STRONGLY CONVERGENT INERTIAL FORWARD-BACKWARD-FORWARD ALGORITHM WITHOUT ON-LINE RULE FOR VARIATIONAL INEQUALITIES

This paper studies a strongly convergent inertial forward-backward-forward algorithm for the variational inequality problem in Hilbert spaces.In our convergence analysis,we do not assume the on-line rule of the inertial parameters and the iterates,which have been assumed by several authors whenever a strongly convergent algorithm with an inertial extrapolation step is proposed for a variational inequality problem.Consequently,our proof arguments are different from what is obtainable in the relevant literature.Finally,we give numerical tests to confirm the theoretical analysis and show that our proposed algorithm is superior to related ones in the literature.

A Sharding Scheme Based on Graph Partitioning Algorithm for Public Blockchain

Blockchain technology,with its attributes of decentralization,immutability,and traceability,has emerged as a powerful catalyst for enhancing traditional industries in terms of optimizing business processes.However,transaction performance and scalability has become the main challenges hindering the widespread adoption of blockchain.Due to its inability to meet the demands of high-frequency trading,blockchain cannot be adopted in many scenarios.To improve the transaction capacity,researchers have proposed some on-chain scaling technologies,including lightning networks,directed acyclic graph technology,state channels,and shardingmechanisms,inwhich sharding emerges as a potential scaling technology.Nevertheless,excessive cross-shard transactions and uneven shard workloads prevent the sharding mechanism from achieving the expected aim.This paper proposes a graphbased sharding scheme for public blockchain to efficiently balance the transaction distribution.Bymitigating crossshard transactions and evening-out workloads among shards,the scheme reduces transaction confirmation latency and enhances the transaction capacity of the blockchain.Therefore,the scheme can achieve a high-frequency transaction as well as a better blockchain scalability.Experiments results show that the scheme effectively reduces the cross-shard transaction ratio to a range of 35%-56%and significantly decreases the transaction confirmation latency to 6 s in a blockchain with no more than 25 shards.

Performance Analysis of Support Vector Machine (SVM) on Challenging Datasets for Forest Fire Detection

This article delves into the analysis of performance and utilization of Support Vector Machines (SVMs) for the critical task of forest fire detection using image datasets. With the increasing threat of forest fires to ecosystems and human settlements, the need for rapid and accurate detection systems is of utmost importance. SVMs, renowned for their strong classification capabilities, exhibit proficiency in recognizing patterns associated with fire within images. By training on labeled data, SVMs acquire the ability to identify distinctive attributes associated with fire, such as flames, smoke, or alterations in the visual characteristics of the forest area. The document thoroughly examines the use of SVMs, covering crucial elements like data preprocessing, feature extraction, and model training. It rigorously evaluates parameters such as accuracy, efficiency, and practical applicability. The knowledge gained from this study aids in the development of efficient forest fire detection systems, enabling prompt responses and improving disaster management. Moreover, the correlation between SVM accuracy and the difficulties presented by high-dimensional datasets is carefully investigated, demonstrated through a revealing case study. The relationship between accuracy scores and the different resolutions used for resizing the training datasets has also been discussed in this article. These comprehensive studies result in a definitive overview of the difficulties faced and the potential sectors requiring further improvement and focus.

Unscented Kalman filter for a low-cost GNSS/IMU-based mobile mapping application under demanding conditions

