OPTIMAL SCHEME FOR SEQUENTIAL COMPUTATIONS OF F_m(z) INTEGRALS IN AB INITIO CALCULATIONS----COMBINATORY USE OF UPWARD AND DOWNWARD RECURSIONS

The quantitative rules of the transfer and variation of errors,when the Gaussian integral functions F.(z) are evaluated sequentially by recurring,have been expounded.The traditional viewpoint to negate the applicability and reliability of upward recursive formula in principle is amended.An optimal scheme of upward-and downward-joint recursions has been developed for the sequential F(z) computations.No additional accuracy is needed with the fundamental term of recursion because the absolute error of Fn(z) always decreases with the recursive approach.The scheme can be employed in modifying any of existent subprograms for Fn<z> computations.In the case of p-d-f-and g-type Gaussians,combining this method with Schaad's formulas can reduce,at least,the additive operations by a factor 40%;the multiplicative and exponential operations by a factor 60%.

On the Use of the Initial Values of Recursions

In this paper we make a study of the use of the iniiai values of a recursion skilfully, so that the count for finding a solution of any recursion will be more simplified. Finally, we give out the "moving forth prineiple" of initial values of a recursion.

Carleman Linearization and Systems of Arbitrary Depth Polynomial Recursions

New approach to systems of polynomial recursions is developed based on the Carleman linearization procedure. The article is divided into two main sections: firstly, we focus on the case of uni-variable depth-one polynomial recurrences. Subsequently, the systems of depth-one polynomial recurrence relations are discussed. The corresponding transition matrix is constructed and upper triangularized. Furthermore, the powers of the transition matrix are calculated using the back substitution procedure. The explicit expression for a solution to a broad family of recurrence relations is obtained. We investigate to which recurrences the framework can be applied and construct sufficient conditions for the method to work. It is shown how introduction of auxiliary variables can be used to reduce arbitrary depth systems to the depth-one system of recurrences dealt with earlier. Finally, the limitations of the method are discussed, outlining possible directions for future research.

Distributed Dynamic Load in Structural Dynamics by the Impulse-Based Force Estimation Algorithm

This paper proposes a novel approach for identifying distributed dynamic loads in the time domain.Using polynomial andmodal analysis,the load is transformed intomodal space for coefficient identification.This allows the distributed dynamic load with a two-dimensional form in terms of time and space to be simultaneously identified in the form of modal force,thereby achieving dimensionality reduction.The Impulse-based Force Estimation Algorithm is proposed to identify dynamic loads in the time domain.Firstly,the algorithm establishes a recursion scheme based on convolution integral,enabling it to identify loads with a long history and rapidly changing forms over time.Secondly,the algorithm introduces moving mean and polynomial fitting to detrend,enhancing its applicability in load estimation.The aforementioned methodology successfully accomplishes the reconstruction of distributed,instead of centralized,dynamic loads on the continuum in the time domain by utilizing acceleration response.To validate the effectiveness of the method,computational and experimental verification were conducted.

A multi-scale second-order autoregressive recursive filter approach for the sea ice concentration analysis

To effectively extract multi-scale information from observation data and improve computational efficiency,a multi-scale second-order autoregressive recursive filter(MSRF)method is designed.The second-order autoregressive filter used in this study has been attempted to replace the traditional first-order recursive filter used in spatial multi-scale recursive filter(SMRF)method.The experimental results indicate that the MSRF scheme successfully extracts various scale information resolved by observations.Moreover,compared with the SMRF scheme,the MSRF scheme improves computational accuracy and efficiency to some extent.The MSRF scheme can not only propagate to a longer distance without the attenuation of innovation,but also reduce the mean absolute deviation between the reconstructed sea ice concentration results and observations reduced by about 3.2%compared to the SMRF scheme.On the other hand,compared with traditional first-order recursive filters using in the SMRF scheme that multiple filters are executed,the MSRF scheme only needs to perform two filter processes in one iteration,greatly improving filtering efficiency.In the two-dimensional experiment of sea ice concentration,the calculation time of the MSRF scheme is only 1/7 of that of SMRF scheme.This means that the MSRF scheme can achieve better performance with less computational cost,which is of great significance for further application in real-time ocean or sea ice data assimilation systems in the future.

