Impact of heterogeneous link qualities and network connectivity on binary consensus

In this paper we consider a network that is trying to reach consensus over the occurrence of an event while communicating over Additive White Gaussian Noise (AWGN) channels. We characterize the impact of different link qualities and network connectivity on consensus performance by analyzing both the asymptotic and transient behaviors. More specifically, we derive a tight approximation for the second largest eigenvalue of the probability transition matrix. We furthermore characterize the dynamics of each individual node. © 2009 AACC.

Bypass transition to sustained thermoacoustic oscillations in a linearly stable rijke tube

In this paper we examine triggering in a simple linearly-stable thermoacoustic system using techniques from flow instability and optimal control. Firstly, for a noiseless system, we find the initial states that have highest energy growth over given times and from given energies. Secondly, by varying the initial energy, we find the lowest energy that just triggers to a stable periodic solution. We show that the corresponding initial state grows first towards an unstable periodic solution and, from there, to the stable periodic solution. This exploits linear transient growth, which arises due to nonnormality in the governing equations and is directly analogous to bypass transition to turbulence. Thirdly, we introduce noise that has similar spectral characteristics to this initial state. We show that, when triggering from low noise levels, the system grows to high amplitude self-sustained oscillations by first growing towards the unstable periodic solution of the noiseless system. This helps to explain the experimental observation that linearly-stable systems can trigger to self-sustained oscillations even with low background noise. © 2010 by University of Cambridge. Published by the American Institute of Aeronautics and Astronautics, Inc.

Auto-calibration of a camera system using Image Alignment

Calibration of a camera system is a necessary step in any stereo metric process. It correlates all cameras to a common coordinate system by measuring the intrinsic and extrinsic parameters of each camera. Currently, manual calibration of a camera system is the only way to achieve calibration in civil engineering operations that require stereo metric processes (photogrammetry, videogrammetry, vision based asset tracking, etc). This type of calibration however is time-consuming and labor-intensive. Furthermore, in civil engineering operations, camera systems are exposed to open, busy sites. In these conditions, the position of presumably stationary cameras can easily be changed due to external factors such as wind, vibrations or due to an unintentional push/touch from personnel on site. In such cases manual calibration must be repeated. In order to address this issue, several self-calibration algorithms have been proposed. These algorithms use Projective Geometry, Absolute Conic and Kruppa Equations and variations of these to produce processes that achieve calibration. However, most of these methods do not consider all constraints of a camera system such as camera intrinsic constraints, scene constraints, camera motion or varying camera intrinsic properties. This paper presents a novel method that takes all constraints into consideration to auto-calibrate cameras using an image alignment algorithm originally meant for vision based tracking. In this method, image frames are taken from cameras. These frames are used to calculate the fundamental matrix that gives epipolar constraints. Intrinsic and extrinsic properties of cameras are acquired from this calculation. Test results are presented in this paper with recommendations for further improvement.

A Hierarchical Model for Ordinal Matrix Factorization

This paper proposes a hierarchical probabilistic model for ordinal matrix factorization. Unlike previous approaches, we model the ordinal nature of the data and take a principled approach to incorporating priors for the hidden variables. Two algorithms are presented for inference, one based on Gibbs sampling and one based on variational Bayes. Importantly, these algorithms may be implemented in the factorization of very large matrices with missing entries. The model is evaluated on a collaborative filtering task, where users have rated a collection of movies and the system is asked to predict their ratings for other movies. The Netflix data set is used for evaluation, which consists of around 100 million ratings. Using root mean-squared error (RMSE) as an evaluation metric, results show that the suggested model outperforms alternative factorization techniques. Results also show how Gibbs sampling outperforms variational Bayes on this task, despite the large number of ratings and model parameters. Matlab implementations of the proposed algorithms are available from cogsys.imm.dtu.dk/ordinalmatrixfactorization.