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.

Optical modular arithmetic

NASA Astrophysics Data System (ADS)

Pavlichin, Dmitri S.; Mabuchi, Hideo

2014-06-01

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

A novel approach for SEMG signal classification with adaptive local binary patterns.

PubMed

Ertuğrul, Ömer Faruk; Kaya, Yılmaz; Tekin, Ramazan

2016-07-01

Feature extraction plays a major role in the pattern recognition process, and this paper presents a novel feature extraction approach, adaptive local binary pattern (aLBP). aLBP is built on the local binary pattern (LBP), which is an image processing method, and one-dimensional local binary pattern (1D-LBP). In LBP, each pixel is compared with its neighbors. Similarly, in 1D-LBP, each data in the raw is judged against its neighbors. 1D-LBP extracts feature based on local changes in the signal. Therefore, it has high a potential to be employed in medical purposes. Since, each action or abnormality, which is recorded in SEMG signals, has its own pattern, and via the 1D-LBP these (hidden) patterns may be detected. But, the positions of the neighbors in 1D-LBP are constant depending on the position of the data in the raw. Also, both LBP and 1D-LBP are very sensitive to noise. Therefore, its capacity in detecting hidden patterns is limited. To overcome these drawbacks, aLBP was proposed. In aLBP, the positions of the neighbors and their values can be assigned adaptively via the down-sampling and the smoothing coefficients. Therefore, the potential to detect (hidden) patterns, which may express an illness or an action, is really increased. To validate the proposed feature extraction approach, two different datasets were employed. Achieved accuracies by the proposed approach were higher than obtained results by employed popular feature extraction approaches and the reported results in the literature. Obtained accuracy results were brought out that the proposed method can be employed to investigate SEMG signals. In summary, this work attempts to develop an adaptive feature extraction scheme that can be utilized for extracting features from local changes in different categories of time-varying signals.

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.

SEARCHING FOR BINARY Y DWARFS WITH THE GEMINI MULTI-CONJUGATE ADAPTIVE OPTICS SYSTEM (GeMS)

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

Opitz, Daniela; Tinney, C. G.; Faherty, Jacqueline K.

The NASA Wide-field Infrared Survey Explorer (WISE) has discovered almost all the known members of the new class of Y-type brown dwarfs. Most of these Y dwarfs have been identified as isolated objects in the field. It is known that binaries with L- and T-type brown dwarf primaries are less prevalent than either M-dwarf or solar-type primaries, they tend to have smaller separations and are more frequently detected in near-equal mass configurations. The binary statistics for Y-type brown dwarfs, however, are sparse, and so it is unclear if the same trends that hold for L- and T-type brown dwarfs alsomore » hold for Y-type ones. In addition, the detection of binary companions to very cool Y dwarfs may well be the best means available for discovering even colder objects. We present results for binary properties of a sample of five WISE Y dwarfs with the Gemini Multi-Conjugate Adaptive Optics System. We find no evidence for binary companions in these data, which suggests these systems are not equal-luminosity (or equal-mass) binaries with separations larger than ∼0.5–1.9 AU. For equal-mass binaries at an age of 5 Gyr, we find that the binary binding energies ruled out by our observations (i.e., 10{sup 42} erg) are consistent with those observed in previous studies of hotter ultra-cool dwarfs.« less

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.

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

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

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…

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),…

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…

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…

Comparison of NRZ and duo-binary format in adaptive equalization assisted 10G-optics based 25G-EPON

NASA Astrophysics Data System (ADS)

Xia, Junqi; Li, Zhengxuan; Li, Yingchun; Xu, Tingting; Chen, Jian; Song, Yingxiong; Wang, Min

2018-03-01

We investigate and compare the requirements of FFE/DFE based adaptive equalization techniques for NRZ and Duo-binary based 25-Gb/s transmission, which are two of the most promising schemes for 25G-EPON. A 25-Gb/s transmission system based on 10G optical transceivers is demonstrated and the performance of only FFE and combination of FFE and DFE with different number of taps are compared with two modulation formats. The FFE/DFE based Duo-binary receiver shows better performance than NRZ receiver. For Duo-binary receiver, only 13-tap FFE is needed for BtB case and the combination of 17-tap FFE and 5-tap DFE can achieve a sensitivity of -23.45 dBm in 25 km transmission case, which is ∼0.6 dB better than the best performance of NRZ equalization. In addition, the requirements of training sequence length for FFE/DFE based adaptive equalization is verified. Experimental results show that 400 symbols training length is optimal for the two modulations, which shows a small packet preamble in up-stream burst-mode transmission.

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…

An adaptable binary entropy coder

NASA Technical Reports Server (NTRS)

Kiely, A.; Klimesh, M.

2001-01-01

We present a novel entropy coding technique which is based on recursive interleaving of variable-to-variable length binary source codes. We discuss code design and performance estimation methods, as well as practical encoding and decoding algorithms.

Efficient algorithms for dilated mappings of binary trees

NASA Technical Reports Server (NTRS)

Iqbal, M. Ashraf

1990-01-01

The problem is addressed to find a 1-1 mapping of the vertices of a binary tree onto those of a target binary tree such that the son of a node on the first binary tree is mapped onto a descendent of the image of that node in the second binary tree. There are two natural measures of the cost of this mapping, namely the dilation cost, i.e., the maximum distance in the target binary tree between the images of vertices that are adjacent in the original tree. The other measure, expansion cost, is defined as the number of extra nodes/edges to be added to the target binary tree in order to ensure a 1-1 mapping. An efficient algorithm to find a mapping of one binary tree onto another is described. It is shown that it is possible to minimize one cost of mapping at the expense of the other. This problem arises when designing pipelined arithmetic logic units (ALU) for special purpose computers. The pipeline is composed of ALU chips connected in the form of a binary tree. The operands to the pipeline can be supplied to the leaf nodes of the binary tree which then process and pass the results up to their parents. The final result is available at the root. As each new application may require a distinct nesting of operations, it is useful to be able to find a good mapping of a new binary tree over existing ALU tree. Another problem arises if every distinct required binary tree is known beforehand. Here it is useful to hardwire the pipeline in the form of a minimal supertree that contains all required binary trees.

Non-symbolic arithmetic in adults and young children.

PubMed

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

2006-01-01

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

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…

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.

All-optical conversion scheme from binary to its MTN form with the help of nonlinear material based tree-net architecture

NASA Astrophysics Data System (ADS)

Maiti, Anup Kumar; Nath Roy, Jitendra; Mukhopadhyay, Sourangshu

2007-08-01

In the field of optical computing and parallel information processing, several number systems have been used for different arithmetic and algebraic operations. Therefore an efficient conversion scheme from one number system to another is very important. Modified trinary number (MTN) has already taken a significant role towards carry and borrow free arithmetic operations. In this communication, we propose a tree-net architecture based all optical conversion scheme from binary number to its MTN form. Optical switch using nonlinear material (NLM) plays an important role.

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;…

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…

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

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…

Astrometric and photometric measurements of binary stars with adaptive optics: observations from 2001 to 2006

NASA Astrophysics Data System (ADS)

Roberts, Lewis C.; Mason, Brian D.

2018-02-01

The adaptive optics system at the 3.6 m Advanced Electro-Optical System telescope was used to measure the astrometry and differential magnitude in I band of binary star systems between 2002 and 2006. We report 413 astrometric and photometric measurements of 373 stellar pairs. The astrometric measurements will be of use for future orbital determination, and the photometric measurements will be of use in estimating the spectral types of the component stars. For 21 binaries that had not been observed in decades, we are able to confirm that the systems share common proper motion. Candidate new companions were detected in 24 systems; for these we show the discovery images. Follow-up observations should be able to determine if these systems share common proper motion and are gravitationally bound objects. We computed orbits for nine binaries. Of these, the orbits of five systems are improved compared to prior orbits and four systems have their orbits computed for the first time. In addition, 315 stars were unresolved and the full-width half maxima of the images are presented.

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

NASA Astrophysics Data System (ADS)

Schudlo, Larissa C.; Chau, Tom

2014-02-01

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

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…

Fostering Formal Commutativity Knowledge with Approximate Arithmetic

PubMed Central

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

2015-01-01

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

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.

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.

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.

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.

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.

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…

Predator Arithmetic

ERIC Educational Resources Information Center

Shutler, Paul M. E.; Fong, Ng Swee

2010-01-01

Modern Hindu-Arabic numeration is the end result of a long period of evolution, and is clearly superior to any system that has gone before, but is it optimal? We compare it to a hypothetical base 5 system, which we dub Predator arithmetic, and judge which of the two systems is superior from a mathematics education point of view. We find that…

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…

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.

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

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

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.

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.

Reconstruction based finger-knuckle-print verification with score level adaptive binary fusion.

PubMed

Gao, Guangwei; Zhang, Lei; Yang, Jian; Zhang, Lin; Zhang, David

2013-12-01

Recently, a new biometrics identifier, namely finger knuckle print (FKP), has been proposed for personal authentication with very interesting results. One of the advantages of FKP verification lies in its user friendliness in data collection. However, the user flexibility in positioning fingers also leads to a certain degree of pose variations in the collected query FKP images. The widely used Gabor filtering based competitive coding scheme is sensitive to such variations, resulting in many false rejections. We propose to alleviate this problem by reconstructing the query sample with a dictionary learned from the template samples in the gallery set. The reconstructed FKP image can reduce much the enlarged matching distance caused by finger pose variations; however, both the intra-class and inter-class distances will be reduced. We then propose a score level adaptive binary fusion rule to adaptively fuse the matching distances before and after reconstruction, aiming to reduce the false rejections without increasing much the false acceptances. Experimental results on the benchmark PolyU FKP database show that the proposed method significantly improves the FKP verification accuracy.

Polarization-multiplexed rate-adaptive non-binary-quasi-cyclic-LDPC-coded multilevel modulation with coherent detection for optical transport networks.

PubMed

Arabaci, Murat; Djordjevic, Ivan B; Saunders, Ross; Marcoccia, Roberto M

2010-02-01

In order to achieve high-speed transmission over optical transport networks (OTNs) and maximize its throughput, we propose using a rate-adaptive polarization-multiplexed coded multilevel modulation with coherent detection based on component non-binary quasi-cyclic (QC) LDPC codes. Compared to prior-art bit-interleaved LDPC-coded modulation (BI-LDPC-CM) scheme, the proposed non-binary LDPC-coded modulation (NB-LDPC-CM) scheme not only reduces latency due to symbol- instead of bit-level processing but also provides either impressive reduction in computational complexity or striking improvements in coding gain depending on the constellation size. As the paper presents, compared to its prior-art binary counterpart, the proposed NB-LDPC-CM scheme addresses the needs of future OTNs, which are achieving the target BER performance and providing maximum possible throughput both over the entire lifetime of the OTN, better.

FBC: a flat binary code scheme for fast Manhattan hash retrieval

NASA Astrophysics Data System (ADS)

Kong, Yan; Wu, Fuzhang; Gao, Lifa; Wu, Yanjun

2018-04-01

Hash coding is a widely used technique in approximate nearest neighbor (ANN) search, especially in document search and multimedia (such as image and video) retrieval. Based on the difference of distance measurement, hash methods are generally classified into two categories: Hamming hashing and Manhattan hashing. Benefitting from better neighborhood structure preservation, Manhattan hashing methods outperform earlier methods in search effectiveness. However, due to using decimal arithmetic operations instead of bit operations, Manhattan hashing becomes a more time-consuming process, which significantly decreases the whole search efficiency. To solve this problem, we present an intuitive hash scheme which uses Flat Binary Code (FBC) to encode the data points. As a result, the decimal arithmetic used in previous Manhattan hashing can be replaced by more efficient XOR operator. The final experiments show that with a reasonable memory space growth, our FBC speeds up more than 80% averagely without any search accuracy loss when comparing to the state-of-art Manhattan hashing methods.

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

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

A comparison of adaptive sampling designs and binary spatial models: A simulation study using a census of Bromus inermis

USGS Publications Warehouse

Irvine, Kathryn M.; Thornton, Jamie; Backus, Vickie M.; Hohmann, Matthew G.; Lehnhoff, Erik A.; Maxwell, Bruce D.; Michels, Kurt; Rew, Lisa

2013-01-01

Commonly in environmental and ecological studies, species distribution data are recorded as presence or absence throughout a spatial domain of interest. Field based studies typically collect observations by sampling a subset of the spatial domain. We consider the effects of six different adaptive and two non-adaptive sampling designs and choice of three binary models on both predictions to unsampled locations and parameter estimation of the regression coefficients (species–environment relationships). Our simulation study is unique compared to others to date in that we virtually sample a true known spatial distribution of a nonindigenous plant species, Bromus inermis. The census of B. inermis provides a good example of a species distribution that is both sparsely (1.9 % prevalence) and patchily distributed. We find that modeling the spatial correlation using a random effect with an intrinsic Gaussian conditionally autoregressive prior distribution was equivalent or superior to Bayesian autologistic regression in terms of predicting to un-sampled areas when strip adaptive cluster sampling was used to survey B. inermis. However, inferences about the relationships between B. inermis presence and environmental predictors differed between the two spatial binary models. The strip adaptive cluster designs we investigate provided a significant advantage in terms of Markov chain Monte Carlo chain convergence when trying to model a sparsely distributed species across a large area. In general, there was little difference in the choice of neighborhood, although the adaptive king was preferred when transects were randomly placed throughout the spatial domain.

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.

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.

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.

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

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.,…

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.

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.

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.

Learning, Realizability and Games in Classical Arithmetic

NASA Astrophysics Data System (ADS)

Aschieri, Federico

2010-12-01

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

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.

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.

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.

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…

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…

Local binary pattern variants-based adaptive texture features analysis for posed and nonposed facial expression recognition

NASA Astrophysics Data System (ADS)

Sultana, Maryam; Bhatti, Naeem; Javed, Sajid; Jung, Soon Ki

2017-09-01

Facial expression recognition (FER) is an important task for various computer vision applications. The task becomes challenging when it requires the detection and encoding of macro- and micropatterns of facial expressions. We present a two-stage texture feature extraction framework based on the local binary pattern (LBP) variants and evaluate its significance in recognizing posed and nonposed facial expressions. We focus on the parametric limitations of the LBP variants and investigate their effects for optimal FER. The size of the local neighborhood is an important parameter of the LBP technique for its extraction in images. To make the LBP adaptive, we exploit the granulometric information of the facial images to find the local neighborhood size for the extraction of center-symmetric LBP (CS-LBP) features. Our two-stage texture representations consist of an LBP variant and the adaptive CS-LBP features. Among the presented two-stage texture feature extractions, the binarized statistical image features and adaptive CS-LBP features were found showing high FER rates. Evaluation of the adaptive texture features shows competitive and higher performance than the nonadaptive features and other state-of-the-art approaches, respectively.

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.

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.

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

ERIC Educational Resources Information Center

Berg, Derek H.; Hutchinson, Nancy L.

2010-01-01

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

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...

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.

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

NASA Astrophysics Data System (ADS)

Bogdanov, Alexander; Khramushin, Vasily

2016-02-01

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

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.

Learning Rotation-Invariant Local Binary Descriptor.

PubMed

Duan, Yueqi; Lu, Jiwen; Feng, Jianjiang; Zhou, Jie

2017-08-01

In this paper, we propose a rotation-invariant local binary descriptor (RI-LBD) learning method for visual recognition. Compared with hand-crafted local binary descriptors, such as local binary pattern and its variants, which require strong prior knowledge, local binary feature learning methods are more efficient and data-adaptive. Unlike existing learning-based local binary descriptors, such as compact binary face descriptor and simultaneous local binary feature learning and encoding, which are susceptible to rotations, our RI-LBD first categorizes each local patch into a rotational binary pattern (RBP), and then jointly learns the orientation for each pattern and the projection matrix to obtain RI-LBDs. As all the rotation variants of a patch belong to the same RBP, they are rotated into the same orientation and projected into the same binary descriptor. Then, we construct a codebook by a clustering method on the learned binary codes, and obtain a histogram feature for each image as the final representation. In order to exploit higher order statistical information, we extend our RI-LBD to the triple rotation-invariant co-occurrence local binary descriptor (TRICo-LBD) learning method, which learns a triple co-occurrence binary code for each local patch. Extensive experimental results on four different visual recognition tasks, including image patch matching, texture classification, face recognition, and scene classification, show that our RI-LBD and TRICo-LBD outperform most existing local descriptors.

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

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…

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

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.

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

ERIC Educational Resources Information Center

Gilmore, Camilla K.; Bryant, Peter

2006-01-01

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

The 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

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

Specific arithmetic calculation deficits in children with Turner syndrome.

PubMed

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

1994-12-01

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

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.

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.

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

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).

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.

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.

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)).

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.

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…

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.

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.

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

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.

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.

Computer-Based Arithmetic Test Generation

ERIC Educational Resources Information Center

Trocchi, Robert F.

1973-01-01

The computer can be a welcome partner in the instructional process, but only if there is man-machine interaction. Man should not compromise system design because of available hardware; the computer must fit the system design for the result to represent an acceptable solution to instructional technology. The Arithmetic Test Generator system fits…

Simple arithmetic: not so simple for highly math anxious individuals

PubMed Central

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

2017-01-01

Abstract Fluency with simple arithmetic, typically achieved in early elementary school, is thought to be one of the building blocks of mathematical competence. Behavioral studies with adults indicate that math anxiety (feelings of tension or apprehension about math) is associated with poor performance on cognitively demanding math problems. However, it remains unclear whether there are fundamental differences in how high and low math anxious individuals approach overlearned simple arithmetic problems that are less reliant on cognitive control. The current study used functional magnetic resonance imaging to examine the neural correlates of simple arithmetic performance across high and low math anxious individuals. We implemented a partial least squares analysis, a data-driven, multivariate analysis method to measure distributed patterns of whole-brain activity associated with performance. Despite overall high simple arithmetic performance across high and low math anxious individuals, performance was differentially dependent on the fronto-parietal attentional network as a function of math anxiety. Specifically, low—compared to high—math anxious individuals perform better when they activate this network less—a potential indication of more automatic problem-solving. These findings suggest that low and high math anxious individuals approach even the most fundamental math problems differently. PMID:29140499

Evaluation of a Computer-Based Training Program for Enhancing Arithmetic Skills and Spatial Number Representation in Primary School Children.

PubMed

Rauscher, Larissa; Kohn, Juliane; Käser, Tanja; Mayer, Verena; Kucian, Karin; McCaskey, Ursina; Esser, Günter; von Aster, Michael

2016-01-01

Calcularis is a computer-based training program which focuses on basic numerical skills, spatial representation of numbers and arithmetic operations. The program includes a user model allowing flexible adaptation to the child's individual knowledge and learning profile. The study design to evaluate the training comprises three conditions (Calcularis group, waiting control group, spelling training group). One hundred and thirty-eight children from second to fifth grade participated in the study. Training duration comprised a minimum of 24 training sessions of 20 min within a time period of 6-8 weeks. Compared to the group without training (waiting control group) and the group with an alternative training (spelling training group), the children of the Calcularis group demonstrated a higher benefit in subtraction and number line estimation with medium to large effect sizes. Therefore, Calcularis can be used effectively to support children in arithmetic performance and spatial number representation.

The Development of Arithmetical Abilities

ERIC Educational Resources Information Center

Butterworth, Brian

2005-01-01

Background: Arithmetical skills are essential to the effective exercise of citizenship in a numerate society. How these skills are acquired, or fail to be acquired, is of great importance not only to individual children but to the organisation of formal education and its role in society. Method: The evidence on the normal and abnormal…

On Arithmetic-Geometric-Mean Polynomials

ERIC Educational Resources Information Center

Griffiths, Martin; MacHale, Des

2017-01-01

We study here an aspect of an infinite set "P" of multivariate polynomials, the elements of which are associated with the arithmetic-geometric-mean inequality. In particular, we show in this article that there exist infinite subsets of probability "P" for which every element may be expressed as a finite sum of squares of real…

The MONGOOSE Rational Arithmetic Toolbox.

PubMed

Le, Christopher; Chindelevitch, Leonid

2018-01-01

The modeling of metabolic networks has seen a rapid expansion following the complete sequencing of thousands of genomes. The constraint-based modeling framework has emerged as one of the most popular approaches to reconstructing and analyzing genome-scale metabolic models. Its main assumption is that of a quasi-steady-state, requiring that the production of each internal metabolite be balanced by its consumption. However, due to the multiscale nature of the models, the large number of reactions and metabolites, and the use of floating-point arithmetic for the stoichiometric coefficients, ensuring that this assumption holds can be challenging.The MONGOOSE toolbox addresses this problem by using rational arithmetic, thus ensuring that models are analyzed in a reproducible manner and consistently with modeling assumptions. In this chapter we present a protocol for the complete analysis of a metabolic network model using the MONGOOSE toolbox, via its newly developed GUI, and describe how it can be used as a model-checking platform both during and after the model construction process.

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

Orbital motion in pre-main sequence binaries

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

Schaefer, G. H.; Prato, L.; Simon, M.

2014-06-01

We present results from our ongoing program to map the visual orbits of pre-main sequence (PMS) binaries in the Taurus star forming region using adaptive optics imaging at the Keck Observatory. We combine our results with measurements reported in the literature to analyze the orbital motion for each binary. We present preliminary orbits for DF Tau, T Tau S, ZZ Tau, and the Pleiades binary HBC 351. Seven additional binaries show curvature in their relative motion. Currently, we can place lower limits on the orbital periods for these systems; full solutions will be possible with more orbital coverage. Five othermore » binaries show motion that is indistinguishable from linear motion. We suspect that these systems are bound and might show curvature with additional measurements in the future. The observations reported herein lay critical groundwork toward the goal of measuring precise masses for low-mass PMS stars.« less

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.

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

NASA Astrophysics Data System (ADS)

Wang, Li-Qun; Saito, Masao

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

Bondi-Hoyle-Lyttleton Accretion onto Binaries

NASA Astrophysics Data System (ADS)

Antoni, Andrea; MacLeod, Morgan; Ramírez-Ruiz, Enrico

2018-01-01

Binary stars are not rare. While only close binary stars will eventually interact with one another, even the widest binary systems interact with their gaseous surroundings. The rates of accretion and the gaseous drag forces arising in these interactions are the key to understanding how these systems evolve. This poster examines accretion flows around a binary system moving supersonically through a background gas. We perform three-dimensional hydrodynamic simulations of Bondi-Hoyle-Lyttleton accretion using the adaptive mesh refinement code FLASH. We simulate a range of values of semi-major axis of the orbit relative to the gravitational focusing impact parameter of the pair. On large scales, gas is gravitationally focused by the center-of-mass of the binary, leading to dynamical friction drag and to the accretion of mass and momentum. On smaller scales, the orbital motion imprints itself on the gas. Notably, the magnitude and direction of the forces acting on the binary inherit this orbital dependence. The long-term evolution of the binary is determined by the timescales for accretion, slow down of the center-of-mass, and decay of the orbit. We use our simulations to measure these timescales and to establish a hierarchy between them. In general, our simulations indicate that binaries moving through gaseous media will slow down before the orbit decays.

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

PubMed

Fehr, Thorsten; Code, Chris; Herrmann, Manfred

2007-10-03

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

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 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.

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

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.

Arithmetic functions in torus and tree networks

DOEpatents

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

2007-12-25

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

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

NASA Astrophysics Data System (ADS)

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

2008-08-01

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

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

PubMed

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

2017-12-01

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

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…

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.

Measuring Close Binary Stars with Speckle Interferometry

DTIC Science & Technology

2014-09-01

extra effort to be measured. One method of observing such binary star systems is to use adaptive optics to correct the atmospheric blur in real-time...simplicity, and with no loss in generalization, this analysis will be reduced to one dimension . From equation (4), it can be seen that the frequency (u...the binary pair are systematically too large , due to the displacement of the minima of the fringes by the atmospheric OTF, when left uncorrected

Fatigue damage prognosis using affine arithmetic

NASA Astrophysics Data System (ADS)

Gbaguidi, Audrey; Kim, Daewon

2014-02-01

Among the essential steps to be taken in structural health monitoring systems, damage prognosis would be the field that is least investigated due to the complexity of the uncertainties. This paper presents the possibility of using Affine Arithmetic for uncertainty propagation of crack damage in damage prognosis. The structures examined are thin rectangular plates made of titanium alloys with central mode I cracks and a composite plate with an internal delamination caused by mixed mode I and II fracture modes, under a harmonic uniaxial loading condition. The model-based method for crack growth rates are considered using the Paris Erdogan law model for the isotropic plates and the delamination growth law model proposed by Kardomateas for the composite plate. The parameters for both models are randomly taken and their uncertainties are considered as defined by an interval instead of a probability distribution. A Monte Carlo method is also applied to check whether Affine Arithmetic (AA) leads to tight bounds on the lifetime of the structure.

Binary statistics among population II stars

NASA Astrophysics Data System (ADS)

Zinnecker, H.; Köhler, R.; Jahreiß, H.

2004-08-01

Population II stars are old, metal-poor, Galactic halo stars with high proper motion. We have carried out a visual binary survey of 164 halo stars in the solar neighborhood (median distance 100 pc), using infrared speckle interferometry, adaptive optics, and wide field direct imaging. The sample is based on the lists of Population II stars of Carney et al. (1994) and Norris (1986), with reliable distances from HIPPARCOS measurements. At face value, we found 33 binaries, 6 triples, and 1 quadruple system. When we limit ourselves to K-band flux ratios larger than 0.1 (to avoid background contamination), the numbers drop to 9 binaries and 1 triple, corresponding to a binary frequency of 6 - 7 % above our angular resolution limit of about 0.1 arcsec. If we count all systems with K-band flux ratios greater than 0.01, we obtain 15 more binaries and 3 more triples, corresponding to a binary frequency for projected separations in excess of 10 AU of around 20 %. This is to be compared with the frequency of spectroscopic binaries (up to a period of 3000 days) of Population II stars of about 15 % (Latham et al. 2002). We also determined a semi-major axis distribution for our visual Population II binary and triple systems, which appears to be remarkably different from that of Population I stars. Second epoch-observations must help confirm the reality of our results.

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)

When listening to rain sounds boosts arithmetic ability

PubMed Central

De Benedetto, Francesco; Ferrari, Maria Vittoria; Ferrarini, Giorgia

2018-01-01

Studies in the literature have provided conflicting evidence about the effects of background noise or music on concurrent cognitive tasks. Some studies have shown a detrimental effect, while others have shown a beneficial effect of background auditory stimuli. The aim of this study was to investigate the influence of agitating, happy or touching music, as opposed to environmental sounds or silence, on the ability of non-musician subjects to perform arithmetic operations. Fifty university students (25 women and 25 men, 25 introverts and 25 extroverts) volunteered for the study. The participants were administered 180 easy or difficult arithmetic operations (division, multiplication, subtraction and addition) while listening to heavy rain sounds, silence or classical music. Silence was detrimental when participants were faced with difficult arithmetic operations, as it was associated with significantly worse accuracy and slower RTs than music or rain sound conditions. This finding suggests that the benefit of background stimulation was not music-specific but possibly due to an enhanced cerebral alertness level induced by the auditory stimulation. Introverts were always faster than extroverts in solving mathematical problems, except when the latter performed calculations accompanied by the sound of heavy rain, a condition that made them as fast as introverts. While the background auditory stimuli had no effect on the arithmetic ability of either group in the easy condition, it strongly affected extroverts in the difficult condition, with RTs being faster during agitating or joyful music as well as rain sounds, compared to the silent condition. For introverts, agitating music was associated with faster response times than the silent condition. This group difference may be explained on the basis of the notion that introverts have a generally higher arousal level compared to extroverts and would therefore benefit less from the background auditory stimuli. PMID:29466472

When listening to rain sounds boosts arithmetic ability.

PubMed

Proverbio, Alice Mado; De Benedetto, Francesco; Ferrari, Maria Vittoria; Ferrarini, Giorgia

2018-01-01

Studies in the literature have provided conflicting evidence about the effects of background noise or music on concurrent cognitive tasks. Some studies have shown a detrimental effect, while others have shown a beneficial effect of background auditory stimuli. The aim of this study was to investigate the influence of agitating, happy or touching music, as opposed to environmental sounds or silence, on the ability of non-musician subjects to perform arithmetic operations. Fifty university students (25 women and 25 men, 25 introverts and 25 extroverts) volunteered for the study. The participants were administered 180 easy or difficult arithmetic operations (division, multiplication, subtraction and addition) while listening to heavy rain sounds, silence or classical music. Silence was detrimental when participants were faced with difficult arithmetic operations, as it was associated with significantly worse accuracy and slower RTs than music or rain sound conditions. This finding suggests that the benefit of background stimulation was not music-specific but possibly due to an enhanced cerebral alertness level induced by the auditory stimulation. Introverts were always faster than extroverts in solving mathematical problems, except when the latter performed calculations accompanied by the sound of heavy rain, a condition that made them as fast as introverts. While the background auditory stimuli had no effect on the arithmetic ability of either group in the easy condition, it strongly affected extroverts in the difficult condition, with RTs being faster during agitating or joyful music as well as rain sounds, compared to the silent condition. For introverts, agitating music was associated with faster response times than the silent condition. This group difference may be explained on the basis of the notion that introverts have a generally higher arousal level compared to extroverts and would therefore benefit less from the background auditory stimuli.

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.

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…

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.

Adaptive optics imaging of the MBM 12 association. Seven binaries and an edge-on disk in a quadruple system

NASA Astrophysics Data System (ADS)

Chauvin, G.; Ménard, F.; Fusco, T.; Lagrange, A.-M.; Beuzit, J.-L.; Mouillet, D.; Augereau, J.-C.

2002-11-01

We report adaptive optics (AO) observations of the young and nearby association MBM 12 obtained with the Canada-France-Hawaii Telescope. Our main observational result is the discovery of six new binary systems, LkHα 264, E 0255+2018, RX J0255.4+2005, S18, MBM 12-10, RX J0255.3+1915, and the confirmation of HD 17332, already known as a binary. We also detected a possible quadruple system. It is composed of the close binary LkHα 263 AB (separation of ~ 0.41''), of LkHα 262 located ~ 15.25'' from LkHα 263 A, and of LkHα 263 C, located ~ 4.1'' from LkHα 263 A. A preliminary study of the binary fraction suggests a binary excess in the MBM 12 association as compared to the field and IC 348. Because of the high binarity rate, previous estimations of spectral types and measurements of IR excesses for several candidate members of MBM 12 have to be revised. LkHα 263 C is a nebulous object that we interpret as a disk oriented almost perfectly edge-on and seen in scattered light. This object has already been reported by Jayawardhana et al. (\\cite{Jayawardhana2002}). Scattered light models allow us to estimate some of the structural parameters (i.e. inclination, diameter and to a lesser extent dust mass) of the circumstellar disk. We find an inclination of 89o and a outer radius for the disk, ~ 165 AU if the distance to MBM 12 is 275 pc. With the present data set, we do not attempt to re-assess the distance to MBM 12. We estimate however that the distance to the candidate member RX J0255.3+1915 is d > 175 pc. Based on data collected at the Canada-France-Hawaii Telescope. The CFHT corporation is funded by the Governments of Canada and France, and by the University of Hawaii.

Nonverbal arithmetic in humans: light from noise.

