall "dominance" model. Only two of these areas presented a lateralization during sentence listening and reading which correlated strongly with the lateralization of two regions active during calculation. Specifically, the profile of asymmetry in the posterior superior temporal sulcus during sentence processing covaried with the asymmetry of calculation-induced activation in the intraparietal sulcus, and a similar colateralization linked the middle frontal gyrus with the superior posterior parietal lobule. Given recent neuroimaging results suggesting a late emergence of hemispheric asymmetries for symbolic arithmetic during childhood, we speculate that these colateralizations might constitute developmental traces of how the acquisition of linguistic symbols affects the cerebral organization of the arithmetic network.

Combining Automated Theorem Provers with Symbolic Algebraic Systems: Position Paper

NASA Technical Reports Server (NTRS)

Schumann, Johann; Koga, Dennis (Technical Monitor)

1999-01-01

In contrast to pure mathematical applications where automated theorem provers (ATPs) are quite capable, proof tasks arising form real-world applications from the area of Software Engineering show quite different characteristics: they usually do not only contain much arithmetic (albeit often quite simple one), but they also often contain reasoning about specific structures (e.g. graphics, sets). Thus, an ATP must be capable of performing reasoning together with a fair amount of simplification, calculation and solving. Therefore, powerful simplifiers and other (symbolic and semi-symbolic) algorithms seem to be ideally suited to augment ATPs. In the following we shortly describe two major points of interest in combining SASs (symbolic algebraic systems) with top-down automated theorem provers (here: SETHEO [Let92, GLMS94]).

Performance Indicators Workbook: Edition I, for Calculating School District Performance in Elementary School Reading and Arithmetic.

ERIC Educational Resources Information Center

New York State Education Dept., Albany. Bureau of School Programs Evaluation.

The Performance Indicators in Education program is designed to develop methods of measuring the performance in reading and arithmetic achievement at the elementary school level of the schools of New York State. From data on file at the State Education Department, a set of profiles was developed for each of 628 school districts indicating how the…

40 CFR 60.2943 - How do I convert my 1-hour arithmetic averages into the appropriate averaging times and units?

Code of Federal Regulations, 2014 CFR

2014-07-01

...) Use Equation 2 in § 60.2975 to calculate the 12-hour rolling averages for concentrations of carbon... averages into the appropriate averaging times and units? 60.2943 Section 60.2943 Protection of Environment... 16, 2006 Monitoring § 60.2943 How do I convert my 1-hour arithmetic averages into the appropriate...

40 CFR 60.2943 - How do I convert my 1-hour arithmetic averages into the appropriate averaging times and units?

Code of Federal Regulations, 2013 CFR

2013-07-01

...) Use Equation 2 in § 60.2975 to calculate the 12-hour rolling averages for concentrations of carbon... averages into the appropriate averaging times and units? 60.2943 Section 60.2943 Protection of Environment... 16, 2006 Monitoring § 60.2943 How do I convert my 1-hour arithmetic averages into the appropriate...

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

The calculating hemispheres: studies of a split-brain patient.

PubMed

Funnell, Margaret G; Colvin, Mary K; Gazzaniga, Michael S

2007-06-11

The purpose of the study was to investigate simple calculation in the two cerebral hemispheres of a split-brain patient. In a series of four experiments, the left hemisphere was superior to the right in simple calculation, confirming the previously reported left hemisphere specialization for calculation. In two different recognition paradigms, right hemisphere performance was at chance for all arithmetic operations, with the exception of subtraction in a two-alternative forced choice paradigm (performance was at chance when the lure differed from the correct answer by a magnitude of 1 but above chance when the magnitude difference was 4). In a recall paradigm, the right hemisphere performed above chance for both addition and subtraction, but performed at chance levels for multiplication and division. The error patterns in that experiment suggested that for subtraction and addition, the right hemisphere does have some capacity for approximating the solution even when it is unable to generate the exact solution. Furthermore, right hemisphere accuracy in addition and subtraction was higher for problems with small operands than with large operands. An additional experiment assessed approximate and exact addition in the two hemispheres for problems with small and large operands. The left hemisphere was equally accurate in both tasks but the right hemisphere was more accurate in approximate addition than in exact addition. In exact addition, right hemisphere accuracy was higher for problems with small operands than large, but the opposite pattern was found for approximate addition.

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

Process and representation in graphical displays

NASA Technical Reports Server (NTRS)

Gillan, Douglas J.; Lewis, Robert; Rudisill, Marianne

1990-01-01

How people comprehend graphics is examined. Graphical comprehension involves the cognitive representation of information from a graphic display and the processing strategies that people apply to answer questions about graphics. Research on representation has examined both the features present in a graphic display and the cognitive representation of the graphic. The key features include the physical components of a graph, the relation between the figure and its axes, and the information in the graph. Tests of people's memory for graphs indicate that both the physical and informational aspect of a graph are important in the cognitive representation of a graph. However, the physical (or perceptual) features overshadow the information to a large degree. Processing strategies also involve a perception-information distinction. In order to answer simple questions (e.g., determining the value of a variable, comparing several variables, and determining the mean of a set of variables), people switch between two information processing strategies: (1) an arithmetic, look-up strategy in which they use a graph much like a table, looking up values and performing arithmetic calculations; and (2) a perceptual strategy in which they use the spatial characteristics of the graph to make comparisons and estimations. The user's choice of strategies depends on the task and the characteristics of the graph. A theory of graphic comprehension is presented.

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.

Passive hand movements disrupt adults' counting strategies.

PubMed

Imbo, Ineke; Vandierendonck, André; Fias, Wim

2011-01-01

In the present study, we experimentally tested the role of hand motor circuits in simple-arithmetic strategies. Educated adults solved simple additions (e.g., 8 + 3) or simple subtractions (e.g., 11 - 3) while they were required to retrieve the answer from long-term memory (e.g., knowing that 8 + 3 = 11), to transform the problem by making an intermediate step (e.g., 8 + 3 = 8 + 2 + 1 = 10 + 1 = 11) or to count one-by-one (e.g., 8 + 3 = 8…9…10…11). During the process of solving the arithmetic problems, the experimenter did or did not move the participants' hand on a four-point matrix. The results show that passive hand movements disrupted the counting strategy while leaving the other strategies unaffected. This pattern of results is in agreement with a procedural account, showing that the involvement of hand motor circuits in adults' mathematical abilities is reminiscent of finger counting during childhood.

Non-symbolic halving in an Amazonian indigene group

PubMed Central

McCrink, Koleen; Spelke, Elizabeth S.; Dehaene, Stanislas; Pica, Pierre

2014-01-01

Much research supports the existence of an Approximate Number System (ANS) that is recruited by infants, children, adults, and non-human animals to generate coarse, non-symbolic representations of number. This system supports simple arithmetic operations such as addition, subtraction, and ordering of amounts. The current study tests whether an intuition of a more complex calculation, division, exists in an indigene group in the Amazon, the Mundurucu, whose language includes no words for large numbers. Mundurucu children were presented with a video event depicting a division transformation of halving, in which pairs of objects turned into single objects, reducing the array's numerical magnitude. Then they were tested on their ability to calculate the outcome of this division transformation with other large-number arrays. The Mundurucu children effected this transformation even when non-numerical variables were controlled, performed above chance levels on the very first set of test trials, and exhibited performance similar to urban children who had access to precise number words and a surrounding symbolic culture. We conclude that a halving calculation is part of the suite of intuitive operations supported by the ANS. PMID:23587042

Groping and Hoping for a Consensus on Calculator Use.

ERIC Educational Resources Information Center

Mathematics Education Dialogues, 1999

1999-01-01

This issue of Mathematics Education Dialogues focuses on the use of calculators in the mathematics classroom. The eleven articles on this theme include: (1) "Groping and Hoping for a Consensus on Calculator Use" (Zalman Usiskin); (2) "Let's Abolish Pencil-and-Paper Arithmetic" (Anthony Ralston); (3) "Do We Need Calculators?" (Kim Mackey); (4) "How…

[Effect of mental arithmetic and verbal fluency on blood flow velocity in the middle cerebral arteries].

PubMed

Amrein, Ilona; Pálvölgyi, László; Debreczeni, Róbert; Kamondi, Anita; Szirmai, Imre

2004-01-20

Using transcranial Doppler sonography (TCD), changes in blood flow velocity (BFV) can be measured in the Medial Cerebral Artery (MCA) during cognitive effort. Our goal was to define the time-course and laterality of BFV in healthy volunteers during arithmetic and verbal fluency tasks according to handedness. Twelve subjects (8 right-handed, 4 left-handed) were assessed. The TCD registered BFV in both MCA simultaneously. Heart rate was also recorded using TCD. Finally we included a 16-channel EEG. BFV laterality index (LI) was calculated. Participants were asked to count silently and generate words beginning with a specified letter. To estimate hemispheric differences in BFV, two-tailed Wilcoxon tests were utilized along with correlational analyses. During cognitive effort the BFV changed in a tri-phasic manner in all participants. A 6-8% elevation of BFV was observed in MCAs without latency at the time of the evoking signal. Laterality of BFV developed after 5-13 seconds during cognitive effort in right-, and several seconds later in left-handed subjects. During tasks the BFV increased in the dominant hemisphere up to 2.6-4.7% compared to the subdominant one. We also calculated the LI. During the verbal task the LI agreed with the handedness in 9 out of 12 subjects. During the mental arithmetic task, agreement was found in 6 out of 12 subjects. According to LI results we found a discrepancy between verbal and arithmetic tests in 3 out of 12 subjects. Cognitive effort elicites significant bilateral BFV increases in the MCAs, which suggests fast neurogenic regulation. The course of BFV during mental arithmetic proved to be different from course BFV assessed during the word fluency task. Based on the laterality of the BFV, the word-generation task was more sensitive in determining the dominant hemisphere when compared to the mental arithmetic task. The use of LI may help to estimate hemispheric functions even in pathologic circumstances.

Arithmetic and Brain Connectivity: Mental Calculation in Adolescents with Periventricular Lesions

ERIC Educational Resources Information Center

Pavlova, Marina; Sokolov, Alexander N.; Krageloh-Mann, Ingeborg

2009-01-01

The ability for mental calculation represents a fundamental prerequisite for development of intelligence, which is predictive for educational and professional success in life. Many individuals with calculation difficulties are survivors of premature birth. The brain mechanisms of these deficits are, however, largely unknown. In this work, we…

Nursing students' confidence in medication calculations predicts math exam performance.

PubMed

Andrew, Sharon; Salamonson, Yenna; Halcomb, Elizabeth J

2009-02-01

The aim of this study was to examine the psychometric properties, including predictive validity, of the newly-developed nursing self-efficacy for mathematics (NSE-Math). The NSE-Math is a 12 item scale that comprises items related to mathematic and arithmetic concepts underpinning medication calculations. The NSE-Math instrument was administered to second year Bachelor of Nursing students enrolled in a nursing practice subject. Students' academic results for a compulsory medication calculation examination for this subject were collected. One-hundred and twelve students (73%) completed both the NSE-Math instrument and the drug calculation assessment task. The NSE-Math demonstrated two factors 'Confidence in application of mathematic concepts to nursing practice' and 'Confidence in arithmetic concepts' with 63.5% of variance explained. Cronbach alpha for the scale was 0.90. The NSE-Math demonstrated predictive validity with the medication calculation examination results (p=0.009). Psychometric testing suggests the NSE-Math is a valid measure of mathematics self-efficacy of second year nursing students.

Mathematical difficulties in nonverbal learning disability or co-morbid dyscalculia and dyslexia.

PubMed

Mammarella, Irene C; Bomba, Monica; Caviola, Sara; Broggi, Fiorenza; Neri, Francesca; Lucangeli, Daniela; Nacinovich, Renata

2013-01-01

The main goal of the present study was to shed further light on the weaknesses of children with different profiles of mathematical difficulties, testing children with nonverbal learning disability (NLD), co-morbid dyscalculia and dyslexia (D&D), or typical development (TD). Sixteen children with NLD, 15 with D&D, and 16 with TD completed tasks derived from Butterworth (2003 ) and divided into: a capacity subscale (i.e., a number-dots comparison task, a number comparison task, and a dots comparison task); and an achievement subscale (i.e., mental calculations and arithmetical fact retrieval). Children with NLD were impaired in the dots comparison task, children with D&D in the mental calculation and arithmetical facts.

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.

High-precision arithmetic in mathematical physics

DOE PAGES

Bailey, David H.; Borwein, Jonathan M.

2015-05-12

For many scientific calculations, particularly those involving empirical data, IEEE 32-bit floating-point arithmetic produces results of sufficient accuracy, while for other applications IEEE 64-bit floating-point is more appropriate. But for some very demanding applications, even higher levels of precision are often required. Furthermore, this article discusses the challenge of high-precision computation, in the context of mathematical physics, and highlights what facilities are required to support future computation, in light of emerging developments in computer architecture.

Propagation of Significant Figures.

ERIC Educational Resources Information Center

Schwartz, Lowell M.

1985-01-01

Shows that the rules of thumb for propagating significant figures through arithmetic calculations frequently yield misleading results. Also describes two procedures for performing this propagation more reliably than the rules of thumb. However, both require considerably more calculational effort than do the rules. (JN)

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 .

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

NASA Astrophysics Data System (ADS)

Chung, Kun-Jen

2012-08-01

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

Spacing and the Transition from Calculation to Retrieval

ERIC Educational Resources Information Center

Rickard, Timothy C.; Lau, Jonas; Pashler, Harold

2008-01-01

Many arithmetic problems can be solved in two ways: by a calculation involving several steps, and by direct retrieval of the answer. With practice on particular problems, memory retrieval tends to supplant calculation--an important aspect of skill learning. We asked how the distribution of practice on particular problems affects this kind of…

Cryptography: Cracking Codes.

ERIC Educational Resources Information Center

Myerscough, Don; And Others

1996-01-01

Describes an activity whose objectives are to encode and decode messages using linear functions and their inverses; to use modular arithmetic, including use of the reciprocal for simple equation solving; to analyze patterns and make and test conjectures; to communicate procedures and algorithms; and to use problem-solving strategies. (ASK)

Towards constructing multi-bit binary adder based on Belousov-Zhabotinsky reaction

NASA Astrophysics Data System (ADS)

Zhang, Guo-Mao; Wong, Ieong; Chou, Meng-Ta; Zhao, Xin

2012-04-01

It has been proposed that the spatial excitable media can perform a wide range of computational operations, from image processing, to path planning, to logical and arithmetic computations. The realizations in the field of chemical logical and arithmetic computations are mainly concerned with single simple logical functions in experiments. In this study, based on Belousov-Zhabotinsky reaction, we performed simulations toward the realization of a more complex operation, the binary adder. Combining with some of the existing functional structures that have been verified experimentally, we designed a planar geometrical binary adder chemical device. Through numerical simulations, we first demonstrated that the device can implement the function of a single-bit full binary adder. Then we show that the binary adder units can be further extended in plane, and coupled together to realize a two-bit, or even multi-bit binary adder. The realization of chemical adders can guide the constructions of other sophisticated arithmetic functions, ultimately leading to the implementation of chemical computer and other intelligent systems.

Plotting equation for gaussian percentiles and a spreadsheet program for generating probability plots

USGS Publications Warehouse

Balsillie, J.H.; Donoghue, J.F.; Butler, K.M.; Koch, J.L.

2002-01-01

Two-dimensional plotting tools can be of invaluable assistance in analytical scientific pursuits, and have been widely used in the analysis and interpretation of sedimentologic data. We consider, in this work, the use of arithmetic probability paper (APP). Most statistical computer applications do not allow for the generation of APP plots, because of apparent intractable nonlinearity of the percentile (or probability) axis of the plot. We have solved this problem by identifying an equation(s) for determining plotting positions of Gaussian percentiles (or probabilities), so that APP plots can easily be computer generated. An EXCEL example is presented, and a programmed, simple-to-use EXCEL application template is hereby made publicly available, whereby a complete granulometric analysis including data listing, moment measure calculations, and frequency and cumulative APP plots, is automatically produced.

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

Non-Symbolic Halving in an Amazonian Indigene Group

ERIC Educational Resources Information Center

McCrink, Koleen; Spelke, Elizabeth S.; Dehaene, Stanislas; Pica, Pierre

2013-01-01

Much research supports the existence of an Approximate Number System (ANS) that is recruited by infants, children, adults, and non-human animals to generate coarse, non-symbolic representations of number. This system supports simple arithmetic operations such as addition, subtraction, and ordering of amounts. The current study tests whether an…

A novel bit-wise adaptable entropy coding technique

NASA Technical Reports Server (NTRS)

Kiely, A.; Klimesh, M.

2001-01-01

We present a novel entropy coding technique which is adaptable in that each bit to be encoded may have an associated probability esitmate which depends on previously encoded bits. The technique may have advantages over arithmetic coding. The technique can achieve arbitrarily small redundancy and admits a simple and fast decoder.

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.

Statistics without Tears: Complex Statistics with Simple Arithmetic

ERIC Educational Resources Information Center

Smith, Brian

2011-01-01

One of the often overlooked aspects of modern statistics is the analysis of time series data. Modern introductory statistics courses tend to rush to probabilistic applications involving risk and confidence. Rarely does the first level course linger on such useful and fascinating topics as time series decomposition, with its practical applications…

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...

40 CFR 98.243 - Calculating GHG emissions.

Code of Federal Regulations, 2010 CFR

2010-07-01

...) through (b)(3). (c) Mass balance for each petrochemical process unit. Calculate the emissions of CO2 from...). (3) Collect a sample of each feedstock and product at least once per month and determine the carbon... carbon content measurements are made during the monthly measurement period, average them arithmetically...

Interactive Software For Astrodynamical Calculations

NASA Technical Reports Server (NTRS)

Schlaifer, Ronald S.; Skinner, David L.; Roberts, Phillip H.

1995-01-01

QUICK computer program provides user with facilities of sophisticated desk calculator performing scalar, vector, and matrix arithmetic; propagate conic-section orbits; determines planetary and satellite coordinates; and performs other related astrodynamic calculations within FORTRAN-like software environment. QUICK is interpreter, and no need to use compiler or linker to run QUICK code. Outputs plotted in variety of formats on variety of terminals. Written in RATFOR.

Calculator Use Need Not Undermine Direct-Access Ability: The Roles of Retrieval, Calculation, and Calculator Use in the Acquisition of Arithmetic Facts

ERIC Educational Resources Information Center

Pyke, Aryn A.; LeFevre, Jo-Anne

2011-01-01

Why is subsequent recall sometimes better for self-generated answers than for answers obtained from an external source (e.g., calculator)? In this study, we explore the relative contribution of 2 processes, recall attempts and self-computation, to this "generation effect" (i.e., enhanced answer recall relative to when problems are practiced with a…

Test Review: Reynolds, C. R., Voress, J. V., Kamphaus, R. W. (2015), "Mathematics Fluency and Calculation Tests (MFaCTs) review." PRO-ED

ERIC Educational Resources Information Center

Marbach, Joshua

2017-01-01

The Mathematics Fluency and Calculation Tests (MFaCTs) are a series of measures designed to assess for arithmetic calculation skills and calculation fluency in children ages 6 through 18. There are five main purposes of the MFaCTs: (1) identifying students who are behind in basic math fact automaticity; (2) evaluating possible delays in arithmetic…

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

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

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).

Simulator of human visual perception

NASA Astrophysics Data System (ADS)

Bezzubik, Vitalii V.; Belashenkov, Nickolai R.

2016-04-01

Difference of Circs (DoC) model allowing to simulate the response of neurons - ganglion cells as a reaction to stimuli is represented and studied in relation with representation of receptive fields of human retina. According to this model the response of neurons is reduced to execution of simple arithmetic operations and the results of these calculations well correlate with experimental data in wide range of stimuli parameters. The simplicity of the model and reliability of reproducing of responses allow to propose the conception of a device which can simulate the signals generated by ganglion cells as a reaction to presented stimuli. The signals produced according to DoC model are considered as a result of primary processing of information received from receptors independently of their type and may be sent to higher levels of nervous system of living creatures for subsequent processing. Such device may be used as a prosthesis for disabled organ.

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.

Decidable and undecidable arithmetic functions in actin filament networks

NASA Astrophysics Data System (ADS)

Schumann, Andrew

2018-01-01

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

A seismic data compression system using subband coding

NASA Technical Reports Server (NTRS)

Kiely, A. B.; Pollara, F.

1995-01-01

This article presents a study of seismic data compression techniques and a compression algorithm based on subband coding. The algorithm includes three stages: a decorrelation stage, a quantization stage that introduces a controlled amount of distortion to allow for high compression ratios, and a lossless entropy coding stage based on a simple but efficient arithmetic coding method. Subband coding methods are particularly suited to the decorrelation of nonstationary processes such as seismic events. Adaptivity to the nonstationary behavior of the waveform is achieved by dividing the data into separate blocks that are encoded separately with an adaptive arithmetic encoder. This is done with high efficiency due to the low overhead introduced by the arithmetic encoder in specifying its parameters. The technique could be used as a progressive transmission system, where successive refinements of the data can be requested by the user. This allows seismologists to first examine a coarse version of waveforms with minimal usage of the channel and then decide where refinements are required. Rate-distortion performance results are presented and comparisons are made with two block transform methods.

Text Comprehension and Oral Language as Predictors of Word-Problem Solving: Insights into Word-Problem Solving as a Form of Text Comprehension

PubMed Central

Fuchs, Lynn S.; Gilbert, Jennifer K.; Fuchs, Douglas; Seethaler, Pamela M.; Martin, BrittanyLee N.

2018-01-01

This study was designed to deepen insights on whether word-problem (WP) solving is a form of text comprehension (TC) and on the role of language in WPs. A sample of 325 second graders, representing high, average, and low reading and math performance, was assessed on (a) start-of-year TC, WP skill, language, nonlinguistic reasoning, working memory, and foundational skill (word identification, arithmetic) and (b) year-end WP solving, WP-language processing (understanding WP statements, without calculation demands), and calculations. Multivariate, multilevel path analysis, accounting for classroom and school effects, indicated that TC was a significant and comparably strong predictor of all outcomes. Start-of-year language was a significantly stronger predictor of both year-end WP outcomes than of calculations, whereas start-of-year arithmetic was a significantly stronger predictor of calculations than of either WP measure. Implications are discussed in terms of WP solving as a form of TC and a theoretically coordinated approach, focused on language, for addressing TC and WP-solving instruction. PMID:29643723

Improving Foundational Number Representations through Simple Arithmetical Training

ERIC Educational Resources Information Center

Kallai, Arava Y.; Schunn, Christian D.; Ponting, Andrea L.; Fiez, Julie A.

2011-01-01

The aim of this study was to test a training program intended to fine-tune the mental representations of double-digit numbers, thus increasing the discriminability of such numbers. The authors' assumption was that increased fluency in math could be achieved by improving the analogic representations of numbers. The study was completed in the…

Identities for Generalized Fibonacci Numbers: A Combinatorial Approach

ERIC Educational Resources Information Center

Plaza, A.; Falcon, S.

2008-01-01

This note shows a combinatorial approach to some identities for generalized Fibonacci numbers. While it is a straightforward task to prove these identities with induction, and also by arithmetical manipulations such as rearrangements, the approach used here is quite simple to follow and eventually reduces the proof to a counting problem. (Contains…

Eating breakfast enhances the efficiency of neural networks engaged during mental arithmetic in school-aged children

USDA-ARS?s Scientific Manuscript database

To determine the influence of a morning meal on complex mental functions in children (8-11 y), time-frequency analyses were applied to electroencephalographic (EEG) activity recorded while children solved simple addition problems after an overnight fast and again after having either eaten or skipped...

Eating breakfast enhances the efficiency of neural networks engaged during mental arithmetic in school-aged children

USDA-ARS?s Scientific Manuscript database

Are there effects of morning nutrition on brain functions important for learning and performance in children? We used time-frequency analyses of EEG activity recorded while children solved simple math problems to study how brain processes were influenced by eating or skipping breakfast. Participants...

Systems Engineering of Education V: Quantitative Concepts for Education Systems.

ERIC Educational Resources Information Center

Silvern, Leonard C.

