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

NASA Astrophysics Data System (ADS)

McCullough, Christopher; Bettadpur, Srinivas

2015-04-01

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

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

NASA Technical Reports Server (NTRS)

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

1976-01-01

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

A parallel solver for huge dense linear systems

NASA Astrophysics Data System (ADS)

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

2011-11-01

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

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

PubMed

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

2008-04-28

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

The fault-tree compiler

NASA Technical Reports Server (NTRS)

Martensen, Anna L.; Butler, Ricky W.

1987-01-01

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

The Fault Tree Compiler (FTC): Program and mathematics

NASA Technical Reports Server (NTRS)

Butler, Ricky W.; Martensen, Anna L.

1989-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2014-08-01

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

Peer-to-peer Monte Carlo simulation of photon migration in topical applications of biomedical optics

NASA Astrophysics Data System (ADS)

Doronin, Alexander; Meglinski, Igor

2012-09-01

In the framework of further development of the unified approach of photon migration in complex turbid media, such as biological tissues we present a peer-to-peer (P2P) Monte Carlo (MC) code. The object-oriented programming is used for generalization of MC model for multipurpose use in various applications of biomedical optics. The online user interface providing multiuser access is developed using modern web technologies, such as Microsoft Silverlight, ASP.NET. The emerging P2P network utilizing computers with different types of compute unified device architecture-capable graphics processing units (GPUs) is applied for acceleration and to overcome the limitations, imposed by multiuser access in the online MC computational tool. The developed P2P MC was validated by comparing the results of simulation of diffuse reflectance and fluence rate distribution for semi-infinite scattering medium with known analytical results, results of adding-doubling method, and with other GPU-based MC techniques developed in the past. The best speedup of processing multiuser requests in a range of 4 to 35 s was achieved using single-precision computing, and the double-precision computing for floating-point arithmetic operations provides higher accuracy.

Peer-to-peer Monte Carlo simulation of photon migration in topical applications of biomedical optics.

PubMed

Doronin, Alexander; Meglinski, Igor

2012-09-01

In the framework of further development of the unified approach of photon migration in complex turbid media, such as biological tissues we present a peer-to-peer (P2P) Monte Carlo (MC) code. The object-oriented programming is used for generalization of MC model for multipurpose use in various applications of biomedical optics. The online user interface providing multiuser access is developed using modern web technologies, such as Microsoft Silverlight, ASP.NET. The emerging P2P network utilizing computers with different types of compute unified device architecture-capable graphics processing units (GPUs) is applied for acceleration and to overcome the limitations, imposed by multiuser access in the online MC computational tool. The developed P2P MC was validated by comparing the results of simulation of diffuse reflectance and fluence rate distribution for semi-infinite scattering medium with known analytical results, results of adding-doubling method, and with other GPU-based MC techniques developed in the past. The best speedup of processing multiuser requests in a range of 4 to 35 s was achieved using single-precision computing, and the double-precision computing for floating-point arithmetic operations provides higher accuracy.

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

NASA Technical Reports Server (NTRS)

Swarztrauber, Paul N.

1989-01-01

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

Inexact hardware for modelling weather & climate

NASA Astrophysics Data System (ADS)

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

2014-05-01

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

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

PubMed Central

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

2017-01-01

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

Reliable and efficient solution of genome-scale models of Metabolism and macromolecular Expression

DOE PAGES

Ma, Ding; Yang, Laurence; Fleming, Ronan M. T.; ...

2017-01-18

Currently, Constraint-Based Reconstruction and Analysis (COBRA) is the only methodology that permits integrated modeling of Metabolism and macromolecular Expression (ME) at genome-scale. Linear optimization computes steady-state flux solutions to ME models, but flux values are spread over many orders of magnitude. Data values also have greatly varying magnitudes. Furthermore, standard double-precision solvers may return inaccurate solutions or report that no solution exists. Exact simplex solvers based on rational arithmetic require a near-optimal warm start to be practical on large problems (current ME models have 70,000 constraints and variables and will grow larger). We also developed a quadrupleprecision version of ourmore » linear and nonlinear optimizer MINOS, and a solution procedure (DQQ) involving Double and Quad MINOS that achieves reliability and efficiency for ME models and other challenging problems tested here. DQQ will enable extensive use of large linear and nonlinear models in systems biology and other applications involving multiscale data.« less

Reliable and efficient solution of genome-scale models of Metabolism and macromolecular Expression

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

Ma, Ding; Yang, Laurence; Fleming, Ronan M. T.

Currently, Constraint-Based Reconstruction and Analysis (COBRA) is the only methodology that permits integrated modeling of Metabolism and macromolecular Expression (ME) at genome-scale. Linear optimization computes steady-state flux solutions to ME models, but flux values are spread over many orders of magnitude. Data values also have greatly varying magnitudes. Furthermore, standard double-precision solvers may return inaccurate solutions or report that no solution exists. Exact simplex solvers based on rational arithmetic require a near-optimal warm start to be practical on large problems (current ME models have 70,000 constraints and variables and will grow larger). We also developed a quadrupleprecision version of ourmore » linear and nonlinear optimizer MINOS, and a solution procedure (DQQ) involving Double and Quad MINOS that achieves reliability and efficiency for ME models and other challenging problems tested here. DQQ will enable extensive use of large linear and nonlinear models in systems biology and other applications involving multiscale data.« less

Basic mathematical function libraries for scientific computation

NASA Technical Reports Server (NTRS)

Galant, David C.

1989-01-01

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

Efficient and portable acceleration of quantum chemical many-body methods in mixed floating point precision using OpenACC compiler directives

NASA Astrophysics Data System (ADS)

Eriksen, Janus J.

2017-09-01

It is demonstrated how the non-proprietary OpenACC standard of compiler directives may be used to compactly and efficiently accelerate the rate-determining steps of two of the most routinely applied many-body methods of electronic structure theory, namely the second-order Møller-Plesset (MP2) model in its resolution-of-the-identity approximated form and the (T) triples correction to the coupled cluster singles and doubles model (CCSD(T)). By means of compute directives as well as the use of optimised device math libraries, the operations involved in the energy kernels have been ported to graphics processing unit (GPU) accelerators, and the associated data transfers correspondingly optimised to such a degree that the final implementations (using either double and/or single precision arithmetics) are capable of scaling to as large systems as allowed for by the capacity of the host central processing unit (CPU) main memory. The performance of the hybrid CPU/GPU implementations is assessed through calculations on test systems of alanine amino acid chains using one-electron basis sets of increasing size (ranging from double- to pentuple-ζ quality). For all but the smallest problem sizes of the present study, the optimised accelerated codes (using a single multi-core CPU host node in conjunction with six GPUs) are found to be capable of reducing the total time-to-solution by at least an order of magnitude over optimised, OpenMP-threaded CPU-only reference implementations.

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

PubMed

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

2014-01-01

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

Optimized 4-bit Quantum Reversible Arithmetic Logic Unit

NASA Astrophysics Data System (ADS)

Ayyoub, Slimani; Achour, Benslama

2017-08-01

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

Digital Ratiometer

NASA Technical Reports Server (NTRS)

Beer, R.

1985-01-01

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

An Elementary Algorithm to Evaluate Trigonometric Functions to High Precision

ERIC Educational Resources Information Center

Johansson, B. Tomas

2018-01-01

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

AN ADA LINEAR ALGEBRA PACKAGE MODELED AFTER HAL/S

NASA Technical Reports Server (NTRS)

Klumpp, A. R.

1994-01-01

This package extends the Ada programming language to include linear algebra capabilities similar to those of the HAL/S programming language. The package is designed for avionics applications such as Space Station flight software. In addition to the HAL/S built-in functions, the package incorporates the quaternion functions used in the Shuttle and Galileo projects, and routines from LINPAK that solve systems of equations involving general square matrices. Language conventions in this package follow those of HAL/S to the maximum extent practical and minimize the effort required for writing new avionics software and translating existent software into Ada. Valid numeric types in this package include scalar, vector, matrix, and quaternion declarations. (Quaternions are fourcomponent vectors used in representing motion between two coordinate frames). Single precision and double precision floating point arithmetic is available in addition to the standard double precision integer manipulation. Infix operators are used instead of function calls to define dot products, cross products, quaternion products, and mixed scalar-vector, scalar-matrix, and vector-matrix products. The package contains two generic programs: one for floating point, and one for integer. The actual component type is passed as a formal parameter to the generic linear algebra package. The procedures for solving systems of linear equations defined by general matrices include GEFA, GECO, GESL, and GIDI. The HAL/S functions include ABVAL, UNIT, TRACE, DET, INVERSE, TRANSPOSE, GET, PUT, FETCH, PLACE, and IDENTITY. This package is written in Ada (Version 1.2) for batch execution and is machine independent. The linear algebra software depends on nothing outside the Ada language except for a call to a square root function for floating point scalars (such as SQRT in the DEC VAX MATHLIB library). This program was developed in 1989, and is a copyrighted work with all copyright vested in NASA.

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

NASA Technical Reports Server (NTRS)

Manos, P.; Turner, L. R.

1972-01-01

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

Arabidopsis plants perform arithmetic division to prevent starvation at night

PubMed Central

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

2013-01-01

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

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

PubMed

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

2007-11-01

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

Efficient Boundary Extraction of BSP Solids Based on Clipping Operations.

PubMed

Wang, Charlie C L; Manocha, Dinesh

2013-01-01

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

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.

Numerical computation of spherical harmonics of arbitrary degree and order by extending exponent of floating point numbers

NASA Astrophysics Data System (ADS)

Fukushima, Toshio

2012-04-01

By extending the exponent of floating point numbers with an additional integer as the power index of a large radix, we compute fully normalized associated Legendre functions (ALF) by recursion without underflow problem. The new method enables us to evaluate ALFs of extremely high degree as 232 = 4,294,967,296, which corresponds to around 1 cm resolution on the Earth's surface. By limiting the application of exponent extension to a few working variables in the recursion, choosing a suitable large power of 2 as the radix, and embedding the contents of the basic arithmetic procedure of floating point numbers with the exponent extension directly in the program computing the recurrence formulas, we achieve the evaluation of ALFs in the double-precision environment at the cost of around 10% increase in computational time per single ALF. This formulation realizes meaningful execution of the spherical harmonic synthesis and/or analysis of arbitrary degree and order.

Multiplication Fact Fluency Using Doubles

ERIC Educational Resources Information Center

Flowers, Judith M.; Rubenstein, Rheta N.

2010-01-01

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

Evidence of Mixed-mode oscillations and Farey arithmetic in double plasma system in presence of fireball

NASA Astrophysics Data System (ADS)

Mitra, Vramori; Sarma, Bornali; Sarma, Arun

2017-10-01

Plasma fireballs are luminous glowing region formed around a positively biased electrode. The present work reports the observation of mix mode oscillation (MMO) in the dynamics of plasma oscillations that are excited in the presence of fireball in a double plasma device. Source voltage and applied electrode voltage are considered as the controlling parameters for the experiment. Many sequences of distinct multi peaked periodic states reflects the presence of MMO with the variation of control parameter. The sequences of states with two patterns are characterized well by Farey arithmetic, which provides rational approximations of irrational numbers. These states can be characterized by a firing number, the ratio of the number of small amplitude oscillations to the total number of oscillations per period. The dynamical transition in plasma fireball is also demonstrated by spectral analysis, recurrence quantification analysis (RQA) and by statistical measures viz., skewness and kurtosis. The mix mode phenomenon observed in the experiment is consistent with a model that describes the dynamics of ionization instabilities.

Numerical Development

ERIC Educational Resources Information Center

Siegler, Robert S.; Braithwaite, David W.

2016-01-01

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

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.

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

NASA Astrophysics Data System (ADS)

Galli, Reto; Tenca, Alexandre F.

2001-11-01

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

Rigorous high-precision enclosures of fixed points and their invariant manifolds

NASA Astrophysics Data System (ADS)

Wittig, Alexander N.

The well established concept of Taylor Models is introduced, which offer highly accurate C0 enclosures of functional dependencies, combining high-order polynomial approximation of functions and rigorous estimates of the truncation error, performed using verified arithmetic. The focus of this work is on the application of Taylor Models in algorithms for strongly non-linear dynamical systems. A method is proposed to extend the existing implementation of Taylor Models in COSY INFINITY from double precision coefficients to arbitrary precision coefficients. Great care is taken to maintain the highest efficiency possible by adaptively adjusting the precision of higher order coefficients in the polynomial expansion. High precision operations are based on clever combinations of elementary floating point operations yielding exact values for round-off errors. An experimental high precision interval data type is developed and implemented. Algorithms for the verified computation of intrinsic functions based on the High Precision Interval datatype are developed and described in detail. The application of these operations in the implementation of High Precision Taylor Models is discussed. An application of Taylor Model methods to the verification of fixed points is presented by verifying the existence of a period 15 fixed point in a near standard Henon map. Verification is performed using different verified methods such as double precision Taylor Models, High Precision intervals and High Precision Taylor Models. Results and performance of each method are compared. An automated rigorous fixed point finder is implemented, allowing the fully automated search for all fixed points of a function within a given domain. It returns a list of verified enclosures of each fixed point, optionally verifying uniqueness within these enclosures. An application of the fixed point finder to the rigorous analysis of beam transfer maps in accelerator physics is presented. Previous work done by Johannes Grote is extended to compute very accurate polynomial approximations to invariant manifolds of discrete maps of arbitrary dimension around hyperbolic fixed points. The algorithm presented allows for automatic removal of resonances occurring during construction. A method for the rigorous enclosure of invariant manifolds of continuous systems is introduced. Using methods developed for discrete maps, polynomial approximations of invariant manifolds of hyperbolic fixed points of ODEs are obtained. These approximations are outfit with a sharp error bound which is verified to rigorously contain the manifolds. While we focus on the three dimensional case, verification in higher dimensions is possible using similar techniques. Integrating the resulting enclosures using the verified COSY VI integrator, the initial manifold enclosures are expanded to yield sharp enclosures of large parts of the stable and unstable manifolds. To demonstrate the effectiveness of this method, we construct enclosures of the invariant manifolds of the Lorenz system and show pictures of the resulting manifold enclosures. To the best of our knowledge, these enclosures are the largest verified enclosures of manifolds in the Lorenz system in existence.

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

DTIC Science & Technology

2009-12-01

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

Improving Foundational Number Representations through Simple Arithmetical Training

ERIC Educational Resources Information Center

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

2011-01-01

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

Skills for the Future.

ERIC Educational Resources Information Center

Smith, Gary R.

This publication contains two miniunits to help students in grades 7-12 build skills for the future. The exercises can also be adapted for use in grades 4-6. Each of the miniunits contains several exercises to build specific skills. Miniunit One, "The Arithmetic of Growth," deals with two concepts--exponential growth and doubling time. These two…

Fast, Massively Parallel Data Processors

NASA Technical Reports Server (NTRS)

Heaton, Robert A.; Blevins, Donald W.; Davis, ED

1994-01-01

Proposed fast, massively parallel data processor contains 8x16 array of processing elements with efficient interconnection scheme and options for flexible local control. Processing elements communicate with each other on "X" interconnection grid with external memory via high-capacity input/output bus. This approach to conditional operation nearly doubles speed of various arithmetic operations.

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

NASA Astrophysics Data System (ADS)

Kaneda, Yukio

2007-11-01

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

SIVA/DIVA- INITIAL VALUE ORDINARY DIFFERENTIAL EQUATION SOLUTION VIA A VARIABLE ORDER ADAMS METHOD

NASA Technical Reports Server (NTRS)

Krogh, F. T.

1994-01-01

The SIVA/DIVA package is a collection of subroutines for the solution of ordinary differential equations. There are versions for single precision and double precision arithmetic. These solutions are applicable to stiff or nonstiff differential equations of first or second order. SIVA/DIVA requires fewer evaluations of derivatives than other variable order Adams predictor-corrector methods. There is an option for the direct integration of second order equations which can make integration of trajectory problems significantly more efficient. Other capabilities of SIVA/DIVA include: monitoring a user supplied function which can be separate from the derivative; dynamically controlling the step size; displaying or not displaying output at initial, final, and step size change points; saving the estimated local error; and reverse communication where subroutines return to the user for output or computation of derivatives instead of automatically performing calculations. The user must supply SIVA/DIVA with: 1) the number of equations; 2) initial values for the dependent and independent variables, integration stepsize, error tolerance, etc.; and 3) the driver program and operational parameters necessary for subroutine execution. SIVA/DIVA contains an extensive diagnostic message library should errors occur during execution. SIVA/DIVA is written in FORTRAN 77 for batch execution and is machine independent. It has a central memory requirement of approximately 120K of 8 bit bytes. This program was developed in 1983 and last updated in 1987.

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

NASA Technical Reports Server (NTRS)

Swarztrauber, Paul N.

1993-01-01

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

Accelerating scientific computations with mixed precision algorithms

NASA Astrophysics Data System (ADS)

Baboulin, Marc; Buttari, Alfredo; Dongarra, Jack; Kurzak, Jakub; Langou, Julie; Langou, Julien; Luszczek, Piotr; Tomov, Stanimire

2009-12-01

On modern architectures, the performance of 32-bit operations is often at least twice as fast as the performance of 64-bit operations. By using a combination of 32-bit and 64-bit floating point arithmetic, the performance of many dense and sparse linear algebra algorithms can be significantly enhanced while maintaining the 64-bit accuracy of the resulting solution. The approach presented here can apply not only to conventional processors but also to other technologies such as Field Programmable Gate Arrays (FPGA), Graphical Processing Units (GPU), and the STI Cell BE processor. Results on modern processor architectures and the STI Cell BE are presented. Program summaryProgram title: ITER-REF Catalogue identifier: AECO_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AECO_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 7211 No. of bytes in distributed program, including test data, etc.: 41 862 Distribution format: tar.gz Programming language: FORTRAN 77 Computer: desktop, server Operating system: Unix/Linux RAM: 512 Mbytes Classification: 4.8 External routines: BLAS (optional) Nature of problem: On modern architectures, the performance of 32-bit operations is often at least twice as fast as the performance of 64-bit operations. By using a combination of 32-bit and 64-bit floating point arithmetic, the performance of many dense and sparse linear algebra algorithms can be significantly enhanced while maintaining the 64-bit accuracy of the resulting solution. Solution method: Mixed precision algorithms stem from the observation that, in many cases, a single precision solution of a problem can be refined to the point where double precision accuracy is achieved. A common approach to the solution of linear systems, either dense or sparse, is to perform the LU factorization of the coefficient matrix using Gaussian elimination. First, the coefficient matrix A is factored into the product of a lower triangular matrix L and an upper triangular matrix U. Partial row pivoting is in general used to improve numerical stability resulting in a factorization PA=LU, where P is a permutation matrix. The solution for the system is achieved by first solving Ly=Pb (forward substitution) and then solving Ux=y (backward substitution). Due to round-off errors, the computed solution, x, carries a numerical error magnified by the condition number of the coefficient matrix A. In order to improve the computed solution, an iterative process can be applied, which produces a correction to the computed solution at each iteration, which then yields the method that is commonly known as the iterative refinement algorithm. Provided that the system is not too ill-conditioned, the algorithm produces a solution correct to the working precision. Running time: seconds/minutes

An efficient and portable SIMD algorithm for charge/current deposition in Particle-In-Cell codes

NASA Astrophysics Data System (ADS)

Vincenti, H.; Lobet, M.; Lehe, R.; Sasanka, R.; Vay, J.-L.

2017-01-01

In current computer architectures, data movement (from die to network) is by far the most energy consuming part of an algorithm (≈ 20 pJ/word on-die to ≈10,000 pJ/word on the network). To increase memory locality at the hardware level and reduce energy consumption related to data movement, future exascale computers tend to use many-core processors on each compute nodes that will have a reduced clock speed to allow for efficient cooling. To compensate for frequency decrease, machine vendors are making use of long SIMD instruction registers that are able to process multiple data with one arithmetic operator in one clock cycle. SIMD register length is expected to double every four years. As a consequence, Particle-In-Cell (PIC) codes will have to achieve good vectorization to fully take advantage of these upcoming architectures. In this paper, we present a new algorithm that allows for efficient and portable SIMD vectorization of current/charge deposition routines that are, along with the field gathering routines, among the most time consuming parts of the PIC algorithm. Our new algorithm uses a particular data structure that takes into account memory alignment constraints and avoids gather/scatter instructions that can significantly affect vectorization performances on current CPUs. The new algorithm was successfully implemented in the 3D skeleton PIC code PICSAR and tested on Haswell Xeon processors (AVX2-256 bits wide data registers). Results show a factor of × 2 to × 2.5 speed-up in double precision for particle shape factor of orders 1- 3. The new algorithm can be applied as is on future KNL (Knights Landing) architectures that will include AVX-512 instruction sets with 512 bits register lengths (8 doubles/16 singles).

Application of grammar-based codes for lossless compression of digital mammograms

NASA Astrophysics Data System (ADS)

Li, Xiaoli; Krishnan, Srithar; Ma, Ngok-Wah

2006-01-01

A newly developed grammar-based lossless source coding theory and its implementation was proposed in 1999 and 2000, respectively, by Yang and Kieffer. The code first transforms the original data sequence into an irreducible context-free grammar, which is then compressed using arithmetic coding. In the study of grammar-based coding for mammography applications, we encountered two issues: processing time and limited number of single-character grammar G variables. For the first issue, we discover a feature that can simplify the matching subsequence search in the irreducible grammar transform process. Using this discovery, an extended grammar code technique is proposed and the processing time of the grammar code can be significantly reduced. For the second issue, we propose to use double-character symbols to increase the number of grammar variables. Under the condition that all the G variables have the same probability of being used, our analysis shows that the double- and single-character approaches have the same compression rates. By using the methods proposed, we show that the grammar code can outperform three other schemes: Lempel-Ziv-Welch (LZW), arithmetic, and Huffman on compression ratio, and has similar error tolerance capabilities as LZW coding under similar circumstances.

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

DTIC Science & Technology

2008-12-01

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

Enhanced Graphics for Extended Scale Range

NASA Technical Reports Server (NTRS)

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

2012-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

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

PubMed

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

2013-12-01

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

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

PubMed Central

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

2012-01-01

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

Mixed Single/Double Precision in OpenIFS: A Detailed Study of Energy Savings, Scaling Effects, Architectural Effects, and Compilation Effects

NASA Astrophysics Data System (ADS)

Fagan, Mike; Dueben, Peter; Palem, Krishna; Carver, Glenn; Chantry, Matthew; Palmer, Tim; Schlacter, Jeremy

2017-04-01

It has been shown that a mixed precision approach that judiciously replaces double precision with single precision calculations can speed-up global simulations. In particular, a mixed precision variation of the Integrated Forecast System (IFS) of the European Centre for Medium-Range Weather Forecasts (ECMWF) showed virtually the same quality model results as the standard double precision version (Vana et al., Single precision in weather forecasting models: An evaluation with the IFS, Monthly Weather Review, in print). In this study, we perform detailed measurements of savings in computing time and energy using a mixed precision variation of the -OpenIFS- model. The mixed precision variation of OpenIFS is analogous to the IFS variation used in Vana et al. We (1) present results for energy measurements for simulations in single and double precision using Intel's RAPL technology, (2) conduct a -scaling- study to quantify the effects that increasing model resolution has on both energy dissipation and computing cycles, (3) analyze the differences between single core and multicore processing, and (4) compare the effects of different compiler technologies on the mixed precision OpenIFS code. In particular, we compare intel icc/ifort with gnu gcc/gfortran.

A floating-point/multiple-precision processor for airborne applications

NASA Technical Reports Server (NTRS)

Yee, R.

1982-01-01

A compact input output (I/O) numerical processor capable of performing floating-point, multiple precision and other arithmetic functions at execution times which are at least 100 times faster than comparable software emulation is described. The I/O device is a microcomputer system containing a 16 bit microprocessor, a numerical coprocessor with eight 80 bit registers running at a 5 MHz clock rate, 18K random access memory (RAM) and 16K electrically programmable read only memory (EPROM). The processor acts as an intelligent slave to the host computer and can be programmed in high order languages such as FORTRAN and PL/M-86.

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

NASA Astrophysics Data System (ADS)

Kobus, Jacek

2013-03-01

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

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

NASA Astrophysics Data System (ADS)

Lieu, Richard

2018-01-01

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

On Matrices, Automata, and Double Counting

NASA Astrophysics Data System (ADS)

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

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

A double sealing technique for increasing the precision of headspace-gas chromatographic analysis.

PubMed

Xie, Wei-Qi; Yu, Kong-Xian; Gong, Yi-Xian

2018-01-19

This paper investigates a new double sealing technique for increasing the precision of the headspace gas chromatographic method. The air leakage problem caused by the high pressure in the headspace vial during the headspace sampling process has a great impact to the measurement precision in the conventional headspace analysis (i.e., single sealing technique). The results (using ethanol solution as the model sample) show that the present technique is effective to minimize such a problem. The double sealing technique has an excellent measurement precision (RSD < 0.15%) and accuracy (recovery = 99.1%-100.6%) for the ethanol quantification. The detection precision of the present method was 10-20 times higher than that in earlier HS-GC work that use conventional single sealing technique. The present double sealing technique may open up a new avenue, and also serve as a general strategy for improving the performance (i.e., accuracy and precision) of headspace analysis of various volatile compounds. Copyright © 2017 Elsevier B.V. All rights reserved.

