Related papers: Study of a general growth model
Longitudinal processes often unfold concurrently where the growth of two or more longitudinal outcomes are associated. Additionally, if the study under investigation is long, the growth curves may exhibit nonconstant change with respect to…
Using continuation methods, we study the global solution structure of periodic solutions for a class of periodically forced equations, generalizing the case of relativistic pendulum. We obtain results on the existence and multiplicity of…
Random growth models are fundamental objects in modern probability theory, have given rise to new mathematics, and have numerous applications, including tumor growth and fluid flow in porous media. In this article, we introduce some of the…
The paper examines random dynamical systems related to the classical von Neumann and Gale models of economic growth. Such systems are defined in terms of multivalued operators in spaces of random vectors, possessing certain properties of…
A broader definition of generalized truncations of graphs is introduced followed by an exploration of some standard concepts and parameters with regard to generalized truncations.
Development and growth are complex and tumultuous processes. Modern economic growth theories identify some key determinants of economic growth. However, the relative importance of the determinants remains unknown, and additional variables…
The dynamics of linear stochastic growth equations on growing substrates is studied. The substrate is assumed to grow in time following the power law $t^\gamma$, where the growth index $\gamma$ is an arbitrary positive number. Two different…
Random features models play a distinguished role in the theory of deep learning, describing the behavior of neural networks close to their infinite-width limit. In this work, we present a thorough analysis of the generalization performance…
We study the growth dynamics of the size of manufacturing firms considering competition and normal distribution of competency. We start with the fact that all components of the system struggle with each other for growth as happened in real…
The learning curve expresses the error rate of a predictive modeling procedure as a function of the sample size of the training dataset. It typically is a decreasing, convex function with a positive limiting value. An estimate of the…
Diffusion models are a class of generative models that serve to establish a stochastic transport map between an empirically observed, yet unknown, target distribution and a known prior. Despite their remarkable success in real-world…
In this pedagogical study, carried out by adopting standard mathematical methods of nonlinear dynamics, we have presented some simple analytical models to understand terminal behaviour in industrial growth. This issue has also been…
Regression curves for studying trait relationships are developed herein. The adaptive evolution model is considered an Ornstein-Uhlenbeck system whose parameters are estimated by a novel engagement of generalized least-squares and…
Graphical modelling has a long history in statistics as a tool for the analysis of multivariate data, starting from Wright's path analysis and Gibbs' applications to statistical physics at the beginning of the last century. In its modern…
Mathematical models are increasingly a part of microbiological research. Here, we share our perspective on how modeling advances the discipline by: (i) enforcing logical consistency, (ii) enabling quantitative prediction, (iii) extracting…
A macroscopic model of the tumor Gompertzian growth is proposed. The new approach is based on the energetic balance among the different cell activities, described by methods of statistical mechanics and related to the growth inhibitor…
In this contribution we consider stochastic growth models in the Kardar-Parisi-Zhang universality class in 1+1 dimension. We discuss the large time distribution and processes and their dependence on the class on initial condition. This…
Determining the mathematical dynamics and associated parameter values that should be used to accurately reflect tumor growth continues to be of interest to mathematical modelers, experimentalists and practitioners. However, while there are…
In a series of papers we classify the possible torsion structures of rational elliptic curves base-extended to number fields of a fixed degree. In this paper we turn our attention to the question of how the torsion of an elliptic curve with…
The fundamental purpose of the present research article is to introduce the basic principles of Dimensional Analysis in the context of the neoclassical economic theory, in order to apply such principles to the fundamental relations that…