The presence of dispersive fading and inter-carrier interference (ICI) constitute the major impediment to reliable communications in orthogonal frequency-division multiplexing (OFDM) systems. Recently iterative (``Turbo'') processing techniques, which have been successfully applied to many detection/decoding problems, have received considerable attention. In this thesis, we first aim on the design of iterative receiver for single antenna OFDM system with frequency offset and dispersive fading. Further work is then extended to space-time block coded (STBC) OFDM system. At last, the technique is applied to STBC-OFDM system through a newly built channel model, which is based on a physical description of the propagation environment. The performance of such systems are verified by computer simulations. The simulation results show that the iterative techniques work well in OFDM systems.

The transition fundions for the correlated random walk with two absorbing boundaries are derived by means of a combinatorial construction which is based on Krattenthaler's Theorem for counting lattice paths with turns. Results for walks with one boundary and for unrestricted walks are presented as special cases. Finally we give an asymptotic formula, which proves to be useful for computational purposes. (author's abstract) / Series: Forschungsberichte / Institut für Statistik

The research described in this dissertation concerns two fields of theoretical chemistry: Part I concerns applications of Density Functional Theory, and part II high accuracy calculations within the Born-Oppenheimer approximation using explicitly correlated Gaussian functions.In the first part, after a brief introduction to Density Functional Theory and Hartree Fock methods, the candidate's research in Density Functional Theory is described in two chapters. One treats the charge transport in B-DNA, specifically (GC)$_N$ oligomers solvated by water. The second chapter treats the charge transfer between the Lithium atom and Fullerene-C$_{60}$ in the endohedral complex Li@C$_{60}$. In both applications Density Functional Theory was the central quantum mechanical technique that allowed the approaching of such large molecular systems.In the second part of this dissertation, the candidate's development of a FORTRAN code using explicitly correlated Gaussian functions within the Born-Oppenheimer approximation is presented.Every item of the author's research during his graduate studies has been published in co-authorship with the author's scientific advisor and other collaborators in peer-reviewed journals. A total of 8 scientific articles and one letter have been published by the author while at The University of Arizona.

The presence of dispersive fading and inter-carrier interference (ICI) constitute the major impediment to reliable communications in orthogonal frequency-division multiplexing (OFDM) systems. Recently iterative (``Turbo'') processing techniques, which have been successfully applied to many detection/decoding problems, have received considerable attention. In this thesis, we first aim on the design of iterative receiver for single antenna OFDM system with frequency offset and dispersive fading. Further work is then extended to space-time block coded (STBC) OFDM system. At last, the technique is applied to STBC-OFDM system through a newly built channel model, which is based on a physical description of the propagation environment. The performance of such systems are verified by computer simulations. The simulation results show that the iterative techniques work well in OFDM systems.

In this paper we consider optimum design of experiments for correlated observations. We approximate the error component of the process by an eigenvector expansion of the corresponding covariance function. Furthermore we study the limit behavior of an additional white noise as a regularization tool. The approach is illustrated by some typical examples. (authors' abstract) / Series: Research Report Series / Department of Statistics and Mathematics

This thesis extends Kim and Nelson's (1999) plucking model for real GDP to include correlated innovations. The resulting correlated innovations unobserved components (UC) model allows for both asymmetric transitory movements and correlation between the permanent and transitory innovations. Applying the extended model to U.S., Canadian and Australian GDP, I show that the GDP series can be usefully decomposed into a permanent component, a symmetric transitory component, and an additional occasional asymmetric transitory shock. Incorporating correlated innovations in the model changes the allocation of volatility between the permanent and transitory components. For the U.S., correlated innovations were found to be significant and the permanent component accounted for a larger share of the volatility in GDP. For Canada and Australia, correlated innovations were not significant and the fitted model produced smooth permanent component and volatile transitory component estimates. / Graduate

