From the viewpoints of both fuzzy system and fuzzy reasoning, a new fuzzy reasoning method which contains the α- triple I restriction method as its particular case is proposed. The previous α-triple I restriction pr...From the viewpoints of both fuzzy system and fuzzy reasoning, a new fuzzy reasoning method which contains the α- triple I restriction method as its particular case is proposed. The previous α-triple I restriction principles are improved, and then the optimal restriction solutions of this new method are achieved, especially for seven familiar implications. As its special case, the corresponding results of α-triple I restriction method are obtained and improved. Lastly, it is found by examples that this new method is more reasonable than the α-triple I restriction method.展开更多
The face recognition with expression and occlusion variation becomes the greatest challenge in biometric applications to recognize people. The proposed work concentrates on recognizing occlusion and seven kinds of exp...The face recognition with expression and occlusion variation becomes the greatest challenge in biometric applications to recognize people. The proposed work concentrates on recognizing occlusion and seven kinds of expression variations such as neutral, surprise, happy, sad, fear, disgust and angry. During enrollment process, principle component analysis (PCA) detects facial regions on the input image. The detected facial region is converted into fuzzy domain data to make decision during recognition process. The Haar wavelet transform extracts features from the detected facial regions. The Nested Hidden markov model is employed to train these features and each feature of face image is considered as states in a Markov chain to perform learning among the features. The maximum likelihood for the input image was estimated by using Baum Welch algorithm and these features were kept on database. During recognition process, the expression and occlusion varied face image is taken as the test image and maximum likelihood for test image is found by following same procedure done in enrollment process. The matching score between maximum likelihood of input image and test image is computed and it is utilized by fuzzy rule based method to decide whether the test image belongs to authorized or unauthorized. The proposed work was tested among several expression varied and occluded face images of JAFFE and AR datasets respectively.展开更多
We propose two error control techniques for numerical integrations in fast multiscale collocation methods for solving Fredholm integral equations of the second kind with weakly singular kernels. Both techniques utiliz...We propose two error control techniques for numerical integrations in fast multiscale collocation methods for solving Fredholm integral equations of the second kind with weakly singular kernels. Both techniques utilize quadratures for singular integrals using graded points. One has a polynomial order of accuracy if the integrand has a polynomial order of smoothness except at the singular point and the other has exponential order of accuracy if the integrand has an infinite order of smoothness except at the singular point. We estimate the order of convergence and computational complexity of the corresponding approximate solutions of the equation. We prove that the second technique preserves the order of convergence and computational complexity of the original collocation method. Numerical experiments are presented to illustrate the theoretical estimates.展开更多
A kind of nondecreasing subgradient algorithm with appropriate stopping rule has been proposed for nonsmooth constrained minimization problem. The dual theory is invoked in dealing with the stopping rule and general g...A kind of nondecreasing subgradient algorithm with appropriate stopping rule has been proposed for nonsmooth constrained minimization problem. The dual theory is invoked in dealing with the stopping rule and general global minimiizing algorithm is employed as a subroutine of the algorithm. The method is expected to tackle a large class of nonsmooth constrained minimization problem.展开更多
The distribution of sampling data influences completeness of rule base so that extrapolating missing rules is very difficult. Based on data mining, a self-learning method is developed for identifying fuzzy model and e...The distribution of sampling data influences completeness of rule base so that extrapolating missing rules is very difficult. Based on data mining, a self-learning method is developed for identifying fuzzy model and extrapolating missing rules, by means of confidence measure and the improved gradient descent method. The proposed approach can not only identify fuzzy model, update its parameters and determine optimal output fuzzy sets simultaneously, but also resolve the uncontrollable problem led by the regions that data do not cover. The simulation results show the effectiveness and accuracy of the proposed approach with the classical truck backer-upper control problem verifying.展开更多
This paper applies the analytical transfer matrix method （ATMM） to calculate energy eigenvalues of a particle in low dimensional sharp confining potential for the first time, and deduces the quantization rules of th...This paper applies the analytical transfer matrix method （ATMM） to calculate energy eigenvalues of a particle in low dimensional sharp confining potential for the first time, and deduces the quantization rules of this system. It presents three cases in which the applied method works very well. In the first quantum dot, the energy eigenvalues and eigenfunction are obtained, and compared with those acquired from the exact numerical analysis and the WKB （Wentzel, Kramers and Brillouin） method; in the second or the third case, we get the energy eigenvalues by the ATMM, and compare them with the EBK （Einstein, Brillouin and Keller） results or the wavefunction outcomes. From the comparisons, we find that the semiclassical method （WKB, EBK or wavefunction） is inexact in such systems.展开更多
