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Support Vector Machines (SVMs) can learn from high-dimensional and small amounts of training data, thanks to effective optimization methods and a diverse set of kernel functions (KFs). The adaptability of SVM to numerous real-world problems has increased interest in the SVM method, and studies conducted with this method carry significant weight in various fields. The fixed parameter "AtanK" for KFs must be specified before the SVM model training process. Therefore, determining the appropriate kernel parameter values can be timE−consuming and may lead to slow convergence of the SVM model. On the other hand, the method provides faster and more robust convergence due to the adaptive parameter in the SVM model. In this study, a new Adaptive Arctan (AA) KF, tailored to the characteristics of different datasets, is proposed as an enhancement to the AtanK KF for the SVM algorithm. The proposed AA KF is compared with experimental results on 30 public KEEL and UCI datasets, alongside AtanK, adaptive Gaussian, Radial Basis Function, linear, and polynomial KFs. The results demonstrate that the proposed AA KF outperforms the other KFs, and it exhibits superior learning ability. [ABSTRACT FROM AUTHOR]

The goal of this paper is to establish Green function estimates for a class of purely discontinuous symmetric Markov processes with jump kernels degenerate at the boundary and critical killing potentials. The jump kernel and the killing potential depend on several parameters. We establish sharp two-sided estimates on the Green functions of these processes for all admissible values of the parameters involved. Depending on the regions where the parameters belong, the estimates on the Green functions are different. In fact, the estimates have three different forms. As applications, we prove that the boundary Harnack principle holds in certain region of the parameters and fails in some other region of the parameters. Together with the main results of our previous paper [Potential Anal., online, 2021], we completely determine the region of the parameters where the boundary Harnack principle holds. [ABSTRACT FROM AUTHOR]

Suppose V ν (·) is the pseudo-variance function of the Cauchy–Stieltjes Kernel (CSK) family K - (ν) generated by a non degenerate probability measure ν on the positive real line. Denote by Φ (ν) the law of large numbers for free multiplicative convolution given in [17]. An explicit expression of Φ (ν) is given in [14] in terms of the pseudo-variance function V ν (.) . In this paper, we give explicitly in terms of the pseudo-variance function V ν (.) the limiting distributions Φ (ν ⊠ t) , Φ ((D 1 / s (ν ⊞ s)) ⊠ t) , Φ ((D 1 / r (ν ⊎ r)) ⊠ t) and Φ ((B r (ν)) ⊠ t) for s > 1 , t > 1 and r > 0 , where B r (ν) = (ν ⊞ 1 + r) ⊎ 1 1 + r and D c (ν) denotes the dilation of measure ν by a number c ≠ 0 . Some examples of calculations of Φ (ν ⊠ t) , Φ ((D 1 / s (ν ⊞ s)) ⊠ t) , Φ ((D 1 / r (ν ⊎ r)) ⊠ t) and Φ ((B r (ν)) ⊠ t) are given for probability measures ν of importance in noncommutative probability. [ABSTRACT FROM AUTHOR]

Kernel methods are often used for nonlinear regression and classification in statistics and machine learning because they are computationally cheap and accurate. The wavelet kernel functions based on wavelet analysis can efficiently approximate any nonlinear functions. In this article, we construct a novel wavelet kernel function in terms of random wavelet bases and define a linear vector space that captures nonlinear structures in reproducing kernel Hilbert spaces (RKHS). Based on the wavelet transform, the data are mapped into a low-dimensional randomized feature space and convert kernel function into operations of a linear machine. We then propose a new Bayesian approximate kernel model with the random wavelet expansion and use the Gibbs sampler to compute the model's parameters. Finally, some simulation studies and two real datasets analyses are carried out to demonstrate that the proposed method displays good stability, prediction performance compared to some other existing methods. [ABSTRACT FROM AUTHOR]

In this paper, the static and dynamic analysis of the higher-order shear deformation nanobeam is investigated within the framework of the two-phase local/nonlocal integral model, in which, the stress is described as the integral convolution form between the strain field and a decay kernel function to address the long-range force interactions in the domain. Based on the principle of minimum potential energy, the finite element formulation of the nonlocal higher-order shear deformation theory nanobeams is derived in a general sense through finite element method (FEM). The explicit expressions of the stiffness, geometric stiffness and mass stiffness matrix of the higher-order shear deformation theory nanobeams are derived directly. The efficiency and accuracy of the developed finite element model of higher-order shear deformation nanobeam are validated by conducting a comparation with the existing analysis results in the researches. Furthermore, under different loading and supported conditions, the effect of nonlocal parameter, nonlocal phase parameter and slenderness ratio on the bending, buckling and free vibration responses of higher-order shear deformation theory nanobeams is investigated in detail. [ABSTRACT FROM AUTHOR]

In this paper, we address the challenge of ensuring stability in bipedal walking robots and exoskeletons. We explore the feasibility of real-time implementation for the Predicted Step Viability algorithm (PSV), a complex multi-step optimization criterion for planning future steps in bipedal gait. To overcome the high computational cost of the PSV algorithm, we performed an analysis using 11 classification algorithms and a stacking strategy to predict if a step will be stable or not. We generated three datasets of increasing complexity through PSV simulations to evaluate the classification performance. Among the classifiers, k Nearest Neighbors, Support Vector Machine with Radial Basis Function Kernel, Decision Tree, and Random Forest exhibited superior performance. Multi-Layer Perceptron also consistently performed well, while linear-based algorithms showed lower performance. Importantly, the use of stacking did not significantly improve performance. Our results suggest that the feature vector applied with this approach is applicable across various robotic models and datasets, provided that training data is balanced and sufficient points are used. Notably, by leveraging classifiers, we achieved rapid computation of results in less than 1 ms, with minimal computational cost. [ABSTRACT FROM AUTHOR]

