Статті в журналах: "Accurate summation"

1

Rump, Siegfried M. "Ultimately Fast Accurate Summation." SIAM Journal on Scientific Computing 31, no. 5 (January 2009): 3466–502. http://dx.doi.org/10.1137/080738490.

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2

Demmel, James, and Yozo Hida. "Accurate and Efficient Floating Point Summation." SIAM Journal on Scientific Computing 25, no. 4 (January 2004): 1214–48. http://dx.doi.org/10.1137/s1064827502407627.

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3

Cooker, Mark J. "The Accurate Summation of Some Awkward Series." Mathematical Gazette 82, no. 493 (March 1998): 48. http://dx.doi.org/10.2307/3620150.

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4

McNamee, John Michael. "A comparison of methods for accurate summation." ACM SIGSAM Bulletin 38, no. 1 (March 2004): 1–7. http://dx.doi.org/10.1145/980175.980177.

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5

Eisinberg, A., and G. Fedele. "Accurate floating-point summation: a new approach." Applied Mathematics and Computation 189, no. 1 (June 2007): 410–24. http://dx.doi.org/10.1016/j.amc.2006.11.095.

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6

Song, Jiming, and Sidharath Jain. "Midpoint Summation: A Method for Accurate and Efficient Summation of Series Appearing in Electromagnetics." IEEE Antennas and Wireless Propagation Letters 9 (2010): 1084–87. http://dx.doi.org/10.1109/lawp.2010.2091488.

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7

Blanchard, Pierre, Nicholas J. Higham, and Theo Mary. "A Class of Fast and Accurate Summation Algorithms." SIAM Journal on Scientific Computing 42, no. 3 (January 2020): A1541—A1557. http://dx.doi.org/10.1137/19m1257780.

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8

Rump, Siegfried M., Takeshi Ogita, and Shin'ichi Oishi. "Accurate Floating-Point Summation Part I: Faithful Rounding." SIAM Journal on Scientific Computing 31, no. 1 (January 2008): 189–224. http://dx.doi.org/10.1137/050645671.

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9

Lindbo, Dag, and Anna-Karin Tornberg. "Spectrally accurate fast summation for periodic Stokes potentials." Journal of Computational Physics 229, no. 23 (November 2010): 8994–9010. http://dx.doi.org/10.1016/j.jcp.2010.08.026.

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10

Akbari, Hesam, Muhammad Tariq Sadiq, Malih Payan, Somayeh Saraf Esmaili, Hourieh Baghri, and Hamed Bagheri. "Depression Detection Based on Geometrical Features Extracted from SODP Shape of EEG Signals and Binary PSO." Traitement du Signal 38, no. 1 (February 28, 2021): 13–26. http://dx.doi.org/10.18280/ts.380102.

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Late detection of depression is having detrimental consequences including suicide thus there is a serious need for an accurate computer-aided system for early diagnosis of depression. In this research, we suggested a novel strategy for the diagnosis of depression based on several geometric features derived from the Electroencephalography (EEG) signal shape of the second-order differential plot (SODP). First, various geometrical features of normal and depression EEG signals were derived from SODP including standard descriptors, a summation of the angles between consecutive vectors, a summation of distances to coordinate, a summation of the triangle area using three successive points, a summation of the shortest distance from each point relative to the 45-degree line, a summation of the centroids to centroid distance of successive triangles, central tendency measure and summation of successive vector lengths. Second, Binary Particle Swarm Optimization was utilized for the selection of suitable features. At last, the features were fed to support vector machine and k-nearest neighbor (KNN) classifiers for the identification of normal and depressed signals. The performance of the proposed framework was evaluated by the recorded bipolar EEG signals from 22 normal and 22 depressed subjects. The results provide an average classification accuracy of 98.79% with the KNN classifier using city-block distance in a ten-fold cross-validation strategy. The proposed system is accurate and can be used for the early diagnosis of depression. We showed that the proposed geometrical features are better than extracted features in the time, frequency, time-frequency domains as it helps in visual inspection and provide up to 17.56% improvement in classification accuracy in contrast to those features.

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11

GRØNBECH-JENSEN, NIELS. "SUMMATION OF LOGARITHMIC INTERACTIONS IN PERIODIC MEDIA." International Journal of Modern Physics C 07, no. 06 (December 1996): 873–81. http://dx.doi.org/10.1142/s0129183196000727.

