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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]

In this study, we consider an epidemic model for susceptible-infected-susceptible populations with nonlocal dffusion, described by convolution operators. Our main objective is to model different diffusion strategies for the susceptible and infected populations by using distinct kernel functions in the convolution operator to model the different movements of individuals for each class. This approach eliminates the simplification of reducing the stationary problem to a single equation, which makes the analysis more challenging. However, we have shown the existence of at least one positive endemic steady state when the basic reproduction number is greater than one, using the index degree theory of Leray-Schauder. Additionally, we investigated the asymptotic profile of the endemic equilibrium state for both, large and small diffusion rates, to demonstrate the persistence or extinction of the disease. Overall, our study indicates that restricting individual movements only partially cannot eliminate the disease unless the total population size is small. [ABSTRACT FROM AUTHOR]

To describe the probabilistic characteristics of critical chloride concentration (CCC) and calibrate the computational accuracy of traditional prediction models, a probabilistic prediction model of CCC for reinforcement corrosion in concrete was developed based on an improved Gaussian process regression (GPR) model. Firstly, a new hybrid kernel function for the GPR model was developed by combining the radial basis function with the rational quartic kernel according to the sum of single kernel functions and automatic relevance determination function. The hyperparameters of the improved GPR model were determined based on Bayesian theory and the maximum likelihood estimation. Subsequently, a probabilistic prediction model of CCC for reinforcement corrosion in concrete was developed based on the improved GPR model and a total of 591 sets of experimental data. The accuracy and applicability of the proposed probabilistic prediction (PPP) model was validated by comparing with traditional kernel functions, machine learning models and empirical theoretical models. The results showed that the PPP model based on the new hybrid kernel function has high accuracy and generalisation capability. The PPP model provides an efficient way to describe the probabilistic characteristics of CCC for reinforcement corrosion in concrete and to calibrate the computational accuracy of traditional prediction models based on the probability density function and confidence intervals. [ABSTRACT FROM AUTHOR]

This paper presents an estimation method for assessing the damage to the rear wall of spacecraft protective structures caused by hypervelocity impacts of space debris. Utilizing the smoothed particle hydrodynamics for numerical simulation, a kernel-function based kinetic energy mapping method is employed to analyze the kinetic energy distribution of the debris cloud generated by the initial impact upon the rear wall. This study establishes a correlation between the kinetic energy of the debris cloud and the resulting damage to the rear wall. This correlation allows for the estimation of damage characteristics, including the depth and volume of impact craters on the rear wall following exposure to a debris cloud. Taking the hypervelocity impacts of an Al-2017 projectile on an Al-6061 thin plate as examples, experimental validation has demonstrated the effectiveness, robustness and versatility of this method over a range of particle sizes and grid resolutions. This method enables rapid estimation of damage to protective structures and assessment of their residual protective performance. • Improving robustness in kinetic energy mapping via kernel function integration. • Estimation method links debris cloud energy to rear wall damage. • Assessing residual protective capability of impacted structures. [ABSTRACT FROM AUTHOR]

Gaussian process regression (GPR) is a commonly used approach for establishing the nonparametric models of ship maneuvering motion, and its performance depends on the selection of the kernel function. However, no single kernel function can be universally applied to all nonparametric models of ship maneuvering motion, which may compromise the robustness of GPR. To address this issue, an adaptive ensemble of multi-kernel GPRs based on heuristic model screening (AEGPR-HMS) is proposed in this paper. In the proposed method, four kernel functions are involved in constructing the ensemble model. The HMS method is introduced to determine the weights of individual-based GPR models, which can be adaptively assigned according to the baseline GPR model. To determine the hyper-parameters of these kernel functions, the genetic algorithm is also employed to compute the optimal values. The KVLCC2 tanker provided by the SIMMAN 2008 workshop is used to validate the performance of the proposed method. The results demonstrate that the AEGPR-HMS is an efficient and robust method for nonparametric modeling of ship maneuvering motion. [ABSTRACT FROM AUTHOR]

The advent of single-cell RNA sequencing (scRNA-seq) technology enables researchers to gain deep insights into cellular heterogeneity. However, the high dimensionality and noise of scRNA-seq data pose significant challenges to clustering. Therefore, we propose a new single-cell type identification method, called CHLSPCA, to address these challenges. In this model, we innovatively combine correntropy with PCA to address the noise and outliers inherent in scRNA-seq data. Meanwhile, we integrate the hypergraph into the model to extract more valuable information from the local structure of the original data. Subsequently, to capture crucial similarity information not considered by the PCA model, we employ the Gaussian kernel function and the Euclidean metric to mine the similarity information between cells, and incorporate this information into the model as the similarity constraint. Furthermore, the principal components (PCs) of PCA are very dense. A new sparse constraint is introduced into the model to gain sparse PCs. Finally, based on the principal direction matrix learned from CHLSPCA, we conduct extensive downstream analyses on real scRNA-seq datasets. The experimental results show that CHLSPCA performs better than many popular clustering methods and is expected to promote the understanding of cellular heterogeneity in scRNA-seq data analysis and support biomedical research. [ABSTRACT FROM AUTHOR]

