A large number of learning algorithms, for example, spectral clustering, kernel Principal Components Analysis and many manifold methods are based on estimating eigenvalues and eigenfunctions of operators defined by a ...

Spectral methods have become increasingly popular in designing fast algorithms for modern highdimensional datasets. This thesis looks at several problems in which spectral methods play a central role. In some cases, we ...

This thesis focuses on the evolution of zonal flows in self-gravitating accretion discs and their resulting effect on disc stability; it also studies the process of disc gravito-turbulence, with particular emphasis given ...