Related papers: The nature of mathematical models
There are versions of "calculus" in many settings, with various mixtures of algebra and analysis. In these informal notes we consider a few examples that suggest a lot of interesting questions.
Exploring further the connection between exponentiation on real closed fields and the existence of an integer part modelling strong fragments of arithmetic, we demonstrate that each model of true arithmetic is an integer part of an…
In modern science, computer models are often used to understand complex phenomena, and a thriving statistical community has grown around analyzing them. This review aims to bring a spotlight to the growing prevalence of stochastic computer…
Given a collection of computational models that all estimate values of the same natural process, we compare the performance of the average of the collection to the individual member whose estimates are nearest a given set of observations.…
A recent trend in mathematical modeling is to publish the computer code together with the research findings. Here we explore the formal question, whether and in which sense a computer implementation is distinct from the mathematical model.…
Understanding the mechanisms of interactions within cells, tissues, and organisms is crucial to driving developments across biology and medicine. Mathematical modeling is an essential tool for simulating biological systems and revealing…
Modelling quantum devices is to find a model according to quantum theory that can explain the result of experiments in a quantum device. We find that usually we cannot correctly identify the model describing the actual physics of the device…
The concept of random dynamical system is a comparatively recent development combining ideas and methods from the well developed areas of probability theory and dynamical systems. Due to our inaccurate knowledge of the particular physical…
We study a physically motivated representation of an algebra of operators in gravitational and non gravitational theories called the covariant representation of an algebra. This is a representation where the symmetries of the operator…
In many applications of interacting systems, we are only interested in the dynamic behavior of a subset of all possible active species. For example, this is true in combustion models (many transient chemical species are not of interest in a…
The 2-matrix model has been introduced to study Ising model on random surfaces. Since then, the link between matrix models and combinatorics of discrete surfaces has strongly tightened. This manuscript aims to investigate these deep links…
Mathematical modeling is an essential step, for example, to analyze the transient behavior of a dynamical process and to perform engineering studies such as optimization and control. With the help of first-principles and expert knowledge, a…
The effects of any quantum measurement can be described by a collection of measurement operators {M_m} acting on the quantum state of the measured system. However, the Hilbert space formalism tends to obscure the relationship between the…
Physical processes rarely occur in isolation, rather they influence and interact with one another. Thus, there is great benefit in modeling potential dependence between both spatial locations and different processes. It is the interaction…
In this article, numerical integration is formulated as evaluation of a matrix function of a matrix that is obtained as a projection of the multiplication operator on a finite-dimensional basis. The idea is to approximate the continuous…
Models continue to increase their already broad use across industry as well as their sophistication. Worldwide regulation oblige financial institutions to manage and address model risk with the same severity as any other type of risk, which…
In consciousness science, several promising approaches have been developed for how to represent conscious experience in terms of mathematical spaces and structures. What is missing, however, is an explicit definition of what a 'mathematical…
Modeling processes are the activities of capturing and representing processes and control of their dynamic behavior. Desired features of the model include capture of relevant aspects of a real phenomenon, understandability, and completeness…
Probabilistic programming is related to a compositional approach to stochastic modeling by switching from discrete to continuous time dynamics. In continuous time, an operator-algebra semantics is available in which processes proceeding in…
Computational simulations are a popular method for testing hypotheses about the emergence of communication. This kind of research is performed in a variety of traditions including language evolution, developmental psychology, cognitive…