Non-Perturbative Methods in Quantum Field Theory and Quantum Gravity

This thesis considers non-perturbative methods in quantum field theory with applications to gravity and cosmology. In particular, there are chapters on black hole holography, inflationary model building, and the conformal bootstrap.

TRANSFORMATIONS OF TASK-DEPENDENT PLASTICITY FROM A1 TO HIGHER-ORDER AUDITORY CORTEX

Everyday, humans and animals navigate complex acoustic environments, where multiple sound sources overlap. Somehow, they effortlessly perform an acoustic scene analysis and extract relevant signals from background noise. Constant updating of the behavioral relevance of ambient sounds requires the representation and integration of incoming acoustical information with internal representations such as behavioral goals, expectations and memories of previous sound-meaning associations. Rapid plasticity of auditory representations may contribute to our ability to attend and focus on relevant sounds. In order to better understand how auditory representations are transformed in the brain to incorporate behavioral contextual information, we explored task-dependent plasticity in neural responses recorded at four levels of the auditory cortical processing hierarchy of ferrets: the primary auditory cortex (A1), two higher-order auditory areas (dorsal PEG and ventral-anterior PEG) and dorso-lateral frontal cortex. In one study we explored the laminar profile of rapid-task related plasticity in A1 and found that plasticity occurred at all depths, but was greatest in supragranular layers. This result suggests that rapid task-related plasticity in A1 derives primarily from intracortical modulation of neural selectivity. In two other studies we explored task-dependent plasticity in two higher-order areas of the ferret auditory cortex that may correspond to belt (secondary) and parabelt (tertiary) auditory areas. We found that representations of behaviorally-relevant sounds are progressively enhanced during performance of auditory tasks. These selective enhancement effects became progressively larger as you ascend the auditory cortical hierarchy. We also observed neuronal responses to non-auditory, task-related information (reward timing, expectations) in the parabelt area that were very similar to responses previously described in frontal cortex. These results suggests that auditory representations in the brain are transformed from the more veridical spectrotemporal information encoded in earlier auditory stages to a more abstract representation encoding sound behavioral meaning in higher-order auditory areas and dorso-lateral frontal cortex.

An Acoustic Analysis of Valveless Pulsejet Engines

Valveless pulsejets are extremely simple aircraft engines; essentially cleverly designed tubes with no moving parts. These engines utilize pressure waves, instead of machinery, for thrust generation, and have demonstrated thrust-to-weight ratios over 8 and thrust specific fuel consumption levels below 1 lbm/lbf-hr – performance levels that can rival many gas turbines. Despite their simplicity and competitive performance, they have not seen widespread application due to extremely high noise and vibration levels, which have persisted as an unresolved challenge primarily due to a lack of fundamental insight into the operation of these engines. This thesis develops two theories for pulsejet operation (both based on electro-acoustic analogies) that predict measurements better than any previous theory reported in the literature, and then uses them to devise and experimentally validate effective noise reduction strategies. The first theory analyzes valveless pulsejets as acoustic ducts with axially varying area and temperature. An electro-acoustic analogy is used to calculate longitudinal mode frequencies and shapes for prescribed area and temperature distributions inside an engine. Predicted operating frequencies match experimental values to within 6% with the use of appropriate end corrections. Mode shapes are predicted and used to develop strategies for suppressing higher modes that are responsible for much of the perceived noise. These strategies are verified experimentally and via comparison to existing models/data for valveless pulsejets in the literature. The second theory analyzes valveless pulsejets as acoustic systems/circuits in which each engine component is represented by an acoustic impedance. These are assembled to form an equivalent circuit for the engine that is solved to find the frequency response. The theory is used to predict the behavior of two interacting pulsejet engines. It is validated via comparison to experiment and data in the literature. The technique is then used to develop and experimentally verify a method for operating two engines in anti-phase without interfering with thrust production. Finally, Helmholtz resonators are used to suppress higher order modes that inhibit noise suppression via anti-phasing. Experiments show that the acoustic output of two resonator-equipped pulsejets operating in anti-phase is 9 dBA less than the acoustic output of a single pulsejet.

SEEKING CULTURAL FAIRNESS IN A MEASURE OF RELATIONAL REASONING

Relational reasoning, or the ability to identify meaningful patterns within any stream of information, is a fundamental cognitive ability associated with academic success across a variety of domains of learning and levels of schooling. However, the measurement of this construct has been historically problematic. For example, while the construct is typically described as multidimensional—including the identification of multiple types of higher-order patterns—it is most often measured in terms of a single type of pattern: analogy. For that reason, the Test of Relational Reasoning (TORR) was conceived and developed to include three other types of patterns that appear to be meaningful in the educational context: anomaly, antinomy, and antithesis. Moreover, as a way to focus on fluid relational reasoning ability, the TORR was developed to include, except for the directions, entirely visuo-spatial stimuli, which were designed to be as novel as possible for the participant. By focusing on fluid intellectual processing, the TORR was also developed to be fairly administered to undergraduate students—regardless of the particular gender, language, and ethnic groups they belong to. However, although some psychometric investigations of the TORR have been conducted, its actual fairness across those demographic groups has yet to be empirically demonstrated. Therefore, a systematic investigation of differential-item-functioning (DIF) across demographic groups on TORR items was conducted. A large (N = 1,379) sample, representative of the University of Maryland on key demographic variables, was collected, and the resulting data was analyzed using a multi-group, multidimensional item-response theory model comparison procedure. Using this procedure, no significant DIF was found on any of the TORR items across any of the demographic groups of interest. This null finding is interpreted as evidence of the cultural-fairness of the TORR, and potential test-development choices that may have contributed to that cultural-fairness are discussed. For example, the choice to make the TORR an untimed measure, to use novel stimuli, and to avoid stereotype threat in test administration, may have contributed to its cultural-fairness. Future steps for psychometric research on the TORR, and substantive research utilizing the TORR, are also presented and discussed.