Date of Award

Fall 2005

Document Type

Dissertation - Restricted

Degree Name

Doctor of Philosophy (PhD)


Mathematics, Statistics and Computer Science

First Advisor

Tonellato, Peter

Second Advisor

Bansal, Naveen

Third Advisor

Clough, Anne


This thesis uses Markov chain decomposition techniques to extract informative traits from arterial pressure recordings of hypertensive rats and humans. The feedback mechanisms, such as baroreceptor and renin angiotensin system, acting on blood pressure are quantified by the Cheeger ratios of specific levels and patterns of blood pressure. Statistical properties of Cheeger ratios and related quantities are established in a central limit theorem. The results show the dependence of the error on the spectral gap, length of recordings and relative frequencies of the estimated sets. These quantities are shown to be statistically different between normal and hypertensive rats, and heritable for the human population. New lower and upper bounds for the convergence rate (spectral gap) of the chain are derived via decomposition techniques. Linkage analysis and multi-trait linkage are used to find QTL for the estimated Cheeger ratios. Principal components are used to reduce the number of tests and increase the linkage power. Conditions for maximizing the power are derived and applied for humans.



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