Network Localization by Shadow Edges

Localization is a fundamental task for sensor networks. Traditional network construction approaches allow to obtain localized networks requiring the nodes to be at least tri-connected (in 2D), i.e., the communication graph needs to be globally rigid. In this paper we exploit, besides the information on the neighbors sensed by each robot/sensor, also the information about the lack of communication among nodes. The result is a framework where the nodes are required to be bi-connected and the communication graph has to be rigid. This is possible considering a novel typology of link, namely Shadow Edges, that account for the lack of communication among nodes and allow to reduce the uncertainty associated to the position of the nodes.Comment: preprint submitted to 2013 European Control Conference, July 17-19 2013, Zurich, Switzerlan

A graphical, scalable and intuitive method for the placement and the connection of biological cells

We introduce a graphical method originating from the computer graphics domain that is used for the arbitrary and intuitive placement of cells over a two-dimensional manifold. Using a bitmap image as input, where the color indicates the identity of the different structures and the alpha channel indicates the local cell density, this method guarantees a discrete distribution of cell position respecting the local density function. This method scales to any number of cells, allows to specify several different structures at once with arbitrary shapes and provides a scalable and versatile alternative to the more classical assumption of a uniform non-spatial distribution. Furthermore, several connection schemes can be derived from the paired distances between cells using either an automatic mapping or a user-defined local reference frame, providing new computational properties for the underlying model. The method is illustrated on a discrete homogeneous neural field, on the distribution of cones and rods in the retina and on a coronal view of the basal ganglia.Comment: Corresponding code at https://github.com/rougier/spatial-computatio

Robust Localization from Incomplete Local Information

We consider the problem of localizing wireless devices in an ad-hoc network embedded in a d-dimensional Euclidean space. Obtaining a good estimation of where wireless devices are located is crucial in wireless network applications including environment monitoring, geographic routing and topology control. When the positions of the devices are unknown and only local distance information is given, we need to infer the positions from these local distance measurements. This problem is particularly challenging when we only have access to measurements that have limited accuracy and are incomplete. We consider the extreme case of this limitation on the available information, namely only the connectivity information is available, i.e., we only know whether a pair of nodes is within a fixed detection range of each other or not, and no information is known about how far apart they are. Further, to account for detection failures, we assume that even if a pair of devices is within the detection range, it fails to detect the presence of one another with some probability and this probability of failure depends on how far apart those devices are. Given this limited information, we investigate the performance of a centralized positioning algorithm MDS-MAP introduced by Shang et al., and a distributed positioning algorithm, introduced by Savarese et al., called HOP-TERRAIN. In particular, for a network consisting of n devices positioned randomly, we provide a bound on the resulting error for both algorithms. We show that the error is bounded, decreasing at a rate that is proportional to R/Rc, where Rc is the critical detection range when the resulting random network starts to be connected, and R is the detection range of each device.Comment: 40 pages, 13 figure