A hardware architecture for a context-adaptive binary arithmetic coder
NASA Astrophysics Data System (ADS)
Sudharsanan, Subramania; Cohen, Adam
2005-03-01
The H.264 video compression standard uses a context-adaptive binary arithmetic coder (CABAC) as an entropy coding mechanism. While the coder provides excellent compression efficiency, it is computationally demanding. On typical general-purpose processors, it can take up to hundreds of cycles to encode a single bit. In this paper, we propose an architecture for a CABAC encoder that can easily be incorporated into system-on-chip designs for H.264 compression. The CABAC is inherently serial and we divide the problem into several stages to derive a design that can provide a throughput of two cycles per encoded bit. The engine proposed is capable of handling binarization of the syntactical elements and provides the coded bit-stream via a first-in first-out buffer. The design is implemented on an Altera FPGA platform that can run at 50 MHz enabling a 25 Mbps encoding rate.
Context adaptive binary arithmetic coding-based data hiding in partially encrypted H.264/AVC videos
NASA Astrophysics Data System (ADS)
Xu, Dawen; Wang, Rangding
2015-05-01
A scheme of data hiding directly in a partially encrypted version of H.264/AVC videos is proposed which includes three parts, i.e., selective encryption, data embedding and data extraction. Selective encryption is performed on context adaptive binary arithmetic coding (CABAC) bin-strings via stream ciphers. By careful selection of CABAC entropy coder syntax elements for selective encryption, the encrypted bitstream is format-compliant and has exactly the same bit rate. Then a data-hider embeds the additional data into partially encrypted H.264/AVC videos using a CABAC bin-string substitution technique without accessing the plaintext of the video content. Since bin-string substitution is carried out on those residual coefficients with approximately the same magnitude, the quality of the decrypted video is satisfactory. Video file size is strictly preserved even after data embedding. In order to adapt to different application scenarios, data extraction can be done either in the encrypted domain or in the decrypted domain. Experimental results have demonstrated the feasibility and efficiency of the proposed scheme.
NASA Astrophysics Data System (ADS)
Karwowski, Damian; Domański, Marek
2016-01-01
An improved context-based adaptive binary arithmetic coding (CABAC) is presented. The idea for the improvement is to use a more accurate mechanism for estimation of symbol probabilities in the standard CABAC algorithm. The authors' proposal of such a mechanism is based on the context-tree weighting technique. In the framework of a high-efficiency video coding (HEVC) video encoder, the improved CABAC allows 0.7% to 4.5% bitrate saving compared to the original CABAC algorithm. The application of the proposed algorithm marginally affects the complexity of HEVC video encoder, but the complexity of video decoder increases by 32% to 38%. In order to decrease the complexity of video decoding, a new tool has been proposed for the improved CABAC that enables scaling of the decoder complexity. Experiments show that this tool gives 5% to 7.5% reduction of the decoding time while still maintaining high efficiency in the data compression.
Binary Arithmetic From Hariot (CA, 1600 A.D.) to the Computer Age.
ERIC Educational Resources Information Center
Glaser, Anton
This history of binary arithmetic begins with details of Thomas Hariot's contribution and includes specific references to Hariot's manuscripts kept at the British Museum. A binary code developed by Sir Francis Bacon is discussed. Briefly mentioned are contributions to binary arithmetic made by Leibniz, Fontenelle, Gauss, Euler, Benzout, Barlow,…
Arithmetic Fourier transform and adaptive delta modulation: A symbiosis for high speed computation
Tufts, D.W.; Sadasiv, G.
1988-01-01
This report presents preliminary results on the VLSI design and implementation of a novel and promising algorithm for accurate high-speed Fourier analysis and synthesis. The Arithmetic Fourier Transform is based on the number -theoretic method of Mobius inversion. Its computations proceed in parallel and the individual operations are very simple. Except for a small number of scalings in one stage of the computation, only multiplications by 0, +1, and -1 are required. If the input samples were not quantized and if deal real-number operations were used internally, then the results would be exact. The accuracy of the computation is limited only by the input A/D conversion process, any constraints on the word lengths of internal accumulating registers, and the implementation of the few scaling operations. Motivated by the goal of efficient, effective, high-speed realization of the algorithm in an integrated circuit, we introduce further simplicities by the use of delta modulation to represent the input function in digital form. The result is that only binary (or preferably, ternary) sequences need to be processed in the parallel computations. And the required accumulations can be replaced by up/down counters. The dynamic range of the resulting transformation can be increased by the use of adaptive delta modulation.
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.
Lakhani, Gopal
2013-04-01
This article presents four modifications to the JPEG arithmetic coding (JAC) algorithm, a topic not studied well before. It then compares the compression performance of the modified JPEG with JPEG XR, the latest block-based image coding standard. We first show that the bulk of inter/intra-block redundancy, caused due to the use of the block-based approach by JPEG, can be captured by applying efficient prediction coding. We propose the following modifications to JAC to take advantages of our prediction approach. 1) We code a totally different DC difference. 2) JAC tests a DCT coefficient by considering its bits in the increasing order of significance for coding the most significant bit position. It causes plenty of redundancy because JAC always begins with the zeroth bit. We modify this coding order and propose alternations to the JPEG coding procedures. 3) We predict the sign of significant DCT coefficients, a problem is not addressed from the perspective of the JPEG decoder before. 4) We reduce the number of binary tests that JAC codes to mark end-of-block. We provide experimental results for two sets of eight-bit gray images. The first set consists of nine classical test images mostly of size 512 × 512 pixels. The second set consists of 13 images of size 2000 × 3000 pixels or more. Our modifications to JAC obtain extra-ordinary amount of code reduction without adding any kind of losses. More specifically, when we quantize the images using the default quantizers, our modifications reduce the total JAC code size of the images of these two sets by about 8.9 and 10.6%, and the JPEG Huffman code size by about 16.3 and 23.4%, respectively, on the average. Gains are even higher for coarsely quantized images. Finally, we compare the modified JAC with two settings of JPEG XR, one with no block overlapping and the other with the default transform (we denote them by JXR0 and JXR1, respectively). Our results show that for the finest quality rate image coding, the modified
Adaptive Mesh Refinement Simulations of Relativistic Binaries
NASA Astrophysics Data System (ADS)
Motl, Patrick M.; Anderson, M.; Lehner, L.; Olabarrieta, I.; Tohline, J. E.; Liebling, S. L.; Rahman, T.; Hirschman, E.; Neilsen, D.
2006-09-01
We present recent results from our efforts to evolve relativistic binaries composed of compact objects. We simultaneously solve the general relativistic hydrodynamics equations to evolve the material components of the binary and Einstein's equations to evolve the space-time. These two codes are coupled through an adaptive mesh refinement driver (had). One of the ultimate goals of this project is to address the merger of a neutron star and black hole and assess the possible observational signature of such systems as gamma ray bursts. This work has been supported in part by NSF grants AST 04-07070 and PHY 03-26311 and in part through NASA's ATP program grant NAG5-13430. The computations were performed primarily at NCSA through grant MCA98N043 and at LSU's Center for Computation & Technology.
Cheng, J. ); Olbright, G.R.; Bryan, R.P. )
1991-10-20
We outline an architecture for performing binary addition by using optical symbolic substitution and optical logic gates based on heterojunction phototransistors and vertical-cavity surface-emitting lasers.
Context-Adaptive Arithmetic Coding Scheme for Lossless Bit Rate Reduction of MPEG Surround in USAC
NASA Astrophysics Data System (ADS)
Yoon, Sungyong; Pang, Hee-Suk; Sung, Koeng-Mo
We propose a new coding scheme for lossless bit rate reduction of the MPEG Surround module in unified speech and audio coding (USAC). The proposed scheme is based on context-adaptive arithmetic coding for efficient bit stream composition of spatial parameters. Experiments show that it achieves the significant lossless bit reduction of 9.93% to 12.14% for spatial parameters and 8.64% to 8.96% for the overall MPEG Surround bit streams compared to the original scheme. The proposed scheme, which is not currently included in USAC, can be used for the improved coding efficiency of MPEG Surround in USAC, where the saved bits can be utilized by the other modules in USAC.
Belda, Petra M; Mielck, Jobst B
2006-11-01
The theoretically expected breaking strength of tablets from powder mixtures is often calculated by the weighted arithmetic mean from the breaking strength of the single components, which corresponds to a linear interpolation. The validity of this additivity of fracture strength shall be evaluated by the underlying model of parallel couplings. It assumes the components linked in parallel with respect to the direction of loading during diametrical strength testing. Parallel couplings were experimentally realised by the preparation of double layer tablets from crystalline and spray-dried lactose on the one hand and from maltitol and metamizol-sodium on the other. Constant total true volumes of the single substances and of layered powders in varying ratios of true volume were compressed on an eccentric tabletting machine to constant geometric mean punch force. Simulated crushing profiles of parallel couplings were derived from force-displacement profiles measured during diametrical compression of the one-component tablets. At given finely graded deformation levels, the forces exerted by the components during loading were added in the proportion of the true volume fractions of the components in the coupling. The results from the experiments and from the simulations are in good accordance. They demonstrate that a linear change of the crushing strength in dependence on the true volume fraction of the components can only be assumed if the single components deform to the same extent up to the point of fracture. This behaviour was approximately found with the parallel lactose system. In all other cases it must be expected that the crushing strength of parallel systems will be lowered beneath the weighted arithmetic mean values or even below the crushing strength of the single components. The latter was observed with the maltitol-metamizol combinations. Thus, if tablets from binary powder mixtures exhibit a crushing strength depression, this is not necessarily an indication
Adaptive Optics Photometry and Astrometry of Binary Stars
NASA Astrophysics Data System (ADS)
Roberts, Lewis C., Jr.; Turner, Nils H.; Bradford, L. William; ten Brummelaar, Theo A.; Oppenheimer, Ben R.; Kuhn, Jeff R.; Whitman, Kathryn; Perrin, Marshall D.; Graham, James R.
2005-11-01
We present astrometric and photometric measurements of 39 binary stars made with the adaptive optics system on the 3.6 m Advanced Electro-Optical System (AEOS) telescope, taken from 2002 November to 2003 March. The binaries have separations ranging from 0.08" to 5.11" and differential magnitudes ranging from 0.096 to 7.9. Also, we include a list of observations of 23 known binaries that we were unable to resolve. In the process of these measurements, we discovered three new companions to two previously known binary stars. We also discuss the effects of scintillation and anisoplanatism on measurements of binary star photometry in adaptive optics images. Suggestions on how to minimize these effects are then given. Based on observations made at the Maui Space Surveillance System operated by Detachment 15 of the US Air Force Research Laboratory's Directed Energy Directorate.
Adaptive filters for detection of gravitational waves from coalescing binaries
Eleuteri, Antonio; Milano, Leopoldo; De Rosa, Rosario; Garufi, Fabio; Acernese, Fausto; Barone, Fabrizio; Giordano, Lara; Pardi, Silvio
2006-06-15
In this work we propose use of infinite impulse response adaptive line enhancer (IIR ALE) filters for detection of gravitational waves from coalescing binaries. We extend our previous work and define an adaptive matched filter structure. Filter performance is analyzed in terms of the tracking capability and determination of filter parameters. Furthermore, following the Neyman-Pearson strategy, receiver operating characteristics are derived, with closedform expressions for detection threshold, false alarm, and detection probability. Extensive tests demonstrate the effectiveness of adaptive filters both in terms of small computational cost and robustness.
Zhao, Hong-Quan; Kasai, Seiya; Shiratori, Yuta; Hashizume, Tamotsu
2009-06-17
A two-bit arithmetic logic unit (ALU) was successfully fabricated on a GaAs-based regular nanowire network with hexagonal topology. This fundamental building block of central processing units can be implemented on a regular nanowire network structure with simple circuit architecture based on graphical representation of logic functions using a binary decision diagram and topology control of the graph. The four-instruction ALU was designed by integrating subgraphs representing each instruction, and the circuitry was implemented by transferring the logical graph structure to a GaAs-based nanowire network formed by electron beam lithography and wet chemical etching. A path switching function was implemented in nodes by Schottky wrap gate control of nanowires. The fabricated circuit integrating 32 node devices exhibits the correct output waveforms at room temperature allowing for threshold voltage variation.
NASA Astrophysics Data System (ADS)
Shutler, Paul M. E.; Swee Fong, Ng
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 complex calculations such as long multiplication can be carried out more efficiently in base 5 than in base 10, and that base 5 is in fact close to being optimal in this regard. We also show that base 5 is small enough so that the intuitiveness of simple grouping and the efficiency of fully ciphered numerals can be combined effectively in a single notation, something which Hindu-Arabic numeration tries but fails to achieve. Furthermore, as a consequence of these notational advantages, we show that the basic operations of arithmetic, addition and subtraction, also borrowing and carrying (regrouping), are easier to teach and to learn in base 5 than in base 10. Finally we show that, even though a shift from base 10 to base 5 may not be a realistic possibility, there are many ways in which the teaching of elementary arithmetic could be improved significantly, along the lines of Predator arithmetic, and which could be implemented at little cost within our current Hindu-Arabic system.
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…
Adaptive allocation for binary outcomes using decreasingly informative priors.
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.
Discovery of a 66 mas Ultracool Binary with Laser Guide Star Adaptive Optics
Siegler, N; Close, L; Burgasser, A; Cruz, K; Marois, C; Macintosh, B; Barman, T
2007-02-02
We present the discovery of 2MASS J21321145+1341584AB as a closely separated (0.066'') very low-mass field dwarf binary resolved in the near-infrared by the Keck II Telescope using laser guide star adaptive optics. Physical association is deduced from the angular proximity of the components and constraints on their common proper motion. We have obtained a near-infrared spectrum of the binary and find that it is best described by an L5{+-}0.5 primary and an L7.5{+-}0.5 secondary. Model-dependent masses predict that the two components straddle the hydrogen burning limit threshold with the primary likely stellar and the secondary likely substellar. The properties of this sytem - close projected separation (1.8{+-}0.3AU) and near unity mass ratio - are consistent with previous results for very low-mass field binaries. The relatively short estimated orbital period of this system ({approx}7-12 yr) makes it a good target for dynamical mass measurements. Interestingly, the system's angular separation is the tightest yet for any very low-mass binary published from a ground-based telescope and is the tightest binary discovered with laser guide star adaptive optics to date.
Covariate-adjusted response-adaptive designs for binary response.
Rosenberger, W F; Vidyashankar, A N; Agarwal, D K
2001-11-01
An adaptive allocation design for phase III clinical trials that incorporates covariates is described. The allocation scheme maps the covariate-adjusted odds ratio from a logistic regression model onto [0, 1]. Simulations assume that both staggered entry and time to response are random and follow a known probability distribution that can depend on the treatment assigned, the patient's response, a covariate, or a time trend. Confidence intervals on the covariate-adjusted odds ratio is slightly anticonservative for the adaptive design under the null hypothesis, but power is similar to equal allocation under various alternatives for n = 200. For similar power, the net savings in terms of expected number of treatment failures is modest, but enough to make this design attractive for certain studies where known covariates are expected to be important and stratification is not desired, and treatment failures have a high ethical cost.
ERIC Educational Resources Information Center
Rousselle, Laurence; Noel, Marie-Pascale
2008-01-01
The adaptive use of approximate calculation was examined using a verification task with 18 third graders with mathematics learning disabilities, 22 typically achieving third graders, and 21 typically achieving second graders. Participants were asked to make true-false decisions on simple and complex addition problems while the distance between the…
[Acquisition of arithmetic knowledge].
Fayol, Michel
2008-01-01
The focus of this paper is on contemporary research on the number counting and arithmetical competencies that emerge during infancy, the preschool years, and the elementary school. I provide a brief overview of the evolution of children's conceptual knowledge of arithmetic knowledge, the acquisition and use of counting and how they solve simple arithmetic problems (e.g. 4 + 3). PMID:18198117
Liu, Dong; Wang, Shengsheng; Huang, Dezhi; Deng, Gang; Zeng, Fantao; Chen, Huiling
2016-05-01
Medical image recognition is an important task in both computer vision and computational biology. In the field of medical image classification, representing an image based on local binary patterns (LBP) descriptor has become popular. However, most existing LBP-based methods encode the binary patterns in a fixed neighborhood radius and ignore the spatial relationships among local patterns. The ignoring of the spatial relationships in the LBP will cause a poor performance in the process of capturing discriminative features for complex samples, such as medical images obtained by microscope. To address this problem, in this paper we propose a novel method to improve local binary patterns by assigning an adaptive neighborhood radius for each pixel. Based on these adaptive local binary patterns, we further propose a spatial adjacent histogram strategy to encode the micro-structures for image representation. An extensive set of evaluations are performed on four medical datasets which show that the proposed method significantly improves standard LBP and compares favorably with several other prevailing approaches. PMID:27058283
Liu, Dong; Wang, Shengsheng; Huang, Dezhi; Deng, Gang; Zeng, Fantao; Chen, Huiling
2016-05-01
Medical image recognition is an important task in both computer vision and computational biology. In the field of medical image classification, representing an image based on local binary patterns (LBP) descriptor has become popular. However, most existing LBP-based methods encode the binary patterns in a fixed neighborhood radius and ignore the spatial relationships among local patterns. The ignoring of the spatial relationships in the LBP will cause a poor performance in the process of capturing discriminative features for complex samples, such as medical images obtained by microscope. To address this problem, in this paper we propose a novel method to improve local binary patterns by assigning an adaptive neighborhood radius for each pixel. Based on these adaptive local binary patterns, we further propose a spatial adjacent histogram strategy to encode the micro-structures for image representation. An extensive set of evaluations are performed on four medical datasets which show that the proposed method significantly improves standard LBP and compares favorably with several other prevailing approaches.
Rousselle, Laurence; Noël, Marie-Pascale
2008-01-01
The adaptive use of approximate calculation was examined using a verification task with 18 third graders with mathematics learning disabilities, 22 typically achieving third graders, and 21 typically achieving second graders. Participants were asked to make true-false decisions on simple and complex addition problems while the distance between the proposed and the correct answer was manipulated. Both typically achieving groups were sensitive to answer plausibility on simple problems, were faster at rejecting extremely incorrect results than at accepting correct answers on complex addition problems, and showed a reduction of the complexity effect on implausible problems, attesting to the use of approximate calculation. Conversely, children with mathematics disabilities were unaffected by answer plausibility on simple addition problems, processed implausible and correct sums with equal speed on complex problems, and exhibited a smaller reduction of the complexity effect on implausible problems. They also made more errors on implausible problems. Different hypotheses are discussed to account for these results. PMID:18443150
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.
Binary stars observed with adaptive optics at the starfire optical range
Drummond, Jack D.
2014-03-01
In reviewing observations taken of binary stars used as calibration objects for non-astronomical purposes with adaptive optics on the 3.5 m Starfire Optical Range telescope over the past 2 years, one-fifth of them were found to be off-orbit. In order to understand such a high number of discrepant position angles and separations, all previous observations in the Washington Double Star Catalog for these rogue binaries were obtained from the Naval Observatory. Adding our observations to these yields new orbits for all, resolving the discrepancies. We have detected both components of γ Gem for the first time, and we have shown that 7 Cam is an optical pair, not physically bound.
ERIC Educational Resources Information Center
Dominici, Diego
2011-01-01
This work introduces a distance between natural numbers not based on their position on the real line but on their arithmetic properties. We prove some metric properties of this distance and consider a possible extension.
Searching for Binary Y Dwarfs with the Gemini Multi-conjugate Adaptive Optics System (GeMS)
NASA Astrophysics Data System (ADS)
Opitz, Daniela; Tinney, C. G.; Faherty, Jacqueline K.; Sweet, Sarah; Gelino, Christopher R.; Kirkpatrick, J. Davy
2016-03-01
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 also 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., 1042 erg) are consistent with those observed in previous studies of hotter ultra-cool dwarfs.
Reconstruction based finger-knuckle-print verification with score level adaptive binary fusion.
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. PMID:24043391
A scale- and orientation-adaptive extension of Local Binary Patterns for texture classification
Hegenbart, Sebastian; Uhl, Andreas
2015-01-01
Local Binary Patterns (LBPs) have been used in a wide range of texture classification scenarios and have proven to provide a highly discriminative feature representation. A major limitation of LBP is its sensitivity to affine transformations. In this work, we present a scale- and rotation-invariant computation of LBP. Rotation-invariance is achieved by explicit alignment of features at the extraction level, using a robust estimate of global orientation. Scale-adapted features are computed in reference to the estimated scale of an image, based on the distribution of scale normalized Laplacian responses in a scale-space representation. Intrinsic-scale-adaption is performed to compute features, independent of the intrinsic texture scale, leading to a significantly increased discriminative power for a large amount of texture classes. In a final step, the rotation- and scale-invariant features are combined in a multi-resolution representation, which improves the classification accuracy in texture classification scenarios with scaling and rotation significantly. PMID:26240440
Lucky Imaging Adaptive Optics of the brown dwarf binary GJ569Bab
NASA Astrophysics Data System (ADS)
Femenía, B.; Rebolo, R.; Pérez-Prieto, J. A.; Hildebrandt, S. R.; Labadie, L.; Pérez-Garrido, A.; Béjar, V. J. S.; Díaz-Sánchez, A.; Villó, I.; Oscoz, A.; López, R.; Rodríguez, L. F.; Piqueras, J.
2011-05-01
The potential of combining Adaptive Optics (AO) and Lucky Imaging (LI) to achieve high-precision astrometry and differential photometry in the optical is investigated by conducting observations of the close 0.1 arcsec brown dwarf binary GJ569Bab. We took 50 000 I-band images with our LI instrument FastCam attached to NAOMI, the 4.2-m William Herschel Telescope (WHT) AO facility. In order to extract the most of the astrometry and photometry of the GJ569Bab system we have resorted to a PSF fitting technique using the primary star GJ569A as a suitable PSF reference which exhibits an I-band magnitude of 7.78 ± 0.03. The AO+LI observations at WHT were able to resolve the binary system GJ569Bab located at 4.92 ± 0.05 arcsec from GJ569A. We measure a separation of 98.4 ± 1.1 mas and I-band magnitudes of 13.86 ± 0.03 and 14.48 ± 0.03 and I-J colours of 2.72 ± 0.08 and 2.83 ± 0.08 for the Ba and Bb components, respectively. Our study rules out the presence of any other companion to GJ569A down to magnitude I˜ 17 at distances larger than 1 arcsec. The I-J colours measured are consistent with M8.5-M9 spectral types for the Ba and Bb components. The available dynamical, photometric and spectroscopic data are consistent with a binary system with Ba being slightly (10-20 per cent) more massive than Bb. We obtain new orbital parameters which are in good agreement with those in the literature. Based on service observations made with the 4.2-m William Herschel Telescope (WHT) operated on the island of La Palma by the Isaac Newton Group and on observations made with the Nordic Optical Telescope (NOT), operated on the island of La Palma jointly by Denmark, Finland, Iceland, Norway and Sweden, in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofísica de Canarias.
Lining up Arithmetic Sequences
ERIC Educational Resources Information Center
Bell, Carol J.
2011-01-01
Most future teachers are familiar with number patterns that represent an arithmetic sequence, and most are able to determine the general representation of the "n"th number in the pattern. However, when they are given a visual representation instead of the numbers in the pattern, it is not always easy for them to make the connection between the…
Connecting Arithmetic to Algebra
ERIC Educational Resources Information Center
Darley, Joy W.; Leapard, Barbara B.
2010-01-01
Algebraic thinking is a top priority in mathematics classrooms today. Because elementary school teachers lay the groundwork to develop students' capacity to think algebraically, it is crucial for teachers to have a conceptual understanding of the connections between arithmetic and algebra and be confident in communicating these connections. Many…
Arithmetic Learning Difficulties in Children
ERIC Educational Resources Information Center
Micallef, Silvana; Prior, Margot
2004-01-01
This study explored the arithmetic skills of 39 children with arithmetic learning difficulties (ALD), compared to two control groups, one consisting of normally achieving children matched to the ALD sample for chronological age (n =28), and another comprising younger normally achieving children matched to the ALD sample for arithmetic level (n…
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)).
Hildebrandt, K Jannis; Benda, Jan; Hennig, R Matthias
2011-10-01
Sensory pathways process behaviorally relevant signals in various contexts and therefore have to adapt to differing background conditions. Depending on changes in signal statistics, this adjustment might be a combination of two fundamental computational operations: subtractive adaptation shifting a neuron's threshold and divisive gain control scaling its sensitivity. The cricket auditory system has to deal with highly stereotyped conspecific songs at low carrier frequencies, and likely much more variable predator signals at high frequencies. We proposed that due to the differences between the two signal classes, the operation that is implemented by adaptation depends on the carrier frequency. We aimed to identify the biophysical basis underlying the basic computational operations of subtraction and division. We performed in vivo intracellular and extracellular recordings in a first-order auditory interneuron (AN2) that is active in both mate recognition and predator avoidance. We demonstrated subtractive shifts at the carrier frequency of conspecific songs and division at the predator-like carrier frequency. Combined application of current injection and acoustic stimuli for each cell allowed us to demonstrate the subtractive effect of cell-intrinsic adaptation currents. Pharmacological manipulation enabled us to demonstrate that presynaptic inhibition is most likely the source of divisive gain control. We showed that adjustment to the sensory context can depend on the class of signals that are relevant to the animal. We further revealed that presynaptic inhibition is a simple mechanism for divisive operations. Unlike other proposed mechanisms, it is widely available in the sensory periphery of both vertebrates and invertebrates.
Stability of Arithmetic Disability Subtypes.
ERIC Educational Resources Information Center
Silver, Cheryl H.; Pennett, H. Deborah-Lynne; Black, Jeffrey L.; Fair, George W.; Balise, Raymond R.
1999-01-01
A study examined the stability over 19 months of academic subtyping classification of 80 children (ages 9 to 13) representing four subtypes of arithmetic disabilities (AD). Approximately half of the sample retained AD regardless of identification method. Children with deficits in arithmetic, reading, and spelling disabilities exhibited the…
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
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 spike
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 spike
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.
Fast Arithmetic Using Signed Digit Numbers and Ternary Logic
NASA Astrophysics Data System (ADS)
Saxena, Rakesh Kumar; Sharma, Neelam; Wadhwani, A. K.
2009-07-01
Redundant Binary Signed Digit Number System may not be convenient for manual computations but may be useful in designing high-speed arithmetic machines. This number system is gaining popularity in computationally intensive environments particularly due to possessing of the carry-free addition/subtraction properties. This property has enabled arithmetic operations such as addition, multiplication, division, square root, etc., to be performed much faster than with conventional binary number systems. In RBSD number system carry propagation chains are eliminated which reduces the computational time substantially, thus enhancing the speed of the machine. The credit of RBSD number system goes to Robertson, who proposed it in 1959 and Avizienis in 1961. In this paper, some of the recent contributions in the area of design of redundant arithmetic based addition and multiplication algorithms and architectures are briefly discussed. Also use of parallel implementation for architectures is discussed so that the enhancement in speed through the use of redundant arithmetic is possible. Also, in this paper, RBSD adder is designed. After calculation and comparison it is concluded that efficiency of RBSD adder is much better than the other adders. An addition of two's complement circuit will make an RBSD subtractor. These Adders/Subtractors can further be used as building blocks for fast multiplication, division and square root operation.
A Substituting Meaning for the Equals Sign in Arithmetic Notating Tasks
ERIC Educational Resources Information Center
Jones, Ian; Pratt, Dave
2012-01-01
Three studies explore arithmetic tasks that support both substitutive and basic relational meanings for the equals sign. The duality of meanings enabled children to engage meaningfully and purposefully with the structural properties of arithmetic statements in novel ways. Some, but not all, children were successful at the adapted task and were…
Mental arithmetic activates analogic representations of internally generated sums.
Kallai, Arava Y; Schunn, Christian D; Fiez, Julie A
2012-08-01
The internal representation of numbers generated during calculation has received little attention. Much of the mathematics learning literature focuses on symbolic retrieval of math facts; in contrast, we critically test the hypothesis that internally generated numbers are represented analogically, using an approximate number system. In an fMRI study, the spontaneous processing of arithmetical expressions was tested. Participants passively viewed a sequence of double-digit addition expressions that summed to the same number. Adaptation was found in number-related regions in a fronto-parietal network. Following adaptation, arrays of dots were introduced, differing in their numerical distance from the sum of the addition expressions. Activation in voxels that showed adaptation to a repeated sum was also sensitive to the distance of the dot quantity from the sum. We conclude that participants exhibited adaptation to an internally generated number, that adapted representations were analogic in nature, and that these analogic representations may undergird arithmetic calculation. PMID:22732492
Bit-wise arithmetic coding for data compression
NASA Technical Reports Server (NTRS)
Kiely, A. B.
1994-01-01
This article examines the problem of compressing a uniformly quantized independent and identically distributed (IID) source. We present a new compression technique, bit-wise arithmetic coding, that assigns fixed-length codewords to the quantizer output and uses arithmetic coding to compress the codewords, treating the codeword bits as independent. We examine the performance of this method and evaluate the overhead required when used block-adaptively. Simulation results are presented for Gaussian and Laplacian sources. This new technique could be used as the entropy coder in a transform or subband coding system.
Stability of arithmetic disability subtypes.
Silver, C H; Pennett, H D; Black, J L; Fair, G W; Balise, R R
1999-01-01
Cross-sectional research has identified subtypes of children with learning disabilities who may have distinctive cognitive ability patterns. This study examined the stability over 19 months of academic subtyping classifications for 80 children ages 9 to 13 representing four subtypes of arithmetic disabilities (AD), using three criteria for learning disability identification. Approximately half of the sample retained AD regardless of identification method. Children with pervasive deficits in arithmetic, reading, and spelling displayed the greatest subtype stability. Only one third of the children with the other subtypes, including those with isolated arithmetic deficits, retained their original subtypes. Thus, drawing conclusions and making recommendations based on academic subtyping at a single point in time may be unwise. PMID:15499712
Simple arithmetic development in school age: The coactivation and selection of arithmetic facts.
Megías, Patricia; Macizo, Pedro
2015-10-01
We evaluated the possible inhibitory mechanism responsible for selecting arithmetic facts in children from 8 or 9 years to 12 or 13 years of age. To this end, we used an adapted version of the negative priming paradigm (NP paradigm) in which children received additions and they decided whether they were correct or not. When an addition was incorrect but the result was that of multiplying the operands (e.g., 2 + 4 = 8), only children from 10 or 11 years of age onward took more time to respond compared with control additions with unrelated results, suggesting that they coactivated arithmetic knowledge of multiplications even when it was irrelevant to perform the task. Furthermore, children from 10 or 11 years of age onward were slower to respond when the result of multiplying the operands was presented again in a correct addition problem (e.g., 2 + 6 = 8). This result showed the development of an inhibitory mechanism involved in the selection of arithmetic facts through formal education. PMID:26037404
NASA Astrophysics Data System (ADS)
Chakraborty, Shibalik; Boolchand, Punit
2014-03-01
Binary GexS100-x glasses reveal elastic and chemical phase transitions driven by network topology. With increasing Ge content x, well defined rigidity (xc(1) =19.3%) and stress(xc(2) =24.85%) transitions and associated optical elasticity power-laws are observed in Raman scattering. Calorimetric measurements reveal a square-well like minimum with window walls that coincide with the two elastic phase transitions. Molar volumes show a trapezoidal-like minimum with edges that nearly coincide with the reversibility window. These results are signatures of the isostatically rigid nature of the elastic phase formed between the rigidity and stress transitions. Complex Cp measurements show melt fragility index, m(x) to also show a global minimum in the reversibility window, underscoring that melt dynamics encode the elastic behavior of the glass formed at Tg. The strong nature of melts formed in the IP has an important practical consequence; they lead to slow homogenization of non-stoichiometric batch compositions reacted at high temperatures. Homogenization of chalcogenides melts/glasses over a scale of a few microns is a pre-requisite to observe the intrinsic physical properties of these materials. Supported by NSF Grant DMR 0853957.
Predicting Arithmetic Abilities: The Role of Preparatory Arithmetic Markers and Intelligence
ERIC Educational Resources Information Center
Stock, Pieter; Desoete, Annemie; Roeyers, Herbert
2009-01-01
Arithmetic abilities acquired in kindergarten are found to be strong predictors for later deficient arithmetic abilities. This longitudinal study (N = 684) was designed to examine if it was possible to predict the level of children's arithmetic abilities in first and second grade from their performance on preparatory arithmetic abilities in…
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…
Traces, ideals, and arithmetic means
Kaftal, Victor; Weiss, Gary
2002-01-01
This article grew out of recent work of Dykema, Figiel, Weiss, and Wodzicki (Commutator structure of operator ideals) which inter alia characterizes commutator ideals in terms of arithmetic means. In this paper we study ideals that are arithmetically mean (am) stable, am-closed, am-open, soft-edged and soft-complemented. We show that many of the ideals in the literature possess such properties. We apply these notions to prove that for all the ideals considered, the linear codimension of their commutator space (the “number of traces on the ideal”) is either 0, 1, or ∞. We identify the largest ideal which supports a unique nonsingular trace as the intersection of certain Lorentz ideals. An application to elementary operators is given. We study properties of arithmetic mean operations on ideals, e.g., we prove that the am-closure of a sum of ideals is the sum of their am-closures. We obtain cancellation properties for arithmetic means: for principal ideals, a necessary and sufficient condition for first order cancellations is the regularity of the generator; for second order cancellations, sufficient conditions are that the generator satisfies the exponential Δ2-condition or is regular. We construct an example where second order cancellation fails, thus settling an open question. We also consider cancellation properties for inclusions. And we find and use lattice properties of ideals associated with the existence of “gaps.” PMID:12032287
Adaptive particle swarm optimization for optimal orbital elements of binary stars
NASA Astrophysics Data System (ADS)
Attia, Abdel-Fattah
2016-10-01
The paper presents an adaptive particle swarm optimization (APSO) as an alternative method to determine the optimal orbital elements of the star η Bootis of MK type G0 IV. The proposed algorithm transforms the problem of finding periodic orbits into the problem of detecting global minimizers as a function, to get a best fit of Keplerian and Phase curves. The experimental results demonstrate that the proposed approach of APSO generally more accurate than the standard particle swarm optimization (PSO) and other published optimization algorithms, in terms of solution accuracy, convergence speed and algorithm reliability.
The Duality of Zero in the Transition from Arithmetic to Algebra
ERIC Educational Resources Information Center
Gallardo, Aurora; Hernandez, Abraham
2005-01-01
This article shows that the recognition of the dualities in equality (operator-equivalent) of the minus sign (unary-binary) and the zero (nullity-totality) during the transitional process from arithmetic to algebra by 12-13 year-old students constitutes a possible way to achieve the extension of the natural number domain to the integers. (Contains…
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.
Electro-Photo-Sensitive Memristor for Neuromorphic and Arithmetic Computing
NASA Astrophysics Data System (ADS)
Maier, P.; Hartmann, F.; Emmerling, M.; Schneider, C.; Kamp, M.; Höfling, S.; Worschech, L.
2016-05-01
We present optically and electrically tunable conductance modifications of a site-controlled quantum-dot memristor. The conductance of the device is tuned by electron localization on a quantum dot. The control of the conductance with voltage and low-power light pulses enables applications in neuromorphic and arithmetic computing. As in neural networks, applying pre- and postsynaptic voltage pulses to the memristor allows us to increase (potentiation) or decrease (depression) the conductance by tuning the time difference between the electrical pulses. Exploiting state-dependent thresholds for potentiation and depression, we are able to demonstrate a memory-dependent induction of learning. The discharging of the quantum dot can further be induced by low-power light pulses in the nanowatt range. In combination with the state-dependent threshold voltage for discharging, this enables applications as generic building blocks to perform arithmetic operations in bases ranging from binary to decimal with low-power optical excitation. Our findings allow the realization of optoelectronic memristor-based synapses in artificial neural networks with a memory-dependent induction of learning and enhanced functionality by performing arithmetic operations.
Liu, Michael C.; Dupuy, Trent J.; Leggett, S. K.
