Composition Analysis and Identification of Ancient Glass Products Based on L1 Regularization Logistic Regression

In view of the composition analysis and identification of ancient glass products, L1 regularization, K-Means cluster analysis, elbow rule and other methods were comprehensively used to build logical regression, cluster analysis, hyper-parameter test and other models, and SPSS, Python and other tools were used to obtain the classification rules of glass products under different fluxes, sub classification under different chemical compositions, hyper-parameter K value test and rationality analysis. Research can provide theoretical support for the protection and restoration of ancient glass relics.

Enhanced Differentiable Architecture Search Based on Asymptotic Regularization

In differentiable search architecture search methods,a more efficient search space design can significantly improve the performance of the searched architecture,thus requiring people to carefully define the search space with different complexity according to various operations.Meanwhile rationalizing the search strategies to explore the well-defined search space will further improve the speed and efficiency of architecture search.With this in mind,we propose a faster and more efficient differentiable architecture search method,AllegroNAS.Firstly,we introduce a more efficient search space enriched by the introduction of two redefined convolution modules.Secondly,we utilize a more efficient architectural parameter regularization method,mitigating the overfitting problem during the search process and reducing the error brought about by gradient approximation.Meanwhile,we introduce a natural exponential cosine annealing method to make the learning rate of the neural network training process more suitable for the search procedure.Moreover,group convolution and data augmentation are employed to reduce the computational cost.Finally,through extensive experiments on several public datasets,we demonstrate that our method can more swiftly search for better-performing neural network architectures in a more efficient search space,thus validating the effectiveness of our approach.

Low-Rank Multi-View Subspace Clustering Based on Sparse Regularization

Multi-view Subspace Clustering (MVSC) emerges as an advanced clustering method, designed to integrate diverse views to uncover a common subspace, enhancing the accuracy and robustness of clustering results. The significance of low-rank prior in MVSC is emphasized, highlighting its role in capturing the global data structure across views for improved performance. However, it faces challenges with outlier sensitivity due to its reliance on the Frobenius norm for error measurement. Addressing this, our paper proposes a Low-Rank Multi-view Subspace Clustering Based on Sparse Regularization (LMVSC- Sparse) approach. Sparse regularization helps in selecting the most relevant features or views for clustering while ignoring irrelevant or noisy ones. This leads to a more efficient and effective representation of the data, improving the clustering accuracy and robustness, especially in the presence of outliers or noisy data. By incorporating sparse regularization, LMVSC-Sparse can effectively handle outlier sensitivity, which is a common challenge in traditional MVSC methods relying solely on low-rank priors. Then Alternating Direction Method of Multipliers (ADMM) algorithm is employed to solve the proposed optimization problems. Our comprehensive experiments demonstrate the efficiency and effectiveness of LMVSC-Sparse, offering a robust alternative to traditional MVSC methods.

Echo State Network With Probabilistic Regularization for Time Series Prediction

Recent decades have witnessed a trend that the echo state network(ESN)is widely utilized in field of time series prediction due to its powerful computational abilities.However,most of the existing research on ESN is conducted under the assumption that data is free of noise or polluted by the Gaussian noise,which lacks robustness or even fails to solve real-world tasks.This work handles this issue by proposing a probabilistic regularized ESN(PRESN)with robustness guaranteed.Specifically,we design a novel objective function for minimizing both the mean and variance of modeling error,and then a scheme is derived for getting output weights of the PRESN.Furthermore,generalization performance,robustness,and unbiased estimation abilities of the PRESN are revealed by theoretical analyses.Finally,experiments on a benchmark dataset and two real-world datasets are conducted to verify the performance of the proposed PRESN.The source code is publicly available at https://github.com/LongJinlab/probabilistic-regularized-echo-state-network.

Comparisons between Isotropic and Anisotropic TV Regularizations in Inverse Acoustic Scattering

This article compares the isotropic and anisotropic TV regularizations used in inverse acoustic scattering. It is observed that compared with the traditional Tikhonov regularization, isotropic and anisotropic TV regularizations perform better in the sense of edge preserving. While anisotropic TV regularization will cause distortions along axes. To minimize the energy function with isotropic and anisotropic regularization terms, we use split Bregman scheme. We do several 2D numerical experiments to validate the above arguments.

