{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/88189"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/88189","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Dynamics of a fully stochastic discretized neuronal model with excitatory and inhibitory neurons","abstract":"We consider here an extension and generalization of the stochastic neuronal network model developed by DeVille et al.; their model corresponded to an all-to-all network of discretized integrate-and-fire excitatory neurons where synapses are failure-prone. It was shown that this model exhibits different metastable phases of asynchronous and synchronous behavior, since the model limits on a mean-field deterministic system with multiple attractors. Our work investigates adding inhibition into the model. The new model exhibits the same metastable phases, but also exhibits new non-monotonic behavior that was not seen in the DeVille et al. model. The techniques used by DeVille et al. for finding the mean-field limit are not suitable for this new model. We explore early attempts at obtaining a new mean-field deterministic system that would give us an understanding of the behavior seen in the new model. After redefining the process we do find a mean-field deterministic system that the model limits on, and we investigate the behavior of the new model studying the mean-field system.","abstract_html":"We consider here an extension and generalization of the stochastic neuronal network model developed by DeVille et al.; their model corresponded to an all-to-all network of discretized integrate-and-fire excitatory neurons where synapses are failure-prone. It was shown that this model exhibits different metastable phases of asynchronous and synchronous behavior, since the model limits on a mean-field deterministic system with multiple attractors. Our work investigates adding inhibition into the model. The new model exhibits the same metastable phases, but also exhibits new non-monotonic behavior that was not seen in the DeVille et al. model. The techniques used by DeVille et al. for finding the mean-field limit are not suitable for this new model. We explore early attempts at obtaining a new mean-field deterministic system that would give us an understanding of the behavior seen in the new model. After redefining the process we do find a mean-field deterministic system that the model limits on, and we investigate the behavior of the new model studying the mean-field system.","abstract_has_math":false,"creators":["Berning, Stephen R"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["DeVille, Lee","Rapti, Zoi","Kirkpatrick, Kay L","Zharnitsky, Vadim"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-09-29T20:49:56Z","date_published":"2015-09-29T20:49:56Z","updated_at":"2026-07-22T22:26:31Z","subjects":["neural network","neuronal network","inhibitory neurons","inhibition","non-monotonic","synchrony","mean-field analysis","integrate-and-fire","limit theorem"],"languages":["en"],"rights":["Copyright 2015 Stephen Berning"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/88189","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["DeVille, Lee","Rapti, Zoi","Kirkpatrick, Kay L","Zharnitsky, Vadim"]},{"key":"dc:creator","label":"Author","values":["Berning, Stephen R"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2015-09-29T20:49:56Z","2017-09-30T09:15:18Z","2015-08","2015-07-16","2015-8"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"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":["neural network","neuronal network","inhibitory neurons","inhibition","non-monotonic","synchrony","mean-field analysis","integrate-and-fire","limit theorem"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2015 Stephen Berning"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/88189"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["We consider here an extension and generalization of the stochastic neuronal network model developed by DeVille et al.; their model corresponded to an all-to-all network of discretized integrate-and-fire excitatory neurons where synapses are failure-prone. It was shown that this model exhibits different metastable phases of asynchronous and synchronous behavior, since the model limits on a mean-field deterministic system with multiple attractors. Our work investigates adding inhibition into the model. The new model exhibits the same metastable phases, but also exhibits new non-monotonic behavior that was not seen in the DeVille et al. model. The techniques used by DeVille et al. for finding the mean-field limit are not suitable for this new model. We explore early attempts at obtaining a new mean-field deterministic system that would give us an understanding of the behavior seen in the new model. After redefining the process we do find a mean-field deterministic system that the model limits on, and we investigate the behavior of the new model studying the mean-field system.","Submission published under a 24 month embargo labeled 'U of I only', the embargo will last until 2017-08-01","The student, Stephen Berning, accepted the attached license on 2015-07-15 at 01:11.","The student, Stephen Berning, submitted this Dissertation for approval on 2015-07-15 at 01:27.","This Dissertation was approved for publication on 2015-07-16 at 13:11.","DSpace SAF Submission Ingestion Package generated from Vireo submission #8443 on 2015-09-29 at 14:59:30","Made available in DSpace on 2015-09-29T20:49:56Z (GMT). No. of bitstreams: 2 BERNING-DISSERTATION-2015.pdf: 1635741 bytes, checksum: da1fdb31589b35b5e007f82c475a8d3f (MD5) LICENSE.txt: 4212 bytes, checksum: 0012e51ab1906fe2020270b5f192ac22 (MD5) Previous issue date: 2015-07-16","Embargo set by: Seth Robbins for item 89469 Lift date: 2017-09-29T20:50:34Z Reason: Author requested U of Illinois access only (OA after 2yrs) in Vireo ETD system","U of I Only Restriction Lifted for Item 89469 on 2017-09-30T09:15:18Z."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Dynamics of a fully stochastic discretized neuronal model with excitatory and inhibitory neurons"]}]}],"canonical_facts":{"dc:contributor":["DeVille, Lee","Rapti, Zoi","Kirkpatrick, Kay L","Zharnitsky, Vadim"],"dc:creator":["Berning, Stephen R"],"dc:date":["2015-09-29T20:49:56Z","2017-09-30T09:15:18Z","2015-08","2015-07-16","2015-8"],"dc:description":["We consider here an extension and generalization of the stochastic neuronal network model developed by DeVille et al.; their model corresponded to an all-to-all network of discretized integrate-and-fire excitatory neurons where synapses are failure-prone. It was shown that this model exhibits different metastable phases of asynchronous and synchronous behavior, since the model limits on a mean-field deterministic system with multiple attractors. Our work investigates adding inhibition into the model. The new model exhibits the same metastable phases, but also exhibits new non-monotonic behavior that was not seen in the DeVille et al. model. The techniques used by DeVille et al. for finding the mean-field limit are not suitable for this new model. We explore early attempts at obtaining a new mean-field deterministic system that would give us an understanding of the behavior seen in the new model. After redefining the process we do find a mean-field deterministic system that the model limits on, and we investigate the behavior of the new model studying the mean-field system.","Submission published under a 24 month embargo labeled 'U of I only', the embargo will last until 2017-08-01","The student, Stephen Berning, accepted the attached license on 2015-07-15 at 01:11.","The student, Stephen Berning, submitted this Dissertation for approval on 2015-07-15 at 01:27.","This Dissertation was approved for publication on 2015-07-16 at 13:11.","DSpace SAF Submission Ingestion Package generated from Vireo submission #8443 on 2015-09-29 at 14:59:30","Made available in DSpace on 2015-09-29T20:49:56Z (GMT). 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