AIM To develop a framework to incorporate background domain knowledge into classification rule learning for knowledge discovery in biomedicine.METHODS Bayesian rule learning(BRL) is a rule-based classifier that uses a...AIM To develop a framework to incorporate background domain knowledge into classification rule learning for knowledge discovery in biomedicine.METHODS Bayesian rule learning(BRL) is a rule-based classifier that uses a greedy best-first search over a space of Bayesian belief-networks(BN) to find the optimal BN to explain the input dataset, and then infers classification rules from this BN. BRL uses a Bayesian score to evaluate the quality of BNs. In this paper, we extended the Bayesian score to include informative structure priors, which encodes our prior domain knowledge about the dataset. We call this extension of BRL as BRL_p. The structure prior has a λ hyperparameter that allows the user to tune the degree of incorporation of the prior knowledge in the model learning process. We studied the effect of λ on model learning using a simulated dataset and a real-world lung cancer prognostic biomarker dataset, by measuring the degree of incorporation of our specified prior knowledge. We also monitored its effect on the model predictive performance. Finally, we compared BRL_p to other stateof-the-art classifiers commonly used in biomedicine.RESULTS We evaluated the degree of incorporation of prior knowledge into BRL_p, with simulated data by measuring the Graph Edit Distance between the true datagenerating model and the model learned by BRL_p. We specified the true model using informative structurepriors. We observed that by increasing the value of λ we were able to increase the influence of the specified structure priors on model learning. A large value of λ of BRL_p caused it to return the true model. This also led to a gain in predictive performance measured by area under the receiver operator characteristic curve(AUC). We then obtained a publicly available real-world lung cancer prognostic biomarker dataset and specified a known biomarker from literature [the epidermal growth factor receptor(EGFR) gene]. We again observed that larger values of λ led to an increased incorporation of EGFR into the final BRL_p model. This relevant background knowledge also led to a gain in AUC.CONCLUSION BRL_p enables tunable structure priors to be incorporated during Bayesian classification rule learning that integrates data and knowledge as demonstrated using lung cancer biomarker data.展开更多
In the present research, a simple quasi-continuum model, the Cauchy-Born rule model, is used to investigate the size effects of elastic modulus for fcc metals. By considering a nanoplate model and calculating the stra...In the present research, a simple quasi-continuum model, the Cauchy-Born rule model, is used to investigate the size effects of elastic modulus for fcc metals. By considering a nanoplate model and calculating the strain energy for the nano-sized plate under tension and bending, the relationship between the elastic modulus and the plate thickness is found. Size effects of the elastic modulus are displayed by the relative differences of the elastic modulus between the nano-sized plate sample and the bulk sample. By comparing the present results with those of others, the effectiveness of the Cauchy-Born rule model in studying the size effects of material properties are shown.展开更多
A job shop scheduling problem with a combination processing in complex production environment is proposed. Based on the defining of ＂non-elastic combination processing relativity＂ and ＂virtual process＂, the proble...A job shop scheduling problem with a combination processing in complex production environment is proposed. Based on the defining of ＂non-elastic combination processing relativity＂ and ＂virtual process＂, the problem can be simplified and transformed to a traditional one. On the basis of the dispatching rules select engine and considered factors of complex production environment, a heuristic method is designed. The algorithm has been applied to a mould enterprise in Shenzhen for half a year. The practice showed that by using the method suggested the number of delayed orders was decreased about 20% and the productivity was increased by 10 to 20%.展开更多
This paper proposes the Laplace Discrete Adomian Decomposition Method and its application for solving nonlinear integro-differential equations. This method is based upon the Laplace Adomian decomposition method couple...This paper proposes the Laplace Discrete Adomian Decomposition Method and its application for solving nonlinear integro-differential equations. This method is based upon the Laplace Adomian decomposition method coupled with some quadrature rules of numerical integration. Four numerical examples of integro-differential equations in both Volterra and Fredholm integrals are used to be solved by the proposed method. The performance of the proposed method is verified through absolute error measures between the approximated solutions and exact solutions. The series of experimental numerical results show that our proposed method performs in high accuracy and efficiency. The study clearly highlights that the proposed method could be used to overcome the analytical approaches in solving nonlinear integro-differential equations.展开更多
