{"id":"https://openalex.org/W2068536004","doi":"https://doi.org/10.3934/nhm.2011.6.279","title":"Gaussian estimates on networks with applications to optimal control","display_name":"Gaussian estimates on networks with applications to optimal control","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W2068536004","doi":"https://doi.org/10.3934/nhm.2011.6.279","mag":"2068536004"},"language":"en","primary_location":{"id":"doi:10.3934/nhm.2011.6.279","is_oa":true,"landing_page_url":"https://doi.org/10.3934/nhm.2011.6.279","pdf_url":"https://www.aimsciences.org/data/article/export-pdf?id=b5463cd9-277d-49d5-804d-02f9a7a5687a","source":{"id":"https://openalex.org/S21752972","display_name":"Networks and Heterogeneous Media","issn_l":"1556-1801","issn":["1556-1801","1556-181X"],"is_oa":false,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks & Heterogeneous Media","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.aimsciences.org/data/article/export-pdf?id=b5463cd9-277d-49d5-804d-02f9a7a5687a","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5082110029","display_name":"Luca Di Persio","orcid":"https://orcid.org/0000-0002-0317-4351"},"institutions":[{"id":"https://openalex.org/I193223587","display_name":"University of Trento","ror":"https://ror.org/05trd4x28","country_code":"IT","type":"education","lineage":["https://openalex.org/I193223587"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Luca Di Persio","raw_affiliation_strings":["University of Trento"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Trento","institution_ids":["https://openalex.org/I193223587"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5004394878","display_name":"Giacomo Ziglio","orcid":"https://orcid.org/0009-0009-4791-5666"},"institutions":[{"id":"https://openalex.org/I193223587","display_name":"University of Trento","ror":"https://ror.org/05trd4x28","country_code":"IT","type":"education","lineage":["https://openalex.org/I193223587"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Giacomo Ziglio","raw_affiliation_strings":["Department of Mathematics University of Trento Povo (TN), 38123, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics University of Trento Povo (TN), 38123, Italy","institution_ids":["https://openalex.org/I193223587"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5082110029"],"corresponding_institution_ids":["https://openalex.org/I193223587"],"apc_list":null,"apc_paid":null,"fwci":0.6522,"has_fulltext":true,"cited_by_count":14,"citation_normalized_percentile":{"value":0.70537186,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"6","issue":"2","first_page":"279","last_page":"296"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.998199999332428,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.998199999332428,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.996999979019165,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13234","display_name":"advanced mathematical theories","score":0.9789000153541565,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.7432647943496704},{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.6993923783302307},{"id":"https://openalex.org/keywords/semigroup","display_name":"Semigroup","score":0.659623384475708},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5428812503814697},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.49871134757995605},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.48867014050483704},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.4530846178531647},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.4521619379520416},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.43525347113609314},{"id":"https://openalex.org/keywords/gaussian-random-field","display_name":"Gaussian random field","score":0.43060582876205444},{"id":"https://openalex.org/keywords/gaussian-process","display_name":"Gaussian process","score":0.3442382514476776},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3306729793548584},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.29165124893188477},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10911881923675537}],"concepts":[{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.7432647943496704},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.6993923783302307},{"id":"https://openalex.org/C207405024","wikidata":"https://www.wikidata.org/wiki/Q207348","display_name":"Semigroup","level":2,"score":0.659623384475708},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5428812503814697},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.49871134757995605},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.48867014050483704},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4530846178531647},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.4521619379520416},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.43525347113609314},{"id":"https://openalex.org/C51267290","wikidata":"https://www.wikidata.org/wiki/Q5527848","display_name":"Gaussian random field","level":4,"score":0.43060582876205444},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.3442382514476776},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3306729793548584},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.29165124893188477},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10911881923675537},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3934/nhm.2011.6.279","is_oa":true,"landing_page_url":"https://doi.org/10.3934/nhm.2011.6.279","pdf_url":"https://www.aimsciences.org/data/article/export-pdf?id=b5463cd9-277d-49d5-804d-02f9a7a5687a","source":{"id":"https://openalex.org/S21752972","display_name":"Networks