Fuzzy clustering algorithms are widely applied in the field of traffic driving, aiding in the classification of driving behaviors from massive traffic data and enhancing traffic safety levels. However, classical Fuzzy C-Means (FCM) algorithms are sensitive to noise during the clustering process, leading to suboptimal performance when dealing with traffic datasets with lower accuracy. Moreover, single-kernel clustering algorithms are greatly influenced by kernel function selection. To address these issues, this paper proposes a Possibility Weighted Multi-Kernel Fuzzy Clustering Algorithm (PMWFCM). By integrating possibility-based fuzzy clustering with FCM and introducing a multi-kernel weighting mechanism, PMWFCM effectively reduces FCM's sensitivity to outliers while resolving issues of clustering consistency in Possibilistic C-Means (PCM) algorithms, overcoming the challenges associated with kernel function selection. Validation on three different types of datasets demonstrates that the PMWFCM algorithm performs exceptionally well in terms of average accuracy, normalized information, average time, robustness, and convergence. When applied to the evaluation of driving behaviors in traffic datasets. Therefore, the improved FCM algorithm proposed in this paper can accurately and comprehensively reflect changes in traffic data, providing a solid theoretical foundation for identifying and assessing major risk types among passenger drivers. [ABSTRACT FROM AUTHOR]

The widespread adoption of internet of things (IoT) devices has brought about unprecedented levels of connectivity and convenience. However, it has also introduced significant challenges, particularly in the areas of security and privacy. This study addresses the critical issue of intrusion detection within IoT environments, with a specific focus on analyzing the Iot-23 dataset. Our methodology involves employing principal component analysis (PCA) and kernel PCA for dimensionality reduction. Subsequently, we utilize the k-nearest neighbors (KNN) algorithm for classification purposes. To optimize the performance of the KNN algorithm, we experiment with various feature scaling techniques, such as StandardScaler, MinMaxScaler, and RobustScaler, utilizing different distance metrics. In our analysis, we discovered that employing the cosine distance metric in combination with KNN resulted in superior intrusion detection performance when utilizing PCA. Additionally, when utilizing kernel PCA, we evaluated multiple kernel functions and determined that the radial basis function and sigmoid kernel yielded the most favorable results. [ABSTRACT FROM AUTHOR]

Analysis of spatial patterns can provide an efficient answer to the problem of locating global or local patterns of the spatial distribution of traffic crashes. Approximately 21% of vehicle crashes in the United States occur due to inclement weather, costing the U.S. economy more than $217.5 billion yearly. One major road winter maintenance activity is snowplow and spreading salt on the road surface to improve the driving condition. The potential for rear-end collisions or conflicts between motorists and Snowplow Trucks (SPTs) is a major safety concern. This study extensively applies Ripley's K-function, the global Moran's I measure and the Getis–Ord Gi* function along with Kernel Density Estimation and Network-based Kernel Density Estimations with the aim of analysing snowplow-involved crash hotspots in the state of Wyoming. The positive Moran's I, the high z-scores and the small p values indicate that Snowplow truck crashes were spatially clustered. [ABSTRACT FROM AUTHOR]

Hydrogen-fueled Wankel rotary engine is considered the potential carbon-free power device. Due to the special structure and operating mode, the heat release process of the Wankel rotary engine is significantly different from the piston engine. To understand the heat release process and further optimize its combustion, the present work conducts a series of experiments, such as engine speed, excess air ratio and qualitative control experiments, to analyze the key combustion parameters under different conditions. The main results are as follows: Both engine speed and excess air ratio play important roles in flame development and propagation. In particular, the excess air ratio only affects the early stage of flame propagation due to its impact on the later stage is covered by in-cylinder turbulence. CA0-10 is prolonged from 15.9 to 11.2°CA while CA50-90 does not show regular changes when the excess air ratio is reduced from 2.0 to 1.2. For qualitative control mode, variation of combustion parameters will become the obstacle to expanding lean flammable limits. In particular, the distribution of CA10 and CA50 or CA90 and CA50 can be fitted by linear regression, and the gradient and intercept of the fitted line can be used to represent engine speed and excess air ratio. 1000 r/min corresponds to 1.07 gradient and 2500 r/min is 1.27. NO emission is closely related to time-based CA0-10 and CA10-90 that can be applied as the independent variable of the Support Vector Machine with radial basis function kernel function to predict NO emission, and the maximum coefficient of determination is 0.92. • Key combustion parameters of hydrogen Wankel rotary engine are analyzed in depth. • The impacts of excess air ratio on combustion only can be reflected before CA50. • Engine speed shows diverse impacts on time and crank angle-based burning parameters. • The derivative of combustion parameter can quantitatively signify engine speed and λ. • NO emission can be effectively predicted by combustion parameters with SVM methods. [ABSTRACT FROM AUTHOR]

The complex nonlinear and strongly coupled dynamics of small unmanned helicopters make mathematical modeling challenging. Traditional approaches often rely on least squares support vector machine (LSSVM) algorithms using standard kernel functions, which are limited in their learning and generalization capabilities, resulting in insufficient accuracy for flight control systems. This paper proposes an adaptive particle swarm optimization-based LSSVM (APSO-LSSVM) method, incorporating a self-constructed kernel function. Using Mercer’s theorem, the custom kernel addresses the limitations of conventional kernels and is integrated into the LSSVM framework. An adaptive particle swarm optimization algorithm, capable of dynamically adjusting inertia weights and learning factors, optimizes the model parameters, overcoming the standard particle swarm optimization’s tendency to get trapped in local optima. The model is trained using flight test data from a self-developed small unmanned helicopter, and its identification performance is cross-validated in the time domain against traditional models. Experimental results show that the proposed method significantly improves the modeling accuracy of small unmanned helicopters. [ABSTRACT FROM AUTHOR]

