In this article we consider the asymptotic behavior of extreme distribution with the extreme value index γ>0 . The rates of uniform convergence for Fréchet distribution are constructed under the second-order ...In this article we consider the asymptotic behavior of extreme distribution with the extreme value index γ>0 . The rates of uniform convergence for Fréchet distribution are constructed under the second-order regular variation condition.展开更多
The subset sum problem is a combinatorial optimization problem,and its complexity belongs to the nondeterministic polynomial time complete(NP-Complete)class.This problem is widely used in encryption,planning or schedu...The subset sum problem is a combinatorial optimization problem,and its complexity belongs to the nondeterministic polynomial time complete(NP-Complete)class.This problem is widely used in encryption,planning or scheduling,and integer partitions.An accurate search algorithm with polynomial time complexity has not been found,which makes it challenging to be solved on classical computers.To effectively solve this problem,we translate it into the quantum Ising model and solve it with a variational quantum optimization method based on conditional values at risk.The proposed model needs only n qubits to encode 2ndimensional search space,which can effectively save the encoding quantum resources.The model inherits the advantages of variational quantum algorithms and can obtain good performance at shallow circuit depths while being robust to noise,and it is convenient to be deployed in the Noisy Intermediate Scale Quantum era.We investigate the effects of the scalability,the variational ansatz type,the variational depth,and noise on the model.Moreover,we also discuss the performance of the model under different conditional values at risk.Through computer simulation,the scale can reach more than nine qubits.By selecting the noise type,we construct simulators with different QVs and study the performance of the model with them.In addition,we deploy the model on a superconducting quantum computer of the Origin Quantum Technology Company and successfully solve the subset sum problem.This model provides a new perspective for solving the subset sum problem.展开更多
In this paper, necessary optimality conditions for a class of Semi-infinite Variational Problems are established which are further generalized to a class of Multi-objective Semi-Infinite Variational Problems. These co...In this paper, necessary optimality conditions for a class of Semi-infinite Variational Problems are established which are further generalized to a class of Multi-objective Semi-Infinite Variational Problems. These conditions are responsible for the development of duality theory which is an extremely important feature for any class of problems, but the literature available so far lacks these necessary optimality conditions for the stated problem. A lemma is also proved to find the topological dual of as it is required to prove the desired result.展开更多
A class of quasilinear elliptic variational inequalities with double degenerate is discussed in this paper. We extend the Keldys-Fichera boundary value problem and the first boundary problem of degenerate elliptic equ...A class of quasilinear elliptic variational inequalities with double degenerate is discussed in this paper. We extend the Keldys-Fichera boundary value problem and the first boundary problem of degenerate elliptic equation to the variationalinequalities. We establish the existence and uniqueness of the weak solution of ocrresspending problem under nonstandard growth conditions.展开更多
Generative AI models for music and the arts in general are increasingly complex and hard to understand.The field of ex-plainable AI(XAI)seeks to make complex and opaque AI models such as neural networks more understan...Generative AI models for music and the arts in general are increasingly complex and hard to understand.The field of ex-plainable AI(XAI)seeks to make complex and opaque AI models such as neural networks more understandable to people.One ap-proach to making generative AI models more understandable is to impose a small number of semantically meaningful attributes on gen-erative AI models.This paper contributes a systematic examination of the impact that different combinations of variational auto-en-coder models(measureVAE and adversarialVAE),configurations of latent space in the AI model(from 4 to 256 latent dimensions),and training datasets(Irish folk,Turkish folk,classical,and pop)have on music generation performance when 2 or 4 meaningful musical at-tributes are imposed on the generative model.To date,there have been no systematic comparisons of such models at this level of com-binatorial detail.Our findings show that measureVAE has better reconstruction performance than adversarialVAE which has better musical attribute independence.Results demonstrate that measureVAE was able to generate music across music genres with inter-pretable musical dimensions of control,and performs best with low complexity music such as pop and rock.We recommend that a 32 or 64 latent dimensional space is optimal for 4 regularised dimensions when using measureVAE to generate music across genres.Our res-ults are the first detailed comparisons of configurations of state-of-the-art generative AI models for music and can be used to help select and configure AI models,musical features,and datasets for more understandable generation of music.展开更多