and Heterogeneous Media","issn_l":"1556-1801","issn":["1556-1801","1556-181X"],"is_oa":false,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks & Heterogeneous Media","raw_type":"journal-article"},{"id":"pmh:oai:eprints.biblio.unitn.it:1793","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306400311","display_name":"Unitn Eprints Research (Universit\u00e0 Degli Studi di Trento)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I193223587","host_organization_name":"University of Trento","host_organization_lineage":["https://openalex.org/I193223587"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Departmental Technical Report"},{"id":"pmh:oai:doaj.org/article:4e07d1e303c542939703fd9106f5bde0","is_oa":false,"landing_page_url":"https://doaj.org/article/4e07d1e303c542939703fd9106f5bde0","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Networks and Heterogeneous Media, Vol 6, Iss 2, Pp 279-296 (2011)","raw_type":"article"},{"id":"pmh:oai:iris.unitn.it:11572/358383","is_oa":true,"landing_page_url":"https://hdl.handle.net/11572/358383","pdf_url":null,"source":{"id":"https://openalex.org/S4306401913","display_name":"Institutional Research Information System (Universit\u00e0 degli Studi di Trento)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I193223587","host_organization_name":"University of Trento","host_organization_lineage":["https://openalex.org/I193223587"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/other"}],"best_oa_location":{"id":"doi:10.3934/nhm.2011.6.279","is_oa":true,"landing_page_url":"https://doi.org/10.3934/nhm.2011.6.279","pdf_url":"https://www.aimsciences.org/data/article/export-pdf?id=b5463cd9-277d-49d5-804d-02f9a7a5687a","source":{"id":"https://openalex.org/S21752972","display_name":"Networks and Heterogeneous Media","issn_l":"1556-1801","issn":["1556-1801","1556-181X"],"is_oa":false,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks & Heterogeneous Media","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320326086","display_name":"Provincia Autonoma di Trento","ror":"https://ror.org/017e99q89"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2068536004.pdf","grobid_xml":"https://content.openalex.org/works/W2068536004.grobid-xml"},"referenced_works_count":36,"referenced_works":["https://openalex.org/W60166153","https://openalex.org/W1514849282","https://openalex.org/W1530927473","https://openalex.org/W1540614089","https://openalex.org/W1558902221","https://openalex.org/W1970530131","https://openalex.org/W1982820061","https://openalex.org/W1982852315","https://openalex.org/W2008518695","https://openalex.org/W2016070429","https://openalex.org/W2031050023","https://openalex.org/W2050294302","https://openalex.org/W2063225484","https://openalex.org/W2065161337","https://openalex.org/W2076851893","https://openalex.org/W2096057796","https://openalex.org/W2125420885","https://openalex.org/W2148621751","https://openalex.org/W2151875493","https://openalex.org/W2161290048","https://openalex.org/W2164094632","https://openalex.org/W2171586580","https://openalex.org/W2209557103","https://openalex.org/W2491647376","https://openalex.org/W2573279179","https://openalex.org/W2612743911","https://openalex.org/W2788847437","https://openalex.org/W2809513156","https://openalex.org/W3100238364","https://openalex.org/W3106131738","https://openalex.org/W4213388037","https://openalex.org/W4237997615","https://openalex.org/W6630607406","https://openalex.org/W6684365759","https://openalex.org/W6737361061","https://openalex.org/W6748304233"],"related_works":["https://openalex.org/W2033341479","https://openalex.org/W4389109202","https://openalex.org/W2054439726","https://openalex.org/W4298202464","https://openalex.org/W4312290701","https://openalex.org/W3134701830","https://openalex.org/W2072210242","https://openalex.org/W2774655044","https://openalex.org/W2168207680","https://openalex.org/W4385819757"],"abstract_inverted_index":{"We":[0,90],"study":[1],"a":[2,9,16,40],"class":[3],"of":[4,18,108],"reaction-diffusion":[5],"type":[6],"equations":[7,78],"on":[8,72,79],"finite":[10],"network":[11],"with":[12,81,87],"continuity":[13],"assumptions":[14],"and":[15],"kind":[17],"non-local,":[19],"stationary":[20],"Kirchhoff's":[21],"conditions":[22,84],"at":[23],"the":[24,33,47,51],"nodes.":[25],"A":[26],"multiplicative":[27],"random":[28],"Gaussian":[29,44,73],"perturbation":[30],"acting":[31],"along":[32],"edges":[34],"is":[35,67],"also":[36],"included.":[37],"For":[38],"such":[39],"problem":[41],"we":[42],"prove":[43],"estimates":[45],"for":[46,76],"semigroup":[48],"generated":[49],"by":[50,114],"evolution":[52],"operator,":[53],"hence":[54],"generalizing":[55],"similar":[56],"results":[57,71,95],"previously":[58],"obtained":[59],"in":[60,103],"[21].":[61],"In":[62],"particular":[63],"our":[64,94],"main":[65],"goal":[66],"to":[68,85,99,105],"extend":[69],"known":[70],"upper":[74],"bounds":[75],"heat":[77],"networks":[80],"local":[82],"boundary":[83],"those":[86],"non-local":[88],"ones.":[89],"conclude":[91],"showing":[92],"how":[93],"can":[96],"be":[97],"used":[98],"apply":[100],"techniques":[101],"developed":[102],"[13]":[104],"solve":[106],"aclass":[107],"Stochastic":[109],"Optimal":[110],"Control":[111],"Problems":[112],"inspired":[113],"neurological":[115],"dynamics.":[116]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}