Existence of Conformal Metrics on Spheres with Prescribed Paneitz Curvature

In this paper we study the problem of prescribing a fourth order conformal invariant (the Paneitz curvature) on the $n$-sphere, with $n\geq 5$. Using tools from the theory of critical points at infinity, we provide some topological conditions on the level sets of a given positive function under which we prove the existene of a metric, conformally equivalent to the standard metric, with prescribed Paneitz curvature.Comment: 20 page

The Paneitz Curvature Problem on Lower Dimensional Spheres

In this paper we prescribe a fourth order conformal invariant 9the Paneitz Curvature) on five and six spheres. Using dynamical and topological methods involving the study of critical points at infinity of the associated variational problem, we prove some existence results.Comment: 34 page

DOPE: Distributed Optimization for Pairwise Energies

We formulate an Alternating Direction Method of Mul-tipliers (ADMM) that systematically distributes the computations of any technique for optimizing pairwise functions, including non-submodular potentials. Such discrete functions are very useful in segmentation and a breadth of other vision problems. Our method decomposes the problem into a large set of small sub-problems, each involving a sub-region of the image domain, which can be solved in parallel. We achieve consistency between the sub-problems through a novel constraint that can be used for a large class of pair-wise functions. We give an iterative numerical solution that alternates between solving the sub-problems and updating consistency variables, until convergence. We report comprehensive experiments, which demonstrate the benefit of our general distributed solution in the case of the popular serial algorithm of Boykov and Kolmogorov (BK algorithm) and, also, in the context of non-submodular functions.Comment: Accepted at CVPR 201

Lyee Program Execution Patterns

National audienceThe research undertaken aims to find regularities in Lyee program execution traces and to relate the trace chunks to well defined types of Lyee design situations. Our findings take the form of Lyee execution patterns, each pattern coupling a situation with a trace chunk. The paper presents and illustrate them with an example