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.

DEVELOPMENT OF A NUCLEIC ACID-BASED SPECIFIC GROWTH MODEL FOR JUVENILE BLUE CRAB, CALLINECTES SAPIDUS

The evaluation and identification of habitats that function as nurseries for marine species has the potential to improve conservation and management. A key assessment of nursery habitat is estimating individual growth. However, the discrete growth of crustaceans presents a challenge for many traditional in situ techniques to accurately estimate growth over a short temporal scale. To evaluate the use of nucleic acid ratios (R:D) for juvenile blue crab (Callinectes sapidus), I developed and validated an R:D-based index of growth in the laboratory. R:D based growth estimates of crabs collected in the Patuxent River, MD indicated growth ranged from 0.8-25.9 (mg·g-1·d-1). Overall, there was no effect of size on growth, whereas there was a weak, but significant effect of date. These data provide insight into patterns of habitat-specific growth. These results highlight the complexity of the biological and physical factors which regulate growth of juvenile blue crabs in the field.