The fifth (of 14) volume of the Education and Training Consultant's (ETC) series on systems engineering of education is designed for readers who have completed others in the series. It reviews arithmetic and algebraic procedures and applies these to simple education and training systems. Flowchart models of example problems are developed and…

Self-Regulated Learning of Basic Arithmetic Skills: A Longitudinal Study

ERIC Educational Resources Information Center

Throndsen, Inger

2011-01-01

Background: Several studies have examined young primary school children's use of strategies when solving simple addition and subtraction problems. Most of these studies have investigated students' strategy use as if they were isolated processes. To date, we have little knowledge about how math strategies in young students are related to other…

Duality of Mathematical Thinking When Making Sense of Simple Word Problems: Theoretical Essay

ERIC Educational Resources Information Center

Polotskaia, Elena; Savard, Annie; Freiman, Viktor

2015-01-01

This essay proposes a reflection on the learning difficulties and teaching approaches associated with arithmetic word problem solving. We question the development of word problem solving skills in the early grades of elementary school. We are trying to revive the discussion because first, the knowledge in question--reversibility of arithmetic…

Real-time Continuous Assessment Method for Mental and Physiological Condition using Heart Rate Variability

NASA Astrophysics Data System (ADS)

Yoshida, Yutaka; Yokoyama, Kiyoko; Ishii, Naohiro

It is necessary to monitor the daily health condition for preventing stress syndrome. In this study, it was proposed the method assessing the mental and physiological condition, such as the work stress or the relaxation, using heart rate variability at real time and continuously. The instantanuous heart rate (HR), and the ratio of the number of extreme points (NEP) and the number of heart beats were calculated for assessing mental and physiological condition. In this method, 20 beats heart rate were used to calculate these indexes. These were calculated in one beat interval. Three conditions, which are sitting rest, performing mental arithmetic and watching relaxation movie, were assessed using our proposed algorithm. The assessment accuracies were 71.9% and 55.8%, when performing mental arithmetic and watching relaxation movie respectively. In this method, the mental and physiological condition was assessed using only 20 regressive heart beats, so this method is considered as the real time assessment method.

Dexterity with numbers: rTMS over left angular gyrus disrupts finger gnosis and number processing.

PubMed

Rusconi, Elena; Walsh, Vincent; Butterworth, Brian

2005-01-01

Since the original description of Gerstmann's syndrome with its four cardinal symptoms, among which are finger agnosia and acalculia, the neuro-cognitive relationship between fingers and calculation has been debated. We asked our participants to perform four different tasks, two of which involved fingers and the other two involving numbers, during repetitive transcranial magnetic stimulation (rTMS) over the posterior parietal lobe of either hemisphere. In the finger tasks, they were required to transform a tactile stimulus randomly delivered on one of their fingers into a speeded key-press response either with the same or with the homologous finger on the opposite hand. In the numerical tasks, they were asked to perform a magnitude or a parity matching on pairs of single digits, in the context of arithmetically related or unrelated numerical primes. In accordance with the original anatomical hypothesis put forward by Gerstmann [Gerstmann, J. (1924). Fingeragnosie: eine umschriebene Stoerung der Orienterung am eigenen Koerper. Wiener clinische Wochenschrift, 37, 1010-12], we found that rTMS over the left angular gyrus disrupted tasks requiring access to the finger schema and number magnitude processing in the same group of participants. In addition to the numerous studies which have employed special populations such as neurological patients and children, our data confirm the presence of a relationship between numbers and body knowledge in skilled adults who no longer use their fingers for solving simple arithmetical tasks.

Young children's use of derived fact strategies for addition and subtraction

PubMed Central

Dowker, Ann

2014-01-01

Forty-four children between 6;0 and 7;11 took part in a study of derived fact strategy use. They were assigned to addition and subtraction levels on the basis of calculation pretests. They were then given Dowker's (1998) test of derived fact strategies in addition, involving strategies based on the Identity, Commutativity, Addend +1, Addend −1, and addition/subtraction Inverse principles; and test of derived fact strategies in subtraction, involving strategies based on the Identity, Minuend +1, Minuend −1, Subtrahend +1, Subtrahend −1, Complement and addition/subtraction Inverse principles. The exact arithmetic problems given varied according to the child's previously assessed calculation level and were selected to be just a little too difficult for the child to solve unaided. Children were given the answer to a problem and then asked to solve another problem that could be solved quickly by using this answer, together with the principle being assessed. The children also took the WISC Arithmetic subtest. Strategies differed greatly in difficulty, with Identity being the easiest, and the Inverse and Complement principles being most difficult. The Subtrahend +1 and Subtrahend −1 problems often elicited incorrect strategies based on an overextension of the principles of addition to subtraction. It was concluded that children may have difficulty with understanding and applying the relationships between addition and subtraction. Derived fact strategy use was significantly related to both calculation level and to WISC Arithmetic scaled score. PMID:24431996

Validation of Calculations in a Digital Thermometer Firmware

NASA Astrophysics Data System (ADS)

Batagelj, V.; Miklavec, A.; Bojkovski, J.

2014-04-01

State-of-the-art digital thermometers are arguably remarkable measurement instruments, measuring outputs from resistance thermometers and/or thermocouples. Not only that they can readily achieve measuring accuracies in the parts-per-million range, but they also incorporate sophisticated algorithms for the transformation calculation of the measured resistance or voltage to temperature. These algorithms often include high-order polynomials, exponentials and logarithms, and must be performed using both standard coefficients and particular calibration coefficients. The numerical accuracy of these calculations and the associated uncertainty component must be much better than the accuracy of the raw measurement in order to be negligible in the total measurement uncertainty. In order for the end-user to gain confidence in these calculations as well as to conform to formal requirements of ISO/IEC 17025 and other standards, a way of validation of these numerical procedures performed in the firmware of the instrument is required. A software architecture which allows a simple validation of internal measuring instrument calculations is suggested. The digital thermometer should be able to expose all its internal calculation functions to the communication interface, so the end-user can compare the results of the internal measuring instrument calculation with reference results. The method can be regarded as a variation of the black-box software validation. Validation results on a thermometer prototype with implemented validation ability show that the calculation error of basic arithmetic operations is within the expected rounding error. For conversion functions, the calculation error is at least ten times smaller than the thermometer effective resolution for the particular probe type.

Relation Between Mathematical Performance, Math Anxiety, and Affective Priming in Children With and Without Developmental Dyscalculia.

PubMed

Kucian, Karin; Zuber, Isabelle; Kohn, Juliane; Poltz, Nadine; Wyschkon, Anne; Esser, Günter; von Aster, Michael

2018-01-01

Many children show negative emotions related to mathematics and some even develop mathematics anxiety. The present study focused on the relation between negative emotions and arithmetical performance in children with and without developmental dyscalculia (DD) using an affective priming task. Previous findings suggested that arithmetic performance is influenced if an affective prime precedes the presentation of an arithmetic problem. In children with DD specifically, responses to arithmetic operations are supposed to be facilitated by both negative and mathematics-related primes (= negative math priming effect ).We investigated mathematical performance, math anxiety, and the domain-general abilities of 172 primary school children (76 with DD and 96 controls). All participants also underwent an affective priming task which consisted of the decision whether a simple arithmetic operation (addition or subtraction) that was preceded by a prime (positive/negative/neutral or mathematics-related) was true or false. Our findings did not reveal a negative math priming effect in children with DD. Furthermore, when considering accuracy levels, gender, or math anxiety, the negative math priming effect could not be replicated. However, children with DD showed more math anxiety when explicitly assessed by a specific math anxiety interview and showed lower mathematical performance compared to controls. Moreover, math anxiety was equally present in boys and girls, even in the earliest stages of schooling, and interfered negatively with performance. In conclusion, mathematics is often associated with negative emotions that can be manifested in specific math anxiety, particularly in children with DD. Importantly, present findings suggest that in the assessed age group, it is more reliable to judge math anxiety and investigate its effects on mathematical performance explicitly by adequate questionnaires than by an affective math priming task.

Relation Between Mathematical Performance, Math Anxiety, and Affective Priming in Children With and Without Developmental Dyscalculia

PubMed Central

Kucian, Karin; Zuber, Isabelle; Kohn, Juliane; Poltz, Nadine; Wyschkon, Anne; Esser, Günter; von Aster, Michael

2018-01-01

Many children show negative emotions related to mathematics and some even develop mathematics anxiety. The present study focused on the relation between negative emotions and arithmetical performance in children with and without developmental dyscalculia (DD) using an affective priming task. Previous findings suggested that arithmetic performance is influenced if an affective prime precedes the presentation of an arithmetic problem. In children with DD specifically, responses to arithmetic operations are supposed to be facilitated by both negative and mathematics-related primes (=negative math priming effect).We investigated mathematical performance, math anxiety, and the domain-general abilities of 172 primary school children (76 with DD and 96 controls). All participants also underwent an affective priming task which consisted of the decision whether a simple arithmetic operation (addition or subtraction) that was preceded by a prime (positive/negative/neutral or mathematics-related) was true or false. Our findings did not reveal a negative math priming effect in children with DD. Furthermore, when considering accuracy levels, gender, or math anxiety, the negative math priming effect could not be replicated. However, children with DD showed more math anxiety when explicitly assessed by a specific math anxiety interview and showed lower mathematical performance compared to controls. Moreover, math anxiety was equally present in boys and girls, even in the earliest stages of schooling, and interfered negatively with performance. In conclusion, mathematics is often associated with negative emotions that can be manifested in specific math anxiety, particularly in children with DD. Importantly, present findings suggest that in the assessed age group, it is more reliable to judge math anxiety and investigate its effects on mathematical performance explicitly by adequate questionnaires than by an affective math priming task. PMID:29755376

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.

Investigation the Arithmetical or Tabular Islamic calendar

NASA Astrophysics Data System (ADS)

Rashed, M. G.; Moklof, M. G.; Hamza, Alaa E.

2018-06-01

Arithmetical calendar (or tabular calendar) is sometimes referred to as the Fātimid calendar but this is in fact one of several almost identical tabular Islamic calendars. This calendar introduced by Muslim astronomers in the 9th century CE to predict the approximate begin of the months in the Islamic lunar calendar. Chronologists adopted 11 leap years in a 30 year cycle. In the case of leap Hijri year they add one day to the last month of the Hijri year. The cycle of this calendar agree with the Smaller cycles (2-5.333 years) discovered by Galal and Rashed (2011) and coincide with the lag criterion given by Galal (1988). We suggested the Islamic tabular calendar. The Leap years of this suggested Islamic tabular calendar may be 2, 5, 7, 10, 13, 15, 18, 21, 23, 26 and 29. Our suggested Arithmetical calendar satisfies the mathematical patterns, while the old Arithmetical calendar (or tabular calendar) does not satisfy a known fixed rule. We conclude empirical formula for our suggested Islamic tabular calendar. From this empirical formula, we can calculate if the Hijric year after immigration is a leap or a non-leap year.

A componential model of human interaction with graphs: 1. Linear regression modeling

NASA Technical Reports Server (NTRS)

Gillan, Douglas J.; Lewis, Robert

1994-01-01

Task analyses served as the basis for developing the Mixed Arithmetic-Perceptual (MA-P) model, which proposes (1) that people interacting with common graphs to answer common questions apply a set of component processes-searching for indicators, encoding the value of indicators, performing arithmetic operations on the values, making spatial comparisons among indicators, and repsonding; and (2) that the type of graph and user's task determine the combination and order of the components applied (i.e., the processing steps). Two experiments investigated the prediction that response time will be linearly related to the number of processing steps according to the MA-P model. Subjects used line graphs, scatter plots, and stacked bar graphs to answer comparison questions and questions requiring arithmetic calculations. A one-parameter version of the model (with equal weights for all components) and a two-parameter version (with different weights for arithmetic and nonarithmetic processes) accounted for 76%-85% of individual subjects' variance in response time and 61%-68% of the variance taken across all subjects. The discussion addresses possible modifications in the MA-P model, alternative models, and design implications from the MA-P model.

Mathematics learning disabilities in girls with fragile X or Turner syndrome during late elementary school.

PubMed

Murphy, Melissa M; Mazzocco, Michèle M M

2008-01-01

The present study focuses on math and related skills among 32 girls with fragile X (n = 14) or Turner (n = 18) syndrome during late elementary school. Performance in each syndrome group was assessed relative to Full Scale IQ-matched comparison groups of girls from the general population (n = 32 and n = 89 for fragile X syndrome and Turner syndrome, respectively). Differences between girls with fragile X and their comparison group emerged on untimed arithmetic calculations, mastery of counting skills, and arithmetic problem verification accuracy. Relative to girls in the comparison group, girls with Turner syndrome did not differ on untimed arithmetic calculations or problem verification accuracy, but they had limited mastery of counting skills and longer response times to complete the problem verification task. Girls with fragile X or Turner syndrome also differed from their respective comparison groups on math-related abilities, including visual-spatial, working memory, and reading skills, and the associations between math and those related skills. Together, these findings support the notion that difficulty with math and related skills among girls with fragile X or Turner syndrome continues into late elementary school and that the profile of math and related skill difficulty distinguishes the two syndrome groups from each other.

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…

Numerical and Calculation Abilities in Children with ADHD

ERIC Educational Resources Information Center

Colomer, Carla; Re, Anna M.; Miranda, Ana; Lucangeli, Daniela

2013-01-01

The aim of this study was to investigate the specific numerical and calculation abilities of 28 children with ADHD without comorbid mathematical learning disabilities (LD), ranging from the 1st to the 5th grade of primary school, and to examine the stability or the development of the arithmetic profile. Our results showed that a high percentage of…

The Y2K Problem: Will It Just Be Another New Year's Eve?

ERIC Educational Resources Information Center

Iwanowski, Jay

1998-01-01

Potential problems for college and university computing functions posed by arrival of the year 2000 (Y2K) are discussed, including arithmetic calculations and sorting functions based on two-digit year dates, embedding of two-digit dates in archival data, system coordination for data exchange, unique number generation, and leap year calculations. A…

Use of Neuroimaging to Clarify How Human Brains Perform Mental Calculations

ERIC Educational Resources Information Center

Ortiz, Enrique

2010-01-01

The purpose of this study was to analyze participants' levels of hemoglobin as they performed arithmetic mental calculations using Optical Topography (OT, helmet type brain-scanning system, also known as Functional Near-Infrared Spectroscopy or fNIRS). A central issue in cognitive neuroscience involves the study of how the human brain encodes and…

Development of Wearable Sheet-Type Shear Force Sensor and Measurement System that is Insusceptible to Temperature and Pressure.

PubMed

Toyama, Shigeru; Tanaka, Yasuhiro; Shirogane, Satoshi; Nakamura, Takashi; Umino, Tokio; Uehara, Ryo; Okamoto, Takuma; Igarashi, Hiroshi

2017-07-31

A sheet-type shear force sensor and a measurement system for the sensor were developed. The sensor has an original structure where a liquid electrolyte is filled in a space composed of two electrode-patterned polymer films and an elastic rubber ring. When a shear force is applied on the surface of the sensor, the two electrode-patterned films mutually move so that the distance between the internal electrodes of the sensor changes, resulting in current increase or decrease between the electrodes. Therefore, the shear force can be calculated by monitoring the current between the electrodes. Moreover, it is possible to measure two-dimensional shear force given that the sensor has multiple electrodes. The diameter and thickness of the sensor head were 10 mm and 0.7 mm, respectively. Additionally, we also developed a measurement system that drives the sensor, corrects the baseline of the raw sensor output, displays data, and stores data as a computer file. Though the raw sensor output was considerably affected by the surrounding temperature, the influence of temperature was drastically decreased by introducing a simple arithmetical calculation. Moreover, the influence of pressure simultaneously decreased after the same calculation process. A demonstrative measurement using the sensor revealed the practical usefulness for on-site monitoring.

Brain Hyper-Connectivity and Operation-Specific Deficits during Arithmetic Problem Solving in Children with Developmental Dyscalculia

ERIC Educational Resources Information Center

Rosenberg-Lee, Miriam; Ashkenazi, Sarit; Chen, Tianwen; Young, Christina B.; Geary, David C.; Menon, Vinod

2015-01-01

Developmental dyscalculia (DD) is marked by specific deficits in processing numerical and mathematical information despite normal intelligence (IQ) and reading ability. We examined how brain circuits used by young children with DD to solve simple addition and subtraction problems differ from those used by typically developing (TD) children who…

Introducing Algebraic Structures through Solving Equations: Vertical Content Knowledge for K-12 Mathematics Teachers

ERIC Educational Resources Information Center

Wasserman, Nicholas H.

2014-01-01

Algebraic structures are a necessary aspect of algebraic thinking for K-12 students and teachers. An approach for introducing the algebraic structure of groups and fields through the arithmetic properties required for solving simple equations is summarized; the collective (not individual) importance of these axioms as a foundation for algebraic…

A Program Complexity Metric Based on Variable Usage for Algorithmic Thinking Education of Novice Learners

ERIC Educational Resources Information Center

Fuwa, Minori; Kayama, Mizue; Kunimune, Hisayoshi; Hashimoto, Masami; Asano, David K.

2015-01-01

We have explored educational methods for algorithmic thinking for novices and implemented a block programming editor and a simple learning management system. In this paper, we propose a program/algorithm complexity metric specified for novice learners. This metric is based on the variable usage in arithmetic and relational formulas in learner's…

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)

Oppugning the assumptions of spatial averaging of segment and joint orientations.

PubMed

Pierrynowski, Michael Raymond; Ball, Kevin Arthur

2009-02-09

Movement scientists frequently calculate "arithmetic averages" when examining body segment or joint orientations. Such calculations appear routinely, yet are fundamentally flawed. Three-dimensional orientation data are computed as matrices, yet three-ordered Euler/Cardan/Bryant angle parameters are frequently used for interpretation. These parameters are not geometrically independent; thus, the conventional process of averaging each parameter is incorrect. The process of arithmetic averaging also assumes that the distances between data are linear (Euclidean); however, for the orientation data these distances are geodesically curved (Riemannian). Therefore we question (oppugn) whether use of the conventional averaging approach is an appropriate statistic. Fortunately, exact methods of averaging orientation data have been developed which both circumvent the parameterization issue, and explicitly acknowledge the Euclidean or Riemannian distance measures. The details of these matrix-based averaging methods are presented and their theoretical advantages discussed. The Euclidian and Riemannian approaches offer appealing advantages over the conventional technique. With respect to practical biomechanical relevancy, examinations of simulated data suggest that for sets of orientation data possessing characteristics of low dispersion, an isotropic distribution, and less than 30 degrees second and third angle parameters, discrepancies with the conventional approach are less than 1.1 degrees . However, beyond these limits, arithmetic averaging can have substantive non-linear inaccuracies in all three parameterized angles. The biomechanics community is encouraged to recognize that limitations exist with the use of the conventional method of averaging orientations. Investigations requiring more robust spatial averaging over a broader range of orientations may benefit from the use of matrix-based Euclidean or Riemannian calculations.

Dyscalculia and the Calculating Brain.

PubMed

Rapin, Isabelle

2016-08-01

Dyscalculia, like dyslexia, affects some 5% of school-age children but has received much less investigative attention. In two thirds of affected children, dyscalculia is associated with another developmental disorder like dyslexia, attention-deficit disorder, anxiety disorder, visual and spatial disorder, or cultural deprivation. Infants, primates, some birds, and other animals are born with the innate ability, called subitizing, to tell at a glance whether small sets of scattered dots or other items differ by one or more item. This nonverbal approximate number system extends mostly to single digit sets as visual discrimination drops logarithmically to "many" with increasing numerosity (size effect) and crowding (distance effect). Preschoolers need several years and specific teaching to learn verbal names and visual symbols for numbers and school agers to understand their cardinality and ordinality and the invariance of their sequence (arithmetic number line) that enables calculation. This arithmetic linear line differs drastically from the nonlinear approximate number system mental number line that parallels the individual number-tuned neurons in the intraparietal sulcus in monkeys and overlying scalp distribution of discrete functional magnetic resonance imaging activations by number tasks in man. Calculation is a complex skill that activates both visual and spatial and visual and verbal networks. It is less strongly left lateralized than language, with approximate number system activation somewhat more right sided and exact number and arithmetic activation more left sided. Maturation and increasing number skill decrease associated widespread non-numerical brain activations that persist in some individuals with dyscalculia, which has no single, universal neurological cause or underlying mechanism in all affected individuals. Copyright © 2016 Elsevier Inc. All rights reserved.

Investigation of learning environment for arithmetic word problems by problem posing as sentence integration in Indonesian language

NASA Astrophysics Data System (ADS)

Hasanah, N.; Hayashi, Y.; Hirashima, T.

2017-02-01

Arithmetic word problems remain one of the most difficult area of teaching mathematics. Learning by problem posing has been suggested as an effective way to improve students’ understanding. However, the practice in usual classroom is difficult due to extra time needed for assessment and giving feedback to students’ posed problems. To address this issue, we have developed a tablet PC software named Monsakun for learning by posing arithmetic word problems based on Triplet Structure Model. It uses the mechanism of sentence-integration, an efficient implementation of problem-posing that enables agent-assessment of posed problems. The learning environment has been used in actual Japanese elementary school classrooms and the effectiveness has been confirmed in previous researches. In this study, ten Indonesian elementary school students living in Japan participated in a learning session of problem posing using Monsakun in Indonesian language. We analyzed their learning activities and show that students were able to interact with the structure of simple word problem using this learning environment. The results of data analysis and questionnaire suggested that the use of Monsakun provides a way of creating an interactive and fun environment for learning by problem posing for Indonesian elementary school students.

Conformity and statistical tolerancing

NASA Astrophysics Data System (ADS)

Leblond, Laurent; Pillet, Maurice

2018-02-01

Statistical tolerancing was first proposed by Shewhart (Economic Control of Quality of Manufactured Product, (1931) reprinted 1980 by ASQC), in spite of this long history, its use remains moderate. One of the probable reasons for this low utilization is undoubtedly the difficulty for designers to anticipate the risks of this approach. The arithmetic tolerance (worst case) allows a simple interpretation: conformity is defined by the presence of the characteristic in an interval. Statistical tolerancing is more complex in its definition. An interval is not sufficient to define the conformance. To justify the statistical tolerancing formula used by designers, a tolerance interval should be interpreted as the interval where most of the parts produced should probably be located. This tolerance is justified by considering a conformity criterion of the parts guaranteeing low offsets on the latter characteristics. Unlike traditional arithmetic tolerancing, statistical tolerancing requires a sustained exchange of information between design and manufacture to be used safely. This paper proposes a formal definition of the conformity, which we apply successively to the quadratic and arithmetic tolerancing. We introduce a concept of concavity, which helps us to demonstrate the link between tolerancing approach and conformity. We use this concept to demonstrate the various acceptable propositions of statistical tolerancing (in the space decentring, dispersion).

Basic math in monkeys and college students.

PubMed

Cantlon, Jessica F; Brannon, Elizabeth M

2007-12-01

Adult humans possess a sophisticated repertoire of mathematical faculties. Many of these capacities are rooted in symbolic language and are therefore unlikely to be shared with nonhuman animals. However, a subset of these skills is shared with other animals, and this set is considered a cognitive vestige of our common evolutionary history. Current evidence indicates that humans and nonhuman animals share a core set of abilities for representing and comparing approximate numerosities nonverbally; however, it remains unclear whether nonhuman animals can perform approximate mental arithmetic. Here we show that monkeys can mentally add the numerical values of two sets of objects and choose a visual array that roughly corresponds to the arithmetic sum of these two sets. Furthermore, monkeys' performance during these calculations adheres to the same pattern as humans tested on the same nonverbal addition task. Our data demonstrate that nonverbal arithmetic is not unique to humans but is instead part of an evolutionarily primitive system for mathematical thinking shared by monkeys.

Multistate Memristive Tantalum Oxide Devices for Ternary Arithmetic

PubMed Central

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

2016-01-01

Redox-based resistive switching random access memory (ReRAM) offers excellent properties to implement future non-volatile memory arrays. Recently, the capability of two-state ReRAMs to implement Boolean logic functionality gained wide interest. Here, we report on seven-states Tantalum Oxide Devices, which enable the realization of an intrinsic modular arithmetic using a ternary number system. Modular arithmetic, a fundamental system for operating on numbers within the limit of a modulus, is known to mathematicians since the days of Euclid and finds applications in diverse areas ranging from e-commerce to musical notations. We demonstrate that multistate devices not only reduce the storage area consumption drastically, but also enable novel in-memory operations, such as computing using high-radix number systems, which could not be implemented using two-state devices. The use of high radix number system reduces the computational complexity by reducing the number of needed digits. Thus the number of calculation operations in an addition and the number of logic devices can be reduced. PMID:27834352

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.

