{"id":"https://openalex.org/W2736852635","doi":"https://doi.org/10.1109/tit.2018.2837878","title":"A Factor-Graph Approach to Algebraic Topology, With Applications to Kramers\u2013Wannier Duality","display_name":"A Factor-Graph Approach to Algebraic Topology, With Applications to Kramers\u2013Wannier Duality","publication_year":2018,"publication_date":"2018-05-17","ids":{"openalex":"https://openalex.org/W2736852635","doi":"https://doi.org/10.1109/tit.2018.2837878","mag":"2736852635"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2018.2837878","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2018.2837878","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"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 Information Theory","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1607.02361","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Ali Al-Bashabsheh","orcid":"https://orcid.org/0000-0003-0462-7727"},"institutions":[{"id":"https://openalex.org/I4210165198","display_name":"Beijing Advanced Sciences and Innovation Center","ror":"https://ror.org/05qm21180","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165198"]},{"id":"https://openalex.org/I82880672","display_name":"Beihang University","ror":"https://ror.org/00wk2mp56","country_code":"CN","type":"education","lineage":["https://openalex.org/I82880672"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ali Al-Bashabsheh","raw_affiliation_strings":["Beijing Advanced Innovation Center for Big Data and Brain Computing, Beihang University, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0003-0462-7727","affiliations":[{"raw_affiliation_string":"Beijing Advanced Innovation Center for Big Data and Brain Computing, Beihang University, Beijing, China","institution_ids":["https://openalex.org/I4210165198","https://openalex.org/I82880672"]}]},{"author_position":"last","author":{"id":null,"display_name":"Pascal O. Vontobel","orcid":"https://orcid.org/0000-0002-6180-258X"},"institutions":[{"id":"https://openalex.org/I177725633","display_name":"Chinese University of Hong Kong","ror":"https://ror.org/00t33hh48","country_code":"HK","type":"education","lineage":["https://openalex.org/I177725633"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Pascal O. Vontobel","raw_affiliation_strings":["Department of Information Engineering, Institute of Theoretical Computer Science and Communications, The Chinese University of Hong Kong, Hong Kong"],"raw_orcid":"https://orcid.org/0000-0002-6180-258X","affiliations":[{"raw_affiliation_string":"Department of Information Engineering, Institute of Theoretical Computer Science and Communications, The Chinese University of Hong Kong, Hong Kong","institution_ids":["https://openalex.org/I177725633"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.3809,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.54506686,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"64","issue":"12","first_page":"7488","last_page":"7510"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.15889999270439148,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T11476","display_name":"Graph theory and applications","score":0.15889999270439148,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.15809999406337738,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.13379999995231628,"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/ising-model","display_name":"Ising model","score":0.7890999913215637},{"id":"https://openalex.org/keywords/potts-model","display_name":"Potts model","score":0.6984999775886536},{"id":"https://openalex.org/keywords/partition-function","display_name":"Partition function (quantum field theory)","score":0.6901999711990356},{"id":"https://openalex.org/keywords/duality","display_name":"Duality (order theory)","score":0.6421999931335449},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5985000133514404},{"id":"https://openalex.org/keywords/algebraic-topology","display_name":"Algebraic topology","score":0.5532000064849854},{"id":"https://openalex.org/keywords/square-lattice-ising-model","display_name":"Square-lattice Ising model","score":0.4693000018596649},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.44670000672340393}],"concepts":[{"id":"https://openalex.org/C51329190","wikidata":"https://www.wikidata.org/wiki/Q1076349","display_name":"Ising model","level":2,"score":0.7890999913215637},{"id":"https://openalex.org/C98925819","wikidata":"https://www.wikidata.org/wiki/Q7235385","display_name":"Potts model","level":3,"score":0.6984999775886536},{"id":"https://openalex.org/C2778401447","wikidata":"https://www.wikidata.org/wiki/Q7140637","display_name":"Partition function (quantum field theory)","level":2,"score":0.6901999711990356},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6601999998092651},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.6421999931335449},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5985000133514404},{"id":"https://openalex.org/C145054310","wikidata":"https://www.wikidata.org/wiki/Q212803","display_name":"Algebraic