Browsing by Author "Alexander Powell"
Now showing items 1-14 of 14
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Spaeth, Anneliese Heidi (2013-08-01)Department: MathematicsWe consider various types of generalized bases in spaces of the type L^p(T), where T=[0,1]. More specifically, we determine whether there exists a system {f_n}_n, of the type under consideration, with the property f_n(t)>=0 ...
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Huo, Xi (2014-06-26)Department: MathematicsThe work in this dissertation is about modeling the spread of an infectious disease in a closed community with two basic public health interventions: (i) identifying and isolating symptomatic cases, and (ii) tracing and ...
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Kapitanov, Georgi (2012-06-25)Department: MathematicsThere is evidence that cancer develops when cells acquire a sequence of mutations. This sequence determines a hierarchy among the cells, based on how many more mutations they need to accumulate in order to become cancerous. ...
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Li, Shiying (2019-07-11)Department: MathematicsSplines have been used to approximate the solutions of differential equations for a while. In the first part of this thesis, adaptive algorithms based on the finite element method and splines on triangulations with hanging ...
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Lee, Chang Hsin (2017-06-19)Department: MathematicsA fundamental problem in signal processing called signal reconstruction, or signal recovery, is the determination of a signal from a sequence of samples obtained from the signal. The sampling process can be viewed as ...
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Leshen, Sara (2019-03-21)Department: MathematicsThe uncertainty principle implies that a function and its Fourier transform cannot both be well-localized. The Balian-Low theorem is a version of the uncertainty principle for generators of Gabor orthonormal bases. This ...
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Northington, Michael Carr V (2016-04-09)Department: MathematicsShift-invariant spaces and Gabor systems are frequently used in approximation theory and signal processing. In these settings, it is advantageous for the generators of such spaces to be localized and for the spaces to be ...
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Su, Yujian (2015-11-30)Department: MathematicsLet $Lambda$ be a lattice in $R^d$ with positive co-volume. Among $Lambda$-periodic $N$-point configurations, we consider the minimal renormalized Riesz $s$-energy $mathcal{E}_{s,Lambda}(N)$. While the dominant term ...
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Petrosyan, Armenak (2017-05-17)Department: MathematicsThe main problem in sampling theory is to reconstruct a function from its values (samples) on some discrete subset <font face=symbol>W</font> of its domain. However, taking samples on an appropriate sampling set <font ...
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LeCrone, Jeremy (2012-05-23)Department: MathematicsIn this thesis, we establish analytic results for the axisymmetric surface diffusion flow (ASD), a fourth-order geometric evolution law. In the first part of the work, we develop a general theory establishing maximal ...
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Jiang, Jiayi (2016-04-08)Department: MathematicsQuantization is an important part of signal processing. Several issues influence the performance of a quantization algorithm. One is the “basis” we choose to represent the signal, another is how we quantize the “basis” ...
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Ren, Yunxiang (2017-08-15)Department: MathematicsModern subfactor theory was initiated by Jones by proving the significant result, Jones' index theorem. Later, Jones gave the topological axiomatization of the standard invariant of subfactors. This topological perspective ...
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Chen, Xuemei (2012-06-06)Department: MathematicsThis dissertation consists of two topics: compressed sensing and the Kaczmarz algorithm. Compressed sensing addresses the problem of recovering an unknown signal $z_0in mathbb{R}^d$ from a small number of linear measurements ...
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Sekmen, Ali Safak (2012-04-18)Department: MathematicsThis thesis developed theory and associated algorithms to solve subspace segmentation problem. Given a set of data W={w_1,...,w_N} in R^D that comes from a union of subspaces, we focused on determining a nonlinear model ...