The Convergence Rate of Fréchet Distribution under the Second-Order Regular Variation Condition

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.

On the 4D Variational Data Assimilation with Constraint Conditions

An investigation is carried out on the problem involved in 4D variational data assimilation (VDA) with constraint conditions based on a finite-element shallow-water equation model. In the investigation, the adjoint technology, penalty method and augmented Lagrangian method are used in constraint optimization field to minimize the defined constraint objective functions. The results of the numerical experiments show that the optimal solutions are obtained if the functions reach the minima. VDA with constraint conditions controlling the growth of gravity oscillations is efficient to eliminate perturbation and produces optimal initial field. It seems that this method can also be applied to the problem in numerical weather prediction. Key words Variational data assimilation - Constraint conditions - Penalty methods - finite-element model This research is supported by National Natural Science Foundation of China (Grant No. 49575269) and by National Key Basic Research on the Formation Mechanism and Prediction Theory of Severe Synoptic Disasters (Grant No. G1998040910).

Solving the subset sum problem by the quantum Ising model with variational quantum optimization based on conditional values at risk

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.

Necessary Optimality Conditions for Multi-Objective Semi-Infinite Variational Problem

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.

THE ELLIPTIC VARIATIONAL INEQUALITIES WITH DOUBLE DEGENERATE AND GENERAL GROWTH CONDITIONS

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.

SNP site-drug association prediction algorithm based on denoising variational auto-encoder

Single nucletide polymorphism(SNP)is an important factor for the study of genetic variation in human families and animal and plant strains.Therefore,it is widely used in the study of population genetics and disease related gene.In pharmacogenomics research,identifying the association between SNP site and drug is the key to clinical precision medication,therefore,a predictive model of SNP site and drug association based on denoising variational auto-encoder(DVAE-SVM)is proposed.Firstly,k-mer algorithm is used to construct the initial SNP site feature vector,meanwhile,MACCS molecular fingerprint is introduced to generate the feature vector of the drug module.Then,we use the DVAE to extract the effective features of the initial feature vector of the SNP site.Finally,the effective feature vector of the SNP site and the feature vector of the drug module are fused input to the support vector machines(SVM)to predict the relationship of SNP site and drug module.The results of five-fold cross-validation experiments indicate that the proposed algorithm performs better than random forest(RF)and logistic regression(LR)classification.Further experiments show that compared with the feature extraction algorithms of principal component analysis(PCA),denoising auto-encoder(DAE)and variational auto-encode(VAE),the proposed algorithm has better prediction results.

Exploring Variational Auto-encoder Architectures, Configurations, and Datasets for Generative Music Explainable AI

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.

Feature-aided pose estimation approach based on variational auto-encoder structure for spacecrafts

Real-time 6 Degree-of-Freedom(DoF)pose estimation is of paramount importance for various on-orbit tasks.Benefiting from the development of deep learning,Convolutional Neural Networks(CNNs)in feature extraction has yielded impressive achievements for spacecraft pose estimation.To improve the robustness and interpretability of CNNs,this paper proposes a Pose Estimation approach based on Variational Auto-Encoder structure(PE-VAE)and a Feature-Aided pose estimation approach based on Variational Auto-Encoder structure(FA-VAE),which aim to accurately estimate the 6 DoF pose of a target spacecraft.Both methods treat the pose vector as latent variables,employing an encoder-decoder network with a Variational Auto-Encoder(VAE)structure.To enhance the precision of pose estimation,PE-VAE uses the VAE structure to introduce reconstruction mechanism with the whole image.Furthermore,FA-VAE enforces feature shape constraints by exclusively reconstructing the segment of the target spacecraft with the desired shape.Comparative evaluation against leading methods on public datasets reveals similar accuracy with a threefold improvement in processing speed,showcasing the significant contribution of VAE structures to accuracy enhancement,and the additional benefit of incorporating global shape prior features.

A novel deep learning framework with variational auto-encoder for indoor air quality prediction

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.