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We present a set of expressions for evaluating energies and forces between particles interacting logarithmically in a finite two-dimensional system with periodic boundary conditions. The formalism can be used for fast and accurate, dynamical or Monte Carlo, simulations of interacting line charges or interactions between point and line charges. The expressions are shown to converge to usual computer accuracy (~10–16) by adding only few terms in a single sum of standard trigonometric functions.

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12

Fern�ndez, Francisco M. "Fast and accurate method for summation of divergent series." International Journal of Quantum Chemistry 81, no. 4 (2001): 268–79. http://dx.doi.org/10.1002/1097-461x(2001)81:4<268::aid-qua4>3.0.co;2-w.

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13

Verstraeten, Matthias, Anuschka Liekens, and Gert Desmet. "Accurate determination of extra-column band broadening using peak summation." Journal of Separation Science 35, no. 4 (January 26, 2012): 519–29. http://dx.doi.org/10.1002/jssc.201100771.

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14

Fernández, F. M., and C. G. Diaz. "Accurate summation of the perturbation series for periodic eigenvalue problems." European Physical Journal D 15, no. 1 (July 2001): 41–46. http://dx.doi.org/10.1007/s100530170181.

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15

Huang, Xianyong, Shanhe Wu, and Bicheng Yang. "A More Accurate Half-Discrete Hilbert-Type Inequality Involving One upper Limit Function and One Partial Sum." Symmetry 13, no. 8 (August 23, 2021): 1548. http://dx.doi.org/10.3390/sym13081548.

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In this paper, by virtue of the symmetry principle, we construct proper weight coefficients and use them to establish a more accurate half-discrete Hilbert-type inequality involving one upper limit function and one partial sum. Then, we prove the new inequality with the help of the Euler–Maclaurin summation formula and Abel’s partial summation formula. Finally, we illustrate how the obtained results can generate some new half-discrete Hilbert-type inequalities.

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16

Merzlikin, Dmitrii, and Sergey Fomel. "Analytical path-summation imaging of seismic diffractions." GEOPHYSICS 82, no. 1 (January 1, 2017): S51—S59. http://dx.doi.org/10.1190/geo2016-0140.1.

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Diffraction imaging aims to emphasize small subsurface objects, such as faults, fracture swarms, and channels. Similar to classical reflection imaging, velocity analysis is crucially important for accurate diffraction imaging. Path-summation migration provides an imaging method that produces an image of the subsurface without picking a velocity model. Previous methods of path-summation imaging involve a discrete summation of the images corresponding to all possible migration velocity distributions within a predefined integration range and thus involve a significant computational cost. We have developed a direct analytical formula for path-summation imaging based on the continuous integration of the images along the velocity dimension, which reduces the cost to that of only two fast Fourier transforms. The analytic approach also enabled automatic migration velocity extraction from diffractions using a double path-summation migration framework. Synthetic and field data examples confirm the efficiency of the proposed techniques.

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17

Leung, Shingyu, Jianliang Qian, and Robert Burridge. "Eulerian Gaussian beams for high-frequency wave propagation." GEOPHYSICS 72, no. 5 (September 2007): SM61—SM76. http://dx.doi.org/10.1190/1.2752136.

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We design an Eulerian Gaussian beam summation method for solving Helmholtz equations in the high-frequency regime. The traditional Gaussian beam summation method is based on Lagrangian ray tracing and local ray-centered coordinates. We propose a new Eulerian formulation of Gaussian beam theory which adopts global Cartesian coordinates, level sets, and Liouville equations, yielding uniformly distributed Eulerian traveltimes and amplitudes in phase space simultaneously for multiple sources. The time harmonic wavefield can be constructed by summing up Gaussian beams with ingredients provided by the new Eulerian formulation. The conventional Gaussian beam summation method can be derived from the proposed method. There are three advantages of the new method: (1) We have uniform resolution of ray distribution. (2) We can obtain wavefields excited at different sources by varying only source locations in the summation formula. (3) We can obtain wavefields excited at different frequencies by varying only frequencies in the summation formula. Numerical experiments indicate that the Gaussian beam summation method yields accurate asymptotic wavefields even at caustics. The new method may be used for seismic modeling and migration.

