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In the study of stochastic systems, the committor function describes the probability that a system starting from an initial configuration x will reach a set B before a set A. This paper introduces an efficient and interpretable algorithm for approximating the committor, called the "fast committor machine" (FCM). The FCM uses simulated trajectory data to build a kernel-based model of the committor. The kernel function is constructed to emphasize low-dimensional subspaces that optimally describe the A to B transitions. The coefficients in the kernel model are determined using randomized linear algebra, leading to a runtime that scales linearly with the number of data points. In numerical experiments involving a triple-well potential and alanine dipeptide, the FCM yields higher accuracy and trains more quickly than a neural network with the same number of parameters. The FCM is also more interpretable than the neural net. [ABSTRACT FROM AUTHOR]

This study uses the triple-phase lag model to investigate how higher-order fractional order and memory-dependent derivatives affect reflection at the free surface of an orthotropic piezo-thermoelastic medium. The performance of both kinds of derivatives is studied using the normal mode analysis technique. Four different types of coupled reflected plane waves are identified and explore the impact of various parameters, fractional order parameter, kernel function, the higher-order time differential fractional, and memory-dependent heat conduction parameters on energy distribution with respect to the angle of incidence. The results are presented graphically, providing numerical data for reflected waves, amplitude, and energy ratios. [ABSTRACT FROM AUTHOR]

Modeling the network topology of the human brain within the mesoscale has become an increasing focus within the neuroscientific community due to its variation across diverse cognitive processes, in the presence of neuropsychiatric disease or injury, and over the lifespan. Much research has been done on the creation of algorithms to detect these mesoscopic structures, called communities or modules, but less has been done to conduct inference on these structures. The literature on analysis of these community detection algorithms has focused on comparing them within the same subject. These approaches, however, either do not accommodate a more general association between community structure and an outcome or cannot accommodate additional covariates that may confound the association of interest. We propose a semiparametric kernel machine regression model for either a continuous or binary outcome, where covariate effects are modeled parametrically and brain connectivity measures are measured nonparametrically. By incorporating notions of similarity between network community structures into a kernel distance function, the high-dimensional feature space of brain networks, defined on input pairs, can be generalized to non-linear spaces, allowing for a wider class of distance-based algorithms. We evaluate our proposed methodology on both simulated and real datasets. Author summary: Parcellating the brain into clusters, which can be characterized as a way to describe the balance between dense relationships among areas highly engaged in the same processing tasks as well as sparser relationships between regions with different processing assignments, has been an area of recent focus within the neuroscientific community. While many algorithms exist to discover and characterize these clusters, there is a paucity of literature seeking to conduct inference on these parcellations between subjects. We have proposed a semiparametric kernel machine regression framework that can accommodate either a binary or continuous outcome, where brain connectivity measures are modeled nonparametrically and any additional covariates of interest (e.g., age, sex, etc.) are modeled parametrically. Evaluating our proposed methodology on both simulated and real datasets, we provide evidence of the robustness of this method within a single layer of clusters, thus showing the potential utility in the rapidly-changing field of network neuroscience. [ABSTRACT FROM AUTHOR]

Summary How carbon (sucrose) and nitrogen (amino acid) accumulation is coordinatively controlled in cereal grains remains largely enigmatic. We found that overexpression of the strigolactone (SL) biosynthesis gene CAROTENOID CLEAVAGE DIOXYGENASE 8 (CCD8) resulted in greater ear diameter and enhanced sucrose and amino acid accumulation in maize kernels. Loss of ZmCCD8 function reduced kernel growth with lower sugar and amino acid concentrations. Transcriptomic analysis showed down‐regulation of the transcription factors ZmMYB42 and ZmMYB63 in ZmCCD8 overexpression alleles and up‐regulation in zmccd8 null alleles. Importantly, ZmMYB42 and ZmMYB63 were negatively regulated by the SL signalling component UNBRANCHED 3, and repressed expression of the sucrose transporters ZmSWEET10 and ZmSWEET13c and the lysine/histidine transporter ZmLHT14. Consequently, null alleles of ZmMYB42 or ZmMYB63 promoted accumulation of soluble sugars and free amino acids in maize kernels, whereas ZmLHT14 overexpression enhanced amino acid accumulation in kernels. Moreover, overexpression of the SL receptor DWARF 14B resulted in more sucrose and amino acid accumulation in kernels, down‐regulation of ZmMYB42 and ZmMYB63 expression, and up‐regulation of ZmSWEETs and ZmLHT14 transcription. Together, we uncover a distinct SL signalling pathway that regulates sucrose and amino acid accumulation in kernels. Significant association of two SNPs in the 5′ upstream region of ZmCCD8 with ear and cob diameter implicates its potential in breeding toward higher yield and nitrogen efficiency. [ABSTRACT FROM AUTHOR]

In this work, the concept of quasi‐type Kernel polynomials with respect to a moment functional is introduced. Difference equation satisfied by these polynomials along with the criterion for orthogonality conditions are discussed. The process of recovering orthogonality for the linear combination of a quasi‐type kernel polynomial with another orthogonal polynomial, which is identified by involving linear spectral transformation, is provided. This process involves an expression of ratio of iterated kernel polynomials. This leads to considering the limiting case of ratio of kernel polynomials involving continued fractions. Special cases of such ratios in terms of certain continued fractions are exhibited. Moreover, examples are discussed for obtaining the orthogonality of quasi‐type kernel polynomials of order 1. [ABSTRACT FROM AUTHOR]

To explore the mechanical properties and fracture modes of basalt fiber-reinforced concrete, single-doped and hybrid-doped basalt fiber-reinforced concrete was prepared, and uniaxial failure tests under different basalt fiber-reinforced concrete contents were carried out. At the same time, the smooth kernel function in the traditional SPH method was improved, and the basalt fiber random generation algorithm was embedded in the SPH program to realize the simulation of the progressive failure of basalt fiber-reinforced concrete. The results show that under the circumstance with no basalt fiber, the specimen final failure mode is damage on the upper and lower surface, as well as the side edge, while the interior of the specimen center is basically intact, indicating that there is an obvious stress concentration phenomenon on the upper and lower surface when the specimen is compressed. Under the circumstance with basalt fiber, longitudinal cracks begin to appear inside the specimen. With the increase in the content, the crack location gradually develops from the edge to the middle, and the crack number gradually increases. This indicates that appropriately increasing the fiber content in concrete may improve the stress state of concrete, change the eccentric compression to axial compression, and indirectly increase the compressive strength of concrete. The numerical simulation results are consistent with the test results, verifying the rationality of the numerical simulation algorithm. For the concrete model without the basalt fiber, shear cracks are generated around the model. For the concrete model with basalt fiber, in addition to shear cracks, the tensile cracks generated at the basalt fiber inside the model eventually lead to the splitting failure of the model. The strength of concrete samples with basalt content of 0.1%, 0.2%, and 0.3% is increased by 1.69%, 5.10%, and 4.31%, respectively, compared to the concrete sample without basalt fiber. It can be seen that with the increase in the content of single-doped basalt fiber, the concrete strength is improved to a certain extent, but the improvement degree is not high; For hybrid-doped basalt fiber-reinforced concrete, the strength of concrete samples with basalt content of 0.1%, 0.2%, and 0.3% is increased by 14.51%, 15.02%, and 30.31%, respectively, compared to the concrete sample without basalt fiber. Therefore, compared with the single-doped basalt fiber process, hybrid doping is easier to improve the strength of concrete. [ABSTRACT FROM AUTHOR]

