Anisotropic Fast-Marching on cartesian grids using Lattice Basis Reduction

We introduce a modification of the Fast Marching Algorithm, which solves the generalized eikonal equation associated to an arbitrary continuous riemannian metric, on a two or three dimensional domain. The algorithm has a logarithmic complexity in the maximum anisotropy ratio of the riemannian metric, which allows to handle extreme anisotropies for a reduced numerical cost. We prove the consistence of the algorithm, and illustrate its efficiency by numerical experiments. The algorithm relies on the computation at each grid point of a special system of coordinates: a reduced basis of the cartesian grid, with respect to the symmetric positive definite matrix encoding the desired anisotropy at this point.Comment: 28 pages, 12 figure

Quantitative Estimates on the Binding Energy for Hydrogen in Non-Relativistic QED. II. The spin case

The hydrogen binding energy in the Pauli-Fierz model with the spin Zeeman term is determined up to the order alpha cube, where alpha denotes the fine-structure constant

Noisy Channel-Output Feedback Capacity of the Linear Deterministic Interference Channel

In this paper, the capacity region of the two-user linear deterministic (LD) interference channel with noisy output feedback (IC-NOF) is fully characterized. This result allows the identification of several asymmetric scenarios in which imple- menting channel-output feedback in only one of the transmitter- receiver pairs is as beneficial as implementing it in both links, in terms of achievable individual rate and sum-rate improvements w.r.t. the case without feedback. In other scenarios, the use of channel-output feedback in any of the transmitter-receiver pairs benefits only one of the two pairs in terms of achievable individual rate improvements or simply, it turns out to be useless, i.e., the capacity regions with and without feedback turn out to be identical even in the full absence of noise in the feedback links.Comment: 5 pages, 9 figures, see proofs in V. Quintero, S. M. Perlaza, and J.-M. Gorce, "Noisy channel-output feedback capacity of the linear deterministic interference channel," INRIA, Tech. Rep. 456, Jan. 2015. This was submitted and accepted in IEEE ITW 201

Precision and accuracy of fish length measurements obtained with two visual underwater methods

During the VITAL cruise in the Bay of Biscay in summer 2002, two devices for measuring the length of swimming fish were tested: 1) a mechanical crown that emitted a pair of parallel laser beams and that was mounted on the main camera and 2) an underwater auto-focus video camera. The precision and accuracy of these devices were compared and the various sources of measurement errors were estimated by repeatedly measuring fixed and mobile objects and live fish. It was found that fish mobility is the main source of error for these devices because they require that the objects to be measured are perpendicular to the field of vision. The best performance was obtained with the laser method where a video-replay of laser spots (projected on fish bodies) carrying real-time size information was used. The auto-focus system performed poorly because of a delay in obtaining focus and because of some technical problems