Stability analysis for periodic solutions of fuzzy shunting inhibitory CNNs with delays

https://advancesindifferenceequations.springeropen.com/articles/10.1186/s13662-019-2321-z#rightslinkWe consider fuzzy shunting inhibitory cellular neural networks (FSICNNs) with time-varying coefficients and constant delays. By virtue of continuation theorem of coincidence degree theory and Cauchy–Schwartz inequality, we prove the existence of periodic solutions for FSICNNs. Furthermore, by employing a suitable Lyapunov functional we establish sufficient criteria which ensure global exponential stability of the periodic solutions. Numerical simulations that support the theoretical discussions are depicted

Experimental study of Pac-Man conditions for learn-ability of discrete linear dynamical systems

Submitted to the Department of Mathematics on May 1, 2019, in partial fulfillment of the requirements for the degree of Master of Applied MathematicsIn this work, we are going to reconstruct parameters of a discrete dynamical system with a hidden layer, given by a quadruple of matrices (,,,), from system’s past behaviour. First, we reproduced experimentally the well-known result of Hardt et al. that the reconstruction can be made under some conditions, called Pac-Man conditions. Then we demonstrated experimentally that the system approaches the global minimum even if an input is a sequence of i.i.d. random variables with a nongaussian distribution. We also formulated hypotheses beyond Pac-Man conditions that Gradient Descent solves the problem if the operator norm (or alternatively, the spectral radius) of transition matrix is bounded by 1 and obtained the negative result, i.e. a counterexample to those conjectures

Experimental study of Pac-Man conditions for learn-ability of discrete linear dynamical systems

Submitted to the Department of Mathematics on May 1, 2019, in partial fulfillment of the requirements for the degree of Master of Applied MathematicsIn this work, we are going to reconstruct parameters of a discrete dynamical system with a hidden layer, given by a quadruple of matrices (,,,), from system’s past behaviour. First, we reproduced experimentally the well-known result of Hardt et al. that the reconstruction can be made under some conditions, called Pac-Man conditions. Then we demonstrated experimentally that the system approaches the global minimum even if an input is a sequence of i.i.d. random variables with a nongaussian distribution. We also formulated hypotheses beyond Pac-Man conditions that Gradient Descent solves the problem if the operator norm (or alternatively, the spectral radius) of transition matrix is bounded by 1 and obtained the negative result, i.e. a counterexample to those conjectures