The geometry of nondegeneracy conditions in completely integrable systems

Nondegeneracy conditions need to be imposed in K.A.M. theorems to insure that the set of diophantine tori has a large measure. Although they are usually expressed in action coordinates, it is possible to give a geometrical formulation using the notion of regular completely integrable systems defined by a fibration of a symplectic manifold by lagrangian tori together with a Hamiltonian function constant on the fibers. In this paper, we give a geometrical definition of different nondegeneracy conditions, we show the implication relations that exist between them, and we show the uniqueness of the fibration for non-degenerate Hamiltonians

Semi-classical approach for Anosov diffeomorphisms and Ruelle resonances

In this paper, we show that some spectral properties of Anosov diffeomorphisms can be obtained by semi-classical analysis. In particular the Ruelle resonances which are eigenvalues of the Ruelle transfer operator acting in suitable anisotropic Sobolev spaces and which govern the decay of dynamical correlations, can be treated as the quantum resonances of open quantum systems in the Aguilar-Baslev-Combes theory or the more recent Helffer-Sjostrand phase-space theory.Comment: 48 page

Heterogeneous multireference alignment: a single pass approach

Multireference alignment (MRA) is the problem of estimating a signal from many noisy and cyclically shifted copies of itself. In this paper, we consider an extension called heterogeneous MRA, where $K$ signals must be estimated, and each observation comes from one of those signals, unknown to us. This is a simplified model for the heterogeneity problem notably arising in cryo-electron microscopy. We propose an algorithm which estimates the $K$ signals without estimating either the shifts or the classes of the observations. It requires only one pass over the data and is based on low-order moments that are invariant under cyclic shifts. Given sufficiently many measurements, one can estimate these invariant features averaged over the $K$ signals. We then design a smooth, non-convex optimization problem to compute a set of signals which are consistent with the estimated averaged features. We find that, in many cases, the proposed approach estimates the set of signals accurately despite non-convexity, and conjecture the number of signals $K$ that can be resolved as a function of the signal length $L$ is on the order of $\sqrt{L}$.Comment: 6 pages, 3 figure

Ligand-dependent opening of the multiple AMPA receptor conductance states: a concerted model

Modulation of the properties of AMPA receptors at the post-synaptic membrane is one of the main suggested mechanisms behind synaptic plasticity in the central nervous system of vertebrates. Electrophysiological recordings of single channels stimulated with agonists showed that both recombinant and native AMPA receptors visit multiple conductance states in an agonist concentration dependent manner. We propose an allosteric model of the multiple conductance states based on concerted conformational transitions of the four subunits, as an iris diaphragm. Our model predicts that the thermodynamic behaviour of the conductance states upon full and partial agonist stimulations can be described with increased affinity of receptors as they progress to higher conductance states. The model also predicts existence of AMPA receptors in non-liganded conductive substates. However, spontaneous openings probability decreases with increasing conductances. Finally, we predict that the large conductance states are stabilized within the rise phase of a whole-cell EPSC in glutamatergic hippocampal neurons. Our model provides a mechanistic link between ligand concentration and conductance states that can explain thermodynamic and kinetic features of AMPA receptor gating.Comment: 4 figures, models available on demand. They will be published by BioModels Database upon publication of the articl

Heterogeneity in Technical Efficiency of the French Urban Transport: 1995 to 2002

In this paper, we analyze the heterogeneity in the technical efficiency of a sample of French urban transport companies with a translog production frontier model. The model generates efficiency disentangling homogenous and heterogeneous variables. Our study concluded that outputs and inputs play a major role in transport efficiency and we find that the efficiency scores vary along the sample. Policy implication is derived.Urban Transport; France, Translog random Frontier Model and Decision-Making Unit.