Central Acceptance Testing for Camera Technologies for CTA

The Cherenkov Telescope Array (CTA) is an international initiative to build the next generation ground based very-high energy gamma-ray observatory. It will consist of telescopes of three different sizes, employing several different technologies for the cameras that detect the Cherenkov light from the observed air showers. In order to ensure the compliance of each camera technology with CTA requirements, CTA will perform central acceptance testing of each camera technology. To assist with this, the Camera Test Facilities (CTF) work package is developing a detailed test program covering the most important performance, stability, and durability requirements, including setting up the necessary equipment. Performance testing will include a wide range of tests like signal amplitude, time resolution, dead-time determination, trigger efficiency, performance testing under temperature and humidity variations and several others. These tests can be performed on fully-integrated cameras using a portable setup at the camera construction sites. In addition, two different setups for performance tests on camera sub-units are being built, which can provide early feedback for camera development. Stability and durability tests will include the long-term functionality of movable parts, water tightness of the camera housing, temperature and humidity cycling, resistance to vibrations during transport or due to possible earthquakes, UV-resistance of materials and several others. Some durability tests will need to be contracted out because they will need dedicated equipment not currently available within CTA. The planned test procedures and the current status of the test facilities will be presented.Comment: 8 pages, 3 figures. In Proceedings of the 34th International Cosmic Ray Conference (ICRC2015), The Hague, The Netherlands. All CTA contributions at arXiv:1508.0589

Asymptotics of Bernoulli random walks, bridges, excursions and meanders with a given number of peaks

A Bernoulli random walk is a random trajectory starting from 0 and having i.i.d. increments, each of them being $+1$ or -1, equally likely. The other families cited in the title are Bernoulli random walks under various conditionings. A peak in a trajectory is a local maximum. In this paper, we condition the families of trajectories to have a given number of peaks. We show that, asymptotically, the main effect of setting the number of peaks is to change the order of magnitude of the trajectories. The counting process of the peaks, that encodes the repartition of the peaks in the trajectories, is also studied. It is shown that suitably normalized, it converges to a Brownian bridge which is independent of the limiting trajectory. Applications in terms of plane trees and parallelogram polyominoes are also provided

Tightness of the maximum likelihood semidefinite relaxation for angular synchronization

Maximum likelihood estimation problems are, in general, intractable optimization problems. As a result, it is common to approximate the maximum likelihood estimator (MLE) using convex relaxations. In some cases, the relaxation is tight: it recovers the true MLE. Most tightness proofs only apply to situations where the MLE exactly recovers a planted solution (known to the analyst). It is then sufficient to establish that the optimality conditions hold at the planted signal. In this paper, we study an estimation problem (angular synchronization) for which the MLE is not a simple function of the planted solution, yet for which the convex relaxation is tight. To establish tightness in this context, the proof is less direct because the point at which to verify optimality conditions is not known explicitly. Angular synchronization consists in estimating a collection of $n$ phases, given noisy measurements of the pairwise relative phases. The MLE for angular synchronization is the solution of a (hard) non-bipartite Grothendieck problem over the complex numbers. We consider a stochastic model for the data: a planted signal (that is, a ground truth set of phases) is corrupted with non-adversarial random noise. Even though the MLE does not coincide with the planted signal, we show that the classical semidefinite relaxation for it is tight, with high probability. This holds even for high levels of noise.Comment: 2 figure

Rehabilitation of shoulder impingement syndrome and rotator cuff injuries: an evidence-based review

Rehabilitation of the patient with glenohumeral impingement requires a complete understanding of the structures involved and the underlying mechanism creating the impingement response. A detailed clinical examination and comprehensive treatment programme including specific interventions to address pain, scapular dysfunction and rotator cuff weakness are recommended. The inclusion of objective testing to quantify range of motion and both muscular strength and balance in addition to the manual orthopaedic clinical tests allows clinicians to design evidence-based rehabilitation programmes as well as measure progression and patient improvement

Conflict-Free Coloring of Intersection Graphs of Geometric Objects

In FOCS'2002, Even et al. introduced and studied the notion of conflict-free colorings of geometrically defined hypergraphs. They motivated it by frequency assignment problems in cellular networks. This notion has been extensively studied since then. A conflict-free coloring of a graph is a coloring of its vertices such that the neighborhood (pointed or closed) of each vertex contains a vertex whose color differs from the colors of all other vertices in that neighborhood. In this paper we study conflict-colorings of intersection graphs of geometric objects. We show that any intersection graph of n pseudo-discs in the plane admits a conflict-free coloring with O(\log n) colors, with respect to both closed and pointed neighborhoods. We also show that the latter bound is asymptotically sharp. Using our methods, we also obtain a strengthening of the two main results of Even et al. which we believe is of independent interest. In particular, in view of the original motivation to study such colorings, this strengthening suggests further applications to frequency assignment in wireless networks. Finally, we present bounds on the number of colors needed for conflict-free colorings of other classes of intersection graphs, including intersection graphs of axis-parallel rectangles and of \rho-fat objects in the plane.Comment: 18 page

On the Power of Manifold Samples in Exploring Configuration Spaces and the Dimensionality of Narrow Passages

We extend our study of Motion Planning via Manifold Samples (MMS), a general algorithmic framework that combines geometric methods for the exact and complete analysis of low-dimensional configuration spaces with sampling-based approaches that are appropriate for higher dimensions. The framework explores the configuration space by taking samples that are entire low-dimensional manifolds of the configuration space capturing its connectivity much better than isolated point samples. The contributions of this paper are as follows: (i) We present a recursive application of MMS in a six-dimensional configuration space, enabling the coordination of two polygonal robots translating and rotating amidst polygonal obstacles. In the adduced experiments for the more demanding test cases MMS clearly outperforms PRM, with over 20-fold speedup in a coordination-tight setting. (ii) A probabilistic completeness proof for the most prevalent case, namely MMS with samples that are affine subspaces. (iii) A closer examination of the test cases reveals that MMS has, in comparison to standard sampling-based algorithms, a significant advantage in scenarios containing high-dimensional narrow passages. This provokes a novel characterization of narrow passages which attempts to capture their dimensionality, an attribute that had been (to a large extent) unattended in previous definitions.Comment: 20 page