A theory of hypoellipticity and unique ergodicity for semilinear stochastic PDEs

We present a theory of hypoellipticity and unique ergodicity for semilinear parabolic stochastic PDEs with "polynomial" nonlinearities and additive noise, considered as abstract evolution equations in some Hilbert space. It is shown that if Hörmander's bracket condition holds at every point of this Hilbert space, then a lower bound on the Malliavin covariance operatorμt can be obtained. Informally, this bound can be read as "Fix any finite-dimensional projection on a subspace of sufficiently regular functions. Then the eigenfunctions of μt with small eigenvalues have only a very small component in the image of Π." We also show how to use a priori bounds on the solutions to the equation to obtain good control on the dependency of the bounds on the Malliavin matrix on the initial condition. These bounds are sufficient in many cases to obtain the asymptotic strong Feller property introduced in [HM06]. One of the main novel technical tools is an almost sure bound from below on the size of "Wiener polynomials," where the coefficients are possibly non-adapted stochastic processes satisfying a Lips chitz condition. By exploiting the polynomial structure of the equations, this result can be used to replace Norris' lemma, which is unavailable in the present context. We conclude by showing that the two-dimensional stochastic Navier-Stokes equations and a large class of reaction-diffusion equations fit the framework of our theory.

Furnishing a Globalized World: Local Distinctiveness in the International Furniture Industry

Advances in technology, communication, and transportation over the past thirty years have led to tighter linkages and enhanced collaboration across traditional borders between nations, institutions, and cultures. This thesis uses the furniture industry as a lens to examine the impacts of globalization on individual countries and companies as they interact on an international scale. Using global value chain analysis and international trade data, I break down the furniture production process and explore how countries have specialized in particular stages of production to differentiate themselves from competitors and maximize the benefits of global involvement. Through interviews with company representatives and evaluation of branding strategies such as advertisements, webpages, and partnerships, I investigate across four country cases how furniture companies construct strong brands in an effort to stand out as unique to consumers with access to products made around the globe. Branding often serves to highlight distinctiveness and associate companies with national identities, thus revealing that in today’s globalized and interconnected society, local differences and diversity are more significant than ever.

Three-dimensional dispersive metallic photonic crystals with a bandgap and a high cutoff frequency.

The goal of this work is to analyze three-dimensional dispersive metallic photonic crystals (PCs) and to find a structure that can provide a bandgap and a high cutoff frequency. The determination of the band structure of a PC with dispersive materials is an expensive nonlinear eigenvalue problem; in this work we propose a rational-polynomial method to convert such a nonlinear eigenvalue problem into a linear eigenvalue problem. The spectral element method is extended to rapidly calculate the band structure of three-dimensional PCs consisting of realistic dispersive materials modeled by Drude and Drude-Lorentz models. Exponential convergence is observed in the numerical experiments. Numerical results show that, at the low frequency limit, metallic materials are similar to a perfect electric conductor, where the simulation results tend to be the same as perfect electric conductor PCs. Band structures of the scaffold structure and semi-woodpile structure metallic PCs are investigated. It is found that band structures of semi-woodpile PCs have a very high cutoff frequency as well as a bandgap between the lowest two bands and the higher bands.

Sensory information and associative cues used in food detection by wild vervet monkeys.

Understanding animals' spatial perception is a critical step toward discerning their cognitive processes. The spatial sense is multimodal and based on both the external world and mental representations of that world. Navigation in each species depends upon its evolutionary history, physiology, and ecological niche. We carried out foraging experiments on wild vervet monkeys (Chlorocebus pygerythrus) at Lake Nabugabo, Uganda, to determine the types of cues used to detect food and whether associative cues could be used to find hidden food. Our first and second set of experiments differentiated between vervets' use of global spatial cues (including the arrangement of feeding platforms within the surrounding vegetation) and/or local layout cues (the position of platforms relative to one another), relative to the use of goal-object cues on each platform. Our third experiment provided an associative cue to the presence of food with global spatial, local layout, and goal-object cues disguised. Vervets located food above chance levels when goal-object cues and associative cues were present, and visual signals were the predominant goal-object cues that they attended to. With similar sample sizes and methods as previous studies on New World monkeys, vervets were not able to locate food using only global spatial cues and local layout cues, unlike all five species of platyrrhines thus far tested. Relative to these platyrrhines, the spatial location of food may need to stay the same for a longer time period before vervets encode this information, and goal-object cues may be more salient for them in small-scale space.

They’re There, Now What?: The Identities, Behaviors, and Perceptions of Black Judges

Prior to the Civil Rights Movement, fewer than 50 Black judges had been elected or appointed to the judiciary. As of August 2015, there are over 1,000 Black state and federal judges. As the number of black judges has increased, one question arises: have American courts been altered purely by this substantial increase? One expectation—and, at times, a prediction—behind the increased descriptive representation of Black judges is that their mere presence would alter the judiciary. It was supposed that these judges would substantively represent Black interests in the decisions they made. In other words, it was suspected, and predicted, that Blacks in the judiciary would enhance equality and justice by being aware of, responsive to, and advocating for African Americans. This theory about the likely role of Black judges derives from theoretical work on political representation and racial group consciousness, and empirical studies of Black elite behavior in other political institutions.

Despite such predictions, there is no corresponding scholarly consensus regarding whether Black judges possess a racial group consciousness and have racially distinctive judicial behavior. Therefore, the theory undergirding the demand for increased diversification, as a means to transform the judiciary, remains unsubstantiated. This is precisely where this project, “They’re There, Now What?: The Identities, Behavior, and Perceptions of Black Judges,” seeks to intervene in and explore, if not settle, the matter of whether black judges possess a racial group consciousness and exhibit racially-distinctive judicial behavior. It addresses a set of interrelated questions relevant to understanding whether we can view Black judges as representatives in ways that are similar to how we view other Black political officials. I examine these questions using a multi-method approach. For my analyses, I draw on diverse materials: the published biographies of every Black judge appointed to the federal bench, a survey experiment with a nationally-representative adult sample, and semi-structured interviews with 30 Black judges.

