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.

Dielectric studies of Liquid Crystal Nanocomposites and Nanomaterial systems.

Liquid crystals (LCs) have revolutionized the display and communication technologies. Doping of LCs with inorganic nanoparticles such as carbon nanotubes, gold nanoparticles and ferroelectric nanoparticles have garnered the interest of research community as they aid in improving the electro-optic performance. In this thesis, we examine a hybrid nanocomposite comprising of 5CB liquid crystal and block copolymer functionalized barium titanate ferroelectric nanoparticles. This hybrid system exhibits a giant soft-memory effect. Here, spontaneous polarization of ferroelectric nanoparticles couples synergistically with the radially aligned BCP chains to create nanoscopic domains that can be rotated electromechanically and locked in space even after the removal of the applied electric field. The resulting non-volatile memory is several times larger than the non-functionalized sample and provides an insight into the role of non-covalent polymer functionalization. We also present the latest results from the dielectric and spectroscopic study of field assisted alignment of gold nanorods.

Advanced Analytical Microscopy at the Nanoscale: Applications in Wide Bandgap and Solid Oxide Fuel Cell Materials

The atomic-level structure and chemistry of materials ultimately dictate their observed macroscopic properties and behavior. As such, an intimate understanding of these characteristics allows for better materials engineering and improvements in the resulting devices. In our work, two material systems were investigated using advanced electron and ion microscopy techniques, relating the measured nanoscale traits to overall device performance. First, transmission electron microscopy and electron energy loss spectroscopy (TEM-EELS) were used to analyze interfacial states at the semiconductor/oxide interface in wide bandgap SiC microelectronics. This interface contains defects that significantly diminish SiC device performance, and their fundamental nature remains generally unresolved. The impacts of various microfabrication techniques were explored, examining both current commercial and next-generation processing strategies. In further investigations, machine learning techniques were applied to the EELS data, revealing previously hidden Si, C, and O bonding states at the interface, which help explain the origins of mobility enhancement in SiC devices. Finally, the impacts of SiC bias temperature stressing on the interfacial region were explored. In the second system, focused ion beam/scanning electron microscopy (FIB/SEM) was used to reconstruct 3D models of solid oxide fuel cell (SOFC) cathodes. Since the specific degradation mechanisms of SOFC cathodes are poorly understood, FIB/SEM and TEM were used to analyze and quantify changes in the microstructure during performance degradation. Novel strategies for microstructure calculation from FIB-nanotomography data were developed and applied to LSM-YSZ and LSCF-GDC composite cathodes, aged with environmental contaminants to promote degradation. In LSM-YSZ, migration of both La and Mn cations to the grain boundaries of YSZ was observed using TEM-EELS. Few substantial changes however, were observed in the overall microstructure of the cells, correlating with a lack of performance degradation induced by the H2O. Using similar strategies, a series of LSCF-GDC cathodes were analyzed, aged in H2O, CO2, and Cr-vapor environments. FIB/SEM observation revealed considerable formation of secondary phases within these cathodes, and quantifiable modifications of the microstructure. In particular, Cr-poisoning was observed to cause substantial byproduct formation, which was correlated with drastic reductions in cell performance.