Related papers: Improved phenomenological nuclear charge radius fo…
The Garvey-Kelson relations (GKRs) are algebraic expressions originally developed to predict nuclear masses. In this letter we show that the GKRs provide a fruitful framework for the prediction of other physical observables that also…
A new formula for the nuclear charge radius is proposed, dependent on the mass number (A) and neutron excess (N-Z) in the nucleus. It is simple and it reproduces all the experimentally available mean square radii and their isotopic shifts…
In this work, we investigate high-dimensional kernel ridge regression (KRR) on i.i.d. Gaussian data with anisotropic power-law covariance. This setting differs fundamentally from the classical source & capacity conditions for KRR, where…
Motivated by the studies of neural networks (e.g.,the neural tangent kernel theory), we perform a study on the large-dimensional behavior of kernel ridge regression (KRR) where the sample size $n \asymp d^{\gamma}$ for some $\gamma > 0$.…
The first determination of the nuclear charge radius by laser spectroscopy for a five-electron system is reported. This is achieved by combining high-accuracy ab initio mass-shift calculations and a high-resolution measurement of the…
With the help of radial basis function (RBF) and the Garvey-Kelson relation, the accuracy and predictive power of some global nuclear mass models are significantly improved. The rms deviation between predictions from four models and 2149…
Random feature (RF) has been widely used for node consistency in decentralized kernel ridge regression (KRR). Currently, the consistency is guaranteed by imposing constraints on coefficients of features, necessitating that the random…
We provide uniform confidence bands for kernel ridge regression (KRR), a widely used nonparametric regression estimator for nonstandard data such as preferences, sequences, and graphs. Despite the prevalence of these data--e.g., student…
Charge radius is one of the most fundamental properties of a nucleus. However, a precise description of the evolution of charge radii along an isotopic chain is highly nontrivial, as reinforced by recent experimental measurements. In this…
Correlation between the rms nucleus charge radius and their deformation, isospin asymmetry, mass and charge numbers are presented. Four parameters radius parametrization formula is proposed. Ratio of experimental to theoretical value…
The generator coordinate method (GCM) is an important tool of choice for modeling large-amplitude collective motion in atomic nuclei. The computational complexity of the GCM increases rapidly with the number of collective coordinates. It…
The information about sizes and nuclear density distributions in unstable (radioactive) nuclei is usually extracted from the data on interaction of radioactive nuclear beams with a nuclear target. We show that in the case of nucleus-nucleus…
The distribution of electric charge in atomic nuclei is fundamental to our understanding of the complex nuclear dynamics and a quintessential observable to validate nuclear structure models. We explore a novel approach that combines…
We find a new method to deduce nuclear radii from proton-nucleus elastic scattering data. In this method a nucleus is viewed as a ``black'' sphere. A diffraction pattern of protons by this sphere is equivalent to that of the Fraunhofer…
The size is a key property of a nucleus. Accurate nuclear radii are extracted from elastic electron scattering, laser spectroscopy, and muonic atom spectroscopy. The results are not always compatible, as the proton-radius puzzle has shown…
Kernel ridge regression (KRR) has recently attracted renewed interest due to its potential for explaining the transient effects, such as double descent, that emerge during neural network training. In this work, we study how the alignment…
Radial Basis Function (RBF), or Gaussian, kernels are among the most widely used parametric kernels in machine learning, particularly in methods such as Support Vector Machines (SVM) and kernel-based subspace approaches. The kernel…
The model inputs play a key role in the performance of the Bayesian optimization approach. In this paper, we investigate the influence of the inputs on the improved predictions of phenomenological nuclear charge radius formulas using an…
Ridge regression (RR) is a regularization technique that penalizes the L2-norm of the coefficients in linear regression. One of the challenges of using RR is the need to set a hyperparameter ($\alpha$) that controls the amount of…
We investigate the properties of random feature ridge regression (RFRR) given by a two-layer neural network with random Gaussian initialization. We study the non-asymptotic behaviors of the RFRR with nearly orthogonal deterministic…