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.

Non-Recursive Base Conversion Using a Deterministic Markov Process

We prove that non-recursive base conversion can always be implemented by using a deterministic Markov process. Our paper discusses the pros and cons of recursive and non-recursive methods, in general. And we include a comparison between non-recursion and a deterministic Markov process, proving that the Markov process is twice as efficient.

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.

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.

Poststack reverse-time migration using a non-reflecting recursive algorithm on surface relief

Presently the research based on the accurate seismic imaging methods for surface relief, complex structure, and complicated velocity distributions is of great significance. Reverse-time migration is considered to be one of highly accurate methods. In this paper, we propose a new non-reflecting recursive algorithm for reverse-time migration by introducing the wave impedance function into the acoustic wave equation and the algorithm for the surface relief case is derived from the coordinate transformation principle. Using the exploding reflector principle and the zero-time imaging condition of poststack reverse- time migration, poststack numerical simulation and reverse-time migration with complex conditions can be realized. The results of synthetic and real data calculations show that the method effectively suppresses unwanted internal reflections and also deals with the seismic imaging problems resulting from surface relief. So, we prove that this method has strong adaptability and practicality.

Calculation connectivity reliability of road networks based on recursive decomposition arithmetic

In order to decrease the calculation complexity of connectivity reliability of road networks, an improved recursive decomposition arithmetic is proposed. First, the basic theory of recursive decomposition arithmetic is reviewed. Then the characteristics of road networks, which are different from general networks, are analyzed. Under this condition, an improved recursive decomposition arithmetic is put forward which fits road networks better. Furthermore, detailed calculation steps are presented which are convenient for the computer, and the advantage of the approximate arithmetic is analyzed based on this improved arithmetic. This improved recursive decomposition arithmetic directly produces disjoint minipaths and avoids the non-polynomial increasing problems. And because the characteristics of road networks are considered, this arithmetic is greatly simplified. Finally, an example is given to prove its validity.

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

With the development and deployment of observation systems in the ocean,more precise passive and active microwave data are becoming available for the weather forecasting and the climate monitoring.Due to the complicated variability of the sea ice concentration(SIC)in the marginal ice zone and the scarcity of high-precision sea ice data,how to use less data to accurately reconstruct the sea ice field has become an urgent problem to be solved.A reconstruction method for gridding observations using the variational optimization technique,called the multi-scale high-order recursive filter(MHRF),which is a combination of Van Vliet fourth-order recursive filter and the three-dimensional variational(3D-VAR)analysis,has been designed in this study to reproduce the refined structure of sea ice field.Compared with the existing spatial multi-scale first-order recursive filter(SMRF)in which left and right filter iterative processes are executed many times,the MHRF scheme only executes the same filter process once to reduce the analysis errors caused by multiple filters and improve the filter precision.Furthermore,the series connected transfer function in the high-order recursive filter is equivalently replaced by the paralleled one,which can carry out the independent filter process in every direction in order to improve the filter efficiency.Experimental results demonstrate that this method possesses a good potential in extracting the observation information to successfully reconstruct the SIC field in computational efficiency.

Recursive and Nonrecursive Traversal Algorithms for Dynamically Created Binary Trees

The modeling of dynamical systems from a time series implemented by our DSA program introduces binary trees of height D with all leaves on the same level, and the related subtrees of height L 〈 D. These are called e-trees and e-subtrees. The recursive and nonrecursive versions of the traversal algorithms for the trees with dynamically created nodes are discussed. The original nonrecursive algorithms that return the pointer to the next node in preorder, inorder and postorder traversals are presented. The space-time complexity analysis shows and the execution time measurements confirm that for these O（2D） algorithms, the recursive versions have approximately 10-25% better time constants. Still, the use of nonrecursive algorithms may be more appropriate in several occasions.

FAST RECURSIVE LEAST SQUARES LEARNING ALGORITHM FOR PRINCIPAL COMPONENT ANALYSIS

Based on the least-square minimization a computationally efficient learning algorithm for the Principal Component Analysis(PCA) is derived. The dual learning rate parameters are adaptively introduced to make the proposed algorithm providing the capability of the fast convergence and high accuracy for extracting all the principal components. It is shown that all the information needed for PCA can be completely represented by the unnormalized weight vector which is updated based only on the corresponding neuron input-output product. The convergence performance of the proposed algorithm is briefly analyzed.The relation between Oja’s rule and the least squares learning rule is also established. Finally, a simulation example is given to illustrate the effectiveness of this algorithm for PCA.

FOUR-PARAMETER AUTOMATIC TRANSMISSION TECHNOLOGY FOR CONSTRUCTION VEHICLE BASED ON ELMAN RECURSIVE NEURAL NETWORK

From the viewpoint of energy saving and improving transmission efficiency, the ZL50E wheel loader is taken as the study object. And the system model is analyzed based on the transmission system of the construction vehicle. A new four-parameter shift schedule is presented, which can keep the torque converter working in the high efficiency area. The control algorithm based on the Elman recursive neural network is applied, and four-parameter control system is developed which is based on industrial computer. The system is used to collect data accurately and control 4D180 power-shift gearbox of ZL50E wheel loader shift timely. An experiment is done on automatic transmission test-bed, and the result indicates that the control system could reliably and safely work and improve the efficiency of hydraulic torque converter. Four-parameter shift strategy that takes into account the power consuming of the working pump has important operating significance and reflects the actual working status of construction vehicle.

