Related papers: Improved phenomenological nuclear charge radius fo…

The charge radii of octet-baryons obtained in quenched lattice-QCD calculations are extrapolated within heavy-baryon chiral perturbation theory. Finite-range regularization (FRR) is applied to improve the convergence of the chiral expansion…

We show that the charge radii of neighboring atomic nuclei, independent of atomic number and charge, follow remarkably very simple relations, despite the fact that atomic nuclei are complex finite many-body systems governed by the laws of…

Conditionally positive definite (CPD) kernels are defined with respect to a function class $\mathcal{F}$. It is well known that such a kernel $K$ is associated with its native space (defined analogously to an RKHS), which in turn gives rise…

A unified theoretical model reproducing charge radii of known atomic nuclei plays an essential role in making extrapolations for unknown nuclei. Recently developed new ansatz which phenomenologically takes into account the neutron-proton…

Systematic trends in nuclear charge radii are of great interest due to universal shell effects and odd-even staggering (OES). The modified root mean square (rms) charge radius formula, which phenomenologically accounts for the formation of…

Random Fourier features is one of the most popular techniques for scaling up kernel methods, such as kernel ridge regression. However, despite impressive empirical results, the statistical properties of random Fourier features are still not…

We study the risk (i.e. generalization error) of Kernel Ridge Regression (KRR) for a kernel $K$ with ridge $\lambda>0$ and i.i.d. observations. For this, we introduce two objects: the Signal Capture Threshold (SCT) and the Kernel Alignment…

The kink observed in the nuclear charge radius of Sn isotopes around neutron number $N = 82$ is investigated within the relativistic mean-field (RMF) framework using the NL3$^*$ parameter set. It is shown that the small components of the…

I present a critical review of absolute root-mean-square charge radii of stable nuclei from $Z=3$ to $Z=32$, which includes a previously overlooked uncertainty in the combined analysis of muonic x-ray and electron scattering experiments.…

The radial basis function (RBF) approach has been used to improve the mass predictions of nuclear models. However, systematic deviations exist between the improved masses and the experimental data for nuclei with different odd-even parities…

The root-mean-square (rms) nuclear charge radius of ^8He, the most neutron-rich of all particle-stable nuclei, has been determined for the first time to be 1.93(3) fm. In addition, the rms charge radius of ^6He was measured to be 2.068(11)…

We derive new bounds for the condition number of kernel matrices, which we then use to enhance existing non-asymptotic test error bounds for kernel ridgeless regression (KRR) in the over-parameterized regime for a fixed input dimension. For…

The random feature (RF) approach is a well-established and efficient tool for scalable kernel methods, but existing literature has primarily focused on kernel ridge regression with random features (KRR-RF), which has limitations in handling…

Kernel ridge regression (KRR) is a fundamental computational tool, appearing in problems that range from computational chemistry to health analytics, with a particular interest due to its starring role in Gaussian process regression.…

Collinear laser spectroscopy measurements were performed on $^{68-74}$Ge isotopes ($Z = 32$) at ISOLDE-CERN, by probing the $4s^2 4p^2 \, ^3\!P_1 \rightarrow 4s^2 4p 5s \, ^3\!P_1^o$ atomic transition (269~nm) of germanium. Nuclear charge…

Kernel balancing weights provide confidence intervals for average treatment effects, based on the idea of balancing covariates for the treated group and untreated group in feature space, often with ridge regularization. Previous works on…

Kernel Ridge Regression (KRR) is a simple yet powerful technique for non-parametric regression whose computation amounts to solving a linear system. This system is usually dense and highly ill-conditioned. In addition, the dimensions of the…

Kernel ridge regression (KRR), also known as the least-squares support vector machine, is a fundamental method for learning functions from finite samples. While most existing analyses focus on the noisy setting with constant-level label…

Based on the systematic investigation of the data available for $A \geq 40$, a $Z^{1/3}$ dependence for the nuclear charge radii is shown to be superior to the generally accepted $A^{1/3}$ law. A delicate scattering of data around…

This paper conducts a comprehensive study of the learning curves of kernel ridge regression (KRR) under minimal assumptions. Our contributions are three-fold: 1) we analyze the role of key properties of the kernel, such as its spectral…