A Hybrid Regularization-Based Multi-Frame Super-Resolution Using Bayesian Framework

The prime purpose for the image reconstruction of a multi-frame super-resolution is to reconstruct a higher-resolution image through incorporating the knowledge obtained from a series of relevant low-resolution images,which is useful in numerousfields.Nevertheless,super-resolution image reconstruction methods are usually damaged by undesirable restorative artifacts,which include blurring distortion,noises,and stair-casing effects.Consequently,it is always challenging to achieve balancing between image smoothness and preservation of the edges inside the image.In this research work,we seek to increase the effectiveness of multi-frame super-resolution image reconstruction by increasing the visual information and improving the automated machine perception,which improves human analysis and interpretation processes.Accordingly,we propose a new approach to the image reconstruction of multi-frame super-resolution,so that it is created through the use of the regularization framework.In the proposed approach,the bilateral edge preserving and bilateral total variation regularizations are employed to approximate a high-resolution image generated from a sequence of corresponding images with low-resolution to protect significant features of an image,including sharp image edges and texture details while preventing artifacts.The experimental results of the synthesized image demonstrate that the new proposed approach has improved efficacy both visually and numerically more than other approaches.

Regularization Methods to Approximate Solutions of Variational Inequalities

In this paper, we study the regularization methods to approximate the solutions of the variational inequalities with monotone hemi-continuous operator having perturbed operators arbitrary. Detail, we shall study regularization methods to approximate solutions of following variational inequalities: and with operator A being monotone hemi-continuous form real Banach reflexive X into its dual space X*, but instead of knowing the exact data (y0, A), we only know its approximate data satisfying certain specified conditions and D is a nonempty convex closed subset of X;the real function f defined on X is assumed to be lower semi-continuous, convex and is not identical to infinity. At the same time, we will evaluate the convergence rate of the approximate solution. The regularization methods here are different from the previous ones.

Diverse Deep Matrix Factorization With Hypergraph Regularization for Multi-View Data Representation

Deep matrix factorization(DMF)has been demonstrated to be a powerful tool to take in the complex hierarchical information of multi-view data(MDR).However,existing multiview DMF methods mainly explore the consistency of multi-view data,while neglecting the diversity among different views as well as the high-order relationships of data,resulting in the loss of valuable complementary information.In this paper,we design a hypergraph regularized diverse deep matrix factorization(HDDMF)model for multi-view data representation,to jointly utilize multi-view diversity and a high-order manifold in a multilayer factorization framework.A novel diversity enhancement term is designed to exploit the structural complementarity between different views of data.Hypergraph regularization is utilized to preserve the high-order geometry structure of data in each view.An efficient iterative optimization algorithm is developed to solve the proposed model with theoretical convergence analysis.Experimental results on five real-world data sets demonstrate that the proposed method significantly outperforms stateof-the-art multi-view learning approaches.

Brain Functional Networks with Dynamic Hypergraph Manifold Regularization for Classification of End-Stage Renal Disease Associated with Mild Cognitive Impairment

The structure and function of brain networks have been altered in patients with end-stage renal disease(ESRD).Manifold regularization(MR)only considers the pairing relationship between two brain regions and cannot represent functional interactions or higher-order relationships between multiple brain regions.To solve this issue,we developed a method to construct a dynamic brain functional network(DBFN)based on dynamic hypergraph MR(DHMR)and applied it to the classification of ESRD associated with mild cognitive impairment(ESRDaMCI).The construction of DBFN with Pearson’s correlation(PC)was transformed into an optimization model.Node convolution and hyperedge convolution superposition were adopted to dynamically modify the hypergraph structure,and then got the dynamic hypergraph to form the manifold regular terms of the dynamic hypergraph.The DHMR and L_(1) norm regularization were introduced into the PC-based optimization model to obtain the final DHMR-based DBFN(DDBFN).Experiment results demonstrated the validity of the DDBFN method by comparing the classification results with several related brain functional network construction methods.Our work not only improves better classification performance but also reveals the discriminative regions of ESRDaMCI,providing a reference for clinical research and auxiliary diagnosis of concomitant cognitive impairments.

