A von Bertalanffy Based Model for the Estimation of Oyster (Crassostrea virginica) Growth on Restored Oyster Reefs in Chesapeake Bay

A model to estimate the mean monthly growth of Crassostrea virginica oysters in Chesapeake Bay was developed. This model is based on the classic von Bertalanffy growth function, however the growth constant is changed every monthly timestep in response to short term changes in temperature and salinity. Using a dynamically varying growth constant allows the model to capture seasonal oscillations in growth, and growth responses to changing environmental conditions that previous applications of the von Bertalanffy model do not capture. This model is further expanded to include an estimation of Perkinsus marinus impacts on growth rates as well as estimations of ecosystem services provided by a restored oyster bar over time. The model was validated by comparing growth estimates from the model to oyster shell height observations from a variety of restoration sites in the upper Chesapeake Bay. Without using the P. marinus impact on growth, the model consistently overestimates mean oyster growth. However, when P. marinus effects are included in the model, the model estimates match the observed mean shell height closely for at least the first 3 years of growth. The estimates of ecosystem services suggested by this model imply that even with high levels of mortality on an oyster reef, the ecosystem services provided by that reef can still be maintained by growth for several years. Because larger oyster filter more water than smaller ones, larger oysters contribute more to the filtration and nutrient removal ecosystem services of the reef. Therefore a reef with an abundance of larger oysters will provide better filtration and nutrient removal. This implies that if an oyster restoration project is trying to improve water quality through oyster filtration, it is important to maintain the larger older oysters on the reef.

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.