We consider conditions on a given system F of vectors in Hilbert space H, forming a frame, which turn H into a reproducing kernel Hilbert space. It is assumed that the vectors in F are functions on some set Ω . We then identify conditions on these fu...
Self-supervised learning (SSL) has emerged as a powerful paradigm for representation learning by optimizing geometric objectives, such as invariance to augmentations, variance preservation, and feature decorrelation, without requiring labels. However...
The theory of reproducing kernel Hilbert spaces (RKHSs) has been developed into a powerful tool in mathematics and has lots of applications in many fields, especially in kernel machine learning. Fractal theory provides new technologies for making com...
The reproducing kernel particle method (RKPM) is one of the most universal meshless methods. However, when solving three-dimensional (3D) problems, the computational efficiency is relatively low because of the complexity of the shape function. To ove...
The aim of this article was to provide improved estimates for the
We apply the reproducing kernel method and group preserving scheme for investigating the Lane–Emden equation. The reproducing kernel method is implemented by the useful reproducing kernel functions and the numerical approximations are given. These ap...
The aim of this paper is to establish an inversion and Calderón formulas for the generalized Gabor transform associated with a class of Sturm–Liouville operators. We also investigate several problems related to reproducing kernel theory...
Fractional-order calculus has become a useful mathematical framework to describe the complex super-diffusive process; however, numerical solutions of the two-sided space-fractional super-diffusive model with variable coefficients are difficult to obt...
In this article, a new reproducing kernel approach is developed for obtaining a numerical solution of multi-order fractional nonlinear three-point boundary value problems. This approach is based on a reproducing kernel, which is constructed by shifte...
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 th...
In this research, obtaining of approximate solution for fractional-order Burgers’ equation will be presented in reproducing kernel Hilbert space (RKHS). Some special reproducing kernel spaces are identified according to inner products and norms...
The direct strong-form collocation method with reproducing kernel approximation is introduced to efficiently and effectively solve the natural convection problem within a parallelogrammic enclosure. As the convection behavior in the fluid-saturated p...
Electrical Tomography (ET) technology is widely used in multiphase flow detection due to its advantages of low cost, visualization, fast response, non-radiation, and non-invasiveness. However, ill-posed solutions lead to low image reconstruction reso...
The regularization parameter plays an important role in regularization-based electrical tomography (ET) algorithms, but the existing methods generally cannot determine the parameter. Moreover, these methods are not real-time since a thorough search m...
Functional data analysis has important applications in biomedical, health studies and other areas. In this paper, we develop a general framework for a mean curve estimation for functional data using a reproducing kernel Hilbert space (RKHS) and deriv...
This paper deals with the numerical solutions and convergence analysis for general singular Lane–Emden type models of fractional order, with appropriate constraint initial conditions. A modified reproducing kernel discretization technique is us...
Handcrafted radiomics features (HRFs) are quantitative features extracted from medical images to decode biological information to improve clinical decision making. Despite the potential of the field, limitations have been identified. The most importa...
Fractional differential equations are becoming more and more indispensable for modeling real-life problems. Modeling and then analyzing these fractional differential equations assists researchers in comprehending and predicting the system they want t...
Motivated by the fact that the Fibonacci sequence is the simplest nontrivial second-order recurrence with a rational generating function, we develop a Fibonacci-weighted Hardy theory for bicomplex holomorphic functions. Starting from the coefficient...
The underlying function in reproducing kernel Hilbert space (RKHS) may be degraded by outliers or deviations, resulting in a symmetry ill-posed problem. This paper proposes a nonconvex minimization model with
A meshless, quasi-convex reproducing kernel particle framework for three-dimensional steady-state thermomechanical coupling problems is presented in this paper. A meshfree, second-order, quasi-convex reproducing kernel scheme is employed to approxima...
In statistical analyses, especially those using a multiresponse regression model approach, a mathematical model that describes a functional relationship between more than one response variables and one or more predictor variables is often involved. T...
In this paper, we implement reproducing kernel Hilbert space method to tenth order boundary value problems. These problems are important for mathematicians. Different techniques were applied to get approximate solutions of such problems. We obtain so...
We give a systematic investigation on the reproducing property of the zonal translation network and apply this property to kernel regularized regression. We propose the concept of the Marcinkiewicz–Zygmund setting (MZS) for the scattered nodes...
Software-defined networking (SDN) requires adaptive control strategies to handle dynamic traffic conditions and heterogeneous network environments. Reinforcement learning (RL) has emerged as a promising solution, yet deep RL methods often face instab...
Achieving high feature reproducibility while preserving biological information is one of the main challenges for the generalizability of current radiomics studies. Non-clinical imaging variables, such as reconstruction kernels, have shown to signific...