Shrimp fry counting is an important task for biomass estimation in aquaculture. Accurate counting of the number of shrimp fry in tanks can not only assess the production of mature shrimp but also assess the density of shrimp fry in the tanks, which is very helpful for the subsequent growth status, transportation management, and yield assessment. However, traditional manual counting methods are often inefficient and prone to counting errors; a more efficient and accurate method for shrimp fry counting is urgently needed. In this paper, we first collected and labeled the images of shrimp fry in breeding tanks according to the constructed experimental environment and generated corresponding density maps using the Gaussian kernel function. Then, we proposed a multi-scale attention fusion-based shrimp fry counting network called the SFCNet. Experiments showed that our proposed SFCNet model reached the optimal performance in terms of shrimp fry counting compared to CNN-based baseline counting models, with MAEs and RMSEs of 3.96 and 4.682, respectively. This approach was able to effectively calculate the number of shrimp fry and provided a better solution for accurately calculating the number of shrimp fry. [ABSTRACT FROM AUTHOR]

When overdispersion and zero-inflated feature are both concerned, Zero-inflated negative binomial (ZINB) model tends to be more appropriate than the popular Zero-inflated Poisson (ZIP) model most used. Moreover, when some variables that model the mean response and the probability of zero-excess have missing data, ignoring the missing or using inappropriate methods is likely to produce questionable estimates. To remedy this problem, we propose a non-parametric and parametric inverse probability weighting (IPW) estimators to estimate parameters of the ZINB models. In particular, the generalized additive models (GAMs), the indicator or kernel smoothing functions are considered for the non-parametric approaches. Meanwhile, logistic model is used to estimate selection probability in parametric method. The performance of our proposed methods are investigated by conducting several simulation studies and exploring a real example analysis. We aim to develop and compare several IPW estimators in order to recommend the most accurate approaches. Numerical illustrations support that the semiparametric IPW methods which were based on the kernel smoothing or indicator function weights tend to produce the best results, because they tend to outperform the GAMs and parametric IPW estimates in terms of efficiency. Hence we recommend that the first approach to be used in the analysis for the ZINB model should be the semiparametric IPW based on the kernel smoothing or indicator function weights. The GAM and parametric weighting estimators are also quite good, as long as their related estimated weights are correct. • This study proposes the parameter estimations on Zero-inflated Negative Binomial (ZINB) model with missing data. • The inverse probability weighting (IPW) method is considered in this work. • We propose the three different approaches include: parametric, non-parametric and generalized additive models. • We compared the proposed approaches with the easiest method of this topic which is the complete case (CC) method. • Many numerical simulations and a real data sets includes the infected blood cells (IBC) was conducted in this study. [ABSTRACT FROM AUTHOR]

The goal of blind image super-resolution (BISR) is to recover the corresponding high-resolution image from a given low-resolution image with unknown degradation. Prior related research has primarily focused effectively on utilizing the kernel as prior knowledge to recover the high-frequency components of image. However, they overlooked the function of structural prior information within the same image, which resulted in unsatisfactory recovery performance for textures with strong self-similarity. To address this issue, we propose a two stage blind super-resolution network that is based on kernel estimation strategy and is capable of integrating structural texture as prior knowledge. In the first stage, we utilize a dynamic kernel estimator to achieve degradation presentation embedding. Then, we propose a triple path attention groups consists of triple path attention blocks and a global feature fusion block to extract structural prior information to assist the recovery of details within images. The quantitative and qualitative results on standard benchmarks with various degradation settings, including Gaussian8 and DIV2KRK, validate that our proposed method outperforms the state-of-the-art methods in terms of fidelity and recovery of clear details. The relevant code is made available on this link as open source. [ABSTRACT FROM AUTHOR]

Due to the restrictive growth and/or monotonicity requirements inherent in their employment, classical iterative fixed-point theorems are rarely used to approximate solutions to an integral operator with Green's function kernel whose fixed points are solutions of a boundary value problem. In this paper, we show how one can decompose a fixed-point problem into multiple fixed-point problems that one can easily iterate to approximate a solution of a differential equation satisfying one boundary condition, then apply a bisection method in an intermediate value theorem argument to meet a second boundary condition. Error estimates on the iterates are also established. The technique will be illustrated on a second-order right focal boundary value problem, with an example provided showing how to apply the results. [ABSTRACT FROM AUTHOR]

This study proposes multivariate kernel density estimation by stagewise minimization algorithm based on U-divergence and a simple dictionary. The dictionary consists of an appropriate scalar bandwidth matrix and a part of the original data. The resulting estimator brings us data-adaptive weighting parameters and bandwidth matrices, and provides a sparse representation of kernel density estimation. We develop the non-asymptotic error bound of the estimator that we obtained via the proposed stagewise minimization algorithm. It is confirmed from simulation studies that the proposed estimator performs as well as, or sometimes better than, other well-known density estimators. [ABSTRACT FROM AUTHOR]

The quality of visual media is critically impacted by low illumination and the presence of airborne particulates, leading to challenges in brightness balance, color saturation, and texture clarity which are detrimental to various applications in image processing and computer vision. Addressing these challenges, this study introduces a novel image enhancement algorithm that significantly improves the quality of degraded images. Our proposed method, the multi-channel phase activation and multi-constraint dark channel prior (MMDCP), leverages an innovative approach by integrating the phase-adjusted Gaussian kernel function for brightness channel optimization in the Fourier transform frequency domain. This optimization is enhanced through the application of a saturated dark channel prior, achieving simultaneous brightness enhancement and color fidelity. Furthermore, we refine the dark channel prior deblurring algorithm by incorporating intensity, brightness, and color constraints to correct overexposure issues and color offsets in the reconstructed images. The efficacy of the MMDCP algorithm is demonstrated through extensive experimentation, comparing it against six contemporary image enhancement algorithms using two types of objective indicators and subjective assessments across four public datasets. The MMDCP algorithm consistently outperforms the existing methods, with a notable average improvement of 20% in PSNR and 19.6% in SSIM metrics, substantiating its superiority in enhancing brightness, detail, and color accuracy. This study's results underline the MMDCP algorithm's robustness and versatility in improving image quality across various conditions, including daytime, nighttime, indoor, and outdoor settings. [ABSTRACT FROM AUTHOR]

The use of tunable metasurface technology to realize the underwater tracking function of submarines, which is one of the hotspots and difficulties in submarine design. The structure-to-sound-field metasurface design approach is a highly iterative process based on trial and error. The process is cumbersome and inefficient. Therefore, an inverse design method was proposed based on parallel deep neural networks. The method took the global and local target sound field feature information as input and the metasurface physical structure parameters as output. The deep neural network was trained using a kernel loss function based on a radial basis kernel function, which established an inverse mapping relationship between the desired sound field to the metasurface physical structure parameters. Finally, the sound field intensity modulation at a localized target range was achieved. The results indicated that within the regulated target range, this method achieved an average prediction error of less than 5 dB for 92.9% of the sample data. [ABSTRACT FROM AUTHOR]