Exposure to poor indoor air conditions poses significant risks to human health, increasing morbidity and mortality rates. Soft measurement modeling is suitable for stable and accurate monitoring of air pollutants and ...Exposure to poor indoor air conditions poses significant risks to human health, increasing morbidity and mortality rates. Soft measurement modeling is suitable for stable and accurate monitoring of air pollutants and improving air quality. Based on partial least squares (PLS), we propose an indoor air quality prediction model that utilizes variational auto-encoder regression (VAER) algorithm. To reduce the negative effects of noise, latent variables in the original data are extracted by PLS in the first step. Then, the extracted variables are used as inputs to VAER, which improve the accuracy and robustness of the model. Through comparative analysis with traditional methods, we demonstrate the superior performance of our PLS-VAER model, which exhibits improved prediction performance and stability. The root mean square error (RMSE) of PLS-VAER is reduced by 14.71%, 26.47%, and 12.50% compared to single VAER, PLS-SVR, and PLS-ANN, respectively. Additionally, the coefficient of determination (R2) of PLS-VAER improves by 13.70%, 30.09%, and 11.25% compared to single VAER, PLS-SVR, and PLS-ANN, respectively. This research offers an innovative and environmentally-friendly approach to monitor and improve indoor air quality.展开更多
Invariant conditions for conformable fractional problems of the calculus of variations under the presence of external forces in the dynamics are studied. Depending on the type of transformations considered, different ...Invariant conditions for conformable fractional problems of the calculus of variations under the presence of external forces in the dynamics are studied. Depending on the type of transformations considered, different necessary conditions of invariance are obtained. As particular cases, we prove fractional versions of Noether's symmetry theorem. Invariant conditions for fractional optimal control problems, using the Hamiltonian formalism, are also investigated. As an example of potential application in Physics, we show that with conformable derivatives it is possible to formulate an Action Principle for particles under frictional forces that is far simpler than the one obtained with classical fractional derivatives.展开更多
In this work, a new class of variational inclusion involving T-accretive operators in Banach spaces is introduced and studied. New iterative algorithms for stability for their class of variational inclusions and its c...In this work, a new class of variational inclusion involving T-accretive operators in Banach spaces is introduced and studied. New iterative algorithms for stability for their class of variational inclusions and its convergence results are established.展开更多
In this paper, a new variational formulation for a reaction-diffusion problem in broken Sobolev space is proposed. And the new formulation in the broken Sobolev space will be proved that it is well-posed and equivalen...In this paper, a new variational formulation for a reaction-diffusion problem in broken Sobolev space is proposed. And the new formulation in the broken Sobolev space will be proved that it is well-posed and equivalent to the standard Galerkin variational formulation. The method will be helpful to easily solve the original partial differential equation numerically. And the method is novel and interesting, which can be used to deal with some complicated problem, such as the low regularity problem, the differential-integral problem and so on.展开更多
One existence integral condition was obtained for the adapted solution of the general backward stochastic differential equations(BSDEs). Then by solving the integral constraint condition, and using a limit procedure, ...One existence integral condition was obtained for the adapted solution of the general backward stochastic differential equations(BSDEs). Then by solving the integral constraint condition, and using a limit procedure, a new approach method is proposed and the existence of the solution was proved for the BSDEs if the diffusion coefficients satisfy the locally Lipschitz condition. In the special case the solution was a Brownian bridge. The uniqueness is also considered in the meaning of "F0-integrable equivalent class" . The new approach method would give us an efficient way to control the main object instead of the "noise".展开更多
