Tensor robust principal component analysis（TRPCA） problem aims to separate a low-rank tensor and a sparse tensor from their sum. This problem has recently attracted considerable research attention due to its wide ra...Tensor robust principal component analysis（TRPCA） problem aims to separate a low-rank tensor and a sparse tensor from their sum. This problem has recently attracted considerable research attention due to its wide range of potential applications in computer vision and pattern recognition. In this paper, we propose a new model to deal with the TRPCA problem by an alternation minimization algorithm along with two adaptive rankadjusting strategies. For the underlying low-rank tensor, we simultaneously perform low-rank matrix factorizations to its all-mode matricizations; while for the underlying sparse tensor,a soft-threshold shrinkage scheme is applied. Our method can be used to deal with the separation between either an exact or an approximate low-rank tensor and a sparse one. We established the subsequence convergence of our algorithm in the sense that any limit point of the iterates satisfies the KKT conditions. When the iteration stops, the output will be modified by applying a high-order SVD approach to achieve an exactly low-rank final result as the accurate rank has been calculated. The numerical experiments demonstrate that our method could achieve better results than the compared methods.展开更多
The present paper spreads the principal axis intrinsic method to the highdimensional case and discusses the solution of the tensor equation AX --XA = C
Based on the equivalence between the Sylvester tensor equation and the linear equation obtained by discretization of partial differential equations(PDEs),an overlapping Schwarz alternative method based on the tensor f...Based on the equivalence between the Sylvester tensor equation and the linear equation obtained by discretization of partial differential equations(PDEs),an overlapping Schwarz alternative method based on the tensor format and an overlapping parallel Schwarz method based on the tensor format for solving high-dimensional PDEs are proposed.The complexity of the new algorithms is discussed.Finally,the feasibility and effectiveness of the new methods are verified by some numerical examples.展开更多
Conventional methods for quantifying thermoelectric anisotropy rely on precisely aligned crystals,which are time-consuming and error-prone.To address this,we propose a tensor inversion method integrating transport mea...Conventional methods for quantifying thermoelectric anisotropy rely on precisely aligned crystals,which are time-consuming and error-prone.To address this,we propose a tensor inversion method integrating transport measurements with EBSD-derived Euler angles to determine the intrinsic tensors of as-grown bismuth crystals.This method reconstructs the full second-rank thermoelectric tensors—including electrical resistivity,thermal conductivity,and the Seebeck coefficient—by transforming transport data between the sample coordinate system and the crystal coordinate system.The inverted tensor components of pure bismuth show excellent agreement with reported principal-axis values,validating the accuracy of this method.Moreover,the reversibility of the tensor inversion approach allows for complete visualization of the directional dependence of the thermoelectric figure of merit(zT),revealing its full angular and crystallographic orientation distribution for the first time.This bidirectional framework not only provides a convenient pathway for the reconstruction of intrinsic transport tensors but also enables the prediction of orientation-dependent properties,thereby offering a robust tool for analyzing anisotropic transport behavior and guiding the optimization of thermoelectric performance.展开更多
Thermoelectric(TE)materials,which enable direct conversion between thermal and electrical energy,have long held promise for applications in waste heat recovery,solid-state refrigeration,and deep-space exploration.[1-3...Thermoelectric(TE)materials,which enable direct conversion between thermal and electrical energy,have long held promise for applications in waste heat recovery,solid-state refrigeration,and deep-space exploration.[1-3]Their energy conversion efficiency is governed by the dimensionless figure of merit zT=S^(2)T/ρκ,where the Seebeck coefficient(S).展开更多
We introduce a new tensor integration method for time-dependent partial differential equations(PDEs)that controls the tensor rank of the PDE solution via time-dependent smooth coordinate transformations.Such coordinat...We introduce a new tensor integration method for time-dependent partial differential equations(PDEs)that controls the tensor rank of the PDE solution via time-dependent smooth coordinate transformations.Such coordinate transformations are obtained by solving a sequence of convex optimization problems that minimize the component of the PDE operator responsible for increasing the tensor rank of the PDE solution.The new algorithm improves upon the non-convex algorithm we recently proposed in Dektor and Venturi(2023)which has no guarantee of producing globally optimal rank-reducing coordinate transformations.Numerical applications demonstrating the effectiveness of the new coordinate-adaptive tensor integration method are presented and discussed for prototype Liouville and Fokker-Planck equations.展开更多
Tensor methods have gained increasingly attention from various applications,including machine learning,quantum chemistry,healthcare analytics,social network analysis,data mining,and signal processing,to name a few.Spa...Tensor methods have gained increasingly attention from various applications,including machine learning,quantum chemistry,healthcare analytics,social network analysis,data mining,and signal processing,to name a few.Sparse tensors and their algorithms become critical to further improve the performance of these methods and enhance the interpretability of their output.This work presents a sparse tensor algorithm benchmark suite(PASTA)for single-and multi-core CPUs.To the best of our knowledge,this is the first benchmark suite for sparse tensor world.PASTA targets on:(1)helping application users to evaluate different computer systems using its representative computational workloads;(2)providing insights to better utilize existed computer architecture and systems and inspiration for the future design.This benchmark suite is publicly released at https://gitla b.com/tenso rworl d/pasta,under version 0.1.0.展开更多
Several new series of approximately mutually unbiased bases are constructed by using Gauss sums and Jacobi sums over Galois rings GR(p2, r), and the tensor method.
