Related papers: Improved phenomenological nuclear charge radius fo…
We study the spectrum of inner-product kernel matrices, i.e., $n \times n$ matrices with entries $h (\langle \textbf{x}_i ,\textbf{x}_j \rangle/d)$ where the $( \textbf{x}_i)_{i \leq n}$ are i.i.d.~random covariates in $\mathbb{R}^d$. In…
The variation in mean-square nuclear charge radius of xenon isotopes was measured utilizing a new method based on extreme ultraviolet spectroscopy of highly charged Na-like ions. The isotope shift of the Na-like D1 (3s $^{2}$S$_{1/2}$ - 3p…
Quantum chemistry calculations are often performed using atom-centered basis sets which are chosen to balance accuracy and cost. While they are systematically improvable, the total energy converges slowly with basis set size towards the…
This work describes the formalism for estimating thermonuclear reaction rates for astrophysical applications, emphasizing modern statistical approaches such as Monte-Carlo sampling and Bayesian models. We discuss related topics including…
Kernel ridge regression (KRR) is a foundational tool in machine learning, with recent work emphasizing its connections to neural networks. However, existing theory primarily addresses the i.i.d. setting, while real-world data often exhibits…
Reinforcement Learning (RL) problems are being considered under increasingly more complex structures. While tabular and linear models have been thoroughly explored, the analytical study of RL under nonlinear function approximation,…
In this paper, we develop a quadrature framework for large-scale kernel machines via a numerical integration representation. Considering that the integration domain and measure of typical kernels, e.g., Gaussian kernels, arc-cosine kernels,…
Study of the ground-state properties of Kr, Sr and Zr isotopes has been performed in the framework of the relativistic mean field (RMF) theory using the recently proposed relativistic parameter set NL-SH. It is shown that the RMF theory…
Global and national efforts to deliver high-quality nuclear data to users have a broad impact across applications such as national security, reactor operation, basic science, medical fields, and more. Cross section evaluation is a large…
The nuclear recoil effect, known also as the mass shift, is one of theoretical contributions to the energy levels in muonic atoms. Accurate theoretical predictions are therefore needed for extracting e.g. the nuclear charge radii from…
This paper proposes and studies a numerical method for approximation of posterior expectations based on interpolation with a Stein reproducing kernel. Finite-sample-size bounds on the approximation error are established for posterior…
We present a high-accuracy calculation of the deuteron structure radius in chiral effective field theory. Our analysis employs the state-of-the-art semilocal two-nucleon potentials and takes into account two-body contributions to the charge…
Lattice QCD calculations of nucleon form factors are restricted to discrete values of the Euclidean four-momentum transfer. Therefore, the extraction of radii typically relies on parametrizing and fitting the lattice QCD data to obtain its…
The nuclear charge radius of $^{12}$Be was precisely determined using the technique of collinear laser spectroscopy on the $2s_{1/2}\rightarrow 2p_{1/2, 3/2}$ transition in the Be$^{+}$ ion. The mean square charge radius increases from…
Collinear-laser spectroscopy with bunched-beams technique was used for the study of neutron deficient Rb isotopes, out to $^{74}$Rb ($N=Z=37$) at TRIUMF. The measured hyperfine coupling constants of $^{76,78m}$Rb were in agreement with…
In this paper, we propose a fast surrogate leverage weighted sampling strategy to generate refined random Fourier features for kernel approximation. Compared to the current state-of-the-art method that uses the leverage weighted scheme…
Complete flavour decompositions of the scalar, axial and tensor charges of the proton, deuteron, diproton and $^3$He at SU(3)-symmetric values of the quark masses corresponding to a pion mass $m_\pi\sim806$ MeV are determined using lattice…
Kernel methods give powerful, flexible, and theoretically grounded approaches to solving many problems in machine learning. The standard approach, however, requires pairwise evaluations of a kernel function, which can lead to scalability…
We propose an experiment to measure the nuclear charge radii of light elements with up to 20~times higher accuracy. These are essential both for understanding nuclear physics at low energies, and for experimental and theoretical…
Reinforcement learning utilizing kernel ridge regression to predict the expected value function represents a powerful method with great representational capacity. This setting is a highly versatile framework amenable to analytical results.…