Recursive Least Square Vehicle Mass Estimation Based on Acceleration Partition

Vehicle mass is an important parameter in vehicle dynamics control systems. Although many algorithms have been developed for the estimation of mass, none of them have yet taken into account the different types of resistance that occur under different conditions. This paper proposes a vehicle mass estimator. The estimator incorporates road gradient information in the longitudinal accelerometer signal, and it removes the road grade from the longitudinal dynamics of the vehicle. Then, two different recursive least square method （RLSM） schemes are proposed to estimate the driving resistance and the mass independently based on the acceleration partition under different conditions. A 6 DOF dynamic model of four In-wheel Motor Vehicle is built to assist in the design of the algorithm and in the setting of the parameters. The acceleration limits are determined to not only reduce the estimated error but also ensure enough data for the resistance estimation and mass estimation in some critical situations. The modification of the algorithm is also discussed to improve the result of the mass estimation. Experiment data on asphalt road, plastic runway, and gravel road and on sloping roads are used to validate the estimation algorithm. The adaptability of the algorithm is improved by using data collected under several critical operating conditions. The experimental results show the error of the estimation process to be within 2.6%, which indicates that the algorithm can estimate mass with great accuracy regardless of the road surface and gradient changes and that it may be valuable in engineering applications. This paper proposes a recursive least square vehicle mass estimation method based on acceleration partition.

Recursive Partitioning Analysis Classification and Graded Prognostic Assessment for Non-Small Cell Lung Cancer Patients with Brain Metastasis:A Retrospective Cohort Study

Objective：To assess prognostic factors and validate the effectiveness of recursive partitioning analysis （RPA） classes and graded prognostic assessment （GPA） in 290 non-small cell lung cancer （NSCLC） patients with brain metastasis （BM）.Methods：From Jan 2008 to Dec 2009,the clinical data of 290 NSCLC cases with BM treated with multiple modalities including brain irradiation,systemic chemotherapy and tyrosine kinase inhibitors （TKIs） in two institutes were analyzed.Survival was estimated by Kaplan-Meier method.The differences of survival rates in subgroups were assayed using log-rank test.Multivariate Cox＇s regression method was used to analyze the impact of prognostic factors on survival.Two prognostic indexes models （RPA and GPA） were validated respectively.Results：All patients were followed up for 1-44 months,the median survival time after brain irradiation and its corresponding 95% confidence interval （95% CI） was 14 （12.3-15.8） months.1-,2-and 3-year survival rates in the whole group were 56.0%,28.3%,and 12.0%,respectively.The survival curves of subgroups,stratified by both RPA and GPA,were significantly different （P0.001）.In the multivariate analysis as RPA and GPA entered Cox＇s regression model,Karnofsky performance status （KPS） ≥ 70,adenocarcinoma subtype,longer administration of TKIs remained their prognostic significance,RPA classes and GPA also appeared in the prognostic model.Conclusion：KPS ≥70,adenocarcinoma subtype,longer treatment of molecular targeted drug,and RPA classes and GPA are the independent prognostic factors affecting the survival rates of NSCLC patients with BM.

Accelerated Recursive Feature Elimination Based on Support Vector Machine for Key Variable Identification

Key variable identification for classifications is related to many trouble-shooting problems in process indus-tries. Recursive feature elimination based on support vector machine (SVM-RFE) has been proposed recently in applica-tion for feature selection in cancer diagnosis. In this paper, SVM-RFE is used to the key variable selection in fault diag-nosis, and an accelerated SVM-RFE procedure based on heuristic criterion is proposed. The data from Tennessee East-man process (TEP) simulator is used to evaluate the effectiveness of the key variable selection using accelerated SVM-RFE (A-SVM-RFE). A-SVM-RFE integrates computational rate and algorithm effectiveness into a consistent framework. It not only can correctly identify the key variables, but also has very good computational rate. In comparison with contribution charts combined with principal component aralysis (PCA) and other two SVM-RFE algorithms, A-SVM-RFE performs better. It is more fitting for industrial application.

A feature selection method combined with ridge regression and recursive feature elimination in quantitative analysis of laser induced breakdown spectroscopy

In the spectral analysis of laser-induced breakdown spectroscopy,abundant characteristic spectral lines and severe interference information exist simultaneously in the original spectral data.Here,a feature selection method called recursive feature elimination based on ridge regression(Ridge-RFE)for the original spectral data is recommended to make full use of the valid information of spectra.In the Ridge-RFE method,the absolute value of the ridge regression coefficient was used as a criterion to screen spectral characteristic,the feature with the absolute value of minimum weight in the input subset features was removed by recursive feature elimination(RFE),and the selected features were used as inputs of the partial least squares regression(PLS)model.The Ridge-RFE method based PLS model was used to measure the Fe,Si,Mg,Cu,Zn and Mn for 51 aluminum alloy samples,and the results showed that the root mean square error of prediction decreased greatly compared to the PLS model with full spectrum as input.The overall results demonstrate that the Ridge-RFE method is more efficient to extract the redundant features,make PLS model for better quantitative analysis results and improve model generalization ability.