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

NASA Astrophysics Data System (ADS)

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

2018-07-01

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

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

Allada, Veerendra, Benjegerdes, Troy; Bode, Brett

Commodity clusters augmented with application accelerators are evolving as competitive high performance computing systems. The Graphical Processing Unit (GPU) with a very high arithmetic density and performance per price ratio is a good platform for the scientific application acceleration. In addition to the interconnect bottlenecks among the cluster compute nodes, the cost of memory copies between the host and the GPU device have to be carefully amortized to improve the overall efficiency of the application. Scientific applications also rely on efficient implementation of the BAsic Linear Algebra Subroutines (BLAS), among which the General Matrix Multiply (GEMM) is considered as themore » workhorse subroutine. In this paper, they study the performance of the memory copies and GEMM subroutines that are critical to port the computational chemistry algorithms to the GPU clusters. To that end, a benchmark based on the NetPIPE framework is developed to evaluate the latency and bandwidth of the memory copies between the host and the GPU device. The performance of the single and double precision GEMM subroutines from the NVIDIA CUBLAS 2.0 library are studied. The results have been compared with that of the BLAS routines from the Intel Math Kernel Library (MKL) to understand the computational trade-offs. The test bed is a Intel Xeon cluster equipped with NVIDIA Tesla GPUs.« less

Numerically stable formulas for a particle-based explicit exponential integrator

NASA Astrophysics Data System (ADS)

Nadukandi, Prashanth

2015-05-01

Numerically stable formulas are presented for the closed-form analytical solution of the X-IVAS scheme in 3D. This scheme is a state-of-the-art particle-based explicit exponential integrator developed for the particle finite element method. Algebraically, this scheme involves two steps: (1) the solution of tangent curves for piecewise linear vector fields defined on simplicial meshes and (2) the solution of line integrals of piecewise linear vector-valued functions along these tangent curves. Hence, the stable formulas presented here have general applicability, e.g. exact integration of trajectories in particle-based (Lagrangian-type) methods, flow visualization and computer graphics. The Newton form of the polynomial interpolation definition is used to express exponential functions of matrices which appear in the analytical solution of the X-IVAS scheme. The divided difference coefficients in these expressions are defined in a piecewise manner, i.e. in a prescribed neighbourhood of removable singularities their series approximations are computed. An optimal series approximation of divided differences is presented which plays a critical role in this methodology. At least ten significant decimal digits in the formula computations are guaranteed to be exact using double-precision floating-point arithmetic. The worst case scenarios occur in the neighbourhood of removable singularities found in fourth-order divided differences of the exponential function.

Design and algorithm research of high precision airborne infrared touch screen

NASA Astrophysics Data System (ADS)

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

2016-10-01

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

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

NASA Astrophysics Data System (ADS)

Kalmykov, M. Yu.; Sheplyakov, A.

2005-10-01

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

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

NASA Astrophysics Data System (ADS)

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

2015-04-01

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

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

PubMed Central

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

2010-01-01

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

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

PubMed

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

2010-10-18

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

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

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

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

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

Lieu, Richard

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

Study on Dynamic Alignment Technology of COIL Resonator

NASA Astrophysics Data System (ADS)

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

2006-10-01

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

Triangle Geometry Processing for Surface Modeling and Cartesian Grid Generation

NASA Technical Reports Server (NTRS)

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

2002-01-01

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

Triangle geometry processing for surface modeling and cartesian grid generation

DOEpatents

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

2002-09-03

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

Implementation details of the coupled QMR algorithm

NASA Technical Reports Server (NTRS)

Freund, Roland W.; Nachtigal, Noel M.

1992-01-01

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

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

PubMed

Kalinina, Elizabeth A

2013-08-01

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

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

NASA Astrophysics Data System (ADS)

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

2009-07-01

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

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

PubMed

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

2015-12-01

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

Quality of Arithmetic Education for Children with Cerebral Palsy

ERIC Educational Resources Information Center

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

2010-01-01

The aim of this exploratory study was to investigate the quality of arithmetic education for children with cerebral palsy. The use of individual educational plans, amount of arithmetic instruction time, arithmetic instructional grouping, and type of arithmetic teaching method were explored in three groups: children with cerebral palsy (CP) in…

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

PubMed

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

2018-03-01

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

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

PubMed

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

2012-01-01

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

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

PubMed

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

2015-11-15

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

Implicit Learning of Arithmetic Regularities Is Facilitated by Proximal Contrast

PubMed Central

Prather, Richard W.

2012-01-01

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

Arithmetic Circuit Verification Based on Symbolic Computer Algebra

NASA Astrophysics Data System (ADS)

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

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

Cognitive Analysis of Educational Games: The Number Game.

PubMed

van der Maas, Han L J; Nyamsuren, Enkhbold

2017-04-01

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

The neural circuits for arithmetic principles.

PubMed

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

2017-02-15

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

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…

Double resonance calibration of g factor standards: Carbon fibers as a high precision standard

NASA Astrophysics Data System (ADS)

Herb, Konstantin; Tschaggelar, Rene; Denninger, Gert; Jeschke, Gunnar

2018-04-01

The g factor of paramagnetic defects in commercial high performance carbon fibers was determined by a double resonance experiment based on the Overhauser shift due to hyperfine coupled protons. Our carbon fibers exhibit a single, narrow and perfectly Lorentzian shaped ESR line and a g factor slightly higher than gfree with g = 2.002644 =gfree · (1 + 162ppm) with a relative uncertainty of 15ppm . This precisely known g factor and their inertness qualify them as a high precision g factor standard for general purposes. The double resonance experiment for calibration is applicable to other potential standards with a hyperfine interaction averaged by a process with very short correlation time.

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

ERIC Educational Resources Information Center

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

2017-01-01

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

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

PubMed

Foley, Alana E; Vasilyeva, Marina; Laski, Elida V

2017-06-01

This study examined the mediating role of children's use of decomposition strategies in the relation between visuospatial memory (VSM) and arithmetic accuracy. Children (N = 78; Age M = 9.36) completed assessments of VSM, arithmetic strategies, and arithmetic accuracy. Consistent with previous findings, VSM predicted arithmetic accuracy in children. Extending previous findings, the current study showed that the relation between VSM and arithmetic performance was mediated by the frequency of children's use of decomposition strategies. Identifying the role of arithmetic strategies in this relation has implications for increasing the math performance of children with lower VSM. Statement of contribution What is already known on this subject? The link between children's visuospatial working memory and arithmetic accuracy is well documented. Frequency of decomposition strategy use is positively related to children's arithmetic accuracy. Children's spatial skill positively predicts the frequency with which they use decomposition. What does this study add? Short-term visuospatial memory (VSM) positively relates to the frequency of children's decomposition use. Decomposition use mediates the relation between short-term VSM and arithmetic accuracy. Children with limited short-term VSM may struggle to use decomposition, decreasing accuracy. © 2016 The British Psychological Society.

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

PubMed

Huber, Maria; Kipman, Ulrike; Pletzer, Belinda

2014-07-01

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

The Los Alamos National Laboratory precision double crystal spectrometer

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

Morgan, D.V.; Stevens, C.J.; Liefield, R.J.

1994-03-01

This report discusses the following topics on the LANL precision double crystal X-ray spectrometer: Motivation for construction of the instrument; a brief history of the instrument; mechanical systems; motion control systems; computer control system; vacuum system; alignment program; scan programs; observations of the copper K{alpha} lines; and characteristics and specifications.

Precision Tests of a Quantum Hall Effect Device DC Equivalent Circuit Using Double-Series and Triple-Series Connections

PubMed Central

Jeffery, A.; Elmquist, R. E.; Cage, M. E.

1995-01-01

Precision tests verify the dc equivalent circuit used by Ricketts and Kemeny to describe a quantum Hall effect device in terms of electrical circuit elements. The tests employ the use of cryogenic current comparators and the double-series and triple-series connection techniques of Delahaye. Verification of the dc equivalent circuit in double-series and triple-series connections is a necessary step in developing the ac quantum Hall effect as an intrinsic standard of resistance. PMID:29151768

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

NASA Astrophysics Data System (ADS)

Xu, Yefeng; He, Mengke

2008-10-01

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

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

PubMed

Berg, Derek H

2008-04-01

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

High precision calcium isotope analysis using 42Ca-48Ca double-spike TIMS technique

NASA Astrophysics Data System (ADS)

Feng, L.; Zhou, L.; Gao, S.; Tong, S. Y.; Zhou, M. L.

2014-12-01

Double spike techniques are widely used for determining calcium isotopic compositions of natural samples. The most important factor controlling precision of the double spike technique is the choice of appropriate spike isotope pair, the composition of double spikes and the ratio of spike to sample（CSp/CN）. We propose an optimal 42Ca-48Ca double spike protocol which yields the best internal precision for calcium isotopic composition determinations among all kinds of spike pairs and various spike compositions and ratios of spike to sample, as predicted by linear error propagation method. It is suggested to use spike composition of 42Ca/(42Ca+48Ca) = 0.44 mol/mol and CSp/(CN+ CSp)= 0.12mol/mol because it takes both advantages of the largest mass dispersion between 42Ca and 48Ca (14%) and lowest spike cost. Spiked samples were purified by pass through homemade micro-column filled with Ca special resin. K, Ti and other interference elements were completely separated, while 100% calcium was recovered with negligible blank. Data collection includes integration time, idle time, focus and peakcenter frequency, which were all carefully designed for the highest internal precision and lowest analysis time. All beams were automatically measured in a sequence by Triton TIMS so as to eliminate difference of analytical conditions between samples and standards, and also to increase the analytical throughputs. The typical internal precision of 100 duty cycles for one beam is 0.012‒0.015 ‰ (2δSEM), which agrees well with the predicted internal precision of 0.0124 ‰ (2δSEM). Our methods improve internal precisions by a factor of 2‒10 compared to previous methods of determination of calcium isotopic compositions by double spike TIMS. We analyzed NIST SRM 915a, NIST SRM 915b and Pacific Seawater as well as interspersed geological samples during two months. The obtained average δ44/40Ca (all relative to NIST SRM 915a) is 0.02 ± 0.02 ‰ (n=28), 0.72±0.04 ‰ (n=10) and 1.93±0.03 ‰ (n=21) for NIST SRM 915a, NIST SRM 915b and Pacific Seawater, respectively. The long-term reproducibility is 0.10‰ (2 δSD), which is comparable to the best external precision of 0.04 ‰ (2 δSD) of previous methods, but our sample throughputs are doubled with significant reduction in amount of spike used for single samples.

Design of permanent magnet synchronous motor speed control system based on SVPWM

NASA Astrophysics Data System (ADS)

Wu, Haibo

2017-04-01

The control system is designed to realize TMS320F28335 based on the permanent magnet synchronous motor speed control system, and put it to quoting all electric of injection molding machine. The system of the control method used SVPWM, through the sampling motor current and rotating transformer position information, realize speed, current double closed loop control. Through the TMS320F28335 hardware floating-point processing core, realize the application for permanent magnet synchronous motor in the floating point arithmetic, to replace the past fixed-point algorithm, and improve the efficiency of the code.

Children's multiplicative transformations of discrete and continuous quantities.

PubMed

Barth, Hilary; Baron, Andrew; Spelke, Elizabeth; Carey, Susan

2009-08-01

Recent studies have documented an evolutionarily primitive, early emerging cognitive system for the mental representation of numerical quantity (the analog magnitude system). Studies with nonhuman primates, human infants, and preschoolers have shown this system to support computations of numerical ordering, addition, and subtraction involving whole number concepts prior to arithmetic training. Here we report evidence that this system supports children's predictions about the outcomes of halving and perhaps also doubling transformations. A total of 138 kindergartners and first graders were asked to reason about the quantity resulting from the doubling or halving of an initial numerosity (of a set of dots) or an initial length (of a bar). Controls for dot size, total dot area, and dot density ensured that children were responding to the number of dots in the arrays. Prior to formal instruction in symbolic multiplication, division, or rational number, halving (and perhaps doubling) computations appear to be deployed over discrete and possibly continuous quantities. The ability to apply simple multiplicative transformations to analog magnitude representations of quantity may form a part of the toolkit that children use to construct later concepts of rational number.

Inconsistencies in Numerical Simulations of Dynamical Systems Using Interval Arithmetic

NASA Astrophysics Data System (ADS)

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

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

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

PubMed Central

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

2016-01-01

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

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

ERIC Educational Resources Information Center

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

2017-01-01

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

Personal Experience and Arithmetic Meaning in Semantic Dementia

ERIC Educational Resources Information Center

Julien, Camille L.; Neary, David; Snowden, Julie S.

2010-01-01

Arithmetic skills are generally claimed to be preserved in semantic dementia (SD), suggesting functional independence of arithmetic knowledge from other aspects of semantic memory. However, in a recent case series analysis we showed that arithmetic performance in SD is not entirely normal. The finding of a direct association between severity of…

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

NASA Astrophysics Data System (ADS)

Johnson, Chris; Kennedy, A. D.

2013-03-01

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

Precision improving of double beam shadow moiré interferometer by phase shifting interferometry for the stress of flexible substrate

NASA Astrophysics Data System (ADS)

Huang, Kuo-Ting; Chen, Hsi-Chao; Lin, Ssu-Fan; Lin, Ke-Ming; Syue, Hong-Ye

2012-09-01

While tin-doped indium oxide (ITO) has been extensively applied in flexible electronics, the problem of the residual stress has many obstacles to overcome. This study investigated the residual stress of flexible electronics by the double beam shadow moiré interferometer, and focused on the precision improvement with phase shifting interferometry (PSI). According to the out-of-plane displacement equation, the theoretical error depends on the grating pitch and the angle between incident light and CCD. The angle error could be reduced to 0.03% by the angle shift of 10° as a result of the double beam interferometer was a symmetrical system. But the experimental error of the double beam moiré interferometer still reached to 2.2% by the noise of the vibration and interferograms. In order to improve the measurement precision, PSI was introduced to the double shadow moiré interferometer. Wavefront phase was reconstructed by the five interferograms with the Hariharan algorithm. The measurement results of standard cylinder indicating the error could be reduced from 2.2% to less than 1% with PSI. The deformation of flexible electronic could be reconstructed fast and calculated the residual stress with the Stoney correction formula. This shadow moiré interferometer with PSI could improve the precision of residual stress for flexible electronics.

Double resonance calibration of g factor standards: Carbon fibers as a high precision standard.

PubMed

Herb, Konstantin; Tschaggelar, Rene; Denninger, Gert; Jeschke, Gunnar

2018-04-01

The g factor of paramagnetic defects in commercial high performance carbon fibers was determined by a double resonance experiment based on the Overhauser shift due to hyperfine coupled protons. Our carbon fibers exhibit a single, narrow and perfectly Lorentzian shaped ESR line and a g factor slightly higher than g free with g=2.002644=g free ·(1+162ppm) with a relative uncertainty of 15ppm. This precisely known g factor and their inertness qualify them as a high precision g factor standard for general purposes. The double resonance experiment for calibration is applicable to other potential standards with a hyperfine interaction averaged by a process with very short correlation time. Copyright © 2018 The Authors. Published by Elsevier Inc. All rights reserved.

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

PubMed

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

2016-10-01

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

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

PubMed

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

2016-12-01

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

[Acquisition of arithmetic knowledge].

PubMed

Fayol, Michel

2008-01-01

The focus of this paper is on contemporary research on the number counting and arithmetical competencies that emerge during infancy, the preschool years, and the elementary school. I provide a brief overview of the evolution of children's conceptual knowledge of arithmetic knowledge, the acquisition and use of counting and how they solve simple arithmetic problems (e.g. 4 + 3).

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

ERIC Educational Resources Information Center

Prather, Richard W.; Alibali, Martha W.

2009-01-01

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

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

PubMed Central

Park, Joonkoo; Brannon, Elizabeth M.

2017-01-01

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

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

PubMed

Artemenko, Christina; Soltanlou, Mojtaba; Ehlis, Ann-Christine; Nuerk, Hans-Christoph; Dresler, Thomas

2018-03-10

Arithmetic processing in adults is known to rely on a frontal-parietal network. However, neurocognitive research focusing on the neural and behavioral correlates of arithmetic development has been scarce, even though the acquisition of arithmetic skills is accompanied by changes within the fronto-parietal network of the developing brain. Furthermore, experimental procedures are typically adjusted to constraints of functional magnetic resonance imaging, which may not reflect natural settings in which children and adolescents actually perform arithmetic. Therefore, we investigated the longitudinal neurocognitive development of processes involved in performing the four basic arithmetic operations in 19 adolescents. By using functional near-infrared spectroscopy, we were able to use an ecologically valid task, i.e., a written production paradigm. A common pattern of activation in the bilateral fronto-parietal network for arithmetic processing was found for all basic arithmetic operations. Moreover, evidence was obtained for decreasing activation during subtraction over the course of 1 year in middle and inferior frontal gyri, and increased activation during addition and multiplication in angular and middle temporal gyri. In the self-paced block design, parietal activation in multiplication and left angular and temporal activation in addition were observed to be higher for simple than for complex blocks, reflecting an inverse effect of arithmetic complexity. In general, the findings suggest that the brain network for arithmetic processing is already established in 12-14 year-old adolescents, but still undergoes developmental changes.

Effect of the combination of ginseng, oriental bezoar and glycyrrhiza on autonomic nervous activity and immune system under mental arithmetic stress.

PubMed

Zheng, Aisong; Moritani, Toshio

2008-06-01

Stress reduces physical and mental tolerances (immune potential) of humans and it induces progression of existing illness or causes latent disorders to become active. Thus, the control and suppression of stress plays an important role in the improvement of quality of life and prevention of diseases. Ginseng, oriental bezoar and glycyrrhiza have been used for Kampo (herbal treatment) for thousand years and a number of pharmacological and clinical studies have reported their effects. However, it has not been previously described how the combination of these most commonly used herbs affect mental stress. This is a randomized, double-blind, placebo-controlled experiment to examine the effectiveness of reducing stress response by taking Kampo. Ten healthy males (mean age 27+/-1) participated in the study. The effectiveness of stress reduction was assessed by measuring ECG, salivary chromogranin A (CgA), blood glucose, WBC, granulocytes, lymphocytes, NK cell activity, etc. Salivary and blood measurement values of pre- and post-mental arithmetic stress were compared. In addition, ECG measurement values of pre- and mid-mental arithmetic stress were compared. we observed a higher HF power and a lower SNS index, HR, CgA, WBC and granulocytes in the Kampo trial than those in the placebo trial. The HR, HF power and SNS index were changed significantly (p<0.05) and CgA, WBC and granulocytes tended to show some differences between the two trials (p<0.1). However, blood glucose, lymphocytes, and NK cell activity showed no significant differences between the Kampo and placebo trials. The result suggests that the Kampo should be useful in reducing mental stress.

Fiber optic combiner and duplicator

NASA Technical Reports Server (NTRS)

1979-01-01

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

Approximate Arithmetic Training Improves Informal Math Performance in Low Achieving Preschoolers

PubMed Central

Szkudlarek, Emily; Brannon, Elizabeth M.

2018-01-01

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

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

PubMed

Szkudlarek, Emily; Brannon, Elizabeth M

2018-01-01

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

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

PubMed Central

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

2011-01-01

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

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

PubMed

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

1993-01-01

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

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

PubMed

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

2012-01-01

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

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

ERIC Educational Resources Information Center

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

2016-01-01

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

Non-symbolic arithmetic in adults and young children.

PubMed

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

2006-01-01

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

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

PubMed

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

2006-06-01

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

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

PubMed

Fehr, Thorsten; Code, Chris; Herrmann, Manfred

2007-10-03

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

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

PubMed

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

2017-02-01

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

Microfluidic approach for encapsulation via double emulsions.

PubMed

Wang, Wei; Zhang, Mao-Jie; Chu, Liang-Yin

2014-10-01

Double emulsions, with inner drops well protected by the outer shells, show great potential as compartmentalized systems to encapsulate multiple components for protecting actives, masking flavor, and targetedly delivering and controllably releasing drugs. Precise control of the encapsulation characteristics of each component is critical to achieve an optimal therapeutic efficacy for pharmaceutical applications. Such controllable encapsulation can be realized by using microfluidic approaches for producing monodisperse double emulsions with versatile and controllable structures as the encapsulation system. The size, number and composition of the emulsion drops can be accurately manipulated for optimizing the encapsulation of each component for pharmaceutical applications. In this review, we highlight the outstanding advantages of controllable microfluidic double emulsions for highly efficient and precisely controllable encapsulation. Copyright © 2014 Elsevier Ltd. All rights reserved.

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

PubMed Central

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

2013-01-01

Arithmetic skill is of critical importance for academic achievement, professional success and everyday life, and childhood is the key period to acquire this skill. Neuroimaging studies have identified that left parietal regions are a key neural substrate for representing arithmetic skill. Although the relationship between functional brain activity in left parietal regions and arithmetic skill has been studied in detail, it remains unclear about the relationship between arithmetic achievement and structural properties in left inferior parietal area in schoolchildren. The current study employed a combination of voxel-based morphometry (VBM) for high-resolution T1-weighted images and fiber tracking on diffusion tensor imaging (DTI) to examine the relationship between structural properties in the inferior parietal area and arithmetic achievement in 10-year-old schoolchildren. VBM of the T1-weighted images revealed that individual differences in arithmetic scores were significantly and positively correlated with the gray matter (GM) volume in the left intraparietal sulcus (IPS). Fiber tracking analysis revealed that the forceps major, left superior longitudinal fasciculus (SLF), bilateral inferior longitudinal fasciculus (ILF) and inferior fronto-occipital fasciculus (IFOF) were the primary pathways connecting the left IPS with other brain areas. Furthermore, the regression analysis of the probabilistic pathways revealed a significant and positive correlation between the fractional anisotropy (FA) values in the left SLF, ILF and bilateral IFOF and arithmetic scores. The brain structure-behavior correlation analyses indicated that the GM volumes in the left IPS and the FA values in the tract pathways connecting left IPS were both related to children's arithmetic achievement. The present findings provide evidence that individual structural differences in the left IPS are associated with arithmetic scores in schoolchildren. PMID:24367320

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

PubMed

Hinault, T; Lemaire, P

2016-01-01

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

Reconfigurable data path processor

NASA Technical Reports Server (NTRS)

Donohoe, Gregory (Inventor)

2005-01-01

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

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

ERIC Educational Resources Information Center

Berg, Derek H.; Hutchinson, Nancy L.

2010-01-01

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

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

NASA Astrophysics Data System (ADS)

Wang, Li-Qun; Saito, Masao

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

On Kedlaya-type inequalities for weighted means.

PubMed

Páles, Zsolt; Pasteczka, Paweł

2018-01-01

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

Boundary implications for frequency response of interval FIR and IIR filters

NASA Technical Reports Server (NTRS)

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

1991-01-01

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

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

PubMed Central

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

2015-01-01

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

Double-trap measurement of the proton magnetic moment at 0.3 parts per billion precision.

PubMed

Schneider, Georg; Mooser, Andreas; Bohman, Matthew; Schön, Natalie; Harrington, James; Higuchi, Takashi; Nagahama, Hiroki; Sellner, Stefan; Smorra, Christian; Blaum, Klaus; Matsuda, Yasuyuki; Quint, Wolfgang; Walz, Jochen; Ulmer, Stefan

2017-11-24

Precise knowledge of the fundamental properties of the proton is essential for our understanding of atomic structure as well as for precise tests of fundamental symmetries. We report on a direct high-precision measurement of the magnetic moment μ p of the proton in units of the nuclear magneton μ N The result, μ p = 2.79284734462 (±0.00000000082) μ N , has a fractional precision of 0.3 parts per billion, improves the previous best measurement by a factor of 11, and is consistent with the currently accepted value. This was achieved with the use of an optimized double-Penning trap technique. Provided a similar measurement of the antiproton magnetic moment can be performed, this result will enable a test of the fundamental symmetry between matter and antimatter in the baryonic sector at the 10 -10 level. Copyright © 2017, American Association for the Advancement of Science.

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

PubMed Central

Rapoport, Shirley; Rubinsten, Orly; Katzir, Tami

2016-01-01

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

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

PubMed

Rapoport, Shirley; Rubinsten, Orly; Katzir, Tami

2016-01-01

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

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

PubMed

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

2018-04-01

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

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

PubMed

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

2017-12-01

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

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

PubMed

Van Rooijen, M; Verhoeven, L; Smits, D W; Dallmeijer, A J; Becher, J G; Steenbergen, B

2014-04-01

The aim of this study was to examine the development of arithmetic performance and its cognitive precursors in children with CP from 7 till 9 years of age. Previous research has shown that children with CP are generally delayed in arithmetic performance compared to their typically developing peers. In children with CP, the developmental trajectory of the ability to solve addition- and subtraction tasks has, however, rarely been studied, as well as the cognitive factors affecting this trajectory. Sixty children (M=7.2 years, SD=.23 months at study entry) with CP participated in this study. Standardized tests were administered to assess arithmetic performance, word decoding skills, non-verbal intelligence, and working memory. The results showed that the ability to solve addition- and subtraction tasks increased over a two year period. Word decoding skills were positively related to the initial status of arithmetic performance. In addition, non-verbal intelligence and working memory were associated with the initial status and growth rate of arithmetic performance from 7 till 9 years of age. The current study highlights the importance of non-verbal intelligence and working memory to the development of arithmetic performance of children with CP. Copyright © 2014 Elsevier Ltd. All rights reserved.