Sickle cell disease is a monogenic blood disorder in which the clinical course and disease severity vary widely among patients. In order for physicians to make more informed decisions regarding the treatment and management of disease, it would be useful to be able to predict disease severity. We focus on two primary modulators of disease severity in sickle cell patients, hemolysis and fetal hemoglobin (HbF). This dissertation evaluates methodology to identify genetic variants associated with severity of sickle cell disease and develops new methodology of genetic risk prediction to predict disease severity in sickle cell patients based on levels of HbF. Hemolysis is a trait that is influenced by multiple correlated phenotypes (lactate dehydrogenase, reticulocytes, bilirubin and aspartate transaminase). There are several approaches to statistical analyses of multiple correlated phenotypes. The first part of this dissertation evaluates the use of principal component analysis (PCA) and compares it to the alternative approach of examining the results of multiple univariate phenotypes individually. We will focus on the question of if and under what conditions we gain more power using a summarized phenotype from PCA in a genome wide association study (GWAS) rather than conducting multiple individual GWAS. We find that the there is more power gained from the PCA approach when there is a strong intercorrelation between the phenotypes. The second part of this dissertation proposes a novel method of genetic risk prediction for continuous traits using an ensemble of genetic models. We aim to show through a simulation and prediction of HbF that the proposed method is more robust to the inclusion of false positives and yields more stable predictions than computing a GRS and 10 fold cross validation. The third part of this dissertation introduces a Bayesian-based clustering approach to produce clusters of sickle cell anemia patients based on their "predicted genetic profiles" of HbF. We then examine the genetic profiles of individuals in the extreme clusters to determine which genes contribute more prominently to the genetic profile so that we may potentially identify genes that are highly influential in the regulation of extremely high and low values of HbF.

In this dissertation, we examine quantum ferromagnets and determine various effects of the magnetic Goldstone modes or "magnons'' in these systems. Firstly, we calculate the magnon contribution to the transport relaxation rate of conduction electrons in metallic ferromagnets and find that at asymptotically low temperatures, the contribution behaves as T^2 exp(-T_0/T) and not as T^2 predicted previously. To perform these calculations, we derive and use a very general effective theory for metallic ferromagnets. This activation barrier-like behavior is due to the fact that spin waves only couple electrons from different Stoner subbands that arise from the splitting of the conduction band in presence of a nonzero magnetization. The T^2 behavior is found to be valid only in a pre-asymptotic temperature window. The temperature scale T_0 is the energy of the least energetic ferromagnon that couples electrons of different spins. Second, we discuss magnon-induced long-range correlation functions in quantum magnets. In the ordered phases of both classical ferromagnets and antiferromagnets, the long-range correlations induced by the magnons lead to a singular wavenumber dependence of the longitudinal order-parameter susceptibility in spatial dimensions 2<d<4. We investigate the quantum analog of this singularity using a nonlinear sigma model. In a quantum antiferromagnet at $T=0$, a weaker nonanalytic behavior is obtained, which is consistent with power counting. The analogous result for a quantum ferromagnet is absent if the magnon damping is neglected. This is due to the lack of magnon number fluctuations in the quantum ferromagnetic ground state. Magnon damping due to quenched disorder restores the expected nonanalyticity. Finally, we use an effective field theory for clean, strongly interacting electron systems to calculate the magnon contribution to the density of states, the longitudinal magnetic susceptibility and the conductivity in an itinerant ferromagnet. Utilizing a loop expansion that does not assume the electron-electron interaction to be a small parameter, we obtain the leading nonanalytic corrections to the Stoner saddle-point results for these observables, as functions of the frequency and wavenumber in the hydrodynamic limit. The dissertation includes previously published and unpublished co-authored material.

The study of gene families critically depends on the correct reconstruction of gene genealogies, as for instance in the case of transcription factor genes like Hox genes and Dlx gene families. Proteins belonging to the same family are likely to share some of the same protein interaction partners and may thus face a similar selective environment. This common selective environment can induce co-evolutionary pressures and thus can give rise to correlated rates and patterns of evolution among members of a gene family. In this study, we simulate the evolution of a family of sequences which share a set of interaction partners. Depending on the amount of sequence dedicated to protein–protein interaction and the relative rate parameters of sequence evolution three outcomes are possible: if the fraction of the sequence dedicated to interaction with common co-factors is low and the time since divergence is small, the trees based on sequence information tend to be correct. If the time since gene duplication is long two possible outcomes are observed in our simulations. If the rate of evolution of the interaction partner is small compared to the rate of evolution of the focal protein family, the reconstructed trees tend towards star phylogenies. As the rate of evolution of the interaction partner approaches that of the focal protein family the reconstructed phylogenies tend to be incorrectly resolved. We conclude that the genealogies of gene families can be hard to estimate, in particular if the proteins interact with a conserved set of binding partners, as is likely the case for transcription factors.

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