For the last two decades,low-cost Global Navigation Satellite System(GNSS)receivers have been used in various applications.These receivers are mini-size,less expensive than geodetic-grade receivers,and in high demand.Irrespective of these outstanding features,low-cost GNSS receivers are potentially poorer hardwares with internal signal processing,resulting in lower quality.They typically come with low-cost GNSS antenna that has lower performance than their counterparts,particularly for multipath mitigation.Therefore,this research evaluated the low-cost GNSS device performance using a high-rate kinematic survey.For this purpose,these receivers were assembled with an Inertial Measurement Unit(IMU)sensor,which actively transmited data on acceleration and orientation rate during the observation.The position and navigation parameter data were obtained from the IMU readings,even without GNSS signals via the U-blox F9R GNSS/IMU device mounted on a vehicle.This research was conducted in an area with demanding conditions,such as an open sky area,an urban environment,and a shopping mall basement,to examine the device’s performance.The data were processed by two approaches:the Single Point Positioning-IMU(SPP/IMU)and the Differential GNSS-IMU(DGNSS/IMU).The Unscented Kalman Filter(UKF)was selected as a filtering algorithm due to its excellent performance in handling nonlinear system models.The result showed that integrating GNSS/IMU in SPP processing mode could increase the accuracy in eastward and northward components up to 68.28%and 66.64%.Integration of DGNSS/IMU increased the accuracy in eastward and northward components to 93.02%and 93.03%compared to the positioning of standalone GNSS.In addition,the positioning accuracy can be improved by reducing the IMU noise using low-pass and high-pass filters.This application could still not gain the expected position accuracy under signal outage conditions.

Redundant Data Detection and Deletion to Meet Privacy Protection Requirements in Blockchain-Based Edge Computing Environment

With the rapid development of information technology,IoT devices play a huge role in physiological health data detection.The exponential growth of medical data requires us to reasonably allocate storage space for cloud servers and edge nodes.The storage capacity of edge nodes close to users is limited.We should store hotspot data in edge nodes as much as possible,so as to ensure response timeliness and access hit rate;However,the current scheme cannot guarantee that every sub-message in a complete data stored by the edge node meets the requirements of hot data;How to complete the detection and deletion of redundant data in edge nodes under the premise of protecting user privacy and data dynamic integrity has become a challenging problem.Our paper proposes a redundant data detection method that meets the privacy protection requirements.By scanning the cipher text,it is determined whether each sub-message of the data in the edge node meets the requirements of the hot data.It has the same effect as zero-knowledge proof,and it will not reveal the privacy of users.In addition,for redundant sub-data that does not meet the requirements of hot data,our paper proposes a redundant data deletion scheme that meets the dynamic integrity of the data.We use Content Extraction Signature(CES)to generate the remaining hot data signature after the redundant data is deleted.The feasibility of the scheme is proved through safety analysis and efficiency analysis.

Two-Dimensional Riemann Problems:Transonic Shock Waves and Free Boundary Problems

We are concerned with global solutions of multidimensional(M-D)Riemann problems for nonlinear hyperbolic systems of conservation laws,focusing on their global configurations and structures.We present some recent developments in the rigorous analysis of two-dimensional(2-D)Riemann problems involving transonic shock waves through several prototypes of hyperbolic systems of conservation laws and discuss some further M-D Riemann problems and related problems for nonlinear partial differential equations.In particular,we present four different 2-D Riemann problems through these prototypes of hyperbolic systems and show how these Riemann problems can be reformulated/solved as free boundary problems with transonic shock waves as free boundaries for the corresponding nonlinear conservation laws of mixed elliptic-hyperbolic type and related nonlinear partial differential equations.

Machine Learning With Data Assimilation and Uncertainty Quantification for Dynamical Systems:A Review

Data assimilation(DA)and uncertainty quantification(UQ)are extensively used in analysing and reducing error propagation in high-dimensional spatial-temporal dynamics.Typical applications span from computational fluid dynamics(CFD)to geoscience and climate systems.Recently,much effort has been given in combining DA,UQ and machine learning(ML)techniques.These research efforts seek to address some critical challenges in high-dimensional dynamical systems,including but not limited to dynamical system identification,reduced order surrogate modelling,error covariance specification and model error correction.A large number of developed techniques and methodologies exhibit a broad applicability across numerous domains,resulting in the necessity for a comprehensive guide.This paper provides the first overview of state-of-the-art researches in this interdisciplinary field,covering a wide range of applications.This review is aimed at ML scientists who attempt to apply DA and UQ techniques to improve the accuracy and the interpretability of their models,but also at DA and UQ experts who intend to integrate cutting-edge ML approaches to their systems.Therefore,this article has a special focus on how ML methods can overcome the existing limits of DA and UQ,and vice versa.Some exciting perspectives of this rapidly developing research field are also discussed.Index Terms-Data assimilation(DA),deep learning,machine learning(ML),reduced-order-modelling,uncertainty quantification(UQ).

