Recovering the low-rank structure of data matrix from sparse errors arises in the principal component pursuit （PCP）. This paper exploits the higher-order generalization of matrix recovery, named higher-order princip...Recovering the low-rank structure of data matrix from sparse errors arises in the principal component pursuit （PCP）. This paper exploits the higher-order generalization of matrix recovery, named higher-order principal component pursuit （HOPCP）, since it is critical in multi-way data analysis. Unlike the convexification （nuclear norm） for matrix rank function, the tensorial nuclear norm is stil an open problem. While existing preliminary works on the tensor completion field provide a viable way to indicate the low complexity estimate of tensor, therefore, the paper focuses on the low multi-linear rank tensor and adopt its convex relaxation to formulate the convex optimization model of HOPCP. The paper further propose two algorithms for HOPCP based on alternative minimization scheme： the augmented Lagrangian alternating direction method （ALADM） and its truncated higher-order singular value decomposition （ALADM-THOSVD） version. The former can obtain a high accuracy solution while the latter is more efficient to handle the computationally intractable problems. Experimental results on both synthetic data and real magnetic resonance imaging data show the applicability of our algorithms in high-dimensional tensor data processing.展开更多
Analysis of volatile components in herbal pair (HP) herba schizonepetae-ramulus cinnamomi (HS-RC), single herb HS and RC was carried out by gas chromatography-mass spectrometry (GC-MS) data and chemometric resolution ...Analysis of volatile components in herbal pair (HP) herba schizonepetae-ramulus cinnamomi (HS-RC), single herb HS and RC was carried out by gas chromatography-mass spectrometry (GC-MS) data and chemometric resolution method (CRM). The two-dimensional data obtained from GC-MS instruments were resolved into a pure chromatogram and a mass spectrum of each chemical compound by CRM. In total, 47, 61 and 51 chemical components in volatile oil of HS, RC, and HP HS-RC were respectively determined qualitatively and quantitatively, accounting for 90.52%, 88.37%, and 88.72% total contents of volatile oil of HS, RC, and HP HS-RC, respectively. The number of the volatile components of HP HS-RC is almost the addition of that of two single herbs, but their relative contents are changed.展开更多
The deformation performance index limits of high reinforced concrete （RC） shear wall components based on Chinese codes were discussed by the nonlinear finite element method. Two typical RC shear wall specimens in th...The deformation performance index limits of high reinforced concrete （RC） shear wall components based on Chinese codes were discussed by the nonlinear finite element method. Two typical RC shear wall specimens in the previous work were first used to verify the correctness of the nonlinear finite element method. Then, the nonlinear finite element method was applied to study the deformability of a set of high RC shear wall components designed according to current Chinese codes and with shear span ratio λ≥2.0. Parametric studies were made on the influence of shear span ratio, axial compression ratio, ratio of flexural capacity to shear capacity and main flexural reinforcement ratio of confined botmdary members. Finally, the deformation performance index and its limits of high RC shear wall components under severe earthquakes were proposed by the finite element model results, which offers a reference in determining the performance status of RC shear wall components designed based on Chinese codes.展开更多
基金supported by the National Natural Science Foundationof China(51275348)
文摘Recovering the low-rank structure of data matrix from sparse errors arises in the principal component pursuit （PCP）. This paper exploits the higher-order generalization of matrix recovery, named higher-order principal component pursuit （HOPCP）, since it is critical in multi-way data analysis. Unlike the convexification （nuclear norm） for matrix rank function, the tensorial nuclear norm is stil an open problem. While existing preliminary works on the tensor completion field provide a viable way to indicate the low complexity estimate of tensor, therefore, the paper focuses on the low multi-linear rank tensor and adopt its convex relaxation to formulate the convex optimization model of HOPCP. The paper further propose two algorithms for HOPCP based on alternative minimization scheme： the augmented Lagrangian alternating direction method （ALADM） and its truncated higher-order singular value decomposition （ALADM-THOSVD） version. The former can obtain a high accuracy solution while the latter is more efficient to handle the computationally intractable problems. Experimental results on both synthetic data and real magnetic resonance imaging data show the applicability of our algorithms in high-dimensional tensor data processing.
基金Project(20235020) supported by the National Natural Science Foundation of China
文摘Analysis of volatile components in herbal pair (HP) herba schizonepetae-ramulus cinnamomi (HS-RC), single herb HS and RC was carried out by gas chromatography-mass spectrometry (GC-MS) data and chemometric resolution method (CRM). The two-dimensional data obtained from GC-MS instruments were resolved into a pure chromatogram and a mass spectrum of each chemical compound by CRM. In total, 47, 61 and 51 chemical components in volatile oil of HS, RC, and HP HS-RC were respectively determined qualitatively and quantitatively, accounting for 90.52%, 88.37%, and 88.72% total contents of volatile oil of HS, RC, and HP HS-RC, respectively. The number of the volatile components of HP HS-RC is almost the addition of that of two single herbs, but their relative contents are changed.
基金Project(2009ZA04) supported by the Independent Research Foundation of State Key Laboratory of Subtropical Architecture Science,China
文摘The deformation performance index limits of high reinforced concrete （RC） shear wall components based on Chinese codes were discussed by the nonlinear finite element method. Two typical RC shear wall specimens in the previous work were first used to verify the correctness of the nonlinear finite element method. Then, the nonlinear finite element method was applied to study the deformability of a set of high RC shear wall components designed according to current Chinese codes and with shear span ratio λ≥2.0. Parametric studies were made on the influence of shear span ratio, axial compression ratio, ratio of flexural capacity to shear capacity and main flexural reinforcement ratio of confined botmdary members. Finally, the deformation performance index and its limits of high RC shear wall components under severe earthquakes were proposed by the finite element model results, which offers a reference in determining the performance status of RC shear wall components designed based on Chinese codes.
