Related papers: The evolution equation: an application of groupoid…
Due to the inherently nonlinear nature of gravity cosmological N-body simulations have become an invaluable tool when the growth of structure is being studied and modelled closer to the present epoch. Large simulations with high dynamical…
Mutations are typically classified by their effects on the nucleotide sequence and by their size. Here, we argue that if our main aim is to understand the effect of mutations on evolutionary outcomes (such as adaptation or speciation), we…
A Lie groupoid, called \textit{material Lie groupoid}, is associated in a natural way to any elastic material. The corresponding Lie algebroid, called \textit{material algebroid}, is used to characterize the uniformity and the homogeneity…
Associated to each material body $\mathcal{B}$ there exists a groupoid $\Omega \left( \mathcal{B} \right)$ consisting of all the material isomorphisms connecting the points of $\mathcal{B}$. The uniformity character of $\mathcal{B}$ is…
Numerical simulation of evolution of a cluster of a finite number of gravitating bodies interacting only by their intrinsic gravity has been carried out. The goal of the study was to reveal the main characteristic phases of the spatial…
Darwin's theory of evolution is considered to be one of the greatest scientific gems in modern science. It not only gives us a description of how living things evolve, but also shows how a population evolves through time and also, why only…
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…
The goal of this paper is to set up a framework designed to take into account the characteristics of sediment particles when transported by water. Our protocol consists in describing the characteristics of sediment particles via an…
Evolution and learning are two of the fundamental mechanisms by which life adapts in order to survive and to transcend limitations. These biological phenomena inspired successful computational methods such as evolutionary algorithms and…
We derive a class of thermodynamically consistent variants of Maxwell/Oldroyd-B type models for viscoelastic fluids. In particular, we study the models that allow one to consider temperature dependent material coefficients. This naturally…
A dynamical theory for the evolution of the genetic code is presented, which accounts for its universality and optimality. The central concept is that a variety of collective, but non-Darwinian, mechanisms likely to be present in early…
We introduce the notion of evolution on sets and study several sets endowed with this structure and obtain some results about this new notion.
This expository paper recounts the development and application of the concept of the diffeological groupoid, from its introduction in 1985 to its use in current research. We demonstrate how this single concept has served as a powerful and…
We consider a new approach to the description of the collective behavior of complex systems of mathematical biology based on the evolution equations for observables of such systems. This representation of the kinetic evolution seems, in…
In this paper we use group, action and orbit to understand how evolutionary solve nonconvex optimization problems.
Understanding why we age is a long-lived open problem in evolutionary biology. Aging is prejudicial to the individual and evolutionary forces should prevent it, but many species show signs of senescence as individuals age. Here, I will…
This paper introduces a variational formulation of natural selection, paying special attention to the nature of "things" and the way that different "kinds" of "things" are individuated from - and influence - each other. We use the Bayesian…
We first review the historical developments, both in physics and in mathematics, that preceded (and in some sense provided the background of) deformation quantization. Then we describe the birth of the latter theory and its evolution in the…
This is a survey on recent results on the Loewner theory in one and several complex manifolds
This study presents the approach to analyzing the evolution of an arbitrary complex system whose behavior is characterized by a set of different time-dependent factors. The key requirement for these factors is only that they must contain an…