Gaussian Radial Basis Function Kernels are the most-often-employed kernel function in artificial intelligence for providing the optimal results in contrast to their respective counterparts. However, our understanding surrounding the utilization of the Generalized Gaussian Radial Basis Function across different machine learning algorithms, such as kernel regression, support vector machines, and pattern recognition via neural networks is incomplete. The results delivered by the Generalized Gaussian Radial Basis Function Kernel in the previously mentioned applications remarkably outperforms those of the Gaussian Radial Basis Function Kernel, the Sigmoid function, and the ReLU function in terms of accuracy and misclassification. This article provides a concrete illustration of the utilization of the Generalized Gaussian Radial Basis Function Kernel as mentioned earlier. We also provide an explicit description of the reproducing kernel Hilbert space by embedding the Generalized Gaussian Radial Basis Function as an L 2 − measure, which is utilized in implementing the analysis support vector machine. Finally, we provide the conclusion that we draw from the empirical experiments considered in the manuscript along with the possible future directions in terms of spectral decomposition of the Generalized Gaussian Radial Basis Function. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the viscoelastic wave equation with variable coefficients and a delay, which is subject to nonlinear and nonlocal boundary dissipation. The existence of strong and weak solutions is obtained by means of Faedo-Galerkin approximation and denseness argument. By introducing an equivalent energy functional and using the Riemannian geometry method, we show the general decay rate of energy when kernel function satisfies some sufficient small conditions that we provide the range accurately. [ABSTRACT FROM AUTHOR]

This article studies the error function and its invariance properties in the convolutional kernel function of bone fractal operators. Specifically, the following contents are included: (1) demonstrating the correlation between the convolution kernel function and error function of bone fractal operators; (2) focusing on the main part of bone fractal operators: p + α 2 -type differential operator, discussing the convolutional kernel function image; (3) exploring the fractional-order correlation between the error function and other special functions from the perspective of fractal operators. [ABSTRACT FROM AUTHOR]

Asymmetry plays a significant role in the transmission dynamics in novel discrete fractional calculus. Few studies have mathematically modeled such asymmetry properties, and none have developed discrete models that incorporate different symmetry developmental stages. This paper introduces a Taylor monomial falling function and presents some properties of this function in a delta fractional model with Green's function kernel. In the deterministic case, Green's function will be non-negative, and this shows that the function has an upper bound for its maximum point. More precisely, in this paper, based on the properties of the Taylor monomial falling function, we investigate Lyapunov-type inequalities for a delta fractional boundary value problem of Riemann–Liouville type. [ABSTRACT FROM AUTHOR]

We present results for the short-distance window observable of the hadronic vacuum polarization contribution to the muon g – 2, computed via the time-momentum representation (TMR) in lattice QCD. A key novelty of our calculation is the reduction of discretization effects by a suitable subtraction applied to the TMR kernel function, which cancels the leading -behaviour at short distances. To compensate for the subtraction, one must substitute a term that can be reliably computed in perturbative QCD. We apply this strategy to our data for the vector current collected on ensembles generated with 2 + 1 flavours of O(a)-improved Wilson quarks at six values of the lattice spacing and pion masses in the range 130 – 420 MeV. Our estimate at the physical point contains a full error budget and reads = 68.85(14)stat (42)syst·10−10, which corresponds to a relative precision of 0.7%. We discuss the implications of our result for the observed tensions between lattice and data-driven evaluations of the hadronic vacuum polarization. [ABSTRACT FROM AUTHOR]

In this paper, Gaussian Process Regression (GPR)‐based models which use the Bayesian approach to regression analysis problem such as load forecasting (LF) are proposed. The GPR is a non‐parametric kernel‐based learning method having the ability to provide correct predictions with uncertainty in measurements. The proposed model provides an hourly and monthly load forecast for an Australian city and four Indian cities in the Maharashtra state. Twelve GPR models are trained with historical datasets including hourly load and environmental data. To evaluate the trained model, the actual and predicted load demand curve is plotted and mean average percentage error (MAPE) is calculated corresponding to different kernel functions of the GPR model. To the best of the author's knowledge, the prediction of load demand using GPR for Indian cities of Maharashtra state has been made for the first time. The calculated MAPE in LF is 0.15% for Australia and 0.002%, 0.209%, 0.077%, and 0.140% for Indian cities viz. Nasik, Bhusawal, Kolhapur, and Aurangabad, respectively. The test results illustrate that minimum MAPE in load prediction is obtained using the proposed model that is GPR with 'Exponential' kernel functions. Furthermore, the comparative analysis with the existing approaches confirms the dominance of the proposed model. [ABSTRACT FROM AUTHOR]

Snow cover has a significant impact on numerous ecological, climatic, and hydrological processes, particularly in high-latitude areas. Remote sensing data estimates of snow cover ranges than traditional surveying methods. Thus, the present study used Sentinel-2B satellite images to compare the performance of support vector machine (SVM) kernel functions and object-oriented fuzzy operators to estimate the snow cover area (SCA) on Alvand Mountain. The research data included four Sentinel-2B 10 m spatial resolution bands (B2, B3, B4, and B8) that were launched on March 6, 2020. In this study, linear, polynomial, radial, and sigmoid SVM kernel functions, as well as the object-oriented fuzzy operators (AND, OR, MGE, MAR, MGWE, and ALP), were used. The results indicated that AND algorithm, which represents a logical commonality, had the lowest return fuzzy value of 98% compared to other algorithms, thus, providing the overall highest accuracy. Based on these findings, the object-oriented processing method in digital image classification could provide the highest accuracy compared to the SVM kernel functions; that is because a wide range of information, such as texture, shape, position, content, and bandwidth, is associated with the objects in this classification method. Finally, the SCA in Alvand Mountain was estimated to be 604 km2 based on the object-based AND fuzzy operator. [ABSTRACT FROM AUTHOR]

