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  • The Inria's Research Teams produce an annual Activity Report presenting their activities and their results of the year. These reports include the team members, the scientific program, the software developed by the team and the new results of the year. The report also describes the grants, contracts and the activities of dissemination and teaching. Finally, the report gives the list of publications of the year.

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Section: New Results

Group synchronization on grids

Group synchronization requires to estimate unknown elements (θv)vV of a compact group 𝔾 associated to the vertices of a graph G=(V,E), using noisy observations of the group differences associated to the edges. This model is relevant to a variety of applications ranging from structure from motion in computer vision to graph localization and positioning, to certain families of community detection problems.

We focus on the case in which the graph G is the d-dimensional grid. Since the unknowns θv are only determined up to a global action of the group, we consider the following weak recovery question. Can we determine the group difference θu-1θv between far apart vertices u,v better than by random guessing? We prove that weak recovery is possible (provided the noise is small enough) for d3 and, for certain finite groups, for d2. Vice-versa, for some continuous groups, we prove that weak recovery is impossible for d=2. Finally, for strong enough noise, weak recovery is always impossible.