Related papers: Asymptotic analysis of a selection model with spac…
We consider statistical inference in high-dimensional regression problems under affine constraints on the parameter space. The theoretical study of this is motivated by the study of genetic determinants of diseases, such as diabetes, using…
We propose a model for describing the growth on an untreated tumor, which is characterized in a simple way by a minimal number of parameters with a well-defined physical interpretation. The model is motivated by invoking the Master Equation…
Adaptive therapy (AT) is designed to postpone the emergence of drug resistance by exploiting evolutionary competition among tumor subclones. Most mathematical models of AT assume a binary population structure of drug-sensitive and…
In this paper, we study the asymptotic (large time) behavior of a selection-mutation-competition model for a population structured with respect to a phenotypic trait, when the rate of mutation is very small. We assume that the reproduction…
We consider a one--spatial dimensional tumour growth model [2, 3, 4] that consists of three dependent variables of space and time: volume fraction of tumour cells, velocity of tumour cells, and nutrient concentration. The model variables…
We investigate the large time behavior of an agent based model describing tumor growth. The microscopic model combines short-range repulsion and cell division. As the number of cells increases exponentially in time, the microscopic model is…
Geographic ranges of communities of species evolve in response to environmental, ecological, and evolutionary forces. Understanding the effects of these forces on species' range dynamics is a major goal of spatial ecology. Previous…
We consider two minimal mathematical models for cancer dynamics and self-adaptation. We aim to capture the interplay between the rapid progression of cancer growth and the possibility to leverage and enhance self-adaptive defense mechanisms…
Fisher's geometric model was originally introduced to argue that complex adaptations must occur in small steps because of pleiotropic constraints. When supplemented with the assumption of additivity of mutational effects on phenotypic…
We consider a model describing the evolution of a tumor inside a host tissue in terms of the parameters $\varphi_p$, $\varphi_d$ (proliferating and dead cells, respectively), $u$ (cell velocity) and $n$ (nutrient concentration). The…
Within the framework of classical field theory, the connection between the Dirac field as the field of matter and the spacetime metric is discussed. Polarization structure of the Dirac field is shown to be rich enough to determine the…
The evolution of dispersal is a classical question in evolutionary ecology, which has been widely studied with several mathematical models. The main question is to define the fittest dispersal rate for a population in a bounded domain, and,…
The interplay between space and evolution is an important issue in population dynamics, that is in particular crucial in the emergence of polymorphism and spatial patterns. Recently, biological studies suggest that invasion and evolution…
For a large number of random constraint satisfaction problems, such as random k-SAT and random graph and hypergraph coloring, there are very good estimates of the largest constraint density for which solutions exist. Yet, all known…
Phenotypic evolution implies sequential fixations of new genomic sequences. The speed at which these mutations fixate depends, in part, on the relative fitness (selection coefficient) of the mutant vs. the ancestor. Using a simple…
We consider a diffuse interface model of tumor growth proposed by A.~Hawkins-Daruud et al. This model consists of the Cahn-Hilliard equation for the tumor cell fraction $\varphi$ nonlinearly coupled with a reaction-diffusion equation for…
We analyse a non-local parabolic integro-differential equation modelling the evolutionary dynamics of a phenotypically-structured population in a changing environment. Such models arise in a variety of contexts from climate change to…
We consider integro-differential models describing the evolution of a population structured by a quantitative trait. Individuals interact competitively, creating a strong selection pressure on the population. On the other hand, mutations…
The availability of cancer measurements over time enables the personalised assessment of tumour growth and therapeutic response dynamics. However, many tumours are treated after diagnosis without collecting longitudinal data, and cancer…
Statistical analysis of alignments of large numbers of protein sequences has revealed "sectors" of collectively coevolving amino acids in several protein families. Here, we show that selection acting on any functional property of a protein,…