The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform
Volker Schulz - One of the best experts on this subject based on the ideXlab platform.
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tensor product method for fast solution of optimal control problems with fractional multidimensional laplacian in constraints
Journal of Computational Physics, 2021Co-Authors: Gennadij Heidel, Boris N Khoromskij, Venera Khoromskaia, Volker SchulzAbstract:Abstract We introduce the tensor numerical method for solution of the d-dimensional optimal control problems ( d = 2 , 3 ) with spectral fractional Laplacian type operators in constraints discretized on large n ⊗ d tensor-product Cartesian grids. The approach is based on the rank-Structured approximation of the matrix valued functions of the corresponding fractional finite difference Laplacian. We solve the equation for the control function, where the system matrix includes the sum of the spectral fractional d-dimensional Laplacian and its inverse. The matrix valued functions of discrete Laplace operator on a tensor grid are diagonalized by using the fast Fourier transform (FFT). Then the low rank approximation of the d-dimensional tensors obtained by folding of the corresponding large diagonal matrices of eigenvalues are computed, which allows to solve the governing equation for the control function in a tensor-Structured Format. The existence of low rank canonical approximation to the class of matrix valued functions involved is justified by using the sinc quadrature approximation method applied to the Laplace transform of the generating function. The linear system of equations for the control function is solved by the PCG iterative method with the rank truncation at each iteration step, where the low Kronecker rank preconditioner is pre-computed. The right-hand side, the solution vector, and the governing system matrix are maintained in the rank-Structured tensor Format which beneficially reduces the numerical cost to O ( n log n ) , outperforming the standard FFT based methods of complexity O ( n 3 log n ) for 3D case. Numerical tests for the 2D and 3D control problems confirm the linear complexity scaling of the method in the univariate grid size n.
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tensor method for optimal control problems constrained by fractional 3d elliptic operator with variable coefficients
arXiv: Numerical Analysis, 2020Co-Authors: Britta Schmitt, Boris N Khoromskij, Venera Khoromskaia, Volker SchulzAbstract:We introduce the tensor numerical method for solving optimal control problems that are constrained by fractional 2D and 3D elliptic operators with variable coefficients. We solve the governing equation for the control function which includes a sum of the fractional operator and its inverse, both discretized over large 3D $n\times n \times n$ spacial grids. Using the diagonalization of the arising matrix valued functions in the eigenbasis of the 1D Sturm-Liouville operators, we construct the rank-Structured tensor approximation with controllable precision for the discretized fractional elliptic operators and the respective preconditioner. The right-hand side in the constraining equation (the optimal design function) is supposed to be represented in a form of a low-rank canonical tensor. Then the equation for the control function is solved in a tensor Structured Format by using preconditioned CG iteration with the adaptive rank truncation procedure that also ensures the accuracy of calculations, given an $\varepsilon$-threshold. This method reduces the numerical cost for solving the control problem to $O(n \log n)$ (plus the quadratic term $O(n^2)$ with a small weight), which is superior to the approaches based on the traditional linear algebra tools that yield at least $O(n^3 \log n)$ complexity in the 3D case. The storage for the representation of all 3D nonlocal operators and functions involved is also estimated by $O(n \log n)$. This essentially outperforms the traditional methods operating with fully populated $n^3 \times n^3$ matrices and vectors in $\mathbb{R}^{n^3}$. Numerical tests for 2D/3D control problems indicate the almost linear complexity scaling of the rank truncated PCG iteration in the univariate grid size $n$.
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tensor product method for fast solution of optimal control problems with fractional multidimensional laplacian in constraints
arXiv: Numerical Analysis, 2018Co-Authors: Gennadij Heidel, Boris N Khoromskij, Venera Khoromskaia, Volker SchulzAbstract:We introduce the tensor numerical method for solution of the $d$-dimensional optimal control problems with fractional Laplacian type operators in constraints discretized on large $n^{\otimes d}$ tensor-product Cartesian grids. The approach is based on the rank-Structured approximation of the matrix valued functions of the corresponding fractional finite difference Laplacian. We solve the equation for the control function, where the system matrix includes the sum of the fractional $d$-dimensional Laplacian and its inverse. The matrix valued functions of discrete Laplace operator on a tensor grid are diagonalized by using the fast Fourier transform (FFT). Then the low rank approximation of the $d$-dimensional tensors obtained by folding of the corresponding large diagonal matrices of eigenvalues are computed, which allows to solve the governing equation for the control function in a tensor-Structured Format. The existence of low rank canonical approximation to the class of matrix valued functions involved is justified by using the sinc quadrature approximation method applied to the Laplace transform of the generating function. The linear system of equations for the control function is solved by the PCG iterative method with the rank truncation at each iteration step, where the low Kronecker rank preconditioner is precomputed. The right-hand side, the solution vector, and the governing system matrix are maintained in the rank-Structured tensor Format which beneficially reduces the numerical cost to $O(n\log n)$, outperforming the standard FFT based methods of complexity $O(n^3\log n)$ for 3D case. Numerical tests for the 2D and 3D control problems confirm the linear complexity scaling of the method in the univariate grid size $n$.