In this paper, we firstly give a counterexample to indicate that the chain rule is lack of accuracy. After that, we put forward the fractional Riccati expansion method. No need to use the chain rule, we apply this met...In this paper, we firstly give a counterexample to indicate that the chain rule is lack of accuracy. After that, we put forward the fractional Riccati expansion method. No need to use the chain rule, we apply this method to fractional KdV-type and fractional Telegraph equations and obtain the tangent and cotangent functions solutions of these fractional equations for the first time.展开更多
An inverse problem for identification of the coefficient in heat-conduction equation is considered. After reducing the problem to a nonlinear ill-posed operator equation, Newton type iterative methods are considered. ...An inverse problem for identification of the coefficient in heat-conduction equation is considered. After reducing the problem to a nonlinear ill-posed operator equation, Newton type iterative methods are considered. The implicit iterative method is applied to the linearized Newton equation, and the key step in the process is that a new reasonable a posteriori stopping rule for the inner iteration is presented. Numerical experiments for the new method as well as for Tikhonov method and Bakushikskii method are given, and these results show the obvious advantages of the new method over the other ones.展开更多
on the basis of linguistics, psychology and other related theory, we should carry outgame teaching method to make students learn easily and happily because of the lack of interestand other problems in some parts of ou...on the basis of linguistics, psychology and other related theory, we should carry outgame teaching method to make students learn easily and happily because of the lack of interestand other problems in some parts of our country.展开更多
The classical composite rectangle (constant) rule for the computation of Cauchy principle value integral with the singular kernel is discussed. We show that the superconvergence rate of the composite midpoint ru...The classical composite rectangle (constant) rule for the computation of Cauchy principle value integral with the singular kernel is discussed. We show that the superconvergence rate of the composite midpoint rule occurs at certain local coodinate of each subinterval and obtain the corresponding superconvergence error estimate. Then collation methods are presented to solve certain kind of Hilbert singular integral equation. At last, some numerical examples are provided to validate the theoretical analysis.展开更多
The Burzynski criterion is developed for anisotropic asymmetric metals with the non-associated flow rule （NAFR） for plane stress problems. The presented pressure depending on the yield criterion can be calibrated wi...The Burzynski criterion is developed for anisotropic asymmetric metals with the non-associated flow rule （NAFR） for plane stress problems. The presented pressure depending on the yield criterion can be calibrated with ten experimental data, i.e., the tensile yield stresses at 0°, 45°, and 90°, the compressive yield stresses at 0°, 15°, 30°, 45°, 75°, and 90° from the rolling direction, and the biaxial tensile yield stress. The corresponding pressure independent plastic potential function can be calibrated with six experimental data, i.e., the tensile R-values at 0°, 15°, 45°, 75°, and 90° from the rolling direction and the tensile biaxial R-value. The downhill simplex method is used to solve these ten and six high nonlinear equations for the yield and plastic potential functions, respectively. The results show that the presented new criterion is appropriate for anisotropic asymmetric metals.展开更多
基金supported by the National Natural Science Foundation of China (61105076 61070124)+2 种基金the National High Technology Research and Development Program of China (863 Program) (2012AA011103)the Open Project of State Key Laboratory of Virtual Reality Technology and Systems of China (BUAA-VR-10KF-5)the Fundamental Research Funds for the Central Universities (2011HGZY0004)
文摘From the viewpoints of both fuzzy system and fuzzy reasoning, a new fuzzy reasoning method which contains the α- triple I restriction method as its particular case is proposed. The previous α-triple I restriction principles are improved, and then the optimal restriction solutions of this new method are achieved, especially for seven familiar implications. As its special case, the corresponding results of α-triple I restriction method are obtained and improved. Lastly, it is found by examples that this new method is more reasonable than the α-triple I restriction method.
文摘The face recognition with expression and occlusion variation becomes the greatest challenge in biometric applications to recognize people. The proposed work concentrates on recognizing occlusion and seven kinds of expression variations such as neutral, surprise, happy, sad, fear, disgust and angry. During enrollment process, principle component analysis (PCA) detects facial regions on the input image. The detected facial region is converted into fuzzy domain data to make decision during recognition process. The Haar wavelet transform extracts features from the detected facial regions. The Nested Hidden markov model is employed to train these features and each feature of face image is considered as states in a Markov chain to perform learning among the features. The maximum likelihood for the input image was estimated by using Baum Welch algorithm and these features were kept on database. During recognition process, the expression and occlusion varied face image is taken as the test image and maximum likelihood for test image is found by following same procedure done in enrollment process. The matching score between maximum likelihood of input image and test image is computed and it is utilized by fuzzy rule based method to decide whether the test image belongs to authorized or unauthorized. The proposed work was tested among several expression varied and occluded face images of JAFFE and AR datasets respectively.