PubMed

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

2007-10-01

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

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

PubMed

Berg, Derek H

2008-04-01

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

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…

Arabidopsis plants perform arithmetic division to prevent starvation at night

PubMed Central

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

2013-01-01

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

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

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.

Secret Codes, Remainder Arithmetic, and Matrices.

ERIC Educational Resources Information Center

Peck, Lyman C.

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

Cognition, emotion, and arithmetic in primary school: A cross-cultural investigation.

PubMed

Rodic, Maja; Cui, Jiaxin; Malykh, Sergey; Zhou, Xinlin; Gynku, Elena I; Bogdanova, Elena L; Zueva, Dina Y; Y Bogdanova, Olga; Kovas, Yulia

2018-06-01

The study investigated cross-cultural differences in variability and average performance in arithmetic, mathematical reasoning, symbolic and non-symbolic magnitude processing, intelligence, spatial ability, and mathematical anxiety in 890 6- to 9-year-old children from the United Kingdom, Russia, and China. Cross-cultural differences explained 28% of the variance in arithmetic and 17.3% of the variance in mathematical reasoning, with Chinese children outperforming the other two groups. No cross-cultural differences were observed for spatial ability and mathematical anxiety. In all samples, symbolic magnitude processing and mathematical reasoning were independently related to early arithmetic. Other factors, such as non-symbolic magnitude processing, mental rotation, intelligence, and mathematical anxiety, produced differential patterns across the populations. The results are discussed in relation to potential influences of parental practice, school readiness, and linguistic factors on individual differences in early mathematics. Statement of contribution What is already known on this subject? Cross-cultural differences in mathematical ability are present in preschool children. Similar mechanisms of mathematical development operate in preschool children from the United Kingdom, Russia, and China. Tasks that require understanding of numbers are best predictors of arithmetic in preschool children. What does this study add? Cross-cultural differences in mathematical ability become greater with age/years of formal education. Similar mechanisms of mathematical development operate in early primary school children from the United Kingdom, Russia, and China. Symbolic number magnitude and mathematical reasoning are the main predictors of arithmetic in all three populations. © 2018 The Authors British Journal of Developmental Psychology published by John Wiley & Sons Ltd on behalf of British Psychological Society.

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.

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…

Real-time mental arithmetic task recognition from EEG signals.

PubMed

Wang, Qiang; Sourina, Olga

2013-03-01

Electroencephalography (EEG)-based monitoring the state of the user's brain functioning and giving her/him the visual/audio/tactile feedback is called neurofeedback technique, and it could allow the user to train the corresponding brain functions. It could provide an alternative way of treatment for some psychological disorders such as attention deficit hyperactivity disorder (ADHD), where concentration function deficit exists, autism spectrum disorder (ASD), or dyscalculia where the difficulty in learning and comprehending the arithmetic exists. In this paper, a novel method for multifractal analysis of EEG signals named generalized Higuchi fractal dimension spectrum (GHFDS) was proposed and applied in mental arithmetic task recognition from EEG signals. Other features such as power spectrum density (PSD), autoregressive model (AR), and statistical features were analyzed as well. The usage of the proposed fractal dimension spectrum of EEG signal in combination with other features improved the mental arithmetic task recognition accuracy in both multi-channel and one-channel subject-dependent algorithms up to 97.87% and 84.15% correspondingly. Based on the channel ranking, four channels were chosen which gave the accuracy up to 97.11%. Reliable real-time neurofeedback system could be implemented based on the algorithms proposed in this paper.

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…

Hybrid Black-Hole Binary Initial Data

NASA Technical Reports Server (NTRS)

Mundim, Bruno C.; Kelly, Bernard J.; Nakano, Hiroyuki; Zlochower, Yosef; Campanelli, Manuela

2010-01-01

"Traditional black-hole binary puncture initial data is conformally flat. This unphysical assumption is coupled with a lack of radiation signature from the binary's past life. As a result, waveforms extracted from evolutions of this data display an abrupt jump. In Kelly et al. [Class. Quantum Grav. 27:114005 (2010)], a new binary black-hole initial data with radiation contents derived in the post-Newtonian (PN) calculations was adapted to puncture evolutions in numerical relativity. This data satisfies the constraint equations to the 2.5PN order, and contains a transverse-traceless "wavy" metric contribution, violating the standard assumption of conformal flatness. Although the evolution contained less spurious radiation, there were undesired features; the unphysical horizon mass loss and the large initial orbital eccentricity. Introducing a hybrid approach to the initial data evaluation, we significantly reduce these undesired features."

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).

Instabilities caused by floating-point arithmetic quantization.

NASA Technical Reports Server (NTRS)

Phillips, C. L.

1972-01-01

It is shown that an otherwise stable digital control system can be made unstable by signal quantization when the controller operates on floating-point arithmetic. Sufficient conditions of instability are determined, and an example of loss of stability is treated when only one quantizer is operated.

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 .

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…

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…

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

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.

The Impact of Binary Companions on Planetary Systems

NASA Astrophysics Data System (ADS)

Kraus, Adam L.; Ireland, Michael; Dupuy, Trent; Mann, Andrew; Huber, Daniel

2018-01-01

The majority of solar-type stars are found in binary systems, and the dynamical influence of binary companions is expected to profoundly influence planetary systems. However, the difficulty of identifying planets in binary systems has left the magnitude of this effect uncertain; despite numerous theoretical hurdles to their formation and survival, at least some binary systems clearly host planets. We present high-resolution imaging of nearly 500 Kepler Objects of Interest (KOIs) obtained using adaptive-optics imaging and nonredundant aperture-mask interferometry on the Keck II telescope. We super-resolve some binary systems to projected separations of under 5 AU, showing that planets might form in these dynamically active environments. However, the full distribution of projected separations for our planet-host sample more broadly reveals a deep paucity of binary companions at solar-system scales. Our results demonstrate that a fifth of all solar-type stars in the Milky Way are disallowed from hosting planetary systems due to the influence of a binary companion. We now update these results with multi-epoch imaging to reject non-comoving background stars and securely identify even the least massive stellar companions, as well as tracing out the orbital motion of stellar companions. These results are beginning to reveal not just the fraction of binaries that do not host planets, but also potential explanations for planet survival even in some very close, dynamically active binary systems.

Black hole binaries dynamically formed in globular clusters

NASA Astrophysics Data System (ADS)

Park, Dawoo; Kim, Chunglee; Lee, Hyung Mok; Bae, Yeong-Bok; Belczynski, Krzysztof

2017-08-01

We investigate properties of black hole (BH) binaries formed in globular clusters via dynamical processes, using directN-body simulations. We pay attention to effects of BH mass function on the total mass and mass ratio distributions of BH binaries ejected from clusters. First, we consider BH populations with two different masses in order to learn basic differences from models with single-mass BHs only. Secondly, we consider continuous BH mass functions adapted from recent studies on massive star evolution in a low metallicity environment, where globular clusters are formed. In this work, we consider only binaries that are formed by three-body processes and ignore stellar evolution and primordial binaries for simplicity. Our results imply that most BH binary mergers take place after they get ejected from the cluster. Also, mass ratios of dynamically formed binaries should be close to 1 or likely to be less than 2:1. Since the binary formation efficiency is larger for higher-mass BHs, it is likely that a BH mass function sampled by gravitational-wave observations would be weighed towards higher masses than the mass function of single BHs for a dynamically formed population. Applying conservative assumptions regarding globular cluster populations such as small BH mass fraction and no primordial binaries, the merger rate of BH binaries originated from globular clusters is estimated to be at least 6.5 yr-1 Gpc-3. Actual rate can be up to more than several times of our conservative estimate.

A simple transferable adaptive potential to study phase separation in large-scale xMgO-(1-x)SiO2 binary glasses.

PubMed

Bidault, Xavier; Chaussedent, Stéphane; Blanc, Wilfried

2015-10-21

A simple transferable adaptive model is developed and it allows for the first time to simulate by molecular dynamics the separation of large phases in the MgO-SiO2 binary system, as experimentally observed and as predicted by the phase diagram, meaning that separated phases have various compositions. This is a real improvement over fixed-charge models, which are often limited to an interpretation involving the formation of pure clusters, or involving the modified random network model. Our adaptive model, efficient to reproduce known crystalline and glassy structures, allows us to track the formation of large amorphous Mg-rich Si-poor nanoparticles in an Mg-poor Si-rich matrix from a 0.1MgO-0.9SiO2 melt.

A Telescopic Binary Learning Machine for Training Neural Networks.

PubMed

Brunato, Mauro; Battiti, Roberto

2017-03-01

This paper proposes a new algorithm based on multiscale stochastic local search with binary representation for training neural networks [binary learning machine (BLM)]. We study the effects of neighborhood evaluation strategies, the effect of the number of bits per weight and that of the maximum weight range used for mapping binary strings to real values. Following this preliminary investigation, we propose a telescopic multiscale version of local search, where the number of bits is increased in an adaptive manner, leading to a faster search and to local minima of better quality. An analysis related to adapting the number of bits in a dynamic way is presented. The control on the number of bits, which happens in a natural manner in the proposed method, is effective to increase the generalization performance. The learning dynamics are discussed and validated on a highly nonlinear artificial problem and on real-world tasks in many application domains; BLM is finally applied to a problem requiring either feedforward or recurrent architectures for feedback control.

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.

Entropy coders for image compression based on binary forward classification

NASA Astrophysics Data System (ADS)

Yoo, Hoon; Jeong, Jechang

2000-12-01

Entropy coders as a noiseless compression method are widely used as final step compression for images, and there have been many contributions to increase of entropy coder performance and to reduction of entropy coder complexity. In this paper, we propose some entropy coders based on the binary forward classification (BFC). The BFC requires overhead of classification but there is no change between the amount of input information and the total amount of classified output information, which we prove this property in this paper. And using the proved property, we propose entropy coders that are the BFC followed by Golomb-Rice coders (BFC+GR) and the BFC followed by arithmetic coders (BFC+A). The proposed entropy coders introduce negligible additional complexity due to the BFC. Simulation results also show better performance than other entropy coders that have similar complexity to the proposed coders.

Toward more intuitive brain-computer interfacing: classification of binary covert intentions using functional near-infrared spectroscopy

NASA Astrophysics Data System (ADS)

Hwang, Han-Jeong; Choi, Han; Kim, Jeong-Youn; Chang, Won-Du; Kim, Do-Won; Kim, Kiwoong; Jo, Sungho; Im, Chang-Hwan

2016-09-01

In traditional brain-computer interface (BCI) studies, binary communication systems have generally been implemented using two mental tasks arbitrarily assigned to "yes" or "no" intentions (e.g., mental arithmetic calculation for "yes"). A recent pilot study performed with one paralyzed patient showed the possibility of a more intuitive paradigm for binary BCI communications, in which the patient's internal yes/no intentions were directly decoded from functional near-infrared spectroscopy (fNIRS). We investigated whether such an "fNIRS-based direct intention decoding" paradigm can be reliably used for practical BCI communications. Eight healthy subjects participated in this study, and each participant was administered 70 disjunctive questions. Brain hemodynamic responses were recorded using a multichannel fNIRS device, while the participants were internally expressing "yes" or "no" intentions to each question. Different feature types, feature numbers, and time window sizes were tested to investigate optimal conditions for classifying the internal binary intentions. About 75% of the answers were correctly classified when the individual best feature set was employed (75.89% ±1.39 and 74.08% ±2.87 for oxygenated and deoxygenated hemoglobin responses, respectively), which was significantly higher than a random chance level (68.57% for p<0.001). The kurtosis feature showed the highest mean classification accuracy among all feature types. The grand-averaged hemodynamic responses showed that wide brain regions are associated with the processing of binary implicit intentions. Our experimental results demonstrated that direct decoding of internal binary intention has the potential to be used for implementing more intuitive and user-friendly communication systems for patients with motor disabilities.

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

PubMed Central

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

2012-01-01

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

Arithmetic Word-Problem-Solving in Huntington's Disease

ERIC Educational Resources Information Center

Allain, P.; Verny, C.; Aubin, G.; Pinon, K.; Bonneau, D.; Dubas, F.; Gall, D.L.

2005-01-01

The purpose of this study was to examine executive functioning in patients with Huntington's disease using an arithmetic word-problem-solving task including eight solvable problems of increasing complexity and four aberrant problems. Ten patients with Huntington's disease and 12 normal control subjects matched by age and education were tested.…

Processing Of Binary Images

NASA Astrophysics Data System (ADS)

Hou, H. S.

1985-07-01

An overview of the recent progress in the area of digital processing of binary images in the context of document processing is presented here. The topics covered include input scan, adaptive thresholding, halftoning, scaling and resolution conversion, data compression, character recognition, electronic mail, digital typography, and output scan. Emphasis has been placed on illustrating the basic principles rather than descriptions of a particular system. Recent technology advances and research in this field are also mentioned.

Rational Arithmetic in Floating-Point.

DTIC Science & Technology

1986-09-01

RD-RI75 190 RATIONAL ARITHMETIC IN FLOTING-POINT(U) CALIFORNIA~UNIY BERKELEY CENTER FOR PURE AND APPLIED MATHEMATICS USI FE N KAHAN SEP 86 PRM-343...8217 ," .’,.-.’ .- " .- . ,,,.". ".. .. ". CENTER FOR PURE AND APPLIED MATHEMATICS UNIVERSITY OF CALIFORNIA, BERKELEY PAf4343 0l RATIONAL ARITHMIETIC IN FLOATING-POINT W. KAHAN SETMER18 SEPTEMBE...delicate balance between, on the one hand, the simplicity and aesthetic appeal of the specifications and, on the other hand, the complexity and

Close Binaries in the η Chamaeleontis Cluster

NASA Astrophysics Data System (ADS)

Köhler, Rainer; Petr-Gotzens, Monika G.

2002-11-01

We have used speckle interferometry and adaptive optics observations to search for multiple systems among 13 stars in the η Chamaeleontis cluster. We discovered two previously unknown subarcsecond binaries. Placing the components in infrared color-magnitude diagrams shows that most members of η Cha are coeval. Repeated observations of the binary RECX 1 allow us to determine a preliminary orbit and derive a system mass of about 2 Msolar. Based on observations obtained at the European Southern Observatory, La Silla, proposals 56.E-0197, 62.I-0399, 65.I-0350, 65.I-0086, 67.C-0354, and 68.C-0539.

The Young Visual Binary Database

NASA Astrophysics Data System (ADS)

Prato, Lisa A.; Avilez, Ian; Allen, Thomas; Zoonematkermani, Saeid; Biddle, Lauren; Muzzio, Ryan; Wittal, Matthew; Schaefer, Gail; Simon, Michal

2017-01-01

We have obtained adaptive optics imaging and high-resolution H-band and in some cases K-band spectra of each component in close to 100 young multiple systems in the nearby star forming regions of Taurus, Ophiuchus, TW Hya, and Orion. The binary separations for the pairs in our sample range from 30 mas to 3 arcseconds. The imaging and most of our spectra were obtained with instruments behind adaptive optics systems in order to resolve even the closest companions. We are in the process of determining fundamental stellar and circumstellar properties, such as effective temperature, Vsin(i), veiling, and radial velocity, for each component in the entire sample. The beta version of our database includes systems in the Taurus region and provides plots, downloadable ascii spectra, and values of the stellar and circumstellar properties for both stars in each system. This resource is openly available to the community at http://jumar.lowell.edu/BinaryStars/. In this poster we describe initial results from our analysis of the survey data. Support for this research was provided in part by NSF award AST-1313399 and by NASA Keck KPDA funding.

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…

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)…

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.

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

New Binaries in the ɛ Cha Association

NASA Astrophysics Data System (ADS)

Briceño, César; Tokovinin, Andrei

2017-11-01

We present Adaptive Optics-aided speckle observations of 47 young stars in the ɛ Cha association made at the 4 m Southern Astrophysical Research Telescope in the I-band. We resolved 10 new binary pairs, 5 previously known binaries, and 2 triple systems, also previously known. In the separation range between 4 and 300 au, the 30 association members of spectral types G0 and later host 6 binary companions, leading to the raw companion frequency of 0.010 ± 0.04 per decade of separation, comparable to the main sequence dwarfs in the field. On the other hand, all five massive association members of spectral types A and B have companions in this range. We discuss the newly resolved and known binaries in our sample. Observed motions in the triple system ɛ Cha, composed of three similar B9V stars, can be described by tentative orbits with periods 13 and ˜900 years and a large mutual inclination. Based on observations obtained at the Southern Astrophysical Research (SOAR) telescope.

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…

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.

File compression and encryption based on LLS and arithmetic coding

NASA Astrophysics Data System (ADS)

Yu, Changzhi; Li, Hengjian; Wang, Xiyu

2018-03-01

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

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.

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.

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

Differences in arithmetic performance between Chinese and German adults are accompanied by differences in processing of non-symbolic numerical magnitude

PubMed Central

Lonnemann, Jan; Li, Su; Zhao, Pei; Li, Peng; Linkersdörfer, Janosch; Lindberg, Sven; Hasselhorn, Marcus; Yan, Song

2017-01-01

Human beings are assumed to possess an approximate number system (ANS) dedicated to extracting and representing approximate numerical magnitude information. The ANS is assumed to be fundamental to arithmetic learning and has been shown to be associated with arithmetic performance. It is, however, still a matter of debate whether better arithmetic skills are reflected in the ANS. To address this issue, Chinese and German adults were compared regarding their performance in simple arithmetic tasks and in a non-symbolic numerical magnitude comparison task. Chinese participants showed a better performance in solving simple arithmetic tasks and faster reaction times in the non-symbolic numerical magnitude comparison task without making more errors than their German peers. These differences in performance could not be ascribed to differences in general cognitive abilities. Better arithmetic skills were thus found to be accompanied by a higher speed of retrieving non-symbolic numerical magnitude knowledge but not by a higher precision of non-symbolic numerical magnitude representations. The group difference in the speed of retrieving non-symbolic numerical magnitude knowledge was fully mediated by the performance in arithmetic tasks, suggesting that arithmetic skills shape non-symbolic numerical magnitude processing skills. PMID:28384191

Young Binaries and Early Stellar Evolution

NASA Astrophysics Data System (ADS)

Brandner, Wolfgang

1996-07-01

Most main-sequence stars are members of binary or multiple systems. The same is true for pre-main-sequence (PMS) stars, as recent surveys have shown. Therefore studying star formation means to a large extent studying the formation of binary systems. Similarly, studying early stellar evolution primarily involves PMS binary systems. In this thesis I have studied the binary frequency among ROSAT selected T Tauri stars in the Chamaeleon T association and the Scorpius-Centaurus OB association, and the evolutionary status of Hα-selected PMS binaries in the T associations of Chamaeleon, Lupus, and ρ Ophiuchi. The direct imaging and spectroscopic observations in the optical have been carried out under subarcsec seeing conditions at the ESO New Technology Telescope (NTT) at La Silla. Furthermore, high-spatial resolution images of selected PMS stars in the near infrared were obtained with the ESO adaptive optics system COME-ON+/ADONIS. Among 195 T Tauri stars observed using direct imaging 31 binaries could be identified, 12 of them with subarcsec separation. Based on statistical arguments alone I conclude that almost all of them are indeed physical (i.e. gravitationally bound) binary or multiple systems. Using astrometric measurements of some binaries I showed that the components of these binaries are common proper motion pairs, very likely in a gravitationally bound orbit around each other. The overall binary frequency among T Tauri stars with a range of separations between 120 and 1800 AU is in agreement with the binary frequency observed among main-sequence stars in the solar neighbourhood. However, within individual regions the spatial distribution of binaries is non-uniform. In particular, in Upper Scorpius, weak-line T Tauri stars in the vicinity of early type stars seem to be almost devoid of multiple systems, whereas in another area in Upper Scorpius half of all weak-line T Tauri stars have a companion in a range of separation between 0.''7 and 3.''0. For a sample

The Ruinous Influence of Close Binary Companions on Planetary Systems

NASA Astrophysics Data System (ADS)

Kraus, Adam L.; Ireland, Michael; Mann, Andrew; Huber, Daniel; Dupuy, Trent J.

2017-01-01

The majority of solar-type stars are found in binary systems, and the dynamical influence of binary companions is expected to profoundly influence planetary systems. However, the difficulty of identifying planets in binary systems has left the magnitude of this effect uncertain; despite numerous theoretical hurdles to their formation and survival, at least some binary systems clearly host planets. We present high-resolution imaging of nearly 500 Kepler Objects of Interest (KOIs) obtained using adaptive-optics imaging and nonredundant aperture-mask interferometry on the Keck II telescope. We super-resolve some binary systems to projected separations of under 5 AU, showing that planets might form in these dynamically active environments. However, the full distribution of projected separations for our planet-host sample more broadly reveals a deep paucity of binary companions at solar-system scales. When the binary population is parametrized with a semimajor axis cutoff a cut and a suppression factor inside that cutoff S bin, we find with correlated uncertainties that inside acut = 47 +59/-23 AU, the planet occurrence rate in binary systems is only Sbin = 0.34 +0.14/-0.15 times that of wider binaries or single stars. Our results demonstrate that a fifth of all solar-type stars in the Milky Way are disallowed from hosting planetary systems due to the influence of a binary companion.

The Ruinous Influence of Close Binary Companions on Planetary Systems

NASA Astrophysics Data System (ADS)

Kraus, Adam L.; Ireland, Michael; Mann, Andrew; Huber, Daniel; Dupuy, Trent J.

2017-06-01

The majority of solar-type stars are found in binary systems, and the dynamical influence of binary companions is expected to profoundly influence planetary systems. However, the difficulty of identifying planets in binary systems has left the magnitude of this effect uncertain; despite numerous theoretical hurdles to their formation and survival, at least some binary systems clearly host planets. We present high-resolution imaging of nearly 500 Kepler Objects of Interest (KOIs) obtained using adaptive-optics imaging and nonredundant aperture-mask interferometry on the Keck II telescope. We super-resolve some binary systems to projected separations of under 5 AU, showing that planets might form in these dynamically active environments. However, the full distribution of projected separations for our planet-host sample more broadly reveals a deep paucity of binary companions at solar-system scales. When the binary population is parametrized with a semimajor axis cutoff a cut and a suppression factor inside that cutoff S bin, we find with correlated uncertainties that inside acut = 47 +59/-23 AU, the planet occurrence rate in binary systems is only Sbin = 0.34+0.14/-0.15 times that of wider binaries or single stars. Our results demonstrate that a fifth of all solar-type stars in the Milky Way are disallowed from hosting planetary systems due to the influence of a binary companion.

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

PubMed

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

2017-05-01

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

Improvements to the construction of binary black hole initial data

NASA Astrophysics Data System (ADS)

Ossokine, Serguei; Foucart, Francois; Pfeiffer, Harald P.; Boyle, Michael; Szilágyi, Béla

2015-12-01

Construction of binary black hole initial data is a prerequisite for numerical evolutions of binary black holes. This paper reports improvements to the binary black hole initial data solver in the spectral Einstein code, to allow robust construction of initial data for mass-ratio above 10:1, and for dimensionless black hole spins above 0.9, while improving efficiency for lower mass-ratios and spins. We implement a more flexible domain decomposition, adaptive mesh refinement and an updated method for choosing free parameters. We also introduce a new method to control and eliminate residual linear momentum in initial data for precessing systems, and demonstrate that it eliminates gravitational mode mixing during the evolution. Finally, the new code is applied to construct initial data for hyperbolic scattering and for binaries with very small separation.

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

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 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.

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)

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…

Toward more intuitive brain-computer interfacing: classification of binary covert intentions using functional near-infrared spectroscopy.

PubMed

Hwang, Han-Jeong; Choi, Han; Kim, Jeong-Youn; Chang, Won-Du; Kim, Do-Won; Kim, Kiwoong; Jo, Sungho; Im, Chang-Hwan

2016-09-01

In traditional brain-computer interface (BCI) studies, binary communication systems have generally been implemented using two mental tasks arbitrarily assigned to “yes” or “no” intentions (e.g., mental arithmetic calculation for “yes”). A recent pilot study performed with one paralyzed patient showed the possibility of a more intuitive paradigm for binary BCI communications, in which the patient’s internal yes/no intentions were directly decoded from functional near-infrared spectroscopy (fNIRS). We investigated whether such an “fNIRS-based direct intention decoding” paradigm can be reliably used for practical BCI communications. Eight healthy subjects participated in this study, and each participant was administered 70 disjunctive questions. Brain hemodynamic responses were recorded using a multichannel fNIRS device, while the participants were internally expressing “yes” or “no” intentions to each question. Different feature types, feature numbers, and time window sizes were tested to investigate optimal conditions for classifying the internal binary intentions. About 75% of the answers were correctly classified when the individual best feature set was employed (75.89% ± 1.39 and 74.08% ± 2.87 for oxygenated and deoxygenated hemoglobin responses, respectively), which was significantly higher than a random chance level (68.57% for p < 0.001). The kurtosis feature showed the highest mean classification accuracy among all feature types. The grand-averaged hemodynamic responses showed that wide brain regions are associated with the processing of binary implicit intentions. Our experimental results demonstrated that direct decoding of internal binary intention has the potential to be used for implementing more intuitive and user-friendly communication systems for patients with motor disabilities.

Updating Working Memory and Arithmetical Attainment in School

ERIC Educational Resources Information Center

Iuculano, Teresa; Moro, Raffaella; Butterworth, Brian

2011-01-01

Here we wished to determine how the sub-components of Working Memory (Phonological-Loop and Central Executive) influence children's arithmetical development. Specifically, we aimed at distinguishing between Working Memory inhibition and updating processes within the Central Executive, and the domain-specificity (words and numbers) of both…

Flare Activity of Wide Binary Stars with Kepler

NASA Astrophysics Data System (ADS)

Clarke, Riley W.; Davenport, James R. A.; Covey, Kevin R.; Baranec, Christoph

2018-01-01

We present an analysis of flare activity in wide binary stars using a combination of value-added data sets from the NASA Kepler mission. The target list contains a set of previously discovered wide binary star systems identified by proper motions in the Kepler field. We cross-matched these systems with estimates of flare activity for ∼200,000 stars in the Kepler field, allowing us to compare relative flare luminosity between stars in coeval binaries. From a sample of 184 previously known wide binaries in the Kepler field, we find 58 with detectable flare activity in at least 1 component, 33 of which are similar in mass (q > 0.8). Of these 33 equal-mass binaries, the majority display similar (±1 dex) flare luminosity between both stars, as expected for stars of equal mass and age. However, we find two equal-mass pairs where the secondary (lower mass) star is more active than its counterpart, and two equal-mass pairs where the primary star is more active. The stellar rotation periods are also anomalously fast for stars with elevated flare activity. Pairs with discrepant rotation and activity qualitatively seem to have lower mass ratios. These outliers may be due to tidal spin-up, indicating these wide binaries could be hierarchical triple systems. We additionally present high-resolution adaptive optics images for two wide binary systems to test this hypothesis. The demographics of stellar rotation and magnetic activity between stars in wide binaries may be useful indicators for discerning the formation scenarios of these systems.

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…

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.

Deficit of Wide Binaries in the η Chamaeleontis Young Cluster

NASA Astrophysics Data System (ADS)

Brandeker, Alexis; Jayawardhana, Ray; Khavari, Parandis; Haisch, Karl E., Jr.; Mardones, Diego

2006-12-01

We have carried out a sensitive high-resolution imaging survey of stars in the young (6-8 Myr), nearby (97 pc) compact cluster around η Chamaeleontis to search for stellar and substellar companions. Our data were obtained using the NACO adaptive optics system on the ESO Very Large Telescope (VLT). Given its youth and proximity, any substellar companions are expected to be luminous, especially in the near-infrared, and thus easier to detect next to their parent stars. Here, we present VLT NACO adaptive optics imaging with companion detection limits for 17 η Cha cluster members, and follow-up VLT ISAAC near-infrared spectroscopy for companion candidates. The widest binary detected is ~0.2", corresponding to the projected separation 20 AU, despite our survey being sensitive down to substellar companions outside 0.3", and planetary-mass objects outside 0.5". This implies that the stellar companion probability outside 0.3" and the brown dwarf companion probability outside 0.5" are less than 0.16 with 95% confidence. We compare the wide binary frequency of η Cha to that of the similarly aged TW Hydrae association and estimate the statistical likelihood that the wide binary probability is equal in both groups to be less than 2×10-4. Even though the η Cha cluster is relatively dense, stellar encounters in its present configuration cannot account for the relative deficit of wide binaries. We thus conclude that the difference in wide binary probability in these two groups provides strong evidence for multiplicity properties being dependent on environment. In two appendices we derive the projected separation probability distribution for binaries, used to constrain physical separations from observed projected separations, and summarize statistical tools useful for multiplicity studies.

The True Ultracool Binary Fraction Using Spectral Binaries

NASA Astrophysics Data System (ADS)

Bardalez Gagliuffi, Daniella; Burgasser, Adam J.; Schmidt, Sarah J.; Gagné, Jonathan; Faherty, Jacqueline K.; Cruz, Kelle; Gelino, Chris

2018-01-01

Brown dwarfs bridge the gap between stars and giant planets. While the essential mechanisms governing their formation are not well constrained, binary statistics are a direct outcome of the formation process, and thus provide a means to test formation theories. Observational constraints on the brown dwarf binary fraction place it at 10 ‑ 20%, dominated by imaging studies (85% of systems) with the most common separation at 4 AU. This coincides with the resolution limit of state-of-the-art imaging techniques, suggesting that the binary fraction is underestimated. We have developed a separation-independent method to identify and characterize tightly-separated (< 5 AU) binary systems of brown dwarfs as spectral binaries by identifying traces of methane in the spectra of late-M and early-L dwarfs. Imaging follow-up of 17 spectral binaries yielded 3 (18%) resolved systems, corroborating the observed binary fraction, but 5 (29%) known binaries were missed, reinforcing the hypothesis that the short-separation systems are undercounted. In order to find the true binary fraction of brown dwarfs, we have compiled a volume-limited, spectroscopic sample of M7-L5 dwarfs and searched for T dwarf companions. In the 25 pc volume, 4 candidates were found, three of which are already confirmed, leading to a spectral binary fraction of 0.95 ± 0.50%, albeit for a specific combination of spectral types. To extract the true binary fraction and determine the biases of the spectral binary method, we have produced a binary population simulation based on different assumptions of the mass function, age distribution, evolutionary models and mass ratio distribution. Applying the correction fraction resulting from this method to the observed spectral binary fraction yields a true binary fraction of 27 ± 4%, which is roughly within 1σ of the binary fraction obtained from high resolution imaging studies, radial velocity and astrometric monitoring. This method can be extended to identify giant

Coding efficiency of AVS 2.0 for CBAC and CABAC engines

NASA Astrophysics Data System (ADS)

Cui, Jing; Choi, Youngkyu; Chae, Soo-Ik

2015-12-01

In this paper we compare the coding efficiency of AVS 2.0[1] for engines of the Context-based Binary Arithmetic Coding (CBAC)[2] in the AVS 2.0 and the Context-Adaptive Binary Arithmetic Coder (CABAC)[3] in the HEVC[4]. For fair comparison, the CABAC is embedded in the reference code RD10.1 because the CBAC is in the HEVC in our previous work[5]. The rate estimation table is employed only for RDOQ in the RD code. To reduce the computation complexity of the video encoder, therefore we modified the RD code so that the rate estimation table is employed for all RDO decision. Furthermore, we also simplify the complexity of rate estimation table by reducing the bit depth of its fractional part to 2 from 8. The simulation result shows that the CABAC has the BD-rate loss of about 0.7% compared to the CBAC. It seems that the CBAC is a little more efficient than that the CABAC in the AVS 2.0.