Purpose: To find the quasi-static thermoelastic stress and displacement, the proposed model looks at how the microstructures interact with each other and how the temperature changes inside a rod. It uses the fractional-order dual-phase-lag (FODPL) theory to derive analytical solutions for one-dimensional problems in nonsimple media within the MDD framework. The dimensionless equations are used to analyze a finite rod experiencing the heat sources continuously distributed over a finite portion of the rod which vary with time according to the ramp-type function with other sectional heat supplies kept at zero temperature. The study introduces a technique using integral transforms for exact solutions in the Laplace transform domain for different kernel functions. Design/methodology/approach: A novel mathematical model incorporating dual-phase-lags, two-temperatures and Riesz space-fractional operators via memory-dependent derivatives has been established to analyze the effects of thermal stress and displacement in a finite rod. The model takes into account the continuous distribution of heat sources over a finite portion of the rod and their time variation according to the ramp-type function. It incorporates the finite Riesz fractional derivative in two-temperature thermoelasticity with dual-phase-lags via memory effect, and its solution is obtained using Laplace transform with respect to time and sine-Fourier transform with respect to spatial coordinates defined over finite domains. Findings: In memory-dependent derivatives, thermal field variables are strongly influenced by the phase-lag heat flux and temperature gradient. The non-Fourier effects of memory-dependent derivatives substantially impact the distribution and history of the thermal field response, and energy dissipation may result in a reduction in temperature without heat transfer. The temperature, displacement and stress profile exhibit a reduced magnitude with the MDD effect compared to when the memory effect is absent (without MDD). To advance future research, a new categorization system for materials based on memory-dependent derivative parameters, in accordance with the principles of two-temperature thermoelasticity theory, must be constructed. Research limitations/implications: The one-dimensional assumption introduces limitations. For example, local heating of a one-dimensional plate will not extend radially, and heating one side will not heat the surrounding sides. Furthermore, while estimating heat transfer, object shape limits may apply. Originality/value: This paper aims to revise the classical Fourier law of heat conduction and develop analytical solutions for one-dimensional problems using fractional-order dual-phase-lag (FODPL) theory in nonsimple media in the context of MDD. [ABSTRACT FROM AUTHOR]

We prove two compactness results for function spaces with finite Dirichlet energy of half‐space nonlocal gradients. In each of these results, we provide sufficient conditions on a sequence of kernel functions that guarantee the asymptotic compact embedding of the associated nonlocal function spaces into the class of square‐integrable functions. Moreover, we will demonstrate that the sequence of nonlocal function spaces converges in an appropriate sense to a limiting function space. As an application, we prove uniform Poincaré‐type inequalities for sequence of half‐space gradient operators. We also apply the compactness result to demonstrate the convergence of appropriately parameterized nonlocal heterogeneous anisotropic diffusion problems. We will construct asymptotically compatible schemes for these type of problems. Another application concerns the convergence and robust discretization of a nonlocal optimal control problem. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the nonlocal‐in‐time Allen‐Cahn equation (NiTACE), which incorporates a nonlocal operator in time with a finite nonlocal memory. Our objective is to examine the well‐posedness of the NiTACE by establishing the maximal Lp$$ {L}^p $$ regularity for the nonlocal‐in‐time parabolic equations with fractional power kernels. Furthermore, we derive a uniform energy bound by leveraging the positive definite property of kernel functions. We also develop an energy‐stable time stepping scheme specifically designed for the NiTACE. Additionally, we analyze the discrete maximum principle and energy dissipation law, which hold significant importance for phase field models. To ensure convergence, we verify the asymptotic compatibility of the proposed stable scheme. Lastly, we provide several numerical examples to illustrate the accuracy and effectiveness of our method. [ABSTRACT FROM AUTHOR]

Human action recognition is one of the most challenging tasks in computer vision due to background noise interference and video frame redundancy. Therefore, we propose a two-stream Convolutional Neural Network based on Spatial-Temporal Multiscale Feature Optimization (ST-MFO). Specifically, multiscale features generated by a pyramid pooling network are combined with improved coordinate attention, which results in richer feature representation and reduces background noise interference. Meanwhile, we introduce density peak clustering based on a nonlinear kernel function, which can extract more representative key frames. To improve classification efficiency, we also assign varying degrees of attention to key frames through temporal attention. In addition, we propose an attention-based spatial-temporal information interaction module that optimizes temporal and spatial features with complementarity between temporal and spatial information. Experimental results on four benchmark video datasets show that ST-MFO achieves comparable or better performance than state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Existing nonlocal diffusion models are mainly classified into two categories: bond-based models, which involve a single-fold integral and usually simulate isotropic diffusion, and state-based models, which contain a double-fold integral and can additionally prototype anisotropic diffusion. While bond-based models exhibit more computational efficiency, they sometimes could be limited in modeling capabilities. In this paper, we successfully develop a novel bond-based nonlocal model for the diffusion process with matrix-valued coefficients in non-divergence form. Our approach incorporates the coefficients into a covariance matrix and employs the multivariate Gaussian function with truncation to define the kernel function, and subsequently model the nonlocal diffusion through the bond-based formulation. We establish the well-posedness of the proposed model along with deriving some of its properties on maximum principle and mass conservation. Furthermore, an efficient linear collocation scheme is designed for numerical solution of our model. Comprehensive experiments in two and three dimensions are conducted to showcase application of the proposed nonlocal model to both isotropic and anisotropic diffusion problems, and to demonstrate high-order accuracy and conditional δ -convergence of the proposed collocation scheme. [ABSTRACT FROM AUTHOR]

