Hybrid Approach for Privacy Enhancement in Data Mining Using Arbitrariness and Perturbation

Imagine numerous clients,each with personal data;individual inputs are severely corrupt,and a server only concerns the collective,statistically essential facets of this data.In several data mining methods,privacy has become highly critical.As a result,various privacy-preserving data analysis technologies have emerged.Hence,we use the randomization process to reconstruct composite data attributes accurately.Also,we use privacy measures to estimate how much deception is required to guarantee privacy.There are several viable privacy protections;however,determining which one is the best is still a work in progress.This paper discusses the difficulty of measuring privacy while also offering numerous random sampling procedures and statistical and categorized data results.Further-more,this paper investigates the use of arbitrary nature with perturbations in privacy preservation.According to the research,arbitrary objects(most notably random matrices)have"predicted"frequency patterns.It shows how to recover crucial information from a sample damaged by a random number using an arbi-trary lattice spectral selection strategy.Thisfiltration system's conceptual frame-work posits,and extensive practicalfindings indicate that sparse data distortions preserve relatively modest privacy protection in various situations.As a result,the research framework is efficient and effective in maintaining data privacy and security.

Arbitrariness and motivation in linguistic signs： Integrative and dialectical reflections

Sausssurean revolution is defined by, among others, his controversial hypothesis of linguistic arbitrariness. This, however, fails to embrace a unanimous acceptation by scholars thereafter and the debates over linguistic signs in terms of arbitrariness and motivation, due to the regrettably understood terms, have imbued the development of linguistics, nurturing a myriad of sustainably productive branches in linguistic studies. Based on refreshing interpretation of the key terms, the paper adopts an integrative and dialectical approach to linguistic signs and argues that arbitrariness is more a matter of degree than one of presence or absence, hopefully to bring home that duality as whole features linguistic signs fundamentally.

Arbitrariness in Saussure＇s View

In the current debates over Saussure＇s principle of arbitrariness, there have occurred some confusions and misunderstandings, especially in the equation of Saussure＇s notion of arbitrariness with the classical notion of arbitrariness. In this article, the uniqueness of Saussure＇s arbitrariness is illustrated in, relation to the classical arbitrariness.

Arbitrariness of the general solution of the partial differential equations and its applications

Using the framework of formal theory of partial differential equations, we consider a method of computation of the bi-Hilbert polynomial (i.e. Hilbert polynomial in two variables). Furthermore, present an approach to compute the number of arbitrary functions of positive differential order in the general solution. Then, under the "AC=BD" model for mathematics mechanization developed by Hong-qing ZHANG, we present a method to reduce an overdetermined system to a well-determined one. As applications, the Maxwell equations and weakly overdetermined equations are considered.

Complete-basis-reprogrammable coding metasurface for generating dynamicallycontrolled holograms under arbitrary polarization states

Reprogrammable metasurfaces,which establish a fascinating bridge between physical and information domains,can dynamically control electromagnetic(EM)waves in real time and thus have attracted great attentions from researchers around the world.To control EM waves with an arbitrary polarization state,it is desirable that a complete set of basis states be controlled independently since incident EM waves with an arbitrary polarization state can be decomposed as a linear sum of these basis states.In this work,we present the concept of complete-basis-reprogrammable coding metasurface(CBR-CM)in reflective manners,which can achieve independently dynamic controls over the reflection phases while maintaining the same amplitude for left-handed circularly polarized(LCP)waves and right-handed circularly polarized(RCP)waves.Since LCP and RCP waves together constitute a complete basis set of planar EM waves,dynamicallycontrolled holograms can be generated under arbitrarily polarized wave incidence.The dynamically reconfigurable metaparticle is implemented to demonstrate the CBR-CM’s robust capability of controlling the longitudinal and transverse positions of holograms under LCP and RCP waves independently.It’s expected that the proposed CBR-CM opens up ways of realizing more sophisticated and advanced devices with multiple independent information channels,which may provide technical assistance for digital EM environment reproduction.