The smoothed particle hydrodynamic technique is strongly based on the proper choice of interpolation functions. This statement is particularly relevant for the study of subsonic fluxes and turbulence, where inherent small errors in the averaging procedures introduce excessive damping on the smallest scales. To mitigate these errors, we can increase both the number of interpolating points and the order of the interpolating kernel function. However, this approach leads to a higher computational burden across all fluid regions. Ideally, the development of a single kernel function capable of effectively accommodating varying numbers of interpolating points in different fluid regions, providing good resolution and minimal errors would be highly desirable. In this work, we revisit and extend the main properties of a family of interpolators called Sinc kernels and compare them with the widely used family of Wendland kernels. We show that a linear combination of low- and high-order Sinc kernels generates good-quality interpolators, which are resistant to pairing instability while maintaining good sampling properties in a wide range of neighbour interpolating points, 60 ≤ nb ≤ 400. We show that a particular case of this linear mix of Sincs produces a well-balanced and robust kernel that improves previous results in the Gresho–Chan vortex experiment even when the number of neighbours is not large, while yielding a good convergence rate. Although such a mixing technique is ideally suited for Sinc kernels owing to their excellent flexibility, it can be easily applied to other interpolating families such as the B-splines and Wendland kernels. [ABSTRACT FROM AUTHOR]

This study focuses on adapting spectral clustering, a numeric data-clustering technique, for categorical and mixed-type data. The method enhances spectral clustering for categorical and mixed-type data with novel kernel functions, showing improved accuracy in real-world applications. Despite achieving better clustering for datasets with mixed variables, challenges remain in identifying suitable kernel functions for categorical relationships. [ABSTRACT FROM AUTHOR]

Spatiotemporally mapping winter wheat is imperative for informing and shaping global food security policies. Traditional mapping methods heavily rely on sufficient and reliable samples obtained through labor-intensive fieldwork and manual sample collection. However, these methods are time-consuming, costly, and lack timely and continuous data collection. To address these challenges and fully leverage remote sensing big data and cloud computing platforms like Google Earth Engine (GEE), this paper developed an algorithm for Auto-Generating Winter Wheat Samples for mapping (AGWWS). The AGWWS utilizes historical samples to determine the optimal migration threshold by measuring Spectral Angle Distance (SAD), Euclidean Distance (ED), and Near-Infrared band Difference Index (NIRDI). This facilitates the auto-generation of winter wheat sample sets for the years 2000, 2005, 2010, 2015, and 2021. Approximately two-thirds of the samples were allocated for training, with the remaining one-third used for validating the mapping method, employing the One-Class Support Vector Machine (OCSVM). The Huang–Huai–Hai (HHH) Plain, a major winter wheat production region, was selected to perform the algorithm and subsequent analysis on. Different combinations of the hyper-parameters, gamma and nu, of the OCSVM based on the Gaussian Radial Basis Function Kernel were tested for each year. Following correlation analysis between the winter wheat area derived from the generated maps and the national statistical dataset at the city level, the map with the highest corresponding R2 was chosen as the AGWWS map for each year (0.77, 0.77, 0.80, 0.86, and 0.87 for 2000, 2005, 2010, 2015, and 2021, respectively). The AGWWS maps ultimately achieved an average Overall Accuracy of 81.65%. The study then explores the Non-Grain Production of Winter Wheat (NGPOWW) by analyzing winter wheat change maps from 2000–2005, 2005–2010, 2005–2010, and 2015–2021 in the HHH Plain. Despite an overall increase in the total planted area of winter wheat, the NGPOWW phenomena has led to concerning winter wheat planting marginalization. Compensatory winter wheat areas are notably situated in mountainous and suburban cultivated lands with low qualities. Consequently, despite the apparent expansion in planted areas, winter wheat production is anticipated to be adversely affected. The findings highlight the necessity for improved cultivated land protection policies monitoring the land quality of the compensation and setting strict quota limits on occupations. [ABSTRACT FROM AUTHOR]

In this paper, we develop surrogate models that can replace expensive predictive models and account for uncertainties in real-time treatment planning for irreversible electroporation of liver tumors. Standard non-intrusive surrogate modeling techniques that account for the model uncertainty and reduce the computational cost, such as polynomial chaos expansion and Gaussian process regression with conventional kernels, often do not capture the true physical behavior of the treatment outcome as required in the context of treatment planning. We improve the Gaussian process regression model by modifying the kernel function to a non-stationary Gibbs kernel with a support vector machine-based classifier in its length scale definition. This proposed model is compared with the standard surrogates in terms of their performance and accuracy. Our model is able to accurately replicate the behavior of the biophysics-based predictive model. There is a decrease of at least 81% in the overall root-mean-square error for treatment outcome when compared to the Gaussian process regression model with conventional kernels. Furthermore, we illustrate the application of the proposed surrogate model in treatment planning to address a voltage optimization problem for complete tumor ablation. Surrogate-assisted treatment planning exhibited good performance while maintaining similar levels of accuracy in comparison to treatment planning based on biophysical models. Finally, the effect of uncertainty in tissue electrical conductivities on the optimal voltage value is discussed. • Gaussian process regression-based surrogates can replace physics-based predictive models for irreversible electroporation. • Gibbs kernel with a support vector machine-based classifier is able to model relative tumor ablation for treatment planning. • Numerical illustrations indicate good accuracy with the use of the proposed kernel when compared to popular kernel choices. • Surrogate-assisted treatment planning was performed to solve a voltage optimization problem for complete tumor ablation. • The effect of uncertainty in electrical conductivities on the optimal voltage for irreversible electroporation is studied. [ABSTRACT FROM AUTHOR]

This study introduces a novel method for predicting drilling pressure in bolt support systems by optimizing Gaussian process time series regression (GPR) using hybrid optimization algorithms. The research initially identified significant variations in prediction outcomes based on different kernel functions and historical points combinations in the GPR algorithm. To address this, we explored 160 distinct schemes combining 10 kernel functions and 16 historical points for numerical analysis. Applying three hybrid optimization algorithms—Genetic Algorithm-GPR (GA-GPR), Particle Swarm Optimization-GPR (PSO-GPR), and Ant Colony Algorithm-GPR (ACA-GPR)—we iteratively optimized these key parameters. The PSO-GPR algorithm emerged as the most effective, achieving an 80% prediction accuracy with a deviation range of 1–2 MPa, acceptable in practical drilling operations. This optimization led to the RQ kernel function with 18 historical points as the optimal combination, yielding an RMSE value of 0.0047246, in contrast to the least effective combination (E kernel function with 6 historical points) producing an RMSE of 0.035704. The final outcome of this study is a robust and efficient prediction system for underground bolt support drilling pressure, verified through practical application. This approach significantly enhances the accuracy and efficiency of support systems in geotechnical engineering, demonstrating the practical applicability of the PSO-GPR model in real-world scenarios. [ABSTRACT FROM AUTHOR]