The weighted reproducing kernel collocation method exhibits high accuracy and efficiency in solving inverse problems as compared with traditional mesh-based methods. Nevertheless, it is known that computing higher order reproducing kernel (RK) shape...
In this paper, we find the solutions of fourth order fractional boundary value problems by using the reproducing kernel Hilbert space method. Firstly, the reproducing kernel Hilbert space method is introduced and then the method is applied to this ki...
Compression-based dissimilarities such as the normalized compression distance are widely used, but direct exponentiation need not produce a positive semidefinite kernel. We develop a systematic interface between prefix algorithmic information theory...
The weighted gradient reproducing kernel collocation method is introduced to recover the heat source described by Poisson’s equation. As it is commonly known that there is no unique solution to the inverse heat source problem, the weak solution...
Nonlinear state estimation plays an important role in aerospace sensing applications, where estimation accuracy must be balanced against computational efficiency. In this paper, a sparse-grid Gaussian kernel quadrature Kalman filter (SGKQKF) is propo...
Numerical methods play an important role in modern mathematical research, especially studying the symmetry analysis and obtaining the numerical solutions of fractional differential equation. In the current work, we use two numerical schemes to deal w...
This paper presents a co-rotational beam formulation, which is used for geometric nonlinear analysis with the differential reproducing kernel (DRK) approximation collocation method. The present formulation, based on the Timoshenko beam hypothesis, is...
It is well known that meshless methods are effective for solving fractional differential equations on both regular and irregular domains. However, many commonly used basis functions such as Legendre wavelets and B-splines are naturally defined on rec...
The Kudryashov–Sinelshchikov equation (KSE) is crucial in modeling pressure waves in liquids containing gas bubbles, capturing both nonlinear wave phenomena and dispersion effects. This article applies the reproducing kernel Hilbert space metho...
Many dimensionality and model reduction techniques rely on estimating dominant eigenfunctions of associated dynamical operators from data. Important examples include the Koopman operator and its generator, but also the Schrödinger operator. We p...
It is shown that symmetric products of Heine–Stieltjes quasi-polynomials satisfy an addition formula. The formula follows from the relationship between Heine–Stieltjes quasi-polynomials and spaces of generalized spherical harmonics, and f...
In this paper, we present an accurate numerical approach based on the reproducing kernel method (RKM) for solving second-order fuzzy initial value problems (FIVP) with symmetry coefficients such as symmetric triangles and symmetric trapezoids. Findin...
In this paper, we study the regularized Huber regression algorithm in a reproducing kernel Hilbert space (RKHS), which is applicable to both fully supervised and semi-supervised learning schemes. Our focus in the work is two-fold: first, we provide t...
Recently, a new fractional derivative operator has been introduced so that it presents the combination of the Riemann–Liouville integral and Caputo derivative. This paper aims to enhance the reproducing kernel Hilbert space method (RKHSM, for s...
In this paper, we discuss the problem of channel identification by using eight algorithms. The first three algorithms are based on higher-order cumulants, the next three algorithms are based on binary output measurement, and the last two algorithms a...
Due to their flexibility and interpretability, additive models are powerful tools for high-dimensional mean regression and variable selection. However, the least-squares loss-based mean regression models suffer from sensitivity to non-Gaussian noises...
The central problem of this study is to represent any holomorphic and square integrable function on the Kepler manifold in the series form based on Fourier analysis. Because these function spaces are reproducing kernel Hilbert spaces (RKHS), three di...
Building on recent approaches to generalized Berezin norms by by Albeladi, Feki, and Taha, this paper establishes several refined upper bounds for the
Many methods have been developed to study nonparametric function-on-function regression models. Nevertheless, there is a lack of model selection approach to the regression function as a functional function with functional covariate inputs. To study i...
In the present paper, we investigate the influence of the choice of continuous linear operator for obtaining the approximate periodic solutions of ordinary second-order differential equations. In most of these problems, the periods are unknown, and t...
In this paper, we introduce and study the
In the framework of statistical learning, we study the online gradient descent algorithm generated by the correntropy-induced losses in Reproducing kernel Hilbert spaces (RKHS). As a generalized correlation measurement, correntropy has been widely ap...
This study aimed at investigating a local radial basis function collocation method (LRBFCM) in the reproducing kernel Hilbert space. This method was, in fact, a meshless one which applied the local sub-clusters of domain nodes for the approximation o...
A reproducing kernel Hilbert space (RKHS) approximation problem arising from learning theory is investigated. Some K-functionals and moduli of smoothness with respect to RKHSs are defined with Fourier–Bessel series and Fourier–Bessel tran...
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