D Cibula - One of the best experts on this subject based on the ideXlab platform.
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european society of gynaecological oncology quality indicators for surgical treatment of cervical cancer
International Journal of Gynecological Cancer, 2020Co-Authors: D Cibula, Francois Planchamp, D Fischerova, Christina Fotopoulou, Christhardt Kohler, Fabio Landoni, Patrice Mathevet, Raj Naik, Jordi PonceAbstract:Background Optimizing and ensuring the quality of surgical care is essential to improve the management and outcome of patients with cervical cancer. To develop a list of quality indicators for surgical treatment of cervical cancer that can be used to audit and improve clinical practice. Methods Quality indicators were developed using a four-step evaluation process that included a systematic literature search to identify potential quality indicators, in-person meetings of an ad hoc group of international experts, an internal validation process, and external review by a large panel of European clinicians and patient representatives. Results Fifteen structural, process, and outcome indicators were selected. Using a Structured Format, each quality indicator has a description specifying what the indicator is measuring. Measurability specifications are also detailed to define how the indicator will be measured in practice. Each indicator has a target which gives practitioners and health administrators a quantitative basis for improving care and organizational processes. Discussion Implementation of institutional quality assurance programs can improve quality of care, even in high-volume centers. This set of quality indicators from the European Society of Gynaecological Cancer may be a major instrument to improve the quality of surgical treatment of cervical cancer.
Boris N Khoromskij - One of the best experts on this subject based on the ideXlab platform.
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tensor product method for fast solution of optimal control problems with fractional multidimensional laplacian in constraints
Journal of Computational Physics, 2021Co-Authors: Gennadij Heidel, Boris N Khoromskij, Venera Khoromskaia, Volker SchulzAbstract:Abstract We introduce the tensor numerical method for solution of the d-dimensional optimal control problems ( d = 2 , 3 ) with spectral fractional Laplacian type operators in constraints discretized on large n ⊗ d tensor-product Cartesian grids. The approach is based on the rank-Structured approximation of the matrix valued functions of the corresponding fractional finite difference Laplacian. We solve the equation for the control function, where the system matrix includes the sum of the spectral fractional d-dimensional Laplacian and its inverse. The matrix valued functions of discrete Laplace operator on a tensor grid are diagonalized by using the fast Fourier transform (FFT). Then the low rank approximation of the d-dimensional tensors obtained by folding of the corresponding large diagonal matrices of eigenvalues are computed, which allows to solve the governing equation for the control function in a tensor-Structured Format. The existence of low rank canonical approximation to the class of matrix valued functions involved is justified by using the sinc quadrature approximation method applied to the Laplace transform of the generating function. The linear system of equations for the control function is solved by the PCG iterative method with the rank truncation at each iteration step, where the low Kronecker rank preconditioner is pre-computed. The right-hand side, the solution vector, and the governing system matrix are maintained in the rank-Structured tensor Format which beneficially reduces the numerical cost to O ( n log n ) , outperforming the standard FFT based methods of complexity O ( n 3 log n ) for 3D case. Numerical tests for the 2D and 3D control problems confirm the linear complexity scaling of the method in the univariate grid size n.