To reveal the multivariate relationships between man-made and meteorological factors on dust storm frequency, the LUCC data, NDVI remote sensing data and meteorological data for the period of 1983-2013 were combined w...To reveal the multivariate relationships between man-made and meteorological factors on dust storm frequency, the LUCC data, NDVI remote sensing data and meteorological data for the period of 1983-2013 were combined with dust storm frequency data, and the possible impacts of meteorological and anthropogenic factors on dust storm frequency were analyzed by using regression analysis and PCA (Principal Component Analysis). Results show that the inter-annual dust storm frequency increased gradually. In particular, an increasing trend in recent years, after 2009, is conspicuous. The monthly frequency of dust storms shows higher values between the months of February and May, with the highest mean number of events occurring in April, which accounts for 29% of the annual dust storm frequency. The annual dust storm frequency is positively correlated with wind speed and negatively correlated with precipitation;the monthly dust storm frequency is positively correlated with wind speed, but no significant correlation can be found with precipitation. The relationship between temperature and dust storms is not simply linear, however, a certain correlation with an unremarkable statistical significance can be found between them. Human activities also affect the dynamics of dust storms indirectly via changing vegetation coverage and direct dust emissions. The multivariate analysis further confirmed the association between dust storm frequency and meteorological factors and NDVI. The high loadings of dust storm frequency, wind speed, precipitation and NDVI on a PC indicate that the increased precipitation and NDVI will decrease dust storm frequency, and increased wind speed will increase dust storm frequency.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
The authors consider optimization methods for box constrained variational inequalities. First, the authors study the KKT-conditions problem based on the original problem. A merit function for the KKT-conditions proble...The authors consider optimization methods for box constrained variational inequalities. First, the authors study the KKT-conditions problem based on the original problem. A merit function for the KKT-conditions problem is proposed, and some desirable properties of the merit function are obtained. Through the merit function, the original problem is reformulated as minimization with simple constraints. Then, the authors show that any stationary point of the optimization problem is a solution of the original problem. Finally, a descent algorithm is presented for the optimization problem, and global convergence is shown.展开更多
The variational analysis of the Pseudo-potential function-vortex-potential function model, a new mathematical model, was developed and by which the flow field with transonic speed and curl was decided, and different s...The variational analysis of the Pseudo-potential function-vortex-potential function model, a new mathematical model, was developed and by which the flow field with transonic speed and curl was decided, and different sorts of the variational principle for vortex potential function were established by transforming the original equation for vortex-function, the boundary conditions for vortex-potential function was raised.展开更多
文摘In this article we consider the asymptotic behavior of extreme distribution with the extreme value index γ>0 . The rates of uniform convergence for Fréchet distribution are constructed under the second-order regular variation condition.
基金supported by the National Key R&D Program of China(Grant No.2019YFA0308700)the Innovation Program for Quantum Science and Technology(Grant No.2021ZD0301500)。
文摘The subset sum problem is a combinatorial optimization problem,and its complexity belongs to the nondeterministic polynomial time complete(NP-Complete)class.This problem is widely used in encryption,planning or scheduling,and integer partitions.An accurate search algorithm with polynomial time complexity has not been found,which makes it challenging to be solved on classical computers.To effectively solve this problem,we translate it into the quantum Ising model and solve it with a variational quantum optimization method based on conditional values at risk.The proposed model needs only n qubits to encode 2ndimensional search space,which can effectively save the encoding quantum resources.The model inherits the advantages of variational quantum algorithms and can obtain good performance at shallow circuit depths while being robust to noise,and it is convenient to be deployed in the Noisy Intermediate Scale Quantum era.We investigate the effects of the scalability,the variational ansatz type,the variational depth,and noise on the model.Moreover,we also discuss the performance of the model under different conditional values at risk.Through computer simulation,the scale can reach more than nine qubits.By selecting the noise type,we construct simulators with different QVs and study the performance of the model with them.In addition,we deploy the model on a superconducting quantum computer of the Origin Quantum Technology Company and successfully solve the subset sum problem.This model provides a new perspective for solving the subset sum problem.