In this paper, a kernel fraction low-power adaptive filtering algorithm based on lncosh function (KFLP-LHCF) is proposed for chaotic time series prediction. The algorithm combines the lncosh function with the kernel fractional low-power algorithm. The nonlinear saturation characteristic of the lncosh function is used to achieve resistance to impulse noise, and the fractional low power is used to suppress the influence of error mutation on the performance of the algorithm. In addition, by adjusting the scale factor, a balance can be achieved between convergence speed as well as steady-state performance. In the alpha noise environment, the proposed algorithm is used to predict and simulate two typical chaotic time series of Lorenz and Mackey–Glass. Experimental results show that the algorithm has better steady-state performance and lower steady-state error than other kernel adaptive filtering algorithms, provided that the convergence speed is similar. [ABSTRACT FROM AUTHOR]

Traffic time series anomaly detection has been intensively studied for years because of its potential applications in intelligent transportation. However, classical traffic anomaly detection methods often overlook the evolving dynamic associations between road network nodes, which leads to challenges in capturing the long-term temporal correlations, spatial characteristics, and abnormal node behaviors in datasets with high periodicity and trends, such as morning peak travel periods. In this paper, we propose a mirror temporal graph autoencoder (MTGAE) framework to explore anomalies and capture unseen nodes and the spatiotemporal correlation between nodes in the traffic network. Specifically, we propose the mirror temporal convolutional module to enhance feature extraction capabilities and capture hidden node-to-node features in the traffic network. Morever, we propose the graph convolutional gate recurrent unit cell (GCGRU CELL) module. This module uses Gaussian kernel functions to map data into a high-dimensional space, and enables the identification of anomalous information and potential anomalies within the complex interdependencies of the traffic network, based on prior knowledge and input data. We compared our work with several other advanced deep-learning anomaly detection models. Experimental results on the NYC dataset illustrate that our model works best compared to other models for traffic anomaly detection. [ABSTRACT FROM AUTHOR]

The diameter distribution of a given species of deciduous trees is well approximated by a Gamma distribution. Here we give new experimental evidence for this conjecture by analyzing deciduous tree size data in mature semi-natural forest and ancient, traditionally managed wood-pasture from Central Europe. These distribution functions collapse on a universal shape if the tree sizes are normalized to the mean value in the considered sample. A new evolutionary master equation is used to model the observed distribution. The model incorporates four ecological processes: tree growth, mortality, recruitment, and diversification. Utilizing simple and realistic kernel functions describing the first three, along with an assumed multiplicative dilution due to diversification, the stationary solution of the master equation yields the experimentally observed Gamma distribution. The model as it is formulated allows an analytically compact solution and has only two fitting parameters whose values are consistent with the experimental data related to these processes. We found that the equilibrium size distribution of tree species with different ecology, originating from two contrastingly different semi-natural ecosystem types can be accurately described by a single dynamical mean-field model. [ABSTRACT FROM AUTHOR]

Exploiting crossing symmetry, the hadron scale pion valence quark distribution function is used to predict the kindred elementary valence quark fragmentation function (FF). This function defines the kernel of a quark jet fragmentation equation, which is solved to obtain the full pion FFs. After evolution to a scale typical of FF fits to data, the results for quark FFs are seen to compare favourably with such fits. However, the gluon FF is markedly different. Notably, although FF evolution equations do not themselves guarantee momentum conservation, inclusion of a gluon FF which, for four quark flavours, distributes roughly 11% of the total light-front momentum fraction, is sufficient to restore momentum conservation under evolution. Overall, significant uncertainty is attached to FFs determined via fits to data; hence, the features of the predictions described herein could potentially provide useful guidance for future such studies. [ABSTRACT FROM AUTHOR]

A method for estimating the conditional average treatment effect under the condition of censored time-to-event data, called BENK (the Beran Estimator with Neural Kernels), is proposed. The main idea behind the method is to apply the Beran estimator for estimating the survival functions of controls and treatments. Instead of typical kernel functions in the Beran estimator, it is proposed to implement kernels in the form of neural networks of a specific form, called neural kernels. The conditional average treatment effect is estimated by using the survival functions as outcomes of the control and treatment neural networks, which consist of a set of neural kernels with shared parameters. The neural kernels are more flexible and can accurately model a complex location structure of feature vectors. BENK does not require a large dataset for training due to its special way for training networks by means of pairs of examples from the control and treatment groups. The proposed method extends a set of models that estimate the conditional average treatment effect. Various numerical simulation experiments illustrate BENK and compare it with the well-known T-learner, S-learner and X-learner for several types of control and treatment outcome functions based on the Cox models, the random survival forest and the Beran estimator with Gaussian kernels. The code of the proposed algorithms implementing BENK is publicly available. [ABSTRACT FROM AUTHOR]

This paper proposes algorithms to model fractional (dynamical) behaviors using non-singular rational kernels whose interest is first demonstrated on a pure power law function. Two algorithms are then proposed to find a non-singular rational kernel that allows the input-output data to be fitted. The first one derives the impulse response of the modeled system from the data. The second one finds the interlaced poles and zeros of the rational function that fits the impulse response found using the first algorithm. Several applications show the efficiency of the proposed work. [ABSTRACT FROM AUTHOR]

We study the second-order scalar and density perturbations generated by Gaussian curvature perturbations and primordial gravitational waves in the radiation-dominated era. After presenting all the possible second-order source terms, we obtain the explicit expressions of the kernel functions and the power spectra of the second-order scalar perturbations. We show that the primordial gravitational waves might affect second-order energy density perturbation δ (2) = δ ρ (2) / ρ (0) significantly. The effects of primordial gravitational waves are studied in terms of different kinds of primordial power spectra. [ABSTRACT FROM AUTHOR]

