Have you ever wondered how complex and massive problems are solved efficiently on computers? The answer lies in the interplay of structured data and fast algorithms. This talk will explore how data sparsity arises in such key problems and introduce key ideas like high-rank decompositions and sparse representations that enable such fast algorithms, all without assuming any background other than linear algebra at a first-year level!!
Prof. Manas Rachh is a mathematician whose research explores integral equation formulations and numerical methods to solve the same, as well as developing and studying novel algorithms to work with statistics, structured matrices and data analysis.
Abstract: Structured matrices are ubiquitous in many areas of science and engineering such as molecular dynamics, antenna and speaker modeling, medical imaging, microfluidic device design, computational statistics, and data visualization to name a few. Traditionally, these matrices tend to be dense and the cost of applying N x N matrices scales like O(N^2). However, large sub-blocks of these matrices tend to be data-sparse. This structure can be exploited to apply matvecs in O(N) CPU time — thus enabling the simulation of much larger computational problems with the same computational budget. This is true, not only in first principle simulations, but also as core components of data analysis pipelines.
The purpose of this talk is two-fold: a) to understand how this data-sparsity manifests itself both for the construction of low dimensional embeddings in bioinformatics (scRNA-seq) and for the computation of N-body sums arising in mathematical physics; and b) to present key recurrent ideas (low-rank decompositions, additive/multiplicative sparse representations, sum of exponential representations, etc) that are used in the development of fast algorithms. These ideas are bringing us a step closer to accurate and efficient large-scale simulation, which I will illustrate with an example from acoustic speaker design.
For more information, check out Prof. Manas Rachh's profile at https://mrachh.github.io/
