{"id":"https://openalex.org/W2972448471","doi":"https://doi.org/10.1137/18m1220030","title":"Propagation of Spiking Moments in Linear Hawkes Networks","display_name":"Propagation of Spiking Moments in Linear Hawkes Networks","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W2972448471","doi":"https://doi.org/10.1137/18m1220030","mag":"2972448471"},"language":"en","primary_location":{"id":"doi:10.1137/18m1220030","is_oa":true,"landing_page_url":"https://doi.org/10.1137/18m1220030","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/18M1220030","source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Dynamical Systems","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://epubs.siam.org/doi/pdf/10.1137/18M1220030","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5091205167","display_name":"Matthieu Gilson","orcid":"https://orcid.org/0000-0002-6726-7207"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Matthieu Gilson","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-6726-7207","affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5061157913","display_name":"Jean-Pascal Pfister","orcid":"https://orcid.org/0000-0002-1847-3389"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jean-Pascal Pfister","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00345524,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"19","issue":"2","first_page":"828","last_page":"859"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10581","display_name":"Neural dynamics and brain function","score":0.998199999332428,"subfield":{"id":"https://openalex.org/subfields/2805","display_name":"Cognitive Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},"topics":[{"id":"https://openalex.org/T10581","display_name":"Neural dynamics and brain function","score":0.998199999332428,"subfield":{"id":"https://openalex.org/subfields/2805","display_name":"Cognitive Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T13187","display_name":"Diffusion and Search Dynamics","score":0.9975000023841858,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T10077","display_name":"Neuroscience and Neuropharmacology Research","score":0.9866999983787537,"subfield":{"id":"https://openalex.org/subfields/2804","display_name":"Cellular and Molecular Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/cumulant","display_name":"Cumulant","score":0.7913603782653809},{"id":"https://openalex.org/keywords/point-process","display_name":"Point process","score":0.609958291053772},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5368839502334595},{"id":"https://openalex.org/keywords/intuition","display_name":"Intuition","score":0.5220482349395752},{"id":"https://openalex.org/keywords/refractory-period","display_name":"Refractory period","score":0.5195489525794983},{"id":"https://openalex.org/keywords/spike","display_name":"Spike (software development)","score":0.5161277055740356},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.44862252473831177},{"id":"https://openalex.org/keywords/spike-train","display_name":"Spike train","score":0.4268413484096527},{"id":"https://openalex.org/keywords/biological-neuron-model","display_name":"Biological neuron model","score":0.4134683609008789},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.35232430696487427},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.20420163869857788},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1716127097606659},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1610480546951294},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.09852990508079529}],"concepts":[{"id":"https://openalex.org/C172686274","wikidata":"https://www.wikidata.org/wiki/Q746007","display_name":"Cumulant","level":2,"score":0.7913603782653809},{"id":"https://openalex.org/C88871306","wikidata":"https://www.wikidata.org/wiki/Q7208287","display_name":"Point process","level":2,"score":0.609958291053772},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5368839502334595},{"id":"https://openalex.org/C132010649","wikidata":"https://www.wikidata.org/wiki/Q189222","display_name":"Intuition","level":2,"score":0.5220482349395752},{"id":"https://openalex.org/C70616116","wikidata":"https://www.wikidata.org/wiki/Q1736732","display_name":"Refractory period","level":2,"score":0.5195489525794983},{"id":"https://openalex.org/C2781390188","wikidata":"https://www.wikidata.org/wiki/Q25203449","display_name":"Spike (software development)","level":2,"score":0.5161277055740356},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.44862252473831177},{"id":"https://openalex.org/C2909946758","wikidata":"https://www.wikidata.org/wiki/Q194277","display_name":"Spike train","level":3,"score":0.4268413484096527},{"id":"https://openalex.org/C186565885","wikidata":"https://www.wikidata.org/wiki/Q1651163","display_name":"Biological neuron model","level":3,"score":0.4134683609008789},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.35232430696487427},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.20420163869857788},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1716127097606659},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1610480546951294},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.09852990508079529},{"id":"https://openalex.org/C115903868","wikidata":"https://www.wikidata.org/wiki/Q80993","display_name":"Software