This paper investigates a phase-space density control based on configuration invariant for large-scale spacecraft swarms. By introducing Jordan-reduced dynamics and the configuration invariant to characterize relative orbits, the macroscopic swarm dynamics is presented with respect to the temporal evolution of phase space density. The density migration of the spacecraft swarm in phase space is modeled as a specific convection–diffusion process, where the diffusion term promotes swarm spreading and the convection term guides the swarm towards a designated region for uniform distribution. Through local density estimation and defining the convection and diffusion terms, the feedback control's specific form is proposed and its exponential stability is proved. Particularly, the formulation of the convection term outside the target region and the combined kernel function for local density estimation help in avoiding sporadic isolated spacecraft. Numerical results of spacecraft swarm deployment validate the effectiveness and superiority of phase-space density control. [ABSTRACT FROM AUTHOR]

Simple Summary: Porcine facial recognition technology is critical for the intelligent husbandry and precision management of pigs. There is a significant demand for the deployment of this technology in mobile and embedded applications within small to medium-sized pig farms. Consequently, to enhance the model's applicability to these farms, this study integrates LDA preprocessing into the conventional approach. Experimental results indicate that the model is well suited for small and medium-sized pig farms, facilitating the intelligent transformation of swine management practices. In this study, the implementation of traditional machine learning models in the intelligent management of swine is explored, focusing on the impact of LDA preprocessing on pig facial recognition using an SVM. Through experimental analysis, the kernel functions for two testing protocols, one utilizing an SVM exclusively and the other employing a combination of LDA and an SVM, were identified as polynomial and RBF, both with coefficients of 0.03. Individual identification tests conducted on 10 pigs demonstrated that the enhanced protocol improved identification accuracy from 83.66% to 86.30%. Additionally, the training and testing durations were reduced to 0.7% and 0.3% of the original times, respectively. These findings suggest that LDA preprocessing significantly enhances the efficiency of individual pig identification using an SVM, providing empirical evidence for the deployment of SVM classifiers in mobile and embedded systems. [ABSTRACT FROM AUTHOR]

In this paper, we propose a smoothing estimation method for censored quantile regression models. The method associates the convolutional smoothing estimation with the loss function, which is quadratically derivable and globally convex by using a non-negative kernel function. Thus, the parameters of the regression model can be computed by using the gradient-based iterative algorithm. We demonstrate the convergence speed and asymptotic properties of the smoothing estimation for large samples in high dimensions. Numerical simulations show that the smoothing estimation method for censored quantile regression models improves the estimation accuracy, computational speed, and robustness over the classical parameter estimation method. The simulation results also show that the parametric methods perform better than the KM method in estimating the distribution function of the censored variables. Even if there is an error setting in the distribution estimation, the smoothing estimation does not fluctuate too much. [ABSTRACT FROM AUTHOR]

The traditional finite element program is executed on the CPU; however, it is challenging for the CPU to compute the ultra-large scale finite element model. In this paper, we present a set of efficient algorithms based on GPU acceleration technology for the dynamic response of fluid-saturated porous media, named PNAM, encompassing the assembly of the global matrix and the iterative solution of equations. In the assembly part, the CSR storage format of the global matrix is directly obtained from the element matrix. For data with two million degrees of freedom, it merely takes approximately 1 s to generate all the data of global matrices, which is significantly superior to the CPU version. Regarding the iterative solution of equations, a novel algorithm based on the CUDA kernel function is proposed. For a data set with two million degrees of freedom, it takes only about 0.05 s to compute an iterative step and transfer the data to the CPU. The program is designed to calculate either in single or double precision. The change in precision has little impact on the assembly of the global matrix, but the calculation time of double precision is generally 1.5 to 2 times that of single precision in the iterative solution part for a model with 2 million degrees of freedom. PNAM has high computational efficiency and great compatibility, which can be used to solve not only saturated fluid problems but also a variety of other problems. [ABSTRACT FROM AUTHOR]

Summary: Optical transport has emerged as a candidate solution to cope with the rising data transmission challenges of enormously evolving data. In the bufferless environment, only the ingress node beholds the buffering to speed up the data transfer in the form of data bursts. However, such networks are prone to data contention issues that degrade the overall performance and eventually result in burst loss. The paper proposes a machine learning (ML) inspired deflection routing (DR) algorithm to overcome contention issues in optical burst switching (OBS) network. The contending burst is first evaluated and assigned the priority order as per the available bits. Based on the burst traffic analysis, support vector machine (SVM) kernels are trained to select an alternate route and redirected the bursts to a new output node. It has been observed that for 65% of cases, radial basis function (RBF) kernel demonstrated the best results among the three kernel functions. The work further shows that ML offers a wiser decision to avoid and overcome contention in the deflection of the route of the contenting bursts. Moreover, the proposed DR scheme has achieved the highest throughput and packet delivery ratio (PDR) with an average delay of 9.66 s using an OBS network deployed with 10 groups of nodes. When compared against the contention scenario and the existing work, the proposed DR outperformed the existing technique with a 4% to 11% margin. [ABSTRACT FROM AUTHOR]

This work addresses a value problem concerning a system of high-order nonlinear equations with viscoelastic terms acting in both equations and homogeneous Dirichlet conditions. Initially, we demonstrate that the system has a weak local solution by combining fixed point theory and Galerkin's method. Under certain conditions on the variable exponents p (.) , as well as conditions related to the kernel functions η (t) ≤ μ (t) , for all t ≥ 0 , we establish that the solution with positive initial energy exhibits exponential growth. In addition, we study some numerical examples to illustrate our theoretical results and demonstrate the effectiveness of our new approach. [ABSTRACT FROM AUTHOR]