2010-10-10
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 most 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
Memory Updating and Mental Arithmetic
Han, Cheng-Ching; Yang, Tsung-Han; Lin, Chia-Yuan; Yen, Nai-Shing
2016-01-01
Is domain-general memory updating ability predictive of calculation skills or are such skills better predicted by the capacity for updating specifically numerical information? Here, we used multidigit mental multiplication (MMM) as a measure for calculating skill as this operation requires the accurate maintenance and updating of information in addition to skills needed for arithmetic more generally. In Experiment 1, we found that only individual differences with regard to a task updating numerical information following addition (MUcalc) could predict the performance of MMM, perhaps owing to common elements between the task and MMM. In Experiment 2, new updating tasks were designed to clarify this: a spatial updating task with no numbers, a numerical task with no calculation, and a word task. The results showed that both MUcalc and the spatial task were able to predict the performance of MMM but only with the more difficult problems, while other updating tasks did not predict performance. It is concluded that relevant processes involved in updating the contents of working memory support mental arithmetic in adults. PMID:26869971
Memory Updating and Mental Arithmetic.
Han, Cheng-Ching; Yang, Tsung-Han; Lin, Chia-Yuan; Yen, Nai-Shing
2016-01-01
Is domain-general memory updating ability predictive of calculation skills or are such skills better predicted by the capacity for updating specifically numerical information? Here, we used multidigit mental multiplication (MMM) as a measure for calculating skill as this operation requires the accurate maintenance and updating of information in addition to skills needed for arithmetic more generally. In Experiment 1, we found that only individual differences with regard to a task updating numerical information following addition (MUcalc) could predict the performance of MMM, perhaps owing to common elements between the task and MMM. In Experiment 2, new updating tasks were designed to clarify this: a spatial updating task with no numbers, a numerical task with no calculation, and a word task. The results showed that both MUcalc and the spatial task were able to predict the performance of MMM but only with the more difficult problems, while other updating tasks did not predict performance. It is concluded that relevant processes involved in updating the contents of working memory support mental arithmetic in adults. PMID:26869971
Arithmetic for First Graders Lacking Number Concepts
ERIC Educational Resources Information Center
Kamii, Constance; Rummelsburg, Judith
2008-01-01
To build cognitive foundation for number, twenty-six low-performing, low-SES first graders did mathematical physical-knowledge activities, such as "bowling," during the first half of the year. As their arithmetic readiness developed, they tried more word problems and games. At the end of the year, these children did better in mental arithmetic and…
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;…
Prevalence of Combined Reading and Arithmetic Disabilities
ERIC Educational Resources Information Center
Dirks, Evelien; Spyer, Ginny; van Lieshout, Ernest C. D. M.; de Sonneville, Leo
2008-01-01
This study assesses the prevalence of combined reading and arithmetic disabilities in 799 Dutch schoolchildren using standardized school achievement tests. Scores of arithmetic, word recognition, reading comprehension, and spelling of children in fourth and fifth grade were used. The main interest involved the co-occurrence of word recognition and…
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…
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…
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…
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.
Plain Polynomial Arithmetic on GPU
NASA Astrophysics Data System (ADS)
Anisul Haque, Sardar; Moreno Maza, Marc
2012-10-01
As for serial code on CPUs, parallel code on GPUs for dense polynomial arithmetic relies on a combination of asymptotically fast and plain algorithms. Those are employed for data of large and small size, respectively. Parallelizing both types of algorithms is required in order to achieve peak performances. In this paper, we show that the plain dense polynomial multiplication can be efficiently parallelized on GPUs. Remarkably, it outperforms (highly optimized) FFT-based multiplication up to degree 212 while on CPU the same threshold is usually at 26. We also report on a GPU implementation of the Euclidean Algorithm which is both work-efficient and runs in linear time for input polynomials up to degree 218 thus showing the performance of the GCD algorithm based on systolic arrays.
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…
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…
Statistical based MQ arithmetic coder
NASA Astrophysics Data System (ADS)
Noikaew, Nopphol; Chitsobhuk, Orachat
2014-01-01
Embedded block coding with optimized truncation (EBCOT) is a key algorithm in JPEG 2000 image compression system. Recently, the bit-plane coder architectures are capable of producing symbols at a higher rate than the capability of the existing MQ arithmetic coders. To solve this problem, a design of a multiple-symbol processor for statistical MQ coder architecture on FPGA is proposed. The proposed architecture takes advantage of simplicity of single-symbol architecture while integrates several techniques in order to increase the coding rate (more than one symbol per clock), reduce critical path, thus accelerate the coding speed. The repeated symbol statistics has been analyzed prior to the proposed architecture using lookahead technique. This allows the proposed architecture to support encoding rate of maximum 8 symbols per clock cycle without stalls and without excessively increasing the hardware cost. This helps to accelerate encoding process, which leads to greatly increase throughput. From the experiments, for lossy wavelet transform, the proposed architecture offers high throughput of at least 233.07 MCxD/S with effectively reducing the number of clock cycles more than 35.51%.
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…
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.
Quality of arithmetic education for children with cerebral palsy.
Jenks, Kathleen M; de Moor, Jan; van Lieshout, Ernest C D M; Withagen, Floortje
2010-03-01
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 special (CP-special; n = 41) and mainstream schools (CP-mainstream; n = 16) and a control group in mainstream schools (n = 16). The majority of individual educational plans did not include well-formulated arithmetic goals and many were not based on optimal assessment. Special schools scheduled much less arithmetic instruction time. Many CP-mainstream children received individualized instruction, which may help to explain why their arithmetic performance did not differ from controls. Remedial arithmetic teaching methods used in special schools did not seem to be optimal, but more research is required. Suggestions to improve arithmetic education to children with CP were discussed.
Fostering Formal Commutativity Knowledge with Approximate Arithmetic.
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
Fostering Formal Commutativity Knowledge with Approximate Arithmetic
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
NASA Astrophysics Data System (ADS)
Gayen, Dilip Kumar; Nath Roy, Jitendra
2008-03-01
An all-optical arithmetic unit with the help of terahertz-optical-asymmetric-demultiplexer (TOAD)-based tree architecture is proposed. We describe the all-optical arithmetic unit by using a set of all-optical multiplexer, all-optical full-adder, and optical switch. The all-optical arithmetic unit can be used to perform a fast central processor unit using optical hardware components. We have tried to exploit the advantages of both optical tree architecture and TOAD-based switch to design an integrated all-optical circuit that can perform binary addition, addition with carry, subtract with borrow, subtract (2's complement), double, increment, decrement, and transfer operations.
Business and Consumer Arithmetic Curriculum Guide.
ERIC Educational Resources Information Center
District of Columbia Public Schools, Washington, DC. Dept. of Career Development.
The focus of this guide is directed upon arithmetic experiences and skills needed for every day business, however it is also designed to develop skill in basic mathematical functions, and to deal with the specific mathematical concepts applicable to personal use and to fields of employment. Fourteen units are included: General Review of Basic…
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…
Arithmetic and Cognitive Contributions to Algebra
ERIC Educational Resources Information Center
Cirino, Paul T.; Tolar, Tammy D.; Fuchs, Lynn S.
2013-01-01
Algebra is a prerequisite for access to STEM careers and occupational success (NMAP, 2008a), yet algebra is difficult for students through high school (US DOE, 2008). Growth in children's conceptual and procedural arithmetical knowledge is reciprocal, although conceptual knowledge has more impact on procedural knowledge than the reverse…
WE USE ARITHMETIC. A SUPPLEMENTARY BULLETIN.
ERIC Educational Resources Information Center
CROSBY, MURIEL
THE PURPOSE OF SYSTEMATIC TEACHING AND LEARNING IN ARITHMETIC IS TO HELP CHILDREN DEVELOP IDEAS OF PROCEDURE, METHODS OF THINKING, MEANING INHERENT IN NUMBER REACTIONS AND ARRANGEMENT IN ORDER THAT THE QUANTITATIVE SITUATIONS OF LIFE MAY BE HANDLED INTELLIGENTLY. AT THE KINDERGARTEN-PRIMARY LEVEL THE NUMBER CONCEPTS TO BE FOSTERED ARE--PUTTING…
Towards sensible floating-point arithmetic
Cody, W.J.
1980-01-01
Efforts to promote the development of high-quality transportable numerical software show that few, if any, of the floating-point arithmetic systems in existing computers are completely satisfactory for serious numerical computation. Examination of the defects in these systems leads to specifications for a sensible floating-point system from a numerical analyst's viewpoint. 1 table.
Number variance for arithmetic hyperbolic surfaces
NASA Astrophysics Data System (ADS)
Luo, W.; Sarnak, P.
1994-03-01
We prove that the number variance for the spectrum of an arithmetic surface is highly nonrigid in part of the universal range. In fact it is close to having a Poisson behavior. This fact was discovered numerically by Schmit, Bogomolny, Georgeot and Giannoni. It has its origin in the high degeneracy of the length spectrum, first observed by Selberg.
CURRICULUM HANDBOOK. SCIENCE, HEALTH, ARITHMETIC ELEMENTARY GRADES.
ERIC Educational Resources Information Center
BEVERLY, LOUISE; AND OTHERS
THE ARITHMETIC CURRICULUM BEGINS WITH GROUPING AND MANIPULATION OF OBJECTS, CONSTRUCTING AND MEASURING THINGS, AND DRAMATIZING NUMBER SITUATIONS. THE CHILD SHOULD NOT BE ALLOWED TO REMAIN IN THE MANIPULATIVE STATE BUT SHOULD BECOME PROFICIENT IN USING NUMBERS ABSTRACTLY. THE SUBJECT MATTER IN THE FIRST GRADE INCLUDES COUNTING, WORKING WITH…
Readings in Geometry from the Arithmetic Teacher.
ERIC Educational Resources Information Center
Brydegaard, Marguerite; Inskeep, James E., Jr.
This is a book of readings from the "Arithmetic Teacher" on selected topics in geometry. The articles chosen are samples of material published in the journal from its beginning in February 1954 through February 1970. The articles are of three major types. The first is classified "involvement." These articles describe geometry units in which the…
Price, Gavin R; Mazzocco, Michèle M M; Ansari, Daniel
2013-01-01
Do individual differences in the brain mechanisms for arithmetic underlie variability in high school mathematical competence? Using functional magnetic resonance imaging, we correlated brain responses to single digit calculation with standard scores on the Preliminary Scholastic Aptitude Test (PSAT) math subtest in high school seniors. PSAT math scores, while controlling for PSAT Critical Reading scores, correlated positively with calculation activation in the left supramarginal gyrus and bilateral anterior cingulate cortex, brain regions known to be engaged during arithmetic fact retrieval. At the same time, greater activation in the right intraparietal sulcus during calculation, a region established to be involved in numerical quantity processing, was related to lower PSAT math scores. These data reveal that the relative engagement of brain mechanisms associated with procedural versus memory-based calculation of single-digit arithmetic problems is related to high school level mathematical competence, highlighting the fundamental role that mental arithmetic fluency plays in the acquisition of higher-level mathematical competence. PMID:23283330
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…
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.
Spatial Ability Explains the Male Advantage in Approximate Arithmetic
Wei, Wei; Chen, Chuansheng; Zhou, Xinlin
2016-01-01
Previous research has shown that females consistently outperform males in exact arithmetic, perhaps due to the former’s advantage in language processing. Much less is known about gender difference in approximate arithmetic. Given that approximate arithmetic is closely associated with visuospatial processing, which shows a male advantage we hypothesized that males would perform better than females in approximate arithmetic. In two experiments (496 children in Experiment 1 and 554 college students in Experiment 2), we found that males showed better performance in approximate arithmetic, which was accounted for by gender differences in spatial ability. PMID:27014124
Hybrid content addressable memory MSD arithmetic
NASA Astrophysics Data System (ADS)
Li, Yao; Kim, Dai Hyun; Kostrzewski, Andrew A.; Eichmann, George
1990-07-01
The modified signed-digit (MSD) number system, because of its inherent weak interdigit dependance, has been suggested as a useful means for a fast and parallel digital arithmetic. To maintain a fast processing speed, a single-stage holographic optical content-addressable memory (CAM) based MSD algorithm was suggested. In this paper, a novel non-holographic opto-electronic CAM based fast MSD addition processing architecture is proposed. The proposed concept has been verified with our first-order proof-of-principle experiments. A figure of merit comparison of this and other existing approaches is also presented. Based on this key opto-electronic CAM element, implementation of more sophisticated I'VISD arithmetic, such as optical MSD subtraction and multiplication operations, are proposed.
Arithmetic coding with constrained carry operations
NASA Astrophysics Data System (ADS)
Mahfoodh, Abo-Talib; Said, Amir; Yea, Sehoon
2015-03-01
Buffer or counter-based techniques are adequate for dealing with carry propagation in software implementations of arithmetic coding, but create problems in hardware implementations due to the difficulty of handling worst-case scenarios, defined by very long propagations. We propose a new technique for constraining the carry propagation, similar to "bit-stuffing," but designed for encoders that generate data as bytes instead of individual bits, and is based on the fact that the encoder and decoder can maintain the same state, and both can identify the situations when it desired to limit carry propagation. The new technique adjusts the coding interval in a way that corresponds to coding an unused data symbol, but selected to minimize overhead. Our experimental results demonstrate that the loss in compression can be made very small using regular precision for arithmetic operations.
Interpolating Quantifier-Free Presburger Arithmetic
NASA Astrophysics Data System (ADS)
Kroening, Daniel; Leroux, Jérôme; Rümmer, Philipp
Craig interpolation has become a key ingredient in many symbolic model checkers, serving as an approximative replacement for expensive quantifier elimination. In this paper, we focus on an interpolating decision procedure for the full quantifier-free fragment of Presburger Arithmetic, i.e., linear arithmetic over the integers, a theory which is a good fit for the analysis of software systems. In contrast to earlier procedures based on quantifier elimination and the Omega test, our approach uses integer linear programming techniques: relaxation of interpolation problems to the rationals, and a complete branch-and-bound rule tailored to efficient interpolation. Equations are handled via a dedicated polynomial-time sub-procedure. We have fully implemented our procedure on top of the SMT-solver OpenSMT and present an extensive experimental evaluation.
Arithmetic for Public-Key Cryptography
NASA Astrophysics Data System (ADS)
Sakiyama, Kazuo; Batina, Lejla
In this chapter, we discuss arithmetic algorithms used for implementing public-key cryptography (PKC). More precisely, we explore the various algorithms for RSA exponentiation and point/divisor multiplication for curve-based cryptography. The selection of the algorithms has a profound impact on the trade-off between cost, performance, and security. The goal of this chapter is to introduce the different recoding techniques to reduce the number of computations efficiently.
High-precision arithmetic in mathematical physics
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.
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.
Arithmetic functions in torus and tree networks
Bhanot, Gyan; Blumrich, Matthias A.; Chen, Dong; Gara, Alan G.; Giampapa, Mark E.; Heidelberger, Philip; Steinmacher-Burow, Burkhard D.; Vranas, Pavlos M.
2007-12-25
Methods and systems for performing arithmetic functions. In accordance with a first aspect of the invention, methods and apparatus are provided, working in conjunction of software algorithms and hardware implementation of class network routing, to achieve a very significant reduction in the time required for global arithmetic operation on the torus. Therefore, it leads to greater scalability of applications running on large parallel machines. The invention involves three steps in improving the efficiency and accuracy of global operations: (1) Ensuring, when necessary, that all the nodes do the global operation on the data in the same order and so obtain a unique answer, independent of roundoff error; (2) Using the topology of the torus to minimize the number of hops and the bidirectional capabilities of the network to reduce the number of time steps in the data transfer operation to an absolute minimum; and (3) Using class function routing to reduce latency in the data transfer. With the method of this invention, every single element is injected into the network only once and it will be stored and forwarded without any further software overhead. In accordance with a second aspect of the invention, methods and systems are provided to efficiently implement global arithmetic operations on a network that supports the global combining operations. The latency of doing such global operations are greatly reduced by using these methods.
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.
NASA Astrophysics Data System (ADS)
Bargatze, L. F.
2015-12-01
Active Data Archive Product Tracking (ADAPT) is a collection of software routines that permits one to generate XML metadata files to describe and register data products in support of the NASA Heliophysics Virtual Observatory VxO effort. ADAPT is also a philosophy. The ADAPT concept is to use any and all available metadata associated with scientific data to produce XML metadata descriptions in a consistent, uniform, and organized fashion to provide blanket access to the full complement of data stored on a targeted data server. In this poster, we present an application of ADAPT to describe all of the data products that are stored by using the Common Data File (CDF) format served out by the CDAWEB and SPDF data servers hosted at the NASA Goddard Space Flight Center. These data servers are the primary repositories for NASA Heliophysics data. For this purpose, the ADAPT routines have been used to generate data resource descriptions by using an XML schema named Space Physics Archive, Search, and Extract (SPASE). SPASE is the designated standard for documenting Heliophysics data products, as adopted by the Heliophysics Data and Model Consortium. The set of SPASE XML resource descriptions produced by ADAPT includes high-level descriptions of numerical data products, display data products, or catalogs and also includes low-level "Granule" descriptions. A SPASE Granule is effectively a universal access metadata resource; a Granule associates an individual data file (e.g. a CDF file) with a "parent" high-level data resource description, assigns a resource identifier to the file, and lists the corresponding assess URL(s). The CDAWEB and SPDF file systems were queried to provide the input required by the ADAPT software to create an initial set of SPASE metadata resource descriptions. Then, the CDAWEB and SPDF data repositories were queried subsequently on a nightly basis and the CDF file lists were checked for any changes such as the occurrence of new, modified, or deleted
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.
Arithmetic, mutually unbiased bases and complementary observables
NASA Astrophysics Data System (ADS)
Sheppeard, M. D.
2010-02-01
Complementary observables in quantum mechanics may be viewed as Frobenius structures in a dagger monoidal category, such as the category of finite dimensional Hilbert spaces over the complex numbers. On the other hand, their properties crucially depend on the discrete Fourier transform and its associated quantum torus, requiring only the finite fields that underlie mutually unbiased bases. In axiomatic topos theory, the complex numbers are difficult to describe and should not be invoked unnecessarily. This paper surveys some fundamentals of quantum arithmetic using finite field complementary observables, with a view considering more general axiom systems.
Aztec arithmetic: positional notation and area calculation.
Harvey, H R; Williams, B J
1980-10-31
Texcocan-Aztec peoples in the Valley of Mexico used both picture symbols and lines and dots for numerical notation. Decipherment and analysis of mid-16th-century native pictorial land documents from the Texcocan region indicate that the line-and-dot system incorporated a symbol for zero and used position to ascribe values. Positional line-and-dot notation was used to record areas of agricultural fields, and analysis of the documentary data suggests that areas were calculated arithmetically. These findings demonstrate that neither positional notation nor the zero were unique to the Maya area, and they imply an equally sophisticated mathematical development among the Aztecs. PMID:17841389
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.
Iglesias-Sarmiento, Valentín; Deaño, Manuel
2016-01-01
This study analyzed the cognitive functioning underlying arithmetical difficulties and explored the predictors of arithmetic achievement in the last three grades of Spanish Primary Education. For this purpose, a group of 165 students was selected and divided into three groups of arithmetic competence: Mathematical Learning Disability group (MLD, n = 27), Low Achieving group (LA, n = 39), and Typical Achieving group (TA, n = 99). Students were assessed in domain-general abilities (working memory and PASS cognitive processes), and numerical competence (counting and number processing) during the last two months of the academic year. Performance of children from the MLD group was significantly poorer than that of the LA group in writing dictated Arabic numbers (d = -0.88), reading written verbal numbers (d = -0.84), transcoding written verbal numbers to Arabic numbers (-0.75) and comprehension of place value (d = -0.69), as well as in simultaneous (d = -0.62) and successive (d = -0.59) coding. In addition, a specific developmental sequence was observed in both groups, the implications of which are discussed. Hierarchical regression analysis revealed simultaneous coding (β = .47, t(155) = 6.18, p < .001) and number processing (β = .23, t(155) = 3.07, p < .01) as specific predictors of arithmetical performance. PMID:27320030
Wiemers, Michael; Bekkering, Harold; Lindemann, Oliver
2014-01-01
Recent research on spatial number representations suggests that the number space is not necessarily horizontally organized and might also be affected by acquired associations between magnitude and sensory experiences in vertical space. Evidence for this claim is, however, controversial. The present study now aims to compare vertical and horizontal spatial associations in mental arithmetic. In Experiment 1, participants solved addition and subtraction problems and indicated the result verbally while moving their outstretched right arm continuously left-, right-, up-, or downwards. The analysis of the problem-solving performances revealed a motion-arithmetic compatibility effect for spatial actions along both the horizontal and the vertical axes. Performances in additions was impaired while making downward compared to upward movements as well as when moving left compared to right and vice versa in subtractions. In Experiment 2, instead of being instructed to perform active body movements, participants calculated while the problems moved in one of the four relative directions on the screen. For visual motions, only the motion-arithmetic compatibility effect for the vertical dimension could be replicated. Taken together, our findings provide first evidence for an impact of spatial processing on mental arithmetic. Moreover, the stronger effect of the vertical dimension supports the idea that mental calculations operate on representations of numerical magnitude that are grounded in a vertically organized mental number space. PMID:24483946
Marghetis, Tyler; Núñez, Rafael; Bergen, Benjamin K
2014-01-01
Mathematics requires precise inferences about abstract objects inaccessible to perception. How is this possible? One proposal is that mathematical reasoning, while concerned with entirely abstract objects, nevertheless relies on neural resources specialized for interacting with the world-in other words, mathematics may be grounded in spatial or sensorimotor systems. Mental arithmetic, for instance, could involve shifts in spatial attention along a mental "number-line", the product of cultural artefacts and practices that systematically spatialize number and arithmetic. Here, we investigate this hypothesized spatial processing during exact, symbolic arithmetic (e.g., 4 + 3 = 7). Participants added and subtracted single-digit numbers and selected the exact solution from responses in the top corners of a computer monitor. While they made their selections using a computer mouse, we recorded the movement of their hand as indexed by the streaming x, y coordinates of the computer mouse cursor. As predicted, hand movements during addition and subtraction were systematically deflected toward the right and the left, respectively, as if calculation involved simultaneously simulating motion along a left-to-right mental number-line. This spatial-arithmetical bias, moreover, was distinct from-but correlated with-individuals' spatial-numerical biases (i.e., spatial-numerical association of response codes, SNARC, effect). These results are the first evidence that exact, symbolic arithmetic prompts systematic spatial processing associated with mental calculation. We discuss the possibility that mathematical calculation relies, in part, on an integrated system of spatial processes. PMID:25051274
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.
ERIC Educational Resources Information Center
Stock, Pieter; Desoete, Annemie; Roeyers, Herbert
2010-01-01
In a 3-year longitudinal study, 471 children were classified, based on their performances on arithmetic tests in first and second grade, as having persistent arithmetic disabilities (AD), persistent low achieving (LA), persistent typical achieving, inconsistent arithmetic disabilities (DF1), or inconsistent low achieving in arithmetic. Significant…
12 CFR Appendix E to Part 1024 - Arithmetic Steps
Code of Federal Regulations, 2012 CFR
2012-01-01
... 12 Banks and Banking 8 2012-01-01 2012-01-01 false Arithmetic Steps E Appendix E to Part 1024 Banks and Banking BUREAU OF CONSUMER FINANCIAL PROTECTION REAL ESTATE SETTLEMENT PROCEDURES ACT (REGULATION X) Pt. 102, App. E Appendix E to Part 1024—Arithmetic Steps I. Example Illustrating...
12 CFR Appendix E to Part 1024 - Arithmetic Steps
Code of Federal Regulations, 2013 CFR
2013-01-01
... 12 Banks and Banking 8 2013-01-01 2013-01-01 false Arithmetic Steps E Appendix E to Part 1024 Banks and Banking BUREAU OF CONSUMER FINANCIAL PROTECTION REAL ESTATE SETTLEMENT PROCEDURES ACT (REGULATION X) Pt. 1024, App. E Appendix E to Part 1024—Arithmetic Steps I. Example Illustrating...
Understanding and Using Principles of Arithmetic: Operations Involving Negative Numbers
ERIC Educational Resources Information Center
Prather, Richard W.; Alibali, Martha W.
2008-01-01
Previous work has investigated adults' knowledge of principles for arithmetic with positive numbers (Dixon, Deets, & Bangert, 2001). The current study extends this past work to address adults' knowledge of principles of arithmetic with a negative number, and also investigates links between knowledge of principles and problem representation.…
Numeral Writing Skill and Elementary Arithmetic Mental Calculations
ERIC Educational Resources Information Center
Johansson, Bo S.
2005-01-01
The paper reports three studies addressing the role of numeral writing for arithmetic performance. About 650 children in the age range 5-7 years participated in the studies. The results demonstrate a positive correlation between number of digits correctly written and number of arithmetic problems solved. The correlations between number of reversed…
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.,…
Arithmetic versus Geometric Means for Environmental Concentration Data.
ERIC Educational Resources Information Center
Parkhurst, David F.
1998-01-01
Concentrations of chemical substances and microorganisms are often averaged using geometric means. Argues that the arithmetic mean is a better choice for summarizing data because arithmetic means are unbiased, easier to calculate and understand, scientifically more meaningful, and more protective of public health. Results of a simulation study…
24 CFR Appendix E to Part 3500 - Arithmetic Steps
Code of Federal Regulations, 2011 CFR
2011-04-01
... 24 Housing and Urban Development 5 2011-04-01 2011-04-01 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...
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…
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…
The Arithmetic Tie Effect Is Mainly Encoding-based.
ERIC Educational Resources Information Center
Blankenberger, Sven
2001-01-01
Examined two possible explanations for the arithmetic tie effect: faster encoding of tie problems versus faster access to arithmetic facts. Found that the tie effect vanished with heterogeneous addition problems, and for seven out of eight participants, the effect vanished with heterogeneous multiplication problems. Concludes that the tie effect…
Paczynacuteski, B
1984-07-20
Most stars in the solar neighborhood are either double or multiple systems. They provide a unique opportunity to measure stellar masses and radii and to study many interesting and important phenomena. The best candidates for black holes are compact massive components of two x-ray binaries: Cygnus X-1 and LMC X-3. The binary radio pulsar PSR 1913 + 16 provides the best available evidence for gravitational radiation. Accretion disks and jets observed in close binaries offer a very good testing ground for models of active galactic nuclei and quasars.
Paczynacuteski, B
1984-07-20
Most stars in the solar neighborhood are either double or multiple systems. They provide a unique opportunity to measure stellar masses and radii and to study many interesting and important phenomena. The best candidates for black holes are compact massive components of two x-ray binaries: Cygnus X-1 and LMC X-3. The binary radio pulsar PSR 1913 + 16 provides the best available evidence for gravitational radiation. Accretion disks and jets observed in close binaries offer a very good testing ground for models of active galactic nuclei and quasars. PMID:17749544
Image processing and the Arithmetic Fourier Transform
Tufts, D.W.; Fan, Z.; Cao, Z.
1989-01-01
A new Fourier technique, the Arithmetic Fourier Transform (AFT) was recently developed for signal processing. This approach is based on the number-theoretic method of Mobius inversion. The AFT needs only additions except for a small amount of multiplications by prescribed scale factors. This new algorithm is also well suited to parallel processing. And there is no accumulation of rounding errors in the AFT algorithm. In this reprint, the AFT is used to compute the discrete cosine transform and is also extended to 2-D cases for image processing. A 2-D Mobius inversion formula is proved. It is then applied to the computation of Fourier coefficients of a periodic 2-D function. It is shown that the output of an array of delay-line (or transversal) filters is the Mobius transform of the input harmonic terms. The 2-D Fourier coefficients can therefore be obtained through Mobius inversion of the output of the filter array.
On the arithmetic sums of Cantor sets
NASA Astrophysics Data System (ADS)
Ilgar Eroglu, Kemal
2007-05-01
Let Cλ and Cγ be two affine Cantor sets in \\mathbb{R} with similarity dimensions dλ and dγ, respectively. We define an analogue of the Bandt-Graf condition for self-similar systems and use it to give necessary and sufficient conditions for having \\xyHa^{d_\\xyla+d_\\xyga}(C_\\xyla + C_\\xyga)>0 where Cλ + Cγ denotes the arithmetic sum of the sets. We use this result to analyse the orthogonal projection properties of sets of the form Cλ × Cγ. We prove that for Lebesgue almost all directions θ for which the projection is not one-to-one, the projection has zero (dλ + dγ)-dimensional Hausdorff measure. We demonstrate the results in the case when Cλ and Cγ are the middle-(1-2λ) and middle-(1-2γ) sets.
Growth model of binary alloy nanopowders for thermal plasma synthesis
NASA Astrophysics Data System (ADS)
Shigeta, Masaya; Watanabe, Takayuki
2010-08-01
A new model is developed for numerical analysis of the entire growth process of binary alloy nanopowders in thermal plasma synthesis. The model can express any nanopowder profile in the particle size-composition distribution (PSCD). Moreover, its numerical solution algorithm is arithmetic and straightforward so that the model is easy to use. By virtue of these features, the model effectively simulates the collective and simultaneous combined process of binary homogeneous nucleation, binary heterogeneous cocondensation, and coagulation among nanoparticles. The effect of the freezing point depression due to nanoscale particle diameters is also considered in the model. In this study, the metal-silicon systems are particularly chosen as representative binary systems involving cocondensation processes. In consequence, the numerical calculation with the present model reveals the growth mechanisms of the Mo-Si and Ti-Si nanopowders by exhibiting their PSCD evolutions. The difference of the materials' saturation pressures strongly affects the growth behaviors and mature states of the binary alloy nanopowder.
Growth model of binary alloy nanopowders for thermal plasma synthesis
Shigeta, Masaya; Watanabe, Takayuki
2010-08-15
A new model is developed for numerical analysis of the entire growth process of binary alloy nanopowders in thermal plasma synthesis. The model can express any nanopowder profile in the particle size-composition distribution (PSCD). Moreover, its numerical solution algorithm is arithmetic and straightforward so that the model is easy to use. By virtue of these features, the model effectively simulates the collective and simultaneous combined process of binary homogeneous nucleation, binary heterogeneous cocondensation, and coagulation among nanoparticles. The effect of the freezing point depression due to nanoscale particle diameters is also considered in the model. In this study, the metal-silicon systems are particularly chosen as representative binary systems involving cocondensation processes. In consequence, the numerical calculation with the present model reveals the growth mechanisms of the Mo-Si and Ti-Si nanopowders by exhibiting their PSCD evolutions. The difference of the materials' saturation pressures strongly affects the growth behaviors and mature states of the binary alloy nanopowder.
Similarity interference in learning and retrieving arithmetic facts.
De Visscher, A; Noël, M-P
2016-01-01
Storing the solution of simple calculations in long-term memory is an important learning in primary school that is subsequently essential in adult daily living. While most children succeed in storing arithmetic facts to which they have been trained at school, huge individual differences are reported, particularly in children with developmental dyscalculia, who show a severe and persistent deficit in arithmetic facts learning. This chapter reports important advances in the understanding of the development of an arithmetic facts network and focuses on the detrimental effect of similarity interference. First, at the retrieval stage, connectionist models highlighted that the similarity of the neighbor problems in the arithmetic facts network creates interference. More recently, the similarity interference during the learning stage was pointed out in arithmetic facts learning. The interference parameter, that captures the proactive interference that a problem receives from previously learned problems, was shown as a substantial determinant of the performance across multiplication problems. This proactive interference was found both in children and adults and showed that when a problem is highly similar to previously learned ones, it is more difficult to remember it. Furthermore, the sensitivity to this similarity interference determined individual differences in the learning and retrieving of arithmetic facts, giving new insights for interindividual differences. Regarding the atypical development, hypersensitivity-to-interference in memory was related to arithmetic facts deficit in a single case of developmental dyscalculia and in a group of fourth-grade children with low arithmetic facts knowledge. In sum, the impact of similarity interference is shown in the learning stage of arithmetic facts and concerns the typical and atypical development. PMID:27339011
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.
Early occipital injury affects numerosity counting but not simple arithmetic.
Zhang, Han; Chen, Chuansheng; Sun, Zhaohui; Lin, Jiuluan; Zhou, Wenjing; Zhou, Xinlin
2016-01-01
This study investigated the effects of early occipital injury on the development of counting and simple arithmetic abilities in an occipital epileptic patient. This patient had obvious softening lesions in the bilateral occipital regions due to viral encephalitis at the age of 1.5 years. Results showed that she could perform subitizing and simple arithmetic very well, but could not perform numerosity counting tasks. These results suggest that the occipital cortex plays an important role in the development of numerosity counting skills, but not in the development of subitizing and simple arithmetic. PMID:25771703
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.
How Modulo Arithmetic is Used in Book Publishing
ERIC Educational Resources Information Center
Dean, Peter G.
1975-01-01
The system of International Standard Book Numbers uses a check code based on modular arithmetic. This system, the use of a simple machine to compute check digits, and related classroom activities are described. (SD)
Statistical properties of an iterated arithmetic mapping
Feix, M.R.; Rouet, J.L.
1994-07-01
We study the (3x = 1)/2 problem from a probabilistic viewpoint and show a forgetting mechanism for the last k binary digits of the seed after k iterations. The problem is subsequently generalized to a trifurcation process, the (lx + m)/3 problem. Finally the sequence of a set of seeds is empirically shown to be equivalent to a random walk of the variable log{sub 2}x (or log{sub 3} x) though computer simulations.
Is integer arithmetic fundamental to mental processing?: the mind's secret arithmetic.
Snyder, A W; Mitchell, D J
1999-01-01
Unlike the ability to acquire our native language, we struggle to learn multiplication and division. It may then come as a surprise that the mental machinery for performing lightning-fast integer arithmetic calculations could be within us all even though it cannot be readily accessed, nor do we have any idea of its primary function. We are led to this provocative hypothesis by analysing the extraordinary skills of autistic savants. In our view such individuals have privileged access to lower levels of information not normally available through introspection. PMID:10212449
NASA Astrophysics Data System (ADS)
Ryan, Keegan; Nakajima, Miki; Stevenson, David J.
2014-11-01
Can a bound pair of similar mass terrestrial planets exist? We are interested here in bodies with a mass ratio of ~ 3:1 or less (so Pluto/Charon or Earth/Moon do not qualify) and we do not regard the absence of any such discoveries in the Kepler data set to be significant since the tidal decay and merger of a close binary is prohibitively fast well inside of 1AU. SPH simulations of equal mass “Earths” were carried out to seek an answer to this question, assuming encounters that were only slightly more energetic than parabolic (zero energy). We were interested in whether the collision or near collision of two similar mass bodies would lead to a binary in which the two bodies remain largely intact, effectively a tidal capture hypothesis though with the tidal distortion being very large. Necessarily, the angular momentum of such an encounter will lead to bodies separated by only a few planetary radii if capture occurs. Consistent with previous work, mostly by Canup, we find that most impacts are disruptive, leading to a dominant mass body surrounded by a disk from which a secondary forms whose mass is small compared to the primary, hence not a binary planet by our adopted definition. However, larger impact parameter “kissing” collisions were found to produce binaries because the dissipation upon first encounter was sufficient to provide a bound orbit that was then rung down by tides to an end state where the planets are only a few planetary radii apart. The long computational times for these simulation make it difficult to fully map the phase space of encounters for which this outcome is likely but the indications are that the probability is not vanishingly small and since planetary encounters are a plausible part of planet formation, we expect binary planets to exist and be a non-negligible fraction of the larger orbital radius exoplanets awaiting discovery.
De Smedt, Bert; Holloway, Ian D; Ansari, Daniel
2011-08-01
Most studies on mathematics learning in the field of educational neuroscience have focused on the neural correlates of very elementary numerical processing skills in children. Little is known about more complex mathematical skills that are formally taught in school, such as arithmetic. Using functional magnetic resonance imaging, the present study investigated how brain activation during single-digit addition and subtraction is modulated by problem size and arithmetic operation in 28 children aged 10-12 years with different levels of arithmetical fluency. Commensurate with adult data, large problems and subtractions activated a fronto-parietal network, including the intraparietal sulci, the latter of which indicates the influence of quantity-based processes during procedural strategy execution. Different from adults, the present findings revealed that particularly the left hippocampus was active during the solution of those problems that are expected to be solved by means of fact retrieval (i.e. small problems and addition), suggesting a specific role of the hippocampus in the early stages of learning arithmetic facts. Children with low levels of arithmetical fluency showed higher activation in the right intraparietal sulcus during the solution of problems with a relatively small problem size, indicating that they continued to rely to a greater extent on quantity-based strategies on those problems that the children with relatively higher arithmetical fluency already retrieved from memory. This might represent a neural correlate of fact retrieval impairments in children with mathematical difficulties. PMID:21182966
Mangarevan invention of binary steps for easier calculation.