基金The NNSF (10371137 and 10201034) of Chinathe Foundation (20030558008) of Doctoral Program of National Higher Education, Guangdong Provincial Natural Science Foundation (1011170) of China and the Advanced Research Foundation of Zhongshan UniversityThe US National Science Foundation (9973427 and 0312113)NSF (10371122) of China and the Chinese Academy of Sciences under the program of "Hundred Distinguished Young Chinese Scientists."
文摘We propose two error control techniques for numerical integrations in fast multiscale collocation methods for solving Fredholm integral equations of the second kind with weakly singular kernels. Both techniques utilize quadratures for singular integrals using graded points. One has a polynomial order of accuracy if the integrand has a polynomial order of smoothness except at the singular point and the other has exponential order of accuracy if the integrand has an infinite order of smoothness except at the singular point. We estimate the order of convergence and computational complexity of the corresponding approximate solutions of the equation. We prove that the second technique preserves the order of convergence and computational complexity of the original collocation method. Numerical experiments are presented to illustrate the theoretical estimates.
文摘A kind of nondecreasing subgradient algorithm with appropriate stopping rule has been proposed for nonsmooth constrained minimization problem. The dual theory is invoked in dealing with the stopping rule and general global minimiizing algorithm is employed as a subroutine of the algorithm. The method is expected to tackle a large class of nonsmooth constrained minimization problem.
基金This project was supported by State Science &Technology Pursuing Project (2001BA204B01) of China and Foundation forUniversity Key Teacher by the Ministry of Education of China.
文摘The distribution of sampling data influences completeness of rule base so that extrapolating missing rules is very difficult. Based on data mining, a self-learning method is developed for identifying fuzzy model and extrapolating missing rules, by means of confidence measure and the improved gradient descent method. The proposed approach can not only identify fuzzy model, update its parameters and determine optimal output fuzzy sets simultaneously, but also resolve the uncontrollable problem led by the regions that data do not cover. The simulation results show the effectiveness and accuracy of the proposed approach with the classical truck backer-upper control problem verifying.
文摘This paper applies the analytical transfer matrix method （ATMM） to calculate energy eigenvalues of a particle in low dimensional sharp confining potential for the first time, and deduces the quantization rules of this system. It presents three cases in which the applied method works very well. In the first quantum dot, the energy eigenvalues and eigenfunction are obtained, and compared with those acquired from the exact numerical analysis and the WKB （Wentzel, Kramers and Brillouin） method; in the second or the third case, we get the energy eigenvalues by the ATMM, and compare them with the EBK （Einstein, Brillouin and Keller） results or the wavefunction outcomes. From the comparisons, we find that the semiclassical method （WKB, EBK or wavefunction） is inexact in such systems.
基金Supported by National Institute of General Medical Sciences of the National Institutes of Health,No.R01GM100387
文摘AIM To develop a framework to incorporate background domain knowledge into classification rule learning for knowledge discovery in biomedicine.METHODS Bayesian rule learning(BRL) is a rule-based classifier that uses a greedy best-first search over a space of Bayesian belief-networks(BN) to find the optimal BN to explain the input dataset, and then infers classification rules from this BN. BRL uses a Bayesian score to evaluate the quality of BNs. In this paper, we extended the Bayesian score to include informative structure priors, which encodes our prior domain knowledge about the dataset. We call this extension of BRL as BRL_p. The structure prior has a λ hyperparameter that allows the user to tune the degree of incorporation of the prior knowledge in the model learning process. We studied the effect of λ on model learning using a simulated dataset and a real-world lung cancer prognostic biomarker dataset, by measuring the degree of incorporation of our specified prior knowledge. We also monitored its effect on the model predictive performance. Finally, we compared BRL_p to other stateof-the-art classifiers commonly used in biomedicine.RESULTS We evaluated the degree of incorporation of prior knowledge into BRL_p, with simulated data by measuring the Graph Edit Distance between the true datagenerating model and the model learned by BRL_p. We specified the true model using informative structurepriors. We observed that by increasing the value of λ we were able to increase the influence of the specified structure priors on model learning. A large value of λ of BRL_p caused it to return the true model. This also led to a gain in predictive performance measured by area under the receiver operator characteristic curve(AUC). We then obtained a publicly available real-world lung cancer prognostic biomarker dataset and specified a known biomarker from literature [the epidermal growth factor receptor(EGFR) gene]. We again observed that larger values of λ led to an increased incorporation of EGFR into the final BRL_p model. This relevant background knowledge also led to a gain in AUC.CONCLUSION BRL_p enables tunable structure priors to be incorporated during Bayesian classification rule learning that integrates data and knowledge as demonstrated using lung cancer biomarker data.