Variational Calculus With Conformable Fractional Derivatives

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.

Stable Perturbed Algorithms for a New Class of Generalized Nonlinear Implicit Quasi Variational Inclusions in Banach Spaces

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.

A New Variational Formulation for a Kind of Reaction-diffusion Problem in Broken Sobolev Space

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.

Variational Approach for the Adapted Solution of Backw ard Stochastic Differential Equations with Locally Lipschitz Diffusion Coefficients

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".

Variation Trends of Dust Storms in Relation to Meteorological Conditions and Anthropogenic Impacts in the Northeast Edge of the Taklimakan Desert, China

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.

New smooth gap function for box constrained variational inequalities

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.

MERIT FUNCTION AND GLOBAL ALGORITHMFOR BOX CONSTRAINED VARIATIONALINEQUALITIES

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.

QUASI-VARIATIONAL PRINCIPLE FOR THE VORTEX-POTENTIAL FUNCTION OF ROTATIONAL FLOW IN THREE-DIMENSION PIPE

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.

基于条件变分自编码器和贝叶斯神经网络的短期电力负荷概率预测

考虑到输入信息和预测模型的不确定性对负荷预测结果的影响,本文提出一种基于条件变分自编码器和贝叶斯神经网络的短期电力负荷概率预测方法.通过条件变分自编码器生成指定天气因素预测值和日历特征条件下实际天气因素可能的多个随机样本,以模拟天气预测信息的不确定性;构建GRU-S2S贝叶斯神经网络学习模型参数的分布特征,以反映预测模型的不确定性,并结合MC dropout技术获得多个可能的负荷预测值;遍历天气因素全部模拟样本,将预测模型输出的负荷预测值构成集合,并通过核密度估计获得预测时段内各时刻预测负荷服从的概率分布.实际算例结果表明,该方法在短期负荷概率预测中具有更高的分位数预测精度和更可靠稳定的区间预测结果.

2000-2020年内蒙古NDVI时空动态及其对水热条件的响应

[目的]了解植被生态现状,剖析植被变化影响因素,为区域生态环境治理和规划提供科学依据。[方法]基于MOD13A3 NDVI数据和气象数据,采用Sen趋势分析、M-K检验、Hurst指数、相关系数等方法研究了内蒙古地区NDVI时空变化及其对水热条件的响应。[结果]内蒙古NDVI显著增长(p<0.01),空间分布呈东高西低的特征,大部分地区NDVI以增加趋势为主,耕地增长率最大且呈增加趋势面积占比最大。研究期内NDVI变化相对稳定,林地的稳定性最好。未来内蒙古NDVI变化以反持续性为主,反持续性和持续性面积占比分别为76.51%,23.49%。NDVI与气温呈负相关的区域占78.25%,其中极显著和显著负相关的区域占19.92%;与降水、土壤湿度呈正相关的区域占93.16%,93.53%,其中极显著和显著正相关的区域分别占51.37%,55.85%。[结论]内蒙古地区植被生态整体趋于改善,未来植被生态可能退化,土壤湿度是影响内蒙古植被生长的主导因子。

DCVAE与DPC融合的网络入侵检测模型研究

入侵检测是主动防御网络中攻击行为的技术,以往入侵检测模型因正常网络流量与未知攻击内在特征区分度不足,导致对未知攻击识别率不够高,本文设计基于判别条件变分自编码器与密度峰值聚类算法的入侵检测模型(DCVAE-DPC).利用判别条件变分自编码器能够生成指定类别样本的能力,学习正常网络流量特征的隐空间表示并计算其重建误差,增加其与未知攻击间的特征区分度,并使用密度峰值聚类算法求出正常网络流量重建误差的分布,提高未知攻击识别率.实验结果表明,在NSL-KDD数据集中与当前流行的入侵检测模型相比,模型的分类准确率可以达到97.08%,具有更高的未知攻击检测能力,面对当前复杂网络环境,有更强的入侵检测性能.