Weyl quantization of degree 2 symplectic graded manifolds

Let $S$ be a spinor bundle of a pseudo-Euclidean vector bundle $(E,\mathrm{g})$ of even rank. We introduce a new filtration on the algebra $\mathcal{D}(M,S)$ of differential operators on $S$. As main property, the associated graded algebra $\mathrm{gr}\mathcal{D}(M,S)$ is isomorphic to the algebra $\mathcal{O}(\mathcal{M})$ of functions on $\mathcal{M}$, where $\mathcal{M}$ is the symplectic graded manifold of degree $2$ canonically associated to $(E,\mathrm{g})$. Accordingly, we define the Weyl quantization on $\mathcal{M}$ as a map $\mathcal{WQ}_\hbar:\mathcal{O}(\mathcal{M})\to\mathcal{D}(M,S)$, and prove that $\mathcal{WQ}_\hbar$ satisfies all desired usual properties. As an application, we obtain a bijection between Courant algebroid structures $(E,\mathrm{g},\rho,[\cdot,\cdot])$, that are encoded by Hamiltonian generating functions on $\mathcal{M}$, and skew-symmetric Dirac generating operators $D\in\mathcal{D}(M,S)$. The operator $D^2$ gives a new invariant of $(E,\mathrm{g},\rho,[\cdot,\cdot])$, which generalizes the square norm of the Cartan $3$-form of a quadratic Lie algebra. We study in detail the particular case of $E$ being the double of a Lie bialgebroid $(A,A^*)$.Comment: 41 page

Predicting the Impact of Measures Against P2P Networks on the Transient Behaviors

The paper has two objectives. The first is to study rigorously the transient behavior of some P2P networks whenever information is replicated and disseminated according to epidemic-like dynamics. The second is to use the insight gained from the previous analysis in order to predict how efficient are measures taken against peer-to-peer (P2P) networks. We first introduce a stochastic model which extends a classical epidemic model and characterize the P2P swarm behavior in presence of free riding peers. We then study a second model in which a peer initiates a contact with another peer chosen randomly. In both cases the network is shown to exhibit a phase transition: a small change in the parameters causes a large change in the behavior of the network. We show, in particular, how the phase transition affects measures that content provider networks may take against P2P networks that distribute non-authorized music or books, and what is the efficiency of counter-measures.Comment: IEEE Infocom (2011

Multi-sensor based object detection in driving scenes

The work done in this internship consists in two main part. The first part is the design of an experimental platform to acquire data for testing and training. To design the experiments, onboard and onroad sensors have been considered. A calibration process has been conducted in order to integrated all the data from different sources. The second part was the use of a stereo system and a laser scanner to extract the free navigable space and to detect obstacles. This has been conducted through the use of an occupancy grid map representation

Adapting the Virtual Platooning Concept to Roundabout Crossing

International audienc

LiDAR based relative pose and covariance estimation for communicating vehicles exchanging a polygonal model of their shape

International audienc

Facial expression aftereffect revealed by adaption to emotion-invisible dynamic bubbled faces

Visual adaptation is a powerful tool to probe the short-term plasticity of the visual system. Adapting to local features such as the oriented lines can distort our judgment of subsequently presented lines, the tilt aftereffect. The tilt aftereffect is believed to be processed at the low-level of the visual cortex, such as V1. Adaptation to faces, on the other hand, can produce significant aftereffects in high-level traits such as identity, expression, and ethnicity. However, whether face adaptation necessitate awareness of face features is debatable. In the current study, we investigated whether facial expression aftereffects (FEAE) can be generated by partially visible faces. We first generated partially visible faces using the bubbles technique, in which the face was seen through randomly positioned circular apertures, and selected the bubbled faces for which the subjects were unable to identify happy or sad expressions. When the subjects adapted to static displays of these partial faces, no significant FEAE was found. However, when the subjects adapted to a dynamic video display of a series of different partial faces, a significant FEAE was observed. In both conditions, subjects could not identify facial expression in the individual adapting faces. These results suggest that our visual system is able to integrate unrecognizable partial faces over a short period of time and that the integrated percept affects our judgment on subsequently presented faces. We conclude that FEAE can be generated by partial face with little facial expression cues, implying that our cognitive system fills-in the missing parts during adaptation, or the subcortical structures are activated by the bubbled faces without conscious recognition of emotion during adaptation

Reasoning in evidential networks with conditional belief functions

AbstractIn the existing evidential networks applicable to belief functions, the relations among the variables are always represented by joint belief functions on the product space of the variables involved. In this paper, we use conditional belief functions to represent such relations in the network and show some relations between these two kinds of representations. We also present a propagation algorithm for such networks. By analyzing the properties of some special networks with conditional belief functions, called networks with partial dependency, we show that the computation for reasoning can be simplified