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.

"Natural Enemies" or Intentional Allies? Teachers' & Parents' Perspectives on Middle School Boys of Color

This study examined the perspectives and “shared knowledge” of parents and teachers of boys of color. The following overarching research question guided this study: “What do parents and teachers want each other to know about their middle school son or student of color regarding academics, engagement, and behavior?” Additionally, it explored the challenges and opportunities for shared knowledge and understanding of their (respective) son’s’ or students’ academics and engagement. The methodology was qualitative in nature and the intent in conducting this case study was to describe, interpret, and explain the “shared knowledge” between these stakeholders at a predominantly minority middle school. A sample of seven parents and seven teachers from one school in a mid-Atlantic state participated in interviews and focus groups. Results indicated that parents and teachers of boys of color viewed each other as “intentional allies.” Results further showed that parents and teachers were aware of the challenges faced by boys of color in and out of school. That awareness was reflected in strategies that both groups employed to support, prepare, and protect their son/students. Lastly, the study found that teachers received no formal training in building parent-teacher partnerships, but gathered experimental knowledge on how to build those relationships. These findings have implications for teacher education programs, schools, parents, and teachers.

Measurement and Simulation of Suppression Effects in a Buoyant Turbulent Line Fire

An experimental and numerical study of turbulent fire suppression is presented. For this work, a novel and canonical facility has been developed, featuring a buoyant, turbulent, methane or propane-fueled diffusion flame suppressed via either nitrogen dilution of the oxidizer or application of a fine water mist. Flames are stabilized on a slot burner surrounded by a co-flowing oxidizer, which allows controlled delivery of either suppressant to achieve a range of conditions from complete combustion through partial and total flame quenching. A minimal supply of pure oxygen is optionally applied along the burner to provide a strengthened flame base that resists liftoff extinction and permits the study of substantially weakened turbulent flames. The carefully designed facility features well-characterized inlet and boundary conditions that are especially amenable to numerical simulation. Non-intrusive diagnostics provide detailed measurements of suppression behavior, yielding insight into the governing suppression processes, and aiding the development and validation of advanced suppression models. Diagnostics include oxidizer composition analysis to determine suppression potential, flame imaging to quantify visible flame structure, luminous and radiative emissions measurements to assess sooting propensity and heat losses, and species-based calorimetry to evaluate global heat release and combustion efficiency. The studied flames experience notable suppression effects, including transition in color from bright yellow to dim blue, expansion in flame height and structural intermittency, and reduction in radiative heat emissions. Still, measurements indicate that the combustion efficiency remains close to unity, and only near the extinction limit do the flames experience an abrupt transition from nearly complete combustion to total extinguishment. Measurements are compared with large eddy simulation results obtained using the Fire Dynamics Simulator, an open-source computational fluid dynamics software package. Comparisons of experimental and simulated results are used to evaluate the performance of available models in predicting fire suppression. Simulations in the present configuration highlight the issue of spurious reignition that is permitted by the classical eddy-dissipation concept for modeling turbulent combustion. To address this issue, simple treatments to prevent spurious reignition are developed and implemented. Simulations incorporating these treatments are shown to produce excellent agreement with the experimentally measured data, including the global combustion efficiency.