相关论文: Mass concentration in a nonlocal model of clonal s…

We consider the continuum limit of some products of random matrices in $\text{SL}(d,{\mathbb R})$ that arise as discretisations of incompressible renewing flows -- that is, of flows corresponding to a divergence-free velocity field that…

It is widely recognized that reciprocal interactions between cells and their microenvironment, via mechanical forces and biochemical signaling pathways, regulate cell behaviors during normal development, homeostasis and disease progression…

Telomeres are repetitive sequences of nucleotides at the end of chromosomes, whose evolution over time is intrinsically related to biological ageing. In most cells, with each cell division, telomeres shorten due to the so-called end…

A mathematical model of genome degradation is proposed that takes into account a variable rate of mutation and increasing number of cells in a developing human organism. The model explains known properties of cancer development, in…

We study the mathematical properties of a general model of cell division structured with several internal variables. We begin with a simpler and specific model with two variables, we solve the eigenvalue problem with strong or weak…

Stochastic resonance induced by external factor is considering to investigate the complex dynamics of tumor. The surrounding environment and the treatment effects on the tumor growth are considered as additive and multiplicative noises in…

This paper investigates dynamic behaviors of the tumor-immune system perturbed by environmental noise. The model describes the response of the cytotoxic T lymphocyte (CTL) to the growth of an immunogenic tumour. The main methods are…

In line with the stability theory of continuous dynamical systems, Lyapunov exponents of cellular automata (CAs) have been conceived two decades ago to quantify to what extent their dynamics changes following a perturbation of their initial…

Development of resistance limits transferability of most anticancer therapies into curative treatment and understanding mechanisms beyond it remains a big challenge. Many high resolution experimental observations show enormous intratumor…

We construct a continuum model for biological aggregations in which individuals experience long-range social attraction and short range dispersal. For the case of one spatial dimension, we study the steady states analytically and…

Background: A fundamental problem in cancer research is identifying the cell type that is capable of sustaining neoplastic growth and its origin from normal tissue cells. Recent investigations of a variety of tumor types have shown that…

We analyse the long term behaviour of the measure-valued solutions of a class of linear renewal equations modelling physiologically structured populations. The renewal equations that we consider are characterised by a regularisation…

Understanding tumor invasion and metastasis is of crucial importance for both fundamental cancer research and clinical practice. In vitro experiments have established that the invasive growth of malignant tumors is characterized by the…

Stochastic resetting models diverse phenomena across numerous scientific disciplines. Current understanding stems from the renewal framework, which relates systems subject to global resetting to their non-resetting counterparts. Yet, in…

We consider a non-local tumour growth model of phase-field type, describing the evolution of tumour cells through proliferation in presence of a nutrient. The model consists of a coupled system, incorporating a non-local Cahn-Hilliard…

We consider a special case of the Patlak-Keller-Segel system in a disc, which arises in the modelling of chemotaxis phenomena. For a critical value of the total mass, the solutions are known to be global in time but with density becoming…

Given a matrix of distribution functions and a quasi-stochastic matrix, i.e. an irreducible nonnegative matrix with maximal eigenvalue one and associated unique positive left and right eigenvectors, the article studies the properties of an…

Most neoplastic tumors originate from a single cell, and their evolution can be genetically traced through lineages characterized by common alterations such as small somatic mutations (SSMs), copy number alterations (CNAs), structural…

This paper concerns multiphase models of tumor growth in interaction with a surrounding tissue, taking into account also the interplay with diffusible nutrients feeding the cells. Models specialize in nonlinear systems of possibly…

Generative models based on static scalar energy functions represent an emerging paradigm in which a single time independent potential drives sample generation through its gradient field, eliminating the need for time conditioning entirely.…