文摘In this paper, necessary optimality conditions for a class of Semi-infinite Variational Problems are established which are further generalized to a class of Multi-objective Semi-Infinite Variational Problems. These conditions are responsible for the development of duality theory which is an extremely important feature for any class of problems, but the literature available so far lacks these necessary optimality conditions for the stated problem. A lemma is also proved to find the topological dual of as it is required to prove the desired result.
文摘A class of quasilinear elliptic variational inequalities with double degenerate is discussed in this paper. We extend the Keldys-Fichera boundary value problem and the first boundary problem of degenerate elliptic equation to the variationalinequalities. We establish the existence and uniqueness of the weak solution of ocrresspending problem under nonstandard growth conditions.
文摘Generative AI models for music and the arts in general are increasingly complex and hard to understand.The field of ex-plainable AI(XAI)seeks to make complex and opaque AI models such as neural networks more understandable to people.One ap-proach to making generative AI models more understandable is to impose a small number of semantically meaningful attributes on gen-erative AI models.This paper contributes a systematic examination of the impact that different combinations of variational auto-en-coder models(measureVAE and adversarialVAE),configurations of latent space in the AI model(from 4 to 256 latent dimensions),and training datasets(Irish folk,Turkish folk,classical,and pop)have on music generation performance when 2 or 4 meaningful musical at-tributes are imposed on the generative model.To date,there have been no systematic comparisons of such models at this level of com-binatorial detail.Our findings show that measureVAE has better reconstruction performance than adversarialVAE which has better musical attribute independence.Results demonstrate that measureVAE was able to generate music across music genres with inter-pretable musical dimensions of control,and performs best with low complexity music such as pop and rock.We recommend that a 32 or 64 latent dimensional space is optimal for 4 regularised dimensions when using measureVAE to generate music across genres.Our res-ults are the first detailed comparisons of configurations of state-of-the-art generative AI models for music and can be used to help select and configure AI models,musical features,and datasets for more understandable generation of music.
基金supported by the Opening Project of Guangxi Key Laboratory of Clean Pulp&Papermaking and Pollution Control,China(No.2021KF11)the Shandong Provincial Natural Science Foundation,China(No.ZR2021MF135)+1 种基金the National Natural Science Foundation of China(No.52170001)the Natural Science Foundation of Jiangsu Provincial Universities,China(No.22KJA530003).
文摘Exposure to poor indoor air conditions poses significant risks to human health, increasing morbidity and mortality rates. Soft measurement modeling is suitable for stable and accurate monitoring of air pollutants and improving air quality. Based on partial least squares (PLS), we propose an indoor air quality prediction model that utilizes variational auto-encoder regression (VAER) algorithm. To reduce the negative effects of noise, latent variables in the original data are extracted by PLS in the first step. Then, the extracted variables are used as inputs to VAER, which improve the accuracy and robustness of the model. Through comparative analysis with traditional methods, we demonstrate the superior performance of our PLS-VAER model, which exhibits improved prediction performance and stability. The root mean square error (RMSE) of PLS-VAER is reduced by 14.71%, 26.47%, and 12.50% compared to single VAER, PLS-SVR, and PLS-ANN, respectively. Additionally, the coefficient of determination (R2) of PLS-VAER improves by 13.70%, 30.09%, and 11.25% compared to single VAER, PLS-SVR, and PLS-ANN, respectively. This research offers an innovative and environmentally-friendly approach to monitor and improve indoor air quality.
基金supported by CNPq and CAPES(Brazilian research funding agencies)Portuguese funds through the Center for Research and Development in Mathematics and Applications(CIDMA)the Portuguese Foundation for Science and Technology(FCT),within project UID/MAT/04106/2013
文摘Invariant conditions for conformable fractional problems of the calculus of variations under the presence of external forces in the dynamics are studied. Depending on the type of transformations considered, different necessary conditions of invariance are obtained. As particular cases, we prove fractional versions of Noether's symmetry theorem. Invariant conditions for fractional optimal control problems, using the Hamiltonian formalism, are also investigated. As an example of potential application in Physics, we show that with conformable derivatives it is possible to formulate an Action Principle for particles under frictional forces that is far simpler than the one obtained with classical fractional derivatives.
