ADDITIVE PERTURBATIONS OF LOCAL C-SEMIGROUPS

In this paper, we apply the contraction mapping theorem to establish some bounded and unbounded additive perturbation theorems concerning local C-semigroups. Some growth conditions of perturbations of local C-semigroups axe also established.

Research on mode localization of reticulated shell structures

Reticulated shell structures （RSSs） are characterized as cyclically periodic structures. Mistuning of RSSs will induce structural mode localization. Mode localization has the following two features： some modal vectors of the structure change remarkably when the values of its physical parameters （mass or stiffness） have a slight change; and the vibration of some modes is mainly restricted in some local areas of the structure. In this paper, two quantitative assessment indexes are introduced that correspond to these two features. The first feature is studied through a numerical example of a RSS, and its induced causes are analyzed by using the perturbation theory. The analysis showed that internally, mode localization is closely related to structural frequencies and externally, slight changes of the physical parameters of the structure cause instability to the RSS. A scaled model experiment to examine mode localization was carried out on a Kiewit single-layer spherical RSS, and both features of mode localization are studied. Eight tests that measured the changes of the physical parameters were carried out in the experiment. Since many modes make their contribution in structural dynamic response, six strong vibration modes were tested at random in the experimental analysis. The change and localization of the six modes are analyzed for each test. The results show that slight changes to the physical parameters are likely to induce remarkable changes and localization of some modal vectors in the RSSs.

A NUMERICAL PERTURBATION EXPANSIONMETHOD FOR THE SOLUTION OF ALIENARD-TYPE INITIAL-VALUE PROBLEMWITH PERIODIC DECAYING FORCING TERM

A numerical perturbation expansion method is developed, analysed and implemented for the numerical solution of a second-order initial-value problem. The differential equation in this problem exhibits cubic damping, a cubic restoring force and a decaying forcing-term which is periodic with constant frequency. The method is compared with the numerical method by Twizell [1]. In fact, the later is first perturbation approximate solution in the present paper.

KSKV:Key-Strategy for Key-Value Data Collection with Local Differential Privacy

In recent years,the research field of data collection under local differential privacy(LDP)has expanded its focus fromelementary data types to includemore complex structural data,such as set-value and graph data.However,our comprehensive review of existing literature reveals that there needs to be more studies that engage with key-value data collection.Such studies would simultaneously collect the frequencies of keys and the mean of values associated with each key.Additionally,the allocation of the privacy budget between the frequencies of keys and the means of values for each key does not yield an optimal utility tradeoff.Recognizing the importance of obtaining accurate key frequencies and mean estimations for key-value data collection,this paper presents a novel framework:the Key-Strategy Framework forKey-ValueDataCollection under LDP.Initially,theKey-StrategyUnary Encoding(KS-UE)strategy is proposed within non-interactive frameworks for the purpose of privacy budget allocation to achieve precise key frequencies;subsequently,the Key-Strategy Generalized Randomized Response(KS-GRR)strategy is introduced for interactive frameworks to enhance the efficiency of collecting frequent keys through group-anditeration methods.Both strategies are adapted for scenarios in which users possess either a single or multiple key-value pairs.Theoretically,we demonstrate that the variance of KS-UE is lower than that of existing methods.These claims are substantiated through extensive experimental evaluation on real-world datasets,confirming the effectiveness and efficiency of the KS-UE and KS-GRR strategies.

Local existence and uniqueness of solutions to the evolutionary model for magnetoviscoelasticity

In this paper,we prove the local existence and uniqueness of solutions to the evolutionary model for magnetoviscoelasticity in R^(2),R^(3).This model consists of an incompressible Navier-Stokes,a regularized system for the evolution of the deformation gradient and the Landau-Lifshitz-Gilbert system for the dynamics of the mag-netization.Our approach depends on approximating the system with a sequence of perturbed systems.

Safeguarding cross-silo federated learning with local differential privacy

Federated Learning(FL)is a new computing paradigm in privacy-preserving Machine Learning(ML),where the ML model is trained in a decentralized manner by the clients,preventing the server from directly accessing privacy-sensitive data from the clients.Unfortunately,recent advances have shown potential risks for user-level privacy breaches under the cross-silo FL framework.In this paper,we propose addressing the issue by using a three-plane framework to secure the cross-silo FL,taking advantage of the Local Differential Privacy(LDP)mechanism.The key insight here is that LDP can provide strong data privacy protection while still retaining user data statistics to preserve its high utility.Experimental results on three real-world datasets demonstrate the effectiveness of our framework.