Natural frequency analysis of laminated piezoelectric beams with arbitrary polarization directions

Piezoelectric devices exhibit unique properties that vary with different vibration modes,closely influenced by their polarization direction.This paper presents an analysis on the free vibration of laminated piezoelectric beams with varying polarization directions,using a state-space-based differential quadrature method.First,based on the electro-elasticity theory,the state-space method is extended to anisotropic piezoelectric materials,establishing state-space equations for arbitrary polarized piezoelectric beams.A semi-analytical solution for the natural frequency is then obtained via the differential quadrature method.The study commences by examining the impact of a uniform polarization direction,and then proceeds to analyze six polarization schemes relevant to the current research and applications.Additionally,the effects of geometric dimensions and gradient index on the natural frequencies are explored.The numerical results demonstrate that varying the polarization direction can significantly influence the natural frequencies,offering distinct advantages for piezoelectric elements with different polarizations.This research provides both theoretical insights and numerical methods for the structural design of piezoelectric devices.

A New Efficient Explicit Deferred Correction Framework:Analysis and Applications to Hyperbolic PDEs and Adaptivity

The deferred correction(DeC)is an iterative procedure,characterized by increasing the accuracy at each iteration,which can be used to design numerical methods for systems of ODEs.The main advantage of such framework is the automatic way of getting arbitrarily high order methods,which can be put in the Runge-Kutta(RK)form.The drawback is the larger computational cost with respect to the most used RK methods.To reduce such cost,in an explicit setting,we propose an efcient modifcation:we introduce interpolation processes between the DeC iterations,decreasing the computational cost associated to the low order ones.We provide the Butcher tableaux of the new modifed methods and we study their stability,showing that in some cases the computational advantage does not afect the stability.The fexibility of the novel modifcation allows nontrivial applications to PDEs and construction of adaptive methods.The good performances of the introduced methods are broadly tested on several benchmarks both in ODE and PDE contexts.

Distributed Stochastic Optimization with Compression for Non-Strongly Convex Objectives

We are investigating the distributed optimization problem,where a network of nodes works together to minimize a global objective that is a finite sum of their stored local functions.Since nodes exchange optimization parameters through the wireless network,large-scale training models can create communication bottlenecks,resulting in slower training times.To address this issue,CHOCO-SGD was proposed,which allows compressing information with arbitrary precision without reducing the convergence rate for strongly convex objective functions.Nevertheless,most convex functions are not strongly convex(such as logistic regression or Lasso),which raises the question of whether this algorithm can be applied to non-strongly convex functions.In this paper,we provide the first theoretical analysis of the convergence rate of CHOCO-SGD on non-strongly convex objectives.We derive a sufficient condition,which limits the fidelity of compression,to guarantee convergence.Moreover,our analysis demonstrates that within the fidelity threshold,this algorithm can significantly reduce transmission burden while maintaining the same convergence rate order as its no-compression equivalent.Numerical experiments further validate the theoretical findings by demonstrating that CHOCO-SGD improves communication efficiency and keeps the same convergence rate order simultaneously.And experiments also show that the algorithm fails to converge with low compression fidelity and in time-varying topologies.Overall,our study offers valuable insights into the potential applicability of CHOCO-SGD for non-strongly convex objectives.Additionally,we provide practical guidelines for researchers seeking to utilize this algorithm in real-world scenarios.

CVTD: A Robust Car-Mounted Video Text Detector

Text perception is crucial for understanding the semantics of outdoor scenes,making it a key requirement for building intelligent systems for driver assistance or autonomous driving.Text information in car-mounted videos can assist drivers in making decisions.However,Car-mounted video text images pose challenges such as complex backgrounds,small fonts,and the need for real-time detection.We proposed a robust Car-mounted Video Text Detector(CVTD).It is a lightweight text detection model based on ResNet18 for feature extraction,capable of detecting text in arbitrary shapes.Our model efficiently extracted global text positions through the Coordinate Attention Threshold Activation(CATA)and enhanced the representation capability through stacking two Feature Pyramid Enhancement Fusion Modules(FPEFM),strengthening feature representation,and integrating text local features and global position information,reinforcing the representation capability of the CVTD model.The enhanced feature maps,when acted upon by Text Activation Maps(TAM),effectively distinguished text foreground from non-text regions.Additionally,we collected and annotated a dataset containing 2200 images of Car-mounted Video Text(CVT)under various road conditions for training and evaluating our model’s performance.We further tested our model on four other challenging public natural scene text detection benchmark datasets,demonstrating its strong generalization ability and real-time detection speed.This model holds potential for practical applications in real-world scenarios.

