The purpose of time-series analysis is to detect basic properties of the system that engenders a time series. The hope of predicting the system's future evolution is closely related to the possibility of such detection. The most easily predictable components of a system's evolution are the regular, deterministic ones; hence we look for trends and periodic oscillations. In doing so, it is often ...

In this lecture, we discuss some spectral techniques and their applications. The goal of spectral techniques is to study and deduce the characteristics of a matrix by looking at its spectrum (i.e. eigenvalues of matrix). Although spectral methods can be applied to any problem instance with matrix representation, we will be focussing on graph theoretic problems in this lecture. Over the past two...