Related papers: Using Principal Component Analysis to Distinguish …
Principal Component Analysis (PCA) is a well-known technique used to decorrelate a set of vectors. It has been applied to explore the star formation history of galaxies or to determine distances of mass-lossing stars. Here we apply PCA to…
We discuss the use of Langevin molecular dynamics in the investigation of the non-equilibrium properties of disordered vortex matter. Our special focus is set on values of system parameters that are realistic for disordered high-$T_c$…
We study effects of pinning on the dynamics of a vortex lattice in a type II superconductor in the strong-pinning situation and determine the force--velocity (or current--voltage) characteristic combining analytical and numerical methods.…
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…
Avalanche dynamics is found in many phenomena spanning from earthquakes to the evolution of species. It can be also found in vortex matter when a type II superconductor is externally driven, for example, by increasing the magnetic field.…
Principal component analysis is performed on Birkeland or field-aligned current (FAC) measurements from the Active Magnetosphere and Planetary Electrodynamics Response Experiment. Principal component analysis (PCA) identifies the patterns…
We experimentally characterize the transverse vortex motion and observed some striking features. We found large structures and peaks in the Hall resistance, which can be attributed to the long-range inhomogeneous vortex flow present in some…
Dynamics of vortices reflects the electronic states of quasiparticles in the core. To understand this, we investigated the following three issues. (1) We investigated the complex surface impedance, Zs, of YBa2Cu3Oy as a function of magnetic…
Sparse Principal Component Analysis (sPCA) is a cardinal technique for obtaining combinations of features, or principal components (PCs), that explain the variance of high-dimensional datasets in an interpretable manner. This involves…
Big data is transforming our world, revolutionizing operations and analytics everywhere, from financial engineering to biomedical sciences. The complexity of big data often makes dimension reduction techniques necessary before conducting…
Within the class of stochastic cellular automata models of traffic flows, we look at the velocity dependent randomization variant (VDR-TCA) whose parameters take on a specific set of extreme values. These initial conditions lead us to the…
The last decade has been marked by great interest in the dynamics of vortices moving at high ($>$10\,km/s) velocities in superconductors. However, the flux-flow instability (FFI) prevents its exploration and sets practical limits for the…
In superconductors, the search for special vortex states such as giant vortices focuses on laterally confined or nanopatterned thin superconducting films, disks, rings, or polygons. We examine the possibility to realize giant vortex states…
A simple model of the driven motion of interacting particles in a two dimensional random medium is analyzed, focusing on the critical behavior near to the threshold that separates a static phase from a flowing phase with a steady-state…
Order-disorder transitions take place in many physical systems, but observing them in detail in real materials is difficult. In two- or quasi-two-dimensional systems, the transition has been studied by computer simulations and…
The interplay between superconductivity and magnetism gives rise to many intriguing and exciting phenomena. In this Letter we report about a novel manifestation of this interplay: a temperature induced phase transition between different…
In type-II superconductors exposed to magnetic fields between upper and lower critical values, $H_{c1}$ and $H_{c2}$, penetrating magnetic flux forms a lattice of vortices whose motion can induce dissipation. Consequently, the magnetization…
We investigate the behavior of vortices of multi-component superconductivity, realized in $\rm{MgB_2}$ and Fe-based superconductors, within the framework of Ginzburg-Landau (GL) theory in terms of numerical calculations of the…
We present quasicyclic principal component analysis (QPCA), a generalization of principal component analysis (PCA), that determines an optimized basis for a dataset in terms of families of shift-orthogonal principal vectors. This is of…
This is a tutorial and survey paper on factor analysis, probabilistic Principal Component Analysis (PCA), variational inference, and Variational Autoencoder (VAE). These methods, which are tightly related, are dimensionality reduction and…