Mathematical Physics (MP)
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Fractional Diffusion and Medium Heterogeneity: The Case of the Continuos Time Random Walk
(20210724)In this contribution we show that fractional diffusion emerges from a simple Markovian Gaussian random walk when the medium displays a powerlaw heterogeneity. Within the framework of the continuous time random walk, the ... 
Stochastic Properties of Colliding Hard Spheres in a Nonequilibrium Thermal Bath
(20210724)We consider the problem of describing the dynamics of a test particle moving in a thermal bath using the stochastic differential equations. We briefly recall the stochastic approach to the Brownian based on the statistical ... 
Image Milnor Number Formulas for WeightedHomogeneous MapGerms
(20210705)We give formulas for the image Milnor number of a weightedhomogeneous mapgerm $(\mathbb{C}^n,0)\to(\mathbb{C}^{n+1},0)$, for $n=4$ and $5$, in terms of weights and degrees. Our expressions are obtained by a purely ... 
Classification of smooth factorial affine surfaces of Kodaira dimension zero with trivial units
(20210731)We give a corrected statement of (Gurjar and Miyanishi 1988, Theorem 2), which classifies smooth affine surfaces of Kodaira dimension zero, whose coordinate ring is factorial and has trivial units. Denote the class of such ... 
Some contributions to the theory of singularities and their characteristic classes
(20210602)In this Ph.D. thesis, we give some contributions to the theory of singularities, as well as to the theory of characteristic classes of singular spaces. The first part of this thesis is devoted to the theory of singularities ... 
Stochastic resetting by a random amplitude
(20210518)Stochastic resetting, a diffusive process whose amplitude is reset to the origin at random times, is a vividly studied strategy to optimize encounter dynamics, e.g., in chemical reactions. Here we generalize the resetting ... 
Macroscopic Dynamics of the StrongCoupling BCSHubbard Model
(2020)The aim of the current paper is to illustrate, in a simple example, our recent, very general, rigorous results on the dynamical properties of fermions and quantumspin systems with longrange, or meanfield, interactions, ... 
Quantum Fluctuations and Large Deviation Principle for Microscopic Currents of Free Fermions in Disordered Media
(2020)We contribute an extension of largedeviation results obtained in [N.J.B. Aza, J.B. Bru, W. de Siqueira Pedra, A. Ratsimanetrimanana, J. Math. Pures Appl. 125 (2019) 209] on conductivity theory at atomic scale of free ... 
Weak* Hypertopologies with Application to Genericity of Convex Sets
(2022)We propose a new class of hypertopologies, called here weak$^{\ast }$ hypertopologies, on the dual space $\mathcal{X}^{\ast }$ of a real or complex topological vector space $\mathcal{X}$. The most wellstudied and wellknown ... 
Large Deviations in Weakly Interacting Fermions  Generating Functions as Gaussian Berezin Integrals and Bounds on Large Pfaffians
(2021)We prove that the G\"{a}rtnerEllis generating function of probability distributions associated with KMS states of weakly interacting fermions on the lattice can be written as the limit of logarithms of Gaussian Berezin ... 
Exact distributions of the maximum and range of random diffusivity processes
(20210209)We study the extremal properties of a stochastic process $x_t$ defined by the Langevin equation ${\dot {x}}_{t}=\sqrt{2{D}_{t}}\enspace {\xi }_{t}$, in which $\xi_t$ is a Gaussian white noise with zero mean and $D_t$ is a ... 
Surrogate based Global Sensitivity Analysis of ADM1based Anaerobic Digestion Model
(2021)In order to calibrate the model parameters, Sensitivity Analysis routines are mandatory to rank the parameters by their relevance and fix to nominal values the least influential factors. Despite the high number of works ... 
Study of Wound Healing Dynamics by Single PseudoParticle Tracking in Phase Contrast Images Acquired in TimeLapse
(202103)Cellular contacts modify the way cells migrate in a cohesive group with respect to a free single cell. The resulting motion is persistent and correlated, with cells’ velocities selfaligning in time. The presence of a dense ... 
SHOULD I STAY OR SHOULD I GO? ZEROSIZE JUMPS IN RANDOM WALKS FOR LÉVY FLIGHTS
(202102)We study Markovian continuoustime random walk models for Lévy flights and we show an example in which the convergence to stable densities is not guaranteed when jumps follow a bimodal powerlaw distribution that is equal ... 
Exact firstpassage time distributions for three random diffusivity models
(20210104)We study the extremal properties of a stochastic process $x_t$ defined by a Langevin equation $\dot{x}= \sqrt{2D_o V (B_t )} \xi_t$, where $\xi$ is a Gaussian white noise with zero mean, $D_0$ is a constant scale factor, ... 
Decomposition theorem and torus actions of complexity one
(2020)We algorithmically compute the intersection cohomology Betti numbers of any complete normal algebraic variety with a torus action of complexity one. 
The abel map for surface singularities II. Generic analytic structure
(2019)We study the analytic and topological invariants associated with complex normal surface singularities. Our goal is to provide topological formulae for several discrete analytic invariants whenever the analytic structure ... 
Reflection maps
(2020)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 ... 
The random diffusivity approach for diffusion in heterogeneous systems
(20201216)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 ... 
Gut microbiota ecology: Biodiversity estimated from hybrid neutralniche model increases with health status and aging
(20201030)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 ...