ASSESSMENT OF LOCAL INFLUENCE IN MULTIVARIATE ANALYSIS

A recent method for assessing the local influence is introduced by Cook(1986), in which the normal curvature of the influence graph based on the likelihood displacement is used to monitor the influence of small perturbation. Since then this method has been applied to various kind of models. However, the local influence in multivariate analysis is still an unexplored area because the influence for many statistics in multivariate analysis is not convenient to handle based on the Cook's likelihood displacement. In this paper, we suggest a method with a slight modification in Cook's approach to assess the local influence of small perturbation on a certain statistic. The local influence of the perturbation on eigenvalue and eigenvector of variance-covariance matrix in theoretical and sample version is assessed, some results for the other statistics in multivariate analysis such as generalized variance, canonical correlations are studied. Finally, two examples are analysed for illustration.

LOCALIZED NODAL SOLUTIONS FOR SCHRODINGER-POISSON SYSTEMS

In this paper,we study the existence of localized nodal solutions for Schrodinger-Poisson systems with critical growth{−ε^(2)Δv+V(x)v+λψv=v^(5)+μ|v|^(q−2)v,in R^(3),−ε^(2)Δψ=v^(2),in R^(3);v(x)→0,ψ(x)→0as|x|→∞.We establish,for smallε,the existence of a sequence of localized nodal solutions concentrating near a given local minimum point of the potential function via the perturbation method,and employ some new analytical skills to overcome the obstacles caused by the nonlocal term φu(x)=1/4π∫R^(3)u^(2)(y)/|x−y|dy.Our results improve and extend related ones in the literature.

Anomalous Cell Detection with Kernel Density-Based Local Outlier Factor

Since data services are penetrating into our daily life rapidly, the mobile network becomes more complicated, and the amount of data transmission is more and more increasing. In this case, the traditional statistical methods for anomalous cell detection cannot adapt to the evolution of networks, and data mining becomes the mainstream. In this paper, we propose a novel kernel density-based local outlier factor(KLOF) to assign a degree of being an outlier to each object. Firstly, the notion of KLOF is introduced, which captures exactly the relative degree of isolation. Then, by analyzing its properties, including the tightness of upper and lower bounds, sensitivity of density perturbation, we find that KLOF is much greater than 1 for outliers. Lastly, KLOFis applied on a real-world dataset to detect anomalous cells with abnormal key performance indicators(KPIs) to verify its reliability. The experiment shows that KLOF can find outliers efficiently. It can be a guideline for the operators to perform faster and more efficient trouble shooting.

LOCAL INFLUENCE ANALYSIS BASED ON THE K－L DISTANCE AND THE INFORMATION DISTANCE

In this paper, the invariance of the K-L distance and that of the infor-mation distance under some parameter transformations are derived; the equiva-lence of the local influence matrix corresponding to the K-L distance, the informa-tion distance and the l

Variations of water's local-structure induced by solvation of NaCl

The researches on the structure of water and its changes induced by solutes are of enduring interests. The changes of the local structure of liquid water induced by NaCl solute under ambient conditions are studied and presented quantitatively with some order parameters and visualized with 2-body and 3-body correlation functions. The results show that, after the NaCl are solvated, the translational order t of water is decreased for the suppression of the second hydration shells around H20 molecules; the tetrahedral order （q） of water is also decreased and its favorite distribution peak moves from 0.76 to 0.5. In addition, the orientational freedom k and the diffusion coefficient D of water molecules are reduced because of new formed hydrogen-bonding structures between water and solvated ions.

The Conversion Relationship between the Local Earthquake Magnitude and Surface Wave Magnitude in the Inner Mongolia Digital Seismic Network

Using 116 earthquakes over M_L3.8 in the Inner Mongolia region from 2008 to 2015, the local earthquake magnitude M_L and surface wave magnitude M_S are remeasured. Based on norm linear regression(SR1 and SR2) and norm(OR) orthogonal regression method, we established the conversion relationship between M_L and M_S. The results were tested with Gaussian disturbance. The result shows that the orthogonal regression method(OR) result has the best fitting curve, and the conversion relation is M_S=0.96 M_L-0.10. The difference between our result and Guo Lücan's(M_S=1.13 M_L-1.08) may be caused by regional tectonic characteristics. M_(S Inner Mongolia) value is significantly higher than the M_(S empirical) value, with an average difference of 0.23, the difference distribution of empirical relation and the rectified relation is in the range of 0.2-0.3.

