Related papers: The Lost Art of Mathematical Modelling
Mathematical modelling allows us to concisely describe fundamental principles in biology. Analysis of models can help to both explain known phenomena, and predict the existence of new, unseen behaviours. Model analysis is often a complex…
Quantitative methods and mathematical modeling are playing an increasingly important role across disciplines. As a result, interdisciplinary mathematics courses are increasing in popularity. However, teaching such courses at an advanced…
The goal of this paper is to advance an extensible theory of living systems using an approach to biomathematics and biocomputation that suitably addresses self-organized, self-referential and anticipatory systems with multi-temporal…
Machine learning (ML) is becoming increasingly crucial in many fields of engineering but has not yet played out its full potential in bioprocess engineering. While experimentation has been accelerated by increasing levels of lab automation,…
This paper outlines the implications of neural-level accounts of insight, and models of the conceptual interactions that underlie creativity, for a theory of cultural evolution. Since elements of human culture exhibit cumulative, adaptive,…
Much of current machine learning (ML) research has lost its connection to problems of import to the larger world of science and society. From this perspective, there exist glaring limitations in the data sets we investigate, the metrics we…
Simulation serves as a third way of doing science, in contrast to both induction and deduction. The web based modeling may considerably facilitate the execution of simulations by other people. We present examples of agent-based and…
Mathematical methods provide useful framework for the analysis and design of complex systems. In newer contexts such as biology, however, there is a need to both adapt existing methods as well as to develop new ones. Using a combination of…
This paper presents a comprehensive overview on the applications of artificial intelligence (AI) in mathematical research, highlighting the transformative role AI has begun to play in this domain. Traditionally, AI advancements have heavily…
The applicability of computational models to the biological world is an active topic of debate. We argue that a useful path forward results from abandoning hard boundaries between categories and adopting an observer-dependent, pragmatic…
Mathematical understanding is built in many ways. Among these, illustration has been a companion and tool for research for as long as research has taken place. We use the term illustration to encompass any way one might bring a mathematical…
The growing disconnection of the majority of population from mathematics is becoming a phenomenon that is increasingly difficult to ignore. This paper attempts to point to deeper roots of this cultural and social phenomenon. It concentrates…
There is a growing need to integrate sustainability into tertiary mathematics education given the urgency of addressing global environmental challenges. This paper presents four case studies from Australian university courses that…
Modeling and simulation (M&S) has revolutionized the way modern engineered products are designed, tested and evaluated. Yet modeling and simulation is much less frequently applied in the study of natural biological and active matter…
This paper is a first step to chase the ambitious objective of developing a mathmatical theory of living systems. The contents refer modeling large systems of interacting living entities with the aim of describing their collective behaviors…
Computing in the life sciences has undergone a transformative evolution, from early computational models in the 1950s to the applications of artificial intelligence (AI) and machine learning (ML) seen today. This paper highlights key…
This review is an introduction to theoretical models and mathematical calculations for biological evolution, aimed at physicists. The methods in the field are naturally very similar to those used in statistical physics, although the…
The theoretical biologist Robert Rosen developed a highly original approach for investigating the question "What is life?", the most fundamental problem of biology. Considering that Rosen made extensive use of mathematics it might seem…
In the emerging era of big data, larger available clinical datasets and computational advances have sparked a massive interest in machine learning-based approaches. The number of manuscripts related to machine learning or artificial…
Standard economic theory uses mathematics as its main means of understanding, and this brings clarity of reasoning and logical power. But there is a drawback: algebraic mathematics restricts economic modeling to what can be expressed only…