BINARY STORAGE ELEMENT

DOEpatents

Chu, J.C.

1958-06-10

A binary storage device is described comprising a toggle provided with associsted improved driver circuits adapted to produce reliable action of the toggle during clearing of the toggle to one of its two states. or transferring information into and out of the toggle. The invention resides in the development of a self-regulating driver circuit to minimize the fluctuation of the driving voltages for the toggle. The disclosed driver circuit produces two pulses in response to an input pulse: a first or ''clear'' pulse beginning nt substantially the same time but endlrg slightly sooner than the second or ''transfer'' output pulse.

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

NASA Astrophysics Data System (ADS)

Taani, Osama

2014-01-01

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

Fault-tolerant arithmetic via time-shared TMR

NASA Astrophysics Data System (ADS)

Swartzlander, Earl E.

1999-11-01

Fault tolerance is increasingly important as society has come to depend on computers for more and more aspects of daily life. The current concern about the Y2K problems indicates just how much we depend on accurate computers. This paper describes work on time- shared TMR, a technique which is used to provide arithmetic operations that produce correct results in spite of circuit faults.

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).

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

PubMed Central

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

2015-01-01

Developmental dyscalculia (DD) is a disability that impacts math learning and skill acquisition in school-age children. Here we investigate arithmetic problem solving deficits in young children with DD using univariate and multivariate analysis of fMRI data. During fMRI scanning, 17 children with DD (ages 7–9, grades 2 and 3) and 17 IQ- and reading ability-matched typically developing (TD) children performed complex and simple addition problems which differed only in arithmetic complexity. While the TD group showed strong modulation of brain responses with increasing arithmetic complexity, children with DD failed to show such modulation. Children with DD showed significantly reduced activation compared to TD children in the intraparietal sulcus, superior parietal lobule, supramarginal gyrus and bilateral dorsolateral prefrontal cortex in relation to arithmetic complexity. Critically, multivariate representational similarity revealed that brain response patterns to complex and simple problems were less differentiated in the DD group in bilateral anterior IPS, independent of overall differences in signal level. Taken together, these results show that children with DD not only under-activate key brain regions implicated in mathematical cognition, but they also fail to generate distinct neural responses and representations for different arithmetic problems. Our findings provide novel insights into the neural basis of DD. PMID:22682904

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

PubMed Central

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

2013-01-01

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

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

PubMed

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

2005-11-01

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

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

PubMed

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

2012-02-15

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

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.

Adaptive Optics Imaging of the Circumbinary Disk around the T Tauri Binary UY Aurigae: Estimates of the Binary Mass and Circumbinary Dust Grain Size Distribution

NASA Astrophysics Data System (ADS)

Close, L. M.; Dutrey, A.; Roddier, F.; Guilloteau, S.; Roddier, C.; Northcott, M.; Ménard, F.; Duvert, G.; Graves, J. E.; Potter, D.

1998-05-01

We have obtained high-resolution (FWHM = 0.15") deep images of the UY Aur binary at J, H, and K' with the University of Hawaii adaptive optics instrument. We clearly detect an R ~ 500 AU circumbinary disk discovered with millimeter interferometry, making UY Aur the second young binary with a confirmed circumbinary disk. It appears that the disk is inclined ~42° from face on. We find that the near side of the disk is brighter than the far side by factors of 2.6, 2.7, and 6.5 times at K', H, and J, respectively. The original GG Tau circumbinary disk has been reexamined and is found to have similar flux ratios of 1.5, 2.6, and 3.6 at K', H, and J, respectively. A realistic power-law distribution (p = 4.7) of spherical dust aggregates (composed of silicates, amorphous carbon, and graphite) that reproduces the observed ISM extinction curve also predicts these observed flux ratios from Mie scattering theory. We find the observed preference of forward-scattering over back-scattering is well fitted (global χ2 minimization) by Mie scattering off particles in the range amin = 0.03 μm to amax = 0.5-0.6 μm. The existence of a significant population of grain radii larger than 0.6 μm is not supported by the scattering observations. Based on the observed disk inclination we derive an orbit for UY Aur where the mass for the binary is 1.6+0.47-0.67 M⊙. Based on the observed K7 and M0 spectral types for UY Aur A and B, accretion disk models for the inner disks around the central stars were constructed. The models suggest that small (lower limit R ~ 5-10 AU) inner disks exist around B and A. It appears that B is accreting ~5 times faster than A, and that both inner disks may be exhausted in ~102-103 yr without replenishment from the outer circumbinary disk. Our images suggest that these inner disks may indeed be resupplied with material through thin streamers of material that penetrate inside the circumbinary disk. Currently it appears that such a streamer may be a close to UY

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.

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

Computer-Assisted Instruction: Stanford's 1965-66 Arithmetic Program.

ERIC Educational Resources Information Center

Suppes, Patrick; And Others

A review of the possibilities and challenges of computer-assisted instruction (CAI), and a brief history of CAI projects at Stanford serve to give the reader the context of the particular program described and analyzed in this book. The 1965-66 arithmetic drill-and-practice program is described, summarizing the curriculum and project operation. An…

Arithmetical Strategies of a Student with Down Syndrome

ERIC Educational Resources Information Center

Rumiati, Rumi

2014-01-01

Kayla was a 15 years old girl with Down syndrome attending a special education school in Indonesia. A modification of Wright et al.'s (2006) approach to assessment documented her number knowledge and arithmetical strategies. This paper discusses the assessment process and the results focusing on her ability to solve number problems. Results show…

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

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.

Arithmetic learning with the use of graphic organiser

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

Multistate Memristive Tantalum Oxide Devices for Ternary Arithmetic

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.

Using Self-Generated Drawings to Solve Arithmetic Word Problems.

ERIC Educational Resources Information Center

Van Essen, Gerard; Hamaker, Christiaan

1990-01-01

Results are presented from two intervention studies which investigate whether encouraging elementary students to generate drawings of arithmetic word problems facilitates problem-solving performance. Findings indicate that fifth graders (N=50) generated many drawings of word problems and improved problem solutions after the intervention, whereas…

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.

Learning to assign binary weights to binary descriptor

NASA Astrophysics Data System (ADS)

Huang, Zhoudi; Wei, Zhenzhong; Zhang, Guangjun

2016-10-01

Constructing robust binary local feature descriptors are receiving increasing interest due to their binary nature, which can enable fast processing while requiring significantly less memory than their floating-point competitors. To bridge the performance gap between the binary and floating-point descriptors without increasing the computational cost of computing and matching, optimal binary weights are learning to assign to binary descriptor for considering each bit might contribute differently to the distinctiveness and robustness. Technically, a large-scale regularized optimization method is applied to learn float weights for each bit of the binary descriptor. Furthermore, binary approximation for the float weights is performed by utilizing an efficient alternatively greedy strategy, which can significantly improve the discriminative power while preserve fast matching advantage. Extensive experimental results on two challenging datasets (Brown dataset and Oxford dataset) demonstrate the effectiveness and efficiency of the proposed method.

Arithmetic in Daily Life and Literacy. Literacy Lessons.

ERIC Educational Resources Information Center

Dalbera, Claude

In order not to waste the time of the people working hard and sacrificing to become literate, literacy must offer them a real opportunity to change their life situation. Although many literacy programs are designed to fit the everyday lives and situations of their students, the same is not true for programs that teach arithmetic. Most adults…

Unique Factorization and the Fundamental Theorem of Arithmetic

ERIC Educational Resources Information Center

Sprows, David

2017-01-01

The fundamental theorem of arithmetic is one of those topics in mathematics that somehow "falls through the cracks" in a student's education. When asked to state this theorem, those few students who are willing to give it a try (most have no idea of its content) will say something like "every natural number can be broken down into a…

Bit-Wise Arithmetic Coding For Compression Of Data

NASA Technical Reports Server (NTRS)

Kiely, Aaron

1996-01-01

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

Relational Thinking: The Bridge between Arithmetic and Algebra

ERIC Educational Resources Information Center

Kiziltoprak, Ayhan; Köse, Nilüfer Yavuzsoy

2017-01-01

The purpose of this study is to investigate the development of relational thinking skill, which is an important component of the transition from arithmetic to algebra, of 5th grade students. In the study, the qualitative research method of teaching experiment was used. The research data were collected from six secondary school 5th grade students…

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.

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.

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

PubMed

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

2017-08-01

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

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.

Cardiorespiratory Information Dynamics during Mental Arithmetic and Sustained Attention

PubMed Central

Widjaja, Devy; Montalto, Alessandro; Vlemincx, Elke; Marinazzo, Daniele; Van Huffel, Sabine; Faes, Luca

2015-01-01

An analysis of cardiorespiratory dynamics during mental arithmetic, which induces stress, and sustained attention was conducted using information theory. The information storage and internal information of heart rate variability (HRV) were determined respectively as the self-entropy of the tachogram, and the self-entropy of the tachogram conditioned to the knowledge of respiration. The information transfer and cross information from respiration to HRV were assessed as the transfer and cross-entropy, both measures of cardiorespiratory coupling. These information-theoretic measures identified significant nonlinearities in the cardiorespiratory time series. Additionally, it was shown that, although mental stress is related to a reduction in vagal activity, no difference in cardiorespiratory coupling was found when several mental states (rest, mental stress, sustained attention) are compared. However, the self-entropy of HRV conditioned to respiration was very informative to study the predictability of RR interval series during mental tasks, and showed higher predictability during mental arithmetic compared to sustained attention or rest. PMID:26042824

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…

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 + __),…

Number word structure in first and second language influences arithmetic skills

PubMed Central

Prior, Anat; Katz, Michal; Mahajna, Islam; Rubinsten, Orly

2015-01-01

Languages differ in how they represent numerical information, and specifically whether the verbal notation of numbers follows the same order as the symbolic notation (in non-inverted languages, e.g., Hebrew, “25, twenty-five”) or whether the two notations diverge (in inverted languages, e.g., Arabic, “25, five-and-twenty”). We examined how the structure of number–words affects how arithmetic operations are processed by bilingual speakers of an inverted and a non-inverted language. We examined Arabic–Hebrew bilinguals’ performance in the first language, L1 (inverted) and in the second language, L2 (non-inverted). Their performance was compared to that of Hebrew L1 speakers, who do not speak an inverted language. Participants judged the accuracy of addition problems presented aurally in L1, aurally in L2 or in visual symbolic notation. Problems were presented such that they matched or did not match the structure of number words in the language. Arabic–Hebrew bilinguals demonstrated both flexibility in processing and adaptation to the language of aural–verbal presentation – they were more accurate for the inverted order of presentation in Arabic, but more accurate for non-inverted order of presentation in Hebrew, thus exhibiting the same pattern found for native Hebrew speakers. In addition, whereas native Hebrew speakers preferred the non-inverted order in visual symbolic presentation as well, the Arabic–Hebrew bilinguals showed enhanced flexibility, without a significant preference for one order over the other, in either speed or accuracy. These findings suggest that arithmetic processing is sensitive to the linguistic representations of number words. Moreover, bilinguals exposed to inverted and non-inverted languages showed influence of both systems, and enhanced flexibility in processing. Thus, the L1 does not seem to have exclusive power in shaping numerical mental representations, but rather the system remains open to influences from a

Constructing binary black hole initial data with high mass ratios and spins

NASA Astrophysics Data System (ADS)

Ossokine, Serguei; Foucart, Francois; Pfeiffer, Harald; Szilagyi, Bela; Simulating Extreme Spacetimes Collaboration

2015-04-01

Binary black hole systems have now been successfully modelled in full numerical relativity by many groups. In order to explore high-mass-ratio (larger than 1:10), high-spin systems (above 0.9 of the maximal BH spin), we revisit the initial-data problem for binary black holes. The initial-data solver in the Spectral Einstein Code (SpEC) was not able to solve for such initial data reliably and robustly. I will present recent improvements to this solver, among them adaptive mesh refinement and control of motion of the center of mass of the binary, and will discuss the much larger region of parameter space this code can now address.

Floating point arithmetic in future supercomputers

NASA Technical Reports Server (NTRS)

Bailey, David H.; Barton, John T.; Simon, Horst D.; Fouts, Martin J.

1989-01-01

Considerations in the floating-point design of a supercomputer are discussed. Particular attention is given to word size, hardware support for extended precision, format, and accuracy characteristics. These issues are discussed from the perspective of the Numerical Aerodynamic Simulation Systems Division at NASA Ames. The features believed to be most important for a future supercomputer floating-point design include: (1) a 64-bit IEEE floating-point format with 11 exponent bits, 52 mantissa bits, and one sign bit and (2) hardware support for reasonably fast double-precision arithmetic.

High Resolution Imaging of Very Low Mass Spectral Binaries: Three Resolved Systems and Detection of Orbital Motion in an L/T Transition Binary

NASA Astrophysics Data System (ADS)

Bardalez Gagliuffi, Daniella C.; Gelino, Christopher R.; Burgasser, Adam J.

2015-11-01

We present high resolution Laser Guide Star Adaptive Optics imaging of 43 late-M, L and T dwarf systems with Keck/NIRC2. These include 17 spectral binary candidates, systems whose spectra suggest the presence of a T dwarf secondary. We resolve three systems: 2MASS J1341-3052, SDSS J1511+0607 and SDSS J2052-1609 the first two are resolved for the first time. All three have projected separations <8 AU and estimated periods of 14-80 years. We also report a preliminary orbit determination for SDSS J2052-1609 based on six epochs of resolved astrometry between 2005 and 2010. Among the 14 unresolved spectral binaries, 5 systems were confirmed binaries but remained unresolved, implying a minimum binary fraction of {47}-11+12% for this sample. Our inability to resolve most of the spectral binaries, including the confirmed binaries, supports the hypothesis that a large fraction of very low mass systems have relatively small separations and are missed with direct imaging. Some of the data presented herein were obtained at the W.M. Keck Observatory, which is operated as a scientific partnership among the California Institute of Technology, the University of California, and the National Aeronautics and Space Administration. The Observatory was made possible by the generous financial support of the W.M. Keck Foundation.

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

PubMed

Shaki, Samuel; Fischer, Martin H

2017-01-01

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

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

PubMed

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

2007-11-01

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

Desirable floating-point arithmetic and elementary functions for numerical computation

NASA Technical Reports Server (NTRS)

Hull, T. E.

1978-01-01

The topics considered are: (1) the base of the number system, (2) precision control, (3) number representation, (4) arithmetic operations, (5) other basic operations, (6) elementary functions, and (7) exception handling. The possibility of doing without fixed-point arithmetic is also mentioned. The specifications are intended to be entirely at the level of a programming language such as FORTRAN. The emphasis is on convenience and simplicity from the user's point of view. Conforming to such specifications would have obvious beneficial implications for the portability of numerical software, and for proving programs correct, as well as attempting to provide facilities which are most suitable for the user. The specifications are not complete in every detail, but it is intended that they be complete in spirit - some further details, especially syntatic details, would have to be provided, but the proposals are otherwise relatively complete.

Stability of binaries. Part 1: Rigid binaries

NASA Astrophysics Data System (ADS)

Sharma, Ishan

2015-09-01

We consider the stability of binary asteroids whose members are possibly granular aggregates held together by self-gravity alone. A binary is said to be stable whenever each member is orbitally and structurally stable to both orbital and structural perturbations. To this end, we extend the stability test for rotating granular aggregates introduced by Sharma (Sharma, I. [2012]. J. Fluid Mech., 708, 71-99; Sharma, I. [2013]. Icarus, 223, 367-382; Sharma, I. [2014]. Icarus, 229, 278-294) to the case of binary systems comprised of rubble members. In part I, we specialize to the case of a binary with rigid members subjected to full three-dimensional perturbations. Finally, we employ the stability test to critically appraise shape models of four suspected binary systems, viz., 216 Kleopatra, 25143 Itokawa, 624 Hektor and 90 Antiope.

Why Is Learning Fraction and Decimal Arithmetic so Difficult?

ERIC Educational Resources Information Center

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

2015-01-01

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

Versatile analog pulse height computer performs real-time arithmetic operations

NASA Technical Reports Server (NTRS)

Brenner, R.; Strauss, M. G.

1967-01-01

Multipurpose analog pulse height computer performs real-time arithmetic operations on relatively fast pulses. This computer can be used for identification of charged particles, pulse shape discrimination, division of signals from position sensitive detectors, and other on-line data reduction techniques.

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…

DISCOVERY OF A HIGHLY UNEQUAL-MASS BINARY T DWARF WITH KECK LASER GUIDE STAR ADAPTIVE OPTICS: A COEVALITY TEST OF SUBSTELLAR THEORETICAL MODELS AND EFFECTIVE TEMPERATURES

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

Liu, Michael C.; Dupuy, Trent J.; Leggett, S. K., E-mail: mliu@ifa.hawaii.ed

Highly unequal-mass ratio binaries are rare among field brown dwarfs, with the mass ratio distribution of the known census described by q {sup (4.9{+-}0.7)}. However, such systems enable a unique test of the joint accuracy of evolutionary and atmospheric models, under the constraint of coevality for the individual components (the 'isochrone test'). We carry out this test using two of the most extreme field substellar binaries currently known, the T1 + T6 {epsilon} Ind Bab binary and a newly discovered 0.''14 T2.0 + T7.5 binary, 2MASS J12095613-1004008AB, identified with Keck laser guide star adaptive optics. The latter is the mostmore » extreme tight binary resolved to date (q {approx} 0.5). Based on the locations of the binary components on the Hertzsprung-Russell (H-R) diagram, current models successfully indicate that these two systems are coeval, with internal age differences of log(age) = -0.8 {+-} 1.3(-1.0{sup +1.2}{sub -1.3}) dex and 0.5{sup +0.4}{sub -0.3}(0.3{sup +0.3}{sub -0.4}) dex for 2MASS J1209-1004AB and {epsilon} Ind Bab, respectively, as inferred from the Lyon (Tucson) models. However, the total mass of {epsilon} Ind Bab derived from the H-R diagram ({approx} 80 M{sub Jup} using the Lyon models) is strongly discrepant with the reported dynamical mass. This problem, which is independent of the assumed age of the {epsilon} Ind Bab system, can be explained by a {approx} 50-100 K systematic error in the model atmosphere fitting, indicating slightly warmer temperatures for both components; bringing the mass determinations from the H-R diagram and the visual orbit into consistency leads to an inferred age of {approx} 6 Gyr for {epsilon} Ind Bab, older than previously assumed. Overall, the two T dwarf binaries studied here, along with recent results from T dwarfs in age and mass benchmark systems, yield evidence for small ({approx}100 K) errors in the evolutionary models and/or model atmospheres, but not significantly larger. Future parallax, resolved

Optical systolic array processor using residue arithmetic

NASA Technical Reports Server (NTRS)

Jackson, J.; Casasent, D.

1983-01-01

The use of residue arithmetic to increase the accuracy and reduce the dynamic range requirements of optical matrix-vector processors is evaluated. It is determined that matrix-vector operations and iterative algorithms can be performed totally in residue notation. A new parallel residue quantizer circuit is developed which significantly improves the performance of the systolic array feedback processor. Results are presented of a computer simulation of this system used to solve a set of three simultaneous equations.

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.…

Syntactic Awareness and Arithmetic Word Problem Solving in Children With and Without Learning Disabilities.

PubMed

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

2015-01-01

Arithmetic word problem (AWP) solving is a highly demanding task for children with learning disabilities (LD) since verbal and mathematical information have to be integrated. This study examines specifically how syntactic awareness (SA), the ability to manage the grammatical structures of language, affects AWP solving. Three groups of children in elementary education were formed: children with arithmetic learning disabilities (ALD), children with reading learning disabilities (RLD), and children with comorbid arithmetic and reading learning disabilities (ARLD). Mediation analysis confirmed that SA was a mediator variable for both groups of children with reading disabilities when solving AWPs, but not for children in the ALD group. All groups performed below the control group in the problem solving task. When SA was controlled for, semantic structure and position of the unknown set were variables that affected both groups with ALD. Specifically, children with ALD only were more affected by the place of the unknown set. © Hammill Institute on Disabilities 2014.

The Posing of Arithmetic Problems by Mathematically Talented Students

ERIC Educational Resources Information Center

Espinoza González, Johan; Lupiáñez Gómez, José Luis; Segovia Alex, Isidoro

2016-01-01

Introduction: This paper analyzes the arithmetic problems posed by a group of mathematically talented students when given two problem-posing tasks, and compares these students' responses to those given by a standard group of public school students to the same tasks. Our analysis focuses on characterizing and identifying the differences between the…

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…

Math anxiety and its relationship with basic arithmetic skills among primary school children.

PubMed

Sorvo, Riikka; Koponen, Tuire; Viholainen, Helena; Aro, Tuija; Räikkönen, Eija; Peura, Pilvi; Dowker, Ann; Aro, Mikko

2017-09-01

Children have been found to report and demonstrate math anxiety as early as the first grade. However, previous results concerning the relationship between math anxiety and performance are contradictory, with some studies establishing a correlation between them while others do not. These contradictory results might be related to varying operationalizations of math anxiety. In this study, we aimed to examine the prevalence of math anxiety and its relationship with basic arithmetic skills in primary school children, with explicit focus on two aspects of math anxiety: anxiety about failure in mathematics and anxiety in math-related situations. The participants comprised 1,327 children at grades 2-5. Math anxiety was assessed using six items, and basic arithmetic skills were assessed using three assessment tasks. Around one-third of the participants reported anxiety about being unable to do math, one-fifth about having to answer teachers' questions, and one tenth about having to do math. Confirmatory factor analysis indicated that anxiety about math-related situations and anxiety about failure in mathematics are separable aspects of math anxiety. Structural equation modelling suggested that anxiety about math-related situations was more strongly associated with arithmetic fluency than anxiety about failure. Anxiety about math-related situations was most common among second graders and least common among fifth graders. As math anxiety, particularly about math-related situations, was related to arithmetic fluency even as early as the second grade, children's negative feelings and math anxiety should be identified and addressed from the early primary school years. © 2017 The British Psychological Society.

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...

Binary Plutinos

NASA Astrophysics Data System (ADS)

Noll, Keith S.

2015-08-01

The Pluto-Charon binary was the first trans-neptunian binary to be identified in 1978. Pluto-Charon is a true binary with both components orbiting a barycenter located between them. The Pluto system is also the first, and to date only, known binary with a satellite system consisting of four small satellites in near-resonant orbits around the common center of mass. Seven other Plutinos, objects in 3:2 mean motion resonance with Neptune, have orbital companions including 2004 KB19 reported here for the first time. Compared to the Cold Classical population, the Plutinos differ in the frequency of binaries, the relative sizes of the components, and their inclination distribution. These differences point to distinct dynamical histories and binary formation processes encountered by Plutinos.

A Learning Trajectory for Teaching Social Arithmetic using RME Approach

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

The Binary Toxin CDT of Clostridium difficile as a Tool for Intracellular Delivery of Bacterial Glucosyltransferase Domains.

PubMed

Beer, Lara-Antonia; Tatge, Helma; Schneider, Carmen; Ruschig, Maximilian; Hust, Michael; Barton, Jessica; Thiemann, Stefan; Fühner, Viola; Russo, Giulio; Gerhard, Ralf

2018-06-01

Binary toxins are produced by several pathogenic bacteria. Examples are the C2 toxin from Clostridium botulinum , the iota toxin from Clostridium perfringens, and the CDT from Clostridium difficile . All these binary toxins have ADP-ribosyltransferases (ADPRT) as their enzymatically active component that modify monomeric actin in their target cells. The binary C2 toxin was intensively described as a tool for intracellular delivery of allogenic ADPRTs. Here, we firstly describe the binary toxin CDT from C. difficile as an effective tool for heterologous intracellular delivery. Even 60 kDa glucosyltransferase domains of large clostridial glucosyltransferases can be delivered into cells. The glucosyltransferase domains of five tested large clostridial glucosyltransferases were successfully introduced into cells as chimeric fusions to the CDTa adapter domain (CDTaN). Cell uptake was demonstrated by the analysis of cell morphology, cytoskeleton staining, and intracellular substrate glucosylation. The fusion toxins were functional only when the adapter domain of CDTa was N -terminally located, according to its native orientation. Thus, like other binary toxins, the CDTaN/b system can be used for standardized delivery systems not only for bacterial ADPRTs but also for a variety of bacterial glucosyltransferase domains.

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.

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

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

NASA Astrophysics Data System (ADS)

Heikalabad, Saeed Rasouli; Gadim, Mahya Rahimpour

2018-06-01

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

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

NASA Astrophysics Data System (ADS)

Heikalabad, Saeed Rasouli; Gadim, Mahya Rahimpour

2018-03-01

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

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.

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

ERIC Educational Resources Information Center

Berg, Derek H.

2008-01-01

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

Patterns of Problem-Solving in Children's Literacy and Arithmetic

ERIC Educational Resources Information Center

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

2009-01-01

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 1 and 2 on the…

On the structure of arithmetic sums of Cantor sets with constant ratios of dissection

NASA Astrophysics Data System (ADS)

Anisca, Razvan; Chlebovec, Christopher

2009-09-01

We investigate conditions which imply that the topological structure of the arithmetic sum of two Cantor sets with constant ratios of dissection at each step is either: a Cantor set, a finite union of closed intervals, or three mixed models (L, R and M-Cantorval). We obtain general results that apply in particular for the case of homogeneous Cantor sets, thus generalizing the results of Mendes and Oliveira. The method used here is new in this context. We also produce results regarding the arithmetic sum of two affine Cantor sets of a special kind.

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

PubMed

Buelow, Melissa T; Frakey, Laura L

2013-06-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

Dynamic fisheye grids for binary black hole simulations

NASA Astrophysics Data System (ADS)

Zilhão, Miguel; Noble, Scott C.

2014-03-01

We present a new warped gridding scheme adapted to simulating gas dynamics in binary black hole spacetimes. The grid concentrates grid points in the vicinity of each black hole to resolve the smaller scale structures there, and rarefies grid points away from each black hole to keep the overall problem size at a practical level. In this respect, our system can be thought of as a ‘double’ version of the fisheye coordinate system, used before in numerical relativity codes for evolving binary black holes. The gridding scheme is constructed as a mapping between a uniform coordinate system—in which the equations of motion are solved—to the distorted system representing the spatial locations of our grid points. Since we are motivated to eventually use this system for circumbinary disc calculations, we demonstrate how the distorted system can be constructed to asymptote to the typical spherical polar coordinate system, amenable to efficiently simulating orbiting gas flows about central objects with little numerical diffusion. We discuss its implementation in the Harm3d code, tailored to evolve the magnetohydrodynamics equations in curved spacetimes. We evaluate the performance of the system’s implementation in Harm3d with a series of tests, such as the advected magnetic field loop test, magnetized Bondi accretion, and evolutions of hydrodynamic discs about a single black hole and about a binary black hole. Like we have done with Harm3d, this gridding scheme can be implemented in other unigrid codes as a (possibly) simpler alternative to adaptive mesh refinement.

Equations with Arithmetic Functions of Pell Numbers

DTIC Science & Technology

2014-01-01

Bull. Math. Soc. Sci. Math. Roumanie Tome 57(105) No. 4, 2014, 409–413 Equations with arithmetic functions of Pell numbers by 1Florian Luca...2Pantelimon Stănică Abstract Here, we prove some diophantine results about the Euler function of Pell numbers and their Pell –Lucas companion sequence. For...example, if the Euler function of the nth Pell number Pn or Pell –Lucas companion number Qn is a power of 2, then n ≤ 8. Key Words: Euler function, Pell

Stability of binaries. Part II: Rubble-pile binaries

NASA Astrophysics Data System (ADS)

Sharma, Ishan

2016-10-01

We consider the stability of the binary asteroids whose members are granular aggregates held together by self-gravity alone. A binary is said to be stable whenever both its members are orbitally and structurally stable to both orbital and structural perturbations. To this end, we extend the stability analysis of Sharma (Sharma [2015] Icarus, 258, 438-453), that is applicable to binaries with rigid members, to the case of binary systems with rubble members. We employ volume averaging (Sharma et al. [2009] Icarus, 200, 304-322), which was inspired by past work on elastic/fluid, rotating and gravitating ellipsoids. This technique has shown promise when applied to rubble-pile ellipsoids, but requires further work to settle some of its underlying assumptions. The stability test is finally applied to some suspected binary systems, viz., 216 Kleopatra, 624 Hektor and 90 Antiope. We also see that equilibrated binaries that are close to mobilizing their maximum friction can sustain only a narrow range of shapes and, generally, congruent shapes are preferred.

R144: a very massive binary likely ejected from R136 through a binary-binary encounter

NASA Astrophysics Data System (ADS)

Oh, Seungkyung; Kroupa, Pavel; Banerjee, Sambaran

2014-02-01

R144 is a recently confirmed very massive, spectroscopic binary which appears isolated from the core of the massive young star cluster R136. The dynamical ejection hypothesis as an origin for its location is claimed improbable by Sana et al. due to its binary nature and high mass. We demonstrate here by means of direct N-body calculations that a very massive binary system can be readily dynamically ejected from an R136-like cluster, through a close encounter with a very massive system. One out of four N-body cluster models produces a dynamically ejected very massive binary system with a mass comparable to R144. The system has a system mass of ≈355 M⊙ and is located at 36.8 pc from the centre of its parent cluster, moving away from the cluster with a velocity of 57 km s-1 at 2 Myr as a result of a binary-binary interaction. This implies that R144 could have been ejected from R136 through a strong encounter with another massive binary or single star. In addition, we discuss all massive binaries and single stars which are ejected dynamically from their parent cluster in the N-body models.

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

ERIC Educational Resources Information Center

Marshall, Sandra P.

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

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…

Finger gnosis predicts a unique but small part of variance in initial arithmetic performance.

PubMed

Wasner, Mirjam; Nuerk, Hans-Christoph; Martignon, Laura; Roesch, Stephanie; Moeller, Korbinian

2016-06-01

Recent studies indicated that finger gnosis (i.e., the ability to perceive and differentiate one's own fingers) is associated reliably with basic numerical competencies. In this study, we aimed at examining whether finger gnosis is also a unique predictor for initial arithmetic competencies at the beginning of first grade-and thus before formal math instruction starts. Therefore, we controlled for influences of domain-specific numerical precursor competencies, domain-general cognitive ability, and natural variables such as gender and age. Results from 321 German first-graders revealed that finger gnosis indeed predicted a unique and relevant but nevertheless only small part of the variance in initial arithmetic performance (∼1%-2%) as compared with influences of general cognitive ability and numerical precursor competencies. Taken together, these results substantiated the notion of a unique association between finger gnosis and arithmetic and further corroborate the theoretical idea of finger-based representations contributing to numerical cognition. However, the only small part of variance explained by finger gnosis seems to limit its relevance for diagnostic purposes. Copyright © 2016. Published by Elsevier Inc.

An algorithm for the arithmetic classification of multilattices.

PubMed

Indelicato, Giuliana

2013-01-01

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

Stellar and Circumstellar Properties of Low-Mass, Young, Subarcsecond Binaries

NASA Astrophysics Data System (ADS)

Bruhns, Sara; Prato, L. A.

