We review and compare two definitions of rough set approximations.One is defined by a pair of sets in the universe and the other by a pair of sets in the quotient universe.The latter definition,although less studied,i...We review and compare two definitions of rough set approximations.One is defined by a pair of sets in the universe and the other by a pair of sets in the quotient universe.The latter definition,although less studied,is semantically superior for interpreting rule induction and is closely related to granularity switching in granular computing.Numerical measures about the accuracy and quality of approximations are examined.Several semantics difficulties are commented.展开更多
In this work it is shown that the kinetic energy and the exchange-correlation energy are mutual dependent on each other.This aspect is first derived in an orbital-free context.It is shown that the total Fermi potentia...In this work it is shown that the kinetic energy and the exchange-correlation energy are mutual dependent on each other.This aspect is first derived in an orbital-free context.It is shown that the total Fermi potential depends on the density only,the individual parts,the Pauli kinetic energy and the exchange-correlation energy,however,are orbital dependent and as such mutually influence each other.The numerical investigation is performed for the orbital-based non-interacting Kohn-Sham system in order to avoid additional effects due to further approximations of the kinetic energy.The numerical influence of the exchange-correlation functional on the non-interacting kinetic energy is shown to be of the orderof a few Hartrees.For chemical purposes,however,the energetic performance as a function of the nuclear coordinates is much more important than total energies.Therefore,the effect on the bond dissociation curve was studied exemplarily for the carbon monoxide.The data reveals that,the mutual influence between the exchange-correlation functional and the kinetic energy has a significant influence on bond dissociation energies and bond distances.Therefore,the effect of the exchange-correlation treatment must be considered in the design of orbital-free density functional approximations for the kinetic energy.展开更多
In this paper,we construct a power type functional which is the approximation functional of the Singular Trudinger-Moser functional.Moreover,we obtain the concentration level of the functional and show it converges to...In this paper,we construct a power type functional which is the approximation functional of the Singular Trudinger-Moser functional.Moreover,we obtain the concentration level of the functional and show it converges to the concentration level of singular Trudinger-Moser functional on the unit ball.展开更多
This paper studies the Smoluchowski–Kramers approximation for a discrete-time dynamical system modeled as the motion of a particle in a force field.We show that the approximation holds for the drift-implicit Euler–M...This paper studies the Smoluchowski–Kramers approximation for a discrete-time dynamical system modeled as the motion of a particle in a force field.We show that the approximation holds for the drift-implicit Euler–Maruyama discretization and derive its convergence rate.In particular,the solution of the discretized system converges to the solution of the first-order limit equation in the mean-square sense,and this convergence is independent of the order in which the mass parameterμand the step size h tend to zero.展开更多
The Stackelberg prediction game(SPG)is a bilevel optimization frame-work for modeling strategic interactions between a learner and a follower.Existing meth-ods for solving this problem with general loss functions are ...The Stackelberg prediction game(SPG)is a bilevel optimization frame-work for modeling strategic interactions between a learner and a follower.Existing meth-ods for solving this problem with general loss functions are computationally expensive and scarce.We propose a novel hyper-gradient type method with a warm-start strategy to address this challenge.Particularly,we first use a Taylor expansion-based approach to obtain a good initial point.Then we apply a hyper-gradient descent method with an ex-plicit approximate hyper-gradient.We establish the convergence results of our algorithm theoretically.Furthermore,when the follower employs the least squares loss function,our method is shown to reach an e-stationary point by solving quadratic subproblems.Numerical experiments show our algorithms are empirically orders of magnitude faster than the state-of-the-art.展开更多
The Majorana zero modes in vortex cores are of extensive interest in the context of topological quantum computing.However,a zero-energy bound state may arise accidentally but is not necessarily a Majorana zero mode.Su...The Majorana zero modes in vortex cores are of extensive interest in the context of topological quantum computing.However,a zero-energy bound state may arise accidentally but is not necessarily a Majorana zero mode.Such accidental zero modes should be carefully ruled out in experiment in order to identify the genuine Majorana zero modes.We show that in a spin-orbital coupled multi-band superconductor,such as the iron-selenide superconductor,accidental zero modes indeed arise in the vortex core if the pairing symmetry is the so-called nodeless d-wave(defined in the absence of spin-orbital coupling).Instead,if the pairing sym-metry is s_(++)or s_(+−)with respect to the Fermi pockets split by the spin-orbital coupling,the accidental zero modes do not appear in the limit of weak spin-orbital coupling.Our results are not only important in the experimental identification of Majorana zero modes,but also provide an avenue to pinpoint the pairing symmetry of the iron-selenide superconductor.展开更多