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

PubMed

Avancini, Chiara; Soltész, Fruzsina; Szűcs, Dénes

2015-08-01

In studies of arithmetic verification, participants typically encounter two operands and they carry out an operation on these (e.g. adding them). Operands are followed by a proposed answer and participants decide whether this answer is correct or incorrect. However, interpretation of results is difficult because multiple parallel, temporally overlapping numerical and non-numerical processes of the human brain may contribute to task execution. In order to overcome this problem here we used a novel paradigm specifically designed to tease apart the overlapping cognitive processes active during arithmetic verification. Specifically, we aimed to separate effects related to detection of arithmetic correctness, detection of the violation of strategic expectations, detection of physical stimulus properties mismatch and numerical magnitude comparison (numerical distance effects). Arithmetic correctness, physical stimulus properties and magnitude information were not task-relevant properties of the stimuli. We distinguished between a series of temporally highly overlapping cognitive processes which in turn elicited overlapping ERP effects with distinct scalp topographies. We suggest that arithmetic verification relies on two major temporal phases which include parallel running processes. Our paradigm offers a new method for investigating specific arithmetic verification processes in detail. Copyright © 2015 Elsevier Ltd. All rights reserved.

Do Children Understand Fraction Addition?

ERIC Educational Resources Information Center

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

2017-01-01

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

Distribución Espacial de Ancho Equivalente del Triplete del CaII a partir de Imágenes GMOS

NASA Astrophysics Data System (ADS)

Díaz, R. J.; Mast, D.

Using Gemini+GMOS imagery obtained through the filters i, z and CaT, we developed a technique for estimating the value of the Ca II triplet (CaT) equivalent width (EW). The map generated through arithmetic operations with the near infrared images was calibrated with long slit spectra obtained with REOSC spectrograph at CASLEO. We apply this technique to the study of M 83 central region and present the preliminary results on the spatial distribution of the EW(CaT) within an area of 40 per 40 square arcsec around the double nucleus of M 83, with a spatial resolution of 0.8 arcsec. FULL TEXT IN SPANISH.

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

PubMed

Avancini, Chiara; Galfano, Giovanni; Szűcs, Dénes

2014-12-01

Event-related potential (ERP) studies have detected several characteristic consecutive amplitude modulations in both implicit and explicit mental arithmetic tasks. Implicit tasks typically focused on the arithmetic relatedness effect (in which performance is affected by semantic associations between numbers) while explicit tasks focused on the distance effect (in which performance is affected by the numerical difference of to-be-compared numbers). Both task types elicit morphologically similar ERP waves which were explained in functionally similar terms. However, to date, the relationship between these tasks has not been investigated explicitly and systematically. In order to fill this gap, here we examined whether ERP effects and their underlying cognitive processes in implicit and explicit mental arithmetic tasks differ from each other. The same group of participants performed both an implicit number-matching task (in which arithmetic knowledge is task-irrelevant) and an explicit arithmetic-verification task (in which arithmetic knowledge is task-relevant). 129-channel ERP data differed substantially between tasks. In the number-matching task, the arithmetic relatedness effect appeared as a negativity over left-frontal electrodes whereas the distance effect was more prominent over right centro-parietal electrodes. In the verification task, all probe types elicited similar N2b waves over right fronto-central electrodes and typical centro-parietal N400 effects over central electrodes. The distance effect appeared as an early-rising, long-lasting left parietal negativity. We suggest that ERP effects in the implicit task reflect access to semantic memory networks and to magnitude discrimination, respectively. In contrast, effects of expectation violation are more prominent in explicit tasks and may mask more delicate cognitive processes. Copyright © 2014 The Authors. Published by Elsevier B.V. All rights reserved.

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

PubMed Central

Avancini, Chiara; Galfano, Giovanni; Szűcs, Dénes

2014-01-01

Event-related potential (ERP) studies have detected several characteristic consecutive amplitude modulations in both implicit and explicit mental arithmetic tasks. Implicit tasks typically focused on the arithmetic relatedness effect (in which performance is affected by semantic associations between numbers) while explicit tasks focused on the distance effect (in which performance is affected by the numerical difference of to-be-compared numbers). Both task types elicit morphologically similar ERP waves which were explained in functionally similar terms. However, to date, the relationship between these tasks has not been investigated explicitly and systematically. In order to fill this gap, here we examined whether ERP effects and their underlying cognitive processes in implicit and explicit mental arithmetic tasks differ from each other. The same group of participants performed both an implicit number-matching task (in which arithmetic knowledge is task-irrelevant) and an explicit arithmetic-verification task (in which arithmetic knowledge is task-relevant). 129-channel ERP data differed substantially between tasks. In the number-matching task, the arithmetic relatedness effect appeared as a negativity over left-frontal electrodes whereas the distance effect was more prominent over right centro-parietal electrodes. In the verification task, all probe types elicited similar N2b waves over right fronto-central electrodes and typical centro-parietal N400 effects over central electrodes. The distance effect appeared as an early-rising, long-lasting left parietal negativity. We suggest that ERP effects in the implicit task reflect access to semantic memory networks and to magnitude discrimination, respectively. In contrast, effects of expectation violation are more prominent in explicit tasks and may mask more delicate cognitive processes. PMID:25450162

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

PubMed

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

2008-04-04

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

Reconfigurable pipelined processor

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

Saccardi, R.J.

1989-09-19

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

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

PubMed Central

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

2014-01-01

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

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

PubMed

Deaño, Manuel Deaño; Alfonso, Sonia; Das, Jagannath Prasad

2015-03-01

This study reports the cognitive and arithmetic improvement of a mathematical model based on the program PASS Remedial Program (PREP), which aims to improve specific cognitive processes underlying academic skills such as arithmetic. For this purpose, a group of 20 students from the last four grades of Primary Education was divided into two groups. One group (n=10) received training in the program and the other served as control. Students were assessed at pre and post intervention in the PASS cognitive processes (planning, attention, simultaneous and successive processing), general level of intelligence, and arithmetic performance in calculus and solving problems. Performance of children from the experimental group was significantly higher than that of the control group in cognitive process and arithmetic. This joint enhancement of cognitive and arithmetic processes was a result of the operationalization of training that promotes the encoding task, attention and planning, and learning by induction, mediation and verbalization. The implications of this are discussed. Copyright © 2014 Elsevier Ltd. All rights reserved.

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

PubMed Central

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

2012-01-01

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

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

PubMed

Lambert, Kevin

2013-06-01

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

An Application of Response Surface Methodology to a Macroeconomic Model.

DTIC Science & Technology

1985-12-01

L21,ILI,ISl ,KI,SBI,PYl ,MI,P11,Q1 double precision TE,TW,TC,TN,TR,G,W2,R2,T,H,NP,NL,N8,NE,FR, :: & PF,LB A double precision CLI, SCLI ,PCL1IDL1 ,WlLl...TCLI-TNLI- SCLI )*PILI/PRLI) & .0.012*FR)+0.5*R1 PR=0.5*(-131. 17+2.32.PI)+0.5*PR *The monetary sector is omitted (See Chapter IV) C L1=0.5*(0.14*(M-TW

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

PubMed

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

2009-07-01

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

A Pacific Ocean general circulation model for satellite data assimilation

NASA Technical Reports Server (NTRS)

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

1991-01-01

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

Conceptual Knowledge of Fraction Arithmetic

ERIC Educational Resources Information Center

Siegler, Robert S.; Lortie-Forgues, Hugues

2015-01-01

Understanding an arithmetic operation implies, at minimum, knowing the direction of effects that the operation produces. However, many children and adults, even those who execute arithmetic procedures correctly, may lack this knowledge on some operations and types of numbers. To test this hypothesis, we presented preservice teachers (Study 1),…

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

ERIC Educational Resources Information Center

Rourke, Byron P.; Conway, James A.

1997-01-01

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

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

ERIC Educational Resources Information Center

Braithwaite, David W.; Siegler, Robert S.

2018-01-01

Fraction arithmetic is among the most important and difficult topics children encounter in elementary and middle school mathematics. Braithwaite, Pyke, and Siegler (2017) hypothesized that difficulties learning fraction arithmetic often reflect reliance on associative knowledge--rather than understanding of mathematical concepts and procedures--to…

A Computational Model of Fraction Arithmetic

ERIC Educational Resources Information Center

Braithwaite, David W.; Pyke, Aryn A.; Siegler, Robert S.

2017-01-01

Many children fail to master fraction arithmetic even after years of instruction, a failure that hinders their learning of more advanced mathematics as well as their occupational success. To test hypotheses about why children have so many difficulties in this area, we created a computational model of fraction arithmetic learning and presented it…

Arithmetic 400. A Computer Educational Program.

ERIC Educational Resources Information Center

Firestein, Laurie

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

Simulating Network Retrieval of Arithmetic Facts.

ERIC Educational Resources Information Center

Ashcraft, Mark H.

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

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

ERIC Educational Resources Information Center

Gilmore, Camilla K.; Bryant, Peter

2006-01-01

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

The Practice of Arithmetic in Liberian Schools.

ERIC Educational Resources Information Center

Brenner, Mary E.

1985-01-01

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

From Arithmetic Sequences to Linear Equations

ERIC Educational Resources Information Center

Matsuura, Ryota; Harless, Patrick

2012-01-01

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

Baby Arithmetic: One Object Plus One Tone

ERIC Educational Resources Information Center

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

2004-01-01

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

Conceptual Knowledge of Decimal Arithmetic

ERIC Educational Resources Information Center

Lortie-Forgues, Hugues; Siegler, Robert S.

2016-01-01

In two studies (N's = 55 and 54), we examined a basic form of conceptual understanding of rational number arithmetic, the direction of effect of decimal arithmetic operations, at a level of detail useful for informing instruction. Middle school students were presented tasks examining knowledge of the direction of effects (e.g., "True or…

IBM system/360 assembly language interval arithmetic software

NASA Technical Reports Server (NTRS)

Phillips, E. J.

1972-01-01

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

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

PubMed

Egeland, Jens; Bosnes, Ole; Johansen, Hans

2009-09-01

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

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

PubMed

Siemann, Julia; Petermann, Franz

2018-01-01

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

If Gravity is Geometry, is Dark Energy just Arithmetic?

NASA Astrophysics Data System (ADS)

Czachor, Marek

2017-04-01

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

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

PubMed

Braithwaite, David W; Siegler, Robert S

2018-04-26

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

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

PubMed

Cipora, Krzysztof; Nuerk, Hans-Christoph

2013-01-01

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

How GNSS Enables Precision Farming

DOT National Transportation Integrated Search

2014-12-01

Precision farming: Feeding a Growing Population Enables Those Who Feed the World. Immediate and Ongoing Needs - population growth (more to feed) - urbanization (decrease in arable land) Double food production by 2050 to meet world demand. To meet thi...

A dual-core double emulsion platform for osmolarity-controlled microreactor triggered by coalescence of encapsulated droplets.

PubMed

Guan, Xuewei; Hou, Likai; Ren, Yukun; Deng, Xiaokang; Lang, Qi; Jia, Yankai; Hu, Qingming; Tao, Ye; Liu, Jiangwei; Jiang, Hongyuan

2016-05-01

Droplet-based microfluidics has provided a means to generate multi-core double emulsions, which are versatile platforms for microreactors in materials science, synthetic biology, and chemical engineering. To provide new opportunities for double emulsion platforms, here, we report a glass capillary microfluidic approach to first fabricate osmolarity-responsive Water-in-Oil-in-Water (W/O/W) double emulsion containing two different inner droplets/cores and to then trigger the coalescence between the encapsulated droplets precisely. To achieve this, we independently control the swelling speed and size of each droplet in the dual-core double emulsion by controlling the osmotic pressure between the inner droplets and the collection solutions. When the inner two droplets in one W/O/W double emulsion swell to the same size and reach the instability of the oil film interface between the inner droplets, core-coalescence happens and this coalescence process can be controlled precisely. This microfluidic methodology enables the generation of highly monodisperse dual-core double emulsions and the osmolarity-controlled swelling behavior provides new stimuli to trigger the coalescence between the encapsulated droplets. Such swelling-caused core-coalescence behavior in dual-core double emulsion establishes a novel microreactor for nanoliter-scale reactions, which can protect reaction materials and products from being contaminated or released.

A dual-core double emulsion platform for osmolarity-controlled microreactor triggered by coalescence of encapsulated droplets

PubMed Central

Guan, Xuewei; Hou, Likai; Ren, Yukun; Deng, Xiaokang; Lang, Qi; Jia, Yankai; Hu, Qingming; Tao, Ye; Liu, Jiangwei; Jiang, Hongyuan

2016-01-01

Droplet-based microfluidics has provided a means to generate multi-core double emulsions, which are versatile platforms for microreactors in materials science, synthetic biology, and chemical engineering. To provide new opportunities for double emulsion platforms, here, we report a glass capillary microfluidic approach to first fabricate osmolarity-responsive Water-in-Oil-in-Water (W/O/W) double emulsion containing two different inner droplets/cores and to then trigger the coalescence between the encapsulated droplets precisely. To achieve this, we independently control the swelling speed and size of each droplet in the dual-core double emulsion by controlling the osmotic pressure between the inner droplets and the collection solutions. When the inner two droplets in one W/O/W double emulsion swell to the same size and reach the instability of the oil film interface between the inner droplets, core-coalescence happens and this coalescence process can be controlled precisely. This microfluidic methodology enables the generation of highly monodisperse dual-core double emulsions and the osmolarity-controlled swelling behavior provides new stimuli to trigger the coalescence between the encapsulated droplets. Such swelling-caused core-coalescence behavior in dual-core double emulsion establishes a novel microreactor for nanoliter-scale reactions, which can protect reaction materials and products from being contaminated or released. PMID:27279935

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

NASA Astrophysics Data System (ADS)

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

2007-12-01

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

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

PubMed

Gilmore, Camilla K; Bryant, Peter

2006-06-01

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

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

PubMed

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

2018-05-01

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

A Substituting Meaning for the Equals Sign in Arithmetic Notating Tasks

ERIC Educational Resources Information Center

Jones, Ian; Pratt, Dave

2012-01-01

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

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

ERIC Educational Resources Information Center

Prather, Richard; Alibali, Martha W.

2011-01-01

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

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

ERIC Educational Resources Information Center

Koontz, Kristine L.; Berch, Daniel B.

1996-01-01

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

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

ERIC Educational Resources Information Center

Glaser, Anton

This history of binary arithmetic begins with details of Thomas Hariot's contribution and includes specific references to Hariot's manuscripts kept at the British Museum. A binary code developed by Sir Francis Bacon is discussed. Briefly mentioned are contributions to binary arithmetic made by Leibniz, Fontenelle, Gauss, Euler, Benzout, Barlow,…

ASIC For Complex Fixed-Point Arithmetic

NASA Technical Reports Server (NTRS)

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

1995-01-01

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

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

ERIC Educational Resources Information Center

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

2012-01-01

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

Cognitive Arithmetic: Evidence for the Development of Automaticity.

ERIC Educational Resources Information Center

LeFevre, Jo-Anne; Bisanz, Jeffrey

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

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

ERIC Educational Resources Information Center

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

2010-01-01

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

Fostering Formal Commutativity Knowledge with Approximate Arithmetic

PubMed Central

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

2015-01-01

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

Frontoparietal white matter diffusion properties predict mental arithmetic skills in children

PubMed Central

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

2009-01-01

Functional MRI studies of mental arithmetic consistently report blood oxygen level–dependent signals in the parietal and frontal regions. We tested whether white matter pathways connecting these regions are related to mental arithmetic ability by using diffusion tensor imaging (DTI) to measure these pathways in 28 children (age 10–15 years, 14 girls) and assessing their mental arithmetic skills. For each child, we identified anatomically the anterior portion of the superior longitudinal fasciculus (aSLF), a pathway connecting parietal and frontal cortex. We measured fractional anisotropy in a core region centered along the length of the aSLF. Fractional anisotropy in the left aSLF positively correlates with arithmetic approximation skill, as measured by a mental addition task with approximate answer choices. The correlation is stable in adjacent core aSLF regions but lower toward the pathway endpoints. The correlation is not explained by shared variance with other cognitive abilities and did not pass significance in the right aSLF. These measurements used DTI, a structural method, to test a specific functional model of mental arithmetic. PMID:19948963

Airborne Double Pulsed 2-Micron IPDA Lidar for Atmospheric CO2 Measurement

NASA Technical Reports Server (NTRS)

Yu, Jirong; Petros, Mulugeta; Refaat, Tamer; Singh, Upendra

2015-01-01

We have developed an airborne 2-micron Integrated Path Differential Absorption (IPDA) lidar for atmospheric CO2 measurements. The double pulsed, high pulse energy lidar instrument can provide high-precision CO2 column density measurements.

Identifying Blocks Formed by Curbed Fractures Using Exact Arithmetic

NASA Astrophysics Data System (ADS)

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

2015-12-01

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

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

ERIC Educational Resources Information Center

Berg, Derek H.

2008-01-01

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

Arithmetic Achievement in Children with Cerebral Palsy or Spina Bifida Meningomyelocele

ERIC Educational Resources Information Center

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

2009-01-01

The aim of this study was to establish whether children with a physical disability resulting from central nervous system disorders (CNSd) show a level of arithmetic achievement lower than that of non-CNSd children and whether this is related to poor automaticity of number facts or reduced arithmetic instruction time. Twenty-two children with CNSd…

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

ERIC Educational Resources Information Center

Singer, Vivian; Strasser, Kathernie

2017-01-01

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

24 CFR Appendix E to Part 3500 - Arithmetic Steps

Code of Federal Regulations, 2010 CFR

2010-04-01

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

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

ERIC Educational Resources Information Center

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

2015-01-01

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

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

ERIC Educational Resources Information Center

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

2009-01-01

Background: Although it is believed that children with cerebral palsy are at high risk for learning difficulties and arithmetic difficulties in particular, few studies have investigated this issue. Methods: Arithmetic ability was longitudinally assessed in children with cerebral palsy in special (n = 41) and mainstream education (n = 16) and…

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

ERIC Educational Resources Information Center

Berg, Derek H.

2008-01-01

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

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

ERIC Educational Resources Information Center

Yang, Ma Tzu-Lin; Cobb, Paul

1995-01-01

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

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

ERIC Educational Resources Information Center

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

2016-01-01

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

Changes of brain response induced by simulated weightlessness

NASA Astrophysics Data System (ADS)

Wei, Jinhe; Yan, Gongdong; Guan, Zhiqiang

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

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

PubMed

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

2009-05-01

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

The MasPar MP-1 As a Computer Arithmetic Laboratory

PubMed Central

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

1996-01-01

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

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

PubMed Central

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

2016-01-01

In this article, we tested, using a 1-year longitudinal design, whether symbolic numerical magnitude processing or children’s numerical representation of Arabic digits, is as important to arithmetic as phonological awareness is to reading. Children completed measures of symbolic comparison, phonological awareness, arithmetic, reading at the start of third grade and the latter two were retested at the start of fourth grade. Cross-sectional and longitudinal correlations indicated that symbolic comparison was a powerful domain-specific predictor of arithmetic and that phonological awareness was a unique predictor of reading. Crucially, the strength of these independent associations was not significantly different. This indicates that symbolic numerical magnitude processing is as important to arithmetic development as phonological awareness is to reading and suggests that symbolic numerical magnitude processing is a good candidate for screening children at risk for developing mathematical difficulties. PMID:26942935

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

NASA Astrophysics Data System (ADS)

Cherri, Abdallah K.

1998-08-01

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

Visuospatial and verbal memory in mental arithmetic.

PubMed

Clearman, Jack; Klinger, Vojtěch; Szűcs, Dénes

2017-09-01

Working memory allows complex information to be remembered and manipulated over short periods of time. Correlations between working memory and mathematics achievement have been shown across the lifespan. However, only a few studies have examined the potentially distinct contributions of domain-specific visuospatial and verbal working memory resources in mental arithmetic computation. Here we aimed to fill this gap in a series of six experiments pairing addition and subtraction tasks with verbal and visuospatial working memory and interference tasks. In general, we found higher levels of interference between mental arithmetic and visuospatial working memory tasks than between mental arithmetic and verbal working memory tasks. Additionally, we found that interference that matched the working memory domain of the task (e.g., verbal task with verbal interference) lowered working memory performance more than mismatched interference (verbal task with visuospatial interference). Findings suggest that mental arithmetic relies on domain-specific working memory resources.

The semantic system is involved in mathematical problem solving.

PubMed

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

2018-02-01

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

Exact method for numerically analyzing a model of local denaturation in superhelically stressed DNA

NASA Astrophysics Data System (ADS)

Fye, Richard M.; Benham, Craig J.

1999-03-01

Local denaturation, the separation at specific sites of the two strands comprising the DNA double helix, is one of the most fundamental processes in biology, required to allow the base sequence to be read both in DNA transcription and in replication. In living organisms this process can be mediated by enzymes which regulate the amount of superhelical stress imposed on the DNA. We present a numerically exact technique for analyzing a model of denaturation in superhelically stressed DNA. This approach is capable of predicting the locations and extents of transition in circular superhelical DNA molecules of kilobase lengths and specified base pair sequences. It can also be used for closed loops of DNA which are typically found in vivo to be kilobases long. The analytic method consists of an integration over the DNA twist degrees of freedom followed by the introduction of auxiliary variables to decouple the remaining degrees of freedom, which allows the use of the transfer matrix method. The algorithm implementing our technique requires O(N2) operations and O(N) memory to analyze a DNA domain containing N base pairs. However, to analyze kilobase length DNA molecules it must be implemented in high precision floating point arithmetic. An accelerated algorithm is constructed by imposing an upper bound M on the number of base pairs that can simultaneously denature in a state. This accelerated algorithm requires O(MN) operations, and has an analytically bounded error. Sample calculations show that it achieves high accuracy (greater than 15 decimal digits) with relatively small values of M (M<0.05N) for kilobase length molecules under physiologically relevant conditions. Calculations are performed on the superhelical pBR322 DNA sequence to test the accuracy of the method. With no free parameters in the model, the locations and extents of local denaturation predicted by this analysis are in quantitatively precise agreement with in vitro experimental measurements. Calculations performed on the fructose-1,6-bisphosphatase gene sequence from yeast show that this approach can also accurately treat in vivo denaturation.

An efficient mixed-precision, hybrid CPU-GPU implementation of a nonlinearly implicit one-dimensional particle-in-cell algorithm

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

Chen, Guangye; Chacon, Luis; Barnes, Daniel C

2012-01-01

Recently, a fully implicit, energy- and charge-conserving particle-in-cell method has been developed for multi-scale, full-f kinetic simulations [G. Chen, et al., J. Comput. Phys. 230, 18 (2011)]. The method employs a Jacobian-free Newton-Krylov (JFNK) solver and is capable of using very large timesteps without loss of numerical stability or accuracy. A fundamental feature of the method is the segregation of particle orbit integrations from the field solver, while remaining fully self-consistent. This provides great flexibility, and dramatically improves the solver efficiency by reducing the degrees of freedom of the associated nonlinear system. However, it requires a particle push per nonlinearmore » residual evaluation, which makes the particle push the most time-consuming operation in the algorithm. This paper describes a very efficient mixed-precision, hybrid CPU-GPU implementation of the implicit PIC algorithm. The JFNK solver is kept on the CPU (in double precision), while the inherent data parallelism of the particle mover is exploited by implementing it in single-precision on a graphics processing unit (GPU) using CUDA. Performance-oriented optimizations, with the aid of an analytical performance model, the roofline model, are employed. Despite being highly dynamic, the adaptive, charge-conserving particle mover algorithm achieves up to 300 400 GOp/s (including single-precision floating-point, integer, and logic operations) on a Nvidia GeForce GTX580, corresponding to 20 25% absolute GPU efficiency (against the peak theoretical performance) and 50-70% intrinsic efficiency (against the algorithm s maximum operational throughput, which neglects all latencies). This is about 200-300 times faster than an equivalent serial CPU implementation. When the single-precision GPU particle mover is combined with a double-precision CPU JFNK field solver, overall performance gains 100 vs. the double-precision CPU-only serial version are obtained, with no apparent loss of robustness or accuracy when applied to a challenging long-time scale ion acoustic wave simulation.« less

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

ERIC Educational Resources Information Center

Education Development Center, Inc., Newton, MA.

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

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

ERIC Educational Resources Information Center

Lynn, Richard; Irwing, Paul

2008-01-01

Meta-analyses are presented of sex differences in (1) the (mental) arithmetic subtest of the Wechsler intelligence tests for children and adolescents (the WISC and WPPSI tests), showing that boys obtained a mean advantage of 0.11d; (2) the (mental) arithmetic subtest of the Wechsler intelligence tests for adults (the WAIS tests) showing a mean…

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

ERIC Educational Resources Information Center

Barrouillet, Pierre; Poirier, Louise

1997-01-01

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

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

ERIC Educational Resources Information Center

Andersson, Ulf

2008-01-01

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

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

ERIC Educational Resources Information Center

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

2012-01-01

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

Error-correcting codes in computer arithmetic.

NASA Technical Reports Server (NTRS)

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

1972-01-01

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

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

ERIC Educational Resources Information Center

McNeil, Nicole M.

