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We extend the correlated basis functions theory (CBF) for nuclei with different number of protons and neutrons and in j-j coupling scheme. By means of the Fermi hypernetted chain integral equations, in conjunction with the single operator…
Regularized variants of Principal Components Analysis, especially Sparse PCA and Functional PCA, are among the most useful tools for the analysis of complex high-dimensional data. Many examples of massive data, have both sparse and…
Principal Component Analysis (PCA) is a dimension reduction technique. It produces inconsistent estimators when the dimensionality is moderate to high, which is often the problem in modern large-scale applications where algorithm…
Nuclear density functional theory is the prevalent theoretical framework for accurately describing nuclear properties at the scale of the entire chart of nuclides. Given an energy functional and a many-body scheme (e.g., single- or…
We applied principal component analysis (PCA) to the study of five ground level enhancement (GLE) of cosmic ray (CR) events. The nature of the multivariate data involved makes PCA a useful tool for this study. A subroutine program written…
The idea of representation has been used in various fields of study from data analysis to political science. In this paper, we define representativeness and describe a method to isolate data points that can represent the entire data set.…
The concept of quantum correlation matrix for observables leads to the application of the PCA (Principal Component Analysis) also for quantum system in Hilbert space. It is shown that, in the case of a 2x2 spin system where the observables…
Relativistic energy density functionals have become a standard framework for nuclear structure studies of ground-state properties and collective excitations over the entire nuclide chart. We review recent developments in modeling nuclear…
Principal Component Analysis (PCA) via Singular Value Decomposition (SVD) of large datasets is an adaptive exploratory method to uncover natural patterns underlying the data. Several recent applications of the PCA-SVD to event-by-event…
Principal Component Analysis (PCA) is a transform for finding the principal components (PCs) that represent features of random data. PCA also provides a reconstruction of the PCs to the original data. We consider an extension of PCA which…
Muonic atom transitions have been measured for almost all stable nuclei to extract nuclear structure properties, including nuclear charge radii and quadrupole moment. To investigate the possibilities of extracting higher-order radial…
Principal component analysis (PCA) is widely used for dimensionality reduction, with well-documented merits in various applications involving high-dimensional data, including computer vision, preference measurement, and bioinformatics. In…
Classical Principal Component Analysis (PCA) approximates data in terms of projections on a small number of orthogonal vectors. There are simple procedures to efficiently compute various functions of the data from the PCA approximation. The…
The nuclear ground state properties of 67 80As nuclei have been investigated within the framework of relativistic mean field (RMF) approach. The RMF model with density dependent (DDME2) interaction is utilized for the calculation of…
Principal Component Analysis (PCA) is the most widely used tool for linear dimensionality reduction and clustering. Still it is highly sensitive to outliers and does not scale well with respect to the number of data samples. Robust PCA…
When the dimension of data is comparable to or larger than the number of data samples, Principal Components Analysis (PCA) may exhibit problematic high-dimensional noise. In this work, we propose an Empirical Bayes PCA method that reduces…
The model independent procedure of extracting charge density distributions from elastic electron scattering data is investigated. The charge density distributions are expanded on an orthonormal basis and the parameters of the expansions are…
We present a technique to perform dimensionality reduction on data that is subject to uncertainty. Our method is a generalization of traditional principal component analysis (PCA) to multivariate probability distributions. In comparison to…
Principal Component Analysis (PCA) is a cornerstone of dimensionality reduction, yet its classical formulation relies critically on second-order moments and is therefore fragile in the presence of heavy-tailed data and impulsive noise.…
Linear density response functions are calculated for symmetric nuclear matter of normal density by time-evolving two-time Green's functions in real time. The feasability and convenience of this approach to this particular problem has been…