Let F/F^+ be a quadratic imaginary field extension of a totally real field F^+, and pi cong \tilde{\pi} otimes xi be a cuspidal automorphic representation of GL_n(AA_F) obtained from tilde{pi} by twisting a Hecke character xi. In the case of F^+ = QQ, Michael Harris defined arithmetic automorphic periods for certain tilde{pi} in his Crelle paper 1997, and showed that critical values of automorphic L-functions for pi can be interpreted in terms of these arithmetic automorphic periods. Lin Jie generalized his construction and results to the general totally real field F^+ in her thesis. On the other hand, for certain cuspidal representation Pi of GL_{2n}(F^+), which admits a Shalika model, Grobner and Raghuram related their critical values of L-functions to a non-zero complex number (called Shalika periods). We noticed that the automorphic induction AI(pi) of pi, considered by Harris and Lin, will automatically have a Shalika model, and by comparing common critical values of their identical L-functions, we relate the Shalika periods of AI(pi) with arithmetic automorphic periods of tilde{pi}. In the case F^+=QQ, this comparison will express each arithmetic automorphic period in terms of the corresponding Shalika periods.

Thesis (Ph.D.)--Baylor University, 2009. / Includes bibliographical references (p. 77-79).

Platform trials evaluating multiple treatment arms against a shared control are an efficient alternative to multiple two-arm trials. Motivated by a randomized clinical trial of the effectiveness of two neuroprotection devices during aortic valve surgery against a control, this dissertation addresses two open questions in the optimal design of these trials. First, to explore whether multiplicity adjustments are necessary in a platform design, simulation studies evaluating the operating characteristics of platform designs relative to independent two-arm trials were conducted. Under the global null hypothesis, relative to a set of two-arm trials, we found that platform trials have slightly lower familywise error; however, conditional error rates for an experimental treatment being declared effective given another was declared effective are above the nominal alpha-level. Adjusting for multiplicity reduces familywise error, but has little impact on conditional error. These studies show that multiplicity adjustments are unnecessary in platform trials of unrelated treatments. Second, to determine the optimal approach for comparing delayed entry arms to the shared control, five methods for incorporating historical controls into two-arm trials were applied to the analyses of simulated open platform trials and compared to pooling all controls. We found that when response rates are constant, pooling yields the lowest error and most precise, unbiased estimates. However, if drift occurs, pooling results in type I error inflation or deflation depending on the direction of drift, as well as biased estimates. Although superior to naive pooling, none of the alternatives explored guarantee error control or unbiased estimates in the presence of drift. Thus, only concurrent controls should be used as comparators in the primary analysis of confirmatory studies. Finally, these findings were applied to assess the design and analysis of the neuroprotection trial.