2008-01-01

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

Arithmetic Data Cube as a Data Intensive Benchmark

NASA Technical Reports Server (NTRS)

Frumkin, Michael A.; Shabano, Leonid

2003-01-01

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

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

PubMed

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

2009-11-01

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

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

PubMed Central

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

2014-01-01

The current study investigated the influence of cardiorespiratory fitness on arithmetic cognition in forty 9–10 year old children. Measures included a standardized mathematics achievement test to assess conceptual and computational knowledge, self-reported strategy selection, and an experimental arithmetic verification task (including small and large addition problems), which afforded the measurement of event-related brain potentials (ERPs). No differences in math achievement were observed as a function of fitness level, but all children performed better on math concepts relative to math computation. Higher fit children reported using retrieval more often to solve large arithmetic problems, relative to lower fit children. During the arithmetic verification task, higher fit children exhibited superior performance for large problems, as evidenced by greater d' scores, while all children exhibited decreased accuracy and longer reaction time for large relative to small problems, and incorrect relative to correct solutions. On the electrophysiological level, modulations of early (P1, N170) and late ERP components (P3, N400) were observed as a function of problem size and solution correctness. Higher fit children exhibited selective modulations for N170, P3, and N400 amplitude relative to lower fit children, suggesting that fitness influences symbolic encoding, attentional resource allocation and semantic processing during arithmetic tasks. The current study contributes to the fitness-cognition literature by demonstrating that the benefits of cardiorespiratory fitness extend to arithmetic cognition, which has important implications for the educational environment and the context of learning. PMID:24829556

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

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

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

NASA Astrophysics Data System (ADS)

Zhang, Shuang; Zhong, Yuning; Xu, Zhongbao

2008-12-01

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

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

NASA Astrophysics Data System (ADS)

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

2017-05-01

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

Optical computation using residue arithmetic.

PubMed

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

1979-01-15

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

Arithmetic learning in advanced age.

PubMed

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

2018-01-01

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

Arithmetic learning in advanced age

PubMed Central

Kremser, Christian; Pertl, Marie-Theres; Gizewski, Elke; Benke, Thomas; Delazer, Margarete

2018-01-01

Acquisition of numerical knowledge and understanding of numerical information are crucial for coping with the changing demands of our digital society. In this study, we assessed arithmetic learning in older and younger individuals in a training experiment including brain imaging. In particular, we assessed age-related effects of training intensity, prior arithmetic competence, and neuropsychological variables on the acquisition of new arithmetic knowledge and on the transfer to new, unknown problems. Effects were assessed immediately after training and after 3 months. Behavioural results showed higher training effects for younger individuals than for older individuals and significantly better performance after 90 problem repetitions than after 30 repetitions in both age groups. A correlation analysis indicated that older adults with lower memory and executive functions at baseline could profit more from intensive training. Similarly, training effects in the younger group were higher for those individuals who had lower arithmetic competence and executive functions prior to intervention. In younger adults, successful transfer was associated with higher executive functions. Memory and set-shifting emerged as significant predictors of training effects in the older group. For the younger group, prior arithmetic competence was a significant predictor of training effects, while cognitive flexibility was a predictor of transfer effects. After training, a subgroup of participants underwent an MRI assessment. A voxel-based morphometry analysis showed a significant interaction between training effects and grey matter volume of the right middle temporal gyrus extending to the angular gyrus for the younger group relative to the older group. The reverse contrast (older group vs. younger group) did not yield any significant results. These results suggest that improvements in arithmetic competence are supported by temporo-parietal areas in the right hemisphere in younger participants, while learning in older people might be more widespread. Overall, our study indicates that arithmetic learning depends on the training intensity as well as on person-related factors including individual age, arithmetic competence before training, memory, and executive functions. In conclusion, we suggest that major progress can be also achieved by older participants, but that interventions have to take into account individual variables in order to provide maximal benefit. PMID:29489905

One way Doppler Extractor. Volume 2: Digital VCO technique

NASA Technical Reports Server (NTRS)

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

1974-01-01

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

Parameter estimation by decoherence in the double-slit experiment

NASA Astrophysics Data System (ADS)

Matsumura, Akira; Ikeda, Taishi; Kukita, Shingo

2018-06-01

We discuss a parameter estimation problem using quantum decoherence in the double-slit interferometer. We consider a particle coupled to a massive scalar field after the particle passing through the double slit and solve the dynamics non-perturbatively for the coupling by the WKB approximation. This allows us to analyze the estimation problem which cannot be treated by master equation used in the research of quantum probe. In this model, the scalar field reduces the interference fringes of the particle and the fringe pattern depends on the field mass and coupling. To evaluate the contrast and the estimation precision obtained from the pattern, we introduce the interferometric visibility and the Fisher information matrix of the field mass and coupling. For the fringe pattern observed on the distant screen, we derive a simple relation between the visibility and the Fisher matrix. Also, focusing on the estimation precision of the mass, we find that the Fisher information characterizes the wave-particle duality in the double-slit interferometer.

Numerical predictors of arithmetic success in grades 1-6.

PubMed

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

2014-09-01

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

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

PubMed

Guthrie, Lisa G; Vallée-Tourangeau, Frédéric

2018-02-03

Previous research indicates that interactive arithmetic tasks may alleviate the deleterious impact of maths anxiety on arithmetic performance. Our aim here was to further test the impact of interactivity on maths-anxious individuals and those with poorer numeracy skills. In the experiment reported here participants completed sums in two interactivity contexts. In a low-interactivity condition, sums were completed with hands down. In a second, high-interactivity condition, participants used moveable number tokens. As anticipated, accuracy and efficiency were greater in the high compared to the low-interactivity condition. Correlational analyses indicated that maths anxiety, objective numeracy, measures of maths expertise and working memory were stronger predictors of performance in the low- than in the high-interactivity conditions. Interactivity transformed the deployment of arithmetic skills, improved performance, and reduced the gap between high- and low-ability individuals. These findings suggest that traditional psychometric efforts that identify the cognitive capacities and dispositions involved in mental arithmetic should take into account the degree of interactivity afforded by the task environment.

FAST TRACK COMMUNICATION: Reversible arithmetic logic unit for quantum arithmetic

NASA Astrophysics Data System (ADS)

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

2010-09-01

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

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

PubMed

Abikoff, H; Courtney, M E; Szeibel, P J; Koplewicz, H S

1996-05-01

This study evaluated the impact of extra-task stimulation on the academic task performance of children with attention-deficit/hyperactivity disorder (ADHD). Twenty boys with ADHD and 20 nondisabled boys worked on an arithmetic task during high stimulation (music), low stimulation (speech), and no stimulation (silence). The music "distractors" were individualized for each child, and the arithmetic problems were at each child's ability level. A significant Group x Condition interaction was found for number of correct answers. Specifically, the nondisabled youngsters performed similarly under all three auditory conditions. In contrast, the children with ADHD did significantly better under the music condition than speech or silence conditions. However, a significant Group x Order interaction indicated that arithmetic performance was enhanced only for those children with ADHD who received music as the first condition. The facilitative effects of salient auditory stimulation on the arithmetic performance of the children with ADHD provide some support for the underarousal/optimal stimulation theory of ADHD.

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

PubMed

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

2012-11-13

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

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

ERIC Educational Resources Information Center

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

2002-01-01

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

Gauss Elimination: Workhorse of Linear Algebra.

DTIC Science & Technology

1995-08-05

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

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

Treesearch

KaDonna Randolph

2010-01-01

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

Perceiving fingers in single-digit arithmetic problems.

PubMed

Berteletti, Ilaria; Booth, James R

2015-01-01

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

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

PubMed

De Visscher, Alice; Noël, Marie-Pascale

2013-01-01

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

Perceiving fingers in single-digit arithmetic problems

PubMed Central

Berteletti, Ilaria; Booth, James R.

2015-01-01

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

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

PubMed Central

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

2015-01-01

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

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

PubMed Central

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

2013-01-01

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

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

PubMed

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

2005-11-01

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

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

PubMed

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

2012-02-15

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

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

PubMed

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

2014-11-01

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

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

PubMed

Rubinsten, Orly

2015-01-01

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

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

PubMed Central

Van Rinsveld, Amandine; Brunner, Martin; Landerl, Karin; Schiltz, Christine; Ugen, Sonja

2015-01-01

Solving arithmetic problems is a cognitive task that heavily relies on language processing. One might thus wonder whether this language-reliance leads to qualitative differences (e.g., greater difficulties, error types, etc.) in arithmetic for bilingual individuals who frequently have to solve arithmetic problems in more than one language. The present study investigated how proficiency in two languages interacts with arithmetic problem solving throughout language acquisition in adolescents and young adults. Additionally, we examined whether the number word structure that is specific to a given language plays a role in number processing over and above bilingual proficiency. We addressed these issues in a German–French educational bilingual setting, where there is a progressive transition from German to French as teaching language. Importantly, German and French number naming structures differ clearly, as two-digit number names follow a unit-ten order in German, but a ten-unit order in French. We implemented a transversal developmental design in which bilingual pupils from grades 7, 8, 10, 11, and young adults were asked to solve simple and complex additions in both languages. The results confirmed that language proficiency is crucial especially for complex addition computation. Simple additions in contrast can be retrieved equally well in both languages after extended language practice. Additional analyses revealed that over and above language proficiency, language-specific number word structures (e.g., unit-ten vs. ten-unit) also induced significant modulations of bilinguals' arithmetic performances. Taken together, these findings support the view of a strong relation between language and arithmetic in bilinguals. PMID:25821442

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

PubMed Central

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

2014-01-01

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

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

PubMed

Evans, Tanya M; Flowers, D Lynn; Napoliello, Eileen M; Olulade, Olumide A; Eden, Guinevere F

2014-11-01

Some arithmetic procedures, such as addition of small numbers, rely on fact retrieval mechanisms supported by left hemisphere perisylvian language areas, while others, such as subtraction, rely on procedural-based mechanisms subserved by bilateral parietal cortices. Previous work suggests that developmental dyslexia, a reading disability, is accompanied by subtle deficits in retrieval-based arithmetic, possibly because of compromised left hemisphere function. To test this prediction, we compared brain activity underlying arithmetic problem solving in children with and without dyslexia during addition and subtraction operations using a factorial design. The main effect of arithmetic operation (addition versus subtraction) for both groups combined revealed activity during addition in the left superior temporal gyrus and activity during subtraction in the bilateral intraparietal sulcus, the right supramarginal gyrus and the anterior cingulate, consistent with prior studies. For the main effect of diagnostic group (dyslexics versus controls), we found less activity in dyslexic children in the left supramarginal gyrus. Finally, the interaction analysis revealed that while the control group showed a strong response in the right supramarginal gyrus for subtraction but not for addition, the dyslexic group engaged this region for both operations. This provides physiological evidence in support of the theory that children with dyslexia, because of disruption to left hemisphere language areas, use a less optimal route for retrieval-based arithmetic, engaging right hemisphere parietal regions typically used by good readers for procedural-based arithmetic. Our results highlight the importance of language processing for mathematical processing and illustrate that children with dyslexia have impairments that extend beyond reading. Copyright © 2014 Elsevier Inc. All rights reserved.

Specific Learning Disorder: Prevalence and Gender Differences

PubMed Central

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

2014-01-01

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

Specific learning disorder: prevalence and gender differences.

PubMed

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

2014-01-01

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

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

PubMed Central

Evans, Tanya M.; Flowers, D. Lynn; Napoliello, Eileen M.; Olulade, Olumide A.; Eden, Guinevere F.

2014-01-01

Some arithmetic procedures, such as addition of small numbers, rely on fact retrieval mechanisms supported by left hemisphere perisylvian language areas, while others, such as subtraction, rely on procedural-based mechanisms subserved by bilateral parietal cortices. Previous work suggests that developmental dyslexia, a reading disability, is accompanied by subtle deficits in retrieval-based arithmetic, possibly because of compromised left hemisphere function. To test this prediction, we compared brain activity underlying arithmetic problem solving in children with and without dyslexia during addition and subtraction operations using a factorial design. The main effect of arithmetic operation (addition versus subtraction) for both groups combined revealed activity during addition in the left superior temporal gyrus and activity during subtraction in bilateral intraparietal sulcus, right supramarginal gyrus and the anterior cingulate, consistent with prior studies. For the main effect of diagnostic group (dyslexics versus controls), we found less activity in dyslexic children in the left supramarginal gyrus. Finally, the interaction analysis revealed that while the control group showed a strong response in right supramarginal gyrus for subtraction but not for addition, the dyslexic group engaged this region for both operations. This provides physiological evidence in support of the theory that children with dyslexia, because of disruption to left hemisphere language areas, use a less optimal route for retrieval-based arithmetic, engaging right hemisphere parietal regions typically used by good readers for procedural-based arithmetic. Our results highlight the importance of language processing for mathematical processing and illustrate that children with dyslexia have impairments that extend beyond reading. PMID:25067820

Pulse intensity characterization of the LCLS nanosecond double-bunch mode of operation

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

Sun, Yanwen; Decker, Franz-Josef; Turner, James

The recent demonstration of the 'nanosecond double-bunch' operation mode,i.e.two X-ray pulses separated in time between 0.35 and hundreds of nanoseconds and by increments of 0.35 ns, offers new opportunities to investigate ultrafast dynamics in diverse systems of interest. However, in order to reach its full potential, this mode of operation requires the precise characterization of the intensity of each X-ray pulse within each pulse pair for any time separation. Here, a transmissive single-shot diagnostic that achieves this goal for time separations larger than 0.7 ns with a precision better than 5% is presented. Lastly, it also provides real-time monitoring feedbackmore » to help tune the accelerator parameters to deliver double pulse intensity distributions optimized for specific experimental goals.« less

Pulse intensity characterization of the LCLS nanosecond double-bunch mode of operation

DOE PAGES

Sun, Yanwen; Decker, Franz-Josef; Turner, James; ...

2018-03-27

The recent demonstration of the 'nanosecond double-bunch' operation mode,i.e.two X-ray pulses separated in time between 0.35 and hundreds of nanoseconds and by increments of 0.35 ns, offers new opportunities to investigate ultrafast dynamics in diverse systems of interest. However, in order to reach its full potential, this mode of operation requires the precise characterization of the intensity of each X-ray pulse within each pulse pair for any time separation. Here, a transmissive single-shot diagnostic that achieves this goal for time separations larger than 0.7 ns with a precision better than 5% is presented. Lastly, it also provides real-time monitoring feedbackmore » to help tune the accelerator parameters to deliver double pulse intensity distributions optimized for specific experimental goals.« less

Precise Hypocenter Determination around Palu Koro Fault: a Preliminary Results

NASA Astrophysics Data System (ADS)

Fawzy Ismullah, M. Muhammad; Nugraha, Andri Dian; Ramdhan, Mohamad; Wandono

2017-04-01

Sulawesi area is located in complex tectonic pattern. High seismicity activity in the middle of Sulawesi is related to Palu Koro fault (PKF). In this study, we determined precise hypocenter around PKF by applying double-difference method. We attempt to investigate of the seismicity rate, geometry of the fault and distribution of focus depth around PKF. We first re-pick P-and S-wave arrival time of the PKF events to determine the initial hypocenter location using Hypoellipse method through updated 1-D seismic velocity. Later on, we relocated the earthquake event using double-difference method. Our preliminary results show the distribution of relocated events are located around PKF and have smaller residual time than the initial location. We will enhance the hypocenter location through updating of arrival time by applying waveform cross correlation method as input for double-difference relocation.

Double Arm Linkage precision Linear motion (DALL) Carriage, a simplified, rugged, high performance linear motion stage for the moving mirror of an Fourier Transform Spectrometer or other system requiring precision linear motion

NASA Astrophysics Data System (ADS)

Johnson, Kendall B.; Hopkins, Greg

2017-08-01

The Double Arm Linkage precision Linear motion (DALL) carriage has been developed as a simplified, rugged, high performance linear motion stage. Initially conceived as a moving mirror stage for the moving mirror of a Fourier Transform Spectrometer (FTS), it is applicable to any system requiring high performance linear motion. It is based on rigid double arm linkages connecting a base to a moving carriage through flexures. It is a monolithic design. The system is fabricated from one piece of material including the flexural elements, using high precision machining. The monolithic design has many advantages. There are no joints to slip or creep and there are no CTE (coefficient of thermal expansion) issues. This provides a stable, robust design, both mechanically and thermally and is expected to provide a wide operating temperature range, including cryogenic temperatures, and high tolerance to vibration and shock. Furthermore, it provides simplicity and ease of implementation, as there is no assembly or alignment of the mechanism. It comes out of the machining operation aligned and there are no adjustments. A prototype has been fabricated and tested, showing superb shear performance and very promising tilt performance. This makes it applicable to both corner cube and flat mirror FTS systems respectively.

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

NASA Astrophysics Data System (ADS)

Zevenbergen, Robyn; Hyde, Merv; Power, Des

2001-12-01

There has been limited examination of the intersection between language and arithmetic in the performance of deaf students, although some previous research has shown that deaf and hearing-impaired1 students are delayed in both their language acquisition and arithmetic performance. This paper examines the performance of deaf and hearing-impaired students in South-East Queensland, Australia, in solving arithmetic word problems. It was found that the subjects' solutions of word problems confirmed trends for hearing students, but that their performance was delayed in comparison. The results confirm other studies where deaf and hearing-impaired students are delayed in their language acquisition and this impacts on their capacity to successfully undertake the resolution of word problems.

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

PubMed

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

2005-08-22

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

In trans paired nicking triggers seamless genome editing without double-stranded DNA cutting.

PubMed

Chen, Xiaoyu; Janssen, Josephine M; Liu, Jin; Maggio, Ignazio; 't Jong, Anke E J; Mikkers, Harald M M; Gonçalves, Manuel A F V

2017-09-22

Precise genome editing involves homologous recombination between donor DNA and chromosomal sequences subjected to double-stranded DNA breaks made by programmable nucleases. Ideally, genome editing should be efficient, specific, and accurate. However, besides constituting potential translocation-initiating lesions, double-stranded DNA breaks (targeted or otherwise) are mostly repaired through unpredictable and mutagenic non-homologous recombination processes. Here, we report that the coordinated formation of paired single-stranded DNA breaks, or nicks, at donor plasmids and chromosomal target sites by RNA-guided nucleases based on CRISPR-Cas9 components, triggers seamless homology-directed gene targeting of large genetic payloads in human cells, including pluripotent stem cells. Importantly, in addition to significantly reducing the mutagenicity of the genome modification procedure, this in trans paired nicking strategy achieves multiplexed, single-step, gene targeting, and yields higher frequencies of accurately edited cells when compared to the standard double-stranded DNA break-dependent approach.CRISPR-Cas9-based gene editing involves double-strand breaks at target sequences, which are often repaired by mutagenic non-homologous end-joining. Here the authors use Cas9 nickases to generate coordinated single-strand breaks in donor and target DNA for precise homology-directed gene editing.

Stress-evoked opioid release inhibits pain in major depressive disorder.

PubMed

Frew, Ashley K; Drummond, Peter D

2008-10-15

To determine whether stress-evoked release of endogenous opioids might account for hypoalgesia in major depressive disorder (MDD), the mu-opioid antagonist naltrexone (50mg) or placebo was administered double-blind to 24 participants with MDD and to 31 non-depressed controls. Eighty minutes later participants completed a painful foot cold pressor test and, after a 5-min interval, began a 25-min arithmetic task interspersed with painful electric shocks. Ten minutes later participants completed a second cold pressor test. Negative affect was greater in participants with MDD than in non-depressed controls throughout the experiment, and increased significantly in both groups during mental arithmetic. Before the math task, naltrexone unmasked direct linear relationships between severity of depression, negative affect while resting quietly, and cold-induced pain in participants with MDD. In contrast, facilitatory effects of naltrexone on cold- and shock-induced pain were greatest in controls with the lowest depression scores. Naltrexone strengthened the relationship between negative affect and shock-induced pain during the math task, particularly in the depressed group, and heightened anxiety in both groups toward the end of the task. Thus, mu-opioid activity apparently masked a positive association between negative affect and pain in the most distressed participants. These findings suggest that psychological distress inhibits pain via stress-evoked release of opioid peptides in severe cases of MDD. In addition, tonic endogenous opioid neurotransmission could inhibit depressive symptoms and pain in people with low depression scores.

Enhancement of DRPE performance with a novel scheme based on new RAC: Principle, security analysis and FPGA implementation

NASA Astrophysics Data System (ADS)

Neji, N.; Jridi, M.; Alfalou, A.; Masmoudi, N.

2016-02-01

The double random phase encryption (DRPE) method is a well-known all-optical architecture which has many advantages especially in terms of encryption efficiency. However, the method presents some vulnerabilities against attacks and requires a large quantity of information to encode the complex output plane. In this paper, we present an innovative hybrid technique to enhance the performance of DRPE method in terms of compression and encryption. An optimized simultaneous compression and encryption method is applied simultaneously on the real and imaginary components of the DRPE output plane. The compression and encryption technique consists in using an innovative randomized arithmetic coder (RAC) that can well compress the DRPE output planes and at the same time enhance the encryption. The RAC is obtained by an appropriate selection of some conditions in the binary arithmetic coding (BAC) process and by using a pseudo-random number to encrypt the corresponding outputs. The proposed technique has the capabilities to process video content and to be standard compliant with modern video coding standards such as H264 and HEVC. Simulations demonstrate that the proposed crypto-compression system has presented the drawbacks of the DRPE method. The cryptographic properties of DRPE have been enhanced while a compression rate of one-sixth can be achieved. FPGA implementation results show the high performance of the proposed method in terms of maximum operating frequency, hardware occupation, and dynamic power consumption.

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

PubMed

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

2017-06-01

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

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

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

Cody, W. J.; Mathematics and Computer Science

1993-12-01

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

Relation between arithmetic performance and phonological working memory in children.

PubMed

Silva, Kelly da; Zuanetti, Patrícia Aparecida; Borcat, Vanessa Trombini Ribeiro; Guedes-Granzotti, Raphaela Barroso; Kuroishi, Rita Cristina Sadako; Domenis, Daniele Ramos; Fukuda, Marisa Tomoe Hebihara

2017-08-17

To compare the results of Loop Phonological Working Memory (LPWM) in children without global learning alterations, with lower and average/higher arithmetic performance. The study was conducted with 30 children, between the ages of seven and nine years old, who attended the second or third grade of elementary school in the public network. Exclusion criteria were children with suggestive signs of hearing loss, neurological disorders, poor performance in the reading comprehension test or in speech therapy. The children included in the study were submitted to the subtest of arithmetic of Academic Achievement Test for division into two groups (G1 and G2). The G1 was composed of children with low performance in arithmetic and G2 for children with average/higher performance in arithmetic. All children were submitted to PWM assessment through the repetition of pseudowords test. Statistical analysis was performed using the Mann-Whitney test and a p-value <0.05 was considered significant. The study included 20 girls and 10 boys, mean age 8.7 years. The G1 was composed of 17 children and G2 of 13 children. There was a statistically significant difference between the groups studied for the repetition of pseudowords with three and four syllables. The results of this study provide support for the hypothesis that changes in phonological working memory are related to difficulties in arithmetic tests.

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

PubMed

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

2013-10-01

Baddeley and Hitch's multi-component working memory (WM) model has played an enduring and influential role in our understanding of cognitive abilities. Very little is known, however, about the neural basis of this multi-component WM model and the differential role each component plays in mediating arithmetic problem solving abilities in children. Here, we investigate the neural basis of the central executive (CE), phonological (PL) and visuo-spatial (VS) components of WM during a demanding mental arithmetic task in 7-9 year old children (N=74). The VS component was the strongest predictor of math ability in children and was associated with increased arithmetic complexity-related responses in left dorsolateral and right ventrolateral prefrontal cortices as well as bilateral intra-parietal sulcus and supramarginal gyrus in posterior parietal cortex. Critically, VS, CE and PL abilities were associated with largely distinct patterns of brain response. Overlap between VS and CE components was observed in left supramarginal gyrus and no overlap was observed between VS and PL components. Our findings point to a central role of visuo-spatial WM during arithmetic problem-solving in young grade-school children and highlight the usefulness of the multi-component Baddeley and Hitch WM model in fractionating the neural correlates of arithmetic problem solving during development. Copyright © 2013 Elsevier Ltd. All rights reserved.

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

PubMed

Chen, Yalin; Yanke, Jill; Campbell, Jamie I D

2016-04-01

The role of language in memory for arithmetic facts remains controversial. Here, we examined transfer of memory training for evidence that bilinguals may acquire language-specific memory stores for everyday arithmetic facts. Chinese-English bilingual adults (n = 32) were trained on different subsets of simple addition and multiplication problems. Each operation was trained in one language or the other. The subsequent test phase included all problems with addition and multiplication alternating across trials in two blocks, one in each language. Averaging over training language, the response time (RT) gains for trained problems relative to untrained problems were greater in the trained language than in the untrained language. Subsequent analysis showed that English training produced larger RT gains for trained problems relative to untrained problems in English at test relative to the untrained Chinese language. In contrast, there was no evidence with Chinese training that problem-specific RT gains differed between Chinese and the untrained English language. We propose that training in Chinese promoted a translation strategy for English arithmetic (particularly multiplication) that produced strong cross-language generalization of practice, whereas training in English strengthened relatively weak, English-language arithmetic memories and produced little generalization to Chinese (i.e., English training did not induce an English translation strategy for Chinese language trials). The results support the existence of language-specific strengthening of memory for everyday arithmetic facts.

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

PubMed

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

2017-03-01

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

A 1D radiative transfer benchmark with polarization via doubling and adding

NASA Astrophysics Data System (ADS)

Ganapol, B. D.

