In this paper, we consider nonlinear control systems and discuss the existence of a separable Lyapunov function. To end, assume that system can be decomposed into subsystems formulate conditions such weighted sum functions yields function overall system. Since deep neural networks are capable approximating without suffering from curse dimensionality, thus identify where an efficient approximati...

Designing an optimal deep neural network for a given task is important and challenging in many machine learning applications. To address this issue, we introduce self-adaptive algorithm: the adaptive enhancement (ANE) method, written as loops of formtrain→estimate→enhance. Starting with small two-layer (NN), step train to solve optimization problem at current NN; estimate compute posteriori est...

It is shown that artificial neural networks may serve as perfect candidate/ importance densities in Markov chain Monte Carlo and Importance Sampling methods for two reasons. First, artificial neural network functions possess a universal approximation property. Second, it is also easy to sample pseudo random draws from such networks. Given this existence property, several procedures are presente...

Image segmentation plays a crucial role in many medical imaging applications and is an important but inherently difficult problem. This paper discusses the method that classifies unsupervised image using a Kohonen self-organizing map neural network. This method has two problems: training time of the network is too long and the classified result and quantity are much easily influenced by the noi...

Capabilities of linear and neural-network models are compared from the point of view of requirements on the growth of model complexity with an increasing accuracy of approximation. Upper bounds on worst-case errors in approximation by neural networks are compared with lower bounds on these errors in linear approximation. The bounds are formulated in terms of singular numbers of certain operator...