Privacy-Preserving Collaborative Filtering Algorithm Based on Local Differential Privacy

Mobile edge computing(MEC)is an emerging technolohgy that extends cloud computing to the edge of a network.MEC has been applied to a variety of services.Specially,MEC can help to reduce network delay and improve the service quality of recommendation systems.In a MEC-based recommendation system,users’rating data are collected and analyzed by the edge servers.If the servers behave dishonestly or break down,users’privacy may be disclosed.To solve this issue,we design a recommendation framework that applies local differential privacy(LDP)to collaborative filtering.In the proposed framework,users’rating data are perturbed to satisfy LDP and then released to the edge servers.The edge servers perform partial computing task by using the perturbed data.The cloud computing center computes the similarity between items by using the computing results generated by edge servers.We propose a data perturbation method to protect user’s original rating values,where the Harmony mechanism is modified so as to preserve the accuracy of similarity computation.And to enhance the protection of privacy,we propose two methods to protect both users’rating values and rating behaviors.Experimental results on real-world data demonstrate that the proposed methods perform better than existing differentially private recommendation methods.

Local imperceptible adversarial attacks against human pose estimation networks

Deep neural networks are vulnerable to attacks from adversarial inputs.Corresponding attack research on human pose estimation(HPE),particularly for body joint detection,has been largely unexplored.Transferring classification-based attack methods to body joint regression tasks is not straightforward.Another issue is that the attack effectiveness and imperceptibility contradict each other.To solve these issues,we propose local imperceptible attacks on HPE networks.In particular,we reformulate imperceptible attacks on body joint regression into a constrained maximum allowable attack.Furthermore,we approximate the solution using iterative gradient-based strength refinement and greedy-based pixel selection.Our method crafts effective perceptual adversarial attacks that consider both human perception and attack effectiveness.We conducted a series of imperceptible attacks against state-of-the-art HPE methods,including HigherHRNet,DEKR,and ViTPose.The experimental results demonstrate that the proposed method achieves excellent imperceptibility while maintaining attack effectiveness by significantly reducing the number of perturbed pixels.Approximately 4%of the pixels can achieve sufficient attacks on HPE.

Localization and Degree of Damage Based on Relative Curvature Difference and Frequency Perturbation

This study proposed a damage identification method compared with the existing ones,based on relative curvature difference and frequency perturbation theory,showing sensitivity to local damage by changes in the curvature mode and high recognition accuracy of frequencies.Considering the relative curvature difference as a damage index,numerical simulation is used for a simply supported beam under single and multiple damage conditions for different damage degrees.The damage is located according to the curvature mode curves,and the damage degree is qualitatively determined.Based on the perturbation theory,the damage equations are established by the changes between frequencies before and after damage,and the damage localization and degree are verified and determined.Effectiveness of the proposed method for identifying damage at different conditions is numerically investigated.This method potentially promotes the development of damage identification of beam structures.

Wavelet multiresolution interpolation Galerkin method for nonlinear boundary value problems with localized steep gradients

The wavelet multiresolution interpolation for continuous functions defined on a finite interval is developed in this study by using a simple alternative of transformation matrix.The wavelet multiresolution interpolation Galerkin method that applies this interpolation to represent the unknown function and nonlinear terms independently is proposed to solve the boundary value problems with the mixed Dirichlet-Robin boundary conditions and various nonlinearities,including transcendental ones,in which the discretization process is as simple as that in solving linear problems,and only common two-term connection coefficients are needed.All matrices are independent of unknown node values and lead to high efficiency in the calculation of the residual and Jacobian matrices needed in Newton’s method,which does not require numerical integration in the resulting nonlinear discrete system.The validity of the proposed method is examined through several nonlinear problems with interior or boundary layers.The results demonstrate that the proposed wavelet method shows excellent accuracy and stability against nonuniform grids,and high resolution of localized steep gradients can be achieved by using local refined multiresolution grids.In addition,Newton’s method converges rapidly in solving the nonlinear discrete system created by the proposed wavelet method,including the initial guess far from real solutions.