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tensor method for optimal control problems constrained by fractional 3d elliptic operator with variable coefficients
arXiv: Numerical Analysis, 2020Co-Authors: Britta Schmitt, Boris N Khoromskij, Venera Khoromskaia, Volker SchulzAbstract:We introduce the tensor numerical method for solving optimal control problems that are constrained by fractional 2D and 3D elliptic operators with variable coefficients. We solve the governing equation for the control function which includes a sum of the fractional operator and its inverse, both discretized over large 3D $n\times n \times n$ spacial grids. Using the diagonalization of the arising matrix valued functions in the eigenbasis of the 1D Sturm-Liouville operators, we construct the rank-Structured tensor approximation with controllable precision for the discretized fractional elliptic operators and the respective preconditioner. The right-hand side in the constraining equation (the optimal design function) is supposed to be represented in a form of a low-rank canonical tensor. Then the equation for the control function is solved in a tensor Structured Format by using preconditioned CG iteration with the adaptive rank truncation procedure that also ensures the accuracy of calculations, given an $\varepsilon$-threshold. This method reduces the numerical cost for solving the control problem to $O(n \log n)$ (plus the quadratic term $O(n^2)$ with a small weight), which is superior to the approaches based on the traditional linear algebra tools that yield at least $O(n^3 \log n)$ complexity in the 3D case. The storage for the representation of all 3D nonlocal operators and functions involved is also estimated by $O(n \log n)$. This essentially outperforms the traditional methods operating with fully populated $n^3 \times n^3$ matrices and vectors in $\mathbb{R}^{n^3}$. Numerical tests for 2D/3D control problems indicate the almost linear complexity scaling of the rank truncated PCG iteration in the univariate grid size $n$.
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tensor product method for fast solution of optimal control problems with fractional multidimensional laplacian in constraints
arXiv: Numerical Analysis, 2018Co-Authors: Gennadij Heidel, Boris N Khoromskij, Venera Khoromskaia, Volker SchulzAbstract:We introduce the tensor numerical method for solution of the $d$-dimensional optimal control problems with fractional Laplacian type operators in constraints discretized on large $n^{\otimes d}$ tensor-product Cartesian grids. The approach is based on the rank-Structured approximation of the matrix valued functions of the corresponding fractional finite difference Laplacian. We solve the equation for the control function, where the system matrix includes the sum of the fractional $d$-dimensional Laplacian and its inverse. The matrix valued functions of discrete Laplace operator on a tensor grid are diagonalized by using the fast Fourier transform (FFT). Then the low rank approximation of the $d$-dimensional tensors obtained by folding of the corresponding large diagonal matrices of eigenvalues are computed, which allows to solve the governing equation for the control function in a tensor-Structured Format. The existence of low rank canonical approximation to the class of matrix valued functions involved is justified by using the sinc quadrature approximation method applied to the Laplace transform of the generating function. The linear system of equations for the control function is solved by the PCG iterative method with the rank truncation at each iteration step, where the low Kronecker rank preconditioner is precomputed. The right-hand side, the solution vector, and the governing system matrix are maintained in the rank-Structured tensor Format which beneficially reduces the numerical cost to $O(n\log n)$, outperforming the standard FFT based methods of complexity $O(n^3\log n)$ for 3D case. Numerical tests for the 2D and 3D control problems confirm the linear complexity scaling of the method in the univariate grid size $n$.
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numerical solution of the hartree fock equation in multilevel tensor Structured Format
SIAM Journal on Scientific Computing, 2011Co-Authors: Boris N Khoromskij, Venera Khoromskaia, Heinzjurgen FladAbstract:In this paper, we describe a novel method for a robust and accurate iterative solution of the self-consistent Hartree-Fock equation in $\mathbb{R}^3$ based on the idea of tensor-Structured computation of the electron density and the nonlinear Hartree and (nonlocal) exchange operators at all steps of the iterative process. We apply the self-consistent field (SCF) iteration to the Galerkin discretization in a set of low separation rank basis functions that are solely specified by the respective values on a three-dimensional Cartesian grid. The approximation error is estimated by $O(h^3)$, where $h=O(n^{-1})$ is the mesh size of an $n\times n\times n$ tensor grid, while the numerical complexity to compute the Galerkin matrices scales linearly in $n\log n$. We propose the tensor-truncated version of the SCF iteration using the traditional direct inversion in the iterative subspace scheme enhanced by the multilevel acceleration with the grid-dependent termination criteria at each discretization level. This implies that the overall computational cost scales almost linearly in the univariate problem size $n$. Numerical illustrations are presented for the all electron case of H$_2$O and the pseudopotential case of CH$_4$ and CH$_3$OH molecules. The proposed scheme is not restricted to a priori given rank-1 basis sets, allowing analytically integrable convolution transform with the Newton kernel that opens further perspectives for promotion of the tensor-Structured methods in computational quantum chemistry.
Jacqueline S Dron - One of the best experts on this subject based on the ideXlab platform.