2017-11-01

Highly precise numerical solutions to the radiative transfer equation with polarization present a special challenge. Here, we establish a precise numerical solution to the radiative transfer equation with combined Rayleigh and isotropic scattering in a 1D-slab medium with simple polarization. The 2-Stokes vector solution for the fully discretized radiative transfer equation in space and direction derives from the method of doubling and adding enhanced through convergence acceleration. Updates to benchmark solutions found in the literature to seven places for reflectance and transmittance as well as for angular flux follow. Finally, we conclude with the numerical solution in a partially randomly absorbing heterogeneous medium.

Elliptic Solvers for Mediterranean Sea Ocean Modeling,

DTIC Science & Technology

1984-05-01

KWSP =21*(112+2*21+6) C PARAMETER (NX=IH-2, NY=JHS-2, KQ=NY*((NX+7)/4+1)+(NY+3)/2+8) 9C DOUBLE PRECISION AX,AY,AC(KH),ACKL DIMENSION HD(IH,JH),HT(IH...JH),RS(IH,JH) C COMMON/BV/ W1(IH,JHS),W2(IH,JHS),W3(IH,JHS),W4(IH,JHS) DOUBLE PRECISION WQ DIMENSION MAP(IH,JHS),WQ(JHS,5),WC( KWSP ) EQUIVALENCE (W1(1...AND ALL OTHER MODES C ( TYPICALLY MXKC1 .GE. MXKC2 .GE .MXKC3 ), C MXKC3 = MAX SIZE OF CV FOR RESTART T.S. C ( TYPICALLY MXKC3 = MXKP*3 ). C KWSP

Accuracy of the lattice-Boltzmann method using the Cell processor

NASA Astrophysics Data System (ADS)

Harvey, M. J.; de Fabritiis, G.; Giupponi, G.

2008-11-01

Accelerator processors like the new Cell processor are extending the traditional platforms for scientific computation, allowing orders of magnitude more floating-point operations per second (flops) compared to standard central processing units. However, they currently lack double-precision support and support for some IEEE 754 capabilities. In this work, we develop a lattice-Boltzmann (LB) code to run on the Cell processor and test the accuracy of this lattice method on this platform. We run tests for different flow topologies, boundary conditions, and Reynolds numbers in the range Re=6 350 . In one case, simulation results show a reduced mass and momentum conservation compared to an equivalent double-precision LB implementation. All other cases demonstrate the utility of the Cell processor for fluid dynamics simulations. Benchmarks on two Cell-based platforms are performed, the Sony Playstation3 and the QS20/QS21 IBM blade, obtaining a speed-up factor of 7 and 21, respectively, compared to the original PC version of the code, and a conservative sustained performance of 28 gigaflops per single Cell processor. Our results suggest that choice of IEEE 754 rounding mode is possibly as important as double-precision support for this specific scientific application.

A high-finesse Fabry-Perot cavity with a frequency-doubled green laser for precision Compton polarimetry at Jefferson Lab

DOE PAGES

Rakhman, A.; Hafez, Mohamed A.; Nanda, Sirish K.; ...

2016-03-31

Here, a high-finesse Fabry-Perot cavity with a frequency-doubled continuous wave green laser (532 nm) has been built and installed in Hall A of Jefferson Lab for high precision Compton polarimetry. The infrared (1064 nm) beam from a ytterbium-doped fiber amplifier seeded by a Nd:YAG nonplanar ring oscillator laser is frequency doubled in a single-pass periodically poled MgO:LiNbO 3 crystal. The maximum achieved green power at 5 W infrared pump power is 1.74 W with a total conversion efficiency of 34.8%. The green beam is injected into the optical resonant cavity and enhanced up to 3.7 kW with a corresponding enhancementmore » of 3800. The polarization transfer function has been measured in order to determine the intra-cavity circular laser polarization within a measurement uncertainty of 0.7%. The PREx experiment at Jefferson Lab used this system for the first time and achieved 1.0% precision in polarization measurements of an electron beam with energy and current of 1.0 GeV and 50 μA.« less

Neurofunctional Differences Associated with Arithmetic Processing in Turner Syndrome

PubMed Central

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

2011-01-01

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

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

PubMed

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

2017-01-01

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

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

PubMed Central

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

2014-01-01

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

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

PubMed

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

2015-01-01

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

Computations of Eisenstein series on Fuchsian groups

NASA Astrophysics Data System (ADS)

Avelin, Helen

2008-09-01

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

Concurrent error detecting codes for arithmetic processors

NASA Technical Reports Server (NTRS)

Lim, R. S.

1979-01-01

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

A precision device needs precise simulation: Software description of the CBM Silicon Tracking System

NASA Astrophysics Data System (ADS)

Malygina, Hanna; Friese, Volker; CBM Collaboration

2017-10-01

Precise modelling of detectors in simulations is the key to the understanding of their performance, which, in turn, is a prerequisite for the proper design choice and, later, for the achievement of valid physics results. In this report, we describe the implementation of the Silicon Tracking System (STS), the main tracking device of the CBM experiment, in the CBM software environment. The STS makes uses of double-sided silicon micro-strip sensors with double metal layers. We present a description of transport and detector response simulation, including all relevant physical effects like charge creation and drift, charge collection, cross-talk and digitization. Of particular importance and novelty is the description of the time behaviour of the detector, since its readout will not be externally triggered but continuous. We also cover some aspects of local reconstruction, which in the CBM case has to be performed in real-time and thus requires high-speed algorithms.

Compositional Verification with Abstraction, Learning, and SAT Solving

DTIC Science & Technology

2015-05-01

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

LSI (Large Scale Integrated) Design for Testability. Final Report of Design, Demonstration, and Testability Analysis.

DTIC Science & Technology

1983-11-01

compound operations, with status. (h) Pre-programmed CRC and double-precision multiply/divide algo- rithms. (i) Double length accumulator with full...IH1.25 _ - MICROCOP ’ RESOLUTION TEST CHART NATIONAL BUREAU OF STANDARDS-1963-A .4 ’* • • . - . .. •. . . . . . . . . . . . . . • - -. .• ,. o. . . .- "o

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

NASA Astrophysics Data System (ADS)

McIlhenny, Robert D.; Ercegovac, Milos D.

2009-08-01

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

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

NASA Astrophysics Data System (ADS)

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

2013-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2012-04-01

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

Changing computing paradigms towards power efficiency

PubMed Central

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

2014-01-01

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

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

PubMed

Daitch, Amy L; Parvizi, Josef

2018-05-01

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

Sparse Matrix Software Catalog, Sparse Matrix Symposium 1982, Fairfield Glade, Tennessee, October 24-27, 1982,

DTIC Science & Technology

1982-10-27

are buried within * a much larger, special purpose package. We regret such omissions, but to have reached the practi- tioners in each of the diverse...sparse matrix (form PAQ ) 4. Method of solution: Distribution count sort 5. Programming language: FORTRAN g Precision: Single and double precision 7

Measurement of theta13 in the double Chooz experiment

NASA Astrophysics Data System (ADS)

Yang, Guang

Neutrino oscillation has been established for over a decade. The mixing angle theta13 is one of the parameters that is most difficult to measure due to its small value. Currently, reactor antineutrino experiments provide the best knowledge of theta13, using the electron antineutrino disappearance phenomenon. The most compelling advantage is the high intensity of the reactor antineutrino rate. The Double Chooz experiment, located on the border of France and Belgium, is such an experiment, which aims to have one of the most precise theta 13 measurements in the world. Double Chooz has a single-detector phase and a double-detector phase. For the single-detector phase, the limit of the theta 13 sensitivity comes mostly from the reactor flux. However, the uncertainty on the reactor flux is highly suppressed in the double-detector phase. Oscillation analyses for the two phases have different strategies but need similar inputs, including background estimation, detection systematics evaluation, energy reconstruction and so on. The Double Chooz detectors are filled with gadolinium (Gd) doped liquid scintillator and use the inverse beta decay (IBD) signal so that for each phase, there are two independent theta13 measurements based on different neutron capturer (Gd or hydrogen). Multiple oscillation analyses are performed to provide the best 13 results. In addition to the 13 measurement, Double Chooz is also an excellent \\playground" to do diverse physics research. For example, a 252Cf calibration source study has been done to understand the spontaneous decay of this radioactive source. Further, Double Chooz also has the ability to do a sterile neutrino search in a certain mass region. Moreover, some new physics ideas can be tested in Double Chooz. In this thesis, the detailed methods to provide precise theta13 measurement will be described and the other physics topics will be introduced.

New high-precision orbital and physical parameters of the double-lined low-mass spectroscopic binary BY Draconis

NASA Astrophysics Data System (ADS)

Hełminiak, K. G.; Konacki, M.; Muterspaugh, M. W.; Browne, S. E.; Howard, A. W.; Kulkarni, S. R.

2012-01-01

We present the most precise to date orbital and physical parameters of the well-known short period (P= 5.975 d), eccentric (e= 0.3) double-lined spectroscopic binary BY Draconis (BY Dra), a prototype of a class of late-type, active, spotted flare stars. We calculate the full spectroscopic/astrometric orbital solution by combining our precise radial velocities (RVs) and the archival astrometric measurements from the Palomar Testbed Interferometer (PTI). The RVs were derived based on the high-resolution echelle spectra taken between 2004 and 2008 with the Keck I/high-resolution echelle spectrograph, Shane/CAT/HamSpec and TNG/SARG telescopes/spectrographs using our novel iodine-cell technique for double-lined binary stars. The RVs and available PTI astrometric data spanning over eight years allow us to reach 0.2-0.5 per cent level of precision in Msin 3i and the parallax but the geometry of the orbit (i≃ 154°) hampers the absolute mass precision to 3.3 per cent, which is still an order of magnitude better than for previous studies. We compare our results with a set of Yonsei-Yale theoretical stellar isochrones and conclude that BY Dra is probably a main-sequence system more metal rich than the Sun. Using the orbital inclination and the available rotational velocities of the components, we also conclude that the rotational axes of the components are likely misaligned with the orbital angular momentum. Given BY Dra's main-sequence status, late spectral type and the relatively short orbital period, its high orbital eccentricity and probable spin-orbit misalignment are not in agreement with the tidal theory. This disagreement may possibly be explained by smaller rotational velocities of the components and the presence of a substellar mass companion to BY Dra AB.

Precision measurements of the RSA method using a phantom model of hip prosthesis.

PubMed

Mäkinen, Tatu J; Koort, Jyri K; Mattila, Kimmo T; Aro, Hannu T

2004-04-01

Radiostereometric analysis (RSA) has become one of the recommended techniques for pre-market evaluation of new joint implant designs. In this study we evaluated the effect of repositioning of X-ray tubes and phantom model on the precision of the RSA method. In precision measurements, we utilized mean error of rigid body fitting (ME) values as an internal control for examinations. ME value characterizes relative motion among the markers within each rigid body and is conventionally used to detect loosening of a bone marker. Three experiments, each consisting of 10 double examinations, were performed. In the first experiment, the X-ray tubes and the phantom model were not repositioned between one double examination. In experiments two and three, the X-ray tubes were repositioned between one double examination. In addition, the position of the phantom model was changed in experiment three. Results showed that significant differences could be found in 2 of 12 comparisons when evaluating the translation and rotation of the prosthetic components. Repositioning procedures increased ME values mimicking deformation of rigid body segments. Thus, ME value seemed to be a more sensitive parameter than migration values in this study design. These results confirmed the importance of standardized radiographic technique and accurate patient positioning for RSA measurements. Standardization and calibration procedures should be performed with phantom models in order to avoid unnecessary radiation dose of the patients. The present model gives the means to establish and to follow the intra-laboratory precision of the RSA method. The model is easily applicable in any research unit and allows the comparison of the precision values in different laboratories of multi-center trials.

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

NASA Astrophysics Data System (ADS)

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

2016-12-01

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

40 CFR 60.58b - Compliance and performance testing.

Code of Federal Regulations, 2010 CFR

2010-07-01

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

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

PubMed

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

2007-01-01

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

Specific arithmetic calculation deficits in children with Turner syndrome.

PubMed

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

1994-12-01

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

STT Doubles with Large Delta M - Part VII: Andromeda, Pisces, Auriga

NASA Astrophysics Data System (ADS)

Knapp, Wilfried; Nanson, John

2017-01-01

The results of visual double star observing sessions suggested a pattern for STT doubles with large DM of being harder to resolve than would be expected based on the WDS catalog data. It was felt this might be a problem with expectations on one hand, and on the other might be an indication of a need for new precise measurements, so we decided to take a closer look at a selected sample of STT doubles and do some research. Similar to the other objects covered so far several of the components show parameters quite different from the current WDS data.

Influence of double stimulation on sound-localization behavior in barn owls.

PubMed

Kettler, Lutz; Wagner, Hermann

2014-12-01

Barn owls do not immediately approach a source after they hear a sound, but wait for a second sound before they strike. This represents a gain in striking behavior by avoiding responses to random incidents. However, the first stimulus is also expected to change the threshold for perceiving the subsequent second sound, thus possibly introducing some costs. We mimicked this situation in a behavioral double-stimulus paradigm utilizing saccadic head turns of owls. The first stimulus served as an adapter, was presented in frontal space, and did not elicit a head turn. The second stimulus, emitted from a peripheral source, elicited the head turn. The time interval between both stimuli was varied. Data obtained with double stimulation were compared with data collected with a single stimulus from the same positions as the second stimulus in the double-stimulus paradigm. Sound-localization performance was quantified by the response latency, accuracy, and precision of the head turns. Response latency was increased with double stimuli, while accuracy and precision were decreased. The effect depended on the inter-stimulus interval. These results suggest that waiting for a second stimulus may indeed impose costs on sound localization by adaptation and this reduces the gain obtained by waiting for a second stimulus.

Representation of natural numbers in quantum mechanics

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

Benioff, Paul

2001-03-01

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

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

PubMed

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

2017-12-01

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

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

PubMed Central

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

2017-01-01

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

Simple arithmetic: not so simple for highly math anxious individuals

PubMed Central

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

2017-01-01

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

Marijuana Primes, Marijuana Expectancies, and Arithmetic Efficiency*

PubMed Central

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

2009-01-01

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

Exploring Hill Ciphers with Graphing Calculators.

ERIC Educational Resources Information Center

St. John, Dennis

1998-01-01

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

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

PubMed

De Biase, G A; Massini, A

1993-02-10

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

Trinary signed-digit arithmetic using an efficient encoding scheme

NASA Astrophysics Data System (ADS)

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

2000-09-01

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

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

NASA Astrophysics Data System (ADS)

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

2000-11-01

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

Bit-wise arithmetic coding for data compression

NASA Technical Reports Server (NTRS)

Kiely, A. B.

1994-01-01

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

The Double Star Orbit Initial Value Problem

NASA Astrophysics Data System (ADS)

Hensley, Hagan

2018-04-01

Many precise algorithms exist to find a best-fit orbital solution for a double star system given a good enough initial value. Desmos is an online graphing calculator tool with extensive capabilities to support animations and defining functions. It can provide a useful visual means of analyzing double star data to arrive at a best guess approximation of the orbital solution. This is a necessary requirement before using a gradient-descent algorithm to find the best-fit orbital solution for a binary system.

Overcoming the Power Wall by Exploiting Application Inexactness and Emerging COTS Architectural Features

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

Fagan, Mike; Schlachter, Jeremy; Yoshii, Kazutomo

Abstract—Energy and power consumption are major limitations to continued scaling of computing systems. Inexactness where the quality of the solution can be traded for energy savings has been proposed as a counterintuitive approach to overcoming those limitation. However, in the past, inexactness has been necessitated the need for highly customized or specialized hardware. In order to move away from customization, in earlier work [4], it was shown that by interpreting precision in the computation to be the parameter to trade to achieve inexactness, weather prediction and page rank could both benefit in terms of yielding energy savings through reduced precision,more » while preserving the quality of the application. However, this required representations of numbers that were not readily available on commercial off-the-shelf (COTS) processors. In this paper, we provide opportunities for extending the the notion of trading precision for energy savings into the world COTS. We provide a model and analyze the opportunities and behavior of all three IEEE compliant precision values available on COTS processors: (i) double (ii) single, and (iii) half. Through measurements, we show through a limit study energy savings in going from double to half precision can potentially exceed a factor of four, largely due to memory and cache effects.« less

The Duality Principle in Teaching Arithmetic and Geometric Series

ERIC Educational Resources Information Center

Yeshurun, Shraga

1978-01-01

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

Modified-Signed-Digit Optical Computing Using Fan-Out

NASA Technical Reports Server (NTRS)

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

1996-01-01

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

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

PubMed Central

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

2015-01-01

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

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

PubMed

Singer, Vivian; Strasser, Kathernie

2017-12-01

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

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

PubMed Central

Sasanguie, Delphine; Reynvoet, Bert

2014-01-01

Several studies have shown that performance on symbolic number tasks is related to individual differences in arithmetic. However, it is not clear which process is responsible for this association, i.e. fast, automatic processing of symbols per se or access to the underlying non-symbolic representation of the symbols. To dissociate between both options, adult participants performed an audiovisual matching paradigm. Auditory presented number words needed to be matched with either Arabic digits or dot patterns. The results revealed that a distance effect was present in the dots-number word matching task and absent in the digit-number word matching task. Crucially, only performance in the digit task contributed to the variance in arithmetical abilities. This led us to conclude that adults' arithmetic builds on the ability to quickly and automatically process Arabic digits, without the underlying non-symbolic magnitude representation being activated. PMID:24505308

The cognitive foundations of reading and arithmetic skills in 7- to 10-year-olds.

PubMed

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

2005-06-01

A range of possible predictors of arithmetic and reading were assessed in a large sample (N=162) of children between ages 7 years 5 months and 10 years 4 months. A confirmatory factor analysis of the predictors revealed a good fit to a model consisting of four latent variables (verbal ability, nonverbal ability, search speed, and phonological memory) and two manifest variables (digit comparison and phoneme deletion). A path analysis showed that digit comparison and verbal ability were unique predictors of variations in arithmetic skills, whereas phoneme deletion and verbal ability were unique predictors of variations in reading skills. These results confirm earlier findings that phoneme deletion ability appears to be a critical foundation for learning to read (decode). In addition, variations in the speed of accessing numerical quantity information appear to be a critical foundation for the development of arithmetic skills.

High Precision Material Study at Near Millimeter Wavelengths.

DTIC Science & Technology

1983-08-30

propagating through these tubes , the beams are allowed to expand for a short distance in free space before they are combined by a mylar -film beam- splitter...Laser Precision Rkp-5200). 22 6 The attenuation of the low-loss EH mode in circular plexiglass tubes of I.D. 0.95 cm, and of various lengths. he...pyroelectric detectors (Laser Precision Rkp-545): L L, and L TPx lens; BS1, wire-mesh beam splitter; BS, mylar -film beam splitter; DPC, double-prism coupler

Precision manometer gauge

DOEpatents

McPherson, Malcolm J.; Bellman, Robert A.

1984-01-01

A precision manometer gauge which locates a zero height and a measured height of liquid using an open tube in communication with a reservoir adapted to receive the pressure to be measured. The open tube has a reference section carried on a positioning plate which is moved vertically with machine tool precision. Double scales are provided to read the height of the positioning plate accurately, the reference section being inclined for accurate meniscus adjustment, and means being provided to accurately locate a zero or reference position.

Precision manometer gauge

DOEpatents

McPherson, M.J.; Bellman, R.A.

1982-09-27

A precision manometer gauge which locates a zero height and a measured height of liquid using an open tube in communication with a reservoir adapted to receive the pressure to be measured. The open tube has a reference section carried on a positioning plate which is moved vertically with machine tool precision. Double scales are provided to read the height of the positioning plate accurately, the reference section being inclined for accurate meniscus adjustment, and means being provided to accurately locate a zero or reference position.

Programmable single-cell mammalian biocomputers.

PubMed

Ausländer, Simon; Ausländer, David; Müller, Marius; Wieland, Markus; Fussenegger, Martin

2012-07-05

Synthetic biology has advanced the design of standardized control devices that program cellular functions and metabolic activities in living organisms. Rational interconnection of these synthetic switches resulted in increasingly complex designer networks that execute input-triggered genetic instructions with precision, robustness and computational logic reminiscent of electronic circuits. Using trigger-controlled transcription factors, which independently control gene expression, and RNA-binding proteins that inhibit the translation of transcripts harbouring specific RNA target motifs, we have designed a set of synthetic transcription–translation control devices that could be rewired in a plug-and-play manner. Here we show that these combinatorial circuits integrated a two-molecule input and performed digital computations with NOT, AND, NAND and N-IMPLY expression logic in single mammalian cells. Functional interconnection of two N-IMPLY variants resulted in bitwise intracellular XOR operations, and a combinatorial arrangement of three logic gates enabled independent cells to perform programmable half-subtractor and half-adder calculations. Individual mammalian cells capable of executing basic molecular arithmetic functions isolated or coordinated to metabolic activities in a predictable, precise and robust manner may provide new treatment strategies and bio-electronic interfaces in future gene-based and cell-based therapies.

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

PubMed

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

2018-06-01

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

The relative importance of two different mathematical abilities to mathematical achievement.

PubMed

Nunes, Terezinha; Bryant, Peter; Barros, Rossana; Sylva, Kathy

2012-03-01

Two distinct abilities, mathematical reasoning and arithmetic skill, might make separate and specific contributions to mathematical achievement. However, there is little evidence to inform theory and educational practice on this matter. The aims of this study were (1) to assess whether mathematical reasoning and arithmetic make independent contributions to the longitudinal prediction of mathematical achievement over 5 years and (2) to test the specificity of this prediction. Data from Avon Longitudinal Study of Parents and Children (ALSPAC) were available on 2,579 participants for analyses of KS2 achievement and on 1,680 for the analyses of KS3 achievement. Hierarchical regression analyses were used to assess the independence and specificity of the contribution of mathematical reasoning and arithmetic skill to the prediction of achievement in KS2 and KS3 mathematics, science, and English. Age, intelligence, and working memory (WM) were controls in these analyses. Mathematical reasoning and arithmetic did make independent contributions to the prediction of mathematical achievement; mathematical reasoning was by far the stronger predictor of the two. These predictions were specific in so far as these measures were more strongly related to mathematics than to science or English. Intelligence and WM were non-specific predictors; intelligence contributed more to the prediction of science than of maths, and WM predicted maths and English equally well. There is clear justification for making a distinction between mathematical reasoning and arithmetic skills. The implication is that schools must plan explicitly to improve mathematical reasoning as well as arithmetic skills. ©2011 The British Psychological Society.

Brain Correlates of Mathematical Competence in Processing Mathematical Representations

PubMed Central

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

2011-01-01

The ability to extract numerical information from different representation formats (e.g., equations, tables, or diagrams) is a key component of mathematical competence but little is known about its neural correlate. Previous studies comparing mathematically less and more competent adults have focused on mental arithmetic and reported differences in left angular gyrus (AG) activity which were interpreted to reflect differential reliance on arithmetic fact retrieval during problem solving. The aim of the present functional magnetic resonance imaging study was to investigate the brain correlates of mathematical competence in a task requiring the processing of typical mathematical representations. Twenty-eight adults of lower and higher mathematical competence worked on a representation matching task in which they had to evaluate whether the numerical information of a symbolic equation matches that of a bar chart. Two task conditions without and one condition with arithmetic demands were administered. Both competence groups performed equally well in the non-arithmetic conditions and only differed in accuracy in the condition requiring calculation. Activation contrasts between the groups revealed consistently stronger left AG activation in the more competent individuals across all three task conditions. The finding of competence-related activation differences independently of arithmetic demands suggests that more and less competent individuals differ in a cognitive process other than arithmetic fact retrieval. Specifically, it is argued that the stronger left AG activity in the more competent adults may reflect their higher proficiency in processing mathematical symbols. Moreover, the study demonstrates competence-related parietal activation differences that were not accompanied by differential experimental performance. PMID:22069387

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

ERIC Educational Resources Information Center

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

2005-01-01

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

Arithmetic and Hyperbolic Structures in String Theory

NASA Astrophysics Data System (ADS)

Persson, Daniel

2010-01-01

This monograph is an updated and extended version of the author's PhD thesis. It consists of an introductory text followed by two separate parts which are loosely related but may be read independently of each other. In Part I we analyze certain hyperbolic structures arising when studying gravity in the vicinity of a spacelike singularity (the "BKL-limit"). In this limit, spatial points decouple and the dynamics exhibits ultralocal behaviour which may be described in terms of a (possibly chaotic) hyperbolic billiard. In all supergravities arising as low-energy limits of string theory or M-theory, the billiard dynamics takes place within the fundamental Weyl chambers of certain hyperbolic Kac-Moody algebras, suggesting that these algebras generate hidden infinite-dimensional symmetries of the theory. Part II of the thesis is devoted to a study of how (U-)dualities in string theory provide powerful constraints on perturbative and non-perturbative quantum corrections. These dualities are described by certain arithmetic groups G(Z) which are conjectured to be preserved in the effective action. The exact couplings are given by automorphic forms on the double quotient G(Z)G/K. We discuss in detail various methods of constructing automorphic forms, with particular emphasis on non-holomorphic Eisenstein series. We provide detailed examples for the physically relevant cases of SL(2,Z) and SL(3,Z), for which we construct their respective Eisenstein series and compute their (non-abelian) Fourier expansions. We also show how these techniques can be applied to hypermultiplet moduli spaces in type II Calabi-Yau compactifications, and we provide a detailed analysis for the universal hypermultiplet.

Meat supplementation improves growth, cognitive, and behavioral outcomes in Kenyan children.

