Sensor graphs for guaranteed cooperative localization performance

A group of mobile robots can localize cooperatively, using relative position and absolute orientation measurements, fused through an extended Kalman filter (ekf). The topology of the graph of relative measurements is known to affect the steady-state value of the position error covariance matrix. Classes of sensor graphs are identified, for which tight bounds for the trace of the covariance matrix can be obtained based on the algebraic properties of the underlying relative measurement graph. The string and the star graph topologies are considered, and the explicit form of the eigenvalues of error covariance matrix is given. More general sensor graph topologies are considered as combinations of the string and star topologies, when additional edges are added. It is demonstrated how the addition of edges increases the trace of the steady-state value of the position error covariance matrix, and the theoretical predictions are verified through simulation analysis.

The most persistent soft-clique in a set of sampled graphs

When searching for characteristic subpatterns in potentially noisy graph data, it appears self-evident that having multiple observations would be better than having just one. However, it turns out that the inconsistencies introduced when different graph instances have different edge sets pose a serious challenge. In this work we address this challenge for the problem of finding maximum weighted cliques. We introduce the concept of most persistent soft-clique. This is subset of vertices, that 1) is almost fully or at least densely connected, 2) occurs in all or almost all graph instances, and 3) has the maximum weight. We present a measure of clique-ness, that essentially counts the number of edge missing to make a subset of vertices into a clique. With this measure, we show that the problem of finding the most persistent soft-clique problem can be cast either as: a) a max-min two person game optimization problem, or b) a min-min soft margin optimization problem. Both formulations lead to the same solution when using a partial Lagrangian method to solve the optimization problems. By experiments on synthetic data and on real social network data we show that the proposed method is able to reliably find soft cliques in graph data, even if that is distorted by random noise or unreliable observations. Copyright 2012 by the author(s)/owner(s).

Random function priors for exchangeable arrays with applications to graphs and relational data

A fundamental problem in the analysis of structured relational data like graphs, networks, databases, and matrices is to extract a summary of the common structure underlying relations between individual entities. Relational data are typically encoded in the form of arrays; invariance to the ordering of rows and columns corresponds to exchangeable arrays. Results in probability theory due to Aldous, Hoover and Kallenberg show that exchangeable arrays can be represented in terms of a random measurable function which constitutes the natural model parameter in a Bayesian model. We obtain a flexible yet simple Bayesian nonparametric model by placing a Gaussian process prior on the parameter function. Efficient inference utilises elliptical slice sampling combined with a random sparse approximation to the Gaussian process. We demonstrate applications of the model to network data and clarify its relation to models in the literature, several of which emerge as special cases.

Model reductions for inference: generality of pairwise, binary, and planar factor graphs.

We offer a solution to the problem of efficiently translating algorithms between different types of discrete statistical model. We investigate the expressive power of three classes of model-those with binary variables, with pairwise factors, and with planar topology-as well as their four intersections. We formalize a notion of "simple reduction" for the problem of inferring marginal probabilities and consider whether it is possible to "simply reduce" marginal inference from general discrete factor graphs to factor graphs in each of these seven subclasses. We characterize the reducibility of each class, showing in particular that the class of binary pairwise factor graphs is able to simply reduce only positive models. We also exhibit a continuous "spectral reduction" based on polynomial interpolation, which overcomes this limitation. Experiments assess the performance of standard approximate inference algorithms on the outputs of our reductions.

Fabrication and electrical integration of robust carbon nanotube micropillars by self-directed elastocapillary densification

Vertically aligned carbon nanotube (CNT) 'forest' microstructures fabricated by chemical vapor deposition (CVD) using patterned catalyst films typically have a low CNT density per unit area. As a result, CNT forests have poor bulk properties and are too fragile for integration with microfabrication processing. We introduce a new self-directed capillary densification method where a liquid is controllably condensed onto and evaporated from the CNT forests. Compared to prior approaches, where the substrate with CNTs is immersed in a liquid, our condensation approach gives significantly more uniform structures and enables precise control of the CNT packing density. We present a set of design rules and parametric studies of CNT micropillar densification by self-directed capillary action, and show that self-directed capillary densification enhances Young's modulus and electrical conductivity of CNT micropillars by more than three orders of magnitude. Owing to the outstanding properties of CNTs, this scalable process will be useful for the integration of CNTs as a functional material in microfabricated devices for mechanical, electrical, thermal and biomedical applications. © 2011 IOP Publishing Ltd.

Europium-directed self-assembly of a luminescent supramolecular gel from a tripodal terpyridine-based ligand.

Eu(III), the last piece in the puzzle: Europium-induced self-assembly of ligands having a C(3)-symmetrical benzene-1,3,5-tricarboxamide core results in the formation of luminescent gels. Supramolecular polymers are formed through hydrogen bonding between the ligands. The polymers are then brought together into the gel assembly through the coordination of terpyridine ends by Eu(III) ions (blue dashed arrow: distance between two ligands in the strand direction).

Detecting bipedal motion from correlated probabilistic trajectories

This paper is about detecting bipedal motion in video sequences by using point trajectories in a framework of classification. Given a number of point trajectories, we find a subset of points which are arising from feet in bipedal motion by analysing their spatio-temporal correlation in a pairwise fashion. To this end, we introduce probabilistic trajectories as our new features which associate each point over a sufficiently long time period in the presence of noise. They are extracted from directed acyclic graphs whose edges represent temporal point correspondences and are weighted with their matching probability in terms of appearance and location. The benefit of the new representation is that it practically tolerates inherent ambiguity for example due to occlusions. We then learn the correlation between the motion of two feet using the probabilistic trajectories in a decision forest classifier. The effectiveness of the algorithm is demonstrated in experiments on image sequences captured with a static camera, and extensions to deal with a moving camera are discussed. © 2013 Elsevier B.V. All rights reserved.

Light-directed writing of chemically tunable narrow-band holographic sensors

This tunable holographic sensor offers interrogation and a reporting transducer as well as an analyte-responsive hydrogel, rendering it label-free and reusable. A single 6 ns laser pulse is used to fabricate holographic sensors consisting of silver nanoparticles arranged periodically within a polymer film. The tunability of the sensor is demonstrated through pH sensing of artificial urine and validated through computational modeling. © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.