Generative Adversarial Networks (GANs) are powerful Machine Learning models capable of generating fully synthetic samples a desired phenomenon with high resolution. Despite their success, the training process GAN is highly unstable and typically it necessary to implement several accessory heuristics networks reach an acceptable convergence model. In this paper, we introduce novel method analyze...

Reduced-order models of the flow in a plane channel flow are constructed in two regimes: a minimal flow unit in which turbulence is sustained, and a transitional flow linearized about the laminar profile. Proper orthogonal decomposition (POD) of data from a direct numerical simulation of a channel flow in a minimal flow unit is performed in order to examine the coherent structures and their dyn...

We consider in this article the analysis of multicomponent signals, defined as superpositions of modulated waves also called modes. More precisely, we focus on the analysis of a variant of the second-order synchrosqueezing transform, which was introduced recently, to deal with modes containing strong frequency modulation. Before going into this analysis, we revisit the case where the modes are ...

Large scale simulations of electrically coupled neuronal oscillators often employ the phase coupled oscillator paradigm to understand and predict network behavior. We study the nature of the interaction between such coupled oscillators using weakly coupled oscillator theory. By employing piecewise linear approximations for phase response curves and voltage time courses and parametrizing their s...