With the advancement of the Internet, social media platforms have gradually become powerful in spreading crisis-related content. Identifying informative tweets associated with natural disasters is beneficial for the rescue operation. When faced with massive text data, choosing the pivotal features, reducing the calculation expense, and increasing the model classification performance is a significant challenge. Therefore, this study proposes a multi-strategy improved black-winged kite algorithm (MSBKA) for feature selection of natural disaster tweets classification based on the wrapper method's principle. Firstly, BKA is improved by utilizing the enhanced Circle mapping, integrating the hierarchical reverse learning, and introducing the Nelder–Mead method. Then, MSBKA is combined with the excellent classifier SVM (RBF kernel function) to construct a hybrid model. Finally, the MSBKA-SVM model performs feature selection and tweet classification tasks. The empirical analysis of the data from four natural disasters shows that the proposed model has achieved an accuracy of 0.8822. Compared with GA, PSO, SSA, and BKA, the accuracy is increased by 4.34%, 2.13%, 2.94%, and 6.35%, respectively. This research proves that the MSBKA-SVM model can play a supporting role in reducing disaster risk. [ABSTRACT FROM AUTHOR]

Diesel engines employed in non-road machinery are significant contributors to nanoparticulate matters. This paper presents a novel device based on the principle of split-stream rushing to mitigate particulate matter emissions from these engines. By organizing and intensifying the airflow movement of the jet in the rushing region, the probability of collisions between nanoparticles is enhanced. This accelerates the growth and coagulation of nanoparticles, reducing the number density of fine particulate matter. This, in turn, facilitates the capture or sedimentation of particulate matter in the diesel engine exhaust aftertreatment system. The coagulation kernel function tailored for diesel engine exhaust nanoparticles is developed. Then, the particle balance equation is solved to investigate the evolution and coagulation characteristics. Afterwards, three-dimensional numerical simulations are performed to study the flow field characteristics of the split-stream rushing device and the particle evolution within it. The results show that the device achieves a maximum coagulation efficiency of 59.73%, increasing the average particle diameter from 96 nm to 121 nm. The particle number density uniformity index exceeded 0.93 in most flow regions, highlighting the effectiveness of the device in ensuring consistent particle distribution. [ABSTRACT FROM AUTHOR]

A kinetic exchange model is developed to investigate wealth distribution in a market. The model incorporates a value function that captures the agents' psychological traits, governing their wealth allocation based on behavioral responses to perceived potential losses and returns. To account for the impact of transaction frequency on wealth dynamics, a non-Maxwellian collision kernel is introduced. Applying quasi-invariant limits and Boltzmann-type equations, a Fokker–Planck equation is derived. We obtain an entropy explicit stationary solution that exhibits exponential convergence to a lognormal wealth distribution. Numerical experiments support the theoretical insights and highlight the model's significance in understanding wealth distribution. [ABSTRACT FROM AUTHOR]

In this paper, we study self-normalized moderate deviations for degenerate U-statistics of order 2. Let { X i , i ≥ 1 } be i.i.d. random variables and consider symmetric and degenerate kernel functions in the form h (x , y) = ∑ l = 1 ∞ λ l g l (x) g l (y) , where λ l > 0 , E g l (X 1) = 0 , and g l (X 1) is in the domain of attraction of a normal law for all l ≥ 1 . Under the condition ∑ l = 1 ∞ λ l < ∞ and some truncated conditions for { g l (X 1) : l ≥ 1 } , we show that log P ( ∑ 1 ≤ i ≠ j ≤ n h (X i , X j) max 1 ≤ l < ∞ λ l V n , l 2 ≥ x n 2) ∼ − x n 2 2 for x n → ∞ and x n = o (n) , where V n , l 2 = ∑ i = 1 n g l 2 (X i) . As application, a law of the iterated logarithm is also obtained. [ABSTRACT FROM AUTHOR]

This paper aims to study the non parametric Negative Binomial Quasi-Maximum Likelihood Estimation (NBQMLE) for locally stationary integer valued processes. So, we have considered two locally stationary integer-valued models of negative binomial type, namely: INARCH (p) and INGARCH (p , q) models. Imposing some contraction arguments, we have extended the stationary negative-binomial QMLE to a localized one in our non-stationary environment. This estimation method is based on a kernel function that achieves the convergence rates of n h n order. Under some regularity assumptions, the consistency, as well as the asymptotic normality of the obtained estimator, are established. The performances of the established estimators are evaluated via a simulation study and an application to real data set. [ABSTRACT FROM AUTHOR]

Purpose: A binary-tree subdivision method (BTSM) for numerical evaluation of weakly singular integrals with discontinuous kernel in the three-dimensional (3D) boundary element method (BEM) is presented in this paper. Design/methodology/approach: In this method, the singular boundary element is split into two sub-elements and subdivided recursively until the termination criterion is met and the subdivision is stopped. Then, the source point is surrounded by one or more spherical cavities determined by the discontinuous kernel function. The sub-elements located in spherical cavities will be eliminated, and the regular triangular or rectangle elements are employed to fill the spherical cavities. Findings: With the proposed method, the obtained sub-elements are automatically refined as they approach the source point, and they are "good" in shape and size for standard Gaussian quadrature. Thus, the proposed method can be used to evaluate singular integrals owing discontinuous kernel function accurately for cases of different element shapes and various source point locations. Originality/value: Numerical examples show that the BTSM is suitable for planar and curved elements of arbitrary regular or irregular shape at various source point locations, and the results have much better accuracy and robustness than conventional subdivision method (CSM) when the kernel function is discontinuous. [ABSTRACT FROM AUTHOR]