Multistate Memristive Tantalum Oxide Devices for Ternary Arithmetic.

PubMed

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

2016-11-11

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

Multistate Memristive Tantalum Oxide Devices for Ternary Arithmetic

NASA Astrophysics Data System (ADS)

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

2016-11-01

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

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

Numerical Aspects of Atomic Physics: Helium Basis Sets and Matrix Diagonalization

NASA Astrophysics Data System (ADS)

Jentschura, Ulrich; Noble, Jonathan

2014-03-01

We present a matrix diagonalization algorithm for complex symmetric matrices, which can be used in order to determine the resonance energies of auto-ionizing states of comparatively simple quantum many-body systems such as helium. The algorithm is based in multi-precision arithmetic and proceeds via a tridiagonalization of the complex symmetric (not necessarily Hermitian) input matrix using generalized Householder transformations. Example calculations involving so-called PT-symmetric quantum systems lead to reference values which pertain to the imaginary cubic perturbation (the imaginary cubic anharmonic oscillator). We then proceed to novel basis sets for the helium atom and present results for Bethe logarithms in hydrogen and helium, obtained using the enhanced numerical techniques. Some intricacies of ``canned'' algorithms such as those used in LAPACK will be discussed. Our algorithm, for complex symmetric matrices such as those describing cubic resonances after complex scaling, is faster than LAPACK's built-in routines, for specific classes of input matrices. It also offer flexibility in terms of the calculation of the so-called implicit shift, which is used in order to ``pivot'' the system toward the convergence to diagonal form. We conclude with a wider overview.

29 CFR 778.327 - Temporary or sporadic reduction in schedule.

Code of Federal Regulations, 2013 CFR

2013-07-01

... is obvious that as a matter of simple arithmetic an employer might adopt a series of different rates... employee would earn no more than his straight time rate no matter how many hours he worked. If he set the... $5.45 for workweeks of 50 hours, and so on, the employee would always receive (for straight time and...

29 CFR 778.327 - Temporary or sporadic reduction in schedule.

Code of Federal Regulations, 2010 CFR

2010-07-01

... is obvious that as a matter of simple arithmetic an employer might adopt a series of different rates... employee would earn no more than his straight time rate no matter how many hours he worked. If he set the... $5.45 for workweeks of 50 hours, and so on, the employee would always receive (for straight time and...

29 CFR 778.327 - Temporary or sporadic reduction in schedule.

Code of Federal Regulations, 2014 CFR

2014-07-01

... is obvious that as a matter of simple arithmetic an employer might adopt a series of different rates... employee would earn no more than his straight time rate no matter how many hours he worked. If he set the... $5.45 for workweeks of 50 hours, and so on, the employee would always receive (for straight time and...

29 CFR 778.327 - Temporary or sporadic reduction in schedule.

Code of Federal Regulations, 2012 CFR

2012-07-01

... is obvious that as a matter of simple arithmetic an employer might adopt a series of different rates... employee would earn no more than his straight time rate no matter how many hours he worked. If he set the... $5.45 for workweeks of 50 hours, and so on, the employee would always receive (for straight time and...

Pictorial Representations of Simple Arithmetic Problems Are Not Always Helpful: A Cognitive Load Perspective

ERIC Educational Resources Information Center

van Lieshout, Ernest C. D. M.; Xenidou-Dervou, Iro

2018-01-01

At the start of mathematics education children are often presented with addition and subtraction problems in the form of pictures. They are asked to solve the problems by filling in corresponding number sentences. One type of problem concerns the representation of an increase or a decrease in a depicted amount. A decrease is, however, more…

Teaching Computer Literacy in an Elementary School: A Comparison of Two Methods Using Microcomputers. Report No. 81:18.

ERIC Educational Resources Information Center

Nordman, R.; Parker, J.

This report compares two methods of teaching BASIC programming used to develop computer literacy among children in grades three through seven in British Columbia. Phase one of the project was designed to instruct children in grades five to seven on the arithmetic operations of writing simple BASIC programs. Instructional methods included using job…

Respiratory-phase domain analysis of heart rate variability can accurately estimate cardiac vagal activity during a mental arithmetic task.

PubMed

Kotani, Kiyoshi; Takamasu, Kiyoshi; Tachibana, Makoto

2007-01-01

The objectives of this paper were to present a method to extract the amplitude of RSA in the respiratory-phase domain, to compare that with subjective or objective indices of the MWL (mental workload), and to compare that with a conventional frequency analysis in terms of its accuracy during a mental arithmetic task. HRV (heart rate variability), ILV (instantaneous lung volume), and motion of the throat were measured under a mental arithmetic experiment and subjective and objective indices were also obtained. The amplitude of RSA was extracted in the respiratory-phase domain, and its correlation with the load level was compared with the results of the frequency domain analysis, which is the standard analysis of the HRV. The subjective and objective indices decreased as the load level increased, showing that the experimental protocol was appropriate. Then, the amplitude of RSA in the respiratory-phase domain also decreased with the increase in the load level. The results of the correlation analysis showed that the respiratory-phase domain analysis has higher negative correlations, -0.84 and -0.82, with the load level as determined by simple correlation and rank correlation, respectively, than does frequency analysis, for which the correlations were found to be -0.54 and -0.63, respectively. In addition, it was demonstrated that the proposed method could be applied to the short-term extraction of RSA amplitude. We proposed a simple and effective method to extract the amplitude of the respiratory sinus arrhythmia (RSA) in the respiratory-phase domain and the results show that this method can estimate cardiac vagal activity more accurately than frequency analysis.

Probabilistic arithmetic automata and their applications.

PubMed

Marschall, Tobias; Herms, Inke; Kaltenbach, Hans-Michael; Rahmann, Sven

2012-01-01

We present a comprehensive review on probabilistic arithmetic automata (PAAs), a general model to describe chains of operations whose operands depend on chance, along with two algorithms to numerically compute the distribution of the results of such probabilistic calculations. PAAs provide a unifying framework to approach many problems arising in computational biology and elsewhere. We present five different applications, namely 1) pattern matching statistics on random texts, including the computation of the distribution of occurrence counts, waiting times, and clump sizes under hidden Markov background models; 2) exact analysis of window-based pattern matching algorithms; 3) sensitivity of filtration seeds used to detect candidate sequence alignments; 4) length and mass statistics of peptide fragments resulting from enzymatic cleavage reactions; and 5) read length statistics of 454 and IonTorrent sequencing reads. The diversity of these applications indicates the flexibility and unifying character of the presented framework. While the construction of a PAA depends on the particular application, we single out a frequently applicable construction method: We introduce deterministic arithmetic automata (DAAs) to model deterministic calculations on sequences, and demonstrate how to construct a PAA from a given DAA and a finite-memory random text model. This procedure is used for all five discussed applications and greatly simplifies the construction of PAAs. Implementations are available as part of the MoSDi package. Its application programming interface facilitates the rapid development of new applications based on the PAA framework.

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)

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.

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.

Non-invasive mapping of calculation function by repetitive navigated transcranial magnetic stimulation.

PubMed

Maurer, Stefanie; Tanigawa, Noriko; Sollmann, Nico; Hauck, Theresa; Ille, Sebastian; Boeckh-Behrens, Tobias; Meyer, Bernhard; Krieg, Sandro M

2016-11-01

Concerning calculation function, studies have already reported on localizing computational function in patients and volunteers by functional magnetic resonance imaging and transcranial magnetic stimulation. However, the development of accurate repetitive navigated TMS (rTMS) with a considerably higher spatial resolution opens a new field in cognitive neuroscience. This study was therefore designed to evaluate the feasibility of rTMS for locating cortical calculation function in healthy volunteers, and to establish this technique for future scientific applications as well as preoperative mapping in brain tumor patients. Twenty healthy subjects underwent rTMS calculation mapping using 5 Hz/10 pulses. Fifty-two previously determined cortical spots of the whole hemispheres were stimulated on both sides. The subjects were instructed to perform the calculation task composed of 80 simple arithmetic operations while rTMS pulses were applied. The highest error rate (80 %) for all errors of all subjects was observed in the right ventral precentral gyrus. Concerning division task, a 45 % error rate was achieved in the left middle frontal gyrus. The subtraction task showed its highest error rate (40 %) in the right angular gyrus (anG). In the addition task a 35 % error rate was observed in the left anterior superior temporal gyrus. Lastly, the multiplication task induced a maximum error rate of 30 % in the left anG. rTMS seems feasible as a way to locate cortical calculation function. Besides language function, the cortical localizations are well in accordance with the current literature for other modalities or lesion studies.

Learner Perceptions of Realism and Magic in Computer Simulations.

ERIC Educational Resources Information Center

Hennessy, Sara; O'Shea, Tim

1993-01-01

Discusses the possible lack of credibility in educational interactive computer simulations. Topics addressed include "Shopping on Mars," a collaborative adventure game for arithmetic calculation that uses direct manipulation in the microworld; the Alternative Reality Kit, a graphical animated environment for creating interactive…

Methodological pitfalls in the analysis of contraceptive failure.

PubMed

Trussell, J

1991-02-01

Although the literature on contraceptive failure is vast and is expanding rapidly, our understanding of the relative efficacy of methods is quite limited because of defects in the research design and in the analytical tools used by investigators. Errors in the literature range from simple arithmetical mistakes to outright fraud. In many studies the proportion of the original sample lost to follow-up is so large that the published results have little meaning. Investigators do not routinely use life table techniques to control for duration of exposure; many employ the Pearl index, which suffers from the same problem as does the crude death rate as a measure of mortality. Investigators routinely calculate 'method' failure rates by eliminating 'user' failures from the numerator (pregnancies) but fail to eliminate 'imperfect' use from the denominator (exposure); as a consequence, these 'method' rates are biased downward. This paper explores these and other common biases that snare investigators and establishes methodological guidelines for future research.

Developmental dyscalculia.

PubMed

Price, Gavin R; Ansari, Daniel

2013-01-01

Developmental dyscalculia (DD) is a learning disorder affecting the acquisition of school level arithmetic skills present in approximately 3-6% of the population. At the behavioral level DD is characterized by poor retrieval of arithmetic facts from memory, the use of immature calculation procedures and counting strategies, and the atypical representation and processing of numerical magnitude. At the neural level emerging evidence suggests DD is associated with atypical structure and function in brain regions associated with the representation of numerical magnitude. The current state of knowledge points to a core deficit in numerical magnitude representation in DD, but further work is required to elucidate causal mechanisms underlying the disorder. Copyright © 2013 Elsevier B.V. All rights reserved.

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

WASP (Write a Scientific Paper) using Excel - 1: Data entry and validation.

PubMed

Grech, Victor

2018-02-01

Data collection for the purposes of analysis, after the planning and execution of a research study, commences with data input and validation. The process of data entry and analysis may appear daunting to the uninitiated, but as pointed out in the 1970s in a series of papers by British Medical Journal Deputy Editor TDV Swinscow, modern hardware and software (he was then referring to the availability of hand calculators) permits the performance of statistical testing outside a computer laboratory. In this day and age, modern software, such as the ubiquitous and almost universally familiar Microsoft Excel™ greatly facilitates this process. This first paper comprises the first of a collection of papers which will emulate Swinscow's series, in his own words, "addressed to readers who want to start at the beginning, not to those who are already skilled statisticians." These papers will have less focus on the actual arithmetic, and more emphasis on how to actually implement simple statistics, step by step, using Excel, thereby constituting the equivalent of Swinscow's papers in the personal computer age. Data entry can be facilitated by several underutilised features in Excel. This paper will explain Excel's little-known form function, data validation implementation at input stage, simple coding tips and data cleaning tools. Copyright © 2018 Elsevier B.V. All rights reserved.

Estimate of standard deviation for a log-transformed variable using arithmetic means and standard deviations.

PubMed

Quan, Hui; Zhang, Ji

2003-09-15

Analyses of study variables are frequently based on log transformations. To calculate the power for detecting the between-treatment difference in the log scale, we need an estimate of the standard deviation of the log-transformed variable. However, in many situations a literature search only provides the arithmetic means and the corresponding standard deviations. Without individual log-transformed data to directly calculate the sample standard deviation, we need alternative methods to estimate it. This paper presents methods for estimating and constructing confidence intervals for the standard deviation of a log-transformed variable given the mean and standard deviation of the untransformed variable. It also presents methods for estimating the standard deviation of change from baseline in the log scale given the means and standard deviations of the untransformed baseline value, on-treatment value and change from baseline. Simulations and examples are provided to assess the performance of these estimates. Copyright 2003 John Wiley & Sons, Ltd.

Fast and accurate 3D tensor calculation of the Fock operator in a general basis

NASA Astrophysics Data System (ADS)

Khoromskaia, V.; Andrae, D.; Khoromskij, B. N.

2012-11-01

The present paper contributes to the construction of a “black-box” 3D solver for the Hartree-Fock equation by the grid-based tensor-structured methods. It focuses on the calculation of the Galerkin matrices for the Laplace and the nuclear potential operators by tensor operations using the generic set of basis functions with low separation rank, discretized on a fine N×N×N Cartesian grid. We prove the Ch2 error estimate in terms of mesh parameter, h=O(1/N), that allows to gain a guaranteed accuracy of the core Hamiltonian part in the Fock operator as h→0. However, the commonly used problem adapted basis functions have low regularity yielding a considerable increase of the constant C, hence, demanding a rather large grid-size N of about several tens of thousands to ensure the high resolution. Modern tensor-formatted arithmetics of complexity O(N), or even O(logN), practically relaxes the limitations on the grid-size. Our tensor-based approach allows to improve significantly the standard basis sets in quantum chemistry by including simple combinations of Slater-type, local finite element and other basis functions. Numerical experiments for moderate size organic molecules show efficiency and accuracy of grid-based calculations to the core Hamiltonian in the range of grid parameter N3˜1015.

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.

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

PubMed

Zhao, Hong-Quan; Kasai, Seiya; Shiratori, Yuta; Hashizume, Tamotsu

2009-06-17

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

An Analytical Time–Domain Expression for the Net Ripple Produced by Parallel Interleaved Converters

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

Johnson, Brian B.; Krein, Philip T.

We apply modular arithmetic and Fourier series to analyze the superposition of N interleaved triangular waveforms with identical amplitudes and duty-ratios. Here, interleaving refers to the condition when a collection of periodic waveforms with identical periods are each uniformly phase-shifted across one period. The main result is a time-domain expression which provides an exact representation of the summed and interleaved triangular waveforms, where the peak amplitude and parameters of the time-periodic component are all specified in closed-form. Analysis is general and can be used to study various applications in multi-converter systems. This model is unique not only in that itmore » reveals a simple and intuitive expression for the net ripple, but its derivation via modular arithmetic and Fourier series is distinct from prior approaches. The analytical framework is experimentally validated with a system of three parallel converters under time-varying operating conditions.« less

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.

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

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

PubMed

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

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

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.

Spectra-temporal patterns underlying mental addition: an ERP and ERD/ERS study.

PubMed

Ku, Yixuan; Hong, Bo; Gao, Xiaorong; Gao, Shangkai

2010-03-12

Functional neuroimaging data have shown that mental calculation involves fronto-parietal areas that are composed of different subsystems shared with other cognitive functions such as working memory and language. Event-related potential (ERP) analysis has also indicated sequential information changes during the calculation process. However, little is known about the dynamic properties of oscillatory networks in this process. In the present study, we applied both ERP and event-related (de-)synchronization (ERS/ERD) analyses to EEG data recorded from normal human subjects performing tasks for sequential visual/auditory mental addition. Results in the study indicate that the late positive components (LPCs) can be decomposed into two separate parts. The earlier element LPC1 (around 360ms) reflects the computing attribute and is more prominent in calculation tasks. The later element LPC2 (around 590ms) indicates an effect of number size and appears larger only in a more complex 2-digit addition task. The theta ERS and alpha ERD show modality-independent frontal and parietal differential patterns between the mental addition and control groups, and discrepancies are noted in the beta ERD between the 2-digit and 1-digit mental addition groups. The 2-digit addition (both visual and auditory) results in similar beta ERD patterns to the auditory control, which may indicate a reliance on auditory-related resources in mental arithmetic, especially with increasing task difficulty. These results coincide with the theory of simple calculation relying on the visuospatial process and complex calculation depending on the phonological process. Copyright 2010 Elsevier Ireland Ltd. All rights reserved.

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.

Mathematics--A Search for Harmony.

ERIC Educational Resources Information Center

Arnold, Stephen

1991-01-01

The harmonic mean, neglected in favor of arithmetic and geometric means in modern mathematics, is defined and its historical relationship to music as presented by Pythagoras is described. Two geometric constructions present a picture of harmony, and an application in calculating the square root of a number is given. (MDH)

Thermodynamic properties of anthophyllite and talc: corrections and discussion of calorimetric data

USGS Publications Warehouse

Hemingway, B.S.

1991-01-01

Arithmetic errors in calculating heat capacity values (Krupka, 1984; Krupka et al, 1985a) for anthophyllite and several errors in the Hess cycles utilized to derive enthalpies of formation of anthophyllite and talc are identified, and revised values are reported. -from Author

The Definition and Implementation of a Computer Programming Language Based on Constraints.

DTIC Science & Technology

1980-08-01

though not quite reached, is a complete programming system which will implicitly support the constraint paradigm to the same extent that IISP , say...and detecting and resolving conflicts, just as iisp provides certain services such as automatic storage management, which records given dala in a...defined- it permits the statement of equalities and some simple arithmetic relationships. An implementation representation is chosen, and IISP code for a

Coding For Compression Of Low-Entropy Data

NASA Technical Reports Server (NTRS)

Yeh, Pen-Shu

1994-01-01

Improved method of encoding digital data provides for efficient lossless compression of partially or even mostly redundant data from low-information-content source. Method of coding implemented in relatively simple, high-speed arithmetic and logic circuits. Also increases coding efficiency beyond that of established Huffman coding method in that average number of bits per code symbol can be less than 1, which is the lower bound for Huffman code.

On the Problem-Size Effect in Small Additions: Can We Really Discard Any Counting-Based Account?

ERIC Educational Resources Information Center

Barrouillet, Pierre; Thevenot, Catherine

2013-01-01

The problem-size effect in simple additions, that is the increase in response times (RTs) and error rates with the size of the operands, is one of the most robust effects in cognitive arithmetic. Current accounts focus on factors that could affect speed of retrieval of the answers from long-term memory such as the occurrence of interference in a…

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

Hypnosis and Hypothesis: A New Graphic Concept

PubMed Central

McDonald, Robert Charles

1979-01-01

This paper outlines a conceptual framework in order to promote a new understanding of what hypnosis does. The term hypnosis is rejected and a new label (the Selective Attention—Selective Inattention state or SASI state) is proposed. The SASI state is regarded as a modified waking state. The concept of depth is also discussed and a simple new arithmetical scoring scale is outlined for measurement of achieved levels of SASI.

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…

Ancient Babylonian astronomers calculated Jupiter’s position from the area under a time-velocity graph

NASA Astrophysics Data System (ADS)

Ossendrijver, Mathieu

2016-01-01

The idea of computing a body’s displacement as an area in time-velocity space is usually traced back to 14th-century Europe. I show that in four ancient Babylonian cuneiform tablets, Jupiter’s displacement along the ecliptic is computed as the area of a trapezoidal figure obtained by drawing its daily displacement against time. This interpretation is prompted by a newly discovered tablet on which the same computation is presented in an equivalent arithmetical formulation. The tablets date from 350 to 50 BCE. The trapezoid procedures offer the first evidence for the use of geometrical methods in Babylonian mathematical astronomy, which was thus far viewed as operating exclusively with arithmetical concepts.

Online with Integers

ERIC Educational Resources Information Center

Siegel, Jonathan W.; Siegel, P. B.

2011-01-01

Integers are sometimes used in physics problems to simplify the mathematics so the arithmetic does not distract students from the physics concepts. This is particularly important in exams where students should not have to spend a lot of time using their calculators. Common uses of integers in physics problems include integer solutions to…

Interpreting Bivariate Regression Coefficients: Going beyond the Average

ERIC Educational Resources Information Center

Halcoussis, Dennis; Phillips, G. Michael

2010-01-01

Statistics, econometrics, investment analysis, and data analysis classes often review the calculation of several types of averages, including the arithmetic mean, geometric mean, harmonic mean, and various weighted averages. This note shows how each of these can be computed using a basic regression framework. By recognizing when a regression model…

40 CFR 141.134 - Reporting and recordkeeping requirements.

Code of Federal Regulations, 2010 CFR

2010-07-01

... quarterly for TOC under the requirements of § 141.132(d) and required to meet the enhanced coagulation or... period that paired samples were taken, the arithmetic average of the percent reduction of TOC for each paired sample and the required TOC percent removal. (iv) Calculations for determining compliance with the...

A New Approach to Teaching Business Oriented Students.

ERIC Educational Resources Information Center

Merchant, Ronald

1980-01-01

Describes a competency based business mathematics course offered at Spokane Falls Community College (Washington) in which students, through the use of calculators, master mathematical concepts without having to mentally add columns of figures or perform complex arithmetic problems on paper. Examines both the mathematical and 10-key skills…

10 CFR 431.12 - Definitions.

Code of Federal Regulations, 2014 CFR

2014-01-01

... method or AEDM means, with respect to an electric motor, a method of calculating the total power loss and average full load efficiency. Average full load efficiency means the arithmetic mean of the full load efficiencies of a population of electric motors of duplicate design, where the full load efficiency of each...

Pathways to Arithmetic Fact Retrieval and Percentage Calculation in Adolescents

ERIC Educational Resources Information Center

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

2017-01-01

Background: Developing sufficient mathematical skills is a prerequisite to function adequately in society today. Given this, an important task is to increase our understanding regarding the cognitive mechanisms underlying young people's acquisition of early number skills and formal mathematical knowledge. Aims: The purpose was to examine whether…

Using the Relational Paradigm: Effects on Pupils' Reasoning in Solving Additive Word Problems

ERIC Educational Resources Information Center

Polotskaia, Elena; Savard, Annie

2018-01-01

Pupils' difficulties in solving word problems continue to attract attention: while researchers highlight the importance of relational reasoning and modelling, school curricula typically use short word problems to develop pupils' knowledge of arithmetic operations and calculation strategies. The Relational Paradigm attributes the leading role in…

Determining productivity gains from herbaceous vegetation management with 'age-shift' calculations

Treesearch

David B. South; James H. Miller; Mark O. Kimberley; Curtis L. Vanderschaaf

2006-01-01

Gains in stand volume that result from competition control and fertilization are sometimes reported as 'percentage gains'. Because percentage gains arithmetically decline over time asstand volume increases, plantation managers have difficultyin using percentage gains to project growth and revenues. The 'age-shift' method quantifies the year...

40 CFR 98.315 - Procedures for estimating missing data.

Code of Federal Regulations, 2010 CFR

2010-07-01

... measured parameters used in the GHG emissions calculations is required (e.g., carbon content values, etc... such estimates. (a) For each missing value of the monthly carbon content of calcined petroleum coke the substitute data value shall be the arithmetic average of the quality-assured values of carbon contents for...

Findings of Studies on Dyscalculia--A Synthesis

ERIC Educational Resources Information Center

Raja, B. William Dharma; Kumar, S. Praveen

2012-01-01

Children with learning disabilities face problems in acquiring the basic skills needed for learning. Dyscalculia is one among those learning disorders which affects the ability to acquire arithmetic skills that are needed to perform mathematical calculations. However this is a learning difficulty which is often not recognized. The objectives of…

Investigating the Group-Level Impact of Advanced Dual-Echo fMRI Combinations

PubMed Central

Kettinger, Ádám; Hill, Christopher; Vidnyánszky, Zoltán; Windischberger, Christian; Nagy, Zoltán

2016-01-01

Multi-echo fMRI data acquisition has been widely investigated and suggested to optimize sensitivity for detecting the BOLD signal. Several methods have also been proposed for the combination of data with different echo times. The aim of the present study was to investigate whether these advanced echo combination methods provide advantages over the simple averaging of echoes when state-of-the-art group-level random-effect analyses are performed. Both resting-state and task-based dual-echo fMRI data were collected from 27 healthy adult individuals (14 male, mean age = 25.75 years) using standard echo-planar acquisition methods at 3T. Both resting-state and task-based data were subjected to a standard image pre-processing pipeline. Subsequently the two echoes were combined as a weighted average, using four different strategies for calculating the weights: (1) simple arithmetic averaging, (2) BOLD sensitivity weighting, (3) temporal-signal-to-noise ratio weighting and (4) temporal BOLD sensitivity weighting. Our results clearly show that the simple averaging of data with the different echoes is sufficient. Advanced echo combination methods may provide advantages on a single-subject level but when considering random-effects group level statistics they provide no benefit regarding sensitivity (i.e., group-level t-values) compared to the simple echo-averaging approach. One possible reason for the lack of clear advantages may be that apart from increasing the average BOLD sensitivity at the single-subject level, the advanced weighted averaging methods also inflate the inter-subject variance. As the echo combination methods provide very similar results, the recommendation is to choose between them depending on the availability of time for collecting additional resting-state data or whether subject-level or group-level analyses are planned. PMID:28018165

Is 1/f sound more effective than simple resting in reducing stress response?

