A universal regression-tensor approach is developed in the mathematical modeling of optimal parameters of chemical-technological process of complex mechanical products. The testing of developed algorithms was performe...A universal regression-tensor approach is developed in the mathematical modeling of optimal parameters of chemical-technological process of complex mechanical products. The testing of developed algorithms was performed on the example of multi-factorial process of low-temperature sulfur-chromium plating of precision mechanical parts.展开更多
This paper constructs and studies a nonlinear multivariate regression-tensor model for substantiation of necessary/sufficient conditions of optimization of technological calculation of multifactor physical and chemica...This paper constructs and studies a nonlinear multivariate regression-tensor model for substantiation of necessary/sufficient conditions of optimization of technological calculation of multifactor physical and chemical process of hardening of complex composite media for metal coatings. An adaptive a posteriori procedure for parametric formation of the target quality functional of integrative physical and mechanical properties of the designed metal coating has been proposed. The results of the research may serve as elements of a mathematical language when creating automated design of precision nanotechnologies for surface hardening of complex composite metal coatings on the basis of complex tribological and anticorrosive tests.展开更多
Diffusion tensor MRI （DT-MRI or DTI） is emerging as an important non-invasive technology for elucidating intemal brain structures. It has recently been utilized to diagnose a series of diseases that affect the integ...Diffusion tensor MRI （DT-MRI or DTI） is emerging as an important non-invasive technology for elucidating intemal brain structures. It has recently been utilized to diagnose a series of diseases that affect the integrity of neural systems to provide a basis for neuroregenerative studies. Results from the present study suggested that neural tissue is reconstructed with multiple diffusion-weighted gradient directions DTI, which varies from traditional imaging methods that utilize 6 gradient directions. Simultaneously, the diffusion tensor matrix is obtained by multiple linear regressions from an equation of echo signal intensity. The condition number value and standard deviation of fractional anisotropy for each scheme can be used to evaluate image quality. Results demonstrated that increasing gradient direction to some extent resulted in improved effects. Therefore, the traditional 6 and 15 directions should not be considered optimal scan protocols for clinical DTI application. In a scheme with 20 directions, the condition number and standard deviation of fractional anisotropy of the encoding gradients matrix were significantly reduced, and resulted in more clearly and accurately displayed neural tissue. Results demonstrated that the scheme with 20 diffusion gradient directions provided better accuracy of structural renderings and could be an optimal scan protocol for clinical DTI application.展开更多
The multivariate resistant regression spline (MURRS) method for estimatingan underlying smooth J-variate function by using noisy data is based on approximatingit with tensor products of B-splines and minimizing a sum ...The multivariate resistant regression spline (MURRS) method for estimatingan underlying smooth J-variate function by using noisy data is based on approximatingit with tensor products of B-splines and minimizing a sum of the ρ-functions of the residuals to obtain a robust estimator of the regression function, where the spline knots areautomatically chosen through a parallel of information criterion. When the knots are deterministically given, it is proved that the MURRS estimator achieves the optimal globalconvergence rates established by Stone under some mild conditions. Examples are givento illustrate the utility of the proposed methodology. Usually, only a few tensor productsof B-splines are enough to fit even complicated functions.展开更多
In this article, we put forward a new approach to estimate multiple conditional regression quantiles simultaneously. Unlike the double summation method in most of the literatures, our proposed model allows continuous ...In this article, we put forward a new approach to estimate multiple conditional regression quantiles simultaneously. Unlike the double summation method in most of the literatures, our proposed model allows continuous variety for the quantile level over(0,1). As a result, all the quantile curves can be obtained via a 2-dimensional surface simultaneously. Most importantly, the proposed minimizing criterion can be readily transformed to a linear programming problem. We use tensor product bi-linear quantile smoothing B-splines tofit it. The asymptotic property of the estimator is derived and a real data set is analyzed to demonstrate the proposed method.展开更多
This letter presents a novel prediction scheme employed for fast visual tracking. The proposed multilinear predictor is formulated as a higher order tensor, instead of the existing vector representations. This predict...This letter presents a novel prediction scheme employed for fast visual tracking. The proposed multilinear predictor is formulated as a higher order tensor, instead of the existing vector representations. This predictor is based on emploing the Canonical/Parallel factors (CP) decomposition to decompose a tensor as a sum of rank one tensors. In that way, the proposed scheme efficiently retains the underlying structural information of the input data, while reduces at the same time the computational complexity by employing separable filter operations applied at different directions. The efficiency of the proposed scheme is demonstrated in the conducted experiments.展开更多
文摘A universal regression-tensor approach is developed in the mathematical modeling of optimal parameters of chemical-technological process of complex mechanical products. The testing of developed algorithms was performed on the example of multi-factorial process of low-temperature sulfur-chromium plating of precision mechanical parts.