Numerical Comparison of Shapeless Radial Basis Function Networks in Pattern Recognition

This work focuses on radial basis functions containing no parameters with themain objective being to comparatively explore more of their effectiveness.For this,a total of sixteen forms of shapeless radial basis functions are gathered and investigated under the context of the pattern recognition problem through the structure of radial basis function neural networks,with the use of the Representational Capability(RC)algorithm.Different sizes of datasets are disturbed with noise before being imported into the algorithm as‘training/testing’datasets.Each shapeless radial basis function is monitored carefully with effectiveness criteria including accuracy,condition number(of the interpolation matrix),CPU time,CPU-storage requirement,underfitting and overfitting aspects,and the number of centres being generated.For the sake of comparison,the well-known Multiquadric-radial basis function is included as a representative of shape-contained radial basis functions.The numerical results have revealed that some forms of shapeless radial basis functions show good potential and are even better than Multiquadric itself indicating strongly that the future use of radial basis function may no longer face the pain of choosing a proper shape when shapeless forms may be equally(or even better)effective.

Performance of GPS and IMU sensor fusion using unscented Kalman filter for precise i-Boat navigation in infinite wide waters

The Unmanned Surface Vehicle(USV)navigation system needs an accurate,firm,and reliable performance to avoid obstacles,as well as carry out automatic movements during missions.The Global Positioning System(GPS)is often used in these systems to provide absolute position information.However,the GPS measurements are affected by external conditions such as atmospheric bias and multipath effects.This leads to the inability of the stand-alone GPS to provide accurate positioning for the USV systems.One of the solutions to correct the errors of this sensor is by conducting GPS and Inertial Measurement Unit(IMU)fusion.The IMU sensor is complementary to the GPS and not affected by external conditions.However,it accumulates noise as time elapses.Therefore,this study aims to determine the fusion of the GPS and IMU sensors for the i-Boat navigation system,which is a USV developed by Institut Teknologi Sepuluh Nopember(ITS)Surabaya.Using the Unscented Kalman filter(UKF),sensor fusion was carried out based on the state equation defined by the dynamic and kinematic mathematical model of ship motion in 6 degrees of freedom.Then the performance of this model was tested through several simulations using different combinations of attitude measurement data.Two scenarios were conducted in the simulations:attitude measurement inclusion and exclusion(Scenarios I and II,respectively).The results showed that the position estimation in Scenario II was better than in Scenario I,with the Root Mean Square Error(RMSE)value of 0.062 m.Further simulations showed that the presence of attitude measurement data caused a decrease in the fusion accuracy.The UKF simulation with eight measurement parameters(Scenarios A,B and C)and seven measurement parameters(Scenarios D,E and F),as well as analytical attitude movement,indicated that yaw data had the largest noise accumulation compared to roll and pitch.

Predicting Wavelet-Transformed Stock Prices Using a Vanishing Gradient Resilient Optimized Gated Recurrent Unit with a Time Lag

The development of accurate prediction models continues to be highly beneficial in myriad disciplines. Deep learning models have performed well in stock price prediction and give high accuracy. However, these models are largely affected by the vanishing gradient problem escalated by some activation functions. This study proposes the use of the Vanishing Gradient Resilient Optimized Gated Recurrent Unit (OGRU) model with a scaled mean Approximation Coefficient (AC) time lag which should counter slow convergence, vanishing gradient and large error metrics. This study employed the Rectified Linear Unit (ReLU), Hyperbolic Tangent (Tanh), Sigmoid and Exponential Linear Unit (ELU) activation functions. Real-life datasets including the daily Apple and 5-minute Netflix closing stock prices were used, and they were decomposed using the Stationary Wavelet Transform (SWT). The decomposed series formed a decomposed data model which was compared to an undecomposed data model with similar hyperparameters and different default lags. The Apple daily dataset performed well with a Default_1 lag, using an undecomposed data model and the ReLU, attaining 0.01312, 0.00854 and 3.67 minutes for RMSE, MAE and runtime. The Netflix data performed best with the MeanAC_42 lag, using decomposed data model and the ELU achieving 0.00620, 0.00487 and 3.01 minutes for the same metrics.

