{"id":"https://openalex.org/W1833573971","doi":"https://doi.org/10.18452/14355","title":"Phase transitions in the evolution of partially ordered sets","display_name":"Phase transitions in the evolution of partially ordered sets","publication_year":1999,"publication_date":"1999-01-06","ids":{"openalex":"https://openalex.org/W1833573971","doi":"https://doi.org/10.18452/14355","mag":"1833573971"},"language":"de","primary_location":{"id":"pmh:oai:edoc.hu-berlin.de:18452/15007","is_oa":true,"landing_page_url":"http://edoc.hu-berlin.de/18452/15007","pdf_url":"http://edoc.hu-berlin.de/18452/15007","source":{"id":"https://openalex.org/S4306400923","display_name":"edoc Publication server (Humboldt University of Berlin)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I39343248","host_organization_name":"Humboldt-Universit\u00e4t zu Berlin","host_organization_lineage":["https://openalex.org/I39343248"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"doctoralThesis"},"type":"dissertation","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://edoc.hu-berlin.de/18452/15007","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5007248146","display_name":"Anuschirawan Ralf Taraz","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Taraz, Anuschirawan Ralf","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5007248146"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9988999962806702,"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"}},"topics":[{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9988999962806702,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9944999814033508,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9911999702453613,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/phase","display_name":"Phase (matter)","score":0.45872896909713745},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2208912968635559},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.0673997700214386}],"concepts":[{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.45872896909713745},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2208912968635559},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0673997700214386}],"mesh":[],"locations_count":6,"locations":[{"id":"pmh:oai:edoc.hu-berlin.de:18452/15007","is_oa":true,"landing_page_url":"http://edoc.hu-berlin.de/18452/15007","pdf_url":"http://edoc.hu-berlin.de/18452/15007","source":{"id":"https://openalex.org/S4306400923","display_name":"edoc Publication server (Humboldt University of Berlin)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I39343248","host_organization_name":"Humboldt-Universit\u00e4t zu Berlin","host_organization_lineage":["https://openalex.org/I39343248"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"doctoralThesis"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.17.5378","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.17.5378","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://dochost.rz.hu-berlin.de/dissertationen/informatik/taraz-anuschirawan-ralf/PS/Taraz.ps","raw_type":"text"},{"id":"pmh:oai:aleph.bib-bvb.de:BVB01-008945659","is_oa":false,"landing_page_url":"http://d-nb.info/95851545X/34","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Hochschulschrift"},{"id":"pmh:oai:cds.cern.ch:547253","is_oa":false,"landing_page_url":"http://cds.cern.ch/record/547253","pdf_url":null,"source":{"id":"https://openalex.org/S4306402195","display_name":"CERN Document Server (European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":null},{"id":"doi:10.18452/14355","is_oa":true,"landing_page_url":"https://doi.org/10.18452/14355","pdf_url":null,"source":{"id":"https://openalex.org/S4306400923","display_name":"edoc Publication server (Humboldt University of Berlin)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I39343248","host_organization_name":"Humboldt-Universit\u00e4t zu Berlin","host_organization_lineage":["https://openalex.org/I39343248"],"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":"article-journal"},{"id":"mag:1833573971","is_oa":false,"landing_page_url":"http://cds.cern.ch/record/547253/files/sis-2002-191.pdf","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":null}],"best_oa_location":{"id":"pmh:oai:edoc.hu-berlin.de:18452/15007","is_oa":true,"landing_page_url":"http://edoc.hu-berlin.de/18452/15007","pdf_url":"http://edoc.hu-berlin.de/18452/15007","source":{"id":"https://openalex.org/S4306400923","display_name":"edoc Publication server (Humboldt University of Berlin)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I39343248","host_organization_name":"Humboldt-Universit\u00e4t zu Berlin","host_organization_lineage":["https://openalex.org/I39343248"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"doctoralThesis"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/13","score":0.550000011920929,"display_name":"Climate