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18

Appelö, Daniel, Gunilla Kreiss, and Siyang Wang. "An Explicit Hermite-Taylor Method for the Schrödinger Equation." Communications in Computational Physics 21, no. 5 (March 27, 2017): 1207–30. http://dx.doi.org/10.4208/cicp.080815.211116a.

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AbstractAn explicit spectrally accurate order-adaptive Hermite-Taylor method for the Schrödinger equation is developed. Numerical experiments illustrating the properties of the method are presented. The method, which is able to use very coarse grids while still retaining high accuracy, compares favorably to an existing exponential integrator – high order summation-by-parts finite difference method.

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19

Liu, Chen Xi, Wei Jin, and Ding Ye. "Study on Integral Summation Algorithm for Measurement of Superfine Scale Based on Fraunhofer Diffraction." Advanced Materials Research 499 (April 2012): 478–81. http://dx.doi.org/10.4028/www.scientific.net/amr.499.478.

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The paper introduces a new method, integral summation algorithm, to measure superfine scale based on Fraunhofer Diffraction. Be different from the traditional method, the paper simulates a series of curve of diffraction luminance distribution on different given size based on Fraunhofer Diffraction theory and researches the closest one to the diffraction curve of unknown slot measured. In order to get more accurate measurement result, the curve is taken by the integral summation algorithm and be compared on the integration area difference instead of comparing the standard deviation. The result shows that the size of given slot is closer to the size of unknown slot than standard deviation method, which somewhat improves the accuracy of the measurement.

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20

Demmel, James, and Yozo Hida. "Fast and Accurate Floating Point Summation with Application to Computational Geometry." Numerical Algorithms 37, no. 1-4 (December 2004): 101–12. http://dx.doi.org/10.1023/b:numa.0000049458.99541.38.

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21

Lindbo, Dag, and Anna-Karin Tornberg. "Fast and spectrally accurate Ewald summation for 2-periodic electrostatic systems." Journal of Chemical Physics 136, no. 16 (April 28, 2012): 164111. http://dx.doi.org/10.1063/1.4704177.

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22

Stenqvist, Björn, and Mikael Lund. "On short-ranged pair-potentials for long-range electrostatics." Physical Chemistry Chemical Physics 21, no. 44 (2019): 24787–92. http://dx.doi.org/10.1039/c9cp03875b.

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23

Khanizadeh, Shahrokh, Deborah Buszard, and Constantinos G. Zarkadas. "Comparison of Three Methods for Calculating Protein Content in Developing Apple Flower Buds." Journal of AOAC INTERNATIONAL 75, no. 4 (July 1, 1992): 734–37. http://dx.doi.org/10.1093/jaoac/75.4.734.

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Abstract Three methods (Kjeldahl, sulfuric acid-hydrogen peroxide, and summation of amino acid content) for determining and calculating the protein content of apple flower buds were compared. Quantitation of protein content based on summation of amino acids appears to be the most accurate method. A new nitrogen:protein conversion factor (5.51) was calculated based on total amino acid analysis. This new conversion factor could replace the conventional 6.25 factor for estimating total protein content of apple flower bud by the Kjeldahl method. However, Kjeldahl is not an accurate method for estimating protein content in apple flower bud tissue, regardless of the conversion factor, and probably would not be a good method for estimation of protein in other plant species.

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24

Kim, Jun, Byung Kim, Minsu Jang, Kyumin Kang, Dae Kim, Byeong-Kwon Ju, and Jinseok Kim. "Wearable Hand Module and Real-Time Tracking Algorithms for Measuring Finger Joint Angles of Different Hand Sizes with High Accuracy Using FBG Strain Sensor." Sensors 20, no. 7 (March 30, 2020): 1921. http://dx.doi.org/10.3390/s20071921.