大规模交易数据库的一种有效聚类算法(英文)

研究大规模交易数据库的聚类问题 ,提出了一种二次聚类算法—— CATD.该算法首先将数据库划分成若干分区 ,在每个分区内利用层次聚类算法进行局部聚类 ,把交易初步划分成若干亚聚类 ,亚聚类的个数由聚类间的距离参数控制 .然后对所有的亚聚类进行全局聚类 ,同时识别出噪声 .由于采用了分区方法和聚类的支持向量表示法 ,该算法只需扫描一次数据库 ,聚类过程在内存中进行 ,因此能处理大规模的数据库 .

THEORETICAL AMPLITUDE AND PERIOD OF PRECURSOR SOLITON GENERATION IN TWO-LAYER FLOW

An fKdV equation of two-layer how and an averaged fKdV equation (AfKdV equation) with respect to phase are derived to determine the theoretical amplitude and period of the precursor solitons in the present paper. In terms of the AfKdV equation derived by the authors, a new theory on the precursor soliton generation based on Lee et al.'s concept is presented. Concepts of asymptotic mean hydraulic fall and level are introduced in our analysis, and the theoretical amplitude and period both depend on the asymptotic mi-an levels and stratified parameters. From the present theoretical results, it is obtained that when the moving velocity of the topography is at the resonant points, there exist two general relations: (1) amplitude relation (A) over circle = 2F, (2) period relation <(tau)over circle> = -8m(1)m(3)(-1)root 6m(4)m(3)(-1)F, in which (A) over circle and <(tau)over circle> are the amplitude and period of the precursor solitons at the resonant points respectively, m(1), m(3) and m(4) are coefficients of the fKdV equation, and F is asymptotic mean half-hydraulic fall at subcritical cutoff points. The theoretical results of this paper are compared with experiments and numerical calculations of two-layer flow over a semicircular topography and all these results are in good agreement. Due to the canonical character of the coefficients of fKdV equations, this theory also holds for any two-dimensional system, which can be reduced to fKdV equations.

STABILITY OF STEADY MULTI-WAVE CONFIGURATIONS FOR THE FULL EULER EQUATIONS OF COMPRESSIBLE FLUID FLOW

We are concerned with the stability of steady multi-wave configurations for the full Euler equations of compressible fluid flow. In this paper, we focus on the stability of steady four-wave configurations that are the solutions of the Riemann problem in the flow direction, consisting of two shocks, one vortex sheet, and one entropy wave, which is one of the core multi-wave configurations for the two-dimensional Euler equations. It is proved that such steady four-wave configurations in supersonic flow are stable in structure globally, even under the BV perturbation of the incoming flow in the flow direction. In order to achieve this, we first formulate the problem as the Cauchy problem （initial value problem） in the flow direction, and then develop a modified Glimm difference scheme and identify a Glimm-type functional to obtain the required BV estimates by tracing the interactions not only between the strong shocks and weak waves, but also between the strong vortex sheet/entropy wave and weak waves. The key feature of the Euler equations is that the reflection coefficient is always less than 1, when a weak wave of different family interacts with the strong vortex sheet/entropy wave or the shock wave, which is crucial to guarantee that the Glimm functional is decreasing. Then these estimates are employed to establish the convergence of the approximate solutions to a global entropy solution, close to the background solution of steady four-wave configuration.

RITT-WU'S CHARACTERISTIC SET METHOD FOR ORDINARY DIFFERENCE POLYNOMIAL SYSTEMS WITH ARBITRARY ORDERING

In this paper, a Ritt-Wu＇s characteristic set method for ordinary difference systems is proposed, which is valid for any admissible ordering. New definition for irreducible chains and new zero decomposition algorithms are also proposed.