基金Project supported by the National Natural Science Foundation of China(Nos.11021262,10932011 and 91216108)the National Basic Research Program of China(2012CB937500)
文摘In the present research, a simple quasi-continuum model, the Cauchy-Born rule model, is used to investigate the size effects of elastic modulus for fcc metals. By considering a nanoplate model and calculating the strain energy for the nano-sized plate under tension and bending, the relationship between the elastic modulus and the plate thickness is found. Size effects of the elastic modulus are displayed by the relative differences of the elastic modulus between the nano-sized plate sample and the bulk sample. By comparing the present results with those of others, the effectiveness of the Cauchy-Born rule model in studying the size effects of material properties are shown.
基金Supported by Research Fund for the Doctoral Program of Higher Education of China(20060487072)National Key Technology R&D Program(2006BAF01A43)
文摘A job shop scheduling problem with a combination processing in complex production environment is proposed. Based on the defining of ＂non-elastic combination processing relativity＂ and ＂virtual process＂, the problem can be simplified and transformed to a traditional one. On the basis of the dispatching rules select engine and considered factors of complex production environment, a heuristic method is designed. The algorithm has been applied to a mould enterprise in Shenzhen for half a year. The practice showed that by using the method suggested the number of delayed orders was decreased about 20% and the productivity was increased by 10 to 20%.
文摘This paper proposes the Laplace Discrete Adomian Decomposition Method and its application for solving nonlinear integro-differential equations. This method is based upon the Laplace Adomian decomposition method coupled with some quadrature rules of numerical integration. Four numerical examples of integro-differential equations in both Volterra and Fredholm integrals are used to be solved by the proposed method. The performance of the proposed method is verified through absolute error measures between the approximated solutions and exact solutions. The series of experimental numerical results show that our proposed method performs in high accuracy and efficiency. The study clearly highlights that the proposed method could be used to overcome the analytical approaches in solving nonlinear integro-differential equations.
文摘In this paper, we firstly give a counterexample to indicate that the chain rule is lack of accuracy. After that, we put forward the fractional Riccati expansion method. No need to use the chain rule, we apply this method to fractional KdV-type and fractional Telegraph equations and obtain the tangent and cotangent functions solutions of these fractional equations for the first time.
文摘An inverse problem for identification of the coefficient in heat-conduction equation is considered. After reducing the problem to a nonlinear ill-posed operator equation, Newton type iterative methods are considered. The implicit iterative method is applied to the linearized Newton equation, and the key step in the process is that a new reasonable a posteriori stopping rule for the inner iteration is presented. Numerical experiments for the new method as well as for Tikhonov method and Bakushikskii method are given, and these results show the obvious advantages of the new method over the other ones.
文摘on the basis of linguistics, psychology and other related theory, we should carry outgame teaching method to make students learn easily and happily because of the lack of interestand other problems in some parts of our country.
文摘The classical composite rectangle (constant) rule for the computation of Cauchy principle value integral with the singular kernel is discussed. We show that the superconvergence rate of the composite midpoint rule occurs at certain local coodinate of each subinterval and obtain the corresponding superconvergence error estimate. Then collation methods are presented to solve certain kind of Hilbert singular integral equation. At last, some numerical examples are provided to validate the theoretical analysis.
文摘The Burzynski criterion is developed for anisotropic asymmetric metals with the non-associated flow rule （NAFR） for plane stress problems. The presented pressure depending on the yield criterion can be calibrated with ten experimental data, i.e., the tensile yield stresses at 0°, 45°, and 90°, the compressive yield stresses at 0°, 15°, 30°, 45°, 75°, and 90° from the rolling direction, and the biaxial tensile yield stress. The corresponding pressure independent plastic potential function can be calibrated with six experimental data, i.e., the tensile R-values at 0°, 15°, 45°, 75°, and 90° from the rolling direction and the tensile biaxial R-value. The downhill simplex method is used to solve these ten and six high nonlinear equations for the yield and plastic potential functions, respectively. The results show that the presented new criterion is appropriate for anisotropic asymmetric metals.
