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Integral of Two-dimensional Fine-computable Functions
2008
Electronical Notes in Theoretical Computer Science
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We discuss effective integrability and effectivization of Fubini's Theorem for a Fine-computable function F (x, y) on the upper-right open unit square. ...
The core objective is Fine-computability of f (x) = R [0,1) F (x, y)dy as a function on [0, 1). ...
In Section 3, we define the two-dimensional Fine-space and notions of Finecomputability and prove that f (x) is uniformly Fine-computable if F (x, y) is uniformly Fine-computable (Theorem 3.6). ...
doi:10.1016/j.entcs.2008.12.013
fatcat:7alh666ikbcjvdygbmqlf56wrm
Dimension reduction in heterogeneous neural networks: Generalized Polynomial Chaos (gPC) and ANalysis-Of-VAriance (ANOVA)
2016
The European Physical Journal Special Topics
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2016 pre-print arXiv:1603.06643v1 fatcat:kvhlyc4h5bdo5hro2bfgx4ve5a
We propose, and illustrate via a neural network example, two different approaches to coarse-graining large heterogeneous networks. ...
The hospitality and support of the Institute for Advanced Study at the T. U. Muenchen, where I.G.K was a Hans Fischer Senior Fellow, and C.L. a visitor is gratefully acknowledged. ...
Then the integral of a high-dimensional function is represented by the integral of a series of low-order functions, which can be easily computed by standard numerical integration techniques. ...
doi:10.1140/epjst/e2016-02662-3
fatcat:wqyjejnaajbk3cylwrhzm4j7om
Fast visualization of volume emissions using conservative subdivision
2004
Mathematics and Computers in Simulation
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A sparse hierarchical wavelet-based representation of the directional volume emission rate function is constructed top-down and then projected onto the image plane. ...
The algorithm is especially well suited when the directional volume emission rate is computationally expensive to evaluate, since the sparse representation minimizes the number of function evaluations ...
Acknowledgements I thank Timothy Sergienko for helping me understand the nomenclature of radiometry. ...
doi:10.1016/j.matcom.2003.11.015
fatcat:izgloqm7krhuzkjufoj7qj3j5m
Multigrid High Order Mesh Refinement Techniques
[article]
1998
arXiv
pre-print
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Applications for all electron quantum chemical computations are discussed. ...
A method for performing high order mesh refinement multigrid computations is presented. ...
I would like to acknowledge the support of NSF grant CHE-9632309. ...
arXiv:physics/9805025v2
fatcat:lky3gqhbxfgsbjjeaycd5zpqte
Multiscale enrichment based on partition of unity for nonperiodic fields and nonlinear problems
2006
Computational Mechanics
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MEPU is aimed at extending the range of applicability of the mathematical homogenization theory to nonlinear nonperiodic systems with inseparable fine and coarse scales. ...
We present a generalization of the Multiscale Enrichment based on Partition of Unity (MEPU) formulation originally reported in [1] to account for boundary layers, nonperiodic fields and nonlinear systems ...
Predict the fine scale strain increment using the influence functions computed from the previous time step Use one of the standard stress integration procedures compute the fine scale stress Corrector ...
doi:10.1007/s00466-006-0095-0
fatcat:3gc7dujkdbd3pahcsklhw7qidq
Page 8270 of Mathematical Reviews Vol. , Issue 2001K
[page]
2001
Mathematical Reviews
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The authors show that (not surprisingly) in both the one- and two-dimensional cases, the least ky occurs when the roots of unity are computed by “direct call”, i.e., by making N/2 calls to library routines ...
A projection-iteration algorithm is constructed for a weakly non- linear integral equation of the second kind with some additional integral restrictions for the sought-for function. ...
Modeling multiscale diffusion processes in random heterogeneous media
2008
Computer Methods in Applied Mechanics and Engineering
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A data-driven approach coupled with a non-linear dimension reduction algorithm is used to construct a low-dimensional stochastic descriptor of the fine-scale variation of the stochastic conductivity. ...
Incomplete characterization of the fine-scale variation necessitates posing the thermal conductivity as a stochastic multiscale random field. ...
The computing was conducted using the resources of the Cornell Center for Advanced Computing.