PubMed

Oh, Eun-Joo; Cho, Il-Young; Park, Soon-Kwon

2014-01-01

It has been previously demonstrated that listening to 1/f sound effectively reduces stress. However, these findings have been inconsistent and further study on the relationship between 1/f sound and the stress response is consequently necessary. The present study examined whether sound with 1/f properties (1/f sound) affects stress-induced electroencephalogram (EEG) changes. Twenty-six subjects who voluntarily participated in the study were randomly assigned to the experimental or control group. Data from four participants were excluded because of EEG artifacts. A mental arithmetic task was used as a stressor. Participants in the experiment group listened to 1/f sound for 5 minutes and 33 seconds, while participants in the control group sat quietly for the same duration. EEG recordings were obtained at various points throughout the experiment. After the experiment, participants completed a questionnaire on the affective impact of the 1/f sound. The results indicated that the mental arithmetic task effectively induced a stress response measurable by EEG. Relative theta power at all electrode sites was significantly lower than baseline in both the control and experimental group. Relative alpha power was significantly lower, and relative beta power was significantly higher in the T3 and T4 areas. Secondly, 1/f sound and simple resting affected task-associated EEG changes in a similar manner. Finally, participants reported in the questionnaire that they experienced a positive feeling in response to the 1/f sound. Our results suggest that a commercialized 1/f sound product is not more effective than simple resting in alleviating the physiological stress response.

Solving fully fuzzy transportation problem using pentagonal fuzzy numbers

NASA Astrophysics Data System (ADS)

Maheswari, P. Uma; Ganesan, K.

2018-04-01

In this paper, we propose a simple approach for the solution of fuzzy transportation problem under fuzzy environment in which the transportation costs, supplies at sources and demands at destinations are represented by pentagonal fuzzy numbers. The fuzzy transportation problem is solved without converting to its equivalent crisp form using a robust ranking technique and a new fuzzy arithmetic on pentagonal fuzzy numbers. To illustrate the proposed approach a numerical example is provided.

Self-Regulation as an Aid to Human Effectiveness and Biocybernetics Technology and Behavior

DTIC Science & Technology

1976-01-01

feedback and two measures of information-processing capacity: short-term memory for digits and choice-reaction times. In this study, Beatty selected...Kamiya, like Beatty, found EEG activity unrelated to both memory for words and a simple reaction-time test. In another study, Kamiya (1972...creative intelligence, visual memory , mental arithmetic, digit memory span, and i,une tracking. The results were negative. Kamiya concluded that the self

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…

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

PubMed

Wong, Terry Tin-Yau

2017-12-01

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

Variational calculation of second-order reduced density matrices by strong N-representability conditions and an accurate semidefinite programming solver.

PubMed

Nakata, Maho; Braams, Bastiaan J; Fujisawa, Katsuki; Fukuda, Mituhiro; Percus, Jerome K; Yamashita, Makoto; Zhao, Zhengji

2008-04-28

The reduced density matrix (RDM) method, which is a variational calculation based on the second-order reduced density matrix, is applied to the ground state energies and the dipole moments for 57 different states of atoms, molecules, and to the ground state energies and the elements of 2-RDM for the Hubbard model. We explore the well-known N-representability conditions (P, Q, and G) together with the more recent and much stronger T1 and T2(') conditions. T2(') condition was recently rederived and it implies T2 condition. Using these N-representability conditions, we can usually calculate correlation energies in percentage ranging from 100% to 101%, whose accuracy is similar to CCSD(T) and even better for high spin states or anion systems where CCSD(T) fails. Highly accurate calculations are carried out by handling equality constraints and/or developing multiple precision arithmetic in the semidefinite programming (SDP) solver. Results show that handling equality constraints correctly improves the accuracy from 0.1 to 0.6 mhartree. Additionally, improvements by replacing T2 condition with T2(') condition are typically of 0.1-0.5 mhartree. The newly developed multiple precision arithmetic version of SDP solver calculates extraordinary accurate energies for the one dimensional Hubbard model and Be atom. It gives at least 16 significant digits for energies, where double precision calculations gives only two to eight digits. It also provides physically meaningful results for the Hubbard model in the high correlation limit.

Validity of hearing impairment calculation methods for prediction of self-reported hearing handicap.

PubMed

John, Andrew B; Kreisman, Brian M; Pallett, Stephen

2012-01-01

Worker's compensation for hearing loss caused by occupational noise exposure is calculated by varying methods, from state to state within the United States (US), with many employing arithmetic formulas based on the pure-tone audiogram, to quantify hearing loss. Several assumptions unsupported or weakly supported by empirical data underlie these formulas. The present study evaluated the ability of various arithmetic hearing impairment calculations to predict a self-reported hearing handicap in a sample of presenting with sensorineural hearing loss. 204 adults (127 male, 77 female) ranging in age from 18 to 94 served as participants. The sample was selected to exclude patients who had been referred for hearing testing for a medicolegal examination or a hearing conservation appointment. A hearing handicap was measured by the Hearing Handicap Inventory for Adults/for the Elderly (HHIA/E). The covariance analysis of linear structural equations was used to assess the relative strength of correlation with the HHIA/E score among the six formulas and various forms of pure-tone average. The results revealed that all the hearing impairment calculations examined were significantly, but weakly, correlated with the self-reported hearing impairment scores. No significant differences among the predictive abilities of the impairment calculations were evident; however, the average binaural impairment assigned differed significantly among the six calculations examined. Individuals who demonstrated 0% impairment had significantly lower (i.e., better) HHIA/E scores compared to those with non-zero impairment for each formula. These results supported the idea that audiometric data provided an insufficient explanation for real-world hearing difficulties.

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

Development of preschool and academic skills in children born very preterm.

PubMed

Aarnoudse-Moens, Cornelieke Sandrine Hanan; Oosterlaan, Jaap; Duivenvoorden, Hugo Joseph; van Goudoever, Johannes Bernard; Weisglas-Kuperus, Nynke

2011-01-01

To examine performance in preschool and academic skills in very preterm (gestational age ≤ 30 weeks) and term-born comparison children aged 4 to 12 years. Very preterm children (n = 200; mean age, 8.2 ± 2.5 years) born between 1996 and 2004 were compared with 230 term-born children (mean age, 8.3 ± 2.3). The Dutch National Pupil Monitoring System was used to measure preschool numerical reasoning and early linguistics, and primary school simple and complex word reading, reading comprehension, spelling, and mathematics/arithmetic. With univariate analyses of variance, we assessed the effects of preterm birth on performance across grades and on grade retention. In preschool, very preterm children performed comparably with term-born children in early linguistics, but perform more poorly (0.7 standard deviation [SD]) in numerical reasoning skills. In primary school, very preterm children scored 0.3 SD lower in complex word reading and 0.6 SD lower in mathematics/arithmetic, but performed comparably with peers in reading comprehension and spelling. They had a higher grade repeat rate (25.5%), although grade repeat did not improve their academic skills. Very preterm children do well in early linguistics, reading comprehension, and spelling, but have clinically significant deficits in numerical reasoning skills and mathematics/arithmetic, which persist with time. Copyright © 2011 Mosby, Inc. All rights reserved.

Some connectivity indices and zagreb index of polyhex nanotubes.

PubMed

Farahani, Mohammad Reza

2012-12-01

Several topological indices are investigated in polyhex nanotubes: Randić connectivity index, sum-connectivity index, atom-bond connectivity index, geometric-arithmetic index, First and Second Zagreb indices and Zagreb polynomials. Formulas for calculating the above topological descriptors in polyhex zigzag TUZC6[m,n] and armchair TUAC6[m,n] nanotube families are given.

Teacher Candidates' Attitudes towards the Teaching Profession in Turkey

ERIC Educational Resources Information Center

Tok, Turkay Nuri

2012-01-01

This study examined the attitudes of teacher candidates in Turkey towards the teaching profession. Descriptive surveys were used and the research data was obtained from Pamukkale University Classroom Teaching students. During data analysis, the arithmetic means and standard deviations of the groups were calculated and a t-test and One-Way ANOVA…

Special Topic: What's Worth Fighting against in Grading?

ERIC Educational Resources Information Center

Reeves, Douglas; Jung, Lee Ann; O'Connor, Ken

2017-01-01

Arguing that there is a "glaring" disconnect between recommended policy and actual practice in the area of grading, the authors outline four common grading practices that they say can impair instructional integrity and distort academic outcomes: 1) the use of the an average, or arithmetic mean, of performances to calculate a final grade;…

Optical Topography of Evoked Brain Activity during Mental Tasks Involving Whole Number Operations

ERIC Educational Resources Information Center

Ortiz, Enrique

2014-01-01

Students start to memorize arithmetic facts from early elementary school mathematics activities. Their fluency or lack of fluency with these facts could affect their efforts as they carry out mental calculations as adults. This study investigated participants' levels of brain activation and possible reasons for these levels as they solved…

Children's Understanding of Addition and Subtraction Concepts

ERIC Educational Resources Information Center

Robinson, Katherine M.; Dube, Adam K.

2009-01-01

After the onset of formal schooling, little is known about the development of children's understanding of the arithmetic concepts of inversion and associativity. On problems of the form a+b-b (e.g., 3+26-26), if children understand the inversion concept (i.e., that addition and subtraction are inverse operations), then no calculations are needed…

Blood money: Harvey's De motu cordis (1628) as an exercise in accounting.

PubMed

Neuss, Michael J

2018-04-13

William Harvey's famous quantitative argument from De motu cordis (1628) about the circulation of blood explained how a small amount of blood could recirculate and nourish the entire body, upending the Galenic conception of the blood's motion. This paper argues that the quantitative argument drew on the calculative and rhetorical skills of merchants, including Harvey's own brothers. Modern translations of De motu cordis obscure the language of accountancy that Harvey himself used. Like a merchant accounting for credits and debits, intake and output, goods and moneys, Harvey treated venous and arterial blood as essentially commensurate, quantifiable and fungible. For Harvey, the circulation (and recirculation) of blood was an arithmetical necessity. The development of Harvey's circulatory model followed shifts in the epistemic value of mercantile forms of knowledge, including accounting and arithmetic, also drawing on an Aristotelian language of reciprocity and balance that Harvey shared with mercantile advisers to the royal court. This paper places Harvey's calculations in a previously underappreciated context of economic crisis, whose debates focused largely on questions of circulation.

QUENCH: A software package for the determination of quenching curves in Liquid Scintillation counting.

PubMed

Cassette, Philippe

2016-03-01

In Liquid Scintillation Counting (LSC), the scintillating source is part of the measurement system and its detection efficiency varies with the scintillator used, the vial and the volume and the chemistry of the sample. The detection efficiency is generally determined using a quenching curve, describing, for a specific radionuclide, the relationship between a quenching index given by the counter and the detection efficiency. A quenched set of LS standard sources are prepared by adding a quenching agent and the quenching index and detection efficiency are determined for each source. Then a simple formula is fitted to the experimental points to define the quenching curve function. The paper describes a software package specifically devoted to the determination of quenching curves with uncertainties. The experimental measurements are described by their quenching index and detection efficiency with uncertainties on both quantities. Random Gaussian fluctuations of these experimental measurements are sampled and a polynomial or logarithmic function is fitted on each fluctuation by χ(2) minimization. This Monte Carlo procedure is repeated many times and eventually the arithmetic mean and the experimental standard deviation of each parameter are calculated, together with the covariances between these parameters. Using these parameters, the detection efficiency, corresponding to an arbitrary quenching index within the measured range, can be calculated. The associated uncertainty is calculated with the law of propagation of variances, including the covariance terms. Copyright © 2015 Elsevier Ltd. All rights reserved.

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.

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.

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…

Network-Physics(NP) Bec DIGITAL(#)-VULNERABILITY Versus Fault-Tolerant Analog

NASA Astrophysics Data System (ADS)

Alexander, G. K.; Hathaway, M.; Schmidt, H. E.; Siegel, E.

2011-03-01

Siegel[AMS Joint Mtg.(2002)-Abs.973-60-124] digits logarithmic-(Newcomb(1881)-Weyl(1914; 1916)-Benford(1938)-"NeWBe"/"OLDbe")-law algebraic-inversion to ONLY BEQS BEC:Quanta/Bosons= digits: Synthesis reveals EMP-like SEVERE VULNERABILITY of ONLY DIGITAL-networks(VS. FAULT-TOLERANT ANALOG INvulnerability) via Barabasi "Network-Physics" relative-``statics''(VS.dynamics-[Willinger-Alderson-Doyle(Not.AMS(5/09)]-]critique); (so called)"Quantum-computing is simple-arithmetic(sans division/ factorization); algorithmic-complexities: INtractibility/ UNdecidability/ INefficiency/NONcomputability / HARDNESS(so MIScalled) "noise"-induced-phase-transitions(NITS) ACCELERATION: Cook-Levin theorem Reducibility is Renormalization-(Semi)-Group fixed-points; number-Randomness DEFINITION via WHAT? Query(VS. Goldreich[Not.AMS(02)] How? mea culpa)can ONLY be MBCS "hot-plasma" versus digit-clumping NON-random BEC; Modular-arithmetic Congruences= Signal X Noise PRODUCTS = clock-model; NON-Shor[Physica A,341,586(04)] BEC logarithmic-law inversion factorization:Watkins number-thy. U stat.-phys.); P=/=NP TRIVIAL Proof: Euclid!!! [(So Miscalled) computational-complexity J-O obviation via geometry.

Design of RISC Processor Using VHDL and Cadence

NASA Astrophysics Data System (ADS)

Moslehpour, Saeid; Puliroju, Chandrasekhar; Abu-Aisheh, Akram

The project deals about development of a basic RISC processor. The processor is designed with basic architecture consisting of internal modules like clock generator, memory, program counter, instruction register, accumulator, arithmetic and logic unit and decoder. This processor is mainly used for simple general purpose like arithmetic operations and which can be further developed for general purpose processor by increasing the size of the instruction register. The processor is designed in VHDL by using Xilinx 8.1i version. The present project also serves as an application of the knowledge gained from past studies of the PSPICE program. The study will show how PSPICE can be used to simplify massive complex circuits designed in VHDL Synthesis. The purpose of the project is to explore the designed RISC model piece by piece, examine and understand the Input/ Output pins, and to show how the VHDL synthesis code can be converted to a simplified PSPICE model. The project will also serve as a collection of various research materials about the pieces of the circuit.

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

Arithmetic processing in the brain shaped by cultures

PubMed Central

Tang, Yiyuan; Zhang, Wutian; Chen, Kewei; Feng, Shigang; Ji, Ye; Shen, Junxian; Reiman, Eric M.; Liu, Yijun

2006-01-01

The universal use of Arabic numbers in mathematics raises a question whether these digits are processed the same way in people speaking various languages, such as Chinese and English, which reflect differences in Eastern and Western cultures. Using functional MRI, we demonstrated a differential cortical representation of numbers between native Chinese and English speakers. Contrasting to native English speakers, who largely employ a language process that relies on the left perisylvian cortices for mental calculation such as a simple addition task, native Chinese speakers, instead, engage a visuo-premotor association network for the same task. Whereas in both groups the inferior parietal cortex was activated by a task for numerical quantity comparison, functional MRI connectivity analyses revealed a functional distinction between Chinese and English groups among the brain networks involved in the task. Our results further indicate that the different biological encoding of numbers may be shaped by visual reading experience during language acquisition and other cultural factors such as mathematics learning strategies and education systems, which cannot be explained completely by the differences in languages per se. PMID:16815966

Radon Concentrations in Drinking Water in Beijing City, China and Contribution to Radiation Dose

PubMed Central

Wu, Yun-Yun; Ma, Yong-Zhong; Cui, Hong-Xing; Liu, Jian-Xiang; Sun, Ya-Ru; Shang, Bing; Su, Xu

2014-01-01

222Rn concentrations in drinking water samples from Beijing City, China, were determined based on a simple method for the continuous monitoring of radon using a radon-in-air monitor coupled to an air-water exchanger. A total of 89 water samples were sampled and analyzed for their 222Rn content. The observed radon levels ranged from detection limit up to 49 Bq/L. The calculated arithmetic and geometric means of radon concentrations in all measured samples were equal to 5.87 and 4.63 Bq/L, respectively. The average annual effective dose from ingestion of radon in drinking water was 2.78 μSv, and that of inhalation of water-borne radon was 28.5 μSv. It is concluded that it is not the ingestion of waterborne radon, but inhalation of the radon escaping from water that is a substantial part of the radiological hazard. Radon in water is a big concern for public health, especially for consumers who directly use well water with very high radon concentration. PMID:25350007

Tiled architecture of a CNN-mostly IP system

NASA Astrophysics Data System (ADS)

Spaanenburg, Lambert; Malki, Suleyman

2009-05-01

Multi-core architectures have been popularized with the advent of the IBM CELL. On a finer grain the problems in scheduling multi-cores have already existed in the tiled architectures, such as the EPIC and Da Vinci. It is not easy to evaluate the performance of a schedule on such architecture as historical data are not available. One solution is to compile algorithms for which an optimal schedule is known by analysis. A typical example is an algorithm that is already defined in terms of many collaborating simple nodes, such as a Cellular Neural Network (CNN). A simple node with a local register stack together with a 'rotating wheel' internal communication mechanism has been proposed. Though the basic CNN allows for a tiled implementation of a tiled algorithm on a tiled structure, a practical CNN system will have to disturb this regularity by the additional need for arithmetical and logical operations. Arithmetic operations are needed for instance to accommodate for low-level image processing, while logical operations are needed to fork and merge different data streams without use of the external memory. It is found that the 'rotating wheel' internal communication mechanism still handles such mechanisms without the need for global control. Overall the CNN system provides for a practical network size as implemented on a FPGA, can be easily used as embedded IP and provides a clear benchmark for a multi-core compiler.

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

ERIC Educational Resources Information Center

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

2017-01-01

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

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.

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.

Arithmetic Processing in Children with Spina Bifida: Calculation Accuracy, Strategy Use, and Fact Retrieval Fluency

ERIC Educational Resources Information Center

Barnes, Marcia A.; Wilkinson, Margaret; Khemani, Ekta; Boudesquie, Amy; Dennis, Maureen; Fletcher, Jack M.

2006-01-01

Three studies compared 98 children with spina bifida myelomeningocele (SBM)--a disorder associated with high rates of math disability and spatial deficits--to 94 typically developing children on multidigit subtraction and cognitive addition tasks. Children with SBM were classified into those with reading decoding and math disability, only math…

Compound Interest Is As Easy As Pi. Teacher's Guide [and] Student Manual.

ERIC Educational Resources Information Center

Auman, L. Charles

This document provides teaching guidelines and student material for a unit intended for use in 12th grade algebra classes. Time allotment is from four to six hours of classroom time. The objective of this capsule is to teach students how to solve compound interest problems using arithmetic, logorithms, and calculators. Prerequisites for the unit…

Private Speech Use in Arithmetical Calculation: Contributory Role of Phonological Awareness in Children with and without Mathematical Difficulties

ERIC Educational Resources Information Center

Ostad, Snorre A.

2013-01-01

The majority of recent studies conclude that children's private speech development (private speech internalization) is related to and important for mathematical development and disabilities. It is far from clear, however, whether private speech internalization itself plays any causal role in the development of mathematical competence. The main…

Design of a Microprogram Control Unit with Concurrent Error Detection.

DTIC Science & Technology

1984-08-01

I fxoot Office of Naval Research N/A N00039-80-C-0556 ta. ADDRESS (City. St.. and ZIP Cod 10. SOURCE OF FUNOING N0. -PROGRAM PROJECT TASK WORK UNIT...However, the CED concept is mainly applied to various codes data transmission, and simple functional units, such as arithmetic units. Little work has...been done in the control unit area. Previous work is primarily in the use of clanical self-checking circuits, using bit slicin& parity, and m-out-of-n

Issues in Benchmark Metric Selection

NASA Astrophysics Data System (ADS)

Crolotte, Alain

It is true that a metric can influence a benchmark but will esoteric metrics create more problems than they will solve? We answer this question affirmatively by examining the case of the TPC-D metric which used the much debated geometric mean for the single-stream test. We will show how a simple choice influenced the benchmark and its conduct and, to some extent, DBMS development. After examining other alternatives our conclusion is that the “real” measure for a decision-support benchmark is the arithmetic mean.

Slimeware: engineering devices with slime mold.

PubMed

Adamatzky, Andrew

2013-01-01

The plasmodium of the acellular slime mold Physarum polycephalum is a gigantic single cell visible to the unaided eye. The cell shows a rich spectrum of behavioral patterns in response to environmental conditions. In a series of simple experiments we demonstrate how to make computing, sensing, and actuating devices from the slime mold. We show how to program living slime mold machines by configurations of repelling and attracting gradients and demonstrate the workability of the living machines on tasks of computational geometry, logic, and arithmetic.

Comparison of surgically induced astigmatism following different glaucoma operations.

PubMed

Tanito, Masaki; Matsuzaki, Yukari; Ikeda, Yoshifumi; Fujihara, Etsuko

2017-01-01

To compare surgically induced astigmatism (SIA) among glaucomatous eyes treated with trabeculectomy (LEC), EX-PRESS ® shunt (EXP), ab externo trabeculotomy (exLOT), or microhook ab interno trabeculotomy (μLOT). Eighty right eyes of 80 subjects who underwent LEC (n=20), EXP (n=20), exLOT (n=20), or μLOT (n=20) were included. The dataset including the best-corrected visual acuity (BCVA), intraocular pressure (IOP), and keratometry recordings preoperatively and 3 months postoperatively was collected by chart review. The means of the vector magnitude, vector meridian, and arithmetic magnitude of the preoperative and postoperative astigmatism and SIA were calculated. The correlations among the SIA magnitude, postoperative BCVA, and IOP were assessed. The mean astigmatic arithmetic magnitudes did not differ significantly ( P =0.0732) preoperatively among the four groups, but the magnitude was significantly ( P =0.0002) greater in the LEC group than the other groups postoperatively. The mean SIA vectors were calculated to be 1.01 D at 56°, 0.62 D at 74°, 0.23 D at 112°, and 0.12 D at 97° for the LEC, EXP, exLOT, and μLOT groups, respectively. The mean SIA arithmetic magnitudes were significantly ( P <0.0001) greater in the LEC group than the other groups. Three months postoperatively, the SIA magnitude was correlated positively with the logarithm of the minimum angle of resolution (logMAR) BCVA ( r =0.3538) and negatively with the IOP ( r =-0.3265); the logMAR BCVA was correlated negatively with the IOP ( r =-0.3105). EXP, exLOT, and μLOT induce less corneal astigmatism than LEC in the early postoperative period.

Calculations of actual corneal astigmatism using total corneal refractive power before and after myopic keratorefractive surgery.

