{"id":"https://openalex.org/W2048980698","doi":"https://doi.org/10.1109/tsmc.1973.4309215","title":"Measurement-Free Tests of Linearity in Biological Systems","display_name":"Measurement-Free Tests of Linearity in Biological Systems","publication_year":1973,"publication_date":"1973-05-01","ids":{"openalex":"https://openalex.org/W2048980698","doi":"https://doi.org/10.1109/tsmc.1973.4309215","mag":"2048980698"},"language":"en","primary_location":{"id":"doi:10.1109/tsmc.1973.4309215","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsmc.1973.4309215","pdf_url":null,"source":{"id":"https://openalex.org/S76152103","display_name":"IEEE Transactions on Systems Man and Cybernetics","issn_l":"0018-9472","issn":["0018-9472","2168-2909"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Systems, Man, and Cybernetics","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/A5016821325","display_name":"David H. Krantz","orcid":"https://orcid.org/0000-0001-6062-6628"},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan\u2013Ann Arbor","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"David H. Krantz","raw_affiliation_strings":["University of Michigan, Ann Arbor, MI, USA"],"affiliations":[{"raw_affiliation_string":"University of Michigan, Ann Arbor, MI, USA","institution_ids":["https://openalex.org/I27837315"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5016821325"],"corresponding_institution_ids":["https://openalex.org/I27837315"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.27660655,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"SMC-3","issue":"3","first_page":"266","last_page":"271"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10876","display_name":"Fault Detection and Control Systems","score":0.9631999731063843,"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"}},"topics":[{"id":"https://openalex.org/T10876","display_name":"Fault Detection and Control Systems","score":0.9631999731063843,"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/T11236","display_name":"Control Systems and Identification","score":0.9453999996185303,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/distortion","display_name":"Distortion (music)","score":0.6957857608795166},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6852184534072876},{"id":"https://openalex.org/keywords/linearity","display_name":"Linearity","score":0.6789045333862305},{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.5474924445152283},{"id":"https://openalex.org/keywords/superposition-principle","display_name":"Superposition principle","score":0.5326069593429565},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5018870830535889},{"id":"https://openalex.org/keywords/convolution","display_name":"Convolution (computer science)","score":0.4649193584918976},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.4555370807647705},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.4453250467777252},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.388694167137146},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.35423803329467773},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3523408770561218},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.20683428645133972},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.08767929673194885},{"id":"https://openalex.org/keywords/electronic-engineering","display_name":"Electronic engineering","score":0.06826663017272949}],"concepts":[{"id":"https://openalex.org/C126780896","wikidata":"https://www.wikidata.org/wiki/Q899871","display_name":"Distortion (music)","level":4,"score":0.6957857608795166},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6852184534072876},{"id":"https://openalex.org/C77170095","wikidata":"https://www.wikidata.org/wiki/Q1753188","display_name":"Linearity","level":2,"score":0.6789045333862305},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.5474924445152283},{"id":"https://openalex.org/C27753989","wikidata":"https://www.wikidata.org/wiki/Q284885","display_name":"Superposition principle","level":2,"score":0.5326069593429565},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5018870830535889},{"id":"https://openalex.org/C45347329","wikidata":"https://www.wikidata.org/wiki/Q5166604","display_name":"Convolution (computer science)","level":3,"score":0.4649193584918976},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.4555370807647705},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.4453250467777252},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.388694167137146},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.35423803329467773},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3523408770561218},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.20683428645133972},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.08767929673194885},{"id":"https://openalex.org/C24326235","wikidata":"https://www.wikidata.org/wiki/Q126095","display_name":"Electronic engineering","level":1,"score":0.06826663017272949},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C2776257435","wikidata":"https://www.wikidata.org/wiki/Q1576430","display_name":"Bandwidth (computing)","level":2,"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/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","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},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C194257627","wikidata":"https://www.wikidata.org/wiki/Q211554","display_name":"Amplifier","level":3,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tsmc.1973.4309215","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsmc.1973.4309215","pdf_url":null,"source":{"id":"https://openalex.org/S76152103","display_name":"IEEE Transactions on Systems Man and Cybernetics","issn_l":"0018-9472","issn":["0018-9472","2168-2909"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Systems, Man, and Cybernetics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":3,"referenced_works":["https://openalex.org/W2105114716","https://openalex.org/W2328099513","https://openalex.org/W2344433746"],"related_works":["https://openalex.org/W4308749380","https://openalex.org/W2037841693","https://openalex.org/W2372481764","https://openalex.org/W2610947892","https://openalex.org/W1977264433","https://openalex.org/W2746368218","https://openalex.org/W4308448008","https://openalex.org/W2170853726","https://openalex.org/W1486810997","https://openalex.org/W4205536354"],"abstract_inverted_index":{"It":[0,69],"is":[1,24,33,70,131,138],"desirable":[2],"to":[3,97,115],"test":[4,56,130,154],"the":[5,28,35,60,64,98,106,111,116,125,143,148,152],"linearity":[6],"of":[7,13,27,59,75,88,105,118],"a":[8,25,73,163],"system":[9,36,149],"without":[10],"interval-scale":[11],"measurement":[12],"its":[14],"input":[15,46,61,65,80,89],"and":[16,48,66],"output.":[17],"Four":[18],"tests":[19],"are":[20,92],"proposed.":[21],"The":[22,54,128],"first":[23,144],"generalization":[26],"superposition":[29,112],"principle.":[30],"If":[31],"it":[32,109,137,158],"satisfied,":[34,139],"can":[37,159],"be":[38,160],"regarded":[39],"as":[40,140,142,162],"an":[41,77],"integral":[42,99],"operator,":[43],"with":[44,95,134],"variable":[45,49,79],"distortion":[47,62,81],"but":[50],"monotonic":[51],"output":[52,67,107,126],"distortion.":[53],"second":[55],"concerns":[57,103],"invariance":[58,104],"over":[63],"domains.":[68],"based":[71],"on":[72],"method":[74],"reconstructing":[76],"unknown":[78],"by":[82],"constructing":[83],"standard":[84],"sequences":[85,87],"(i.e.,":[86],"values":[90],"that":[91],"equally":[93],"spaced":[94],"respect":[96],"operator).":[100],"Test":[101],"three":[102],"distortion;":[108],"generalizes":[110],"principle":[113],"further,":[114],"case":[117],"comparing":[119],"outputs":[120],"across":[121],"different":[122],"points":[123],"in":[124,156],"domain.":[127],"fourth":[129],"simply":[132],"commutativity":[133],"translations;":[135],"if":[136],"well":[141],"two":[145],"tests,":[146],"then":[147],"also":[150],"satisfies":[151],"third":[153],"and,":[155],"addition,":[157],"written":[161],"convolution":[164],"integral.":[165]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}