Genomic surveillance of SARS-CoV-2 Spike gene by sanger sequencing.

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.

N-body dynamics on closed surfaces: the axioms of mechanics.

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).

Epidemics Modelings: Some New Challenges.

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.

Point-vortex cluster formation in the plane and on the sphere: an energy bifurcation condition.

The dynamics of a system of point vortices is considered in the plane and on the sphere. Particular attention is given to the formation of vortex clusters and to global vortex dynamics, especially in the spherical case. For integrable systems and systems with given symmetries, we show the existence of a critical energy above or below which (depending on the geometry of the surface) the system splits into clusters and vortex dynamics is confined to a particular region. The case of nonidentical vortices is of particular interest since we observe quite different global dynamics depending on the energy and the initial conditions. Furthermore we identify all the relative equilibria configurations as critical points of the reduced energy and we give an instability criterion to deduce instability for certain configurations.