Common Hadoop and Blob Storage Integration Errors

AbstractBy using the stability condition and general formulas developed by Fukushima (1998 = Paper I) we discovered that, just as in the case of the explicit symmetric multistep methods (Quinlan and Tremaine, 1990), when integrating orbital motions of celestial bodies, the implicit symmetric multistep methods used in the predictor-corrector manner lead to integration errors in position which grow linearly with the integration time if the stepsizes adopted are sufficiently small and if the number of corrections is sufficiently large, say two or three. We confirmed also that the symmetric methods (explicit or implicit) would produce the stepsize-dependent instabilities/resonances, which was discovered by A. Toomre in 1991 and confirmed by G.D. Quinlan for some high order explicit methods. Although the implicit methods require twice or more computational time for the same stepsize than the explicit symmetric ones do, they seem to be preferable since they reduce these undesirable features significantly.

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QMC integration errors and quasi-asymptotics

Monte Carlo Methods and Applications ◽

10.1515/mcma-2020-2067 ◽

2020 ◽

Vol 26 (3) ◽

pp. 171-176

Author(s):

Ilya M. Sobol ◽

Boris V. Shukhman

Keyword(s):

Monte Carlo ◽

Error Estimate ◽

Numerical Experiments ◽

Probable Error ◽

Quasi Monte Carlo ◽

Integration Error ◽

Asymptotic Error ◽

Dimensional Cube ◽

Integration Errors ◽

Mc Method

AbstractA crude Monte Carlo (MC) method allows to calculate integrals over a d-dimensional cube. As the number N of integration nodes becomes large, the rate of probable error of the MC method decreases as {O(1/\sqrt{N})}. The use of quasi-random points instead of random points in the MC algorithm converts it to the quasi-Monte Carlo (QMC) method. The asymptotic error estimate of QMC integration of d-dimensional functions contains a multiplier {1/N}. However, the multiplier {(\ln N)^{d}} is also a part of the error estimate, which makes it virtually useless. We have proved that, in the general case, the QMC error estimate is not limited to the factor {1/N}. However, our numerical experiments show that using quasi-random points of Sobol sequences with {N=2^{m}} with natural m makes the integration error approximately proportional to {1/N}. In our numerical experiments, {d\leq 15}, and we used {N\leq 2^{40}} points generated by the SOBOLSEQ16384 code published in 2011. In this code, {d\leq 2^{14}} and {N\leq 2^{63}}.

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Property-based sensitivity analysis: An approach to identify model implementation and integration errors

Environmental Modelling & Software ◽

10.1016/j.envsoft.2021.105013 ◽

2021 ◽

pp. 105013

Author(s):

Takuya Iwanaga ◽

Xifu Sun ◽

Qian Wang ◽

Joseph H.A. Guillaume ◽

Barry F.W. Croke ◽

...

Keyword(s):

Sensitivity Analysis ◽

Integration Errors

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A high-fidelity realization of the Euclid code comparison N-body simulation with Abacus

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/stz634 ◽

2019 ◽

Vol 485 (3) ◽

pp. 3370-3377 ◽

Cited By ~ 8

Author(s):

Lehman H Garrison ◽

Daniel J Eisenstein ◽

Philip A Pinto

Keyword(s):