The three common genetic models(or modes of inheritance)in association analysis are the dominant,additive,and recessive models.It is known that the Cochran-Armitage trend test(CATT)which correctly incorporates informa...The three common genetic models(or modes of inheritance)in association analysis are the dominant,additive,and recessive models.It is known that the Cochran-Armitage trend test(CATT)which correctly incorporates information from genetic models,is more powerful than the commonly used Pearson’s chi-square test.However,the true genetic model is usually unknown in practice,and the power of the CAT test could be substantially reduced with a wrongly specified genetic model.To achieve a power that is close to that of a correctly specified CAT test,it is natural to apply trend tests under different possible genetic models and to report the most significant test result.This results in a MAX-type testing procedure,and it was found that this test is usually more powerful than the Pearson’s chi-square test.Although the signi-ficance(i.e.,p value)of the MAX-type test can be accessed by either large sample approximation or permutation methods,requirements for sample size or simulation replicates are demanding with respect to accuracy and efficiency.This paper proposes an approach to calculate the exact p values of MAX-type tests based on the combinatorial counting method.The simulation results show that the exact method is more accurate than the large sample approximation methods and more computationally efficient than the permutation method,and our method can be readily applied to genome-wide association studies(GWASs).The proposed methodis built in an R package,MaXact,which is available at the https://github.com/Myuan 2019/MaXact/.展开更多
General neural network inverse adaptive controller has two flaws: the first is the slow convergence speed; the second is the invalidation to the non-minimum phase system. These defects limit the scope in which the neu...General neural network inverse adaptive controller has two flaws: the first is the slow convergence speed; the second is the invalidation to the non-minimum phase system. These defects limit the scope in which the neural network inverse adaptive controller is used. We employ Davidon least squares in training the multi-layer feedforward neural network used in approximating the inverse model of plant to expedite the convergence, and then through constructing the pseudo-plant, a neural network inverse adaptive controller is put forward which is still effective to the nonlinear non-minimum phase system. The simulation results show the validity of this scheme.展开更多
A relaxation least squares-based learning algorithm for neual networks is proposed. Not only does it have a fast convergence rate, but it involves less computation quantity. Therefore, it is suitable to deal with the ...A relaxation least squares-based learning algorithm for neual networks is proposed. Not only does it have a fast convergence rate, but it involves less computation quantity. Therefore, it is suitable to deal with the case when a network has a large scale but the number of training data is very limited. It has been used in converting furnace process modelling, and impressive result has been obtained.展开更多
According to time-sharing valuation principle (TSVP) of power supply, the relationships of current density and current efficiency at different acidities are obtained based on the processed data of electrolytic deposit...According to time-sharing valuation principle (TSVP) of power supply, the relationships of current density and current efficiency at different acidities are obtained based on the processed data of electrolytic deposition process of zinc (EDPZ) with the least square method (LSM). Thus an optimal model of time-sharing power supply system for EDPZ is established, which has been optimized by use of an improved efficient simulated annealing algorithm (SAA). Practical results show that industrial and mining enterprises can obtain enormous economic benefits every year.展开更多
The inverse design of electron lens is realized by two different methods in this paper. One is damped least square method and the other is the artificial neural network method. Their merits and defects are discussed a...The inverse design of electron lens is realized by two different methods in this paper. One is damped least square method and the other is the artificial neural network method. Their merits and defects are discussed according to our calculation results in the paper. In the condition of selecting the learning samples properly, the artificial neural network has obvious advantages in the inverse design of electron lens. It is an effective method to solve the inverse design problem in the electron optic system.展开更多
A robust on-line fault diagnosis methor based on least squares estimate for nonlinear difference-algebraic systems (DAS) with uncertainties is proposed. Based on the known nominal model of the DAS, this method firstly...A robust on-line fault diagnosis methor based on least squares estimate for nonlinear difference-algebraic systems (DAS) with uncertainties is proposed. Based on the known nominal model of the DAS, this method firstly constructs an auxiliary system consisting of a difference equation and an algebraic equation, then, based on the relationship between the state deviation and the faults in the difference equation and the relationship between the algebraic variable deviation and the faults in algebraic equation, it identifies the faults on-line through least squares estimate. This method can not only detect, isolate and identify faults for DAS, but also give the upper bound of the error of fault identification. The simulation results indicate that it can give satisfactory diagnostic results for both abrupt and incipient faults.展开更多
The support vector machine （SVM） is a novel machine learning method, which has the ability to approximate nonlinear functions with arbitrary accuracy. Setting parameters well is very crucial for SVM learning results...The support vector machine （SVM） is a novel machine learning method, which has the ability to approximate nonlinear functions with arbitrary accuracy. Setting parameters well is very crucial for SVM learning results and generalization ability, and now there is no systematic, general method for parameter selection. In this article, the SVM parameter selection for function approximation is regarded as a compound optimization problem and a mutative scale chaos optimization algorithm is employed to search for optimal paraxneter values. The chaos optimization algorithm is an effective way for global optimal and the mutative scale chaos algorithm could improve the search efficiency and accuracy. Several simulation examples show the sensitivity of the SVM parameters and demonstrate the superiority of this proposed method for nonlinear function approximation.展开更多
文摘We review and compare two definitions of rough set approximations.One is defined by a pair of sets in the universe and the other by a pair of sets in the quotient universe.The latter definition,although less studied,is semantically superior for interpreting rule induction and is closely related to granularity switching in granular computing.Numerical measures about the accuracy and quality of approximations are examined.Several semantics difficulties are commented.
