University of Illinois Urbana-Champaign

On geometric & topological methods for analysis of biophysical time series data

Abraham, Ivan T.

Content Files
ABRAHAM-DISSERTATION-2022.pdf

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https://hdl.handle.net/2142/117702

Description

Title
On geometric & topological methods for analysis of biophysical time series data
Author(s)
Abraham, Ivan T.
Issue Date
2022-08-10
Director of Research (if dissertation) or Advisor (if thesis)
  • Baryshnikov, Yuliy M
  • Belabbas, Mohamed-Ali
Doctoral Committee Chair(s)
  • Baryshnikov, Yuliy M
  • Belabbas, Mohamed-Ali
Committee Member(s)
  • Husain, Fatima T
  • Zhao, Zhizhen
Department of Study
Electrical & Computer Eng
Discipline
Electrical & Computer Engr
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
  • time-series
  • geometric diffusions
  • manifold learning
  • cyclicity analysis
  • fmri
  • emg
Abstract
Time series analysis is staple work horse in many fields including climatology, econometrics, stock and derivatives markets, systems engineering, etc. Traditional analysis of time series data is focused on predicting or forecasting future values based on analysis and modeling of past values. In this work we present methods of time series analysis that are based on geometric principles. First cyclicity analysis, a method of analysis of repeating but aperiodic signals is introduced and treated in depth. This method is then used to examine two sets of brain imaging data, specifically functional magnetic resonance imaging data under both resting state and task paradigms. We present results that show our ability to fingerprint individuals using their resting state scans, detect slow cortical waves in the brain and classify between groups in the dataset. Next we apply principles from geometric diffusion process in the context of manifold learning to show how synergy detection in eletcromyography data is best viewed as a nonlinear clustering problem rather than a factor analysis problem. We also present simple kinematic examples where linear methods fail to show that nonlinearity is inherent in even the simplest systems. Finally, we conclude this document with a review of results presented, some comments of a historical nature and ongoing trends in the fields we that supplied the data and what can be expected in the near future.
Graduation Semester
2022-12
Type of Resource
Thesis
Handle URL
https://hdl.handle.net/2142/117702
Copyright and License Information
Copyright 2022 Ivan T. Abraham

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