2014-01-01

We present a study of the stellar and circumstellar characteristics of close (< 1''), young (< 2 to 3 Myr), low-mass (<1 solar mass) binary stars in the Taurus star forming region. Low-resolution (R ~ 2000) spectra were taken in the K-band using adaptive optics to separate the observations for each component and identify the individual spectral types, extinction, and K-band excess. Combining these data with stellar luminosities allows us to estimate the stellar masses and ages. We also measured equivalent widths of the hydrogen Brackett gamma line in order to estimate the strength of gas accretion. We obtained spectra for six binary systems with separations from 1'' down to 0.3''. In the CZ Tau binary we found that the fainter secondary star spectrum appears to be of earlier spectral type than the primary; we speculate on the origin of this inversion.

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

Robust Adaptive Thresholder For Document Scanning Applications

NASA Astrophysics Data System (ADS)

Hsing, To R.

1982-12-01

In document scanning applications, thresholding is used to obtain binary data from a scanner. However, due to: (1) a wide range of different color backgrounds; (2) density variations of printed text information; and (3) the shading effect caused by the optical systems, the use of adaptive thresholding to enhance the useful information is highly desired. This paper describes a new robust adaptive thresholder for obtaining valid binary images. It is basically a memory type algorithm which can dynamically update the black and white reference level to optimize a local adaptive threshold function. The results of high image quality from different types of simulate test patterns can be obtained by this algorithm. The software algorithm is described and experiment results are present to describe the procedures. Results also show that the techniques described here can be used for real-time signal processing in the varied applications.

Arithmetical functions and irrationality of Lambert series

NASA Astrophysics Data System (ADS)

Duverney, Daniel

2011-09-01

We use a method of Erdös in order to prove the linear independence over Q of the numbers 1, ∑ n = 1+∞1/qn2-1, ∑ n = 1+∞n/qn2-1 for every q∈Z, with |q|≥2. The main idea consists in considering the two above series as Lambert series. This allows to expand them as power series of 1/q. The Taylor coefficients of these expansions are arithmetical functions, whose properties allow to apply an elementary irrationality criterion, which yields the result.

Noncommutative geometry and arithmetics

NASA Astrophysics Data System (ADS)

Almeida, P.

2009-09-01

We intend to illustrate how the methods of noncommutative geometry are currently used to tackle problems in class field theory. Noncommutative geometry enables one to think geometrically in situations in which the classical notion of space formed of points is no longer adequate, and thus a “noncommutative space” is needed; a full account of this approach is given in [3] by its main contributor, Alain Connes. The class field theory, i.e., number theory within the realm of Galois theory, is undoubtedly one of the main achievements in arithmetics, leading to an important algebraic machinery; for a modern overview, see [23]. The relationship between noncommutative geometry and number theory is one of the many themes treated in [22, 7-9, 11], a small part of which we will try to put in a more down-to-earth perspective, illustrating through an example what should be called an “application of physics to mathematics,” and our only purpose is to introduce nonspecialists to this beautiful area.

Bounds for the price of discrete arithmetic Asian options

NASA Astrophysics Data System (ADS)

Vanmaele, M.; Deelstra, G.; Liinev, J.; Dhaene, J.; Goovaerts, M. J.

2006-01-01

In this paper the pricing of European-style discrete arithmetic Asian options with fixed and floating strike is studied by deriving analytical lower and upper bounds. In our approach we use a general technique for deriving upper (and lower) bounds for stop-loss premiums of sums of dependent random variables, as explained in Kaas et al. (Ins. Math. Econom. 27 (2000) 151-168), and additionally, the ideas of Rogers and Shi (J. Appl. Probab. 32 (1995) 1077-1088) and of Nielsen and Sandmann (J. Financial Quant. Anal. 38(2) (2003) 449-473). We are able to create a unifying framework for European-style discrete arithmetic Asian options through these bounds, that generalizes several approaches in the literature as well as improves the existing results. We obtain analytical and easily computable bounds. The aim of the paper is to formulate an advice of the appropriate choice of the bounds given the parameters, investigate the effect of different conditioning variables and compare their efficiency numerically. Several sets of numerical results are included. We also discuss hedging using these bounds. Moreover, our methods are applicable to a wide range of (pricing) problems involving a sum of dependent random variables.

Neural computation of arithmetic functions

NASA Technical Reports Server (NTRS)

Siu, Kai-Yeung; Bruck, Jehoshua

1990-01-01

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

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

PubMed

Macdonald, R I

1987-10-01

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

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…

Sex Differences in Arithmetical Performance Scores: Central Tendency and Variability

ERIC Educational Resources Information Center

Martens, R.; Hurks, P. P. M.; Meijs, C.; Wassenberg, R.; Jolles, J.

2011-01-01

The present study aimed to analyze sex differences in arithmetical performance in a large-scale sample of 390 children (193 boys) frequenting grades 1-9. Past research in this field has focused primarily on average performance, implicitly assuming homogeneity of variance, for which support is scarce. This article examined sex differences in…

Using Microcomputers To Help Learning Disabled Student with Arithmetic Difficulties.

ERIC Educational Resources Information Center

Brevil, Margarette

The use of microcomputers to help the learning disabled increase their arithmetic skills is examined. The microcomputer should be used to aid the learning disabled student to practice the concepts taught by the teacher. Computer-aided instruction such as drill and practice may help the learning disabled student because it gives immediate feedback…

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

PubMed

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

2017-01-01

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

Final binary star results from the ESO VLT Lunar occultations program

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

Richichi, A.; Fors, O.; Cusano, F.

2014-03-01

We report on 13 subarcsecond binaries, detected by means of lunar occultations in the near-infrared at the ESO Very Large Telescope (VLT). They are all first-time detections except for the visual binary HD 158122, which we resolved for the first time in the near-infrared. The primaries have magnitudes in the range K = 4.5-10.0, and companions in the range K = 6.8-11.1. The magnitude differences have a median value of 2.4, with the largest being 4.6. The projected separations are in the range of 4-168 mas, with a median of 13 mas. We discuss and compare our results with themore » available literature. With this paper, we conclude the mining for binary star detections in the 1226 occultations recorded at the VLT with the ISAAC instrument. We expect that the majority of these binaries may be unresolvable by adaptive optics on current telescopes, and they might be challenging for long-baseline interferometry. However, they constitute an interesting sample for future larger telescopes and for astrometric missions such as GAIA.« less

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

PubMed Central

Demir, Özlem Ece; Prado, Jérôme; Booth, James R.

2014-01-01

We examine the relations of verbal and spatial WM ability to the neural bases of arithmetic in school-age children. We independently localize brain regions subserving verbal versus spatial representations. For multiplication, higher verbal WM ability is associated with greater recruitment of the left temporal cortex, identified by the verbal localizer. For multiplication and subtraction, higher spatial WM ability is associated with greater recruitment of right parietal cortex, identified by the spatial localizer. Depending on their WM ability, children engage different neural systems that manipulate different representations to solve arithmetic problems. PMID:25144257

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

ERIC Educational Resources Information Center

De Visscher, Alice; Noël, Marie-Pascale

2014-01-01

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

KIC 7177553: A QUADRUPLE SYSTEM OF TWO CLOSE BINARIES

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

Lehmann, H.; Borkovits, T.; Rappaport, S. A.

2016-03-01

KIC 7177553 was observed by the Kepler satellite to be an eclipsing eccentric binary star system with an 18-day orbital period. Recently, an eclipse timing study of the Kepler binaries has revealed eclipse timing variations (ETVs) in this object with an amplitude of ∼100 s and an outer period of 529 days. The implied mass of the third body is that of a super-Jupiter, but below the mass of a brown dwarf. We therefore embarked on a radial velocity (RV) study of this binary to determine its system configuration and to check the hypothesis that it hosts a giant planet. Frommore » the RV measurements, it became immediately obvious that the same Kepler target contains another eccentric binary, this one with a 16.5-day orbital period. Direct imaging using adaptive optics reveals that the two binaries are separated by 0.″4 (∼167 AU) and have nearly the same magnitude (to within 2%). The close angular proximity of the two binaries and very similar γ velocities strongly suggest that KIC 7177553 is one of the rare SB4 systems consisting of two eccentric binaries where at least one system is eclipsing. Both systems consist of slowly rotating, nonevolved, solar-like stars of comparable masses. From the orbital separation and the small difference in γ velocity, we infer that the period of the outer orbit most likely lies in the range of 1000–3000 yr. New images taken over the next few years, as well as the high-precision astrometry of the Gaia satellite mission, will allow us to set much narrower constraints on the system geometry. Finally, we note that the observed ETVs in the Kepler data cannot be produced by the second binary. Further spectroscopic observations on a longer timescale will be required to prove the existence of the massive planet.« less

Unconscious Addition: When We Unconsciously Initiate and Follow Arithmetic Rules

ERIC Educational Resources Information Center

Ric, Francois; Muller, Dominique

2012-01-01

This research shows that people can unconsciously initiate and follow arithmetic rules (e.g., addition). Participants were asked to detect whether a symbol was a digit. This symbol was preceded by 2 digits and a subliminal instruction: "add" or a control instruction. Participants were faster at identifying a symbol as a number when the…

Neural Correlates of Arithmetic and Language Comprehension: A Common Substrate?

ERIC Educational Resources Information Center

Baldo, Juliana V.; Dronkers, Nina F.

2007-01-01

There is debate as to the relationship between mathematical ability and language. Some research has suggested that common processes underlie arithmetic and grammar while other research has suggested that these are distinct processes. The current study aimed to address this issue in a large group of 68 left hemisphere stroke patients who were all…

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…

Developing an effective multimedia in education for special education (MESE): An introduction to arithmetic

NASA Astrophysics Data System (ADS)

Munir, Kusnendar, Jajang; Rahmadhani

2016-02-01

This research aims to develop and test the effectiveness of multimedia in education for special education (MESE) of students with cognitive disabilities in introducing Arithmetic. Students with cognitive disabilities are those who have a level of intelligence under the normal ones. They think concretely and tend to have a very limited memory, switched concentration and forgot easily. The mastery of words is minimal, and also requires a long time to learn. These limitations will interfere in introduction learning to Arithmetic, with the material of numbers 1 to 10. The study resulted that MESE is worth to be used and enhanced the ability of the students.

Discovery of a Highly Unequal-mass Binary T Dwarf with Keck Laser Guide Star Adaptive Optics: A Coevality Test of Substellar Theoretical Models and Effective Temperatures

NASA Astrophysics Data System (ADS)

Liu, Michael C.; Dupuy, Trent J.; Leggett, S. K.

2010-10-01

Highly unequal-mass ratio binaries are rare among field brown dwarfs, with the mass ratio distribution of the known census described by q (4.9±0.7). However, such systems enable a unique test of the joint accuracy of evolutionary and atmospheric models, under the constraint of coevality for the individual components (the "isochrone test"). We carry out this test using two of the most extreme field substellar binaries currently known, the T1 + T6 epsilon Ind Bab binary and a newly discovered 0farcs14 T2.0 + T7.5 binary, 2MASS J12095613-1004008AB, identified with Keck laser guide star adaptive optics. The latter is the most extreme tight binary resolved to date (q ≈ 0.5). Based on the locations of the binary components on the Hertzsprung-Russell (H-R) diagram, current models successfully indicate that these two systems are coeval, with internal age differences of log(age) = -0.8 ± 1.3(-1.0+1.2 -1.3) dex and 0.5+0.4 -0.3(0.3+0.3 -0.4) dex for 2MASS J1209-1004AB and epsilon Ind Bab, respectively, as inferred from the Lyon (Tucson) models. However, the total mass of epsilon Ind Bab derived from the H-R diagram (≈ 80 M Jup using the Lyon models) is strongly discrepant with the reported dynamical mass. This problem, which is independent of the assumed age of the epsilon Ind Bab system, can be explained by a ≈ 50-100 K systematic error in the model atmosphere fitting, indicating slightly warmer temperatures for both components; bringing the mass determinations from the H-R diagram and the visual orbit into consistency leads to an inferred age of ≈ 6 Gyr for epsilon Ind Bab, older than previously assumed. Overall, the two T dwarf binaries studied here, along with recent results from T dwarfs in age and mass benchmark systems, yield evidence for small (≈100 K) errors in the evolutionary models and/or model atmospheres, but not significantly larger. Future parallax, resolved spectroscopy, and dynamical mass measurements for 2MASS J1209-1004AB will enable a more

Nonsymbolic, Approximate Arithmetic in Children: Abstract Addition Prior to Instruction

ERIC Educational Resources Information Center

Barth, Hilary; Beckmann, Lacey; Spelke, Elizabeth S.

2008-01-01

Do children draw upon abstract representations of number when they perform approximate arithmetic operations? In this study, kindergarten children viewed animations suggesting addition of a sequence of sounds to an array of dots, and they compared the sum to a second dot array that differed from the sum by 1 of 3 ratios. Children performed this…

Fluency, Accuracy, and Gender Predict Developmental Trajectories of Arithmetic Strategies

ERIC Educational Resources Information Center

Carr, Martha; Alexeev, Natalia

2011-01-01

The purpose of this study was to determine whether there are different growth trajectories of arithmetic strategies and whether these trajectories result in different achievement outcomes. Longitudinal data were collected on 240 students who began the study as 2nd graders. In the 1st year of the study, the 2nd-grade students were assessed on…

Spontaneous Meta-Arithmetic as a First Step toward School Algebra

ERIC Educational Resources Information Center

Caspi, Shai; Sfard, Anna

2012-01-01

Taking as the point of departure the vision of school algebra as a formalized meta-discourse of arithmetic, we have been following five pairs of 7th grade students as they progress in algebraic discourse during 24 months, from their informal algebraic talk to the formal algebraic discourse, as taught in school. Our analysis follows changes that…

Adaptive allocation for binary outcomes using decreasingly informative priors.

PubMed

Sabo, Roy T

2014-01-01

A method of outcome-adaptive allocation is presented using Bayes methods, where a natural lead-in is incorporated through the use of informative yet skeptical prior distributions for each treatment group. These prior distributions are modeled on unobserved data in such a way that their influence on the allocation scheme decreases as the trial progresses. Simulation studies show this method to behave comparably to the Bayesian adaptive allocation method described by Thall and Wathen (2007), who incorporate a natural lead-in through sample-size-based exponents.

Redesigning Arithmetic for Student Success: Supporting Faculty to Teach in New Ways

ERIC Educational Resources Information Center

Bickerstaff, Susan; Lontz, Barbara; Cormier, Maria Scott; Xu, Di

2014-01-01

This chapter describes a promising new approach to teaching developmental arithmetic and prealgebra, and presents research findings that demonstrate how a faculty support network helped instructors adopt new teaching strategies and gain confidence in teaching the reformed course.

GUIELOA: Adaptive Optics System for the 2.1-m SPM UNAM Telescope

NASA Astrophysics Data System (ADS)

Cuevas, S.; Iriarte, A.; Martínez, L. A.; Garfias, F.; Sánchez, L.; Chapa, O.; Ruelas, R. A.

2004-08-01

GUIELOA is the adaptive optics system project for the 2.1-m SPM telescope. This is a 19 sub-apertures curvature-type system. It corrects 8 Zernike terms. GUIELOA is very similar to PUEO, the CFHT adaptive optics system and compensates the atmospheric turbulence from the R band to the K band. Among the planned applications of GUIELOA are the study of OB binary systems, the detection of close binary stars, and the study of disks, jets and other phenomena associated with young stars.

The Codevelopment of Children's Fraction Arithmetic Skill and Fraction Magnitude Understanding

ERIC Educational Resources Information Center

Bailey, Drew H.; Hansen, Nicole; Jordan, Nancy C.

2017-01-01

The importance of fraction knowledge to later mathematics achievement, along with U.S. students' poor knowledge of fraction concepts and procedures, has prompted research on the development of fraction learning. In the present study, participants' (N = 536) development of fraction magnitude understanding and fraction arithmetic skills was assessed…

Dynamic and scalable audio classification by collective network of binary classifiers framework: an evolutionary approach.

PubMed

Kiranyaz, Serkan; Mäkinen, Toni; Gabbouj, Moncef

2012-10-01

In this paper, we propose a novel framework based on a collective network of evolutionary binary classifiers (CNBC) to address the problems of feature and class scalability. The main goal of the proposed framework is to achieve a high classification performance over dynamic audio and video repositories. The proposed framework adopts a "Divide and Conquer" approach in which an individual network of binary classifiers (NBC) is allocated to discriminate each audio class. An evolutionary search is applied to find the best binary classifier in each NBC with respect to a given criterion. Through the incremental evolution sessions, the CNBC framework can dynamically adapt to each new incoming class or feature set without resorting to a full-scale re-training or re-configuration. Therefore, the CNBC framework is particularly designed for dynamically varying databases where no conventional static classifiers can adapt to such changes. In short, it is entirely a novel topology, an unprecedented approach for dynamic, content/data adaptive and scalable audio classification. A large set of audio features can be effectively used in the framework, where the CNBCs make appropriate selections and combinations so as to achieve the highest discrimination among individual audio classes. Experiments demonstrate a high classification accuracy (above 90%) and efficiency of the proposed framework over large and dynamic audio databases. Copyright © 2012 Elsevier Ltd. All rights reserved.

A cellular automaton - finite volume method for the simulation of dendritic and eutectic growth in binary alloys using an adaptive mesh refinement

NASA Astrophysics Data System (ADS)

Dobravec, Tadej; Mavrič, Boštjan; Šarler, Božidar

2017-11-01

A two-dimensional model to simulate the dendritic and eutectic growth in binary alloys is developed. A cellular automaton method is adopted to track the movement of the solid-liquid interface. The diffusion equation is solved in the solid and liquid phases by using an explicit finite volume method. The computational domain is divided into square cells that can be hierarchically refined or coarsened using an adaptive mesh based on the quadtree algorithm. Such a mesh refines the regions of the domain near the solid-liquid interface, where the highest concentration gradients are observed. In the regions where the lowest concentration gradients are observed the cells are coarsened. The originality of the work is in the novel, adaptive approach to the efficient and accurate solution of the posed multiscale problem. The model is verified and assessed by comparison with the analytical results of the Lipton-Glicksman-Kurz model for the steady growth of a dendrite tip and the Jackson-Hunt model for regular eutectic growth. Several examples of typical microstructures are simulated and the features of the method as well as further developments are discussed.

Neutron-Star-Black-Hole Binaries Produced by Binary-Driven Hypernovae

NASA Astrophysics Data System (ADS)

Fryer, Chris L.; Oliveira, F. G.; Rueda, J. A.; Ruffini, R.

2015-12-01

Binary-driven hypernovae (BdHNe) within the induced gravitational collapse paradigm have been introduced to explain energetic (Eiso≳1052 erg ), long gamma-ray bursts (GRBs) associated with type Ic supernovae (SNe). The progenitor is a tight binary composed of a carbon-oxygen (CO) core and a neutron-star (NS) companion, a subclass of the newly proposed "ultrastripped" binaries. The CO-NS short-period orbit causes the NS to accrete appreciable matter from the SN ejecta when the CO core collapses, ultimately causing it to collapse to a black hole (BH) and producing a GRB. These tight binaries evolve through the SN explosion very differently than compact binaries studied in population synthesis calculations. First, the hypercritical accretion onto the NS companion alters both the mass and the momentum of the binary. Second, because the explosion time scale is on par with the orbital period, the mass ejection cannot be assumed to be instantaneous. This dramatically affects the post-SN fate of the binary. Finally, the bow shock created as the accreting NS plows through the SN ejecta transfers angular momentum, braking the orbit. These systems remain bound even if a large fraction of the binary mass is lost in the explosion (well above the canonical 50% limit), and even large kicks are unlikely to unbind the system. Indeed, BdHNe produce a new family of NS-BH binaries unaccounted for in current population synthesis analyses and, although they may be rare, the fact that nearly 100% remain bound implies that they may play an important role in the compact merger rate, important for gravitational waves that, in turn, can produce a new class of ultrashort GRBs.

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

ERIC Educational Resources Information Center

Persky, Ronald L.

2003-01-01

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

Pulsars in binary systems: probing binary stellar evolution and general relativity.

PubMed

Stairs, Ingrid H

2004-04-23

Radio pulsars in binary orbits often have short millisecond spin periods as a result of mass transfer from their companion stars. They therefore act as very precise, stable, moving clocks that allow us to investigate a large set of otherwise inaccessible astrophysical problems. The orbital parameters derived from high-precision binary pulsar timing provide constraints on binary evolution, characteristics of the binary pulsar population, and the masses of neutron stars with different mass-transfer histories. These binary systems also test gravitational theories, setting strong limits on deviations from general relativity. Surveys for new pulsars yield new binary systems that increase our understanding of all these fields and may open up whole new areas of physics, as most spectacularly evidenced by the recent discovery of an extremely relativistic double-pulsar system.

How I Learned to Stop Worrying and Love Eclipsing Binaries

NASA Astrophysics Data System (ADS)

Moe, Maxwell Cassady

producing sinusoidal variations in perceived brightness as they orbit. These nascent eclipsing binaries are embedded in the hearts of star-forming emission nebulae, and therefore provide a unique snapshot into the formation and evolution of massive binaries and stellar nurseries. We next examine a large sample of B-type eclipsing binaries with intermediate orbital periods. To achieve such a task, we develop an automated pipeline to classify the eclipsing binaries, measure their physical properties from the observed light curves, and recover the intrinsic binary statistics by correcting for selection effects. We find the population of massive binaries at intermediate separations differ from those orbiting in close proximity. Close massive binaries favor small eccentricities and have correlated component masses, demonstrating they coevolved via competitive accretion during their formation in the circumbinary disk. Meanwhile, B-type binaries at slightly wider separations are born with large eccentricities and are weighted toward extreme mass ratios, indicating the components formed relatively independently and subsequently evolved to their current configurations via dynamical interactions. By using eclipsing binaries as accurate age indicators, we also reveal that the binary orbital eccentricities and the line-of-sight dust extinctions are anticorrelated with respect to time. These empirical relations provide robust constraints for tidal evolution in massive binaries and the evolution of the dust content in their surrounding environments. Finally, we compile observations of early-type binaries identified via spectroscopy, eclipses, long-baseline interferometry, adaptive optics, lucky imaging, high-contrast photometry, and common proper motion. We combine the samples from the various surveys and correct for their respective selection effects to determine a comprehensive nature of the intrinsic binary statistics of massive stars. We find the probability distributions of primary

Adaptation and focusing of optode configurations for fluorescence optical tomography by experimental design methods.

PubMed

Freiberger, Manuel; Clason, Christian; Scharfetter, Hermann

2010-01-01

Fluorescence tomography excites a fluorophore inside a sample by light sources on the surface. From boundary measurements of the fluorescent light, the distribution of the fluorophore is reconstructed. The optode placement determines the quality of the reconstructions in terms of, e.g., resolution and contrast-to-noise ratio. We address the adaptation of the measurement setup. The redundancy of the measurements is chosen as a quality criterion for the optodes and is computed from the Jacobian of the mathematical formulation of light propagation. The algorithm finds a subset with minimum redundancy in the measurements from a feasible pool of optodes. This allows biasing the design in order to favor reconstruction results inside a given region. Two different variations of the algorithm, based on geometric and arithmetic averaging, are compared. Both deliver similar optode configurations. The arithmetic averaging is slightly more stable, whereas the geometric averaging approach shows a better conditioning of the sensitivity matrix and mathematically corresponds more closely with entropy optimization. Adapted illumination and detector patterns are presented for an initial set of 96 optodes placed on a cylinder with focusing on different regions. Examples for the attenuation of fluorophore signals from regions outside the focus are given.

Arithmetic Practice Can Be Modified to Promote Understanding of Mathematical Equivalence

ERIC Educational Resources Information Center

McNeil, Nicole M.; Fyfe, Emily R.; Dunwiddie, April E.

2015-01-01

This experiment tested if a modified version of arithmetic practice facilitates understanding of math equivalence. Children within 2nd-grade classrooms (N = 166) were randomly assigned to practice single-digit addition facts using 1 of 2 workbooks. In the control workbook, problems were presented in the traditional "operations = answer"…

The Role of the Updating Function in Solving Arithmetic Word Problems

ERIC Educational Resources Information Center

Mori, Kanetaka; Okamoto, Masahiko

2017-01-01

We investigated how the updating function supports the integration process in solving arithmetic word problems. In Experiment 1, we measured reading time, that is, translation and integration times, when undergraduate and graduate students (n = 78) were asked to solve 2 types of problems: those containing only necessary information and those…

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

PubMed Central

2012-01-01

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

Neutron-star–black-hole binaries produced by binary-driven hypernovae

DOE PAGES

Fryer, Chris L.; Oliveira, F. G.; Rueda, Jorge A.; ...

2015-12-04

Here, binary-driven hypernovae (BdHNe) within the induced gravitational collapse paradigm have been introduced to explain energetic (E iso ≳10 52 erg), long gamma-ray bursts (GRBs) associated with type Ic supernovae (SNe). The progenitor is a tight binary composed of a carbon-oxygen (CO) core and a neutron-star (NS) companion, a subclass of the newly proposed “ultrastripped” binaries. The CO-NS short-period orbit causes the NS to accrete appreciable matter from the SN ejecta when the CO core collapses, ultimately causing it to collapse to a black hole (BH) and producing a GRB. These tight binaries evolve through the SN explosion very differentlymore » than compact binaries studied in population synthesis calculations. First, the hypercritical accretion onto the NS companion alters both the mass and the momentum of the binary. Second, because the explosion time scale is on par with the orbital period, the mass ejection cannot be assumed to be instantaneous. This dramatically affects the post-SN fate of the binary. Finally, the bow shock created as the accreting NS plows through the SN ejecta transfers angular momentum, braking the orbit. These systems remain bound even if a large fraction of the binary mass is lost in the explosion (well above the canonical 50% limit), and even large kicks are unlikely to unbind the system. Indeed, BdHNe produce a new family of NS-BH binaries unaccounted for in current population synthesis analyses and, although they may be rare, the fact that nearly 100% remain bound implies that they may play an important role in the compact merger rate, important for gravitational waves that, in turn, can produce a new class of ultrashort GRBs.« less

Neutron-Star-Black-Hole Binaries Produced by Binary-Driven Hypernovae.

PubMed

Fryer, Chris L; Oliveira, F G; Rueda, J A; Ruffini, R

2015-12-04

Binary-driven hypernovae (BdHNe) within the induced gravitational collapse paradigm have been introduced to explain energetic (E_{iso}≳10^{52}  erg), long gamma-ray bursts (GRBs) associated with type Ic supernovae (SNe). The progenitor is a tight binary composed of a carbon-oxygen (CO) core and a neutron-star (NS) companion, a subclass of the newly proposed "ultrastripped" binaries. The CO-NS short-period orbit causes the NS to accrete appreciable matter from the SN ejecta when the CO core collapses, ultimately causing it to collapse to a black hole (BH) and producing a GRB. These tight binaries evolve through the SN explosion very differently than compact binaries studied in population synthesis calculations. First, the hypercritical accretion onto the NS companion alters both the mass and the momentum of the binary. Second, because the explosion time scale is on par with the orbital period, the mass ejection cannot be assumed to be instantaneous. This dramatically affects the post-SN fate of the binary. Finally, the bow shock created as the accreting NS plows through the SN ejecta transfers angular momentum, braking the orbit. These systems remain bound even if a large fraction of the binary mass is lost in the explosion (well above the canonical 50% limit), and even large kicks are unlikely to unbind the system. Indeed, BdHNe produce a new family of NS-BH binaries unaccounted for in current population synthesis analyses and, although they may be rare, the fact that nearly 100% remain bound implies that they may play an important role in the compact merger rate, important for gravitational waves that, in turn, can produce a new class of ultrashort GRBs.

Multireader multicase reader studies with binary agreement data: simulation, analysis, validation, and sizing.

PubMed

Chen, Weijie; Wunderlich, Adam; Petrick, Nicholas; Gallas, Brandon D

2014-10-01

We treat multireader multicase (MRMC) reader studies for which a reader's diagnostic assessment is converted to binary agreement (1: agree with the truth state, 0: disagree with the truth state). We present a mathematical model for simulating binary MRMC data with a desired correlation structure across readers, cases, and two modalities, assuming the expected probability of agreement is equal for the two modalities ([Formula: see text]). This model can be used to validate the coverage probabilities of 95% confidence intervals (of [Formula: see text], [Formula: see text], or [Formula: see text] when [Formula: see text]), validate the type I error of a superiority hypothesis test, and size a noninferiority hypothesis test (which assumes [Formula: see text]). To illustrate the utility of our simulation model, we adapt the Obuchowski-Rockette-Hillis (ORH) method for the analysis of MRMC binary agreement data. Moreover, we use our simulation model to validate the ORH method for binary data and to illustrate sizing in a noninferiority setting. Our software package is publicly available on the Google code project hosting site for use in simulation, analysis, validation, and sizing of MRMC reader studies with binary agreement data.

Trojan Binaries

NASA Astrophysics Data System (ADS)

Noll, K. S.

2017-12-01

The Jupiter Trojans, in the context of giant planet migration models, can be thought of as an extension of the small body populations found beyond Neptune in the Kuiper Belt. Binaries are a distinctive feature of small body populations in the Kuiper Belt with an especially high fraction apparent among the brightest Cold Classicals. The binary fraction, relative sizes, and separations in the dynamically excited populations (Scattered, Resonant) reflects processes that may have eroded a more abundant initial population. This trend continues in the Centaurs and Trojans where few binaries have been found. We review new evidence including a third resolved Trojan binary and lightcurve studies to understand how the Trojans are related to the small body populations that originated in the outer protoplanetary disk.

Parallel computations and control of adaptive structures

NASA Technical Reports Server (NTRS)

Park, K. C.; Alvin, Kenneth F.; Belvin, W. Keith; Chong, K. P. (Editor); Liu, S. C. (Editor); Li, J. C. (Editor)

1991-01-01

The equations of motion for structures with adaptive elements for vibration control are presented for parallel computations to be used as a software package for real-time control of flexible space structures. A brief introduction of the state-of-the-art parallel computational capability is also presented. Time marching strategies are developed for an effective use of massive parallel mapping, partitioning, and the necessary arithmetic operations. An example is offered for the simulation of control-structure interaction on a parallel computer and the impact of the approach presented for applications in other disciplines than aerospace industry is assessed.

Robust image region descriptor using local derivative ordinal binary pattern

NASA Astrophysics Data System (ADS)

Shang, Jun; Chen, Chuanbo; Pei, Xiaobing; Liang, Hu; Tang, He; Sarem, Mudar

2015-05-01

Binary image descriptors have received a lot of attention in recent years, since they provide numerous advantages, such as low memory footprint and efficient matching strategy. However, they utilize intermediate representations and are generally less discriminative than floating-point descriptors. We propose an image region descriptor, namely local derivative ordinal binary pattern, for object recognition and image categorization. In order to preserve more local contrast and edge information, we quantize the intensity differences between the central pixels and their neighbors of the detected local affine covariant regions in an adaptive way. These differences are then sorted and mapped into binary codes and histogrammed with a weight of the sum of the absolute value of the differences. Furthermore, the gray level of the central pixel is quantized to further improve the discriminative ability. Finally, we combine them to form a joint histogram to represent the features of the image. We observe that our descriptor preserves more local brightness and edge information than traditional binary descriptors. Also, our descriptor is robust to rotation, illumination variations, and other geometric transformations. We conduct extensive experiments on the standard ETHZ and Kentucky datasets for object recognition and PASCAL for image classification. The experimental results show that our descriptor outperforms existing state-of-the-art methods.