Temperature Probability distribution function ...
doi:10.1016/j.cma.2008.03.020
fatcat:5ibcl6fpvvaslgwc6l75pk7i5e
Unifying via conformal mapping coarse-mesh neutron diffusion calculations in Cartesian and hexagonal geometries
1995
Journal of Computational and Applied Mathematics
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Thus applications to the two different geometries can be unified in a single nodal code. ...
Modern design methodology for nuclear reactor core designs performs routinely three-dimensional core modeling. ...
Thus the three-dimensional computation time in this approach is determined by the speed of performing the calculation for the three-dimensional global smooth nodal solution. ...
doi:10.1016/0377-0427(95)00090-9
fatcat:sfarxhdft5hpfcagnb3jyn2onq
Accuracy of Determining Stress Intensity Factors in Some Numerical Programs
2001
Acta Polytechnica
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Further numerical computations of the MARC program and analytical solutions of stress intensity factors were included to compare the results with each other. ...
The influence of mesh fineness on the results was also investigated in all programs. The distributions of the stress intensity factors show good agreement in quality. ...
Franc2d (two-dimensional FRActure ANalysis Code) is based on the finite element method and enables analyses of two-dimensional problems with arbitrary component and crack geometries. ...
doaj:416e60cff6a34fa58085b7c3c90b8dc4
fatcat:fxjcdo2vwja3nbgjxwnxy4aj5e
Page 83 of Journal of Aircraft Vol. 12, Issue 2
[page]
1975
Journal of Aircraft
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And before the computations reach the sec- tion of no boundary layer, the radius a(t) may change rapidly (for such a closed-ended body as the ellipsoid) such that very fine integration meshes are required ...
These results may be fortuitous since the implication is that the separation of a three dimensional (probably) turbulent boundary layer is describable by a two- dimensional unsteady laminar boundary layer ...
AMR on the CM-2
1994
Applied Numerical Mathematics
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We develop a data layout scheme that preserves locality even for communication between fine and coarse grids.On 8K of a 32K machine we achieve performance slightly less than 1 CPU of the Cray Y-MP. ...
Y We describe the development of a structured adaptive mesh algorithm (AMR) for the CM-2. ...
It is a pleasure to acknowledge discussions with Scott Baden, Yanmin Sun, and Steve Hammond during the course of this work. M. ...
doi:10.1016/0168-9274(94)90028-0
fatcat:grtzwtjfbfcyhckijnn7kdwyhm
From CDF to PDF --- A Density Estimation Method for High Dimensional Data
[article]
2018
arXiv
pre-print
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Experiments of this method for one-dimensional data shows promising results. ...
CDF2PDF is a method of PDF estimation by approximating CDF. The original idea of it was previously proposed in [1] called SIC. ...
However, the integration part of this method suffers from the difficulty of numerical integration for high dimensional data. ...
arXiv:1804.05316v1
fatcat:aosic7rk6bgcdns3rpemecwama
Fast and Accurate Calculation of a Computationally Intensive Statistic for Mapping Disease Genes
2009
Journal of Computational Biology
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The new method is shown to require far fewer function evaluations compared to the alternatives while matching or exceeding the best of them in terms of accuracy. ...
Many statistical methods in biology utilize numerical integration in order to deal with moderately high-dimensional parameter spaces without closed form integrals. ...
Thus the calculation of the BR is now divided into two separate integrations: the one-dimensional integration corresponds to the inner-most layer of our three-layer scheme, and any function evaluation ...
doi:10.1089/cmb.2008.0175
pmid:19432537
pmcid:PMC3148122
fatcat:bjqarg3s4feytfdpt5qwicmi3y
Page 1286 of American Society of Civil Engineers. Collected Journals Vol. 116, Issue HY11
[page]
1990
American Society of Civil Engineers. Collected Journals
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Individual differences between measured and two-dimensional computed depth-integrated transport rates are also 25% or less in the shallow part of the stream tube. ...
CONCLUSIONS
Detailed flow-velocity and sediment-concentration measurements were performed in a tidal channel with a fine sand bed (Ds. = 200 to 300 ym) to verify two-dimensional vertical and three-dimensional ...
Error Estimation and Grid Adaptation Using Euler Adjoint Method
2006
Journal of Aircraft
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. | for two- dimensional triangle cells and three-dimensional tetrahedral cells. ...
The error in an integral output functional of interest is estimated by a dot product of the residual error and adjoint variable vector. ...
doi:10.2514/1.19603
fatcat:wjonq25od5ghjbqmnenzunhdkq
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