Dr. Mileyko is the recipient of a collaborative grant from the Division Of Mathematical Sciences at the National Science Foundation for a total amount of $220,000 (starting date August 1st, 2016 and a duration of 3 years).
The project is titled “Topological Invariants for Enhanced Data Analysis”. The general goal of this project, which will be carried out in collaboration with Prof. Yuliy Baryshnikov from the University of Illinois at Urbana-Champaign (UIUC), is to develop a theoretical foundation as well as practical tools for recovering local topological structure of complex datasets. Introduction of topological techniques into the toolbox of data analysis was one of the major advances of the past decade, and the field of Topological Data Analysis has emerged as a powerful alternative to the mainstream methods of data analysis. The main premise of the topological approach is that the data in any given problem have a shape, and this shape matters, having a potential to reveal otherwise hidden patterns which characterize the underlying process. Moreover, local shape of data and the corresponding shape distributions, which have been largely overlooked, may produce a wealth of additional, previously unexplored information capable of providing crucial insights in a variety of scientific and engineering problems. More specifically, the developed toolkit is planned to be employed to capture transient behavior in power networks such as on onset of dangerous oscillations, characterize complex networks such as the Internet or plant root systems, and investigate brain activity with a focus on neural characteristics of
various tinnitus related conditions.
The grant also includes funding for graduate as well as undergraduate students, and thus presents an excellent opportunity for the students to engage in interdisciplinary research activities. Students will have a chance to work at the frontiers of science with mathematicians, engineers, biologists, and medical professionals at UH Mānoa and UIUC, and see first hand how STEM disciplines come together to tackle important real world problems. The students' experience will also be enriched by engagement in public awareness and early engagement activities at middle schools and high schools with the goal of promoting and improving K-12 STEM education.
Yuriy Mileyko obtained his Ph.D. in mathematical sciences in 2005 from the New Jersey Institute of Technology and Rutgers University. This was followed by a three year position as research associate in the department of computer science at Duke University from 2005-2008, a one year post-doc at the school of Biology at Georgia Institute of Technology from 2008-2009, a three year visiting assistant professor position in the department of mathematics at Duke University from 2009-2012 and one year as a visiting scholar in the coordinated science lab & department of mathematics at the University of Illinois at Urbana Champaign. He joined the Department of Mathematics at UH Mānoa in August 2013.