Local gamma-band (~30-100Hz) oscillations in the brain, produced by feedback inhibition on a characteristic timescale, appear in multiple areas of the brain and are associated with a wide range of cognitive functions. Some regions producing gamma also receive gamma-rhythmic input, and the interaction and coordination of these rhythms has been hypothesized to serve various functional roles. This thesis consists of three stand-alone chapters, each of which considers the response of a gamma-rhythmic neuronal circuit to input in an analytical framework. In the first, we demonstrate that several related models of a gamma-generating circuit under periodic forcing are asymptotically drawn onto an attracting invariant torus due to the convergence of inhibition trajectories at spikes and the convergence of voltage trajectories during sustained inhibition, and therefore display a restricted range of dynamics. In the second, we show that a model of a gamma-generating circuit under forcing by square pulses cannot maintain multiple stably phase-locked solutions. In the third, we show that a separation of time scales of membrane potential dynamics and synaptic decay causes the gamma model to phase align its spiking such that periodic forcing pulses arrive under minimal inhibition. When two of these models are mutually coupled, the same effect causes excitatory pulses from the faster oscillator to arrive at the slower under minimal inhibition, while pulses from the slower to the faster arrive under maximal inhibition. We also show that such a time scale separation allows the model to respond sensitively to input pulse coherence to an extent that is not possible for a simple one-dimensional oscillator. We draw on a wide range of mathematical tools and structures including return maps, saltation matrices, contraction methods, phase response formalism, and singular perturbation theory in order to show that the neuronal mechanism of gamma oscillations is uniquely suited to reliably phase lock across brain regions and facilitate the selective transmission of information.

<pre><p>Difficulty understanding speech in background noise is the most common hearing complaint. Elucidating the neurophysiological mechanisms underlying speech intelligibility in everyday environments with multiple sound sources and distortions is hence important for any technology that aims to improve real-world listening. Using a combination of behavioral, electroencephalography (EEG), and computational modeling experiments, this dissertation provides insight into how the brain analyzes such complex scenes, and what roles different acoustic cues play in facilitating this process and in conveying phonetic content. Experiment #1 showed that brain oscillations selectively track the temporal envelopes (i.e., modulations) of attended speech in a mixture of competing talkers, and that the strength and pattern of this attention effect differs between individuals. Experiment #2 showed that the fidelity of neural tracking of attended-speech envelopes is strongly shaped by the modulations in interfering sounds as well as the temporal fine structure (TFS) conveyed by the cochlea, and predicts speech intelligibility in diverse listening environments. Results from Experiments #1 and #2 support the theory that temporal coherence of sound elements across envelopes and/or TFS shapes scene analysis and speech intelligibility. Experiment #3 tested this theory further by measuring and computationally modeling consonant categorization behavior in a range of background noises and distortions. We found that a physiologically plausible model that incorporated temporal-coherence effects predicted consonant confusions better than conventional speech-intelligibility models, providing independent evidence that temporal coherence influences scene analysis. Finally, results from Experiment #3 also showed that TFS is used to extract speech content (voicing) for consonant categorization even when intact envelope cues are available. Together, the novel insights provided by our results can guide future models of speech intelligibility and scene analysis, clinical diagnostics, improved assistive listening devices, and other audio technologies.</p></pre>