ABSTRACT
Simulating the behavior of a human heart, predicting tomorrow's weather, optimizing the aerodynamics of a sailboat, finding the ideal cooking time for a hamburger: to solve these problems, cardiologists, meteorologists, sportsmen, and engineers can count on math help. This book will lead you to the discovery of a magical world, made up of equations, in which a huge variety of important problems for our life can find useful answers. © The Editor(s) (if applicable) and The Author(s), under exclusive licence to Springer Nature Switzerland AG 2022. All rights reserved.
ABSTRACT
Numerical algorithms are widely used in different applications, therefore, the execution time of the functions involved in numerical algorithms is important, and, in some cases, decisive, for example, in machine learning algorithms. Given a finite set of independent functions A(x), B(x), …, Z(x) with domains defined by disjoint, consecutive, and not necessarily adjacent intervals, the main goal is to integrate into a single function F(x) = k1×A(x) + k2×B(x) + … + kn×Z(x), where each activation coefficient k, is one if x is in the interval of the respective domain and zero otherwise. The novelty of this work is the presentation and formal demonstration of two general forms of integration of functions in a single function: The first is the mathematical version and the second is the computational version (with the AND function at the bit level), which is characterized by its efficiency. The result is applied in a case study (Peru), where two regression functions were obtained that integrate all the waves of Covid-19, that is, the epidemic curve of the variable global number of deaths/infected per day, the adjustment provided a highly statistically significant measure of correlation, a Pearson's product-moment correlation of 0.96 and 0.98 respectively. Finally, the size of the epidemic was projected for the next 30 days © 2022, International Journal of Advanced Computer Science and Applications.All Rights Reserved.
ABSTRACT
We analyze a mathematical model of COVID-19 transmission control, which includes the interactions among different groups of the population: vaccinated, susceptible, exposed, infectious, super-spreaders, hospitalized and fatality, based on a system of ordinary differential equations, which describes compartment model of a disease and its treatment. The aim of the model is to predict the development disease under different types of treatment during some fixed time period. We develop a game theoretic approach and a dual dynamic programming method to formulate optimal conditions of the treatment for an administration of a vaccine. Next, we calculate numerically an optimal treatment. © 2022, The Author(s), under exclusive licence to Springer Nature B.V.