Analytical Solution to a Third-Order Rational Difference Equation.

Inspired by some open conjectures in a rational dynamical system by G. Ladas and Palladino, in this paper, we consider the problem of solving a third-order difference equation. We comment the conjecture by Ladas. A third-order rational difference equation is solved analytically. The solution is compared with the solution to the linearized equation. We show that the solution to the linearized equation is not good, in general. The methods employed here may be used to solve other rational difference equations. The period of the solution is calculated. We illustrate the accuracy of the obtained solutions in concrete examples.

Artificial neural network-based heuristic to solve COVID-19 model including government strategies and individual responses.

The current work aims to design a computational framework based on artificial neural networks (ANNs) and the optimization procedures of global and local search approach to solve the nonlinear dynamics of the spread of COVID-19, i.e., the SEIR-NDC model. The combination of the Genetic algorithm (GA) and active-set approach (ASA), i.e., GA-ASA, works as a global-local search scheme to solve the SEIR-NDC model. An error-based fitness function is optimized through the hybrid combination of the GA-ASA by using the differential SEIR-NDC model and its initial conditions. The numerical performances of the SEIR-NDC nonlinear model are presented through the procedures of ANNs along with GA-ASA by taking ten neurons. The correctness of the designed scheme is observed by comparing the obtained results based on the SEIR-NDC model and the reference Adams method. The absolute error performances are performed in suitable ranges for each dynamic of the SEIR-NDC model. The statistical analysis is provided to authenticate the reliability of the proposed scheme. Moreover, performance indices graphs and convergence measures are provided to authenticate the exactness and constancy of the proposed stochastic scheme.

A Cloud-Based Machine Learning Approach to Reduce Noise in ECG Arrhythmias for Smart Healthcare Services.

ECG (electrocardiogram) identifies and traces targets and is commonly employed in cardiac disease detection. It is necessary for monitoring precise target trajectories. Estimations of ECG are nonlinear as the parameters TDEs (time delays) and Doppler shifts are computed on receipt of echoes where EKFs (extended Kalman filters) and electrocardiogram have not been examined for computations. ECG, certain times, results in poor accuracies and low SNRs (signal-to-noise ratios), especially while encountering complicated environments. This work proposes to track online filter performances while using optimization techniques to enhance outcomes with the removal of noise in the signal. The use of cost functions can assist state corrections while lowering costs. A new parameter is optimized using IMCEHOs (Improved Mutation Chaotic Elephant Herding Optimizations) by linearly approximating system nonlinearity where multi-iterative function (Optimized Iterative UKFs) predicts a target's unknown parameters. To obtain optimal solutions theoretically, multi-iterative function takes less iteration, resulting in shorter execution times. The proposed multi-iterative function provides numerical approximations, which are derivative-free implementations. Signals are updated in the cloud environment; the updates are received by the patients from home. The simulation evaluation results with estimators show better performances in terms of reduced NMSEs (normalized mean square errors), RMSEs (root mean squared errors), SNRs, variances, and better accuracies than current approaches. Machine learning algorithms have been used to predict the stages of heart disease, which is updated to the patient in the cloud environment. The proposed work has a 91.0% accuracy rate with an error rate of 0.05% by reducing noise levels.