[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.

Improving Preschoolers’ Arithmetic through Number Magnitude Training: The Impact of Non-Symbolic and Symbolic Training

PubMed Central

2016-01-01

The numerical cognition literature offers two views to explain numerical and arithmetical development. The unique-representation view considers the approximate number system (ANS) to represent the magnitude of both symbolic and non-symbolic numbers and to be the basis of numerical learning. In contrast, the dual-representation view suggests that symbolic and non-symbolic skills rely on different magnitude representations and that it is the ability to build an exact representation of symbolic numbers that underlies math learning. Support for these hypotheses has come mainly from correlative studies with inconsistent results. In this study, we developed two training programs aiming at enhancing the magnitude processing of either non-symbolic numbers or symbolic numbers and compared their effects on arithmetic skills. Fifty-six preschoolers were randomly assigned to one of three 10-session-training conditions: (1) non-symbolic training (2) symbolic training and (3) control training working on story understanding. Both numerical training conditions were significantly more efficient than the control condition in improving magnitude processing. Moreover, symbolic training led to a significantly larger improvement in arithmetic than did non-symbolic training and the control condition. These results support the dual-representation view. PMID:27875540

Numerical Simulations of Wind Accretion in Symbiotic Binaries

NASA Astrophysics Data System (ADS)

de Val-Borro, M.; Karovska, M.; Sasselov, D.

2009-08-01

About half of the binary systems are close enough to each other for mass to be exchanged between them at some point in their evolution, yet the accretion mechanism in wind accreting binaries is not well understood. We study the dynamical effects of gravitational focusing by a binary companion on winds from late-type stars. In particular, we investigate the mass transfer and formation of accretion disks around the secondary in detached systems consisting of an asymptotic giant branch (AGB) mass-losing star and an accreting companion. The presence of mass outflows is studied as a function of mass-loss rate, wind temperature, and binary orbital parameters. A two-dimensional hydrodynamical model is used to study the stability of mass transfer in wind accreting symbiotic binary systems. In our simulations we use an adiabatic equation of state and a modified version of the isothermal approximation, where the temperature depends on the distance from the mass losing star and its companion. The code uses a block-structured adaptive mesh refinement method that allows us to have high resolution at the position of the secondary and resolve the formation of bow shocks and accretion disks. We explore the accretion flow between the components and formation of accretion disks for a range of orbital separations and wind parameters. Our results show the formation of stream flow between the stars and accretion disks of various sizes for certain orbital configurations. For a typical slow and massive wind from an AGB star the flow pattern is similar to a Roche lobe overflow with accretion rates of 10% of the mass loss from the primary. Stable disks with exponentially decreasing density profiles and masses of the order 10-4 solar masses are formed when wind acceleration occurs at several stellar radii. The disks are geometrically thin with eccentric streamlines and close to Keplerian velocity profiles. The formation of tidal streams and accretion disks is found to be weakly dependent on

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

PubMed

Oyama, Katsunori; Sakatani, Kaoru

2016-01-01

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

Bit-systolic arithmetic arrays using dynamic differential gallium arsenide circuits

NASA Technical Reports Server (NTRS)

Beagles, Grant; Winters, Kel; Eldin, A. G.

1992-01-01

A new family of gallium arsenide circuits for fine grained bit-systolic arithmetic arrays is introduced. This scheme combines features of two recent techniques of dynamic gallium arsenide FET logic and differential dynamic single-clock CMOS logic. The resulting circuits are fast and compact, with tightly constrained series FET propagation paths, low fanout, no dc power dissipation, and depletion FET implementation without level shifting diodes.

An Experimental Comparison of an Intrinsically Programed Text and a Narrative Text.

ERIC Educational Resources Information Center

Senter, R. J.; And Others

The study compared three methods of instruction in binary and octal arithmetic, i.e., (1) Norman Crowder's branched programed text, "The Arithmetic of Computers," (2) another version of this text modified so that subjects could not see the instructional material while answering "branching" questions, and (3) a narrative text…

Testing the Binary Black Hole Nature of a Compact Binary Coalescence

NASA Astrophysics Data System (ADS)

Krishnendu, N. V.; Arun, K. G.; Mishra, Chandra Kant

2017-09-01

We propose a novel method to test the binary black hole nature of compact binaries detectable by gravitational wave (GW) interferometers and, hence, constrain the parameter space of other exotic compact objects. The spirit of the test lies in the "no-hair" conjecture for black holes where all properties of a Kerr black hole are characterized by its mass and spin. The method relies on observationally measuring the quadrupole moments of the compact binary constituents induced due to their spins. If the compact object is a Kerr black hole (BH), its quadrupole moment is expressible solely in terms of its mass and spin. Otherwise, the quadrupole moment can depend on additional parameters (such as the equation of state of the object). The higher order spin effects in phase and amplitude of a gravitational waveform, which explicitly contains the spin-induced quadrupole moments of compact objects, hence, uniquely encode the nature of the compact binary. Thus, we argue that an independent measurement of the spin-induced quadrupole moment of the compact binaries from GW observations can provide a unique way to distinguish binary BH systems from binaries consisting of exotic compact objects.

Testing the Binary Black Hole Nature of a Compact Binary Coalescence.

PubMed

Krishnendu, N V; Arun, K G; Mishra, Chandra Kant

2017-09-01

We propose a novel method to test the binary black hole nature of compact binaries detectable by gravitational wave (GW) interferometers and, hence, constrain the parameter space of other exotic compact objects. The spirit of the test lies in the "no-hair" conjecture for black holes where all properties of a Kerr black hole are characterized by its mass and spin. The method relies on observationally measuring the quadrupole moments of the compact binary constituents induced due to their spins. If the compact object is a Kerr black hole (BH), its quadrupole moment is expressible solely in terms of its mass and spin. Otherwise, the quadrupole moment can depend on additional parameters (such as the equation of state of the object). The higher order spin effects in phase and amplitude of a gravitational waveform, which explicitly contains the spin-induced quadrupole moments of compact objects, hence, uniquely encode the nature of the compact binary. Thus, we argue that an independent measurement of the spin-induced quadrupole moment of the compact binaries from GW observations can provide a unique way to distinguish binary BH systems from binaries consisting of exotic compact objects.

An Application of the Rasch Model to Computerized Adaptive Testing.

ERIC Educational Resources Information Center

Wisniewski, Dennis R.

Three questions concerning the Binary Search Method (BSM) of computerized adaptive testing were studied: (1) whether it provided a reliable and valid estimation of examinee ability; (2) its effect on examinee attitudes toward computerized adaptive testing and conventional paper-and-pencil testing; and (3) the relationship between item response…

The Performance of Chinese Primary School Students on Realistic Arithmetic Word Problems

ERIC Educational Resources Information Center

Xin, Ziqiang; Lin, Chongde; Zhang, Li; Yan, Rong

2007-01-01

Compared with standard arithmetic word problems demanding only the direct use of number operations and computations, realistic problems are harder to solve because children need to incorporate "real-world" knowledge into their solutions. Using the realistic word problem testing materials developed by Verschaffel, De Corte, and Lasure…

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.

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

NASA Astrophysics Data System (ADS)

Galli, Reto; Tenca, Alexandre F.

2001-11-01

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

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.

Full Ionisation In Binary-Binary Encounters With Small Positive Energies

NASA Astrophysics Data System (ADS)

Sweatman, W. L.

2006-08-01

Interactions between binary stars and single stars and binary stars and other binary stars play a key role in the dynamics of a dense stellar system. Energy can be transferred between the internal dynamics of a binary and the larger scale dynamics of the interacting objects. Binaries can be destroyed and created by the interaction. In a binary-binary encounter, full ionisation occurs when both of the binary stars are destroyed in the interaction to create four single stars. This is only possible when the total energy of the system is positive. For very small energies the probability of this occurring is very low and it tends towards zero as the total energy tends towards zero. Here the case is considered for which all the stars have equal masses. An asymptotic power law is predicted relating the probability of full ionisation with the total energy when this latter quantity is small. The exponent, which is approximately 2.31, is compared with the results from numerical scattering experiments. The theoretical approach taken is similar to one used previously in the three-body problem. It makes use of the fact that the most dramatic changes in scale and energies of a few-body system occur when its components pass near to a central configuration. The position, and number, of these configurations is not known for the general four-body problem, however, with equal masses there are known to be exactly five different cases. Separate consideration and comparison of the properties of orbits close to each of these five central configurations enables the prediction of the form of the cross-section for full ionisation for the case of small positive total energy. This is the relation between total energy and the probability of total ionisation described above.

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.

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

ERIC Educational Resources Information Center

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

2014-01-01

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

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

PubMed

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

2018-01-01

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

Use of promethazine to hasten adaptation to provocative motion

NASA Technical Reports Server (NTRS)

Lackner, J. R.; Graybiel, A.

1994-01-01

In an earlier study, the authors found that severely motion sick individuals could be greatly relieved of their symptoms by intramuscular injections of promethazine (50 mg) or scopolamine (.5 mg). Comparable 50-mg injections of promethazine also have been found effective in alleviating symptoms of space motion sickness. The concern has risen, however, that such drugs may delay or retard the acquisition of adaptation to stressful environments. In the current study, we controlled arousal using a mental arithmetic task and precisely equated the exposure history (number of head movements during rotation) of a placebo, control group and an experimental group who had received promethazine. No differences in total adaptation or in rates of adaptation were present between the two groups. Another experimental group also received promethazine and was allowed to make as many head movements as they could, before reaching nausea, up to 800. This group showed a greater level of adaptation than the placebo group. These results suggest a strategy for dealing with space motion sickness that is described.

Activities for Students: Averaging Rates--Deciding when to Use the Harmonic or Arithmetic Mean

ERIC Educational Resources Information Center

Brown, S. L.; Rizzardi, M. A.

2005-01-01

The article describes the harmonic mean and explores situations for using it. Activities that involve hands-on practice for students are provided. Students learn to recognize which mean, harmonic or arithmetic, is appropriate.

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.

Fast large-scale object retrieval with binary quantization

NASA Astrophysics Data System (ADS)

Zhou, Shifu; Zeng, Dan; Shen, Wei; Zhang, Zhijiang; Tian, Qi

2015-11-01

The objective of large-scale object retrieval systems is to search for images that contain the target object in an image database. Where state-of-the-art approaches rely on global image representations to conduct searches, we consider many boxes per image as candidates to search locally in a picture. In this paper, a feature quantization algorithm called binary quantization is proposed. In binary quantization, a scale-invariant feature transform (SIFT) feature is quantized into a descriptive and discriminative bit-vector, which allows itself to adapt to the classic inverted file structure for box indexing. The inverted file, which stores the bit-vector and box ID where the SIFT feature is located inside, is compact and can be loaded into the main memory for efficient box indexing. We evaluate our approach on available object retrieval datasets. Experimental results demonstrate that the proposed approach is fast and achieves excellent search quality. Therefore, the proposed approach is an improvement over state-of-the-art approaches for object retrieval.

Multireader multicase reader studies with binary agreement data: simulation, analysis, validation, and sizing

PubMed Central

Chen, Weijie; Wunderlich, Adam; Petrick, Nicholas; Gallas, Brandon D.

2014-01-01

Abstract. We treat multireader multicase (MRMC) reader studies for which a reader’s diagnostic assessment is converted to binary agreement (1: agree with the truth state, 0: disagree with the truth state). We present a mathematical model for simulating binary MRMC data with a desired correlation structure across readers, cases, and two modalities, assuming the expected probability of agreement is equal for the two modalities (P1=P2). This model can be used to validate the coverage probabilities of 95% confidence intervals (of P1, P2, or P1−P2 when P1−P2=0), validate the type I error of a superiority hypothesis test, and size a noninferiority hypothesis test (which assumes P1=P2). To illustrate the utility of our simulation model, we adapt the Obuchowski–Rockette–Hillis (ORH) method for the analysis of MRMC binary agreement data. Moreover, we use our simulation model to validate the ORH method for binary data and to illustrate sizing in a noninferiority setting. Our software package is publicly available on the Google code project hosting site for use in simulation, analysis, validation, and sizing of MRMC reader studies with binary agreement data. PMID:26158051

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

PubMed

Tschentscher, Nadja; Hauk, Olaf

2015-01-01

Mental arithmetic is a powerful paradigm to study problem solving using neuroimaging methods. However, the evaluation of task complexity varies significantly across neuroimaging studies. Most studies have parameterized task complexity by objective features such as the number size. Only a few studies used subjective rating procedures. In fMRI, we provided evidence that strategy self-reports control better for task complexity across arithmetic conditions than objective features (Tschentscher and Hauk, 2014). Here, we analyzed the relative predictive value of self-reported strategies and objective features for performance in addition and multiplication tasks, by using a paradigm designed for neuroimaging research. We found a superiority of strategy ratings as predictor of performance above objective features. In a Principal Component Analysis on reaction times, the first component explained over 90 percent of variance and factor loadings reflected percentages of self-reported strategies well. In multiple regression analyses on reaction times, self-reported strategies performed equally well or better than objective features, depending on the operation type. A Receiver Operating Characteristic (ROC) analysis confirmed this result. Reaction times classified task complexity better when defined by individual ratings. This suggests that participants' strategy ratings are reliable predictors of arithmetic complexity and should be taken into account in neuroimaging research.

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

PubMed Central

Tschentscher, Nadja; Hauk, Olaf

2015-01-01

Mental arithmetic is a powerful paradigm to study problem solving using neuroimaging methods. However, the evaluation of task complexity varies significantly across neuroimaging studies. Most studies have parameterized task complexity by objective features such as the number size. Only a few studies used subjective rating procedures. In fMRI, we provided evidence that strategy self-reports control better for task complexity across arithmetic conditions than objective features (Tschentscher and Hauk, 2014). Here, we analyzed the relative predictive value of self-reported strategies and objective features for performance in addition and multiplication tasks, by using a paradigm designed for neuroimaging research. We found a superiority of strategy ratings as predictor of performance above objective features. In a Principal Component Analysis on reaction times, the first component explained over 90 percent of variance and factor loadings reflected percentages of self-reported strategies well. In multiple regression analyses on reaction times, self-reported strategies performed equally well or better than objective features, depending on the operation type. A Receiver Operating Characteristic (ROC) analysis confirmed this result. Reaction times classified task complexity better when defined by individual ratings. This suggests that participants’ strategy ratings are reliable predictors of arithmetic complexity and should be taken into account in neuroimaging research. PMID:26321997

In-situ observation of switchable nanoscale topography for y-shaped binary brushes in fluids.

PubMed

Lin, Yen-Hsi; Teng, Jing; Zubarev, Eugene R; Shulha, Hennady; Tsukruk, Vladimir V

2005-03-01

Direct, in-fluid observation of the surface morphology and nanomechanical properties of the mixed brushes composed of Y-shaped binary molecules PS-PAA revealed nanoscale network-like surface topography formed by coexisting stretched soluble PAA arms and collapsed insoluble PS chains in water. Placement of Y-shaped brushes in different fluids resulted in dramatic reorganization ranging from soft repellent layer covered by swollen PS arms in toluene to an adhesive, mixed layer composed of coexisting swollen PAA and collapsed PS arms in water. These binary layers with the overall nanoscale thickness can serve as adaptive nanocoatings with stimuli-responsive properties.

Brief non-symbolic, approximate number practice enhances subsequent exact symbolic arithmetic in children

PubMed Central

Spelke, Elizabeth S.

2014-01-01

Recent research reveals a link between individual differences in mathematics achievement and performance on tasks that activate the approximate number system (ANS): a primitive cognitive system shared by diverse animal species and by humans of all ages. Here we used a brief experimental paradigm to test one causal hypothesis suggested by this relationship: activation of the ANS may enhance children's performance of symbolic arithmetic. Over 2 experiments, children who briefly practiced tasks that engaged primitive approximate numerical quantities performed better on subsequent exact, symbolic arithmetic problems than did children given other tasks involving comparison and manipulation of non-numerical magnitudes (brightness and length). The practice effect appeared specific to mathematics, as no differences between groups were observed on a comparable sentence completion task. These results move beyond correlational research and provide evidence that the exercise of non-symbolic numerical processes can enhance children's performance of symbolic mathematics. PMID:24462713

Mathematics/Arithmetic Knowledge-Based Way of Thinking and Its Maintenance Needed for Engineers

NASA Astrophysics Data System (ADS)

Harada, Shoji

Examining curriculum among universities revealed that no significant difference in math class or related subjects can be seen. However, amount and depth of those studies, in general, differed depending on content of curriculum and the level of achievement at entrance to individual university. Universalization of higher education shows that students have many problems in learning higher level of traditional math and that the memory of math they learned quickly fades away after passing in exam. It means that further development of higher math knowledgebased engineer after graduation from universities. Under these circumstances, the present author, as one of fun of math, propose how to maintain way of thinking generated by math knowledge. What necessary for engineer is to pay attention to common books, dealing with elementary mathematics or arithmetic- related matters. This surely leads engineer to nourish math/arithmetic knowledge-based way of thinking.

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

On r-circulant matrices with Fibonacci and Lucas numbers having arithmetic indices

NASA Astrophysics Data System (ADS)

Bueno, Aldous Cesar F.

2017-11-01

We investigate r-circulant matrices whose entries are Fibonacci and Lucas numbers having arithmetic indices. We then solve for the eigenvalues, determinant, Euclidean norm and the bounds for the spectral norm of the matrices. We also present some special cases and some results on identities and divisibility. Lastly, we present an open problem.

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…

A Precise Physical Orbit for the M-dwarf Binary Gliese 268

NASA Astrophysics Data System (ADS)

Barry, R. K.; Demory, B.-O.; Ségransan, D.; Forveille, T.; Danchi, W. C.; Di Folco, E.; Queloz, D.; Spooner, H. R.; Torres, G.; Traub, W. A.; Delfosse, X.; Mayor, M.; Perrier, C.; Udry, S.

2012-11-01

We report high-precision interferometric and radial velocity (RV) observations of the M-dwarf binary Gl 268. Combining measurements conducted using the IOTA interferometer and the ELODIE and Harvard Center for Astrophysics RV instruments leads to a mass of 0.22596 ± 0.00084 M ⊙ for component A and 0.19230 ± 0.00071 M ⊙ for component B. The system parallax as determined by these observations is 0.1560 ± 0.0030 arcsec—a measurement with 1.9% uncertainty in excellent agreement with Hipparcos (0.1572 ± 0.0033). The absolute H-band magnitudes of the component stars are not well constrained by these measurements; however, we can place an approximate upper limit of 7.95 and 8.1 for Gl 268A and B, respectively. We test these physical parameters against the predictions of theoretical models that combine stellar evolution with high fidelity, non-gray atmospheric models. Measured and predicted values are compatible within 2σ. These results are among the most precise masses measured for visual binaries and compete with the best adaptive optics and eclipsing binary results.

Binary Sources and Binary Lenses in Microlensing Surveys of MACHOs

NASA Astrophysics Data System (ADS)

Petrovic, N.; Di Stefano, R.; Perna, R.

2003-12-01

Microlensing is an intriguing phenomenon which may yield information about the nature of dark matter. Early observational searches identified hundreds of microlensing light curves. The data set consisted mainly of point-lens light curves and binary-lens events in which the light curves exhibit caustic crossings. Very few mildly perturbed light curves were observed, although this latter type should constitute the majority of binary lens light curves. Di Stefano (2001) has suggested that the failure to take binary effects into account may have influenced the estimates of optical depth derived from microlensing surveys. The work we report on here is the first step in a systematic analysis of binary lenses and binary sources and their impact on the results of statistical microlensing surveys. In order to asses the problem, we ran Monte-Carlo simulations of various microlensing events involving binary stars (both as the source and as the lens). For each event with peak magnification > 1.34, we sampled the characteristic light curve and recorded the chi squared value when fitting the curve with a point lens model; we used this to asses the perturbation rate. We also recorded the parameters of each system, the maximum magnification, the times at which each light curve started and ended and the number of caustic crossings. We found that both the binarity of sources and the binarity of lenses increased the lensing rate. While the binarity of sources had a negligible effect on the perturbation rates of the light curves, the binarity of lenses had a notable effect. The combination of binary sources and binary lenses produces an observable rate of interesting events exhibiting multiple "repeats" in which the magnification rises above and dips below 1.34 several times. Finally, the binarity of lenses impacted both the durations of the events and the maximum magnifications. This work was supported in part by the SAO intern program (NSF grant AST-9731923) and NASA contracts NAS8

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.

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.

Automatic target detection using binary template matching

NASA Astrophysics Data System (ADS)

Jun, Dong-San; Sun, Sun-Gu; Park, HyunWook

2005-03-01

This paper presents a new automatic target detection (ATD) algorithm to detect targets such as battle tanks and armored personal carriers in ground-to-ground scenarios. Whereas most ATD algorithms were developed for forward-looking infrared (FLIR) images, we have developed an ATD algorithm for charge-coupled device (CCD) images, which have superior quality to FLIR images in daylight. The proposed algorithm uses fast binary template matching with an adaptive binarization, which is robust to various light conditions in CCD images and saves computation time. Experimental results show that the proposed method has good detection performance.

Finding the General Term for an Arithmetic Progression: Alternatives to the Formula

ERIC Educational Resources Information Center

Yeo, Joseph B. W.

2010-01-01

Secondary school students in Singapore are expected to find an expression for the general or "nth" term of an arithmetic progression (AP) without using the AP formula T[subscript n] = a + (n-1)d, where "a" is the first term, "n" is the number of terms and "d" is the common difference between successive…

Spatial Working Memory and Arithmetic Deficits in Children with Nonverbal Learning Difficulties

ERIC Educational Resources Information Center

Mammarella, Irene Cristina; Lucangeli, Daniela; Cornoldi, Cesare

2010-01-01

Visuospatial working memory and its involvement in arithmetic were examined in two groups of 7- to 11-year-olds: one comprising children described by teachers as displaying symptoms of nonverbal learning difficulties (N = 21), the other a control group without learning disabilities (N = 21). The two groups were matched for verbal abilities, age,…

A novel asynchronous access method with binary interfaces

PubMed Central

2008-01-01

Background Traditionally synchronous access strategies require users to comply with one or more time constraints in order to communicate intent with a binary human-machine interface (e.g., mechanical, gestural or neural switches). Asynchronous access methods are preferable, but have not been used with binary interfaces in the control of devices that require more than two commands to be successfully operated. Methods We present the mathematical development and evaluation of a novel asynchronous access method that may be used to translate sporadic activations of binary interfaces into distinct outcomes for the control of devices requiring an arbitrary number of commands to be controlled. With this method, users are required to activate their interfaces only when the device under control behaves erroneously. Then, a recursive algorithm, incorporating contextual assumptions relevant to all possible outcomes, is used to obtain an informed estimate of user intention. We evaluate this method by simulating a control task requiring a series of target commands to be tracked by a model user. Results When compared to a random selection, the proposed asynchronous access method offers a significant reduction in the number of interface activations required from the user. Conclusion This novel access method offers a variety of advantages over traditionally synchronous access strategies and may be adapted to a wide variety of contexts, with primary relevance to applications involving direct object manipulation. PMID:18959797

Development of a Yorùbá Arithmetic Multimedia Learning System

ERIC Educational Resources Information Center

Eludiora, Safiriyu

2017-01-01

In recent times, the endangerment of Yorùbá has highly been speculated among Yorùbá intellectuals, indigenes and enthusiasts alike. In an effort to promote the learning and use of Yorùbá numeral system in carrying out day-to-day activities and transactions, the development of a Yorùbá arithmetic learning system will help bridge the gap between…

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.

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

PubMed

Daches Cohen, Lital; Rubinsten, Orly

2017-01-01

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

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

ERIC Educational Resources Information Center

Kidd, Teresa A.; Saudargas, Richard A.

1988-01-01

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

Arithmetical Computation: Competence after Three Years of Learning under Differing Instructional Programs.

ERIC Educational Resources Information Center

Brownell, William A.; And Others

Reported are the results and conclusions of an arithmetic investigation made in the schools of Scotland in the spring and fall of 1966. The first problem in this investigation was to ascertain which, if either, of two unlike programs of instruction was more effective in developing skill in computation. The second was to determine the value of an…

The Design and Testing of Multimedia for Teaching Arithmetic to Deaf Learners

ERIC Educational Resources Information Center

Techaraungrong, Piyaporn; Suksakulchai, Surachai; Kaewprapan, Wacheerapan; Murphy, Elizabeth

2017-01-01

The purpose of the study reported on in this paper was to design and test multimedia for deaf and hard of hearing (DHH) learners. The study focused on counting, addition and subtraction with grade one (age 7) DHH learners in Thailand. The multimedia created for the study was informed by design considerations for DHH learners of arithmetic and…

Interference and Shaping in Sensorimotor Adaptations with Rewards

PubMed Central

Darshan, Ran; Leblois, Arthur; Hansel, David

2014-01-01

When a perturbation is applied in a sensorimotor transformation task, subjects can adapt and maintain performance by either relying on sensory feedback, or, in the absence of such feedback, on information provided by rewards. For example, in a classical rotation task where movement endpoints must be rotated to reach a fixed target, human subjects can successfully adapt their reaching movements solely on the basis of binary rewards, although this proves much more difficult than with visual feedback. Here, we investigate such a reward-driven sensorimotor adaptation process in a minimal computational model of the task. The key assumption of the model is that synaptic plasticity is gated by the reward. We study how the learning dynamics depend on the target size, the movement variability, the rotation angle and the number of targets. We show that when the movement is perturbed for multiple targets, the adaptation process for the different targets can interfere destructively or constructively depending on the similarities between the sensory stimuli (the targets) and the overlap in their neuronal representations. Destructive interferences can result in a drastic slowdown of the adaptation. As a result of interference, the time to adapt varies non-linearly with the number of targets. Our analysis shows that these interferences are weaker if the reward varies smoothly with the subject's performance instead of being binary. We demonstrate how shaping the reward or shaping the task can accelerate the adaptation dramatically by reducing the destructive interferences. We argue that experimentally investigating the dynamics of reward-driven sensorimotor adaptation for more than one sensory stimulus can shed light on the underlying learning rules. PMID:24415925

Language, Arithmetic Word Problems, and Deaf Students: Linguistic Strategies Used To Solve Tasks.

ERIC Educational Resources Information Center

Zevenbergen, Robyn; Hyde, Merv; Power, Des

2001-01-01

Examines the performance of deaf and hearing-impaired students in Queensland, Australia when solving arithmetic word problems. Subjects' solutions of word problems confirmed trends for learning students but their performance was delayed in comparison. Confirms other studies in which deaf and hearing-impaired students are delayed in their language…

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

ERIC Educational Resources Information Center

Desoete, Annemie

2008-01-01

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

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

A neural net based architecture for the segmentation of mixed gray-level and binary pictures

NASA Technical Reports Server (NTRS)

Tabatabai, Ali; Troudet, Terry P.

1991-01-01

A neural-net-based architecture is proposed to perform segmentation in real time for mixed gray-level and binary pictures. In this approach, the composite picture is divided into 16 x 16 pixel blocks, which are identified as character blocks or image blocks on the basis of a dichotomy measure computed by an adaptive 16 x 16 neural net. For compression purposes, each image block is further divided into 4 x 4 subblocks; a one-bit nonparametric quantizer is used to encode 16 x 16 character and 4 x 4 image blocks; and the binary map and quantizer levels are obtained through a neural net segmentor over each block. The efficiency of the neural segmentation in terms of computational speed, data compression, and quality of the compressed picture is demonstrated. The effect of weight quantization is also discussed. VLSI implementations of such adaptive neural nets in CMOS technology are described and simulated in real time for a maximum block size of 256 pixels.

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

PubMed

Humphries, Ailsa; Chen, Zhe; Neumann, Ewald

2017-01-01

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

Binary-disk interaction. II. Gap-opening criteria for unequal-mass binaries

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

Del Valle, Luciano; Escala, Andrés, E-mail: ldelvalleb@gmail.com

We study the interaction of an unequal-mass binary with an isothermal circumbinary disk, motivated by the theoretical and observational evidence that after a major merger of gas-rich galaxies, a massive gaseous disk with a supermassive black hole binary will be formed in the nuclear region. We focus on the gravitational torques that the binary exerts on the disk and how these torques can drive the formation of a gap in the disk. This exchange of angular momentum between the binary and the disk is mainly driven by the gravitational interaction between the binary and a strong nonaxisymmetric density perturbation thatmore » is produced in the disk, in response to the presence of the binary. Using smoothed particle hydrodynamics numerical simulations, we test two gap-opening criteria, one that assumes the geometry of the density perturbation is an ellipsoid/thick spiral and another that assumes a flat spiral geometry for the density perturbation. We find that the flat spiral gap-opening criterion successfully predicts which simulations will have a gap in the disk and which will not. We also study the limiting cases predicted by the gap-opening criteria. Since the viscosity in our simulations is considerably smaller than the expected value in the nuclear regions of gas-rich merging galaxies, we conclude that in such environments the formation of a circumbinary gap is unlikely.« less

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…

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

ERIC Educational Resources Information Center

Siegler, Robert S.; Lortie-Forgues, Hugues

2017-01-01

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

Effects of lipid extraction on stable isotope ratios in avian egg yolk: Is arithmetic correction a reliable alternative?

USGS Publications Warehouse

Oppel, S.; Federer, R.N.; O'Brien, D. M.; Powell, A.N.; Hollmén, Tuula E.

2010-01-01

Many studies of nutrient allocation to egg production in birds use stable isotope ratios of egg yolk to identify the origin of nutrients. Dry egg yolk contains >50% lipids, which are known to be depleted in 13C. Currently, researchers remove lipids from egg yolk using a chemical lipid-extraction procedure before analyzing the isotopic composition of protein in egg yolk. We examined the effects of chemical lipid extraction on ??13C, ??15N, and ??34S of avian egg yolk and explored the utility of an arithmetic lipid correction model to adjust whole yolk ??13C for lipid content. We analyzed the dried yolk of 15 captive Spectacled Eider (Somateriafischeri) and 20 wild King Eider (S. spectabilis) eggs, both as whole yolk and after lipid extraction with a 2:1 chloroform:methanol solution. We found that chemical lipid extraction leads to an increase of (mean ?? SD) 3.3 ?? 1.1% in ??13C, 1.1 ?? 0.5% in ??15N, and 2.3 ?? 1.1% in ??34S. Arithmetic lipid correction provided accurate values for lipid-extracted S13C in captive Spectacled Eiders fed on a homogeneous high-quality diet. However, arithmetic lipid correction was unreliable for wild King Eiders, likely because of their differential incorporation of macronutrients from isotopically distinct environments during migration. For that reason, we caution against applying arithmetic lipid correction to the whole yolk ??13C of migratory birds, because these methods assume that all egg macronutrients are derived from the same dietary sources. ?? 2010 The American Ornithologists' Union.