PubMed

Neumann, Charlotte G; Murphy, Suzanne P; Gewa, Connie; Grillenberger, Monika; Bwibo, Nimrod O

2007-04-01

A randomized, controlled school feeding study was conducted in rural Embu District, Kenya to test for a causal link between animal-source food intake and changes in micronutrient nutrition and growth, cognitive, and behavioral outcomes. Twelve primary schools were randomly assigned to 1 of 4 groups. Children in Standard I classes received the local plant-based dish githeri as a midmorning school snack supplemented with meat, milk, or fat added to equalize energy content in all feedings. The Control children received no feedings but participated in data collection. Main outcome measures assessed at baseline and longitudinally were 24-h food intake recall, anthropometry, cognitive function, physical activity, and behaviors during school free play. For cognitive function, the Meat group showed the steepest rate of increase on Raven's Progressive Matrices scores and in zone-wide school end-term total and arithmetic test scores. The Plain githeri and Meat groups performed better over time than the Milk and Control groups (P < 0.02-0.03) on arithmetic tests. The Meat group showed the greatest increase in percentage time in high levels of physical activity and in initiative and leadership behaviors compared with all other groups. For growth, in the Milk group only younger and stunted children showed a greater rate of gain in height. The Meat group showed near doubling of upper midarm muscle area, and the Milk group a smaller degree of increase. This is the first randomized, controlled feeding study to examine the effect of meat- vs. milk- vs. plant-based snacks on functional outcomes in children.

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

NASA Astrophysics Data System (ADS)

Gilbreth, C. N.; Alhassid, Y.

2015-03-01

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

Supercomputing on massively parallel bit-serial architectures

NASA Technical Reports Server (NTRS)

Iobst, Ken

1985-01-01

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

Changing computing paradigms towards power efficiency.

PubMed

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

2014-06-28

Power awareness is fast becoming immensely important in computing, ranging from the traditional high-performance computing applications to the new generation of data centric workloads. In this work, we describe our efforts towards a power-efficient computing paradigm that combines low- and high-precision arithmetic. We showcase our ideas for the widely used kernel of solving systems of linear equations that finds numerous applications in scientific and engineering disciplines as well as in large-scale data analytics, statistics and machine learning. Towards this goal, we developed tools for the seamless power profiling of applications at a fine-grain level. In addition, we verify here previous work on post-FLOPS/W metrics and show that these can shed much more light in the power/energy profile of important applications. © 2014 The Author(s) Published by the Royal Society. All rights reserved.

Probability Quantization for Multiplication-Free Binary Arithmetic Coding

NASA Technical Reports Server (NTRS)

Cheung, K. -M.

1995-01-01

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

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

PubMed

Shaki, Samuel; Fischer, Martin H

2017-01-01

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

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

NASA Astrophysics Data System (ADS)

Anisca, Razvan; Chlebovec, Christopher

2009-09-01

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

Fast reversible wavelet image compressor

NASA Astrophysics Data System (ADS)

Kim, HyungJun; Li, Ching-Chung

1996-10-01

We present a unified image compressor with spline biorthogonal wavelets and dyadic rational filter coefficients which gives high computational speed and excellent compression performance. Convolutions with these filters can be preformed by using only arithmetic shifting and addition operations. Wavelet coefficients can be encoded with an arithmetic coder which also uses arithmetic shifting and addition operations. Therefore, from the beginning to the end, the while encoding/decoding process can be done within a short period of time. The proposed method naturally extends form the lossless compression to the lossy but high compression range and can be easily adapted to the progressive reconstruction.

Fault tolerant computing: A preamble for assuring viability of large computer systems

NASA Technical Reports Server (NTRS)

Lim, R. S.

1977-01-01

The need for fault-tolerant computing is addressed from the viewpoints of (1) why it is needed, (2) how to apply it in the current state of technology, and (3) what it means in the context of the Phoenix computer system and other related systems. To this end, the value of concurrent error detection and correction is described. User protection, program retry, and repair are among the factors considered. The technology of algebraic codes to protect memory systems and arithmetic codes to protect memory systems and arithmetic codes to protect arithmetic operations is discussed.

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

PubMed Central

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

2014-01-01

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

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.

STT Doubles with Large Delta_M - Part VIII: Tau Per Ori Cam Mon Cnc Peg

NASA Astrophysics Data System (ADS)

Knapp, Wilfried; Nanson, John

2017-04-01

The results of visual double star observing sessions suggested a pattern for STT doubles with large delta_M of being harder to resolve than would be expected based on the WDS catalog data. It was felt this might be a problem with expectations on one hand, and on the other might be an indication of a need for new precise measurements, so we decided to take a closer look at a selected sample of STT doubles and do some research. Again like for the other STT objects covered so far several of the components show parameters quite different from the current WDS data.

Fabrication of large diffractive optical elements in thick film on a concave lens surface.

PubMed

Xie, Yongjun; Lu, Zhenwu; Li, Fengyou

2003-05-05

We demonstrate experimentally the technique of fabricating large diffractive optical elements (DOEs) in thick film on a concave lens surface (mirrors) with precise alignment by using the strategy of double exposure. We adopt the method of double exposure to overcome the difficulty of processing thick photoresist on a large curved substrate. A uniform thick film with arbitrary thickness on a concave lens can be obtained with this technique. We fabricate a large concentric circular grating with a 10-ìm period on a concave lens surface in film with a thickness of 2.0 ìm after development. It is believed that this technique can also be used to fabricate larger DOEs in thicker film on the concave or convex lens surface with precise alignment. There are other potential applications of this technique, such as fabrication of micro-optoelectromechanical systems (MOEMS) or microelectromechanical systems (MEMS) and fabrication of microlens arrays on a large concave lens surface or convex lens surface with precise alignment.

Precision Measurements of $$A_1^n$$ in the Deep Inelastic Regime

DOE PAGES

Parno, Diana; Flay, David; Posik, Matthew; ...

2015-04-07

We have performed precision measurements of the double-spin virtual-photon asymmetry A₁ on the neutron in the deep inelastic scattering regime, using an open-geometry, large-acceptance spectrometer and a longitudinally and transversely polarized ³He target. Our data cover a wide kinematic range 0.277 ≤ x ≤ 0.5480 at an average Q² value of 3.078 (GeV/c)², doubling the available high-precision neutron data in this x range. We have combined our results with world data on proton targets to make a leading-order extraction of the ratio of polarized-to-unpolarized parton distribution functions for up quarks and for down quarks in the same kinematic range. Ourmore » data are consistent with a previous observation of an View the MathML source A 1 n zero crossing near x=0.5. We find no evidence of a transition to a positive slope in (Δd+Δd¯)/(d+d¯) up to x=0.548.« less

High-precision two-dimensional atom localization from four-wave mixing in a double-Λ four-level atomic system

NASA Astrophysics Data System (ADS)

Shui, Tao; Yang, Wen-Xing; Chen, Ai-Xi; Liu, Shaopeng; Li, Ling; Zhu, Zhonghu

2018-03-01

We propose a scheme for high-precision two-dimensional (2D) atom localization via the four-wave mixing (FWM) in a four-level double-Λ atomic system. Due to the position-dependent atom-field interaction, the 2D position information of the atoms can be directly determined by the measurement of the normalized light intensity of output FWM-generated field. We further show that, when the position-dependent generated FWM field has become sufficiently intense, efficient back-coupling to the FWM generating state becomes important. This back-coupling pathway leads to competitive multiphoton destructive interference of the FWM generating state by three supplied and one internally generated fields. We find that the precision of 2D atom localization can be improved significantly by the multiphoton destructive interference and depends sensitively on the frequency detunings and the pump field intensity. Interestingly enough, we show that adjusting the frequency detunings and the pump field intensity can modify significantly the FWM efficiency, and consequently lead to a redistribution of the atoms. As a result, the atom can be localized in one of four quadrants with holding the precision of atom localization.

SU (2) lattice gauge theory simulations on Fermi GPUs

NASA Astrophysics Data System (ADS)

Cardoso, Nuno; Bicudo, Pedro

2011-05-01

In this work we explore the performance of CUDA in quenched lattice SU (2) simulations. CUDA, NVIDIA Compute Unified Device Architecture, is a hardware and software architecture developed by NVIDIA for computing on the GPU. We present an analysis and performance comparison between the GPU and CPU in single and double precision. Analyses with multiple GPUs and two different architectures (G200 and Fermi architectures) are also presented. In order to obtain a high performance, the code must be optimized for the GPU architecture, i.e., an implementation that exploits the memory hierarchy of the CUDA programming model. We produce codes for the Monte Carlo generation of SU (2) lattice gauge configurations, for the mean plaquette, for the Polyakov Loop at finite T and for the Wilson loop. We also present results for the potential using many configurations (50,000) without smearing and almost 2000 configurations with APE smearing. With two Fermi GPUs we have achieved an excellent performance of 200× the speed over one CPU, in single precision, around 110 Gflops/s. We also find that, using the Fermi architecture, double precision computations for the static quark-antiquark potential are not much slower (less than 2× slower) than single precision computations.

Double the dates and go for Bayes - Impacts of model choice, dating density and quality on chronologies

NASA Astrophysics Data System (ADS)

Blaauw, Maarten; Christen, J. Andrés; Bennett, K. D.; Reimer, Paula J.

2018-05-01

Reliable chronologies are essential for most Quaternary studies, but little is known about how age-depth model choice, as well as dating density and quality, affect the precision and accuracy of chronologies. A meta-analysis suggests that most existing late-Quaternary studies contain fewer than one date per millennium, and provide millennial-scale precision at best. We use existing and simulated sediment cores to estimate what dating density and quality are required to obtain accurate chronologies at a desired precision. For many sites, a doubling in dating density would significantly improve chronologies and thus their value for reconstructing and interpreting past environmental changes. Commonly used classical age-depth models stop becoming more precise after a minimum dating density is reached, but the precision of Bayesian age-depth models which take advantage of chronological ordering continues to improve with more dates. Our simulations show that classical age-depth models severely underestimate uncertainty and are inaccurate at low dating densities, and also perform poorly at high dating densities. On the other hand, Bayesian age-depth models provide more realistic precision estimates, including at low to average dating densities, and are much more robust against dating scatter and outliers. Indeed, Bayesian age-depth models outperform classical ones at all tested dating densities, qualities and time-scales. We recommend that chronologies should be produced using Bayesian age-depth models taking into account chronological ordering and based on a minimum of 2 dates per millennium.

The Use of Scale-Dependent Precision to Increase Forecast Accuracy in Earth System Modelling

NASA Astrophysics Data System (ADS)

Thornes, Tobias; Duben, Peter; Palmer, Tim

2016-04-01

At the current pace of development, it may be decades before the 'exa-scale' computers needed to resolve individual convective clouds in weather and climate models become available to forecasters, and such machines will incur very high power demands. But the resolution could be improved today by switching to more efficient, 'inexact' hardware with which variables can be represented in 'reduced precision'. Currently, all numbers in our models are represented as double-precision floating points - each requiring 64 bits of memory - to minimise rounding errors, regardless of spatial scale. Yet observational and modelling constraints mean that values of atmospheric variables are inevitably known less precisely on smaller scales, suggesting that this may be a waste of computer resources. More accurate forecasts might therefore be obtained by taking a scale-selective approach whereby the precision of variables is gradually decreased at smaller spatial scales to optimise the overall efficiency of the model. To study the effect of reducing precision to different levels on multiple spatial scales, we here introduce a new model atmosphere developed by extending the Lorenz '96 idealised system to encompass three tiers of variables - which represent large-, medium- and small-scale features - for the first time. In this chaotic but computationally tractable system, the 'true' state can be defined by explicitly resolving all three tiers. The abilities of low resolution (single-tier) double-precision models and similar-cost high resolution (two-tier) models in mixed-precision to produce accurate forecasts of this 'truth' are compared. The high resolution models outperform the low resolution ones even when small-scale variables are resolved in half-precision (16 bits). This suggests that using scale-dependent levels of precision in more complicated real-world Earth System models could allow forecasts to be made at higher resolution and with improved accuracy. If adopted, this new paradigm would represent a revolution in numerical modelling that could be of great benefit to the world.

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

ERIC Educational Resources Information Center

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

2014-01-01

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

Versatile analog pulse height computer performs real-time arithmetic operations

NASA Technical Reports Server (NTRS)

Brenner, R.; Strauss, M. G.

1967-01-01

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

Pre-schoolers Learn at Home.

ERIC Educational Resources Information Center

Smith, Penny

1985-01-01

Reviews: "ArithMagic (Counting, Addition, Subtraction)" which uses graphics to illustrate/review basic arithmetic concepts; "The Sweet Shop" which uses graphics (and a character called Mr. Jellybean) to teach arithmetic concepts; and "Math Magic," a monster-filled arcade game that teaches addition and subtraction.…

Efficient Probabilistic Diagnostics for Electrical Power Systems

NASA Technical Reports Server (NTRS)

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

2008-01-01

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

Learning, Realizability and Games in Classical Arithmetic

NASA Astrophysics Data System (ADS)

Aschieri, Federico

2010-12-01

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

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

NASA Astrophysics Data System (ADS)

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

2008-08-01

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

Validation of a particle tracking analysis method for the size determination of nano- and microparticles

NASA Astrophysics Data System (ADS)

Kestens, Vikram; Bozatzidis, Vassili; De Temmerman, Pieter-Jan; Ramaye, Yannic; Roebben, Gert

2017-08-01

Particle tracking analysis (PTA) is an emerging technique suitable for size analysis of particles with external dimensions in the nano- and sub-micrometre scale range. Only limited attempts have so far been made to investigate and quantify the performance of the PTA method for particle size analysis. This article presents the results of a validation study during which selected colloidal silica and polystyrene latex reference materials with particle sizes in the range of 20 nm to 200 nm were analysed with NS500 and LM10-HSBF NanoSight instruments and video analysis software NTA 2.3 and NTA 3.0. Key performance characteristics such as working range, linearity, limit of detection, limit of quantification, sensitivity, robustness, precision and trueness were examined according to recommendations proposed by EURACHEM. A model for measurement uncertainty estimation following the principles described in ISO/IEC Guide 98-3 was used for quantifying random and systematic variations. For nominal 50 nm and 100 nm polystyrene and a nominal 80 nm silica reference materials, the relative expanded measurement uncertainties for the three measurands of interest, being the mode, median and arithmetic mean of the number-weighted particle size distribution, varied from about 10% to 12%. For the nominal 50 nm polystyrene material, the relative expanded uncertainty of the arithmetic mean of the particle size distributions increased up to 18% which was due to the presence of agglomerates. Data analysis was performed with software NTA 2.3 and NTA 3.0. The latter showed to be superior in terms of sensitivity and resolution.

Effect of Mental Arithmetic on heart rate responses during Parabolic Flights: the Barcelona Zero-G Challenge

NASA Astrophysics Data System (ADS)

Osborne, Jeffrey R.; Alonsopérez Lanza, María Victoria; Desclaux, David Ferrer; Goswami, Nandu; González Alonso, Daniel Ventura; Moser, Maximilian; Grote, Vincent; Garcia-Cuadrado, Gloria; Perez-Poch, Antoni

2014-07-01

When an astronaut transitions from a low to high gravitational environment, fluid shifts from the head towards the feet resulting in orthostatic intolerance and syncope. Ground based experiments have shown that by stimulating the cardiovascular system via simple mental stressors, syncope can be delayed, potentially enabling astronauts to reach assistance before loss of consciousness. However, the effect of mental stressors on the stimulation of the cardiovascular system in gravitational environments different than that of Earth's is unknown. As such, this paper investigates the effects that mental stressors under various gravitational environments. To do this, a pilot study was performed in which two participants were flown on two separate parabolic flights that simulated hyper and hypogravity conditions. The plane used was an Aerobatic Single-Engine Cap-10B plane (twin seater), and each participant executed 11 parabolas. The participants were the winners of the Barcelona Zero-G Challenge 2011 organized by UPC Universitat Politècnica de Catalunya-BarcelonaTech and Aeroclub Barcelona-Sabadell. Measurements were made of the participants' hemodynamic and autonomic response throughout the parabolas, using a Chronocord: high precision HRV monitor. Comparisons of the baseline response without mental stressors, and the response with mental stressors during different gravitational loading conditions were made. It was observed that there is an increase in cardiovascular activity during hypo- and hyper-gravity when performing mental arithmetic. Our results show that the twin seater aerobatic single engine CAP-10B aicraft can provide changing gravitational loading conditions for enough periods to study changes in physiological systems.

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

ERIC Educational Resources Information Center

Persky, Ronald L.

2003-01-01

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

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

PubMed

Macdonald, R I

1987-10-01

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

Instabilities caused by floating-point arithmetic quantization.

NASA Technical Reports Server (NTRS)

Phillips, C. L.

1972-01-01

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

Babies and Math: A Meta-Analysis of Infants' Simple Arithmetic Competence

ERIC Educational Resources Information Center

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

2017-01-01

Wynn's (1992) seminal research reported that infants looked longer at stimuli representing "incorrect" versus "correct" solutions of basic addition and subtraction problems and concluded that infants have innate arithmetical abilities. Since then, infancy researchers have attempted to replicate this effect, yielding mixed…

Phonology and arithmetic in the language-calculation network.

PubMed

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

2015-04-01

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

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

PubMed

Oyama, Katsunori; Sakatani, Kaoru

2016-01-01

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

Developmental and Individual Differences in Understanding of Fractions

PubMed Central

Siegler, Robert S.; Pyke, Aryn A.

2014-01-01

We examined developmental and individual differences in 6th and 8th graders’ fraction arithmetic and overall mathematics achievement and related them to differences in understanding of fraction magnitudes, whole number division, executive functioning, and metacognitive judgments within a cross sectional design. Results indicated that the difference between low achieving and higher achieving children’s fraction arithmetic knowledge, already substantial in 6th grade, was much greater in 8th grade. The fraction arithmetic knowledge of low achieving children was similar in the two grades, whereas higher achieving children showed much greater knowledge in 8th than 6th grade, despite both groups having been in the same classrooms, using the same textbooks, and having the same teachers and classmates. Individual differences in both fraction arithmetic and mathematics achievement test scores were predicted by differences in fraction magnitude knowledge and whole number division, even after the contributions of reading achievement and executive functioning were statistically controlled. Instructional implications of the findings are discussed. PMID:23244401

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

PubMed

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

2015-01-01

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

Arithmetic of five-part of leukocytes based on image process

NASA Astrophysics Data System (ADS)

Li, Yian; Wang, Guoyou; Liu, Jianguo

2007-12-01

This paper apply computer image processing and pattern recognizition methods to solve the problem of auto classification and counting of leukocytes (white blood cell) in peripheral blood. In this paper a new leukocyte arithmetic of five-part based on image process and pattern recognizition is presented, which relized auto classify of leukocyte. The first aim is detect the leukocytes . A major requirement of the whole system is to classify these leukocytes to 5 classes. This arithmetic bases on notability mechanism of eyes, process image by sequence, divides up leukocytes and pick up characters. Using the prior kwonledge of cells and image shape information, this arithmetic divides up the probable shape of Leukocyte first by a new method based on Chamfer and then gets the detail characters. It can reduce the mistake judge rate and the calculation greatly. It also has the learning fuction. This paper also presented a new measurement of karyon's shape which can provide more accurate information. This algorithm has great application value in clinical blood test .

[Reflex epilepsy evoked by decision making: report of a case (author's transl)].

PubMed

Mutani, R; Ganga, A; Agnetti, V

1980-01-01

A 17-year-old girl with a story of Gran Mal attacks occurring during lessons of mathematics or solving mathematical problems, was investigated with prolonged EEG recordings. During the sessions, relax periods were alternated with arithmetical or mathematical testing, with card or checkers games and solution of puzzles and crossword problems, and with different neuropsychological tests. EGG recordings were characterized by the appearance, on a normal background, of bilaterally synchronous and symmetrical spike-and-wave and polispike-and-wave discharges, associated with loss of consciousness. During relax their mean frequency was one/54 min., it doubled during execution of tests involved with nonsequential decision making, and was eight times as high (one/7 min.) during tests involving sequential decision making. Some tension, challenge and complexity of the performance were also important as precipitating factors. Their lack deprived sequential tests of their efficacy, while on the contrary their presence sometimes gave nonsequential tests full efficacy.

Physics of Electronic Materials

NASA Astrophysics Data System (ADS)

Rammer, Jørgen

2017-03-01

1. Quantum mechanics; 2. Quantum tunneling; 3. Standard metal model; 4. Standard conductor model; 5. Electric circuit theory; 6. Quantum wells; 7. Particle in a periodic potential; 8. Bloch currents; 9. Crystalline solids; 10. Semiconductor doping; 11. Transistors; 12. Heterostructures; 13. Mesoscopic physics; 14. Arithmetic, logic and machines; Appendix A. Principles of quantum mechanics; Appendix B. Dirac's delta function; Appendix C. Fourier analysis; Appendix D. Classical mechanics; Appendix E. Wave function properties; Appendix F. Transfer matrix properties; Appendix G. Momentum; Appendix H. Confined particles; Appendix I. Spin and quantum statistics; Appendix J. Statistical mechanics; Appendix K. The Fermi-Dirac distribution; Appendix L. Thermal current fluctuations; Appendix M. Gaussian wave packets; Appendix N. Wave packet dynamics; Appendix O. Screening by symmetry method; Appendix P. Commutation and common eigenfunctions; Appendix Q. Interband coupling; Appendix R. Common crystal structures; Appendix S. Effective mass approximation; Appendix T. Integral doubling formula; Bibliography; Index.

Scheduling of flow shop problems on 3 machines in fuzzy environment with double transport facility

NASA Astrophysics Data System (ADS)

Sathish, Shakeela; Ganesan, K.

2016-06-01

Flow shop scheduling is a decision making problem in production and manufacturing field which has a significant impact on the performance of an organization. When the machines on which jobs are to be processed are placed at different places, the transportation time plays a significant role in production. Further two different transport agents where 1st takes the job from 1st machine to 2nd machine and then returns back to the first machine and the 2nd takes the job from 2nd machine to 3rd machine and then returns back to the 2nd machine are also considered. We propose a method to minimize the total make span; without converting the fuzzy processing time to classical numbers by using a new type of fuzzy arithmetic and a fuzzy ranking method. A numerical example is provided to explain the proposed method.

Relationship between carbon dioxide levels and reported headaches on the international space station.

PubMed

Law, Jennifer; Van Baalen, Mary; Foy, Millennia; Mason, Sara S; Mendez, Claudia; Wear, Mary L; Meyers, Valerie E; Alexander, David

2014-05-01

Because of anecdotal reports of CO(2)-related symptoms onboard the International Space Station (ISS), the relationship between CO(2) and in-flight headaches was analyzed. Headache reports and CO(2) measurements were obtained, and arithmetic means and single-point maxima were determined for 24-hour and 7-day periods. Multiple imputation addressed missing data, and logistic regression modeled the relationship between CO(2), headache probability, and covariates. CO(2) level, age at launch, time in-flight, and data source were significantly associated with headache. For each 1-mm Hg increase in CO(2), the odds of a crew member reporting a headache doubled. To keep the risk of headache below 1%, average 7-day CO(2) would need to be maintained below 2.5 mm Hg (current ISS range: 1 to 9 mm Hg). Although headache incidence was not high, results suggest an increased susceptibility to physiological effects of CO(2) in-flight.

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

Grout, Ray W. S.

Convergence of spectral deferred correction (SDC), where low-order time integration methods are used to construct higher-order methods through iterative refinement, can be accelerated in terms of computational effort by using mixed-precision methods. Using ideas from multi-level SDC (in turn based on FAS multigrid ideas), some of the SDC correction sweeps can use function values computed in reduced precision without adversely impacting the accuracy of the final solution. This is particularly beneficial for the performance of combustion solvers such as S3D [6] which require double precision accuracy but are performance limited by the cost of data motion.

File compression and encryption based on LLS and arithmetic coding

NASA Astrophysics Data System (ADS)

Yu, Changzhi; Li, Hengjian; Wang, Xiyu

2018-03-01

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

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

NASA Astrophysics Data System (ADS)

Munir, Kusnendar, Jajang; Rahmadhani

2016-02-01

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

The ALARM Experiment

ERIC Educational Resources Information Center

Gerhardt, Ira

2015-01-01

An experiment was conducted over three recent semesters of an introductory calculus course to test whether it was possible to quantify the effect that difficulty with basic algebraic and arithmetic computation had on individual performance. Points lost during the term were classified as being due to either algebraic and arithmetic mistakes…

Updating Working Memory and Arithmetical Attainment in School

ERIC Educational Resources Information Center

Iuculano, Teresa; Moro, Raffaella; Butterworth, Brian

2011-01-01

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

Does Your Graphing Software Real-ly Work?

ERIC Educational Resources Information Center

Marchand, R. J.; McDevitt, T. J.; Bosse, Michael J.; Nandakumar, N. R.

2007-01-01

Many popular mathematical software products including Maple, Mathematica, Derive, Mathcad, Matlab, and some of the TI calculators produce incorrect graphs because they use complex arithmetic instead of "real" arithmetic. This article expounds on this issue, provides possible remedies for instructors to share with their students, and demonstrates…

Using Self-Generated Drawings to Solve Arithmetic Word Problems.

ERIC Educational Resources Information Center

Van Essen, Gerard; Hamaker, Christiaan

1990-01-01

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

Attentional bias induced by solving simple and complex addition and subtraction problems.

