The paper uses Euclidean Jordan algebras as a basic tool to extend smoothing functions, which include the Chen-Mangasarian class and the Fischer-Burmeister smoothing functions, to symmetric cone complementarity proble...The paper uses Euclidean Jordan algebras as a basic tool to extend smoothing functions, which include the Chen-Mangasarian class and the Fischer-Burmeister smoothing functions, to symmetric cone complementarity problems. Computable formulas for these functions and their Jacobians are derived. In addition, it is shown that these functions are Lipschitz continuous with respect to parameter # and continuously differentiable on J × J for any μ 〉 0.展开更多
This paper is aimed at the derivation of a discrete data smoothing function for the discrete Dirichlet condition in a regular grid on the surface of a spheroid.The method employed here is the local L^2-seminorm minimi...This paper is aimed at the derivation of a discrete data smoothing function for the discrete Dirichlet condition in a regular grid on the surface of a spheroid.The method employed here is the local L^2-seminorm minimization,through Euler-Lagrange method,for the Beltrami operator.The method results in a weighted average of the surrounding points in a te mplate based on the first order Taylor expansion of the unknown function under consideration.The coefficients of the weighted average are calculated and used to smooth the Geoid height data in Iran,derived from the EGM2008 geopotential model.展开更多
Let M(u) be an N function, A=D r+∑r-1k=0a k(x)D k a linear differential operator and W M(A) the Sobolev Orlicz class defined by M(u) and A. In this paper we give the asymptotic estimates...Let M(u) be an N function, A=D r+∑r-1k=0a k(x)D k a linear differential operator and W M(A) the Sobolev Orlicz class defined by M(u) and A. In this paper we give the asymptotic estimates of the n K width d n(W M(A),L 2[0,1]) .展开更多
Most material distribution-based topology optimization methods work on a relaxed form of the optimization problem and then push the solution toward the binary limits.However,when benchmarking these methods,researchers...Most material distribution-based topology optimization methods work on a relaxed form of the optimization problem and then push the solution toward the binary limits.However,when benchmarking these methods,researchers use known solutions to only a single form of benchmark problem.This paper proposes a comparison platform for systematic benchmarking of topology optimization methods using both binary and relaxed forms.A greyness measure is implemented to evaluate how far a solution is from the desired binary form.The well-known ZhouRozvany(ZR)problem is selected as the benchmarking problem here,making use of available global solutions for both its relaxed and binary forms.The recently developed non-penalization Smooth-edged Material Distribution for Optimizing Topology(SEMDOT),well-established Solid Isotropic Material with Penalization(SIMP),and continuation methods are studied on this platform.Interestingly,in most cases,the grayscale solutions obtained by SEMDOT demonstrate better performance in dealing with the ZR problem than SIMP.The reasons are investigated and attributed to the usage of two different regularization techniques,namely,the Heaviside smooth function in SEMDOT and the power-law penalty in SIMP.More importantly,a simple-to-use benchmarking graph is proposed for evaluating newly developed topology optimization methods.展开更多
Let M(u) be an N function, A=D r+∑r-1k=0a k(x)D k a linear differential operator and W M(A) the Sobolev Orlicz class defined by M(u) and A. In this paper we give the asymptotic estimates...Let M(u) be an N function, A=D r+∑r-1k=0a k(x)D k a linear differential operator and W M(A) the Sobolev Orlicz class defined by M(u) and A. In this paper we give the asymptotic estimates of the n K width d n(W M(A),L 2[0,1]) .展开更多
Smooth support vector machine （SSVM） changs the normal support vector machine （SVM） into the unconstrained op- timization by using the smooth sigmoid function. The method can be solved under the Broyden-Fletcher-G...Smooth support vector machine （SSVM） changs the normal support vector machine （SVM） into the unconstrained op- timization by using the smooth sigmoid function. The method can be solved under the Broyden-Fletcher-Goldfarb-Shanno （BFGS） algorithm and the Newdon-Armijio （NA） algorithm easily, however the accuracy of sigmoid function is not as good as that of polyno- mial smooth function. Furthermore, the method cannot reduce the influence of outliers or noise in dataset. A fuzzy smooth support vector machine （FSSVM） with fuzzy membership and polynomial smooth functions is introduced into the SVM. The fuzzy member- ship considers the contribution rate of each sample to the optimal separating hyperplane and makes the optimization problem more accurate at the inflection point. Those changes play a positive role on trials. The results of the experiments show that those FSSVMs can obtain a better accuracy and consume the shorter time than SSVM and lagrange support vector machine （LSVM）.展开更多
In this paper,the kernel of the cubic spline interpolation is given.An optimal error bound for the cu- bic spline interpolation of lower smooth functions is obtained.