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This paper presents a wearable hand module which was made of five fiber Bragg grating (FBG) strain sensor and algorithms to achieve high accuracy even when worn on different hand sizes of users. For real-time calculation with high accuracy, FBG strain sensors move continuously according to the size of the hand and the bending of the joint. Representatively, four algorithms were proposed; point strain (PTS), area summation (AREA), proportional summation (PS), and PS/interference (PS/I or PS/I_ α ). For more accurate and efficient assessments, 3D printed hand replica with different finger sizes was adopted and quantitative evaluations were performed for index~little fingers (77 to 117 mm) and thumb (68~78 mm). For index~little fingers, the optimized algorithms were PS and PS/I_ α . For thumb, the optimized algorithms were PS/I_ α and AREA. The average error angle of the wearable hand module was observed to be 0.47 ± 2.51° and mean absolute error (MAE) was achieved at 1.63 ± 1.97°. These results showed that more accurate hand modules than other glove modules applied to different hand sizes can be manufactured using FBG strain sensors which move continuously and algorithms for tracking this movable FBG sensors.

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25

BYATT-SMITH, J. G. B. "Formulation and summation of hyperasymptotic expansions obtained from integrals." European Journal of Applied Mathematics 9, no. 2 (April 1998): 159–85. http://dx.doi.org/10.1017/s0956792597003392.

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Formal hyperasymptotic expansions of integrals are obtained from the Poincaré asymptotic expansion by re-expanding the remainder term. We show that for the integrals under consideration these hyperasymptotic expansions can be made accurate to any desired exponentially-small order.

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26

Graillat, Stef, and Valérie Ménissier-Morain. "Accurate summation, dot product and polynomial evaluation in complex floating point arithmetic." Information and Computation 216 (July 2012): 57–71. http://dx.doi.org/10.1016/j.ic.2011.09.003.

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27

Chu, Chunlei, and Paul L. Stoffa. "Efficient 3D frequency response modeling with spectral accuracy by the rapid expansion method." GEOPHYSICS 77, no. 4 (July 1, 2012): T117—T123. http://dx.doi.org/10.1190/geo2011-0415.1.

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Frequency responses of seismic wave propagation can be obtained either by directly solving the frequency domain wave equations or by transforming the time domain wavefields using the Fourier transform. The former approach requires solving systems of linear equations, which becomes progressively difficult to tackle for larger scale models and for higher frequency components. On the contrary, the latter approach can be efficiently implemented using explicit time integration methods in conjunction with running summations as the computation progresses. Commonly used explicit time integration methods correspond to the truncated Taylor series approximations that can cause significant errors for large time steps. The rapid expansion method (REM) uses the Chebyshev expansion and offers an optimal solution to the second-order-in-time wave equations. When applying the Fourier transform to the time domain wavefield solution computed by the REM, we can derive a frequency response modeling formula that has the same form as the original time domain REM equation but with different summation coefficients. In particular, the summation coefficients for the frequency response modeling formula corresponds to the Fourier transform of those for the time domain modeling equation. As a result, we can directly compute frequency responses from the Chebyshev expansion polynomials rather than the time domain wavefield snapshots as do other time domain frequency response modeling methods. When combined with the pseudospectral method in space, this new frequency response modeling method can produce spectrally accurate results with high efficiency.

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28

Song, Shengli, Rui Jiang, Xieda Song, Yuxuan Cao, and Zhidan Sun. "Driving Performance Assessment Based on Accurate Position Tracking." Wireless Communications and Mobile Computing 2019 (August 8, 2019): 1–8. http://dx.doi.org/10.1155/2019/5256180.

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A driving performance assessment (DPA) system has been proposed in this paper to evaluate drivers’ skills in training. The system is based on centimeter-level localization of the vehicles, thanks to differential BeiDou Navigation Satellite System (BDS). Given a vehicle’s dimensions, its envelopment has been discretized both temporally and spatially as binary images, while the training area is modeled as a grayscale image where the intensity denotes the penalty of the certain area in unit time. The performance index can be obtained from the summation of images along with time. Experiments have been conducted to demonstrate the accuracy of vehicle tracking and the effectiveness of the proposed assessment system.

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29

SUN, HAO, and BARRY B. LEE. "A single mechanism for both luminance and chromatic grating vernier tasks: Evidence from temporal summation." Visual Neuroscience 21, no. 3 (May 2004): 315–20. http://dx.doi.org/10.1017/s0952523804213232.

