Papers by Stefanella Boatto
Assimilation de données par filtrage particulaire régularisé dans un modèle d'épidémiologie
International audienc
A Bacteria-based Experimental Platform to Test Parameters Raised by Mathematical Models on Population Dynamics
Bacterial populations are current models to assay biological effects of a number of different tre... more Bacterial populations are current models to assay biological effects of a number of different treatments on the basis of a high-number statistics. One typical bacterial inoculum grows at doubling rates as fast as some 30 min per generation, reaching up to ~109 cells per ml of medium in a few hours. Given the features of such experimental protocol, it is easy to test the impact of environmental modifications during bacteria growth, by scoring doubling rates time, final cell concentration, oxygen consumption, mutagenesis rates, cell viability under different selective pressures, etc. The drawing of a actual dose-response or kinetic curves can feed parameters on a given mathematical model on population dynamics by weighting each equation term. The purpose of this talk is to present experimental schemes with bacterial populations so as to serve as parallel two-hands testing of different mathematical models on populations dynamics.
PLOS ONE
The SARS-CoV-2 responsible for the ongoing COVID pandemic reveals particular evolutionary dynamic... more The SARS-CoV-2 responsible for the ongoing COVID pandemic reveals particular evolutionary dynamics and an extensive polymorphism, mainly in Spike gene. Monitoring the S gene mutations is crucial for successful controlling measures and detecting variants that can evade vaccine immunity. Even after the costs reduction resulting from the pandemic, the new generation sequencing methodologies remain unavailable to a large number of scientific groups. Therefore, to support the urgent surveillance of SARS-CoV-2 S gene, this work describes a new feasible protocol for complete nucleotide sequencing of the S gene using the Sanger technique. Such a methodology could be easily adopted by any laboratory with experience in sequencing, adding to effective surveillance of SARS-CoV-2 spreading and evolution.
Bilhares rugosos e dinâmica das part́ıculas a longo prazo
Uma questão fundamental na literatura sobre bilhares e ́ a de caracterizar o movimento de uma pa... more Uma questão fundamental na literatura sobre bilhares e ́ a de caracterizar o movimento de uma part́ıcula livre refletida no bordo de uma região dada e, em particular, determinar se a dinâmica e ́ integrável, ergódica (ou mais ainda difusa). Em geral, os ingredientes principais nessa análise são: • a geometria da região M onde a dinâmica ocorre. Uma classicação usual consiste em caracterizar os bilhares em eleticos, hiperbólicos e parabólicos, dependendo da geometria da curva do bordo ∂M e da superf́ıcie M (veja Tabachikov, Young). A curva do bordo pode ser, nos casos mais extremos, diferenciável por partes. • a lei de reflexão no bordo (i.e. elástica, inelástica ou mista). No caso elástico (lei de Fresnel) o ângulo de reflexão e ́ igual ao ângulo de in-cidência. No caso inelástico ha ́ várias escolhas posśıveis. Em geral, para um ângulo de incidência dado corresponde uma distribução de posśıveis ângulos de reflexão. • se a região considerada e ́ limi...
Point-Vortex Dynamics
Encyclopedia of Mathematical Physics, 2006
Symposium on Mathematical Methods in Biophysics and Genomics
Epidemics modeling has been particularly growing in the past years. In epidemics studies, mathema... more Epidemics modeling has been particularly growing in the past years. In epidemics studies, mathematical modeling is used in particular to reach a better understanding of some neglected diseases (dengue, malaria, ...) and of new emerging ones (SARS, influenza A,....) of big agglomerates. Such studies offer new challenges both from the modeling point of view (searching for simple models which capture the main characteristics of the disease spreading), data analysis and mathematical complexity. We are facing often with complex networks especially when modeling the city dynamics. Such networks can be static (in first approximation) and homogeneous, static and not homogeneous and/or not static (when taking into account the city structure, micro-climates, people circulation, etc.). The objective being studying epidemics dynamics and being able to predict its spreading.
Physica D: Nonlinear Phenomena, 2008
Vortex modeling has a long history. Descartes (1644) used it as a model for the solar systems. J.... more Vortex modeling has a long history. Descartes (1644) used it as a model for the solar systems. J. J. Thomsom (1883) used it as a model for the atom. We consider point-vortex systems, which can be regarded as "discrete" solutions of the Euler equation. Their dynamics is described by a Hamiltonian system of equations. We are interested in polygonal configurations and how their stability depends upon various dynamical variables. In the plane a polygon with seven vortices has been shown to be a special boundary case: polygons with N < 7 vortices are (linearly and nonlinearly) stable while polygons with N > 7 vortices are unstable. Why should N = 7 be special? Celestial Mechanics helped us to simplify a problem that has been studied for over a century, and to show that the case of Thomson's Heptagon is actually a case of bifurcation at infinity. This becomes particularly clear when considering the corresponding problem of a ring on a sphere with two polar vortices of variable intensities Γ N and Γ S , at the North and South Pole, respectively.
