{"id":"https://openalex.org/W1970482569","doi":"https://doi.org/10.1137/090768102","title":"P-Splines Using Derivative Information","display_name":"P-Splines Using Derivative Information","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W1970482569","doi":"https://doi.org/10.1137/090768102","mag":"1970482569","pmid":"https://pubmed.ncbi.nlm.nih.gov/21691592"},"language":"en","primary_location":{"id":"doi:10.1137/090768102","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090768102","pdf_url":null,"source":{"id":"https://openalex.org/S4357572","display_name":"Multiscale Modeling and Simulation","issn_l":"1540-3459","issn":["1540-3459","1540-3467"],"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":"Multiscale Modeling & Simulation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/3117255","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5048551115","display_name":"Christopher P. Calderon","orcid":"https://orcid.org/0000-0001-8024-9081"},"institutions":[{"id":"https://openalex.org/I74775410","display_name":"Rice University","ror":"https://ror.org/008zs3103","country_code":"US","type":"education","lineage":["https://openalex.org/I74775410"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Christopher P. Calderon","raw_affiliation_strings":["Department of Computational and Applied Mathematics, Rice University, Houston, TX 77005"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computational and Applied Mathematics, Rice University, Houston, TX 77005","institution_ids":["https://openalex.org/I74775410"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008253161","display_name":"Josue G. Martinez","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Josue G. Martinez","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5000822072","display_name":"Raymond J. Carroll","orcid":"https://orcid.org/0000-0002-5465-9682"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Raymond J. Carroll","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5109874470","display_name":"Danny C. Sorensen","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Danny C. Sorensen","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.3153,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.85962039,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"8","issue":"4","first_page":"1562","last_page":"1580"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13487","display_name":"Statistical and numerical algorithms","score":0.9947999715805054,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T13487","display_name":"Statistical and numerical algorithms","score":0.9947999715805054,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9915000200271606,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9868999719619751,"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/derivative","display_name":"Derivative (finance)","score":0.5390064716339111},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5333248376846313},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4468306005001068},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4272543787956238},{"id":"https://openalex.org/keywords/business","display_name":"Business","score":0.11176624894142151}],"concepts":[{"id":"https://openalex.org/C111771559","wikidata":"https://www.wikidata.org/wiki/Q66295","display_name":"Derivative (finance)","level":2,"score":0.5390064716339111},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5333248376846313},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4468306005001068},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4272543787956238},{"id":"https://openalex.org/C144133560","wikidata":"https://www.wikidata.org/wiki/Q4830453","display_name":"Business","level":0,"score":0.11176624894142151},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/090768102","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090768102","pdf_url":null,"source":{"id":"https://openalex.org/S4357572","display_name":"Multiscale Modeling and Simulation","issn_l":"1540-3459","issn":["1540-3459","1540-3467"],"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":"Multiscale Modeling & Simulation","raw_type":"journal-article"},{"id":"pmid:21691592","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/21691592","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Multiscale modeling & simulation : a SIAM interdisciplinary journal","raw_type":null},{"id":"pmh:oai:pubmedcentral.nih.gov:3117255","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/3117255","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Multiscale Model Simul","raw_type":"Text"},{"id":"pmh:oai:repository.kaust.edu.sa:10754/599129","is_oa":false,"landing_page_url":"http://hdl.handle.net/10754/599129","pdf_url":null,"source":{"id":"https://openalex.org/S4306401596","display_name":"King Abdullah University of Science and Technology Repository (King Abdullah University of Science and Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I71920554","host_organization_name":"King Abdullah University of Science and Technology","host_organization_lineage":["https://openalex.org/I71920554"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:scholarship.rice.edu:1911/102118","is_oa":false,"landing_page_url":"http://hdl.handle.net/1911/102118","pdf_url":null,"source":{"id":"https://openalex.org/S4306401268","display_name":"Rice Digital Scholarship Archive (Rice University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I74775410","host_organization_name":"Rice University","host_organization_lineage":["https://openalex.org/I74775410"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Technical