PubMed

Seo, Kyoung Yul; Yang, Hun; Kim, Wook Kyum; Nam, Sang Min

2017-01-01

To calculate actual corneal astigmatism using the total corneal refractive astigmatism for the 4-mm apex zone of the Pentacam (TCRP4astig) and keratometric astigmatism (Kastig) before and after photorefractive keratectomy or laser in situ keratomileusis. Uncomplicated 56 eyes after more than 6 months from the surgery were recruited by chart review. Various corneal astigmatisms were measured using the Pentacam and autokeratometer before and after surgery. Three eyes were excluded and 53 eyes of 38 subjects with with-the-rule astigmatism (WTR) were finally included. The astigmatisms were investigated using polar value analysis. When TCRP4astig was set as an actual astigmatism, the efficacy of arithmetic or coefficient adjustment of Kastig was evaluated using bivariate analysis. The difference between the simulated keratometer astigmatism of the Pentacam (SimKastig) and Kastig was strongly correlated with the difference between TCRP4astig and Kastig. TCRP4astig was different from Kastig in magnitude rather than meridian before and after surgery; the preoperative difference was due to the posterior cornea only; however, the postoperative difference was observed in both anterior and posterior parts. For arithmetic adjustment, 0.28 D and 0.27 D were subtracted from the preoperative and postoperative magnitudes of Kastig, respectively. For coefficient adjustment, the preoperative and postoperative magnitudes of Kastig were multiplied by 0.80 and 0.66, respectively. By arithmetic or coefficient adjustment, the difference between TCRP4astig and adjusted Kastig would be less than 0.75 D in magnitude for 95% of cases. Kastig was successfully adjusted to TCPR4astig before and after myopic keratorefractive surgery in cases of WTR. For use of TCRP4astig directly, SimKastig and Kastig should be matched.

Calculations of actual corneal astigmatism using total corneal refractive power before and after myopic keratorefractive surgery

PubMed Central

Seo, Kyoung Yul; Yang, Hun; Kim, Wook Kyum; Nam, Sang Min

2017-01-01

Purpose To calculate actual corneal astigmatism using the total corneal refractive astigmatism for the 4-mm apex zone of the Pentacam (TCRP4astig) and keratometric astigmatism (Kastig) before and after photorefractive keratectomy or laser in situ keratomileusis Methods Uncomplicated 56 eyes after more than 6 months from the surgery were recruited by chart review. Various corneal astigmatisms were measured using the Pentacam and autokeratometer before and after surgery. Three eyes were excluded and 53 eyes of 38 subjects with with-the-rule astigmatism (WTR) were finally included. The astigmatisms were investigated using polar value analysis. When TCRP4astig was set as an actual astigmatism, the efficacy of arithmetic or coefficient adjustment of Kastig was evaluated using bivariate analysis. Results The difference between the simulated keratometer astigmatism of the Pentacam (SimKastig) and Kastig was strongly correlated with the difference between TCRP4astig and Kastig. TCRP4astig was different from Kastig in magnitude rather than meridian before and after surgery; the preoperative difference was due to the posterior cornea only; however, the postoperative difference was observed in both anterior and posterior parts. For arithmetic adjustment, 0.28 D and 0.27 D were subtracted from the preoperative and postoperative magnitudes of Kastig, respectively. For coefficient adjustment, the preoperative and postoperative magnitudes of Kastig were multiplied by 0.80 and 0.66, respectively. By arithmetic or coefficient adjustment, the difference between TCRP4astig and adjusted Kastig would be less than 0.75 D in magnitude for 95% of cases. Conclusions Kastig was successfully adjusted to TCPR4astig before and after myopic keratorefractive surgery in cases of WTR. For use of TCRP4astig directly, SimKastig and Kastig should be matched. PMID:28403194

Comparison of surgically induced astigmatism following different glaucoma operations

PubMed Central

Tanito, Masaki; Matsuzaki, Yukari; Ikeda, Yoshifumi; Fujihara, Etsuko

2017-01-01

Aim To compare surgically induced astigmatism (SIA) among glaucomatous eyes treated with trabeculectomy (LEC), EX-PRESS® shunt (EXP), ab externo trabeculotomy (exLOT), or microhook ab interno trabeculotomy (μLOT). Subjects and methods Eighty right eyes of 80 subjects who underwent LEC (n=20), EXP (n=20), exLOT (n=20), or μLOT (n=20) were included. The dataset including the best-corrected visual acuity (BCVA), intraocular pressure (IOP), and keratometry recordings preoperatively and 3 months postoperatively was collected by chart review. The means of the vector magnitude, vector meridian, and arithmetic magnitude of the preoperative and postoperative astigmatism and SIA were calculated. The correlations among the SIA magnitude, postoperative BCVA, and IOP were assessed. Results The mean astigmatic arithmetic magnitudes did not differ significantly (P=0.0732) preoperatively among the four groups, but the magnitude was significantly (P=0.0002) greater in the LEC group than the other groups postoperatively. The mean SIA vectors were calculated to be 1.01 D at 56°, 0.62 D at 74°, 0.23 D at 112°, and 0.12 D at 97° for the LEC, EXP, exLOT, and μLOT groups, respectively. The mean SIA arithmetic magnitudes were significantly (P<0.0001) greater in the LEC group than the other groups. Three months postoperatively, the SIA magnitude was correlated positively with the logarithm of the minimum angle of resolution (logMAR) BCVA (r=0.3538) and negatively with the IOP (r=−0.3265); the logMAR BCVA was correlated negatively with the IOP (r=−0.3105). Conclusion EXP, exLOT, and μLOT induce less corneal astigmatism than LEC in the early postoperative period. PMID:29238159

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.

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

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.

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…

Midline Dose Verification with Diode In Vivo Dosimetry for External Photon Therapy of Head and Neck and Pelvis Cancers During Initial Large-Field Treatments

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

Tung, Chuan-Jong; Department of Biomedical Engineering and Environmental Sciences, National Tsing Hua University, Hsinchu, Taiwan; Yu, Pei-Chieh

2010-01-01

During radiotherapy treatments, quality assurance/control is essential, particularly dose delivery to patients. This study was designed to verify midline doses with diode in vivo dosimetry. Dosimetry was studied for 6-MV bilateral fields in head and neck cancer treatments and 10-MV bilateral and anteroposterior/posteroanterior (AP/PA) fields in pelvic cancer treatments. Calibrations with corrections of diodes were performed using plastic water phantoms; 190 and 100 portals were studied for head and neck and pelvis treatments, respectively. Calculations of midline doses were made using the midline transmission, arithmetic mean, and geometric mean algorithms. These midline doses were compared with the treatment planning systemmore » target doses for lateral or AP (PA) portals and paired opposed portals. For head and neck treatments, all 3 algorithms were satisfactory, although the geometric mean algorithm was less accurate and more uncertain. For pelvis treatments, the arithmetic mean algorithm seemed unacceptable, whereas the other algorithms were satisfactory. The random error was reduced by using averaged midline doses of paired opposed portals because the asymmetric effect was averaged out. Considering the simplicity of in vivo dosimetry, the arithmetic mean and geometric mean algorithm should be adopted for head/neck and pelvis treatments, respectively.« less

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.

Learning Mathematics in a Visuospatial Format: A Randomized, Controlled Trial of Mental Abacus Instruction

ERIC Educational Resources Information Center

Barner, David; Alvarez, George; Sullivan, Jessica; Brooks, Neon; Srinivasan, Mahesh; Frank, Michael C.

2016-01-01

Mental abacus (MA) is a technique of performing fast, accurate arithmetic using a mental image of an abacus; experts exhibit astonishing calculation abilities. Over 3 years, 204 elementary school students (age range at outset: 5-7 years old) participated in a randomized, controlled trial to test whether MA expertise (a) can be acquired in standard…

Surface EEG Shows that Functional Segregation via Phase Coupling Contributes to the Neural Substrate of Mental Calculations

ERIC Educational Resources Information Center

Dimitriadis, Stavros I.; Kanatsouli, Kassiani; Laskaris, Nikolaos A.; Tsirka, Vasso; Vourkas, Michael; Micheloyannis, Sifis

2012-01-01

Multichannel EEG traces from healthy subjects are used to investigate the brain's self-organisation tendencies during two different mental arithmetic tasks. By making a comparison with a control-state in the form of a classification problem, we can detect and quantify the changes in coordinated brain activity in terms of functional connectivity.…

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…

Refining the quantitative pathway of the Pathways to Mathematics model.

PubMed

Sowinski, Carla; LeFevre, Jo-Anne; Skwarchuk, Sheri-Lynn; Kamawar, Deepthi; Bisanz, Jeffrey; Smith-Chant, Brenda

2015-03-01

In the current study, we adopted the Pathways to Mathematics model of LeFevre et al. (2010). In this model, there are three cognitive domains--labeled as the quantitative, linguistic, and working memory pathways--that make unique contributions to children's mathematical development. We attempted to refine the quantitative pathway by combining children's (N=141 in Grades 2 and 3) subitizing, counting, and symbolic magnitude comparison skills using principal components analysis. The quantitative pathway was examined in relation to dependent numerical measures (backward counting, arithmetic fluency, calculation, and number system knowledge) and a dependent reading measure, while simultaneously accounting for linguistic and working memory skills. Analyses controlled for processing speed, parental education, and gender. We hypothesized that the quantitative, linguistic, and working memory pathways would account for unique variance in the numerical outcomes; this was the case for backward counting and arithmetic fluency. However, only the quantitative and linguistic pathways (not working memory) accounted for unique variance in calculation and number system knowledge. Not surprisingly, only the linguistic pathway accounted for unique variance in the reading measure. These findings suggest that the relative contributions of quantitative, linguistic, and working memory skills vary depending on the specific cognitive task. Copyright © 2014 Elsevier Inc. All rights reserved.

[Study of correlation dimension on EEG].

PubMed

Yang, Hao; Fang, Liang; He, Wei

2004-02-01

The study of non-linear EEG is of great significance in clinical practice and research work. This paper has gone into the feasibility of calculating the correlation dimension and has developed some subjects with the characters of correlation dimension and the difference under four conditions: (1) passive eyes closed(PEC); (2) mental arithmetic with eyes closed(MAEC); (3) passive eyes open(PEO); (4) mental reasoning with eyes open (MRED). The results show it is feasible and meaningful to calculate correlation dimension and the correlation dimension can reflect the regular patterns of mental activity.

Construction of the Fock Matrix on a Grid-Based Molecular Orbital Basis Using GPGPUs.

PubMed

Losilla, Sergio A; Watson, Mark A; Aspuru-Guzik, Alán; Sundholm, Dage

2015-05-12

We present a GPGPU implementation of the construction of the Fock matrix in the molecular orbital basis using the fully numerical, grid-based bubbles representation. For a test set of molecules containing up to 90 electrons, the total Hartree-Fock energies obtained from reference GTO-based calculations are reproduced within 10(-4) Eh to 10(-8) Eh for most of the molecules studied. Despite the very large number of arithmetic operations involved, the high performance obtained made the calculations possible on a single Nvidia Tesla K40 GPGPU card.

Development of hardware accelerator for molecular dynamics simulations: a computation board that calculates nonbonded interactions in cooperation with fast multipole method.

PubMed

Amisaki, Takashi; Toyoda, Shinjiro; Miyagawa, Hiroh; Kitamura, Kunihiro

2003-04-15

Evaluation of long-range Coulombic interactions still represents a bottleneck in the molecular dynamics (MD) simulations of biological macromolecules. Despite the advent of sophisticated fast algorithms, such as the fast multipole method (FMM), accurate simulations still demand a great amount of computation time due to the accuracy/speed trade-off inherently involved in these algorithms. Unless higher order multipole expansions, which are extremely expensive to evaluate, are employed, a large amount of the execution time is still spent in directly calculating particle-particle interactions within the nearby region of each particle. To reduce this execution time for pair interactions, we developed a computation unit (board), called MD-Engine II, that calculates nonbonded pairwise interactions using a specially designed hardware. Four custom arithmetic-processors and a processor for memory manipulation ("particle processor") are mounted on the computation board. The arithmetic processors are responsible for calculation of the pair interactions. The particle processor plays a central role in realizing efficient cooperation with the FMM. The results of a series of 50-ps MD simulations of a protein-water system (50,764 atoms) indicated that a more stringent setting of accuracy in FMM computation, compared with those previously reported, was required for accurate simulations over long time periods. Such a level of accuracy was efficiently achieved using the cooperative calculations of the FMM and MD-Engine II. On an Alpha 21264 PC, the FMM computation at a moderate but tolerable level of accuracy was accelerated by a factor of 16.0 using three boards. At a high level of accuracy, the cooperative calculation achieved a 22.7-fold acceleration over the corresponding conventional FMM calculation. In the cooperative calculations of the FMM and MD-Engine II, it was possible to achieve more accurate computation at a comparable execution time by incorporating larger nearby regions. Copyright 2003 Wiley Periodicals, Inc. J Comput Chem 24: 582-592, 2003

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.

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…

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.

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.

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

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.

Multinode reconfigurable pipeline computer

NASA Technical Reports Server (NTRS)

Nosenchuck, Daniel M. (Inventor); Littman, Michael G. (Inventor)

1989-01-01

A multinode parallel-processing computer is made up of a plurality of innerconnected, large capacity nodes each including a reconfigurable pipeline of functional units such as Integer Arithmetic Logic Processors, Floating Point Arithmetic Processors, Special Purpose Processors, etc. The reconfigurable pipeline of each node is connected to a multiplane memory by a Memory-ALU switch NETwork (MASNET). The reconfigurable pipeline includes three (3) basic substructures formed from functional units which have been found to be sufficient to perform the bulk of all calculations. The MASNET controls the flow of signals from the memory planes to the reconfigurable pipeline and vice versa. the nodes are connectable together by an internode data router (hyperspace router) so as to form a hypercube configuration. The capability of the nodes to conditionally configure the pipeline at each tick of the clock, without requiring a pipeline flush, permits many powerful algorithms to be implemented directly.

Learning Mathematics in a Visuospatial Format: A Randomized, Controlled Trial of Mental Abacus Instruction.

PubMed

Barner, David; Alvarez, George; Sullivan, Jessica; Brooks, Neon; Srinivasan, Mahesh; Frank, Michael C

2016-07-01

Mental abacus (MA) is a technique of performing fast, accurate arithmetic using a mental image of an abacus; experts exhibit astonishing calculation abilities. Over 3 years, 204 elementary school students (age range at outset: 5-7 years old) participated in a randomized, controlled trial to test whether MA expertise (a) can be acquired in standard classroom settings, (b) improves students' mathematical abilities (beyond standard math curricula), and (c) is related to changes in basic cognitive capacities like working memory. MA students outperformed controls on arithmetic tasks, suggesting that MA expertise can be achieved by children in standard classrooms. MA training did not alter basic cognitive abilities; instead, differences in spatial working memory at the beginning of the study mediated MA learning. © 2016 The Authors. Child Development © 2016 Society for Research in Child Development, Inc.

Efficient implementation of the 3D-DDA ray traversal algorithm on GPU and its application in radiation dose calculation.

PubMed

Xiao, Kai; Chen, Danny Z; Hu, X Sharon; Zhou, Bo

2012-12-01

The three-dimensional digital differential analyzer (3D-DDA) algorithm is a widely used ray traversal method, which is also at the core of many convolution∕superposition (C∕S) dose calculation approaches. However, porting existing C∕S dose calculation methods onto graphics processing unit (GPU) has brought challenges to retaining the efficiency of this algorithm. In particular, straightforward implementation of the original 3D-DDA algorithm inflicts a lot of branch divergence which conflicts with the GPU programming model and leads to suboptimal performance. In this paper, an efficient GPU implementation of the 3D-DDA algorithm is proposed, which effectively reduces such branch divergence and improves performance of the C∕S dose calculation programs running on GPU. The main idea of the proposed method is to convert a number of conditional statements in the original 3D-DDA algorithm into a set of simple operations (e.g., arithmetic, comparison, and logic) which are better supported by the GPU architecture. To verify and demonstrate the performance improvement, this ray traversal method was integrated into a GPU-based collapsed cone convolution∕superposition (CCCS) dose calculation program. The proposed method has been tested using a water phantom and various clinical cases on an NVIDIA GTX570 GPU. The CCCS dose calculation program based on the efficient 3D-DDA ray traversal implementation runs 1.42 ∼ 2.67× faster than the one based on the original 3D-DDA implementation, without losing any accuracy. The results show that the proposed method can effectively reduce branch divergence in the original 3D-DDA ray traversal algorithm and improve the performance of the CCCS program running on GPU. Considering the wide utilization of the 3D-DDA algorithm, various applications can benefit from this implementation method.

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…

Disentangling the effects of working memory, language, parental education, and non-verbal intelligence on children’s mathematical abilities

PubMed Central

Pina, Violeta; Fuentes, Luis J.; Castillo, Alejandro; Diamantopoulou, Sofia

2014-01-01

It is assumed that children’s performance in mathematical abilities is influenced by several factors such as working memory (WM), verbal ability, intelligence, and socioeconomic status. The present study explored the contribution of those factors to mathematical performance taking a componential view of both WM and mathematics. We explored the existing relationship between different WM components (verbal and spatial) with tasks that make differential recruitment of the central executive, and simple and complex mathematical skills in a sample of 102 children in grades 4–6. The main findings point to a relationship between the verbal WM component and complex word arithmetic problems, whereas language and non-verbal intelligence were associated with knowledge of quantitative concepts and arithmetic ability. The spatial WM component was associated with the subtest Series, whereas the verbal component was with the subtest Concepts. The results also suggest a positive relationship between parental educational level and children’s performance on Quantitative Concepts. These findings suggest that specific cognitive skills might be trained in order to improve different aspects of mathematical ability. PMID:24847306

Validity and reliability of dental age estimation of teeth root translucency based on digital luminance determination.

PubMed

Ramsthaler, Frank; Kettner, Mattias; Verhoff, Marcel A

2014-01-01

In forensic anthropological casework, estimating age-at-death is key to profiling unknown skeletal remains. The aim of this study was to examine the reliability of a new, simple, fast, and inexpensive digital odontological method for age-at-death estimation. The method is based on the original Lamendin method, which is a widely used technique in the repertoire of odontological aging methods in forensic anthropology. We examined 129 single root teeth employing a digital camera and imaging software for the measurement of the luminance of the teeth's translucent root zone. Variability in luminance detection was evaluated using statistical technical error of measurement analysis. The method revealed stable values largely unrelated to observer experience, whereas requisite formulas proved to be camera-specific and should therefore be generated for an individual recording setting based on samples of known chronological age. Multiple regression analysis showed a highly significant influence of the coefficients of the variables "arithmetic mean" and "standard deviation" of luminance for the regression formula. For the use of this primer multivariate equation for age-at-death estimation in casework, a standard error of the estimate of 6.51 years was calculated. Step-by-step reduction of the number of embedded variables to linear regression analysis employing the best contributor "arithmetic mean" of luminance yielded a regression equation with a standard error of 6.72 years (p < 0.001). The results of this study not only support the premise of root translucency as an age-related phenomenon, but also demonstrate that translucency reflects a number of other influencing factors in addition to age. This new digital measuring technique of the zone of dental root luminance can broaden the array of methods available for estimating chronological age, and furthermore facilitate measurement and age classification due to its low dependence on observer experience.

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.

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.

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.

Measuring Timber Truck Loads With Image Processing In Paper Mills

NASA Astrophysics Data System (ADS)

Silva, M. Santos; Carvalho, Fernando D.; Rodrigues, F. Carvalho; Goncalves, Ana N. R.

1989-04-01

The raw material for the paper industry is wood. To have an exact account of the stock of piled sawn tree trunks every truck load entering the plant's stockyard must be measured as to the amount of wood being brought in. Weighting down the trucks has its own problems, mainly, due to the high capacity of the tree trunks to absorb water. This problem is further enhanced when calculations must be made to arrive at the mass of sawn tree trunks which must go into the process of producing a certain quantity of paper pulp. The method presented here is based on two fixed cameras which take the image of the truck load. One takes a view of the trunks in order to get information on the average length of the tree trunks. The other obtains a side view which is digitised and by just discriminating against a grey level the area covered by the tree trunk cross section is measured. A simple arithmetic operation gives the volume of wood in the trunk. The same computer, a PC, will register the trucks particulars is almost independent of weather the wood is wet or dry and it serves trucks of any size.

A source-attractor approach to network detection of radiation sources

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

Wu, Qishi; Barry, M. L..; Grieme, M.

Radiation source detection using a network of detectors is an active field of research for homeland security and defense applications. We propose Source-attractor Radiation Detection (SRD) method to aggregate measurements from a network of detectors for radiation source detection. SRD method models a potential radiation source as a magnet -like attractor that pulls in pre-computed virtual points from the detector locations. A detection decision is made if a sufficient level of attraction, quantified by the increase in the clustering of the shifted virtual points, is observed. Compared with traditional methods, SRD has the following advantages: i) it does not requiremore » an accurate estimate of the source location from limited and noise-corrupted sensor readings, unlike the localizationbased methods, and ii) its virtual point shifting and clustering calculation involve simple arithmetic operations based on the number of detectors, avoiding the high computational complexity of grid-based likelihood estimation methods. We evaluate its detection performance using canonical datasets from Domestic Nuclear Detection Office s (DNDO) Intelligence Radiation Sensors Systems (IRSS) tests. SRD achieves both lower false alarm rate and false negative rate compared to three existing algorithms for network source detection.« less

FuzzObserver

NASA Technical Reports Server (NTRS)

Howard, Ayanna; Bayard, David

2006-01-01

Fuzzy Feature Observation Planner for Small Body Proximity Observations (FuzzObserver) is a developmental computer program, to be used along with other software, for autonomous planning of maneuvers of a spacecraft near an asteroid, comet, or other small astronomical body. Selection of terrain features and estimation of the position of the spacecraft relative to these features is an essential part of such planning. FuzzObserver contributes to the selection and estimation by generating recommendations for spacecraft trajectory adjustments to maintain the spacecraft's ability to observe sufficient terrain features for estimating position. The input to FuzzObserver consists of data from terrain images, including sets of data on features acquired during descent toward, or traversal of, a body of interest. The name of this program reflects its use of fuzzy logic to reason about the terrain features represented by the data and extract corresponding trajectory-adjustment rules. Linguistic fuzzy sets and conditional statements enable fuzzy systems to make decisions based on heuristic rule-based knowledge derived by engineering experts. A major advantage of using fuzzy logic is that it involves simple arithmetic calculations that can be performed rapidly enough to be useful for planning within the short times typically available for spacecraft maneuvers.

Simultaneous measurement for thermal conductivity, diffusivity, and specific heat of methane hydrate bearing sediments recovered from Nankai-Trough wells

NASA Astrophysics Data System (ADS)

Muraoka, M.; Ohtake, M.; Susuki, N.; Yamamoto, Y.; Suzuki, K.; Tsuji, T.

2014-12-01

This study presents the results of the measurements of the thermal constants of natural methane-hydrate-bearing sediments samples recovered from the Tokai-oki test wells (Nankai-Trough, Japan) in 2004. The thermal conductivity, thermal diffusivity, and specific heat of the samples were simultaneously determined using the hot-disk transient method. The thermal conductivity of natural hydrate-bearing sediments decreases slightly with increasing porosity. In addition, the thermal diffusivity of hydrate-bearing sediment decrease as porosity increases. We also used simple models to calculate the thermal conductivity and thermal diffusivity. The results of the distribution model (geometric-mean model) are relatively consistent with the measurement results. In addition, the measurement results are consistent with the thermal diffusivity, which is estimated by dividing the thermal conductivity obtained from the distribution model by the specific heat obtained from the arithmetic mean. In addition, we discuss the relation between the thermal conductivity and mineral composition of core samples in conference. Acknowledgments. This work was financially supported by MH21 Research Consortium for Methane Hydrate Resources in Japan on the National Methane Hydrate Exploitation Program planned by the Ministry of Economy, Trade and Industry.

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

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.

How verbal and spatial manipulation networks contribute to calculation: an fMRI study.

PubMed

Zago, Laure; Petit, Laurent; Turbelin, Marie-Renée; Andersson, Frédéric; Vigneau, Mathieu; Tzourio-Mazoyer, Nathalie

2008-01-01

The manipulation of numbers required during calculation is known to rely on working memory (WM) resources. Here, we investigated the respective contributions of verbal and/or spatial WM manipulation brain networks during the addition of four numbers performed by adults, using functional magnetic resonance imaging (fMRI). Both manipulation and maintenance tasks were proposed with syllables, locations, or two-digit numbers. As compared to their maintenance, numbers manipulation (addition) elicited increased activation within a widespread cortical network including inferior temporal, parietal, and prefrontal regions. Our results demonstrate that mastery of arithmetic calculation requires the cooperation of three WM manipulation systems: an executive manipulation system conjointly recruited by the three manipulation tasks, including the anterior cingulate cortex (ACC), the orbital part of the inferior frontal gyrus, and the caudate nuclei; a left-lateralized, language-related, inferior fronto-temporal system elicited by numbers and syllables manipulation tasks required for retrieval, selection, and association of symbolic information; and a right superior and posterior fronto-parietal system elicited by numbers and locations manipulation tasks for spatial WM and attentional processes. Our results provide new information that the anterior intraparietal sulcus (IPS) is involved in tasks requiring a magnitude processing with symbolic (numbers) and nonsymbolic (locations) stimuli. Furthermore, the specificity of arithmetic processing is mediated by a left-hemispheric specialization of the anterior and posterior parts of the IPS as compared to a spatial task involving magnitude processing with nonsymbolic material.