文摘In this work, a new class of variational inclusion involving T-accretive operators in Banach spaces is introduced and studied. New iterative algorithms for stability for their class of variational inclusions and its convergence results are established.
基金Supported by the Natural Science Foundation of Henan Province(162300410031) Supported by the Excellent Youth Program of the Basic Research Operating Expenses Program of Henan Province (yqpy20140039)
文摘In this paper, a new variational formulation for a reaction-diffusion problem in broken Sobolev space is proposed. And the new formulation in the broken Sobolev space will be proved that it is well-posed and equivalent to the standard Galerkin variational formulation. The method will be helpful to easily solve the original partial differential equation numerically. And the method is novel and interesting, which can be used to deal with some complicated problem, such as the low regularity problem, the differential-integral problem and so on.
基金National Natural Science Foundation of China ( No. 11171062 ) Natural Science Foundation for the Youth,China ( No.11101077) Innovation Program of Shanghai Municipal Education Commission,China ( No. 12ZZ063)
文摘One existence integral condition was obtained for the adapted solution of the general backward stochastic differential equations(BSDEs). Then by solving the integral constraint condition, and using a limit procedure, a new approach method is proposed and the existence of the solution was proved for the BSDEs if the diffusion coefficients satisfy the locally Lipschitz condition. In the special case the solution was a Brownian bridge. The uniqueness is also considered in the meaning of "F0-integrable equivalent class" . The new approach method would give us an efficient way to control the main object instead of the "noise".
文摘To reveal the multivariate relationships between man-made and meteorological factors on dust storm frequency, the LUCC data, NDVI remote sensing data and meteorological data for the period of 1983-2013 were combined with dust storm frequency data, and the possible impacts of meteorological and anthropogenic factors on dust storm frequency were analyzed by using regression analysis and PCA (Principal Component Analysis). Results show that the inter-annual dust storm frequency increased gradually. In particular, an increasing trend in recent years, after 2009, is conspicuous. The monthly frequency of dust storms shows higher values between the months of February and May, with the highest mean number of events occurring in April, which accounts for 29% of the annual dust storm frequency. The annual dust storm frequency is positively correlated with wind speed and negatively correlated with precipitation;the monthly dust storm frequency is positively correlated with wind speed, but no significant correlation can be found with precipitation. The relationship between temperature and dust storms is not simply linear, however, a certain correlation with an unremarkable statistical significance can be found between them. Human activities also affect the dynamics of dust storms indirectly via changing vegetation coverage and direct dust emissions. The multivariate analysis further confirmed the association between dust storm frequency and meteorological factors and NDVI. The high loadings of dust storm frequency, wind speed, precipitation and NDVI on a PC indicate that the increased precipitation and NDVI will decrease dust storm frequency, and increased wind speed will increase dust storm frequency.
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.
基金the National Natural Science Foundation of China(No.19971002)
文摘The authors consider optimization methods for box constrained variational inequalities. First, the authors study the KKT-conditions problem based on the original problem. A merit function for the KKT-conditions problem is proposed, and some desirable properties of the merit function are obtained. Through the merit function, the original problem is reformulated as minimization with simple constraints. Then, the authors show that any stationary point of the optimization problem is a solution of the original problem. Finally, a descent algorithm is presented for the optimization problem, and global convergence is shown.
文摘The variational analysis of the Pseudo-potential function-vortex-potential function model, a new mathematical model, was developed and by which the flow field with transonic speed and curl was decided, and different sorts of the variational principle for vortex potential function were established by transforming the original equation for vortex-function, the boundary conditions for vortex-potential function was raised.