Berry-Esseen bounds for nonlinear statistics, and asymptotic relative efficiency between correlation statistics

Four papers, written in collaboration with the author’s graduate school advisor, are presented. In the first paper, uniform and non-uniform Berry-Esseen (BE) bounds on the convergence to normality of a general class of nonlinear statistics are provided; novel applications to specific statistics, including the non-central Student’s, Pearson’s, and the non-central Hotelling’s, are also stated. In the second paper, a BE bound on the rate of convergence of the F-statistic used in testing hypotheses from a general linear model is given. The third paper considers the asymptotic relative efficiency (ARE) between the Pearson, Spearman, and Kendall correlation statistics; conditions sufficient to ensure that the Spearman and Kendall statistics are equally (asymptotically) efficient are provided, and several models are considered which illustrate the use of such conditions. Lastly, the fourth paper proves that, in the bivariate normal model, the ARE between any of these correlation statistics possesses certain monotonicity properties; quadratic lower and upper bounds on the ARE are stated as direct applications of such monotonicity patterns.

Cloning and characterization of the genes involved in cambial growth in response to elevated [CO2]

Aspen (Populus tremuloides) trees growing under elevated [CO2] at a free-air CO2 enrichment (FACE) site have produced significantly more biomass compared to control trees. The molecular mechanisms underlying the observed increase in biomass productivity was investigated by producing transcriptomic profiles of the vascular cambium zone (VCZ) and leaves, followed by a comparative study to identify genes and pathways that showed significant changes following long-term exposure to elevated [CO2]. This study is mainly to verify if genetic modification of a few selected candidate genes including CAP1, CKX6, and ASML2 that are expressed in vascular cambium in response to elevated [CO2] can cause the changes in plant growth and development. To this end, these three genes were cloned into both sense and antisense constructs. Then antisense and sense transgenic lines of above-mentioned genes were developed. 15 events were generated for 5 constructs, which were confirmed with regular PCR and RT-PCR. Confirmed plants were planted in greenhouse for growth and phenotypic characterization. The expression of CAP1, CKX6 and ASML2 in antisense plants was measured by real-time RT-PCR, and the changes caused by gene interference in cambial growth were studies by analyzing the microscopic sections made from the antisense transgenic plants. It has been found that 1) CAP1 is mainly expressed in xylem and root. 2) RNAi suppression of CAP1 significantly affected height and diameter. 3) CAP1, ASML2 and CKX6 affected xylem and phloem cell proliferation and elongation. Due to the delay in regenerating sense transgenic plants, the characterization of sense transgenic plants is limited to growth only.

ANALYSIS OF POPULUS TREMULOIDES CLONAL VARIATION AND DELINEATION IN THE OTTAWA NATIONAL FOREST

The technique of delineating Populus tremuloides (Michx.) clonal colonies based on morphology and phenology has been utilized in many studies and forestry applications since the 1950s. Recently, the availability and robustness of molecular markers has challenged the validity of such approaches for accurate clonal identification. However, genetically sampling an entire stand is largely impractical or impossible. For that reason, it is often necessary to delineate putative genet boundaries for a more selective approach when genetically analyzing a clonal population. Here I re-evaluated the usefulness of phenotypic delineation by: (1) genetically identifying clonal colonies using nuclear microsatellite markers, (2) assessing phenotypic inter- and intraclonal agreement, and (3) determining the accuracy of visible characters to correctly assign ramets to their respective genets. The long-term soil productivity study plot 28 was chosen for analysis and is located in the Ottawa National Forest, MI (46° 37'60.0" N, 89° 12'42.7" W). In total, 32 genets were identified from 181 stems using seven microsatellite markers. The average genet size was 5.5 ramets and six of the largest were selected for phenotypic analyses. Phenotypic analyses included budbreak timing, DBH, bark thickness, bark color or brightness, leaf senescence, leaf serrations, and leaf length ratio. All phenotypic characters, except for DBH, were useful for the analysis of inter- and intraclonal variation and phenotypic delineation. Generally, phenotypic expression was related to genotype with multiple response permutation procedure (MRPP) intraclonal distance values ranging from 0.148 and 0.427 and an observed MRPP delta value=0.221 when the expected delta=0.5. The phenotypic traits, though, overlapped significantly among some clones. When stems were assigned into phenotypic groups, six phenotypic groups were identified with each group containing a dominant genotype or clonal colony. All phenotypic groups contained stems from at least two clonal colonies and no clonal colony was entirely contained within one phenotypic group. These results demonstrate that phenotype varies with genotype and stand clonality can be determined using phenotypic characters, but phenotypic delineation is less precise. I therefore recommend that some genetic identification follow any phenotypic delineation. The amount of genetic identification required for clonal confirmation is likely to vary based on stand and environmental conditions. Further analysis, however, is needed to test these findings in other forest stands and populations.

AN ASSESSMENT OF FLOW REGIME MAPS AND A NUMERICAL HEAT TRANSFER CORRELATION FOR THE STRATIFIED/ANNULAR REGIME OF SHEAR-DRIVEN INTERNAL CONDENSING FLOWS

Several modern-day cooling applications require the incorporation of mini/micro-channel shear-driven flow condensers. There are several design challenges that need to be overcome in order to meet those requirements. The difficulty in developing effective design tools for shear-driven flow condensers is exacerbated due to the lack of a bridge between the physics-based modelling of condensing flows and the current, popular approach based on semi-empirical heat transfer correlations. One of the primary contributors of this disconnect is a lack of understanding caused by the fact that typical heat transfer correlations eliminate the dependence of the heat transfer coefficient on the method of cooling employed on the condenser surface when it may very well not be the case. This is in direct contrast to direct physics-based modeling approaches where the thermal boundary conditions have a direct and huge impact on the heat transfer coefficient values. Typical heat transfer correlations instead introduce vapor quality as one of the variables on which the value of the heat transfer coefficient depends. This study shows how, under certain conditions, a heat transfer correlation from direct physics-based modeling can be equivalent to typical engineering heat transfer correlations without making the same apriori assumptions. Another huge factor that raises doubts on the validity of the heat-transfer correlations is the opacity associated with the application of flow regime maps for internal condensing flows. It is well known that flow regimes influence heat transfer rates strongly. However, several heat transfer correlations ignore flow regimes entirely and present a single heat transfer correlation for all flow regimes. This is believed to be inaccurate since one would expect significant differences in the heat transfer correlations for different flow regimes. Several other studies present a heat transfer correlation for a particular flow regime - however, they ignore the method by which extents of the flow regime is established. This thesis provides a definitive answer (in the context of stratified/annular flows) to: (i) whether a heat transfer correlation can always be independent of the thermal boundary condition and represented as a function of vapor quality, and (ii) whether a heat transfer correlation can be independently obtained for a flow regime without knowing the flow regime boundary (even if the flow regime boundary is represented through a separate and independent correlation). To obtain the results required to arrive at an answer to these questions, this study uses two numerical simulation tools - the approximate but highly efficient Quasi-1D simulation tool and the exact but more expensive 2D Steady Simulation tool. Using these tools and the approximate values of flow regime transitions, a deeper understanding of the current state of knowledge in flow regime maps and heat transfer correlations in shear-driven internal condensing flows is obtained. The ideas presented here can be extended for other flow regimes of shear-driven flows as well. Analogous correlations can also be obtained for internal condensers in the gravity-driven and mixed-driven configuration.