This paper deals with the effect of fractional order on the fractional Euler-Bernoulli beams model. This model is based on the elastic curve that can be approximated using tangent lines and the osculating circle. We introduce a general form of the fractional Green's function for the highest-order term 1 < α ≤ 2 , which gives a unique solution for the geometrical fractional bending beams with an inhomogeneous fractional differential equation. The analytical closed-form responses were obtained by inverse problem technique and integration over Green's function kernel. The theory and properties of fractional Green's function method are described by generalizing classical theory to the initial and two-point fractional boundary value problems. Static analysis of the numerical examples, such as determinate and indeterminate beams with typical loads and beam property boundary conditions, are presented and discussed. The results were verified using the direct integration method. The fractional conventional ratio indicates the beam's deformation deviation from its classical state. The analysis results reveal that changing the fractional parameter significantly impacts the deflection behavior of flexural beams due to the beam's characteristics and the fractional order. The behavior of the fractional beam is identical to the classical state when the fractional parameter is an integer number. [ABSTRACT FROM AUTHOR]

The effective inclusion of a priori knowledge when embedding known data in physics‐based models of dynamical systems can ensure that the reconstructed model respects physical principles, while simultaneously improving the accuracy of the solution in the previously unseen regions of state space. This paper presents a physics‐constrained data‐driven discrepancy modeling method that variationally embeds known data in the modeling framework. The hierarchical structure of the method yields fine scale variational equations that facilitate the derivation of residuals which are comprised of the first‐principles theory and sensor‐based data from the dynamical system. The embedding of the sensor data via residual terms leads to discrepancy‐informed closure models that yield a method which is driven not only by boundary and initial conditions, but also by measurements that are taken at only a few observation points in the target system. Specifically, the data‐embedding term serves as residual‐based least‐squares loss function, thus retaining variational consistency. Another important relation arises from the interpretation of the stabilization tensor as a kernel function, thereby incorporating a priori knowledge of the problem and adding computational intelligence to the modeling framework. Numerical test cases show that when known data is taken into account, the data driven variational (DDV) method can correctly predict the system response in the presence of several types of discrepancies. Specifically, the damped solution and correct energy time histories are recovered by including known data in the undamped situation. Morlet wavelet analyses reveal that the surrogate problem with embedded data recovers the fundamental frequency band of the target system. The enhanced stability and accuracy of the DDV method is manifested via reconstructed displacement and velocity fields that yield time histories of strain and kinetic energies which match the target systems. The proposed DDV method also serves as a procedure for restoring eigenvalues and eigenvectors of a deficient dynamical system when known data is taken into account, as shown in the numerical test cases presented here. [ABSTRACT FROM AUTHOR]

Twin Support Vector Machine (TSVM) transforms a single large quadratic programming problem (QPP) in support vector machine (SVM) into two smaller QPPs by finding two non-parallel classification hyperplanes, so that its computational time is reduced to a quarter of what the traditional SVM takes. However, TSVM ignores the data distribution of class, which makes TSVM sensitive to noise. In this paper, a fuzzy twin support vector machine based on centered kernel alignment (FTSVM-CKA) is proposed to solve the problem that TSVM is sensitive to noise. Firstly, a feature-weighted kernel function is constructed by using the information gain, and it is applied to the calculation of the centered kernel alignment (CKA). This assigns greater weight to strongly correlated features, emphasizing their classification importance over weakly correlated features. Secondly, the CKA method is utilized to derive a heuristic function for calculating the dependency between samples and their corresponding labels, which assigns fuzzy membership to different samples. Based on this, a fuzzy membership assignment strategy is proposed that can effectively address the sensitivity of TSVM to noise. Thirdly, this strategy is combined with TSVM to propose the FTSVM-CKA model. Moreover, this study employs a coordinate descent strategy with shrinking by active set to tackle the computational complexity arising from high-dimensional inputs. This can effectively accelerate the training speed of the model while ensuring classification performance. In order to evaluate the performance of FTSVM-CKA, this study conducts experiments designed on artificial and UCI datasets. The results demonstrate that FTSVM-CKA can efficiently and quickly solve binary classification problems with noise. [ABSTRACT FROM AUTHOR]

In the context of the triple-phase lag model, comparison studies are conducted between the memory-dependent derivative and fractional order derivative on the propagation of plane waves in a half-space of initially stressed transversely isotropic piezothermoelastic material. The coupled governing equations of the considered model involving relaxation time, time delay, fractional order parameter, and kernel function are selected according to specific problems and solved using the normal mode analysis technique and obtaining the analytical expression. The non-dimensional temperature, displacement, electrical displacements, and stresses at different values of the fractional order parameter and time delay factor are obtained graphically. [ABSTRACT FROM AUTHOR]

Remaining useful life (RUL) is a key indicator for assessing the health status of lithium (Li)-ion batteries, and realizing accurate and reliable RUL prediction is crucial for the proper operation of battery systems. As high-capacity Li batteries have more complex chemical properties, most of the current RUL prediction methods rely mainly on a priori knowledge to make judgments. As a result, prediction accuracy is not high. In this study, we developed a health indicator-capacity (HI-C) dual Gaussian process regression (GPR) model based on incremental capacity analysis (ICA) and optimized its kernel function to achieve accurate RUL prediction for 280 Ah high-capacity Li batteries. Validation against the United States National Aeronautics and Space Administration's four battery test datasets showed that the use of the HI-C dual GPR model resulted in a mean absolute percentage error and root mean square error of less than 0.02 and 0.04, respectively, for the four battery-rated capacity predictions. Additionally, this model achieved an absolute error of less than five battery failure turns. Compared with a single model, the HI-C dual GPR model not only had high accuracy but also solved the problem that the HI was not measurable in the actual battery operation, which made it more suitable for RUL prediction of Li batteries. [ABSTRACT FROM AUTHOR]

River sediment load estimation poses a critical challenge for water engineers due to its complex and nonlinear hydrological processes. This study assessed the amount of suspended sediment at the Bagh-e-Kalayeh hydrometric station on the Alamut River in the Qazvin province of Iran using two hydrological and meteorological variables, including discharge and rainfall, by considering three scenarios (discharge, discharge + monthly rainfall, and discharge + monthly rainfall + daily rainfall). For modeling, kernel-based data-driven methods, including Gaussian process regression (GPR) and support vector regression (SVR), and tree models, including the M5 tree, random forest (RF), random tree (RT), extra trees, reduced error pruning tree (REPT), and multi-search methods, were used. The results showed that the best performance was achieved by the SVR, with r = 0.948, Wilmot index = 0.965, and RMSE = 0.011 in the first scenario (only discharge). Discharge had the most significant impact on sediment estimation compared to rainfall. It was determined that the suspended sediment load in the Alamut River can be successfully estimated by the SVR method, where only the discharge was used as the input parameter. Additionally, the results indicated that given its characteristics and inherent features, the multi-search method can be used as a complementary approach in sediment modeling, especially in situations where the data volume is not extensive. [ABSTRACT FROM AUTHOR]