Bender, Andrea; Beller, Sieghard
2014-01-28
When Leibniz demonstrated the advantages of the binary system for computations as early as 1703, he laid the foundation for computing machines. However, is a binary system also suitable for human cognition? One of two number systems traditionally used on Mangareva, a small island in French Polynesia, had three binary steps superposed onto a decimal structure. Here, we show how this system functions, how it facilitated arithmetic, and why it is unique. The Mangarevan invention of binary steps, centuries before their formal description by Leibniz, attests to the advancements possible in numeracy even in the absence of notation and thereby highlights the role of culture for the evolution of and diversity in numerical cognition.
Mangarevan invention of binary steps for easier calculation
Bender, Andrea; Beller, Sieghard
2014-01-01
When Leibniz demonstrated the advantages of the binary system for computations as early as 1703, he laid the foundation for computing machines. However, is a binary system also suitable for human cognition? One of two number systems traditionally used on Mangareva, a small island in French Polynesia, had three binary steps superposed onto a decimal structure. Here, we show how this system functions, how it facilitated arithmetic, and why it is unique. The Mangarevan invention of binary steps, centuries before their formal description by Leibniz, attests to the advancements possible in numeracy even in the absence of notation and thereby highlights the role of culture for the evolution of and diversity in numerical cognition. PMID:24344278
Mangarevan invention of binary steps for easier calculation.
Bender, Andrea; Beller, Sieghard
2014-01-28
When Leibniz demonstrated the advantages of the binary system for computations as early as 1703, he laid the foundation for computing machines. However, is a binary system also suitable for human cognition? One of two number systems traditionally used on Mangareva, a small island in French Polynesia, had three binary steps superposed onto a decimal structure. Here, we show how this system functions, how it facilitated arithmetic, and why it is unique. The Mangarevan invention of binary steps, centuries before their formal description by Leibniz, attests to the advancements possible in numeracy even in the absence of notation and thereby highlights the role of culture for the evolution of and diversity in numerical cognition. PMID:24344278
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.
Perceiving fingers in single-digit arithmetic problems
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
Optimization Approaches for Designing Quantum Reversible Arithmetic Logic Unit
NASA Astrophysics Data System (ADS)
Haghparast, Majid; Bolhassani, Ali
2016-03-01
Reversible logic is emerging as a promising alternative for applications in low-power design and quantum computation in recent years due to its ability to reduce power dissipation, which is an important research area in low power VLSI and ULSI designs. Many important contributions have been made in the literatures towards the reversible implementations of arithmetic and logical structures; however, there have not been many efforts directed towards efficient approaches for designing reversible Arithmetic Logic Unit (ALU). In this study, three efficient approaches are presented and their implementations in the design of reversible ALUs are demonstrated. Three new designs of reversible one-digit arithmetic logic unit for quantum arithmetic has been presented in this article. This paper provides explicit construction of reversible ALU effecting basic arithmetic operations with respect to the minimization of cost metrics. The architectures of the designs have been proposed in which each block is realized using elementary quantum logic gates. Then, reversible implementations of the proposed designs are analyzed and evaluated. The results demonstrate that the proposed designs are cost-effective compared with the existing counterparts. All the scales are in the NANO-metric area.
Effect of language switching on arithmetic: a bilingual FMRI study.
Venkatraman, Vinod; Siong, Soon Chun; Chee, Michael W L; Ansari, Daniel
2006-01-01
The role of language in performing numerical computations has been a topic of special interest in cognition. The "Triple Code Model" proposes the existence of a language-dependent verbal code involved in retrieving arithmetic facts related to addition and multiplication, and a language-independent analog magnitude code subserving tasks such as number comparison and estimation. Neuroimaging studies have shown dissociation between dependence of arithmetic computations involving exact and approximate processing on language-related circuits. However, a direct manipulation of language using different arithmetic tasks is necessary to assess the role of language in forming arithmetic representations and in solving problems in different languages. In the present study, 20 English-Chinese bilinguals were trained in two unfamiliar arithmetic tasks in one language and scanned using fMRI on the same problems in both languages (English and Chinese). For the exact "base-7 addition" task, language switching effects were found in the left inferior frontal gyrus (LIFG) and left inferior parietal lobule extending to the angular gyrus. In the approximate "percentage estimation" task, language switching effects were found predominantly in the bilateral posterior intraparietal sulcus and LIFG, slightly dorsal to the LIFG activation seen for the base-7 addition task. These results considerably strengthen the notion that exact processing relies on verbal and language-related networks, whereas approximate processing engages parietal circuits typically involved in magnitude-related processing. PMID:16417683
Patterns of problem-solving in children's literacy and arithmetic.
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.
Number processing and arithmetic skills in children with cochlear implants
Pixner, Silvia; Leyrer, Martin; Moeller, Korbinian
2014-01-01
Though previous findings report that hearing impaired children exhibit impaired language and arithmetic skills, our current understanding of how hearing and the associated language impairments may influence the development of arithmetic skills is still limited. In the current study numerical/arithmetic performance of 45 children with a cochlea implant were compared to that of controls matched for hearing age, intelligence and sex. Our main results were twofold disclosing that children with CI show general as well as specific numerical/arithmetic impairments. On the one hand, we found an increased percentage of children with CI with an indication of dyscalculia symptoms, a general slowing in multiplication and subtraction as well as less accurate number line estimations. On the other hand, however, children with CI exhibited very circumscribed difficulties associated with place-value processing. Performance declined specifically when subtraction required a borrow procedure and number line estimation required the integration of units, tens, and hundreds instead of only units and tens. Thus, it seems that despite initially atypical language development, children with CI are able to acquire arithmetic skills in a qualitatively similar fashion as their normal hearing peers. Nonetheless, when demands on place-value understanding, which has only recently been proposed to be language mediated, hearing impaired children experience specific difficulties. PMID:25566152
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.
Age-related differences in arithmetic strategy sequential effects.
Lemaire, Patrick
2016-03-01
In this article, I review a series of new findings concerning how age-related changes in strategic variations are modulated by sequential effects. Sequential effects refer to how strategy selection and strategy execution on current problems are influenced by which strategy is used on immediately preceding problems. Two sequential effects during strategy selection (i.e., strategy revisions and strategy perseverations) and during strategy execution (i.e., strategy switch costs and modulations of poorer strategy effects) are presented. I also discuss how these effects change with age during adulthood. These phenomena are important, as they shed light on arithmetic processes and how these processes change with age during adulthood. In particular, they speak to the role of executive control while participants select and execute arithmetic strategies. Finally, I discuss the implications of sequential effects for theories of strategies and of arithmetic.
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. PMID:27445889
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. PMID:27445889
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.
Towards constructing multi-bit binary adder based on Belousov-Zhabotinsky reaction
NASA Astrophysics Data System (ADS)
Zhang, Guo-Mao; Wong, Ieong; Chou, Meng-Ta; Zhao, Xin
2012-04-01
It has been proposed that the spatial excitable media can perform a wide range of computational operations, from image processing, to path planning, to logical and arithmetic computations. The realizations in the field of chemical logical and arithmetic computations are mainly concerned with single simple logical functions in experiments. In this study, based on Belousov-Zhabotinsky reaction, we performed simulations toward the realization of a more complex operation, the binary adder. Combining with some of the existing functional structures that have been verified experimentally, we designed a planar geometrical binary adder chemical device. Through numerical simulations, we first demonstrated that the device can implement the function of a single-bit full binary adder. Then we show that the binary adder units can be further extended in plane, and coupled together to realize a two-bit, or even multi-bit binary adder. The realization of chemical adders can guide the constructions of other sophisticated arithmetic functions, ultimately leading to the implementation of chemical computer and other intelligent systems.
Logical and arithmetic circuits in Belousov-Zhabotinsky encapsulated disks
NASA Astrophysics Data System (ADS)
Holley, Julian; Jahan, Ishrat; de Lacy Costello, Ben; Bull, Larry; Adamatzky, Andrew
2011-11-01
Excitation waves on a subexcitable Belousov-Zhabotinsky (BZ) substrate can be manipulated by chemical variations in the substrate and by interactions with other waves. Symbolic assignment and interpretation of wave dynamics can be used to perform logical and arithmetic computations. We present chemical analogs of elementary logic and arithmetic circuits created entirely from interconnected arrangements of individual BZ encapsulated cell-like disk. Interdisk wave migration is confined in carefully positioned connecting pores. This connection limits wave expansion and unifies the input-output characteristic of the disks. Circuit designs derived from numeric simulations are optically encoded onto a homogeneous photosensitive BZ substrate.
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…
24 CFR Appendix E to Part 3500 - Arithmetic Steps
Code of Federal Regulations, 2013 CFR
2013-04-01
... 24 Housing and Urban Development 5 2013-04-01 2013-04-01 false Arithmetic Steps E Appendix E to Part 3500 Housing and Urban Development Regulations Relating to Housing and Urban Development... URBAN DEVELOPMENT REAL ESTATE SETTLEMENT PROCEDURES ACT Pt. 3500, App. E Appendix E to Part...
24 CFR Appendix E to Part 3500 - Arithmetic Steps
Code of Federal Regulations, 2012 CFR
2012-04-01
... 24 Housing and Urban Development 5 2012-04-01 2012-04-01 false Arithmetic Steps E Appendix E to Part 3500 Housing and Urban Development Regulations Relating to Housing and Urban Development... URBAN DEVELOPMENT REAL ESTATE SETTLEMENT PROCEDURES ACT Pt. 3500, App. E Appendix E to Part...
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…
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…
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.…
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…
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…
Learning by Seeing by Doing: Arithmetic Word Problems
ERIC Educational Resources Information Center
Weber-Russell, Sylvia; LeBlanc, Mark D.
2004-01-01
"Learning by doing" in pursuit of real-world goals has received much attention from education researchers but has been unevenly supported by mathematics education software at the elementary level, particularly as it involves arithmetic word problems. In this article, we give examples of doing-oriented tools that might promote children's ability to…
The Reorganization of Arithmetic Practice in the Kitchen.
ERIC Educational Resources Information Center
De La Rocha, Olivia
1985-01-01
The relations between a cultural fund of general knowledge and knowledge-in-use were investigated by observing the arithmetical practices of ten women enrolled in the Weight Watchers program. Apparently, the precision of dieters' measurements is dependent on situation and everyday context. Often, subjects' knowledge-in-use exceeded the general…
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 Part 3500 Housing and Urban Development Regulations Relating to Housing and Urban Development... URBAN DEVELOPMENT REAL ESTATE SETTLEMENT PROCEDURES ACT Pt. 3500, App. E Appendix E to Part...
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…
Toward a Student-Centred Process of Teaching Arithmetic
ERIC Educational Resources Information Center
Eriksson, Gota
2011-01-01
This article describes a way toward a student-centred process of teaching arithmetic, where the content is harmonized with the students' conceptual levels. At school start, one classroom teacher is guided in recurrent teaching development meetings in order to develop teaching based on the students' prerequisites and to successively learn the…
Beginners' Progress in Early Arithmetic in the Swedish Compulsory School
ERIC Educational Resources Information Center
Eriksson, Gota
2008-01-01
This article focuses on spontaneous knowledge-building in the field of "the arithmetic "of" the child." The aim is to investigate the conceptual progress of fifteen children during their early school years in the compulsory school. The study is based on the epistemology of radical constructivism and the methodology of "multiple clinical…
Relational Thinking: Learning Arithmetic in Order to Promote Algebraic Thinking
ERIC Educational Resources Information Center
Napaphun, Vishnu
2012-01-01
Trends in the curriculum reform propose that algebra should be taught throughout the grades, starting in elementary school. The aim should be to decrease the discontinuity between the arithmetic in elementary school and the algebra in upper grades. This study was conducted to investigate and characterise upper elementary school students…
Feasibility of a New Basis for School Arithmetic. Final Report.
ERIC Educational Resources Information Center
Klein, George
The objective of this study was to explore methods of using commonplace mechanical devices at the fourth grade level to expedite and extend the treatment of two important segments of the lower elementary arithmetic curriculum. The experimental testing of classroom materials took place at the Middle School of the Laboratory Schools of the…
Thinking Mathematically: Integrating Arithmetic and Algebra in Elementary School.
ERIC Educational Resources Information Center
Carpenter, Thomas P.; Franke, Megan Loef; Levi, Linda
This book is designed to help teachers understand children's intuitive problem solving and computational processes and to figure out how to use that knowledge to enhance students' understanding of arithmetic. This book provides numerous examples of classroom dialogues that indicate how algebraic ideas emerge in children's thinking and what…
Single-Digit Arithmetic in Children with Dyslexia
ERIC Educational Resources Information Center
Boets, Bart; De Smedt, Bert
2010-01-01
It has been suggested that individuals with dyslexia show poorer performance on those aspects of arithmetic that involve the manipulation of verbal representations, such as the use of fact retrieval strategies. The present study examined this in 13 children with dyslexia who showed normal general mathematics achievement and 16 matched controls.…
Representations in the Sixteenth-Century Arithmetic Books
ERIC Educational Resources Information Center
Madrid, María José; Maz-Machado, Alexander; León-Mantero, Carmen
2015-01-01
The research on the History of Mathematics and Mathematics Education has on textbook a useful tool to provide diverse types of information; this fact has led to the realization of many different studies focus on them. In this context, this work analyzes eight different sixteenth-century arithmetic books to know the different types of…
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…
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…
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…
ARITHMETIC DRILLS AND REVIEW ON A COMPUTER-BASED TELETYPE.
ERIC Educational Resources Information Center
SUPPES, PATRICK; AND OTHERS
FIFTEEN DAILY DRILLS EMPHASIZING MASTERY OF BASIC NUMBER FACTS, SUCH AS ARITHMETIC OPERATIONS AND UNITS OF MEASUREMENT WERE CONSTRUCTED TO ENCOMPASS 7 PREVIOUSLY REPORTED ATTRIBUTES OF AN EFFECTIVE DRILL. ATTRIBUTES ARE MIXED DRILL, TIME LIMIT, INCREASINGLY DIFFICULT EXAMPLES, THOROUGH COVERAGE, FREQUENT AND SMALL AMOUNTS, VERBAL PROBLEMS,…
Operation-Specific Encoding in Single-Digit Arithmetic
ERIC Educational Resources Information Center
Zhou, Xinlin
2011-01-01
Solving simple arithmetic problems involves three stages: encoding the problem, retrieving or calculating the answer, and reporting the answer. This study compared the event-related potentials elicited by single-digit addition and multiplication problems to examine the relationship between encoding and retrieval/calculation stages. Results showed…
Arithmetic word problem solving: a Situation Strategy First framework.
Brissiaud, Rémi; Sander, Emmanuel
2010-01-01
Before instruction, children solve many arithmetic word problems with informal strategies based on the situation described in the problem. A Situation Strategy First framework is introduced that posits that initial representation of the problem activates a situation-based strategy even after instruction: only when it is not efficient for providing the numerical solution is the representation of the problem modified so that the relevant arithmetic knowledge might be used. Three experiments were conducted with Year 3 and Year 4 children. Subtraction, multiplication and division problems were created in two versions involving the same wording but different numerical values. The first version could be mentally solved with a Situation strategy (Si version) and the second with a Mental Arithmetic strategy (MA version). Results show that Si-problems are easier than MA-problems even after instruction, and, when children were asked to report their strategy by writing a number sentence, equations that directly model the situation were predominant for Si-problems but not for MA ones. Implications of the Situation Strategy First framework regarding the relation between conceptual and procedural knowledge and the development of arithmetic knowledge are discussed.
Arithmetic Word Problem Solving: A Situation Strategy First Framework
ERIC Educational Resources Information Center
Brissiaud, Remi; Sander, Emmanuel
2010-01-01
Before instruction, children solve many arithmetic word problems with informal strategies based on the situation described in the problem. A Situation Strategy First framework is introduced that posits that initial representation of the problem activates a situation-based strategy even after instruction: only when it is not efficient for providing…
Exploring Working Memory in Children with Low Arithmetical Achievement
ERIC Educational Resources Information Center
D'Amico, A.; Guarnera, M.
2005-01-01
This research aimed at exploring the working memory functions in children with low arithmetical achievement and normal reading, compared to age matched controls (mean age 9 years). All the children completed a series of working memory tasks, involving the central executive functions (using both linguistic and numerical material), the phonological…
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…
Numerical Predictors of Arithmetic Success in Grades 1-6
ERIC Educational Resources Information Center
Lyons, Ian M.; Price, Gavin R.; Vaessen, Anniek; Blomert, Leo; Ansari, Daniel
2014-01-01
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…
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…
ERIC Educational Resources Information Center
Garcia, Ana I.; Jimenez, Juan E.; Hess, Stephany
2006-01-01
This study was designed to determine a word problem difficulty classification in children with arithmetic learning disabilities (ALD; n = 104) in comparison with typically achieving students (n = 44). We tested variables such as (a) semantic structure (Change, Combine, Compare, and Equalize), (b) operation (subtraction and addition), and (c)…
Park, Joonkoo; Brannon, Elizabeth M.
2014-01-01
A nonverbal primitive number sense allows approximate estimation and mental manipulations on numerical quantities without the use of numerical symbols. In a recent randomized controlled intervention study in adults, we demonstrated that repeated training on a non-symbolic approximate arithmetic task resulted in improved exact symbolic arithmetic performance, suggesting a causal relationship between the primitive number sense and arithmetic competence. Here, we investigate the potential mechanisms underlying this causal relationship. We constructed multiple training conditions designed to isolate distinct cognitive components of the approximate arithmetic task. We then assessed the effectiveness of these training conditions in improving exact symbolic arithmetic in adults. We found that training on approximate arithmetic, but not on numerical comparison, numerical matching, or visuo-spatial short-term memory, improves symbolic arithmetic performance. In addition, a second experiment revealed that our approximate arithmetic task does not require verbal encoding of number, ruling out an alternative explanation that participants use exact symbolic strategies during approximate arithmetic training. Based on these results, we propose that nonverbal numerical quantity manipulation is one key factor that drives the link between the primitive number sense and symbolic arithmetic competence. Future work should explore implications from this finding that training young children on approximate arithmetic tasks even before they solidify the symbolic number understanding may be fruitful for improving readiness for math education. PMID:25044247
Arithmetic facts storage deficit: the hypersensitivity-to-interference in memory hypothesis.
De Visscher, Alice; Noël, Marie-Pascale
2014-05-01
Dyscalculia, or mathematics learning disorders, is currently known to be heterogeneous (Wilson & Dehaene, ). 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, ; Jordan & Montani, ; Slade & Russel, ). Arithmetic facts are simple arithmetic problems that are solved by direct retrieval from memory. Recently, De Visscher and Noël () showed hypersensitivity-to-interference in memory in an adult suffering from a specific deficit of arithmetic facts storage. According to the authors, arithmetic facts share many features. The overlapping of these features between arithmetic facts may provoke interference. Consequently, learners who are hypersensitive-to-interference could have considerable difficulties in storing arithmetic facts. The present study aims at testing this new hypothesis on fourth-grade children who are learning multiplication tables. Among 101 children that were assessed, 23 low arithmetic facts learners were selected because of their low score in arithmetic facts fluency (controlling for processing speed). Twenty-three control children were selected, matched for classroom, gender, and age. In addition to a subtest of global reasoning, these participants were given a multiplication production task and a memorization task of low- and high-interference associations. The results show that children with low arithmetic fluencies experience hypersensitivity-to-interference in memory compared with children with typical arithmetic fluencies.
Eye-movement models for arithmetic and reading performance.
Suppes, P
1990-01-01
Three stochastic eye-movement models for arithmetic and reading performance have been proposed, one for arithmetic and two for reading. Each model characterizes a real-time stochastic process in terms of fixation durations and saccadic movement, but only direction and length of saccades are considered, not acceleration or velocity. Aspects of the models that are emphasized, partly because of their general neglect in the literature, are the probability distribution of fixation durations and the random walk of saccade directions. The distributions of fixation duration are approximately exponential, but systematic deviations can be accounted for in the models, even though the fit to data is not perfect. In the case of the arithmetic algorithms of addition and subtraction, the random walk of the normative model has only two possible moves. Data are also presented on backtracking, skipping and wandering eye movements, each of which has a significant relative frequency. The first reading model is called a minimal control model, because it does not take account of the effects of many local variables, e.g., word length, that have been extensively studied. The axioms on fixation duration for the minimal control model are the same as for the arithmetic model. Abstracting from the different arrangement of stimuli in arithmetic algorithms and in linear text, the axioms on saccadic motion for the two models are also essentially identical. The stochastic nature of both models is strongly supported by data on the independence of fixation durations from previous fixation durations. Additional detailed evidence is presented for the arithmetic model. To better account for a great variety of experimental results concerning significant effects on eye movements in reading, a text-dependent probabilistic model of reading is introduced. Significant local effects fall into three classes, identified as line, word and grammatical variables. The revised axioms embody five features of text
Interval arithmetic operations for uncertainty analysis with correlated interval variables
NASA Astrophysics Data System (ADS)
Jiang, Chao; Fu, Chun-Ming; Ni, Bing-Yu; Han, Xu
2016-08-01
A new interval arithmetic method is proposed to solve interval functions with correlated intervals through which the overestimation problem existing in interval analysis could be significantly alleviated. The correlation between interval parameters is defined by the multidimensional parallelepiped model which is convenient to describe the correlative and independent interval variables in a unified framework. The original interval variables with correlation are transformed into the standard space without correlation, and then the relationship between the original variables and the standard interval variables is obtained. The expressions of four basic interval arithmetic operations, namely addition, subtraction, multiplication, and division, are given in the standard space. Finally, several numerical examples and a two-step bar are used to demonstrate the effectiveness of the proposed method.
Arithmetic difficulties in females with the fragile X premutation.
Lachiewicz, Ave M; Dawson, Deborah V; Spiridigliozzi, Gail A; McConkie-Rosell, Allyn
2006-04-01
Females with the fragile X full mutation have been reported to have difficulty learning mathematics. Women with the fragile X premutation often give a history of mathematics difficulties in themselves especially with higher level math. In order to evaluate whether women with the premutation have difficulty with math, we asked women with both the fragile X premutation and full mutation to complete the Wide Range Achievement Test-3. For the group of 39 women with the fragile X premutation, the median standard score on the Arithmetic portion was 93, which was significantly lower (P = 0.001) than the median of the standardized norm of 100. Only nine of the women had Arithmetic scores at or above the 50th centile, while over half of the women had standard scores at or above the 50th centile in Reading and Spelling. The eight women with the full mutation also had lower Arithmetic scores than Reading and Spelling scores. These data suggest that mathematics may be an area of relative weakness for the women with the premutation as well as the full mutation. This possibility should be evaluated further by using other measures. This information is important both for counseling purposes and to understand whether a mathematics deficit is evidence of low expression of the FMR1 gene in the premutation state.
Arabidopsis plants perform arithmetic division to prevent starvation at night
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
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 +…
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. PMID:24128690
Spectral Investigation of Binary Asteroids
NASA Astrophysics Data System (ADS)
Birlan, Mirel; Nedelcu, D.; Descamps, P.; Berthier, J.; Marchis, F.; Merouane, S.
2008-09-01
The number of binary asteroids increased in a significant manner during the last years. Multiple types of observations obtained in adaptive optics, photometry, and radar, allow the rethinking not only the dynamics of the asteroids, but also their physics. The spectroscopy of a binary system can play a key role for establish the mineralogical composition of components, and implicitly the range of their density. By the application of these considerations to the physical and dynamical models, the physical parameters such as the macro-porosity or the "rubble pile” structures could be derived. Observations of binary asteroid (854) Frostia, and binary candidates (1333) Cevenola, and (3632) Chaplin were carried out in the 0.8-2.5 µm spectral range using SpeX/IRTF in LowRes mode. The asteroids present features in both 1 and 2 µm regions, suggesting the presence of silicates in the surface composition. The analysis of slopes, band strengths, and the most probable mineralogical models will be presented.
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
Number word structure in first and second language influences arithmetic skills
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
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.
Rinne, Luke F; Mazzocco, Michèle M M
2014-01-01
Does knowing when mental arithmetic judgments are right--and when they are wrong--lead to more accurate judgments over time? We hypothesize that the successful detection of errors (and avoidance of false alarms) may contribute to the development of mental arithmetic performance. Insight into error detection abilities can be gained by examining the "calibration" of mental arithmetic judgments-that is, the alignment between confidence in judgments and the accuracy of those judgments. Calibration may be viewed as a measure of metacognitive monitoring ability. We conducted a developmental longitudinal investigation of the relationship between the calibration of children's mental arithmetic judgments and their performance on a mental arithmetic task. Annually between Grades 5 and 8, children completed a problem verification task in which they rapidly judged the accuracy of arithmetic expressions (e.g., 25 + 50 = 75) and rated their confidence in each judgment. Results showed that calibration was strongly related to concurrent mental arithmetic performance, that calibration continued to develop even as mental arithmetic accuracy approached ceiling, that poor calibration distinguished children with mathematics learning disability from both low and typically achieving children, and that better calibration in Grade 5 predicted larger gains in mental arithmetic accuracy between Grades 5 and 8. We propose that good calibration supports the implementation of cognitive control, leading to long-term improvement in mental arithmetic accuracy. Because mental arithmetic "fluency" is critical for higher-level mathematics competence, calibration of confidence in mental arithmetic judgments may represent a novel and important developmental predictor of future mathematics performance. PMID:24988539
Rinne, Luke F.; Mazzocco, Michèle M. M.
2014-01-01
Does knowing when mental arithmetic judgments are right—and when they are wrong—lead to more accurate judgments over time? We hypothesize that the successful detection of errors (and avoidance of false alarms) may contribute to the development of mental arithmetic performance. Insight into error detection abilities can be gained by examining the “calibration” of mental arithmetic judgments—that is, the alignment between confidence in judgments and the accuracy of those judgments. Calibration may be viewed as a measure of metacognitive monitoring ability. We conducted a developmental longitudinal investigation of the relationship between the calibration of children's mental arithmetic judgments and their performance on a mental arithmetic task. Annually between Grades 5 and 8, children completed a problem verification task in which they rapidly judged the accuracy of arithmetic expressions (e.g., 25+50 = 75) and rated their confidence in each judgment. Results showed that calibration was strongly related to concurrent mental arithmetic performance, that calibration continued to develop even as mental arithmetic accuracy approached ceiling, that poor calibration distinguished children with mathematics learning disability from both low and typically achieving children, and that better calibration in Grade 5 predicted larger gains in mental arithmetic accuracy between Grades 5 and 8. We propose that good calibration supports the implementation of cognitive control, leading to long-term improvement in mental arithmetic accuracy. Because mental arithmetic “fluency” is critical for higher-level mathematics competence, calibration of confidence in mental arithmetic judgments may represent a novel and important developmental predictor of future mathematics performance. PMID:24988539
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.
Oscillatory EEG Correlates of Arithmetic Strategies: A Training Study
Grabner, Roland H.; De Smedt, Bert
2012-01-01
There has been a long tradition of research on mathematics education showing that children and adults use different strategies to solve arithmetic problems. Neurophysiological studies have recently begun to investigate the brain correlates of these strategies. The existing body of data, however, reflect static end points of the learning process and do not provide information on how brain activity changes in response to training or intervention. In this study, we explicitly address this issue by training participants in using fact retrieval strategies. We also investigate whether brain activity related to arithmetic fact learning is domain-specific or whether this generalizes to other learning materials, such as the solution of figural-spatial problems. Twenty adult students were trained on sets of two-digit multiplication problems and figural-spatial problems. After the training, they were presented with the trained and untrained problems while their brain activity was recorded by means of electroencephalography (EEG). In both problem types, the training resulted in accuracies over 90% and significant decreases in solution times. Analyses of the oscillatory EEG data also revealed training effects across both problem types. Specifically, we observed training-related activity increases in the theta band (3–6 Hz) and decreases in the lower alpha band (8–10 Hz), especially over parietooccipital and parietal brain regions. These results provide the first evidence that a short-term fact retrieval training results in significant changes in oscillatory EEG activity. These findings further corroborate the role of the theta band in the retrieval of semantic information from memory and suggest that theta activity is sensitive to fact retrieval not only in mental arithmetic but also in other domains. PMID:23162495
Oscillatory EEG correlates of arithmetic strategies: a training study.
Grabner, Roland H; De Smedt, Bert
2012-01-01
There has been a long tradition of research on mathematics education showing that children and adults use different strategies to solve arithmetic problems. Neurophysiological studies have recently begun to investigate the brain correlates of these strategies. The existing body of data, however, reflect static end points of the learning process and do not provide information on how brain activity changes in response to training or intervention. In this study, we explicitly address this issue by training participants in using fact retrieval strategies. We also investigate whether brain activity related to arithmetic fact learning is domain-specific or whether this generalizes to other learning materials, such as the solution of figural-spatial problems. Twenty adult students were trained on sets of two-digit multiplication problems and figural-spatial problems. After the training, they were presented with the trained and untrained problems while their brain activity was recorded by means of electroencephalography (EEG). In both problem types, the training resulted in accuracies over 90% and significant decreases in solution times. Analyses of the oscillatory EEG data also revealed training effects across both problem types. Specifically, we observed training-related activity increases in the theta band (3-6 Hz) and decreases in the lower alpha band (8-10 Hz), especially over parietooccipital and parietal brain regions. These results provide the first evidence that a short-term fact retrieval training results in significant changes in oscillatory EEG activity. These findings further corroborate the role of the theta band in the retrieval of semantic information from memory and suggest that theta activity is sensitive to fact retrieval not only in mental arithmetic but also in other domains.
Quantum error correcting codes and 4-dimensional arithmetic hyperbolic manifolds
NASA Astrophysics Data System (ADS)
Guth, Larry; Lubotzky, Alexander
2014-08-01
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 nɛ. Their rate is evaluated via Euler characteristic arguments and their distance using {Z}_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),
A real time correlator architecture using distributed arithmetic principles
NASA Technical Reports Server (NTRS)
Premkumar, A. Benjamin; Srikanthan, T.
1992-01-01
A real time correlator design based on the principles of Distributed Arithmetic (DA) is described. This design is shown to be more efficient in terms of memory requirement than the direct DA implementation, especially when the number of coefficients is large. Since the proposed architecture implements the sum of product evaluation, it can be easily extended to finite and infinite response filters. Methods to further reduce the memory requirements are also discussed. A brief comparison is made between the proposed method and different DA implementations.
Arithmetic coding as a non-linear dynamical system
NASA Astrophysics Data System (ADS)
Nagaraj, Nithin; Vaidya, Prabhakar G.; Bhat, Kishor G.
2009-04-01
In order to perform source coding (data compression), we treat messages emitted by independent and identically distributed sources as imprecise measurements (symbolic sequence) of a chaotic, ergodic, Lebesgue measure preserving, non-linear dynamical system known as Generalized Luröth Series (GLS). GLS achieves Shannon's entropy bound and turns out to be a generalization of arithmetic coding, a popular source coding algorithm, used in international compression standards such as JPEG2000 and H.264. We further generalize GLS to piecewise non-linear maps (Skewed-nGLS). We motivate the use of Skewed-nGLS as a framework for joint source coding and encryption.
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.
Quantum error correcting codes and 4-dimensional arithmetic hyperbolic manifolds
Guth, Larry; Lubotzky, Alexander
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.
Strategy-Enhanced Interactive Proving and Arithmetic Simplification for PVS
NASA Technical Reports Server (NTRS)
diVito, Ben L.
2003-01-01
We describe an approach to strategy-based proving for improved interactive deduction in specialized domains. An experimental package of strategies (tactics) and support functions called Manip has been developed for PVS to reduce the tedium of arithmetic manipulation. Included are strategies aimed at algebraic simplification of real-valued expressions. A general deduction architecture is described in which domain-specific strategies, such as those for algebraic manipulation, are supported by more generic features, such as term-access techniques applicable in arbitrary settings. An extended expression language provides access to subterms within a sequent.
Binary mask programmable hologram.
Tsang, P W M; Poon, T-C; Zhou, Changhe; Cheung, K W K
2012-11-19
We report, for the first time, the concept and generation of a novel Fresnel hologram called the digital binary mask programmable hologram (BMPH). A BMPH is comprised of a static, high resolution binary grating that is overlaid with a lower resolution binary mask. The reconstructed image of the BMPH can be programmed to approximate a target image (including both intensity and depth information) by configuring the pattern of the binary mask with a simple genetic algorithm (SGA). As the low resolution binary mask can be realized with less stringent display technology, our method enables the development of simple and economical holographic video display.
NASA Astrophysics Data System (ADS)
Noll, Keith S.; Grundy, W. M.; Ryan, E. L.; Benecchi, S. D.
2015-11-01
We have reexamined 41 Trojan asteroids observed with the Hubble Space Telescope (HST) to search for unresolved binaries. We have identified one candidate binary with a separation of 53 milliarcsec, about the width of the diffraction limited point-spread function (PSF). Sub-resolution-element detection of binaries is possible with HST because of the high signal-to-noise ratio of the observations and the stability of the PSF. Identification and confirmation of binary Trojans is important because a Trojan Tour is one of five possible New Frontiers missions. A binary could constitute a potentially high value target because of the opportunity to study two objects and to test models of the primordial nature of binaries. The potential to derive mass-based physical information from the binary orbit could yield more clues to the origin of Trojans.
Why are pharmacokinetic data summarized by arithmetic means?
Julious, S A; Debarnot, C A
2000-02-01
The main aim of many studies in clinical pharmacology is to describe the pharmacokinetic activity of a given compound. This pharmacokinetic activity for an individual is then evaluated through a series of summary parameters, such as area under the concentration-time curve (AUC), maximum concentration (Cmax) and the rate constant lambda, and it is evaluated across individuals by descriptive statistics of these parameters, such as the mean and range and a measure of spread such as the standard deviation. How the pharmacokinetic parameters are derived is described here. It is demonstrated that the assumption of an exponential half-life is often fundamental to the derivation of pharmacokinetic parameters. Given this fact, one would think it logical that data are analyzed with the appropriate statistics on the log-scale and not by summary statistics, such as arithmetic means, on the original scale. Why arithmetic means are used to describe the data is explored and the special nature of the log-transformation highlighted. PMID:10709801
Working memory failures in children with arithmetical difficulties.
Passolunghi, Maria Chiara; Cornoldi, Cesare
2008-09-01
A large body of literature has examined the relationship between working memory and arithmetic achievement, but results are still ambiguous. To examine this relationship, we compared the performance of third and fifth graders with arithmetic difficulties (AD) and controls of the same age, grade, and verbal intelligence on a battery of working memory tasks, differentiating between different aspects of working memory. Children with AD scored significantly lower on active working memory tasks requiring manipulation of the to-be-recalled information (Listening Completion task, Corsi Span Backwards, Digit Backwards), but not in passive working memory tasks, requiring the recall of information in the same format in which it had been presented (Digit, Word, and Corsi Forwards Span tasks), nor in tasks involving word processing (word articulation rate, forwards and backwards word spans). A regression analysis showed that the best predictors of differences between AD children and the control group were the Corsi Span Backwards, the Listening Completion task, and the rate of articulation of pseudowords. The analysis of strategies used by children in mental calculation revealed the greater tendency of children with AD to rely on more primitive strategies: finger use never appeared as the most frequent strategy in skilled children, whereas it was the most used strategy in children with AD. Verbal and visual strategies appeared associated with successful performance in third graders, but in fifth grade, the most successful strategy was verbalization. PMID:18608224
Why are pharmacokinetic data summarized by arithmetic means?
Julious, S A; Debarnot, C A
2000-02-01
The main aim of many studies in clinical pharmacology is to describe the pharmacokinetic activity of a given compound. This pharmacokinetic activity for an individual is then evaluated through a series of summary parameters, such as area under the concentration-time curve (AUC), maximum concentration (Cmax) and the rate constant lambda, and it is evaluated across individuals by descriptive statistics of these parameters, such as the mean and range and a measure of spread such as the standard deviation. How the pharmacokinetic parameters are derived is described here. It is demonstrated that the assumption of an exponential half-life is often fundamental to the derivation of pharmacokinetic parameters. Given this fact, one would think it logical that data are analyzed with the appropriate statistics on the log-scale and not by summary statistics, such as arithmetic means, on the original scale. Why arithmetic means are used to describe the data is explored and the special nature of the log-transformation highlighted.