Identification of time-varying system and energy-based optimization of adaptive control in seismically excited structure

The combination of structural health monitoring and vibration control is of great importance to provide components of smart structures.While synthetic algorithms have been proposed,adaptive control that is compatible with changing conditions still needs to be used,and time-varying systems are required to be simultaneously estimated with the application of adaptive control.In this research,the identification of structural time-varying dynamic characteristics and optimized simple adaptive control are integrated.First,reduced variations of physical parameters are estimated online using the multiple forgetting factor recursive least squares(MFRLS)method.Then,the energy from the structural vibration is simultaneously specified to optimize the control force with the identified parameters to be operational.Optimization is also performed based on the probability density function of the energy under the seismic excitation at any time.Finally,the optimal control force is obtained by the simple adaptive control(SAC)algorithm and energy coefficient.A numerical example and benchmark structure are employed to investigate the efficiency of the proposed approach.The simulation results revealed the effectiveness of the integrated online identification and optimal adaptive control in systems.

Control method based on DRFNN sliding mode for multifunctional flexible multistate switch

To address the low accuracy and stability when applying classical control theory in distribution networks with distributed generation,a control method involving flexible multistate switches(FMSs)is proposed in this study.This approach is based on an improved double-loop recursive fuzzy neural network(DRFNN)sliding mode,which is intended to stably achieve multiterminal power interaction and adaptive arc suppression for single-phase ground faults.First,an improved DRFNN sliding mode control(SMC)method is proposed to overcome the chattering and transient overshoot inherent in the classical SMC and reduce the reliance on a precise mathematical model of the control system.To improve the robustness of the system,an adaptive parameter-adjustment strategy for the DRFNN is designed,where its dynamic mapping capabilities are leveraged to improve the transient compensation control.Additionally,a quasi-continuous second-order sliding mode controller with a calculus-driven sliding mode surface is developed to improve the current monitoring accuracy and enhance the system stability.The stability of the proposed method and the convergence of the network parameters are verified using the Lyapunov theorem.A simulation model of the three-port FMS with its control system is constructed in MATLAB/Simulink.The simulation result confirms the feasibility and effectiveness of the proposed control strategy based on a comparative analysis.

Sound event localization and detection based on deep learning

Acoustic source localization(ASL)and sound event detection(SED)are two widely pursued independent research fields.In recent years,in order to achieve a more complete spatial and temporal representation of sound field,sound event localization and detection(SELD)has become a very active research topic.This paper presents a deep learning-based multioverlapping sound event localization and detection algorithm in three-dimensional space.Log-Mel spectrum and generalized cross-correlation spectrum are joined together in channel dimension as input features.These features are classified and regressed in parallel after training by a neural network to obtain sound recognition and localization results respectively.The channel attention mechanism is also introduced in the network to selectively enhance the features containing essential information and suppress the useless features.Finally,a thourough comparison confirms the efficiency and effectiveness of the proposed SELD algorithm.Field experiments show that the proposed algorithm is robust to reverberation and environment and can achieve higher recognition and localization accuracy compared with the baseline method.

Asymptotic stability of monostable wavefronts in discrete-time integral recursions

The aim of this work is to study the traveling wavefronts in a discrete-time integral recursion with a Gauss kernel in R2.We first establish the existence of traveling wavefronts as well as their precise asymptotic behavior.Then,by employing the comparison principle and upper and lower solutions technique,we prove the asymptotic stability and uniqueness of such monostable wavefronts in the sense of phase shift and circumnutation.We also obtain some similar results in R.

Online Identification of Lithium-ion Battery Model Parameters with Initial Value Uncertainty and Measurement Noise

Online parameter identification is essential for the accuracy of the battery equivalent circuit model(ECM).The traditional recursive least squares(RLS)method is easily biased with the noise disturbances from sensors,which degrades the modeling accuracy in practice.Meanwhile,the recursive total least squares(RTLS)method can deal with the noise interferences,but the parameter slowly converges to the reference with initial value uncertainty.To alleviate the above issues,this paper proposes a co-estimation framework utilizing the advantages of RLS and RTLS for a higher parameter identification performance of the battery ECM.RLS converges quickly by updating the parameters along the gradient of the cost function.RTLS is applied to attenuate the noise effect once the parameters have converged.Both simulation and experimental results prove that the proposed method has good accuracy,a fast convergence rate,and also robustness against noise corruption.

