Method of multi-level recursive and application to nonlinear dynamic deformation forecasting

The time-dependence bilinear mixed-regression deformation model and time-dependence bilinear dynamic system deformation model are established for deformation observation series. According to the multi- level recursive method, the time-dependence parameters are first traced and predicted, and then the dynamic system states. Due to the method considering time-dependence of deformation and having stronger adaptability to time-dependence system, it can improve forecast’s precision. It is very effective for data processing of nonlinear dynamic deformation monitoring to make multi-step forecasting.

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.

Scheme Based on Multi-Level Patch Attention and Lesion Localization for Diabetic Retinopathy Grading

Early screening of diabetes retinopathy(DR)plays an important role in preventing irreversible blindness.Existing research has failed to fully explore effective DR lesion information in fundus maps.Besides,traditional attention schemes have not considered the impact of lesion type differences on grading,resulting in unreasonable extraction of important lesion features.Therefore,this paper proposes a DR diagnosis scheme that integrates a multi-level patch attention generator(MPAG)and a lesion localization module(LLM).Firstly,MPAGis used to predict patches of different sizes and generate a weighted attention map based on the prediction score and the types of lesions contained in the patches,fully considering the impact of lesion type differences on grading,solving the problem that the attention maps of lesions cannot be further refined and then adapted to the final DR diagnosis task.Secondly,the LLM generates a global attention map based on localization.Finally,the weighted attention map and global attention map are weighted with the fundus map to fully explore effective DR lesion information and increase the attention of the classification network to lesion details.This paper demonstrates the effectiveness of the proposed method through extensive experiments on the public DDR dataset,obtaining an accuracy of 0.8064.

Deep neural network based on multi-level wavelet and attention for structured illumination microscopy

Structured illumination microscopy(SIM)is a popular and powerful super-resolution(SR)technique in biomedical research.However,the conventional reconstruction algorithm for SIM heavily relies on the accurate prior knowledge of illumination patterns and signal-to-noise ratio(SNR)of raw images.To obtain high-quality SR images,several raw images need to be captured under high fluorescence level,which further restricts SIM’s temporal resolution and its applications.Deep learning(DL)is a data-driven technology that has been used to expand the limits of optical microscopy.In this study,we propose a deep neural network based on multi-level wavelet and attention mechanism(MWAM)for SIM.Our results show that the MWAM network can extract high-frequency information contained in SIM raw images and accurately integrate it into the output image,resulting in superior SR images compared to those generated using wide-field images as input data.We also demonstrate that the number of SIM raw images can be reduced to three,with one image in each illumination orientation,to achieve the optimal tradeoff between temporal and spatial resolution.Furthermore,our MWAM network exhibits superior reconstruction ability on low-SNR images compared to conventional SIM algorithms.We have also analyzed the adaptability of this network on other biological samples and successfully applied the pretrained model to other SIM systems.

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.

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.

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.

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 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.

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.

Research on SINS Error Recursive Model of Ballistic Missile

The strap-down inertial navigation system (SINS) error of ballistic missile is generated by the mutual influence of gyroscope and accelerometer, and the recursive model is completely different from that of gimbaled INS. In the paper, a discrete error recursive model was obtained by studying the applied SINS error model of ballistic missile, and the discrete Kalman filtering simulation based on the model was carried out. The simulated results show that the model can depict the SINS error exactly and provide the advantages for research on integrated guidance and improved hit accuracy.

RECURSIVE FORMULA FOR CALCULATING THE CHROMATIC POLYNOMIAL OF A GRAPH BY VERTEX DELETION

A new recursive vertex-deleting formula for the computation of the chromatic polynomial of a graph is obtained in this paper. This algorithm is not only a good tool for further studying chromatic polynomials but also the fastest among all the algorithms for the computation of chromatic polynomials.

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.

Minimal cut-based recursive decomposition algorithm for seismic reliability evaluation of lifeline networks

In this paper, a new probabilistic analytical approach, the minimal cut-based recursive decomposition algorithm （MCRDA）, is presented to evaluate the seismic reliability of large-scale lifeline systems. Based on the minimal cut searching algorithm, the approach calculates the disjoint minimal cuts one by one using the basic procedure of the recursive decomposition method. At the same time, the process obtains the disjoint minimal paths of the system. In order to improve the computation efficiency, probabilistic inequality is used to calculate a solution that satisfies the prescribed error bound. A series of case studies show that MCRDA converges rapidly when the edges of the systems have low reliabilities. Therefore, the approach can be used to evaluate large-scale lifeline systems subjected to strong seismic wave excitation.

RECURSIVE UTILITY,PRODUCTIVE GOVERNMENT EXPENDITURE AND OPTIMAL FISCAL POLICY

This paper employs a stochastic endogenous growth model extended to the case of a recursive utility function which can disentangle intertemporal substitution from risk aversion to analyze productive government expenditure and optimal fiscal policy, particularly stresses the importance of factor income. First, the explicit solutions of the central planner＇s stochastic optimization problem are derived, the growth maximizing and welfare-maximizing government expenditure policies are obtained and their standing in conflict or coincidence depends upon intertemporal substitution. Second, the explicit solutions of the representative individual＇s stochastic optimization problem which permits to tax on capital income and labor income separately are derived ,and it is found that the effect of risk on growth crucially depends on the degree of risk aversion,the intertemporal elasticity of substitution and the capital income share. Finally, a flexible optimal tax policy which can be internally adjusted to a certain extent is derived, and it is found that the distribution of factor income plays an important role in designing the optimal tax policy.

RECURSIVE STRUCTURE AND QUASI-RECURSIVE STRUCTURE OF ADAPTIVE VOLTERRA FILTER AND THEIR ALGORITHMS AND APPLICATIONS

The recursive structure and quasi-recursive structure of Adaptive Volterra Fil-ter(AVF) are put forward, their algorithms are given, and their characteristics and applications are discussed. The introduction of recursive structure can remarkably reduce the parameters and computational cost of AVF.