Noise-induced behaviors in neural mean field dynamics

The collective behavior of cortical neurons is strongly affected by the presence of noise at the level of individual cells. In order to study these phenomena in large-scale assemblies of neurons, we consider networks of firing-rate neurons with linear intrinsic dynamics and nonlinear coupling, belonging to a few types of cell populations and receiving noisy currents. Asymptotic equations as the number of neurons tends to infinity (mean field equations) are rigorously derived based on a probabilistic approach. These equations are implicit on the probability distribution of the solutions which generally makes their direct analysis difficult. However, in our case, the solutions are Gaussian, and their moments satisfy a closed system of nonlinear ordinary differential equations (ODEs), which are much easier to study than the original stochastic network equations, and the statistics of the empirical process uniformly converge towards the solutions of these ODEs. Based on this description, we analytically and numerically study the influence of noise on the collective behaviors, and compare these asymptotic regimes to simulations of the network. We observe that the mean field equations provide an accurate description of the solutions of the network equations for network sizes as small as a few hundreds of neurons. In particular, we observe that the level of noise in the system qualitatively modifies its collective behavior, producing for instance synchronized oscillations of the whole network, desynchronization of oscillating regimes, and stabilization or destabilization of stationary solutions. These results shed a new light on the role of noise in shaping collective dynamics of neurons, and gives us clues for understanding similar phenomena observed in biological networks

Camera motion estimation through planar deformation determination

In this paper, we propose a global method for estimating the motion of a camera which films a static scene. Our approach is direct, fast and robust, and deals with adjacent frames of a sequence. It is based on a quadratic approximation of the deformation between two images, in the case of a scene with constant depth in the camera coordinate system. This condition is very restrictive but we show that provided translation and depth inverse variations are small enough, the error on optical flow involved by the approximation of depths by a constant is small. In this context, we propose a new model of camera motion, that allows to separate the image deformation in a similarity and a ``purely'' projective application, due to change of optical axis direction. This model leads to a quadratic approximation of image deformation that we estimate with an M-estimator; we can immediatly deduce camera motion parameters.Comment: 21 pages, version modifi\'ee accept\'e le 20 mars 200

Dirac fermions at the H point of graphite: Magneto-transmission studies

We report on far infrared magneto-transmission measurements on a thin graphite sample prepared by exfoliation of highly oriented pyrolytic graphite. In magnetic field, absorption lines exhibiting a blue-shift proportional to sqrtB are observed. This is a fingerprint for massless Dirac holes at the H point in bulk graphite. The Fermi velocity is found to be c*=1.02x10^6 m/s and the pseudogap at the H point is estimated to be below 10 meV. Although the holes behave to a first approximation as a strictly 2D gas of Dirac fermions, the full 3D band structure has to be taken into account to explain all the observed spectral features.Comment: 4 pages, 4 figures, to appear in Phys. Rev. Let

Graphite from the viewpoint of Landau level spectroscopy: An effective graphene bilayer and monolayer

We describe an infrared transmission study of a thin layer of bulk graphite in magnetic fields up to B = 34 T. Two series of absorption lines whose energy scales as sqrtB and B are present in the spectra and identified as contributions of massless holes at the H point and massive electrons in the vicinity of the K point, respectively. We find that the optical response of the K point electrons corresponds, over a wide range of energy and magnetic field, to a graphene bilayer with an effective inter-layer coupling 2\gamma_1, twice the value for a real graphene bilayer, which reflects the crystal ordering of bulk graphite along the c-axis. The K point electrons thus behave as massive Dirac fermions with a mass enhanced twice in comparison to a true graphene bilayer.Comment: 4 pages, 2 figure

Electron-phonon coupling in the two phonon mode ternary alloy Al0.25In0.75As/Ga0.25In0.75AsAl_{0.25}In_{0.75}As/Ga_{0.25}In_{0.75}As quantum well

We have investigated the infrared transmission of a two-dimensional (2DEG) electron gas confined in a $Al_{0.25}In_{0.75}As/Ga_{0.25}In_{0.75}As$ single quantum well in order to study the electron optical phonon interaction in a two phonon mode system. Infrared transmission experiments have been performed in both the perpendicular Faraday (PF) and tilted Faraday (TF) configurations for which the growth axis of the sample is tilted with respect to the incident light propagation direction and to the magnetic field direction. The experimental results lead to question the validity of the concept of polaron mass in a real material.Comment: 7 pages, 3 figure

Fine structure of "zero-mode" Landau levels in HgTe/HgCdTe quantum wells

HgTe/HgCdTe quantum wells with the inverted band structure have been probed using far infrared magneto-spectroscopy. Realistic calculations of Landau level diagrams have been performed to identify the observed transitions. Investigations have been greatly focused on the magnetic field dependence of the peculiar pair of "zero-mode" Landau levels which characteristically split from the upper conduction and bottom valence bands, and merge under the applied magnetic field. The observed avoided crossing of these levels is tentatively attributed to the bulk inversion asymmetry of zinc blend compounds.Comment: 5 pages, 4 figure

Evidence for magnetoplasmon character of the cyclotron resonance response of a two-dimensional electron gas

Experimental results on the absolute magneto-transmission of a series of high density, high mobility GaAs quantum wells are compared with the predictions of a recent magnetoplasmon theory for values of the filling factor above 2. We show that the magnetoplasmon picture can explain the non-linear features observed in the magnetic field evolution of the cyclotron resonance energies and of the absorption oscillator strength. This provides experimental evidence that inter Landau level excitations probed by infrared spectroscopy need to be considered as many body excitations in terms of magnetoplasmons: this is especially true when interpreting the oscillator strengths of the cyclotron transitions

Frohlich mass in GaAs-based structures

The Frohlich interaction is one of the main electron-phonon intrinsic interactions in polar materials originating from the coupling of one itinerant electron with the macroscopic electric field generated by any longitudinal optical (LO) phonon. Infra-red magneto-absorption measurements of doped GaAs quantum wells structures have been carried out in order to test the concept of Frohlich interaction and polaron mass in such systems. These new experimental results lead to question the validity of this concept in a real system.Comment: 4 pages, 3 figure

The relative contribution of noise and adaptation to competition during tri-stable motion perception

Animals exploit antagonistic interactions for sensory processing and these can cause oscillations between competing states. Ambiguous sensory inputs yield such perceptual multi-stability. Despite numerous empirical studies using binocular rivalry or plaid pattern motion, the driving mechanisms behind the spontaneous transitions between alternatives remain unclear. In the current work, we used a tri-stable barberpole motion stimulus combining empirical and modelling approaches to elucidate the contributions of noise and adaptation to underlying competition. We first robustly characterised the coupling between perceptual reports of transitions and continuously recorded eye direction, identifying a critical window of 480ms before button presses within which both measures were most strongly correlated. Second, we identified a novel non monotonic relationship between stimulus contrast and average perceptual switching rate with an initially rising rate before a gentle reduction at higher contrasts. A neural fields model of the underlying dynamics introduced in previous theoretical work and incorporating noise and adaptation mechanisms was adapted, extended and empirically validated. Noise and adaptation contributions were confirmed to dominate at the lower, and higher, contrasts respectively. Model simulations with two free parameters, controlling adaptation dynamics and direction thresholds, captured the measured mean transition rates for participants. We verified the shift from noise dominated towards adaptation-driven in both the eye direction distributions and inter-transition duration statistics. This work combines modelling and empirical evidence to demonstrate the signal strength dependent interplay between noise and adaptation during tri- stability. We propose that the findings generalise beyond the barberpole stimulus case to ambiguous perception in continuous feature space