The linear request problem

We propose a simple approach to a problem introduced by Galatolo and Pollicott, consisting in perturbing a dynamical system in order for its absolutely continuous invariant measure to change in a prescribed way. Instead of using transfer operators, we observe that restricting to an infinitesimal conjugacy already yields a solution. This allows us to work in any dimension and dispense from any dynamical hypothesis. In particular, we don't need to assume hyperbolicity to obtain a solution, although expansion moreover ensures the existence of an infinite-dimensional space of solutions.Comment: v2: the approach has been further simplified, only basic differential calculus is in fact needed instead of basic PD

Optimal Cooperative MAC Protocol with Efficient Selection of Relay Terminals

A new cooperative protocol is proposed in the context of wireless mesh networks. The protocol implements ondemand cooperation, i.e. cooperation between a source terminal and a destination terminal is activated only when needed. In that case, only the best relay among a set of available terminals is re-transmitting the source message to the destination terminal. This typical approach is improved using three additional features. First, a splitting algorithm is implemented to select the best relay. This ensures a fast selection process. Moreover, the duration of the selection process is now completely characterized. Second, only terminals that improve the outage probability of the direct link are allowed to participate to the relay selection. By this means, inefficient cooperation is now avoided. Finally, the destination terminal discards the source message when it fails to decode it. This saves processing time since the destination terminal does not need to combine the replicas of the source message: the one from the source terminal and the one from the best relay. We prove that the proposed protocol achieves an optimal performance in terms of Diversity-Multiplexing Tradeoff (DMT)

A Pontryagin Maximum Principle in Wasserstein Spaces for Constrained Optimal Control Problems

In this paper, we prove a Pontryagin Maximum Principle for constrained optimal control problems in the Wasserstein space of probability measures. The dynamics, is described by a transport equation with non-local velocities and is subject to end-point and running state constraints. Building on our previous work, we combine the classical method of needle-variations from geometric control theory and the metric differential structure of the Wasserstein spaces to obtain a maximum principle stated in the so-called Gamkrelidze form.Comment: 35 page

Overview of MHz air shower radio experiments and results

In this paper, I present a review of the main results obtained in the last 10 years in the field of radio-detection of cosmic-ray air showers in the MHz range. All results from all experiments cannot be reported here so that I will focus on the results more than on the experiments themselves. Modern experiments started in 2003 with CODALEMA and LOPES. In 2006, small-size autonomous prototypes setup were installed at the Pierre Auger Observatory site, to help the design of the Auger Engineering Radio Array (AERA). We will discuss the principal aspects of the radio data analysis and the determination of the primary cosmic ray characteristics: the arrival direction, the lateral distribution of the electric field, the correlation with the primary energy, the emission mechanisms and the sensitivity to the composition of the cosmic rays.Comment: Proceedings of the ARENA2012 conference (Erlangen, Germany), to be published in AIP Conference Proceeding

Observation of diffraction and measurement of the forward energy flow with the CMS detector

The observation of inclusive diffraction with the CMS detector at the LHC is presented for centre-of-mass energies \sqrt s = 0.9 TeV and 2.36 TeV. Diffractive events are selected by the presence of a Large Rapidity Gap in the forward region of the CMS detector and uncorrected data are compared with Monte Carlo simulations based on the event generators PYTHIA and PHOJET. The measurement of the forward energy flow, in the pseudorapidity region 3.15 < |\eta| < 4.9, is also presented at \sqrt s = 0.9 TeV, 2.36 TeV and 7 TeV. Uncorrected data are compared with Monte Carlo simulations based on PYTHIA.Comment: 4 pages - 2 figures - proceedings of Physics at LHC 2010, 7-12 June 2010, DESY, Hambur