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Vernier thresholds are determined by luminance rather than chromatic contrast when both are present in vernier targets. The role of luminance and chromatic mechanisms in vernier performance under equiluminant conditions remains uncertain. Temporal summation functions for vernier thresholds with luminance and red–green equiluminant gratings were compared to those for detection thresholds with similar stimuli. Vernier thresholds showed similar temporal summation for luminance and chromatic gratings, which is consistent with a single mechanism underlying vernier performance in the two conditions. However, detection thresholds showed a shorter temporal summation duration for luminance gratings than for chromatic gratings, which suggests that two different mechanisms underlie detection thresholds. Analysis of physiological data supports the hypothesis that the frequency-doubled response of ganglion cells in the magnocellular pathway can provide accurate spatiotemporal information for vernier performance at equiluminance.

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30

Gao, Lin, Fang Chen, Hao Yi Yang, Gao Hua Yan, and Guo Xiu Zhong. "Determination of Cd(II) in Water Samples by Summable Spectrophotometry of Positive-Negative Peaks after Cloud Point Extraction." Advanced Materials Research 573-574 (October 2012): 48–52. http://dx.doi.org/10.4028/www.scientific.net/amr.573-574.48.

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Cadmium has been determined by summable spectrophotometry of positive-negative peaks with cadion and Triton X-114 after cloud point preconcentration. Influence factors on cloud point extraction, color reaction and absorbance were investigated by studying the summation absorbance of color compounds at 480 nm and 570 nm. The sensitivity and absorbance of this method are at least five times higher when compared with that of usual cadion spectrophotometry due to the summation of positive and negative peak. The proposed method is sensitive, simple, accurate and environmentally-friendly in the determination of cadmium in environment water.

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31

Allen, Robert D., Mark S. Beasley, and Bruce C. Branson. "Improving Analytical Procedures: A Case of Using Disaggregate Multilocation Data." AUDITING: A Journal of Practice & Theory 18, no. 2 (September 1, 1999): 128–42. http://dx.doi.org/10.2308/aud.1999.18.2.128.

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According to SAS No. 56, Analytical Procedures, the use of disaggregate, individual location data can improve the effectiveness of analytical procedures used in multilocation audits. Using a case-study approach, we investigate whether improvements in the accuracy and precision of account balance expectations can be obtained by using disaggregate, individual location data in a large, multilocation company. Specifically, we examine two issues: (1) whether the summation of individual location expectations generates more accurate and precise expectations of company-wide account balances than expectations based on company-wide data only and (2) whether the accuracy and precision of analytical procedures is enhanced by including peer location observations of the account balance in individual location expectation models. We find that for the multilocation company examined in this case study the summation of individual location account balance expectations is not more accurate or precise than an expectation derived from aggregate models unless the individual location models include peer location observations of the account balance. When the individual location models include the same account observations from other peer locations within the company, the company-wide account balance expectations developed from disaggregate models are more accurate and precise (less variable) than expectations developed using aggregate, company-wide data only. The results from this case study indicate that when auditors are generating expectations of company-wide balances, disaggregate models incorporating peer location account observations provide account balance expectations that are both more accurate and more precise than company-wide, aggregate models. Given the limitations of a case-study approach, future research should be directed at establishing the generalizability of these findings.

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32

Abakumov, Yu G., M. A. Verhoturova, and E. S. Kogan. "ABOUT ONE PROBLEM OF THE APPROXIMATION THEORY." Vestnik of Samara University. Natural Science Series 18, no. 3.1 (June 7, 2017): 5–13. http://dx.doi.org/10.18287/2541-7525-2012-18-3.1-5-13.

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In the given article the solution of the problem of ﬁnding of accurate constants by methods of summation of Fourier series is considered. The number of results belonging to the constants , the existence of parameters are also set forth.

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33

Grønbech-Jensen, Niels. "Lekner Summation of Long Range Interactions in Periodic Systems." International Journal of Modern Physics C 08, no. 06 (December 1997): 1287–97. http://dx.doi.org/10.1142/s0129183197001144.

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We present a complete set of practical expressions for fast and accurate evaluation of Coulomb interactions, forces and energies, in any rectangular periodic medium. This analysis also includes explicit expressions for energy constants and self-energies of charged particles in periodic lattices. Energy constants and self-energies are further evaluated for logarithmic interactions in two-dimensional rectangular systems with periodic boundary conditions. The expressions are optimized for computational speed and tested by direct numerical implementation.

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34

Tyagi, Sandeep, Axel Arnold, and Christian Holm. "ICMMM2D: An accurate method to include planar dielectric interfaces via image charge summation." Journal of Chemical Physics 127, no. 15 (October 21, 2007): 154723. http://dx.doi.org/10.1063/1.2790428.