Rolling bearings are a key component for ensuring the safe and smooth operation of rotating machinery and are very prone to failure. Therefore, intelligent fault diagnosis research on rolling bearings has become a crucial task in the field of mechanical fault diagnosis. This paper proposes research on the fault diagnosis of rolling bearings based on an adaptive nearest neighbor strategy and the discriminative fusion of multi-feature information using supervised manifold learning (AN-MFIDFS-Isomap). Firstly, an adaptive nearest neighbor strategy is proposed using the Euclidean distance and cosine similarity to optimize the selection of neighboring points. Secondly, three feature space transformation and feature information extraction methods are proposed, among which an innovative exponential linear kernel function is introduced to provide new feature information descriptions for the data, enhancing feature sensitivity. Finally, under the adaptive nearest neighbor strategy, a novel AN-MFIDFS-Isomap algorithm is proposed for rolling bearing fault diagnosis by fusing various feature information and classifiers through discriminative fusion with label information. The proposed AN-MFIDFS-Isomap algorithm is validated on the CWRU open dataset and our experimental dataset. The experiments show that the proposed method outperforms other traditional manifold learning methods in terms of data clustering and fault diagnosis. [ABSTRACT FROM AUTHOR]

The present paper deals with the study of the approximation properties of the well-known sampling Kantorovich (SK) operators in "Sobolev-like settings". More precisely, a convergence theorem in case of functions belonging to the usual Sobolev spaces for the SK operators has been established. In order to get such a result, suitable Strang-Fix type conditions have been required on the kernel functions defining the above sampling type series. As a consequence, certain open problems related to the convergence in variation for the SK operators have been solved. Then, we considered the above operators in a fractional-type setting. It is well-known that, in the literature, several notions of fractional Sobolev spaces are available, such as, the Gagliardo Sobolev spaces (GSs) defined by means of the Gagliardo semi-norm, or the weak Riemann-Liouville Sobolev spaces (wRLSs) defined by the weak (left and right) Riemann-Liouville fractional derivatives and so on. Here, in order to face the above convergence problem, we introduced a new definition of fractional Sobolev spaces, that we called the tight fractional Sobolev spaces (tfSs) and generated as the intersection of the GSs and the symmetric Sobolev spaces (i.e., that given by the intersection of the left and the right wRLSs). In the latter setting, we obtain one of the main results of the paper, that is a convergence theorem for the SK operators with respect to a suitable norm on tfSs. [ABSTRACT FROM AUTHOR]

This article studies the kinetics of ψ -fractional differential equations (ψ -FDEs). Above all, some new fractional inequalities are presented, which are the cornerstone of the later stability analysis. The continuous dependence of the solutions to the ψ -FDEs on some particular parameters is established. Then, the comparison theorems for ψ -fractional systems are given. What is more, based on the properties of ψ -fractional calculus and the generalized Laplace transform, some sufficient conditions about the stability of fractional systems involving ψ -Riemann-Liouville or ψ -Caputo derivatives are attained. Last but not least, numerical simulations with some new kernel functions are given to validate the stability results. [ABSTRACT FROM AUTHOR]

The flow of water through a horizontal small-scale Venturi tube of rectangular cross-section is simulated using a modified version of the open-source code DualSPHysics, which is based on Smoothed Particle Hydrodynamics (SPH) methods. Water is simulated using the Murnaghan-Tait equation of state so that weak compressibility is allowed. The hydrodynamics is coupled to a Large-Eddy Simulation (LES) turbulence model. The convergence properties of SPH are improved by adopting a C 2 Wendland function as the interpolation kernel, increased number of neighboring particles and non-reflective open boundary conditions at the outlet of the Venturi tube. The flow structure and differential pressure as well as the mainstream velocity profiles at different stations are compared with calibrated experimental data. A resolution independence test shows that good convergence to the experimental measurements is achieved using four million particles. At this resolution the simulations predict the experimental centerline velocity profile along the Venturi meter for a volumetric flow rate of ten liters per minutes (lpm) with a root-mean-square error of 4.3%. This error grows to 7.1% when the volumetric flow rate increases to 25 lpm. The predicted differential pressure matches the experimental data with errors varying from 1.4% (for 10 lpm) to 6.8% (for 25 lpm). Cross-sectional velocity profiles within the throat and divergent sections differ from the experimental measurements in less than 5.5%. In general, it is shown that the SPH model can provide an efficient and accurate method for recalibrating flow meters at moderately high Reynolds numbers instead of using costly experimental tests. [ABSTRACT FROM AUTHOR]

Accurate carbon price prediction is a reference that allows market participants to make decisions. This study adopts a total of 1,857 trading days of data from April 2, 2014, to June 15, 2022, in the Hubei carbon market, one of the first and largest pilot carbon markets in China for carbon price prediction. We propose a new framework based on the GA-VMD-CNN-BiLSTM-Attention hybrid model: a genetic algorithm (GA) is adopted to search the optimal parameter combination of variational mode decomposition (VMD); a convolutional neural network (CNN) is established to discover the relationship between influencing factors and carbon prices; a bidirectional long and short-term memory network (BiLSTM) is applied to extract time series information; and an attention mechanism is used to strengthen the influence of important information on carbon prices. Compared to 11 other models, the GA-VMD-CNN-BiLSTM-Attention model has a higher accuracy and stronger model reliability. In addition to deterministic point prediction, this study uses non-parametric kernel density estimation with the Gaussian kernel function (KDE-Gaussian) for interval forecasting. The forecasting can quantify the uncertainty of carbon prices and serve as a more practical reference for decision-makers. By revealing the particularly challenging issue that underlies carbon price forecasting, our analysis also sheds light on current low-carbon policies in China. The GA-VMD method achieves more accurate decomposition results. A hybrid prediction model is established based on CNN and BiLSTM. An attention mechanism is proposed for enhancing the impact of key information. Kernel density estimation with Gaussian function is adopted for interval forecasting. [ABSTRACT FROM AUTHOR]

