Related papers: Reciprocally induced coevolution: A computational …
In this book a multitude of Diophantine equations and their partial or complete solutions are presented. How should we solve, for example, the equation {\eta}({\pi}(x)) = {\pi}({\eta}(x)), where {\eta} is the Smarandache function and {\pi}…
Evolution is a fundamental process that shapes the biological world we inhabit, and reinforcement learning is a powerful tool used in artificial intelligence to develop intelligent agents that learn from their environment. In recent years,…
We survey some of our recent results on inverse problems for evolution equations. The goal is to provide a unified approach to solve various types of evolution equations. The inverse problems we consider consist in determining unknown…
The main topic of this thesis is the analysis of evolution equations reflecting issues in ecology and population dynamics. In mathematical modelling, the impact of environmental elements and the interaction between species is read into the…
Biological systems like long-lived clonal organisms, holobionts and clades challenge traditional evolutionary thinking since they adapt without populations or reproduction. This paper aims to provide an overarching theoretical framework…
Many of the mathematical frameworks describing natural selection are equivalent to Bayes Theorem, also known as Bayesian updating. By definition, a process of Bayesian Inference is one which involves a Bayesian update, so we may conclude…
Sweepstakes reproduction may be generated by chance matching of reproduction with favorable environmental conditions. Gene genealogies generated by sweepstakes reproduction are in the domain of attraction of multiple-merger coalescents…
Combinatorial evolution - the creation of new things through the combination of existing things - can be a powerful way to evolve rather than design technical objects such as electronic circuits. Intriguingly, this seems to be an ongoing…
Innovation and evolution are two processes of paramount relevance for social and biological systems. In general, the former allows to introduce elements of novelty, while the latter is responsible for the motion of a system in its phase…
These notes represent an extended version of a talk I gave for the participants of the IMO 2009 and other interested people. We introduce diophantine equations and show evidence that it can be hard to solve them. Then we demonstrate how one…
Cooperation is a widespread natural phenomenon yet current evolutionary thinking is dominated by the paradigm of selfish competition. Recent advanced in many fronts of Biology and Non-linear Physics are helping to bring cooperation to its…
Natural evolution gives the impression of leading to an open-ended process of increasing diversity and complexity. If our goal is to produce such open-endedness artificially, this suggests an approach driven by evolutionary metaphor. On the…
Population expansions trigger many biomedical and ecological transitions, from tumor growth to invasions of non-native species. Although population spreading often selects for more invasive phenotypes, we show that this outcome is far from…
Genome rearrangements are evolutionary events that shuffle genomic architectures. Most frequent genome rearrangements are reversals, translocations, fusions, and fissions. While there are some more complex genome rearrangements such as…
Concomitant with the evolution of biological diversity must have been the evolution of mechanisms that facilitate evolution, due to the essentially infinite complexity of protein sequence space. We describe how evolvability can be an object…
Reciprocal transformations mix the role of the dependent and independent variables to achieve simpler versions or even linearized versions of nonlinear PDEs. These transformations help in the identification of a plethora of PDEs available…
This research is concerned with evolution equations and their forward-backward discretizations. Our first contribution is an estimation for the distance between iterates of sequences generated by forward-backward schemes, useful in the…
Deep learning is used in computer vision problems with important applications in several scientific fields. In ecology for example, there is a growing interest in deep learning for automatizing repetitive analyses on large amounts of…
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…
Evolutionary and bioinspired computation are crucial for efficiently addressing complex optimization problems across diverse application domains. By mimicking processes observed in nature, like evolution itself, these algorithms offer…