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.

LARGE MOTION VISUALIZATION AND ESTIMATION FOR FLAPPING WING SYSTEMS

Studies of fluid-structure interactions associated with flexible structures such as flapping wings require the capture and quantification of large motions of bodies that may be opaque. Motion capture of a free flying insect is considered by using three synchronized high-speed cameras. A solid finite element representation is used as a reference body and successive snapshots in time of the displacement fields are reconstructed via an optimization procedure. An objective function is formulated, and various shape difference definitions are considered. The proposed methodology is first studied for a synthetic case of a flexible cantilever structure undergoing large deformations, and then applied to a Manduca Sexta (hawkmoth) in free flight. The three-dimensional motions of this flapping system are reconstructed from image date collected by using three cameras. The complete deformation geometry of this system is analyzed. Finally, a computational investigation is carried out to understand the flow physics and aerodynamic performance by prescribing the body and wing motions in a fluid-body code. This thesis work contains one of the first set of such motion visualization and deformation analyses carried out for a hawkmoth in free flight. The tools and procedures used in this work are widely applicable to the studies of other flying animals with flexible wings as well as synthetic systems with flexible body elements.