This paper considers the Kolmogorov width,the Gelfand width and the Linear width of the periodic smooth functions with boundary conditions in Orlicz space.Further,the relationships among these three types of width are...This paper considers the Kolmogorov width,the Gelfand width and the Linear width of the periodic smooth functions with boundary conditions in Orlicz space.Further,the relationships among these three types of width are obtained.展开更多
A new smooth gap function for the box constrained variational inequality problem （VIP） is proposed based on an integral global optimality condition. The smooth gap function is simple and has some good differentiable...A new smooth gap function for the box constrained variational inequality problem （VIP） is proposed based on an integral global optimality condition. The smooth gap function is simple and has some good differentiable properties. The box constrained VIP can be reformulated as a differentiable optimization problem by the proposed smooth gap function. The conditions, under which any stationary point of the optimization problem is the solution to the box constrained VIP, are discussed. A simple frictional contact problem is analyzed to show the applications of the smooth gap function. Finally, the numerical experiments confirm the good theoretical properties of the method.展开更多
In this note, we establish a new formulation of smoothness conditions for piecewise polynomial (: =pp) functions in terms of the B-net representation in the general n-dimensional setting. It plays an important role fo...In this note, we establish a new formulation of smoothness conditions for piecewise polynomial (: =pp) functions in terms of the B-net representation in the general n-dimensional setting. It plays an important role for 2-dimensional setting in the constructive proof of the fact that the spaces of polynomial splines with smoothness rand total degree k≥3r+2 over arbitrary triangulations achieve the optimal approximation order with the approximation constant depending only on k and the smallest angle of the partition in [5].展开更多
In this paper, a class of smoothing modulus-based iterative method was presented for solving implicit complementarity problems. The main idea was to transform the implicit complementarity problem into an equivalent im...In this paper, a class of smoothing modulus-based iterative method was presented for solving implicit complementarity problems. The main idea was to transform the implicit complementarity problem into an equivalent implicit fixed-point equation, then introduces a smoothing function to obtain its approximation solutions. The convergence analysis of the algorithm was given, and the efficiency of the algorithms was verified by numerical experiments.展开更多
Three dimensional frictional contact problems are formulated as linear complementarity problems based on the parametric variational principle. Two aggregate-functionbased algorithms for solving complementarity problem...Three dimensional frictional contact problems are formulated as linear complementarity problems based on the parametric variational principle. Two aggregate-functionbased algorithms for solving complementarity problems are proposed. One is called the self-adjusting interior point algorithm, the other is called the aggregate function smoothing algorithm. Numerical experiment shows the efficiency of the proposed two algorithms.展开更多
The system of generalized absolute value equations(GAVE)has attracted more and more attention in the optimization community.In this paper,by introducing a smoothing function,we develop a smoothing Newton algorithm wit...The system of generalized absolute value equations(GAVE)has attracted more and more attention in the optimization community.In this paper,by introducing a smoothing function,we develop a smoothing Newton algorithm with non-monotone line search to solve the GAVE.We show that the non-monotone algorithm is globally and locally quadratically convergent under a weaker assumption than those given in most existing algorithms for solving the GAVE.Numerical results are given to demonstrate the viability and efficiency of the approach.展开更多