New recursive algorithm for matrix inversion

To reduce the computational complexity of matrix inversion, which is the majority of processing in many practical applications, two numerically efficient recursive algorithms （called algorithms I and II, respectively） are presented. Algorithm I is used to calculate the inverse of such a matrix, whose leading principal minors are all nonzero. Algorithm II, whereby, the inverse of an arbitrary nonsingular matrix can be evaluated is derived via improving the algorithm I. The implementation, for algorithm II or I, involves matrix-vector multiplications and vector outer products. These operations are computationally fast and highly parallelizable. MATLAB simulations show that both recursive algorithms are valid.

Piecewise linear recursive convolution FDTD method for magnetized plasmas

The piecewise linear recursive convolution （PLRC） finite-different time-domain （FDTD） method greatly improves accuracy over the original recursive convolution （RC） FDTD approach but retains its speed and efficiency advantages. A PLRC-FDTD formulation for magnetized plasma which incorporates both anisotropy and frequency dispersion at the same time is presented, enabled the transient analysis of magnetized plasma media. The technique is illustrated by numerical simulations the reflection and transmission coefficients through a magnetized plasma layer. The results show that the PLRC-FDTD method has significantly improved the accuracy over the original RC method.

Recursive State-space Model Identification of Non-uniformly Sampled Systems Using Singular Value Decomposition

In this paper a recursive state-space model identification method is proposed for non-uniformly sampled systems in industrial applications. Two cases for measuring all states and only output(s) of such a system are considered for identification. In the case of state measurement, an identification algorithm based on the singular value decomposition(SVD) is developed to estimate the model parameter matrices by using the least-squares fitting. In the case of output measurement only, another identification algorithm is given by combining the SVD approach with a hierarchical identification strategy. An example is used to demonstrate the effectiveness of the proposed identification method.

An efficient stock market prediction model using hybrid feature reduction method based on variational autoencoders and recursive feature elimination

In this study,the hourly directions of eight banking stocks in Borsa Istanbul were predicted using linear-based,deep-learning(LSTM)and ensemble learning(Light-GBM)models.These models were trained with four different feature sets and their performances were evaluated in terms of accuracy and F-measure metrics.While the first experiments directly used the own stock features as the model inputs,the second experiments utilized reduced stock features through Variational AutoEncoders(VAE).In the last experiments,in order to grasp the effects of the other banking stocks on individual stock performance,the features belonging to other stocks were also given as inputs to our models.While combining other stock features was done for both own(named as allstock_own)and VAE-reduced(named as allstock_VAE)stock features,the expanded dimensions of the feature sets were reduced by Recursive Feature Elimination.As the highest success rate increased up to 0.685 with allstock_own and LSTM with attention model,the combination of allstock_VAE and LSTM with the attention model obtained an accuracy rate of 0.675.Although the classification results achieved with both feature types was close,allstock_VAE achieved these results using nearly 16.67%less features compared to allstock_own.When all experimental results were examined,it was found out that the models trained with allstock_own and allstock_VAE achieved higher accuracy rates than those using individual stock features.It was also concluded that the results obtained with the VAE-reduced stock features were similar to those obtained by own stock features.

Fast recursive algorithm for two-dimensional Tsallis entropy thresholding method

Recently, a two-dimensional （2-D） Tsallis entropy thresholding method has been proposed as a new method for image segmentation. But the computation complexity of 2-D Tsallis entropy is very large and becomes an obstacle to real time image processing systems. A fast recursive algorithm for 2-D Tsallis entropy thresholding is proposed. The key variables involved in calculating 2-D Tsallis entropy are written in recursive form. Thus, many repeating calculations are avoided and the computation complexity reduces to O（L2） from O（L4）. The effectiveness of the proposed algorithm is illustrated by experimental results.

Recursive weighted least squares estimation algorithm based on minimum model error principle

Kalman filter is commonly used in data filtering and parameters estimation of nonlinear system,such as projectile's trajectory estimation and control.While there is a drawback that the prior error covariance matrix and filter parameters are difficult to be determined,which may result in filtering divergence.As to the problem that the accuracy of state estimation for nonlinear ballistic model strongly depends on its mathematical model,we improve the weighted least squares method(WLSM)with minimum model error principle.Invariant embedding method is adopted to solve the cost function including the model error.With the knowledge of measurement data and measurement error covariance matrix,we use gradient descent algorithm to determine the weighting matrix of model error.The uncertainty and linearization error of model are recursively estimated by the proposed method,thus achieving an online filtering estimation of the observations.Simulation results indicate that the proposed recursive estimation algorithm is insensitive to initial conditions and of good robustness.