Cooperating or Fighting with Control Noise in the Optimal Manipulation of Quantum Dynamics

This paper investigates the impact of control field noise on the optimal manipulation of quantum dynamics. Simulations are performed on several multilevel quantum systems with the goal of population transfer in the presence of significant control noise. The noise enters as run-to-run variations in the control amplitude and phase with the observation being an ensemble average over many runs as is commonly done in the laboratory. A genetic algorithm with an improved elitism operator is used to find the optimal field that either fights against or cooperates with control field noise. When seeking a high control yield it is possible to find fields that successfully fight with the noise while attaining good quality stable results. When seeking modest control yields, fields can be found which are optimally shaped to cooperate with the noise and thereby drive the dynamics more efficiently. In general, noise reduces the coherence of the dynamics, but the results indicate that population transfer objectives can be met by appropriately either fighting or cooperating with noise, even when it is intense.Comment: Scientific Workplace Late

Design and Association Methods for Next-generation Sequencing Studies for Quantitative Traits.

Advances in exome sequencing and the development of exome genotyping arrays are enabling explorations of association between rare coding variants and complex traits using sequencing-based GWAS. However, the cost of sequencing remains high, optimal study design for sequencing-based association studies is an open question, powerful association methods and software to detect trait-associated rare and low-frequency variants are in great need. Containing 5% of information in human genome, chromosome X analysis has been largely neglected in routine GWAS analysis. In this dissertation, I focus on three topics: First, I describe a computationally efficient approach to re-construct gene-level association test statistics from single-variant summary statistics and their covariance matrices for single studies and meta-analyses. By simulation and real data examples, I evaluate our methods under the null, investigate scenarios when family samples have larger power than population samples, compare power of different types of gene-level tests under various trait-generating models, and demonstrate the usage of our methods and the C++ software, RAREMETAL, by meta-analyzing SardiNIA and HUNT data on lipids levels. Second, I describe a variance component approach and a series of gene-level tests for X-linked rare variants analysis. By simulations, I demonstrate that our methods are well controlled under the null. I evaluate power to detect an autosomal or X-linked gene of same effect size, and investigate the effect of sex ratio in a sample to power of detecting an X-linked gene. Finally I demonstrate usage of our method and the C++ software by analyzing various quantitative traits measured in the SardiNIA study and report detected X-linked variants and genes. Third, I describe a novel likelihood-based approach and the C++ software, RAREFY, to prioritize samples that are more likely to be carriers of trait-associated variants in a sample, with limited budget. I first describe the statistical method for small pedigrees and then describe an MCMC approach to make our method computationally feasible for large pedigrees. By simulations and real data analysis, I compare our approach with other methods in both trait-associated allele discovery power and association power, and demonstrate the usage of our method on pedigrees from the SardiNIA study.PhDBiostatisticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/113521/1/sfengsph_1.pd

Early Afterglows of Gamma-Ray Bursts in a Stratified Medium with a Power-Law Density Distribution

A long-duration gamma-ray burst (GRB) has been widely thought to arise from the collapse of a massive star, and it has been suggested that its ambient medium is a homogenous interstellar medium (ISM) or a stellar wind. There are two shocks when an ultra-relativistic fireball that has been ejected during the prompt gamma-ray emission phase sweeps up the circumburst medium: a reverse shock that propagates into the fireball, and a forward shock that propagates into the ambient medium. In this paper, we investigate the temporal evolution of the dynamics and emission of these two shocks in an environment with a general density distribution of $n\propto R^{-k}$ (where $R$ is the radius) by considering thick-shell and thin-shell cases. A GRB afterglow with one smooth onset peak at early times is understood to result from such external shocks. Thus, we can determine the medium density distribution by fitting the onset peak appearing in the light curve of an early optical afterglow. We apply our model to 19 GRBs, and find that their $k$ values are in the range of 0.4 - 1.4, with a typical value of $k\sim1$, implying that this environment is neither a homogenous interstellar medium with $k=0$ nor a typical stellar wind with $k=2$. This shows that the progenitors of these GRBs might have undergone a new mass-loss evolution.Comment: 32 pages, 5 figures, 1 table, published in Ap