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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…
In many reacting flow systems, the thermo-chemical state-space is known or assumed to evolve close to a low-dimensional manifold (LDM). Various approaches are available to obtain those manifolds and subsequently express the original…
Principal Component Analysis (PCA) is a powerful tool in statistics and machine learning. While existing study of PCA focuses on the recovery of principal components and their associated eigenvalues, there are few precise characterizations…
We study the distributed computing setting in which there are multiple servers, each holding a set of points, who wish to compute functions on the union of their point sets. A key task in this setting is Principal Component Analysis (PCA),…
In this paper, we consider clustering based on principal component analysis (PCA) for high-dimension, low-sample-size (HDLSS) data. We give theoretical reasons why PCA is effective for clustering HDLSS data. First, we derive a geometric…
A full understanding of the spacetime evolution of the QCD matter created in a heavy ion collision requires understanding the properties of the initial stages. In the weak coupling picture these are dominated by classical gluon fields,…
The initial temperature $T_{i}$, energy density $\varepsilon_{i}$, and formation time $\tau_{i}$ of the initial state of the QGP formed in the heavy ion collisions at RHIC and LHC energies are determined using the data driven Color String…
We consider estimation of large approximate factor models in high-dimensional panels of stationary time series using Principal Component Analysis (PCA). We review the key results establishing the necessary and sufficient conditions for…
The Principal Component Analysis (PCA) is a data dimensionality reduction technique well-suited for processing data from sensor networks. It can be applied to tasks like compression, event detection, and event recognition. This technique is…
In heavy-ion collisions, momentum-dependent pair correlations can be characterized by a principal component analysis (PCA), in which subleading modes are expected to reveal new information on flow fluctuations. However, we find that, as…
Principal Component Analysis (PCA) is a well-known multivariate technique used to decorrelate a set of vectors. PCA has been extensively applied in the past to the classification of stellar and galaxy spectra. Here we apply PCA to the…
Fluctuations are one of the main probes of the physics of the new state of hot and dense nuclear matter called the Quark Gluon Plasma (QGP) which is created in the ultra-relativistic heavy ion collisions. In this dissertation we extend and…
Four models for the initial conditions of a fluid dynamic description of high energy heavy ion collisions are analysed and compared. We study expectation values and event-by-event fluctuations in the initial transverse energy density…
Principal Component Analysis (PCA) is one of the most commonly used statistical methods for data exploration, and for dimensionality reduction wherein the first few principal components account for an appreciable proportion of the…
(Abridged) Environmental differences in the stellar populations of early-type galaxies are explored using principal component analysis (PCA), focusing on differences between elliptical galaxies in Hickson Compact Groups (HCGs) and in the…
The PYTHIA Monte Carlo (PMC) has been applied broadly to simulations of high-energy $p$-$p$ and $p$-$\bar p$ collisions. The PMC is based on several assumptions, such as that most hadrons result from jet production (multiple parton…
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…
This work investigates the possibility of accessing the initial geometric shape of the proton in proton-proton and proton-nucleus collisions at the LHC. In particular, we look for manifestations of the configuration in which the proton is…
We initialize the Quantum Chromodynamic conserved charges of baryon number, strangeness, and electric charge arising from gluon splitting into quark-antiquark pairs for the initial conditions of relativistic heavy-ion collisions. A new…
We investigate the sensitivity of low-energy nuclear collisions to intrinsic nuclear structure by studying the interplay between initial-state geometry and final-state observables in C+C and C+Pb collisions at $\sqrt{s_{NN}}=2.36$~GeV,…