action"},{"id":"https://metadata.un.org/sdg/11","score":0.44999998807907104,"display_name":"Sustainable cities and communities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1833573971.pdf","grobid_xml":"https://content.openalex.org/works/W1833573971.grobid-xml"},"referenced_works_count":43,"referenced_works":["https://openalex.org/W120382638","https://openalex.org/W947400629","https://openalex.org/W1540243329","https://openalex.org/W1555293549","https://openalex.org/W1571051474","https://openalex.org/W1587590810","https://openalex.org/W1593970265","https://openalex.org/W1603384057","https://openalex.org/W1769381271","https://openalex.org/W1911186902","https://openalex.org/W1965482388","https://openalex.org/W1967223908","https://openalex.org/W1974575606","https://openalex.org/W1976442532","https://openalex.org/W1977349791","https://openalex.org/W1977647548","https://openalex.org/W1994399760","https://openalex.org/W2004621408","https://openalex.org/W2018472031","https://openalex.org/W2018663595","https://openalex.org/W2018883342","https://openalex.org/W2021434280","https://openalex.org/W2028457162","https://openalex.org/W2030001549","https://openalex.org/W2038080222","https://openalex.org/W2044935944","https://openalex.org/W2045472305","https://openalex.org/W2049947556","https://openalex.org/W2050228009","https://openalex.org/W2080961710","https://openalex.org/W2081735788","https://openalex.org/W2084131533","https://openalex.org/W2085531476","https://openalex.org/W2086388790","https://openalex.org/W2096001230","https://openalex.org/W2111007781","https://openalex.org/W2116537669","https://openalex.org/W2145702572","https://openalex.org/W2146162554","https://openalex.org/W2153478982","https://openalex.org/W2171919542","https://openalex.org/W2325654786","https://openalex.org/W2905110430"],"related_works":["https://openalex.org/W3106157583","https://openalex.org/W2037411454","https://openalex.org/W2984154242","https://openalex.org/W3099095348","https://openalex.org/W67621383","https://openalex.org/W2344791152","https://openalex.org/W2523555186","https://openalex.org/W31673381","https://openalex.org/W762437628"],"abstract_inverted_index":{"Unter":[0],"dem":[1],"Evolutionsproze\u00df":[2,83],"eines":[3],"Objekts,":[4],"das":[5,15],"aus":[6,132,156],"einer":[7,93,202],"gegebenen":[8,94],"Klasse":[9,25,103],"zuf\u00e4llig":[10],"ausgew\u00e4hlt":[11],"wird,":[12],"versteht":[13],"man":[14,27],"folgende":[16],"Gedankenexperiment.":[17],"Zu":[18],"einem":[19],"geeigneten":[20],"Parameter":[21,35],"der":[22,24,60,165],"Objekte":[23,56],"betrachtet":[26],"die":[28,44,66,69,88,102,200],"Teilklasse":[29,53],"derjenigen":[30],"Objekte,":[31],"bei":[32],"denen":[33],"dieser":[34,52,206],"einen":[36],"bestimmten":[37,137],"Wert":[38],"x":[39,75],"annimmt.":[40],"Dadurch":[41],"stellen":[42],"sich":[43,65,74,199],"folgenden":[45],"Fragen:":[46],"Wie":[47,63],"sieht":[48],"ein":[49,169],"typisches":[50],"Objekt":[51],"aus?":[54],"Wieviele":[55],"gibt":[57],"es":[58,190],"in":[59],"Teilklasse?":[61],"Und:":[62],"ver\u00e4ndern":[64],"Antworten":[67],"auf":[68],"ersten":[70],"beiden":[71],"Fragen,":[72],"wenn":[73],"ver\u00e4ndert?":[76],"Die":[77],"vorliegende":[78],"Dissertation":[79,166],"behandelt":[80],"Phasen\u00fcberg\u00e4nge":[81,193],"im":[82,118,142,179],"teilweiser":[84,90],"Ordnungen":[85,91,106],"und":[86,110,125,139,149,187],"bestimmt":[87],"Anzahl":[89,95],"mit":[92,107],"vergleichbarer":[96],"Paare.":[97],"Wir":[98,176],"bezeichnen":[99],"durch":[100],"Pn,d":[101],"aller":[104],"teilweisen":[105],"n":[108],"Punkten":[109],"dn2":[111],"vergleichbaren":[112],"Paaren.":[113],"1978":[114],"bestimmte":[115],"Dhar":[116],"|Pn,d|":[117,141,178],"Intervall":[119,143,181],"1/8":[120,148],"<":[121,123,145,147,183,185],"d":[122,146,184],"3/16":[124],"zeigte,":[126],"da\u00df":[127,151,189],"hier":[128,152],"eine":[129,153],"typische":[130,154],"Ordnung":[131,155,204],"drei":[133],"\"Ebenen\"":[134],"besteht.":[135],"1979":[136],"Kleitman":[138],"Rothschild":[140],"0":[144,182],"zeigten,":[150],"zwei":[157],"Ebenen":[158],"besteht,":[159],"also":[160],"bipartit":[161],"ist.":[162],"Das":[163],"Hauptergebnis":[164],"ist":[167],"es,":[168],"vollst\u00e4ndiges":[170],"Bild":[171],"des":[172],"Evolutionsprozesses":[173],"zu":[174],"geben.":[175],"bestimmen":[177],"gesamten":[180],"1/2":[186],"zeigen,":[188],"unendlich":[191],"viele":[192],"gibt.":[194],"Abschlie\u00dfend":[195],"beschreiben":[196],"wir,":[197],"wie":[198],"Struktur":[201],"typischen":[203],"w\u00e4hrend":[205],"Phasen":[207],"ver\u00e4ndert.":[208]},"counts_by_year":[{"year":2015,"cited_by_count":1}],"updated_date":"2026-08-27T14:10:00.468798","created_date":"2025-10-10T00:00:00"}