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

Acoustic simulation in architecture with parallel algorithm

NASA Astrophysics Data System (ADS)

Li, Xiaohong; Zhang, Xinrong; Li, Dan

2004-03-01

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

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.

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

Space of symmetry matrices with elements 0, ±1 and complete geometric description; its properties and application.

PubMed

Stróż, Kazimierz

2011-09-01

A fixed set, that is the set of all lattice metrics corresponding to the arithmetic holohedry of a primitive lattice, is a natural tool for keeping track of the symmetry changes that may occur in a deformable lattice [Ericksen (1979). Arch. Rat. Mech. Anal. 72, 1-13; Michel (1995). Symmetry and Structural Properties of Condensed Matter, edited by T. Lulek, W. Florek & S. Walcerz. Singapore: Academic Press; Pitteri & Zanzotto (1996). Acta Cryst. A52, 830-838; and references quoted therein]. For practical applications it is desirable to limit the infinite number of arithmetic holohedries, and simplify their classification and construction of the fixed sets. A space of 480 matrices with cyclic consecutive powers, determinant 1, elements from {0, ±1} and geometric description were analyzed and offered as the framework for dealing with the symmetry of reduced lattices. This matrix space covers all arithmetic holohedries of primitive lattice descriptions related to the three shortest lattice translations in direct or reciprocal spaces, and corresponds to the unique list of 39 fixed points with integer coordinates in six-dimensional space of lattice metrics. Matrices are presented by the introduced dual symbol, which sheds some light on the lattice and its symmetry-related properties, without further digging into matrices. By the orthogonal lattice distortion the lattice group-subgroup relations are easily predicted. It was proven and exemplified that new symbols enable classification of lattice groups on an absolute basis, without metric considerations. In contrast to long established but sophisticated methods for assessing the metric symmetry of a lattice, simple filtering of the symmetry operations from the predefined set is proposed. It is concluded that the space of symmetry matrices with elements from {0, ±1} is the natural environment of lattice symmetries related to the reduced cells and that complete geometric characterization of matrices in the arithmetic holohedry provides a useful tool for solving practical lattice-related problems, especially in the context of lattice deformation. © 2011 International Union of Crystallography

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.

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.

Nuclear Poincaré cycle synchronizes with the incident de Broglie wave to predict regularity in neutron resonance energies

NASA Astrophysics Data System (ADS)

Ohkubo, Makio

2016-06-01

In observed neutron resonances, long believed to be a form of quantum chaos, regular family structures are found in the s-wave resonances of many even-even nuclei in the tens keV to MeV region [M.Ohkubo, Phys. Rev. C 87, 014608(2013)]. Resonance reactions take place when the incident de Broglie wave synchronizes with the Poincaré cycle of the compound nucleus, which is composed of several normal modes with periods that are time quantized by inverse Fermi energy. Based on the breathing model of the compound nucleus, neutron resonance energies in family structures are written by simple arithmetic expressions using Sn and small integers. Family structures in observed resonances of 40Ca+n and 37Cl+n are described as simple cases. A model for time quantization is discussed.

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…

[Numbers, counting and calculating problems in view of cognitive neurology].

PubMed

Márkus, Attila

2010-03-30

The ability to count and calculate is a human-specific skill comprised of understanding numeric values and categories and performing numerical operations; it is an acoustic-verbal symbolic activity that may be expressed in writing and understood by reading. The neuronal bases and precursors of cognitive systems have been supplied to mankind by the process of evolution. Abilities to create symbols (speech, visual letter and number symbols) must have played a decisive role in the emergence of man from the world of primates. Although counting and calculating problems are classified into numerous types, two main forms of dyscalculia have practical importance: the acquired one (the loss of learned knowledge) and the developmental one (the disturbance of the acquisition of arithmetical knowledge).

Operational momentum in large-number addition and subtraction by 9-month-olds.

PubMed

McCrink, Koleen; Wynn, Karen

2009-08-01

Recent studies on nonsymbolic arithmetic have illustrated that under conditions that prevent exact calculation, adults display a systematic tendency to overestimate the answers to addition problems and underestimate the answers to subtraction problems. It has been suggested that this operational momentum results from exposure to a culture-specific practice of representing numbers spatially; alternatively, the mind may represent numbers in spatial terms from early in development. In the current study, we asked whether operational momentum is present during infancy, prior to exposure to culture-specific representations of numbers. Infants (9-month-olds) were shown videos of events involving the addition or subtraction of objects with three different types of outcomes: numerically correct, too large, and too small. Infants looked significantly longer only at those incorrect outcomes that violated the momentum of the arithmetic operation (i.e., at too-large outcomes in subtraction events and too-small outcomes in addition events). The presence of operational momentum during infancy indicates developmental continuity in the underlying mechanisms used when operating over numerical representations.

Overprotective social support leads to increased cardiovascular and subjective stress reactivity.

PubMed

Zniva, Richard; Pauli, Paul; Schulz, Stefan M

2017-02-01

Self-determination theory suggests that autonomy-enhancing social support helps individuals to perceive stressors as challenging rather than stressing. Overprotective support may reduce stress in the short-run but undermines autonomy, thus hampering stress-coping in the long run, particularly when social support is terminated. Heartrate, blood-pressure and ratings were examined in N=44 undergraduate students receiving autonomy support (calculation steps) or overprotection (solutions) from a close friend or no support for solving arithmetic tasks as well as during a subsequent stress-challenge (solving arithmetic tasks alone). Overprotection resulted in increased heartrate, diastolic blood-pressure, stress ratings, and decreased subjective control during stress-challenge. Autonomy support did not lead to unfavorable stress responding. The current findings are in line with assumptions derived from self-determination theory and indicate that autonomy support can help to prevent stress. Overprotection does not buffer stress and is associated with increased stress when discontinued. Copyright © 2016 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

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

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

Single-digit arithmetic processing—anatomical evidence from statistical voxel-based lesion analysis

PubMed Central

Mihulowicz, Urszula; Willmes, Klaus; Karnath, Hans-Otto; Klein, Elise

2014-01-01

Different specific mechanisms have been suggested for solving single-digit arithmetic operations. However, the neural correlates underlying basic arithmetic (multiplication, addition, subtraction) are still under debate. In the present study, we systematically assessed single-digit arithmetic in a group of acute stroke patients (n = 45) with circumscribed left- or right-hemispheric brain lesions. Lesion sites significantly related to impaired performance were found only in the left-hemisphere damaged (LHD) group. Deficits in multiplication and addition were related to subcortical/white matter brain regions differing from those for subtraction tasks, corroborating the notion of distinct processing pathways for different arithmetic tasks. Additionally, our results further point to the importance of investigating fiber pathways in numerical cognition. PMID:24847238

Application to recognition of ferrography image with fractal neural network

NASA Astrophysics Data System (ADS)

Tian, Xianzhong; Hu, Tongsen; Zhang, Jian

2005-10-01

Because wear particles have fractal characteristics, it is necessary that adding fractal parameters to studying wear particles and diagnosing machine troubles. This paper discusses fractal parameters of wear particles, presents arithmetic calculating fractal dimension, and constructs a fractal neural network which can recognize wear particles image. It is proved by experiments that this fractal neural network can recognize some characteristics of wear particles image, and can also classify wear types.

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.

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.

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.

Mathematical models frame environmental dispute [Review of the article Useless arithmetic: Ten points to ponder when using mathematical models in environmental decision making

USGS Publications Warehouse

Lamb, Berton Lee; Burkardt, Nina

2008-01-01

When Linda Pilkey- Jarvis and Orrin Pilkey state in their article, "Useless Arithmetic," that "mathematical models are simplified, generalized representations of a process or system," they probably do not mean to imply that these models are simple. Rather, the models are simpler than nature and that is the heart of the problem with predictive models. We have had a long professional association with the developers and users of one of these simplifications of nature in the form of a mathematical model known as Physical Habitat Simulation (PHABSIM), which is part of the Instream Flow Incremental Methodology (IFIM). The IFIM is a suite of techniques, including PHABSIM, that allows the analyst to incorporate hydrology , hydraulics, habitat, water quality, stream temperature, and other variables into a tradeoff analysis that decision makers can use to design a flow regime to meet management objectives (Stalnaker et al. 1995). Although we are not the developers of the IFIM, we have worked with those who did design it, and we have tried to understand how the IFIM and PHABSIM are actually used in decision making (King, Burkardt, and Clark 2006; Lamb 1989).

Sources of Group and Individual Differences in Emerging Fraction Skills

PubMed Central

Hecht, Steven A.; Vagi, Kevin J.

2010-01-01

Results from a two year longitudinal study of 181 children from fourth through fifth grade are reported. Levels of growth in children’s computation, word problem, and estimation skills using common fractions were predicted by working memory, attentive classroom behavior, conceptual knowledge about fractions, and simple arithmetic fluency. Comparisons of 55 participants identified as having mathematical difficulties to those without mathematical difficulties revealed that group differences in emerging fraction skills were consistently mediated by attentive classroom behavior and conceptual knowledge about fractions. Neither working memory nor arithmetic fluency mediated group differences in growth in fraction skills. It was also found that the development of basic fraction skills and conceptual knowledge are bidirectional in that conceptual knowledge exerted strong influences on all three types of basic fraction skills, and basic fraction skills exerted a more modest influence on subsequent conceptual knowledge. Results are discussed with reference to how the identification of potentially malleable student characteristics that contribute to the difficulties that some students have with fractions informs interventions and also will contribute to a future theoretical account concerning how domain general and domain specific factors influence the development of basic fraction skills. PMID:21170171

Self-regulated learning of basic arithmetic skills: a longitudinal study.

PubMed

Throndsen, Inger

2011-12-01

Several studies have examined young primary school children's use of strategies when solving simple addition and subtraction problems. Most of these studies have investigated students' strategy use as if they were isolated processes. To date, we have little knowledge about how math strategies in young students are related to other important aspects in self-regulated learning. The main purpose of this study was to examine relations between young primary school children's basic mathematical skills and their use of math strategies, their metacognitive competence and motivational beliefs, and to investigate how students with basic mathematics skills at various levels differ in respect to the different self-regulation components. The participants were comprised of 27 Year 2 students, all from the same class. The data were collected in three stages (autumn Year 2, spring Year 2, and autumn Year 3). The children's arithmetic skills were measured by age relevant tests, while strategy use, metacognitive competence, and motivational beliefs were assessed through individual interviews. The participants were divided into three performance groups; very good students, good students, and not-so-good students. Analyses revealed that young primary school children at different levels of basic mathematics skill may differ in several important aspects of self-regulated learning. Analyses revealed that a good performance in addition and subtraction was related not only to the children's use of advanced mathematics strategies, but also to domain-specific metacognitive competence, ability attribution for success, effort attribution for failure, and high perceived self-efficacy when using specific strategies. The results indicate that instructional efforts to facilitate self-regulated learning of basic arithmetic skills should address cognitive, metacognitive, and motivational aspects of self-regulation. This is particularly important for low-performing students. ©2010 The British Psychological Society.

Licensed operating reactors: Status summary report, data as of December 31, 1995. Volume 20

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

NONE

1996-06-01

The US Nuclear Regulatory Commission`s monthly summary of licensed nuclear power reactor data is based primarily on the operating data report submitted by licensees for each unit. This report is divided into two sections: the first contains summary highlights and the second contains data on each individual unit in commercial operation. Section 1 availability factors, capacity factors, and forced outage rates are simple arithmetic averages. Section 2 items in the cumulative column are generally as reported by the licensees and notes to the use of weighted averages and starting dates other than commercial operation are provided.

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.

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…

A decimal carry-free adder

NASA Astrophysics Data System (ADS)

Nikmehr, Hooman; Phillips, Braden; Lim, Cheng-Chew

2005-02-01

Recently, decimal arithmetic has become attractive in the financial and commercial world including banking, tax calculation, currency conversion, insurance and accounting. Although computers are still carrying out decimal calculation using software libraries and binary floating-point numbers, it is likely that in the near future, all processors will be equipped with units performing decimal operations directly on decimal operands. One critical building block for some complex decimal operations is the decimal carry-free adder. This paper discusses the mathematical framework of the addition, introduces a new signed-digit format for representing decimal numbers and presents an efficient architectural implementation. Delay estimation analysis shows that the adder offers improved performance over earlier designs.

Transforming geographic scale: a comparison of combined population and areal weighting to other interpolation methods.

PubMed

Hallisey, Elaine; Tai, Eric; Berens, Andrew; Wilt, Grete; Peipins, Lucy; Lewis, Brian; Graham, Shannon; Flanagan, Barry; Lunsford, Natasha Buchanan

2017-08-07

Transforming spatial data from one scale to another is a challenge in geographic analysis. As part of a larger, primary study to determine a possible association between travel barriers to pediatric cancer facilities and adolescent cancer mortality across the United States, we examined methods to estimate mortality within zones at varying distances from these facilities: (1) geographic centroid assignment, (2) population-weighted centroid assignment, (3) simple areal weighting, (4) combined population and areal weighting, and (5) geostatistical areal interpolation. For the primary study, we used county mortality counts from the National Center for Health Statistics (NCHS) and population data by census tract for the United States to estimate zone mortality. In this paper, to evaluate the five mortality estimation methods, we employed address-level mortality data from the state of Georgia in conjunction with census data. Our objective here is to identify the simplest method that returns accurate mortality estimates. The distribution of Georgia county adolescent cancer mortality counts mirrors the Poisson distribution of the NCHS counts for the U.S. Likewise, zone value patterns, along with the error measures of hierarchy and fit, are similar for the state and the nation. Therefore, Georgia data are suitable for methods testing. The mean absolute value arithmetic differences between the observed counts for Georgia and the five methods were 5.50, 5.00, 4.17, 2.74, and 3.43, respectively. Comparing the methods through paired t-tests of absolute value arithmetic differences showed no statistical difference among the methods. However, we found a strong positive correlation (r = 0.63) between estimated Georgia mortality rates and combined weighting rates at zone level. Most importantly, Bland-Altman plots indicated acceptable agreement between paired arithmetic differences of Georgia rates and combined population and areal weighting rates. This research contributes to the literature on areal interpolation, demonstrating that combined population and areal weighting, compared to other tested methods, returns the most accurate estimates of mortality in transforming small counts by county to aggregated counts for large, non-standard study zones. This conceptually simple cartographic method should be of interest to public health practitioners and researchers limited to analysis of data for relatively large enumeration units.

Students’ Mathematical Literacy in Solving PISA Problems Based on Keirsey Personality Theory

NASA Astrophysics Data System (ADS)

Masriyah; Firmansyah, M. H.

2018-01-01

This research is descriptive-qualitative research. The purpose is to describe students’ mathematical literacy in solving PISA on space and shape content based on Keirsey personality theory. The subjects are four junior high school students grade eight with guardian, artisan, rational or idealist personality. Data collecting methods used test and interview. Data of Keirsey Personality test, PISA test, and interview were analysed. Profile of mathematical literacy of each subject are described as follows. In formulating, guardian subject identified mathematical aspects are formula of rectangle area and sides length; significant variables are terms/conditions in problem and formula of ever encountered question; translated into mathematical language those are measurement and arithmetic operations. In employing, he devised and implemented strategies using ease of calculation on area-subtraction principle; declared truth of result but the reason was less correct; didn’t use and switch between different representations. In interpreting, he declared result as area of house floor; declared reasonableness according measurement estimation. In formulating, artisan subject identified mathematical aspects are plane and sides length; significant variables are solution procedure on both of daily problem and ever encountered question; translated into mathematical language those are measurement, variables, and arithmetic operations as well as symbol representation. In employing, he devised and implemented strategies using two design comparison; declared truth of result without reason; used symbol representation only. In interpreting, he expressed result as floor area of house; declared reasonableness according measurement estimation. In formulating, rational subject identified mathematical aspects are scale and sides length; significant variables are solution strategy on ever encountered question; translated into mathematical language those are measurement, variable, arithmetic operation as well as symbol and graphic representation. In employing, he devised and implemented strategies using additional plane forming on area-subtraction principle; declared truth of result according calculation process; used and switched between symbol and graphic representation. In interpreting, he declared result as house area within terrace and wall; declared reasonableness according measurement estimation. In formulating, idealist subject identified mathematical aspects are sides length; significant variables are terms/condition in problem; translated into mathematical language those are measurement, variables, arithmetic operations as well as symbol and graphic representation. In employing, he devised and implemented strategies using trial and error and two design in process of finding solutions; declared truth of result according the use of two design of solution; used and switched between symbol and graphic representation. In interpreting, he declared result as floor area of house; declared reasonableness according measurement estimation.

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;…

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…

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.

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).

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.

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.

Dual tasking and balance in those with central and peripheral vision loss.

PubMed

Kotecha, Aachal; Chopra, Reena; Fahy, Rachel T A; Rubin, Gary S

2013-08-09

To investigate the effects of a secondary task on standing balance in patients with glaucoma or AMD compared with age-similar control subjects. Twelve AMD, 12 glaucoma, and 12 control participants underwent posturography under two standing conditions (eyes open on a firm or foam-rubber surface) and two tasks: quiet standing and undertaking a mental arithmetic task. Center of foot-pressure average displacement (root mean square [RMS]; in millimeters) was calculated. The mean (SD) age of the participants in each group was as follows: controls 66.2 (6.4) years, glaucoma 69.2 (4.3) years, and AMD 72.2 (5.3) years. There were significant differences in RMS between controls and AMD patients when undertaking the mental arithmetic task standing on the firm surface (mean difference [SE]: 2.8 [0.8] mm, P = 0.005). There were significant differences between controls and AMD patients when undertaking the mental arithmetic task on the foam surface, with the difference between controls and glaucoma patients approaching significance (mean difference [SE]: control versus AMD = 3.1 [0.9] mm, P = 0.005; control versus glaucoma = 2.2 [0.9] mm, P = 0.06). Postural instability increases with the addition of a secondary task in older persons, which may put them at greater risk of falls. Patients with central losses exhibit greater instability with the addition of a secondary task, particularly during somatosensory perturbations. The negative effects of secondary tasks on balance control in those with peripheral visual losses become more apparent under somatosensory perturbations.

Comparison of newer IOL power calculation methods for post-corneal refractive surgery eyes

PubMed Central

Wang, Li; Tang, Maolong; Huang, David; Weikert, Mitchell P.; Koch, Douglas D.

2015-01-01

Objective To compare the newer formulae, the optical coherence tomography based intraocular lens (IOL) power formula (OCT formula) and the Barrett True-K formula (True-K), to the methods on the ASCRS calculator in eyes with previous myopic LASIK/PRK. Design Prospective case series. Participants One-hundred and four eyes of 80 patients who had previous myopic LASIK/PRK and subsequent cataract surgery and IOL implantation. Methods Using the actual refraction following cataract surgery as target refraction, predicted IOL power for each method was calculated. The IOL prediction error (PE) was obtained by subtracting the predicted IOL power from the power of IOL implanted. Main outcome measures Arithmetic IOL PEs, variances of mean arithmetic IOL PE, median refractive PE and percent of eyes within 0.5 D and 1.0 D of refractive PE. Results OCT produced smaller variance of IOL PE than did Wang-Koch-Maloney, and Shammas (P<0.05). With the OCT, True-K No History, Wang-Koch-Maloney, Shammas, Haigis-L, and Average of these 5 formulas, respectively, the median refractive PEs were 0.35 D, 0.42 D, 0.51 D, 0.48 D, 0.39 D, and 0.35 D, and the % of eyes within 0.5 D of refractive PE were 68.3%, 58.7%, 50.0%, 52.9%, 55.8%, and 67.3%, and within 1.0 D of RPE, 92.3%, 90.4%, 86.9%, 88.5%, 90.4%, and 94.2%, respectively. The OCT formula had smaller refractive PE compared to Wang-Koch-Maloney and Shammas, and the Average approach produced significantly smaller refractive PE than did all methods except OCT (all P<0.05). Conclusions The OCT and True-K No History are promising formulas. The ASCRS IOL calculator has been updated to include the OCT and Barrett True K formulas. Trial registration Intraocular Lens Power Calculation After Laser Refractive Surgery Based on Optical Coherence Tomography (OCT IOL); Identifier: NCT00532051; www.ClinicalTrials.gov PMID:26459996

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…

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,…

How Is Phonological Processing Related to Individual Differences in Children's Arithmetic Skills?

ERIC Educational Resources Information Center

De Smedt, Bert; Taylor, Jessica; Archibald, Lisa; Ansari, Daniel

2010-01-01

While there is evidence for an association between the development of reading and arithmetic, the precise locus of this relationship remains to be determined. Findings from cognitive neuroscience research that point to shared neural correlates for phonological processing and arithmetic as well as recent behavioral evidence led to the present…

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)…

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

Toward a formal verification of a floating-point coprocessor and its composition with a central processing unit

NASA Technical Reports Server (NTRS)

Pan, Jing; Levitt, Karl N.; Cohen, Gerald C.

1991-01-01

Discussed here is work to formally specify and verify a floating point coprocessor based on the MC68881. The HOL verification system developed at Cambridge University was used. The coprocessor consists of two independent units: the bus interface unit used to communicate with the cpu and the arithmetic processing unit used to perform the actual calculation. Reasoning about the interaction and synchronization among processes using higher order logic is demonstrated.

Abacus Training Affects Math and Task Switching Abilities and Modulates Their Relationships in Chinese Children

PubMed Central

Yao, Yuan; Weng, Jian; Hu, Yuzheng; Chen, Feiyan

2015-01-01

Our previous work demonstrated that abacus-based mental calculation (AMC), a traditional Chinese calculation method, could help children improve their math abilities (e.g. basic arithmetical ability) and executive function (e.g. working memory). This study further examined the effects of long-term AMC training on math ability in visual-spatial domain and the task switching component of executive function. More importantly, this study investigated whether AMC training modulated the relationship between math abilities and task switching. The participants were seventy 7-year-old children who were randomly assigned into AMC and control groups at primary school entry. Children in AMC group received 2-hour AMC training every week since primary school entry. On the contrary, children in the control group had never received any AMC training. Math and task switching abilities were measured one year and three years respectively after AMC training began. The results showed that AMC children performed better than their peers on math abilities in arithmetical and visual-spatial domains. In addition, AMC group responded faster than control group in the switching task, while no group difference was found in switch cost. Most interestingly, group difference was present in the relationships between math abilities and switch cost. These results implied the effect of AMC training on math abilities as well as its relationship with executive function. PMID:26444689

Abacus Training Affects Math and Task Switching Abilities and Modulates Their Relationships in Chinese Children.

PubMed

Wang, Chunjie; Geng, Fengji; Yao, Yuan; Weng, Jian; Hu, Yuzheng; Chen, Feiyan

2015-01-01

Our previous work demonstrated that abacus-based mental calculation (AMC), a traditional Chinese calculation method, could help children improve their math abilities (e.g. basic arithmetical ability) and executive function (e.g. working memory). This study further examined the effects of long-term AMC training on math ability in visual-spatial domain and the task switching component of executive function. More importantly, this study investigated whether AMC training modulated the relationship between math abilities and task switching. The participants were seventy 7-year-old children who were randomly assigned into AMC and control groups at primary school entry. Children in AMC group received 2-hour AMC training every week since primary school entry. On the contrary, children in the control group had never received any AMC training. Math and task switching abilities were measured one year and three years respectively after AMC training began. The results showed that AMC children performed better than their peers on math abilities in arithmetical and visual-spatial domains. In addition, AMC group responded faster than control group in the switching task, while no group difference was found in switch cost. Most interestingly, group difference was present in the relationships between math abilities and switch cost. These results implied the effect of AMC training on math abilities as well as its relationship with executive function.

Genetic diversity studies in pea (Pisum sativum L.) using simple sequence repeat markers.