Commission 42: Close Binary Stars

NASA Astrophysics Data System (ADS)

Rucinski, Slavek M.; Ribas, Ignasi; Giménez, Alvaro; Harmanec, Petr; Hilditch, Ronald W.; Kaluzny, Janusz; Niarchos, Panayiotis; Nordström, Birgitta; Oláh, Katalin; Richards, Mercedes T.; Scarfe, Colin D.; Sion, Edward M.; Torres, Guillermo; Vrielmann, Sonja

Two meetings of interest to close binaries took place during the reporting period: A full day session on short-period binary stars mostly CV's (Milone et al. 2008) during the 2006 AAS Spring meeting in Calgary and the very broadly designed IAU Symposium No. 240 on Binary Stars as Critical Tools and Tests in Contemporary Astrophysics in Prague, 2006, with many papers on close binaries [Hartkopf et al. 2007]. In addition, the book by Eggleton (2006), which is a comprehensive summary of evolutionary processes in binary and multiple stars, was published.

The fate of close encounters between binary stars and binary supermassive black holes

NASA Astrophysics Data System (ADS)

Wang, Yi-Han; Leigh, Nathan; Yuan, Ye-Fei; Perna, Rosalba

2018-04-01

The evolution of main-sequence binaries that reside in the Galactic Centre can be heavily influenced by the central supermassive black hole (SMBH). Due to these perturbative effects, the stellar binaries in dense environments are likely to experience mergers, collisions, or ejections through secular and/or non-secular interactions. More direct interactions with the central SMBH are thought to produce hypervelocity stars (HVSs) and tidal disruption events (TDEs). In this paper, we use N-body simulations to study the dynamics of stellar binaries orbiting a central SMBH primary with an outer SMBH secondary orbiting this inner triple. The effects of the secondary SMBH on the event rates of HVSs, TDEs, and stellar mergers are investigated, as a function of the SMBH-SMBH binary mass ratio. Our numerical experiments reveal that, relative to the isolated SMBH case, the TDE and HVS rates are enhanced for, respectively, the smallest and largest mass ratio SMBH-SMBH binaries. This suggests that the observed event rates of TDEs and HVSs have the potential to serve as a diagnostic of the mass ratio of a central SMBH-SMBH binary. The presence of a secondary SMBH also allows for the creation of hypervelocity binaries. Observations of these systems could thus constrain the presence of a secondary SMBH in the Galactic Centre.

Modified signed-digit arithmetic based on redundant bit representation.

PubMed

Huang, H; Itoh, M; Yatagai, T

1994-09-10

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

High accuracy binary black hole simulations with an extended wave zone

NASA Astrophysics Data System (ADS)

Pollney, Denis; Reisswig, Christian; Schnetter, Erik; Dorband, Nils; Diener, Peter

2011-02-01

We present results from a new code for binary black hole evolutions using the moving-puncture approach, implementing finite differences in generalized coordinates, and allowing the spacetime to be covered with multiple communicating nonsingular coordinate patches. Here we consider a regular Cartesian near-zone, with adapted spherical grids covering the wave zone. The efficiencies resulting from the use of adapted coordinates allow us to maintain sufficient grid resolution to an artificial outer boundary location which is causally disconnected from the measurement. For the well-studied test case of the inspiral of an equal-mass nonspinning binary (evolved for more than 8 orbits before merger), we determine the phase and amplitude to numerical accuracies better than 0.010% and 0.090% during inspiral, respectively, and 0.003% and 0.153% during merger. The waveforms, including the resolved higher harmonics, are convergent and can be consistently extrapolated to r→∞ throughout the simulation, including the merger and ringdown. Ringdown frequencies for these modes (to (ℓ,m)=(6,6)) match perturbative calculations to within 0.01%, providing a strong confirmation that the remnant settles to a Kerr black hole with irreducible mass Mirr=0.884355±20×10-6 and spin Sf/Mf2=0.686923±10×10-6.

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

ERIC Educational Resources Information Center

Schoppek, Wolfgang; Tulis, Maria

2010-01-01

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

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

ERIC Educational Resources Information Center

D'Amico, Antonella; Passolunghi, Maria Chiara

2009-01-01

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

Can business and economics students perform elementary arithmetic?

PubMed

Standing, Lionel G; Sproule, Robert A; Leung, Ambrose

2006-04-01

Business and economics majors (N=146) were tested on the D'Amore Test of Elementary Arithmetic, which employs third-grade test items from 1932. Only 40% of the subjects passed the test by answering 10 out of 10 items correctly. Self-predicted scores were a good predictor of actual scores, but performance was not associated with demographic variables, grades in calculus courses, liking for science or computers, or mathematics anxiety. Scores decreased over the subjects' initial years on campus. The hardest test item, with an error rate of 23%, required the subject to evaluate (36 x 7) + (33 x 7). The results are similar to those of Standing in 2006, despite methodological changes intended to maximize performance.

A Precise Physical Orbit For The M-Dwarf Binary Gliese 268

NASA Technical Reports Server (NTRS)

Barry, R. K.; Demory, B. -O.; Segransan, D.; Forveille, T.; Danchi, W. C.; Di Folco, E.; Queloz, D.; Spooner, H. R.; Torres, G.; Traub, W. A.;

Schema Knowledge Structures for Representing and Understanding Arithmetic Story Problems.

DTIC Science & Technology

1987-03-01

do so on a common unit of measure. Implicit in the CP relation is the concept of one-to- one matching of one element in the problem with the other. As...engages in one-to-one matching , removing one member from each set and setting them apart as a matched pair. The smaller of the two sets is the one...to be critical. As we pointed out earlier, some of the semantic * relations can be present in situations that demand any of * the four arithmetic

Binary YORP Effect and Evolution of Binary Asteroids

NASA Astrophysics Data System (ADS)

Steinberg, Elad; Sari, Re'em

2011-02-01

The rotation states of kilometer-sized near-Earth asteroids are known to be affected by the Yarkevsky O'Keefe-Radzievskii-Paddack (YORP) effect. In a related effect, binary YORP (BYORP), the orbital properties of a binary asteroid evolve under a radiation effect mostly acting on a tidally locked secondary. The BYORP effect can alter the orbital elements over ~104-105 years for a Dp = 2 km primary with a Ds = 0.4 km secondary at 1 AU. It can either separate the binary components or cause them to collide. In this paper, we devise a simple approach to calculate the YORP effect on asteroids and the BYORP effect on binaries including J 2 effects due to primary oblateness and the Sun. We apply this to asteroids with known shapes as well as a set of randomly generated bodies with various degrees of smoothness. We find a strong correlation between the strengths of an asteroid's YORP and BYORP effects. Therefore, statistical knowledge of one could be used to estimate the effect of the other. We show that the action of BYORP preferentially shrinks rather than expands the binary orbit and that YORP preferentially slows down asteroids. This conclusion holds for the two extremes of thermal conductivities studied in this work and the assumption that the asteroid reaches a stable point, but may break down for moderate thermal conductivity. The YORP and BYORP effects are shown to be smaller than could be naively expected due to near cancellation of the effects at small scales. Taking this near cancellation into account, a simple order-of-magnitude estimate of the YORP and BYORP effects as a function of the sizes and smoothness of the bodies is calculated. Finally, we provide a simple proof showing that there is no secular effect due to absorption of radiation in BYORP.

New spectroscopic binary companions of giant stars and updated metallicity distribution for binary systems

NASA Astrophysics Data System (ADS)

Bluhm, P.; Jones, M. I.; Vanzi, L.; Soto, M. G.; Vos, J.; Wittenmyer, R. A.; Drass, H.; Jenkins, J. S.; Olivares, F.; Mennickent, R. E.; Vučković, M.; Rojo, P.; Melo, C. H. F.

2016-10-01

We report the discovery of 24 spectroscopic binary companions to giant stars. We fully constrain the orbital solution for 6 of these systems. We cannot unambiguously derive the orbital elements for the remaining stars because the phase coverage is incomplete. Of these stars, 6 present radial velocity trends that are compatible with long-period brown dwarf companions. The orbital solutions of the 24 binary systems indicate that these giant binary systems have a wide range in orbital periods, eccentricities, and companion masses. For the binaries with restricted orbital solutions, we find a range of orbital periods of between ~97-1600 days and eccentricities of between ~0.1-0.4. In addition, we studied the metallicity distribution of single and binary giant stars. We computed the metallicity of a total of 395 evolved stars, 59 of wich are in binary systems. We find a flat distribution for these binary stars and therefore conclude that stellar binary systems, and potentially brown dwarfs, have a different formation mechanism than planets. This result is confirmed by recent works showing that extrasolar planets orbiting giants are more frequent around metal-rich stars. Finally, we investigate the eccentricity as a function of the orbital period. We analyzed a total of 130 spectroscopic binaries, including those presented here and systems from the literature. We find that most of the binary stars with periods ≲30 days have circular orbits, while at longer orbital periods we observe a wide spread in their eccentricities. Based on observations collected at La Silla - Paranal Observatory under programs IDs IDs 085.C-0557, 087.C.0476, 089.C-0524, 090.C-0345, 096.A-9020 and through the Chilean Telescope Time under programs IDs CN2012A-73, CN2012B-47, CN2013A-111, CN2013B-51, CN2014A-52 and CN2015A-48.

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

PubMed Central

Daches Cohen, Lital; Rubinsten, Orly

2017-01-01

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

Heber Binary Project. Binary Cycle Geothermal Demonstration Power Plant (RP1900-1)

NASA Astrophysics Data System (ADS)

Lacy, R. G.; Nelson, T. T.

1982-12-01

The Heber Binary Project (1) demonstrates the potential of moderate temperature (below 410 F) geothermal energy to produce economic electric power with binary cycle conversion technology; (2) allows the scaling up and evaluation of the performance of binary cycle technology in geothermal service; (3) establishes schedule, cost and equipment performance, reservoir performance, and the environmental acceptability of such plants; and (4) resolves uncertainties associated with the reservoir performance, plant operation, and economics.

New Results on Contact Binary Stars

NASA Astrophysics Data System (ADS)

He, J.; Qian, S.; Zhu, L.; Liu, L.; Liao, W.

2014-08-01

Contact binary star is a kind of close binary with the strongest interaction binary system. Their formations and evolutions are unsolved problems in astrophysics. Since 2000, our groups have observed and studied more than half a hundred of contact binaries. In this report, I will summarize our new results of some contact binary stars (e.g. UZ CMi, GSC 03526-01995, FU Dra, GSC 0763-0572, V524 Mon, MR Com, etc.). They are as follow: (1) We discovered that V524 Mon and MR Com are shallow-contact binaries with their period decreasing; (2) GSC 03526-01995 is middle-contact binary without a period increasing or decreasing continuously; (3) UZ CMi, GSC 0763-0572 and FU Dra are middle-contact binaries with the period increasing continuously; (4) UZ CMi, GSC 03526-01995, FU Dra and V524 Mon show period oscillation which may imply the presence of additional components in these contact binaries.

The Tarantula Massive Binary Monitoring. I. Observational campaign and OB-type spectroscopic binaries

NASA Astrophysics Data System (ADS)

Almeida, L. A.; Sana, H.; Taylor, W.; Barbá, R.; Bonanos, A. Z.; Crowther, P.; Damineli, A.; de Koter, A.; de Mink, S. E.; Evans, C. J.; Gieles, M.; Grin, N. J.; Hénault-Brunet, V.; Langer, N.; Lennon, D.; Lockwood, S.; Maíz Apellániz, J.; Moffat, A. F. J.; Neijssel, C.; Norman, C.; Ramírez-Agudelo, O. H.; Richardson, N. D.; Schootemeijer, A.; Shenar, T.; Soszyński, I.; Tramper, F.; Vink, J. S.

2017-02-01

Context. Massive binaries play a crucial role in the Universe. Knowing the distributions of their orbital parameters is important for a wide range of topics from stellar feedback to binary evolution channels and from the distribution of supernova types to gravitational wave progenitors, yet no direct measurements exist outside the Milky Way. Aims: The Tarantula Massive Binary Monitoring project was designed to help fill this gap by obtaining multi-epoch radial velocity (RV) monitoring of 102 massive binaries in the 30 Doradus region. Methods: In this paper we analyze 32 FLAMES/GIRAFFE observations of 93 O- and 7 B-type binaries. We performed a Fourier analysis and obtained orbital solutions for 82 systems: 51 single-lined (SB1) and 31 double-lined (SB2) spectroscopic binaries. Results: Overall, the binary fraction and orbital properties across the 30 Doradus region are found to be similar to existing Galactic samples. This indicates that within these domains environmental effects are of second order in shaping the properties of massive binary systems. A small difference is found in the distribution of orbital periods, which is slightly flatter (in log space) in 30 Doradus than in the Galaxy, although this may be compatible within error estimates and differences in the fitting methodology. Also, orbital periods in 30 Doradus can be as short as 1.1 d, somewhat shorter than seen in Galactic samples. Equal mass binaries (q> 0.95) in 30 Doradus are all found outside NGC 2070, the central association that surrounds R136a, the very young and massive cluster at 30 Doradus's core. Most of the differences, albeit small, are compatible with expectations from binary evolution. One outstanding exception, however, is the fact that earlier spectral types (O2-O7) tend to have shorter orbital periods than later spectral types (O9.2-O9.7). Conclusions: Our results point to a relative universality of the incidence rate of massive binaries and their orbital properties in the

EPIC 219217635: A Doubly Eclipsing Quadruple System Containing an Evolved Binary

NASA Astrophysics Data System (ADS)

Borkovits, T.; Albrecht, S.; Rappaport, S.; Nelson, L.; Vanderburg, A.; Gary, B. L.; Tan, T. G.; Justesen, A. B.; Kristiansen, M. H.; Jacobs, T. L.; LaCourse, D.; Ngo, H.; Wallack, N.; Ruane, G.; Mawet, D.; Howell, S. B.; Tronsgaard, R.

2018-05-01

We have discovered a doubly eclipsing, bound, quadruple star system in the field of K2 Campaign 7. EPIC 219217635 is a stellar image with Kp = 12.7 that contains an eclipsing binary (`EB') with PA = 3.59470 d and a second EB with PB = 0.61825 d. We have obtained followup radial-velocity (`RV') spectroscopy observations, adaptive optics imaging, as well as ground-based photometric observations. From our analysis of all the observations, we derive good estimates for a number of the system parameters. We conclude that (1) both binaries are bound in a quadruple star system; (2) a linear trend to the RV curve of binary A is found over a 2-year interval, corresponding to an acceleration, \\dot{γ }= 0.0024 ± 0.0007 cm s-2; (3) small irregular variations are seen in the eclipse-timing variations (`ETVs') detected over the same interval; (4) the orbital separation of the quadruple system is probably in the range of 8-25 AU; and (5) the orbital planes of the two binaries must be inclined with respect to each other by at least 25°. In addition, we find that binary B is evolved, and the cooler and currently less massive star has transferred much of its envelope to the currently more massive star. We have also demonstrated that the system is sufficiently bright that the eclipses can be followed using small ground-based telescopes, and that this system may be profitably studied over the next decade when the outer orbit of the quadruple is expected to manifest itself in the ETV and/or RV curves.

Item Mass and Complexity and the Arithmetic Computation of Students with Learning Disabilities.

ERIC Educational Resources Information Center

Cawley, John F.; Shepard, Teri; Smith, Maureen; Parmar, Rene S.

1997-01-01

The performance of 76 students (ages 10 to 15) with learning disabilities on four tasks of arithmetic computation within each of the four basic operations was examined. Tasks varied in difficulty level and number of strokes needed to complete all items. Intercorrelations between task sets and operations were examined as was the use of…

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

ERIC Educational Resources Information Center

López, Magdalena

2014-01-01

Introduction: This study has aimed to investigate the relationship between the development of working memory and performance on arithmetic activities. Method: We conducted a 3-year longitudinal study of a sample of 90 children, that was followed during the first, second and third year of primary school. All children were tested on measures of WM…

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

ERIC Educational Resources Information Center

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

2009-01-01

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

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

ERIC Educational Resources Information Center

Maschietto, Michela

2015-01-01

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

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

PubMed

Geurten, Marie; Lemaire, Patrick

2018-04-19

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

Event-related brain potentials to violations of arithmetic syntax represented by place value structure.

PubMed

Szucs, Dénes; Soltész, Fruzsina

2010-05-01

We dissociated ERP markers of semantic (numerical distance) vs. syntactic (place value) incongruence in the domain of arithmetic. Participants verified additions with four-digit numbers. Semantic incongruencies elicited the N400 ERP effect. A centro-parietal (putative P600) effect to place value violations was not related to arithmetic syntax. Rather, this effect was an enlarged P3b reflecting different surprise values of place value vs. non-place value violations. This potential confound should be considered in numerical cognition experiments. The latency of the N400 and P3a effects were differentially affected by place value analysis. The amplitude of the P3a and that of a fronto-central positive effect (FP600) was sensitive to place value analysis and digit content. Results suggest that ERPs can index the syntactical analysis of multi-digit numbers. Both ERP and behavioral data confirmed that multi-digit numbers were decomposed into their constituent digits, rather than evaluated holistically. Copyright 2010 Elsevier B.V. All rights reserved.

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.

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

PubMed

Geurten, Marie; Lemaire, Patrick

2017-10-01

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

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

PubMed

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

2015-01-01

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

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.

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

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.

Binary optics: Trends and limitations

NASA Technical Reports Server (NTRS)

Farn, Michael W.; Veldkamp, Wilfrid B.

1993-01-01

We describe the current state of binary optics, addressing both the technology and the industry (i.e., marketplace). With respect to the technology, the two dominant aspects are optical design methods and fabrication capabilities, with the optical design problem being limited by human innovation in the search for new applications and the fabrication issue being limited by the availability of resources required to improve fabrication capabilities. With respect to the industry, the current marketplace does not favor binary optics as a separate product line and so we expect that companies whose primary purpose is the production of binary optics will not represent the bulk of binary optics production. Rather, binary optics' more natural role is as an enabling technology - a technology which will directly result in a competitive advantage in a company's other business areas - and so we expect that the majority of binary optics will be produced for internal use.

Photometric binary stars in Praesepe and the search for globular cluster binaries

NASA Technical Reports Server (NTRS)

Bolte, Michael

1991-01-01

A radial velocity study of the stars which are located on a second sequence above the single-star zero-age main sequence at a given color in the color-magnitude diagram of the open cluster Praesepe, (NGC 2632) shows that 10, and possibly 11, of 17 are binary systems. Of the binary systems, five have full amplitudes for their velocity variations that are greater than 50 km/s. To the extent that they can be applied to globular clusters, these results suggests that (1) observations of 'second-sequence' stars in globular clusters would be an efficient way of finding main-sequence binary systems in globulars, and (2) current instrumentation on large telescopes is sufficient for establishing unambiguously the existence of main-sequence binary systems in nearby globular clusters.

Probing and exploiting the chaotic dynamics of a hydrodynamic photochemical oscillator to implement all the basic binary logic functions

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

Hayashi, Kenta; Department of Chemistry, Biology, and Biotechnology, University of Perugia, 06123 Perugia; Gotoda, Hiroshi

2016-05-15

The convective motions within a solution of a photochromic spiro-oxazine being irradiated by UV only on the bottom part of its volume, give rise to aperiodic spectrophotometric dynamics. In this paper, we study three nonlinear properties of the aperiodic time series: permutation entropy, short-term predictability and long-term unpredictability, and degree distribution of the visibility graph networks. After ascertaining the extracted chaotic features, we show how the aperiodic time series can be exploited to implement all the fundamental two-inputs binary logic functions (AND, OR, NAND, NOR, XOR, and XNOR) and some basic arithmetic operations (half-adder, full-adder, half-subtractor). This is possible duemore » to the wide range of states a nonlinear system accesses in the course of its evolution. Therefore, the solution of the convective photochemical oscillator results in hardware for chaos-computing alternative to conventional complementary metal-oxide semiconductor-based integrated circuits.« less

BINARY ASTROMETRIC MICROLENSING WITH GAIA

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

Sajadian, Sedighe, E-mail: sajadian@ipm.ir; Department of Physics, Sharif University of Technology, P.O. Box 11155-9161, Tehran

2015-04-15

We investigate whether or not Gaia can specify the binary fractions of massive stellar populations in the Galactic disk through astrometric microlensing. Furthermore, we study whether or not some information about their mass distributions can be inferred via this method. In this regard, we simulate the binary astrometric microlensing events due to massive stellar populations according to the Gaia observing strategy by considering (i) stellar-mass black holes, (ii) neutron stars, (iii) white dwarfs, and (iv) main-sequence stars as microlenses. The Gaia efficiency for detecting the binary signatures in binary astrometric microlensing events is ∼10%–20%. By calculating the optical depth duemore » to the mentioned stellar populations, the numbers of the binary astrometric microlensing events being observed with Gaia with detectable binary signatures, for the binary fraction of about 0.1, are estimated to be 6, 11, 77, and 1316, respectively. Consequently, Gaia can potentially specify the binary fractions of these massive stellar populations. However, the binary fraction of black holes measured with this method has a large uncertainty owing to a low number of the estimated events. Knowing the binary fractions in massive stellar populations helps with studying the gravitational waves. Moreover, we investigate the number of massive microlenses for which Gaia specifies masses through astrometric microlensing of single lenses toward the Galactic bulge. The resulting efficiencies of measuring the mass of mentioned populations are 9.8%, 2.9%, 1.2%, and 0.8%, respectively. The numbers of their astrometric microlensing events being observed in the Gaia era in which the lens mass can be inferred with the relative error less than 0.5 toward the Galactic bulge are estimated as 45, 34, 76, and 786, respectively. Hence, Gaia potentially gives us some information about the mass distribution of these massive stellar populations.« less

KEPLER ECLIPSING BINARIES WITH STELLAR COMPANIONS

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

Gies, D. R.; Matson, R. A.; Guo, Z.

2015-12-15

Many short-period binary stars have distant orbiting companions that have played a role in driving the binary components into close separation. Indirect detection of a tertiary star is possible by measuring apparent changes in eclipse times of eclipsing binaries as the binary orbits the common center of mass. Here we present an analysis of the eclipse timings of 41 eclipsing binaries observed throughout the NASA Kepler mission of long duration and precise photometry. This subset of binaries is characterized by relatively deep and frequent eclipses of both stellar components. We present preliminary orbital elements for seven probable triple stars amongmore » this sample, and we discuss apparent period changes in seven additional eclipsing binaries that may be related to motion about a tertiary in a long period orbit. The results will be used in ongoing investigations of the spectra and light curves of these binaries for further evidence of the presence of third stars.« less

A VLSI architecture for simplified arithmetic Fourier transform algorithm

NASA Technical Reports Server (NTRS)

Reed, Irving S.; Shih, Ming-Tang; Truong, T. K.; Hendon, E.; Tufts, D. W.

1992-01-01

The arithmetic Fourier transform (AFT) is a number-theoretic approach to Fourier analysis which has been shown to perform competitively with the classical FFT in terms of accuracy, complexity, and speed. Theorems developed in a previous paper for the AFT algorithm are used here to derive the original AFT algorithm which Bruns found in 1903. This is shown to yield an algorithm of less complexity and of improved performance over certain recent AFT algorithms. A VLSI architecture is suggested for this simplified AFT algorithm. This architecture uses a butterfly structure which reduces the number of additions by 25 percent of that used in the direct method.

Non-Symbolic Arithmetic Abilities and Mathematics Achievement in the First Year of Formal Schooling

ERIC Educational Resources Information Center

Gilmore, Camilla K.; McCarthy, Shannon E.; Spelke, Elizabeth S.

2010-01-01

Children take years to learn symbolic arithmetic. Nevertheless, non-human animals, human adults with no formal education, and human infants represent approximate number in arrays of objects and sequences of events, and they use these capacities to perform approximate addition and subtraction. Do children harness these abilities when they begin to…

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

ERIC Educational Resources Information Center

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

2015-01-01

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

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

ERIC Educational Resources Information Center

Pareto, Lena

2014-01-01

In this paper we will describe a learning environment designed to foster conceptual understanding and reasoning in mathematics among younger school children. The learning environment consists of 48 2-player game variants based on a graphical model of arithmetic where the mathematical content is intrinsically interwoven with the game idea. The…

Hydrodynamical processes in coalescing binary stars

NASA Astrophysics Data System (ADS)

Lai, Dong

1994-01-01

Coalescing neutron star binaries are considered to be the most promising sources of gravitational waves that could be detected by the planned laser-interferometer LIGO/VIRGO detectors. Extracting gravity wave signals from noisy data requires accurate theoretical waveforms in the frequency range 10-1000 Hz end detailed understanding of the dynamics of the binary orbits. We investigate the quasi-equilibrium and dynamical tidal interactions in coalescing binary stars, with particular focus on binary neutron stars. We develop a new formalism to study the equilibrium and dynamics of fluid stars in binary systems. The stars are modeled as compressible ellipsoids, and satisfy polytropic equation of state. The hydrodynamic equations are reduced to a set of ordinary differential equations for the evolution of the principal axes and other global quantities. The equilibrium binary structure is determined by a set of algebraic equations. We consider both synchronized and nonsynchronized systems, obtaining the generalizations to compressible fluid of the classical results for the ellipsoidal binary configurations. Our method can be applied to a wide variety of astrophysical binary systems containing neutron stars, white dwarfs, main-sequence stars and planets. We find that both secular and dynamical instabilities can develop in close binaries. The quasi-static (secular) orbital evolution, as well as the dynamical evolution of binaries driven by viscous dissipation and gravitational radiation reaction are studied. The development of the dynamical instability accelerates the binary coalescence at small separation, leading to appreciable radial infall velocity near contact. We also study resonant excitations of g-mode oscillations in coalescing binary neutron stars. A resonance occurs when the frequency of the tidal driving force equals one of the intrinsic g-mode frequencies. Using realistic microscopic nuclear equations of state, we determine the g-modes in a cold neutron atar

Coevolution of Binaries and Circumbinary Gaseous Disks

NASA Astrophysics Data System (ADS)

Fleming, David; Quinn, Thomas R.

2018-04-01

The recent discoveries of circumbinary planets by Kepler raise questions for contemporary planet formation models. Understanding how these planets form requires characterizing their formation environment, the circumbinary protoplanetary disk, and how the disk and binary interact. The central binary excites resonances in the surrounding protoplanetary disk that drive evolution in both the binary orbital elements and in the disk. To probe how these interactions impact both binary eccentricity and disk structure evolution, we ran N-body smooth particle hydrodynamics (SPH) simulations of gaseous protoplanetary disks surrounding binaries based on Kepler 38 for 10^4 binary orbital periods for several initial binary eccentricities. We find that nearly circular binaries weakly couple to the disk via a parametric instability and excite disk eccentricity growth. Eccentric binaries strongly couple to the disk causing eccentricity growth for both the disk and binary. Disks around sufficiently eccentric binaries strongly couple to the disk and develop an m = 1 spiral wave launched from the 1:3 eccentric outer Lindblad resonance (EOLR). This wave corresponds to an alignment of gas particle longitude of periastrons. We find that in all simulations, the binary semi-major axis decays due to dissipation from the viscous disk.

Binaries in globular clusters

NASA Technical Reports Server (NTRS)

Hut, Piet; Mcmillan, Steve; Goodman, Jeremy; Mateo, Mario; Phinney, E. S.; Pryor, Carlton; Richer, Harvey B.; Verbunt, Frank; Weinberg, Martin

1992-01-01

Recent observations have shown that globular clusters contain a substantial number of binaries most of which are believed to be primordial. We discuss different successful optical search techniques, based on radial-velocity variables, photometric variables, and the positions of stars in the color-magnitude diagram. In addition, we review searches in other wavelengths, which have turned up low-mass X-ray binaries and more recently a variety of radio pulsars. On the theoretical side, we give an overview of the different physical mechanisms through which individual binaries evolve. We discuss the various simulation techniques which recently have been employed to study the effects of a primordial binary population, and the fascinating interplay between stellar evolution and stellar dynamics which drives globular-cluster evolution.

Spectral properties of binary asteroids

NASA Astrophysics Data System (ADS)

Pajuelo, Myriam; Birlan, Mirel; Carry, Benoît; DeMeo, Francesca E.; Binzel, Richard P.; Berthier, Jérôme

2018-04-01

We present the first attempt to characterize the distribution of taxonomic class among the population of binary asteroids (15% of all small asteroids). For that, an analysis of 0.8-2.5{μ m} near-infrared spectra obtained with the SpeX instrument on the NASA/IRTF is presented. Taxonomic class and meteorite analog is determined for each target, increasing the sample of binary asteroids with known taxonomy by 21%. Most binary systems are bound in the S-, X-, and C- classes, followed by Q and V-types. The rate of binary systems in each taxonomic class agrees within uncertainty with the background population of small near-Earth objects and inner main belt asteroids, but for the C-types which are under-represented among binaries.

A 3D dynamical model of the colliding winds in binary systems

NASA Astrophysics Data System (ADS)

Parkin, E. R.; Pittard, J. M.

2008-08-01

We present a three-dimensional (3D) dynamical model of the orbital-induced curvature of the wind-wind collision region in binary star systems. Momentum balance equations are used to determine the position and shape of the contact discontinuity between the stars, while further downstream the gas is assumed to behave ballistically. An Archimedean spiral structure is formed by the motion of the stars, with clear resemblance to high-resolution images of the so-called `pinwheel nebulae'. A key advantage of this approach over grid or smoothed particle hydrodynamic models is its significantly reduced computational cost, while it also allows the study of the structure obtained in an eccentric orbit. The model is relevant to symbiotic systems and γ-ray binaries, as well as systems with O-type and Wolf-Rayet stars. As an example application, we simulate the X-ray emission from hypothetical O+O and WR+O star binaries, and describe a method of ray tracing through the 3D spiral structure to account for absorption by the circumstellar material in the system. Such calculations may be easily adapted to study observations at wavelengths ranging from the radio to γ-ray.

Practical low-cost visual communication using binary images for deaf sign language.

PubMed

Manoranjan, M D; Robinson, J A

2000-03-01

Deaf sign language transmitted by video requires a temporal resolution of 8 to 10 frames/s for effective communication. Conventional videoconferencing applications, when operated over low bandwidth telephone lines, provide very low temporal resolution of pictures, of the order of less than a frame per second, resulting in jerky movement of objects. This paper presents a practical solution for sign language communication, offering adequate temporal resolution of images using moving binary sketches or cartoons, implemented on standard personal computer hardware with low-cost cameras and communicating over telephone lines. To extract cartoon points an efficient feature extraction algorithm adaptive to the global statistics of the image is proposed. To improve the subjective quality of the binary images, irreversible preprocessing techniques, such as isolated point removal and predictive filtering, are used. A simple, efficient and fast recursive temporal prefiltering scheme, using histograms of successive frames, reduces the additive and multiplicative noise from low-cost cameras. An efficient three-dimensional (3-D) compression scheme codes the binary sketches. Subjective tests performed on the system confirm that it can be used for sign language communication over telephone lines.

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

ERIC Educational Resources Information Center

Taani, Osama

2014-01-01

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

ERP correlates of mental arithmetic in preadolescents: influence of ability and effects of morning nutrition

USDA-ARS?s Scientific Manuscript database

The effects of morning nutritional status on ERP correlates of mental arithmetic were studied in preadolescents differing in experience (age) and mathematical skills. Children [right-handed; IQ > 80), randomly assigned to treatment [eat (B) or skip (SB) breakfast (each, n = 41)], were sub-grouped by...