PHOEBE: PHysics Of Eclipsing BinariEs
NASA Astrophysics Data System (ADS)
Prsa, Andrej; Matijevic, Gal; Latkovic, Olivera; Vilardell, Francesc; Wils, Patrick
2011-06-01
PHOEBE (PHysics Of Eclipsing BinariEs) is a modeling package for eclipsing binary stars, built on top of the widely used WD program (Wilson & Devinney 1971). This introductory paper overviews most important scientific extensions (incorporating observational spectra of eclipsing binaries into the solution-seeking process, extracting individual temperatures from observed color indices, main-sequence constraining and proper treatment of the reddening), numerical innovations (suggested improvements to WD's Differential Corrections method, the new Nelder & Mead's downhill Simplex method) and technical aspects (back-end scripter structure, graphical user interface). While PHOEBE retains 100% WD compatibility, its add-ons are a powerful way to enhance WD by encompassing even more physics and solution reliability.
On the Arithmetization of School Geometry in the Setting of Modern Axiomatics.
ERIC Educational Resources Information Center
Patronis, Tasos; Thomaidis, Yannis
1997-01-01
Analyzes the arithmetized geometry from a semantical point of view and compares it with classical synthetic exposition of school geometry. Also analyzes the didactical use of one particular system of arithmetized geometry--namely Pogorelov's system--in the Greek Lyceum. Contains 33 references. (Author/JRH)
Relationship of Bender Memory to Achievement in Arithmetic by First Graders.
ERIC Educational Resources Information Center
Snyder, Robert T.; And Others
1980-01-01
Arithmetic and reading achievement scores of 84 children were correlated with power and precision of Bender Memory using the Bender Visual Memory Technique (BVMT). Of the 20 correlations, 16 were significant. Support for recommended use of the BVMT as a screening instrument for early assessment of arithmetic skill is provided. (Author/SJL)
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…
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)…
Early Number and Arithmetic Performance of Ecuadorian 4-5-Year-Olds
ERIC Educational Resources Information Center
Bojorque, Gina; Torbeyns, Joke; Moscoso, Jheni; Van Nijlen, Daniël; Verschaffel, Lieven
2015-01-01
This study aimed at (a) constructing a reliable and valid test to assess Ecuadorian 4-5-year olds' number and arithmetic skills; (b) providing empirical data on Ecuadorian 4-5-year olds' number and arithmetic skills; and (c) confronting these children's actual performances with the performances expected by national experts in this domain. We…
A library for prototyping the computer arithmetic level in elliptic curve cryptography
NASA Astrophysics Data System (ADS)
Imbert, Laurent; Peirera, Agostinho; Tisserand, Arnaud
2007-09-01
This paper presents the first version of a software library called PACE ("Prototyping Arithmetic in Cryptography Easily"). This is a C++ library under LGPL license. It provides number systems and algorithms for prototyping the arithmetic layer in cryptographic applications. The first version of PACE includes basic support of prime finite fields and ECC (Elliptic Curve Cryptography) basic algorithms for software implementations.
Spontaneous Meta-Arithmetic as the First Step toward School Algebra
ERIC Educational Resources Information Center
Caspi, Shai; Sfard, Anna
2012-01-01
Taking as a point of departure the vision of school algebra as a formalized meta-discourse of arithmetic, we have been following six pairs of 7th-grade students (12-13 years old) as they gradually modify their spontaneous meta-arithmetic toward the "official" algebraic form of talk. In this paper we take a look at the very beginning of…
Developmental Changes in the Use of Logical Principles in Mental Arithmetic.
ERIC Educational Resources Information Center
Bisanz, Jeffrey; And Others
Because little is presently known about changes in children's knowledge of the logical principles of arithmetic and, more specifically, about how children's developing knowledge is reflected in the use of solution procedures, two types of three-term arithmetic problems were presented for solution to 6-, 7-, 9-, 11-, and 20-year-olds. Problems were…
ERIC Educational Resources Information Center
Weinstein, Lawrence; Laverghetta, Antonio
2009-01-01
Undergraduate and graduate students at Cameron University (N = 158) were given the D'Amore Test of Elementary Arithmetic to test whether or not experience in college mathematics courses might be associated with a relative increase in arithmetic performance compared to those students who had not taken college mathematics courses. We found that only…
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…
Design and Analysis of Fast Text Compression Based on Quasi-Arithmetic Coding.
ERIC Educational Resources Information Center
Howard, Paul G; Vitter, Jeffrey Scott
1994-01-01
Describes a detailed algorithm for fast text compression. Related to the PPM (prediction by partial matching) method, it simplifies the modeling phase by eliminating the escape mechanism and speeds up coding by using a combination of quasi-arithmetic coding and Rice coding. Details of the use of quasi-arithmetic code tables are given, and their…
Application of Schema Theory to the Instruction of Arithmetic Word Problem Solving Skills.
ERIC Educational Resources Information Center
Tsai, Chia-jer; Derry, Sharon J.
An understanding-based approach to teaching arithmetic word problems is used in the Training Arithmetic Problem Solving Skills (TAPS) research project, for which four semantic schemas or problem representations have been revised and adopted: Combine, Compare, Change, and Vary. It is hypothesized that a good problem solver identifies the schema of…
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…
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…
The Impact of Different Teaching Methods on Students' Arithmetic and Self-Regulated Learning Skills
ERIC Educational Resources Information Center
Samuelsson, Joakim
2008-01-01
The present study examines the effect of three different structured methods, traditional, independent and problem-solving, of teaching children arithmetic in the beginning of 7th grade in Sweden, age 13 years. The progress made by these students is presented by measures of their arithmetic ability, calculation and quantitative concept, as well as…
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…
Salillas, Elena; Wicha, Nicole Y Y
2012-07-01
Language and math are intertwined during children's learning of arithmetic concepts, but the importance of language in adult arithmetic processing is less clear. To determine whether early learning plays a critical role in the math-language connection in adults, we tested retrieval of simple multiplication in adult bilinguals who learned arithmetic in only one language. We measured electrophysiological and behavioral responses during correctness judgments for problems presented as digits or as number words in Spanish or English. Problems presented in the language in which participants learned arithmetic elicited larger, more graded, and qualitatively different brain responses than did problems presented in participants' other language, and these responses more closely resembled responses for digits, even when participants' other language was more dominant. These findings suggest that the memory networks for simple multiplication are established when arithmetic concepts are first learned and are independent of language dominance in adulthood. PMID:22707225
Variable-Precision Arithmetic for Solving Inverse Problems of Electrical Impedance Tomography
Tian, H.; Yamada, S.; Iwahara, M.; Yang, H.
2005-04-09
Electrical Impedance Tomography (EIT) is a nondestructive imaging technique, which reconstructs the electrical characteristic tomographys by electrical measurement on the periphery of objects. EIT approximates the spatial distribution of impedance (or conductivity) within the detected objects via employing data of injected electrical currents and boundary electrical potentials. This technique would be used for detecting flaws inside metal materials or providing medical images. In theory EIT belongs to inverse problems of low frequency current field and its reconstruction calculation suffers from ill-posed nonlinear nature. This paper presents variable-precision arithmetic is effective to improve the precision of conventional finite-difference in Newton's method. Comparing with exact symbolic arithmetic and floating-point arithmetic, variable-precision arithmetic achieves a good tradeoff between accuracy and complexity of computing. The simulation results have illustrated that variable-precision arithmetic is valid for solving inverse problems of EIT.
Teachers’ Beliefs and Practices Regarding the Role of Executive Functions in Reading and Arithmetic
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
Salillas, Elena; Wicha, Nicole Y Y
2012-07-01
Language and math are intertwined during children's learning of arithmetic concepts, but the importance of language in adult arithmetic processing is less clear. To determine whether early learning plays a critical role in the math-language connection in adults, we tested retrieval of simple multiplication in adult bilinguals who learned arithmetic in only one language. We measured electrophysiological and behavioral responses during correctness judgments for problems presented as digits or as number words in Spanish or English. Problems presented in the language in which participants learned arithmetic elicited larger, more graded, and qualitatively different brain responses than did problems presented in participants' other language, and these responses more closely resembled responses for digits, even when participants' other language was more dominant. These findings suggest that the memory networks for simple multiplication are established when arithmetic concepts are first learned and are independent of language dominance in adulthood.
Quantifying the Impact of Single Bit Flips on Floating Point Arithmetic
Elliott, James J; Mueller, Frank; Stoyanov, Miroslav K; Webster, Clayton G
2013-08-01
In high-end computing, the collective surface area, smaller fabrication sizes, and increasing density of components have led to an increase in the number of observed bit flips. If mechanisms are not in place to detect them, such flips produce silent errors, i.e. the code returns a result that deviates from the desired solution by more than the allowed tolerance and the discrepancy cannot be distinguished from the standard numerical error associated with the algorithm. These phenomena are believed to occur more frequently in DRAM, but logic gates, arithmetic units, and other circuits are also susceptible to bit flips. Previous work has focused on algorithmic techniques for detecting and correcting bit flips in specific data structures, however, they suffer from lack of generality and often times cannot be implemented in heterogeneous computing environment. Our work takes a novel approach to this problem. We focus on quantifying the impact of a single bit flip on specific floating-point operations. We analyze the error induced by flipping specific bits in the most widely used IEEE floating-point representation in an architecture-agnostic manner, i.e., without requiring proprietary information such as bit flip rates and the vendor-specific circuit designs. We initially study dot products of vectors and demonstrate that not all bit flips create a large error and, more importantly, expected value of the relative magnitude of the error is very sensitive on the bit pattern of the binary representation of the exponent, which strongly depends on scaling. Our results are derived analytically and then verified experimentally with Monte Carlo sampling of random vectors. Furthermore, we consider the natural resilience properties of solvers based on the fixed point iteration and we demonstrate how the resilience of the Jacobi method for linear equations can be significantly improved by rescaling the associated matrix.
All optical binary delta-sigma modulator
NASA Astrophysics Data System (ADS)
Sayeh, Mohammad R.; Siahmakoun, Azad
2005-09-01
This paper describes a novel A/D converter called "Binary Delta-Sigma Modulator" (BDSM) which operates only with nonnegative signal with positive feedback and binary threshold. This important modification to the conventional delta-sigma modulator makes the high-speed (>100GHz) all-optical implementation possible. It has also the capability to modify its own sampling frequency as well as its input dynamic range. This adaptive feature helps designers to optimize the system performance under highly noisy environment and also manage the power consumption of the A/D converters.
ERIC Educational Resources Information Center
KLAUSMEIER, HERBERT J.; AND OTHERS
A COMPARISON OF THE LEARNING EFFICIENCY IN ARITHMETIC OF MENTALLY RETARDED CHILDREN AND CHILDREN OF AVERAGE AND HIGH INTELLIGENCE WAS MADE. THIS STUDY TESTED FIVE HYPOTHESES--(1) UNEVEN PHYSICAL GROWTH ACCOMPANIES LOW EFFICIENCY IN LEARNING ARITHMETIC, (2) SLOW PHYSICAL GROWTH ACCOMPANIES LOW EFFICIENCY IN LEARNING ARITHMETIC, (3) THE LEVEL OF…
Modeling Brain Responses in an Arithmetic Working Memory Task
NASA Astrophysics Data System (ADS)
Hamid, Aini Ismafairus Abd; Yusoff, Ahmad Nazlim; Mukari, Siti Zamratol-Mai Sarah; Mohamad, Mazlyfarina; Manan, Hanani Abdul; Hamid, Khairiah Abdul
2010-07-01
Functional magnetic resonance imaging (fMRI) was used to investigate brain responses due to arithmetic working memory. Nine healthy young male subjects were given simple addition and subtraction instructions in noise and in quiet. The general linear model (GLM) and random field theory (RFT) were implemented in modelling the activation. The results showed that addition and subtraction evoked bilateral activation in Heschl's gyrus (HG), superior temporal gyrus (STG), inferior frontal gyrus (IFG), supramarginal gyrus (SG) and precentral gyrus (PCG). The HG, STG, SG and PCG activate higher number of voxels in noise as compared to in quiet for addition and subtraction except for IFG that showed otherwise. The percentage of signal change (PSC) in all areas is higher in quiet as compared to in noise. Surprisingly addition (not subtraction) exhibits stronger activation.
Can business and economics students perform elementary arithmetic?
Standing, Lionel G; Sproule, Robert A; Leung, Ambrose
2006-04-01
Business and economics majors (N=146) were tested on the D'Amore Test of Elementary Arithmetic, which employs third-grade test items from 1932. Only 40% of the subjects passed the test by answering 10 out of 10 items correctly. Self-predicted scores were a good predictor of actual scores, but performance was not associated with demographic variables, grades in calculus courses, liking for science or computers, or mathematics anxiety. Scores decreased over the subjects' initial years on campus. The hardest test item, with an error rate of 23%, required the subject to evaluate (36 x 7) + (33 x 7). The results are similar to those of Standing in 2006, despite methodological changes intended to maximize performance.
Arithmetic and local circuitry underlying dopamine prediction errors
Eshel, Neir; Bukwich, Michael; Rao, Vinod; Hemmelder, Vivian; Tian, Ju; Uchida, Naoshige
2015-01-01
Dopamine neurons are thought to facilitate learning by comparing actual and expected reward1,2. Despite two decades of investigation, little is known about how this comparison is made. To determine how dopamine neurons calculate prediction error, we combined optogenetic manipulations with extracellular recordings in the ventral tegmental area (VTA) while mice engaged in classical conditioning. By manipulating the temporal expectation of reward, we demonstrate that dopamine neurons perform subtraction, a computation that is ideal for reinforcement learning but rarely observed in the brain. Furthermore, selectively exciting and inhibiting neighbouring GABA neurons in the VTA reveals that these neurons are a source of subtraction: they inhibit dopamine neurons when reward is expected, causally contributing to prediction error calculations. Finally, bilaterally stimulating VTA GABA neurons dramatically reduces anticipatory licking to conditioned odours, consistent with an important role for these neurons in reinforcement learning. Together, our results uncover the arithmetic and local circuitry underlying dopamine prediction errors. PMID:26322583
Short-term memory impairment and arithmetical ability.
Butterworth, B; Cipolotti, L; Warrington, E K
1996-02-01
We document the dissociation of preserved calculation skills in a patient with impaired auditory short-term memory. The patient (MRF) had a memory span of three digits. Furthermore, he showed rapid decrement in performance of single digits and letters with both auditory and visual presentation in the Brown-Peterson forgetting task. Analysis of his calculation skills revealed a normal ability to solve auditorily presented multidigit addition and subtraction problems such as 173 + 68 and to execute the Paced Auditory Serial Addition Task (Sampson, 1956, 1958; Gronwall, 1977). In addition, his performance on other tests, including arithmetic manipulation of natural numbers, decimals and fractions, approximation, magnitude, ratio, and percentage, appeared to be normal (Hitch, 1978b). It is argued that these findings require a revision of Baddeley and Hitch's (1974) concept of the function of working memory. PMID:8920104
Development of ferrite logic devices for an arithmetic processor
NASA Technical Reports Server (NTRS)
Heckler, C. H., Jr.
1972-01-01
A number of fundamentally ultra-reliable, all-magnetic logic circuits are developed using as a basis a single element ferrite structure wired as a logic delay element. By making minor additions or changes to the basic wiring pattern of the delay element other logic functions such as OR, AND, NEGATION, MAJORITY, EXCLUSIVE-OR, and FAN-OUT are developed. These logic functions are then used in the design of a full-adder, a set/reset flip-flop, and an edge detector. As a demonstration of the utility of all the developed devices, an 8-bit, all-magnetic, logic arithmetic unit capable of controlled addition, subtraction, and multiplication is designed. A new basic ferrite logic element and associated complementary logic scheme with the potential of improved performance is also described. Finally, an improved batch process for fabricating joint-free power drive and logic interconnect conductors for this basic class of all-magnetic logic is presented.
Arithmetic and local circuitry underlying dopamine prediction errors.
Eshel, Neir; Bukwich, Michael; Rao, Vinod; Hemmelder, Vivian; Tian, Ju; Uchida, Naoshige
2015-09-10
Dopamine neurons are thought to facilitate learning by comparing actual and expected reward. Despite two decades of investigation, little is known about how this comparison is made. To determine how dopamine neurons calculate prediction error, we combined optogenetic manipulations with extracellular recordings in the ventral tegmental area while mice engaged in classical conditioning. Here we demonstrate, by manipulating the temporal expectation of reward, that dopamine neurons perform subtraction, a computation that is ideal for reinforcement learning but rarely observed in the brain. Furthermore, selectively exciting and inhibiting neighbouring GABA (γ-aminobutyric acid) neurons in the ventral tegmental area reveals that these neurons are a source of subtraction: they inhibit dopamine neurons when reward is expected, causally contributing to prediction-error calculations. Finally, bilaterally stimulating ventral tegmental area GABA neurons dramatically reduces anticipatory licking to conditioned odours, consistent with an important role for these neurons in reinforcement learning. Together, our results uncover the arithmetic and local circuitry underlying dopamine prediction errors.
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
Neighborhood consistency in mental arithmetic: Behavioral and ERP evidence
Domahs, Frank; Domahs, Ulrike; Schlesewsky, Matthias; Ratinckx, Elie; Verguts, Tom; Willmes, Klaus; Nuerk, Hans-Christoph
2007-01-01
Background Recent cognitive and computational models (e.g. the Interacting Neighbors Model) state that in simple multiplication decade and unit digits of the candidate answers (including the correct result) are represented separately. Thus, these models challenge holistic views of number representation as well as traditional accounts of the classical problem size effect in simple arithmetic (i.e. the finding that large problems are answered slower and less accurate than small problems). Empirical data supporting this view are still scarce. Methods Data of 24 participants who performed a multiplication verification task with Arabic digits (e.g. 8 × 4 = 36 - true or false?) are reported. Behavioral (i.e. RT and errors) and EEG (i.e. ERP) measures were recorded in parallel. Results We provide evidence for neighborhood-consistency effects in the verification of simple multiplication problems (e.g. 8 × 4). Behaviorally, we find that decade-consistent lures, which share their decade digit with the correct result (e.g. 36), are harder to reject than matched inconsistent lures, which differ in both digits from the correct result (e.g. 28). This neighborhood consistency effect in product verification is similar to recent observations in the production of multiplication results. With respect to event-related potentials we find significant differences for consistent compared to inconsistent lures in the N400 (increased negativity) and Late Positive Component (reduced positivity). In this respect consistency effects in our paradigm resemble lexico-semantic effects earlier found in simple arithmetic and in orthographic input processing. Conclusion Our data suggest that neighborhood consistency effects in simple multiplication stem at least partly from central (lexico-semantic') stages of processing. These results are compatible with current models on the representation of simple multiplication facts – in particular with the Interacting Neighbors Model – and with the
Practical Algorithm For Computing The 2-D Arithmetic Fourier Transform
NASA Astrophysics Data System (ADS)
Reed, Irving S.; Choi, Y. Y.; Yu, Xiaoli
1989-05-01
Recently, Tufts and Sadasiv [10] exposed a method for computing the coefficients of a Fourier series of a periodic function using the Mobius inversion of series. They called this method of analysis the Arithmetic Fourier Transform(AFT). The advantage of the AFT over the FN 1' is that this method of Fourier analysis needs only addition operations except for multiplications by scale factors at one stage of the computation. The disadvantage of the AFT as they expressed it originally is that it could be used effectively only to compute finite Fourier coefficients of a real even function. To remedy this the AFT developed in [10] is extended in [11] to compute the Fourier coefficients of both the even and odd components of a periodic function. In this paper, the improved AFT [11] is extended to a two-dimensional(2-D) Arithmetic Fourier Transform for calculating the Fourier Transform of two-dimensional discrete signals. This new algorithm is based on both the number-theoretic method of Mobius inversion of double series and the complex conjugate property of Fourier coefficients. The advantage of this algorithm over the conventional 2-D FFT is that the corner-turning problem needed in a conventional 2-D Discrete Fourier Transform(DFT) can be avoided. Therefore, this new 2-D algorithm is readily suitable for VLSI implementation as a parallel architecture. Comparing the operations of 2-D AFT of a MxM 2-D data array with the conventional 2-D FFT, the number of multiplications is significantly reduced from (2log2M)M2 to (9/4)M2. Hence, this new algorithm is faster than the FFT algorithm. Finally, two simulation results of this new 2-D AFT algorithm for 2-D artificial and real images are given in this paper.
García, Ana I; Jiménez, Juan E; Hess, Stephany
2006-01-01
This study was designed to determine a word problem difficulty classification in children with arithmetic learning disabilities (ALD; n = 104) in comparison with typically achieving students (n = 44). We tested variables such as (a) semantic structure (Change, Combine, Compare, and Equalize), (b) operation (subtraction and addition), and (c) position of the unknown quantity in the problem. Facet theory with multidimensional scaling techniques (MINISSA) was used to analyze the underlying dimensions in the responses of each group of participants. Our results indicate that although the word problem difficulty classifications for the 2 groups of children were different, the position of the unknown quantity had a greater influence on the level of difficulty of story problems than other variables. The noncanonical problems--specifically, those with the unknown term in the first place--although difficult for both groups of children, were the most difficult problems for children with ALD.
Are Individual Differences in Arithmetic Fact Retrieval in Children Related to Inhibition?
Bellon, Elien; Fias, Wim; De Smedt, Bert
2016-01-01
Although it has been proposed that inhibition is related to individual differences in mathematical achievement, it is not clear how it is related to specific aspects of mathematical skills, such as arithmetic fact retrieval. The present study therefore investigated the association between inhibition and arithmetic fact retrieval and further examined the unique role of inhibition in individual differences in arithmetic fact retrieval, in addition to numerical magnitude processing. We administered measures of cognitive inhibition (i.e., numerical and non-numerical stroop tasks) and a complementary, more ecologically valid measure of children’s inhibition in the classroom (i.e., teacher questionnaire), as well as numerical magnitude processing (i.e., symbolic and non-symbolic numerical magnitude comparison) and arithmetic fact retrieval (i.e., two verification tasks) in 86 typically developing third graders. We used a correlation, a regression and a Bayesian analysis. This study failed to observe a significant association between inhibition and arithmetic fact retrieval. Consequently, our results did not reveal a unique contribution of inhibition to arithmetic fact retrieval in addition to numerical magnitude processing. On the other hand, symbolic numerical magnitude processing turned out to be a very powerful predictor of arithmetic fact retrieval, as indicated by both frequentist and Bayesian approaches. PMID:27378961
Prieto-Corona, Belén; Rodríguez-Camacho, Mario; Silva-Pereyra, Juan; Marosi, Erzsébet; Fernández, Thalía; Guerrero, Vicente
2010-01-14
Some cognitive abilities of arithmetical calculation depend on retrieval of arithmetic facts from long-term memory. Arithmetic-fact retrieval has been studied in adults through Event-Related Potentials (ERP) experiments. Such information in children, however, has been scarce. It has been reported that from the age of 9 years, children employ a memory retrieval strategy for solving simple multiplication problems. The present study compared arithmetical-fact retrieval in children and adults while they were being subjected to ERP recording. The subjects were asked to make judgments about solutions to simple multiplication problems. Both groups of participants displayed the so-called arithmetic N400 effect for incorrect solutions relative to correct solutions. Adults showed a posterior N400 effect, while children showed a widely distributed N400 effect. Children displayed a larger amplitude and longer latency arithmetic N400 component than adults; this observation could be due to children exerting greater effort involving more widespread cortical activation than adults to solve the experimental problems. The Late Positive Component (LPC), which follows the arithmetic N400 and has been described previously in adult subjects, was observed in the present adult subjects, but was present in children only for correct solutions. These results may indicate that, relative to adults, children showed slower memory retrieval and a different pattern of a verification mechanism for correct and incorrect solutions. PMID:19897015
How is phonological processing related to individual differences in children's arithmetic skills?
De Smedt, Bert; Taylor, Jessica; Archibald, Lisa; Ansari, Daniel
2010-05-01
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 hypothesis that there exists a highly specific association between phonological awareness and single-digit arithmetic with relatively small problem sizes. The present study examined this association in 37 typically developing fourth and fifth grade children. Regression analyses revealed that phonological awareness was specifically and uniquely related to arithmetic problems with a small but not large problem size. Further analysis indicated that problems with a high probability of being solved by retrieval, but not those typically associated with procedural problem-solving strategies, are correlated with phonological awareness. The specific association between phonological awareness and arithmetic problems with a small problem size and those for which a retrieval strategy is most common was maintained even after controlling for general reading ability and phonological short-term memory. The present findings indicate that the quality of children's long-term phonological representations mediates individual differences in single-digit arithmetic, suggesting that more distinct long-term phonological representations are related to more efficient arithmetic fact retrieval.
Hybrid black-hole binary initial data
NASA Astrophysics Data System (ADS)
Mundim, Bruno; Kelly, Bernard; Zlochower, Yosef; Nakano, Hiroyuki; Campanelli, Manuela
2011-04-01
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.Quant.Grav.27:114005,2010], a new binary black-hole initial data with radiation contents derived in the post-Newtonian (PN) calculation 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. Thanks NSF and NASA for support.
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."
Orbital motion in pre-main sequence binaries
Schaefer, G. H.; Prato, L.; Simon, M.; Patience, J.
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 other 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.
Micheloyannis, Sifis; Papanikolaou, Elias; Bizas, Emmanuel; Stam, Cornelis J; Simos, Panagiotis G
2002-06-01
This study examined patterns of variation in the ongoing electroencephalogram during performance of three visual tasks. One task required exact arithmetic calculations on Arabic numerals. A second task involved pseudoword processing as a control for the verbal (phonological) component that is, by definition, part of arithmetic tasks. A third task primarily required visual/graphemic processing, which is also involved in the other two tasks. Spectral power in the alpha range was lowest during the pseudoword task, followed by power during the arithmetic task, and finally by power in the visual task, indicating more prominent desynchronization during engagement in the analysis of word-like printed material. Finally, linear (power in the gamma range) and non-linear measures (correlation dimension) provided evidence of predominant right hemisphere engagement during the arithmetic task.
Single-digit arithmetic processing—anatomical evidence from statistical voxel-based lesion analysis
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
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. PMID:26301447
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.
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
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.
Linguistic and spatial skills predict early arithmetic development via counting sequence knowledge.
Zhang, Xiao; Koponen, Tuire; Räsänen, Pekka; Aunola, Kaisa; Lerkkanen, Marja-Kristiina; Nurmi, Jari-Erik
2014-01-01
Utilizing a longitudinal sample of Finnish children (ages 6-10), two studies examined how early linguistic (spoken vs. written) and spatial skills predict later development of arithmetic, and whether counting sequence knowledge mediates these associations. In Study 1 (N = 1,880), letter knowledge and spatial visualization, measured in kindergarten, predicted the level of arithmetic in first grade, and later growth through third grade. Study 2 (n = 378) further showed that these associations were mediated by counting sequence knowledge measured in first grade. These studies add to the literature by demonstrating the importance of written language for arithmetic development. The findings are consistent with the hypothesis that linguistic and spatial skills can improve arithmetic development by enhancing children's number-related knowledge. PMID:24148144
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
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.
Signatures of Arithmetic Simplicity in Metabolic Network Architecture
Riehl, William J.; Krapivsky, Paul L.; Redner, Sidney; Segrè, Daniel
2010-01-01
Metabolic networks perform some of the most fundamental functions in living cells, including energy transduction and building block biosynthesis. While these are the best characterized networks in living systems, understanding their evolutionary history and complex wiring constitutes one of the most fascinating open questions in biology, intimately related to the enigma of life's origin itself. Is the evolution of metabolism subject to general principles, beyond the unpredictable accumulation of multiple historical accidents? Here we search for such principles by applying to an artificial chemical universe some of the methodologies developed for the study of genome scale models of cellular metabolism. In particular, we use metabolic flux constraint-based models to exhaustively search for artificial chemistry pathways that can optimally perform an array of elementary metabolic functions. Despite the simplicity of the model employed, we find that the ensuing pathways display a surprisingly rich set of properties, including the existence of autocatalytic cycles and hierarchical modules, the appearance of universally preferable metabolites and reactions, and a logarithmic trend of pathway length as a function of input/output molecule size. Some of these properties can be derived analytically, borrowing methods previously used in cryptography. In addition, by mapping biochemical networks onto a simplified carbon atom reaction backbone, we find that properties similar to those predicted for the artificial chemistry hold also for real metabolic networks. These findings suggest that optimality principles and arithmetic simplicity might lie beneath some aspects of biochemical complexity. PMID:20369010
Modulation of human motoneuron activity by a mental arithmetic task.
Bensoussan, Laurent; Duclos, Yann; Rossi-Durand, Christiane
2012-10-01
This study aimed to determine whether the performance of a mental task affects motoneuron activity. To this end, the tonic discharge pattern of wrist extensor motor units was analyzed in healthy subjects while they were required to maintain a steady wrist extension force and to concurrently perform a mental arithmetic (MA) task. A shortening of the mean inter-spike interval (ISI) and a decrease in ISI variability occurred when MA task was superimposed to the motor task. Aloud and silent MA affected equally the rate and variability of motoneuron discharge. Increases in surface EMG activity and force level were consistent with the modulation of the motor unit discharge rate. Trial-by-trial analysis of the characteristics of motor unit firing revealed that performing MA increases activation of wrist extensor SMU. It is suggested that increase in muscle spindle afferent activity, resulting from fusimotor drive activation by MA, may have contributed to the increase in synaptic inputs to motoneurons during the mental task performance, likely together with enhancement in the descending drive. The finding that a mental task affects motoneuron activity could have consequences in assessment of motor disabilities and in rehabilitation in motor pathologies.
Fixed-point arithmetic for mobile devices: a fingerprinting verification case study
NASA Astrophysics Data System (ADS)
Moon, Yiu S.; Luk, Franklin T.; Ho, Ho C.; Tang, T. Y.; Chan, Kit C.; Leung, C. W.
2002-12-01
Mobile devices use embedded processors with low computing capabilities to reduce power consumption. Since floating-point arithmetic units are power hungry, computationally intensive jobs must be accomplished with either digital signal processors or hardware co-processors. In this paper, we propose to perform fixed-point arithmetic on an integer hardware unit. We illustrate the advantages of our approach by implementing fingerprint verification on mobile devices.
Asymptotic free probability for arithmetic functions and factorization of Dirichlet series
NASA Astrophysics Data System (ADS)
Cho, Ilwoo; Gillespie, Timothy; Jorgensen, Palle E. T.
2015-11-01
In this paper, we study a free-probabilistic model on the algebra of arithmetic functions by considering their asymptotic behavior. As an application, we concentrate on arithmetic functions arising from certain representations attached to the general linear group GL_n . We then study conditions under which a Dirichlet series may be factored into a product of automorphic L-functions using asymptotic freeness.
Asymptotic free probability for arithmetic functions and factorization of Dirichlet series
NASA Astrophysics Data System (ADS)
Cho, Ilwoo; Gillespie, Timothy; Jorgensen, Palle E. T.
2016-09-01
In this paper, we study a free-probabilistic model on the algebra of arithmetic functions by considering their asymptotic behavior. As an application, we concentrate on arithmetic functions arising from certain representations attached to the general linear group GL_n. We then study conditions under which a Dirichlet series may be factored into a product of automorphic L-functions using asymptotic freeness.
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.
NASA Astrophysics Data System (ADS)
Sprows, David
2015-04-01
This note uses material involving perfect numbers and Zeno's paradoxes to show that although most students prefer to use base 10 when working with mathematical concepts there are times when the binary system is best.
Double Degenerate Binary Systems
Yakut, K.
2011-09-21
In this study, angular momentum loss via gravitational radiation in double degenerate binary (DDB)systems (NS + NS, NS + WD, WD + WD, and AM CVn) is studied. Energy loss by gravitational waves has been estimated for each type of systems.
Mutual Orbits of Transneptunian Binaries
NASA Astrophysics Data System (ADS)
Grundy, William M.; Noll, K. S.; Roe, H. G.; Porter, S. B.; Trujillo, C. A.; Benecchi, S. D.; Buie, M. W.
2012-10-01
We report the latest results from a program of high spatial resolution imaging to resolve the individual components of binary transneptunian objects. These observations use Hubble Space Telescope and also laser guide star adaptive optics systems on Keck and Gemini telescopes on Mauna Kea. From relative astrometry over multiple epochs, we determine the mutual orbits of the components, and thus the total masses of the systems. Accurate masses anchor subsequent detailed investigations into the physical characteristics of these systems. For instance, dynamical masses enable computation of bulk densities for systems where the component sizes can be estimated from other measurements. Additionally, patterns in the ensemble characteristics of binary orbits offer clues to circumstances in the protoplanetary nebula when these systems formed, as well as carrying imprints of various subsequent dynamical evolution processes. The growing ensemble of known orbits shows intriguing patterns that can shed light on the evolution of this population of distant objects. This work has been supported by an NSF Planetary Astronomy grant and by several Hubble Space Telescope and NASA Keck data analysis grants. The research makes use of data from the Gemini Observatory obtained through NOAO survey program 11A-0017, from a large number of Hubble Space Telescope programs, and from several NASA Keck programs.
Common substrate for mental arithmetic and finger representation in the parietal cortex.
Andres, Michael; Michaux, Nicolas; Pesenti, Mauro
2012-09-01
The history of mathematics provides several examples of the use of fingers to count or calculate. These observations converge with developmental data showing that fingers play a critical role in the acquisition of arithmetic knowledge. Further studies evidenced specific interference of finger movements with arithmetic problem solving in adults, raising the question of whether or not finger and number manipulations rely on common brain areas. In the present study, functional magnetic resonance imaging (fMRI) was used to investigate the possible overlap between the brain areas involved in mental arithmetic and those involved in finger discrimination. Solving subtraction and multiplication problems was found to increase cerebral activation bilaterally in the horizontal part of the intraparietal sulcus (hIPS) and in the posterior part of the superior parietal lobule (PSPL). Finger discrimination was associated with increased activity in a bilateral occipito-parieto-precentral network extending from the extrastriate body area to the primary somatosensory and motor cortices. A conjunction analysis showed common areas for mental arithmetic and finger representation in the hIPS and PSPL bilaterally. Voxelwise correlations further showed that finger discrimination and mental arithmetic induced a similar pattern of activity within the parietal areas only. Pattern similarity was more important for the left than for the right hIPS and for subtraction than for multiplication. These findings provide the first evidence that the brain circuits involved in finger representation also underlie arithmetic operations in adults. PMID:22634854
Profiles of children's arithmetic fact development: a model-based clustering approach.
Vanbinst, Kiran; Ceulemans, Eva; Ghesquière, Pol; De Smedt, Bert
2015-05-01
The current longitudinal study tried to capture profiles of individual differences in children's arithmetic fact development. We used a model-based clustering approach to delineate profiles of arithmetic fact development based on empirically derived differences in parameters of arithmetic fact mastery repeatedly assessed at the start of three subsequent school years: third, fourth, and fifth grades. This cluster analysis revealed three profiles in a random sample-slow and variable (n = 8), average (n = 24), and efficient (n = 20)-that were marked by differences in children's development in arithmetic fact mastery from third grade to fifth grade. These profiles did not differ in terms of age, sex, socioeconomic status, or intellectual ability. In addition, we explored whether these profiles varied in cognitive skills that have been associated with individual differences in single-digit arithmetic. The three profiles differed in nonsymbolic and symbolic numerical magnitude processing as well as phonological processing, but not in digit naming or working memory. After also controlling for cluster differences in general mathematics achievement and reading ability, only differences in symbolic numerical magnitude processing remained significant. Taken together, our longitudinal data reveal that symbolic numerical magnitude processing represents an important variable that contributes to individual variability in children's acquisition of arithmetic facts.
Rütsche, Bruno; Hauser, Tobias U.; Jäncke, Lutz; Grabner, Roland H.
2015-01-01
The problem size effect is a well-established finding in arithmetic problem solving and is characterized by worse performance in problems with larger compared to smaller operand size. Solving small and large arithmetic problems has also been shown to involve different cognitive processes and distinct electroencephalography (EEG) oscillations over the left posterior parietal cortex (LPPC). In this study, we aimed to provide further evidence for these dissociations by using transcranial direct current stimulation (tDCS). Participants underwent anodal (30min, 1.5 mA, LPPC) and sham tDCS. After the stimulation, we recorded their neural activity using EEG while the participants solved small and large arithmetic problems. We found that the tDCS effects on performance and oscillatory activity critically depended on the problem size. While anodal tDCS improved response latencies in large arithmetic problems, it decreased solution rates in small arithmetic problems. Likewise, the lower-alpha desynchronization in large problems increased, whereas the theta synchronization in small problems decreased. These findings reveal that the LPPC is differentially involved in solving small and large arithmetic problems and demonstrate that the effects of brain stimulation strikingly differ depending on the involved neuro-cognitive processes. PMID:25789486
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.
