A Primal-dual Large-update Interior-point Algorithm for P_*(κ)-LCP Based on a New Class of Kernel Functions

In this paper, we propose a large-update primal-dual interior point algorithm for P_＊（κ）-linear complementarity problem. The method is based on a new class of kernel functions which is neither classical logarithmic function nor self-regular functions. It is determines both search directions and the proximity measure between the iterate and the center path. We show that if a strictly feasible starting point is available, then the new algorithm has O（1 ＋ 2κ）p√n（1/plog n ＋ 1）^2 lognε iteration complexity which becomes O（（1 ＋ 2κ）√nlog n logn/ε）with special choice of the parameter p. It is matches the currently best known iteration bound for P＊（κ）-linear complementarity problem. Some computational results have been provided.

Multi-output Gaussian Process Regression Model with Combined Kernel Function for Polyester Esterification Processes

In polyester fiber industrial processes,the prediction of key performance indicators is vital for product quality.The esterification process is an indispensable step in the polyester polymerization process.It has the characteristics of strong coupling,nonlinearity and complex mechanism.To solve these problems,we put forward a multi-output Gaussian process regression(MGPR)model based on the combined kernel function for the polyester esterification process.Since the seasonal and trend decomposition using loess(STL)can extract the periodic and trend characteristics of time series,a combined kernel function based on the STL and the kernel function analysis is constructed for the MGPR.The effectiveness of the proposed model is verified by the actual polyester esterification process data collected from fiber production.

Exploring Motor Imagery EEG: Enhanced EEG Microstate Analysis with GMD-Driven Density Canopy Method

The analysis of microstates in EEG signals is a crucial technique for understanding the spatiotemporal dynamics of brain electrical activity.Traditional methods such as Atomic Agglomerative Hierarchical Clustering(AAHC),K-means clustering,Principal Component Analysis(PCA),and Independent Component Analysis(ICA)are limited by a fixed number of microstate maps and insufficient capability in cross-task feature extraction.Tackling these limitations,this study introduces a Global Map Dissimilarity(GMD)-driven density canopy K-means clustering algorithm.This innovative approach autonomously determines the optimal number of EEG microstate topographies and employs Gaussian kernel density estimation alongside the GMD index for dynamic modeling of EEG data.Utilizing this advanced algorithm,the study analyzes the Motor Imagery(MI)dataset from the GigaScience database,GigaDB.The findings reveal six distinct microstates during actual right-hand movement and five microstates across other task conditions,with microstate C showing superior performance in all task states.During imagined movement,microstate A was significantly enhanced.Comparison with existing algorithms indicates a significant improvement in clustering performance by the refined method,with an average Calinski-Harabasz Index(CHI)of 35517.29 and a Davis-Bouldin Index(DBI)average of 2.57.Furthermore,an information-theoretical analysis of the microstate sequences suggests that imagined movement exhibits higher complexity and disorder than actual movement.By utilizing the extracted microstate sequence parameters as features,the improved algorithm achieved a classification accuracy of 98.41%in EEG signal categorization for motor imagery.A performance of 78.183%accuracy was achieved in a four-class motor imagery task on the BCI-IV-2a dataset.These results demonstrate the potential of the advanced algorithm in microstate analysis,offering a more effective tool for a deeper understanding of the spatiotemporal features of EEG signals.

Landslide prediction based on improved principal component analysis and mixed kernel function least squares support vector regression model

