Related papers: Cosmic-Ray Mass Composition around the Knee via Pr…
Principal component analysis (PCA) represents a standard approach to identify collective variables $\{x_i\}\!=\!\boldsymbol{x}$, which can be used to construct the free energy landscape $\Delta G(\boldsymbol{x})$ of a molecular system.…
This paper examines several applications of principal component analysis (PCA) to physical systems. The first of these demonstrates that the principal components in a basis of appropriate system variables can be employed to identify…
We explore the physical implications of applying principal component analysis (PCA) to translationally invariant classical systems defined on a $d$-dimensional hypercubic lattice. Using Rayleigh-Schr\"odinger perturbation theory, we…
The status and capabilities of the KASCADE-Grande extensive air shower experiment are presented. The installation is located at Forschungszentrum Karlsruhe and comprises a large collecting area (0.5 km^2) electromagnetic array (Grande)…
By accurately measuring composition and energy spectrum of cosmic ray, the origin problem of so called "keen" region (energy > 1 PeV) can be solved. However, up to the present, the results of the spectrum in the knee region obtained by…
Remote sensing observations, products and simulations are fundamental sources of information to monitor our planet and its climate variability. Uncovering the main modes of spatial and temporal variability in Earth data is essential to…
We look for evidence for the evolution in dark energy density by employing Principal Component Analysis (PCA). Distance redshift data from supernovae and baryon acoustic oscillations (BAO) along with WMAP7 distance priors are used to put…
We propose novel methods for predictive (sparse) PCA with spatially misaligned data. These methods identify principal component loading vectors that explain as much variability in the observed data as possible, while also ensuring the…
More than fifty years after the discovery of the knee in the cosmic ray spectra, its physical origin remains a mystery. This is partly due to the ambiguity of the energy spectrum of individual composition. Recently, direct measurements from…
We have carried out a detailed study to understand the observed energy spectrum and composition of cosmic rays with energies up to ~10^18 eV. Our study shows that a single Galactic component with subsequent energy cut-offs in the individual…
We develop an efficient method to represent nuclear densities using basis functions extracted via Principal Component Analysis (PCA). Applying PCA to densities of 75 nuclei calculated with the relativistic continuum Hartree-Bogoliubov…
Principal Component Analysis (PCA) is applied to a variety of blazars to examine X-ray spectral variability. Data from nine different objects are analysed in two ways: long-term, which examines variability trends across years or decades,…
The origin of cosmic rays remains an unresolved fundamental problem in astrophysics. The synergy of multiple observational probes, including the energy spectra, the mass composition, and anisotropy is a viable way to jointly uncover this…
Principal component analysis (PCA) is a classical method for dimensionality reduction based on extracting the dominant eigenvectors of the sample covariance matrix. However, PCA is well known to behave poorly in the ``large $p$, small $n$''…
Principal Component Analysis (PCA) is an important tool of dimension reduction especially when the dimension (or the number of variables) is very high. Asymptotic studies where the sample size is fixed, and the dimension grows [i.e., High…
We study the correlations between the structural parameters of dark matter haloes using Principal Component Analysis (PCA). We consider a set of eight parameters, six of which are commonly used to characterize dark matter halo properties:…
The transition between the Galactic and extragalactic cosmic ray components could take place either in the region of the spectrum known as the second knee or in the ankle. There are several models of the transition but it is not possible to…
We use Principal Component Analysis (PCA) to analyze a volume-limited sample from the SDSS and explore how cosmic web environments affect the interrelations between various galaxy properties, such as $(u-r)$ colour, stellar mass, specific…
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…
Air showers, produced by the interaction of energetic cosmic rays with the atmosphere, are an excellent alternative to study particle physics at energies beyond any human-made particle accelerator. For that, it is necessary to identify…