To explore experimental quantization of stochastic chaos and exact wave tur-bulence in exponential oscillons,it is necessary to construct smooth random functions of time.In the current paper,we develop a new method of...To explore experimental quantization of stochastic chaos and exact wave tur-bulence in exponential oscillons,it is necessary to construct smooth random functions of time.In the current paper,we develop a new method of modeling stochastic variables described by a closed system of ordinary differential and algebraic equations.Primarily,oscillatory and pulsatory dynamic models pro-duced by the first triplet of copolar elliptic functions are studied from the view-point of the Hamiltonian and Newtonian dynamics.Secondly,the Hamilto-nian systems of the first triplet and the first triplet squared are meticulously investigated in the hyperbolic limit that results in oscillations and pulsations with rectangular and point pulses and a variable period.Thirdly,the relative Hamiltonian systems are used to develop two stochastic models of a random oscillatory cn-noise and a random pulsatory cn2-noise.Numerical experi-ments show that for the Bernoulli frequencies the random oscillatory cn-noise approaches a smooth random oscillatory variable with an unbounded period and the Gaussian probability distribution and the random pulsatory cn2-noise tends to a smooth random pulsatory variable with an unbounded period and the truncated Gaussian probability distribution as the number of elliptic modes approaches infinity.展开更多
Two-dimensional finite element mesh generation algorithm for electromagnetic field calculation is proposed in this paper to improve the efficiency and accuracy of electromagnetic calculation. An image boundary extract...Two-dimensional finite element mesh generation algorithm for electromagnetic field calculation is proposed in this paper to improve the efficiency and accuracy of electromagnetic calculation. An image boundary extraction algorithm is developed to map the image on the geometric domain. Identification algorithm for the location of nodes in polygon area is proposed to determine the state of the node. To promote the average quality of the mesh and the efficiency of mesh generation, a novel force-based mesh smoothing algorithm is proposed. One test case and a typical electromagnetic calculation are used to testify the effectiveness and efficiency of the proposed algorithm. The results demonstrate that the proposed algorithm can produce a high-quality mesh with less iteration.展开更多
The aim of this work is to employ a modified cell-based smoothed finite element method(S-FEM)for topology optimization with the domain discretized with arbitrary polygons.In the present work,the linear polynomial basi...The aim of this work is to employ a modified cell-based smoothed finite element method(S-FEM)for topology optimization with the domain discretized with arbitrary polygons.In the present work,the linear polynomial basis function is used as the weight function instead of the constant weight function used in the standard S-FEM.This improves the accuracy and yields an optimal convergence rate.The gradients are smoothed over each smoothing domain,then used to compute the stiffness matrix.Within the proposed scheme,an optimum topology procedure is conducted over the smoothing domains.Structural materials are distributed over each smoothing domain and the filtering scheme relies on the smoothing domain.Numerical tests are carried out to pursue the performance of the proposed optimization by comparing convergence,efficiency and accuracy.展开更多
A novel modulation recognition algorithm is proposed by introducing a Chen-Harker-Kanzow-Smale (CHKS) smooth function into the C-support vector machine deformation algorithm. A set of seven characteristic parameters i...A novel modulation recognition algorithm is proposed by introducing a Chen-Harker-Kanzow-Smale (CHKS) smooth function into the C-support vector machine deformation algorithm. A set of seven characteristic parameters is selected from a range of parameters of communication signals including instantaneous amplitude, phase, and frequency. And the Newton-Armijo algorithm is utilized to train the proposed algorithm, namely, smooth CHKS smooth support vector machine (SCHKS-SSVM). Compared with the existing algorithms, the proposed algorithm not only solves the non-differentiable problem of the second order objective function, but also reduces the recognition error. It significantly improves the training speed and also saves a large amount of storage space through large-scale sorting problems. The simulation results show that the recognition rate of the algorithm can batch training. Therefore, the proposed algorithm is suitable for solving the problem of high dimension and its recognition can exceed 95% when the signal-to-noise ratio is no less than 10 dB.展开更多