Characterization of binary string statistics for syntactic landmine detection

NASA Astrophysics Data System (ADS)

Nasif, Ahmed O.; Mark, Brian L.; Hintz, Kenneth J.

2011-06-01

Syntactic landmine detection has been proposed to detect and classify non-metallic landmines using ground penetrating radar (GPR). In this approach, the GPR return is processed to extract characteristic binary strings for landmine and clutter discrimination. In our previous work, we discussed the preprocessing methodology by which the amplitude information of the GPR A-scan signal can be effectively converted into binary strings, which identify the impedance discontinuities in the signal. In this work, we study the statistical properties of the binary string space. In particular, we develop a Markov chain model to characterize the observed bit sequence of the binary strings. The state is defined as the number of consecutive zeros between two ones in the binarized A-scans. Since the strings are highly sparse (the number of zeros is much greater than the number of ones), defining the state this way leads to fewer number of states compared to the case where each bit is defined as a state. The number of total states is further reduced by quantizing the number of consecutive zeros. In order to identify the correct order of the Markov model, the mean square difference (MSD) between the transition matrices of mine strings and non-mine strings is calculated up to order four using training data. The results show that order one or two maximizes this MSD. The specification of the transition probabilities of the chain can be used to compute the likelihood of any given string. Such a model can be used to identify characteristic landmine strings during the training phase. These developments on modeling and characterizing the string statistics can potentially be part of a real-time landmine detection algorithm that identifies landmine and clutter in an adaptive fashion.

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

ERIC Educational Resources Information Center

Fägerstam, Emilia; Samuelsson, Joakim

2014-01-01

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

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.

Polar alignment of a protoplanetary disc around an eccentric binary II: Effect of binary and disc parameters

NASA Astrophysics Data System (ADS)

Martin, Rebecca G.; Lubow, Stephen H.

2018-06-01

In a recent paper Martin & Lubow showed that a circumbinary disc around an eccentric binary can undergo damped nodal oscillations that lead to the polar (perpendicular) alignment of the disc relative to the binary orbit. The disc angular momentum vector aligns to the eccentricity vector of the binary. We explore the robustness of this mechanism for a low mass disc (0.001 of the binary mass) and its dependence on system parameters by means of hydrodynamic disc simulations. We describe how the evolution depends upon the disc viscosity, temperature, size, binary mass ratio, orbital eccentricity and inclination. We compare results with predictions of linear theory. We show that polar alignment of a low mass disc may occur over a wide range of binary-disc parameters. We discuss the application of our results to the formation of planetary systems around eccentric binary stars.

The European style arithmetic Asian option pricing with stochastic interest rate based on Black Scholes model

NASA Astrophysics Data System (ADS)

Winarti, Yuyun Guna; Noviyanti, Lienda; Setyanto, Gatot R.

2017-03-01

The stock investment is a high risk investment. Therefore, there are derivative securities to reduce these risks. One of them is Asian option. The most fundamental of option is option pricing. Many factors that determine the option price are underlying asset price, strike price, maturity date, volatility, risk free interest rate and dividends. Various option pricing usually assume that risk free interest rate is constant. While in reality, this factor is stochastic process. The arithmetic Asian option is free from distribution, then, its pricing is done using the modified Black-Scholes model. In this research, the modification use the Curran approximation. This research focuses on the arithmetic Asian option pricing without dividends. The data used is the stock daily closing data of Telkom from January 1 2016 to June 30 2016. Finnaly, those option price can be used as an option trading strategy.

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

PubMed

Tschentscher, Nadja; Hauk, Olaf

2014-05-15

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

Spectral properties of binary asteroids

NASA Astrophysics Data System (ADS)

Pajuelo, Myriam; Birlan, Mirel; Carry, Benoît; DeMeo, Francesca E.; Binzel, Richard P.; Berthier, Jérôme

2018-07-01

We present the first attempt to characterize the distribution of taxonomic class among the population of binary asteroids (15 per cent of all small asteroids). For that, an analysis of 0.8-2.5 µm near-infrared spectra obtained with the SpeX instrument on the NASA/IRTF (Infrared Telescope Facility) is presented. Taxonomic class and meteorite analogue is determined for each target, increasing the sample of binary asteroids with known taxonomy by 21 per cent. Most binary systems are bound in the S, X, and C classes, followed by Q and V types. The rate of binary systems in each taxonomic class agrees within uncertainty with the background population of small near-Earth objects and inner main belt asteroids, but for the C types which are under-represented among binaries.

Binary Cepheids: Separations and Mass Ratios in 5 M ⊙ Binaries

NASA Astrophysics Data System (ADS)

Evans, Nancy Evans; Bond, Howard E.; Schaefer, Gail H.; Mason, Brian D.; Karovska, Margarita; Tingle, Evan

2013-10-01

Deriving the distribution of binary parameters for a particular class of stars over the full range of orbital separations usually requires the combination of results from many different observing techniques (radial velocities, interferometry, astrometry, photometry, direct imaging), each with selection biases. However, Cepheids—cool, evolved stars of ~5 M ⊙—are a special case because ultraviolet (UV) spectra will immediately reveal any companion star hotter than early type A, regardless of the orbital separation. We have used International Ultraviolet Explorer UV spectra of a complete sample of all 76 Cepheids brighter than V = 8 to create a list of all 18 Cepheids with companions more massive than 2.0 M ⊙. Orbital periods of many of these binaries are available from radial-velocity studies, or can be estimated for longer-period systems from detected velocity variability. In an imaging survey with the Hubble Space Telescope Wide Field Camera 3, we resolved three of the companions (those of η Aql, S Nor, and V659 Cen), allowing us to make estimates of the periods out to the long-period end of the distribution. Combining these separations with orbital data in the literature, we derive an unbiased distribution of binary separations, orbital periods, and mass ratios. The distribution of orbital periods shows that the 5 M ⊙ binaries have systematically shorter periods than do 1 M ⊙ stars. Our data also suggest that the distribution of mass ratios depends on both binary separation and system multiplicity. The distribution of mass ratios as a function of orbital separation, however, does not depend on whether a system is a binary or a triple. Based in part on observations made with the NASA/ESA Hubble Space Telescope, obtained by the Space Telescope Science Institute. STScI is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555.

Advancing Fourth-Grade Students' Understanding of Arithmetic Properties with Instruction That Promotes Mathematical Argumentation

ERIC Educational Resources Information Center

Rumsey, Chepina Witkowski

2012-01-01

The goals for this study were to investigate how fourth-grade students developed an understanding of the arithmetic properties when instruction promoted mathematical argumentation and to identify the characteristics of students' arguments. Using the emergent perspective as an overarching theoretical perspective helped distinguish between two…

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…

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

ERIC Educational Resources Information Center

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

2015-01-01

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

Multiclass Classification by Adaptive Network of Dendritic Neurons with Binary Synapses Using Structural Plasticity

PubMed Central

Hussain, Shaista; Basu, Arindam

2016-01-01

The development of power-efficient neuromorphic devices presents the challenge of designing spike pattern classification algorithms which can be implemented on low-precision hardware and can also achieve state-of-the-art performance. In our pursuit of meeting this challenge, we present a pattern classification model which uses a sparse connection matrix and exploits the mechanism of nonlinear dendritic processing to achieve high classification accuracy. A rate-based structural learning rule for multiclass classification is proposed which modifies a connectivity matrix of binary synaptic connections by choosing the best “k” out of “d” inputs to make connections on every dendritic branch (k < < d). Because learning only modifies connectivity, the model is well suited for implementation in neuromorphic systems using address-event representation (AER). We develop an ensemble method which combines several dendritic classifiers to achieve enhanced generalization over individual classifiers. We have two major findings: (1) Our results demonstrate that an ensemble created with classifiers comprising moderate number of dendrites performs better than both ensembles of perceptrons and of complex dendritic trees. (2) In order to determine the moderate number of dendrites required for a specific classification problem, a two-step solution is proposed. First, an adaptive approach is proposed which scales the relative size of the dendritic trees of neurons for each class. It works by progressively adding dendrites with fixed number of synapses to the network, thereby allocating synaptic resources as per the complexity of the given problem. As a second step, theoretical capacity calculations are used to convert each neuronal dendritic tree to its optimal topology where dendrites of each class are assigned different number of synapses. The performance of the model is evaluated on classification of handwritten digits from the benchmark MNIST dataset and compared with other

Identifying Blocks Formed by Curbed Fractures Using Exact Arithmetic

NASA Astrophysics Data System (ADS)

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

2015-12-01

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

An exact arithmetic toolbox for a consistent and reproducible structural analysis of metabolic network models

PubMed Central

Chindelevitch, Leonid; Trigg, Jason; Regev, Aviv; Berger, Bonnie

2014-01-01

Constraint-based models are currently the only methodology that allows the study of metabolism at the whole-genome scale. Flux balance analysis is commonly used to analyse constraint-based models. Curiously, the results of this analysis vary with the software being run, a situation that we show can be remedied by using exact rather than floating-point arithmetic. Here we introduce MONGOOSE, a toolbox for analysing the structure of constraint-based metabolic models in exact arithmetic. We apply MONGOOSE to the analysis of 98 existing metabolic network models and find that the biomass reaction is surprisingly blocked (unable to sustain non-zero flux) in nearly half of them. We propose a principled approach for unblocking these reactions and extend it to the problems of identifying essential and synthetic lethal reactions and minimal media. Our structural insights enable a systematic study of constraint-based metabolic models, yielding a deeper understanding of their possibilities and limitations. PMID:25291352

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

PubMed

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

2016-01-01

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

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

PubMed Central

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

2016-01-01

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

Planet Formation in Binaries

NASA Astrophysics Data System (ADS)

Thebault, P.; Haghighipour, N.

Spurred by the discovery of numerous exoplanets in multiple systems, binaries have become in recent years one of the main topics in planet formation research. Numerous studies have investigated to what extent the presence of a stellar companion can affect the planet formation process. Such studies have implications that can reach beyond the sole context of binaries, as they allow to test certain aspects of the planet formation scenario by submitting them to extreme environments. We review here the current understanding on this complex problem. We show in particular how each of the different stages of the planet-formation process is affected differently by binary perturbations. We focus especially on the intermediate stage of kilometre-sized planetesimal accretion, which has proven to be the most sensitive to binarity and for which the presence of some exoplanets observed in tight binaries is difficult to explain by in-situ formation following the "standard" planet-formation scenario. Some tentative solutions to this apparent paradox are presented. The last part of our review presents a thorough description of the problem of planet habitability, for which the binary environment creates a complex situation because of the presence of two irradation sources of varying distance.

An adaptive mesh refinement-multiphase lattice Boltzmann flux solver for simulation of complex binary fluid flows

NASA Astrophysics Data System (ADS)

Yuan, H. Z.; Wang, Y.; Shu, C.

2017-12-01

This paper presents an adaptive mesh refinement-multiphase lattice Boltzmann flux solver (AMR-MLBFS) for effective simulation of complex binary fluid flows at large density ratios. In this method, an AMR algorithm is proposed by introducing a simple indicator on the root block for grid refinement and two possible statuses for each block. Unlike available block-structured AMR methods, which refine their mesh by spawning or removing four child blocks simultaneously, the present method is able to refine its mesh locally by spawning or removing one to four child blocks independently when the refinement indicator is triggered. As a result, the AMR mesh used in this work can be more focused on the flow region near the phase interface and its size is further reduced. In each block of mesh, the recently proposed MLBFS is applied for the solution of the flow field and the level-set method is used for capturing the fluid interface. As compared with existing AMR-lattice Boltzmann models, the present method avoids both spatial and temporal interpolations of density distribution functions so that converged solutions on different AMR meshes and uniform grids can be obtained. The proposed method has been successfully validated by simulating a static bubble immersed in another fluid, a falling droplet, instabilities of two-layered fluids, a bubble rising in a box, and a droplet splashing on a thin film with large density ratios and high Reynolds numbers. Good agreement with the theoretical solution, the uniform-grid result, and/or the published data has been achieved. Numerical results also show its effectiveness in saving computational time and virtual memory as compared with computations on uniform meshes.

Informal Numeracy Skills: The Structure and Relations among Numbering, Relations, and Arithmetic Operations in Preschool

ERIC Educational Resources Information Center

Purpura, David J.; Lonigan, Christopher J.

2013-01-01

Validating the structure of informal numeracy skills is critical to understanding the developmental trajectories of mathematics skills at early ages; however, little research has been devoted to construct evaluation of the Numbering, Relations, and Arithmetic Operations domains. This study was designed to address this knowledge gap by examining…

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

ERIC Educational Resources Information Center

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

2005-01-01

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

DISTINGUISHING COMPACT BINARY POPULATION SYNTHESIS MODELS USING GRAVITATIONAL WAVE OBSERVATIONS OF COALESCING BINARY BLACK HOLES

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

Stevenson, Simon; Ohme, Frank; Fairhurst, Stephen, E-mail: simon.stevenson@ligo.org

2015-09-01

The coalescence of compact binaries containing neutron stars or black holes is one of the most promising signals for advanced ground-based laser interferometer gravitational-wave (GW) detectors, with the first direct detections expected over the next few years. The rate of binary coalescences and the distribution of component masses is highly uncertain, and population synthesis models predict a wide range of plausible values. Poorly constrained parameters in population synthesis models correspond to poorly understood astrophysics at various stages in the evolution of massive binary stars, the progenitors of binary neutron star and binary black hole systems. These include effects such asmore » supernova kick velocities, parameters governing the energetics of common envelope evolution and the strength of stellar winds. Observing multiple binary black hole systems through GWs will allow us to infer details of the astrophysical mechanisms that lead to their formation. Here we simulate GW observations from a series of population synthesis models including the effects of known selection biases, measurement errors and cosmology. We compare the predictions arising from different models and show that we will be able to distinguish between them with observations (or the lack of them) from the early runs of the advanced LIGO and Virgo detectors. This will allow us to narrow down the large parameter space for binary evolution models.« less

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

PubMed

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

2009-12-01

Sex differences in cognitive tasks have been widely investigated. With brain-imaging techniques, the functions of the brain during the performance of tasks can be examined. Mental arithmetic and near-infrared spectroscopy (NIRS) were used to assess sex differences in prefrontal area activation in a functional brain study. Healthy college students were recruited to perform 2 mental arithmetic tasks. In the first (easy) task, students had to subtract a 1-digit number from a 3-digit number. In the second (difficult) task, they had to subtract a 2-digit number from a 3-digit number. Changes in the concentration of oxygenated hemoglobin (oxy-Hgb) in the prefrontal area during the tasks were measured with NIRS. Thirty students (15 men, 15 women; mean [SD] age: 24.9 [2.2] and 24.3 [2.6] years, respectively) were recruited from Southeast University, Nanjing, China, to participate in the study. The concentration of oxy-Hgb increased during both mental arithmetic tasks (difficult task vs easy task, mean [SD] % arbitrary units: 4.36 [4.38] vs 2.26 [2.82]; F(1,28) = 222.80; P < 0.01). Significant interactions of task x sex (F(1,28) = 82.95), time x sex (F(1,28) = 34.48), task x time (F(1,28) = 222.57), and task x time x sex (F(1,28) = 83.09) were obtained (all, P < 0.01). However, for the 2 tasks, no significant differences between men and women were observed in the mean (SD) response time (men vs women, sec: 3.60 [0.74] vs 3.56 [0.49] for the easy task, 6.55 [0.77] vs 6.44 [0.75] for the difficult task; F(1,28) = 0.67; P = NS) or accuracy rate (men vs women, %: 95.33 [7.40] vs 92.77 [8.80] for the easy task, 62.67 [28.56] vs 54.67 [18.75] for the difficult task; F(1,28) = 0.54; P = NS). Male students showed neural efficiency (less prefrontal activation in subjects with better performance) during the difficult task. In these subjects, sex differences in prefrontal response when performing mental arithmetic were associated with the intensity of the task. Compared with men

Gravitational radiation, inspiraling binaries, and cosmology

NASA Technical Reports Server (NTRS)

Chernoff, David F.; Finn, Lee S.

1993-01-01

We show how to measure cosmological parameters using observations of inspiraling binary neutron star or black hole systems in one or more gravitational wave detectors. To illustrate, we focus on the case of fixed mass binary systems observed in a single Laser Interferometer Gravitational-wave Observatory (LIGO)-like detector. Using realistic detector noise estimates, we characterize the rate of detections as a function of a threshold SNR Rho(0), H0, and the binary 'chirp' mass. For Rho(0) = 8, H0 = 100 km/s/Mpc, and 1.4 solar mass neutron star binaries, the sample has a median redshift of 0.22. Under the same assumptions but independent of H0, a conservative rate density of coalescing binaries implies LIGO will observe about 50/yr binary inspiral events. The precision with which H0 and the deceleration parameter q0 may be determined depends on the number of observed inspirals. For fixed mass binary systems, about 100 observations with Rho(0) = 10 in the LIGO will give H0 to 10 percent in an Einstein-DeSitter cosmology, and 3000 will give q0 to 20 percent. For the conservative rate density of coalescing binaries, 100 detections with Rho(0) = 10 will require about 4 yrs.

Contact Binaries on Their Way Towards Merging

NASA Astrophysics Data System (ADS)

Gazeas, K.

2015-07-01

Contact binaries are the most frequently observed type of eclipsing star system. They are small, cool, low-mass binaries belonging to a relatively old stellar population. They follow certain empirical relationships that closely connect a number of physical parameters with each other, largely because of constraints coming from the Roche geometry. As a result, contact binaries provide an excellent test of stellar evolution, specifically for stellar merger scenarios. Observing campaigns by many authors have led to the cataloging of thousands of contact binaries and enabled statistical studies of many of their properties. A large number of contact binaries have been found to exhibit extraordinary behavior, requiring follow-up observations to study their peculiarities in detail. For example, a doubly-eclipsing quadruple system consisting of a contact binary and a detached binary is a highly constrained system offering an excellent laboratory to test evolutionary theories for binaries. A new observing project was initiated at the University of Athens in 2012 in order to investigate the possible lower limit for the orbital period of binary systems before coalescence, prior to merging.

Spatial Skills as a Predictor of First Grade Girls' Use of Higher Level Arithmetic Strategies

ERIC Educational Resources Information Center

Laski, Elida V.; Casey, Beth M.; Yu, Qingyi; Dulaney, Alana; Heyman, Miriam; Dearing, Eric

2013-01-01

Girls are more likely than boys to use counting strategies rather than higher-level mental strategies to solve arithmetic problems. Prior research suggests that dependence on counting strategies may have negative implications for girls' later math achievement. We investigated the relation between first-grade girls' verbal and spatial skills and…

Protoplanetary disk evolution and stellar parameters of T Tauri binaries in Chamaeleon I

NASA Astrophysics Data System (ADS)

Daemgen, S.; Petr-Gotzens, M. G.; Correia, S.; Teixeira, P. S.; Brandner, W.; Kley, W.; Zinnecker, H.

2013-06-01

Aims: This study aims to determine the impact of stellar binary companions on the lifetime and evolution of circumstellar disks in the Chamaeleon I (Cha I) star-forming region by measuring the frequency and strength of accretion and circumstellar dust signatures around the individual components of T Tauri binary stars. Methods: We used high-angular resolution adaptive optics JHKsL' -band photometry and 1.5-2.5 μm spectroscopy of 19 visual binary and 7 triple stars in Cha I - including one newly discovered tertiary component - with separations between ~25 and ~1000 AU. The data allowed us to infer stellar component masses and ages and, from the detection of near-infrared excess emission and the strength of Brackett-γ emission, the presence of ongoing accretion and hot circumstellar dust of the individual stellar components of each binary. Results: Of all the stellar components in close binaries with separations of 25-100 AU, 10+15-5% show signs of accretion. This is less than half of the accretor fraction found in wider binaries, which itself appears significantly reduced (~44%) compared with previous measurements of single stars in Cha I. Hot dust was found around 50+30-15% of the target components, a value that is indistinguishable from that of Cha I single stars. Only the closest binaries (<25 AU) were inferred to have a significantly reduced fraction (≲25%) of components that harbor hot dust. Accretors were exclusively found in binary systems with unequal component masses Msecondary/Mprimary < 0.8, implying that the detected accelerated disk dispersal is a function of mass-ratio. This agrees with the finding that only one accreting secondary star was found, which is also the weakest accretor in the sample. Conclusions: The results imply that disk dispersal is more accelerated the stronger the dynamical disk truncation, i.e., the smaller the inferred radius of the disk. Nonetheless, the overall measured mass accretion rates appear to be independent of the

Classification of prefrontal activity due to mental arithmetic and music imagery using hidden Markov models and frequency domain near-infrared spectroscopy

NASA Astrophysics Data System (ADS)

Power, Sarah D.; Falk, Tiago H.; Chau, Tom

2010-04-01

Near-infrared spectroscopy (NIRS) has recently been investigated as a non-invasive brain-computer interface (BCI). In particular, previous research has shown that NIRS signals recorded from the motor cortex during left- and right-hand imagery can be distinguished, providing a basis for a two-choice NIRS-BCI. In this study, we investigated the feasibility of an alternative two-choice NIRS-BCI paradigm based on the classification of prefrontal activity due to two cognitive tasks, specifically mental arithmetic and music imagery. Deploying a dual-wavelength frequency domain near-infrared spectrometer, we interrogated nine sites around the frontopolar locations (International 10-20 System) while ten able-bodied adults performed mental arithmetic and music imagery within a synchronous shape-matching paradigm. With the 18 filtered AC signals, we created task- and subject-specific maximum likelihood classifiers using hidden Markov models. Mental arithmetic and music imagery were classified with an average accuracy of 77.2% ± 7.0 across participants, with all participants significantly exceeding chance accuracies. The results suggest the potential of a two-choice NIRS-BCI based on cognitive rather than motor tasks.

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

PubMed

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

2017-02-01

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

Tera-Op Reliable Intelligently Adaptive Processing System (TRIPS)

DTIC Science & Technology

2004-04-01

flop creates a loadable FIFO queue, fifo pload. A prototype of the HML simulator is implemented using a functional language OCaml . The language type...Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 7.1.2 Hardware Meta Language ...operates on the TRIPS Intermediate Language (TIL) produced by the Scale compiler. We also adapted the gnu binary utilities to implement an assembler and

Binary Systems and the Initial Mass Function

NASA Astrophysics Data System (ADS)

Malkov, O. Yu.

2017-07-01

In the present paper we discuss advantages and disadvantages of binary stars, which are important for star formation history determination. We show that to make definite conclusions of the initial mass function shape, it is necessary to study binary population well enough to correct the luminosity function for unresolved binaries; to construct the mass-luminosity relation based on wide binaries data, and to separate observational mass functions of primaries, of secondaries, and of unresolved binaries.

Accuracy of binary black hole waveform models for aligned-spin binaries

NASA Astrophysics Data System (ADS)

Kumar, Prayush; Chu, Tony; Fong, Heather; Pfeiffer, Harald P.; Boyle, Michael; Hemberger, Daniel A.; Kidder, Lawrence E.; Scheel, Mark A.; Szilagyi, Bela

2016-05-01

Coalescing binary black holes are among the primary science targets for second generation ground-based gravitational wave detectors. Reliable gravitational waveform models are central to detection of such systems and subsequent parameter estimation. This paper performs a comprehensive analysis of the accuracy of recent waveform models for binary black holes with aligned spins, utilizing a new set of 84 high-accuracy numerical relativity simulations. Our analysis covers comparable mass binaries (mass-ratio 1 ≤q ≤3 ), and samples independently both black hole spins up to a dimensionless spin magnitude of 0.9 for equal-mass binaries and 0.85 for unequal mass binaries. Furthermore, we focus on the high-mass regime (total mass ≳50 M⊙ ). The two most recent waveform models considered (PhenomD and SEOBNRv2) both perform very well for signal detection, losing less than 0.5% of the recoverable signal-to-noise ratio ρ , except that SEOBNRv2's efficiency drops slightly for both black hole spins aligned at large magnitude. For parameter estimation, modeling inaccuracies of the SEOBNRv2 model are found to be smaller than systematic uncertainties for moderately strong GW events up to roughly ρ ≲15 . PhenomD's modeling errors are found to be smaller than SEOBNRv2's, and are generally irrelevant for ρ ≲20 . Both models' accuracy deteriorates with increased mass ratio, and when at least one black hole spin is large and aligned. The SEOBNRv2 model shows a pronounced disagreement with the numerical relativity simulation in the merger phase, for unequal masses and simultaneously both black hole spins very large and aligned. Two older waveform models (PhenomC and SEOBNRv1) are found to be distinctly less accurate than the more recent PhenomD and SEOBNRv2 models. Finally, we quantify the bias expected from all four waveform models during parameter estimation for several recovered binary parameters: chirp mass, mass ratio, and effective spin.

Radial Velocities of 41 Kepler Eclipsing Binaries

NASA Astrophysics Data System (ADS)

Matson, Rachel A.; Gies, Douglas R.; Guo, Zhao; Williams, Stephen J.

2017-12-01

Eclipsing binaries are vital for directly determining stellar parameters without reliance on models or scaling relations. Spectroscopically derived parameters of detached and semi-detached binaries allow us to determine component masses that can inform theories of stellar and binary evolution. Here we present moderate resolution ground-based spectra of stars in close binary systems with and without (detected) tertiary companions observed by NASA’s Kepler mission and analyzed for eclipse timing variations. We obtain radial velocities and spectroscopic orbits for five single-lined and 35 double-lined systems, and confirm one false positive eclipsing binary. For the double-lined spectroscopic binaries, we also determine individual component masses and examine the mass ratio {M}2/{M}1 distribution, which is dominated by binaries with like-mass pairs and semi-detached classical Algol systems that have undergone mass transfer. Finally, we constrain the mass of the tertiary component for five double-lined binaries with previously detected companions.

Photometric detection of a candidate low-mass giant binary system at the Milky Way Galactic Center

NASA Astrophysics Data System (ADS)

Krishna Gautam, Abhimat; Do, Tuan; Ghez, Andrea; Sakai, Shoko; Morris, Mark; Lu, Jessica; Witzel, Gunther; Jia, Siyao; Becklin, Eric Eric; Matthews, Keith

2018-01-01

We present the discovery of a new periodic variable star at the Milky Way Galactic Center (GC). This study uses laser guide-star adaptive optics data collected with the W. M. Keck 10 m telescope in the K‧-band (2.2 µm) over 35 nights spanning an 11 year time baseline, and 5 nights of additional H-band (1.6 µm) data. We implemented an iterative photometric calibration and local correction technique, resulting in a photometric uncertainty of Δm_K‧ ∼ 0.03 to a magnitude of m_K‧ ∼ 16.The periodically variable star has a 39.42 day period. We find that the star is not consistent with known periodically variable star classes in this period range with its observed color and luminosity, nor with an eclipsing binary system. The star's color and luminosity are however consistent with an ellipsoidal binary system at the GC, consisting of a K-giant and a dwarf component with an orbital period of 78.84 days. If a binary system, it represents the first detection of a low-mass giant binary system in the central half parsec of the GC. Such long-period binary systems can easily evaporate in the dense environment of the GC due to interactions with other stars. The existence and properties of a low-mass, long-period binary system can thus place valuable constraints on dynamical models of the GC environment and probe the density of the hypothesized dark cusp of stellar remnants at the GC.

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)…

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…

Eclipsing Stellar Binaries in the Galactic Center

NASA Astrophysics Data System (ADS)

Li, Gongjie; Ginsburg, Idan; Naoz, Smadar; Loeb, Abraham

2017-12-01

Compact stellar binaries are expected to survive in the dense environment of the Galactic center. The stable binaries may undergo Kozai–Lidov oscillations due to perturbations from the central supermassive black hole (Sgr A*), yet the general relativistic precession can suppress the Kozai–Lidov oscillations and keep the stellar binaries from merging. However, it is challenging to resolve the binary sources and distinguish them from single stars. The close separations of the stable binaries allow higher eclipse probabilities. Here, we consider the massive star SO-2 as an example and calculate the probability of detecting eclipses, assuming it is a binary. We find that the eclipse probability is ∼30%–50%, reaching higher values when the stellar binary is more eccentric or highly inclined relative to its orbit around Sgr A*.

Theoretical studies of binaries in astrophysics

NASA Astrophysics Data System (ADS)

Dischler, Johann Sebastian

This thesis introduces and summarizes four papers dealing with computer simulations of astrophysical processes involving binaries. The first part gives the rational and theoretical background to these papers. In paper I and II a statistical approach to studying eclipsing binaries is described. By using population synthesis models for binaries the probabilities for eclipses are calculated for different luminosity classes of binaries. These are compared with Hipparcos data and they agree well if one uses a standard input distribution for the orbit sizes. If one uses a random pairing model, where both companions are independently picked from an IMF, one finds too feclipsing binaries by an order of magnitude. In paper III we investigate a possible scenario for the origin of the stars observed close to the centre of our galaxy, called S stars. We propose that a cluster falls radially cowards the central black hole. The binaries within the cluster can then, if they have small impact parameters, be broken up by the black hole's tidal held and one of the components of the binary will be captured by the black hole. Paper IV investigates how the onset of mass transfer in eccentric binaries depends on the eccentricity. To do this we have developed a new two-phase SPH scheme where very light particles are at tire outer edge of our simulated star. This enables us to get a much better resolution of the very small mass that is transferred in close binaries. Our simulations show that the minimum required distance between the stars to have mass transfer decreases with the eccentricity.

Embedded binaries and their dense cores

NASA Astrophysics Data System (ADS)

Sadavoy, Sarah I.; Stahler, Steven W.

2017-08-01

We explore the relationship between young, embedded binaries and their parent cores, using observations within the Perseus Molecular Cloud. We combine recently published Very Large Array observations of young stars with core properties obtained from Submillimetre Common-User Bolometer Array 2 observations at 850 μm. Most embedded binary systems are found towards the centres of their parent cores, although several systems have components closer to the core edge. Wide binaries, defined as those systems with physical separations greater than 500 au, show a tendency to be aligned with the long axes of their parent cores, whereas tight binaries show no preferred orientation. We test a number of simple, evolutionary models to account for the observed populations of Class 0 and I sources, both single and binary. In the model that best explains the observations, all stars form initially as wide binaries. These binaries either break up into separate stars or else shrink into tighter orbits. Under the assumption that both stars remain embedded following binary break-up, we find a total star formation rate of 168 Myr-1. Alternatively, one star may be ejected from the dense core due to binary break-up. This latter assumption results in a star formation rate of 247 Myr-1. Both production rates are in satisfactory agreement with current estimates from other studies of Perseus. Future observations should be able to distinguish between these two possibilities. If our model continues to provide a good fit to other star-forming regions, then the mass fraction of dense cores that becomes stars is double what is currently believed.

Asteroid Systems: Binaries, Triples, and Pairs

NASA Astrophysics Data System (ADS)

Margot, J.-L.; Pravec, P.; Taylor, P.; Carry, B.; Jacobson, S.

In the past decade, the number of known binary near-Earth asteroids has more than quadrupled and the number of known large main-belt asteroids with satellites has doubled. Half a dozen triple asteroids have been discovered, and the previously unrecognized populations of asteroid pairs and small main-belt binaries have been identified. The current observational evidence confirms that small (≲20 km) binaries form by rotational fission and establishes that the Yarkovsky-O'Keefe-Radzievskii-Paddack (YORP) effect powers the spin-up process. A unifying paradigm based on rotational fission and post-fission dynamics can explain the formation of small binaries, triples, and pairs. Large (>~20 km) binaries with small satellites are most likely created during large collisions.