Early screening of breast cancer through image recognition technology can significantly increase the survival rate of patients. Therefore, breast cancer pathological image is of great significance for medical diagnosis and clinical research. In recent years, numerous deep learning models have been applied to breast cancer image classification, with deep CNN being a typical representative. Due to the use of multi-depth small convolutional kernels in mainstream CNN architectures such as VGG and Inception, the obtained image features often have high dimensionality. Although high dimensionality can bring more fine-grained features, it also increases the computational complexity of subsequent classifiers and may even lead to the curse of dimensionality and overfitting. To address these issues, a novel embedded kernel CNN principal component feature fusion (CNN-PCFF) algorithm is proposed. The constructed kernel function is embedded in the principal component analysis to form the multi-kernel principal component. Multi-kernel principal component analysis is used to fuse the high dimensional features obtained from the convolution base into some representative comprehensive variables, which are called kernel principal components, so as to achieve the purpose of dimensionality reduction. Any type of classifier can be added based on multi-kernel principal components. Through experimental analysis on two public breast cancer image datasets, the results show that the proposed algorithm can improve the performance of the current mainstream CNN architecture and subsequent classifiers. Therefore, the proposed algorithm in this paper is an effective tool for the classification of breast cancer pathological images. [ABSTRACT FROM AUTHOR]

Support vector regression (SVR) is a powerful kernel-based regression prediction algorithm that performs excellently in various application scenarios. However, for real-world data, the general SVR often fails to achieve good predictive performance due to its inability to assess feature contribution accurately. Feature weighting is a suitable solution to address this issue, applying correlation measurement methods to obtain reasonable weights for features based on their contributions to the output. In this paper, based on the idea of a Hilbert–Schmidt independence criterion least absolute shrinkage and selection operator (HSIC LASSO) for selecting features with minimal redundancy and maximum relevance, we propose a novel feature-weighted SVR that considers the importance of features to the output and the redundancy between features. In this approach, the HSIC is utilized to effectively measure the correlation between features as well as that between features and the output. The feature weights are obtained by solving a LASSO regression problem. Compared to other feature weighting methods, our method takes much more comprehensive consideration of weight calculation, and the obtained weighted kernel function can lead to more precise predictions for unknown data. Comprehensive experiments on real datasets from the University of California Irvine (UCI) machine learning repository demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Several authors are interested in the study of limiting distributions for large symmetrical random matrices. Our approach of studying limiting distributions is different and is related to the new concept of variance functions of Cauchy–Stieltjes Kernel (CSK) families of probabilities. By means of the variance functions machinery, some novel limiting probability measures are provided involving the free multiplicative law of large numbers, using both free and Boolean (additive and multiplicative) convolutions. Several examples of these limiting probability measures are given in the context of free probability. [ABSTRACT FROM AUTHOR]

This paper focuses on studying the mapping properties of singular integral operators over product symmetric spaces. The boundedness of such operators is established on Triebel–Lizorkin spaces whenever their rough kernel functions belong to the Grafakos and Stefanov class. Our findings generalize, extend and improve some previously known results on singular integral operators. [ABSTRACT FROM AUTHOR]

In recent years, our research on biomechanical and biophysical problems has involved a series of symmetry issues. We found that the fundamental laws of the aforementioned problems can all be characterized by fractal operators, and each type of operator possesses rich invariant properties. Based on the invariant properties of fractal operators, we discovered that the symmetry evolution laws of functional fractal trees in the physical fractal space can reveal the intrinsic correlations between special functions. This article explores the fractional-order correlation between special functions inspired by bone fractal operators. Specifically, the following contents are included: (1) showing the intrinsic expression in the convolutional kernel function of bone fractal operators and its correlation with special functions; (2) proving the following proposition: the convolutional kernel function of bone fractal operators is still related to the special functions under different input signals (external load, external stimulus); (3) using the bone fractal operators as the background and error function as the core, deriving the fractional-order correlation between different special functions. [ABSTRACT FROM AUTHOR]

In the early stages of aerospace design, reduced-order models (ROMs) are crucial for minimizing computational costs associated with using physics-rich field information in many-query scenarios requiring multiple evaluations. The intricacy of aerospace design demands the use of high-dimensional design spaces to capture detailed features and design variability accurately. However, these spaces introduce significant challenges, including the curse of dimensionality, which stems from both high-dimensional inputs and outputs necessitating substantial training data and computational effort. To address these complexities, this study introduces a novel multifidelity, parametric, and nonintrusive ROM framework designed for high-dimensional contexts. It integrates machine learning techniques for manifold alignment and dimension reduction--employing proper orthogonal decomposition and model-based active subspace--with multifidelity regression for ROM construction. Our approach is validated through two test cases: the 2D RAE 2822 airfoil and the 3D NASA CRM wing, assessing various fidelity levels, training data ratios, and sample sizes. Compared to the single-fidelity principal component-active subspace (PCAS) method, our multifidelity solution offers improved cost-accuracy benefits and achieves better predictive accuracy with reduced computational demands. Moreover, our methodology outperforms the manifold-aligned ROM method by 50% in handling scenarios with large input dimensions, underscoring its efficacy in addressing the complex challenges of aerospace design. [ABSTRACT FROM AUTHOR]

This paper is devoted to the study of the descent problem in the spirit of conjectures proposed by Kahn in characteristic different from 2. The descent problem seeks conditions under which a K$K$‐form (quadratic or bilinear) is defined over F$F$ for a field extension K/F$K/F$. We study this problem in a complete manner for K$K$‐quadratic and bilinear forms up to dimension 4 when F$F$ is a field of characteristic 2 and K$K$ is the function field of a projective quadric. [ABSTRACT FROM AUTHOR]

In this study, pure and hexagonal boron nitride (hBN)-doped zinc oxide (ZnO) nanoparticles with different doping ratios (1, 5 and 10 wt%) were synthesized and their structural morphological properties were investigated. ZnO-hBN nanocomposite particles were used as reinforcement material in AZ91 magnesium alloy. AZ91 powder reinforced with ZnO-hBN nanocomposite particles was combined by powder metallurgy. Hardness of AZ91 matrix composites was measured at 5 different points on each sample and averaged. The specimens were subjected to wear tests in a pin-on-disk test apparatus. As a result of the tests, the hardness value of pure AZ91 alloy was found to be 62 HB, while the hardness value of AZ91-ZnO-10 hBN sample was found to be up to 85 HB. In the wear tests, it was observed that ZnO-hBN additives resulted in low weight losses in wear losses and also decreased the friction coefficient of the hBN additive in the friction coefficient graphs. A hybrid GA (genetic algorithm)-SVR (support vector regression) model was proposed for the prediction of wear quantities of composites. The purpose of using a hybrid system combining SVR and GA is to improve the wear prediction by optimizing the hyperparameters of t and GA. The results are observed using four different kernel functions in the SVR algorithm, and then, a hybrid GA-SVR structure is proposed and compared. With the proposed method, 98.80% prediction success of the wear quantities of the composite is achieved by the hybridized GA. [ABSTRACT FROM AUTHOR]