Landslide probability prediction plays an important role in understanding landslide information in advance and taking preventive measures.Many factors can influence the occurrence of landslides,which is easy to have a curse of dimensionality and thus lead to reduce prediction accuracy.Then the generalization ability of the model will also decline sharply when there are only small samples.To reduce the dimension of calculation and balance the model’s generalization and learning ability,this study proposed a landslide prediction method based on improved principal component analysis(PCA)and mixed kernel function least squares support vector regression(LSSVR)model.First,the traditional PCA was introduced with the idea of linear discrimination,and the dimensions of initial influencing factors were reduced from 8 to 3.The improved PCA can not only weight variables but also extract the original feature.Furthermore,combined with global and local kernel function,the mixed kernel function LSSVR model was framed to improve the generalization ability.Whale optimization algorithm(WOA)was used to optimize the parameters.Moreover,Root Mean Square Error(RMSE),the sum of squared errors(SSE),Mean Absolute Error(MAE),Mean Absolute Precentage Error(MAPE),and reliability were employed to verify the performance of the model.Compared with radial basis function(RBF)LSSVR model,Elman neural network model,and fuzzy decision model,the proposed method has a smaller deviation.Finally,the landslide warning level obtained from the landslide probability can also provide references for relevant decision-making departments in emergency response.

Zeroes of the Bergman Kernels on Some New Hartogs Domains

We obtain the Bergman kernel for a new type of Hartogs domain.The corresponding LU Qi-Keng's problem is considered.

An iterative modified kernel based on training data

To improve performance of a support vector regression, a new method for a modified kernel function is proposed. In this method, information of all samples is included in the kernel function with conformal mapping. Thus the kernel function is data-dependent. With a random initial parameter, the kernel function is modified repeatedly until a satisfactory result is achieved. Compared with the conventional model, the improved approach does not need to select parameters of the kernel function. Sim- ulation is carried out for the one-dimension continuous function and a case of strong earthquakes. The results show that the improved approach has better learning ability and forecasting precision than the traditional model. With the increase of the iteration number, the figure of merit decreases and converges. The speed of convergence depends on the parameters used in the algorithm.

RECURSIVE REPRODUCING KERNELS HILBERT SPACES USING THE THEORY OF POWER KERNELS

The main objective of this work is to decompose orthogonally the reproducing kernels Hilbert space using any conditionally positive definite kernels into smaller ones by introducing the theory of power kernels, and to show how to do this decomposition recur- sively. It may be used to split large interpolation problems into smaller ones with different kernels which are related to the original kernels. To reach this objective, we will reconstruct the reproducing kernels Hilbert space for the normalized and the extended kernels and give the recursive algorithm of this decomposition.

Improved Logistic Regression Algorithm Based on Kernel Density Estimation for Multi-Classification with Non-Equilibrium Samples

Logistic regression is often used to solve linear binary classification problems such as machine vision,speech recognition,and handwriting recognition.However,it usually fails to solve certain nonlinear multi-classification problem,such as problem with non-equilibrium samples.Many scholars have proposed some methods,such as neural network,least square support vector machine,AdaBoost meta-algorithm,etc.These methods essentially belong to machine learning categories.In this work,based on the probability theory and statistical principle,we propose an improved logistic regression algorithm based on kernel density estimation for solving nonlinear multi-classification.We have compared our approach with other methods using non-equilibrium samples,the results show that our approach guarantees sample integrity and achieves superior classification.

APPLICATION OF HOLOMORPHIC INVARIANTS IN REPRODUCING KERNEL

We use holomorphic invariants to calculate the Bergman kernel for generalized quasi-homogeneous Reinhardt-Hartogs domains. In addition, we present a complete orthonormal basis for the Bergman space on bounded Reinhardt-Hartogs domains.

Interior-point algorithm based on general kernel function for monotone linear complementarity problem

A polynomial interior-point algorithm is presented for monotone linear complementarity problem （MLCP） based on a class of kernel functions with the general barrier term, which are called general kernel functions. Under the mild conditions for the barrier term, the complexity bound of algorithm in terms of such kernel function and its derivatives is obtained. The approach is actually an extension of the existing work which only used the specific kernel functions for the MLCP.