Regularization by Multiple Dual Frames for Compressed Sensing Magnetic Resonance Imaging With Convergence Analysis

Plug-and-play priors are popular for solving illposed imaging inverse problems. Recent efforts indicate that the convergence guarantee of the imaging algorithms using plug-andplay priors relies on the assumption of bounded denoisers. However, the bounded properties of existing plugged Gaussian denoisers have not been proven explicitly. To bridge this gap, we detail a novel provable bounded denoiser termed as BMDual,which combines a trainable denoiser using dual tight frames and the well-known block-matching and 3D filtering(BM3D)denoiser. We incorporate multiple dual frames utilized by BMDual into a novel regularization model induced by a solver. The proposed regularization model is utilized for compressed sensing magnetic resonance imaging(CSMRI). We theoretically show the bound of the BMDual denoiser, the bounded gradient of the CSMRI data-fidelity function, and further demonstrate that the proposed CSMRI algorithm converges. Experimental results also demonstrate that the proposed algorithm has a good convergence behavior, and show the effectiveness of the proposed algorithm.

An improved four-dimensional variation source term inversion model with observation error regularization

Aiming at the Four-Dimensional Variation source term inversion algorithm proposed earlier,the observation error regularization factor is introduced to improve the prediction accuracy of the diffusion model,and an improved Four-Dimensional Variation source term inversion algorithm with observation error regularization(OER-4DVAR STI model)is formed.Firstly,by constructing the inversion process and basic model of OER-4DVAR STI model,its basic principle and logical structure are studied.Secondly,the observation error regularization factor estimation method based on Bayesian optimization is proposed,and the error factor is separated and optimized by two parameters:error statistical time and deviation degree.Finally,the scientific,feasible and advanced nature of the OER-4DVAR STI model are verified by numerical simulation and tracer test data.The experimental results show that OER-4DVAR STI model can better reverse calculate the hazard source term information under the conditions of high atmospheric stability and flat underlying surface.Compared with the previous inversion algorithm,the source intensity estimation accuracy of OER-4DVAR STI model is improved by about 46.97%,and the source location estimation accuracy is improved by about 26.72%.

Distributed Optimal Formation Control for Unmanned Surface Vessels by a Regularized Game-Based Approach

Dear Editor,This letter explores optimal formation control for a network of unmanned surface vessels(USVs).By designing an individual objective function for each USV,the optimal formation problem is transformed into a noncooperative game.Under this game theoretic framework,the optimal formation is achieved by seeking the Nash equilibrium of the regularized game.A modular structure consisting of a distributed Nash equilibrium seeker and a regulator is proposed.

THE GLOBAL EXISTENCE AND ANALYTICITY OF A MILD SOLUTION TO THE 3D REGULARIZED MHD EQUATIONS

In this paper,we study the three-dimensional regularized MHD equations with fractional Laplacians in the dissipative and diffusive terms.We establish the global existence of mild solutions to this system with small initial data.In addition,we also obtain the Gevrey class regularity and the temporal decay rate of the solution.

SHARP MORREY REGULARITY THEORY FOR A FOURTH ORDER GEOMETRICAL EQUATION

This paper is a continuation of recent work by Guo-Xiang-Zheng[10].We deduce the sharp Morrey regularity theory for weak solutions to the fourth order nonhomogeneous Lamm-Rivière equation △^{2}u=△(V▽u)+div(w▽u)+(▽ω+F)·▽u+f in B^(4),under the smallest regularity assumptions of V,ω,ω,F,where f belongs to some Morrey spaces.This work was motivated by many geometrical problems such as the flow of biharmonic mappings.Our results deepens the Lp type regularity theory of[10],and generalizes the work of Du,Kang and Wang[4]on a second order problem to our fourth order problems.