PubMed

Masson, Nicolas; Pesenti, Mauro

2014-01-01

The processing of numbers has been shown to induce shifts of spatial attention in simple probe detection tasks, with small numbers orienting attention to the left and large numbers to the right side of space. Recently, the investigation of this spatial-numerical association has been extended to mental arithmetic with the hypothesis that solving addition or subtraction problems may induce attentional displacements (to the right and to the left, respectively) along a mental number line onto which the magnitude of the numbers would range from left to right, from small to large numbers. Here we investigated such attentional shifts using a target detection task primed by arithmetic problems in healthy participants. The constituents of the addition and subtraction problems (first operand; operator; second operand) were flashed sequentially in the centre of a screen, then followed by a target on the left or the right side of the screen, which the participants had to detect. This paradigm was employed with arithmetic facts (Experiment 1) and with more complex arithmetic problems (Experiment 2) in order to assess the effects of the operation, the magnitude of the operands, the magnitude of the results, and the presence or absence of a requirement for the participants to carry or borrow numbers. The results showed that arithmetic operations induce some spatial shifts of attention, possibly through a semantic link between the operation and space.

STT Doubles with Large DM - Part IV: Ophiuchus and Hercules

NASA Astrophysics Data System (ADS)

Knapp, Wilfried; Nanson, John

2016-04-01

The results of visual double star observing sessions suggested a pattern for STT doubles with large DM of being harder to resolve than would be expected based on the WDS catalog data. It was felt this might be a problem with expectations on one hand, and on the other might be an indication of a need for new precise measurements, so we decided to take a closer look at a selected sample of STT doubles and do some research. We found that like in the other constellations covered so far (Gem, Leo, UMa, etc.) at least several of the selected objects in Ophiuchus and Hercules show parameters quite different from the current WDS data.

STT Doubles with Large DM - Part V: Aquila, Delphinus, Cygnus, Aquarius

NASA Astrophysics Data System (ADS)

Knapp, Wilfried; Nanson, John

2016-07-01

The results of visual double star observing sessions suggested a pattern for STT doubles with large DM of being harder to resolve than would be expected based on the WDS catalog data. It was felt this might be a problem with expectations on one hand, and on the other might be an indication of a need for new precise measurements, so we decided to take a closer look at a selected sample of STT doubles and do some research. We found that, as in the other constellations covered so far (Gem, Leo, UMa etc.), at least several of the selected objects in Aql, Del, Cyg and Aqr show parameters quite different from the current WDS data

Stellar Astrophysics with a Dispersed Fourier Transform Spectrograph. II. Orbits of Double-lined Spectroscopic Binaries

NASA Astrophysics Data System (ADS)

Behr, Bradford B.; Cenko, Andrew T.; Hajian, Arsen R.; McMillan, Robert S.; Murison, Marc; Meade, Jeff; Hindsley, Robert

2011-07-01

We present orbital parameters for six double-lined spectroscopic binaries (ι Pegasi, ω Draconis, 12 Boötis, V1143 Cygni, β Aurigae, and Mizar A) and two double-lined triple star systems (κ Pegasi and η Virginis). The orbital fits are based upon high-precision radial velocity (RV) observations made with a dispersed Fourier Transform Spectrograph, or dFTS, a new instrument that combines interferometric and dispersive elements. For some of the double-lined binaries with known inclination angles, the quality of our RV data permits us to determine the masses M 1 and M 2 of the stellar components with relative errors as small as 0.2%.

A novel double fine guide sensor design on space telescope

NASA Astrophysics Data System (ADS)

Zhang, Xu-xu; Yin, Da-yi

2018-02-01

To get high precision attitude for space telescope, a double marginal FOV (field of view) FGS (Fine Guide Sensor) is proposed. It is composed of two large area APS CMOS sensors and both share the same lens in main light of sight. More star vectors can be get by two FGS and be used for high precision attitude determination. To improve star identification speed, the vector cross product in inter-star angles for small marginal FOV different from traditional way is elaborated and parallel processing method is applied to pyramid algorithm. The star vectors from two sensors are then used to attitude fusion with traditional QUEST algorithm. The simulation results show that the system can get high accuracy three axis attitudes and the scheme is feasibility.

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

ERIC Educational Resources Information Center

Marshall, Sandra P.

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

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

ERIC Educational Resources Information Center

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

2007-01-01

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

Counting and RAN: Predictors of Arithmetic Calculation and Reading Fluency

ERIC Educational Resources Information Center

Koponen, Tuire; Salmi, Paula; Eklund, Kenneth; Aro, Tuija

2013-01-01

This study examined whether counting and rapid automatized naming (RAN) could operate as significant predictors of both later arithmetic calculation and reading fluency. The authors also took an important step to clarify the cognitive mechanisms underlying these predictive relationships by controlling for the effect of phonological awareness and…

The Development of Arithmetical Abilities

ERIC Educational Resources Information Center

Butterworth, Brian

2005-01-01

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

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

ERIC Educational Resources Information Center

De Visscher, Alice; Noël, Marie-Pascale

2014-01-01

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

Arithmetic Word-Problem-Solving in Huntington's Disease

ERIC Educational Resources Information Center

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

2005-01-01

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

Numerical Processing Efficiency Improved in Experienced Mental Abacus Children

ERIC Educational Resources Information Center

Wang, Yunqi; Geng, Fengji; Hu, Yuzheng; Du, Fenglei; Chen, Feiyan

2013-01-01

Experienced mental abacus (MA) users are able to perform mental arithmetic calculations with unusual speed and accuracy. However, it remains unclear whether their extraordinary gains in mental arithmetic ability are accompanied by an improvement in numerical processing efficiency. To address this question, the present study, using a numerical…

40 CFR 133.101 - Definitions.

Code of Federal Regulations, 2010 CFR

2010-07-01

... arithmetic mean of pollutant parameter values for samples collected in a period of 7 consecutive days. (b) 30-day average. The arithmetic mean of pollutant parameter values of samples collected in a period of 30... percentile value for the 30-day average effluent quality achieved by a treatment works in a period of at...

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…

Computer-Based Arithmetic Test Generation

ERIC Educational Resources Information Center

Trocchi, Robert F.

1973-01-01

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

Teaching Linear Algebra: Proceeding More Efficiently by Staying Comfortably within Z

ERIC Educational Resources Information Center

Beaver, Scott

2015-01-01

For efficiency in a linear algebra course the instructor may wish to avoid the undue arithmetical distractions of rational arithmetic. In this paper we explore how to write fraction-free problems of various types including elimination, matrix inverses, orthogonality, and the (non-normalizing) Gram-Schmidt process.

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

ERIC Educational Resources Information Center

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

2017-01-01

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

Mathematics: Essential to Marketing. Student's Manual and Teacher's Guide.

ERIC Educational Resources Information Center

Helton, Betty G.; Griffin, Jennie

This document contains both a student's manual and a teacher's guide for high school mathematics essential to marketing. The student's manual contains 34 assignments within the following 11 units: (1) arithmetic fundamentals; (2) application of arithmetic fundamentals; (3) cashiering; (4) inventory procedures; (5) invoices; (6) computing employee…

Basic Mathematics Operations--A Math Practice Booklet.

ERIC Educational Resources Information Center

Herr, Nicholas K.

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

Teacher Actions to Facilitate Early Algebraic Reasoning

ERIC Educational Resources Information Center

Hunter, Jodie

2015-01-01

In recent years there has been an increased emphasis on integrating the teaching of arithmetic and algebra in primary school classrooms. This requires teachers to develop links between arithmetic and algebra and use pedagogical actions that facilitate algebraic reasoning. Drawing on findings from a classroom-based study, this paper provides an…

SMP That Help Foster Algebraic Thinking

ERIC Educational Resources Information Center

Billings, Esther M. H.

2017-01-01

Arithmetic is a major mathematical focus in elementary school curriculum, and researchers such as Mason (2008) claim that "algebraic thinking is required in order to make sense of arithmetic" (p. 58). When adding, subtracting, multiplying, and dividing, learners must rely on a small set of fundamental properties also important for the…

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

ERIC Educational Resources Information Center

Kidd, Teresa A.; Saudargas, Richard A.

1988-01-01

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

Idempotents a la mod

ERIC Educational Resources Information Center

Sibley, Thomas Q.

2012-01-01

An idempotent satisfies the equation x[superscript 2] = x. In ordinary arithmetic, this is so easy to solve it's boring. We delight the mathematical palette here, topping idempotents off with modular arithmetic and a series of exercises determining for which n there are more than two idempotents (mod n) and exactly how many there are.

Early Numeracy in Cerebral Palsy: Review and Future Research

ERIC Educational Resources Information Center

van Rooijen, Maaike; Verhoeven, Ludo; Steenbergen, Bert

2011-01-01

Children with cerebral palsy (CP) often have problems with arithmetic, but the development of numerical abilities in these children has received only minor attention. In comparison, detailed accounts have been written on the arithmetic abilities of typically developing children, but a theoretical framework is still lacking. A promising perspective…

Remedial Instruction to Enhance Mathematical Ability of Dyscalculics

ERIC Educational Resources Information Center

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

2012-01-01

The ability to do arithmetic calculations is essential to school-based learning and skill development in an information rich society. Arithmetic is a basic academic skill that is needed for learning which includes the skills such as counting, calculating, reasoning etc. that are used for performing mathematical calculations. Unfortunately, many…

Airborne 2-Micron Double Pulsed Direct Detection IPDA Lidar for Atmospheric CO2 Measurement

NASA Technical Reports Server (NTRS)

Yu, Jirong; Petros, Mulugeta; Refaat, Tamer F.; Reithmaier, Karl; Remus, Ruben; Singh, Upendra; Johnson, Will; Boyer, Charlie; Fay, James; Johnston, Susan;

An effective method on pornographic images realtime recognition

NASA Astrophysics Data System (ADS)

Wang, Baosong; Lv, Xueqiang; Wang, Tao; Wang, Chengrui

2013-03-01

In this paper, skin detection, texture filtering and face detection are used to extract feature on an image library, training them with the decision tree arithmetic to create some rules as a decision tree classifier to distinguish an unknown image. Experiment based on more than twenty thousand images, the precision rate can get 76.21% when testing on 13025 pornographic images and elapsed time is less than 0.2s. This experiment shows it has a good popularity. Among the steps mentioned above, proposing a new skin detection model which called irregular polygon region skin detection model based on YCbCr color space. This skin detection model can lower the false detection rate on skin detection. A new method called sequence region labeling on binary connected area can calculate features on connected area, it is faster and needs less memory than other recursive methods.

Numerical ‘health check’ for scientific codes: the CADNA approach

NASA Astrophysics Data System (ADS)

Scott, N. S.; Jézéquel, F.; Denis, C.; Chesneaux, J.-M.

2007-04-01

Scientific computation has unavoidable approximations built into its very fabric. One important source of error that is difficult to detect and control is round-off error propagation which originates from the use of finite precision arithmetic. We propose that there is a need to perform regular numerical 'health checks' on scientific codes in order to detect the cancerous effect of round-off error propagation. This is particularly important in scientific codes that are built on legacy software. We advocate the use of the CADNA library as a suitable numerical screening tool. We present a case study to illustrate the practical use of CADNA in scientific codes that are of interest to the Computer Physics Communications readership. In doing so we hope to stimulate a greater awareness of round-off error propagation and present a practical means by which it can be analyzed and managed.

Detection of the Haemophilus somnus antibodies in the bulls' reproductive tract fluids using the ELISA. I. Elaboration of the ELISA for the detection of the specific antibodies in the IgG, IgM and IgA classes.

PubMed

Stefaniak, T

1993-01-01

The conditions of the ELISA for detecting the Haemophilus somnus antibodies in IgG, IgM and IgA classes were elaborated. The test was adapted for examining the seminal plasma, preputial washings and blood serum samples of bulls. In order to obtain the more precise evaluation of results, the tests were made for two different dilutions of the examined material. The arising out of this method difficulty in the evaluation of the intensity of reaction was solved by introducing the specific, semi-quantitative method of classification, using the eleven-degree scale. The mean arithmetic classificational values calculated from absorbance readings were called "absorbance index". The introduced parameter proved to be especially useful while comparing the reaction of antibodies in reproductive tract fluids samples.

[Haptic tracking control for minimally invasive robotic surgery].

PubMed

Xu, Zhaohong; Song, Chengli; Wu, Wenwu

2012-06-01

Haptic feedback plays a significant role in minimally invasive robotic surgery (MIRS). A major deficiency of the current MIRS is the lack of haptic perception for the surgeon, including the commercially available robot da Vinci surgical system. In this paper, a dynamics model of a haptic robot is established based on Newton-Euler method. Because it took some period of time in exact dynamics solution, we used a digital PID arithmetic dependent on robot dynamics to ensure real-time bilateral control, and it could improve tracking precision and real-time control efficiency. To prove the proposed method, an experimental system in which two Novint Falcon haptic devices acting as master-slave system has been developed. Simulations and experiments showed proposed methods could give instrument force feedbacks to operator, and bilateral control strategy is an effective method to master-slave MIRS. The proposed methods could be used to tele-robotic system.

Representing exact number visually using mental abacus.

PubMed

Frank, Michael C; Barner, David

2012-02-01

Mental abacus (MA) is a system for performing rapid and precise arithmetic by manipulating a mental representation of an abacus, a physical calculation device. Previous work has speculated that MA is based on visual imagery, suggesting that it might be a method of representing exact number nonlinguistically, but given the limitations on visual working memory, it is unknown how MA structures could be stored. We investigated the structure of the representations underlying MA in a group of children in India. Our results suggest that MA is represented in visual working memory by splitting the abacus into a series of columns, each of which is independently stored as a unit with its own detailed substructure. In addition, we show that the computations of practiced MA users (but not those of control participants) are relatively insensitive to verbal interference, consistent with the hypothesis that MA is a nonlinguistic format for exact numerical computation.

Fpga based L-band pulse doppler radar design and implementation

NASA Astrophysics Data System (ADS)

Savci, Kubilay

As its name implies RADAR (Radio Detection and Ranging) is an electromagnetic sensor used for detection and locating targets from their return signals. Radar systems propagate electromagnetic energy, from the antenna which is in part intercepted by an object. Objects reradiate a portion of energy which is captured by the radar receiver. The received signal is then processed for information extraction. Radar systems are widely used for surveillance, air security, navigation, weather hazard detection, as well as remote sensing applications. In this work, an FPGA based L-band Pulse Doppler radar prototype, which is used for target detection, localization and velocity calculation has been built and a general-purpose Pulse Doppler radar processor has been developed. This radar is a ground based stationary monopulse radar, which transmits a short pulse with a certain pulse repetition frequency (PRF). Return signals from the target are processed and information about their location and velocity is extracted. Discrete components are used for the transmitter and receiver chain. The hardware solution is based on Xilinx Virtex-6 ML605 FPGA board, responsible for the control of the radar system and the digital signal processing of the received signal, which involves Constant False Alarm Rate (CFAR) detection and Pulse Doppler processing. The algorithm is implemented in MATLAB/SIMULINK using the Xilinx System Generator for DSP tool. The field programmable gate arrays (FPGA) implementation of the radar system provides the flexibility of changing parameters such as the PRF and pulse length therefore it can be used with different radar configurations as well. A VHDL design has been developed for 1Gbit Ethernet connection to transfer digitized return signal and detection results to PC. An A-Scope software has been developed with C# programming language to display time domain radar signals and detection results on PC. Data are processed both in FPGA chip and on PC. FPGA uses fixed point arithmetic operations as it is fast and facilitates source requirement as it consumes less hardware than floating point arithmetic operations. The software uses floating point arithmetic operations, which ensure precision in processing at the expense of speed. The functionality of the radar system has been tested for experimental validation in the field with a moving car and the validation of submodules are tested with synthetic data simulated on MATLAB.

Discrete mathematical physics and particle modeling

NASA Astrophysics Data System (ADS)

Greenspan, D.

The theory and application of the arithmetic approach to the foundations of both Newtonian and special relativistic mechanics are explored. Using only arithmetic, a reformulation of the Newtonian approach is given for: gravity; particle modeling of solids, liquids, and gases; conservative modeling of laminar and turbulent fluid flow, heat conduction, and elastic vibration; and nonconservative modeling of heat convection, shock-wave generation, the liquid drop problem, porous flow, the interface motion of a melting solid, soap films, string vibrations, and solitons. An arithmetic reformulation of special relativistic mechanics is given for theory in one space dimension, relativistic harmonic oscillation, and theory in three space dimensions. A speculative quantum mechanical model of vibrations in the water molecule is also discussed.

Trinary arithmetic and logic unit (TALU) using savart plate and spatial light modulator (SLM) suitable for optical computation in multivalued logic

NASA Astrophysics Data System (ADS)

Ghosh, Amal K.; Bhattacharya, Animesh; Raul, Moumita; Basuray, Amitabha

2012-07-01

Arithmetic logic unit (ALU) is the most important unit in any computing system. Optical computing is becoming popular day-by-day because of its ultrahigh processing speed and huge data handling capability. Obviously for the fast processing we need the optical TALU compatible with the multivalued logic. In this regard we are communicating the trinary arithmetic and logic unit (TALU) in modified trinary number (MTN) system, which is suitable for the optical computation and other applications in multivalued logic system. Here the savart plate and spatial light modulator (SLM) based optoelectronic circuits have been used to exploit the optical tree architecture (OTA) in optical interconnection network.

SU (2) lattice gauge theory simulations on Fermi GPUs

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

Cardoso, Nuno, E-mail: nunocardoso@cftp.ist.utl.p; Bicudo, Pedro, E-mail: bicudo@ist.utl.p

2011-05-10

In this work we explore the performance of CUDA in quenched lattice SU (2) simulations. CUDA, NVIDIA Compute Unified Device Architecture, is a hardware and software architecture developed by NVIDIA for computing on the GPU. We present an analysis and performance comparison between the GPU and CPU in single and double precision. Analyses with multiple GPUs and two different architectures (G200 and Fermi architectures) are also presented. In order to obtain a high performance, the code must be optimized for the GPU architecture, i.e., an implementation that exploits the memory hierarchy of the CUDA programming model. We produce codes formore » the Monte Carlo generation of SU (2) lattice gauge configurations, for the mean plaquette, for the Polyakov Loop at finite T and for the Wilson loop. We also present results for the potential using many configurations (50,000) without smearing and almost 2000 configurations with APE smearing. With two Fermi GPUs we have achieved an excellent performance of 200x the speed over one CPU, in single precision, around 110 Gflops/s. We also find that, using the Fermi architecture, double precision computations for the static quark-antiquark potential are not much slower (less than 2x slower) than single precision computations.« less

Double soft limit of the graviton amplitude from the Cachazo-He-Yuan formalism

NASA Astrophysics Data System (ADS)

Saha, Arnab Priya

2017-08-01

We present a complete analysis for double soft limit of graviton scattering amplitude using the formalism proposed by Cachazo, He, and Yuan. Our results agree with that obtained via Britto-Cachazo-Feng-Witten (BCFW) recursion relations in [T. Klose, T. McLoughlin, D. Nandan, J. Plefka, and G. Travaglini, Double-soft limits of gluons and gravitons, J. High Energy Phys. 07 (2015) 135., 10.1007/JHEP07(2015)135]. In addition we find precise relations between degenerate and nondegenerate solutions of scattering equations with local and nonlocal terms in the soft factor.

BIREFRINGENT FILTER MODEL

NASA Technical Reports Server (NTRS)

Cross, P. L.

1994-01-01

Birefringent filters are often used as line-narrowing components in solid state lasers. The Birefringent Filter Model program generates a stand-alone model of a birefringent filter for use in designing and analyzing a birefringent filter. It was originally developed to aid in the design of solid state lasers to be used on aircraft or spacecraft to perform remote sensing of the atmosphere. The model is general enough to allow the user to address problems such as temperature stability requirements, manufacturing tolerances, and alignment tolerances. The input parameters for the program are divided into 7 groups: 1) general parameters which refer to all elements of the filter; 2) wavelength related parameters; 3) filter, coating and orientation parameters; 4) input ray parameters; 5) output device specifications; 6) component related parameters; and 7) transmission profile parameters. The program can analyze a birefringent filter with up to 12 different components, and can calculate the transmission and summary parameters for multiple passes as well as a single pass through the filter. The Jones matrix, which is calculated from the input parameters of Groups 1 through 4, is used to calculate the transmission. Output files containing the calculated transmission or the calculated Jones' matrix as a function of wavelength can be created. These output files can then be used as inputs for user written programs. For example, to plot the transmission or to calculate the eigen-transmittances and the corresponding eigen-polarizations for the Jones' matrix, write the appropriate data to a file. The Birefringent Filter Model is written in Microsoft FORTRAN 2.0. The program format is interactive. It was developed on an IBM PC XT equipped with an 8087 math coprocessor, and has a central memory requirement of approximately 154K. Since Microsoft FORTRAN 2.0 does not support complex arithmetic, matrix routines for addition, subtraction, and multiplication of complex, double precision variables are included. The Birefringent Filter Model was written in 1987.

In vivo Three-Dimensional Superresolution Fluorescence Tracking using a Double-Helix Point Spread Function

PubMed Central

Lew, Matthew D.; Thompson, Michael A.; Badieirostami, Majid; Moerner, W. E.

2010-01-01

The point spread function (PSF) of a widefield fluorescence microscope is not suitable for three-dimensional super-resolution imaging. We characterize the localization precision of a unique method for 3D superresolution imaging featuring a double-helix point spread function (DH-PSF). The DH-PSF is designed to have two lobes that rotate about their midpoint in any transverse plane as a function of the axial position of the emitter. In effect, the PSF appears as a double helix in three dimensions. By comparing the Cramer-Rao bound of the DH-PSF with the standard PSF as a function of the axial position, we show that the DH-PSF has a higher and more uniform localization precision than the standard PSF throughout a 2 μm depth of field. Comparisons between the DH-PSF and other methods for 3D super-resolution are briefly discussed. We also illustrate the applicability of the DH-PSF for imaging weak emitters in biological systems by tracking the movement of quantum dots in glycerol and in live cells. PMID:20563317

Lack of interaction between a new antihistamine, mizolastine, and lorazepam on psychomotor performance and memory in healthy volunteers.

PubMed

Patat, A; Perault, M C; Vandel, B; Ulliac, N; Zieleniuk, I; Rosenzweig, P

1995-01-01

1. The possible interaction between a new H1 antihistamine, mizolastine, and lorazepam was assessed in a randomised, double-blind, cross-over, placebo-controlled study involving 16 healthy young male volunteers who received mizolastine 10 mg or placebo once daily for 8 days with a 1 week wash-out interval. The interaction of mizolastine, at steady-state, with a single oral dose of lorazepam or placebo was assessed on days 6 or 8 of each treatment period. 2. Psychomotor performance and cognitive function were evaluated using objective tests (critical flicker fusion threshold, choice reaction time, tapping, arithmetic calculation, body sway) and self-ratings (visual analogue scale, ARCI) before and at 2, 4, 6 and 8 h after dosing. Short-term memory (Sternberg memory scanning immediate free recall of a word list) and long-term memory (delayed free recall and recognition of words and pictures) were assessed before and at 3 h after dosing. Pharmacodynamic interactions were evaluated by repeated measures ANOVA in a 2 x 2 factorial interaction model. 3. Mizolastine, 10 mg once daily, at steady-state, was devoid of sedation and detrimental effect on skilled performance and memory. 4. In contrast, a single 2 mg dose of lorazepam produced marked impairment of psychomotor performance, cognitive functions (significant reduction in flicker fusion threshold, tapping and arithmetic calculation and increase in reaction times and body sway) and subjective sedation from 2 to 8 h after dosing. In addition, lorazepam induced an anterograde amnesia, characterised by a decrease in delayed free recall and recognition, and a deficit in short term memory.(ABSTRACT TRUNCATED AT 250 WORDS)

Estimation of satellite position, clock and phase bias corrections

NASA Astrophysics Data System (ADS)

Henkel, Patrick; Psychas, Dimitrios; Günther, Christoph; Hugentobler, Urs

2018-05-01

Precise point positioning with integer ambiguity resolution requires precise knowledge of satellite position, clock and phase bias corrections. In this paper, a method for the estimation of these parameters with a global network of reference stations is presented. The method processes uncombined and undifferenced measurements of an arbitrary number of frequencies such that the obtained satellite position, clock and bias corrections can be used for any type of differenced and/or combined measurements. We perform a clustering of reference stations. The clustering enables a common satellite visibility within each cluster and an efficient fixing of the double difference ambiguities within each cluster. Additionally, the double difference ambiguities between the reference stations of different clusters are fixed. We use an integer decorrelation for ambiguity fixing in dense global networks. The performance of the proposed method is analysed with both simulated Galileo measurements on E1 and E5a and real GPS measurements of the IGS network. We defined 16 clusters and obtained satellite position, clock and phase bias corrections with a precision of better than 2 cm.

