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Largescale optimization Methods for datascience applications
(Massachusetts Institute of Technology, 2019)In this thesis, we present several contributions of large scale optimization methods with the applications in data science and machine learning. In the first part, we present new computational methods and associated ... 
Point processes of representation theoretic origin
(Massachusetts Institute of Technology, 2019)There are two parts to this thesis. In the first part we compute the correlation functions of the 4parameter family of BC type Zmeasures. The result is given explicitly in terms of Gauss's hypergeometric function. The ... 
Hydrodynamic analogues of quantum corrals and Friedel oscillations
(Massachusetts Institute of Technology, 2019)We consider the walking droplet (or 'walker') system discovered in 2005 by Yves Couder and coworkers. We investigate experimentally and theoretically the behaviour of this hydrodynamic pilotwave system in both closed and ...