Investigation on Damage Regularity of Mikania micrantha

[Objectives]The paper was to understand the occurrence and damage regularity of the invasive plant Mikania micrantha in Huadu District of Guangzhou.[Methods]The damage status of M.micranthFa in different forest lands and its annual growth dynamics were investigated by field investigation.[Results]With the change of canopy density from low to high,the occurrence degree of M.micrantha changed from high to low.The occurrence degree of M.micrantha in different forest land types was:abandoned orchard>wasteland>roadside greenbelt>waterside>forest edge>normally managed orchard.[Conclusions]M.micrantha enters the rapid growth period from March to May in spring,with the growth rate gradually slowing down after June.The result provides a theoretical basis and practical guidance for the prevention and control of M.micrantha.

A New Result on Regular Designs under Baseline Parameterization

The study on designs for the baseline parameterization has aroused attention in recent years. This paper focuses on two-level regular designs for the baseline parameterization. A general result on the relationship between K-aberration and word length pattern is developed.

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.

The Regularity of Solutions to Mixed Boundary Value Problems of Second-Order Elliptic Equations with Small Angles

This paper considers the regularity of solutions to mixed boundary value problems in small-angle regions for elliptic equations. By constructing a specific barrier function, we proved that under the assumption of sufficient regularity of boundary conditions and coefficients, as long as the angle is sufficiently small, the regularity of the solution to the mixed boundary value problem of the second-order elliptic equation can reach any order.

Solving Neumann Boundary Problem with Kernel-Regularized Learning Approach

We provide a kernel-regularized method to give theory solutions for Neumann boundary value problem on the unit ball. We define the reproducing kernel Hilbert space with the spherical harmonics associated with an inner product defined on both the unit ball and the unit sphere, construct the kernel-regularized learning algorithm from the view of semi-supervised learning and bound the upper bounds for the learning rates. The theory analysis shows that the learning algorithm has better uniform convergence according to the number of samples. The research can be regarded as an application of kernel-regularized semi-supervised learning.

利用GPS垂直位移反演区域陆地水储量变化的TSVD-Tikhonov正则化方法

利用GPS垂直位移反演区域陆地水储量变化(TWSC)属于典型的病态问题,其关键是如何进行稳定求解并提高反演结果的精度和可靠性.本文引入TSVD-Tikhonov组合正则化方法对利用GPS垂直位移反演区域TWSC的病态问题进行求解,并以四川省TWSC反演为例进行分析与验证.首先,通过数值模拟对TSVD、Tikhonov和TSVD-Tikhonov正则化方法采用不同正则化参数选取策略(RMSE最小准则、GCV法和L-curve法)进行反演,结果显示基于TSVD-Tikhonov正则化反演的TWSC比单独使用TSVD或Tikhonov正则化反演结果的精度和可靠性更高,这三种正则化方法反演2005年1月至12月的TWSC差值的平均STD分别为14.97 mm、7.03 mm和5.04 mm.其次,利用中国地壳运动观测网络(CMONOC)的72个GPS测站的垂直位移数据,基于TSVD-Tikhonov正则化反演了四川省2010年12月至2021年2月的TWSC时间序列,结果表明GPS反演的TWSC与GRACE/GFO Mascon模型(JPL、CSR和GSFC)的空间分布特征及季节性变化符合较好,但其TWSC信号的振幅比GRACE/GFO Mascon模型更强.最后,采用广义三角帽方法(GTCH)融合不同类型的降水、蒸散发和径流数据,并根据水量平衡方程计算的dTWSC/dt序列(PER-dS/dt)对GPS反演的dTWSC/dt序列(GPS-dS/dt)和GRACE/GFO Mascon模型融合的dTWSC/dt序列(GRACE/GFO-dS/dt)进行验证,结果表明这三类dTWSC/dt序列的季节性变化符合较好,平滑后GPS-dS/dt和GRACE/GFO-dS/dt序列与PER-dS/dt序列的相关系数分别为0.78和0.87,但GPS相比GRACE/GFO对降水变化的响应更为敏感.本文研究证明了TSVD-Tikhonov组合正则化方法能够提高GPS垂直位移反演区域TWSC的精度和可靠性,同时也表明GPS观测数据对局部水质量负荷变化更为敏感,可作为GRACE/GFO反演区域TWSC的有益补充.