http://hdl.handle.net/1721.1/49433 Mon, 20 May 2013 21:46:29 GMT 2013-05-20T21:46:29Z http://dspace.mit.edu:80/bitstream/id/812537/ http://hdl.handle.net/1721.1/49433 http://hdl.handle.net/1721.1/78927 Data Assimilation with Gaussian Mixture Models using the Dynamically Orthogonal Field Equations. Part II. Applications Sondergaard, Thomas; Lermusiaux, Pierre F. J. The properties and capabilities of the GMM-DO filter are assessed and exemplified by applications to two dynamical systems: (1) the Double Well Diffusion and (2) Sudden Expansion flows; both of which admit far-from-Gaussian statistics. The former test case, or twin experiment, validates the use of the EM algorithm and Bayesian Information Criterion with Gaussian Mixture Models in a filtering context; the latter further exemplifies its ability to efficiently handle state vectors of non-trivial dimensionality and dynamics with jets and eddies. For each test case, qualitative and quantitative comparisons are made with contemporary filters. The sensitivity to input parameters is illustrated and discussed. Properties of the filter are examined and its estimates are described, including: the equation-based and adaptive prediction of the probability densities; the evolution of the mean field, stochastic subspace modes and stochastic coefficients; the fitting of Gaussian Mixture Models; and, the efficient and analytical Bayesian updates at assimilation times and the corresponding data impacts. The advantages of respecting nonlinear dynamics and preserving non-Gaussian statistics are brought to light. For realistic test cases admitting complex distributions and with sparse or noisy measurements, the GMM-DO filter is shown to fundamentally improve the filtering skill, outperforming simpler schemes invoking the Gaussian parametric distribution. Sun, 01 Jan 2012 05:00:00 GMT http://hdl.handle.net/1721.1/78927 2012-01-01T05:00:00Z http://hdl.handle.net/1721.1/78926 Estimating Phospholipid Membrane Water Partition Coefficients Using Comprehensive Two-Dimensional Gas Chromatography Tcaciuc, Alexandra Patricia; Nelson, Robert Gregory; Reddy, Christopher M.; Gschwend, Philip M. Recent studies have shown that membrane–water partition coefficients of organic chemicals can be used to predict bioaccumulation and type I narcosis toxicity more accurately than the traditional K[subscript OW]-based approach. In this paper, we demonstrate how comprehensive two-dimensional gas chromatography (GC × GC) can be used to estimate such membrane–water partition coefficients (K[subscript PLW]s), focusing in particular on phosphatidyl choline based lipids. This method performed well for a set of 38 compounds, including polycyclic aromatic hydrocarbons, polychlorinated benzenes and biphenyls, and substituted benzenes including some phenols and anilines. The average difference between the estimated and the measured log K[subscript PLW] values of 0.47 log units is smaller than in the case of a log K[subscript OW] correlation approach but larger than seen using a polyparameter linear free energy relationship based approach. However, the GC × GC based method presents the advantage that it can be applied to mixtures of chemicals that are not completely identified, such as petroleum hydrocarbon mixtures. At the same time, our application of the GC × GC method suffered larger errors when applied to certain hydrogen bonding compounds due to the inability of the GC × GC capillary columns phases that we used to interact with analytes via hydrogen bond donation/electron acceptance. Thu, 01 Mar 2012 05:00:00 GMT http://hdl.handle.net/1721.1/78926 2012-03-01T05:00:00Z http://hdl.handle.net/1721.1/78925 Hypothesis testing via a comparator Polyanskiy, Yury This paper investigates the best achievable performance by a hypothesis test satisfying a structural constraint: two functions are computed at two different terminals and the detector consists of a simple comparator verifying whether the functions agree. Such tests arise as part of study of fundamental limits of channel coding, but are also useful in other contexts. A simple expression for the Stein exponent is found and applied to showing a strong converse in the problem of multi-terminal hypothesis testing with rate constraints. Connections to the Gács-Körner common information and to spectral properties of conditional expectation operator are identified. Further tightening of results hinges on finding λ-blocks of minimal weight. Application of Delsarte's linear programming method to this problem is described. Sun, 01 Jul 2012 04:00:00 GMT http://hdl.handle.net/1721.1/78925 2012-07-01T04:00:00Z http://hdl.handle.net/1721.1/78924 Dynamic positioning of beacon vehicles for cooperative underwater navigation Bahr, Alexander; Leonard, John Joseph; Martinoli, Alcherio Autonomous Underwater Vehicles (AUVs) are used for an ever increasing range of applications due to the maturing of the technology. Due to the absence of the GPS signal underwater, the correct estimation of its position is a challenge for submerged vehicles. One promising strategy to mitigate this problem is to use a group of AUVs where one or more assume the role of a beacon vehicle which has a very accurate position estimate due to an expensive navigation suite or frequent surfacings. These beacon vehicles broadcast their position and the remaining survey vehicles can use this position information and intra-vehicle ranges to update their position estimate. The effectiveness of this approach strongly depends on the geometry between the beacon vehicles and the survey vehicles. The trajectories of the beacon vehicles should thus be planned with the goal to minimize the position uncertainty of the survey vehicles. We propose a distributed algorithm which dynamically computes the locally optimal position for a beacon vehicle using only information obtained from broadcast communication of the survey vehicles. It does not need prior information about the survey vehicles' trajectory and can be used for any group size of beacon and survey vehicles. Mon, 01 Oct 2012 04:00:00 GMT http://hdl.handle.net/1721.1/78924 2012-10-01T04:00:00Z