The article is concerned with and analyzes the α -robust error bound for time-fractional diffusion wave equations with weakly singular solutions. Nonuniform L 1-type time meshes are used to handle non-smooth systems, and the sum-of-exponentials (SOEs) approximation for the kernels function is adopted to reduce the memory storage and computational cost. Meanwhile, the virtual element method (VEM), which can deal with complex geometric meshes and achieve arbitrary order of accuracy, is constructed for spatial discretization. Based on the explicit factors and discrete complementary convolution kernels, the optimal error bound of the fully discrete SOEs-VEM scheme in the L 2 -norm is derived in detail and that is α -robust, i.e., the bounds will not explosive growth while α → 2 −. Finally, some numerical experiments are implemented to verify the theoretical results. [ABSTRACT FROM AUTHOR]

We characterize rotation equivariant bounded linear operators from C(\mathbb {S}^{n-1}) to C^2(\mathbb {S}^{n-1}) by the mass distribution of the spherical Laplacian of their kernel function on small polar caps. Using this characterization, we show that every continuous, homogeneous, translation invariant, and rotation equivariant Minkowski valuation \Phi that is weakly monotone maps the space of convex bodies with a C^2 support function into itself. As an application, we prove that if \Phi is in addition even or a mean section operator, then Euclidean balls are its only fixed points in some C^2 neighborhood of the unit ball. Our approach unifies and extends previous results by Ivaki [J. Funct. Anal. 272 (2017), pp. 5144–5161] and the second author together with Schuster [Adv. Math. 392 (2021), paper no. 108017, 33]. [ABSTRACT FROM AUTHOR]

Accurate prediction of remaining useful life (RUL) is crucial for predictive maintenance of industrial systems. Although data-driven RUL prediction methods have received considerable attention, they typically require massive run-to-failure (R2F) data which is often unavailable in practice. If not properly addressed, training with a limited number of R2F trajectories not only leads to large errors in RUL prediction, but also causes difficulty in quantifying the prediction uncertainty. To address the above challenge, this paper proposes a Bayesian ensemble RUL prediction method that combines mode-dependent relevance vector machine (RVM) and trajectory similarity. Firstly, the proposed approach clusters historical R2F trajectories of unequal lengths into different degradation modes, and constructs RVM and similarity based predictions with improved accuracy by using mode-dependent libraries of kernel functions and similar trajectories. Secondly, the proposed Bayesian ensemble scheme fuses the RVM and similarity based predictions, and quantifies the associated prediction uncertainty even though the number of historical R2F trajectories are limited. In two case studies involving bearings and batteries, using only 11 and 16 R2F trajectories as training data, respectively, the proposed method reduces the mean absolute percentage error of RUL prediction by more than 20% compared to three existing methods. • Investigate RUL prediction using a limited number of run-to-failure trajectories. • Perform mode-dependent prediction to address different degradation modes. • Propose a Bayesian ensemble approach fusing RVM and similarity based predictions. • Generate confidence intervals for RUL predictions without using massive data. • Achieve smaller prediction errors with lower variance compared to existing methods. [ABSTRACT FROM AUTHOR]

Learned distance metrics measure the difference of the data according to the intrinsic properties of the data points and classes. Distance metric learning approaches are typically used to linearly distinguish the samples of different classes and do not perform well on real-world nonlinear data classes. A kernel-based nonlinear distance metric learning approach is proposed in this article which exploits the density of multimodal classes to properly differentiate the classes while reducing the within-class separation. Here, multimodality refers to the disjoint distribution of a class, resulting in each class having multiple density components. In the proposed kernel density-based distance metric learning approach, kernel trick is applied on the original data and maps the data to a higher-dimensional space. Then, given the possibility of multimodal classes, a mixture of multivariate Gaussian densities is considered for the distribution of each class. The number of components is calculated using a density-based clustering approach, and then the parameters of the Gaussian components are estimated using maximum a posteriori density estimation. Then, an iterative method is used to maximize the Bhattacharya distance among the classes' Gaussian mixtures. The distance among the external components is increased, while the distance among samples of each component is decreased to provide a wide between-class margin. The results of the experiments show that using the proposed approach significantly improves the efficiency of the simple K nearest neighbor algorithm on the imbalanced data set, but when the imbalance ratio is very high, the kernel function does not have a significant effect on the efficiency of the distance metric. [ABSTRACT FROM AUTHOR]

Interior-point methods (IPMs) for linear programming (LP) are generally based on the logarithmic barrier function. Peng et al. (J. Comput. Technol. 6: 61–80, 2001) were the first to propose non-logarithmic kernel functions (KFs) for solving IPMs. These KFs are strongly convex and smoothly coercive on their domains. Later, Bai et al. (SIAM J. Optim. 15(1): 101–128, 2004) introduced the first KF with a trigonometric barrier term. Since then, no new type of KFs were proposed until 2020, when Touil and Chikouche (Filomat. 34(12): 3957–3969, 2020; Acta Math. Sin. (Engl. Ser.), 38(1): 44–67, 2022) introduced the first hyperbolic KFs for semidefinite programming (SDP). They established that the iteration complexities of algorithms based on their proposed KFs are O (n 2 3 log n ϵ) and O (n 3 4 log n ϵ) for large-update methods, respectively. The aim of this work is to improve the complexity result for large-update method. In fact, we present a new parametric KF with a hyperbolic barrier term. By simple tools, we show that the worst-case iteration complexity of our algorithm for the large-update method is O (n log n log n ϵ) iterations. This coincides with the currently best-known iteration bounds for IPMs based on all existing kind of KFs. The algorithm based on the proposed KF has been tested. Extensive numerical simulations on test problems with different sizes have shown that this KF has promising results. [ABSTRACT FROM AUTHOR]