Quantum error correcting codes and 4-dimensional arithmetic hyperbolic manifolds

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

Guth, Larry, E-mail: lguth@math.mit.edu; Lubotzky, Alexander, E-mail: alex.lubotzky@mail.huji.ac.il

2014-08-15

Using 4-dimensional arithmetic hyperbolic manifolds, we construct some new homological quantum error correcting codes. They are low density parity check codes with linear rate and distance n{sup ε}. Their rate is evaluated via Euler characteristic arguments and their distance using Z{sub 2}-systolic geometry. This construction answers a question of Zémor [“On Cayley graphs, surface codes, and the limits of homological coding for quantum error correction,” in Proceedings of Second International Workshop on Coding and Cryptology (IWCC), Lecture Notes in Computer Science Vol. 5557 (2009), pp. 259–273], who asked whether homological codes with such parameters could exist at all.

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

PubMed

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

2016-01-01

Theta-phase gamma-amplitude coupling (TGC) measurement has recently received attention as a feasible method of assessing brain functions such as neuronal interactions. The purpose of this electroencephalographic (EEG) study is to understand the mechanisms underlying the deficits in attentional control in children with attention deficit/hyperactivity disorder (ADHD) by comparing the power spectra and TGC at rest and during a mental arithmetic task. Nineteen-channel EEGs were recorded from 97 volunteers (including 53 subjects with ADHD) from a camp for hyperactive children under two conditions (rest and task performance). The EEG power spectra and the TGC data were analyzed. Correlation analyses between the Intermediate Visual and Auditory (IVA) continuous performance test (CPT) scores and EEG parameters were performed. No significant difference in the power spectra was detected between the groups at rest and during task performance. However, TGC was reduced during the arithmetic task in the ADHD group compared with the normal group (F = 16.70, p < 0.001). The TGC values positively correlated with the IVA CPT scores but negatively correlated with theta power. Our findings suggest that desynchronization of TGC occurred during the arithmetic task in ADHD children. TGC in ADHD children is expected to serve as a promising neurophysiological marker of network deactivation during attention-demanding tasks.

Binary asteroid population. 2. Anisotropic distribution of orbit poles of small, inner main-belt binaries

NASA Astrophysics Data System (ADS)

Pravec, P.; Scheirich, P.; Vokrouhlický, D.; Harris, A. W.; Kušnirák, P.; Hornoch, K.; Pray, D. P.; Higgins, D.; Galád, A.; Világi, J.; Gajdoš, Š.; Kornoš, L.; Oey, J.; Husárik, M.; Cooney, W. R.; Gross, J.; Terrell, D.; Durkee, R.; Pollock, J.; Reichart, D. E.; Ivarsen, K.; Haislip, J.; LaCluyze, A.; Krugly, Yu. N.; Gaftonyuk, N.; Stephens, R. D.; Dyvig, R.; Reddy, V.; Chiorny, V.; Vaduvescu, O.; Longa-Peña, P.; Tudorica, A.; Warner, B. D.; Masi, G.; Brinsfield, J.; Gonçalves, R.; Brown, P.; Krzeminski, Z.; Gerashchenko, O.; Shevchenko, V.; Molotov, I.; Marchis, F.

2012-03-01

Our photometric observations of 18 main-belt binary systems in more than one apparition revealed a strikingly high number of 15 having positively re-observed mutual events in the return apparitions. Our simulations of the survey showed that it cannot be due to an observational selection effect and that the data strongly suggest that poles of mutual orbits between components of binary asteroids in the primary size range 3-8 km are not distributed randomly: The null hypothesis of an isotropic distribution of the orbit poles is rejected at a confidence level greater than 99.99%. Binary orbit poles concentrate at high ecliptic latitudes, within 30° of the poles of the ecliptic. We propose that the binary orbit poles oriented preferentially up/down-right are due to either of the two processes: (i) the YORP tilt of spin axes of their parent bodies toward the asymptotic states near obliquities 0° and 180° (pre-formation mechanism) or (ii) the YORP tilt of spin axes of the primary components of already formed binary systems toward the asymptotic states near obliquities 0° and 180° (post-formation mechanism). The alternative process of elimination of binaries with poles closer to the ecliptic by dynamical instability, such as the Kozai effect due to gravitational perturbations from the Sun, does not explain the observed orbit pole concentration. This is because for close binary asteroid systems, the gravitational effects of primary’s irregular shape dominate the solar-tide effect.

From wide to close binaries?

NASA Astrophysics Data System (ADS)

Eggleton, Peter P.

The mechanisms by which the periods of wide binaries (mass 8 solar mass or less and period 10-3000 d) are lengthened or shortened are discussed, synthesizing the results of recent theoretical investigations. A system of nomenclature involving seven evolutionary states, three geometrical states, and 10 types of orbital-period evolution is developed and applied; classifications of 71 binaries are presented in a table along with the basic observational parameters. Evolutionary processes in wide binaries (single-star-type winds, magnetic braking with tidal friction, and companion-reinforced attrition), late case B systems, low-mass X-ray binaries, and triple systems are examined in detail, and possible evolutionary paths are shown in diagrams.

Subdwarf B Stars: Tracers Of Binary Evolution

NASA Astrophysics Data System (ADS)

Morales-Rueda, L.; Maxted, P. F. L.; Marsh, T. R.

2007-08-01

Subdwarf B stars are a superb stellar population to study binary evolution. In 2001, Maxted et al. (MNRAS, 326, 1391) found that 21 out of the 36 subdwarf B stars they studied were in short period binaries. These observations inspired new theoretical work that suggests that up to 90 per cent of subdwarf B stars are in binary systems with the remaining apparently single stars being the product of merging pairs. This high binary fraction added to the fact that they are detached binaries that have not changed significantly since they came out of the common envelope, make subdwarf B stars a perfect population to study binary evolution. By comparing the observed orbital period distribution of subdwarf B stars with that obtained from population synthesis calculations we can determine fundamental parameters of binary evolution such as the common envelope ejection efficiency. Here we give an overview of the fraction of short period binaries found from different surveys as well as the most up to date orbital period distribution determined observationally. We also present results from a recent search for subdwarf B stars in long period binaries.

Survival of planets around shrinking stellar binaries

PubMed Central

Muñoz, Diego J.; Lai, Dong

2015-01-01

The discovery of transiting circumbinary planets by the Kepler mission suggests that planets can form efficiently around binary stars. None of the stellar binaries currently known to host planets has a period shorter than 7 d, despite the large number of eclipsing binaries found in the Kepler target list with periods shorter than a few days. These compact binaries are believed to have evolved from wider orbits into their current configurations via the so-called Lidov–Kozai migration mechanism, in which gravitational perturbations from a distant tertiary companion induce large-amplitude eccentricity oscillations in the binary, followed by orbital decay and circularization due to tidal dissipation in the stars. Here we explore the orbital evolution of planets around binaries undergoing orbital decay by this mechanism. We show that planets may survive and become misaligned from their host binary, or may develop erratic behavior in eccentricity, resulting in their consumption by the stars or ejection from the system as the binary decays. Our results suggest that circumbinary planets around compact binaries could still exist, and we offer predictions as to what their orbital configurations should be like. PMID:26159412

Survival of planets around shrinking stellar binaries.

PubMed

Muñoz, Diego J; Lai, Dong

2015-07-28

The discovery of transiting circumbinary planets by the Kepler mission suggests that planets can form efficiently around binary stars. None of the stellar binaries currently known to host planets has a period shorter than 7 d, despite the large number of eclipsing binaries found in the Kepler target list with periods shorter than a few days. These compact binaries are believed to have evolved from wider orbits into their current configurations via the so-called Lidov-Kozai migration mechanism, in which gravitational perturbations from a distant tertiary companion induce large-amplitude eccentricity oscillations in the binary, followed by orbital decay and circularization due to tidal dissipation in the stars. Here we explore the orbital evolution of planets around binaries undergoing orbital decay by this mechanism. We show that planets may survive and become misaligned from their host binary, or may develop erratic behavior in eccentricity, resulting in their consumption by the stars or ejection from the system as the binary decays. Our results suggest that circumbinary planets around compact binaries could still exist, and we offer predictions as to what their orbital configurations should be like.

Real time pipelined system for forming the sum of products in the processing of video data

NASA Technical Reports Server (NTRS)

Wilcox, Brian (Inventor)

1988-01-01

A 3-by-3 convolver utilizes 9 binary arithmetic units connected in cascade for multiplying 12-bit binary pixel values P sub i which are positive or two's complement binary numbers by 5-bit magnitide (plus sign) weights W sub i which may be positive or negative. The weights are stored in registers including the sign bits. For a negative weight, the one's complement of the pixel value to be multiplied is formed at each unit by a bank of 17 exclusive or gates G sub i under control of the sign of the corresponding weight W sub i, and a correction is made by adding the sum of the absolute values of all the negative weights for each 3-by-3 kernel. Since this correction value remains constant as long as the weights are constant, it can be precomputed and stored in a register as a value to be added to the product PW of the first arithmetic unit.

Formation and Evolution of X-ray Binaries

NASA Astrophysics Data System (ADS)

Shao, Y.

2017-07-01

X-ray binaries are a class of binary systems, in which the accretor is a compact star (i.e., black hole, neutron star, or white dwarf). They are one of the most important objects in the universe, which can be used to study not only binary evolution but also accretion disks and compact stars. Statistical investigations of these binaries help to understand the formation and evolution of galaxies, and sometimes provide useful constraints on the cosmological models. The goal of this thesis is to investigate the formation and evolution processes of X-ray binaries including Be/X-ray binaries, low-mass X-ray binaries (LMXBs), ultraluminous X-ray sources (ULXs), and cataclysmic variables. In Chapter 1 we give a brief review on the basic knowledge of the binary evolution. In Chapter 2 we discuss the formation of Be stars through binary interaction. In this chapter we investigate the formation of Be stars resulting from mass transfer in binaries in the Galaxy. Using binary evolution and population synthesis calculations, we find that in Be/neutron star binaries the Be stars have a lower limit of mass ˜ 8 M⊙ if they are formed by a stable (i.e., without the occurrence of common envelope evolution) and nonconservative mass transfer. We demonstrate that the isolated Be stars may originate from both mergers of two main-sequence stars and disrupted Be binaries during the supernova explosions of the primary stars, but mergers seem to play a much more important role. Finally the fraction of Be stars produced by binary interactions in all B type stars can be as high as ˜ 13%-30% , implying that most of Be stars may result from binary interaction. In Chapter 3 we show the evolution of intermediate- and low-mass X-ray binaries (I/LMXBs) and the formation of millisecond pulsars. Comparing the calculated results with the observations of binary radio pulsars, we report the following results: (1) The allowed parameter space for forming binary pulsars in the initial orbital period

Binary ferrihydrite catalysts

DOEpatents

Huffman, Gerald P.; Zhao, Jianmin; Feng, Zhen

1996-01-01

A method of preparing a catalyst precursor comprises dissolving an iron salt and a salt of an oxoanion forming agent, in water so that a solution of the iron salt and oxoanion forming agent salt has a ratio of oxoanion/Fe of between 0.0001:1 to 0.5:1. Next is increasing the pH of the solution to 10 by adding a strong base followed by collecting of precipitate having a binary ferrihydrite structure. A binary ferrihydrite catalyst precursor is also prepared by dissolving an iron salt in water. The solution is brought to a pH of substantially 10 to obtain ferrihydrite precipitate. The precipitate is then filtered and washed with distilled water and subsequently admixed with a hydroxy carboxylic acid solution. The admixture is mixed/agitated and the binary ferrihydrite precipitate is then filtered and recovered.

Binary ferrihydrite catalysts

DOEpatents

Huffman, G.P.; Zhao, J.; Feng, Z.

1996-12-03

A method of preparing a catalyst precursor comprises dissolving an iron salt and a salt of an oxoanion forming agent, in water so that a solution of the iron salt and oxoanion forming agent salt has a ratio of oxoanion/Fe of between 0.0001:1 to 0.5:1. Next is increasing the pH of the solution to 10 by adding a strong base followed by collecting of precipitate having a binary ferrihydrite structure. A binary ferrihydrite catalyst precursor is also prepared by dissolving an iron salt in water. The solution is brought to a pH of substantially 10 to obtain ferrihydrite precipitate. The precipitate is then filtered and washed with distilled water and subsequently admixed with a hydroxy carboxylic acid solution. The admixture is mixed/agitated and the binary ferrihydrite precipitate is then filtered and recovered. 3 figs.

The Influence of Mathematical Ability and Morning Nutrition on Mental Arithmetic in Preadolescents: An ERP study.

USDA-ARS?s Scientific Manuscript database

The effects of eating or skipping breakfast on ERP correlates of mental arithmetic were studied in preadolescents differing in experience (age) and mathematical skills. Participants, randomly assigned to treatment [eat (B) or skip (SB) breakfast (each, n = 41)], were sub-grouped by age [8.8 yrs (B: ...

X-ray binaries

NASA Technical Reports Server (NTRS)

1976-01-01

Satellite X-ray experiments and ground-based programs aimed at observation of X-ray binaries are discussed. Experiments aboard OAO-3, OSO-8, Ariel 5, Uhuru, and Skylab are included along with rocket and ground-based observations. Major topics covered are: Her X-1, Cyg X-3, Cen X-3, Cyg X-1, the transient source A0620-00, other possible X-ray binaries, and plans and prospects for future observational programs.

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

PubMed Central

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

2015-01-01

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

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

PubMed

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

2015-01-01

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

A Comparison of Updating Processes in Children Good or Poor in Arithmetic Word Problem-Solving

ERIC Educational Resources Information Center

Passolunghi, Maria Chiara; Pazzaglia, Francesca

2005-01-01

This study examines the updating ability of poor or good problem solvers. Seventy-eight fourth-graders, 43 good and 35 poor arithmetic word problem-solvers, performed the Updating Test used in Palladino et al. [Palladino, P., Cornoldi, C., De Beni, R., and Pazzaglia F. (2002). Working memory and updating processes in reading comprehension. Memory…

A wavelet approach to binary blackholes with asynchronous multitasking

NASA Astrophysics Data System (ADS)

Lim, Hyun; Hirschmann, Eric; Neilsen, David; Anderson, Matthew; Debuhr, Jackson; Zhang, Bo

2016-03-01

Highly accurate simulations of binary black holes and neutron stars are needed to address a variety of interesting problems in relativistic astrophysics. We present a new method for the solving the Einstein equations (BSSN formulation) using iterated interpolating wavelets. Wavelet coefficients provide a direct measure of the local approximation error for the solution and place collocation points that naturally adapt to features of the solution. Further, they exhibit exponential convergence on unevenly spaced collection points. The parallel implementation of the wavelet simulation framework presented here deviates from conventional practice in combining multi-threading with a form of message-driven computation sometimes referred to as asynchronous multitasking.

The Evolution of Compact Binary Star Systems.

PubMed

Postnov, Konstantin A; Yungelson, Lev R

2006-01-01

We review the formation and evolution of compact binary stars consisting of white dwarfs (WDs), neutron stars (NSs), and black holes (BHs). Binary NSs and BHs are thought to be the primary astrophysical sources of gravitational waves (GWs) within the frequency band of ground-based detectors, while compact binaries of WDs are important sources of GWs at lower frequencies to be covered by space interferometers (LISA). Major uncertainties in the current understanding of properties of NSs and BHs most relevant to the GW studies are discussed, including the treatment of the natal kicks which compact stellar remnants acquire during the core collapse of massive stars and the common envelope phase of binary evolution. We discuss the coalescence rates of binary NSs and BHs and prospects for their detections, the formation and evolution of binary WDs and their observational manifestations. Special attention is given to AM CVn-stars - compact binaries in which the Roche lobe is filled by another WD or a low-mass partially degenerate helium-star, as these stars are thought to be the best LISA verification binary GW sources.

The Evolution of Compact Binary Star Systems.

PubMed

Postnov, Konstantin A; Yungelson, Lev R

2014-01-01

We review the formation and evolution of compact binary stars consisting of white dwarfs (WDs), neutron stars (NSs), and black holes (BHs). Mergings of compact-star binaries are expected to be the most important sources for forthcoming gravitational-wave (GW) astronomy. In the first part of the review, we discuss observational manifestations of close binaries with NS and/or BH components and their merger rate, crucial points in the formation and evolution of compact stars in binary systems, including the treatment of the natal kicks, which NSs and BHs acquire during the core collapse of massive stars and the common envelope phase of binary evolution, which are most relevant to the merging rates of NS-NS, NS-BH and BH-BH binaries. The second part of the review is devoted mainly to the formation and evolution of binary WDs and their observational manifestations, including their role as progenitors of cosmologically-important thermonuclear SN Ia. We also consider AM CVn-stars, which are thought to be the best verification binary GW sources for future low-frequency GW space interferometers.

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

PubMed

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

2017-08-01

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

Separation in 5 Msun Binaries

NASA Astrophysics Data System (ADS)

Evans, Nancy R.; Bond, H. E.; Schaefer, G.; Mason, B. D.; Karovska, M.; Tingle, E.

2013-01-01

Cepheids (5 Msun stars) provide an excellent sample for determining the binary properties of fairly massive stars. International Ultraviolet Explorer (IUE) observations of Cepheids brighter than 8th magnitude resulted in a list of ALL companions more massive than 2.0 Msun uniformly sensitive to all separations. Hubble Space Telescope Wide Field Camera 3 (WFC3) has resolved three of these binaries (Eta Aql, S Nor, and V659 Cen). Combining these separations with orbital data in the literature, we derive an unbiased distribution of binary separations for a sample of 18 Cepheids, and also a distribution of mass ratios. The distribution of orbital periods shows that the 5 Msun binaries prefer shorter periods than 1 Msun stars, reflecting differences in star formation processes.

Research on the Orbital Period of Massive Binaries

NASA Astrophysics Data System (ADS)

Zhao, E.; Qain, S.

2011-12-01

Massive binary is the kind of binary, whose spectral type is earlier than B5. Research on massive binary plays an important role in the mass and angular momentum transfer or loss between the components, and the evolution of binary. Some massive binaries are observed and analyzed, including O-type binary LY Aur, B-type contact binary RZ Pyx and B-type semi-detached binary AI Cru. It is found that all of their periods have a long-term increasing, which indicates that the system is undergoing a Case A slow mass transfer stage on the nuclear time-scale of the secondary. Moreover, analysis show a cyclic change of orbital period, which can be explained by the light-travel effect time of the third body.

A ROSAT Survey of Contact Binary Stars

NASA Astrophysics Data System (ADS)

Geske, M. T.; Gettel, S. J.; McKay, T. A.

2006-01-01

Contact binary stars are common variable stars that are all believed to emit relatively large fluxes of X-rays. In this work we combine a large new sample of contact binary stars derived from the ROTSE-I telescope with X-ray data from the ROSAT All Sky Survey (RASS) to estimate the X-ray volume emissivity of contact binary stars in the Galaxy. We obtained X-ray fluxes for 140 contact binaries from the RASS, as well as two additional stars observed by the XMM-Newton observatory. From these data we confirm the emission of X-rays from all contact binary systems, with typical luminosities of approximately 1.0×1030 ergs s-1. Combining calculated luminosities with an estimated contact binary space density, we find that contact binaries do not have strong enough X-ray emission to account for a significant portion of the Galactic X-ray background.

Constraining Accreting Binary Populations in Normal Galaxies

NASA Astrophysics Data System (ADS)

Lehmer, Bret; Hornschemeier, A.; Basu-Zych, A.; Fragos, T.; Jenkins, L.; Kalogera, V.; Ptak, A.; Tzanavaris, P.; Zezas, A.

2011-01-01

X-ray emission from accreting binary systems (X-ray binaries) uniquely probe the binary phase of stellar evolution and the formation of compact objects such as neutron stars and black holes. A detailed understanding of X-ray binary systems is needed to provide physical insight into the formation and evolution of the stars involved, as well as the demographics of interesting binary remnants, such as millisecond pulsars and gravitational wave sources. Our program makes wide use of Chandra observations and complementary multiwavelength data sets (through, e.g., the Spitzer Infrared Nearby Galaxies Survey [SINGS] and the Great Observatories Origins Deep Survey [GOODS]), as well as super-computing facilities, to provide: (1) improved calibrations for correlations between X-ray binary emission and physical properties (e.g., star-formation rate and stellar mass) for galaxies in the local Universe; (2) new physical constraints on accreting binary processes (e.g., common-envelope phase and mass transfer) through the fitting of X-ray binary synthesis models to observed local galaxy X-ray binary luminosity functions; (3) observational and model constraints on the X-ray evolution of normal galaxies over the last 90% of cosmic history (since z 4) from the Chandra Deep Field surveys and accreting binary synthesis models; and (4) predictions for deeper observations from forthcoming generations of X-ray telesopes (e.g., IXO, WFXT, and Gen-X) to provide a science driver for these missions. In this talk, we highlight the details of our program and discuss recent results.

Galaxy Rotation and Rapid Supermassive Binary Coalescence

NASA Astrophysics Data System (ADS)

Holley-Bockelmann, Kelly; Khan, Fazeel Mahmood

2015-09-01

Galaxy mergers usher the supermassive black hole (SMBH) in each galaxy to the center of the potential, where they form an SMBH binary. The binary orbit shrinks by ejecting stars via three-body scattering, but ample work has shown that in spherical galaxy models, the binary separation stalls after ejecting all the stars in its loss cone—this is the well-known final parsec problem. However, it has been shown that SMBH binaries in non-spherical galactic nuclei harden at a nearly constant rate until reaching the gravitational wave regime. Here we use a suite of direct N-body simulations to follow SMBH binary evolution in both corotating and counterrotating flattened galaxy models. For N > 500 K, we find that the evolution of the SMBH binary is convergent and is independent of the particle number. Rotation in general increases the hardening rate of SMBH binaries even more effectively than galaxy geometry alone. SMBH binary hardening rates are similar for co- and counterrotating galaxies. In the corotating case, the center of mass of the SMBH binary settles into an orbit that is in corotation resonance with the background rotating model, and the coalescence time is roughly a few 100 Myr faster than a non-rotating flattened model. We find that counterrotation drives SMBHs to coalesce on a nearly radial orbit promptly after forming a hard binary. We discuss the implications for gravitational wave astronomy, hypervelocity star production, and the effect on the structure of the host galaxy.

Confirmation of the binary status of Chamaeleon Hα 2 - a very young low-mass binary in Chamaeleon

NASA Astrophysics Data System (ADS)

Schmidt, T. O. B.; Neuhäuser, R.; Vogt, N.; Seifahrt, A.; Roell, T.; Bedalov, A.

2008-06-01

Context: Neuhäuser & Comerón (1998, Science, 282, 83; 1999, A&A, 350, 612) presented direct imaging evidence, as well as first spectra, of several young stellar and sub-stellar M6- to M8-type objects in the Cha I dark cloud. One of these objects is Cha Hα 2, classified as brown dwarf candidate in several publications and suggested as possible binary in Neuhäuser et al. (2002, A&A, 384, 999). Aims: We have searched around Cha Hα 2 for close and faint companions with adaptive optics imaging. Methods: Two epochs of direct imaging data were taken with the Very Large Telescope (VLT) Adaptive Optics instrument NACO in February 2006 and March 2007 in Ks-band together with a Hipparcos binary for astrometric calibration. Moreover, we took a J-band image in March 2007 to get color information. We retrieved an earlier image from 2005 from the European Southern Observatory (ESO) Science Archive Facility, increasing the available time coverage. After confirmation of common proper motion, we deduce physical parameters of the objects by spectroscopy, like temperature and mass. Results: We find Cha Hα 2 to be a very close binary of 0.16 arcsec separation, having a flux ratio of 0.91, thus having almost equal brightness and indistinguishable spectral types within the errors. We show that the two tentative components of Cha Hα 2 form a common proper motion pair, and that neither component is a non-moving background object. We even find evidence for orbital motion. A combined spectrum of both stars spanning optical and near-infrared parts of the spectral energy distribution yields a temperature of 3000 ± 100 K, corresponding to a spectral type of M6 ± 1 and a surface gravity of log{g} = 4.0+0.75-0.5, both from a comparison with GAIA model atmospheres. Furthermore, we obtained an optical extinction of AV ≃ 4.3 mag from this comparison. Conclusions: We derive masses of 0.110 M⊙ (≥0.070 M⊙) and 0.124 M⊙ (≥0.077 M⊙) for the two components of Cha Hα 2, i

Biclustering sparse binary genomic data.

PubMed

van Uitert, Miranda; Meuleman, Wouter; Wessels, Lodewyk

2008-12-01

Genomic datasets often consist of large, binary, sparse data matrices. In such a dataset, one is often interested in finding contiguous blocks that (mostly) contain ones. This is a biclustering problem, and while many algorithms have been proposed to deal with gene expression data, only two algorithms have been proposed that specifically deal with binary matrices. None of the gene expression biclustering algorithms can handle the large number of zeros in sparse binary matrices. The two proposed binary algorithms failed to produce meaningful results. In this article, we present a new algorithm that is able to extract biclusters from sparse, binary datasets. A powerful feature is that biclusters with different numbers of rows and columns can be detected, varying from many rows to few columns and few rows to many columns. It allows the user to guide the search towards biclusters of specific dimensions. When applying our algorithm to an input matrix derived from TRANSFAC, we find transcription factors with distinctly dissimilar binding motifs, but a clear set of common targets that are significantly enriched for GO categories.

Hidden slow pulsars in binaries

NASA Technical Reports Server (NTRS)

Tavani, Marco; Brookshaw, Leigh

1993-01-01

The recent discovery of the binary containing the slow pulsar PSR 1718-19 orbiting around a low-mass companion star adds new light on the characteristics of binary pulsars. The properties of the radio eclipses of PSR 1718-19 are the most striking observational characteristics of this system. The surface of the companion star produces a mass outflow which leaves only a small 'window' in orbital phase for the detection of PSR 1718-19 around 400 MHz. At this observing frequency, PSR 1718-19 is clearly observable only for about 1 hr out of the total 6.2 hr orbital period. The aim of this Letter is twofold: (1) to model the hydrodynamical behavior of the eclipsing material from the companion star of PSR 1718-19 and (2) to argue that a population of binary slow pulsars might have escaped detection in pulsar surveys carried out at 400 MHz. The possible existence of a population of partially or totally hidden slow pulsars in binaries will have a strong impact on current theories of binary evolution of neutron stars.

Eclipsing Binaries in Open Clusters

NASA Astrophysics Data System (ADS)

Southworth, John; Clausen, Jens Viggo

2006-08-01

The study of detached eclipsing binaries in open clusters can provide stringent tests of theoretical stellar evolutionary models, which must simultaneously fit the masses, radii, and luminosities of the eclipsing stars and the radiative properties of every other star in the cluster. We review recent progress in such studies and discuss two unusually interesting objects currently under analysis. GV Carinae is an A0 m + A8 m binary in the Southern open cluster NGC 3532; its eclipse depths have changed by 0.1 mag between 1990 and 2001, suggesting that its orbit is being perturbed by a relatively close third body. DW Carinae is a high-mass unevolved B1 V + B1 V binary in the very young open cluster Collinder 228, and displays double-peaked emission in the centre of the Hα line which is characteristic of Be stars. We conclude by pointing out that the great promise of eclipsing binaries in open clusters can only be satisfied when both the binaries and their parent clusters are well-observed, a situation which is less common than we would like.

Tuning into Scorpius X-1: adapting a continuous gravitational-wave search for a known binary system

NASA Astrophysics Data System (ADS)

Meadors, Grant David; Goetz, Evan; Riles, Keith

2016-05-01

We describe how the TwoSpect data analysis method for continuous gravitational waves (GWs) has been tuned for directed sources such as the low-mass X-ray binary (LMXB), Scorpius X-1 (Sco X-1). A comparison of five search algorithms generated simulations of the orbital and GW parameters of Sco X-1. Whereas that comparison focused on relative performance, here the simulations help quantify the sensitivity enhancement and parameter estimation abilities of this directed method, derived from an all-sky search for unknown sources, using doubly Fourier-transformed data. Sensitivity is shown to be enhanced when the source sky location and period are known, because we can run a fully templated search, bypassing the all-sky hierarchical stage using an incoherent harmonic sum. The GW strain and frequency, as well as the projected semi-major axis of the binary system, are recovered and uncertainty estimated, for simulated signals that are detected. Upper limits for GW strain are set for undetected signals. Applications to future GW observatory data are discussed. Robust against spin-wandering and computationally tractable despite an unknown frequency, this directed search is an important new tool for finding gravitational signals from LMXBs.

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

ERIC Educational Resources Information Center

Pagliaro, Claudia M.; Ansell, Ellen

2011-01-01

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

The Role of Executive Function in Arithmetic Problem-Solving Processes: A Study of Third Graders

ERIC Educational Resources Information Center

Viterbori, Paola; Traverso, Laura; Usai, M. Carmen

2017-01-01

This study investigated the roles of different executive function (EF) components (inhibition, shifting, and working memory) in 2-step arithmetic word problem solving. A sample of 139 children aged 8 years old and regularly attending the 3rd grade of primary school were tested on 6 EF tasks measuring different EF components, a reading task and a…

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

NASA Astrophysics Data System (ADS)

Kim, J. B.; Won, E.

2018-03-01

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

Simulations of binary black hole mergers

NASA Astrophysics Data System (ADS)

Lovelace, Geoffrey

2017-01-01

Advanced LIGO's observations of merging binary black holes have inaugurated the era of gravitational wave astronomy. Accurate models of binary black holes and the gravitational waves they emit are helping Advanced LIGO to find as many gravitational waves as possible and to learn as much as possible about the waves' sources. These models require numerical-relativity simulations of binary black holes, because near the time when the black holes merge, all analytic approximations break down. Following breakthroughs in 2005, many research groups have built numerical-relativity codes capable of simulating binary black holes. In this talk, I will discuss current challenges in simulating binary black holes for gravitational-wave astronomy, and I will discuss the tremendous progress that has already enabled such simulations to become an essential tool for Advanced LIGO.

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

Searching for Unresolved Binary Brown Dwarfs

NASA Astrophysics Data System (ADS)

Albretsen, Jacob; Stephens, Denise

2007-10-01

There are currently L and T brown dwarfs (BDs) with errors in their classification of +/- 1 to 2 spectra types. Metallicity and gravitational differences have accounted for some of these discrepancies, and recent studies have shown unresolved binary BDs may offer some explanation as well. However limitations in technology and resources often make it difficult to clearly resolve an object that may be binary in nature. Stephens and Noll (2006) identified statistically strong binary source candidates from Hubble Space Telescope (HST) images of Trans-Neptunian Objects (TNOs) that were apparently unresolved using model point-spread functions for single and binary sources. The HST archive contains numerous observations of BDs using the Near Infrared Camera and Multi-Object Spectrometer (NICMOS) that have never been rigorously analyzed for binary properties. Using methods developed by Stephens and Noll (2006), BD observations from the HST data archive are being analyzed for possible unresolved binaries. Preliminary results will be presented. This technique will identify potential candidates for future observations to determine orbital information.