{"id":"https://openalex.org/W3096013023","doi":"https://doi.org/10.1137/19m1303940","title":"Variance of Finite Difference Methods for Reaction Networks with Non-Lipschitz Rate Functions","display_name":"Variance of Finite Difference Methods for Reaction Networks with Non-Lipschitz Rate Functions","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3096013023","doi":"https://doi.org/10.1137/19m1303940","mag":"3096013023"},"language":"en","primary_location":{"id":"doi:10.1137/19m1303940","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1303940","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5003071783","display_name":"David F. Anderson","orcid":"https://orcid.org/0000-0002-2344-614X"},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"David F. Anderson","raw_affiliation_strings":["Department of Mathematics, University of Wisconsin, Madison, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Wisconsin, Madison, USA","institution_ids":["https://openalex.org/I135310074"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5029964378","display_name":"Chaojie Yuan","orcid":"https://orcid.org/0009-0002-3128-0642"},"institutions":[{"id":"https://openalex.org/I4210119109","display_name":"Indiana University Bloomington","ror":"https://ror.org/02k40bc56","country_code":"US","type":"education","lineage":["https://openalex.org/I4210119109","https://openalex.org/I592451"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Chaojie Yuan","raw_affiliation_strings":["Department of Mathematics, Indiana University Bloomington, Indiana, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Indiana University Bloomington, Indiana, USA","institution_ids":["https://openalex.org/I4210119109"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5003071783"],"corresponding_institution_ids":["https://openalex.org/I135310074"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.10338012,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"58","issue":"6","first_page":"3125","last_page":"3143"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10621","display_name":"Gene Regulatory Network Analysis","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T10621","display_name":"Gene Regulatory Network Analysis","score":0.9998999834060669,"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.995199978351593,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10848","display_name":"Advanced Multi-Objective Optimization Algorithms","score":0.9549000263214111,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.8858538866043091},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7196961641311646},{"id":"https://openalex.org/keywords/variance","display_name":"Variance (accounting)","score":0.6284178495407104},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.5678975582122803},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.5642297863960266},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5545552968978882},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.5468069314956665},{"id":"https://openalex.org/keywords/coupling","display_name":"Coupling (piping)","score":0.54557204246521},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.544277012348175},{"id":"https://openalex.org/keywords/finite-difference","display_name":"Finite difference","score":0.5384128093719482},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.46179676055908203},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.30122894048690796},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.27289530634880066},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.16317349672317505},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.15515708923339844}],"concepts":[{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.8858538866043091},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7196961641311646},{"id":"https://openalex.org/C196083921","wikidata":"https://www.wikidata.org/wiki/Q7915758","display_name":"Variance (accounting)","level":2,"score":0.6284178495407104},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.5678975582122803},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.5642297863960266},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5545552968978882},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.5468069314956665},{"id":"https://openalex.org/C131584629","wikidata":"https://www.wikidata.org/wiki/Q4308705","display_name":"Coupling (piping)","level":2,"score":0.54557204246521},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.544277012348175},{"id":"https://openalex.org/C181330731","wikidata":"https://www.wikidata.org/wiki/Q2068418","display_name":"Finite