Related papers: Mutation frequencies in a birth-death branching pr…
The shapes of branching trees have been linked to disease transmission patterns. In this paper we use the general Crump-Mode-Jagers branching process to model an outbreak of an infectious disease under mild assumptions. Introducing a new…
Genetic mutations are footprints of tumour growth. While mutation data in bulk samples has been used to infer evolutionary parameters hard to measure in vivo, the advent of single-cell data has led to strong interest in the mutational…
We will study the relationship between two well-known theories, genetic evolution and random matrix theory in the context of many-body systems. It is suggested that genetic evolution can be described by a random matrix theory with…
The proliferation and migration dichotomy of the tumor cell invasion is examined within a two-component continuous time random walk (CTRW) model. The balance equations for the cancer cells of two phenotypes with random switching between…
Phenotype variations define heterogeneity of biological and molecular systems, which play a crucial role in several mechanisms. Heterogeneity has been demonstrated in tumor cells. Here, samples from blood of patients affected from colon…
Stem cells, through their ability to produce daughter stem cells and differentiate into specialized cells, are essential in the growth, maintenance, and repair of biological tissues. Understanding the dynamics of cell populations in the…
Recent progress in microdissection and in DNA sequencing has enabled subsampling of multi-focal cancers in organs such as the liver in several hundred spots, helping to determine the pattern of mutations in each of these spots. This has led…
We study the asymptotic behaviors of stochastic cell fate decision between proliferation and differentiation. We propose a model of a self-replicating Langevin system, where cells choose their fate (i.e. proliferation or differentiation)…
A bit-string model for the evolution of a population of haploid organisms, subject to competition, reproduction with mutation and selection is studied, using mean field theory and Monte Carlo simulations. We show that, depending on…
In this work, we develop a stochastic multiscale model for glioma growth and invasion in the brain, incorporating the effects of therapeutic interventions. The model accounts for tumor cell migration influenced by brain tissue heterogeneity…
Starting with the interpretation of parton evolution with rapidity as a branching-diffusion process, we describe the different kinds of fluctuations of the density of partons which affect the properties of QCD scattering amplitudes at…
We consider a generalization of the classical logistic growth model introducing more than one inflection point. The growth, called multi-sigmoidal, is firstly analyzed from a deterministic point of view in order to obtain the main…
Major efforts to sequence cancer genomes are now occurring throughout the world. Though the emerging data from these studies are illuminating, their reconciliation with epidemiologic and clinical observations poses a major challenge. In the…
Recent methods have been developed to map single-cell lineage statistics to population growth. Because population growth selects for exponentially rare phenotypes, these methods inherently depend on sampling large deviations from finite…
The goal of cancer genome sequencing projects is to determine the genetic alterations that cause common cancers. Many malignancies arise during the clonal expansion of a benign tumor which motivates the study of recurrent selective sweeps…
Understanding how stochastic and non-linear deterministic processes interact is a major challenge in population dynamics theory. After a short review, we introduce a stochastic individual-centered particle model to describe the evolution in…
In this thesis we develop minimal models of the relationship between motility, growth, and evolution of cancer cells. We utilise simple simulations of a population of individual cells in space to examine how changes in mechanical properties…
In order to fulfill cell proliferation and differentiation through cellular hierarchy, stem cells can undergo either asymmetric or symmetric divisions. Recent studies pay special attention to the effect of different modes of stem cell…
Deterministic population growth models with power-law rates can exhibit a large variety of growth behaviors, ranging from algebraic, exponential to hyperexponential (finite time explosion). In this setup, selfsimilarity considerations play…
Cancer cells co-cultured in vitro reveal unexpected differential growth rates that classical exponential growth models cannot account for. Two non-interacting cell lines were grown in the same culture, and counts of each species were…