Based on the theory of nonlocal elasticity and nonlocal heat conduction, a new dual-phase-lag heat conduction model with memory dependent effect is proposed in this article to explore the thermodynamic behavior of functionally graded rotating piezoelectric rods under the action of moving heat sources. Assuming that the material properties of functionally graded piezoelectric rods vary exponentially along the length direction, the end of the rod is rigid and fixed without voltage. Use Laplace transform to transform the problem into the spatial domain and perform analytical solutions, then use inverse Laplace transform to obtain the time-domain solution. Numerical solutions were performed for dimensionless displacement, temperature, electric potential, and stress, and the variation patterns of the physical quantities involved were described in graphical form. The calculation provides the effects of functional gradient non-uniformity index, thermal nonlocal parameters, kernel function, and viscoelastic parameters on the physical quantities involved. [ABSTRACT FROM AUTHOR]

Inclusive green growth (hereafter "IGG"), as a green and intensive development mode that considers both fairness and efficiency, environmental protection and development, is crucial for achieving sustainable development. New quality productive forces (hereafter "NQPFs") have become a novel and significant factor in promoting IGG. This study aims to examine the connection between NQPFs and IGG. Based on the data from 283 Chinese cities between 2010 and 2021, the "CRITIC-entropy value" objective combination weighting method is adopted to establish comprehensive indicator system of NQPFs and IGG in this paper. The spatiotemporal characteristics, mutual relationship and influencing mechanism of NQPFs and IGG are evaluated based on kernel density function, panel fixed effect model and spatial Durbin model. The results show that both NQPFs and IGG in China have shown a steady upward trend. NQPFs can significantly promote IGG, and economic agglomeration and technological innovation are important approaches to their interaction. In the period of high Internet penetration and in developed cities, the role of NQPFs in promoting IGG is more obvious. There is also a double threshold effect of financial development in this promotion process. With financial development improving, this promotion effect is significantly enhanced. Our research advocates promoting IGG by enhancing NQPFs, thereby protecting the earth's ecological environment and attaining long-term sustainability of human society. [ABSTRACT FROM AUTHOR]

The periodical dynamics of a G0 cell cycle model of pluripotential stem cells is analyzed by DDE‐Biftool software. The cell cycle model is impressed by modeling the optional choice of Hill function, which is benefited by Fourier transformation. The cell cycle is based on DDEs with distributed time delay, in which the kernel function is denoted by Gamma‐distribution expression. Hopf bifurcation of the linear version of the cell cycle model with distribution time delay is analyzed analytically. The periodical solution continuation is simulated by the artificial handbook of DDE‐Biftool software. With the discrete time delay, the complex behavior of adding‐period bifurcation and period‐doubling bifurcation are simulated. With distribution time delay, the continuation work of the homoclinic solution is done, and the homoclinic bifurcation line crosses the generalized Hopf point nearly. JEL Classification: 34C25, 34K18, 37G15 [ABSTRACT FROM AUTHOR]

Niche trajectory analysis is a promising framework for modeling spatially continuous variations of the tissue microenvironment. However, the existing approach is limited by its requirement of cell‐type annotation as a necessary input, which can lead to unwanted technical variations. To overcome this limitation, a new kernel‐based strategy is presented that models the structural composition of a niche as a continuous function in the gene expression space, thereby obviating the need for cell‐type annotation. Further integration with cell‐type deconvolution analysis extends its application to datasets with any spatial resolution. Applying this strategy to real datasets indicates enhanced performance in robustness and accuracy and provides new insights into injury or disease‐associated tissue microenvironment changes. As such, a useful tool for spatial transcriptomics data analysis is provided. [ABSTRACT FROM AUTHOR]

A new kernel function, termed the closed-box kernel function, has been developed to address numerical simulation of transient heat conduction in the same medium. Firstly, this method is versatile and not limited to specific industrial scenarios or designated materials. Secondly, the method solves the spatial temperature at each time point only once, eliminating the need for multiple iterations. Thirdly, the method allows for controlled and adjustable simulation speed of heat conduction while maintaining high accuracy. After 24,700 iterations in the transient process, the relative error in temperature values is merely 0.000072. Fourthly, this numerical technique can break data dependency between spatial nodes, making it suitable for parallel computing with Graphics Processing Units (GPUs). The average speedup achieved is 94.0712 times faster compared to Central Processing Unit (CPU) computations. Finally, we provide mathematical examples to verify the correctness and accuracy of this numerical approach and present a computational framework for parallel computing in the Visual Studio (VS) programming environment to demonstrate its practicality in engineering applications. [ABSTRACT FROM AUTHOR]

In this study, we investigate the application of support vector machines utilizing a radial basis function kernel for predicting nuclear -decay half-lives. Our approach integrates a comprehensive set of physics-derived features, including characteristics derived from nuclear structure, to systematically evaluate their impact on predictive accuracy. In addition to traditional parameters such as proton and neutron numbers, as well as terms based on the liquid drop model (e.g., volume, surface, Coulomb features), we incorporate decay energies and orbital angular momentum quantum numbers for both parent and daughter nuclei. Our analysis of 2232 nuclear data points demonstrates that the use of the radial basis function kernel yields predictive models with root mean square errors of 0.819 (for set1) and 0.352 (for set2), aligning with results obtained from comparable machine learning methodologies. Furthermore, Shapley additive explanations values highlight the predominant role of parent nuclei in predicting -decay half-lives within the support vector machines. These results highlight the effectiveness of machine learning in nuclear structure research, opening up new possibilities for predicting the -decay half-lives of previously unstudied nuclei. [ABSTRACT FROM AUTHOR]