High Order ADER-IPDG Methods for the Unsteady Advection-Diffusion Equation

We present a high-order Galerkin method in both space and time for the 1D unsteady linear advection-diffusion equation. Three Interior Penalty Discontinuous Galerkin (IPDG) schemes are detailed for the space discretization, while the time integration is performed at the same order of accuracy thanks to an Arbitrary high order DERivatives (ADER) method. The orders of convergence of the three ADER-IPDG methods are carefully examined through numerical illustrations, showing that the approach is consistent, accurate, and efficient. The numerical results indicate that the symmetric version of IPDG is typically more accurate and more efficient compared to the other approaches.

耦合拉格朗日-欧拉方法及其在海洋工程中的应用

Combining the strengths of Lagrangian and Eulerian descriptions,the coupled Lagrangian–Eulerian methods play an increasingly important role in various subjects.This work reviews their development and application in ocean engineering.Initially,we briefly outline the advantages and disadvantages of the Lagrangian and Eulerian descriptions and the main characteristics of the coupled Lagrangian–Eulerian approach.Then,following the developmental trajectory of these methods,the fundamental formulations and the frameworks of various approaches,including the arbitrary Lagrangian–Eulerian finite element method,the particle-in-cell method,the material point method,and the recently developed Lagrangian–Eulerian stabilized collocation method,are detailedly reviewed.In addition,the article reviews the research progress of these methods with applications in ocean hydrodynamics,focusing on free surface flows,numerical wave generation,wave overturning and breaking,interactions between waves and coastal structures,fluid–rigid body interactions,fluid–elastic body interactions,multiphase flow problems and visualization of ocean flows,etc.Furthermore,the latest research advancements in the numerical stability,accuracy,efficiency,and consistency of the coupled Lagrangian–Eulerian particle methods are reviewed;these advancements enable efficient and highly accurate simulation of complicated multiphysics problems in ocean and coastal engineering.By building on these works,the current challenges and future directions of the hybrid Lagrangian–Eulerian particle methods are summarized.

Least Square Finite Element Model for Analysis of Multilayered Composite Plates under Arbitrary Boundary Conditions

Laminated composites are widely used in many engineering industries such as aircraft, spacecraft, boat hulls, racing car bodies, and storage tanks. We analyze the 3D deformations of a multilayered, linear elastic, anisotropic rectangular plate subjected to arbitrary boundary conditions on one edge and simply supported on other edge. The rectangular laminate consists of anisotropic and homogeneous laminae of arbitrary thicknesses. This study presents the elastic analysis of laminated composite plates subjected to sinusoidal mechanical loading under arbitrary boundary conditions. Least square finite element solutions for displacements and stresses are investigated using a mathematical model, called a state-space model, which allows us to simultaneously solve for these field variables in the composite structure’s domain and ensure that continuity conditions are satisfied at layer interfaces. The governing equations are derived from this model using a numerical technique called the least-squares finite element method (LSFEM). These LSFEMs seek to minimize the squares of the governing equations and the associated side conditions residuals over the computational domain. The model is comprised of layerwise variables such as displacements, out-of-plane stresses, and in- plane strains, treated as independent variables. Numerical results are presented to demonstrate the response of the laminated composite plates under various arbitrary boundary conditions using LSFEM and compared with the 3D elasticity solution available in the literature.

Simulation of extrusion process of complicated aluminium profile and die trial

The arbitrary Lagrangian-Eulerian（ALE） adaptive remeshing technology and the HyperXtrude software of transient finite element simulations were used on analogue simulation of aluminium extrusion processing.The field distributions of strain rate,stress,temperature and velocity of metal flow were obtained.The results are basically consistent with the experiment,which indicates that this method may successfully predict the defects in the actual extrusion process.

ALE框架下几种不同Godunov型格式的数值比较

给出一种有限体积Godunov型的ALE方法,用于求解多介质大变形的可压缩流动问题.由于方法具有任意的网格移动速度,可在拉氏、欧氏和ALE之间切换,具有较强的适应性.通过数值算例对这3种框架下的数值特性进行了比较研究.同时还研究了几种不同Godunov型格式的数值行为特性,分析比较了它们对激波和接触间断的分辨效果.

