Optimal configurations of lines and a statistical application

Motivated by the construction of confidence intervals in statistics, we study optimal configurations of $2^d-1$ lines in real projective space $RP^{d-1}$. For small $d$, we determine line sets that numerically minimize a wide variety of potential functions among all configurations of $2^d-1$ lines through the origin. Numerical experiments verify that our findings enable to assess efficiently the tightness of a bound arising from the statistical literature.Comment: 13 page

Early identification of important patents through network centrality

One of the most challenging problems in technological forecasting is to identify as early as possible those technologies that have the potential to lead to radical changes in our society. In this paper, we use the US patent citation network (1926-2010) to test our ability to early identify a list of historically significant patents through citation network analysis. We show that in order to effectively uncover these patents shortly after they are issued, we need to go beyond raw citation counts and take into account both the citation network topology and temporal information. In particular, an age-normalized measure of patent centrality, called rescaled PageRank, allows us to identify the significant patents earlier than citation count and PageRank score. In addition, we find that while high-impact patents tend to rely on other high-impact patents in a similar way as scientific papers, the patents' citation dynamics is significantly slower than that of papers, which makes the early identification of significant patents more challenging than that of significant papers.Comment: 14 page

Hyperspectral pan-sharpening: a variational convex constrained formulation to impose parallel level lines, solved with ADMM

In this paper, we address the issue of hyperspectral pan-sharpening, which consists in fusing a (low spatial resolution) hyperspectral image HX and a (high spatial resolution) panchromatic image P to obtain a high spatial resolution hyperspectral image. The problem is addressed under a variational convex constrained formulation. The objective favors high resolution spectral bands with level lines parallel to those of the panchromatic image. This term is balanced with a total variation term as regularizer. Fit-to-P data and fit-to-HX data constraints are effectively considered as mathematical constraints, which depend on the statistics of the data noise measurements. The developed Alternating Direction Method of Multipliers (ADMM) optimization scheme enables us to solve this problem efficiently despite the non differentiabilities and the huge number of unknowns.Comment: 4 pages, detailed version of proceedings of conference IEEE WHISPERS 201

Comparison of SAGE and classical multi-antenna algorithms for multipath mitigation in real-world environment

The performance of the Space Alternating Generalized Expectation Maximisation (SAGE) algorithm for multipath mitigation is assessed in this paper. Numerical simulations have already proven the potential of SAGE in navigation context, but practical aspects of the implementation of such a technique in a GNSS receiver are the topic for further investigation. In this paper, we will present the first results of SAGE implementation in a real world environmen

A two-layer shallow flow model with two axes of integration, well-balanced discretization and application to submarine avalanches

We propose a two-layer model with two different axes of integration and a well-balanced finite volume method. The purpose is to study submarine avalanches and generated tsunamis by a depth-averaged model with different averaged directions for the fluid and the granular layers. Two-layer shallow depth-averaged models usually consider either Cartesian or local coordinates for both layers. However, the motion characteristics of the granular layer and the water wave are different: the granular flow velocity is mainly oriented downslope while water motion related to tsunami wave propagation is mostly horizontal. As a result, the shallow approximation and depth-averaging have to be imposed (i) in the direction normal to the topography for the granular flow and (ii) in the vertical direction for the water layer. To deal with this problem, we define a reference plane related to topography variations and use the associated local coordinates to derive the granular layer equations whereas Cartesian coordinates are used for the fluid layer. Depthaveraging is done orthogonally to that reference plane for the granular layer equations and in the vertical direction for the fluid layer equations. Then, a finite volume method is defined based on an extension of the hydrostatic reconstruction. The proposed method is exactly well-balanced for two kind of stationary solutions: the classical one, when both water and granular masses are at rest; the second one, when only the granular mass is at rest. Several tests are presented to get insight into the sensitivity of the granular flow, deposit and generated water waves to the choice of the coordinate systems. Our results show that even for moderate slopes (up to 30◦), strong relative errors on the avalanche dynamics and deposit (up to 60%) and on the generated water waves (up to 120%) are made when using Cartesian coordinates for both layers instead of an appropriate local coordinate system as proposed here.Ministerio de Economía y Competitividad (MINECO). EspañaEuropean Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER)Agence Nationale de la Recherche. FranceEuropean Research Council (ERC