局部遮荫下基于改进金枪鱼算法的光伏最大功率点跟踪控制

光伏阵列在局部遮荫环境下的P-U特性曲线呈现多峰特性,导致传统最大功率点跟踪(MPPT)算法在跟踪最大功率时失效。为此,提出一种基于改进金枪鱼算法的光伏MPPT双层控制模型,在上层中将莱维飞行(Levy)策略和多项式变异策略嵌入金枪鱼算法中,构建莱维-多项式变异金枪鱼算法(LPTSO)来搜索全局功率最大点;在下层中采用扰动观察法对全局最大功率点进行局部跟踪,以降低局部遮荫环境下的功率振荡。将该双层控制模型应用于光伏MPPT仿真系统中,仿真实验结果表明,针对多峰MPPT控制,所提模型在收敛速度、跟踪效率、功率振荡等方面都有较大提升,该光伏MPPT双层控制模型能够有效解决局部遮荫环境下最大功率跟踪失效的问题。

漂移动理学效应对HL-2A托卡马克共振磁扰动等离子体响应的影响

边缘局域模(Edge Localized Modes,ELMs)的控制是国际热核聚变实验堆(International Thermonuclear Experimental Reactor,ITER)及未来磁约束聚变堆安全运行必须解决的一个关键主题。近年来,大量的理论模拟和实验研究证明,共振磁扰动(Resonant Magnetic Perturbation,RMP)是一种非常有效控制边缘局域模的技术。为了更好地理解HL-2A托卡马克中ELMs的控制,本文基于HL-2A托卡马克实验上等离子体和RMP线圈的位形,使用MARS-F/K程序,计算了高约束模式下等离子体对RMP的漂移动理学响应,并与流体模型的结果进行对比;进一步对等离子体平衡压强、环向流以及热粒子碰撞效应等关键参数进行了敏感性研究。结果表明,随着归一化比压βN的增加,流体响应模型预测的等离子体响应幅度最初相对较弱,随后在接近无壁比压极限时发生强烈变化,但这一非物理因素“跳变”在动理学响应模型中得到了修正。此外,在考虑粒子碰撞效应的动理学响应中,捕获热离子的非绝热共振贡献显著;而忽略粒子碰撞效应,捕获热电子的进动漂移共振贡献则更加显著。由此可见在高比压等离子体响应中考虑动理学效应的重要性,尤其是在考虑粒子碰撞效应时,需要考虑捕获粒子的非绝热共振贡献。

同质区共享端元变异性的高光谱混合像元分解

由于不同的照明条件、复杂的大气环境等因素,相同端元的光谱特征在图像的不同位置呈现出可见的差异,这种现象被称为端元的光谱变异性。在相当大的场景中,端元的变异性可能很大,但在适度的局部同质区内,变异性往往很小。扰动线性混合模型(Perturbed Linear Mixing Model,PLMM)在解混的过程中可以减轻端元变异性造成的不利影响,但是对缩放效应造成的变异性的处理能力较弱。为此,本文改进了扰动线性混合模型,引入了尺度因子以处理缩放效应造成的变异性,并结合超像素分割算法划分局部同质区,然后设计出基于局部同质区共享端元变异性的解混算法(Shared Endmember Variability in Unmixing,SEVU)。与扰动线性混合模型,扩展线性混合模型(Extended Linear Mixing Model,ELMM)等算法相比,所提SEVU算法在合成数据集上平均端元光谱角距离(mean Spectral Angle Distance,mSAD)和丰度均方根误差(abundance Root Mean Square Error,aRMSE)最优,分别为0.0855和0.0562;在Jasper Ridge和Cuprite真实数据集上mSAD是最优的,分别为0.0603和0.1003。在合成数据集和两个实测数据集上的实验结果验证了SEVU算法的有效性。

基于主动学习和二次有理核的模型无关局部解释方法

深度学习模型的广泛使用,在更大程度上使人们意识到模型的决策是亟需解决的问题,复杂难以解释的黑盒模型阻碍了算法在实际场景中部署。LIME作为最流行的局部解释方法,生成的扰动数据却具有不稳定性,导致最终的解释产生偏差。针对上述问题,提出了一种基于主动学习和二次有理核的模型无关局部解释方法ActiveLIME,使得局部解释模型更加忠于原始分类器。ActiveLIME生成扰动数据后,通过主动学习的查询策略对扰动数据进行采样,筛选不确定性高的扰动集训练,使用迭代过程中准确度最高的局部模型对感兴趣实例生成解释。并且,针对容易陷入局部过拟合的高维稀疏样本,在模型损失函数中引入了二次有理核来减少过拟合。实验结果表明,所提出的ActiveLIME方法引比传统局部解释方法具有更高的局部保真度和解释质量。