In a hyperspectral image classification (HSIC) task, manually labeling samples requires a lot of manpower and material resources. Therefore, it is of great significance to use small samples to achieve the HSIC task. Recently, convolutional neural networks (CNNs) have shown remarkable performance in HSIC, but they still have some areas for improvement. (1) Convolutional kernel weights are determined through initialization and cannot be adaptively adjusted based on the input data. Therefore, it is difficult to adaptively learn the structural features of the input data. (2) The convolutional kernel size is single per layer, which leads to the loss of local information for a large convolutional kernel or global information for a small convolutional kernel. In order to solve the above problems, we propose a plug-and-play method called dynamic convolution based on structural re-parameterization (DCSRP). The contributions of this method are as follows. Firstly, compared with traditional convolution, dynamic convolution is a non-linear function, so it has more representation power. In addition, it can adaptively capture the contextual information of input data. Secondly, the large convolutional kernel and the small convolutional kernel are integrated into a new large convolutional kernel. The large convolutional kernel shares the advantages of the two convolution kernels, which can capture global information and local information at the same time. The results in three publicly available HSIC datasets show the effectiveness of the DCSRP. [ABSTRACT FROM AUTHOR]

Simple Summary: In large-scale chicken farming, monitoring flock density can help optimize feeding management and improve animal welfare. Traditional manual counting methods are not only prone to errors and omissions but also can cause harm to chickens. In this paper, a counting model for dense chicken flocks is proposed. The method can effectively estimate the number of chickens in real dense scenes. With the development of artificial intelligence, automatically and accurately counting chickens has become a reality. However, insufficient lighting, irregular sizes, and dense flocks make this a challenging task. The existing methods cannot perform accurate and stable counting. In this article, a dense flock of chickens counting network (DFCCNet) is proposed based on density map regression, where features from different levels are merged using feature fusion to obtain more information for distinguishing chickens from the background, resulting in more stable counting results. Multi-scaling is used to detect and count chickens at various scales, which can improve the counting accuracy and ensure stable performance for chickens of different sizes. Feature convolution kernels are adopted to convolve feature maps, which can extract more accurate target information, reduce the impact of occlusion, and achieve more reliable and precise results. A dataset of dense flocks of chickens (namely Dense-Chicken) has been collected and constructed, which contains 600 images of 99,916 chickens, with labeled points and boxes. It can be accessed by researchers as benchmark data. The proposed method was compared with some state-of-the-art algorithms, to validate its effectiveness. With its robustness being verified by counting in three kinds of density situations, with the mean absolute error being 4.26, 9.85, and 19.17, respectively, and a speed of 16.15 FPS. DFCCNet provides an automatic and fast approach to counting chickens in a dense farming environment. It can be easily embedded into handheld devices for application in agricultural engineering. [ABSTRACT FROM AUTHOR]

In the context of intelligent driving, pedestrian detection faces challenges related to low accuracy in target recognition and positioning. To address this issue, a pedestrian detection algorithm is proposed that integrates a large kernel attention mechanism with the YOLOV5 lightweight model. The algorithm aims to enhance long-term attention and dependence during image processing by fusing the large kernel attention module with the C3 module. Furthermore, it addresses the lack of long-distance relationship information in channel and spatial feature extraction and representation by introducing the Coordinate Attention mechanism. This mechanism effectively extracts local information and focused location details, thereby improving detection accuracy. To improve the positioning accuracy of obscured targets, the alpha CIOU bounding box regression loss function is employed. It helps mitigate the impact of occlusions and enhances the algorithm's ability to precisely localize pedestrians. To evaluate the effectiveness of trained model, experiments are conducted on the BDD100K pedestrian dataset as well as the Pascal VOC dataset. Experimental results demonstrate that the improved attention fusion YOLOV5 lightweight model achieves an average accuracy of 60.3%. Specifically, the detection accuracy improves by 1.1% compared to the original YOLOV5 algorithm, and the accuracy performance index reaches 73.0%. These findings strongly indicate the proposed algorithm in significantly enhancing the accuracy of pedestrian detection in road scenes. [ABSTRACT FROM AUTHOR]

Customer churn remains a critical challenge in telecommunications, necessitating effective churn prediction (CP) methodologies. This paper introduces the Enhanced Gradient Boosting Model (EGBM), which uses a Support Vector Machine with a Radial Basis Function kernel (SVMRBF) as a base learner and exponential loss function to enhance the learning process of the GBM. The novel base learner significantly improves the initial classification performance of the traditional GBM and achieves enhanced performance in CP-EGBM after multiple boosting stages by utilizing state-of-the-art decision tree learners. Further, a modified version of Particle Swarm Optimization (PSO) using the consumption operator of the Artificial Ecosystem Optimization (AEO) method to prevent premature convergence of the PSO in the local optima is developed to tune the hyper-parameters of the CP-EGBM effectively. Seven open-source CP datasets are used to evaluate the performance of the developed CP-EGBM model using several quantitative evaluation metrics. The results showed that the CP-EGBM is significantly better than GBM and SVM models. Results are statistically validated using the Friedman ranking test. The proposed CP-EGBM is also compared with recently reported models in the literature. Comparative analysis with state-of-the-art models showcases CP-EGBM's promising improvements, making it a robust and effective solution for churn prediction in the telecommunications industry. [ABSTRACT FROM AUTHOR]

The discriminability and transferability of models are two important factors for the success of domain adaptation methods. Recently, some domain adaptation methods have improved models by adding a discriminant information extraction module. However, these methods need to carefully balance the discriminability and transferability of a model. To address this problem, we propose a new deep domain adaptation method, Gaussian Process-based Transfer Kernel Learning (GPTKL), which can perform domain knowledge transfer and improve the discrimination ability of the model simultaneously. GPTKL uses the kernel similarity between all samples in the source and target domains as a priori information to establish a cross-domain Gaussian process. By maximizing its likelihood function, GPTKL reduces the domain discrepancy between the source and target domains, thereby enhancing generalization across domains. At the same time, GPTKL introduces the deep kernel learning strategy into the cross-domain Gaussian process to learn a transfer kernel function based on deep features. Through transfer kernel learning, GPTKL learns a deep feature space with both discriminability and transferability. In addition, GPTKL uses cross-entropy and mutual information to learn a classification model shared by the source and target domains. Experiments on four benchmarks show that GPTKL achieves superior classification performance over state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Unsupervised classification is used in credit risk assessment to reduce human resource costs and make informed decisions in the shortest possible time. Although several studies show that support vector machine-based methods have better performance in unlabeled datasets, several factors still negatively affect these models, such as unstable results due to random initialization, reduced effectiveness due to kernel dependencies, and noise points and outliers. This paper introduces an unsupervised classification method based on a fuzzy unsupervised quadratic surface support vector machine without a kernel to avoid selecting related kernel parameters for credit risk assessment. In addition, we propose an innovative fuzzy membership function for reducing noise points and outliers in line with the direction of sample density variation. Fuzzy Unsupervised QSSVM (FUS-QSSVM) outperforms well-known SVM-based methods based on numerical tests on public benchmark credit data. In some real-world applications, the proposed method has significant potential as well as being effective, efficient, and robust. The algorithm can therefore increase the number of potential customers of financial institutions as well as increase profitability. [ABSTRACT FROM AUTHOR]