NASA Technical Reports Server (NTRS)
Lopez, Hiram
1987-01-01
Transmission errors for zeros and ones tabulated separately. Binary-symmetry detector employs psuedo-random data pattern used as test message coming through channel. Message then modulo-2 added to locally generated and synchronized version of test data pattern in same manner found in manufactured test sets of today. Binary symmetrical channel shows nearly 50-percent ones to 50-percent zeroes correspondence. Degree of asymmetry represents imbalances due to either modulation, transmission, or demodulation processes of system when perturbed by noise.
NASA Technical Reports Server (NTRS)
Ricks, Douglas W.
1993-01-01
There are a number of sources of scattering in binary optics: etch depth errors, line edge errors, quantization errors, roughness, and the binary approximation to the ideal surface. These sources of scattering can be systematic (deterministic) or random. In this paper, scattering formulas for both systematic and random errors are derived using Fourier optics. These formulas can be used to explain the results of scattering measurements and computer simulations.
NASA Astrophysics Data System (ADS)
Batten, A.; Murdin, P.
2000-11-01
Historically, spectroscopic binary stars were binary systems whose nature was discovered by the changing DOPPLER EFFECT or shift of the spectral lines of one or both of the component stars. The observed Doppler shift is a combination of that produced by the constant RADIAL VELOCITY (i.e. line-of-sight velocity) of the center of mass of the whole system, and the variable shift resulting from the o...
NASA Astrophysics Data System (ADS)
Olevic, D.; Cvetkovic, Z.
In this paper the orbits of binaries WDS 10093+2020 = A 2145, WDS 21074-0814 = BU 368 AB and WDS 22288-0001 = STF 2909 AB are recalculated because of significant deviations of more recent observations from the ephemerides. For binaries WDS 22384-0754 = A 2695, WDS 23474-7118 = FIN 375 Aa and WDS 23578+2508 = McA 76 the orbital elements are calculated for the first time.
Exploring the Birth of Binary Stars
NASA Astrophysics Data System (ADS)
Kohler, Susanna
2016-08-01
More than half of all stars are thought to be in binary or multiple star systems. But how do these systems form? The misaligned spins of some binary protostars might provide a clue.Two Formation ModelsIts hard to tell how multiple-star systems form, since these systems are difficult to observe in their early stages. But based on numerical simulations, there are two proposed models for the formation of stellar binaries:Turbulent fragmentationTurbulence within a single core leads to multiple dense clumps. These clumps independently collapse to form stars that orbit each other.Disk fragmentationGravitational instabilities in a massive accretion disk cause the formation of a smaller, secondary disk within the first, resulting in two stars that orbit each other.Log column density for one of the authors simulated binary systems, just after the formation of two protostars. Diamonds indicate the protostar positions. [Adapted from Offner et al. 2016]Outflows as CluesHow can we differentiate between these formation mechanisms? Led by Stella Offner (University of Massachusetts), a team of scientists has suggested that the key isto examine the alignment of the stars protostellar outflows jets that are often emitted from the poles of young, newly forming stars.Naively, wed expect that disk fragmentation would produce binary stars with common angular momentum. As the stars spins would be aligned, they would therefore also launch protostellar jets that were aligned with each other. Turbulent fragmentation, on the other hand, would cause the stars to have independent angular momentum. This would lead to randomly oriented spins, so the protostellar jets would be misaligned.Snapshots from the authors simulations. Left panel of each pair: column density; green arrows giveprotostellar spin directions. Right panel: synthetic observations produced from the simulations; cyan arrows giveprotostellar outflow directions. [Offner et al. 2016]Simulations of FragmentationIn order to better
Young and Waltzing Binary Stars
NASA Astrophysics Data System (ADS)
2001-10-01
ADONIS Observes Low-mass Eclipsing System in Orion Summary A series of very detailed images of a binary system of two young stars have been combined into a movie . In merely 3 days, the stars swing around each other. As seen from the earth, they pass in front of each other twice during a full revolution, producing eclipses during which their combined brightness diminishes . A careful analysis of the orbital motions has now made it possible to deduce the masses of the two dancing stars . Both turn out to be about as heavy as our Sun. But while the Sun is about 4500 million years old, these two stars are still in their infancy. They are located some 1500 light-years away in the Orion star-forming region and they probably formed just 10 million years ago . This is the first time such an accurate determination of the stellar masses could be achieved for a young binary system of low-mass stars . The new result provides an important piece of information for our current understanding of how young stars evolve. The observations were obtained by a team of astronomers from Italy and ESO [1] using the ADaptive Optics Near Infrared System (ADONIS) on the 3.6-m telescope at the ESO La Silla Observatory. PR Photo 29a/01 : The RXJ 0529.4+0041 system before primary eclipse PR Photo 29b/01 : The RXJ 0529.4+0041 system at mid-primary eclipse PR Photo 29c/01 : The RXJ 0529.4+0041 system after primary eclipse PR Photo 29d/01 : The RXJ 0529.4+0041 system before secondary eclipse PR Photo 29e/01 : The RXJ 0529.4+0041 system at mid-secondary eclipse PR Photo 29f/01 : The RXJ 0529.4+0041 system after secondary eclipse PR Video Clip 06/01 : Video of the RXJ 0529.4+0041 system Binary stars and stellar masses Since some time, astronomers have noted that most stars seem to form in binary or multiple systems. This is quite fortunate, as the study of binary stars is the only way in which it is possible to measure directly one of the most fundamental quantities of a star, its mass. The mass of a
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.
Processes in arithmetic strategy selection: a fMRI study.
Taillan, Julien; Ardiale, Eléonore; Anton, Jean-Luc; Nazarian, Bruno; Félician, Olivier; Lemaire, Patrick
2015-01-01
This neuroimaging (functional magnetic resonance imaging) study investigated neural correlates of strategy selection. Young adults performed an arithmetic task in two different conditions. In both conditions, participants had to provide estimates of two-digit multiplication problems like 54 × 78. In the choice condition, participants had to select the better of two available rounding strategies, rounding-up (RU) strategy (i.e., doing 60 × 80 = 4,800) or rounding-down (RD) strategy (i.e., doing 50 × 70 = 3,500 to estimate product of 54 × 78). In the no-choice condition, participants did not have to select strategy on each problem but were told which strategy to use; they executed RU and RD strategies each on a series of problems. Participants also had a control task (i.e., providing correct products of multiplication problems like 40 × 50). Brain activations and performance were analyzed as a function of these conditions. Participants were able to frequently choose the better strategy in the choice condition; they were also slower when they executed the difficult RU than the easier RD. Neuroimaging data showed greater brain activations in right anterior cingulate cortex (ACC), dorso-lateral prefrontal cortex (DLPFC), and angular gyrus (ANG), when selecting (relative to executing) the better strategy on each problem. Moreover, RU was associated with more parietal cortex activation than RD. These results suggest an important role of fronto-parietal network in strategy selection and have important implications for our further understanding and modeling cognitive processes underlying strategy selection.
NASA Astrophysics Data System (ADS)
Noll, Keith S.
The discovery of binaries in each of the major populations of minor bodies in the solar system is propelling a rapid growth of heretofore unattainable physical information. The availability of mass and density constraints for minor bodies opens the door to studies of internal structure, comparisons with meteorite samples, and correlations between bulk-physical and surface-spectral properties. The number of known binaries is now more than 70 and is growing rapidly. A smaller number have had the extensive followup observations needed to derive mass and albedo information, but this list is growing as well. It will soon be the case that we will know more about the physical parameters of objects in the Kuiper Belt than has been known about asteroids in the Main Belt for the last 200 years. Another important aspect of binaries is understanding the mechanisms that lead to their formation and survival. The relative sizes and separations of binaries in the different minor body populations point to more than one mechanism for forming bound pairs. Collisions appear to play a major role in the Main Belt. Rotational and/or tidal fission may be important in the Near Earth population. For the Kuiper Belt, capture in multi-body interactions may be the preferred formation mechanism. However, all of these conclusions remain tentative and limited by observational and theoretical incompleteness. Observational techniques for identifying binaries are equally varied. High angular resolution observations from space and from the ground are critical for detection of the relatively distant binaries in the Main Belt and the Kuiper Belt. Radar has been the most productive method for detection of Near Earth binaries. Lightcurve analysis is an independent technique that is capable of exploring phase space inaccessible to direct observations. Finally, spacecraft flybys have played a crucial paradigm-changing role with discoveries that unlocked this now-burgeoning field.
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
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.
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
Grabner, Roland H; Rütsche, Bruno; Ruff, Christian C; Hauser, Tobias U
2015-07-01
The successful acquisition of arithmetic skills is an essential step in the development of mathematical competencies and has been associated with neural activity in the left posterior parietal cortex (PPC). It is unclear, however, whether this brain region plays a causal role in arithmetic skill acquisition and whether arithmetic learning can be modulated by means of non-invasive brain stimulation of this key region. In the present study we addressed these questions by applying transcranial direct current stimulation (tDCS) over the left PPC during a short-term training that simulates the typical path of arithmetic skill acquisition (specifically the transition from effortful procedural to memory-based problem-solving strategies). Sixty participants received either anodal, cathodal or sham tDCS while practising complex multiplication and subtraction problems. The stability of the stimulation-induced learning effects was assessed in a follow-up test 24 h after the training. Learning progress was modulated by tDCS. Cathodal tDCS (compared with sham) decreased learning rates during training and resulted in poorer performance which lasted over 24 h after stimulation. Anodal tDCS showed an operation-specific improvement for subtraction learning. Our findings extend previous studies by demonstrating that the left PPC is causally involved in arithmetic learning (and not only in arithmetic performance) and that even a short-term tDCS application can modulate the success of arithmetic knowledge acquisition. Moreover, our finding of operation-specific anodal stimulation effects suggests that the enhancing effects of tDCS on learning can selectively affect just one of several cognitive processes mediated by the stimulated area.
Grabner, Roland H; Rütsche, Bruno; Ruff, Christian C; Hauser, Tobias U
2015-07-01
The successful acquisition of arithmetic skills is an essential step in the development of mathematical competencies and has been associated with neural activity in the left posterior parietal cortex (PPC). It is unclear, however, whether this brain region plays a causal role in arithmetic skill acquisition and whether arithmetic learning can be modulated by means of non-invasive brain stimulation of this key region. In the present study we addressed these questions by applying transcranial direct current stimulation (tDCS) over the left PPC during a short-term training that simulates the typical path of arithmetic skill acquisition (specifically the transition from effortful procedural to memory-based problem-solving strategies). Sixty participants received either anodal, cathodal or sham tDCS while practising complex multiplication and subtraction problems. The stability of the stimulation-induced learning effects was assessed in a follow-up test 24 h after the training. Learning progress was modulated by tDCS. Cathodal tDCS (compared with sham) decreased learning rates during training and resulted in poorer performance which lasted over 24 h after stimulation. Anodal tDCS showed an operation-specific improvement for subtraction learning. Our findings extend previous studies by demonstrating that the left PPC is causally involved in arithmetic learning (and not only in arithmetic performance) and that even a short-term tDCS application can modulate the success of arithmetic knowledge acquisition. Moreover, our finding of operation-specific anodal stimulation effects suggests that the enhancing effects of tDCS on learning can selectively affect just one of several cognitive processes mediated by the stimulated area. PMID:25970697
Kepler's Cool Eclipsing Binaries
NASA Astrophysics Data System (ADS)
Swift, Jonathan; Muirhead, P. S.; Johnson, J. A.; Gonzales, A.; Shporer, A.; Plavchan, P.; Lockwood, A.; Morton, T.
2014-01-01
Some of the most exciting exoplanet results to date have come from the smallest and coolest sample of stars in the Kepler field—the M dwarfs. These cool stars represent the largest stellar population in the Galaxy which in turn harbors one of the largest known exoplanet populations. However, an accurate understanding of their physical properties currently eludes us. Detached, M dwarf eclipsing binary systems provide an accurate and precise, model-independent means of measuring the fundamental properties of low-mass stars shedding light on the rich physics embodied by this spectral class and refining our knowledge of their exoplanets. We have undertaken an observational campaign to obtain masses, radii, and effective temperatures of the Kepler eclipsing binaries having an M dwarf primary with periods between 1 and 60 days. These data will allow detailed comparisons between stellar properties, binary period, rotation, metallicity and activity levels.
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.
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.
Reading and arithmetic in adolescents with autism spectrum disorders: peaks and dips in attainment.
Jones, Catherine R G; Happé, Francesca; Golden, Hannah; Marsden, Anita J S; Tregay, Jenifer; Simonoff, Emily; Pickles, Andrew; Baird, Gillian; Charman, Tony
2009-11-01
In describing academic attainment in autism spectrum disorders (ASD), results are typically reported at the group mean level. This may mask subgroups of individuals for whom academic achievement is incommensurate with intellectual ability. The authors tested the IQ, literacy, and mathematical abilities of a large group (N = 100) of adolescents (14-16 years old) with ASD. Seventy-three percent of the sample had at least one area of literacy or mathematical achievement that was highly discrepant (approximately 14 standard score points) from full-scale IQ (FSIQ). The authors focused on four subgroups with either word reading ("Reading Peak" and "Reading Dip") or arithmetic ("Arithmetic Peak" and "Arithmetic Dip") higher or lower than FSIQ. These subgroups were largely mutually exclusive and were characterized by distinct intellectual profiles. The largest was the "Arithmetic Peak" subgroup of participants, who presented with average intellectual ability alongside superior arithmetic skills and who were predominantly in a mainstream educational setting. Overall, the most pervasive profile was discrepantly poor reading comprehension, which associated with severity of social and communication difficulties. The high rate of uneven academic attainment in ASD has implications for educational practice. PMID:19899830
Language-specific memory for everyday arithmetic facts in Chinese-English bilinguals.
Chen, Yalin; Yanke, Jill; Campbell, Jamie I D
2016-04-01
The role of language in memory for arithmetic facts remains controversial. Here, we examined transfer of memory training for evidence that bilinguals may acquire language-specific memory stores for everyday arithmetic facts. Chinese-English bilingual adults (n = 32) were trained on different subsets of simple addition and multiplication problems. Each operation was trained in one language or the other. The subsequent test phase included all problems with addition and multiplication alternating across trials in two blocks, one in each language. Averaging over training language, the response time (RT) gains for trained problems relative to untrained problems were greater in the trained language than in the untrained language. Subsequent analysis showed that English training produced larger RT gains for trained problems relative to untrained problems in English at test relative to the untrained Chinese language. In contrast, there was no evidence with Chinese training that problem-specific RT gains differed between Chinese and the untrained English language. We propose that training in Chinese promoted a translation strategy for English arithmetic (particularly multiplication) that produced strong cross-language generalization of practice, whereas training in English strengthened relatively weak, English-language arithmetic memories and produced little generalization to Chinese (i.e., English training did not induce an English translation strategy for Chinese language trials). The results support the existence of language-specific strengthening of memory for everyday arithmetic facts.
The Influence of Implicit Hand-Based Representations on Mental Arithmetic
Klein, Elise; Moeller, Korbinian; Willmes, Klaus; Nuerk, Hans-Christoph; Domahs, Frank
2011-01-01
Recently, a strong functional relationship between finger counting and number processing has been suggested. It has been argued that bodily experiences such as finger counting may influence the structure of the basic mental representations of numbers even in adults. However, to date it remains unclear whether the structure of finger counting systems also influences educated adults’ performance in mental arithmetic. In the present study, we pursued this question by examining finger-based sub-base-five effects in an addition production task. With the standard effect of a carry operation (i.e., base-10 crossing) being replicated, we observed an additional sub-base-five effect such that crossing a sub-base-five boundary led to a relative response time increase. For the case of mental arithmetic sub-base-five effects have previously been reported only in children. However, it remains unclear whether finger-based numerical effects in mental arithmetic reflect an important but transitory step in the development of arithmetical skills. The current findings suggest that even in adults embodied representations such as finger counting patterns modulate arithmetic performance. Thus, they support the general idea that even seemingly abstract cognition in adults may at least partly be rooted in our bodily experiences. PMID:21927606
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.
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
Binary Oscillatory Crossflow Electrophoresis
NASA Technical Reports Server (NTRS)
Molloy, Richard F.; Gallagher, Christopher T.; Leighton, David T., Jr.
1996-01-01
We present preliminary results of our implementation of a novel electrophoresis separation technique: Binary Oscillatory Cross flow Electrophoresis (BOCE). The technique utilizes the interaction of two driving forces, an oscillatory electric field and an oscillatory shear flow, to create an active binary filter for the separation of charged species. Analytical and numerical studies have indicated that this technique is capable of separating proteins with electrophoretic mobilities differing by less than 10%. With an experimental device containing a separation chamber 20 cm long, 5 cm wide, and 1 mm thick, an order of magnitude increase in throughput over commercially available electrophoresis devices is theoretically possible.
Identification list of binaries
NASA Astrophysics Data System (ADS)
Malkov,, O.; Karchevsky,, A.; Kaygorodov, P.; Kovaleva, D.
The Identification List of Binaries (ILB) is a star catalogue constructed to facilitate cross-referencing between different catalogues of binary stars. As of 2015, it comprises designations for approximately 120,000 double/multiple systems. ILB contains star coordinates and cross-references to the Bayer/Flemsteed, DM (BD/CD/CPD), HD, HIP, ADS, WDS, CCDM, TDSC, GCVS, SBC9, IGR (and some other X-ray catalogues), PSR designations, as well as identifications in the recently developed BSDB system. ILB eventually became a part of the BDB stellar database.
Binary coding for hyperspectral imagery
NASA Astrophysics Data System (ADS)
Wang, Jing; Chang, Chein-I.; Chang, Chein-Chi; Lin, Chinsu
2004-10-01
Binary coding is one of simplest ways to characterize spectral features. One commonly used method is a binary coding-based image software system, called Spectral Analysis Manager (SPAM) for remotely sensed imagery developed by Mazer et al. For a given spectral signature, the SPAM calculates its spectral mean and inter-band spectral difference and uses them as thresholds to generate a binary code word for this particular spectral signature. Such coding scheme is generally effective and also very simple to implement. This paper revisits the SPAM and further develops three new SPAM-based binary coding methods, called equal probability partition (EPP) binary coding, halfway partition (HP) binary coding and median partition (MP) binary coding. These three binary coding methods along with the SPAM well be evaluated for spectral discrimination and identification. In doing so, a new criterion, called a posteriori discrimination probability (APDP) is also introduced for performance measure.
NASA Technical Reports Server (NTRS)
Tcheng, Ping
1989-01-01
Binary resistors in series tailored to precise value of resistance. Desired value of resistance obtained by cutting appropriate traces across resistors. Multibit, binary-based, adjustable resistor with high resolution used in many applications where precise resistance required.
Binary stars - Formation by fragmentation
NASA Technical Reports Server (NTRS)
Boss, Alan P.
1988-01-01
Theories of binary star formation by capture, separate nuclei, fission and fragmentation are compared, assessing the success of theoretical attempts to explain the observed properties of main-sequence binary stars. The theory of formation by fragmentation is examined, discussing the prospects for checking the theory against observations of binary premain-sequence stars. It is concluded that formation by fragmentation is successful at explaining many of the key properties of main-sequence binary stars.
Characterizing the Eclipsing Binary KOI 1120
NASA Astrophysics Data System (ADS)
Gonzales, Alexandria; Swift, J.; Shporer, A.; Sanchis Ojeda, R.; Johnson, J. A.
2014-01-01
Because the NASA Kepler Mission is primarily a search for exoplanetary objects, its exquisite photometric precision has also opened scientific frontiers in stellar astrophysics. As part of the cool Kepler eclipsing binary program, we present a case study of a particularly interesting KOI false positive—KOI-1120. This K giant/G dwarf eclipsing binary pair reveals a deep secondary eclipse of 16% and a 7% primary eclipse depth with multiple star spot crossing events over the Kepler time baseline. Kepler data supplemented with Keck/HIRES radial velocity measurements, Keck/NIRC2 adaptive optics imaging, and Palomar/TripleSpec near infrared spectra enable precise and accurate modeling of the system. Characterizing this distinctive system will provide important insights into stellar astrophysics and stellar evolution.
Shared structural and temporal integration resources for music and arithmetic processing.
Hoch, L; Tillmann, B
2012-07-01
While previous research has investigated the relationship either between language and music processing or between language and arithmetic processing, the present study investigated the relationship between music and arithmetic processing. Rule-governed number series, with the final number being a correct or incorrect series ending, were visually presented in synchrony with musical sequences, with the final chord functioning as the expected tonic or the less-expected subdominant chord (i.e., tonal function manipulation). Participants were asked to judge the correctness of the final number as quickly and accurately as possible. The results revealed an interaction between the processing of series ending and the processing of the task-irrelevant chords' tonal function, thus suggesting that music and arithmetic processing share cognitive resources. These findings are discussed in terms of general temporal and structural integration resources for linguistic and non-linguistic rule-governed sequences.
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. PMID:24509567
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.
van Harskamp, N J; Cipolotti, L
2001-06-01
This study reports for the first time a selective impairment for simple addition in patient FS. Moreover, patient VP presented with a selective impairment for simple multiplication and patient DT with a selective impairment for simple subtraction. These findings are discussed in the context of two of the most influential models for the organisation of arithmetical facts in memory (Dehaene and Cohen, 1995, 1997, and Dagenbach and McCloskey, 1992). Dehaene and Cohen (1995, 1997) have proposed that dissociation between arithmetical facts result from a selective impairment to two different types of processing: rote verbal memory for multiplication and simple addition vs. quantity processing for subtraction and division. Dagenbach and McCloskey (1992) suggest dissociation between arithmetical facts result from a selective damage to segregated memory networks specific for each operation. We will argue that our findings are problematic for Dehaene's model and in good accord with McCloskey's view. PMID:11485063
Retrieval or nonretrieval strategies in mental arithmetic? An operand recognition paradigm.
Thevenot, Catherine; Fanget, Muriel; Fayol, Michel
2007-09-01
According to LeFevre, Sadesky, and Bisanz, averaging solution latencies in order to study individuals' arithmetic strategies can result in misleading conclusions. Therefore, in addition to classical chronometric data, they collected verbal reports and challenged the assumption that adults rely systematically on retrieval of arithmetic facts from memory to solve simple addition problems. However, Kirk and Ashcraft questioned the validity of such a methodology and concluded that a more appropriate method has to be found. Thus, we developed an operand recognition paradigm that does not rely on verbal reports or on solution latencies. In accordance with LeFevre et al., we show in a first experiment that adults resort to nonretrieval strategies to solve addition problems involving medium numbers. However, in a second experiment, we show that high-skilled individuals can solve the same problems using a retrieval strategy. The benefits of our paradigm to the study of arithmetic strategies are discussed. PMID:18035632
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.
Shared structural and temporal integration resources for music and arithmetic processing.
Hoch, L; Tillmann, B
2012-07-01
While previous research has investigated the relationship either between language and music processing or between language and arithmetic processing, the present study investigated the relationship between music and arithmetic processing. Rule-governed number series, with the final number being a correct or incorrect series ending, were visually presented in synchrony with musical sequences, with the final chord functioning as the expected tonic or the less-expected subdominant chord (i.e., tonal function manipulation). Participants were asked to judge the correctness of the final number as quickly and accurately as possible. The results revealed an interaction between the processing of series ending and the processing of the task-irrelevant chords' tonal function, thus suggesting that music and arithmetic processing share cognitive resources. These findings are discussed in terms of general temporal and structural integration resources for linguistic and non-linguistic rule-governed sequences. PMID:22673068
NASA Technical Reports Server (NTRS)
Frazier, D. O.; Facemire, B. R.; Kaukler, W. F.; Witherow, W. K.; Fanning, U.
1986-01-01
Studies of monotectic alloys and alloy analogs reviewed. Report surveys research on liquid/liquid and solid/liquid separation in binary monotectic alloys. Emphasizes separation processes in low gravity, such as in outer space or in free fall in drop towers. Advances in methods of controlling separation in experiments highlighted.
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 Functional Anatomy of Single-Digit Arithmetic in Children with Developmental Dyslexia
Evans, Tanya M.; Flowers, D. Lynn; Napoliello, Eileen M.; Olulade, Olumide A.; Eden, Guinevere F.
2014-01-01
Some arithmetic procedures, such as addition of small numbers, rely on fact retrieval mechanisms supported by left hemisphere perisylvian language areas, while others, such as subtraction, rely on procedural-based mechanisms subserved by bilateral parietal cortices. Previous work suggests that developmental dyslexia, a reading disability, is accompanied by subtle deficits in retrieval-based arithmetic, possibly because of compromised left hemisphere function. To test this prediction, we compared brain activity underlying arithmetic problem solving in children with and without dyslexia during addition and subtraction operations using a factorial design. The main effect of arithmetic operation (addition versus subtraction) for both groups combined revealed activity during addition in the left superior temporal gyrus and activity during subtraction in bilateral intraparietal sulcus, right supramarginal gyrus and the anterior cingulate, consistent with prior studies. For the main effect of diagnostic group (dyslexics versus controls), we found less activity in dyslexic children in the left supramarginal gyrus. Finally, the interaction analysis revealed that while the control group showed a strong response in right supramarginal gyrus for subtraction but not for addition, the dyslexic group engaged this region for both operations. This provides physiological evidence in support of the theory that children with dyslexia, because of disruption to left hemisphere language areas, use a less optimal route for retrieval-based arithmetic, engaging right hemisphere parietal regions typically used by good readers for procedural-based arithmetic. Our results highlight the importance of language processing for mathematical processing and illustrate that children with dyslexia have impairments that extend beyond reading. PMID:25067820
The functional anatomy of single-digit arithmetic in children with developmental dyslexia.
Evans, Tanya M; Flowers, D Lynn; Napoliello, Eileen M; Olulade, Olumide A; Eden, Guinevere F
2014-11-01
Some arithmetic procedures, such as addition of small numbers, rely on fact retrieval mechanisms supported by left hemisphere perisylvian language areas, while others, such as subtraction, rely on procedural-based mechanisms subserved by bilateral parietal cortices. Previous work suggests that developmental dyslexia, a reading disability, is accompanied by subtle deficits in retrieval-based arithmetic, possibly because of compromised left hemisphere function. To test this prediction, we compared brain activity underlying arithmetic problem solving in children with and without dyslexia during addition and subtraction operations using a factorial design. The main effect of arithmetic operation (addition versus subtraction) for both groups combined revealed activity during addition in the left superior temporal gyrus and activity during subtraction in the bilateral intraparietal sulcus, the right supramarginal gyrus and the anterior cingulate, consistent with prior studies. For the main effect of diagnostic group (dyslexics versus controls), we found less activity in dyslexic children in the left supramarginal gyrus. Finally, the interaction analysis revealed that while the control group showed a strong response in the right supramarginal gyrus for subtraction but not for addition, the dyslexic group engaged this region for both operations. This provides physiological evidence in support of the theory that children with dyslexia, because of disruption to left hemisphere language areas, use a less optimal route for retrieval-based arithmetic, engaging right hemisphere parietal regions typically used by good readers for procedural-based arithmetic. Our results highlight the importance of language processing for mathematical processing and illustrate that children with dyslexia have impairments that extend beyond reading.
Flexible transfer of knowledge in mental arithmetic--an fMRI study.
Ischebeck, Anja; Zamarian, Laura; Schocke, Michael; Delazer, Margarete
2009-02-01
Recent imaging studies could show that fact acquisition in arithmetic is associated with decreasing activation in several frontal and parietal areas, and relatively increasing activation within the angular gyrus, indicating a switch from direct calculation to retrieval of a learned fact from memory. So far, however, little is known about the transfer of learned facts between arithmetic operations. The aim of the present fMRI study was to investigate whether and how newly acquired arithmetic knowledge might transfer from trained multiplication problems to related division problems. On the day before scanning, ten complex multiplication problems were trained. Within the scanner, trained multiplication problems were compared with untrained multiplication problems, and division problems related to multiplication (transfer condition) were compared with unrelated division problems (no-transfer condition). Replicating earlier results, untrained multiplication problems activated several frontal and parietal brain areas more strongly than trained multiplication problems, while trained multiplication problems showed relatively stronger activation in the left angular gyrus than untrained multiplication problems. Concerning division, an ROI analysis indicated that activation in the left angular gyrus was relatively stronger for the transfer condition than for the no-transfer condition. We also observed distinct inter-individual differences with regard to transfer that modulated activation within the left angular gyrus. Activation within the left angular gyrus was generally higher for participants who showed a transfer effect for division problems. In conclusion, the present study yielded some evidence that successful transfer of knowledge between arithmetic operations is accompanied by modifications of brain activation patterns. The left angular gyrus seems not only to be involved in the retrieval of stored arithmetic facts, but also in the transfer between arithmetic
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
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
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.
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.
Compensating arithmetic ability with derived fact strategies in Broca's aphasia: a case report.
Puvanendran, Kalaiyashni; Dowker, Ann; Demeyere, Nele
2016-01-01
We investigated derived fact strategy use in RR, an aphasic patient with severely impaired working memory (no phonological loop), and 16 neurologically healthy matched controls. Participants were tested on derived fact strategy use in multi-digit addition, subtraction, multiplication, and division. RR's accuracy only differed from controls in multiplication. He was as quick as controls in addition and subtraction when able to use the strategies, though significantly slower in addition, division, and multiplication without strategies. Our findings suggest the phonological loop is non-essential for multi-digit arithmetic, and derived fact strategies can help speed up arithmetic in individuals with impaired working memory. PMID:26647359
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.
Young and Waltzing Binary Stars
NASA Astrophysics Data System (ADS)
2001-10-01
ADONIS Observes Low-mass Eclipsing System in Orion Summary A series of very detailed images of a binary system of two young stars have been combined into a movie . In merely 3 days, the stars swing around each other. As seen from the earth, they pass in front of each other twice during a full revolution, producing eclipses during which their combined brightness diminishes . A careful analysis of the orbital motions has now made it possible to deduce the masses of the two dancing stars . Both turn out to be about as heavy as our Sun. But while the Sun is about 4500 million years old, these two stars are still in their infancy. They are located some 1500 light-years away in the Orion star-forming region and they probably formed just 10 million years ago . This is the first time such an accurate determination of the stellar masses could be achieved for a young binary system of low-mass stars . The new result provides an important piece of information for our current understanding of how young stars evolve. The observations were obtained by a team of astronomers from Italy and ESO [1] using the ADaptive Optics Near Infrared System (ADONIS) on the 3.6-m telescope at the ESO La Silla Observatory. PR Photo 29a/01 : The RXJ 0529.4+0041 system before primary eclipse PR Photo 29b/01 : The RXJ 0529.4+0041 system at mid-primary eclipse PR Photo 29c/01 : The RXJ 0529.4+0041 system after primary eclipse PR Photo 29d/01 : The RXJ 0529.4+0041 system before secondary eclipse PR Photo 29e/01 : The RXJ 0529.4+0041 system at mid-secondary eclipse PR Photo 29f/01 : The RXJ 0529.4+0041 system after secondary eclipse PR Video Clip 06/01 : Video of the RXJ 0529.4+0041 system Binary stars and stellar masses Since some time, astronomers have noted that most stars seem to form in binary or multiple systems. This is quite fortunate, as the study of binary stars is the only way in which it is possible to measure directly one of the most fundamental quantities of a star, its mass. The mass of a
ERIC Educational Resources Information Center
Bjorklund, David F.; Hubertz, Martha J.; Reubens, Andrea C.
2004-01-01
We examined the relationship between parents' behaviour and children's use of simple arithmetic strategies while playing a board game in contrast to solving arithmetic problems. In a microgenetic study spanning 3 weeks, 5-year-old children who were just beginning kindergarten played a modified game of "Chutes and Ladders" with one of their…
Code of Federal Regulations, 2010 CFR
2010-07-01
... of 40 CFR part 60, section 4.3, to calculate the daily geometric average concentrations of sulfur... 40 Protection of Environment 8 2010-07-01 2010-07-01 false How do I convert my 1-hour arithmetic... convert my 1-hour arithmetic averages into appropriate averaging times and units? (a) Use the equation...
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…
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.…
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.
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. PMID:25594486
Grabner, Roland H; Ansari, Daniel; Koschutnig, Karl; Reishofer, Gernot; Ebner, Franz; Neuper, Christa
2009-01-01
While there is consistent evidence from neuropsychological and brain imaging studies for an association between the left angular gyrus and mental arithmetic, its specific role in calculation has remained poorly understood. It has been speculated that the angular gyrus mediates the retrieval of arithmetic facts during problem solving, but this hypothesis has not been directly tested. In the present functional Magnetic Resonance Imaging study comprising 28 adults, we used trial-by-trial strategy self-reports to identify brain regions underpinning different strategies in arithmetic problem solving. Analyses revealed stronger activation of the left angular gyrus while solving arithmetic problems for which participants reported fact retrieval whereas the application of procedural strategies was accompanied by widespread activation in a fronto-parietal network. These data directly link the left angular gyrus with arithmetic fact retrieval and show that strategy self-reports can be used to predict differential patterns of brain activation. PMID:19007800
Massive Black Hole Binary Evolution
NASA Astrophysics Data System (ADS)
Merritt, David; Milosavljević, Milos
2005-11-01
Coalescence of binary supermassive black holes (SBHs) would constitute the strongest sources of gravitational waves to be observed by LISA. While the formation of binary SBHs during galaxy mergers is almost inevitable, coalescence requires that the separation between binary components first drop by a few orders of magnitude, due presumably to interaction of the binary with stars and gas in a galactic nucleus. This article reviews the observational evidence for binary SBHs and discusses how they would evolve. No completely convincing case of a bound, binary SBH has yet been found, although a handful of systems (e.g. interacting galaxies; remnants of galaxy mergers) are now believed to contain two SBHs at projected separations of <~ 1kpc. N-body studies of binary evolution in gas-free galaxies have reached large enough particle numbers to reproduce the slow, "diffusive" refilling of the binary's loss cone that is believed to characterize binary evolution in real galactic nuclei. While some of the results of these simulations - e.g. the binary hardening rate and eccentricity evolution - are strongly N-dependent, others - e.g. the "damage" inflicted by the binary on the nucleus - are not. Luminous early-type galaxies often exhibit depleted cores with masses of ~ 1-2 times the mass of their nuclear SBHs, consistent with the predictions of the binary model. Studies of the interaction of massive binaries with gas are still in their infancy, although much progress is expected in the near future. Binary coalescence has a large influence on the spins of SBHs, even for mass ratios as extreme as 10:1, and evidence of spin-flips may have been observed.
NASA Astrophysics Data System (ADS)
Yagi, Kent; Yunes, Nicolás
2016-07-01
When in a tight binary, the mutual tidal deformations of neutron stars get imprinted onto observables, encoding information about their internal structure at supranuclear densities and gravity in the extreme-gravity regime. Gravitational wave (GW) observations of their late binary inspiral may serve as a tool to extract the individual tidal deformabilities, but this is made difficult by degeneracies between them in the GW model. We here resolve this problem by discovering approximately equation-of-state (EoS)-insensitive relations between dimensionless combinations of the individual tidal deformabilities. We show that these relations break degeneracies in the GW model, allowing for the accurate extraction of both deformabilities. Such measurements can be used to better differentiate between EoS models, and improve tests of general relativity and cosmology.
Dark Matter from Binary Tetrahedral Flavor Symmetry
NASA Astrophysics Data System (ADS)
Eby, David; Frampton, Paul
2012-03-01
Binary Tetrahedral Flavor Symmetry, originally developed as a quark family symmetry and later adapted to leptons, has proved both resilient and versatile over the past decade. In 2008 a minimal T' model was developed to accommodate quark and lepton masses and mixings using a family symmetry of (T'xZ2). We examine an expansion of this earlier model using an additional Z2 group that facilitates predictions of WIMP dark matter, the Cabibbo angle, and deviations from Tribimaximal Mixing, while giving hints at the nature of leptogenesis.
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.
NASA Technical Reports Server (NTRS)
Bokhari, Shahid H.; Crockett, Thomas W.; Nicol, David M.
