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Applications of Rapidly Mixing Markov Chains to Problems in Graph Theory

Description: In this dissertation the results of Jerrum and Sinclair on the conductance of Markov chains are used to prove that almost all generalized Steinhaus graphs are rapidly mixing and an algorithm for the uniform generation of 2 - (4k + 1,4,1) cyclic Mendelsohn designs is developed.
Date: August 1993
Creator: Simmons, Dayton C. (Dayton Cooper)
Partner: UNT Libraries

Modeling threat assessments of water supply systems using markov latent effects methodology.

Description: Recent amendments to the Safe Drinking Water Act emphasize efforts toward safeguarding our nation's water supplies against attack and contamination. Specifically, the Public Health Security and Bioterrorism Preparedness and Response Act of 2002 established requirements for each community water system serving more than 3300 people to conduct an assessment of the vulnerability of its system to a terrorist attack or other intentional acts. Integral to evaluating system vulnerability is the threat assessment, which is the process by which the credibility of a threat is quantified. Unfortunately, full probabilistic assessment is generally not feasible, as there is insufficient experience and/or data to quantify the associated probabilities. For this reason, an alternative approach is proposed based on Markov Latent Effects (MLE) modeling, which provides a framework for quantifying imprecise subjective metrics through possibilistic or fuzzy mathematics. Here, an MLE model for water systems is developed and demonstrated to determine threat assessments for different scenarios identified by the assailant, asset, and means. Scenario assailants include terrorists, insiders, and vandals. Assets include a water treatment plant, water storage tank, node, pipeline, well, and a pump station. Means used in attacks include contamination (onsite chemicals, biological and chemical), explosives and vandalism. Results demonstrated highest threats are vandalism events and least likely events are those performed by a terrorist.
Date: December 1, 2006
Creator: Silva, Consuelo Juanita
Partner: UNT Libraries Government Documents Department

Dimension spectrum and graph directed Markov systems.

Description: In this dissertation we study graph directed Markov systems (GDMS) and limit sets associated with these systems. Given a GDMS S, by the Hausdorff dimension spectrum of S we mean the set of all positive real numbers which are the Hausdorff dimension of the limit set generated by a subsystem of S. We say that S has full Hausdorff dimension spectrum (full HD spectrum), if the dimension spectrum is the interval [0, h], where h is the Hausdorff dimension of the limit set of S. We give necessary conditions for a finitely primitive conformal GDMS to have full HD spectrum. A GDMS is said to be regular if the Hausdorff dimension of its limit set is also the zero of the topological pressure function. We show that every number in the Hausdorff dimension spectrum is the Hausdorff dimension of a regular subsystem. In the particular case of a conformal iterated function system we show that the Hausdorff dimension spectrum is compact. We introduce several new systems: the nearest integer GDMS, the Gauss-like continued fraction system, and the Renyi-like continued fraction system. We prove that these systems have full HD spectrum. A special attention is given to the backward continued fraction system that we introduce and we prove that it has full HD spectrum. This system turns out to be a parabolic iterated function system and this makes the analysis more involved. Several examples have been constructed in the past of systems not having full HD spectrum. We give an example of such a system whose limit set has positive Lebesgue measure.
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Date: May 2006
Creator: Ghenciu, Eugen Andrei
Partner: UNT Libraries

Markov sequential pattern recognition : dependency and the unknown class.

Description: The sequential probability ratio test (SPRT) minimizes the expected number of observations to a decision and can solve problems in sequential pattern recognition. Some problems have dependencies between the observations, and Markov chains can model dependencies where the state occupancy probability is geometric. For a non-geometric process we show how to use the effective amount of independent information to modify the decision process, so that we can account for the remaining dependencies. Along with dependencies between observations, a successful system needs to handle the unknown class in unconstrained environments. For example, in an acoustic pattern recognition problem any sound source not belonging to the target set is in the unknown class. We show how to incorporate goodness of fit (GOF) classifiers into the Markov SPRT, and determine the worse case nontarget model. We also develop a multiclass Markov SPRT using the GOF concept.
Date: October 1, 2004
Creator: Malone, Kevin Thomas; Haschke, Greg Benjamin & Koch, Mark William
Partner: UNT Libraries Government Documents Department

Markov models and the ensemble Kalman filter for estimation of sorption rates.

Description: Non-equilibrium sorption of contaminants in ground water systems is examined from the perspective of sorption rate estimation. A previously developed Markov transition probability model for solute transport is used in conjunction with a new conditional probability-based model of the sorption and desorption rates based on breakthrough curve data. Two models for prediction of spatially varying sorption and desorption rates along a one-dimensional streamline are developed. These models are a Markov model that utilizes conditional probabilities to determine the rates and an ensemble Kalman filter (EnKF) applied to the conditional probability method. Both approaches rely on a previously developed Markov-model of mass transfer, and both models assimilate the observed concentration data into the rate estimation at each observation time. Initial values of the rates are perturbed from the true values to form ensembles of rates and the ability of both estimation approaches to recover the true rates is examined over three different sets of perturbations. The models accurately estimate the rates when the mean of the perturbations are zero, the unbiased case. For the cases containing some bias, addition of the ensemble Kalman filter is shown to improve accuracy of the rate estimation by as much as an order of magnitude.
Date: September 1, 2007
Creator: Vugrin, Eric D.; McKenna, Sean Andrew (Sandia National Laboratories, Albuquerque, NM) & Vugrin, Kay White
Partner: UNT Libraries Government Documents Department