Direction of arrival (DOA) estimation with nested arrays has been widely investigated in the field of array signal processing, but most studies assume that the noise is Gaussian white noise. In practical situations, there may exist impulsive noise (a kind of heavy-tailed noise), wherein the performance of traditional subspace-based DOA estimation algorithms deteriorates significantly. In this paper, we propose a correlation entropy-based infinite norm preprocessing algorithm, which can be applicable to any type of impulsive noise. Each snapshot of the sensor array data is processed by an exponential kernel function with the infinite norm, which can effectively combat the outliers. Furthermore, we construct the equivalent second-order covariance matrix and perform DOA estimation using classical subspace methods. Simulation results demonstrate the effectiveness of the proposed method for both symmetric α -stable distribution and the Gaussian mixture model. [ABSTRACT FROM AUTHOR]

This paper explores the potential benefits of quantum coherence and quantum discord in the non-universal quantum computing model called deterministic quantum computing with one qubit (DQC1) in supervised machine learning. We show that the DQC1 model can be leveraged to develop an efficient method for estimating complex kernel functions. We demonstrate a simple relationship between coherence consumption and the kernel function, a crucial element in machine learning. The paper presents an implementation of a binary classification problem on IBM hardware using the DQC1 model and analyzes the impact of quantum coherence and hardware noise. The advantage of our proposal lies in its utilization of quantum discord, which is more resilient to noise than entanglement. [ABSTRACT FROM AUTHOR]

Hypertension is associated with significant cardiovascular morbidity. Blood pressure (BP) control on maintenance hemodialysis (HD) is strongly impacted by volume status. The objective of this study was to assess whether machine learning (ML) is effective in predicting post-HD BP in children and young adults on HD. We collected data on BP, IDWG, pulse, and weights for patients on maintenance HD (> 3 months). Input features included DW, pre-post weight difference, IDWG and pre-HD BP. Seven models were trained and tuned using open-source libraries. Model performance was evaluated using time-series cross-validation on a rolling basis (3–12 month training, 1-day testing). Various regression scores were compared between models. Data for 35 patients (14,375 HD sessions) were analyzed. Extreme gradient boosting (XGB) and vector autoregression with exogenous regressors (VARX) achieved better accuracy in predicting post-dialysis systolic BP than K-nearest neighbor, support vector regression (SVR) with radial basis function kernel and random forest (p < 0.001 for each). The differences in accuracy between XGB, VARX, SVR with linear kernel, random forest and linear regression were not significant. Using clinical parameters, ML models may be useful in predicting post-HD BP, which may help guide DW adjustment and optimizing BP control for maintenance HD patients. [ABSTRACT FROM AUTHOR]

Most works on Support Vector Regression (SVR) focus on kernel or loss functions, with the corresponding support vectors obtained using a fixed-radius ε -tube, affording good predictive performance on datasets. However, the fixed radius limitation prevents the adaptive selection of support vectors according to the data distribution characteristics, compromising the performance of the SVR-based methods. Therefore, this study proposes an "Alterable ε i -Support Vector Regression" (A ε i -SVR) model by applying a novel ε , named "Alterable ε i ," to the SVR model. Based on the data point sparsity at each location, the model solves the different ε i at the corresponding position, and thus zoom-in or zoom-out the ε -tube by changing its radius. Such a variable ε -tube strategy diminishes noise and outliers in the dataset, enhancing the prediction performance of the A ε i -SVR model. Therefore, we suggest a novel non-deterministic algorithm to iteratively solve the complex problem of optimizing ε i associated with every location. Extensive experimental results demonstrate that our approach can improve the accuracy and stability on simulated and real data compared with the baseline methods. [ABSTRACT FROM AUTHOR]

For the sake of conducting distribution network reliability prediction in an accurate and efficient manner, a model for distribution network reliability prediction (IAO-LSSVM) based on an improved Aquila Optimizer (IAO) optimized mixed-kernel Least Squares Support Vector Machine (LSSVM) is thus proposed in this paper. First, the influencing factors that greatly affect the distribution network reliability are screened out through grey relational analysis. Afterwards, the radial basis kernel function and polynomial kernel function are combined and a mixed kernel LSSVM model is constructed, which has better generalization ability. However, for the AO algorithm, it is easy to fall into local extremum. In such case, the AO algorithm is innovatively improved after both the improved tent chaotic initialization strategy and adaptive t-distribution strategy are introduced. Next, the parameters of the mixed-kernel LSSVM model are optimized and the IAO-LSSVM distribution network reliability prediction model is established through using the improved AO algorithm. In the end, the prediction results and errors of the IAO-LSSVM prediction model and other models are compared in the actual distribution network applications. It is revealed that the IAO-LSSVM prediction model proposed in this paper features higher accuracy and better stability. [ABSTRACT FROM AUTHOR]

A novel approach based on the FSMO (fractional sliding model observer) is proposed to address the problem of nonlinear fault diagnosis in analog circuits. First, the fractional transform is extensively analyzed to derive the kernel functions. Next, the kernel functions are calculated and input into the SMO (sliding model observer). Then, the fractional sliding surface data are used to construct the FSMO of the fault feature extraction model. By analyzing the fractional sliding surface data, the digital fault features are extracted and used in the nonlinear fault diagnosis of the analog circuit. Finally, the experiments demonstrate the availability of the proposed method. [ABSTRACT FROM AUTHOR]