The two hallmark features of Brownian motion are the linear growth $\langle x^2(t) \rangle = 2 D d t$ of the mean squared displacement (MSD) with diffusion coefficient $D$ in $d$ spatial dimensions, and the Gaussian ...

In this work we propose an index to estimate the gut microbiota biodiversity using a modeling approach with the aim of describing its relationship with health and aging. The gut microbiota, a complex ecosystem that links ...

It was shown by Henry and Parusiński in 2003 that the bi-Lipschitz right equivalence of function germs admits moduli. In this article, we introduce the notion of Lipschitz simple function germ and present the complete ...

Stochastic models based on random diffusivities, such as the diffusing- diffusivity approach, are popular concepts for the description of non-Gaussian diffusion in heterogeneous media. Studies of these models typically ...

The Stefan problem, involving the tracking of an evolving phase-change front, is the prototypical example of a moving boundary problem. In basic one- dimensional problems it is well known that the front advances as the ...

In this paper we present a classification of a class of globally subanalytic CMC surfaces in $\mathbb{R}^3$ that generalizes the recent classification made by Barbosa and do Carmo in 2016. We show that a globally subanalytic ...

We survey the proof of the Nash conjecture for surfaces and show how geometric and topological ideas developed in previous articles by the authors influenced it. Later, we summarize the main ideas in the higher dimensional ...

This paper is devoted to study multiplicity and regularity of complex analytic sets. We present an equivalence for complex analytical sets, named blow-spherical equivalence and we obtain several applications with this new ...

It was conjectured that multiplicity of a singularity is bi-Lipschitz invariant. We disprove this conjecture constructing examples of bi-Lipschitz equivalent complex algebraic singularities with different values of multiplicity.

Given a reflection group G acting on a complex vector space V , a reflection map is the composition of an embedding X → V with the quotient map V → Cp of G. We show how these maps, which can highly singular, may be studied ...