基金The project was supported by the Fund for Scientific Research in Flanders (FWO-Vlaanderen) for Research Grant G021115N.
文摘In this work it is shown that the kinetic energy and the exchange-correlation energy are mutual dependent on each other.This aspect is first derived in an orbital-free context.It is shown that the total Fermi potential depends on the density only,the individual parts,the Pauli kinetic energy and the exchange-correlation energy,however,are orbital dependent and as such mutually influence each other.The numerical investigation is performed for the orbital-based non-interacting Kohn-Sham system in order to avoid additional effects due to further approximations of the kinetic energy.The numerical influence of the exchange-correlation functional on the non-interacting kinetic energy is shown to be of the orderof a few Hartrees.For chemical purposes,however,the energetic performance as a function of the nuclear coordinates is much more important than total energies.Therefore,the effect on the bond dissociation curve was studied exemplarily for the carbon monoxide.The data reveals that,the mutual influence between the exchange-correlation functional and the kinetic energy has a significant influence on bond dissociation energies and bond distances.Therefore,the effect of the exchange-correlation treatment must be considered in the design of orbital-free density functional approximations for the kinetic energy.
文摘In this paper,we construct a power type functional which is the approximation functional of the Singular Trudinger-Moser functional.Moreover,we obtain the concentration level of the functional and show it converges to the concentration level of singular Trudinger-Moser functional on the unit ball.
基金supported by the PhD Research Startup Foundation of Hubei University of Economics(Grand No.XJ23BS42).
文摘This paper studies the Smoluchowski–Kramers approximation for a discrete-time dynamical system modeled as the motion of a particle in a force field.We show that the approximation holds for the drift-implicit Euler–Maruyama discretization and derive its convergence rate.In particular,the solution of the discretized system converges to the solution of the first-order limit equation in the mean-square sense,and this convergence is independent of the order in which the mass parameterμand the step size h tend to zero.
文摘The Stackelberg prediction game(SPG)is a bilevel optimization frame-work for modeling strategic interactions between a learner and a follower.Existing meth-ods for solving this problem with general loss functions are computationally expensive and scarce.We propose a novel hyper-gradient type method with a warm-start strategy to address this challenge.Particularly,we first use a Taylor expansion-based approach to obtain a good initial point.Then we apply a hyper-gradient descent method with an ex-plicit approximate hyper-gradient.We establish the convergence results of our algorithm theoretically.Furthermore,when the follower employs the least squares loss function,our method is shown to reach an e-stationary point by solving quadratic subproblems.Numerical experiments show our algorithms are empirically orders of magnitude faster than the state-of-the-art.
基金supported by National Key R&D Program of China(Grant No.2022YFA1403201)and National Natural Science Foundation of China(Grant No.12374147,12274205 and 92365203).
文摘The Majorana zero modes in vortex cores are of extensive interest in the context of topological quantum computing.However,a zero-energy bound state may arise accidentally but is not necessarily a Majorana zero mode.Such accidental zero modes should be carefully ruled out in experiment in order to identify the genuine Majorana zero modes.We show that in a spin-orbital coupled multi-band superconductor,such as the iron-selenide superconductor,accidental zero modes indeed arise in the vortex core if the pairing symmetry is the so-called nodeless d-wave(defined in the absence of spin-orbital coupling).Instead,if the pairing sym-metry is s_(++)or s_(+−)with respect to the Fermi pockets split by the spin-orbital coupling,the accidental zero modes do not appear in the limit of weak spin-orbital coupling.Our results are not only important in the experimental identification of Majorana zero modes,but also provide an avenue to pinpoint the pairing symmetry of the iron-selenide superconductor.