PubMed

Kumari, P; Basal, N; Singh, A K; Rai, V P; Srivastava, C P; Singh, P K

2013-03-13

The genetic diversity among 28 pea (Pisum sativum L.) genotypes was analyzed using 32 simple sequence repeat markers. A total of 44 polymorphic bands, with an average of 2.1 bands per primer, were obtained. The polymorphism information content ranged from 0.657 to 0.309 with an average of 0.493. The variation in genetic diversity among these cultivars ranged from 0.11 to 0.73. Cluster analysis based on Jaccard's similarity coefficient using the unweighted pair-group method with arithmetic mean (UPGMA) revealed 2 distinct clusters, I and II, comprising 6 and 22 genotypes, respectively. Cluster II was further differentiated into 2 subclusters, IIA and IIB, with 12 and 10 genotypes, respectively. Principal component (PC) analysis revealed results similar to those of UPGMA. The first, second, and third PCs contributed 21.6, 16.1, and 14.0% of the variation, respectively; cumulative variation of the first 3 PCs was 51.7%.

MM Algorithms for Geometric and Signomial Programming

PubMed Central

Lange, Kenneth; Zhou, Hua

2013-01-01

This paper derives new algorithms for signomial programming, a generalization of geometric programming. The algorithms are based on a generic principle for optimization called the MM algorithm. In this setting, one can apply the geometric-arithmetic mean inequality and a supporting hyperplane inequality to create a surrogate function with parameters separated. Thus, unconstrained signomial programming reduces to a sequence of one-dimensional minimization problems. Simple examples demonstrate that the MM algorithm derived can converge to a boundary point or to one point of a continuum of minimum points. Conditions under which the minimum point is unique or occurs in the interior of parameter space are proved for geometric programming. Convergence to an interior point occurs at a linear rate. Finally, the MM framework easily accommodates equality and inequality constraints of signomial type. For the most important special case, constrained quadratic programming, the MM algorithm involves very simple updates. PMID:24634545

MM Algorithms for Geometric and Signomial Programming.

PubMed

Lange, Kenneth; Zhou, Hua

2014-02-01

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

Simple mental addition in children with and without mild mental retardation.

PubMed

Janssen, R; De Boeck, P; Viaene, M; Vallaeys, L

1999-11-01

The speeded performance on simple mental addition problems of 6- and 7-year-old children with and without mild mental retardation is modeled from a person perspective and an item perspective. On the person side, it was found that a single cognitive dimension spanned the performance differences between the two ability groups. However, a discontinuity, or "jump," was observed in the performance of the normal ability group on the easier items. On the item side, the addition problems were almost perfectly ordered in difficulty according to their problem size. Differences in difficulty were explained by factors related to the difficulty of executing nonretrieval strategies. All findings were interpreted within the framework of Siegler's (e.g., R. S. Siegler & C. Shipley, 1995) model of children's strategy choices in arithmetic. Models from item response theory were used to test the hypotheses. Copyright 1999 Academic Press.

A GPU-based incompressible Navier-Stokes solver on moving overset grids

NASA Astrophysics Data System (ADS)

Chandar, Dominic D. J.; Sitaraman, Jayanarayanan; Mavriplis, Dimitri J.

2013-07-01

In pursuit of obtaining high fidelity solutions to the fluid flow equations in a short span of time, graphics processing units (GPUs) which were originally intended for gaming applications are currently being used to accelerate computational fluid dynamics (CFD) codes. With a high peak throughput of about 1 TFLOPS on a PC, GPUs seem to be favourable for many high-resolution computations. One such computation that involves a lot of number crunching is computing time accurate flow solutions past moving bodies. The aim of the present paper is thus to discuss the development of a flow solver on unstructured and overset grids and its implementation on GPUs. In its present form, the flow solver solves the incompressible fluid flow equations on unstructured/hybrid/overset grids using a fully implicit projection method. The resulting discretised equations are solved using a matrix-free Krylov solver using several GPU kernels such as gradient, Laplacian and reduction. Some of the simple arithmetic vector calculations are implemented using the CU++: An Object Oriented Framework for Computational Fluid Dynamics Applications using Graphics Processing Units, Journal of Supercomputing, 2013, doi:10.1007/s11227-013-0985-9 approach where GPU kernels are automatically generated at compile time. Results are presented for two- and three-dimensional computations on static and moving grids.

Genetic variability in Brazilian wheat cultivars assessed by microsatellite markers

PubMed Central

2009-01-01

Wheat (Triticum aestivum) is one of the most important food staples in the south of Brazil. Understanding genetic variability among the assortment of Brazilian wheat is important for breeding. The aim of this work was to molecularly characterize the thirty-six wheat cultivars recommended for various regions of Brazil, and to assess mutual genetic distances, through the use of microsatellite markers. Twenty three polymorphic microsatellite markers (PMM) delineated all 36 of the samples, revealing a total of 74 simple sequence repeat (SSR) alleles, i.e. an average of 3.2 alleles per locus. Polymorphic information content (PIC value) calculated to assess the informativeness of each marker ranged from 0.20 to 0.79, with a mean of 0.49. Genetic distances among the 36 cultivars ranged from 0.10 (between cultivars Ocepar 18 and BRS 207) to 0.88 (between cultivars CD 101 and Fudancep 46), the mean distance being 0.48. Twelve groups were obtained by using the unweighted pair-group method with arithmetic means analysis (UPGMA), and thirteen through the Tocher method. Both methods produced similar clusters, with one to thirteen cultivars per group. The results indicate that these tools may be used to protect intellectual property and for breeding and selection programs. PMID:21637519

Assessing the genetic relationships of Curcuma alismatifolia varieties using simple sequence repeat markers.

PubMed

Taheri, S; Abdullah, T L; Abdullah, N A P; Ahmad, Z; Karimi, E; Shabanimofrad, M R

2014-09-05

The genus Curcuma is a member of the ginger family (Zingiberaceae) that has recently become popular for use as flowering pot plants, both indoors and as patio and landscape plants. We used PCR-based molecular markers (SSRs) to elucidate genetic variation and relationships between five varieties of Curcuma (Curcuma alismatifolia) cultivated in Malaysia. Of the primers tested, 8 (of 17) SSR primers were selected for their reproducibility and high rates of polymorphism. The number of presumed alleles revealed by the SSR analysis ranged from two to six alleles, with a mean value of 3.25 alleles per locus. The values of HO and HE ranged from 0 to 0.8 (mean value of 0.2) and 0.1837 to 0.7755 (mean value of 0.5102), respectively. Eight SSR primers yielded 26 total amplified fragments and revealed high rates of polymorphism among the varieties studied. The polymorphic information content varied from 0.26 to 0.73. Dice's similarity coefficient was calculated for all pairwise comparisons and used to construct an unweighted pair group method with arithmetic average (UPGMA) dendrogram. Similarity coefficient values from 0.2105 to 0.6667 (with an average of 0.4386) were found among the five varieties examined. A cluster analysis of data using a UPGMA algorithm divided the five varieties/hybrids into 2 groups.

Distributed estimation of sensors position in underwater wireless sensor network

NASA Astrophysics Data System (ADS)

Zandi, Rahman; Kamarei, Mahmoud; Amiri, Hadi

2016-05-01

In this paper, a localisation method for determining the position of fixed sensor nodes in an underwater wireless sensor network (UWSN) is introduced. In this simple and range-free scheme, the node localisation is achieved by utilising an autonomous underwater vehicle (AUV) that transverses through the network deployment area, and that periodically emits a message block via four directional acoustic beams. A message block contains the actual known AUV position as well as a directional dependent marker that allows a node to identify the respective transmit beam. The beams form a fixed angle with the AUV body. If a node passively receives message blocks, it could calculate the arithmetic mean of the coordinates existing in each messages sequence, to find coordinates at two different time instants via two different successive beams. The node position can be derived from the two computed positions of the AUV. The major advantage of the proposed localisation algorithm is that it is silent, which leads to energy efficiency for sensor nodes. The proposed method does not require any synchronisation among the nodes owing to being silent. Simulation results, using MATLAB, demonstrated that the proposed method had better performance than other similar AUV-based localisation methods in terms of the rates of well-localised sensor nodes and positional root mean square error.

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…

Cost analysis of medical device spare parts

PubMed Central

Bektemur, Guven; Muzoglu, Nedim; Arici, Mehmet Ali; Karaaslan, Melike Kaya

2018-01-01

Objective: To establish estimation method on budget management of medical device spare parts and to evaluate the cost of medical device spare parts in affiliated hospitals of Istanbul Public Hospital Unions (PHUs). Methods: While this evaluation was performed, the relationship between paid cost for spare parts according to technological development level of device groups and total inventory value was used. Spare part cost analysis was carried out by using the normalized weighted arithmetic average method. Cost analysis of medical equipment spare parts of Istanbul PHUs was performed by using the data retrieved from Ministry of Health Business Intelligence Decision Support System for spending of spare parts in 2015. Results: The medical device spare part groups were categorized based on technological development. Among 1 to 6 PHUs, the cost ratios were acquired for high, middle, low and simple technology group as 17.31 – 40.08%, 29.14 – 43.36%, 22.62 – 27.44% and 8.16 – 11.89%, respectively. The ratio between the spare part and total inventory costs for 1-6 PHUs were calculated as 1.66%, 2.87%, 3.03%, 3.31%, 2.57% and 4.69% respectively. Expected rates based on normalized weighted method were obtained as follows; 5.76%, 4.67%, 5.31%, 4.87%, 4.34% and 4.27%. Conclusion: The expenditure analysis and budget planning for medical device spare parts in PHU could be predicted more accurately by taking into consideration the expected rate calculated by the normal weight method. In additon, the importance of Clinical Engineering Service Units in management of medical devices has been determined. PMID:29805429

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

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.

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.

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.…

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.

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

DOEpatents

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

2008-11-11

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

Programmable full-adder computations in communicating three-dimensional cell cultures.

PubMed

Ausländer, David; Ausländer, Simon; Pierrat, Xavier; Hellmann, Leon; Rachid, Leila; Fussenegger, Martin

2018-01-01

Synthetic biologists have advanced the design of trigger-inducible gene switches and their assembly into input-programmable circuits that enable engineered human cells to perform arithmetic calculations reminiscent of electronic circuits. By designing a versatile plug-and-play molecular-computation platform, we have engineered nine different cell populations with genetic programs, each of which encodes a defined computational instruction. When assembled into 3D cultures, these engineered cell consortia execute programmable multicellular full-adder logics in response to three trigger compounds.

Numerical Algorithm for Delta of Asian Option

PubMed Central

Zhang, Boxiang; Yu, Yang; Wang, Weiguo

2015-01-01

We study the numerical solution of the Greeks of Asian options. In particular, we derive a close form solution of Δ of Asian geometric option and use this analytical form as a control to numerically calculate Δ of Asian arithmetic option, which is known to have no explicit close form solution. We implement our proposed numerical method and compare the standard error with other classical variance reduction methods. Our method provides an efficient solution to the hedging strategy with Asian options. PMID:26266271

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.

Ballistic Evaluation of 7056 Aluminum

DTIC Science & Technology

2017-02-01

positioned 152 mm (6 inches) behind the target to determine the outcome of each shot. An impact is regarded as a complete penetration ( CP ), or loss, if...not result in a CP , it is considered a partial penetration (PP), or win. To keep results as consistent as possible, only shots conforming to the...defined as the vector sum of the projectile’s pitch and yaw. The V50 is calculated by the arithmetic mean of an equal number of CPs and PPs within an 18

An efficient algorithm for generating random number pairs drawn from a bivariate normal distribution

NASA Technical Reports Server (NTRS)

Campbell, C. W.

1983-01-01

An efficient algorithm for generating random number pairs from a bivariate normal distribution was developed. Any desired value of the two means, two standard deviations, and correlation coefficient can be selected. Theoretically the technique is exact and in practice its accuracy is limited only by the quality of the uniform distribution random number generator, inaccuracies in computer function evaluation, and arithmetic. A FORTRAN routine was written to check the algorithm and good accuracy was obtained. Some small errors in the correlation coefficient were observed to vary in a surprisingly regular manner. A simple model was developed which explained the qualities aspects of the errors.

Intangible heritage for sustainable future: mathematics in the paddy field

NASA Astrophysics Data System (ADS)

Dewanto, Stanley P.; Kusuma, Dianne A.; Nurani Ruchjana, Budi; Setiawan Abdullah, Atje

2017-10-01

Mathematics, as the only general language, can describe all phenomena on earth. Mathematics not only helps us to understand these phenomena, but it also can sustain human activities, consequently ensure that the future development is sustainable. Indonesia, with high cultural diversity, should aware to have its understanding, skills, and philosophies developed by certain societies, with long histories of interaction with their natural surroundings, which will provide a foundation for locally appropriate sustainable development. This paper discussed the condition and situation on certain area in Cigugur, Indonesia, and what skills, knowledge, and concept can be transmitted, regarding simple mathematics (arithmetic). Some examples are provided.

Penetration and Growth Rates of Mobile Phones in Developing Countries: An Analytical Classification

PubMed Central

2010-01-01

This brief paper uses a simple arithmetic framework to classify and explain the performance of developing countries in closing the absolute digital divide. Four categories are created on the basis of two variables, namely, the penetration and rate of growth of mobile phones. The paper answers questions such as: Which countries do well and badly on both variables? Are the countries in these categories drawn from specific regions or similar income levels or is the distribution more random? How can similar countries from the same region appear in two diametrically opposite categories? What does this imply for policy? PMID:20835391

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

Basic numerical capacities and prevalence of developmental dyscalculia: the Havana Survey.

PubMed

Reigosa-Crespo, Vivian; Valdés-Sosa, Mitchell; Butterworth, Brian; Estévez, Nancy; Rodríguez, Marisol; Santos, Elsa; Torres, Paul; Suárez, Ramón; Lage, Agustín

2012-01-01

The association of enumeration and number comparison capacities with arithmetical competence was examined in a large sample of children from 2nd to 9th grades. It was found that efficiency on numerical capacities predicted separately more than 25% of the variance in the individual differences on a timed arithmetical test, and this occurred for both younger and older learners. These capacities were also significant predictors of individual variations in an untimed curriculum-based math achievement test and on the teacher scores of math performance over developmental time. Based on these findings, these numerical capacities were used for estimating the prevalence and gender ratio of basic numerical deficits and developmental dyscalculia (DD) over the grade range defined above (N = 11,652 children). The extent to which DD affects the population with poor ability on calculation was also examined. For this purpose, the prevalence and gender ratio of arithmetical dysfluency (AD) were estimated in the same cohort. The estimated prevalence of DD was 3.4%, and the male:female ratio was 4:1. However, the prevalence of AD was almost 3 times as high (9.35%), and no gender differences were found (male:female ratio = 1.07:1). Basic numerical deficits affect 4.54% of school-age population and affect more boys than girls (2.4:1). The differences between the corresponding estimates were highly significant (α < .01). Based on these contrastive findings, it is concluded that DD, defined as a defective sense of numerosity, could be a distinctive disorder that affects only a portion of children with AD.

Cardiovascular and metabolic activity at rest and during psychological and physical challenge in normotensives and subjects with mildly elevated blood pressure.

PubMed

Sims, J; Carroll, D

1990-03-01

Heart rate, systolic and diastolic blood pressure, and respiratory and metabolic activity were recorded prior to and during mental arithmetic and a video game task in 20 young men with mildly elevated casual systolic blood pressures. Twenty-five unambiguously normotensive young men were tested under the same protocol. For pretask baseline physiological activity, group differences emerged for all cardiovascular and metabolic variables; thus the elevated blood pressure group displayed not only higher resting cardiovascular levels than normotensive subjects, but higher levels of metabolic activity too. With regard to change in physiological activity from rest to task, the group with mildly elevated blood pressure showed reliably larger increases in heart rate to the mental arithmetic task than the normotensive subjects. These effects, however, were not paralleled by group differences in metabolic activity increase. Physiological measures were also taken prior to and during graded dynamic exercise. The subsequent calculation of individual heart rate-oxygen consumption exercise regression lines allowed the comparison of actual and predicted heart rates during psychological challenge. The subjects with mildly elevated blood pressure displayed significantly greater discrepancies between actual and predicted heart rate values than normotensives during the psychological tasks in general and mental arithmetic in particular. Group differences in physiological activity during exercise largely reflected the pattern seen at rest. A possible exception here was systolic blood pressure. Not only were systolic blood pressure levels higher throughout the exercise phase for mildly elevated blood pressure subjects, but this group evidenced more of an increase from rest to exercise than the normotensives.

Effects of First-Grade Number Knowledge Tutoring With Contrasting Forms of Practice.

PubMed

Fuchs, Lynn S; Geary, David C; Compton, Donald L; Fuchs, Douglas; Schatschneider, Christopher; Hamlett, Carol L; Deselms, Jacqueline; Seethaler, Pamela M; Wilson, Julie; Craddock, Caitlin F; Bryant, Joan D; Luther, Kurstin; Changas, Paul

2013-01-01

The purpose of this study was to investigate the effects of 1st-grade number knowledge tutoring with contrasting forms of practice. Tutoring occurred 3 times per week for 16 weeks. In each 30-min session, the major emphasis (25 min) was number knowledge; the other 5 min provided practice in 1 of 2 forms. Nonspeeded practice reinforced relations and principles addressed in number knowledge tutoring. Speeded practice promoted quick responding and use of efficient counting procedures to generate many correct responses. At-risk students were randomly assigned to number knowledge tutoring with speeded practice ( n = 195), number knowledge tutoring with nonspeeded practice ( n = 190), and control (no tutoring, n = 206). Each tutoring condition produced stronger learning than control on all 4 mathematics outcomes. Speeded practice produced stronger learning than nonspeeded practice on arithmetic and 2-digit calculations, but effects were comparable on number knowledge and word problems. Effects of both practice conditions on arithmetic were partially mediated by increased reliance on retrieval, but only speeded practice helped at-risk children compensate for weak reasoning ability.

Passive Resistor Temperature Compensation for a High-Temperature Piezoresistive Pressure Sensor.

PubMed

Yao, Zong; Liang, Ting; Jia, Pinggang; Hong, Yingping; Qi, Lei; Lei, Cheng; Zhang, Bin; Li, Wangwang; Zhang, Diya; Xiong, Jijun

2016-07-22

The main limitation of high-temperature piezoresistive pressure sensors is the variation of output voltage with operating temperature, which seriously reduces their measurement accuracy. This paper presents a passive resistor temperature compensation technique whose parameters are calculated using differential equations. Unlike traditional experiential arithmetic, the differential equations are independent of the parameter deviation among the piezoresistors of the microelectromechanical pressure sensor and the residual stress caused by the fabrication process or a mismatch in the thermal expansion coefficients. The differential equations are solved using calibration data from uncompensated high-temperature piezoresistive pressure sensors. Tests conducted on the calibrated equipment at various temperatures and pressures show that the passive resistor temperature compensation produces a remarkable effect. Additionally, a high-temperature signal-conditioning circuit is used to improve the output sensitivity of the sensor, which can be reduced by the temperature compensation. Compared to traditional experiential arithmetic, the proposed passive resistor temperature compensation technique exhibits less temperature drift and is expected to be highly applicable for pressure measurements in harsh environments with large temperature variations.

Passive Resistor Temperature Compensation for a High-Temperature Piezoresistive Pressure Sensor

PubMed Central

Yao, Zong; Liang, Ting; Jia, Pinggang; Hong, Yingping; Qi, Lei; Lei, Cheng; Zhang, Bin; Li, Wangwang; Zhang, Diya; Xiong, Jijun

2016-01-01

The main limitation of high-temperature piezoresistive pressure sensors is the variation of output voltage with operating temperature, which seriously reduces their measurement accuracy. This paper presents a passive resistor temperature compensation technique whose parameters are calculated using differential equations. Unlike traditional experiential arithmetic, the differential equations are independent of the parameter deviation among the piezoresistors of the microelectromechanical pressure sensor and the residual stress caused by the fabrication process or a mismatch in the thermal expansion coefficients. The differential equations are solved using calibration data from uncompensated high-temperature piezoresistive pressure sensors. Tests conducted on the calibrated equipment at various temperatures and pressures show that the passive resistor temperature compensation produces a remarkable effect. Additionally, a high-temperature signal-conditioning circuit is used to improve the output sensitivity of the sensor, which can be reduced by the temperature compensation. Compared to traditional experiential arithmetic, the proposed passive resistor temperature compensation technique exhibits less temperature drift and is expected to be highly applicable for pressure measurements in harsh environments with large temperature variations. PMID:27455271

Ambulatory stress monitoring with a wearable bluetooth electrocardiographic device.

PubMed

Hong, Sungyoup; Yang, Youngmo; Lee, Jangyoung; Yang, Heebum; Park, Kyungnam; Lee, Suyeul; Lee, Inbum; Jang, Yongwon

2010-01-01

We tried to monitor stress by using a wearable one channel ECG device that can send ECG signals through Bluetooth wireless communication. Noxious physical and mental arithmetic stress was given three times repeatedly to healthy adults, and cortisol and catecholamines were measured serially from peripheral blood. At the same time, time domain and frequency domain parameters of heart rate variability (HRV) were calculated by taking precordial electrocardiogram. The intensity of correlation between subjective visual analogue scale (VAS) and catecholamine, cortisol, and HRV parameters according to stress was analyzed by using concordance correlation coefficients. The HRV triangular index and LF/HF ratio had high concordance correlation with the degree of stress in the physical stress model. In mental arithmetic stress model, the HRV triangular index and LF/HF ratio had weak concordance correlation with the degree of stress, and it had lower predictability than epinephrine. In both models, cortisol had some correlation with catecholamine, but it had little correlation with HRV parameters. HRV parameters using wearable one channel ECG device can be useful in predicting acute stress and also in many other areas.

Effects of First-Grade Number Knowledge Tutoring With Contrasting Forms of Practice

PubMed Central

Fuchs, Lynn S.; Geary, David C.; Compton, Donald L.; Fuchs, Douglas; Schatschneider, Christopher; Hamlett, Carol L.; DeSelms, Jacqueline; Seethaler, Pamela M.; Wilson, Julie; Craddock, Caitlin F.; Bryant, Joan D.; Luther, Kurstin; Changas, Paul

2013-01-01

The purpose of this study was to investigate the effects of 1st-grade number knowledge tutoring with contrasting forms of practice. Tutoring occurred 3 times per week for 16 weeks. In each 30-min session, the major emphasis (25 min) was number knowledge; the other 5 min provided practice in 1 of 2 forms. Nonspeeded practice reinforced relations and principles addressed in number knowledge tutoring. Speeded practice promoted quick responding and use of efficient counting procedures to generate many correct responses. At-risk students were randomly assigned to number knowledge tutoring with speeded practice (n = 195), number knowledge tutoring with nonspeeded practice (n = 190), and control (no tutoring, n = 206). Each tutoring condition produced stronger learning than control on all 4 mathematics outcomes. Speeded practice produced stronger learning than nonspeeded practice on arithmetic and 2-digit calculations, but effects were comparable on number knowledge and word problems. Effects of both practice conditions on arithmetic were partially mediated by increased reliance on retrieval, but only speeded practice helped at-risk children compensate for weak reasoning ability. PMID:24065865

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.

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

Longitudinal Brain Development of Numerical Skills in Typically Developing Children and Children with Developmental Dyscalculia.

PubMed

McCaskey, Ursina; von Aster, Michael; Maurer, Urs; Martin, Ernst; O'Gorman Tuura, Ruth; Kucian, Karin

2017-01-01

Developmental dyscalculia (DD) is a learning disability affecting the acquisition of numerical-arithmetical skills. Studies report persistent deficits in number processing and aberrant functional activation of the fronto-parietal numerical network in DD. However, the neural development of numerical abilities has been scarcely investigated. The present paper provides a first attempt to investigate behavioral and neural trajectories of numerical abilities longitudinally in typically developing (TD) and DD children. During a study period of 4 years, 28 children (8-11 years) were evaluated twice by means of neuropsychological tests and a numerical order fMRI paradigm. Over time, TD children improved in numerical abilities and showed a consistent and well-developed fronto-parietal network. In contrast, DD children revealed persistent deficits in number processing and arithmetic. Brain imaging results of the DD group showed an age-related activation increase in parietal regions (intraparietal sulcus), pointing to a delayed development of number processing areas. Besides, an activation increase in frontal areas was observed over time, indicating the use of compensatory mechanisms. In conclusion, results suggest a continuation in neural development of number representation in DD, whereas the neural network for simple ordinal number estimation seems to be stable or show only subtle changes in TD children over time.

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

PubMed

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

2017-08-01

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

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.

