Abstract:
Combining intracellular electrophysiology and multi-photon calcium imaging in vivo, we studied the relationship between calcium signals (sampled at 500–750？Hz) and spike output in principal neurons in the locust antennal lobe. Our goal was to determine whether the firing rate of individual neurons can be estimated in vivo with calcium imaging and, if so, to measure directly the accuracy and resolution of our estimates. Using the calcium indicator Oregon Green BAPTA-1, we describe a simple method to reconstruct firing rates from dendritic calcium signals with 80–90% accuracy and 50？ms temporal resolution.

Abstract:
Le désenchantement démocratique qui se confirme régulièrement s’explique en partie par la désagrégation de l’espace public de délibération habermassien. Le développement durable offre une chance de redonner du sens et du contenu au débat politique. Parmi les différentes formules de structures de concertation proposées par le corpus législatif, le conseil de développement peut être un lieu offrant des caractéristiques encourageantes pour revivifier la participation des citoyens au débat démocratique, à condition que son fonctionnement prévoit une réelle procédure d’animation du débat public. Si ces deux conditions sont réunies (un lieu, une procédure), alors le conseil de développement peut être un outil de renouvellement de la gouvernance des territoires.

Abstract:
Genetically encoded optical indicators hold the promise of enabling non-invasive monitoring of activity in identified neurons in behaving organisms. However, the interpretation of images of brain activity produced using such sensors is not straightforward. Several recent studies of sensory coding used G-CaMP 1.3—a calcium sensor—as an indicator of neural activity; some of these studies characterized the imaged neurons as having narrow tuning curves, a conclusion not always supported by parallel electrophysiological studies. To better understand the possible cause of these conflicting results, we performed simultaneous in vivo 2-photon imaging and electrophysiological recording of G-CaMP 1.3 expressing neurons in the antennal lobe (AL) of intact fruitflies. We find that G-CaMP has a relatively high threshold, that its signal often fails to capture spiking response kinetics, and that it can miss even high instantaneous rates of activity if those are not sustained. While G-CaMP can be misleading, it is clearly useful for the identification of promising neural targets: when electrical activity is well above the sensor's detection threshold, its signal is fairly well correlated with mean firing rate and G-CaMP does not appear to alter significantly the responses of neurons that express it. The methods we present should enable any genetically encoded sensor, activator, or silencer to be evaluated in an intact neural circuit in vivo in Drosophila.

Abstract:
This paper extends the Method of Particular Solutions (MPS) to the computation of eigenfrequencies and eigenmodes of plates. Specific approximation schemes are developed, with plane waves (MPS-PW) or Fourier-Bessel functions (MPS-FB). This framework also requires a suitable formulation of the boundary conditions. Numerical tests, on two plates with various boundary conditions, demonstrate that the proposed approach provides competitive results with standard numerical schemes such as the Finite Element Method, at reduced complexity, and with large flexibility in the implementation choices.

Abstract:
We study the spectral theory of a reversible Markov chain associated to a hypoelliptic random walk on a manifold M. This random walk depends on a parameter h which is roughly the size of each step of the walk. We prove uniform bounds with respect to h on the rate of convergence to equilibrium, and the convergence when h goes to zero to the associated hypoelliptic diffusion.

Abstract:
We prove a sharp rate of convergence to stationarity for a natural random walk on a compact Riemannian manifold $(M,g)$. The proof includes a detailed study of the spectral theory of the associated operator.

Abstract:
We study two cases of acoustic source localization in a reverberant room, from a number of point-wise narrowband measurements. In the first case, the room is perfectly known. We show that using a sparse recovery algorithm with a dictionary of sources computed a priori requires measurements at multiple frequencies. Furthermore, we study the choice of frequencies for these measurements, and show that one should avoid the modal frequencies of the room. In the second case, when the shape and the boundary conditions of the room are unknown, we propose a model of the acoustical field based on the Vekua theory, still allowing the localization of sources, at the cost of an increased number of measurements. Numerical results are given, using simple adaptations of standard sparse recovery methods.

Abstract:
We examine the recent results of the MACHO collaboration towards the Large Magellanic Cloud (Alcock et al. 1996) in terms of a halo brown dwarf or white dwarf population. The possibility for most of the microlensing events to be due to brown dwarfs is totally excluded by large-scale kinematic properties. The white dwarf scenario is examined in details in the context of the most recent white dwarf cooling theory (Segretain et al. 1994) which includes explicitely the extra source of energy due to carbon-oxygen differentiation at crystallization, and the subsequent Debye cooling. We show that the observational constraints arising from the luminosity function of high-velocity white dwarfs in the solar neighborhood and from the recent HST deep field counts are consistent with a white dwarf contribution to the halo missing mass as large as 50 %, provided i) an IMF strongly peaked around 1.7 Msol and ii) a halo age older than 18 Gyr.

Abstract:
Large HII regions, with angular dimensions exceeding 10 pc, usually enclose numerous massive O-stars. Stellar winds from such stars are expected to play a sizeable role in the dynamical, morphological and chemical evolution of the targeted nebula. Kinematically, stellar winds remain hardly observable i.e., the typical expansion velocities of wind-blown bubbles being often confused with other dynamical processes also regularly found HII regions. However, supersonic shock waves, developed by stellar winds, should favor shock excitation and leave a well-defined spectral signature in the ionized nebular content. In this work, the presence of stellar winds, observed through shock excitation, is investigated in the brightest portions of the Galactic IC 1805 nebula, a giant HII region encompassing at least 10 O-stars from main-sequence O9 to giant and supergiant O4. The use of the imaging Fourier transform spectrometer SpIOMM enabled the simultaneous acquisition of the spectral information associated to the Halpha6563A, [NII]6548, 6584A, and [SII]6716, 6731A ionic lines. Diagnostic diagrams, first introduced by Sabbadin and collaborators, were used to circumscribe portions of the nebula likely subject to shock excitation from other areas dominated by photoionization. The gas compression, expected from supersonic shocks, is investigated by comparing the pre- and post-shocked material's densities computed from the [SII]/[SII] line ratio. The typical [NII]/[NII] line ratio slightly exceeds the theoretical value of 3 expected in low-density regimes. To explain such behavior, a scenario based on collisional de-excitations affecting the [NII]6548A line is proposed.

Abstract:
We consider the inverse problem of reconstructing general solutions to the Helmholtz equation on some domain $\Omega$ from their values at scattered points $x_1,\dots,x_n\subset \Omega$. This problem typically arises when sampling acoustic fields with $n$ microphones for the purpose of reconstructing this field over a region of interest $\Omega$ contained in a larger domain $D$ in which the acoustic field propagates. In many applied settings, the shape of $D$ and the boundary conditions on its border are unknown. Our reconstruction method is based on the approximation of a general solution $u$ by linear combinations of Fourier-Bessel functions or plane waves. We analyze the convergence of the least-squares estimates to $u$ using these families of functions based on the samples $(u(x_i))_{i=1,\dots,n}$. Our analysis describes the amount of regularization needed to guarantee the convergence of the least squares estimate towards $u$, in terms of a condition that depends on the dimension of the approximation subspace, the sample size $n$ and the distribution of the samples. It reveals the advantage of using non-uniform distributions that have more points on the boundary of $\Omega$. Numerical illustrations show that our approach compares favorably with reconstruction methods using other basis functions, and other types of regularization.