基于ALE法的车轮踏面磨损及疲劳性能研究

基于有限元Arbitrary Lagrangian Eulerian(ALE)方法和Archard磨损理论建立了CRH5型动车组车轮的磨损分析模型。通过静态以及稳态分析结合修型运算,获取了车轮在典型工况下的磨损规律,包括车轮踏面磨损程度和磨损量沿踏面分布的动态变化规律。基于以上工作,又对不同磨损程度的车轮进行了疲劳寿命分析,总结了在磨损过程中,车轮的疲劳损伤速率随磨损的动态规律。结果发现:车轮的疲劳损伤速率在初期时呈显著下降趋势,当磨损超过整个仿真磨损量的70%时趋于平稳。

Modeling seismic wave propagation within complex structures

Seismic modeling is a useful tool for studying the propagation of seismic waves within complex structures. However, traditional methods of seismic simulation cannot meet the needs for studying seismic wavefields in the complex geological structures found in seismic exploration of the mountainous area in Northwestern China. More powerful techniques of seismic modeling are demanded for this purpose. In this paper, two methods of finite element-finite difference method （FE-FDM） and arbitrary difference precise integration （ADPI） for seismic forward modeling have been developed and implemented to understand the behavior of seismic waves in complex geological subsurface structures and reservoirs. Two case studies show that the FE-FDM and ADPI techniques are well suited to modeling seismic wave propagation in complex geology.

An Algorithm for Partitioning Polygons into Convex Parts

An algorithm for partitioning arbitrary simple polygons into a number of convex parts was presented. The concave vertices were determined first, and then they were moved by using the method connecting the concave vertices with the vertices of falling into its region B,so that the primary polygon could be partitioned into two subpolygons. Finally, this method was applied recursively to the subpolygons until all the concave vertices were removed. This algorithm partitions the polygon into O(l) convex parts, its time complexity is max(O(n),O(l 2)) multiplications, where n is the number of vertices of the polygon and l is the number of the concave vertices.

坝体考虑流固耦合的动力特性分析

运用ALE(Arbitrary Langrangian-Eulerian)描述流体域,流体域中的网格点按照自由液面的运动和结构与液体接触面的移动而不断更新,从而将运动边界的非线性效应融入到计算中,考虑坝水完全耦合。数值模拟了四川某坝体在地震作用下的坝体的动力特性、库水自由表面重力波影响的问题以及库水域有效影响范围的问题,得出了有益的结论。

Optimized nonhyperbolic moveout correction equation of long-offset seismic data for TI media with an arbitrary spatial orientation

The conventional long-offset nonhyperbolic moveout equation is derived for the transverse isotropic media with a vertical symmetric axis（VTI）.It cannot be extended to the transverse isotropic media with an arbitrary spatial orientation of symmetry axis（ATI）.In this paper,we optimize a modified long-offset nonhyperbolic moveout equation for ATI media based on the conventional nonhyperbolic moveout equation and the exact analytical solution of the quartic moveout coefficient（A_4） and NMO velocity for ATI media that were derived in our previous work.Compared with the exact traveltimes of the ray-tracing algorithm for anisotropic media,this optimized equation can be used to calculate the traveltime varying with survey line azimuth in arbitrary strong or weak ATI media.It can replace the time-consuming, multi-offset,and multi-azimuth ray tracing method for forward modeling of long-offset reflection traveltimes in ATI media,which is useful to further anisotropic parameter inversion using long-offset nonhyperbolic moveout.

ALE方法评估黏土场地的自升式平台桩靴承载力

为研究自升式平台桩靴在黏土场地中的极限承载力,建立Abaqus桩靴-土模型,采用任意拉格朗日-欧拉(Arbitrary Lagrangian-Eulerian,ALE)方法对桩靴的贯入过程进行模拟,提出大值法、中值法、小值法等3种数据处理方法,并拟合桩靴承载力估算公式。将模拟计算结果与SNAME规范公式计算结果进行对比分析,对比结果证明ALE方法模拟桩靴贯入的可行性。为提高工程的安全性,提出对SNAME公式计算结果进行折减的具体公式,以使其与ALE小值法处理结果更吻合。