Related papers: The nature of mathematical models
In this article, the notion of a mathematical model in science is attempted to be enlightened from several points of view. In particular, it is shown that mathematical models are introduced differently and used differently in different…
The problem of mathematical modeling in geography is one of the most important strategies in order to establish the evolution and the prevision of geographical phenomena. Models must have a simplified structure, to reflect essential…
Mathematical models are vital to the field of metrology, playing a key role in the derivation of measurement results and the calculation of uncertainties from measurement data, informed by an understanding of the measurement process. These…
Mathematical modelling has a long history in the context of collective cell migration, with applications throughout development, disease and regenerative medicine. The aim of modelling in this context is to provide a framework in which to…
This text is addressed to mathematicians who are interested in generalized functions and unbounded operators on a Hilbert space. We expose in detail (in a "formal way" - as done by Heisenberg and Pauli - i.e. without mathematical…
The growing complexity of modern practical problems puts high demands on the mathematical modelling. Given that various models can be used for modelling one physical phenomenon, the role of model comparison and model choice becomes…
Basic principles of mathematical modeling are reviewed in this book, with the focus on physics and its practical applications, and examples of selected mathematical methods are presented. Most of the models have been imported from physics…
A mathematical model is a function taking certain arguments and returning a theoretical prediction of a feature of a physical system. The arguments to the mathematical model can be split into two groups; (a) controllable variables of the…
Statistical and mathematical modeling are crucial to describe, interpret, compare and predict the behavior of complex biological systems including the organization of hematopoietic stem and progenitor cells in the bone marrow environment.…
With the rise of computers, simulation models have emerged beside the more traditional statistical and mathematical models as a third pillar for ecological analysis. Broadly speaking, a simulation model is an algorithm, typically…
A primary goal of physics is to create mathematical models that allow both predictions and explanations of physical phenomena. We weave maths extensively into our physics instruction beginning in high school, and the level and complexity of…
The role of mathematical models in physics has for longer been well established. The issue of their proper building and use appears to be less clear. Examples in this regard from relativity and quantum mechanics are mentioned. Comments…
Traditional machine learning models, particularly neural networks, are rooted in finite-dimensional parameter spaces and nonlinear function approximations. This report explores an alternative formulation where learning tasks are expressed…
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…
Unlike computation or the numerical analysis of differential equations, simulation does not have a well established conceptual and mathematical foundation. Simulation is an arguable unique union of modeling and computation. However,…
In recent years, promising mathematical models have been suggested which aim to describe conscious experience and its relation to the physical domain. Whereas the axioms and metaphysical ideas of these theories have been carefully…
Simulation models are an absolute necessity in the human and social sciences, which can only very exceptionally use experimental science methods to construct their knowledge. Models enable the simulation of social processes by replacing the…
Stochastic models share many characteristics with generic parametric models. In some ways they can be regarded as a special case. But for stochastic models there is a notion of weak distribution or generalised random variable, and the same…
The use of mathematical models in the sciences often involves the estimation of unknown parameter values from data. Sloppiness provides information about the uncertainty of this task. In this paper, we develop a precise mathematical…
As the twin movements of open science and open source bring an ever greater share of the scientific process into the digital realm, new opportunities arise for the meta-scientific study of science itself, including of data science and…