topology","level":3,"score":0.5532000064849854},{"id":"https://openalex.org/C49005734","wikidata":"https://www.wikidata.org/wiki/Q7581981","display_name":"Square-lattice Ising model","level":3,"score":0.4693000018596649},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.44670000672340393},{"id":"https://openalex.org/C107277493","wikidata":"https://www.wikidata.org/wiki/Q5101824","display_name":"Chiral Potts curve","level":4,"score":0.41929998993873596},{"id":"https://openalex.org/C2989065042","wikidata":"https://www.wikidata.org/wiki/Q7378971","display_name":"Algebraic properties","level":2,"score":0.4002000093460083},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.38019999861717224},{"id":"https://openalex.org/C148607811","wikidata":"https://www.wikidata.org/wiki/Q746863","display_name":"Algebraic function","level":3,"score":0.35679998993873596},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.35350000858306885},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3346000015735626},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.32829999923706055},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3190999925136566},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3093999922275543},{"id":"https://openalex.org/C2731732","wikidata":"https://www.wikidata.org/wiki/Q7301119","display_name":"Real algebraic geometry","level":3,"score":0.2896000146865845},{"id":"https://openalex.org/C2779782106","wikidata":"https://www.wikidata.org/wiki/Q4724020","display_name":"Algebraic theory","level":3,"score":0.2833999991416931},{"id":"https://openalex.org/C54643580","wikidata":"https://www.wikidata.org/wiki/Q1005603","display_name":"Algebraic combinatorics","level":2,"score":0.2777999937534332}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tit.2018.2837878","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2018.2837878","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"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 Information Theory","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1607.02361","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1607.02361","pdf_url":"https://arxiv.org/pdf/1607.02361","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1607.02361","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1607.02361","pdf_url":"https://arxiv.org/pdf/1607.02361","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2659825867","display_name":null,"funder_award_id":"AoE/E-02/08","funder_id":"https://openalex.org/F4320321019","funder_display_name":"University Grants Committee"}],"funders":[{"id":"https://openalex.org/F4320321019","display_name":"University Grants Committee","ror":"https://ror.org/00djwmt25"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W1622775971","https://openalex.org/W1965511886","https://openalex.org/W1970635910","https://openalex.org/W1976278894","https://openalex.org/W2000512161","https://openalex.org/W2024710200","https://openalex.org/W2055496088","https://openalex.org/W2068674173","https://openalex.org/W2104557113","https://openalex.org/W2124089253","https://openalex.org/W2133068391","https://openalex.org/W2135094946","https://openalex.org/W2135273380","https://openalex.org/W2137813581","https://openalex.org/W2138628599","https://openalex.org/W2139584447","https://openalex.org/W2142486636","https://openalex.org/W2142511915","https://openalex.org/W2150859678","https://openalex.org/W2159793005","https://openalex.org/W2166248051","https://openalex.org/W2171516545","https://openalex.org/W2225144138","https://openalex.org/W2246296081","https://openalex.org/W2319680621","https://openalex.org/W2332615042","https://openalex.org/W2588591589","https://openalex.org/W2607730504","https://openalex.org/W2963518415","https://openalex.org/W6629196920"],"related_works":[],"abstract_inverted_index":{"Algebraic":[0],"topology":[1,27],"studies":[2],"topological":[3],"spaces":[4],"with":[5],"the":[6,57,61,72,76,90,95],"help":[7],"of":[8,16,34,46,51,60,71,75],"tools":[9],"from":[10,25],"abstract":[11],"algebra.":[12],"The":[13],"main":[14],"focus":[15],"this":[17],"paper":[18],"is":[19],"to":[20],"show":[21],"that":[22],"many":[23],"concepts":[24],"algebraic":[26],"can":[28],"be":[29],"conveniently":[30],"expressed":[31],"in":[32,69],"terms":[33,70],"(normal)":[35],"factor":[36],"graphs.":[37],"As":[38],"an":[39,43],"application,":[40],"we":[41,85],"give":[42],"alternative":[44],"proof":[45],"a":[47,66,81],"classical":[48],"duality":[49],"result":[50],"Kramers":[52],"and":[53,94],"Wannier,":[54],"which":[55],"expresses":[56],"partition":[58,73],"function":[59,74],"2-D":[62,77],"Ising":[63,78,92],"model":[64,79,93],"at":[65,80],"low":[67],"temperature":[68],"high":[82],"temperature.":[83],"Moreover,":[84],"discuss":[86],"analogous":[87],"results":[88],"for":[89],"3-D":[91],"Potts":[96],"model.":[97]},"counts_by_year":[{"year":2018,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2017-07-31T00:00:00"}