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Two types of spatiotemporal chaos exhibited by ensembles of coupled nonlinear oscillators are analyzed using independent component analysis (ICA). For diffusively coupled complex Ginzburg-Landau oscillators that exhibit smooth amplitude patterns, ICA extracts localized one-humped basis vectors that reflect the characteristic hole structures of the system, and for nonlocally coupled complex Ginzburg-Landau oscillators with fractal amplitude patterns, ICA extracts localized basis vectors with characteristic gap structures. Statistics of the decomposed signals also provide insight into the complex dynamics of the spatiotemporal chaos.
We study Lyapunov vectors (LVs) corresponding to the largest Lyapunov exponents in systems with spatiotemporal chaos. We focus on characteristic LVs and compare the results with backward LVs obtained via successive Gram-Schmidt orthonormalizations. S
Extreme events such as rogue wave in optics and fluids are often associated with the merging dynamics of coherent structures. We present experimental and numerical results on the physics of extreme events appearance in a spatially extended semiconduc
Independent component analysis (ICA) has been widely used for blind source separation in many fields such as brain imaging analysis, signal processing and telecommunication. Many statistical techniques based on M-estimates have been proposed for esti
Compositional data represent a specific family of multivariate data, where the information of interest is contained in the ratios between parts rather than in absolute values of single parts. The analysis of such specific data is challenging as the a
Fast Independent Component Analysis (FastICA) is a component separation algorithm based on the levels of non-Gaussianity. Here we apply the FastICA to the component separation problem of the microwave background including carbon monoxide (CO) line em