http://hdl.handle.net/1974/6158 Tue, 21 May 2013 07:20:15 GMT 2013-05-21T07:20:15Z http://hdl.handle.net/1974/7819 Title: Feed-Forward Rate Distortion Function and Markov Sources Authors: Asoodeh, Shahab Abstract: The problem of channel coding with feedback has been extensively studied over the last 50 years. Using an ideal feedback link, the encoder knows all previously received channel outputs. Recently the duality between channel coding and rate distortion has been established in [15] and [3], leading to the problem of source coding with feed-forward. In this project we first study the general formula for the feed-forward rate distortion function given by Venkataramanan et al. [8]. They studied the source coding problem when a feed-forward link is available for general sources and general distortion measures. They derived the feed-forward rate distortion function for an arbitrary source in terms of the directed information which was originally introduced by Massey [5]. It is shown that the general formula given for source coding with feed-forward is closely related to the general formula for channel coding with feedback given by Tatikonda [4]. We then study another formula for the feed-forward rate distortion function recently proposed by Naiss et al. which is tractable and computable [17]. They also calculated the exact rate distortion function for first order asymmetric Markov sources. An original contribution of this project is an alternative achievability proof for the feed-forward rate distortion function of first order asymmetric Markov sources. Tue, 19 Feb 2013 05:00:00 GMT http://hdl.handle.net/1974/7819 2013-02-19T05:00:00Z http://hdl.handle.net/1974/7582 Title: Statistical Analysis of Atrial Fibrillation Electrograms Authors: Haley, Charlotte Abstract: Atrial fibrillation (AF) is the single most prevalent sustained cardiac rhythm disorder, arising when the normal electrochemical action potential propagating through the atria is interrupted by randomly ring foci. Current therapies rely on the analysis of electrocardiograms taken inside the atria to determine the amount of atrial activation at any given site on the endocardium. Atrial activation is measured by the appearance of peaks in an endocardial signal, detections occurring close together correspond to sites of greater activation and may be closer to the foci in which the disturbance originates. It is the purpose of this study to use signal processing techniques to determine the occurrence times of the peaks in a digitized electrocardiogram (ECG) signal and to generate from this meaningful statistics about the atrial activation of the site where the ECG was taken. Currently, mean cycle length (CL) of a signal is the most widely used statistic for atrial activation. Frequency domain methods and spectrum analysis give basis to claims that AF is not completely chaotic and that its mechanism can be explained by the substrate through which the signals propagate. Frequency domain analysis is used liberally in this paper to support the development of an algorithm for deflection detection. Little is known presently about the mechanism of AF and algorithms such as the one proposed in this paper will provide more quantitative information about the disease process. Description: A project submitted to the department of mathematics and statistics to complete the degree requirements for the pattern II master of science. Completed and defended August 2009, submitted to Qspace 2012. Tue, 09 Oct 2012 04:00:00 GMT http://hdl.handle.net/1974/7582 2012-10-09T04:00:00Z http://hdl.handle.net/1974/7495 Title: Nonparametric Testing Methods for Treatment-Biomarker Interaction based on Local Partial-Likelihood Authors: Liu, Yicong Abstract: A fair amount of research has been done on the interactions between treatment and biomarkers hoping to avoid failure to recognize effective agents which benefit only a subset of patients in traditional clinical designs and analysis, such as (Bonetti, 2004), (Bonetti et al., 2009), and (Royston and Sauerbrei, 2004). Particularly, Fan et al. (Fan et al., 2006) assumed the treatment effect is an unknown function of a putative biomarker, and proposed techniques to give the local partial likelihood estimation (LPLE) of this treatment effect function using local linear techniques (Fan and Chen, 1999). However, no methods were developed for assessing whether the treatment effect is indeed a function of the biomarker (interaction exists) or just a constant (no interactions). Based on the idea of LPLE, a new nonparametric hypothesis testing methodology, which we call local partial likelihood bootstrap (LPLB) test, is proposed in this work to identify the differences in treatment effects among subgroups of patients with different values of biomarkers in a Phase III clinical trials study. A bootstrap technique is used to evaluate the significance of the test. Meanwhile, the proposed method can also be applied to identify the interactions between a putative biomarker and a collection of covariates (covariate vectors) that are discrete or continuous. Numerical studies show that the LPLB test can provide a substantial improvement in the power of the interaction detection compared with the commonly used method, especially for interactions of complex form. The LPLB test is also applied to a prostate cancer trial with the serum prostatic acid phosphatase (AP) biomarker. Tue, 25 Sep 2012 04:00:00 GMT http://hdl.handle.net/1974/7495 2012-09-25T04:00:00Z http://hdl.handle.net/1974/6923 Title: On Upper Bounding Discrete Entropy Authors: Alnakhli , Razan Abstract: Two upper bounds on the entropy of a discrete random variable are studied. The standard upper bound is derived based on the differential entropy bound for a Gaus- sian random variable. A tighter bound is proved using the transformation formula of the Jacobi theta function and Shannon's inequality. Numerical examples are provided to illustrate their tightness. Thu, 22 Dec 2011 05:00:00 GMT http://hdl.handle.net/1974/6923 2011-12-22T05:00:00Z