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A Universal Approximation Theorem for Tychonoff Spaces with Application to Spaces of Probability and Finite Measures
DownloadFall 2022
Universal approximation refers to the property of a collection of functions to approximate continuous functions. Past literature has demonstrated that neural networks are dense in continuous functions on compact subsets of finite-dimensional spaces, and this document extends those findings to...
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Fall 2012
In this thesis, we develop a novel method of generating CAPTCHAs, which are used to protect online resources from abuse by computer agents. We view CAPTCHA generation as random field simulation and construct a CAPTCHA by evolving an initial state via resimulating pixels until the image becomes...
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Outer Products and Stochastic Approximation Algorithms in a Heavy-tailed and Long-range Dependent Setting
DownloadFall 2015
Classical time-series theories are mainly concerned with the statistical analysis of light-tailed and short-range dependent stationary linear processes. Applications in network theory and financial mathematics lead us to consider time series models with heavy tails and long memory. Heavy-tailed...