Support vector machines （SVMs） have been extensively studied and have shown remarkable success in many applications. A new family of twice continuously differentiable piecewise smooth functions are used to smooth th...Support vector machines （SVMs） have been extensively studied and have shown remarkable success in many applications. A new family of twice continuously differentiable piecewise smooth functions are used to smooth the objective function of uncon- strained SVMs. The three-order piecewise smooth support vector machine （TPWSSVMd） is proposed. The piecewise functions can get higher and higher approximation accuracy as required with the increase of parameter d. The global convergence proof of TPWSSVMd is given with the rough set theory. TPWSSVMd can efficiently handle large scale and high dimensional problems. Nu- merical results demonstrate TPWSSVMa has better classification performance and learning efficiency than other competitive base- lines.展开更多
Angiotensin （Ang）-（1-7） is recognized as a new bioactive peptide in renin-angiotensin system （RAS）. Ang-（1-7） is a counter-regulatory mediator of Ang-II which appears to be protective against cardiovascular di...Angiotensin （Ang）-（1-7） is recognized as a new bioactive peptide in renin-angiotensin system （RAS）. Ang-（1-7） is a counter-regulatory mediator of Ang-II which appears to be protective against cardiovascular disease. Recent studies have found that Ang-（1-7） played an important role in reducing smooth muscle cell proliferation and migration, improving endothelial function and regulating lipid metabolism, leading to inhibition of atherosclerotic lesions and increase of plaque stability. Although clinical application of Ang-（1-7） is restricted due to its pharmacokinetic properties, identification of stabilized compounds, including more stable analogues and specific delivery compounds, has enabled clinical application of Ang-（1-7）. In this review, we discussed recent findings concerning the biological role of Ang-（1-7） and related mechanism during atherosclerosis development. In addition, we highlighted the perspective to develop therapeutic strategies using Ang-（1-7） to treat atherosclerosis.展开更多
In this paper,we study smoothing approximations for some piecewise smooth functions.We first present two approaches for one-dimensional case:a global approach is to construct smoothing approximations over the whole do...In this paper,we study smoothing approximations for some piecewise smooth functions.We first present two approaches for one-dimensional case:a global approach is to construct smoothing approximations over the whole domain and a local approach is to construct smoothing approximations within appropriate neighborhoods of the nonsmooth points.We obtain some error estimate results for both approaches and discuss whether the smoothing approximations can inherit the convexity of the original functions.Furthermore,we extend the global approach to some multiple dimensional cases.展开更多
基金Supported by the Funds of Ministry of Education of China for PhD (20020141013)the NNSF of China (10471015).
文摘The paper uses Euclidean Jordan algebras as a basic tool to extend smoothing functions, which include the Chen-Mangasarian class and the Fischer-Burmeister smoothing functions, to symmetric cone complementarity problems. Computable formulas for these functions and their Jacobians are derived. In addition, it is shown that these functions are Lipschitz continuous with respect to parameter # and continuously differentiable on J × J for any μ 〉 0.
文摘This paper is aimed at the derivation of a discrete data smoothing function for the discrete Dirichlet condition in a regular grid on the surface of a spheroid.The method employed here is the local L^2-seminorm minimization,through Euler-Lagrange method,for the Beltrami operator.The method results in a weighted average of the surrounding points in a te mplate based on the first order Taylor expansion of the unknown function under consideration.The coefficients of the weighted average are calculated and used to smooth the Geoid height data in Iran,derived from the EGM2008 geopotential model.
文摘Let M(u) be an N function, A=D r+∑r-1k=0a k(x)D k a linear differential operator and W M(A) the Sobolev Orlicz class defined by M(u) and A. In this paper we give the asymptotic estimates of the n K width d n(W M(A),L 2[0,1]) .