report"}],"best_oa_location":{"id":"pmh:oai:pubmedcentral.nih.gov:3117255","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/3117255","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Multiscale Model Simul","raw_type":"Text"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/14","score":0.6200000047683716,"display_name":"Life below water"}],"awards":[{"id":"https://openalex.org/G2700991700","display_name":null,"funder_award_id":"(R37-CA057030)","funder_id":"https://openalex.org/F4320337351","funder_display_name":"National Cancer Institute"},{"id":"https://openalex.org/G3097535683","display_name":null,"funder_award_id":"R25 CA090301","funder_id":"https://openalex.org/F4320337351","funder_display_name":"National Cancer Institute"},{"id":"https://openalex.org/G4692642738","display_name":null,"funder_award_id":"T32CA090301","funder_id":"https://openalex.org/F4320337351","funder_display_name":"National Cancer Institute"},{"id":"https://openalex.org/G5234310444","display_name":null,"funder_award_id":"R01 CA057030","funder_id":"https://openalex.org/F4320337351","funder_display_name":"National Cancer Institute"},{"id":"https://openalex.org/G931198179","display_name":null,"funder_award_id":"T90 DK070121","funder_id":"https://openalex.org/F4320337357","funder_display_name":"National Institute of Diabetes and Digestive and Kidney Diseases"}],"funders":[{"id":"https://openalex.org/F4320315254","display_name":"Innovative Research Group Project of the National Natural Science Foundation of China","ror":null},{"id":"https://openalex.org/F4320337351","display_name":"National Cancer Institute","ror":"https://ror.org/040gcmg81"},{"id":"https://openalex.org/F4320337357","display_name":"National Institute of Diabetes and Digestive and Kidney Diseases","ror":"https://ror.org/00adh9b73"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W212854950","https://openalex.org/W564402824","https://openalex.org/W1607200676","https://openalex.org/W1661010298","https://openalex.org/W1970790735","https://openalex.org/W1972974306","https://openalex.org/W1975729486","https://openalex.org/W1982141499","https://openalex.org/W1986156047","https://openalex.org/W1989412209","https://openalex.org/W1990420052","https://openalex.org/W2002026218","https://openalex.org/W2003165787","https://openalex.org/W2019005118","https://openalex.org/W2021651754","https://openalex.org/W2027099938","https://openalex.org/W2027106381","https://openalex.org/W2029667189","https://openalex.org/W2035465993","https://openalex.org/W2039005632","https://openalex.org/W2049813208","https://openalex.org/W2054103452","https://openalex.org/W2068049270","https://openalex.org/W2070808678","https://openalex.org/W2081407528","https://openalex.org/W2081540648","https://openalex.org/W2085571455","https://openalex.org/W2102172821","https://openalex.org/W2105614327","https://openalex.org/W2121807492","https://openalex.org/W2136106655","https://openalex.org/W2150981663","https://openalex.org/W2153675946","https://openalex.org/W2154257821","https://openalex.org/W2162870748","https://openalex.org/W2798909945","https://openalex.org/W3021971632","https://openalex.org/W3098846354"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644"],"abstract_inverted_index":{"Time":[0],"series":[1],"associated":[2,42,65],"with":[3,43,66,149],"single-molecule":[4,99],"experiments":[5],"and/or":[6],"simulations":[7],"contain":[8],"a":[9,21,55,77,91,98],"wealth":[10],"of":[11,23],"multiscale":[12],"information":[13,110],"about":[14],"complex":[15],"biomolecular":[16],"systems.":[17],"We":[18,115],"demonstrate":[19],"how":[20,51,131,144],"collection":[22],"Penalized-splines":[24],"(P-splines)":[25],"can":[26],"be":[27],"useful":[28],"in":[29,54,83,88,165],"quantitatively":[30],"summarizing":[31],"such":[32],"data.":[33],"In":[34],"this":[35],"work,":[36],"functions":[37],"estimated":[38,53],"using":[39,124],"P-splines":[40,81,102],"are":[41,157,183],"stochastic":[44],"differential":[45],"equations":[46],"(SDEs).":[47],"It":[48,128],"is":[49,95,129,164,172],"shown":[50,130],"quantities":[52],"single":[56],"SDE":[57],"summarize":[58],"fast-scale":[59],"phenomena,":[60],"whereas":[61],"variation":[62],"between":[63],"curves":[64],"different":[67],"SDEs":[68,87],"partially":[69],"reflects":[70],"noise":[71],"induced":[72],"by":[73],"motion":[74],"evolving":[75],"on":[76],"slower":[78],"time":[79],"scale.":[80],"assist":[82],"\"semiparametrically\"":[84],"estimating":[85,166],"nonlinear":[86,167],"situations":[89,175],"where":[90,176],"time-dependent":[92],"external":[93],"force":[94],"applied":[96],"to":[97,111,117,174],"system.":[100],"The":[101],"introduced":[103],"simultaneously":[104],"use":[105],"function":[106,179],"and":[107,180],"derivative":[108,181],"scatterplot":[109],"refine":[112],"curve":[113],"estimates.":[114],"refer":[116],"the":[118,121,139,160,169],"approach":[119],"as":[120],"PuDI":[122,140,155,170],"(P-splines":[123],"Derivative":[125],"Information)":[126],"method.":[127,141],"generalized":[132,150],"least":[133,151],"squares":[134,152],"ideas":[135],"fit":[136],"seamlessly":[137],"into":[138],"Applications":[142],"demonstrating":[143],"utilizing":[145],"uncertainty":[146],"information/approximations":[147],"along":[148],"techniques":[153],"improve":[154],"fits":[156],"presented.":[158],"Although":[159],"primary":[161],"application":[162],"here":[163],"SDEs,":[168],"method":[171],"applicable":[173],"both":[177],"unbiased":[178],"estimates":[182],"available.":[184]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2026-08-01T09:00:35.917206","created_date":"2025-10-10T00:00:00"}