{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/117702"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/117702","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"On geometric & topological methods for analysis of biophysical time series data","abstract":"Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2023-04-12 without embargo terms","abstract_html":"Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2023-04-12 without embargo terms","abstract_has_math":false,"creators":["Abraham, Ivan T."],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Electrical & Computer Engr","degree_department":null,"school":null,"contributors":["Baryshnikov, Yuliy M","Belabbas, Mohamed-Ali","Husain, Fatima T","Zhao, Zhizhen"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2022,"date_issued":"2022-12","date_published":"2022-12","updated_at":"2026-07-22T22:24:56Z","subjects":["time-series","geometric diffusions","manifold learning","cyclicity analysis","fmri","emg"],"languages":["en","eng"],"rights":["Copyright 2022 Ivan T. Abraham"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/2142/117702","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Baryshnikov, Yuliy M","Belabbas, Mohamed-Ali","Husain, Fatima T","Zhao, Zhizhen"]},{"key":"dc:creator","label":"Author","values":["Abraham, Ivan T."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2022-12","2022-08-10"]},{"key":"dc:type","label":"Dc Type","values":["text","Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Electrical & Computer Engr"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["time-series","geometric diffusions","manifold learning","cyclicity analysis","fmri","emg"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en","eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2022 Ivan T. Abraham"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://hdl.handle.net/2142/117702"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2023-04-12 without embargo terms","The student, Ivan Abraham, accepted the attached license on 2022-08-06 at 09:41.","The student, Ivan Abraham, submitted this Dissertation for approval on 2022-08-06 at 09:41.","This Dissertation was approved for publication on 2022-08-10 at 13:31.","DSpace SAF Submission Ingestion Package generated from Vireo submission #18450 on 2023-04-12 at 07:22:51","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."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["On geometric & topological methods for analysis of biophysical time series data"]}]}],"canonical_facts":{"dc:contributor":["Baryshnikov, Yuliy M","Belabbas, Mohamed-Ali","Husain, Fatima T","Zhao, Zhizhen"],"dc:creator":["Abraham, Ivan T."],"dc:date":["2022-12","2022-08-10"],"dc:description":["Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2023-04-12 without embargo terms","The student, Ivan Abraham, accepted the attached license on 2022-08-06 at 09:41.","The student, Ivan Abraham, submitted this Dissertation for approval on 2022-08-06 at 09:41.","This Dissertation was approved for publication on 2022-08-10 at 13:31.","DSpace SAF Submission Ingestion Package generated from Vireo submission #18450 on 2023-04-12 at 07:22:51","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."],"dc:format":["application/pdf"],"dc:identifier":["https://hdl.handle.net/2142/117702"],"dc:language":["en","eng"],"dc:rights":["Copyright 2022 Ivan T. Abraham"],"dc:subject":["time-series","geometric diffusions","manifold learning","cyclicity analysis","fmri","emg"],"dc:title":["On geometric & topological methods for analysis of biophysical time series data"],"dc:type":["text","Thesis"],"thesis:degree_discipline":["Electrical & Computer Engr"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:24:56Z"}