Curvature perturbations and stability of a ring of vortices
Discrete and Continuous Dynamical Systems - Series B, 2008
Vortex modeling has a long history. Descartes (1644) used it as a model for the solar system. J.J... more Vortex modeling has a long history. Descartes (1644) used it as a model for the solar system. J.J. Thomson (1883) used it as a model for the atom. We consider point-vortex systems, which can be regarded as “discrete” solutions of the Euler equation. Their dynamics is described by a Hamiltonian system of equations. In particular we are interested in vortex dynamics on simply connected surfaces of constant curvature $K$, i.e. a plane, spheres and hyperbolic surfaces. It is known that polygonal configurations of $N$ point-vortices are relative equilibria of the system. We study the stability of such polygonal configurations, and, more specifically, how stability depends upon the number of vortices $N$ and the curvature $K$ of the surface. To address such a question we have to formulate the problem in a unified geometrical way. The fact that the surfaces of interest can be viewed as Kahler manifolds greatly simplify our task. Nonlinear stability is then studied by making use of the Dirichlet Criterion. Stability ranges are the $K$-intervals for which the Hessian of the Hamiltonian is positive or negative definite, when evaluated at the equilibrium configuration.
SIAM Journal on Applied Mathematics, 2003
We study the nonlinear stability of relative equilibria of configurations of identical point-vort... more We study the nonlinear stability of relative equilibria of configurations of identical point-vortices on the surface of a sphere. In particular, we study how the stability changes as a function of the colatitude θ and of the number of vortices N . By using the integrals of motion, we view the system in a suitable corotating frame where the polygonal vortex configuration is at rest. Then after a sufficient criterion due to Dirichlet, the stability ranges are the θ-intervals for which the Hessian of the Hamiltonian-evaluated at the equilibrium configuration-is positive or negative definite. We find that the stability intervals coincide with those for linear stability determined by Polvani and Dritschel [J.
The dynamics of a passive tracer in the velocity field of four identical point vortices, moving u... more The dynamics of a passive tracer in the velocity field of four identical point vortices, moving under the influence of...
Classes of steady and periodic solutions are investigated for the incompressible Euler equation. ... more Classes of steady and periodic solutions are investigated for the incompressible Euler equation. Of particular interest is the stability of "discrete solutions" of the type of point-vortices on surfaces with constant curvature, on domains without boundaries. The study makes use of an infinite dimensional Hamiltonian formulation of the vorticity equation when the rotation of a planet is taken into account [see T.G. Shepherd, Hamiltonian Dynamics, Encyclopedia of Atmospheric Sciences, Academic Press, pp. 929-938, 2003; B. Khesin and G. Misio lek, Euler equations on homogeneous spaces and Virasoro orbits.
Modelling epidemics dynamics due to Aedes mosquitoes : the example of Rio de Janeiro. How to approximate an epidemic attractor and to estimate the infectivity rate
SIR model with time dependent infectivity parameter : approximating the epidemic attractor and the importance of the initial phase
We consider a SIR model with birth and death terms and time-varying infectivity parameter β (t). ... more We consider a SIR model with birth and death terms and time-varying infectivity parameter β (t). In the particular case of a sinusoidal parameter, we show that the average Basic Reproduction Number ¯ R o , introduced in [Bacaer & Guernaoui, 2006], is not the only relevant parameter and we emphasize the role played by the initial phase, the amplitude and the period. For a (general) periodic infectivity parameter β (t) a periodic orbit exists, as already proved in [Katriel, 2014]. In the case of a slowly varying β (t) an approximation of such a solution is given, which is shown to be asymptotically stable under an extra assumption on the slowness of β (t). For a non necessarily periodic β (t) , all the trajectories of the system are proved to be attracted into a tubular region around a suitable curve, which is then an approximation of the underlying attractor. Numerical simulations are given.
N-body Dynamics on an Infinite Cylinder: the Topological Signature in the Dynamics
Regular and Chaotic Dynamics
The formulation of the dynamics of N -bodies on the surface of an infinite cylinder is considered... more The formulation of the dynamics of N -bodies on the surface of an infinite cylinder is considered. We have chosen such a surface to be able to study the impact of the surface’s topology in the particle’s dynamics. For this purpose we need to make a choice of how to generalize the notion of gravitational potential on a general manifold. Following Boatto, Dritschel and Schaefer [5], we define a gravitational potential as an attractive central force which obeys Maxwell’s like formulas. As a result of our theoretical differential Galois theory and numerical study — Poincaré sections, we prove that the two-body dynamics is not integrable. Moreover, for very low energies, when the bodies are restricted to a small region, the topological signature of the cylinder is still present in the dynamics. A perturbative expansion is derived for the force between the two bodies. Such a force can be viewed as the planar limit plus the topological perturbation. Finally, a polygonal configuration of identical masses (identical charges or identical vortices) is proved to be an unstable relative equilibrium for all N > 2.
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
One contribution of 11 to a theme issue 'Topological and geometrical aspects of mass and vortex d... more One contribution of 11 to a theme issue 'Topological and geometrical aspects of mass and vortex dynamics' .
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
One contribution of 11 to a theme issue 'Topological and geometrical aspects of mass and vortex d... more One contribution of 11 to a theme issue 'Topological and geometrical aspects of mass and vortex dynamics'.
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
A major challenge for our understanding of the mathematical basis of particle dynamics is the for... more A major challenge for our understanding of the mathematical basis of particle dynamics is the formulation of N-body and N-vortex dynamics on Riemann surfaces. In this paper, we show how the two problems are, in fact, closely related when considering the role played by the intrinsic geometry of the surface. This enables a straightforward deduction of the dynamics of point masses, using recently derived results for point vortices on general closed differentiable surfaces M endowed with a metric g . We find, generally, that Kepler's Laws do not hold. What is more, even Newton's First Law (the law of inertia) fails on closed surfaces with variable curvature (e.g. the ellipsoid).
Diffusion approximation of a model Knudsen gas: dependence of the diffusion constant upon the boundary condition
Aps Division of Fluid Dynamics Meeting Abstracts, Nov 1, 2001
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Papers by Stefanella Boatto