Efficient Function Integration and a Case Study with Gompertz Functions for Covid-19 Waves

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.

Analysis of the Epidemic Curve of the Waves of COVID-19 Using Integration of Functions and Neural Networks in Peru

“…We used two versions of the integration of functions method, i.e., the concatenation of functions: the mathematical version and the computational version [14]. The novelty was the use of the sigmoidal-Boltzmann model for all COVID-19 waves.…”

“…, adding feature q to the training data (for example, consecutive numbers) [14], the coefficients are presented in Table 1.…”

“…Sigmoidal models adequately represent and describe COVID-19 waves. There are various works based on specific models, such as those by Gompertz, Brody, and von Berta-Informatics 2024, 11, 40 2 of 17 lanffy [7,[14][15][16][17]. In particular, the sigmoidal-Boltzmann model has a simple representation as compared to other similar examples (e.g., the Gompertz model), which is convenient considering that the execution time is an important factor in numerical algorithms in nonlinear regression.…”

Implementing Bisection Method on Forex Trading Database for Early Diagnosis of Inflection Point

“…Based on these problems, this research is focused on finding a solution by processing a database containing transaction data and forex value movements obtained from the meta trader application connected to the broker server [5][6][7]. From this problem arises the question, how to know the inflection point on a curve that can be seen by the user in real time [8].…”