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35

MacDonald, D. A. "On the highly accurate summation of certain series occurring in plate contact problems." Mathematics of Computation 66, no. 220 (October 1, 1997): 1619–28. http://dx.doi.org/10.1090/s0025-5718-97-00869-7.

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36

Whitelam, Cameron, and Thirimachos Bourlai. "Accurate eye localization in the Short Waved Infrared Spectrum through summation range filters." Computer Vision and Image Understanding 139 (October 2015): 59–72. http://dx.doi.org/10.1016/j.cviu.2015.05.001.

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37

Lampret, Vito. "Simple accurate balanced asymptotic approximation of Wallis' ratio using Euler-Boole alternating summation." Mathematical Inequalities & Applications, no. 4 (2021): 887–96. http://dx.doi.org/10.7153/mia-2021-24-61.

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38

Fu, Bo, Xiu Xiang Fan, Qiong Cheng, Li Li, Bo Li, and Guo Jun Zhang. "Accurate Computation of Zernike Moments in Cartesian Coordinates." Applied Mechanics and Materials 195-196 (August 2012): 615–19. http://dx.doi.org/10.4028/www.scientific.net/amm.195-196.615.

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In this paper, a novel algorithm is proposed to accurately calculate Zernike moments in Cartesian Coordinates. We connect the corners of an image pixel with the origin to construct four triangles and then assign the intensity function value of the pixel to these triangles. The Fourier Mellin moment integration of the pixel is converted to a summation of four integrations within domains of these constructed triangles. By using the trigonometric resolution, we derive the analytic equations of the four integrations of these triangles. Then, the analytic expressions of the Fourier Mellin moments and Zernike moments are obtained. The algorithm eliminates the geometric and discretization errors theoretically. Finally, a set of efficient computational recursive relations is proposed. An experiment is designed to verify the performance of the proposed algorithm.

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39

Zhou, J., E. Pan, and M. Bevis. "A point dislocation in a layered, transversely isotropic and self-gravitating Earth — Part II: accurate Green's functions." Geophysical Journal International 219, no. 3 (August 29, 2019): 1717–28. http://dx.doi.org/10.1093/gji/ggz392.

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SUMMARY We present an accurate approach for calculating the point-dislocation Green's functions (GFs) for a layered, spherical, transversely-isotropic and self-gravitating Earth. The formalism is based on the approach recently used to find analytical solutions for the dislocation Love numbers (DLNs). However, in order to make use of the DLNs, we first analyse their asymptotic behaviour, and then the behaviour of the GFs computed from the DLNs. We note that the summations used for different GF components evolve at different rates towards asymptotic convergence, requiring us to use two new and different truncation values for the harmonic degree (i.e. the index of summation). We exploit this knowledge to design a Kummer transformation that allows us to reduce the computation required to evaluate the GFs at the desired level of accuracy. Numerical examples are presented to clarify these issues and demonstrate the advantages of our approach. Even with the Kummer transformation, DLNs of high degree are still needed when the earth model contains very fine layers, so computational efficiency is important. The effect of anisotropy is assessed by comparing GFs for isotropic and transversely isotropic media. It is shown that this effect, though normally modest, can be significant in certain contexts, even in the far field.

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40

Hurth, A. "Spatial Acuity of the Nociceptive System and Spatial Summation of Pain: Potential Implications for the Clinic." Douleur et Analgésie 34, no. 4 (October 4, 2021): 260–63. http://dx.doi.org/10.3166/dea-2021-0170.

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Previous studies investigating spatial acuity measured by two-point discrimination threshold concluded that the nociceptive system is less accurate than the innocuous tactile system. In the discussed article, the authors point out that the nociceptive system is more accurate than the tactile system when controlling for the stimulus modality and intensity in healthy pain-free individuals. Furthermore, this article shows that the pattern of distance-based and areabased spatial summation of pain is modality independent.

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41

SHAH, ARVIND, and ABDEL-RAHMAN MAHMOUD. "COMPUTATIONAL METHODS FOR GUIDED ULTRASONIC WAVES IN PLATES." International Journal of Computational Methods 03, no. 01 (March 2006): 35–55. http://dx.doi.org/10.1142/s0219876206000576.

