{"id":"https://openalex.org/W4403661686","doi":"https://doi.org/10.48550/arxiv.2409.08389","title":"Higher-Order Topological Directionality and Directed Simplicial Neural\n Networks","display_name":"Higher-Order Topological Directionality and Directed Simplicial Neural\n Networks","publication_year":2024,"publication_date":"2024-09-12","ids":{"openalex":"https://openalex.org/W4403661686","doi":"https://doi.org/10.48550/arxiv.2409.08389"},"language":"en","primary_location":{"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2409.08389","pdf_url":"http://arxiv.org/pdf/2409.08389","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":["Cornell University"],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false},"type":"preprint","type_crossref":"posted-content","indexed_in":["arxiv"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://arxiv.org/pdf/2409.08389","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5029855019","display_name":"Manuel Lecha","orcid":"https://orcid.org/0009-0000-9662-1255"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lecha, Manuel","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101507980","display_name":"Andrea Cavallo","orcid":"https://orcid.org/0009-0006-1226-3926"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Cavallo, Andrea","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080486553","display_name":"Francesca Dominici","orcid":"https://orcid.org/0000-0001-5964-0756"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Dominici, Francesca","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5060836778","display_name":"Elvin Isufi","orcid":"https://orcid.org/0000-0002-1919-260X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Isufi, Elvin","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5062501594","display_name":"Claudio Battiloro","orcid":"https://orcid.org/0000-0003-0090-5355"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Battiloro, Claudio","raw_affiliation_strings":[],"affiliations":[]}],"institution_assertions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.99977,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":84,"max":92},"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9888,"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9888,"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/T10320","display_name":"Neural Networks and Applications","score":0.9715,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9349,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/directionality","display_name":"Directionality","score":0.8477746}],"concepts":[{"id":"https://openalex.org/C29648211","wikidata":"https://www.wikidata.org/wiki/Q1995607","display_name":"Directionality","level":2,"score":0.8477746},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.60979307},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.46296668},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.46123978},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4161741},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.37351114},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.30297786},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.19462448},{"id":"https://openalex.org/C144133560","wikidata":"https://www.wikidata.org/wiki/Q4830453","display_name":"Business","level":0,"score":0.16416636},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.14125198},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2409.08389","pdf_url":"http://arxiv.org/pdf/2409.08389","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":["Cornell University"],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false}],"best_oa_location":{"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2409.08389","pdf_url":"http://arxiv.org/pdf/2409.08389","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":["Cornell University"],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false},"sustainable_development_goals":[],"grants":[],"datasets":[],"versions":[],"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W4232225082","https://openalex.org/W33032069","https://openalex.org/W2950752483","https://openalex.org/W2794987474","https://openalex.org/W2624817431","https://openalex.org/W2473013794","https://openalex.org/W2334790377","https://openalex.org/W2029088481","https://openalex.org/W1599251874"],"abstract_inverted_index":{"Topological":[0],"Deep":[1],"Learning":[2],"(TDL)":[3],"has":[4],"emerged":[5],"as":[6,22],"a":[7,49,97,124],"paradigm":[8],"to":[9,77],"process":[10],"and":[11,55,80,104,141],"learn":[12],"from":[13],"signals":[14],"defined":[15],"on":[16,65,72,123],"higher-order":[17,53,100],"combinatorial":[18],"topological":[19],"spaces,":[20],"such":[21],"simplicial":[23,74],"or":[24],"cell":[25],"complexes.":[26],"Although":[27],"many":[28],"complex":[29,138,147],"systems":[30],"have":[31],"an":[32],"asymmetric":[33,82],"relational":[34],"structure,":[35],"most":[36],"TDL":[37,94],"models":[38],"forcibly":[39],"symmetrize":[40],"these":[41],"relationships.":[42],"In":[43],"this":[44,90],"paper,":[45],"we":[46,56],"first":[47,93],"introduce":[48],"novel":[50],"notion":[51,98],"of":[52,99],"directionality":[54],"then":[57],"design":[58],"Directed":[59],"Simplicial":[60],"Neural":[61],"Networks":[62],"(Dir-SNNs)":[63],"based":[64],"it.":[66],"Dir-SNNs":[67,108,131],"are":[68,109],"message-passing":[69],"networks":[70],"operating":[71],"directed":[73,79,114,120],"complexes":[75],"able":[76],"leverage":[78],"possibly":[81],"interactions":[83],"among":[84],"the":[85,92,136,145],"simplices.":[86],"To":[87],"our":[88],"knowledge,":[89],"is":[91,139,148],"model":[95],"using":[96],"directionality.":[101],"We":[102],"theoretically":[103],"empirically":[105],"prove":[106],"that":[107,130],"more":[110],"expressive":[111],"than":[112],"their":[113],"graph":[115],"counterpart":[116],"in":[117],"distinguishing":[118],"isomorphic":[119],"graphs.":[121],"Experiments":[122],"synthetic":[125],"source":[126],"localization":[127],"task":[128],"demonstrate":[129],"outperform":[132],"undirected":[133],"SNNs":[134],"when":[135,144],"underlying":[137,146],"directed,":[140],"perform":[142],"comparably":[143],"undirected.":[149]},"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W4403661686","counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2025-01-03T05:01:57.695535","created_date":"2024-10-23"}