Thesis (Ph. D.)--School of Physics, Georgia Institute of Technology, 2004. Directed by Kurt Wiesenfeld. / Includes bibliographical references (leaves 122-128).

Graphical model, the marriage between graph theory and probability theory, has been drawing increasing attention because of its many attractive features. In this paper, we consider the problem of learning the structure of graphical model based on observed data through a greedy forward-backward algorithm and with the use of learned model to classify the data into different categories. We establish the graphical model associated with a binary Ising Markov random field. And model selection is implemented by adding and deleting edges between nodes. Our experiments show that: compared with previous methods, the proposed algorithm has better performance in terms of correctness rate and model selection. / text

This thesis is concerned with the utilisation of spatial information in processing of high-frequency sidescan SONAR imagery, and particularly in how such information can be used in developing techniques to assist in mapping functions. Survey applications aim to generate maps of the seabed, but are time consuming and expensive; automatic processing is required to improve efficiency. Current techniques have had some success, but utilise little of the available spatial information. Previously, inclusion of such knowledge was prohibitively expensive; recent improvements in numerical simulations techniques has reduced the costs involved. This thesis attempts to exploit these improvements into a method for including spatial information in SONAR processing and in general to image and signal analysis. Bayesian techniques for inclusion of prior knowledge and structuring complex problems are developed and applied to problems of texture segmentation, object detection and parameter extraction. It is shown through experiments on groundtruth and real datasets that the inclusion of spatial context can be very effective in improving poor techniques or, conversely in allowing simpler techniques to be used with the same objective outcome (with obvious computational advantages). The thesis also considers some of the implementation problems with the techniques used, and develops simple modifications to improve common algorithms.

published_or_final_version / Statistics / Master / Master of Philosophy

It is well known that the perturbed GUE matrix model has a combinatorial interpretation involving graphs embedded in Riemann surfaces. Generating functions for these graphs in the case of an even potential have been studied by many authors. The case of a cubic potential has also been studied. Using string equations, we construct "valence independent" formulas for map generating functions. These formulas hold for arbitrary polynomial potentials. We derive "edge Toda equations," which we use together with our valence independent formulas to generalize formulas of Ercolani, McLaughlin and Pierce to the case of an arbitrary odd or even valence. We derive a valence independent formula for the equilibrium measure for eigenvalues of the matrix model. Using this formula for the equilibrium measure we show that our valence independent formulas for generating functions can also be derived from the Riemann-Hilbert problem for orthogonal polynomials, and from the loop equations.

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