Application of Particle Swarm Optimization to Fault Condition Recognition Based on Kernel Principal Component Analysis

Panicle swarm optimization （PSO） is an optimization algorithm based on the swarm intelligent principle. In this paper the modified PSO is applied to a kernel principal component analysis （ KPCA ） for an optimal kernel function parameter. We first comprehensively considered within-class scatter and between-class scatter of the sample features. Then, the fitness function of an optimized kernel function parameter is constructed, and the particle swarm optimization algorithm with adaptive acceleration （CPSO） is applied to optimizing it. It is used for gearbox condi- tion recognition, and the result is compared with the recognized results based on principal component analysis （PCA）. The results show that KPCA optimized by CPSO can effectively recognize fault conditions of the gearbox by reducing bind set-up of the kernel function parameter, and its results of fault recognition outperform those of PCA. We draw the conclusion that KPCA based on CPSO has an advantage in nonlinear feature extraction of mechanical failure, and is helpful for fault condition recognition of complicated machines.

AN ASYMPTOTIC EXPANSION FORMULA OF KERNEL FUNCTION FOR QUASI FOURIER-LEGENDRE SERIES AND ITS APPLICATION

Is this paper we shall give cm asymptotic expansion formula of the kernel functim for the Quasi Faurier-Legendre series on an ellipse, whose error is 0(1/n2) and then applying it we shall sham an analogue of an exact result in trigonometric series.

ASYMPTOTIC NORMALITY OF KERNEL ESTIMATES OF A DENSITY FUNCTION UNDER ASSOCIATION DEPENDENCE

Let {Xn, n≥1} be a strictly stationary sequence of random variables, which are either associated or negatively associated, f(.) be their common density. In this paper, the author shows a central limit theorem for a kernel estimate of f(.) under certain regular conditions.

Quantifyingα-diversity as a continuous function of location——a case study of a temperate forest

α-diversity describes species diversity at local scales.The Simpson’s and Shannon-Wiener indices are widely used to characterizeα-diversity based on species abundances within a fixed study site(e.g.,a quadrat or plot).Although such indices provide overall diversity estimates that can be analyzed,their values are not spatially continuous nor applicable in theory to any point within the study region,and thus they cannot be treated as spatial covariates for analyses of other variables.Herein,we extended the Simpson’s and Shannon-Wiener indices to create point estimates ofα-diversity for any location based on spatially explicit species occurrences within different bandwidths(i.e.,radii,with the location of interest as the center).For an arbitrary point in the study region,species occurrences within the circle plotting the bandwidth were weighted according to their distance from the center using a tri-cube kernel function,with occurrences closer to the center having greater weight than more distant ones.These novel kernel-basedα-diversity indices were tested using a tree dataset from a 400 m×400 m study region comprising a 200 m×200 m core region surrounded by a 100-m width buffer zone.Our newly extendedα-diversity indices did not disagree qualitatively with the traditional indices,and the former were slightly lower than the latter by<2%at medium and large band widths.The present work demonstrates the feasibility of using kernel-basedα-diversity indices to estimate diversity at any location in the study region and allows them to be used as quantifiable spatial covariates or predictors for other dependent variables of interest in future ecological studies.Spatially continuousα-diversity indices are useful to compare and monitor species trends in space and time,which is valuable for conservation practitioners.

Research on Adaptive TSSA-HKRVM Model for Regression Prediction of Crane Load Spectrum

For the randomness of crane working load leading to the decrease of load spectrum prediction accuracy with time,an adaptive TSSA-HKRVM model for crane load spectrum regression prediction is proposed.The heterogeneous kernel relevance vector machine model(HKRVM)with comprehensive expression ability is established using the complementary advantages of various kernel functions.The combination strategy consisting of refraction reverse learning,golden sine,and Cauchy mutation+logistic chaotic perturbation is introduced to form a multi-strategy improved sparrow algorithm(TSSA),thus optimizing the relevant parameters of HKRVM.The adaptive updatingmechanismof the heterogeneous kernel RVMmodel under themulti-strategy improved sparrow algorithm(TSSA-HKMRVM)is defined by the sliding window design theory.Based on the sample data of the measured load spectrum,the trained adaptive TSSA-HKRVMmodel is employed to complete the prediction of the crane equivalent load spectrum.Applying this method toQD20/10 t×43m×12mgeneral bridge crane,the results show that:compared with other prediction models,although the complexity of the adaptive TSSA-HKRVMmodel is relatively high,the prediction accuracy of the load spectrum under long periods has been effectively improved,and the completeness of the load information during thewhole life cycle is relatively higher,with better applicability.