This research, which engages with scholarship on representation, group consciousness, judicial behavior, and candidate perceptions, offers new insights into the lives, perceptions, and behavior of Black judges, as well as the manifestations of Black substantive representation in the judiciary. My dissertation argues that, despite the general reluctance to use the term “representation” when referring to judges, we can consider Black judges as representatives. Black judges behave as substantive representatives by (1) sharing and understanding the experience, history, and perspectives of Black Americans, (2) challenging language, persons, policies, and laws they feel negatively affect, or violate the rights and liberties of, African Americans, (3) respecting African American litigants, and (4) ensuring the rights of African Americans are protected and the needs of black Americans are being met.

Only through research that considers the perspectives, identities, perceptions, and behavior of Black judges will we arrive at a more comprehensive understanding of the importance of racial diversity in the courts. As this project finds, a link between descriptive representation and substantive representation can, and frequently does exist within the judicial context. Such a link is significant given that Blacks’ liberty and justice through the American legal system continues to be subject to those who exercise judicial power. This dissertation has implications for the discourse surrounding the need for increased descriptive and substantive representation of Blacks in the judiciary, and the factors that affect representation in the justice system.

Contributions Of the Human Medial Prefrontal Cortex To Associative Recognition Memory: Evidence From Functional Neuroimaging

Neuroimaging studies of episodic memory, or memory of events from our personal past, have predominantly focused their attention on medial temporal lobe (MTL). There is growing acknowledgement however, from the cognitive neuroscience of memory literature, that regions outside the MTL can support episodic memory processes. The medial prefrontal cortex is one such region garnering increasing interest from researchers. Using behavioral and functional magnetic resonance imaging measures, over two studies, this thesis provides evidence of a mnemonic role of the medial PFC. In the first study, participants were scanned while judging the extent to which they agreed or disagreed with the sociopolitical views of unfamiliar individuals. Behavioral tests of associative recognition revealed that participants remembered with high confidence viewpoints previously linked with judgments of strong agreement/disagreement. Neurally, the medial PFC mediated the interaction between high-confidence associative recognition memory and beliefs associated with strong agree/disagree judgments. In an effort to generalize this finding to well-established associative information, in the second study, we investigated associative recognition memory for real-world concepts. Object-scene pairs congruent or incongruent with a preexisting schema were presented to participants in a cued-recall paradigm. Behavioral tests of conceptual and perceptual recognition revealed memory enhancements arising from strong resonance between presented pairs and preexisting schemas. Neurally, the medial PFC tracked increases in visual recall of schema-congruent pairs whereas the MTL tracked increases in visual recall of schema-incongruent pairs. Additionally, ventral areas of the medial PFC tracked conceptual components of visual recall specifically for schema-congruent pairs. These findings are consistent with a recent theoretical proposal of medial PFC contributions to memory for schema-related content. Collectively, these studies provide evidence of a role for the medial PFC in associative recognition memory persisting for associative information deployed in our daily social interactions and for those associations formed over multiple learning episodes. Additionally, this set of findings advance our understanding of the cognitive contributions of the medial PFC beyond its canonical role in processes underlying social cognition.

The Perspectives of Gay, Bisexual, and Queer Adolescent Males with Parent-Child Sex Communication

Problem: Gay, bisexual, and queer (GBQ) adolescent males are disproportionately affected by negative sexual health outcomes compared to their heterosexual counterparts. Their sex education needs are not sufficiently addressed in the home and the larger ecological systems. The omission of their sex education needs at a time when they are forming a sexual identity during adolescence compels GBQ males to seek information in unsupervised settings. Evidence-based interventions aimed at ensuring positive sexual health outcomes through sex communication cannot be carried out with these youth as research on how parents and GBQ males discuss sex in the home has been largely uninvestigated.

Methods: This naturalistic qualitative study focused on the interpretive reports of 15- to 20-year-old GBQ males’ discussions about sex-related topics with their parents. From a purposive sample of 30 male adolescents who self-identified as GBQ, participants who could recall at least one conversation about sex with their parents were recruited for one-time interviews and card sorts. This strategy revealed, using Bronfenbrenners’ Bioecological Theory, their perceptions about sex communication in the context of their reciprocal relationship and the ecological systems that GBQ males and their parents navigate.

Results: Parents received poor ratings as sex educators, were generally viewed as not confident in their communication approach, and lacked knowledge about issues pertinent to GBQ sons. Nevertheless, participants viewed parents as their preferred source of sex information and recognized multiple functions of sex communication. The value placed by GBQ youth on sex communication underscores their desire to ensure an uninterrupted parent-child relationship in spite of their GBQ sexual orientation. For GBQ children, inclusive sex communication is a proxy for parental acceptance.

Results show that the timing, prompts, teaching aids, and setting of sex communication for this population are similar to what has been reported with heterosexual samples. However, most GBQ sons rarely had inclusive guidance about sex and sexuality that matched their attraction, behavior, and identities. Furthermore, the assumption of heterosexuality resulted in the early awareness of being different from their peers which led them to covertly search for sex information. The combination of assumed heterosexuality and their early reliance on themselves for applicable information is a missed parental opportunity to positively impact the health of GBQ sons. More importantly, due to the powerful reach of new media, there is a critical period of maximum receptiveness that has been identified which makes inclusive sex communication paramount in the pre-sexual stage for this population. Our findings also indicate that there are plenty of opportunities for systemic improvements to meet this population’s sexual education needs.