Wednesday, July 25, 2018
07/25/2018 - 2:00pm
The past few decades have brought critical challenges in storage and analysis of large datasets. In this talk, I will first briefly survey some important techniques from Applied Harmonic Analysis that address these challenges. Then I will focus on Diffusion Maps, an algorithm in which the eigendecomposition of a graph operator, the Laplacian, is used to efficiently encode important, sometimes hidden, information about datasets. I will show various Diffusion Maps’ applications, including results as crucial as detecting early stages of blindness and some exciting new findings on autism, both via analysis of medical images.
07/25/2018 - 4:00pm
We show that on the n-torus with the matrix valued Hardy space case one can perform a similar Blaschke product decomposition like in the classical case. In the latter case this type decomposition is an implementation of the direct sum decomposition of the Hardy space into zero-based invariant subspaces and the corresponding backward shift invariant subspaces involving the Beurling Theorem.