engineering","level":1,"score":0.0},{"id":"https://openalex.org/C164705383","wikidata":"https://www.wikidata.org/wiki/Q10379","display_name":"Cardiology","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":9,"locations":[{"id":"doi:10.1137/18m1220030","is_oa":true,"landing_page_url":"https://doi.org/10.1137/18m1220030","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/18M1220030","source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Dynamical Systems","raw_type":"journal-article"},{"id":"pmh:oai:repositori-api.upf.edu:10230/46072","is_oa":true,"landing_page_url":"http://hdl.handle.net/10230/46072","pdf_url":null,"source":{"id":"https://openalex.org/S4306402615","display_name":"Repositori digital de la UPF (Universitat Pompeu Fabra)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I170486558","host_organization_name":"Universitat Pompeu Fabra","host_organization_lineage":["https://openalex.org/I170486558"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:arXiv.org:1810.09520","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1810.09520","pdf_url":"https://arxiv.org/pdf/1810.09520","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"mag:2972448471","is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/1810.09520","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:boris.unibe.ch:148868","is_oa":true,"landing_page_url":"https://boris.unibe.ch/148868/","pdf_url":null,"source":{"id":"https://openalex.org/S4306401086","display_name":"Bern Open Repository and Information System (University of Bern)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I118564535","host_organization_name":"University of Bern","host_organization_lineage":["https://openalex.org/I118564535"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Gilson, Matthieu; Pfister, Jean-Pascal (2020). Propagation of Spiking Moments in Linear Hawkes Networks. SIAM journal on applied dynamical systems, 19(2), pp. 828-859. Society for Industrial and Applied Mathematics 10.1137/18M1220030 <http://dx.doi.org/10.1137/18M1220030>","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:www.research-collection.ethz.ch:20.500.11850/426912","is_oa":true,"landing_page_url":"http://hdl.handle.net/20.500.11850/426912","pdf_url":null,"source":{"id":"https://openalex.org/S4306402302","display_name":"Repository for Publications and Research Data (ETH Zurich)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I35440088","host_organization_name":"ETH Zurich","host_organization_lineage":["https://openalex.org/I35440088"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Applied Dynamical Systems, 19 (2)","raw_type":"info:eu-repo/semantics/article"},{"id":"doi:10.48550/arxiv.1810.09520","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1810.09520","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.3929/ethz-b-000426912","is_oa":true,"landing_page_url":"https://doi.org/10.3929/ethz-b-000426912","pdf_url":null,"source":{"id":"https://openalex.org/S7407051236","display_name":"ETH Z\u00fcrich Research Collection","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"},{"id":"doi:10.7892/boris.148868","is_oa":true,"landing_page_url":"https://doi.org/10.7892/boris.148868","pdf_url":null,"source":{"id":"https://openalex.org/S7407053152","display_name":"Open Access CRIS of the University of Bern","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"JournalArticle"}],"best_oa_location":{"id":"doi:10.1137/18m1220030","is_oa":true,"landing_page_url":"https://doi.org/10.1137/18m1220030","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/18M1220030","source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Dynamical Systems","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1918095058","display_name":null,"funder_award_id":"HBP SGA2","funder_id":"https://openalex.org/F4320332999","funder_display_name":"Horizon 2020 Framework Programme"},{"id":"https://openalex.org/G2400705044","display_name":"Biological neural networks: from structure to function","funder_award_id":"656547","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G3345895242","display_name":null,"funder_award_id":"H2020-MSCA","funder_id":"https://openalex.org/F4320332999","funder_display_name":"Horizon 2020 Framework Programme"},{"id":"https://openalex.org/G4956004573","display_name":"Inference and Learning with Spiking Neurons","funder_award_id":"150637","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G5106620330","display_name":"Filtering with Spiking Neurons","funder_award_id":"179060","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G5394833745","display_name":null,"funder_award_id":"HBP-SGA2-785907","funder_id":"https://openalex.org/F4320338337","funder_display_name":"H2020 Marie Sk\u0142odowska-Curie Actions"},{"id":"https://openalex.org/G5766349579","display_name":"Human Brain Project Specific Grant Agreement 2","funder_award_id":"785907","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G6607577419","display_name":null,"funder_award_id":"785907","funder_id":"https://openalex.org/F4320332999","funder_display_name":"Horizon 2020 Framework