In this paper, we consider the principal spectral theory for the nonlocal dispersal eigenvalue problem (1) d ρ p [ ∫ Ω J ρ (x − y) u (y) d y − u (x) ] + κ ρ q [ ∫ Ω G ρ (x − y) u (y) d y − u (x) ] + a (x) u (x) = − λ u (x) , x ∈ Ω ¯ , where Ω ⊂ R N is a bounded smooth domain, J ρ (x) = ρ N J (ρ x) , G ρ (x) = ρ N G (ρ x) , the kernel functions J (x) and G (x) are nonnegative, J (x) is symmetric, the parameter ρ is positive, d , κ are positive, p , q are given constants, and a ∈ C (Ω ¯). We investigate the limiting behavior of the principal spectral point or generalized principal eigenvalue of (1) as ρ → ∞ and ρ → 0. When ρ ≫ 1 , the nonlocal dispersal operator u (⋅) ↦ d ρ p (∫ Ω J ρ (⋅ − y) u (y) d y − u (⋅)) + κ ρ q (∫ Ω G ρ (⋅ − y) u (y) d y − u (⋅)) + a (⋅) u (⋅) with ν 0 ≠ 0 behaves like the elliptic operator u (⋅) ↦ d c 0 ρ p − 2 Δ u − κ ρ q − 1 ν 0 ⋅ ∇ u + a (⋅) u (⋅) on Ω with Dirichlet boundary condition on ∂Ω, where c 0 = 1 2 N ∫ R N J (y) | y | 2 d y , ν 0 = 〈 ∫ R N G (x) x 1 d x , ∫ R N G (x) x 2 d x , ⋯ , ∫ R N G (x) x N d x 〉. The results obtained in the paper are novel when the dispersal kernel function G (x) is asymmetric. Moreover, when G is asymmetric with ν 0 ≠ 0 , and p ≥ 2 , q > p − 1 or p < 2 , q > 1 , it is seen that the limiting behavior of the generalized principal eigenvalue of (1) as ρ → ∞ is strikingly different from the limiting behavior of the principal eigenvalue of the elliptic operator u (⋅) ↦ d c 0 ρ p − 2 Δ u − κ ρ q − 1 ν 0 ⋅ ∇ u + a (⋅) u (⋅) on Ω with Dirichlet boundary condition on ∂Ω. The main results are used to study the asymptotic dynamics of nonlinear nonlocal dispersal problems. [ABSTRACT FROM AUTHOR]

In this paper, we examine the effect of a new free boundary condition on the propagation dynamics of the nonlocal diffusion model considered in [9] , which describes the spreading of a species with density u (t , x) and population range [ g (t) , h (t) ] ⊂ R. The existing free boundary condition can be written as { h ′ (t) = μ ∫ g (t) h (t) u (t , x) W J (h (t) − x) d x , g ′ (t) = − μ ∫ g (t) h (t) u (t , x) W J (x − g (t)) d x , where W J (x) = ∫ x + ∞ J (y) d y , and J is the kernel function of the nonlocal diffusion operator in the model. In the new free boundary condition, we replace W J by a general nonnegative locally Lipschitz continuous function W with W (0) > 0 , independent of J. This represents a very different assumption that the movement of the range boundary of the species is independent of its dispersal strategy, as in [20]. Our analysis shows that the dynamics of the model with the new free boundary condition resembles that of the old model except in the case that J is thin-tailed and ∫ 0 ∞ W (x) d x = ∞ , where new propagation phenomena appear. [ABSTRACT FROM AUTHOR]

This paper concerns a nonlocal diffusion problem with a free boundary. We first give accurate estimates on the longtime behaviors of solution by constructing suitably upper and lower solutions. In particular, for two important kinds of kernel functions, one of which is compactly supported and the other behaves like |x|−γ with γ ∈ (1, 2] near infinity, some sharp estimates on the longtime behaviors and rates of accelerated spreading are obtained. Then the limiting behaviors of the solution pair of a semi-wave problem and asymptotic dynamics of a nonlocal diffusion problem on half space are given, respectively. Finally, we investigate the limiting profiles of this free boundary problem when the expanding coefficient of free boundary converges to 0 and ∞, respectively. [ABSTRACT FROM AUTHOR]

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This manuscript examines the effects of memory-dependent and fractional-order derivatives on a novel generalized piezo-thermo-elastic semiconductor model. The medium is homogenous and orthotropic, subjected to photo-thermal excitation. The governing equations include fractional-order parameters, relaxation time, time delay, and kernel function tailored to specific problem requirements. Normal mode method use to solve the equations, yielding analytical expressions. Graphical representations show physical field distribution across various fractional-order parameters, kernel functions, time delay, and frequency values. This study has the potential to advance precise model development and future simulations. [ABSTRACT FROM AUTHOR]

AbstractMany methods have been developed to analyze complex data, such as non-Euclidean shape, network, and manifold data. However, there is a lack of methods for studying interactions among complex data. In this article, we first propose a novel kernel function for a metric space and construct its associated reproducing kernel Hilbert space. The new nonstationary kernel function provides a flexible and powerful tool for learning complex structures in non-Euclidean data. We then construct an analysis of variance (ANOVA) decomposition of the nonparametric regression function defined on metric space, which provides a hierarchical structure for investigating the main effects and interactions. We develop estimation and computational methods for a semi-parametric model with a multivariate function on a product of metric spaces modeled by the ANOVA decomposition. We establish the convergence rates of parameter and nonparametric function estimates. The application of the proposed methods to the Alzheimer’s Disease Neuroimaging Initiative hippocampus shape data confirms some existing and suggests some new interactions among hippocampal regions. Simulations indicate that the proposed methods work well. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work. [ABSTRACT FROM AUTHOR]

