{"id":"https://openalex.org/W2076106811","doi":"https://doi.org/10.1016/0893-6080(91)90017-y","title":"On probabilistic invariance","display_name":"On probabilistic invariance","publication_year":1991,"publication_date":"1991-01-01","ids":{"openalex":"https://openalex.org/W2076106811","doi":"https://doi.org/10.1016/0893-6080(91)90017-y","mag":"2076106811"},"language":"en","primary_location":{"id":"doi:10.1016/0893-6080(91)90017-y","is_oa":false,"landing_page_url":"https://doi.org/10.1016/0893-6080(91)90017-y","pdf_url":null,"source":{"id":"https://openalex.org/S123019304","display_name":"Neural Networks","issn_l":"0893-6080","issn":["0893-6080","1879-2782"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neural Networks","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/A5005222066","display_name":"Reiner Lenz","orcid":"https://orcid.org/0000-0001-7557-4904"},"institutions":[{"id":"https://openalex.org/I102134673","display_name":"Link\u00f6ping University","ror":"https://ror.org/05ynxx418","country_code":"SE","type":"education","lineage":["https://openalex.org/I102134673"]}],"countries":["SE"],"is_corresponding":true,"raw_author_name":"Reiner Lenz","raw_affiliation_strings":["Link\u00f6ping University Sweden","Link\u00f6ping University, Sweden"],"affiliations":[{"raw_affiliation_string":"Link\u00f6ping University Sweden","institution_ids":["https://openalex.org/I102134673"]},{"raw_affiliation_string":"Link\u00f6ping University, Sweden","institution_ids":["https://openalex.org/I102134673"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5005222066"],"corresponding_institution_ids":["https://openalex.org/I102134673"],"apc_list":{"value":3350,"currency":"USD","value_usd":3350},"apc_paid":null,"fwci":1.0767,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.81728347,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"4","issue":"5","first_page":"627","last_page":"641"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9908999800682068,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T10320","display_name":"Neural Networks and Applications","score":0.9908999800682068,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T10824","display_name":"Image Retrieval and Classification Techniques","score":0.9616000056266785,"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/T11698","display_name":"Underwater Acoustics Research","score":0.9417999982833862,"subfield":{"id":"https://openalex.org/subfields/1910","display_name":"Oceanography"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/invariance-principle","display_name":"Invariance principle","score":0.6569581031799316},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6557763814926147},{"id":"https://openalex.org/keywords/filter","display_name":"Filter (signal processing)","score":0.5936592221260071},{"id":"https://openalex.org/keywords/rotational-invariance","display_name":"Rotational invariance","score":0.5740228891372681},{"id":"https://openalex.org/keywords/transformation","display_name":"Transformation (genetics)","score":0.5687241554260254},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.5420937538146973},{"id":"https://openalex.org/keywords/rotation","display_name":"Rotation (mathematics)","score":0.5227399468421936},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.4681779444217682},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.4634177088737488},{"id":"https://openalex.org/keywords/sketch","display_name":"Sketch","score":0.46204301714897156},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.367408812046051},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3474608063697815},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3349186182022095},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2583455443382263},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.19226166605949402},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.10207042098045349},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10064557194709778},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08240896463394165},{"id":"https://openalex.org/keywords/computer-vision","display_name":"Computer vision","score":0.07045572996139526}],"concepts":[{"id":"https://openalex.org/C156387681","wikidata":"https://www.wikidata.org/wiki/Q6059484","display_name":"Invariance principle","level":2,"score":0.6569581031799316},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6557763814926147},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.5936592221260071},{"id":"https://openalex.org/C33098168","wikidata":"https://www.wikidata.org/wiki/Q108537107","display_name":"Rotational invariance","level":2,"score":0.5740228891372681},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.5687241554260254},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.5420937538146973},{"id":"https://openalex.org/C74050887","wikidata":"https://www.wikidata.org/wiki/Q848368","display_name":"Rotation (mathematics)","level":2,"score":0.5227399468421936},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.4681779444217682},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.4634177088737488},{"id":"https://openalex.org/C2779231336","wikidata":"https://www.wikidata.org/wiki/Q7534724","display_name":"Sketch","level":2,"score":0.46204301714897156},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.367408812046051},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3474608063697815},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3349186182022095},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2583455443382263},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.19226166605949402},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.10207042098045349},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10064557194709778},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08240896463394165},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.07045572996139526},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/0893-6080(91)90017-y","is_oa":false,"landing_page_url":"https://doi.org/10.1016/0893-6080(91)90017-y","pdf_url":null,"source":{"id":"https://openalex.org/S123019304","display_name":"Neural Networks","issn_l":"0893-6080","issn":["0893-6080","1879-2782"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neural Networks","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W382810004","https://openalex.org/W1966781286","https://openalex.org/W1975721872","https://openalex.org/W1989648698","https://openalex.org/W2003600876","https://openalex.org/W2023963201","https://openalex.org/W2049686973","https://openalex.org/W2062570766","https://openalex.org/W2090563615","https://openalex.org/W2121761475","https://openalex.org/W3145013517","https://openalex.org/W4285719527","https://openalex.org/W6647810626","https://openalex.org/W6662899466","https://openalex.org/W6771707327"],"related_works":["https://openalex.org/W2378994405","https://openalex.org/W2385974820","https://openalex.org/W2373478030","https://openalex.org/W2378679551","https://openalex.org/W3149739944","https://openalex.org/W2392363776","https://openalex.org/W2063051341","https://openalex.org/W1494563618","https://openalex.org/W2357022711","https://openalex.org/W2024845998"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