difference","level":2,"score":0.5384128093719482},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.46179676055908203},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.30122894048690796},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.27289530634880066},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.16317349672317505},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.15515708923339844},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C121955636","wikidata":"https://www.wikidata.org/wiki/Q4116214","display_name":"Accounting","level":1,"score":0.0},{"id":"https://openalex.org/C144133560","wikidata":"https://www.wikidata.org/wiki/Q4830453","display_name":"Business","level":0,"score":0.0},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/19m1303940","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1303940","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6307437511","display_name":null,"funder_award_id":"W911NF-18-1-0324","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G7452299184","display_name":null,"funder_award_id":"W911NF","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G8998121839","display_name":null,"funder_award_id":"911NF","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"}],"funders":[{"id":"https://openalex.org/F4320338281","display_name":"Army Research Office","ror":"https://ror.org/05epdh915"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W1982566313","https://openalex.org/W2011963508","https://openalex.org/W2027101131","https://openalex.org/W2034895724","https://openalex.org/W2042321087","https://openalex.org/W2043422021","https://openalex.org/W2047149512","https://openalex.org/W2059053384","https://openalex.org/W2067210175","https://openalex.org/W2080739873","https://openalex.org/W2092309107","https://openalex.org/W2125744693","https://openalex.org/W2139629468","https://openalex.org/W2141688036","https://openalex.org/W2156541178","https://openalex.org/W2168403922","https://openalex.org/W2171280873","https://openalex.org/W2740757730","https://openalex.org/W2963114865","https://openalex.org/W2963502558","https://openalex.org/W2963525067","https://openalex.org/W3104465214"],"related_works":["https://openalex.org/W3185235544","https://openalex.org/W2897842840","https://openalex.org/W2911623553","https://openalex.org/W4297791327","https://openalex.org/W2397777611","https://openalex.org/W1502031429","https://openalex.org/W3122602933","https://openalex.org/W2950038056","https://openalex.org/W1544940847","https://openalex.org/W2289285490"],"abstract_inverted_index":{"Parametric":[0],"sensitivity":[1],"analysis":[2,28,78,186],"is":[3,122],"a":[4,126,146,176,205],"critical":[5],"component":[6],"in":[7,29,61,109,133,171,192,218],"the":[8,30,49,54,58,62,80,83,87,104,118,130,134,164,167,172,185,193,212,219,222],"study":[9,31],"of":[10,13,32,65,79,82,89,103,129,150,166,179,207,215,224],"mathematical":[11],"models":[12,131,208],"physical":[14],"systems.":[15],"Due":[16],"to":[17,43,70,125,159,187],"its":[18],"simplicity,":[19],"finite":[20,45],"difference":[21,46],"methods":[22,39],"are":[23,73],"used":[24],"extensively":[25],"for":[26,145,175,189,211],"this":[27,71,153,157],"stochastically":[33],"modeled":[34],"reaction":[35],"networks.":[36],"Different":[37],"coupling":[38,72],"have":[40],"been":[41],"proposed":[42],"build":[44],"estimators,":[47],"with":[48,199],"\u201csplit":[50],"coupling,\u201d":[51,56],"also":[52],"termed":[53],"\u201cstacked":[55],"yielding":[57],"lowest":[59],"variance":[60,81,165],"vast":[63,213],"majority":[64,214],"cases.":[66],"Analytical":[67],"results":[68,142],"related":[69],"sparse":[74],"and":[75,136],"include":[76],"an":[77],"coupled":[84,168],"processes":[85,169],"under":[86],"assumption":[88,107],"globally":[90],"Lipschitz":[91,106],"intensity":[92],"functions":[93],"[SIAM":[94,110],"J.":[95,111],"Numer.":[96,112],"Anal.,":[97,113],"50":[98,114],"(2012),":[99,115],"pp.":[100,116],"2237--2258].":[101],"Because":[102],"global":[105],"utilized":[108],"2237--2258],":[117],"main":[119],"result":[120],"there":[121],"only":[123],"applicable":[124],"small":[127],"percentage":[128],"found":[132],"literature,":[135,220],"it":[137],"was":[138],"conjectured":[139],"that":[140,209],"similar":[141],"should":[143],"hold":[144],"much":[147],"wider":[148],"class":[149,178,206],"models.":[151,181],"In":[152,195],"paper":[154],"we":[155],"demonstrate":[156],"conjecture":[158],"be":[160],"true":[161],"by":[162],"proving":[163],"scales":[170],"desired":[173],"manner":[174],"large":[177],"non-Lipschitz":[180],"We":[182],"further":[183],"extend":[184],"allow":[188],"time":[190],"dependence":[191],"parameters.":[194],"particular,":[196],"binary":[197],"systems":[198,216],"or":[200],"without":[201],"time-dependent":[202],"rate":[203],"parameters,":[204],"accounts":[210],"considered":[217],"satisfy":[221],"assumptions":[223],"our":[225],"theory.":[226]},"counts_by_year":[],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}