A trustable and accurate ground truth is a key requirement for benchmarking self-localization and mapping algorithms; on the other hand, collection of ground truth is a complex and daunting task, and its validation is a challenging issue. In this paper we propose two techniques for indoor ground truth collection, developed in the framework of the European project RAW S E E D S, which are mutually independent and also independent on the sensors onboard the robot. These techniques are based, respectively, on a network of fixed cameras, and on a network of fixed laser scanners. We show how these systems are implemented and deployed, and, most importantly, we evaluate their performance; moreover, we investigate the possible fusion of their outputs

We study positive entire solutions u = u(x, y) of the critical equationwhere (x, y) ∈ R m × R k , α > 0, and Q = m + k(α + 1). In the first part of the article, exploiting the invariance of the equation with respect to a suitable conformal inversion, we prove a "spherical symmetry" result for solutions. In the second part, we show how to reduce the dimension of the problem using a hyperbolic symmetry argument. Given any positive solution u of (1), after a suitable scaling and a translation in the variable y, the function v(x) = u(x, 0) satisfies the equationwith a mixed boundary condition. Here, p and q are appropriate radial functions. In the last part, we prove that if m = k = 1, the solution of (2) is unique and that for m ≥ 3 and k = 1, problem (2) has a unique solution in the class of x-radial functions.

fieldsAbstract 9 We prove the Poincard inequality for vector fields on the balls of the control distance by integrating along subunit paths. Our method requires that the balls are representable by means of suitable "controllable almost exponential maps".

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We prove a ball-box theorem for nonsmooth Hörmander vector fields of step s ≥ 2.