In this paper, we combine the direct-forcing fictitious domain （DF/FD） method and the sharp interface method to resolve the problem of particle dielectrophoresis in two dimensions. The flow field and the motion of p...In this paper, we combine the direct-forcing fictitious domain （DF/FD） method and the sharp interface method to resolve the problem of particle dielectrophoresis in two dimensions. The flow field and the motion of particles are solved with the DF/FD method, the electric field is solved with the sharp inter- face method, and the electrostatic force on the particles is computed using the Maxwell stress tensor method. The proposed method is validated via three problems： effective conductivity of particle compos- ite between two planar plates, cell trapping in a channel, and motion of particles due to both conventional and traveling wave dielectrophoretic forces.展开更多
基金Supported by the National Natural Science Foundation of China(Grant Nos.6157209961320106008+2 种基金91230103)National Science and Technology Major Project(Grant Nos.2013ZX040050212014ZX04001011)
文摘Tensor robust principal component analysis（TRPCA） problem aims to separate a low-rank tensor and a sparse tensor from their sum. This problem has recently attracted considerable research attention due to its wide range of potential applications in computer vision and pattern recognition. In this paper, we propose a new model to deal with the TRPCA problem by an alternation minimization algorithm along with two adaptive rankadjusting strategies. For the underlying low-rank tensor, we simultaneously perform low-rank matrix factorizations to its all-mode matricizations; while for the underlying sparse tensor,a soft-threshold shrinkage scheme is applied. Our method can be used to deal with the separation between either an exact or an approximate low-rank tensor and a sparse one. We established the subsequence convergence of our algorithm in the sense that any limit point of the iterates satisfies the KKT conditions. When the iteration stops, the output will be modified by applying a high-order SVD approach to achieve an exactly low-rank final result as the accurate rank has been calculated. The numerical experiments demonstrate that our method could achieve better results than the compared methods.
文摘The present paper spreads the principal axis intrinsic method to the highdimensional case and discusses the solution of the tensor equation AX --XA = C
基金supported by the National Natural Science Foundation of China(12161027)the Guangxi Natural Science Foundation of China(2020GXNSFAA159143)partially supported by the Science and Technology Project of Guangxi of China(Guike AD23023002).
文摘Based on the equivalence between the Sylvester tensor equation and the linear equation obtained by discretization of partial differential equations(PDEs),an overlapping Schwarz alternative method based on the tensor format and an overlapping parallel Schwarz method based on the tensor format for solving high-dimensional PDEs are proposed.The complexity of the new algorithms is discussed.Finally,the feasibility and effectiveness of the new methods are verified by some numerical examples.
基金supported by the National Key Research and Development Program of China(Grant No.2021YFA0718700)the National Natural Science Foundation of China(Grant Nos.52172259 and 52472191)+1 种基金the Fujian Science&Technology Innovation Laboratory for Optoelectronic Information of China(Grant No.2021ZZ127)the Natural Science Foundation of Fujian Province of China(Grant No.2025J010017)。
文摘Conventional methods for quantifying thermoelectric anisotropy rely on precisely aligned crystals,which are time-consuming and error-prone.To address this,we propose a tensor inversion method integrating transport measurements with EBSD-derived Euler angles to determine the intrinsic tensors of as-grown bismuth crystals.This method reconstructs the full second-rank thermoelectric tensors—including electrical resistivity,thermal conductivity,and the Seebeck coefficient—by transforming transport data between the sample coordinate system and the crystal coordinate system.The inverted tensor components of pure bismuth show excellent agreement with reported principal-axis values,validating the accuracy of this method.Moreover,the reversibility of the tensor inversion approach allows for complete visualization of the directional dependence of the thermoelectric figure of merit(zT),revealing its full angular and crystallographic orientation distribution for the first time.This bidirectional framework not only provides a convenient pathway for the reconstruction of intrinsic transport tensors but also enables the prediction of orientation-dependent properties,thereby offering a robust tool for analyzing anisotropic transport behavior and guiding the optimization of thermoelectric performance.