Scattering of Surface Waves by the Edge of a Small Undulation on a Porous Bed in an Ocean with Ice-cover

在免费表面有一个冰封面的地方，在有限深度的海洋在一张多孔的床上由小波动的边表面波浪散布作为很小的厚度的一个有弹性的盘子正在被建模，在线性化的水的框架以内被调查波浪理论。在在冰封面下面的表面的表面紧张的效果被忽视。在那里存在宣传在的一个仅仅波浪数字就在冰封面下面。不安分析被采用解决一个方法 Laplace 鈥檚 方程与适当格林鈥檚 功能并且从而的介绍基于格林鈥檚 积分定理管理的边界价值问题近似评估思考和传播系数直到第一份订单。正弦曲线涟漪的一个补丁被看作一个例子，相关系数是坚定的。

MHD stagnation-point flow and heat transfer towards stretching sheet with induced magnetic field

The problem of the steady magnetohydrodynamic （MHD） stagnation-point flow of an incompressible viscous fluid over a stretching sheet is studied. The effect of an induced magnetic field is taken into account. The nonlinear partial differential equations are transformed into ordinary differential equations via the similarity transformation. The transformed boundary layer equations are solved numerically using the shooting method. Numerical results are obtained for various magnetic parameters and Prandtl numbers. The effects of the induced magnetic field on the skin friction coefficient, the local Nusselt number, the velocity, and the temperature profiles are presented graphically and discussed in detail.

Energy transfer in double plate system dynamics

The study of energy transfer between coupled subsystems in a hybrid system is very important for applications. This paper presents an analytical analysis of energy transfer between plates of a visco-elastically connected double-plate system in free transversal vibrations. The analytical analysis shows that the visco-elastic connection between plates is responsible for the appearance of two-frequency regime in the time function, which corresponds to one eigen amplitude function of one mode, and also that time functions of different vibration modes are uncoupled, but energy transfer between plates in one eigen mode appears. It was shown for each shape of vibrations. Series of the two Lyapunov exponents corresponding to the one eigen amplitude mode are expressed by using the energy of the corresponding eigen amplitude time component.

Oblique Water Wave Scattering by Bottom Undulation in a Two-layer Fluid Flowing Through a Channel

在在由二层组成的隧道流动的小变丑上的繁殖被考虑的倾斜的波浪(内部波浪) 的问题。上面的液体被假定被一个僵硬的盖上面跳，它是为免费表面的近似，并且更低的被有小变丑的透不过的底部表面下面围住；隧道在水平方向是无界的。假定无旋的运动，不安技术被采用由与适当草地功能的介绍合适使用草地不可分的定理在二液体计算速度潜力的一阶的修正。那些功能在以包含代表底部变丑的形状功能 c (x) 的积分计算思考和传播系数帮助。三维的线性水波浪理论为提出相关边界价值问题被利用。底部变丑的二个特殊例子被认为验证结果。正弦曲线涟漪的一个补丁的考虑(让一样的波浪数) 思考系数是比率的摆动的功能的表演两次到涟漪波浪数字的波浪数字的 x 部件。当这比率接近一个时，理论预言在床和接口之间的一个反响的相互作用，并且思考系数变得一涟漪的数字多重。如果这个数字大，事件波浪精力的高思考发生。类似的结果为有不同波浪数字的正弦曲线涟漪的一个补丁被观察。为小入射角，反映的精力与直到 / 的另外的入射角相比是更大的，这也被观察 4。这些理论观察被图形的结果支持。

ON CAUCHY-POMPEIU FORMULA FOR FUNCTIONS WITH VALUES IN A UNIVERSAL CLIFFORD ALGEBRA

This paper obtains the Cauchy-Pompeiu formula on certain distinguished boundary for functions with values in a universal Clifford algebra. This formula is just an extension of the Cauchy's integral formula obtained in [11].