This paper investigates the capabilities of the resonant cavity system (ResCav) for detecting tampered integrated circuits (ICs) within supply chains. Prior research showcased ResCav's ability to discern minor circuit variations, this study focuses on enhancing supervised classification results and introduces a one-class support vector machine (SVM) approach with a modified radial basis function kernel for novelty detection. Through finer hyperparameter tuning, the system achieves improved classification accuracy, demonstrating its potential to identify nuanced alterations with even higher precision and recall rates. Additionally, the application of a one-class SVM enables the detection of tampered ICs without reliance on labeled datasets, expanding utility in scenarios where access is limited to golden ICs. These advancements in ResCav's capabilities signify progress in failure prevention methodologies, offering an efficient and non-destructive solution crucial for safeguarding against counterfeit and non-conforming components infiltrating critical supply chains. [ABSTRACT FROM AUTHOR]

The present article contributes a new novel mathematical model influenced with the memory effect that endeavours to record the thermal responses inside a living tissue exposed to an oscillatory heat input on its outer surface. Heat transport inside the tissue is modelled with the hyperbolic equation involving three relaxation times. Analytical solutions of the significant field quantities—temperature, displacement and thermal stress are determined in the frequency domain by adopting the Laplace transform mechanism. Computational results are derived by inverting the field quantities from frequency domain to the physical domain. Memory influences are forecasted on the propagation of the thermo-mechanical waves inside the tissue by obtaining the influences of the kernel functions and time-delay quantity on the physical fields. Impact of the relaxation times is pronounced on the variances of the waves' constituents. Graphical outcomes speculate that inclusion of the phase lags in heat transfer model supresses and stabilizes the speed of the waves. This study may support to the medical practitioners during thermal therapy and to develop the precised clinical equipment. [ABSTRACT FROM AUTHOR]

The Internet of Things (IoT) has grown significantly in recent years, allowing devices with sensors to share data via the internet. Despite the growing popularity of IoT devices, they remain vulnerable to cyber-attacks. To address this issue, researchers have proposed the Hybrid Intrusion Detection System (HIDS) as a way to enhance the security of IoT. This paper presents a novel intrusion detection model, namely QSVM-IGWO, for improving the detection capabilities and reducing false positive alarms of HIDS. This model aims to improve the performance of the Quantum Support Vector Machine (QSVM) by incorporating parameters from the Improved Grey Wolf Optimizer (IGWO) algorithm. IGWO is introduced under the hypothesis that the social hierarchy observed in grey wolves enhances the searching procedure and overcomes the limitations of GWO. In addition, the QSVM model is employed for binary classification by selecting the kernel function to obtain an optimal solution. Experimental results show promising performance of QSVM-IGWO in terms of accuracy, Recall, Precision, F1 score, and ROC curve, when compared with recent detection models. [ABSTRACT FROM AUTHOR]

Image clustering has received significant attention due to the growing importance of image recognition. Researchers have explored Riemannian manifold clustering, which is capable of capturing the non‐linear shapes found in real‐world datasets. However, the complexity of image data poses substantial challenges for modelling and feature extraction. Traditional methods such as covariance matrices and linear subspace have shown promise in image modelling, and they are still in their early stages and suffer from certain limitations. However, these include the uncertainty of representing data using only one Riemannian manifold, limited feature extraction capacity of single kernel functions, and resulting incomplete data representation and redundancy. To overcome these limitations, the authors propose a novel approach called join multiple Riemannian manifold representation and multi‐kernel non‐redundancy for image clustering (MRMNR‐MKC). It combines covariance matrices with linear subspace to represent data and applies multiple kernel functions to map the non‐linear structural data into a reproducing kernel Hilbert space, enabling linear model analysis for image clustering. Additionally, the authors use matrix‐induced regularisation to improve the clustering kernel selection process by reducing redundancy and assigning lower weights to identical kernels. Finally, the authors also conducted numerous experiments to evaluate the performance of our approach, confirming its superiority to state‐of‐the‐art methods on three benchmark datasets. [ABSTRACT FROM AUTHOR]

Information-theoretic measures play a vital role in training learning systems. Many researchers proposed non-parametric entropy estimators that have applications in adaptive systems. In this work, a kernel density estimator using Kapur entropy of order a and type ß has been proposed and discussed with the help of theorems and properties. From the results, it has been observed that the proposed density measure is consistent, minimum, and smooth for the probability density function (PDF) underlying given conditions and validated with the help of theorems and properties. The objective of the paper is to understand the theoretical viewpoint behind the underlying concept. [ABSTRACT FROM AUTHOR]

Defect pattern classification of wafer bin maps (WBMs) assists in identifying the causes of semiconductor manufacturing process failures, thus contributing to the search for appropriate solutions. However, new previously unobserved defect patterns may be generated in real applications, which require classification methods with out-of-distribution (OOD) pattern detection capabilities. In this paper, we propose a novel method called a spectral-normalized neural radial basis function (SNRBF) network to classify defect patterns in WBMs while simultaneously detecting OOD defect patterns by quantifying the predictive uncertainty of a deep neural network. The SNRBF network adds spectral normalization to the weights in each layer of a deep neural network and replaces the output layer with a radial basis function kernel, facilitating high-quality uncertainty quantification and efficient computation. Additionally, we propose a novel regularization method based on singular values of the representation matrix to improve uncertainty quantification. Furthermore, we propose a new noise-filtering method capable of effectively eliminating random defects in WBMs by considering various defect pattern sizes. The proposed method is evaluated on a real WBM dataset and is demonstrated to outperform other competing methods in OOD detection while presenting competitive classification performance. [ABSTRACT FROM AUTHOR]

