Dynamics of a large submersed plant bed in upper Chesapeake Bay

A large SAV bed in upper Chesapeake Bay has experienced several abrupt shifts over the past half-century, beginning with near-complete loss after a record-breaking flood in 1972, followed by an unexpected, rapid resurgence in the early 2000’s, then partial decline in 2011 following another major flood event. Together, these trends and events provide a unique opportunity to study a recovering SAV ecosystem from several different perspectives. First, I analyzed and synthesized existing time series datasets to make inferences about what factors prompted the recovery. Next, I analyzed existing datasets, together with field samples and a simple hydrodynamic model to investigate mechanisms of SAV bed loss and resilience to storm events. Finally, I conducted field deployments and experiments to explore how the bed affects internal physical and biogeochemical processes and what implications those effects have for the dynamics of the system. I found that modest reductions in nutrient loading, coupled with several consecutive dry years likely facilitated the SAV resurgence. Furthermore, positive feedback processes may have played a role in the sudden nature of the recovery because they could have reinforced the state of the bed before and after the abrupt shift. I also found that scour and poor water clarity associated with sediment deposition during the 2011 flood event were mechanisms of plant loss. However, interactions between the bed, water flow, and waves served as mechanisms of resilience because these processes created favorable growing conditions (i.e., clear water, low flow velocities) in the inner core of the bed. Finally, I found that that interactions between physical and biogeochemical processes led to low nutrient concentrations inside the bed relative to outside the bed, which created conditions that precluded algal growth and reinforced vascular plant dominance. This work demonstrates that positive feedbacks play a central role in SAV resilience to both chronic eutrophication as well as acute storm events. Furthermore, I show that analysis of long-term ecological monitoring data, together with field measurements and experiments, can be an effective approach for understanding the mechanisms underlying ecosystem dynamics.

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.