1993-01-01
Binary dissection is widely used to partition non-uniform domains over parallel computers. This algorithm does not consider the perimeter, surface area, or aspect ratio of the regions being generated and can yield decompositions that have poor communication to computation ratio. Parametric Binary Dissection (PBD) is a new algorithm in which each cut is chosen to minimize load + lambda x(shape). In a 2 (or 3) dimensional problem, load is the amount of computation to be performed in a subregion and shape could refer to the perimeter (respectively surface) of that subregion. Shape is a measure of communication overhead and the parameter permits us to trade off load imbalance against communication overhead. When A is zero, the algorithm reduces to plain binary dissection. This algorithm can be used to partition graphs embedded in 2 or 3-d. Load is the number of nodes in a subregion, shape the number of edges that leave that subregion, and lambda the ratio of time to communicate over an edge to the time to compute at a node. An algorithm is presented that finds the depth d parametric dissection of an embedded graph with n vertices and e edges in O(max(n log n, de)) time, which is an improvement over the O(dn log n) time of plain binary dissection. Parallel versions of this algorithm are also presented; the best of these requires O((n/p) log(sup 3)p) time on a p processor hypercube, assuming graphs of bounded degree. How PBD is applied to 3-d unstructured meshes and yields partitions that are better than those obtained by plain dissection is described. Its application to the color image quantization problem is also discussed, in which samples in a high-resolution color space are mapped onto a lower resolution space in a way that minimizes the color error.
1996-04-02
This software is a set of tools for the design and analysis of binary optics. It consists of a series of stand-alone programs written in C and some scripts written in an application-specific language interpreted by a CAD program called DW2000. This software can be used to optimize the design and placement of a complex lens array from input to output and produce contours, mask designs, and data exported for diffractive optic analysis.
Separated Fringe Packet Binaries
NASA Astrophysics Data System (ADS)
Bagnuolo, W. G.; Taylor, S. F.; McAlister, H. A.; ten Brummelaar, T.; Sturmann, L.; Sturmann, J.; Turner, N. H.; Berger, D.; Ridgway, S. T.; CenterHigh Angular Resolution Astronomy (CHARA)
2004-12-01
Individually resolved packets are produced by scans from the CHARA Interferometer Array for binary stars with separations from 10 to 100 milli-arcsec (mas) in the K' band. We have used this data for astrometry of the binary with the goal of improving the visual orbits for these systems. About 12 data sets of 400 scans each can be collected for a star within an hour. The intrinsic accuracy with simple linear/quadratic fits to the time-separation curve yields accuracies of 0.15 mas. But, for systems with separations less than 80 mas, the measured separation is modulated periodically by the secondary star's packet riding over the sidelobes of the primary which provides a phase reference. This "sidelobe verniering" can improve the precision to better than 50 micro-arcsec. These techniques, represents 1-2 orders of magnitude improvement in astrometic accuracy over speckle interferometry techniques. Visual orbits can then be refined via a maximum liklihood technique, which leads to revisions in the stellar masses. We present the results for several binaries that have been observed at the CHARA Array, starting in 2001.
Evolutionary models of binaries
NASA Astrophysics Data System (ADS)
van Rensbergen, Walter; Mennekens, Nicki; de Greve, Jean-Pierre; Jansen, Kim; de Loore, Bert
2011-07-01
We have put on CDS a catalog containing 561 evolutionary models of binaries: J/A+A/487/1129 (Van Rensbergen+, 2008). The catalog covers a grid of binaries with a B-type primary at birth, different values for the initial mass ratio and a wide range of initial orbital periods. The evolution was calculated with the Brussels code in which we introduced the spinning up and the creation of a hot spot on the gainer or its accretion disk, caused by impacting mass coming from the donor. When the kinetic energy of fast rotation added to the radiative energy of the hot spot exceeds the binding energy, a fraction of the transferred matter leaves the system: the evolution is liberal during a short lasting era of rapid mass transfer. The spin-up of the gainer was modulated using both strong and weak tides. The catalog shows the results for both types. For comparison, we included the evolutionary tracks calculated with the conservative assumption. Binaries with an initial primary below 6 Msolar show hardly any mass loss from the system and thus evolve conservatively. Above this limit differences between liberal and conservative evolution grow with increasing initial mass of the primary star.
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…
Preservice Teachers' Use of Multiple Representations in Solving Arithmetic Mean Problems.
ERIC Educational Resources Information Center
Gfeller, Mary K.; Niess, Margaret L.; Lederman, Norman G.
1999-01-01
Examines solutions presented by preservice teachers for solving graphical and numerical problems involving the arithmetic mean. Participants presented two methods: algorithmic computation and balancing deviations about the mean. A significant difference was found between science and mathematics preservice teachers in the use of balancing…
Text Integration and Mathematical Connections: A Computer Model of Arithmetic Word Problem Solving.
ERIC Educational Resources Information Center
LeBlanc, Mark D.; Weber-Russell, Sylvia
1996-01-01
A growing body of empirical and theoretical work indicates that young children (grades K-3) have difficulties solving word problems because of deficient language and text comprehension strategies. Describes a computer simulation designed to model working memory demands in "bottom-up" comprehension of arithmetic word problems, offering a…
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…
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…
Executive Functioning in Children, and Its Relations with Reasoning, Reading, and Arithmetic
ERIC Educational Resources Information Center
van der Sluis, Sophie; de Jong, Peter F.; van der Leij, Aryan
2007-01-01
The aims of this study were to investigate whether the executive functions, inhibition, shifting, and updating, are distinguishable as latent variables (common factors) in children aged 9 to 12, and to examine the relations between these executive functions and reading, arithmetic, and (non)verbal reasoning. Confirmatory factor analysis was used…
Transfer of Strategy Use by Semantic Recoding in Arithmetic Problem Solving
ERIC Educational Resources Information Center
Gamo, Sylvie; Sander, Emmanuel; Richard, Jean-Francois
2010-01-01
Transfer of strategies between problems sharing the same formal structure is facilitated by a semantic recoding that makes evident the structural similarities between the problems. Two experiments were carried out among 4th and 5th grade pupils, with an experimental group trained to compare strategies in order to reinterpret an arithmetic word…
Differences between Flemish and Chinese Primary Students' Mastery of Basic Arithmetic Operations
ERIC Educational Resources Information Center
Zhao, Ningning; Valcke, Martin; Desoete, Annemie; Burny, Elise; Imbo, Ineke
2014-01-01
The present paper investigates differences in the process of mastering the four basic arithmetic operations (addition, subtraction, multiplication and division) between Flemish and Chinese children from Grade 3 till Grade 6 (i.e. from 8 to 11 years old). The results showed, firstly, that Chinese students outperformed Flemish students in each grade…
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…
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)…
Arithmetical Thinking in Children Attending Special Schools for the Intellectually Disabled
ERIC Educational Resources Information Center
Eriksson, Gota
2008-01-01
This article focuses on spontaneous and progressive knowledge building in ''the arithmetic of the child.'' The aim is to investigate variations in the behavior patterns of eight pupils attending a school for the intellectually disabled. The study is based on the epistemology of radical constructivism and the methodology of multiple clinical…
Supervision of Teachers Based on Adjusted Arithmetic Learning in Special Education
ERIC Educational Resources Information Center
Eriksson, Gota
2008-01-01
This article reports on 20 children's learning in arithmetic after teaching was adjusted to their conceptual development. The report covers periods from three months up to three terms in an ongoing intervention study of teachers and children in schools for the intellectually disabled and of remedial teaching in regular schools. The researcher…
Arithmetical Problem Solving: A Program Demonstration by Teachers of the Mentally Handicapped.
ERIC Educational Resources Information Center
Cawley, John F.; Goodman, John O.
The purposes of the study were to investigate the effects of the combination of a trained teacher and a planned program on the problem solving abilities of mentally handicapped children, to develop measures of verbal problem solving (IDES) and arithmetic understanding (PUT), and to analyze the interrelationships among primary mental abilities and…
Eye Gaze Reveals a Fast, Parallel Extraction of the Syntax of Arithmetic Formulas
ERIC Educational Resources Information Center
Schneider, Elisa; Maruyama, Masaki; Dehaene, Stanislas; Sigman, Mariano
2012-01-01
Mathematics shares with language an essential reliance on the human capacity for recursion, permitting the generation of an infinite range of embedded expressions from a finite set of symbols. We studied the role of syntax in arithmetic thinking, a neglected component of numerical cognition, by examining eye movement sequences during the…
Spanish/English Bilingual Students' Comprehension of Arithmetic Story Problem Texts
ERIC Educational Resources Information Center
Ambrose, Rebecca; Molina, Marta
2014-01-01
In this paper we explore some of factors that affect bilingual students' comprehension of story problems: vocabulary, syntax, cultural relevance and understanding of the word problem genre. In an effort to determine how these factors interact, we asked 18 Spanish/English bilingual children to retell and solve arithmetic story problems in…
Is Arithmetic Really Necessary for Algebra? A Case for an Integrated Curriculum.
ERIC Educational Resources Information Center
Palow, William P.
By measuring the performance of 62 students enrolled in a community college introductory algebra course, this study challenges the generally accepted assumption among mathematics instructors that mastery of arithmetic is necessary for the learning of algebra. Study subjects were 35% male, 74% Hispanic, 16% Black, 8% white, and 2% other. A pretest,…
Inhibiting Interference from Prior Knowledge: Arithmetic Intrusions in Algebra Word Problem Solving
ERIC Educational Resources Information Center
Khng, Kiat Hui; Lee, Kerry
2009-01-01
In Singapore, 6-12 year-old students are taught to solve algebra word problems with a mix of arithmetic and pre-algebraic strategies; 13-17 year-olds are typically encouraged to replace these strategies with letter-symbolic algebra. We examined whether algebra problem-solving proficiency amongst beginning learners of letter-symbolic algebra is…
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…
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…
Predicting arithmetical achievement from neuro-psychological performance: a longitudinal study.
Fayol, M; Barrouillet, P; Marinthe, C
1998-08-01
In this article, we show that the performances of 5- to 6-year-old children in arithmetic tests can be predicted from their performances in neuro-psychological tests administered a number of months in advance, independently of their level of development. PMID:9818514
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…
Spatial biases during mental arithmetic: evidence from eye movements on a blank screen
Hartmann, Matthias; Mast, Fred W.; Fischer, Martin H.
2014-01-01
While the influence of spatial-numerical associations in number categorization tasks has been well established, their role in mental arithmetic is less clear. It has been hypothesized that mental addition leads to rightward and upward shifts of spatial attention (along the “mental number line”), whereas subtraction leads to leftward and downward shifts. We addressed this hypothesis by analyzing spontaneous eye movements during mental arithmetic. Participants solved verbally presented arithmetic problems (e.g., 2 + 7, 8–3) aloud while looking at a blank screen. We found that eye movements reflected spatial biases in the ongoing mental operation: Gaze position shifted more upward when participants solved addition compared to subtraction problems, and the horizontal gaze position was partly determined by the magnitude of the operands. Interestingly, the difference between addition and subtraction trials was driven by the operator (plus vs. minus) but was not influenced by the computational process. Thus, our results do not support the idea of a mental movement toward the solution during arithmetic but indicate a semantic association between operation and space. PMID:25657635
Teaching the Four Arithmetic Processes to the EMR Child-Addition
ERIC Educational Resources Information Center
Ogletree, Earl J.
1977-01-01
Available from: Journal for Special Educators of the Mentally Retarded, 179 Sierra Vista Lane, Valley Cottage, New York 10989. Methods of teaching addition and number concepts to educable mentally retarded students through concrete objects, memory exercises, and clock arithmetic are discussed. (CL)
Evaluation of AnimalWatch: An Intelligent Tutoring System for Arithmetic and Fractions
ERIC Educational Resources Information Center
Beal, Carole R.; Arroyo, Ivon M.; Cohen, Paul R.; Woolf, Beverly P.
2010-01-01
Three studies were conducted with middle school students to evaluate a web-based intelligent tutoring system (ITS) for arithmetic and fractions. The studies involved pre and post test comparisons, as well as group comparisons to assess the impact of the ITS on students' math problem solving. Results indicated that students improved from pre to…
Preschoolers' Nonsymbolic Arithmetic with Large Sets: Is Addition More Accurate than Subtraction?
ERIC Educational Resources Information Center
Shinskey, Jeanne L.; Chan, Cindy Ho-man; Coleman, Rhea; Moxom, Lauren; Yamamoto, Eri
2009-01-01
Adult and developing humans share with other animals analog magnitude representations of number that support nonsymbolic arithmetic with large sets. This experiment tested the hypothesis that such representations may be more accurate for addition than for subtraction in children as young as 3 1/2 years of age. In these tasks, the experimenter hid…
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…
ERIC Educational Resources Information Center
BIJOU, SIDNEY W.; AND OTHERS
RESEARCH IN WHICH BEHAVIOR THEORY WAS APPLIED TO TEACHING READING, WRITING, AND ARITHMETIC TO RETARDED CHILDREN IS REPORTED. TWENTY- SEVEN EDUCABLY RETARDED CHILDREN PARTICIPATED IN THE CORE GROUP. THE MEAN MENTAL AGE WAS 11 YEARS AND THE MEAN IQ WAS 63. IN AN EXPERIMENTAL ENVIRONMENT OF APPROVAL, ENCOURAGEMENT, AND TOKEN REINFORCEMENT, A…
Comparison between first geometric-arithmetic index and atom-bond connectivity index
NASA Astrophysics Data System (ADS)
Das, Kinkar Ch.; Trinajstić, N.
2010-09-01
The first geometric-arithmetic index ( GA) [1] and atom-bond connectivity index ( ABC) [2] that are recently introduced, are found to be useful tools in QSPR and QSAR studies. In this letter we compare the GA and ABC indices for chemical trees and molecular graphs. Moreover, we also compare these two indices for general graphs.
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…
ERIC Educational Resources Information Center
Bragman, Ruth; Hardy, Robert C.
1982-01-01
Results from testing 20 first graders in a remedial class in Maryland indicated that: same pattern recognition was significantly higher than reverse pattern recognition; identical pattern recognition did not affect performance on reading and arithmetic achievement; reverse pattern recognition significantly affected performance on reading and…
Arithmetic memory networks established in childhood are changed by experience in adulthood.
Martinez-Lincoln, Amanda; Cortinas, Christina; Wicha, Nicole Y Y
2015-01-01
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
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…
Australian Item Bank Program: Mathematics Item Bank. Book 1: Arithmetic, Algebra.
ERIC Educational Resources Information Center
Australian Council for Educational Research, Hawthorn.
This item bank was compiled by the Australian Council for Educational research (ACER) to help teachers at the secondary school level construct objective tests in arithmetic and algebra. The multiple-choice items were written by teachers who attended ACER writing workshops. The questions are classified according to their subject content and the…
ERIC Educational Resources Information Center
Feygin, Gennady; And Others
1994-01-01
Presents two new algorithms for performing arithmetic coding without employing multiplication and discusses their implementation requirements. The first algorithm, suitable for an alphabet of arbitrary size, reduces the worst case excess length to under 0.8%. The second algorithm, suitable only for alphabets of less than 12 symbols, allows even…
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"…
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…
ERIC Educational Resources Information Center
Kamii, Constance
This book describes and develops an innovative program of teaching arithmetic in the early elementary grades. The educational strategies employed are based on Jean Piaget's constructivist scientific ideas of how children develop logico-mathematical thinking. The book is written in collaboration with a classroom teacher and premised on the…
ERIC Educational Resources Information Center
Pieper, Edward L.; Deshler, Donald D.
The study involving 60 learning disabled (LD) and 30 normal achieving seventh through ninth graders was designed to identify adolescents homogeneously defined as exhibiting a "specific learning disability in arithmetic" and to determine if the cognitive processes (visual-spatial, visual-reasoning, and visual-memory) are related to the academic…
Linguistic and Spatial Skills Predict Early Arithmetic Development via Counting Sequence Knowledge
ERIC Educational Resources Information Center
Zhang, Xiao; Koponen, Tuire; Räsänen, Pekka; Aunola, Kaisa; Lerkkanen, Marja-Kristiina; Nurmi, Jari-Erik
2014-01-01
Utilizing a longitudinal sample of Finnish children (ages 6-10), two studies examined how early linguistic (spoken vs. written) and spatial skills predict later development of arithmetic, and whether counting sequence knowledge mediates these associations. In Study 1 (N = 1,880), letter knowledge and spatial visualization, measured in…
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…
Arithmetic memory networks established in childhood are changed by experience in adulthood
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
Deaf College Students' Comprehension of Relational Language in Arithmetic Compare Problems.
ERIC Educational Resources Information Center
Kelly, Ronald R.; Lang, Harry G.; Mousley, Keith; Davis, Stacey M.
2003-01-01
A study involving 80 undergraduates with deafness enrolled in first-year algebra courses found students were more likely to miscomprehend a relational statement and commit a reversal error when the required arithmetic operation was inconsistent with the statement's relational term. Reading ability influenced performance, and errors decreased as…
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…
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…
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…
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…
Working Memory in Nonsymbolic Approximate Arithmetic Processing: A Dual-Task Study with Preschoolers
ERIC Educational Resources Information Center
Xenidou-Dervou, Iro; van Lieshout, Ernest C. D. M.; van der Schoot, Menno
2014-01-01
Preschool children have been proven to possess nonsymbolic approximate arithmetic skills before learning how to manipulate symbolic math and thus before any formal math instruction. It has been assumed that nonsymbolic approximate math tasks necessitate the allocation of Working Memory (WM) resources. WM has been consistently shown to be an…
Manipulatives and Number Sentences in Computer-Aided Arithmetic Word Problem Solving.
ERIC Educational Resources Information Center
Stellingwerf, Berend P.; van Lieshout, Ernest C. D. M.
1999-01-01
Investigates the relative contribution of two main components often used in the instruction of arithmetic and word-problem solving to first-grade children and children with learning problems: external representation with manipulatives and formal mathematical representation with number sequences. Four computer-aided treatments were developed along…
Arithmetic memory networks established in childhood are changed by experience in adulthood.
Martinez-Lincoln, Amanda; Cortinas, Christina; Wicha, Nicole Y Y
2015-01-01
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-.
ERIC Educational Resources Information Center
Lubin, Amélie; Vidal, Julie; Lanoë, Céline; Houdé, Olivier; Borst, Grégoire
2013-01-01
Solving simple arithmetic word problems is a major ability that children must acquire throughout the primary-grade mathematics curriculum. However, this skill is often challenging for them. For instance, "unknown referent problems" are more difficult to solve than "unknown compare problems." In unknown compare problems, the…
ERIC Educational Resources Information Center
McNeil, Nicole M.; Chesney, Dana L.; Matthews, Percival G.; Fyfe, Emily R.; Petersen, Lori A.; Dunwiddie, April E.; Wheeler, Mary C.
2012-01-01
This experiment tested the hypothesis that organizing arithmetic fact practice by equivalent values facilitates children's understanding of math equivalence. Children (M age = 8 years 6 months, N = 104) were randomly assigned to 1 of 3 practice conditions: (a) equivalent values, in which problems were grouped by equivalent sums (e.g., 3 + 4 = 7, 2…
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…
ERIC Educational Resources Information Center
Fehr, Thorsten; Weber, Jochen; Willmes, Klaus; Herrmann, Manfred
2010-01-01
Prodigies are individuals with exceptional mental abilities. How is it possible that some of these people mentally calculate exponentiations with high accuracy and speed? We examined CP, a mental calculation prodigy, and a control group of 11 normal calculators for moderate mental arithmetic tasks. CP has additionally been tested for exceptionally…
Individual Differences in Memory Updating in Relation to Arithmetic Problem Solving
ERIC Educational Resources Information Center
Passolunghi, Maria Chiara; Pazzaglia, Francesca
2004-01-01
The study investigates the relationship between memory updating and arithmetic word problem solving. Two groups of 35 fourth graders with high and low memory-updating abilities were selected from a sample of 89 children on the basis of an updating task used by Palladino et al. ["Memory & Cognition" 29 (2002) 344]. The two groups were required to…
NASA Technical Reports Server (NTRS)
Griebeler, Elmer L.
2011-01-01
Binary communication through long cables, opto-isolators, isolating transformers, or repeaters can become distorted in characteristic ways. The usual solution is to slow the communication rate, change to a different method, or improve the communication media. It would help if the characteristic distortions could be accommodated at the receiving end to ease the communication problem. The distortions come from loss of the high-frequency content, which adds slopes to the transitions from ones to zeroes and zeroes to ones. This weakens the definition of the ones and zeroes in the time domain. The other major distortion is the reduction of low frequency, which causes the voltage that defines the ones or zeroes to drift out of recognizable range. This development describes a method for recovering a binary data stream from a signal that has been subjected to a loss of both higher-frequency content and low-frequency content that is essential to define the difference between ones and zeroes. The method makes use of the frequency structure of the waveform created by the data stream, and then enhances the characteristics related to the data to reconstruct the binary switching pattern. A major issue is simplicity. The approach taken here is to take the first derivative of the signal and then feed it to a hysteresis switch. This is equivalent in practice to using a non-resonant band pass filter feeding a Schmitt trigger. Obviously, the derivative signal needs to be offset to halfway between the thresholds of the hysteresis switch, and amplified so that the derivatives reliably exceed the thresholds. A transition from a zero to a one is the most substantial, fastest plus movement of voltage, and therefore will create the largest plus first derivative pulse. Since the quiet state of the derivative is sitting between the hysteresis thresholds, the plus pulse exceeds the plus threshold, switching the hysteresis switch plus, which re-establishes the data zero to one transition
Modeling Selective Intergranular Oxidation of Binary Alloys
Xu, Zhijie; Li, Dongsheng; Schreiber, Daniel K.; Rosso, Kevin M.; Bruemmer, Stephen M.
2015-01-07
Intergranular attack of alloys under hydrothermal conditions is a complex problem that depends on metal and oxygen transport kinetics via solid-state and channel-like pathways to an advancing oxidation front. Experiments reveal very different rates of intergranular attack and minor element depletion distances ahead of the oxidation front for nickel-based binary alloys depending on the minor element. For example, a significant Cr depletion up to 9 µm ahead of grain boundary crack tips were documented for Ni-5Cr binary alloy, in contrast to relatively moderate Al depletion for Ni-5Al (~100s of nm). We present a mathematical kinetics model that adapts Wagner’s model for thick film growth to intergranular attack of binary alloys. The transport coefficients of elements O, Ni, Cr, and Al in bulk alloys and along grain boundaries were estimated from the literature. For planar surface oxidation, a critical concentration of the minor element can be determined from the model where the oxide of minor element becomes dominant over the major element. This generic model for simple grain boundary oxidation can predict oxidation penetration velocities and minor element depletion distances ahead of the advancing front that are comparable to experimental data. The significant distance of depletion of Cr in Ni-5Cr in contrast to the localized Al depletion in Ni-5Al can be explained by the model due to the combination of the relatively faster diffusion of Cr along the grain boundary and slower diffusion in bulk grains, relative to Al.
Modeling selective intergranular oxidation of binary alloys
NASA Astrophysics Data System (ADS)
Xu, Zhijie; Li, Dongsheng; Schreiber, Daniel K.; Rosso, Kevin M.; Bruemmer, Stephen M.
2015-01-01
Intergranular attack of alloys under hydrothermal conditions is a complex problem that depends on metal and oxygen transport kinetics via solid-state and channel-like pathways to an advancing oxidation front. Experiments reveal very different rates of intergranular attack and minor element depletion distances ahead of the oxidation front for nickel-based binary alloys depending on the minor element. For example, a significant Cr depletion up to 9 μm ahead of grain boundary crack tips was documented for Ni-5Cr binary alloy, in contrast to relatively moderate Al depletion for Ni-5Al (˜100 s of nm). We present a mathematical kinetics model that adapts Wagner's model for thick film growth to intergranular attack of binary alloys. The transport coefficients of elements O, Ni, Cr, and Al in bulk alloys and along grain boundaries were estimated from the literature. For planar surface oxidation, a critical concentration of the minor element can be determined from the model where the oxide of minor element becomes dominant over the major element. This generic model for simple grain boundary oxidation can predict oxidation penetration velocities and minor element depletion distances ahead of the advancing front that are comparable to experimental data. The significant distance of depletion of Cr in Ni-5Cr in contrast to the localized Al depletion in Ni-5Al can be explained by the model due to the combination of the relatively faster diffusion of Cr along the grain boundary and slower diffusion in bulk grains, relative to Al.
A quintuple star system containing two eclipsing binaries
NASA Astrophysics Data System (ADS)
Rappaport, S.; Lehmann, H.; Kalomeni, B.; Borkovits, T.; Latham, D.; Bieryla, A.; Ngo, H.; Mawet, D.; Howell, S.; Horch, E.; Jacobs, T. L.; LaCourse, D.; Sódor, Á.; Vanderburg, A.; Pavlovski, K.
2016-10-01
We present a quintuple star system that contains two eclipsing binaries. The unusual architecture includes two stellar images separated by 11 arcsec on the sky: EPIC 212651213 and EPIC 212651234. The more easterly image (212651213) actually hosts both eclipsing binaries which are resolved within that image at 0.09 arcsec, while the westerly image (212651234) appears to be single in adaptive optics (AO), speckle imaging, and radial velocity (RV) studies. The `A' binary is circular with a 5.1-d period, while the `B' binary is eccentric with a 13.1-d period. The γ velocities of the A and B binaries are different by ˜10 km s-1. That, coupled with their resolved projected separation of 0.09 arcsec, indicates that the orbital period and separation of the `C' binary (consisting of A orbiting B) are ≃65 yr and ≃25 au, respectively, under the simplifying assumption of a circular orbit. Motion within the C orbit should be discernible via future RV, AO, and speckle imaging studies within a couple of years. The C system (i.e. 212651213) has an RV and proper motion that differ from that of 212651234 by only ˜1.4 km s-1 and ˜3 mas yr-1. This set of similar space velocities in three dimensions strongly implies that these two objects are also physically bound, making this at least a quintuple star system.
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.
Binary optics: Trends and limitations
NASA Astrophysics Data System (ADS)
Farn, Michael W.; Veldkamp, Wilfrid B.
1993-08-01
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.
Binary Stars in Globular Clusters
NASA Astrophysics Data System (ADS)
Mateo, M.; Murdin, P.
2000-11-01
Globular clusters have long been known to be among the richest stellar groupings within our Galaxy, but for many years they were believed to be largely devoid of the most minimal stellar group: binary stars (see BINARY STARS: OVERVIEW). For many years, the only evidence that any binaries existed in these clusters came from the presence of BLUE STRAGGLERS—stars that appear to be significantly you...
ERIC Educational Resources Information Center
Sympson, James B.; And Others
Conventional Armed Services Vocational Aptitude Battery-7 (ASVAB) Arithmetic Reasoning and Word Knowledge tests, were compared with computer-administered adaptive tests as predictors of performance in an Air Force Jet Engine Mechanic training course (n=495). Results supported earlier research in showing somewhat longer examinee response times for…
Evolution of Close Binary Systems
Yakut, K; Eggleton, P
2005-01-24
We collected data on the masses, radii, etc. of three classes of close binary stars: low-temperature contact binaries (LTCBs), near-contact binaries (NCBs), and detached close binaries (DCBs). They restrict themselves to systems where (1) both components are, at least arguably, near the Main Sequence, (2) the periods are less than a day, and (3) there is both spectroscopic and photometric analysis leading to reasonably reliable data. They discuss the possible evolutionary connections between these three classes, emphasizing the roles played by mass loss and angular momentum loss in rapidly-rotating cool stars.
KIC 7177553: A Quadruple System of Two Close Binaries
NASA Astrophysics Data System (ADS)
Lehmann, H.; Borkovits, T.; Rappaport, S. A.; Ngo, H.; Mawet, D.; Csizmadia, Sz.; Forgács-Dajka, E.
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. From 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.
Low autocorrelation binary sequences
NASA Astrophysics Data System (ADS)
Packebusch, Tom; Mertens, Stephan
2016-04-01
Binary sequences with minimal autocorrelations have applications in communication engineering, mathematics and computer science. In statistical physics they appear as groundstates of the Bernasconi model. Finding these sequences is a notoriously hard problem, that so far can be solved only by exhaustive search. We review recent algorithms and present a new algorithm that finds optimal sequences of length N in time O(N {1.73}N). We computed all optimal sequences for N≤slant 66 and all optimal skewsymmetric sequences for N≤slant 119.
NASA Astrophysics Data System (ADS)
Griffin, R. Elizabeth; Ake, Thomas B.
This opening chapter provides a brief historical overview of the ζ Aur stars, with a focus on what K.O. Wright, his predecessors and colleagues at the Dominion Astrophysical Observatory, and his contemporaries further afield, achieved during the era of pre-electronic data. It places the topic within the framework of modern observing, data management and computing, outlines the principal features of the chromospheric-eclipse phenomena which single out the ζ Aur binaries for special study, and describes the considerable potential which this remarkable yet very select group of stars offers for increasing our understanding of stellar physics.
NASA Astrophysics Data System (ADS)
Carey, Michael Richard
Binary porous convection falls into the larger category of pattern formation---a symmetry breaking instability which creates a spatially periodic structure within a homogeneous system. The experiments and model presented in this dissertation indicate that an essential piece of physics is missing from the standard Darcian picture used to describe pattern formation in a porous medium convection system. Present theory predicts a bifurcation to an oscillatory state at onset for a binary mixture in a porous media over a wide range of experimental parameters (Brand and Steinberg, Physics Letters 93A 333 (1983)). This theory is inadequate in explaining the predominant large amplitude, backward, stationary overturning convection state observed in our experiments after transients have decayed. Convection experiments were visualized with magnetic resonance imaging and performed with a foam medium in slot and cylindrical geometries as well as a rectangular, packed bead system with water-ethanol mixtures. We explore the possibility that the difference between theory and experiment is due to enhanced solutal mixing not included in previous theories. The enhanced mixing of the fluid produces an effective diffusion coefficient that largely suppresses gradients in the concentration field, resulting in single-fluid like behavior. We model the experimental system with a Lorenz truncation of the binary Darcy equations with enhanced mixing. This model predicts results qualitatively similar to experiments: a forward bifurcation to small amplitude oscillations with a secondary backward bifurcation to large amplitude stationary convection. We have also developed an experimental nuclear magnetic resonance technique that measures the effective diffusion coefficient, D = D(v), as a function of velocity, v, for the individual species of the binary mixture simultaneously. However, the mixing effect measured in plug flow experiments is roughly two to three orders of magnitude too small to have
Moeller, K; Pixner, S; Zuber, J; Kaufmann, L; Nuerk, H-C
2011-01-01
It is assumed that basic numerical competencies are important building blocks for more complex arithmetic skills. The current study aimed at evaluating this interrelation in a longitudinal approach. It was investigated whether first graders' performance in basic numerical tasks in general as well as specific processes involved (e.g., place-value understanding) reliably predicted performance in an addition task in third grade. The results indicated that early place-value understanding was a reliable predictor for specific aspects of arithmetic performance. Implications of the role of basic numerical competencies for the acquisition of complex arithmetic are discussed. PMID:21498043
Muterspaugh, Matthew W.; O'Connell, J.; Hartkopf, William I.; Lane, Benjamin F.; Williamson, M.; Kulkarni, S. R.; Konacki, Maciej; Burke, Bernard F.; Colavita, M. M.; Shao, M.; Wiktorowicz, Sloane J. E-mail: wih@usno.navy.mi E-mail: maciej@ncac.torun.p
2010-12-15
Differential astrometry measurements from the Palomar High-precision Astrometric Search for Exoplanet Systems have been combined with lower precision single-aperture measurements covering a much longer timespan (from eyepiece measurements, speckle interferometry, and adaptive optics) to determine improved visual orbits for 20 binary stars. In some cases, radial velocity observations exist to constrain the full three-dimensional orbit and determine component masses. The visual orbit of one of these binaries-{alpha} Com (HD 114378)-shows that the system is likely to have eclipses, despite its very long period of 26 years. The next eclipse is predicted to be within a week of 2015 January 24.
NASA Astrophysics Data System (ADS)
Park, Conner; Read, Jocelyn; Flynn, Eric; Lockett-Ruiz, Veronica
2016-03-01
Gravitational waves, predicted by Einstein's Theory of Relativity, are a new frontier in astronomical observation we can use to observe phenomena in the universe. Laser Interferometer Gravitational wave Observatory (LIGO) is currently searching for gravitational wave signals, and requires accurate predictions in order to best extract astronomical signals from all other sources of fluctuations. The focus of my research is in increasing the accuracy of Post-Newtonian models of binary neutron star coalescence to match the computationally expensive Numerical models. Numerical simulations can take months to compute a couple of milliseconds of signal whereas the Post-Newtonian can generate similar signals in seconds. However the Post-Newtonian model is an approximation, e.g. the Taylor T4 Post-Newtonian model assumes that the two bodies in the binary neutron star system are point charges. To increase the effectiveness of the approximation, I added in tidal effects, resonance frequencies, and a windowing function. Using these observed effects from simulations significantly increases the Post-Newtonian model's similarity to the Numerical signal.
Multilevel Models for Binary Data
ERIC Educational Resources Information Center
Powers, Daniel A.
2012-01-01
The methods and models for categorical data analysis cover considerable ground, ranging from regression-type models for binary and binomial data, count data, to ordered and unordered polytomous variables, as well as regression models that mix qualitative and continuous data. This article focuses on methods for binary or binomial data, which are…
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.
Systolic temporal arithmetic; A new formalism for specification and verification of systolic arrays
Ling, N. ); Bayoumi, M.A. )
1990-08-01
This paper introduces a novel formalism named systolic temporal arithmetic (STA) suitable for describing arithmetic operations in dynamic environments. The motivation behind the development of STA is to use it for formal specifications and verifications of systolic arrays at the array architecture level. Besides providing value and operation abstraction from the lower level, it also exploits several features of systolic arrays such as synchrony, regularity, repeatability, modularity, pipelinability, parallel processing ability, as well as spatial and temporal locality. STA provides constructs and verification techniques for simple, efficient, and effective systolic array specification and verification. Verification techniques such as mathematical induction are suggested to exploit these systolic array features so as to speedup the process.
Lightweight Floating-Point Arithmetic: Case Study of Inverse Discrete Cosine Transform
NASA Astrophysics Data System (ADS)
Fang, Fang; Chen, Tsuhan; Rutenbar, Rob A.
2002-12-01
To enable floating-point (FP) signal processing applications in low-power mobile devices, we propose lightweight floating-point arithmetic. It offers a wider range of precision/power/speed/area trade-offs, but is wrapped in forms that hide the complexity of the underlying implementations from both multimedia software designers and hardware designers. Libraries implemented in C++ and Verilog provide flexible and robust floating-point units with variable bit-width formats, multiple rounding modes and other features. This solution bridges the design gap between software and hardware, and accelerates the design cycle from algorithm to chip by avoiding the translation to fixed-point arithmetic. We demonstrate the effectiveness of the proposed scheme using the inverse discrete cosine transform (IDCT), in the context of video coding, as an example. Further, we implement lightweight floating-point IDCT into hardware and demonstrate the power and area reduction.
Hui, Sheldon; Suganthan, Ponnuthurai N
2016-01-01
Multimodal optimization problems consists of multiple equal or comparable spatially distributed solutions. Niching and clustering differential evolution (DE) techniques have been demonstrated to be highly effective for solving such problems. The key challenge in the speciation niching technique is to balance between local solution exploitation and global exploration. Our proposal enhances exploration by applying arithmetic recombination with speciation and improves exploitation of individual peaks by applying neighborhood mutation with ensemble strategies. Our novel algorithm, called ensemble and arithmetic recombination-based speciation DE, is shown to either outperform or perform comparably to the state-of-the-art algorithms on 29 common multimodal benchmark problems. Comparable performance is observed only when some problems are solved perfectly by the algorithms in the literature. PMID:25781971
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.
Individual differences in arithmetic skill reflected in event-related brain potentials.
Núñez-Peña, M Isabel; Gracia-Bafalluy, María; Tubau, Elisabet
2011-05-01
We used event-related brain potentials (ERP) to study the problem-size effect in individuals with high and low arithmetic skill. Participants were presented with a classic equality verification task, and problem size was manipulated by using small (e.g., 3+4), medium (e.g., 7+8) and large problems (e.g., 16+29). ERP analyses were time-locked to the onset of the second operand in order to address brain potentials during the production phase. High-skill individuals showed a positive slow wave when solving large problems and no differences in the ERP pattern when solving small and medium problems. In contrast, low-skill individuals showed a positive slow wave when solving medium and large problems. Given that differences between high and low skill individuals have been related to differences in calculation strategies, these results provide further support to the utility of using ERP as a signature of arithmetic strategy.
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.
Math anxiety differentially affects WAIS-IV arithmetic performance in undergraduates.