Apple core browning not only affects the nutritional quality of apples, but also poses a health risk to consumers. Therefore, there is an urgent need to develop a fast and reliable non-destructive detection method for apple core browning. To deal with the challenges of the long incubation period, strong infectivity, and difficulty in the prevention and control of apple core browning, a novel non-destructive detection method for apple core browning has been developed through combining hyperspectral imaging and dielectric techniques. To reduce the computational complexity of high-dimensional multi-view data, canonical correlation analysis is employed for feature dimensionality reduction. Then, the two low-dimensional vectors extracted from two different sensors are concatenated into one united feature vector; therefore, the information contained in the hyperspectral and dielectric data is fused to improve the detection accuracy of the non-destructive method. At last, five traditional classifiers, such as k-Nearest Neighbors, a support vector machine with radial basis function kernel and polynomial kernel, Decision Tree, and neural network, are trained on the fused feature vectors to discriminate apple core browning. The experimental results on our own constructed dataset have shown that the sensitivity, specificity, and precision of SVM with RBF kernel based on concatenated 70-dimensional feature vectors extracted via canonical correlation analysis reached 99.98%, 99.70%, and 99.70%, respectively, which achieved better results than other models. This study can provide theoretical assurance and technical support for further development of higher accuracy and lower-cost non-destructive detection devices for apple core browning. [ABSTRACT FROM AUTHOR]

Deep Convolutional Neural Networks (DCNNs) are very useful for image-based pattern classification problems because of their efficient feature extraction capabilities. Although DCNNs have good generalization performance, their applicability is limited due to slow learning speed, as they are based on iterative weight-update algorithms. This study presents a new noniterative DCNN that can be trained in real-time. The fundamental block of the proposed DCNN is fixed real number-based filters for convolution operations for multi-feature extraction. After a finite number of feature extraction layers, nonlinear kernel mapping along with pseudo-inverse is used for the classification of extracted feature vectors. The proposed DCNN, named Deep Convolutional Kernelized Classification (DCKC), is noniterative, as the mask coefficients of its convolution operations are fixed real numbers. The kernel function with predefined parameters of DCKC does a nonlinear mapping of extracted features, and pseudo-inverse is used to find its output weights. The proposed noniterative DCKC was evaluated on benchmark face recognition databases, achieving better results and establishing its superiority. [ABSTRACT FROM AUTHOR]

In this manuscript, we study and examine the time‐fractional modified anomalous sub‐diffusion model of distributed‐order. Two numerical approaches are used to study the approximate solutions of the presented model. For the first approach, we use a second‐order difference method based on the L1 formula for the temporal variable. In this case, stability and convergence analysis for time discretization using the L1 formula is displayed. For the second approach, we display and demonstrate the numerical method for the full‐discrete based on the Galerkin weak form based on various kernels and shape functions of reproducing kernel particle method which do not have the δ$$ \delta $$‐Kronecker property. Moreover, in this manuscript, in order to be able to use the necessary boundary conditions, the two straight strategies are used: one is the Lagrange multiplier method, and the other one is the penalty method. By using penalty method, we can the main boundary value model is changed to a new BVP with Robin boundary condition. At the end of the article, some numerical examples are presented and analyzed for the efficiency of the proposed numerical method. Also, the presented numerical method is compared with other numerical approaches, and the results of this comparison are reported in the form of a table. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the fractional hybrid integro-differential equations with Dirichlet boundary conditions. We first prove the existence of a unique solution for the equation using a fixed point technique. Our main goal is to obtain the best approximation using optimal controllers. After studying the stability, we present the reproducing kernel Hilbert space numerical method to obtain approximate solutions to the equation. We finally conclude with numerical results. [ABSTRACT FROM AUTHOR]

Based on small scale sample of accident data from specific scenarios, fully exploring the potential influencing factors of the severity of traffic accidents has become a key and effective research method. In order to analyze the factors mentioned above in the scenario of urban ring roads, this paper collected data records of 1250 traffic accidents involving different severity on urban ring road of a central city in northwest China in the past 3 years. Firstly, the Support Vector Machine (SVM) model of non-parametric method is utilized to analyze the data above, and three kernel functions of linear, inhomogeneous polynomial and Gaussian radial basis are constructed respectively. Considering comprehensively 16 potential influencing factors covering the driver-vehicle-road-environment integrated system, the SVM models of above three kernel functions are verified, accuracy reaches 0.771 and F1 reaches 0.841. Then, Bayesian Optimization (BO), Grids Search (GS) and Rough Set (RS) are utilized as optimizer to adjust the parameters of Gaussian radial basis function SVM model, the performance of BO-SVM is further improved and reaches the optimum, with an average accuracy of 0.875 on the test set and a F1 of 0.886, completely outperforming the benchmark models of GS-SVM, RS-SVM, Bilayer-LSTM and BP. Finally, the sensitivity analysis method is utilized to quantify the sensitivity of the potential influencing factors to the severity of road accidents, and the backward selection method is utilized to screen the core influencing factors that influence the severity of accident, concluded that core influencing factors are age, driving mileage and vehicle type. This paper will provide reference for the analysis of the significant influencing factors for road accidents severity, and to provide theoretical support for the precise formulation of accident improvement strategies. [ABSTRACT FROM AUTHOR]

This article investigates the issue of anti‐modal‐asynchrony sliding mode control (SMC) for discrete semi‐Markov jump systems with bi‐boundary sojourn time. Asynchronous mechanism refers to the mismatch phenomenon between the system mode and the controller mode, in which the modal lag is mode‐dependent to reduce some conservatism compared with traditional mode‐independent lag. In contrast to traditional semi‐Markov jump systems, the sojourn time of each mode in this article is considered to have upper‐and‐lower bounds, representing better characteristics than the upper bound. Based on the semi‐Markov kernel and the Lyapunov function related to the elapsed time of current mode, a sufficient condition is proposed to ensure that the mean‐square stability of the underlying system is achieved under an equivalent SMC mechanism. The conditions for the existence of the designed controller are obtained, which shows that the constructed SMC mechanism is effective against asynchronous mode jumps. An anti‐modal‐asynchrony SMC mechanism is constructed to achieve the reachability of discrete quasi‐sliding mode. Finally, the F‐404 aircraft engine model is given to validate the effectiveness of the control strategy. [ABSTRACT FROM AUTHOR]

In this paper, the well‐posedness of Cauchy's problem of fractional Schrödinger equations with a power‐type nonlinearity on n‐dimensional manifolds with nonnegative Ricci curvature is studied. Under suitable volume conditions, the local solution with initial data in H[n2]+1 will blow up in finite time no matter how small the initial data is, which follows from a new weight function and ODE inequalities. Moreover, the upper‐bound of the lifespan can be estimated. [ABSTRACT FROM AUTHOR]