文摘Most material distribution-based topology optimization methods work on a relaxed form of the optimization problem and then push the solution toward the binary limits.However,when benchmarking these methods,researchers use known solutions to only a single form of benchmark problem.This paper proposes a comparison platform for systematic benchmarking of topology optimization methods using both binary and relaxed forms.A greyness measure is implemented to evaluate how far a solution is from the desired binary form.The well-known ZhouRozvany(ZR)problem is selected as the benchmarking problem here,making use of available global solutions for both its relaxed and binary forms.The recently developed non-penalization Smooth-edged Material Distribution for Optimizing Topology(SEMDOT),well-established Solid Isotropic Material with Penalization(SIMP),and continuation methods are studied on this platform.Interestingly,in most cases,the grayscale solutions obtained by SEMDOT demonstrate better performance in dealing with the ZR problem than SIMP.The reasons are investigated and attributed to the usage of two different regularization techniques,namely,the Heaviside smooth function in SEMDOT and the power-law penalty in SIMP.More importantly,a simple-to-use benchmarking graph is proposed for evaluating newly developed topology optimization methods.
文摘Let M(u) be an N function, A=D r+∑r-1k=0a k(x)D k a linear differential operator and W M(A) the Sobolev Orlicz class defined by M(u) and A. In this paper we give the asymptotic estimates of the n K width d n(W M(A),L 2[0,1]) .
基金supported by the National Natural Science Foundation of China (60974082)
文摘Smooth support vector machine （SSVM） changs the normal support vector machine （SVM） into the unconstrained op- timization by using the smooth sigmoid function. The method can be solved under the Broyden-Fletcher-Goldfarb-Shanno （BFGS） algorithm and the Newdon-Armijio （NA） algorithm easily, however the accuracy of sigmoid function is not as good as that of polyno- mial smooth function. Furthermore, the method cannot reduce the influence of outliers or noise in dataset. A fuzzy smooth support vector machine （FSSVM） with fuzzy membership and polynomial smooth functions is introduced into the SVM. The fuzzy member- ship considers the contribution rate of each sample to the optimal separating hyperplane and makes the optimization problem more accurate at the inflection point. Those changes play a positive role on trials. The results of the experiments show that those FSSVMs can obtain a better accuracy and consume the shorter time than SSVM and lagrange support vector machine （LSVM）.
文摘In this paper,the kernel of the cubic spline interpolation is given.An optimal error bound for the cu- bic spline interpolation of lower smooth functions is obtained.
基金Supported by National Natural Science Foundation of China(Grant No.11761055)Supported by Inner Mongolia Normal University Graduate Research and Innovation Project(Grant No.CXJJS20091).
文摘This paper considers the Kolmogorov width,the Gelfand width and the Linear width of the periodic smooth functions with boundary conditions in Orlicz space.Further,the relationships among these three types of width are obtained.
基金Project supported by the National Natural Science Foundation of China(Nos.10902077,11172209, and 10572031)
文摘A new smooth gap function for the box constrained variational inequality problem （VIP） is proposed based on an integral global optimality condition. The smooth gap function is simple and has some good differentiable properties. The box constrained VIP can be reformulated as a differentiable optimization problem by the proposed smooth gap function. The conditions, under which any stationary point of the optimization problem is the solution to the box constrained VIP, are discussed. A simple frictional contact problem is analyzed to show the applications of the smooth gap function. Finally, the numerical experiments confirm the good theoretical properties of the method.
文摘In this note, we establish a new formulation of smoothness conditions for piecewise polynomial (: =pp) functions in terms of the B-net representation in the general n-dimensional setting. It plays an important role for 2-dimensional setting in the constructive proof of the fact that the spaces of polynomial splines with smoothness rand total degree k≥3r+2 over arbitrary triangulations achieve the optimal approximation order with the approximation constant depending only on k and the smallest angle of the partition in [5].
文摘In this paper, a class of smoothing modulus-based iterative method was presented for solving implicit complementarity problems. The main idea was to transform the implicit complementarity problem into an equivalent implicit fixed-point equation, then introduces a smoothing function to obtain its approximation solutions. The convergence analysis of the algorithm was given, and the efficiency of the algorithms was verified by numerical experiments.
