Speaker: Abhinav Natarajan
Title: Wavelets, Sparsity, and Irregular Domains
Abstract: For many decades, Fourier transforms remained the main tool for analysts and engineers in linear time-invariant signal processing. The emergence of wavelets provided a huge new jungle of linear transforms with several advantages over Fourier transforms, most notably in analysing spatially-localised properties of functions, and in constructing sparse dictionaries for encoding large classes of datasets. I will talk about the basic notions behind wavelet transforms, their applications, some of their sparsity properties, and about recent efforts to extend these wavelet transforms to irregular domains like graphs and manifolds.
Speaker: Adam Tonks
Title: Reducing regional distortions in cartograms produced by flow-based algorithms
Abstract: A cartogram, or density-equalising map, is a transformed map projection such that the area of each geographic region is proportional to a certain data value attributed to it. A contiguous cartogram is a successful data visualisation method of geographical data in that it
achieves two seemingly irreconcilable properties – that the area principle of statistics is satisfied, and that the topology of the original map projection is preserved. The most popular method currently for producing cartograms is the Gastner-Newman algorithm, which is based on the diffusion equation. However, it suffers from boundary distortions for regions that are shrunk or expanded by a large factor. A successful attempt to mitigate the boundary distortions, via edge detection or Tobler’s pycnophylactic interpolation algorithms, will make different regions on a cartogram more easily recognisable for readers, and may result in increased adoption of cartograms in a variety of arenas, be it the mainstream media or the scientific literature.