In this article, we present a cost-benefit analysis of the approximation in tensor products of Hilbert spaces of Sobolev-analytic type. The Sobolev part is defined on a finite dimensional domain, whereas the analytica...
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Algebraic multigrid (AMG) methods for directly solving coupled systems of partial differential equations (PDEs) have been extensively used in various types of numerical simulations in engineering. A necessary conditio...
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The use of biomarkers is becoming increasingly integral to to the contemporary practice of medicine and continues to play a central role in preventive, predictive and personalized medicine. However, the limited number...
The use of biomarkers is becoming increasingly integral to to the contemporary practice of medicine and continues to play a central role in preventive, predictive and personalized medicine. However, the limited number of FDA-approved, in use biomarkers, on one hand, and an increasing number of published potential biomarkers, on the other hand, calls for an accelerated approach to translating biomarker research to clinical application. In this talk, I introduce novel concept of "Biomarker-guided Mechanism Discovery" through an integrative disease modeling approach and present the successful application of this methodology to deciphering the network model of genomic hormone interactions underlying dementia and its translational validation through serendipitous off-target effect. Moreover, the current challenges in biomarker discovery is discussed and results of our proposed Biomarker Ontology in collaboration with pharma industry will be presented.
The original online version of this article (Randrianarivony, M. (June 2014) On DFT Molecular Simulation for Non-Adaptive Kernel Approximation. Advances in Materials Physics and Chemistry, Vol. 4 No. 6, 105-115. http:...
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The original online version of this article (Randrianarivony, M. (June 2014) On DFT Molecular Simulation for Non-Adaptive Kernel Approximation. Advances in Materials Physics and Chemistry, Vol. 4 No. 6, 105-115. http://***/10.4236/ampc.2014.46013) did not contain any acknowledgment. The author wishes to add the following acknowledgements: Acknowledgements: This work was partially supported by Eurostars Project E!6935 funded by German Federal Ministry of Education and Research.
Quantum energies which are used in applications are usually composed of repulsive and attractive terms. The objective of this study is to use an accurate and efficient fitting of the repulsive energy instead of using ...
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Quantum energies which are used in applications are usually composed of repulsive and attractive terms. The objective of this study is to use an accurate and efficient fitting of the repulsive energy instead of using standard parametrizations. The investigation is based on Density Functional Theory and Tight Binding simulations. Our objective is not only to capture the values of the repulsive terms but also to efficiently reproduce the elastic properties and the forces. The elasticity values determine the rigidity of a material when some traction or load is applied on it. The pair-potential is based on an exponential term corrected by B-spline terms. In order to accelerate the computations, one uses a hierarchical optimization for the B-splines on different levels. Carbon graphenes constitute the configurations used in the simulations. We report on some results to show the efficiency of the B-splines on different levels.
In this paper, we present an algorithm for trigonometric interpolation of multivariate functions on generalized sparse grids and study its application for the approximation of functions in periodic Sobolev spaces of d...
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Robust optimization determines how the input variables dispersion is propagated on the output variables. This is of great practical relevance: For example, the quality of a product is influenced decisively by producti...
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ISBN:
(纸本)9789609999465
Robust optimization determines how the input variables dispersion is propagated on the output variables. This is of great practical relevance: For example, the quality of a product is influenced decisively by production tolerances. In industrial applications it is important to characterize the range of variation with appropriate measures. The industry is particularly interested in accurate limits of the output distribution or its centered part. In this article the mathematical characterization of robustness is discussed under the viewpoint of its practical applicability. It is shown, that the usually used robustness measures mean for central tendency and standard deviation for dispersion produce inaccurate limits. Instead several measures based on quantiles are proposed. The median is used as measure of central tendency while different quantile ranges are used as measure of dispersion. They are compared for the robust optimization of mathematical functions and industrial applications. The advantages of the quantile measures are pointed out. The computation of quantiles is expensive, because it needs many function evaluations. Due to their long runtime only a few simulations can be executed in practice. A methodology tailored to this situation is proposed. It is based on the use of metamodels. Starting with a few real simulations a metamodel for the system is build. Further ones for median and dispersion of the output variables are derived from it. This enables the user to perform a full multicriteria robust optimization on the whole parameter range. The methodology takes the tolerances of the metamodels into account. A new measure for the tolerance of metamodels which are derived from metamodels is presented. It is used to estimate the accuracy of the quantile models. The tolerance can easily be integrated in the robust optimization process.
Quantum energies which are used in applications are usually composed of repulsive and attractive terms. The objective of this study is to use an accurate and efficient fitting of the repulsive energy instead of using ...
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Quantum energies which are used in applications are usually composed of repulsive and attractive terms. The objective of this study is to use an accurate and efficient fitting of the repulsive energy instead of using standard parametrizations. The investigation is based on Density Functional Theory and Tight Binding simulations. Our objective is not only to capture the values of the repulsive terms but also to efficiently reproduce the elastic properties and the forces. The elasticity values determine the rigidity of a material when some traction or load is applied on it. The pair-potential is based on an exponential term corrected by B-spline terms. In order to accelerate the computations, one uses a hierarchical optimization for the B-splines on different levels. Carbon graphenes constitute the configurations used in the simulations. We report on some results to show the efficiency of the B-splines on different levels.
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