基金The project supported by the National Natural Science foundation of china(10225212,50178016.10302007)the National Kev Basic Research Special Foundation and the Ministry of Education of China
文摘Three dimensional frictional contact problems are formulated as linear complementarity problems based on the parametric variational principle. Two aggregate-functionbased algorithms for solving complementarity problems are proposed. One is called the self-adjusting interior point algorithm, the other is called the aggregate function smoothing algorithm. Numerical experiment shows the efficiency of the proposed two algorithms.
基金supported by the Natural Science Foundation of Fujian Province(Grant No.2021J01661)by the National Natural Science Foundation of China(Grant No.11901024)+5 种基金supported by the National Natural Science Foundation of China(Grant No.12201275)by the Ministry of Education in China of Humanities and Social Science Project(Grant No.21YJCZH204)by the Liaoning Provincial Department of Education(Grant No.JYTZD2023072)supported by the National Natural Science Foundation of China(Grant No.12131004)by the Ministry of Science and Technology of China(Grant No.2021YFA1003600)supported by the National Key Research and Development Program of China(Grant No.2019YFC0312003).
文摘The system of generalized absolute value equations(GAVE)has attracted more and more attention in the optimization community.In this paper,by introducing a smoothing function,we develop a smoothing Newton algorithm with non-monotone line search to solve the GAVE.We show that the non-monotone algorithm is globally and locally quadratically convergent under a weaker assumption than those given in most existing algorithms for solving the GAVE.Numerical results are given to demonstrate the viability and efficiency of the approach.
基金The support of CAAM and the University of Mount Saint Vincent is gratefully acknowledged。
文摘To explore experimental quantization of stochastic chaos and exact wave tur-bulence in exponential oscillons,it is necessary to construct smooth random functions of time.In the current paper,we develop a new method of modeling stochastic variables described by a closed system of ordinary differential and algebraic equations.Primarily,oscillatory and pulsatory dynamic models pro-duced by the first triplet of copolar elliptic functions are studied from the view-point of the Hamiltonian and Newtonian dynamics.Secondly,the Hamilto-nian systems of the first triplet and the first triplet squared are meticulously investigated in the hyperbolic limit that results in oscillations and pulsations with rectangular and point pulses and a variable period.Thirdly,the relative Hamiltonian systems are used to develop two stochastic models of a random oscillatory cn-noise and a random pulsatory cn2-noise.Numerical experi-ments show that for the Bernoulli frequencies the random oscillatory cn-noise approaches a smooth random oscillatory variable with an unbounded period and the Gaussian probability distribution and the random pulsatory cn2-noise tends to a smooth random pulsatory variable with an unbounded period and the truncated Gaussian probability distribution as the number of elliptic modes approaches infinity.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.52077203 and 61701467)the Natural Science Foundation of Zhejiang Province,China(Grant No.LY19E070003)。
文摘Two-dimensional finite element mesh generation algorithm for electromagnetic field calculation is proposed in this paper to improve the efficiency and accuracy of electromagnetic calculation. An image boundary extraction algorithm is developed to map the image on the geometric domain. Identification algorithm for the location of nodes in polygon area is proposed to determine the state of the node. To promote the average quality of the mesh and the efficiency of mesh generation, a novel force-based mesh smoothing algorithm is proposed. One test case and a typical electromagnetic calculation are used to testify the effectiveness and efficiency of the proposed algorithm. The results demonstrate that the proposed algorithm can produce a high-quality mesh with less iteration.
基金support by Basic Science Research Program through the National Research Foundation(NRF)funded by Korea Ministry of Education(No.2016R1A6A1A0312812).
文摘The aim of this work is to employ a modified cell-based smoothed finite element method(S-FEM)for topology optimization with the domain discretized with arbitrary polygons.In the present work,the linear polynomial basis function is used as the weight function instead of the constant weight function used in the standard S-FEM.This improves the accuracy and yields an optimal convergence rate.The gradients are smoothed over each smoothing domain,then used to compute the stiffness matrix.Within the proposed scheme,an optimum topology procedure is conducted over the smoothing domains.Structural materials are distributed over each smoothing domain and the filtering scheme relies on the smoothing domain.Numerical tests are carried out to pursue the performance of the proposed optimization by comparing convergence,efficiency and accuracy.