How to acquire the exact center of a circular sample is an essential task in object recognition. Present algorithms suffer from the high time consumption and low precision. To tackle these issues, we propose a novel circle center location algorithm based on sample density and adaptive thresholding. After obtaining circular contours through image pre-processing, these contours were segmented using a grid method to obtain the required coordinates. Based on the principle of three points forming a circle, a data set containing a large number of samples with circle center coordinates was constructed. It was highly probable that these circle center samples would fall within the near neighborhood of the actual circle center coordinates. Subsequently, an adaptive bandwidth fast Gaussian kernel was introduced to address the issue of sample point weighting. The mean shift clustering algorithm was employed to compute the optimal solution for the density of candidate circle center sample data. The final optimal center location was obtained by an iteration algorithm. Experimental results demonstrate that in the presence of interference, the average positioning error of this circle center localization algorithm is 0.051 pixels. Its localization accuracy is 64.1 % higher than the Hough transform and 86.4 % higher than the circle fitting algorithm. [ABSTRACT FROM AUTHOR]

A kernel interpolation method for the acoustic transfer function (ATF) between regions constrained by the physics of sound while being adaptive to the data is proposed. Most ATF interpolation methods aim to model the ATF for fixed source by using techniques that fit the estimation to the measurements while not taking the physics of the problem into consideration. We aim to interpolate the ATF for a region-to-region estimation, meaning we account for variation of both source and receiver positions. By using a very general formulation for the reproducing kernel function, we have created a kernel function that considers both directed and residual fields as two separate kernel functions. The directed field kernel considers a sparse selection of reflective field components with large amplitudes and is formulated as a combination of directional kernels. The residual field is composed of the remaining densely distributed components with lower amplitudes. Its kernel weight is represented by a universal approximator, a neural network, in order to learn patterns from the data freely. These kernel parameters are learned using Bayesian inference both under the assumption of Gaussian priors and by using a Markov chain Monte Carlo simulation method to perform inference in a more directed manner. We compare all established kernel formulations with each other in numerical simulations, showing that the proposed kernel model is capable of properly representing the complexities of the ATF. [ABSTRACT FROM AUTHOR]

ABSTRACT This article proposes a novel method to accelerate the boundary feedback control design of cascaded parabolic difference equations (PDEs) through DeepONet. The backstepping method has been widely used in boundary control problems of PDE systems, but solving the backstepping kernel function can be time‐consuming. To address this, a neural operator (NO) learning scheme is leveraged for accelerating the control design of cascaded parabolic PDEs. DeepONet, a class of deep neural networks designed for approximating nonlinear operators, has shown potential for approximating PDE backstepping designs in recent studies. Specifically, we focus on approximating gain kernel PDEs for two cascaded parabolic PDEs. We utilize neural operators to map only two kernel functions, while the other two are computed using the analytical solution, thus simplifying the training process. We establish the continuity and boundedness of the kernels, and demonstrate the existence of arbitrarily close DeepONet approximations to the kernel PDEs. Furthermore, we demonstrate that the DeepONet approximation gain kernels ensure stability when replacing the exact backstepping gain kernels. Notably, DeepONet operator exhibits computation speeds two orders of magnitude faster than PDE solvers for such gain functions, and their theoretically proven stabilizing capability is validated through simulations. [ABSTRACT FROM AUTHOR]

This paper investigates the most optimized Kernel Function in Support Vector Machine (SVM) to be utilized on Received Signal Level ( RSL ) dataset for High Speed Rail (HSR). Commonly, RSL is rapidly fluctuated over a large distance and it becomes weakened when it reaches the receiver. Therefore, Kernel Function in SVM is utilized for a more secure, reliable and stable high dimensional mapping especially when the datasets cannot be linearly separable. The most optimized kernel can handle non-linear decision boundaries. In this research, continuous features in RSL dataset are discretized before mapping them into the appropriate kernels. Accordingly, this paper presents a comparison of four well-known Kernel Functions which are Default Function Kernel, Linear Function Kernel, Radial Basis Function Kernel and Poly Kernel Function Kernel. It is observable that Linear Kernel is proven to be more accurate than other Kernels Functions as it has yielded 89% of accuracy and precision as much as 85%. An excellent Recall score and F1 score as much as 85% has also satisfyingly achieved with a minimum RMSE number as much as 0.32. Finally, choosing the most optimal Kernel Functions will definitely help to comprehend the behavior of datasets especially in investigating the HSR scientific research. [ABSTRACT FROM AUTHOR]

This paper aims to introduce a new fractional extension of the interval Hermite–Hadamard ( H H ), H H –Fejér, and Pachpatte-type inequalities for left- and right-interval-valued harmonically convex mappings ( L R I V H convex mappings) with an exponential function in the kernel. We use fractional operators to develop several generalizations, capturing unique outcomes that are currently under investigation, while also introducing a new operator. Generally, we propose two methods that, in conjunction with more generalized fractional integral operators with an exponential function in the kernel, can address certain novel generalizations of increasing mappings under the assumption of L R I V convexity, yielding some noteworthy results. The results produced by applying the suggested scheme show that the computational effects are extremely accurate, flexible, efficient, and simple to implement in order to explore the path of upcoming intricate waveform and circuit theory research. [ABSTRACT FROM AUTHOR]

Considering the demand for the optimization of the technical factors of spraying for a greater area coverage and minimal drift, field tests were carried out to determine the interaction between the area coverage, number of droplets per cm2, droplet diameter, and drift. The studies were conducted with two different types of sprayers (axial and radial fan) in an apple orchard and a vineyard. The technical factors of the spraying interactions were nozzle type (ISO code 015, code 02, and code 03), working speed (6 and 8 km h−1), and spraying norm (250–400 L h−1). The airflow of both sprayers was adjusted to the plantation leaf mass and the working pressure was set for each repetition separately. A method using water-sensitive paper and a digital image analysis was used to collect data on coverage factors. The data from the field research were processed using four machine learning models: quantile random forest (QRF), support vector regression with radial basis function kernel (SVR), Bayesian Regularization for Feed-Forward Neural Networks (BRNN), and Ensemble Machine Learning (ENS). Nozzle type had the highest predictive value for the properties of number of droplets per cm2 (axial = 69.1%; radial = 66.0%), droplet diameter (axial = 30.6%; radial = 38.2%), and area coverage (axial = 24.6%; radial = 34.8%). Spraying norm had the greatest predictive value for area coverage (axial = 43.3%; radial = 26.9%) and drift (axial = 72.4%; radial = 62.3%). Greater coverage of the treated area and a greater number of droplets were achieved with the radial sprayer, as well as less drift. The accuracy of the machine learning model for the prediction of the treated surface showed a satisfactory accuracy for most properties (R2 = 0.694–0.984), except for the estimation of the droplet diameter for an axial sprayer (R2 = 0.437–0.503). [ABSTRACT FROM AUTHOR]