Buelow, Melissa T; Frakey, Laura L
2013-06-01
Previous research has shown that math anxiety can influence the math performance level; however, to date, it is unknown whether math anxiety influences performance on working memory tasks during neuropsychological evaluation. In the present study, 172 undergraduate students completed measures of math achievement (the Math Computation subtest from the Wide Range Achievement Test-IV), math anxiety (the Math Anxiety Rating Scale-Revised), general test anxiety (from the Adult Manifest Anxiety Scale-College version), and the three Working Memory Index tasks from the Wechsler Adult Intelligence Scale-IV Edition (WAIS-IV; Digit Span [DS], Arithmetic, Letter-Number Sequencing [LNS]). Results indicated that math anxiety predicted performance on Arithmetic, but not DS or LNS, above and beyond the effects of gender, general test anxiety, and math performance level. Our findings suggest that math anxiety can negatively influence WAIS-IV working memory subtest scores. Implications for clinical practice include the utilization of LNS in individuals expressing high math anxiety.
Nested arithmetic progressions of oscillatory phases in Olsen's enzyme reaction model.
Gallas, Marcia R; Gallas, Jason A C
2015-06-01
We report some regular organizations of stability phases discovered among self-sustained oscillations of a biochemical oscillator. The signature of such organizations is a nested arithmetic progression in the number of spikes of consecutive windows of periodic oscillations. In one of them, there is a main progression of windows whose consecutive number of spikes differs by one unit. Such windows are separated by a secondary progression of smaller windows whose number of spikes differs by two units. Another more complex progression involves a fan-like nested alternation of stability phases whose number of spikes seems to grow indefinitely and to accumulate methodically in cycles. Arithmetic progressions exist abundantly in several control parameter planes and can be observed by tuning just one among several possible rate constants governing the enzyme reaction.
A Hand Full of Numbers: A Role for Offloading in Arithmetics Learning?
Costa, Annelise Júlio; Silva, Júlia Beatriz Lopes; Chagas, Pedro Pinheiro; Krinzinger, Helga; Lonneman, Jan; Willmes, Klaus; Wood, Guilherme; Haase, Vitor Geraldi
2011-01-01
Finger counting has been associated to arithmetic learning in children. We examined children with (n = 14) and without (n = 84) mathematics learning difficulties with ages between 8 and 11 years. Deficits in finger gnosia were found in association to mathematical difficulties. Finger gnosia was particularly relevant for the performance in word problems requiring active manipulation of small magnitudes in the range between 1 and 10. Moreover, the deficits in finger gnosia could not be attributed to a shortage in working memory capacity but rather to a specific inability to use fingers to transiently represent magnitudes, tagging to be counted objects, and reducing the cognitive load necessary to solve arithmetic problems. Since finger gnosia was more related to symbolic than to non-symbolic magnitude processing, finger-related representation of magnitude seems to be an important link for learning the mapping of analog onto discrete symbolic magnitudes. PMID:22180748
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
Reactivity to written mental arithmetic: effects of exercise lay-off and habituation.
Szabo, A; Gauvin, L
1992-03-01
The present study examined (i) the effects of exercise lay-off on heart rate (HR) and subjective response to mental stress in 24 individuals highly committed to exercise, and (ii) psychophysiological reactivity to a challenging written mental arithmetic with subjectively controlled difficulty level. Subjects were tested on two occasions one week apart. Exercise withdrawal did not influence psychophysiological stress response. Second exposure to the mental arithmetic resulted in significantly lower HR response, due to habituation; higher pretask resting HR, due to anticipation of performance; and later onset in HR recovery. No changes in task performance and subjective measures were observed from session one to session two, indicating that habituation is rather a physiological than behavioral phenomenon. While these findings do not strengthen the link between exercise and stress response, they demonstrate the significant mediatory roles of habituation and anticipation in laboratory studies employing a test-retest design.
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
Signature Visualization of Software Binaries
Panas, T
2008-07-01
In this paper we present work on the visualization of software binaries. In particular, we utilize ROSE, an open source compiler infrastructure, to pre-process software binaries, and we apply a landscape metaphor to visualize the signature of each binary (malware). We define the signature of a binary as a metric-based layout of the functions contained in the binary. In our initial experiment, we visualize the signatures of a series of computer worms that all originate from the same line. These visualizations are useful for a number of reasons. First, the images reveal how the archetype has evolved over a series of versions of one worm. Second, one can see the distinct changes between version. This allows the viewer to form conclusions about the development cycle of a particular worm.
NASA Technical Reports Server (NTRS)
Manos, P.; Turner, L. R.
1972-01-01
Approximations which can be evaluated with precision using floating-point arithmetic are presented. The particular set of approximations thus far developed are for the function TAN and the functions of USASI FORTRAN excepting SQRT and EXPONENTIATION. These approximations are, furthermore, specialized to particular forms which are especially suited to a computer with a small memory, in that all of the approximations can share one general purpose subroutine for the evaluation of a polynomial in the square of the working argument.
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.
DNA based arithmetic function: a half adder based on DNA strand displacement
NASA Astrophysics Data System (ADS)
Li, Wei; Zhang, Fei; Yan, Hao; Liu, Yan
2016-02-01
Biomolecular programming utilizes the reactions and information stored in biological molecules, such as proteins and nucleic acids, for computational purposes. DNA has proven itself an excellent candidate for building logic operating systems due to its highly predictable molecular behavior. In this work we designed and realized an XOR logic gate and an AND logic gate based on DNA strand displacement reactions. These logic gates utilize ssDNA as input and output signals. The XOR gate and the AND gate were used as building blocks for constructing a half adder logic circuit, which is a primary step in constructing a full adder, a basic arithmetic unit in computing. This work provides the field of DNA molecular programming with a potential universal arithmetic tool.Biomolecular programming utilizes the reactions and information stored in biological molecules, such as proteins and nucleic acids, for computational purposes. DNA has proven itself an excellent candidate for building logic operating systems due to its highly predictable molecular behavior. In this work we designed and realized an XOR logic gate and an AND logic gate based on DNA strand displacement reactions. These logic gates utilize ssDNA as input and output signals. The XOR gate and the AND gate were used as building blocks for constructing a half adder logic circuit, which is a primary step in constructing a full adder, a basic arithmetic unit in computing. This work provides the field of DNA molecular programming with a potential universal arithmetic tool. Electronic supplementary information (ESI) available: Detailed descriptions of DNA logic gate design, materials and methods, and additional data analysis. See DOI: 10.1039/c5nr08497k
Fourier transforms on Cantor sets: A study in non-Diophantine arithmetic and calculus
NASA Astrophysics Data System (ADS)
Aerts, Diederik; Czachor, Marek; Kuna, Maciej
2016-10-01
Fractals equipped with intrinsic arithmetic lead to a natural definition of differentiation, integration and complex numbers. Applying the formalism to the problem of a Fourier transform on fractals we show that the resulting transform has all the expected basic properties. As an example we discuss a sawtooth signal on the ternary middle-third Cantor set. The formalism works also for fractals that are not self-similar.
The Influence of verbalization on the pattern of cortical activation during mental arithmetic
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
Mental arithmetic stress as a test for evaluation of diabetic sympathetic autonomic neuropathy.
Locatelli, A; Franzetti, I; Lepore, G; Maglio, M L; Gaudio, E; Caviezel, F; Pozza, G
1989-08-01
The effects of a 1-min mental arithmetic stress test on heart rate change were studied in 72 Type 1 diabetic patients, 36 without and 36 with diabetic autonomic neuropathy (mean age 33 and 44 yr, respectively), and in 80 matched normal subjects. Variation in hand skin temperature was also recorded in 25 normal subjects and 30 diabetic patients without and 32 with autonomic neuropathy. While mental arithmetic rapidly reduced skin temperature of normal volunteers and of patients without autonomic neuropathy, no effect was found in autonomic neuropath (a drop of 0.63 +/- 0.05 (+/- SE), 0.52 +/- 0.04 and 0.16 +/- 0.02 degrees C (p less than 0.001), respectively). In control subjects and in diabetic patients without and with autonomic neuropathy the heart rate increase was 22.9 +/- 6.8 (+/- SD), 21.4 +/- 8.4 and 7.0 +/- 3.7 beats min-1, respectively (p less than 0.001). The ratio between maximum mental arithmetic-induced heart rate and basal heart rate was 1.29 +/- 0.10, 1.24 +/- 0.10 and 1.07 +/- 0.05 (p less than 0.001) for healthy subjects, non-neuropathic patients, and neuropathic patients. Cut-off values (the low normal limit for these variables) are proposed: skin temperature 0.23 degrees C, heart rate increase 11.6 beats min-1 and heart rate ratio 1.12. Anxiety state, blood glucose concentration (excluding hypoglycaemia), body position, basal heart rate, and age did not interfere with responses to mental arithmetic stress. PMID:2527129
ERIC Educational Resources Information Center
Campbell, Jamie I. D.
2005-01-01
Meuter and Allport (1999) demonstrated greater RT (response time) costs for bilinguals to switch to their first language (L1) from their second language (L2) relative to switching to L2 from L1. Here, analyses of digit naming and simple arithmetic (from 2+2 to 9+9 and from 2x2 to 9x9) by Chinese-English bilinguals demonstrated that these…
BINARY ASTROMETRIC MICROLENSING WITH GAIA
Sajadian, Sedighe
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 due 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.
Evolution of Small Binary Asteroids with the Binary YORP Effect
NASA Astrophysics Data System (ADS)
Frouard, Julien
2013-05-01
Abstract (2,250 Maximum Characters): Small, Near-Earth binaries are believed to be created following the fission of an asteroid spun up by the YORP effect. It is then believed that the YORP effect acting on the secondary (Binary YORP) increases or decreases the binary mutual distance on 10^5 yr timescales. How long this mechanism can apply is not yet fully understood. We investigate the binary orbital and rotational dynamics by using non-averaged, direct numerical simulations, taking into account the relative motion of two ellipsoids (primary and secondary) and the solar perturbation. We add the YORP force and torque on the orbital and rotational motion of the secondary. As a check of our code we obtain a ~ 7.2 cm/yr drift in semi-major axis for 1999 KW4 beta, consistent with the values obtained with former analytical studies. The synchronous rotation of the secondary is required for the Binary YORP to be effective. We investigate the synchronous lock of the secondary in function of different parameters ; mutual distance, shape of the secondary, and heliocentric orbit. For example we show that the secondary of 1999 KW4 can be synchronous only up to 7 Rp (primary radius), where the resonance becomes completely chaotic even for very small eccentricities. We use Gaussian Random Spheres to obtain various secondary shapes, and check the evolution of the binaries with the Binary YORP effect.
Geary, D C; Bow-Thomas, C C; Liu, F; Siegler, R S
1996-10-01
The arithmetical competencies of more than 200 Chinese or American kindergarten, first-, second-, or third-grade children were assessed toward the beginning and toward the end of the U.S. school year. All children were administered a paper-and-pencil test of addition skills, a digit span measure, and an addition strategy assessment. The addition strategy assessment provided information on the types of strategies the children used to solve simple addition problems as well as information on the speed and accuracy of their strategy use. Information on the number of math instruction periods across times of measurement was also obtained for each of the first-, second-, and third-grade children. The pattern of arithmetical development across the academic year and across the Chinese and American children suggests that a mix of cultural and maturational factors influence the emergence of early arithmetical competencies and that the Chinese advantage in early mathematical development is related to a combination of language- and school-related factors. PMID:9022227
Design and quantitative analysis of parametrisable eFPGA-architectures for arithmetic
NASA Astrophysics Data System (ADS)
Neumann, B.; von Sydow, T.; Blume, H.; Noll, T. G.
2006-09-01
Future SoCs will feature embedded FPGAs (eFPGAs) to enable flexible and efficient implementations of high-throughput digital signal processing applications. Current research projects on and emerging products containing FPGAs are mainly based on "standard FPGA"-architectures that are optimised for a very wide range of applications. The implementation costs of these FPGAs are dominated by a very complex interconnect network. This paper presents a method to improve the efficiency of eFPGAs by tailoring them for a certain application domain using a parametrisable architecture template derived from the results of a systematic evaluation of the requirements of the application domain. Two different architectures are discussed, a reference architecture to illustrate the methodology and possible optimisation measures as well as a specialised arithmetic-oriented eFPGA for applications like correlators, decoders, and filters. For the arithmetic-oriented architecture, a novel logic element (LE) and a special interconnect architecture that was designed with respect to the connectivity characteristics of regular datapaths, are presented. For both architecture templates, physically optimised implementations based on an automatic design approach have been created. As a first cost comparison of these implementations with standard FPGAs, the LE-density (number of logic elements per mm2) is evaluated. For the arithmetic-oriented architecture, the LE-density could be increased by an order of magnitude compared to standard architectures.
Dormal, Valérie; Schuller, Anne-Marie; Nihoul, Julie; Pesenti, Mauro; Andres, Michael
2014-07-01
Recent behavioural and brain imaging studies have provided evidence for rightward and leftward attention shifts while solving addition and subtraction problems respectively, suggesting that mental arithmetic makes use of mechanisms akin to those underlying spatial attention. However, this hypothesis mainly relies on correlative data and the causal relevance of spatial attention for mental arithmetic remains unclear. In order to test whether the mechanisms underlying spatial attention are necessary to perform arithmetic operations, we compared the performance of right brain-lesioned patients, with and without left unilateral neglect, and healthy controls in addition and subtraction of two-digit numbers. We predicted that patients with left unilateral neglect would be selectively impaired in the subtraction task while being unimpaired in the addition task. The results showed that neglect patients made more errors than the two other groups to subtract large numbers, whereas they were still able to solve large addition problems matched for difficulty and magnitude of the answer. This finding demonstrates a causal relationship between the ability to attend the left side of space and the solving of large subtraction problems. A plausible account is that attention shifts help localizing the position of the answer on a spatial continuum while subtracting large numbers. PMID:24859525
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 .
Finger gnosis predicts a unique but small part of variance in initial arithmetic performance.
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. PMID:26895483
Multiple Paths to Mathematics Practice in Al-Kashi's Key to Arithmetic
NASA Astrophysics Data System (ADS)
Taani, Osama
2013-07-01
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.
Mace, F C; Neef, N A; Shade, D; Mauro, B C
1996-01-01
Students with learning difficulties participated in two studies that analyzed the effects of problem difficulty and reinforcer quality upon time allocated to two sets of arithmetic problems reinforced according to a concurrent variable-interval 30-s variable-interval 120-s schedule. In Study 1, high- and low-difficulty arithmetic problems were systematically combined with rich and lean concurrent schedules (nickels used as reinforcers) across conditions using a single-subject design. The pairing of the high-difficulty problems with the richer schedule failed to offset time allocated to that alternative. Study 2 investigated the interactive effects of problem difficulty and reinforcer quality (nickels vs. program money) upon time allocation to arithmetic problems maintained by the concurrent schedules of reinforcement. Unlike problem difficulty, the pairing of the lesser quality reinforcer (program money) with the richer schedule reduced the time allocated to that alternative. The magnitude of this effect was greatest when combined with the low-difficulty problems. These studies have important implications for a matching law analysis of asymmetrical reinforcement variables that influence time allocation. PMID:8881341
NASA Technical Reports Server (NTRS)
Truong, Trieu-Kie (Inventor); Hsu, In-Shek (Inventor); Reed, Irving S. (Inventor)
1989-01-01
A pipeline binary updown counter is comprised of simple stages that may be readily replicated. Each stage is defined by the Boolean logic equation: A(sub n)(t) = A(sub n)(t - 1) exclusive OR (U AND P(sub n)) inclusive OR (D AND Q(sub n)), where A(sub n)(t) denotes the value of the nth bit at time t. The input to the counter has three values represented by two binary signals U and D such that if both are zero, the input is zero, if U = 0 and D = 1, the input is -1 and if U = 1 and D = 0, the input is +1. P(sub n) represents a product of A(sub k)'s for 1 is less than or equal to k is less than or equal to -1, while Q(sub n) represents the product of bar A's for 1 is less than or equal to K is less than or equal to n - 1, where bar A(sub k) is the complement of A(sub k) and P(sub n) and Q(sub n) are expressed as the following two equations: P(sub n) = A(sub n - 1) A(sub n - 2)...A(sub 1) and Q(sub n) = bar A(sub n - 1) bar A(sub n - 2)...bar A(sub 1), which can be written in recursive form as P(sub n) = P(sub n - 1) AND bar A(sub n - 1) and Q(sub n) = Q(sub n - 1) AND bar A(sub n - 1) with the initial values P(sub 1) = 1 and Q(sub 1) = 1.
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
ROTATIONAL VELOCITIES OF INDIVIDUAL COMPONENTS IN VERY LOW MASS BINARIES
Konopacky, Q. M.; Macintosh, B. A.; Ghez, A. M.; Fabrycky, D. C.; White, R. J.; Barman, T. S.; Rice, E. L.; Hallinan, G.; Duchene, G. E-mail: konopacky@di.utoronto.ca E-mail: fabrycky@ucolick.org E-mail: barman@lowell.edu E-mail: gh@astro.caltech.edu
2012-05-01
We present rotational velocities for individual components of 11 very low mass (VLM) binaries with spectral types between M7 and L7.5. These results are based on observations taken with the near-infrared spectrograph, NIRSPEC, and the Keck II laser guide star adaptive optics system. We find that the observed sources tend to be rapid rotators (v sin i > 10 km s{sup -1}), consistent with previous seeing-limited measurements of VLM objects. The two sources with the largest v sin i, LP 349-25B and HD 130948C, are rotating at {approx}30% of their break-up speed, and are among the most rapidly rotating VLM objects known. Furthermore, five binary systems, all with orbital semimajor axes {approx}<3.5 AU, have component v sin i values that differ by greater than 3{sigma}. To bring the binary components with discrepant rotational velocities into agreement would require the rotational axes to be inclined with respect to each other, and that at least one component is inclined with respect to the orbital plane. Alternatively, each component could be rotating at a different rate, even though they have similar spectral types. Both differing rotational velocities and inclinations have implications for binary star formation and evolution. We also investigate possible dynamical evolution in the triple system HD 130948A-BC. The close binary brown dwarfs B and C have significantly different v sin i values. We demonstrate that components B and C could have been torqued into misalignment by the primary star, A, via orbital precession. Such a scenario can also be applied to another triple system in our sample, GJ 569A-Bab. Interactions such as these may play an important role in the dynamical evolution of VLM binaries. Finally, we note that two of the binaries with large differences in component v sin i, LP 349-25AB and 2MASS 0746+20AB, are also known radio sources.
NASA Astrophysics Data System (ADS)
Kraus, Adam L.; Ireland, Michael J.; Huber, Daniel; Mann, Andrew W.; Dupuy, Trent J.
2016-07-01
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 382 Kepler Objects of Interest (KOIs) obtained using adaptive-optics imaging and nonredundant aperture-mask interferometry on the Keck II telescope. Among the full sample of 506 candidate binary companions to KOIs, we super-resolve some binary systems to projected separations of <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. For a field binary population, we should have found 58 binary companions with projected separation ρ < 50 au and mass ratio q > 0.4 we instead only found 23 companions (a 4.6σ deficit), many of which must be wider pairs that are only close in projection. 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 {a}{cut}={47}-23+59 au, the planet occurrence rate in binary systems is only {S}{bin}={0.34}-0.15+0.14 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.
Content identification: binary content fingerprinting versus binary content encoding
NASA Astrophysics Data System (ADS)
Ferdowsi, Sohrab; Voloshynovskiy, Svyatoslav; Kostadinov, Dimche
2014-02-01
In this work, we address the problem of content identification. We consider content identification as a special case of multiclass classification. The conventional approach towards identification is based on content fingerprinting where a short binary content description known as a fingerprint is extracted from the content. We propose an alternative solution based on elements of machine learning theory and digital communications. Similar to binary content fingerprinting, binary content representation is generated based on a set of trained binary classifiers. We consider several training/encoding strategies and demonstrate that the proposed system can achieve the upper theoretical performance limits of content identification. The experimental results were carried out both on a synthetic dataset with different parameters and the FAMOS dataset of microstructures from consumer packages.
Binary Oscillatory Crossflow Electrophoresis
NASA Technical Reports Server (NTRS)
Molloy, Richard F.; Gallagher, Christopher T.; Leighton, David T., Jr.
1997-01-01
Electrophoresis has long been recognized as an effective analytic technique for the separation of proteins and other charged species, however attempts at scaling up to accommodate commercial volumes have met with limited success. In this report we describe a novel electrophoretic separation technique - Binary Oscillatory Crossflow Electrophoresis (BOCE). Numerical simulations indicate that the technique has the potential for preparative scale throughputs with high resolution, while simultaneously avoiding many problems common to conventional electrophoresis. The technique utilizes the interaction of an oscillatory electric field and a transverse oscillatory shear flow to create an active binary filter for the separation of charged protein species. An oscillatory electric field is applied across the narrow gap of a rectangular channel inducing a periodic motion of charged protein species. The amplitude of this motion depends on the dimensionless electrophoretic mobility, alpha = E(sub o)mu/(omega)d, where E(sub o) is the amplitude of the electric field oscillations, mu is the dimensional mobility, omega is the angular frequency of oscillation and d is the channel gap width. An oscillatory shear flow is induced along the length of the channel resulting in the separation of species with different mobilities. We present a model that predicts the oscillatory behavior of charged species and allows estimation of both the magnitude of the induced convective velocity and the effective diffusivity as a function of a in infinitely long channels. Numerical results indicate that in addition to the mobility dependence, the steady state behavior of solute species may be strongly affected by oscillating fluid into and out of the active electric field region at the ends of the cell. The effect is most pronounced using time dependent shear flows of the same frequency (cos((omega)t)) flow mode) as the electric field oscillations. Under such conditions, experiments indicate that
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.
Computing Binary Black Hole Initial Data with Discontinuous Galerkin Methods
NASA Astrophysics Data System (ADS)
Vincent, Trevor; Pfeiffer, Harald
2016-03-01
Discontinuous Galerkin (DG) finite element methods have been used to solve hyperbolic PDEs in relativistic simulations and offer advantages over traditional discretization methods. Comparatively little attention has been given towards using the DG method to solve the elliptic PDEs arising from the Einstein initial data equations. We describe how the DG method can be used to create a parallel, adaptive solver for initial data. We discuss the use of our dG code to compute puncture initial data for binary black holes.
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.
Cryptography with DNA binary strands.
Leier, A; Richter, C; Banzhaf, W; Rauhe, H
2000-06-01
Biotechnological methods can be used for cryptography. Here two different cryptographic approaches based on DNA binary strands are shown. The first approach shows how DNA binary strands can be used for steganography, a technique of encryption by information hiding, to provide rapid encryption and decryption. It is shown that DNA steganography based on DNA binary strands is secure under the assumption that an interceptor has the same technological capabilities as sender and receiver of encrypted messages. The second approach shown here is based on steganography and a method of graphical subtraction of binary gel-images. It can be used to constitute a molecular checksum and can be combined with the first approach to support encryption. DNA cryptography might become of practical relevance in the context of labelling organic and inorganic materials with DNA 'barcodes'.
CHAOTIC ZONES AROUND GRAVITATING BINARIES
Shevchenko, Ivan I.
2015-01-20
The extent of the continuous zone of chaotic orbits of a small-mass tertiary around a system of two gravitationally bound primaries of comparable masses (a binary star, a binary black hole, a binary asteroid, etc.) is estimated analytically, as a function of the tertiary's orbital eccentricity. The separatrix map theory is used to demonstrate that the central continuous chaos zone emerges (above a threshold in the primaries' mass ratio) due to overlapping of the orbital resonances corresponding to the integer ratios p:1 between the tertiary and the central binary periods. In this zone, the unlimited chaotic orbital diffusion of the tertiary takes place, up to its ejection from the system. The primaries' mass ratio, above which such a chaotic zone is universally present at all initial eccentricities of the tertiary, is estimated. The diversity of the observed orbital configurations of biplanetary and circumbinary exosystems is shown to be in accord with the existence of the primaries' mass parameter threshold.
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.
Simulating relativistic binaries with Whisky
NASA Astrophysics Data System (ADS)
Baiotti, L.
We report about our first tests and results in simulating the last phase of the coalescence and the merger of binary relativistic stars. The simulations were performed using our code Whisky and mesh refinement through the Carpet driver.
ERIC Educational Resources Information Center
Klinkenberg, S.; Straatemeier, M.; van der Maas, H. L. J.
2011-01-01
In this paper we present a model for computerized adaptive practice and monitoring. This model is used in the Maths Garden, a web-based monitoring system, which includes a challenging web environment for children to practice arithmetic. Using a new item response model based on the Elo (1978) rating system and an explicit scoring rule, estimates of…
Exoplanets bouncing between binary stars
NASA Astrophysics Data System (ADS)
Moeckel, Nickolas; Veras, Dimitri
2012-05-01
Exoplanetary systems are found not only among single stars, but also among binaries of widely varying parameters. Binaries with separations of 100-1000 au are prevalent in the solar neighbourhood; at these separations, planet formation around a binary member may largely proceed as if around a single star. During the early dynamical evolution of a planetary system, planet-planet scattering can eject planets from a star's grasp. In a binary, the motion of a planet ejected from one star has effectively entered a restricted three-body system consisting of itself and the two stars, and the equations of motion of the three-body problem will apply as long as the ejected planet remains far from the remaining planets. Depending on its energy, escape from the binary as a whole may be impossible or delayed until the three-body approximation breaks down, and further close interactions with its planetary siblings boost its energy when it passes close to its parent star. Until then, this planet may be able to transition from the space around one star to the other, and chaotically 'bounce' back and forth. In this paper, we directly simulate scattering planetary systems that are around one member of a circular binary, and quantify the frequency of bouncing in scattered planets. We find that a great majority (70-85 per cent) of ejected planets will pass at least once through the space of it's host's binary companion, and depending on the binary parameters about 35-75 per cent will begin bouncing. The time spent bouncing is roughly lognormally distributed with a peak at about 104 yr, with only a small percentage bouncing for more than 1 Myr. This process may perturb and possibly incite instability among existing planets around the companion star. In rare cases, the presence of multiple planets orbiting both stars may cause post-bouncing capture or planetary swapping.
The indirect binary n-cube array
NASA Technical Reports Server (NTRS)
Pease, M. C.
1977-01-01
The array is built from a large number (hundreds or thousands) of microprocessors or microcomputers linked through a switching network into an indirect binary n-cube array. Control is two level, the array operating synchronously, or in lock step, at the higher level, and with the broadcast commands being locally interpreted into rewritable microinstruction streams in the microprocessors and in the switch control units. The key to the design is the switching array. By properly programming it, the array can be made into a wide variety of virtual arrays which are well adapted to a wide range of applications. It is believed that the flexibility of the switching array can be used to obtain fault avoidance, which appears necessary in any highly parallel design.
NASA Astrophysics Data System (ADS)
Reig, Pablo
2011-03-01
The interest in X/ γ-ray Astronomy has grown enormously in the last decades thanks to the ability to send X-ray space missions above the Earth’s atmosphere. There are more than half a million X-ray sources detected and over a hundred missions (past and currently operational) devoted to the study of cosmic X/ γ rays. With the improved sensibilities of the currently active missions new detections occur almost on a daily basis. Among these, neutron-star X-ray binaries form an important group because they are among the brightest extra-solar objects in the sky and are characterized by dramatic variability in brightness on timescales ranging from milliseconds to months and years. Their main source of power is the gravitational energy released by matter accreted from a companion star and falling onto the neutron star in a relatively close binary system. Neutron-star X-ray binaries divide into high-mass and low-mass systems according to whether the mass of the donor star is above ˜8 or below ˜2 M⊙, respectively. Massive X-ray binaries divide further into supergiant X-ray binaries and Be/X-ray binaries depending on the evolutionary status of the optical companion. Virtually all Be/X-ray binaries show X-ray pulsations. Therefore, these systems can be used as unique natural laboratories to investigate the properties of matter under extreme conditions of gravity and magnetic field. The purpose of this work is to review the observational properties of Be/X-ray binaries. The open questions in Be/X-ray binaries include those related to the Be star companion, that is, the so-called “Be phenomenon”, such as, timescales associated to the formation and dissipation of the equatorial disc, mass-ejection mechanisms, V/ R variability, and rotation rates; those related to the neutron star, such as, mass determination, accretion physics, and spin period evolution; but also, those that result from the interaction of the two constituents, such as, disc truncation and mass
Unsupervised learning of binary vectors
NASA Astrophysics Data System (ADS)
Copelli Lopes da Silva, Mauro
In this thesis, unsupervised learning of binary vectors from data is studied using methods from Statistical Mechanics of disordered systems. In the model, data vectors are distributed according to a single symmetry-breaking direction. The aim of unsupervised learning is to provide a good approximation to this direction. The difference with respect to previous studies is the knowledge that this preferential direction has binary components. It is shown that sampling from the posterior distribution (Gibbs learning) leads, for general smooth distributions, to an exponentially fast approach to perfect learning in the asymptotic limit of large number of examples. If the distribution is non-smooth, then first order phase transitions to perfect learning are expected. In the limit of poor performance, a second order phase transition ("retarded learning") is predicted to occur if the data distribution is not biased. Using concepts from Bayesian inference, the center of mass of the Gibbs ensemble is shown to have maximal average (Bayes-optimal) performance. This upper bound for continuous vectors is extended to a discrete space, resulting in the clipped center of mass of the Gibbs ensemble having maximal average performance among the binary vectors. To calculate the performance of this best binary vector, the geometric properties of the center of mass of binary vectors are studied. The surprising result is found that the center of mass of infinite binary vectors which obey some simple constraints, is again a binary vector. When disorder is taken into account in the calculation, however, a vector with continuous components is obtained. The performance of the best binary vector is calculated and shown to always lie above that of Gibbs learning and below the Bayes-optimal performance. Making use of a variational approach under the replica symmetric ansatz, an optimal potential is constructed in the limits of zero temperature and mutual overlap 1. Minimization of this potential
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
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.
Paranoia.Ada: A diagnostic program to evaluate Ada floating-point arithmetic
NASA Technical Reports Server (NTRS)
Hjermstad, Chris
1986-01-01
Many essential software functions in the mission critical computer resource application domain depend on floating point arithmetic. Numerically intensive functions associated with the Space Station project, such as emphemeris generation or the implementation of Kalman filters, are likely to employ the floating point facilities of Ada. Paranoia.Ada appears to be a valuabe program to insure that Ada environments and their underlying hardware exhibit the precision and correctness required to satisfy mission computational requirements. As a diagnostic tool, Paranoia.Ada reveals many essential characteristics of an Ada floating point implementation. Equipped with such knowledge, programmers need not tremble before the complex task of floating point computation.
A motif extraction algorithm based on hashing and modulo-4 arithmetic.
Sheng, Huitao; Mehrotra, Kishan; Mohan, Chilukuri; Raina, Ramesh
2008-01-01
We develop an algorithm to identify cis-elements in promoter regions of coregulated genes. This algorithm searches for subsequences of desired length whose frequency of occurrence is relatively high, while accounting for slightly perturbed variants using hash table and modulo arithmetic. Motifs are evaluated using profile matrices and higher-order Markov background model. Simulation results show that our algorithm discovers more motifs present in the test sequences, when compared with two well-known motif-discovery tools (MDScan and AlignACE). The algorithm produces very promising results on real data set; the output of the algorithm contained many known motifs. PMID:20058489
Algorithmic solution of arithmetic problems and operands-answer associations in long-term memory.
Thevenot, C; Barrouillet, P; Fayol, M
2001-05-01
Many developmental models of arithmetic problem solving assume that any algorithmic solution of a given problem results in an association of the two operands and the answer in memory (Logan & Klapp, 1991; Siegler, 1996). In this experiment, adults had to perform either an operation or a comparison on the same pairs of two-digit numbers and then a recognition task. It is shown that unlike comparisons, the algorithmic solution of operations impairs the recognition of operands in adults. Thus, the postulate of a necessary and automatic storage of operands-answer associations in memory when young children solve additions by algorithmic strategies needs to be qualified. PMID:11394064
Implementation of Arithmetic and Nonarithmetic Functions on a Label-free and DNA-based Platform
Wang, Kun; He, Mengqi; Wang, Jin; He, Ronghuan; Wang, Jianhua
2016-01-01
A series of complex logic gates were constructed based on graphene oxide and DNA-templated silver nanoclusters to perform both arithmetic and nonarithmetic functions. For the purpose of satisfying the requirements of progressive computational complexity and cost-effectiveness, a label-free and universal platform was developed by integration of various functions, including half adder, half subtractor, multiplexer and demultiplexer. The label-free system avoided laborious modification of biomolecules. The designed DNA-based logic gates can be implemented with readout of near-infrared fluorescence, and exhibit great potential applications in the field of bioimaging as well as disease diagnosis. PMID:27713517
Transcranial random noise stimulation mitigates increased difficulty in an arithmetic learning task
Popescu, Tudor; Krause, Beatrix; Terhune, Devin B.; Twose, Olivia; Page, Thomas; Humphreys, Glyn; Cohen Kadosh, Roi
2016-01-01
Proficiency in arithmetic learning can be achieved by using a multitude of strategies, the most salient of which are procedural learning (applying a certain set of computations) and rote learning (direct retrieval from long-term memory). Here we investigated the effect of transcranial random noise stimulation (tRNS), a non-invasive brain stimulation method previously shown to enhance cognitive training, on both types of learning in a 5-day sham-controlled training study, under two conditions of task difficulty, defined in terms of item repetition. On the basis of previous research implicating the prefrontal and posterior parietal cortex in early and late stages of arithmetic learning, respectively, sham-controlled tRNS was applied to bilateral prefrontal cortex for the first 3 days and to the posterior parietal cortex for the last 2 days of a 5-day training phase. The training involved learning to solve arithmetic problems by applying a calculation algorithm; both trained and untrained problems were used in a brief testing phase at the end of the training phase. Task difficulty was manipulated between subjects by using either a large (“easy” condition) or a small (“difficult” condition) number of repetition of problems during training. Measures of attention and working memory were acquired before and after the training phase. As compared to sham, participants in the tRNS condition displayed faster reaction times and increased learning rate during the training phase; as well as faster reaction times for both trained and untrained (new) problems, which indicated a transfer effect after the end of training. All stimulation effects reached significance only in the “difficult” condition when number of repetition was lower. There were no transfer effects of tRNS on attention or working memory. The results support the view that tRNS can produce specific facilitative effects on numerical cognition – specifically, on arithmetic learning. They also highlight
A motif extraction algorithm based on hashing and modulo-4 arithmetic.
Sheng, Huitao; Mehrotra, Kishan; Mohan, Chilukuri; Raina, Ramesh
2008-01-01
We develop an algorithm to identify cis-elements in promoter regions of coregulated genes. This algorithm searches for subsequences of desired length whose frequency of occurrence is relatively high, while accounting for slightly perturbed variants using hash table and modulo arithmetic. Motifs are evaluated using profile matrices and higher-order Markov background model. Simulation results show that our algorithm discovers more motifs present in the test sequences, when compared with two well-known motif-discovery tools (MDScan and AlignACE). The algorithm produces very promising results on real data set; the output of the algorithm contained many known motifs.
The arithmetic mean iterative method for solving 2D Helmholtz equation
NASA Astrophysics Data System (ADS)
Muthuvalu, Mohana Sundaram; Akhir, Mohd Kamalrulzaman Md; Sulaiman, Jumat; Suleiman, Mohamed; Dass, Sarat Chandra; Singh, Narinderjit Singh Sawaran
2014-10-01
In this paper, application of the Arithmetic Mean (AM) iterative method is extended by solving second order finite difference algebraic equations. The performance of AM method in solving second order finite difference algebraic equations is comparatively studied by their application on two-dimensional Helmholtz equation. Numerical results of AM method in solving two test problems are included and compared with the standard Gauss-Seidel (GS) method. Based on the numerical results obtained, the results show that AM method is better than GS method in the sense of number of iterations and CPU time.
Transcranial random noise stimulation mitigates increased difficulty in an arithmetic learning task.