文摘This paper constructs and studies a nonlinear multivariate regression-tensor model for substantiation of necessary/sufficient conditions of optimization of technological calculation of multifactor physical and chemical process of hardening of complex composite media for metal coatings. An adaptive a posteriori procedure for parametric formation of the target quality functional of integrative physical and mechanical properties of the designed metal coating has been proposed. The results of the research may serve as elements of a mathematical language when creating automated design of precision nanotechnologies for surface hardening of complex composite metal coatings on the basis of complex tribological and anticorrosive tests.
基金supported by the National Natural Science Foundation of China (Key technology of neural fiber reconstruction based on MRI),No. 60703045
文摘Diffusion tensor MRI （DT-MRI or DTI） is emerging as an important non-invasive technology for elucidating intemal brain structures. It has recently been utilized to diagnose a series of diseases that affect the integrity of neural systems to provide a basis for neuroregenerative studies. Results from the present study suggested that neural tissue is reconstructed with multiple diffusion-weighted gradient directions DTI, which varies from traditional imaging methods that utilize 6 gradient directions. Simultaneously, the diffusion tensor matrix is obtained by multiple linear regressions from an equation of echo signal intensity. The condition number value and standard deviation of fractional anisotropy for each scheme can be used to evaluate image quality. Results demonstrated that increasing gradient direction to some extent resulted in improved effects. Therefore, the traditional 6 and 15 directions should not be considered optimal scan protocols for clinical DTI application. In a scheme with 20 directions, the condition number and standard deviation of fractional anisotropy of the encoding gradients matrix were significantly reduced, and resulted in more clearly and accurately displayed neural tissue. Results demonstrated that the scheme with 20 diffusion gradient directions provided better accuracy of structural renderings and could be an optimal scan protocol for clinical DTI application.
文摘The multivariate resistant regression spline (MURRS) method for estimatingan underlying smooth J-variate function by using noisy data is based on approximatingit with tensor products of B-splines and minimizing a sum of the ρ-functions of the residuals to obtain a robust estimator of the regression function, where the spline knots areautomatically chosen through a parallel of information criterion. When the knots are deterministically given, it is proved that the MURRS estimator achieves the optimal globalconvergence rates established by Stone under some mild conditions. Examples are givento illustrate the utility of the proposed methodology. Usually, only a few tensor productsof B-splines are enough to fit even complicated functions.
基金partially supported by the National Natural Science Foundation of China(No.11861042)the Fundamental Research Funds for the Central Universitiesthe Research Funds of Renmin University of China(No.18XNL012)。
文摘In this article, we put forward a new approach to estimate multiple conditional regression quantiles simultaneously. Unlike the double summation method in most of the literatures, our proposed model allows continuous variety for the quantile level over(0,1). As a result, all the quantile curves can be obtained via a 2-dimensional surface simultaneously. Most importantly, the proposed minimizing criterion can be readily transformed to a linear programming problem. We use tensor product bi-linear quantile smoothing B-splines tofit it. The asymptotic property of the estimator is derived and a real data set is analyzed to demonstrate the proposed method.
文摘This letter presents a novel prediction scheme employed for fast visual tracking. The proposed multilinear predictor is formulated as a higher order tensor, instead of the existing vector representations. This predictor is based on emploing the Canonical/Parallel factors (CP) decomposition to decompose a tensor as a sum of rank one tensors. In that way, the proposed scheme efficiently retains the underlying structural information of the input data, while reduces at the same time the computational complexity by employing separable filter operations applied at different directions. The efficiency of the proposed scheme is demonstrated in the conducted experiments.
