ABSTRACT
In this paper we study the oscillatory behavior of a new class of memristor based neural networks with mixed delays and we prove the existence and uniqueness of the periodic solution of the system based on the concept of Filippov solutions of the differential equation with discontinuous right-hand side. In addition, some assumptions are determined to guarantee the globally exponentially stability of the solution. Then, we study the adaptive finite-time complete periodic synchronization problem and by applying Lyapunov-Krasovskii functional approach, a new adaptive controller and adaptive update rule have been developed. A useful finite-time complete synchronization condition is established in terms of linear matrix inequalities. Finally, an illustrative simulation is given to substantiate the main results.
ABSTRACT
The interpretation of biological data such as the ElectroCardioGram (ECG) signal gives clinical information and helps to assess the heart function. There are distinct ECG patterns associated with a specific class of arrhythmia. The convolutional neural network, inspired by findings in the study of biological vision, is currently one of the most commonly employed deep neural network algorithms for ECG processing. However, deep neural network models require many hyperparameters to tune. Selecting the optimal or the best hyperparameter for the convolutional neural network algorithm is a highly challenging task. Often, we end up tuning the model manually with different possible ranges of values until a best fit model is obtained. Automatic hyperparameters tuning using Bayesian Optimization (BO) and evolutionary algorithms can provide an effective solution to current labour-intensive manual configuration approaches. In this paper, we propose to optimize the Residual one Dimensional Convolutional Neural Network model (R-1D-CNN) at two levels. At the first level, a residual convolutional layer and one-dimensional convolutional neural layers are trained to learn patient-specific ECG features over which multilayer perceptron layers can learn to produce the final class vectors of each input. This level is manual and aims to limit the search space and select the most important hyperparameters to optimize. The second level is automatic and based on our proposed BO-based algorithm. Our optimized proposed architecture (BO-R-1D-CNN) is evaluated on two publicly available ECG datasets. Comparative experimental results demonstrate that our BO-based algorithm achieves an optimal rate of 99.95% for the MIT-BIH database to discriminate between five kinds of heartbeats, including normal heartbeats, left bundle branch block, atrial premature, right bundle branch block, and premature ventricular contraction. Moreover, experiments demonstrate that the proposed architecture fine-tuned with BO achieves a higher accuracy tested on the 10,000 ECG patients dataset compared to the other proposed architectures. Our optimized architecture achieves excellent results compared to previous works on the two benchmark datasets.
ABSTRACT
This paper is concerned with the existence and uniqueness of pseudo almost-periodic solutions to recurrent delayed neural networks. Several conditions guaranteeing the existence and uniqueness of such solutions are obtained in a suitable convex domain. Furthermore, several methods are applied to establish sufficient criteria for the globally exponential stability of this system. The approaches are based on constructing suitable Lyapunov functionals and the well-known Banach contraction mapping principle. Moreover, the attractivity and exponential stability of the pseudo almost-periodic solution are also considered for the system. A numerical example is given to illustrate the effectiveness of our results.