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Reducing the general problem of computing three-dimensional Green's function in a transversely isotropic plate to a finite summation of contributions from a series of planar problems can efficiently yield an accurate solution. Hence, solving the planar scattering problem, of the Pressure-Shear-Vertical (PSV) type or the Shear-Horizontal (SH) type, was performed by three different techniques: The boundary element method; the hybrid method; and the perfectly matched layer method. In the pursuit of these methods, the objective was to highlight their pros and cons in terms of accuracy and efficiency.

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Popov, Mikhail M., Nikolay M. Semtchenok, Peter M. Popov, and Arie R. Verdel. "Depth migration by the Gaussian beam summation method." GEOPHYSICS 75, no. 2 (March 2010): S81—S93. http://dx.doi.org/10.1190/1.3361651.

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Seismic depth migration aims to produce an image of seismic reflection interfaces. Ray methods are suitable for subsurface target-oriented imaging and are less costly compared to two-way wave-equation-based migration, but break down in cases when a complex velocity structure gives rise to the appearance of caustics. Ray methods also have difficulties in correctly handling the different branches of the wavefront that result from wave propagation through a caustic. On the other hand, migration methods based on the two-way wave equation, referred to as reverse-time migration, are known to be capable of dealing with these problems. However, they are very expensive, especially in the 3D case. It can be prohibitive if many iterations are needed, such as for velocity-model building. Our method relies on the calculation of the Green functions for the classical wave equation by per-forming a summation of Gaussian beams for the direct and back-propagated wavefields. The subsurface image is obtained by cal-culating the coherence between the direct and backpropagated wavefields. To a large extent, our method combines the advantages of the high computational speed of ray-based migration with the high accuracy of reverse-time wave-equation migration because it can overcome problems with caustics, handle all arrivals, yield good images of steep flanks, and is readily extendible to target-oriented implementation. We have demonstrated the quality of our method with several state-of-the-art benchmark subsurface models, which have velocity variations up to a high degree of complexity. Our algorithm is especially suited for efficient imaging of selected subsurface subdomains, which is a large advantage particularly for 3D imaging and velocity-model refinement applications such as subsalt velocity-model improvement. Because our method is also capable of providing highly accurate migration results in structurally complex subsurface settings, we have also included the concept of true-amplitude imaging in our migration technique.

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Arnold, Axel, and Christian Holm. "MMM2D: A fast and accurate summation method for electrostatic interactions in 2D slab geometries." Computer Physics Communications 148, no. 3 (November 2002): 327–48. http://dx.doi.org/10.1016/s0010-4655(02)00586-6.

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Rump, Siegfried M., Takeshi Ogita, and Shin'ichi Oishi. "Accurate Floating-Point Summation Part II: Sign, K-Fold Faithful and Rounding to Nearest." SIAM Journal on Scientific Computing 31, no. 2 (January 2009): 1269–302. http://dx.doi.org/10.1137/07068816x.

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LEVENDORSKIĬ, SERGEI. "EFFICIENT PRICING AND RELIABLE CALIBRATION IN THE HESTON MODEL." International Journal of Theoretical and Applied Finance 15, no. 07 (November 2012): 1250050. http://dx.doi.org/10.1142/s0219024912500501.

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We suggest a general scheme for improvement of FT-pricing formulas for European options and give efficient recommendations for the choice of the parameters of the numerical scheme, which allow for very accurate and fast calculations. The efficiency of the method stems from the properties of functions analytical in a strip, which were introduced to finance by Feng and Linetsky (2008). We demonstrate that an indiscriminate choice of parameters of a numerical scheme leads to an inaccurate pricing and calibration. As applications, we consider the Heston model and its generalization. For many parameter sets documented in empirical studies of financial markets, relative accuracy better than 0.01% can be achieved by summation of less than 10-20 terms even in the situations in which the standard approach requires more than 200. In some cases, the one-term formula produces an error of several percent, and the summation of two terms — less than 0.5%. Typically, 10 terms and fewer suffice to achieve the error tolerance of several percent and smaller.

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Slominski, Tara N., Jennifer L. Momsen, and Lisa M. Montplaisir. "Drawing on student knowledge of neuroanatomy and neurophysiology." Advances in Physiology Education 41, no. 2 (June 1, 2017): 212–21. http://dx.doi.org/10.1152/advan.00129.2016.