The piezoelectricity of piezoceramics considerably depends on the doped compositions. However, the conventional trial-and-error approach to composition design is time-consuming and inefficient when searching for high-performance piezoceramics with various dopants. In this study, we introduce a data-driven framework to accelerate the design and discovery of lead-free (K,Na)NbO 3 (KNN) materials with enhanced piezoelectric performance. The proposed framework integrates machine learning with feature engineering, surrogate-based optimisation, and experimentation in an active learning loop. Using feature engineering techniques, we demonstrated that the piezoelectric coefficient d 33 of KNN materials can be predicted based on a set of elemental and atomic properties. We evaluated six machine learning models and found that support vector regression with a radial basis function kernel achieved high accuracy in predicting the d 33 values of KNN ceramics. After three iterations of experimentation and optimisation, we identified an optimal composition with a relatively high d 33 of ∼353 pC/N from thousands of possible compositions using a pure exploitation strategy. This study demonstrates an efficient and systematic approach to the composition design of KNN-based piezoceramics, which can be applied to investigate the diverse functional properties of other materials. [ABSTRACT FROM AUTHOR]

The kernel method is a tool that converts data to a kernel space where operation can be performed. When converted to a high-dimensional feature space by using kernel functions, the data samples are more likely to be linearly separable. Traditional machine learning methods can be extended to the kernel space, such as the radial basis function (RBF) network. As a kernel-based method, support vector machine (SVM) is one of the most popular nonparametric classification methods, and is optimal in terms of computational learning theory. Based on statistical learning theory and the maximum margin principle, SVM attempts to determine an optimal hyperplane by addressing a quadratic programming (QP) problem. Using Vapnik–Chervonenkis dimension theory, SVM maximizes generalization performance by finding the widest classification margin within the feature space. In this paper, kernel machines and SVMs are systematically introduced. We first describe how to turn classical methods into kernel machines, and then give a literature review of existing kernel machines. We then introduce the SVM model, its principles, and various SVM training methods for classification, clustering, and regression. Related topics, including optimizing model architecture, are also discussed. We conclude by outlining future directions for kernel machines and SVMs. This article functions both as a state-of-the-art survey and a tutorial. [ABSTRACT FROM AUTHOR]

In this paper, a novel hybrid method based on the finite element method (FEM) and physics-informed kernel function neural network (PIKFNN) is proposed. The method is applied to predict underwater acoustic propagation induced by structural vibrations in diverse ocean environments, including the unbounded ocean, deep ocean, and shallow ocean. In the hybrid method, PIKFNN is regarded as an improved shallow physics-informed neural network (PINN) in which the activation function in the PINN is replaced with a physics-informed kernel function (PIKF). This ensures the integration of prior physical information into the neural network model. Moreover, PIKFNN circumvents embedding the governing equations into the loss function in the PINN and requires only training on boundary data. By using Green's function as PIKF and the structural-acoustic coupling response information obtained from the FEM as training data, PIKFNN can inherently capture the Sommerfeld radiation condition at infinity, which are naturally suitable for predicting ocean acoustic propagation. Numerical experiments demonstrate the accuracy and feasibility of FEM-PIKFNN in comparison with analytical solutions and finite element results. [ABSTRACT FROM AUTHOR]

Small mammal populations fluctuate significantly in abundance over time, affecting the entire food web. However, changes in their occupancy across a landscape receive less attention. While habitat features are relevant for some predators, diet specialization and prey distribution and abundance might play an important role in shaping predator populations. Using a multi‐season occupancy analysis, we examined the spatio‐temporal patterns of Mediterranean mesocarnivores—common genet, stone marten and red fox—focusing on the factors that influence their occupancy dynamics, particularly small mammal occupancy as a prey resource. Data was collected from December 2020 to May 2021 in the Sant Llorenç del Munt i l'Obac Natural Park using a camera‐trap grid. We analysed small mammal occupancy dynamics and used these as covariates in predator occupancy models to explore predator–prey relationships. Additionally, we included the occurrence of each carnivore as a predictor for interspecific analysis, and kernel density functions were used to assess daily activity overlaps. Results showed that interspecific competition significantly affected mesocarnivore occupancy, as genet occupancy was negatively correlated with the red fox occupancy. Although prey occurrence did not influence mesocarnivore occupancy, it did affect detectability, with genet and stone marten detectability being positively related to small mammal presence and high daily activity overlap between predators and prey. This suggests that mesopredators respond rapidly to prey abundance, highlighting the intricate temporal dependence between predator activity and prey occupancy. Dynamic occupancy and activity models provide a deeper understanding of predator–prey relationships at the local scale. [ABSTRACT FROM AUTHOR]

In this article, we present an adaptive residual subsampling scheme designed for kernel based interpolation. For an optimal choice of the kernel shape parameter we consider some cross validation (CV) criteria, using efficient algorithms of k-fold CV and leave-one-out CV (LOOCV) as a special case. In this framework, the selection of the shape parameter within the residual subsampling method is totally automatic, provides highly reliable and accurate results for any kind of kernel, and guarantees existence and uniqueness of the kernel based interpolant. Numerical results show the performance of this new adaptive scheme, also giving a comparison with other computational techniques. [ABSTRACT FROM AUTHOR]