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improving reporting standards for polygenic scores in risk prediction studies
Nature, 2021Co-Authors: Hannah Wand, Samuel A Lambert, Cecelia Tamburro, Michael A Iacocca, Jack W Osullivan, Catherine Sillari, Iftikhar J Kullo, Robb K Rowley, Jacqueline S DronAbstract:Polygenic risk scores (PRSs), which often aggregate results from genome-wide association studies, can bridge the gap between initial discovery efforts and clinical applications for the estimation of disease risk using genetics. However, there is notable heterogeneity in the application and reporting of these risk scores, which hinders the translation of PRSs into clinical care. Here, in a collaboration between the Clinical Genome Resource (ClinGen) Complex Disease Working Group and the Polygenic Score (PGS) Catalog, we present the Polygenic Risk Score Reporting Standards (PRS-RS), in which we update the Genetic Risk Prediction Studies (GRIPS) Statement to reflect the present state of the field. Drawing on the input of experts in epidemiology, statistics, disease-specific applications, implementation and policy, this comprehensive reporting framework defines the minimal inFormation that is needed to interpret and evaluate PRSs, especially with respect to downstream clinical applications. Items span detailed descriptions of study populations, statistical methods for the development and validation of PRSs and considerations for the potential limitations of these scores. In addition, we emphasize the need for data availability and transparency, and we encourage researchers to deposit and share PRSs through the PGS Catalog to facilitate reproducibility and comparative benchmarking. By providing these criteria in a Structured Format that builds on existing standards and ontologies, the use of this framework in publishing PRSs will facilitate translation into clinical care and progress towards defining best practice.
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improving reporting standards for polygenic scores in risk prediction studies
medRxiv, 2020Co-Authors: Hannah Wand, Samuel A Lambert, Cecelia Tamburro, Michael A Iacocca, Jack W Osullivan, Catherine Sillari, Iftikhar J Kullo, Robb K Rowley, Jacqueline S DronAbstract:Over the past decade, genome-wide association studies have identified genetic variation associated with a wide range of human diseases and traits. These findings are now commonly aggregated into polygenic risk scores, which can bridge the gap between the initial discovery efforts and clinical applications for disease risk estimation. However, there is remarkable heterogeneity in the reporting of these risk scores due to a lack of accepted standards for the development, reporting, and application of PRS. This lack of rigorous standards hinders the translation of PRS into clinical care. The ClinGen Complex Disease Working Group, in a collaboration with the Polygenic Score (PGS) Catalog, have developed a novel PRS Reporting Statement (PRS-RS), updating previous standards to the current state of the field. Drawing upon experts in epidemiology, statistics, disease-specific applications, implementation, and policy, this 33-item reporting framework defines the minimal inFormation needed to interpret and evaluate a PRS, especially with respect to any downstream clinical applications. Items span detailed descriptions of the study population (recruitment method, key demographics, inclusion/exclusion criteria, and phenotype definition), statistical methods for both PRS development and validation, and considerations for potential limitations of the published risk score and downstream clinical utility. Additionally, emphasis has been placed on data availability and transparency to facilitate reproducibility and benchmarking against other PRS, such as deposition in the publicly available PGS Catalog. By providing these criteria in a Structured Format that borrows from existing standards and ontologies, the use of this framework in publishing PRS will facilitate PRS translation into clinical care and progress towards defining best practices.
Jordi Ponce - One of the best experts on this subject based on the ideXlab platform.
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european society of gynaecological oncology quality indicators for surgical treatment of cervical cancer
International Journal of Gynecological Cancer, 2020Co-Authors: D Cibula, Francois Planchamp, D Fischerova, Christina Fotopoulou, Christhardt Kohler, Fabio Landoni, Patrice Mathevet, Raj Naik, Jordi PonceAbstract:Background Optimizing and ensuring the quality of surgical care is essential to improve the management and outcome of patients with cervical cancer. To develop a list of quality indicators for surgical treatment of cervical cancer that can be used to audit and improve clinical practice. Methods Quality indicators were developed using a four-step evaluation process that included a systematic literature search to identify potential quality indicators, in-person meetings of an ad hoc group of international experts, an internal validation process, and external review by a large panel of European clinicians and patient representatives. Results Fifteen structural, process, and outcome indicators were selected. Using a Structured Format, each quality indicator has a description specifying what the indicator is measuring. Measurability specifications are also detailed to define how the indicator will be measured in practice. Each indicator has a target which gives practitioners and health administrators a quantitative basis for improving care and organizational processes. Discussion Implementation of institutional quality assurance programs can improve quality of care, even in high-volume centers. This set of quality indicators from the European Society of Gynaecological Cancer may be a major instrument to improve the quality of surgical treatment of cervical cancer.
