Mathematical model with bias and influence coefficients in the theoretical relationship of scientific thought: analysis from the larval bioregulator Gambusia punctata Poey, 1854.

Abstract

The aim of the study was to propose a mathematical model with bias and coefficients of influence in the theoretical relationship of scientific thought: analysis from the larval bio-regulator Gambusia punctata Poey, 1854. The study was conducted between January and April 2024. The mathematical model is based on the independent variable (-Vi), the dependent variable (-Vd), a control coefficient (m), and an exponential function (e^-Vd). A coefficient (s) that adjusts the initial bias is considered. Two equations were proposed as a mathematical model: 1st) -Vi = m ⋅ (1−e^-Vd) + s ⋅ (1−e), and 2nd) -Vd = Ʃⁿ_i=1 [m ⋅ -Vi ⋅ (1−e^-Vd)] + s ⋅ (1−e). The selection will depend on identifying one or several independent variables. The value m was determined through weighted values: -0.2 (minor influence), -0.4 (moderate influence), -0.6 (considerable influence), and -0.8 (significant influence) referring from perceptible but limited changes to fundamental and marked changes in the values or results of the dependent variable. The allocation of weighted values was based on the theoretical understanding of the system where empirical and theoretical data are integrated. The inclusion of the exponential function improves accuracy on complex non-linear cause-effect relationships in natural systems. It is concluded that the proposed mathematical model, supported by weighted assignments and an exponential function, provides a robust tool to understand and predict responses in complex systems. Although initial subjectivity may introduce some uncertainty, a rigorous review of scientific literature minimizes potential biases, ensuring its validity and utility in science.