Periodic motions galore: How to modify nonlinear evolution equations so that they feature a lot of periodic solutions

A simple trick is illustrated, whereby nonlinear evolution equations can be modified so that they feature a lot - or, in some cases, only -- periodic solutions. Several examples (ODEs and PDEs) are exhibited.Comment: arxiv version is already officia

Algebraically Linearizable Dynamical Systems

The main result of this paper is the evidence of an explicit linearization of dynamical systems of Ruijsenaars-Schneider type and of the perturbations introduced by F. Calogero of these systems with all orbits periodic of same period. Several other systems share the existence of this explicit linearization, among them, the Calogero-Moser system (with and without external potential) and the Calogero-Sutherland system. This explicit linearization is compared with the notion of maximal superintegrability which has been discussed in several articles.Comment: 11 pages, Late

Monodromy and the Kowalevskaya top

International audienc

Study of tropospheric correction for intercontinental GPS common-view time transfer

Current practice is to incorporate general empirical models of the troposphere, which depend only on the station height and the elevation of the satellite, in GPS time receivers used for common-view time transfer. Comparisons of these models with a semi-empirical model based on weather measurements show differences of several nanoseconds. This paper reports on a study of tropospheric correction during GPS common-view time transfer over a short baseline of about 700 km, and three long baselines of 6400 km, 9000 km and 9600 km. It is shown that the use of a general empirical model of the troposphere within a region where the climate is similar does not affect time transfer by more than a few hundreds of picoseconds. For the long distance links, differences between the use of a general empirical model and the use of a semi-empirical model reach several nanoseconds

Human Chondrosarcoma Cells Acquire an Epithelial-Like Gene Expression Pattern via an Epigenetic Switch: Evidence for Mesenchymal-Epithelial Transition during Sarcomagenesis

Chondrocytes are mesenchymally derived cells that reportedly acquire some epithelial characteristics; however, whether this is a progression through a mesenchymal to epithelial transition (MET) during chondrosarcoma development is still a matter of investigation. We observed that chondrosarcoma cells acquired the expression of four epithelial markers, E-cadherin,desmocollin 3, maspin, and 14-3-3σ, all of which are governed epigenetically through cytosine methylation. Indeed, loss of cytosine methylation was tightly associated with acquired expression of both maspin and 14-3-3σ in chondrosarcomas. In contrast, chondrocyte cells were negative for maspin and 14-3-3σ and displayed nearly complete DNA methylation. Robust activation of these genes was also observed in chondrocyte cells following 5-aza-dC treatment. We also examined the transcription factor snail which has been reported to be an important mediator of epithelial to mesenchymal transitions (EMTs). In chondrosarcoma cells snail is downregulated suggesting a role for loss of snail expression in lineage maintenance. Taken together, these results document an epigenetic switch associated with an MET-like phenomenon that accompanies chondrosarcoma progression

Higher-order Abel equations: Lagrangian formalism, first integrals and Darboux polynomials

A geometric approach is used to study a family of higher-order nonlinear Abel equations. The inverse problem of the Lagrangian dynamics is studied in the particular case of the second-order Abel equation and the existence of two alternative Lagrangian formulations is proved, both Lagrangians being of a non-natural class (neither potential nor kinetic term). These higher-order Abel equations are studied by means of their Darboux polynomials and Jacobi multipliers. In all the cases a family of constants of the motion is explicitly obtained. The general n-dimensional case is also studied