New Analyses of Double-Bang Events in the Atmosphere

We use CORSIKA+Herwig simulation code to produce ultra-high energy neutrino interactions in the atmosphere. Our aim is to reproduce extensive air showers originated by extragalactic tau-neutrinos. For charged current tau-neutrino interactions in the atmosphere, beside the air shower originated from the neutrino interaction, it is expected that a tau is created and may decay before reaching the ground. That phenomenon makes possible the generation of two related extensive air showers, the so called Double-Bang event. We make an analysis of the main characteristics of Double-Bang events in the atmosphere for mean values of the parameters involved in such phenomenon, like the inelasticity and tau decay length. We discuss what may happen for the ``out of the average'' cases and conclude that it may be possible to observe this kind of event in ultra-high energy cosmic ray observatories such as Pierre Auger or Telescope Array.Comment: 17 pages, 5 figures, final version to appear in BJ

Distributing the Kalman Filter for Large-Scale Systems

This paper derives a \emph{distributed} Kalman filter to estimate a sparsely connected, large-scale, $n-$dimensional, dynamical system monitored by a network of $N$ sensors. Local Kalman filters are implemented on the ($n_l-$dimensional, where $n_l\ll n$) sub-systems that are obtained after spatially decomposing the large-scale system. The resulting sub-systems overlap, which along with an assimilation procedure on the local Kalman filters, preserve an $L$th order Gauss-Markovian structure of the centralized error processes. The information loss due to the $L$th order Gauss-Markovian approximation is controllable as it can be characterized by a divergence that decreases as $L\uparrow$. The order of the approximation, $L$, leads to a lower bound on the dimension of the sub-systems, hence, providing a criterion for sub-system selection. The assimilation procedure is carried out on the local error covariances with a distributed iterate collapse inversion (DICI) algorithm that we introduce. The DICI algorithm computes the (approximated) centralized Riccati and Lyapunov equations iteratively with only local communication and low-order computation. We fuse the observations that are common among the local Kalman filters using bipartite fusion graphs and consensus averaging algorithms. The proposed algorithm achieves full distribution of the Kalman filter that is coherent with the centralized Kalman filter with an $L$th order Gaussian-Markovian structure on the centralized error processes. Nowhere storage, communication, or computation of $n-$dimensional vectors and matrices is needed; only $n_l \ll n$ dimensional vectors and matrices are communicated or used in the computation at the sensors

Service scheduling in garden maintenance

Neoturf is a Portuguese company working in the area of project, building and garden’s maintenance. Neoturf would like to have a procedure for scheduling and routing efficiently the clients from garden maintenance services. The company has two teams available during the whole year and an additional team during summer to handle all the maintenance jobs. Each team consists of two or three employees with a vehicle fully equipped with the tools that allow to carry out every kind of maintenance service. In the beginning of each year, the number and frequency of maintenance interventions to conduct during the year, on each client, are accorded. Each client is assigned to the same team and, usually, time windows are established so that visits to the client should occur only within these periods. As the Neoturf costumers’ are geographically spread over a wide region, the total distance on visiting clients is a factor that has a heavy weight on the costs of the company. Neoturf is concerned with reducing these costs, while satisfying the agreements with the clients

DILAND: An Algorithm for Distributed Sensor Localization with Noisy Distance Measurements

In this correspondence, we present an algorithm for distributed sensor localization with noisy distance measurements (DILAND) that extends and makes the DLRE more robust. DLRE is a distributed sensor localization algorithm in $\mathbb{R}^m$ $(m\geq1)$ introduced in \cite{usman_loctsp:08}. DILAND operates when (i) the communication among the sensors is noisy; (ii) the communication links in the network may fail with a non-zero probability; and (iii) the measurements performed to compute distances among the sensors are corrupted with noise. The sensors (which do not know their locations) lie in the convex hull of at least $m+1$ anchors (nodes that know their own locations.) Under minimal assumptions on the connectivity and triangulation of each sensor in the network, this correspondence shows that, under the broad random phenomena described above, DILAND converges almost surely (a.s.) to the exact sensor locations.Comment: Submitted to the IEEE Transactions on Signal Processing. Initial submission on May 2009. 12 page

Bound-states and polarized charged zero modes in three-dimensional topological insulators induced by a magnetic vortex

By coating a three-dimensional topological insulator (TI) with a ferromagnetic film supporting an in-plane magnetic vortex, one breaks the time-reversal symmetry (TRS) without generating a mass gap. It rather yields electronic states bound to the vortex center which have different probabilities associated with each spin mode. In addition, its associate current (around the vortex center) is partially polarized with an energy gap separating the most excited bound state from the scattered ones. Charged zero-modes also appear as fully polarized modes localized near the vortex center. From the magnetic point of view, the observation of such a special current in a TI-magnet sandwich comes about as an alternative technique for detecting magnetic vortices in magnetic thin films.Comment: 8 pages, 3 figures, new version with more discussions and results accepted for publication in The European Physical Journal