Developing an Energy Policy for the United States

ERIC Educational Resources Information Center

Keefe, Pat

2014-01-01

Al Bartlett's video "Arithmetic, Population, and Energy" spells out many of the complex issues related to energy use in our society. Bartlett makes the point that basic arithmetic is the fundamental obstacle preventing us from being able to grasp the relationships between energy consumption, population, and lifestyles. In an earlier…

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…

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…

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

ERIC Educational Resources Information Center

Zevenbergen, Robyn; Hyde, Merv; Power, Des

2001-01-01

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

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"…

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

ERIC Educational Resources Information Center

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

2014-01-01

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

The Posing of Arithmetic Problems by Mathematically Talented Students

ERIC Educational Resources Information Center

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

2016-01-01

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

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

USDA-ARS?s Scientific Manuscript database

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

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

USDA-ARS?s Scientific Manuscript database

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

The Teachers' Views on Soroban Abacus Training

ERIC Educational Resources Information Center

Altiparmak, Kemal

2016-01-01

Soroban abacus training is called as mental arithmetic training in our country. It is known for mental arithmetic to increase the ability of four mode operations. Besides this, how is the situation for the students which are having Soroban abacus training in the terms of problem solving abilities, creativity, development of concepts, attraction…

The Role of the Updating Function in Solving Arithmetic Word Problems

ERIC Educational Resources Information Center

Mori, Kanetaka; Okamoto, Masahiko

2017-01-01

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

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…

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

ERIC Educational Resources Information Center

Senter, R. J.; And Others

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

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

ERIC Educational Resources Information Center

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

2010-01-01

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

Sign Language for K-8 Mathematics by 3D Interactive Animation

ERIC Educational Resources Information Center

Adamo-Villani, Nicoletta; Doublestein, John; Martin, Zachary

2005-01-01

We present a new highly interactive computer animation tool to increase the mathematical skills of deaf children. We aim at increasing the effectiveness of (hearing) parents in teaching arithmetic to their deaf children, and the opportunity of deaf children to learn arithmetic via interactive media. Using state-of-the-art computer animation…

Using Microcomputers To Help Learning Disabled Student with Arithmetic Difficulties.

ERIC Educational Resources Information Center

Brevil, Margarette

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

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

ERIC Educational Resources Information Center

Rumsey, Chepina Witkowski

2012-01-01

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

On Arithmetic-Geometric-Mean Polynomials

ERIC Educational Resources Information Center

Griffiths, Martin; MacHale, Des

2017-01-01

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

Arithmetical Strategies of a Student with Down Syndrome

ERIC Educational Resources Information Center

Rumiati, Rumi

2014-01-01

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

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

ERIC Educational Resources Information Center

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

2011-01-01

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

Effects of Numerical Surface Form in Arithmetic Word Problems

ERIC Educational Resources Information Center

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

2015-01-01

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

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

ERIC Educational Resources Information Center

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

2014-01-01

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

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

ERIC Educational Resources Information Center

Desoete, Annemie

2008-01-01

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

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

ERIC Educational Resources Information Center

Siegler, Robert S.; Lortie-Forgues, Hugues

2017-01-01

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

Early Integration of Tutorial Support in Beginning Algebra

ERIC Educational Resources Information Center

Copus, Colleen; McKinney, Betsy

2016-01-01

Anecdotal observations reveal that most students with strong arithmetic skills will succeed in the Beginning Algebra course even if they have no previous experience with algebra. In trying to quantify this with an initial teacher-created survey of arithmetic skills, it was observed, for three consecutive semesters, that students who scored in the…

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

ERIC Educational Resources Information Center

Purpura, David J.; Lonigan, Christopher J.

2013-01-01

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

Assessment of Psychological Readiness Situation of Students Starting to Primary School

ERIC Educational Resources Information Center

Halmatov, Medera

2018-01-01

There are important responsibilities expected from primary school students. The most important of these are the learning of reading, writing and arithmetic. There is a "psychological readiness" aspect besides reading, writing and arithmetic in order to be ready for the school. In this study, among the first-grade students, those who were…

Secret Codes, Remainder Arithmetic, and Matrices.

ERIC Educational Resources Information Center

Peck, Lyman C.

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

Cognitive and numerosity predictors of mathematical skills in middle school.

PubMed

Cirino, Paul T; Tolar, Tammy D; Fuchs, Lynn S; Huston-Warren, Emily

2016-05-01

There is a strong research base on the underlying concomitants of early developing math skills. Fewer studies have focused on later developing skills. Here, we focused on direct and indirect contributions of cognitive measures (e.g., language, spatial skills, working memory) and numerosity measures, as well as arithmetic proficiency, on key outcomes of fraction performance, proportional reasoning, and broad mathematics achievement at sixth grade (N=162) via path analysis. We expected a hierarchy of skill development, with predominantly indirect effects of cognitive factors via number and arithmetic. Results controlling for age showed that the combination of cognitive, number, and arithmetic variables cumulatively accounted for 38% to 44% of the variance in fractions, proportional reasoning, and broad mathematics. There was consistency across outcomes, with more proximal skills providing direct effects and with the effects of cognitive skills being mediated by number and by more proximal skills. Results support a hierarchical progression from domain-general cognitive processes through numerosity and arithmetic skills to proportional reasoning to broad mathematics achievement. Copyright © 2016 Elsevier Inc. All rights reserved.

Developmental dyscalculia.

PubMed

Shalev, Ruth S

2004-10-01

Developmental dyscalculia is a specific learning disability affecting the normal acquisition of arithmetic skills. Genetic, neurobiologic, and epidemiologic evidence indicates that dyscalculia, like other learning disabilities, is a brain-based disorder. However, poor teaching and environmental deprivation have also been implicated in its etiology. Because the neural network of both hemispheres comprises the substrate of normal arithmetic skills, dyscalculia can result from dysfunction of either hemisphere, although the left parietotemporal area is of particular significance. The prevalence of developmental dyscalculia is 5 to 6% in the school-aged population and is as common in girls as in boys. Dyscalculia can occur as a consequence of prematurity and low birthweight and is frequently encountered in a variety of neurologic disorders, such as attention-deficit hyperactivity disorder (ADHD), developmental language disorder, epilepsy, and fragile X syndrome. Developmental dyscalculia has proven to be a persisting learning disability, at least for the short term, in about half of affected preteen pupils. Educational interventions for dyscalculia range from rote learning of arithmetic facts to developing strategies for solving arithmetic exercises. The long-term prognosis of dyscalculia and the role of remediation in its outcome are yet to be determined.

The calculating brain: an fMRI study.

PubMed

Rickard, T C; Romero, S G; Basso, G; Wharton, C; Flitman, S; Grafman, J

2000-01-01

To explore brain areas involved in basic numerical computation, functional magnetic imaging (fMRI) scanning was performed on college students during performance of three tasks; simple arithmetic, numerical magnitude judgment, and a perceptual-motor control task. For the arithmetic relative to the other tasks, results for all eight subjects revealed bilateral activation in Brodmann's area 44, in dorsolateral prefrontal cortex (areas 9 and 10), in inferior and superior parietal areas, and in lingual and fusiform gyri. Activation was stronger on the left for all subjects, but only at Brodmann's area 44 and the parietal cortices. No activation was observed in the arithmetic task in several other areas previously implicated for arithmetic, including the angular and supramarginal gyri and the basal ganglia. In fact, angular and supramarginal gyri were significantly deactivated by the verification task relative to both the magnitude judgment and control tasks for every subject. Areas activated by the magnitude task relative to the control were more variable, but in five subjects included bilateral inferior parietal cortex. These results confirm some existing hypotheses regarding the neural basis of numerical processes, invite revision of others, and suggest productive lines for future investigation.

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

PubMed

Humphries, Ailsa; Chen, Zhe; Neumann, Ewald

2017-01-01

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

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

PubMed

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

2016-06-01

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

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

PubMed

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

2017-01-01

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

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

PubMed

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

2015-01-01

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

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

PubMed

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

2017-02-01

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

Fixed-Rate Compressed Floating-Point Arrays.

PubMed

Lindstrom, Peter

2014-12-01

Current compression schemes for floating-point data commonly take fixed-precision values and compress them to a variable-length bit stream, complicating memory management and random access. We present a fixed-rate, near-lossless compression scheme that maps small blocks of 4(d) values in d dimensions to a fixed, user-specified number of bits per block, thereby allowing read and write random access to compressed floating-point data at block granularity. Our approach is inspired by fixed-rate texture compression methods widely adopted in graphics hardware, but has been tailored to the high dynamic range and precision demands of scientific applications. Our compressor is based on a new, lifted, orthogonal block transform and embedded coding, allowing each per-block bit stream to be truncated at any point if desired, thus facilitating bit rate selection using a single compression scheme. To avoid compression or decompression upon every data access, we employ a software write-back cache of uncompressed blocks. Our compressor has been designed with computational simplicity and speed in mind to allow for the possibility of a hardware implementation, and uses only a small number of fixed-point arithmetic operations per compressed value. We demonstrate the viability and benefits of lossy compression in several applications, including visualization, quantitative data analysis, and numerical simulation.

Design and realization of the control system for the three-channel birefringent filter

NASA Astrophysics Data System (ADS)

Zhu, Dan

2008-07-01

Space Solar Telescope is one of the large-scale scientific programs under development in China. In it, an important part is the filter, a birefringent filter with three-channels. It consists of 17 rotatable wave plates. In coordination with other mechanical and optical components, complicated and precise adjustments of their attitudes are necessary, which requests a high-accuracy control system to ensure their concertedness. The paper describes the design and realization of the control system. It mainly has a hardware plate and a software one. The former uses an industrial controller, a control card and step motors, while the latter uses the technique construction of the object oriented. That is modularization design with lengthwise dividing as per functions and breadthwise dividing as per element layers. Shift arithmetic for whole spectrum in programs is for intelligent spectral scanning. At the same time, the control information is roundly recorded in the data base of the system. Tests show that the system is characterized by high precision, good stabilization, high data safety and user-friendly interface, totally meeting the design requirements. Also discussed in this paper is some new conceivability to realize the handiness and miniaturization of the filter to fit the use in space flight in the future.

A simplified Integer Cosine Transform and its application in image compression

NASA Technical Reports Server (NTRS)

Costa, M.; Tong, K.

1994-01-01

A simplified version of the integer cosine transform (ICT) is described. For practical reasons, the transform is considered jointly with the quantization of its coefficients. It differs from conventional ICT algorithms in that the combined factors for normalization and quantization are approximated by powers of two. In conventional algorithms, the normalization/quantization stage typically requires as many integer divisions as the number of transform coefficients. By restricting the factors to powers of two, these divisions can be performed by variable shifts in the binary representation of the coefficients, with speed and cost advantages to the hardware implementation of the algorithm. The error introduced by the factor approximations is compensated for in the inverse ICT operation, executed with floating point precision. The simplified ICT algorithm has potential applications in image-compression systems with disparate cost and speed requirements in the encoder and decoder ends. For example, in deep space image telemetry, the image processors on board the spacecraft could take advantage of the simplified, faster encoding operation, which would be adjusted on the ground, with high-precision arithmetic. A dual application is found in compressed video broadcasting. Here, a fast, high-performance processor at the transmitter would precompensate for the factor approximations in the inverse ICT operation, to be performed in real time, at a large number of low-cost receivers.

The digital compensation technology system for automotive pressure sensor

NASA Astrophysics Data System (ADS)

Guo, Bin; Li, Quanling; Lu, Yi; Luo, Zai

2011-05-01

Piezoresistive pressure sensor be made of semiconductor silicon based on Piezoresistive phenomenon, has many characteristics. But since the temperature effect of semiconductor, the performance of silicon sensor is also changed by temperature, and the pressure sensor without temperature drift can not be produced at present. This paper briefly describe the principles of sensors, the function of pressure sensor and the various types of compensation method, design the detailed digital compensation program for automotive pressure sensor. Simulation-Digital mixed signal conditioning is used in this dissertation, adopt signal conditioning chip MAX1452. AVR singlechip ATMEGA128 and other apparatus; fulfill the design of digital pressure sensor hardware circuit and singlechip hardware circuit; simultaneously design the singlechip software; Digital pressure sensor hardware circuit is used to implementing the correction and compensation of sensor; singlechip hardware circuit is used to implementing to controll the correction and compensation of pressure sensor; singlechip software is used to implementing to fulfill compensation arithmetic. In the end, it implement to measure the output of sensor, and contrast to the data of non-compensation, the outcome indicates that the compensation precision of compensated sensor output is obviously better than non-compensation sensor, not only improving the compensation precision but also increasing the stabilization of pressure sensor.

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

PubMed

Pinel, Philippe; Dehaene, Stanislas

2010-01-01

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

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

PubMed

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

2016-09-01

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

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

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

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

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

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

PubMed

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

2004-01-20

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

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

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

Atomically Precise Interfaces from Non-stoichiometric Deposition

NASA Astrophysics Data System (ADS)

Nie, Yuefeng; Zhu, Ye; Lee, Che-Hui; Kourkoutis, Lena; Mundy, Julia; Junquera, Javier; Ghosez, Philippe; Baek, David; Sung, Suk Hyun; Xi, Xiaoxing; Shen, Kyle; Muller, David; Schlom, Darrell

2015-03-01

Complex oxide heterostructures display some of the most chemically abrupt, atomically precise interfaces, which is advantageous when constructing new interface phases with emergent properties by juxtaposing incompatible ground states. One might assume that atomically precise interfaces result from stoichiometric growth. Here we show that the most precise control is, however, obtained by using deliberate and specific non-stoichiometric growth conditions. For the precise growth of Srn+1TinO3n+1 Ruddlesden-Popper (RP) phases, stoichiometric deposition leads to the loss of the first RP rock-salt double layer, but growing with a strontium-rich surface layer restores the bulk stoichiometry and ordering of the subsurface RP structure. Our results dramatically expand the materials that can be prepared in epitaxial heterostructures with precise interface control--from just the n = 1 end members (perovskites) to the entire RP homologous series--enabling the exploration of novel quantum phenomena at a richer variety of oxide interfaces.

Atomically precise interfaces from non-stoichiometric deposition

NASA Astrophysics Data System (ADS)

Nie, Y. F.; Zhu, Y.; Lee, C.-H.; Kourkoutis, L. F.; Mundy, J. A.; Junquera, J.; Ghosez, Ph.; Baek, D. J.; Sung, S.; Xi, X. X.; Shen, K. M.; Muller, D. A.; Schlom, D. G.

2014-08-01

Complex oxide heterostructures display some of the most chemically abrupt, atomically precise interfaces, which is advantageous when constructing new interface phases with emergent properties by juxtaposing incompatible ground states. One might assume that atomically precise interfaces result from stoichiometric growth. Here we show that the most precise control is, however, obtained by using deliberate and specific non-stoichiometric growth conditions. For the precise growth of Srn+1TinOn+1 Ruddlesden-Popper (RP) phases, stoichiometric deposition leads to the loss of the first RP rock-salt double layer, but growing with a strontium-rich surface layer restores the bulk stoichiometry and ordering of the subsurface RP structure. Our results dramatically expand the materials that can be prepared in epitaxial heterostructures with precise interface control—from just the n=∞ end members (perovskites) to the entire RP homologous series—enabling the exploration of novel quantum phenomena at a richer variety of oxide interfaces.

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

Utama, Muhammad Reza July, E-mail: muhammad.reza@bmkg.go.id; Indonesian Meteorological, Climatological and Geophysical Agency; Nugraha, Andri Dian

The precise hypocenter was determined location using double difference method around subduction zone in Moluccas area eastern part of Indonesia. The initial hypocenter location from MCGA data catalogue of 1,945 earthquake events. Basically the principle of double-difference algorithm assumes if the distance between two earthquake hypocenter distribution is very small compared to the distance between the station to the earthquake source, the ray path can be considered close to both earthquakes. The results show the initial earthquakes with a certain depth (fix depth 10 km) relocated and can be interpreted more reliable in term of seismicity and geological setting. Themore » relocation of the intra slab earthquakes beneath Banda Arc are also clearly observed down to depth of about 400 km. The precise relocated hypocenter will give invaluable seismicity information for other seismological and tectonic studies especially for seismic hazard analysis in this region.« less

Accurate computation of gravitational field of a tesseroid

NASA Astrophysics Data System (ADS)

Fukushima, Toshio

2018-02-01

We developed an accurate method to compute the gravitational field of a tesseroid. The method numerically integrates a surface integral representation of the gravitational potential of the tesseroid by conditionally splitting its line integration intervals and by using the double exponential quadrature rule. Then, it evaluates the gravitational acceleration vector and the gravity gradient tensor by numerically differentiating the numerically integrated potential. The numerical differentiation is conducted by appropriately switching the central and the single-sided second-order difference formulas with a suitable choice of the test argument displacement. If necessary, the new method is extended to the case of a general tesseroid with the variable density profile, the variable surface height functions, and/or the variable intervals in longitude or in latitude. The new method is capable of computing the gravitational field of the tesseroid independently on the location of the evaluation point, namely whether outside, near the surface of, on the surface of, or inside the tesseroid. The achievable precision is 14-15 digits for the potential, 9-11 digits for the acceleration vector, and 6-8 digits for the gradient tensor in the double precision environment. The correct digits are roughly doubled if employing the quadruple precision computation. The new method provides a reliable procedure to compute the topographic gravitational field, especially that near, on, and below the surface. Also, it could potentially serve as a sure reference to complement and elaborate the existing approaches using the Gauss-Legendre quadrature or other standard methods of numerical integration.

Design and initial validation of a wireless control system based on WSN

NASA Astrophysics Data System (ADS)

Yu, Yan; Li, Luyu; Li, Peng; Wang, Xu; Liu, Hang; Ou, Jinping

2013-04-01

At present, cantilever structure used widely in civil structures will generate continuous vibration by external force due to their low damping characteristic, which leads to a serious impact on the working performance and service time. Therefore, it is very important to control the vibration of these structures. The active vibration control is the primary means of controlling the vibration with high precision and strong adaptive ability. Nowadays, there are many researches using piezoelectric materials in the structural vibration control. Piezoelectric materials are cheap, reliable and they can provide braking and sensing method harmless to the structure, therefore they have broad usage. They are used for structural vibration control in a lot of civil engineering research currently. In traditional sensor applications, information exchanges with the monitoring center or a computer system through wires. If wireless sensor networks(WSN) technology is used, cabling links is not needed, thus the cost of the whole system is greatly reduced. Based on the above advantages, a wireless control system is designed and validated through preliminary tests. The system consists of a cantilever, PVDF as sensor, signal conditioning circuit(SCM), A/D acquisition board, control arithmetic unit, D/A output board, power amplifier, piezoelectric bimorph as actuator. DSP chip is used as the control arithmetic unit and PD control algorithm is embedded in it. PVDF collects the parameters of vibration, sends them to the SCM after A/D conversion. SCM passes the data to the DSP through wireless technology, and DSP calculates and outputs the control values according to the control algorithm. The output signal is amplified by the power amplifier to drive the piezoelectric bimorph for vibration control. The structural vibration duration reduces to 1/4 of the uncontrolled case, which verifies the feasibility of the system.

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

ERIC Educational Resources Information Center

Arsic, Sladjana; Eminovic, Fadilj; Stankovic, Ivona

2011-01-01

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

Arithmetic in Daily Life and Literacy. Literacy Lessons.

ERIC Educational Resources Information Center

Dalbera, Claude

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

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

ERIC Educational Resources Information Center

Schoppek, Wolfgang; Tulis, Maria

2010-01-01

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

Unconscious Addition: When We Unconsciously Initiate and Follow Arithmetic Rules

ERIC Educational Resources Information Center

Ric, Francois; Muller, Dominique

2012-01-01

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

BASIC MATHEMATICS I FOR THE SECONDARY SCHOOLS.

ERIC Educational Resources Information Center

MCCARTHY, CHARLES T.; AND OTHERS

THE COURSE IS GEARED TO MEET THE NEEDS OF STUDENTS ENTERING SENIOR HIGH SCHOOL WITH A MATHEMATICS ACHIEVEMENT LEVEL BELOW SIXTH GRADE. SINCE TWO PRINCIPAL CAUSES OF SERIOUS DEFICIENCIES IN ARITHMETIC ARE A LACK OF UNDERSTANDING OF THE DECIMAL SYSTEM OF NOTATION AND A LACK OF KNOWLEDGE OF THE BASIC FUNDAMENTALS OF ARITHMETIC, BASIC CONCEPTS MUST BE…

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…

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

ERIC Educational Resources Information Center

Yeo, Joseph B. W.

2010-01-01

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

Basic Numerical Capacities and Prevalence of Developmental Dyscalculia: The Havana Survey

ERIC Educational Resources Information Center

Reigosa-Crespo, Vivian; Valdes-Sosa, Mitchell; Butterworth, Brian; Estevez, Nancy; Rodriguez, Marisol; Santos, Elsa; Torres, Paul; Suarez, Ramon; Lage, Agustin

2012-01-01

The association of enumeration and number comparison capacities with arithmetical competence was examined in a large sample of children from 2nd to 9th grades. It was found that efficiency on numerical capacities predicted separately more than 25% of the variance in the individual differences on a timed arithmetical test, and this occurred for…

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

ERIC Educational Resources Information Center

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

2008-01-01

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

Unique Factorization and the Fundamental Theorem of Arithmetic

ERIC Educational Resources Information Center

Sprows, David

2017-01-01

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

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

ERIC Educational Resources Information Center

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

1997-01-01

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

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

NASA Astrophysics Data System (ADS)

Bueno, Aldous Cesar F.

2017-11-01

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

Investigating Children's Understanding of Inversion Using the Missing Number Paradigm

ERIC Educational Resources Information Center

Gilmore, Camilla K.

2006-01-01

The development of conceptual understanding in arithmetic is a gradual process and children may make use of a concept in some situations before others. Previous research has demonstrated that when children are given arithmetic problems with an inverse relationship they can infer that the initial and final quantities are the same. However, we do…

Relational Thinking: The Bridge between Arithmetic and Algebra

ERIC Educational Resources Information Center

Kiziltoprak, Ayhan; Köse, Nilüfer Yavuzsoy

2017-01-01

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

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…

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

ERIC Educational Resources Information Center

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

2009-01-01

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

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…

Bit-Wise Arithmetic Coding For Compression Of Data

NASA Technical Reports Server (NTRS)

Kiely, Aaron

1996-01-01

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

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

ERIC Educational Resources Information Center

D'Amico, Antonella; Passolunghi, Maria Chiara

2009-01-01

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

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

ERIC Educational Resources Information Center

Fägerstam, Emilia; Samuelsson, Joakim

2014-01-01

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

Multiplier Architecture for Coding Circuits

NASA Technical Reports Server (NTRS)

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

1986-01-01

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

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

ERIC Educational Resources Information Center

Mogari, David; Faleye, Sunday

2012-01-01

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

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

ERIC Educational Resources Information Center

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

2010-01-01

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

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

ERIC Educational Resources Information Center

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

2015-01-01

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

Predator Arithmetic

ERIC Educational Resources Information Center

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

2010-01-01

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

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

ERIC Educational Resources Information Center

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

2015-01-01

The present study evaluated 626 5-7-year-old children in the UK, China, Russia, and Kyrgyzstan on a cognitive test battery measuring: (1) general skills; (2) non-symbolic number sense; (3) symbolic number understanding; (4) simple arithmetic--operating with numbers; and (5) familiarity with numbers. Although most inter-population differences were…

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

ERIC Educational Resources Information Center

Carr, Martha; Alexeev, Natalia

2011-01-01

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

Spontaneous Meta-Arithmetic as a First Step toward School Algebra

ERIC Educational Resources Information Center

Caspi, Shai; Sfard, Anna

2012-01-01

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

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…

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…

Early Predictors of Middle School Fraction Knowledge

PubMed Central

Bailey, Drew H.; Siegler, Robert S.; Geary, David C.

2014-01-01

Recent findings that earlier fraction knowledge predicts later mathematics achievement raise the question of what predicts later fraction knowledge. Analyses of longitudinal data indicated that whole number magnitude knowledge in first grade predicted knowledge of fraction magnitudes in middle school, controlling for whole number arithmetic proficiency, domain general cognitive abilities, parental income and education, race, and gender. Similarly, knowledge of whole number arithmetic in first grade predicted knowledge of fraction arithmetic in middle school, controlling for whole number magnitude knowledge in first grade and the other control variables. In contrast, neither type of early whole number knowledge uniquely predicted middle school reading achievement. We discuss the implications of these findings for theories of numerical development and for improving mathematics learning. PMID:24576209

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

NASA Technical Reports Server (NTRS)

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

1991-01-01

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

Ramanujan sums for signal processing of low-frequency noise.

PubMed

Planat, Michel; Rosu, Haret; Perrine, Serge

2002-11-01

An aperiodic (low-frequency) spectrum may originate from the error term in the mean value of an arithmetical function such as Möbius function or Mangoldt function, which are coding sequences for prime numbers. In the discrete Fourier transform the analyzing wave is periodic and not well suited to represent the low-frequency regime. In place we introduce a different signal processing tool based on the Ramanujan sums c(q)(n), well adapted to the analysis of arithmetical sequences with many resonances p/q. The sums are quasiperiodic versus the time n and aperiodic versus the order q of the resonance. Different results arise from the use of this Ramanujan-Fourier transform in the context of arithmetical and experimental signals.

Ramanujan sums for signal processing of low-frequency noise

NASA Astrophysics Data System (ADS)

Planat, Michel; Rosu, Haret; Perrine, Serge

2002-11-01

An aperiodic (low-frequency) spectrum may originate from the error term in the mean value of an arithmetical function such as Möbius function or Mangoldt function, which are coding sequences for prime numbers. In the discrete Fourier transform the analyzing wave is periodic and not well suited to represent the low-frequency regime. In place we introduce a different signal processing tool based on the Ramanujan sums cq(n), well adapted to the analysis of arithmetical sequences with many resonances p/q. The sums are quasiperiodic versus the time n and aperiodic versus the order q of the resonance. Different results arise from the use of this Ramanujan-Fourier transform in the context of arithmetical and experimental signals.