Longitudinal Brain Development of Numerical Skills in Typically Developing Children and Children with Developmental Dyscalculia

PubMed Central

McCaskey, Ursina; von Aster, Michael; Maurer, Urs; Martin, Ernst; O'Gorman Tuura, Ruth; Kucian, Karin

2018-01-01

Developmental dyscalculia (DD) is a learning disability affecting the acquisition of numerical-arithmetical skills. Studies report persistent deficits in number processing and aberrant functional activation of the fronto-parietal numerical network in DD. However, the neural development of numerical abilities has been scarcely investigated. The present paper provides a first attempt to investigate behavioral and neural trajectories of numerical abilities longitudinally in typically developing (TD) and DD children. During a study period of 4 years, 28 children (8–11 years) were evaluated twice by means of neuropsychological tests and a numerical order fMRI paradigm. Over time, TD children improved in numerical abilities and showed a consistent and well-developed fronto-parietal network. In contrast, DD children revealed persistent deficits in number processing and arithmetic. Brain imaging results of the DD group showed an age-related activation increase in parietal regions (intraparietal sulcus), pointing to a delayed development of number processing areas. Besides, an activation increase in frontal areas was observed over time, indicating the use of compensatory mechanisms. In conclusion, results suggest a continuation in neural development of number representation in DD, whereas the neural network for simple ordinal number estimation seems to be stable or show only subtle changes in TD children over time. PMID:29354041

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.

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.

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.

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...

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.

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.

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

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.

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.

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

Mapping of Arithmetic Processing by Navigated Repetitive Transcranial Magnetic Stimulation in Patients with Parietal Brain Tumors and Correlation with Postoperative Outcome.

PubMed

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

2018-06-01

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

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.

Finite basis representations with nondirect product basis functions having structure similar to that of spherical harmonics.

PubMed

Czakó, Gábor; Szalay, Viktor; Császár, Attila G

2006-01-07

The currently most efficient finite basis representation (FBR) method [Corey et al., in Numerical Grid Methods and Their Applications to Schrodinger Equation, NATO ASI Series C, edited by C. Cerjan (Kluwer Academic, New York, 1993), Vol. 412, p. 1; Bramley et al., J. Chem. Phys. 100, 6175 (1994)] designed specifically to deal with nondirect product bases of structures phi(n) (l)(s)f(l)(u), chi(m) (l)(t)phi(n) (l)(s)f(l)(u), etc., employs very special l-independent grids and results in a symmetric FBR. While highly efficient, this method is not general enough. For instance, it cannot deal with nondirect product bases of the above structure efficiently if the functions phi(n) (l)(s) [and/or chi(m) (l)(t)] are discrete variable representation (DVR) functions of the infinite type. The optimal-generalized FBR(DVR) method [V. Szalay, J. Chem. Phys. 105, 6940 (1996)] is designed to deal with general, i.e., direct and/or nondirect product, bases and grids. This robust method, however, is too general, and its direct application can result in inefficient computer codes [Czako et al., J. Chem. Phys. 122, 024101 (2005)]. It is shown here how the optimal-generalized FBR method can be simplified in the case of nondirect product bases of structures phi(n) (l)(s)f(l)(u), chi(m) (l)(t)phi(n) (l)(s)f(l)(u), etc. As a result the commonly used symmetric FBR is recovered and simplified nonsymmetric FBRs utilizing very special l-dependent grids are obtained. The nonsymmetric FBRs are more general than the symmetric FBR in that they can be employed efficiently even when the functions phi(n) (l)(s) [and/or chi(m) (l)(t)] are DVR functions of the infinite type. Arithmetic operation counts and a simple numerical example presented show unambiguously that setting up the Hamiltonian matrix requires significantly less computer time when using one of the proposed nonsymmetric FBRs than that in the symmetric FBR. Therefore, application of this nonsymmetric FBR is more efficient than that of the symmetric FBR when one wants to diagonalize the Hamiltonian matrix either by a direct or via a basis-set contraction method. Enormous decrease of computer time can be achieved, with respect to a direct application of the optimal-generalized FBR, by employing one of the simplified nonsymmetric FBRs as is demonstrated in noniterative calculations of the low-lying vibrational energy levels of the H3+ molecular ion. The arithmetic operation counts of the Hamiltonian matrix vector products and the properties of a recently developed diagonalization method [Andreozzi et al., J. Phys. A Math. Gen. 35, L61 (2002)] suggest that the nonsymmetric FBR applied along with this particular diagonalization method is suitable to large scale iterative calculations. Whether or not the nonsymmetric FBR is competitive with the symmetric FBR in large-scale iterative calculations still has to be investigated numerically.

Relationships between magnitude representation, counting and memory in 4- to 7-year-old children: a developmental study.

PubMed

Soltész, Fruzsina; Szucs, Dénes; Szucs, Lívia

2010-02-18

The development of an evolutionarily grounded analogue magnitude representation linked to the parietal lobes is frequently thought to be a major factor in the arithmetic development of humans. We investigated the relationship between counting and the development of magnitude representation in children, assessing also children's knowledge of number symbols, their arithmetic fact retrieval, their verbal skills, and their numerical and verbal short-term memory. The magnitude representation was tested by a non-symbolic magnitude comparison task. We have perfected previous experimental designs measuring magnitude discrimination skills in 65 children kindergarten (4-7-year-olds) by controlling for several variables which were not controlled for in previous similar research. We also used a large number of trials which allowed for running a full factorial ANOVA including all relevant factors. Tests of verbal counting, of short term memory, of number knowledge, of problem solving abilities and of verbal fluency were administered and correlated with performance in the magnitude comparison task. Verbal counting knowledge and performance on simple arithmetic tests did not correlate with non-symbolic magnitude comparison at any age. Older children performed successfully on the number comparison task, showing behavioural patterns consistent with an analogue magnitude representation. In contrast, 4-year-olds were unable to discriminate number independently of task-irrelevant perceptual variables. Sensitivity to irrelevant perceptual features of the magnitude discrimination task was also affected by age, and correlated with memory, suggesting that more general cognitive abilities may play a role in performance in magnitude comparison tasks. We conclude that young children are not able to discriminate numerical magnitudes when co-varying physical magnitudes are methodically pitted against number. We propose, along with others, that a rather domain general magnitude representation provides the later basis for a specialized representation of numerical magnitudes. For this representational specialization, the acquisition of the concept of abstract numbers, together with the development of other cognitive abilities, is indispensable.

Relationships between magnitude representation, counting and memory in 4- to 7-year-old children: A developmental study

PubMed Central

2010-01-01

Background The development of an evolutionarily grounded analogue magnitude representation linked to the parietal lobes is frequently thought to be a major factor in the arithmetic development of humans. We investigated the relationship between counting and the development of magnitude representation in children, assessing also children's knowledge of number symbols, their arithmetic fact retrieval, their verbal skills, and their numerical and verbal short-term memory. Methods The magnitude representation was tested by a non-symbolic magnitude comparison task. We have perfected previous experimental designs measuring magnitude discrimination skills in 65 children kindergarten (4-7-year-olds) by controlling for several variables which were not controlled for in previous similar research. We also used a large number of trials which allowed for running a full factorial ANOVA including all relevant factors. Tests of verbal counting, of short term memory, of number knowledge, of problem solving abilities and of verbal fluency were administered and correlated with performance in the magnitude comparison task. Results and discussion Verbal counting knowledge and performance on simple arithmetic tests did not correlate with non-symbolic magnitude comparison at any age. Older children performed successfully on the number comparison task, showing behavioural patterns consistent with an analogue magnitude representation. In contrast, 4-year-olds were unable to discriminate number independently of task-irrelevant perceptual variables. Sensitivity to irrelevant perceptual features of the magnitude discrimination task was also affected by age, and correlated with memory, suggesting that more general cognitive abilities may play a role in performance in magnitude comparison tasks. Conclusion We conclude that young children are not able to discriminate numerical magnitudes when co-varying physical magnitudes are methodically pitted against number. We propose, along with others, that a rather domain general magnitude representation provides the later basis for a specialized representation of numerical magnitudes. For this representational specialization, the acquisition of the concept of abstract numbers, together with the development of other cognitive abilities, is indispensable. PMID:20167066

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.

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.

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.

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

FPGA-Based Stochastic Echo State Networks for Time-Series Forecasting.

PubMed

Alomar, Miquel L; Canals, Vincent; Perez-Mora, Nicolas; Martínez-Moll, Víctor; Rosselló, Josep L

2016-01-01

Hardware implementation of artificial neural networks (ANNs) allows exploiting the inherent parallelism of these systems. Nevertheless, they require a large amount of resources in terms of area and power dissipation. Recently, Reservoir Computing (RC) has arisen as a strategic technique to design recurrent neural networks (RNNs) with simple learning capabilities. In this work, we show a new approach to implement RC systems with digital gates. The proposed method is based on the use of probabilistic computing concepts to reduce the hardware required to implement different arithmetic operations. The result is the development of a highly functional system with low hardware resources. The presented methodology is applied to chaotic time-series forecasting.

Registration of Heat Capacity Mapping Mission day and night images

NASA Technical Reports Server (NTRS)

Watson, K.; Hummer-Miller, S.; Sawatzky, D. L. (Principal Investigator)

1982-01-01

Neither iterative registration, using drainage intersection maps for control, nor cross correlation techniques were satisfactory in registering day and night HCMM imagery. A procedure was developed which registers the image pairs by selecting control points and mapping the night thermal image to the daytime thermal and reflectance images using an affine transformation on a 1300 by 1100 pixel image. The resulting image registration is accurate to better than two pixels (RMS) and does not exhibit the significant misregistration that was noted in the temperature-difference and thermal-inertia products supplied by NASA. The affine transformation was determined using simple matrix arithmetic, a step that can be performed rapidly on a minicomputer.

[A design of simple ventilator control system based on LabVIEW].

PubMed

Pei, Baoqing; Xu, Shengwei; Li, Hui; Li, Deyu; Pei, Yidong; He, Haixing

2011-01-01

This paper designed a ventilator control system to control proportional valves and motors. It used LabVIEW to control the object mentioned above and design ,validate, evaluate arithmetic, and establish hardware in loop platform. There are two system' s hierarchies. The high layer was used to run non-real time program and the low layer was used to run real time program. The two layers communicated through TCP/IP net. The program can be divided into several modules, which can be expanded and maintained easily. And the harvest in the prototype designing can be seamlessly used to embedded products. From all above, this system was useful in employing OEM products.

FPGA-Based Stochastic Echo State Networks for Time-Series Forecasting

PubMed Central

Alomar, Miquel L.; Canals, Vincent; Perez-Mora, Nicolas; Martínez-Moll, Víctor; Rosselló, Josep L.

2016-01-01

Hardware implementation of artificial neural networks (ANNs) allows exploiting the inherent parallelism of these systems. Nevertheless, they require a large amount of resources in terms of area and power dissipation. Recently, Reservoir Computing (RC) has arisen as a strategic technique to design recurrent neural networks (RNNs) with simple learning capabilities. In this work, we show a new approach to implement RC systems with digital gates. The proposed method is based on the use of probabilistic computing concepts to reduce the hardware required to implement different arithmetic operations. The result is the development of a highly functional system with low hardware resources. The presented methodology is applied to chaotic time-series forecasting. PMID:26880876

Fidelity for kicked atoms with gravity near a quantum resonance.

PubMed

Dubertrand, Rémy; Guarneri, Italo; Wimberger, Sandro

2012-03-01

Kicked atoms under a constant Stark or gravity field are investigated for experimental setups with cold and ultracold atoms. The parametric stability of the quantum dynamics is studied using the fidelity. In the case of a quantum resonance, it is shown that the behavior of the fidelity depends on arithmetic properties of the gravity parameter. Close to a quantum resonance, the long-time asymptotics of the fidelity is studied by means of a pseudoclassical approximation introduced by Fishman et al. [J. Stat. Phys. 110, 911 (2003)]. The long-time decay of fidelity arises from the tunneling out of pseudoclassical stable islands, and a simple ansatz is proposed which satisfactorily reproduces the main features observed in numerical simulations.

Application of a simple cerebellar model to geologic surface mapping

USGS Publications Warehouse

Hagens, A.; Doveton, J.H.

1991-01-01

Neurophysiological research into the structure and function of the cerebellum has inspired computational models that simulate information processing associated with coordination and motor movement. The cerebellar model arithmetic computer (CMAC) has a design structure which makes it readily applicable as an automated mapping device that "senses" a surface, based on a sample of discrete observations of surface elevation. The model operates as an iterative learning process, where cell weights are continuously modified by feedback to improve surface representation. The storage requirements are substantially less than those of a conventional memory allocation, and the model is extended easily to mapping in multidimensional space, where the memory savings are even greater. ?? 1991.

Genetic diversity and relationship analysis of Gossypium arboreum accessions.

PubMed

Liu, F; Zhou, Z L; Wang, C Y; Wang, Y H; Cai, X Y; Wang, X X; Zhang, Z S; Wang, K B

2015-11-19

Simple sequence repeat techniques were used to identify the genetic diversity of 101 Gossypium arboreum accessions collected from India, Vietnam, and the southwest of China (Guizhou, Guangxi, and Yunnan provinces). Twenty-six pairs of SSR primers produced a total of 103 polymorphic loci with an average of 3.96 polymorphic loci per primer. The average of the effective number of alleles, Nei's gene diversity, and Shannon's information index were 0.59, 0.2835, and 0.4361, respectively. The diversity varied among different geographic regions. The result of principal component analysis was consistent with that of unweighted pair group method with arithmetic mean clustering analysis. The 101 G. arboreum accessions were clustered into 2 groups.

On Matrices, Automata, and Double Counting

NASA Astrophysics Data System (ADS)

Beldiceanu, Nicolas; Carlsson, Mats; Flener, Pierre; Pearson, Justin

Matrix models are ubiquitous for constraint problems. Many such problems have a matrix of variables M, with the same constraint defined by a finite-state automaton A on each row of M and a global cardinality constraint gcc on each column of M. We give two methods for deriving, by double counting, necessary conditions on the cardinality variables of the gcc constraints from the automaton A. The first method yields linear necessary conditions and simple arithmetic constraints. The second method introduces the cardinality automaton, which abstracts the overall behaviour of all the row automata and can be encoded by a set of linear constraints. We evaluate the impact of our methods on a large set of nurse rostering problem instances.

Calculating degree-based topological indices of dominating David derived networks

NASA Astrophysics Data System (ADS)

Ahmad, Muhammad Saeed; Nazeer, Waqas; Kang, Shin Min; Imran, Muhammad; Gao, Wei

2017-12-01

An important area of applied mathematics is the Chemical reaction network theory. The behavior of real world problems can be modeled by using this theory. Due to applications in theoretical chemistry and biochemistry, it has attracted researchers since its foundation. It also attracts pure mathematicians because it involves interesting mathematical structures. In this report, we compute newly defined topological indices, namely, Arithmetic-Geometric index (AG1 index), SK index, SK1 index, and SK2 index of the dominating David derived networks [1, 2, 3, 4, 5].

An improved multiple linear regression and data analysis computer program package

NASA Technical Reports Server (NTRS)

Sidik, S. M.

1972-01-01

NEWRAP, an improved version of a previous multiple linear regression program called RAPIER, CREDUC, and CRSPLT, allows for a complete regression analysis including cross plots of the independent and dependent variables, correlation coefficients, regression coefficients, analysis of variance tables, t-statistics and their probability levels, rejection of independent variables, plots of residuals against the independent and dependent variables, and a canonical reduction of quadratic response functions useful in optimum seeking experimentation. A major improvement over RAPIER is that all regression calculations are done in double precision arithmetic.

Development of retrospective quantitative and qualitative job-exposure matrices for exposures at a beryllium processing facility.

PubMed

Couch, James R; Petersen, Martin; Rice, Carol; Schubauer-Berigan, Mary K

2011-05-01

To construct a job-exposure matrix (JEM) for an Ohio beryllium processing facility between 1953 and 2006 and to evaluate temporal changes in airborne beryllium exposures. Quantitative area- and breathing-zone-based exposure measurements of airborne beryllium were made between 1953 and 2006 and used by plant personnel to estimate daily weighted average (DWA) exposure concentrations for sampled departments and operations. These DWA measurements were used to create a JEM with 18 exposure metrics, which was linked to the plant cohort consisting of 18,568 unique job, department and year combinations. The exposure metrics ranged from quantitative metrics (annual arithmetic/geometric average DWA exposures, maximum DWA and peak exposures) to descriptive qualitative metrics (chemical beryllium species and physical form) to qualitative assignment of exposure to other risk factors (yes/no). Twelve collapsed job titles with long-term consistent industrial hygiene samples were evaluated using regression analysis for time trends in DWA estimates. Annual arithmetic mean DWA estimates (overall plant-wide exposures including administration, non-production, and production estimates) for the data by decade ranged from a high of 1.39 μg/m(3) in the 1950s to a low of 0.33 μg/m(3) in the 2000s. Of the 12 jobs evaluated for temporal trend, the average arithmetic DWA mean was 2.46 μg/m(3) and the average geometric mean DWA was 1.53 μg/m(3). After the DWA calculations were log-transformed, 11 of the 12 had a statistically significant (p < 0.05) decrease in reported exposure over time. The constructed JEM successfully differentiated beryllium exposures across jobs and over time. This is the only quantitative JEM containing exposure estimates (average and peak) for the entire plant history.

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.

A decoding procedure for the Reed-Solomon codes

NASA Technical Reports Server (NTRS)

Lim, R. S.

1978-01-01

A decoding procedure is described for the (n,k) t-error-correcting Reed-Solomon (RS) code, and an implementation of the (31,15) RS code for the I4-TENEX central system. This code can be used for error correction in large archival memory systems. The principal features of the decoder are a Galois field arithmetic unit implemented by microprogramming a microprocessor, and syndrome calculation by using the g(x) encoding shift register. Complete decoding of the (31,15) code is expected to take less than 500 microsecs. The syndrome calculation is performed by hardware using the encoding shift register and a modified Chien search. The error location polynomial is computed by using Lin's table, which is an interpretation of Berlekamp's iterative algorithm. The error location numbers are calculated by using the Chien search. Finally, the error values are computed by using Forney's method.

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.

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

Spectroscopic properties of Er3+-doped fluorotellurite glasses containing various modifiers

NASA Astrophysics Data System (ADS)

Burtan-Gwizdała, Bożena; Reben, Manuela; Cisowski, Jan; Grelowska, Iwona; Yousef, El Sayed; Algarni, Hamed; Lisiecki, Radosław; Nosidlak, Natalia

2017-11-01

We have investigated the optical and spectroscopic properties of new Er3+-doped fluorotellurite glasses with the basic molar composition 75%TeO2-10%P2O5-10%ZnO-5%PbF2, modified by replacing 5%TeO2 by four various metal oxides, namely MgO, PbO, SrO and CdO. The ellipsometric data have provided a Sellmeier-type dispersion relation of the refractive index of the investigated glasses. The optical absorption edge has been described within the Urbach approach, while the absorption and fluorescence spectra have been analyzed in terms of the standard Judd-Ofelt theory along with the photoluminescence decay of the 4I13/2 and 4S3/2 levels of the Er3+ ion. The absorption and emission spectra of the 4I15/2 ↔ 4I13/2 infrared transition have been analyzed within the McCumber theory to yield the peak emission cross-section and figure of merit (FOM) for the amplifier gain. It appears that the glass containing MgO as a modifier is characterized by the largest FOM suggesting that the fluorotellurite matrix with this oxide can be a good novel host for Er3+ ion doping. Finally, we propose a new simple method to calculate the mean transition energy of the McCumber approach as the arithmetic average of the barycenter wavenumbers of absorption and emission spectra.

Social support and loneliness in college students: effects on pulse pressure reactivity to acute stress.

PubMed

O'Donovan, Aoife; Hughes, Brian

2007-01-01

Socially supportive relationships at university may buffer against psychological stress in students, particularly in those experiencing loneliness. To examine the relation of social support at university and loneliness with pulse pressure (PP) reactivity to acute psychological stress in a sample of first-year undergraduate students. Sixty-five female, adolescent, first-year university students. Pulse pressure (PP) was calculated as the arithmetic difference between systolic blood pressure and diastolic blood pressure, which were measured during a resting baseline and during a stressful reading task. The difference between baseline and reading task PP represents PP reactivity. The Social Support at University Scale (SSUS) was used to assess social support availability in university, and the Revised UCLA Loneliness Scale was used to assess loneliness. Hierarchical linear regression was used to examine main and interactive effects of SSUS and loneliness on PP change scores, and simple slopes were computed to assist in the interpretation of interaction effects. Social support at university was associated with lower PP reactivity in students reporting medium (t = -2.03, p = .04) or high levels of loneliness (t = -2.93, p = .004), but not in those reporting low levels of loneliness (t = -0.20, p = .83). Psychosocial interventions designed to increase social support available at university, and targeted at students experiencing loneliness may buffer against the harmful effects of acute stressors in lonely first-year students.

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

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

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 language of arithmetic across the hemispheres: An event-related potential investigation.

PubMed

Dickson, Danielle S; Federmeier, Kara D

2017-05-01

Arithmetic expressions, like verbal sentences, incrementally lead readers to anticipate potential appropriate completions. Existing work in the language domain has helped us understand how the two hemispheres differently participate in and contribute to the cognitive process of sentence reading, but comparatively little work has been done with mathematical equation processing. In this study, we address this gap by examining the ERP response to provided answers to simple multiplication problems, which varied both in levels of correctness (given an equation context) and in visual field of presentation (joint attention in central presentation, or biased processing to the left or right hemisphere through contralateral visual field presentation). When answers were presented to any of the visual fields (hemispheres), there was an effect of correctness prior to the traditional N400 timewindow, which we interpret as a P300 in response to a detected target item (the correct answer). In addition to this response, equation answers also elicited a late positive complex (LPC) for incorrect answers. Notably, this LPC effect was most prominent in the left visual field (right hemisphere), and it was also sensitive to the confusability of the wrong answer - incorrect answers that were closely related to the correct answer elicited a smaller LPC. This suggests a special, prolonged role for the right hemisphere during answer evaluation. Copyright © 2017 Elsevier B.V. All rights reserved.

Memristive effects in oxygenated amorphous carbon nanodevices

NASA Astrophysics Data System (ADS)

Bachmann, T. A.; Koelmans, W. W.; Jonnalagadda, V. P.; Le Gallo, M.; Santini, C. A.; Sebastian, A.; Eleftheriou, E.; Craciun, M. F.; Wright, C. D.

2018-01-01

Computing with resistive-switching (memristive) memory devices has shown much recent progress and offers an attractive route to circumvent the von-Neumann bottleneck, i.e. the separation of processing and memory, which limits the performance of conventional computer architectures. Due to their good scalability and nanosecond switching speeds, carbon-based resistive-switching memory devices could play an important role in this respect. However, devices based on elemental carbon, such as tetrahedral amorphous carbon or ta-C, typically suffer from a low cycling endurance. A material that has proven to be capable of combining the advantages of elemental carbon-based memories with simple fabrication methods and good endurance performance for binary memory applications is oxygenated amorphous carbon, or a-CO x . Here, we examine the memristive capabilities of nanoscale a-CO x devices, in particular their ability to provide the multilevel and accumulation properties that underpin computing type applications. We show the successful operation of nanoscale a-CO x memory cells for both the storage of multilevel states (here 3-level) and for the provision of an arithmetic accumulator. We implement a base-16, or hexadecimal, accumulator and show how such a device can carry out hexadecimal arithmetic and simultaneously store the computed result in the self-same a-CO x cell, all using fast (sub-10 ns) and low-energy (sub-pJ) input pulses.

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

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

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

Human computers: the first pioneers of the information age.

PubMed

Grier, D A

2001-03-01

Before computers were machines, they were people. They were men and women, young and old, well educated and common. They were the workers who convinced scientists that large-scale calculation had value. Long before Presper Eckert and John Mauchly built the ENIAC at the Moore School of Electronics, Philadelphia, or Maurice Wilkes designed the EDSAC for Manchester University, human computers had created the discipline of computation. They developed numerical methodologies and proved them on practical problems. These human computers were not savants or calculating geniuses. Some knew little more than basic arithmetic. A few were near equals of the scientists they served and, in a different time or place, might have become practicing scientists had they not been barred from a scientific career by their class, education, gender or ethnicity.

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.

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.

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 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.

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.