{"id":"https://openalex.org/W2946155099","doi":"https://doi.org/10.3390/e25121637","title":"Arrow Contraction and Expansion in Tropical Diagrams","display_name":"Arrow Contraction and Expansion in Tropical Diagrams","publication_year":2023,"publication_date":"2023-12-08","ids":{"openalex":"https://openalex.org/W2946155099","doi":"https://doi.org/10.3390/e25121637","mag":"2946155099","pmid":"https://pubmed.ncbi.nlm.nih.gov/38136517"},"language":"en","primary_location":{"id":"doi:10.3390/e25121637","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e25121637","pdf_url":"https://www.mdpi.com/1099-4300/25/12/1637/pdf?version=1702041297","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/25/12/1637/pdf?version=1702041297","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5040509177","display_name":"Rostislav Matveev","orcid":"https://orcid.org/0000-0001-7027-1939"},"institutions":[{"id":"https://openalex.org/I4210091327","display_name":"Max Planck Institute for Mathematics in the Sciences","ror":"https://ror.org/00ez2he07","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210091327"]},{"id":"https://openalex.org/I4210119712","display_name":"Max Planck Institute for Mathematics","ror":"https://ror.org/02dh8ja68","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210119712"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Rostislav Matveev","raw_affiliation_strings":["Max Planck Institute for Mathematics in the Sciences, 04103 Leipzig, Germany"],"raw_orcid":"https://orcid.org/0000-0001-7027-1939","affiliations":[{"raw_affiliation_string":"Max Planck Institute for Mathematics in the Sciences, 04103 Leipzig, Germany","institution_ids":["https://openalex.org/I4210091327","https://openalex.org/I4210119712"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5018184060","display_name":"Jacobus W. Portegies","orcid":"https://orcid.org/0000-0002-2103-7334"},"institutions":[{"id":"https://openalex.org/I83019370","display_name":"Eindhoven University of Technology","ror":"https://ror.org/02c2kyt77","country_code":"NL","type":"education","lineage":["https://openalex.org/I83019370"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"Jacobus W. Portegies","raw_affiliation_strings":["Department of Mathematics and Computer Science, Eindhoven University of Technology, 5612 AZ Eindhoven, The Netherlands"],"raw_orcid":"https://orcid.org/0000-0002-2103-7334","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, Eindhoven University of Technology, 5612 AZ Eindhoven, The Netherlands","institution_ids":["https://openalex.org/I83019370"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5018184060","https://openalex.org/A5040509177"],"corresponding_institution_ids":["https://openalex.org/I4210091327","https://openalex.org/I4210119712","https://openalex.org/I83019370"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2224},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2224},"fwci":0.1395,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.42163165,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":93},"biblio":{"volume":"25","issue":"12","first_page":"1637","last_page":"1637"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9668999910354614,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9668999910354614,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9549999833106995,"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/T11270","display_name":"Complex Systems and Time Series Analysis","score":0.9517999887466431,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/arrow","display_name":"Arrow","score":0.7907388806343079},{"id":"https://openalex.org/keywords/morphism","display_name":"Morphism","score":0.6884972453117371},{"id":"https://openalex.org/keywords/contraction","display_name":"Contraction (grammar)","score":0.6613427400588989},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5941739678382874},{"id":"https://openalex.org/keywords/diagram","display_name":"Diagram","score":0.45129746198654175},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.34718450903892517},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.32329583168029785},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.23785936832427979},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.08343973755836487}],"concepts":[{"id":"https://openalex.org/C2780339515","wikidata":"https://www.wikidata.org/wiki/Q3074698","display_name":"Arrow","level":2,"score":0.7907388806343079},{"id":"https://openalex.org/C137212723","wikidata":"https://www.wikidata.org/wiki/Q1948412","display_name":"Morphism","level":2,"score":0.6884972453117371},{"id":"https://openalex.org/C163415756","wikidata":"https://www.wikidata.org/wiki/Q126473","display_name":"Contraction (grammar)","level":2,"score":0.6613427400588989},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5941739678382874},{"id":"https://openalex.org/C186399060","wikidata":"https://www.wikidata.org/wiki/Q959962","display_name":"Diagram","level":2,"score":0.45129746198654175},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.34718450903892517},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.32329583168029785},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.23785936832427979},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08343973755836487},{"id":"https://openalex.org/C126322002","wikidata":"https://www.wikidata.org/wiki/Q11180","display_name":"Internal medicine","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":8,"locations":[{"id":"doi:10.3390/e25121637","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e25121637","pdf_url":"https://www.mdpi.com/1099-4300/25/12/1637/pdf?version=1702041297","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},{"id":"pmid:38136517","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/38136517","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":"Entropy (Basel, Switzerland)","raw_type":"Journal Article"},{"id":"pmh:oai:arXiv.org:1905.05597","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1905.05597","pdf_url":"https://arxiv.org/pdf/1905.05597","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:pubmedcentral.nih.gov:10743289","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/10743289","pdf_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC10743289/pdf/entropy-25-01637.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy (Basel)","raw_type":"Text"},{"id":"pmh:oai:pure.tue.nl:publications/c06349cc-1430-402b-bd99-1103c435685a","is_oa":true,"landing_page_url":"https://research.tue.nl/en/publications/c06349cc-1430-402b-bd99-1103c435685a","pdf_url":"https://research.tue.nl/files/259212261/1905.05597v2.pdf","source":{"id":"https://openalex.org/S4406922641","display_name":"TU/e Research Portal","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Matveev, R & Portegies, J W 2019, 'Arrow Contraction and Expansion in Tropical Diagrams', arXiv, vol. 2019, 1905.05597. https://doi.org/10.48550/arXiv.1905.05597","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:doaj.org/article:bc508c28e80c40708b637dc19518e36a","is_oa":true,"landing_page_url":"https://doaj.org/article/bc508c28e80c40708b637dc19518e36a","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 25, Iss 12, p 1637 (2023)","raw_type":"article"},{"id":"pmh:tue:oai:pure.tue.nl:publications/c06349cc-1430-402b-bd99-1103c435685a","is_oa":true,"landing_page_url":"https://research.tue.nl/nl/publications/c06349cc-1430-402b-bd99-1103c435685a","pdf_url":null,"source":{"id":"https://openalex.org/S4406922641","display_name":"TU/e Research Portal","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv, 2019:1905.05597. Cornell University Library","raw_type":"info:eu-repo/semantics/article"},{"id":"doi:10.48550/arxiv.1905.05597","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1905.05597","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.3390/e25121637","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e25121637","pdf_url":"https://www.mdpi.com/1099-4300/25/12/1637/pdf?version=1702041297","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2946155099.pdf","grobid_xml":"https://content.openalex.org/works/W2946155099.grobid-xml"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W390216103","https://openalex.org/W1565516259","https://openalex.org/W1966069596","https://openalex.org/W1993408838","https://openalex.org/W2065264265","https://openalex.org/W2081988641","https://openalex.org/W2130839732","https://openalex.org/W2157376352","https://openalex.org/W2313526252","https://openalex.org/W2895921347","https://openalex.org/W2945930052","https://openalex.org/W2946393891","https://openalex.org/W2963705438","https://openalex.org/W3015255391","https://openalex.org/W3105020139","https://openalex.org/W3105841952","https://openalex.org/W6762844541"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1437213286","https://openalex.org/W3149432069","https://openalex.org/W2083151571","https://openalex.org/W2011564139","https://openalex.org/W102771113","https://openalex.org/W2403473672","https://openalex.org/W26434650","https://openalex.org/W1901793333","https://openalex.org/W2768503191"],"abstract_inverted_index":{"Arrow":[0,61],"contraction":[1,50],"applied":[2],"to":[3,34,51,67],"a":[4,11,44],"tropical":[5],"diagram":[6],"of":[7,13,18,28,57],"probability":[8],"spaces":[9],"is":[10,32,63],"modification":[12],"the":[14,19,29,35,55,58,64,68],"diagram,":[15],"replacing":[16],"one":[17],"morphisms":[20],"with":[21],"an":[22],"isomorphism":[23],"while":[24],"preserving":[25],"other":[26],"parts":[27],"diagram.":[30],"It":[31],"related":[33],"rate":[36],"regions":[37],"introduced":[38],"by":[39],"Ahlswede":[40],"and":[41],"K\u00f6rner.":[42],"In":[43],"companion":[45],"article,":[46],"we":[47],"use":[48],"arrow":[49,69],"derive":[52],"information":[53],"about":[54],"shape":[56],"entropic":[59],"cone.":[60],"expansion":[62],"inverse":[65],"operation":[66],"contraction.":[70]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2026-08-28T12:50:07.497085","created_date":"2019-05-29T00:00:00"}