Dissertation Defense Announcements

We propose methods for functional predictor selection and the estimation of smooth functional coefficients simultaneously in a scalar-on-function regression problem under a high-dimensional multivariate functional data setting. In particular, we develop two methods for functional group-sparse regression under a generic Hilbert space of infinite dimension. We show the convergence of algorithms and the consistency of the estimation and the selection (oracle property) under infinite-dimensional Hilbert spaces. Simulation studies show the effectiveness of the methods in both the selection and the estimation of functional coefficients. The applications to functional magnetic resonance imaging (fMRI) reveal the human brain regions related to ADHD and IQ. In addition, we apply the proposed methods to an econometric data set to find the related functional covariates to GDP of a country. To extend the results, we propose numerical algorithms for more complex models, such as nonlinear (via RKHS), logistic, sparse function--on--function, and standardization of the results of the sparse scalar--on--function models before we list the applications of these extensions to the brain image data analysis.

Climate change has resulted in warming of coastal aquatic habitats around the world at almost every latitude, threatening ecosystems with a significant loss in biodiversity and occurring at a rate that may exceed species’ ability to adapt. Understanding how reef species survive in habitats that currently experience extreme temperatures will help identify the biological processes that will govern future responses to climate change. The Persian/Arabian Gulf experiences the warmest coral reef temperatures on the planet (summer maxima ~35-36°C but can exceed 37°C) and connects to the neighboring Gulf of Oman, which experiences more benign environmental conditions (summer maxima of ~30-32°C). Here, we leverage this unique environmental gradient as a natural laboratory to better understand how the keystone sea urchin Echinometra sp. EZ copes with thermal extremes. Species survival in extreme habitats is dependent on their ability to acclimate over the course of an organisms’ lifetime and adapt over the course of many generations. Two complementary mechanisms for coping with environmental change are shifts in the host-associated microbial community, which can happen on a timescale of hours to days, and classic Darwinian evolution in which selection results in different patterns of alleles between populations over many generations. Here, we identify temperature as a robust predictor of community-level microbial variation and highlight specific bacterial taxa that may be crucial for maintenance of host homeostasis during thermal extremes. Next, we show that while there is a high degree of genetic admixture between all sites and bidirectional gene flow between the two seas, there is also significant population differentiation. We describe nine candidate loci that are under putative selection, including one collagen gene. Finally, we sequence, assemble, and annotate a chromosome-level genome that will add substantial value to future functional genomic datasets. Together, the research composing my dissertation has identified the importance of novel microbiome and genomic variation in the adaptation of a dominant ecosystem engineer to the warmest marine environment on Earth. These integrative results provide a foothold for understanding shared and unique mechanisms for the adaptation of marine species to historic and ongoing climate change.

Background: Current popular conceptualizations of the psychological process Repetitive Thought (RT) appear of limited accuracy due to ample construct proliferation (e.g. equating RT with rumination or worry), tautological definitions, and the construct being studied primarily in mentally disordered populations. This paper sought to unite current disparate lines of research surrounding RT, in order to illuminate and clarify the nature of RT.

Methods: Two studies were completed: First, a systematic literature review was conducted in order to develop a more comprehensive and conceptually coherent model of RT. Second, the structural validity of the model produced by the first study was empirically tested using factor analytic and multiple regression techniques.

Results: Partially Exploratory Factor Analyses revealed a strong general Repetitive Thinking factor, as well as a three-factor model that was empirically most appropriate (Intrusive Repetitive Thought, Deliberate Processing, and Self-Conscious Repetitive Thought). Additional validation analyses confirmed these findings.

Conclusions: This study contributes to our understanding of the nature of Repetitive Thought. Importantly, the three RT factors can be conceptualized as independent dimensions that are all part of a larger RT trait. The empirical and applied implications of the conceptualization of RT, as well as development of a preliminary measure of RT, are discussed.

Stress wave propagation in granular materials subjected to dynamic loadings has attracted much attention for exploring new physical phenomena. One-dimensional (1D) granular systems, a type of artificially designed granular materials consisting of periodically aligned discrete particles, are demonstrated to produce unprecedented wave properties that are notably different from conventional engineering materials. By designing the critical characteristics of 1D granular systems, a remarkable tunability can be achieved, which yields various engineering applications. Therefore, it is of great significance to fundamentally investigate the stress wave propagation and tunability in 1D granular systems.
Firstly, the solitary wave propagation within 1D granular crystals based on composite cylinders is systematically investigated via experiments, numerical simulations, and theoretical analysis. Next, we investigate the properties of Nesterenko solitary wave supported by one-dimensional granular chains and achieve an equivalent wave transmission among various materials and dimensions. Furthermore, we develop efficient and controllable stress wave attenuation approaches by considering I. Strain-softening behaviors; II. Kirigami-based structures. Finally, we design a 1D cylindrical granular system and comprehensively investigate solitary wave tuning strategies based on the system through mass, modulus, and thickness mismatch. Results unlock the unique solitary wave tuning mechanism and provide design guidance for next-generation signal measurement and monitoring systems.