Population balance equations are widely used to study the evolution of aerosols, colloids, liquid–liquid dispersion, raindrop fragmentation, and pharmaceutical granulation. However, these equations are difficult to solve due to the complexity of the kernel structures and initial conditions. The hyperbolic fragmentation equation, in particular, is further complicated by the inclusion of double integrals. These challenges hinder the analytical solutions of number density functions for basic kernel classes with exponential initial distributions. To address these issues, this study introduces a new approach combining the projected differential transform method with Laplace transform and Padé approximants to solve the hyperbolic fragmentation equation. This method aims to provide accurate and efficient explicit solutions to this challenging problem. The approach's applicability is demonstrated through rigorous mathematical derivation and convergence analysis using the Banach contraction principle. Additionally, several numerical examples illustrate the accuracy and robustness of this new method. For the first time, new analytical solutions for number density functions are presented for various fragmentation kernels with gamma and other initial distributions. This method significantly enhances solution quality over extended periods using fewer terms in the truncated series. The solutions are compared and verified against the finite volume method and the homotopy perturbation method, showing that the coupled approach not only estimates number density functions accurately but also captures integral moments with high precision. This research advances computational methods for particle breakage phenomena, offering potential applications in various industrial processes and scientific disciplines. [ABSTRACT FROM AUTHOR]

Two novel crossover models for breast cancer that incorporate Ψ -Caputo fractal variable-order fractional derivatives, fractal fractional-order derivatives, and variable-order fractional stochastic derivatives driven by variable-order fractional Brownian motion and the crossover model for breast cancer that incorporates Atangana–Baleanu Caputo fractal variable-order fractional derivatives, fractal fractional-order derivatives, and variable-order fractional stochastic derivatives driven by variable-order fractional Brownian motion are presented here, where we used a simple nonstandard kernel function Ψ (t) in the first model and a non-singular kernel in the second model. Moreover, we evaluated our models using actual statistics from Saudi Arabia. To ensure consistency with the physical model problem, the symmetry parameter ζ is introduced. We can obtain the fractal variable-order fractional Caputo and Caputo–Katugampola derivatives as special cases from the proposed Ψ -Caputo derivative. The crossover dynamics models define three alternative models: fractal variable-order fractional model, fractal fractional-order model, and variable-order fractional stochastic model over three-time intervals. The stability of the proposed model is analyzed. The Ψ -nonstandard finite-difference method is designed to solve fractal variable-order fractional and fractal fractional models, and the Toufik–Atangana method is used to solve the second crossover model with the non-singular kernel. Also, the nonstandard modified Euler–Maruyama method is used to study the variable-order fractional stochastic model. Numerous numerical tests and comparisons with real data were conducted to validate the methods' efficacy and support the theoretical conclusions. [ABSTRACT FROM AUTHOR]

The Black–Scholes (B–S) equation has been recently extended as a kind of tempered time-fractional B–S equations, which becomes an interesting mathematical model in option pricing. In this study, we provide a fast numerical method to approximate the solution of the tempered time-fractional B–S model. To achieve high-order accuracy in space and overcome the weak initial singularity of exact solution, we combine the compact difference operator with L1-type approximation under nonuniform time steps to yield the numerical scheme. The convergence of the proposed difference scheme is proved to be unconditionally stable. Moreover, the kernel function in the tempered Caputo fractional derivative is approximated by sum-of-exponentials, which leads to a fast unconditionally stable compact difference method that reduces the computational cost. Finally, numerical results demonstrate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

Spherical data arise widely in various settings. Spherical statistics is an analysis of data on a unit hyper-spherical domain. In this paper, we mainly consider the local kernel estimators for regression models with a binary response and the predictors including spherical variables. We apply the random forests kernel to nonparametric binary regression models with spherical predictors. Simulation experiments and real examples are used to validate the performance of the new models. Compared with the classical von Mises–Fisher kernel and the linear-spherical kernel, the random forests kernel has better fitting effect and faster computation speed. Compared with other classifiers, the models proposed in this paper have better classification performance in both low and high dimensional cases. [ABSTRACT FROM AUTHOR]

This paper is devoted to a nonlocal dispersal logistic model with seasonal succession and free boundaries, where the free boundaries represent the expanding front and the seasonal succession accounts for the effect of two different seasons. Technically, this free boundary problem is much more difficult than the case without seasonal succession since the coefficients are all time periodic and piecewise continuous. We prove the existence and uniqueness of global solution, and then examine the long-time dynamical behaviour and the criteria that completely determine when spreading and vanishing can happen, revealing some significant differences from the model without seasonal succession. Moreover, we use a "thin-tail" condition on the kernel function to estimate the asymptotic speeds of (g, h) and the asymptotic spreading speed of u, which is achieved by solving the associated semi-wave problem. [ABSTRACT FROM AUTHOR]

Extended kalman filter (EKF) is widely used to integrated navigation system of global navigation satellite system (GNSS) and strapdown inertial navigation system (SINS). However, non-Gaussian noise and the uncertainty of measurement noise can seriously reduce the performance of EKF, so it is difficult to obtain an optimal GNSS/INS integration solution. At present, non-Gaussian noise processing is still a difficult issue in filter research. In this paper, an adaptive and robust maximum correntropy extended kalman filter (MCEKF) method based on Cauchy kernel function is proposed to solve the above problem. Thanks to the excellent properties of Cauchy kernel function, the proposed method can effectively avoid filter faults and has better stability. However, the performance of MCEKF depends on the select of kernel bandwidth parameter, which is a difficult problem in the engineering application of MCEKF. In this paper, the switching kernel bandwidth algorithm is employed to adaptively estimate the kernel bandwidth parameter to solve the tradeoff between convergence rate and steady-state misalignment in the MCEKF algorithm under constant kernel bandwidth. Finally, the performance of the proposed algorithm is verified by two sets of vehicle-mounted precise point positioning (PPP) and SINS tightly coupled integration experiments in urban environment. The results show that compared with EKF, the proposed method can significantly improve the positioning accuracy, that is, the PPP/SINS positioning accuracy based on GE, GR and GRE system is improved by 25.1 %, 2.5 % and 17.0 % in D196 experiment, and 23.5 %, 16.5 % and 31.8 % in D107 experiment, respectively. The velocity and attitude accuracy of the two methods are similar. The velocity errors of all schemes can reach cm/s level. The roll, pitch and heading errors of navigation-grade inertial sensor are all less than 0.12 degree. The roll and pitch errors of MEMS are less than 1.0 degree, the heading error of the G, GE, GR, and GRE systems are 1.719, 1.464, 1.676, and 1.475 degree, respectively. [ABSTRACT FROM AUTHOR]