A Full-Newton Step Feasible Interior-Point Algorithm for the Special Weighted Linear Complementarity Problems Based on a Kernel Function

In this paper,a new full-Newton step primal-dual interior-point algorithm for solving the special weighted linear complementarity problem is designed and analyzed.The algorithm employs a kernel function with a linear growth term to derive the search direction,and by introducing new technical results and selecting suitable parameters,we prove that the iteration bound of the algorithm is as good as best-known polynomial complexity of interior-point methods.Furthermore,numerical results illustrate the efficiency of the proposed method.

An improved form of smoothed particle hydrodynamics method for crack propagation simulation applied in rock mechanics

The simulation of crack propagation processes in rock engineering has been not only a research hot spot among scholars but also a challenge.Based on this background,a new numerical method named improved kernel of smoothed particle hydrodynamics(IKSPH)has been put forward.By improving the kernel function in the traditional smoothed particle hydrodynamics(SPH)method,the brittle fracture characteristics of the base particles are realized.The particle domain searching method(PDSM)has also been put forward to generate the arbitrary complex fissure networks.Three numerical examples are analyzed to validate the efficiency of IKSPH and PDSM,which can correctly reveal the morphology of wing crack and the laws of crack coalescence compared with previous experimental and numerical studies.Finally,a rock slope model with complex joints is numerically simulated and the progressive failure processes are exhibited,which indicates that the IKSPH method can be well applied to rock mechanics engineering.The research results showed that IKSPH method reduces the programming difficulties and avoids the traditional grid distortion,which can provide some references for the application of IKSPH to rock mechanics engineering and the understanding of rock fracture mechanisms.

Temperature prediction control based on least squares support vector machines

A prediction control algorithm is presented based on least squares support vector machines (LS-SVM) model for a class of complex systems with strong nonlinearity. The nonlinear off-line model of the controlled plant is built by LS-SVM with radial basis function (RBF) kernel. In the process of system running, the off-line model is linearized at each sampling instant, and the generalized prediction control (GPC) algorithm is employed to implement the prediction control for the controlled plant. The obtained algorithm is applied to a boiler temperature control system with complicated nonlinearity and large time delay. The results of the experiment verify the effectiveness and merit of the algorithm.

Study on the detection of abnormal sounding data based on LS-SVM

A new method of detecting abnormal sounding data based on LS-SVM is presented.The theorem proves that the trend surface filter is the especial result of LS-SVM.In order to depict the relationship of trend surface filter and LS-SVM,a contrast is given.The example shows that abnormal sounding data could be detected effectively by LS-SVM when the training samples and kernel function are reasonable.

A Study of the Stability Properties in Simulation of Wave Propagation with SPH Method

When ordinary Smoothed Particle Hydrodynamics （SPH） method is used to simulate wave propagation in a wave tank, it is usually observed that the wave height decays and the wave length elongates along the direction of wave propagation. Accompanied with this phenomenon, the pressure under water decays either and shows a big oscillation simultaneously. The reason is the natural potential tensile instability of modeling water motion with ordinary SPH which is caused by particle negative stress in the computation. I＇o deal with the problems, a new sextic kernel function is proposed to reduce this instability. An appropriate smooth length is given and its computation criterion is also suggested. At the same time, a new kind dynamic boundary condition is introduced. Based on these improvements, the new SPH method named stability improved SPH （SISPH） can simulate the wave propagation well. Both the water surface and pressure can be well expressed and the oscillation of pressure is nearly eliminated. Compared with other improved methods, SISPH can truly reveal the physical reality without bringing some new problems in a simple way.