基金supported by the National Key Research and Development Program of China(Grant No.2025YFE0126500)the National Natural Science Foundation of China(NSFC)(Grant No.52402232)+1 种基金Guangdong Basic and Applied Basic Research Foundation(Grant No.2023A1515110512)Southern University of Science and Technology Grant(Y01796123)。
文摘Thermoelectric(TE)materials,which enable direct conversion between thermal and electrical energy,have long held promise for applications in waste heat recovery,solid-state refrigeration,and deep-space exploration.[1-3]Their energy conversion efficiency is governed by the dimensionless figure of merit zT=S^(2)T/ρκ,where the Seebeck coefficient(S).
基金supported by the U.S.Air Force Office of Scientific Research(AFOSR)grant FA9550-20-1-0174the U.S.Army Research Office(ARO)grant W911NF-18-1-0309.
文摘We introduce a new tensor integration method for time-dependent partial differential equations(PDEs)that controls the tensor rank of the PDE solution via time-dependent smooth coordinate transformations.Such coordinate transformations are obtained by solving a sequence of convex optimization problems that minimize the component of the PDE operator responsible for increasing the tensor rank of the PDE solution.The new algorithm improves upon the non-convex algorithm we recently proposed in Dektor and Venturi(2023)which has no guarantee of producing globally optimal rank-reducing coordinate transformations.Numerical applications demonstrating the effectiveness of the new coordinate-adaptive tensor integration method are presented and discussed for prototype Liouville and Fokker-Planck equations.
基金funded by the US Department of Energy,Office for Advanced Scientific Computing(ASCR)under Award No.66150:“CENATE:The Center for Advanced Technology Evaluation”Pacific Northwest National Laboratory(PNNL)is a multiprogram national laboratory operated for DOE by Battelle Memorial Institute under Contract DE-AC05-76RL01830supported by the High Performance Data Analytics(HPDA)program at Pacific Northwest National Laboratory.
文摘Tensor methods have gained increasingly attention from various applications,including machine learning,quantum chemistry,healthcare analytics,social network analysis,data mining,and signal processing,to name a few.Sparse tensors and their algorithms become critical to further improve the performance of these methods and enhance the interpretability of their output.This work presents a sparse tensor algorithm benchmark suite(PASTA)for single-and multi-core CPUs.To the best of our knowledge,this is the first benchmark suite for sparse tensor world.PASTA targets on:(1)helping application users to evaluate different computer systems using its representative computational workloads;(2)providing insights to better utilize existed computer architecture and systems and inspiration for the future design.This benchmark suite is publicly released at https://gitla b.com/tenso rworl d/pasta,under version 0.1.0.
基金supported by the Natural Science Foundation of China under Grant No.61370089the Tsinghua National Laboratory for Information Science and Technology+1 种基金by the Fundamental Research Funds for the Central Universities under Grant No.JZ2014HGBZ0349by Science and Technology on Information Assurance Lab.KJ-12-01
文摘Several new series of approximately mutually unbiased bases are constructed by using Gauss sums and Jacobi sums over Galois rings GR(p2, r), and the tensor method.
基金support from the National Natural Science Foundation of China(no.10872181)the National Basic Research Program of China(no.2006CB705400)+1 种基金Chinese Universities Scientific Fundthe Major Program of the National Natural Science Foundation of China(no.10632070)
文摘In this paper, we combine the direct-forcing fictitious domain （DF/FD） method and the sharp interface method to resolve the problem of particle dielectrophoresis in two dimensions. The flow field and the motion of particles are solved with the DF/FD method, the electric field is solved with the sharp inter- face method, and the electrostatic force on the particles is computed using the Maxwell stress tensor method. The proposed method is validated via three problems： effective conductivity of particle compos- ite between two planar plates, cell trapping in a channel, and motion of particles due to both conventional and traveling wave dielectrophoretic forces.