Popescu, Tudor; Krause, Beatrix; Terhune, Devin B; Twose, Olivia; Page, Thomas; Humphreys, Glyn; Cohen Kadosh, Roi
2016-01-29
Proficiency in arithmetic learning can be achieved by using a multitude of strategies, the most salient of which are procedural learning (applying a certain set of computations) and rote learning (direct retrieval from long-term memory). Here we investigated the effect of transcranial random noise stimulation (tRNS), a non-invasive brain stimulation method previously shown to enhance cognitive training, on both types of learning in a 5-day sham-controlled training study, under two conditions of task difficulty, defined in terms of item repetition. On the basis of previous research implicating the prefrontal and posterior parietal cortex in early and late stages of arithmetic learning, respectively, sham-controlled tRNS was applied to bilateral prefrontal cortex for the first 3 days and to the posterior parietal cortex for the last 2 days of a 5-day training phase. The training involved learning to solve arithmetic problems by applying a calculation algorithm; both trained and untrained problems were used in a brief testing phase at the end of the training phase. Task difficulty was manipulated between subjects by using either a large ("easy" condition) or a small ("difficult" condition) number of repetition of problems during training. Measures of attention and working memory were acquired before and after the training phase. As compared to sham, participants in the tRNS condition displayed faster reaction times and increased learning rate during the training phase; as well as faster reaction times for both trained and untrained (new) problems, which indicated a transfer effect after the end of training. All stimulation effects reached significance only in the "difficult" condition when number of repetition was lower. There were no transfer effects of tRNS on attention or working memory. The results support the view that tRNS can produce specific facilitative effects on numerical cognition--specifically, on arithmetic learning. They also highlight the importance of
Masson, Nicolas; Pesenti, Mauro
2016-07-01
Solving arithmetic problems has been shown to induce shifts of spatial attention in simple probe-detection tasks, subtractions orienting attention to the left side and additions to the right side of space. Whether these attentional shifts constitute epiphenomena or are critically linked to the calculation process is still unknown. In the present study, we investigate participants' performance on addition and subtraction solving while they have to detect central or lateralized targets. The results show that lateralized distractors presented in the hemifield congruent to the operation to be solved interfere with arithmetical solving: participants are slower to solve subtractions or additions when distractors are located on the left or on the right, respectively. These results converge with previous data to show that attentional shifts underlie not only number processing but also mental arithmetic. They extend them as they reveal the reverse effect of the one previously reported by showing that inducing attention shifts interferes with the solving of arithmetic problems. They also demonstrate that spatial attentional shifts are part of the calculation procedure of solving mentally arithmetic problems. Their functional role is to access, from the first operand, the representation of the result in a direction congruent to the operation.
Ashkenazi, Sarit; Rosenberg-Lee, Miriam; Tenison, Caitlin; Menon, Vinod
2012-02-15
Developmental dyscalculia (DD) is a disability that impacts math learning and skill acquisition in school-age children. Here we investigate arithmetic problem solving deficits in young children with DD using univariate and multivariate analysis of fMRI data. During fMRI scanning, 17 children with DD (ages 7-9, grades 2 and 3) and 17 IQ- and reading ability-matched typically developing (TD) children performed complex and simple addition problems which differed only in arithmetic complexity. While the TD group showed strong modulation of brain responses with increasing arithmetic complexity, children with DD failed to show such modulation. Children with DD showed significantly reduced activation compared to TD children in the intraparietal sulcus, superior parietal lobule, supramarginal gyrus and bilateral dorsolateral prefrontal cortex in relation to arithmetic complexity. Critically, multivariate representational similarity revealed that brain response patterns to complex and simple problems were less differentiated in the DD group in bilateral anterior IPS, independent of overall differences in signal level. Taken together, these results show that children with DD not only under-activate key brain regions implicated in mathematical cognition, but they also fail to generate distinct neural responses and representations for different arithmetic problems. Our findings provide novel insights into the neural basis of DD.
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
Masson, Nicolas; Pesenti, Mauro
2016-07-01
Solving arithmetic problems has been shown to induce shifts of spatial attention in simple probe-detection tasks, subtractions orienting attention to the left side and additions to the right side of space. Whether these attentional shifts constitute epiphenomena or are critically linked to the calculation process is still unknown. In the present study, we investigate participants' performance on addition and subtraction solving while they have to detect central or lateralized targets. The results show that lateralized distractors presented in the hemifield congruent to the operation to be solved interfere with arithmetical solving: participants are slower to solve subtractions or additions when distractors are located on the left or on the right, respectively. These results converge with previous data to show that attentional shifts underlie not only number processing but also mental arithmetic. They extend them as they reveal the reverse effect of the one previously reported by showing that inducing attention shifts interferes with the solving of arithmetic problems. They also demonstrate that spatial attentional shifts are part of the calculation procedure of solving mentally arithmetic problems. Their functional role is to access, from the first operand, the representation of the result in a direction congruent to the operation. PMID:25991551
Planets in Evolved Binary Systems
NASA Astrophysics Data System (ADS)
Perets, Hagai B.
2011-03-01
Exo-planets are typically thought to form in protoplanetary disks left over from protostellar disk of their newly formed host star. However, additional planetary formation and evolution routes may exist in old evolved binary systems. Here we discuss the implications of binary stellar evolution on planetary systems in such environments. In these binary systems stellar evolution could lead to the formation of symbiotic stars, where mass is lost from one star and could be transferred to its binary companion, and may form an accretion disk around it. This raises the possibility that such a disk could provide the necessary environment for the formation of a new, second generation of planets in both circumstellar or circumbinary configurations. Pre-existing first generation planets surviving the post-MS evolution of such systems would be dynamically effected by the mass loss in the systems and may also interact with the newly formed disk. Such planets and/or planetesimals may also serve as seeds for the formation of the second generation planets, and/or interact with them, possibly forming atypical planetary systems. Second generation planetary systems should be typically found in white dwarf binary systems, and may show various observational signatures. Most notably, second generation planets could form in environment which are inaccessible, or less favorable, for first generation planets. The orbital phase space available for the second generation planets could be forbidden (in terms of the system stability) to first generation planets in the pre-evolved progenitor binaries. In addition planets could form in metal poor environments such as globular clusters and/or in double compact object binaries. Observations of exo-planets in such forbidden or unfavorable regions could possibly serve to uniquely identify their second generation character. Finally, we point out a few observed candidate second generation planetary systems, including Gl 86, HD 27442 and all of the
The Michigan Binary Star Program
NASA Astrophysics Data System (ADS)
Lindner, Rudi P.
2007-07-01
At the end of the nineteenth century, William J. Hussey and Robert G. Aitken, both at Lick Observatory, began a systematic search for unrecorded binary stars with the aid of the 12" and 36" refracting telescopes at Lick Observatory. Aitken's work (and book on binary stars) are well known, Hussey's contributions less so. In 1905 Hussey, a Michigan engineering graduate, returned to direct the Ann Arbor astronomy program, and immediately he began to design new instrumentation for the study of binary stars and to train potential observers. For a time, he spent six months a year at the La Plata Observatory, where he discovered a number of new pairs and decided upon a major southern hemisphere campaign. He spent a decade obtaining the lenses for a large refractor, through the vicissitudes of war and depression. Finally, he obtained a site in South Africa, a 26" refractor, and a small corps of observers, but he died in London en route to fulfill his dream. His right hand man, Richard Rossiter, established the observatory and spent the next thirty years discovering and measuring binary stars: his personal total is a record for the field. This talk is an account of the methods, results, and utility of the extraordinary binary star factory in the veldt.
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.
Ling, N.
1989-01-01
A novel formalism, termed Systolic Temporal Arithmetic (STA), is introduced. It provides necessary constructs to describe arithmetic operations in dynamic environments. The motivation behind the development of STA is to use it for systolic array design at the array architecture level. It is particularly useful for formally specifying systolic array designs, and for formally verifying their correctness with respect to the algorithm specifications. Besides providing value and operation abstractions from the lower level, the formalism exploits unique systolic features such as synchrony, regularity, repeatability, modularity, pipelinability, parallel processing ability, as well as spatial and temporal locality, to provide constructs and verification techniques for simple, efficient, and effective systolic array specification verification. STA overcomes many limitations of current specification and verification techniques. It can be used with lower level formalism for multilevel reasoning of systolic arrays. Application examples are given to show how STA can be applied to specify and verify several different systolic arrays. To present a more unified design environment, STA is also extended to describe systolic array synthesis process. A synthesis procedure for systolic arrays is presented which also includes an algorithm transformation technique developed that can improve the computation time of resulting arrays for suitable algorithms, without much increase in area requirement. Several systolic array synthesis examples are also provided in this dissertation.
About the influence of the presentation format on arithmetical-fact retrieval processes.
Noël, M P; Fias, W; Brysbaert, M
1997-06-01
This article presents the results of two experiments. In Experiment 1, French-speaking participants were asked first to retrieve the product of two numbers presented in Arabic or verbal code, and then to perform a number-matching task on the same material to assess the encoding time difference between numerals in the two formats. Experiment 2 involved the same multiplication task with Dutch-speaking participants who name two-digit numbers in reverse order. The format effects obtained by Campbell and Clark (1992); Campbell (1994) for multiplication were replicated. However, several observations suggest that some of these effects may be due to encoding time differences between word and digit numerals. The same size-by-format interaction was found for the number-matching task as for the multiplication task, and the effect disappeared with practice in the multiplication task. Finally, despite the fact that the linguistic structure of number names differs between French and Dutch, the types of error produced in both groups were identical. The last result does not match with the hypothesis that operand intrusion errors are due to interference between reading processes and arithmetical-fact retrieval processes. Implications of these findings for the debate about the nature of arithmetical-fact retrieval are discussed.
Xiang, Yanhui; Jiang, Yiqi; Chao, Xiaomei; Wu, Qihan; Mo, Lei
2016-01-01
Approximate strategies are crucial in daily human life. The studies on the "difficulty effect" seen in approximate complex arithmetic have long been neglected. Here, we aimed to explore the brain mechanisms related to this difficulty effect in the case of complex addition, using event-related potential-based methods. Following previous path-finding studies, we used the inequality paradigm and different split sizes to induce the use of two approximate strategies for different difficulty levels. By comparing dependent variables from the medium- and large-split conditions, we anticipated being able to dissociate the effects of task difficulty based on approximate strategy in electrical components. In the fronto-central region, early P2 (150-250 ms) and an N400-like wave (250-700 ms) were significantly different between different difficulty levels. Differences in P2 correlated with the difficulty of separation of the approximate strategy from the early physical stimulus discrimination process, which is dominant before 200 ms, and differences in the putative N400 correlated with different difficulties of approximate strategy execution. Moreover, this difference may be linked to speech processing. In addition, differences were found in the fronto-central region, which may reflect the regulatory role of this part of the cortex in approximate strategy execution when solving complex arithmetic problems. PMID:27072753
Landerl, Karin
2013-01-01
Numerical processing has been demonstrated to be closely associated with arithmetic skills, however, our knowledge on the development of the relevant cognitive mechanisms is limited. The present longitudinal study investigated the developmental trajectories of numerical processing in 42 children with age-adequate arithmetic development and 41 children with dyscalculia over a 2-year period from beginning of Grade 2, when children were 7; 6 years old, to beginning of Grade 4. A battery of numerical processing tasks (dot enumeration, non-symbolic and symbolic comparison of one- and two-digit numbers, physical comparison, number line estimation) was given five times during the study (beginning and middle of each school year). Efficiency of numerical processing was a very good indicator of development in numerical processing while within-task effects remained largely constant and showed low long-term stability before middle of Grade 3. Children with dyscalculia showed less efficient numerical processing reflected in specifically prolonged response times. Importantly, they showed consistently larger slopes for dot enumeration in the subitizing range, an untypically large compatibility effect when processing two-digit numbers, and they were consistently less accurate in placing numbers on a number line. Thus, we were able to identify parameters that can be used in future research to characterize numerical processing in typical and dyscalculic development. These parameters can also be helpful for identification of children who struggle in their numerical development. PMID:23898310
The arithmetic problem size effect in children: an event-related potential study
Van Beek, Leen; Ghesquièr, Pol; De Smedt, Bert; Lagae, Lieven
2014-01-01
This study used for the first time event-related potentials (ERPs) to examine the well-known arithmetic problem size effect in children. The electrophysiological correlates of this problem size effect have been well documented in adults, but such information in children is lacking. In the present study, 22 typically developing 12-year-olds were asked to solve single-digit addition problems of small (sum ≤ 10) and large problem size (sum > 10) and to speak the solution into a voice key while ERPs were recorded. Children displayed similar early and late components compared to previous adult studies on the problem size effect. There was no effect of problem size on the early components P1, N1, and P2. The peak amplitude of the N2 component showed more negative potentials on left and right anterior electrodes for large additions compared to small additions, which might reflect differences in attentional and working memory resources between large and small problems. The mean amplitude of the late positivity component which follows the N2, was significantly larger for large than for small additions at right parieto-occipital electrodes, in line with previous adult data. The ERPs of the problem size effect during arithmetic might be a useful neural marker for future studies on fact retrieval impairments in children with mathematical difficulties. PMID:25309405
Efficiency of Arithmetic Procedures Modulates the Problem-Size Effect in Subtraction.
Núñez-Peña, M Isabel; Colomé, Angels; Tubau, Elisabet
2015-01-01
The aim of this study was to examine whether differences in strategy selection and/or strategy efficiency can explain the modulation of the problem-size effect by arithmetic skill. More specifically, we wondered whether arithmetic skill increases the use of retrieval strategy in large problems, and/or enhances the efficiency of either retrieval or procedural strategies. The performance of highly-skilled (HS) and less highly-skilled (LS) individuals on a subtraction verification task was analyzed according to problem size and to the strategy reported on a trial-by-trial basis after each problem. The problem size effect was larger for LS individuals than for their HS peers, both in response time and in hit rate. Nevertheless, groups did not differ regarding the strategy reported for each subtraction size. As expected, problems in which retrieval strategy was reported were solved more quickly and more accurately than problems solved by procedural strategies. Responses using retrieval strategy were equally fast in the two groups, but HS individuals performed better than LS when using procedural strategies. The results therefore suggest that the differences in behavioral measures between groups might specifically be due to differences in the efficiency of procedural strategies.
Núñez-Peña, Maria Isabel; Suárez-Pellicioni, Macarena
2012-05-01
This paper focuses on the capacity to solve numerical incongruities in high- and lower-skilled arithmetic problem-solvers by investigating event-related brain potentials elicited by incorrect solutions to additions. Fifteen high-skill and fifteen low-skill individuals were presented with simple addition problems in a verification task. The proposed solution was manipulated by presenting correct solutions and incorrect solutions very close to the correct ones. Incorrect solutions elicited a negative component followed by a late positive component (LPC/P3b), whose amplitude was smaller for the low-skill group than for the high-skill group. Because the LPC/P3b amplitude has been taken as an indicator of the plausibility of the stimulus, this result suggests that incorrect solutions close to the correct ones appear more plausible to low-skilled individuals than to their high-skilled counterparts. This result is interpreted in terms of differences in the strength of association between problems and potential solutions depending on arithmetical skill.
Barrouillet, P; Fayol, M
1998-03-01
A number of theories of mental arithmetic suggest that the ability to solve simple addition and subtraction problems develops from an algorithmic strategy toward a strategy based on the direct retrieval of the result from memory. In the experiment presented here, 2nd and 12th graders were asked to solve two tasks of number and alphabet arithmetic. The subjects transformed series of 1 to 4 numbers or letters (item span) by adding or subtracting an operand varying from 1 to 4 (operation span). Although both the item and operation span were associated with major and identical effects in the case of both numbers and letters at 2nd grade, such effects were clearly observable only in the case of letters for the adult subjects. This suggests the use of an algorithmic strategy for both types of material in the case of the children and for the letters only in the case of the adults, who retrieved numerical results directly from memory. PMID:9584442
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
An arithmetic rule for spatial summation of excitatory and inhibitory inputs in pyramidal neurons
Hao, Jiang; Wang, Xu-dong; Dan, Yang; Poo, Mu-ming; Zhang, Xiao-hui
2009-01-01
Dendritic integration of excitatory and inhibitory inputs is critical for neuronal computation, but the underlying rules remain to be elucidated. Based on realistic modeling and experiments in rat hippocampal slices, we derived a simple arithmetic rule for spatial summation of concurrent excitatory glutamatergic inputs (E) and inhibitory GABAergic inputs (I). The somatic response can be well approximated as the sum of the excitatory postsynaptic potential (EPSP), the inhibitory postsynaptic potential (IPSP), and a nonlinear term proportional to their product (k*EPSP*IPSP), where the coefficient k reflects the strength of shunting effect. The k value shows a pronounced asymmetry in its dependence on E and I locations. For I on the dendritic trunk, k decays rapidly with E–I distance for proximal Es, but remains largely constant for distal Es, indicating a uniformly high shunting efficacy for all distal Es. For I on an oblique branch, the shunting effect is restricted mainly within the branch, with the same proximal/distal asymmetry. This asymmetry can be largely attributed to cable properties of the dendrite. Further modeling studies showed that this rule also applies to the integration of multiple coincident Es and Is. Thus, this arithmetic rule offers a simple analytical tool for studying E–I integration in pyramidal neurons that incorporates the location specificity of GABAergic shunting inhibition. PMID:19955407
Knops, André; Willmes, Klaus
2014-01-01
A prominent proposal in numerical cognition states that our mental calculation abilities are grounded in the approximate number system (ANS). Recently, it was proposed that this association is mediated by numerical ordering abilities. As a first step in elucidating the neural correlates of this link this study tested which areas in the human brain carry information common to both calculation and numerical ordering. While lying in an MR scanner 17 healthy participants (a) decided whether or not a given number triplet was presented in numerically ascending order, and (b) solved simple addition and subtraction problems. Standard general linear model analyses revealed a largely overlapping network in fronto-parietal regions for both tasks. By analyzing the spatial information over voxels using a whole-brain searchlight algorithm we identified a right hemispheric network comprising areas along the intraparietal sulcus and in the inferior frontal cortex which was similarly involved in order judgments and symbolic arithmetic. Functional and anatomical characteristics of this network make it a candidate for linking the ANS to mental arithmetic. PMID:24064069
The arithmetic of elliptic fibrations in gauge theories on a circle
NASA Astrophysics Data System (ADS)
Grimm, Thomas W.; Kapfer, Andreas; Klevers, Denis
2016-06-01
The geometry of elliptic fibrations translates to the physics of gauge theories in F-theory. We systematically develop the dictionary between arithmetic structures on elliptic curves as well as desingularized elliptic fibrations and symmetries of gauge theories on a circle. We show that the Mordell-Weil group law matches integral large gauge transformations around the circle in Abelian gauge theories and explain the significance of Mordell-Weil torsion in this context. We also use Higgs transitions and circle large gauge transformations to introduce a group law for genus-one fibrations with multi-sections. Finally, we introduce a novel arithmetic structure on elliptic fibrations with non-Abelian gauge groups in F-theory. It is defined on the set of exceptional divisors resolving the singularities and divisor classes of sections of the fibration. This group structure can be matched with certain integral non-Abelian large gauge transformations around the circle when studying the theory on the lower-dimensional Coulomb branch. Its existence is required by consistency with Higgs transitions from the non-Abelian theory to its Abelian phases in which it becomes the Mordell-Weil group. This hints towards the existence of a new underlying geometric symmetry.
Adaptive management is an approach to natural resource management that emphasizes learning through management where knowledge is incomplete, and when, despite inherent uncertainty, managers and policymakers must act. Unlike a traditional trial and error approach, adaptive managem...
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.
Testing Atmosphere and Evolution Models with Brown Dwarf Binaries
NASA Astrophysics Data System (ADS)
Barman, Travis S.; Konopacky, Q. M.; Ghez, A. M.
2013-01-01
Precise dynamical masses are available for many brown dwarf binaries, covering late-M, L and T spectral types. With known masses and equal ages within a binary, the range of predicted luminosity, effective temperature, and surface gravity of each dwarf narrows significantly providing important tests for interior and evolution models. Furthermore, the consistency between the basic properties inferred from evolutionary cooling tracks and those inferred only from atmosphere model comparisons is best tested with brown dwarf binaries. Our recent Hubble Space Telescope program extends the spatially resolved photometric coverage of 11 binaries (all with dynamical masses measured to a precision of 10%, or better) into the optical, allowing precise effective temperatures and bolometric luminosities to be determined. By comparing these new data to models, limits are placed on the brown dwarf cooling evolution across a range of masses. In addition to photometry, ground-based spatially resolved near-IR spectroscopy (obtained with the laser guide star adaptive optics system on the W.M. Keck II telescope and the NIRSPAO spectrograph) is used to estimate surface gravities and further constrain the effective temperatures for a few systems.
Gravitational radiation from compact binaries in scalar-tensor gravity
NASA Astrophysics Data System (ADS)
Lang, R. N.
2015-05-01
General relativity (GR) has been extensively tested in the solar system and in binary pulsars, but never in the strong-field, dynamical regime. Soon, gravitational-wave (GW) detectors like Advanced LIGO and eLISA will be able to probe this regime by measuring GWs from inspiraling and merging compact binaries. One particularly interesting alternative to GR is scalar-tensor gravity. We present progress in the calculation of second post-Newtonian (2PN) gravitational waveforms for inspiraling compact binaries in a general class of scalar- tensor theories. The waveforms are constructed using a standard GR method known as “direct integration of the relaxed Einstein equations,” appropriately adapted to the scalar-tensor case. We find that differences from general relativity can be characterized by a reasonably small number of parameters. Among the differences are new hereditary terms which depend on the past history of the source. In one special case, binary black hole systems, we find that the waveform is indistinguishable from that of general relativity. In another, mixed black hole- neutron star systems, all differences from GR can be characterized by only a single parameter.
Gravitational radiation from compact binaries in scalar-tensor gravity
NASA Astrophysics Data System (ADS)
Lang, Ryan
2014-03-01
General relativity (GR) has been extensively tested in the solar system and in binary pulsars, but never in the strong-field, dynamical regime. Soon, gravitational-wave (GW) detectors like Advanced LIGO will be able to probe this regime by measuring GWs from inspiraling and merging compact binaries. One particularly interesting alternative to GR is scalar-tensor gravity. We present the calculation of second post-Newtonian (2PN) gravitational waveforms for inspiraling compact binaries in a general class of scalar-tensor theories. The waveforms are constructed using a standard GR method known as ``Direct Integration of the Relaxed Einstein equations,'' appropriately adapted to the scalar-tensor case. We find that differences from general relativity can be characterized by a reasonably small number of parameters. Among the differences are new hereditary terms which depend on the past history of the source. In one special case, mixed black hole-neutron star systems, all differences from GR can be characterized by only a single parameter. In another, binary black hole systems, we find that the waveform is indistinguishable from that of general relativity.
Ashkenazi, Sarit; Rosenberg-Lee, Miriam; Metcalfe, Arron W S; Swigart, Anna G; Menon, Vinod
2013-09-01
The study of developmental disorders can provide a unique window into the role of domain-general cognitive abilities and neural systems in typical and atypical development. Mathematical disabilities (MD) are characterized by marked difficulty in mathematical cognition in the presence of preserved intelligence and verbal ability. Although studies of MD have most often focused on the role of core deficits in numerical processing, domain-general cognitive abilities, in particular working memory (WM), have also been implicated. Here we identify specific WM components that are impaired in children with MD and then examine their role in arithmetic problem solving. Compared to typically developing (TD) children, the MD group demonstrated lower arithmetic performance and lower visuo-spatial working memory (VSWM) scores with preserved abilities on the phonological and central executive components of WM. Whole brain analysis revealed that, during arithmetic problem solving, left posterior parietal cortex, bilateral dorsolateral and ventrolateral prefrontal cortex, cingulate gyrus and precuneus, and fusiform gyrus responses were positively correlated with VSWM ability in TD children, but not in the MD group. Additional analyses using a priori posterior parietal cortex regions previously implicated in WM tasks, demonstrated a convergent pattern of results during arithmetic problem solving. These results suggest that MD is characterized by a common locus of arithmetic and VSWM deficits at both the cognitive and functional neuroanatomical levels. Unlike TD children, children with MD do not use VSWM resources appropriately during arithmetic problem solving. This work advances our understanding of VSWM as an important domain-general cognitive process in both typical and atypical mathematical skill development.
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
Experience with parametric binary dissection
NASA Technical Reports Server (NTRS)
Bokhari, Shahid H.
1993-01-01
Parametric Binary Dissection (PBD) is a new algorithm that can be used for partitioning graphs embedded in 2- or 3-dimensional space. It partitions explicitly on the basis of nodes + (lambda)x(edges cut), where lambda is the ratio of time to communicate over an edge to the time to compute at a node. The new algorithm is faster than the original binary dissection algorithm and attempts to obtain better partitions than the older algorithm, which only takes nodes into account. The performance of parametric dissection with plain binary dissection on 3 large unstructured 3-d meshes obtained from computational fluid dynamics and on 2 random graphs were compared. It was showm that the new algorithm can usually yield partitions that are substantially superior, but that its performance is heavily dependent on the input data.
On the Brauer group of an arithmetic model of a hyperkähler variety over a number field
NASA Astrophysics Data System (ADS)
Tankeev, S. G.
2015-06-01
We prove Artin's conjecture on the finiteness of the Brauer group for an arithmetic model of a hyperkähler variety V over a number field k\\hookrightarrow C provided that b_2(V\\otimesk C)\\gt 3. We show that the Brauer group of an arithmetic model of a simply connected Calabi-Yau variety over a number field is finite. We also prove that if the l-adic Tate conjecture on divisors holds for a certain smooth projective variety V over a field k of arbitrary characteristic \\operatorname{char}(k)\
Mental Effort in Binary Categorization Aided by Binary Cues
ERIC Educational Resources Information Center
Botzer, Assaf; Meyer, Joachim; Parmet, Yisrael
2013-01-01
Binary cueing systems assist in many tasks, often alerting people about potential hazards (such as alarms and alerts). We investigate whether cues, besides possibly improving decision accuracy, also affect the effort users invest in tasks and whether the required effort in tasks affects the responses to cues. We developed a novel experimental tool…
Terziev, Emil; Law, Nicholas M.; Arcavi, Iair; Baranec, Christoph; Bui, Khanh; Dekany, Richard G.; Kulkarni, S. R.; Riddle, Reed; Tendulkar, Shriharsh P.; Bloom, Joshua S.; Burse, Mahesh P.; Chorida, Pravin; Das, H. K.; Punnadi, Sujit; Ramaprakash, A. N.; Kraus, Adam L.; Nugent, Peter; Ofek, Eran O.; Sullivan, Mark
2013-06-01
The direct detection of binary systems in wide-field surveys is limited by the size of the stars' point-spread functions (PSFs). A search for elongated objects can find closer companions, but is limited by the precision to which the PSF shape can be calibrated for individual stars. Based on a technique from weak-lensing analysis, we have developed the BinaryFinder algorithm to search for close binaries by using precision measurements of PSF ellipticity across wide-field survey images. We show that the algorithm is capable of reliably detecting binary systems down to Almost-Equal-To 1/5 of the seeing limit, and can directly measure the systems' position angles, separations, and contrast ratios. To verify the algorithm's performance we evaluated 100,000 objects in Palomar Transient Factory (PTF) wide-field-survey data for signs of binarity, and then used the Robo-AO robotic laser adaptive optics system to verify the parameters of 44 high-confidence targets. We show that BinaryFinder correctly predicts the presence of close companions with a <11% false-positive rate, measures the detected binaries' position angles within 1 Degree-Sign to 4 Degree-Sign (depending on signal-to-noise ratio and separation), and separations within 25%, and weakly constrains their contrast ratios. When applied to the full PTF data set, we estimate that BinaryFinder will discover and characterize {approx}450,000 physically associated binary systems with separations <2 arcsec and magnitudes brighter than m{sub R} = 18. New wide-field synoptic surveys with high sensitivity and sub-arcsecond angular resolution, such as LSST, will allow BinaryFinder to reliably detect millions of very faint binary systems with separations as small as 0.1 arcsec.
NASA Astrophysics Data System (ADS)
Terziev, Emil; Law, Nicholas M.; Arcavi, Iair; Baranec, Christoph; Bloom, Joshua S.; Bui, Khanh; Burse, Mahesh P.; Chorida, Pravin; Das, H. K.; Dekany, Richard G.; Kraus, Adam L.; Kulkarni, S. R.; Nugent, Peter; Ofek, Eran O.; Punnadi, Sujit; Ramaprakash, A. N.; Riddle, Reed; Sullivan, Mark; Tendulkar, Shriharsh P.
2013-06-01
The direct detection of binary systems in wide-field surveys is limited by the size of the stars' point-spread functions (PSFs). A search for elongated objects can find closer companions, but is limited by the precision to which the PSF shape can be calibrated for individual stars. Based on a technique from weak-lensing analysis, we have developed the BinaryFinder algorithm to search for close binaries by using precision measurements of PSF ellipticity across wide-field survey images. We show that the algorithm is capable of reliably detecting binary systems down to ≈1/5 of the seeing limit, and can directly measure the systems' position angles, separations, and contrast ratios. To verify the algorithm's performance we evaluated 100,000 objects in Palomar Transient Factory (PTF) wide-field-survey data for signs of binarity, and then used the Robo-AO robotic laser adaptive optics system to verify the parameters of 44 high-confidence targets. We show that BinaryFinder correctly predicts the presence of close companions with a <11% false-positive rate, measures the detected binaries' position angles within 1° to 4° (depending on signal-to-noise ratio and separation), and separations within 25%, and weakly constrains their contrast ratios. When applied to the full PTF data set, we estimate that BinaryFinder will discover and characterize ~450,000 physically associated binary systems with separations <2 arcsec and magnitudes brighter than mR = 18. New wide-field synoptic surveys with high sensitivity and sub-arcsecond angular resolution, such as LSST, will allow BinaryFinder to reliably detect millions of very faint binary systems with separations as small as 0.1 arcsec.
Code of Federal Regulations, 2010 CFR
2010-07-01
... 40 Protection of Environment 6 2010-07-01 2010-07-01 false How do I convert my 1-hour arithmetic averages into the appropriate averaging times and units? 60.1265 Section 60.1265 Protection of Environment... Continuous Emission Monitoring § 60.1265 How do I convert my 1-hour arithmetic averages into the...
ERIC Educational Resources Information Center
Chronaki, Anna
2005-01-01
The present study explores the experience of two young Gypsy girls in solving school arithmetic tasks in interaction with an adult who supports their participation. Along with learning the use of arithmetic tools, a basic element concerning the experience of the two girls as they try to gain entry into the school practice is learning about…
ERIC Educational Resources Information Center
Guberman, Raisa
2016-01-01
One of the key courses in the mathematics teacher education program in Israel is arithmetic, which engages in contents which these pre-service mathematics teachers (PMTs) will later teach at school. Teaching arithmetic involves knowledge about the essence of the concept of "number" and the development thereof, calculation methods and…
BINARY YORP EFFECT AND EVOLUTION OF BINARY ASTEROIDS
Steinberg, Elad; Sari, Re'em
2011-02-15
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 {approx}10{sup 4}-10{sup 5} years for a D{sub p} = 2 km primary with a D{sub s} = 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{sub 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.
Hunt, R.L.
1983-12-27
An adapter is disclosed for use with a fireplace. The stove pipe of a stove standing in a room to be heated may be connected to the flue of the chimney so that products of combustion from the stove may be safely exhausted through the flue and outwardly of the chimney. The adapter may be easily installed within the fireplace by removing the damper plate and fitting the adapter to the damper frame. Each of a pair of bolts has a portion which hooks over a portion of the damper frame and a threaded end depending from the hook portion and extending through a hole in the adapter. Nuts are threaded on the bolts and are adapted to force the adapter into a tight fit with the adapter frame.
KEPLER ECLIPSING BINARIES WITH STELLAR COMPANIONS
Gies, D. R.; Matson, R. A.; Guo, Z.; Lester, K. V.; Orosz, J. A.; Peters, G. J. E-mail: rmatson@chara.gsu.edu E-mail: lester@chara.gsu.edu E-mail: gjpeters@mucen.usc.edu
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 among 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.
Observational Properties of Synthetic Visual Binary Catalog
NASA Astrophysics Data System (ADS)
Nurmi, P.
2004-08-01
Forthcoming astrometric missions will observe a huge number of new binaries from which a large fraction will be visual binaries. Detailed planning of optimal detection procedures requires pre-launch information about the observational properties of expected visual binaries. Hence, a synthetic binary catalog is created and analyzed for observational properties of visual binary stars. These results help to understand what kind of binaries we expect to find in the final output catalogs of astrometric missions. These results represent `true' binary distributions if all of them would be observed. All real observational projects or astrometric satellites sample only small fractions of these populations depending on the observational capabilities of the missions. In this study we consider only relative numbers with respect to the total number of binary stars assumed to exist in the sky down to the magnitude limit depending on the astrometric mission.
Blind binary masking for reverberation suppression in cochlear implants.
Hazrati, Oldooz; Lee, Jaewook; Loizou, Philipos C
2013-03-01
A monaural binary time-frequency (T-F) masking technique is proposed for suppressing reverberation. The mask is estimated for each T-F unit by extracting a variance-based feature from the reverberant signal and comparing it against an adaptive threshold. Performance of the estimated binary mask is evaluated in three moderate to relatively high reverberant conditions (T60 = 0.3, 0.6, and 0.8 s) using intelligibility listening tests with cochlear implant users. Results indicate that the proposed T-F masking technique yields significant improvements in intelligibility of reverberant speech even in relatively high reverberant conditions (T60 = 0.8 s). The improvement is hypothesized to result from the recovery of the vowel/consonant boundaries, which are severely smeared in reverberation. PMID:23464030
A Galactic Binary Detection Pipeline
NASA Technical Reports Server (NTRS)
Littenberg, Tyson B.
2011-01-01
The Galaxy is suspected to contain hundreds of millions of binary white dwarf systems, a large fraction of which will have sufficiently small orbital period to emit gravitational radiation in band for space-based gravitational wave detectors such as the Laser Interferometer Space Antenna (LISA). LISA's main science goal is the detection of cosmological events (supermassive black hole mergers, etc.) however the gravitational signal from the galaxy will be the dominant contribution to the data - including instrumental noise over approximately two decades in frequency. The catalogue of detectable binary systems will serve as an unparalleled means of studying the Galaxy. Furthermore, to maximize the scientific return from the mission, the data must be "cleansed" of the galactic foreground. We will present an algorithm that can accurately resolve and subtract 2:: 10000 of these sources from simulated data supplied by the Mock LISA Data Challenge Task Force. Using the time evolution of the gravitational wave frequency, we will reconstruct the position of the recovered binaries and show how LISA will sample the entire compact binary population in the Galaxy.
Discs in misaligned binary systems
NASA Astrophysics Data System (ADS)
Rawiraswattana, Krisada; Hubber, David A.; Goodwin, Simon P.
2016-08-01
We perform SPH simulations to study precession and changes in alignment between the circumprimary disc and the binary orbit in misaligned binary systems. We find that the precession process can be described by the rigid-disc approximation, where the disc is considered as a rigid body interacting with the binary companion only gravitationally. Precession also causes change in alignment between the rotational axis of the disc and the spin axis of the primary star. This type of alignment is of great important for explaining the origin of spin-orbit misaligned planetary systems. However, we find that the rigid-disc approximation fails to describe changes in alignment between the disc and the binary orbit. This is because the alignment process is a consequence of interactions that involve the fluidity of the disc, such as the tidal interaction and the encounter interaction. Furthermore, simulation results show that there are not only alignment processes, which bring the components towards alignment, but also anti-alignment processes, which tend to misalign the components. The alignment process dominates in systems with misalignment angle near 90°, while the anti-alignment process dominates in systems with the misalignment angle near 0° or 180°. This means that highly misaligned systems will become more aligned but slightly misaligned systems will become more misaligned.
Hydrodynamic Simulations of Contact Binaries
NASA Astrophysics Data System (ADS)
Kadam, Kundan; Clayton, Geoffrey C.; Frank, Juhan; Marcello, Dominic; Motl, Patrick M.; Staff, Jan E.
2015-01-01
The motivation for our project is the peculiar case of the 'red nova" V1309 Sco which erupted in September 2008. The progenitor was, in fact, a contact binary system. We are developing a simulation of contact binaries, so that their formation, structural, and merger properties could be studied using hydrodynamics codes. The observed transient event was the disruption of the secondary star by the primary, and their subsequent merger into one star; hence to replicate this behavior, we need a core-envelope structure for both the stars. We achieve this using a combination of Self Consistant Field (SCF) technique and composite polytropes, also known as bipolytropes. So far we have been able to generate close binaries with various mass ratios. Another consequence of using bipolytropes is that according to theoretical calculations, the radius of a star should expand when the core mass fraction exceeds a critical value, resulting in interesting consequences in a binary system. We present some initial results of these simulations.