AIGCrank:A new adaptive algorithm for identifying a set of influential spreaders in complex networks based on gravity centrality

The influence maximization problem in complex networks asks to identify a given size of seed spreaders set to maximize the number of expected influenced nodes at the end of the spreading process.This problem finds many practical applications in numerous areas such as information dissemination,epidemic immunity,and viral marketing.However,most existing influence maximization algorithms are limited by the“rich-club”phenomenon and are thus unable to avoid the influence overlap of seed spreaders.This work proposes a novel adaptive algorithm based on a new gravity centrality and a recursive ranking strategy,named AIGCrank,to identify a set of influential seeds.Specifically,the gravity centrality jointly employs the neighborhood,network location and topological structure information of nodes to evaluate each node's potential of being selected as a seed.We also present a recursive ranking strategy for identifying seed nodes one-byone.Experimental results show that our algorithm competes very favorably with the state-of-the-art algorithms in terms of influence propagation and coverage redundancy of the seed set.

Anti-interference self-alignment algorithm by attitude optimization estimation for SINS on a rocking base

The performance of a strapdown inertial navigation system(SINS)largely depends on the accuracy and rapidness of the initial alignment.A novel anti-interference self-alignment algorithm by attitude optimization estimation for SINS on a rocking base is presented in this paper.The algorithm transforms the initial alignment into the initial attitude determination problem by using infinite vector observations to remove the angular motions,the SINS alignment is heuristically established as an optimiza-tion problem of finding the minimum eigenvector.In order to further improve the alignment precision,an adaptive recursive weighted least squares(ARWLS)curve fitting algorithm is used to fit the translational motion interference-contaminated reference vectors according to their time domain characteristics.Simulation studies and experimental results favorably demonstrate its rapidness,accuracy and robustness.

Recursive recurrent neural network:A novel model for manipulator control with different levels of physical constraints

Manipulators actuate joints to let end effectors to perform precise path tracking tasks.Recurrent neural network which is described by dynamic models with parallel processing capability,is a powerful tool for kinematic control of manipulators.Due to physical limitations and actuation saturation of manipulator joints,the involvement of joint constraints for kinematic control of manipulators is essential and critical.However,current existing manipulator control methods based on recurrent neural networks mainly handle with limited levels of joint angular constraints,and to the best of our knowledge,methods for kinematic control of manipulators with higher order joint constraints based on recurrent neural networks are not yet reported.In this study,for the first time,a novel recursive recurrent network model is proposed to solve the kinematic control issue for manipulators with different levels of physical constraints,and the proposed recursive recurrent neural network can be formulated as a new manifold system to ensure control solution within all of the joint constraints in different orders.The theoretical analysis shows the stability and the purposed recursive recurrent neural network and its convergence to solution.Simulation results further demonstrate the effectiveness of the proposed method in end‐effector path tracking control under different levels of joint constraints based on the Kuka manipulator system.Comparisons with other methods such as the pseudoinverse‐based method and conventional recurrent neural network method substantiate the superiority of the proposed method.

Nyström kernel algorithm based on least logarithmic hyperbolic cosine loss

Kernel adaptive filters(KAFs)have sparked substantial attraction for online non-linear learning applications.It is noted that the effectiveness of KAFs is highly reliant on a rational learning criterion.Concerning this,the logarithmic hyperbolic cosine(lncosh)criterion with better robustness and convergence has drawn attention in recent studies.However,existing lncosh loss-based KAFs use the stochastic gradient descent(SGD)for optimization,which lack a trade-off between the convergence speed and accuracy.But recursion-based KAFs can provide more effective filtering performance.Therefore,a Nyström method-based robust sparse kernel recursive least lncosh loss algorithm is derived in this article.Experiments via measures and synthetic data against the non-Gaussian noise confirm the superiority with regard to the robustness,accuracy performance,and computational cost.

An Intrusion Detection System for SDN Using Machine Learning

Software Defined Networking(SDN)has emerged as a promising and exciting option for the future growth of the internet.SDN has increased the flexibility and transparency of the managed,centralized,and controlled network.On the other hand,these advantages create a more vulnerable environment with substantial risks,culminating in network difficulties,system paralysis,online banking frauds,and robberies.These issues have a significant detrimental impact on organizations,enterprises,and even economies.Accuracy,high performance,and real-time systems are necessary to achieve this goal.Using a SDN to extend intelligent machine learning methodologies in an Intrusion Detection System(IDS)has stimulated the interest of numerous research investigators over the last decade.In this paper,a novel HFS-LGBM IDS is proposed for SDN.First,the Hybrid Feature Selection algorithm consisting of two phases is applied to reduce the data dimension and to obtain an optimal feature subset.In thefirst phase,the Correlation based Feature Selection(CFS)algorithm is used to obtain the feature subset.The optimal feature set is obtained by applying the Random Forest Recursive Feature Elimination(RF-RFE)in the second phase.A LightGBM algorithm is then used to detect and classify different types of attacks.The experimental results based on NSL-KDD dataset show that the proposed system produces outstanding results compared to the existing methods in terms of accuracy,precision,recall and f-measure.