基金supported by the National Natural Science Foundation of China(61401196)the Jiangsu Provincial Natural Science Foundation of China(BK20140954)+1 种基金the Science and Technology on Information Transmission and Dissemination in Communication Networks Laboratory(KX152600015/ITD-U15006)the Beijing Shengfeifan Electronic System Technology Development Co.,Ltd(KY10800150036)
文摘A novel modulation recognition algorithm is proposed by introducing a Chen-Harker-Kanzow-Smale (CHKS) smooth function into the C-support vector machine deformation algorithm. A set of seven characteristic parameters is selected from a range of parameters of communication signals including instantaneous amplitude, phase, and frequency. And the Newton-Armijo algorithm is utilized to train the proposed algorithm, namely, smooth CHKS smooth support vector machine (SCHKS-SSVM). Compared with the existing algorithms, the proposed algorithm not only solves the non-differentiable problem of the second order objective function, but also reduces the recognition error. It significantly improves the training speed and also saves a large amount of storage space through large-scale sorting problems. The simulation results show that the recognition rate of the algorithm can batch training. Therefore, the proposed algorithm is suitable for solving the problem of high dimension and its recognition can exceed 95% when the signal-to-noise ratio is no less than 10 dB.
基金supported by the National Natural Science Foundation of China(6110016561100231+6 种基金5120530961472307)the Natural Science Foundation of Shaanxi Province(2012JQ80442014JM83132010JQ8004)the Foundation of Education Department of Shaanxi Province(2013JK1096)the New Star Team of Xi’an University of Posts and Telecommunications
文摘Support vector machines （SVMs） have been extensively studied and have shown remarkable success in many applications. A new family of twice continuously differentiable piecewise smooth functions are used to smooth the objective function of uncon- strained SVMs. The three-order piecewise smooth support vector machine （TPWSSVMd） is proposed. The piecewise functions can get higher and higher approximation accuracy as required with the increase of parameter d. The global convergence proof of TPWSSVMd is given with the rough set theory. TPWSSVMd can efficiently handle large scale and high dimensional problems. Nu- merical results demonstrate TPWSSVMa has better classification performance and learning efficiency than other competitive base- lines.
基金This work was supported by National Natural Science Foundation of China （NSFC） （No. 81400265 and No. 81270274）, and Peking University People＇s Hospital Research and Development funds （RDB2014-16）.
文摘Angiotensin （Ang）-（1-7） is recognized as a new bioactive peptide in renin-angiotensin system （RAS）. Ang-（1-7） is a counter-regulatory mediator of Ang-II which appears to be protective against cardiovascular disease. Recent studies have found that Ang-（1-7） played an important role in reducing smooth muscle cell proliferation and migration, improving endothelial function and regulating lipid metabolism, leading to inhibition of atherosclerotic lesions and increase of plaque stability. Although clinical application of Ang-（1-7） is restricted due to its pharmacokinetic properties, identification of stabilized compounds, including more stable analogues and specific delivery compounds, has enabled clinical application of Ang-（1-7）. In this review, we discussed recent findings concerning the biological role of Ang-（1-7） and related mechanism during atherosclerosis development. In addition, we highlighted the perspective to develop therapeutic strategies using Ang-（1-7） to treat atherosclerosis.
基金This work was supported in part by the National Natural Science Foundation of China(No.11431004)the Innovation Program of Shanghai Municipal Education Commission.
文摘In this paper,we study smoothing approximations for some piecewise smooth functions.We first present two approaches for one-dimensional case:a global approach is to construct smoothing approximations over the whole domain and a local approach is to construct smoothing approximations within appropriate neighborhoods of the nonsmooth points.We obtain some error estimate results for both approaches and discuss whether the smoothing approximations can inherit the convexity of the original functions.Furthermore,we extend the global approach to some multiple dimensional cases.
