Theses  Pure Mathematics and Mathematical Statistics
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KellerSegelType Models and Kinetic Equations for Interacting Particles: LongTime Asymptotic Analysis
(20170721)This thesis consists of three parts: The first and second parts focus on longtime asymptotics of macroscopic and kinetic models respectively, while in the third part we connect these regimes using different scaling ... 
A concentration inequality based statistical methodology for inference on covariance matrices and operators
(20170623)In the modern era of high and infinite dimensional data, classical statistical methodology is often rendered inefficient and ineffective when confronted with such big data problems as arise in genomics, medical imaging, ... 
Modern kNearest Neighbour Methods in Entropy Estimation, Independence Testing and Classification
(20171001)Nearest neighbour methods are a classical approach in nonparametric statistics. The knearest neighbour classifier can be traced back to the seminal work of Fix and Hodges (1951) and they also enjoy popularity in many other ... 
The Calderón problem for connections
(20171003)This thesis is concerned with the inverse problem of determining a unitary connection $A$ on a Hermitian vector bundle $E$ of rank $m$ over a compact Riemannian manifold $(M, g)$ from the DirichlettoNeumann (DN) ...