Nested Sampling and its Applications in Stable Compressive Covariance Estimation and Phase Retrieval with Near-Minimal Measurements

Compressed covariance sensing using quadratic samplers is gaining increasing interest in recent literature. Covariance matrix often plays the role of a sufficient statistic in many signal and information processing tasks. However, owing to the large dimension of the data, it may become necessary to obtain a compressed sketch of the high dimensional covariance matrix to reduce the associated storage and communication costs. Nested sampling has been proposed in the past as an efficient sub-Nyquist sampling strategy that enables perfect reconstruction of the autocorrelation sequence of Wide-Sense Stationary (WSS) signals, as though it was sampled at the Nyquist rate. The key idea behind nested sampling is to exploit properties of the difference set that naturally arises in quadratic measurement model associated with covariance compression. In this thesis, we will focus on developing novel versions of nested sampling for low rank Toeplitz covariance estimation, and phase retrieval, where the latter problem finds many applications in high resolution optical imaging, X-ray crystallography and molecular imaging. The problem of low rank compressive Toeplitz covariance estimation is first shown to be fundamentally related to that of line spectrum recovery. In absence if noise, this connection can be exploited to develop a particular kind of sampler called the Generalized Nested Sampler (GNS), that can achieve optimal compression rates. In presence of bounded noise, we develop a regularization-free algorithm that provably leads to stable recovery of the high dimensional Toeplitz matrix from its order-wise minimal sketch acquired using a GNS. Contrary to existing TV-norm and nuclear norm based reconstruction algorithms, our technique does not use any tuning parameters, which can be of great practical value. The idea of nested sampling idea also finds a surprising use in the problem of phase retrieval, which has been of great interest in recent times for its convex formulation via PhaseLift, By using another modified version of nested sampling, namely the Partial Nested Fourier Sampler (PNFS), we show that with probability one, it is possible to achieve a certain conjectured lower bound on the necessary measurement size. Moreover, for sparse data, an l1 minimization based algorithm is proposed that can lead to stable phase retrieval using order-wise minimal number of measurements.

A GLOBAL SAMPLING OF PIANO MUSIC FROM 1978 TO 2005

Pianists of the twenty-first century have a wealth of repertoire at their fingertips. They busily study music from the different periods -- Baroque, Classical, Romantic, and some of the twentieth century -- trying to understand the culture and performance practice of the time and the stylistic traits of each composer so they can communicate their music effectively. Unfortunately, this leaves little time to notice the composers who are writing music today. Whether this neglect proceeds from lack of time or lack of curiosity, I feel we should be connected to music that was written in our own lifetime, when we already understand the culture and have knowledge of the different styles that preceded us. Therefore, in an attempt to promote today’s composers, I have selected piano music written during my lifetime, to show that contemporary music is effective and worthwhile and deserves as much attention as the music that preceded it. This dissertation showcases piano music composed from 1978 to 2005. A point of departure in selecting the pieces for this recording project is to represent the major genres in the piano repertoire in order to show a variety of styles, moods, lengths, and difficulties. Therefore, from these recordings, there is enough variety to successfully program a complete contemporary recital from the selected works, and there is enough variety to meet the demands of pianists with different skill levels and recital programming needs. Since we live in an increasingly global society, music from all parts of the world is included to offer a fair representation of music being composed everywhere. Half of the music in this project comes from the United States. The other half comes from Australia, Japan, Russia, and Argentina. The composers represented in these recordings are: Lowell Liebermann, Richard Danielpour, Frederic Rzewski, Judith Lang Zaimont, Samuel Adler, Carl Vine, Nikolai Kapustin, Akira Miyoshi and Osvaldo Golijov. With the exception of one piano concerto, all the works are for solo piano. This recording project dissertation consists of two 60 minute CDs of selected repertoire, accompanied by a substantial document of in-depth program notes. The recordings are documented on compact discs that are housed within the University of Maryland Library System.

ROLE OF ICAM-1-MEDIATED ENDOCYTOSIS IN ENDOTHELIAL FUNCTION AND IMPLICATIONS FOR CARRIER-ASSISTED DRUG DELIVERY

Intercellular adhesion molecule 1 (ICAM-1) is a transmembrane protein found on the surface of vascular endothelial cells (ECs). Its expression is upregulated at inflammatory sites, allowing for targeted delivery of therapeutics using ICAM-1-binding drug carriers. Engagement of multiple copies of ICAM-1 by these drug carriers induces cell adhesion molecule (CAM)-mediated endocytosis, which results in trafficking of carriers to lysosomes and across ECs. Knowledge about the regulation behind CAM-mediated endocytosis can help improve drug delivery, but questions remain about these regulatory mechanisms. Furthermore, little is known about the natural function of this endocytic pathway. To address these gaps in knowledge, we focused on two natural binding partners of ICAM-1 that potentially elicit CAM-mediated endocytosis: leukocytes (which bind ICAM-1 via β₂ integrins) and fibrin polymers (a main component of blood clots which binds ICAM-1 via the γ3 sequence). First, inspired by properties of these natural binding partners, we varied the size and targeting moiety of model drug carriers to determine how these parameters affect CAM-mediated endocytosis. Increasing ICAM-1-targeted carrier size slowed carrier uptake kinetics, reduced carrier trafficking to lysosomes, and increased carrier transport across ECs. Changing targeting moieties from antibodies to peptides decreased particle binding and uptake, lowered trafficking to lysosomes, and increased transport across ECs. Second, using cell culture models of leukocyte/EC interactions, inhibiting regulatory elements of the CAM-mediated pathway disrupted leukocyte sampling, a process crucial to leukocyte crossing of endothelial layers (transmigration). This inhibition also decreased leukocyte transmigration across ECs, specifically through the transcellular route, which occurs through a single EC without disassembly of cell-cell junctions. Third, fibrin meshes, which mimic blood clot fragments/remnants, bound to ECs at ICAM-1-enriched sites and were internalized by the endothelium. Inhibiting the CAM-mediated pathway disrupted this uptake. Following endocytosis, fibrin meshes trafficked to lysosomes where they were degraded. In mouse models, CAM-mediated endocytosis of fibrin meshes appeared to remove fibrin remnants at the endothelial surface, preventing re-initiation of the coagulation cascade. Overall, these results support a link between CAM-mediated endocytosis and leukocyte transmigration as well as uptake of fibrin materials by ECs. Furthermore, these results will guide the future design of ICAM-1-targeted carrier-assisted therapies.