Related papers: Using Principal Component Analysis to Distinguish …
Principal component analysis (PCA) is a powerful method that can identify patterns in large, complex data sets by constructing low-dimensional order parameters from higher-dimensional feature vectors. There are increasing efforts to use…
The principal component analysis (PCA), a mathematical tool commonly used in statistics, has recently been employed to interpret the $p_T$-dependent fluctuations of harmonic flow $v_n$ in terms of leading and subleading flow modes in heavy…
We present results from extensive simulations of driven vortex lattices interacting with periodic arrays of pinning sites. Changing an applied driving force produces a rich variety of novel dynamical plastic flow phases which are very…
In this work we investigate the Principal Component Analysis (PCA) sensitivity to the velocity power spectrum in high opacity regimes of the interstellar medium (ISM). For our analysis we use synthetic Position-Position-Velocity (PPV) cubes…
We perform a principal component analysis (PCA) of two one-dimensional lattice models belonging to distinct nonequilibrium universality classes - directed bond percolation and branching and annihilating random walks with even number of…
In this paper, we implement Principal Component Analysis (PCA) to study the single particle distributions generated from thousands of {\tt VISH2+1} hydrodynamic simulations with an aim to explore if a machine could directly discover flow…
We apply principal component analysis, a method frequently used in image processing and unsupervised machine learning, to characterize particle displacements observed in the steady shear flow of amorphous solids. PCA produces a…
In type-II superconductors, the dynamics of superconducting vortices determine their transport properties. In the Ginzburg-Landau theory, vortices correspond to topological defects in the complex order parameter. Extracting their precise…
In this work, we develop a novel principal component analysis (PCA) for semimartingales by introducing a suitable spectral analysis for the quadratic variation operator. Motivated by high-dimensional complex systems typically found in…
We outline how principal component analysis (PCA) can be applied to particle configuration data to detect a variety of phase transitions in off-lattice systems, both in and out of equilibrium. Specifically, we discuss its application to…
We study experimentally and theoretically, the reorganization of superconducting vortices driven by oscillatory forces near the plastic depinning transition. We show that the system can be taken to configurations that are tagged by the…
We review the depinning and nonequilibrium phases of collectively interacting particle systems driven over random or periodic substrates. This type of system is relevant to vortices in type-II superconductors, sliding charge density waves,…
Principal component analysis (PCA) aims at estimating the direction of maximal variability of a high-dimensional dataset. A natural question is: does this task become easier, and estimation more accurate, when we exploit additional…
Using Langevin dynamics, we have investigated the dynamics of vortices in a disordered two dimensional superconductor subjected to a uniform driving current. The results provide direct numerical evidence for a dynamical phase transition…
The dynamic transition between the ordered flow and the plastic flow is studied for a two-dimensional driven vortex lattice, in the presence of sharp and dense pinning centers, from numerical simulations. For this system, which does not…
We examine vortex pinning and dynamics in thin-film superconductors interacting with square and rectangular pinning arrays for varied vortex densities including densities significantly larger than the pinning density. For both square and…
Principal component analysis (PCA) is often used for analyzing data in the most diverse areas. In this work, we report an integrated approach to several theoretical and practical aspects of PCA. We start by providing, in an intuitive and…
We demonstrate the utility of an unsupervised machine learning tool for the detection of phase transitions in off-lattice systems. We focus on the application of principal component analysis (PCA) to detect the freezing transitions of…
It is shown that Principal Component Analysis (PCA) applied to event-by-event single-particle distributions in A-A collisions allows establishing the most optimal basis for anisotropic flow studies from data itself, in contrast to manual…
In superconductors, the motion of vortices introduces unwanted dissipation that is disruptive to applications. Fortunately, material defects can immobilize vortices, acting as vortex pinning centers, which engenders dramatic improvements in…