Browsing by Subject "Wavelets"
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Item Application of wavelets in few-body problems.(2012-08) Hewawasam, KuraviThis study is an application of wavelet numerical techniques in solving a non-perturbative Yukawa Hamiltonian in light-front quantum field theory. Once the problem is stated in the form of an integral equation, a wavelet basis of a particular scale is used to discretize the problem into a dense matrix. Wavelets are a class of functions with special properties. Daubachies wavelets are a subset of wavelets defined to have vanishing lower order moments, enabling Daubachies 2 and 3 wavelet bases to exactly represent polynomials of degree up to two. These properties make them useful as a basis set for various numerical methods. It was observed that a kernel containing structure in fine scales requires a fine scaling function basis to converge closer to analytical results. Once the kernel matrix is obtained, the wavelet transform followed by an absolute thresholding filters the dense kernel matrix to a sparse matrix. The sparse matrix eigenvalue problem was then solved and compared with the original eigenvalue problem. It was observed that as long as the problem is discretized with a scale fine enough to resolve the features of the kernel, higher levels of filtering would still reproduce eigenvalues that agree with the unfiltered problem.Item The Empirical Behavior of Commodity Prices at High Frequencies(2016-12) Mahon, JosephI analyze the intraday prices and volatility of three exchange-traded agricultural commodities at high-frequencies. The dataset spans only a few trading days, but includes every transaction on the exchanges down to the microsecond. After reviewing some of the empirical issues with high-frequency data and the methods in the literature devoted to estimating volatility from them, I develop an approach that can disentangle the continuous or integrated volatility from discrete jumps in the price process. I illustrate applications to estimating spot volatility and in volatility forecasting, and conclude that these methods provide useful refinements to existing approaches.Item Event detection for post lung transplant based on home monitoring of spirometry and symptoms(2011-12) Wang, XueweThe goal of this dissertation research was to develop, implement, and test an automated decision system to provide early detection of actual acute bronchopulmonary events in a population of lung transplant recipients following a home monitoring protocol. Decision rules were developed using wavelet analysis of spirometry and symptom signal data collected daily at home by the lung transplant recipients, and transmitted weekly to our study data center. Rules were developed based on a learning set of patient home data, and validated with an independent set of patients. Using either FEV1 or symptom-based home data monitoring, the detection algorithm can capture the majority of events (sensitivity > 80%) at an acceptable level of false alarms. Detection occurs 6.6 to 10.8 days earlier than the corresponding events recorded in the patient's clinical records. Combining rules using the Dempster-Shafer theory of evidence incrementally improves performance over a single variable. This framework can be readily implemented as an automatic event detection tool to aid medical discovery and diagnosis of acute pulmonary events.