Sparse Signal Representation in Digital and Biological Systems

Theories of sparse signal representation, wherein a signal is decomposed as the sum of a small number of constituent elements, play increasing roles in both mathematical signal processing and neuroscience. This happens despite the differences between signal models in the two domains. After reviewing preliminary material on sparse signal models, I use work on compressed sensing for the electron tomography of biological structures as a target for exploring the efficacy of sparse signal reconstruction in a challenging application domain. My research in this area addresses a topic of keen interest to the biological microscopy community, and has resulted in the development of tomographic reconstruction software which is competitive with the state of the art in its field. Moving from the linear signal domain into the nonlinear dynamics of neural encoding, I explain the sparse coding hypothesis in neuroscience and its relationship with olfaction in locusts. I implement a numerical ODE model of the activity of neural populations responsible for sparse odor coding in locusts as part of a project involving offset spiking in the Kenyon cells. I also explain the validation procedures we have devised to help assess the model's similarity to the biology. The thesis concludes with the development of a new, simplified model of locust olfactory network activity, which seeks with some success to explain statistical properties of the sparse coding processes carried out in the network.

An Assessment of Professional Development for Astronomy and Physics Faculty: Expanding Our Vision of How to Support Faculty's Learning About Teaching

In this thesis, we will explore approaches to faculty instructional change in astronomy and physics. We primarily focus on professional development (PD) workshops, which are a central mechanism used within our community to help faculty improve their teaching. Although workshops serve a critical role for promoting more equitable instruction, we rarely assess them through careful consideration of how they engage faculty. To encourage a shift towards more reflective, research-informed PD, we developed the Real-Time Professional Development Observation Tool (R-PDOT), to document the form and focus of faculty's engagement during workshops. We then analyze video-recordings of faculty's interactions during the Physics and Astronomy New Faculty Workshop, focusing on instances where faculty might engage in pedagogical sense-making. Finally, we consider insights gained from our own local, team-based effort to improve a course sequence for astronomy majors. We conclude with recommendations for PD leaders and researchers.