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Drawings are an underutilized assessment format in Human Anatomy and Physiology (HA&P), despite their potential to reveal student content understanding and alternative conceptions. This study used student-generated drawings to explore student knowledge in a HA&P course. The drawing tasks in this study focused on chemical synapses between neurons, an abstract concept in HA&P. Using two preinstruction drawing tasks, students were asked to depict synaptic transmission and summation. In response to the first drawing task, 20% of students ( n = 352) created accurate representations of neuron anatomy. The remaining students created drawings suggesting an inaccurate or incomplete understanding of synaptic transmission. Of the 208 inaccurate student-generated drawings, 21% depicted the neurons as touching. When asked to illustrate summation, only 10 students (roughly 4%) were able to produce an accurate drawing. Overall, students were more successful at drawing anatomy (synapse) than physiology (summation) before formal instruction. The common errors observed in student-generated drawings indicate students do not enter the classroom as blank slates. The error of “touching” neurons in a chemical synapse suggests that students may be using intuitive or experiential knowledge when reasoning about physiological concepts. These results 1) support the utility of drawing tasks as a tool to reveal student content knowledge about neuroanatomy and neurophysiology; and 2) suggest students enter the classroom with better knowledge of anatomy than physiology. Collectively, the findings from this study inform both practitioners and researchers about the prevalence and nature of student difficulties in HA&P, while also demonstrating the utility of drawing in revealing student knowledge.

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Banitt, Yoav, Kevan A. C. Martin, and Idan Segev. "Depressed Responses of Facilitatory Synapses." Journal of Neurophysiology 94, no. 1 (July 2005): 865–70. http://dx.doi.org/10.1152/jn.00689.2004.

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We show that when temporal summation takes place, depression of postsynaptic responses may ensue when the underlying synaptic conductance change is constant or even facilitatory. We term this phenomenon “apparent depression.” Such apparent depression is most notable for slow synaptic conductance changes, for high frequency, and when the synapse is located at distal dendritic sites. We show that, when temporal summation ensues, the erroneous estimation of short-term synaptic plasticity arises partially from the conventional measurement of synaptic dynamics at postsynaptic potential peak time. This can be corrected when measuring overlapping synaptic responses at fixed intervals after stimulus time. Somatic voltage clamp also helps to partially correct for the apparent depression, but a good model of the neuron can do even better in providing a more accurate view of the underlying synaptic conductances.

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Petersen, Michael S., Martin D. Weinberg, and Neal Katz. "exp: N-body integration using basis function expansions." Monthly Notices of the Royal Astronomical Society 510, no. 4 (January 8, 2022): 6201–17. http://dx.doi.org/10.1093/mnras/stab3639.

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ABSTRACT We present the N-body simulation techniques implemented in the exp code. exp uses empirically chosen basis functions to expand the potential field of an ensemble of particles. Unlike other basis function expansions, the derived basis functions are adapted to an input mass distribution, enabling accurate expansion of highly non-spherical objects, such as Galactic discs. We measure the force accuracy in three models, one based on a spherical or aspherical halo, one based on an exponential disc, and one based on a bar-based disc model. We find that exp is as accurate as a direct-summation or tree-based calculation, and in some ways is better, while being considerably less computationally intensive. We discuss optimizing the computation of the basis function representation. We also detail numerical improvements for performing orbit integrations, including time-steps.

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Jain, Sidharath, and Ji-Ming Song. "EFFICIENT AND ACCURATE APPROXIMATION OF INFINITE SERIES SUMMATION USING ASYMPTOTIC APPROXIMATION AND FAST CONVERGENT SERIES." Progress In Electromagnetics Research M 22 (2012): 191–203. http://dx.doi.org/10.2528/pierm11100810.

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Wennberg, Christian L., Teemu Murtola, Szilárd Páll, Mark J. Abraham, Berk Hess, and Erik Lindahl. "Direct-Space Corrections Enable Fast and Accurate Lorentz–Berthelot Combination Rule Lennard-Jones Lattice Summation." Journal of Chemical Theory and Computation 11, no. 12 (November 20, 2015): 5737–46. http://dx.doi.org/10.1021/acs.jctc.5b00726.

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