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.

A comprehensive study of multiplicative attribute graph model

Graphs are powerful tools to describe social, technological and biological networks, with nodes representing agents (people, websites, gene, etc.) and edges (or links) representing relations (or interactions) between agents. Examples of real-world networks include social networks, the World Wide Web, collaboration networks, protein networks, etc. Researchers often model these networks as random graphs. In this dissertation, we study a recently introduced social network model, named the Multiplicative Attribute Graph model (MAG), which takes into account the randomness of nodal attributes in the process of link formation (i.e., the probability of a link existing between two nodes depends on their attributes). Kim and Lesckovec, who defined the model, have claimed that this model exhibit some of the properties a real world social network is expected to have. Focusing on a homogeneous version of this model, we investigate the existence of zero-one laws for graph properties, e.g., the absence of isolated nodes, graph connectivity and the emergence of triangles. We obtain conditions on the parameters of the model, so that these properties occur with high or vanishingly probability as the number of nodes becomes unboundedly large. In that regime, we also investigate the property of triadic closure and the nodal degree distribution.

TAXONOMY, MORPHOLOGY, AND RNA-SEQ TRANSCRIPTOMICS OF THE CUBOZOAN ALATINA ALATA, AN EMERGING MODEL CNIDARIAN

Cnidarians are often considered simple animals, but the more than 13,000 estimated species (e.g., corals, hydroids and jellyfish) of the early diverging phylum exhibit a broad diversity of forms, functions and behaviors, some of which are demonstrably complex. In particular, cubozoans (box jellyfish) are cnidarians that have evolved a number of distinguishing features. Some cubozoan species possess complex mating behaviors or particularly potent stings, and all possess well-developed light sensation involving image-forming eyes. Like all cnidarians, cubozoans have specialized subcellular structures called nematocysts that are used in prey capture and defense. The objective of this study is to contribute to the development of the box jellyfish Alatina alata as a model cnidarian. This cubozoan species offers numerous advantages for investigating morphological and molecular traits underlying complex processes and coordinated behavior in free-living medusozoans (i.e., jellyfish), and more broadly throughout Metazoa. First, I provide an overview of Cnidaria with an emphasis on the current understanding of genes and proteins implicated in complex biological processes in a few select cnidarians. Second, to further develop resources for A. alata, I provide a formal redescription of this cubozoan and establish a neotype specimen voucher, which serve to stabilize the taxonomy of the species. Third, I generate the first functionally annotated transcriptome of adult and larval A. alata tissue and apply preliminary differential expression analyses to identify candidate genes implicated broadly in biological processes related to prey capture and defense, vision and the phototransduction pathway and sexual reproduction and gametogenesis. Fourth, to better understand venom diversity and mechanisms controlling venom synthesis in A. alata, I use bioinformatics to investigate gene candidates with dual roles in venom and digestion, and review the biology of prey capture and digestion in cubozoans. The morphological and molecular resources presented herein contribute to understanding the evolution of cubozoan characteristics and serve to facilitate further research on this emerging cubozoan model.

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.