249 research outputs found
Concentration of the first eigenfunction for a second order elliptic operator
We study the semi-classical limits of the first eigenfunction of a positive
second order operator on a compact Riemannian manifold when the diffusion
constant goes to zero. We assume that the first order term is given
by a vector field , whose recurrent components are either hyperbolic points
or cycles or two dimensional torii. The limits of the normalized eigenfunctions
concentrate on the recurrent sets of maximal dimension where the topological
pressure \cite{Kifer90} is attained. On the cycles and torii, the limit
measures are absolutely continuous with respect to the invariant probability
measure on these sets. We have determined these limit measures, using a blow-up
analysis.Comment: Note to appear in C.R.A.
Residence times of receptors in dendritic spines analyzed by simulations in empirical domains
Analysis of high-density superresolution imaging of receptors reveal the
organization of dendrites at the nano-scale resolution. We present here
simulations in empirical live cell images, which allows converting local
information extracted from short range trajectories into simulations of long
range trajectories. Based on these empirical simulations, we compute the
residence time of an AMPA receptor (AMPAR) in dendritic spines that accounts
for receptors local interactions and geometrical organization. We report here
that depending on the type of the spine, the residence time varies from one to
five minutes. Moreover, we show that there exists transient organized
structures, previously described as potential wells that can regulate the
trafficking of AMPARs to dendritic spines.Comment: 19 page
Analysis of single particle trajectories: when things go wrong
To recover the long-time behavior and the statistics of molecular
trajectories from the large number (tens of thousands) of their short
fragments, obtained by super-resolution methods at the single molecule level,
data analysis based on a stochastic model of their non-equilibrium motion is
required. Recently, we characterized the local biophysical properties
underlying receptor motion based on coarse-grained long-range interactions,
corresponding to attracting potential wells of large sizes. The purpose of this
letter is to discuss optimal estimators and show what happens when thing goes
wrong.Comment: 4 page
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