Deep Learning Enabled Social Media Recommendation Based on User Comments

Nowadays,review systems have been developed with social media Recommendation systems(RS).Although research on RS social media is increas-ing year by year,the comprehensive literature review and classification of this RS research is limited and needs to be improved.The previous method did notfind any user reviews within a time,so it gets poor accuracy and doesn’tfilter the irre-levant comments efficiently.The Recursive Neural Network-based Trust Recom-mender System(RNN-TRS)is proposed to overcome this method’s problem.So it is efficient to analyse the trust comment and remove the irrelevant sentence appropriately.Thefirst step is to collect the data based on the transactional reviews of social media.The second step is pre-processing using Imbalanced Col-laborative Filtering(ICF)to remove the null values from the dataset.Extract the features from the pre-processing step using the Maximum Support Grade Scale(MSGS)to extract the maximum number of scaling features in the dataset and grade the weights(length,count,etc.).In the Extracting features for Training and testing method before that in the feature weights evaluating the softmax acti-vation function for calculating the average weights of the features.Finally,In the classification method,the Recursive Neural Network-based Trust Recommender System(RNN-TRS)for User reviews based on the Positive and negative scores is analysed by the system.The simulation results improve the predicting accuracy and reduce time complexity better than previous methods.

Application of Recursive Query on Structured Query Language Server

The advantage of recursive programming is that it is very easy to write and it only requires very few lines of code if done correctly.Structured query language(SQL)is a database language and is used to manipulate data.In Microsoft SQL Server 2000,recursive queries are implemented to retrieve data which is presented in a hierarchical format,but this way has its disadvantages.Common table expression(CTE)construction introduced in Microsoft SQL Server 2005 provides the significant advantage of being able to reference itself to create a recursive CTE.Hierarchical data structures,organizational charts and other parent-child table relationship reports can easily benefit from the use of recursive CTEs.The recursive query is illustrated and implemented on some simple hierarchical data.In addition,one business case study is brought forward and the solution using recursive query based on CTE is shown.At the same time,stored procedures are programmed to do the recursion in SQL.Test results show that recursive queries based on CTEs bring us the chance to create much more complex queries while retaining a much simpler syntax.

Generalized Series of Bernoulli Type

The problem of evaluating an infinite series whose successive terms are reciprocal squares of the natural numbers was posed without a solution being offered in the middle of the seventeenth century. In the modern era, it is part of the theory of the Riemann zeta-function, specifically ζ (2). Jakob Bernoulli attempted to solve it by considering other more tractable series which were superficially similar and which he hoped could be algebraically manipulated to yield a solution to the difficult series. This approach was eventually unsuccessful, however, Bernoulli did produce an early monograph on summation of series. It remained for Bernoulli’s student and countryman Leonhard Euler to ultimately determine the sum to be . We characterize a class of series based on generalizing Bernoulli’s original work by adding two additional parameters to the summations. We also develop a recursion formula that allows summation of any member of the class.

The Bivariate Normal Integral via Owen’s T Function as a Modified Euler’s Arctangent Series

The Owen’s T function is presented in four new ways, one of them as a series similar to the Euler’s arctangent series divided by 2π, which is its majorant series. All possibilities enable numerically stable and fast convergent computation of the bivariate normal integral with simple recursion. When tested computation on a random sample of one million parameter triplets with uniformly distributed components and using double precision arithmetic, the maximum absolute error was 3.45 × 10-16. In additional testing, focusing on cases with correlation coefficients close to one in absolute value, when the computation may be very sensitive to small rounding errors, the accuracy was retained. In rare potentially critical cases, a simple adjustment to the computation procedure was performed—one potentially critical computation was replaced with two equivalent non-critical ones. All new series are suitable for vector and high-precision computation, assuming they are supplemented with appropriate efficient and accurate computation of the arctangent and standard normal cumulative distribution functions. They are implemented by the R package Phi2rho, available on CRAN. Its functions allow vector arguments and are ready to work with the Rmpfr package, which enables the use of arbitrary precision instead of double precision numbers. A special test with up to 1024-bit precision computation is also presented.

金属电极电位与费米能级的对应关系

通过计算机编程,建立了几种典型金属的原子团晶体模型.应用实空间Recursion方法,计算了这几种金属在纯净状态下的费米能级与电子态密度.由此得出随着金属的费米能级的升高,其电极电位会随之下降.而电子局域态密度分布在高能区的金属易失去电子,进行氧化反应.