The Weierstrass subgroup of a curve has maximal rank

We show that the Weierstrass points of the generic curve of genus $g$ over an algebraically closed field of characteristic 0 generate a group of maximal rank in the Jacobian

Quantum confinement effects in Pb Nanocrystals grown on InAs

In the recent work of Ref.\cite{Vlaic2017-bs}, it has been shown that Pb nanocrystals grown on the electron accumulation layer at the (110) surface of InAs are in the regime of Coulomb blockade. This enabled the first scanning tunneling spectroscopy study of the superconducting parity effect across the Anderson limit. The nature of the tunnel barrier between the nanocrystals and the substrate has been attributed to a quantum constriction of the electronic wave-function at the interface due to the large Fermi wavelength of the electron accumulation layer in InAs. In this manuscript, we detail and review the arguments leading to this conclusion. Furthermore, we show that, thanks to this highly clean tunnel barrier, this system is remarkably suited for the study of discrete electronic levels induced by quantum confinement effects in the Pb nanocrystals. We identified three distinct regimes of quantum confinement. For the largest nanocrystals, quantum confinement effects appear through the formation of quantum well states regularly organized in energy and in space. For the smallest nanocrystals, only atomic-like electronic levels separated by a large energy scale are observed. Finally, in the intermediate size regime, discrete electronic levels associated to electronic wave-functions with a random spatial structure are observed, as expected from Random Matrix Theory.Comment: Main 12 pages, Supp: 6 page

Singular perturbation approximation of linear hyperbolic systems of balance laws (full version)

This paper deals with a class of linear hyperbolic systems of balance laws with multiple time scales. The scale of time constants is modeled by a perturbation parameter. This parameter is introduced in both dynamics and boundary conditions. The solution of the full system is approximated by that of the reduced subsystem when the perturbation parameter is small enough. Lyapunov technique is used to prove it. The main result is illustrated by an academic example. Moreover, the boundary control synthesis to a gas flow transport model is shown based on singular perturbation approach

Tikhonov theorem for linear hyperbolic systems

International audienceA class of linear systems of conservation laws with a small perturbation parameter is introduced. By setting the perturbation parameter to zero, two subsystems, the reduced system standing for the slow dynamics and the boundary-layer system representing the fast dynamics, are computed. It is first proved that the exponential stability of the full system implies the stability of both subsystems. Secondly, a counter example is given to indicate that the converse is not true. Moreover a new Tikhonov theorem for this class of the infinite dimensional systems is stated. The solution of the full system can be approximated by that of the reduced system, and this is proved by Lyapunov techniques. An application to boundary feedback stabilization of gas transport model is used to illustrate the results

Stability analysis of a singularly perturbed coupled ODE-PDE system

International audienceThis paper is concerned with a coupled ODE-PDE system with two time scales modeled by a perturbation parameter. Firstly, the perturbation parameter is introduced into the PDE system. We show that the stability of the full system is guaranteed by the stability of the reduced and the boundary-layer subsystems. A numerical simulation on a gas flow transport model is used to illustrate the first result. Secondly, an example is used to show that the full system can be unstable even though both subsystems are stable when the perturbation parameter is introduced into the ODE system

Approximation of singularly perturbed linear hyperbolic systems

International audienceThis paper is concerned with systems modelled by linear singularly perturbed partial differential equations. More precisely a class of linear systems of conservation laws with a small perturbation parameter is investigated. By setting the perturbation parameter to zero, the full system leads to two subsystems, the reduced system standing for the slow dynamics and the boundary-layer system representing the fast dynamics. The exponential stability for both subsystems are obtained by the stability of the overall system of conservation laws. However, the stability of the two subsystems does not imply the stability of the full system. The approximation of the solution for the overall system by the solution for the reduced system is validated via Lyapunov techniques

Lyapunov stability of a singularly perturbed system of two conservation laws

International audienceThis paper is concerned with a class of singularly perturbed systems of two conservation laws. A small perturbation parameter is introduced in the dynamics and the boundary conditions. By setting the perturbation parameter to zero, the singularly perturbed system of conservation laws can be treated as two subsystems of one conservation law: the reduced system and the boundary-layer system. The asymptotic stability of the complete system is investigated via Lyapunov techniques. A Lyapunov function for the singularly perturbed system is obtained as a weighted sum of two Lyapunov functions of the subsystems

A new H2-norm Lyapunov function for the stability of a singularly perturbed system of two conservation laws

International audienceIn this paper a class of singularly perturbed system of conservation laws is considered. The partial differential equations are equipped with boundary conditions which may be studied to derive the exponential stability. Lyapunov stability technique is used to derive sufficient conditions for the exponential stability of this system. A Lyapunov function in H2-norm for a singularly perturbed system of conservation laws is constructed. It is based on the Lyapunov functions of two subsystems in L2-norm

Coding of shape from shading in area V4 of the macaque monkey

<p>Abstract</p> <p>Background</p> <p>The shading of an object provides an important cue for recognition, especially for determining its 3D shape. However, neuronal mechanisms that allow the recovery of 3D shape from shading are poorly understood. The aim of our study was to determine the neuronal basis of 3D shape from shading coding in area V4 of the awake macaque monkey.</p> <p>Results</p> <p>We recorded the responses of V4 cells to stimuli presented parafoveally while the monkeys fixated a central spot. We used a set of stimuli made of 8 different 3D shapes illuminated from 4 directions (from above, the left, the right and below) and different 2D controls for each stimulus. The results show that V4 neurons present a broad selectivity to 3D shape and illumination direction, but without a preference for a unique illumination direction. However, 3D shape and illumination direction selectivities are correlated suggesting that V4 neurons can use the direction of illumination present in complex patterns of shading present on the surface of objects. In addition, a vast majority of V4 neurons (78%) have statistically different responses to the 3D and 2D versions of the stimuli, while responses to 3D are not systematically stronger than those to 2D controls. However, a hierarchical cluster analysis showed that the different classes of stimuli (3D, 2D controls) are clustered in the V4 cells response space suggesting a coding of 3D stimuli based on the population response. The different illumination directions also tend to be clustered in this space.</p> <p>Conclusion</p> <p>Together, these results show that area V4 participates, at the population level, in the coding of complex shape from the shading patterns coming from the illumination of the surface of corrugated objects. Hence V4 provides important information for one of the steps of cortical processing of the 3D aspect of objects in natural light environment.</p