基金This work was supported by the Natural Science Foundation of Anhui Province(2008085MA09)the National Natural Science Foundation of China(11671375).
文摘The three common genetic models(or modes of inheritance)in association analysis are the dominant,additive,and recessive models.It is known that the Cochran-Armitage trend test(CATT)which correctly incorporates information from genetic models,is more powerful than the commonly used Pearson’s chi-square test.However,the true genetic model is usually unknown in practice,and the power of the CAT test could be substantially reduced with a wrongly specified genetic model.To achieve a power that is close to that of a correctly specified CAT test,it is natural to apply trend tests under different possible genetic models and to report the most significant test result.This results in a MAX-type testing procedure,and it was found that this test is usually more powerful than the Pearson’s chi-square test.Although the signi-ficance(i.e.,p value)of the MAX-type test can be accessed by either large sample approximation or permutation methods,requirements for sample size or simulation replicates are demanding with respect to accuracy and efficiency.This paper proposes an approach to calculate the exact p values of MAX-type tests based on the combinatorial counting method.The simulation results show that the exact method is more accurate than the large sample approximation methods and more computationally efficient than the permutation method,and our method can be readily applied to genome-wide association studies(GWASs).The proposed methodis built in an R package,MaXact,which is available at the https://github.com/Myuan 2019/MaXact/.
基金Tianjin Natural Science Foundation !983602011National 863/CIMS Research Foundation !863-511-945-010
文摘General neural network inverse adaptive controller has two flaws: the first is the slow convergence speed; the second is the invalidation to the non-minimum phase system. These defects limit the scope in which the neural network inverse adaptive controller is used. We employ Davidon least squares in training the multi-layer feedforward neural network used in approximating the inverse model of plant to expedite the convergence, and then through constructing the pseudo-plant, a neural network inverse adaptive controller is put forward which is still effective to the nonlinear non-minimum phase system. The simulation results show the validity of this scheme.
基金This project was supported by the National Natural Science Foundation of China (No. 60174021)the Key Project of Tianjin Natural Science Foundation (No.010115).
文摘A relaxation least squares-based learning algorithm for neual networks is proposed. Not only does it have a fast convergence rate, but it involves less computation quantity. Therefore, it is suitable to deal with the case when a network has a large scale but the number of training data is very limited. It has been used in converting furnace process modelling, and impressive result has been obtained.
文摘According to time-sharing valuation principle (TSVP) of power supply, the relationships of current density and current efficiency at different acidities are obtained based on the processed data of electrolytic deposition process of zinc (EDPZ) with the least square method (LSM). Thus an optimal model of time-sharing power supply system for EDPZ is established, which has been optimized by use of an improved efficient simulated annealing algorithm (SAA). Practical results show that industrial and mining enterprises can obtain enormous economic benefits every year.
基金the Scientific Research Foundation for Returned Overseas Chinese Scholars, State EducationCommission.
文摘The inverse design of electron lens is realized by two different methods in this paper. One is damped least square method and the other is the artificial neural network method. Their merits and defects are discussed according to our calculation results in the paper. In the condition of selecting the learning samples properly, the artificial neural network has obvious advantages in the inverse design of electron lens. It is an effective method to solve the inverse design problem in the electron optic system.
文摘A robust on-line fault diagnosis methor based on least squares estimate for nonlinear difference-algebraic systems (DAS) with uncertainties is proposed. Based on the known nominal model of the DAS, this method firstly constructs an auxiliary system consisting of a difference equation and an algebraic equation, then, based on the relationship between the state deviation and the faults in the difference equation and the relationship between the algebraic variable deviation and the faults in algebraic equation, it identifies the faults on-line through least squares estimate. This method can not only detect, isolate and identify faults for DAS, but also give the upper bound of the error of fault identification. The simulation results indicate that it can give satisfactory diagnostic results for both abrupt and incipient faults.
基金the National Nature Science Foundation of China (60775047, 60402024)
文摘The support vector machine （SVM） is a novel machine learning method, which has the ability to approximate nonlinear functions with arbitrary accuracy. Setting parameters well is very crucial for SVM learning results and generalization ability, and now there is no systematic, general method for parameter selection. In this article, the SVM parameter selection for function approximation is regarded as a compound optimization problem and a mutative scale chaos optimization algorithm is employed to search for optimal paraxneter values. The chaos optimization algorithm is an effective way for global optimal and the mutative scale chaos algorithm could improve the search efficiency and accuracy. Several simulation examples show the sensitivity of the SVM parameters and demonstrate the superiority of this proposed method for nonlinear function approximation.