Programme"},{"id":"https://openalex.org/G6754083667","display_name":null,"funder_award_id":"785907","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8512683158","display_name":null,"funder_award_id":"H2020-MSCA","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G8542562305","display_name":null,"funder_award_id":"H2020-MSCA-656547","funder_id":"https://openalex.org/F4320338337","funder_display_name":"H2020 Marie Sk\u0142odowska-Curie Actions"},{"id":"https://openalex.org/G8681506169","display_name":null,"funder_award_id":"HBP SGA2","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320320924","display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung","ror":"https://ror.org/00yjd3n13"},{"id":"https://openalex.org/F4320332999","display_name":"Horizon 2020 Framework Programme","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320338337","display_name":"H2020 Marie Sk\u0142odowska-Curie Actions","ror":null}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W2972448471.pdf"},"referenced_works_count":54,"referenced_works":["https://openalex.org/W138372711","https://openalex.org/W1539015357","https://openalex.org/W1542782021","https://openalex.org/W1594866779","https://openalex.org/W1825637327","https://openalex.org/W1975412204","https://openalex.org/W1984866500","https://openalex.org/W1985440329","https://openalex.org/W1991333841","https://openalex.org/W1993868308","https://openalex.org/W1999535357","https://openalex.org/W1999735946","https://openalex.org/W2001856534","https://openalex.org/W2005073618","https://openalex.org/W2023312327","https://openalex.org/W2043679829","https://openalex.org/W2046350206","https://openalex.org/W2048756013","https://openalex.org/W2052197092","https://openalex.org/W2069519142","https://openalex.org/W2069849731","https://openalex.org/W2078428825","https://openalex.org/W2083659237","https://openalex.org/W2086284736","https://openalex.org/W2089442458","https://openalex.org/W2090212329","https://openalex.org/W2090654022","https://openalex.org/W2106529987","https://openalex.org/W2123820663","https://openalex.org/W2130670899","https://openalex.org/W2141073948","https://openalex.org/W2268656019","https://openalex.org/W2291069302","https://openalex.org/W2323548107","https://openalex.org/W2566356335","https://openalex.org/W2620499422","https://openalex.org/W2738586679","https://openalex.org/W2754514363","https://openalex.org/W2775993691","https://openalex.org/W2788223163","https://openalex.org/W2887070693","https://openalex.org/W2953000845","https://openalex.org/W2962817261","https://openalex.org/W2963051810","https://openalex.org/W2963445010","https://openalex.org/W2963702580","https://openalex.org/W2964026625","https://openalex.org/W2964255676","https://openalex.org/W2964294938","https://openalex.org/W3037972180","https://openalex.org/W3101772483","https://openalex.org/W3121146574","https://openalex.org/W3121182462","https://openalex.org/W3123773610"],"related_works":["https://openalex.org/W2896065021","https://openalex.org/W3128149065","https://openalex.org/W1571545895","https://openalex.org/W2952299971","https://openalex.org/W2050840442","https://openalex.org/W2730863700","https://openalex.org/W2048884755","https://openalex.org/W2971820792","https://openalex.org/W2792690674","https://openalex.org/W3004660996","https://openalex.org/W2346016147","https://openalex.org/W2138433895","https://openalex.org/W956142784","https://openalex.org/W2589632792","https://openalex.org/W2036330324","https://openalex.org/W2062037720","https://openalex.org/W1980773744","https://openalex.org/W2897515426","https://openalex.org/W2120584521","https://openalex.org/W2003264344"],"abstract_inverted_index":{"The":[0],"present":[1],"paper":[2],"provides":[3,88],"exact":[4],"mathematical":[5],"expressions":[6],"for":[7,99,115,127],"the":[8,30,43,63,68,82,92,96,123],"high-order":[9],"moments":[10],"of":[11,19,32,45],"spiking":[12],"activity":[13],"in":[14],"a":[15,33,46],"recurrently":[16],"connected":[17],"network":[18,36,93],"linear":[20],"Hawkes":[21,35],"processes.":[22],"It":[23],"extends":[24],"previous":[25],"studies":[26],"that":[27,111],"have":[28],"explored":[29],"case":[31,44],"(linear)":[34],"driven":[37],"by":[38,48,67,120],"deterministic":[39],"intensity":[40],"functions":[41,52],"to":[42],"stimulation":[47],"external":[49],"inputs":[50],"(rate":[51],"or":[53],"spike":[54],"trains)":[55],"with":[56,117],"arbitrary":[57,74],"correlation":[58],"structure.":[59],"Our":[60],"approach":[61],"describes":[62],"spatio-temporal":[64],"filtering":[65],"induced":[66],"afferent":[69],"and":[70],"recurrent":[71],"connectivities":[72],"(with":[73],"synaptic":[75],"response":[76],"kernels)":[77],"using":[78,108],"operators":[79],"acting":[80],"on":[81],"input":[83],"moments.":[84],"This":[85],"algebraic":[86],"viewpoint":[87],"intuition":[89],"about":[90],"how":[91],"ingredients":[94],"shape":[95],"input-output":[97],"mapping":[98],"moments,":[100],"as":[101,103],"well":[102],"cumulants.":[104],"We":[105],"also":[106],"show":[107],"numerical":[109],"simulation":[110],"our":[112],"results":[113],"hold":[114],"neurons":[116],"refractoriness":[118],"implemented":[119],"self-inhibition,":[121],"provided":[122],"corresponding":[124],"negative":[125],"feedback":[126],"each":[128],"neuron":[129],"only":[130],"mildly":[131],"alters":[132],"its":[133],"mean":[134],"firing":[135],"probability.":[136]},"counts_by_year":[],"updated_date":"2026-08-06T08:24:18.245995","created_date":"2025-10-10T00:00:00"}