Monte Carlo Simulation of a Modified Chi Distribution with Unequal Variances in the Generating Gaussians. A Discrete Methodology to Study Collective Response Times

Editorial of the Special Issue “Skewed (Asymmetrical) Probability Distributions and Applications across Disciplines”

This Special Issue includes a total of 14 articles on skewed probability distributions and applications across disciplines [...]

Evaluation and Mathematical Analysis of a Four-Dimensional Lotka–Volterra-like Equation Designed to Describe the Batch Nisin Production System

Nisin, an antibacterial compound produced by Lactococcus lactis strains, has been approved by the US Food and Drug Administration to be used as a safe food additive to control the growth of undesirable pathogenic bacteria. Nisin is commonly described as a pH-dependent primary metabolite since its production depends on growth and culture pH evolution. However, the relationships between bacteriocin synthesis (BT), biomass production (X), culture pH, and the consumption of the limiting nutrient (total nitrogen: TN) have not been described until now. Therefore, this study aims to develop a competitive four-dimensional Lotka–Volterra-like Equation (predator-prey system) to describe these complex relationships in three series of batch fermentations with L. lactis CECT 539 in diluted whey (DW)-based media. The developed four-dimensional predator-prey system accurately described each individual culture, providing a good description of the relationships between pH, TN, X, and BT, higher values for R2 and F-ratios, lower values (<10%) for the mean relative percentage deviation modulus, with bias and accuracy factor values approximately equal to one. The mathematical analysis of the developed equation showed the existence of one asymptotically stable equilibrium point, and the phase’s diagram obtained did not show the closed elliptic trajectories observed in biological predator-prey systems.

Monte Carlo Simulation of a Modified Chi Distribution Considering Asymmetry in the Generating Functions: Application to the Study of Health-Related Variables

Random variables in biology, social and health sciences commonly follow skewed distributions. Many of these variables can be represented by exGaussian functions; however, in practice, they are sometimes considered as Gaussian functions when statistical analysis is carried out. The asymmetry can play a fundamental role which can not be captured by central tendency estimators such as the mean. By means of Monte Carlo simulations, the effect of a small asymmetry in the generating functions of the chi distribution is studied. To this end, the k generating functions are taken as exGaussian functions. The limits of this approximation are tested numerically for the practical case of three health-related variables: one physical (body mass index) and two cognitive (verbal fluency and short-term memory). This work is in line with our previous works on a physics-inspired mathematical model to represent the reaction times of a group of individuals.

Human Reaction Times: Linking Individual and Collective Behaviour Through Physics Modeling

An individual’s reaction time data to visual stimuli have usually been represented in Experimental Psychology by means of an ex-Gaussian function. In most previous works, researchers have mainly aimed at finding a meaning for the parameters of the ex-Gaussian function which are known to correlate with cognitive disorders. Based on the recent evidence of correlations between the reaction time series to visual stimuli produced by different individuals within a group, we go beyond and propose a Physics-inspired model to represent the reaction time data of a coetaneous group of individuals. In doing so, a Maxwell–Boltzmann-like distribution appeared, the same distribution as for the velocities of the molecules in an Ideal Gas model. We describe step by step the methodology we use to go from the individual reaction times to the distribution of the individuals response within the coetaneous group. In practical terms, by means of this model we also provide a simple entropy-based methodology for the classification of the individuals within the collective they belong to with no need for an external reference which can be applicable in diverse areas of social sciences.