Mathematics Theses and Dissertations
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Nonlinear Analysis of Phase Retrieval and Deep Learning
(2017)Nonlinearity causes information loss. The phase retrieval problem, or the phaseless reconstruction problem, seeks to reconstruct a signal from the magnitudes of linear measurements. With a more complicated design, convolutional ... 
Two GoodnessofFit Tests for the Density Ratio Model
(2017)Under consideration are goodnessoffit tests for the \textit{density ratio model}. The model stipulates that the loglikelihood ratio of two unknown densities is of a known form which depends on finite dimensional parameters ... 
Transfer of Representations and Orbital Integrals of Inner Forms of GL_n
(2016)Let $F$ be a nonarchimedean local field and $D$ an $F$central division algebra. We characterize the Local Langlands Correspondence (LLC) for inner forms of $GL_n$ over $F$ via the JacquetLanglands Correspondence and ... 
Spectral Analysis of Markov Jump Processes with Rare Transitions: A GraphAlgorithmic Approach
(2017)Parameterdependent Markov jump processes with exponentially small transition rates arise in modeling complex systems in physics, chemistry, and biology. Longterm dynamics of these processes are largely governed by the ... 
Exponentiation of Motivic Zeta Functions
(2017)We provide a formula for the generating series of the Weil zeta function $Z(X,t)$ of symmetric powers $\Sym^n X$ of varieties $X$ over finite fields. This realizes the zeta function $Z(X,t)$ as an exponentiable measure ...