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Mathematical modelling has become an established tool for studying the dynamics of biological systems. Current applications range from building models that reproduce quantitative data to identifying systems with predefined qualitative…
We study the off-equilibrium dynamics of a particle in a general $N$-dimensional random potential when $N \to \infty$. We demonstrate the existence of two asymptotic time regimes: {\it i.} stationary dynamics, {\it ii.} slow aging dynamics…
We study Bayesian estimation of finite mixture models in a general setup where the number of components is unknown and allowed to grow with the sample size. An assumption on growing number of components is a natural one as the degree of…
Motivated by observations of heterogeneous domain structure on the surface of cells, we consider a minimal model to describe the dynamics of phase separation on the surface of a spherical particle. Finite-size effects on the curved particle…
A model independent parametrization of an extension of the Standard Model including vector-like quarks, new heavy gauge bosons and an extra scalar, is introduced. Theoretical constraints on the model couplings and hypothetical particle…
The origins of the large differences observed to the rates with which the diverse particles are conveyed along axonal microtubules are still a matter of debate in the literature. There is evidence that certain neurodegenerative diseases may…
This work proposes a framework for multistage adjustable robust optimization that unifies the treatment of three different types of endogenous uncertainty, where decisions, respectively, (i) alter the uncertainty set, (ii) affect the…
In this paper we study a model describing the growth of necrotic tumors in different regimes of vascularisation. The tumor consists of a necrotic core of death cells and a surrounding nonnecrotic shell. The corresponding mathematical…
We compute the oblique parameters, including the three new parameters $ V $, $ W $ and $ X $ introduced recently by the Montreal group, for the case of one scalar multiplet of arbitrary weak isospin $ J $ and weak hypercharge $ Y $. We show…
We consider a class of biologically-motivated stochastic processes in which a unicellular organism divides its resources (volume or damaged proteins, in particular) symmetrically or asymmetrically between its progeny. Assuming the final…
We compute averages of products and ratios of characteristic polynomials associated with Orthogonal, Unitary, and Symplectic Ensembles of Random Matrix Theory. The pfaffian/determinantal formulas for these averages are obtained, and the…
In this work we derive the evolution equation for the density contrast considering open system cosmology, where the influence of adiabatic particle production process on the dynamic of a homogeneous and isotropic is investigated within a…
This paper deals with some mathematical models arising in the theory of epitaxial growth of crystal. We focalize the study on a stationary problem which presents some analytical difficulties. We study the existence of solutions. The central…
A number of novel experimental and theoretical results have recently been obtained on active soft matter, demonstrating the various interesting universal and anomalous features of this kind of driven systems. Here we consider a fundamental…
Nanoparticles introduced in living cells are capable of strongly promoting the aggregation of peptides and proteins. We use here molecular dynamics simulations to characterise in detail the process by which nanoparticle surfaces catalyse…
We present a geometric framework to study the growth-division dynamics of cells and protocells, and demonstrate that self-reproduction emerges only when a system's growth dynamics and division strategy are mutually compatible. Using several…
We study the mathematical properties of a model of cell division structured by two variables, the size and the size increment, in the case of a linear growth rate and a self-similar fragmentation kernel. We first show that one can construct…
Mathematical models are essential tools to study how the cardiovascular system maintains homeostasis. The utility of such models is limited by the accuracy of their predictions, which can be determined by uncertainty quantification (UQ). A…
We study the identification and estimation of structural parameters in dynamic panel data logit models where decisions are forward-looking and the joint distribution of unobserved heterogeneity and observable state variables is…
Biomolecular condensates self-assemble when proteins and nucleic acids spontaneously demix to form droplets within the crowded intracellular milieu. This simple mechanism underlies the formation of a wide variety of membraneless…