Power Spectrum ◽

High Performance ◽

High Fidelity ◽

Step Size ◽

Time Step ◽

Code Comparison ◽

Force Accuracy ◽

Integration Errors ◽

Better Than ◽

Good Agreement

Abstract We present a high-fidelity realization of the cosmological N-body simulation from the Schneider et al. code comparison project. The simulation was performed with our AbacusN-body code, which offers high-force accuracy, high performance, and minimal particle integration errors. The simulation consists of 20483 particles in a $500\ h^{-1}\, \mathrm{Mpc}$ box for a particle mass of $1.2\times 10^9\ h^{-1}\, \mathrm{M}_\odot$ with $10\ h^{-1}\, \mathrm{kpc}$ spline softening. Abacus executed 1052 global time-steps to z = 0 in 107 h on one dual-Xeon, dual-GPU node, for a mean rate of 23 million particles per second per step. We find Abacus is in good agreement with Ramses and Pkdgrav3 and less so with Gadget3. We validate our choice of time-step by halving the step size and find sub-percent differences in the power spectrum and 2PCF at nearly all measured scales, with ${\lt }0.3{{\ \rm per\ cent}}$ errors at $k\lt 10\ \mathrm{Mpc}^{-1}\, h$. On large scales, Abacus reproduces linear theory better than 0.01 per cent. Simulation snapshots are available at http://nbody.rc.fas.harvard.edu/public/S2016.

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Elimination of some integration errors in pesticide residue analyses

Analytical Chemistry ◽

10.1021/ac60364a043 ◽

1975 ◽

Vol 47 (14) ◽

pp. 2485-2486 ◽

Cited By ~ 5

Author(s):

J. M. Zehner ◽

R. A. Simonaitis

Keyword(s):

Pesticide Residue ◽

Integration Errors

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Reproducing kernels of Sobolev spaces on ℝd and applications to embedding constants and tractability

Analysis and Applications ◽

10.1142/s0219530518500094 ◽

2018 ◽

Vol 16 (05) ◽

pp. 693-715 ◽

Cited By ~ 2

Author(s):

Erich Novak ◽

Mario Ullrich ◽

Henryk Woźniakowski ◽

Shun Zhang

Keyword(s):

Sobolev Space ◽

Sobolev Spaces ◽

Reproducing Kernel ◽

Absolute Error ◽

Reproducing Kernels ◽

Worst Case ◽

Reproducing Kernel Formula ◽

Positive Integers ◽

Integration Errors ◽

Exponentially Small

The standard Sobolev space [Formula: see text], with arbitrary positive integers [Formula: see text] and [Formula: see text] for which [Formula: see text], has the reproducing kernel [Formula: see text] for all [Formula: see text], where [Formula: see text] are components of [Formula: see text]-variate [Formula: see text], and [Formula: see text] with non-negative integers [Formula: see text]. We obtain a more explicit form for the reproducing kernel [Formula: see text] and find a closed form for the kernel [Formula: see text]. Knowing the form of [Formula: see text], we present applications on the best embedding constants between the Sobolev space [Formula: see text] and [Formula: see text], and on strong polynomial tractability of integration with an arbitrary probability density. We prove that the best embedding constants are exponentially small in [Formula: see text], whereas worst case integration errors of algorithms using [Formula: see text] function values are also exponentially small in [Formula: see text] and decay at least like [Formula: see text]. This yields strong polynomial tractability in the worst case setting for the absolute error criterion.

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Overcoming Time-Integration Errors in SINDA's FWDBCK Solution Routine

10.4271/840953 ◽

1984 ◽

Cited By ~ 2

Author(s):

Joseph T. Skladany ◽

F. A. Costello

Keyword(s):

Time Integration ◽

Integration Errors

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Application of Data Mining Techniques for Improving Continuous Integration

International Journal of Engineering and Management Research ◽

10.31033/ijemr.8.5.4 ◽

2018 ◽

Vol 8 (5) ◽

Author(s):

Meenakshi Kathayat

Keyword(s):

Data Mining ◽

Development Process ◽

Software Development Process ◽

Data Mining Techniques ◽

Useful Knowledge ◽

Continuous Integration ◽

Integration Data ◽

Integration Problems ◽

Work Done ◽

Integration Errors

Continuous integration is a software development process where members of a team frequently integrate the work done by them. Generally each person integrates at least daily - leading to multiple integrations per day. Integration done by each developer is verified by an automated build (including test) to detect integration errors as quickly as possible. Many teams find that this approach reduces integration problems and allows a team to develop cohesive software rapidly. Continuous Integration doesn’t remove bugs, but it does make them dramatically easier to find and remove. This paper provides an overview of various issues regarding Continuous Integration and how various data mining techniques can be applied in continuous integration data for extracting useful knowledge and solving continuousintegration problems.

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