{"id":"https://openalex.org/W4407735971","doi":"https://doi.org/10.3233/978-1-60750-718-5-135","title":"Discrete Convexity and Its Applications","display_name":"Discrete Convexity and Its Applications","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W4407735971","doi":"https://doi.org/10.3233/978-1-60750-718-5-135"},"language":"en","primary_location":{"id":"doi:10.3233/978-1-60750-718-5-135","is_oa":false,"landing_page_url":"https://doi.org/10.3233/978-1-60750-718-5-135","pdf_url":null,"source":{"id":"https://openalex.org/S4210202636","display_name":"NATO science for peace and security series. D, Information and communication security","issn_l":"1874-6268","issn":["1874-6268","1879-8292"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"NATO Science for Peace and Security Series - D: Information and Communication Security","raw_type":"book-chapter"},"type":"book-chapter","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/A5116325381","display_name":"Koshevoy G.A.","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Koshevoy G.A.","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5116325381"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.50764779,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"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/T12923","display_name":"Digital Image Processing Techniques","score":0.9560999870300293,"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"}},"topics":[{"id":"https://openalex.org/T12923","display_name":"Digital Image Processing Techniques","score":0.9560999870300293,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.7827507257461548},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4321480989456177},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.23338952660560608},{"id":"https://openalex.org/keywords/financial-economics","display_name":"Financial economics","score":0.04771021008491516}],"concepts":[{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.7827507257461548},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4321480989456177},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.23338952660560608},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.04771021008491516}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3233/978-1-60750-718-5-135","is_oa":false,"landing_page_url":"https://doi.org/10.3233/978-1-60750-718-5-135","pdf_url":null,"source":{"id":"https://openalex.org/S4210202636","display_name":"NATO science for peace and security series. D, Information and communication security","issn_l":"1874-6268","issn":["1874-6268","1879-8292"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"NATO Science for Peace and Security Series - D: Information and Communication Security","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W1964872188","https://openalex.org/W2187391117","https://openalex.org/W1981809986","https://openalex.org/W2949367465","https://openalex.org/W2587048717","https://openalex.org/W4235203617","https://openalex.org/W2006359264"],"abstract_inverted_index":{"We":[0,169],"explain":[1],"what":[2,8],"subsets":[3],"of":[4,19,28,47,56,64,75,84,93,102,109,121,146,187],"the":[5,11,20,23,45,57,73,82,99,110,119,122,132,144,162,188],"lattice":[6,12],"\\mathbb{Z}nand":[7],"functions":[9,33,67,173],"on":[10],"\\mathbb{Z}ncould":[13],"be":[14],"called":[15],"convex.":[16],"The":[17,90,107,149],"basis":[18],"theory":[21],"is":[22,51],"following":[24],"three":[25],"main":[26],"postulates":[27],"classical":[29],"convex":[30,94],"analysis:":[31],"concave":[32,49,66,105,153],"are":[34,39,96,113,125,159],"closed":[35,41,114,126],"under":[36,42,79,88,115,127],"sums;":[37],"they":[38],"also":[40],"convolutions;":[43],"and":[44,77,86,118],"superdifferential":[46],"a":[48],"function":[50],"nonempty":[52],"at":[53],"each":[54],"point":[55],"domain.":[58],"Interesting":[59],"(and":[60],"even":[61],"dual)":[62],"classes":[63,92,108,120],"discrete":[65,196],"arise":[68],"if":[69],"we":[70],"require":[71],"either":[72],"existence":[74,83],"superdifferentials":[76,85],"closeness":[78,87],"convolutions":[80],"or":[81],"sums.":[89],"corresponding":[91],"sets":[95,138],"obtained":[97],"as":[98],"affinity":[100],"domains":[101],"such":[103,147,172],"discretely":[104,152],"functions.":[106],"first":[111],"type":[112,124],"(Minkowski)":[116],"sums,":[117],"second":[123],"intersections.":[128],"In":[129],"both":[130],"classes,":[131],"separation":[133],"theorem":[134],"holds":[135],"true.":[136],"Unimodular":[137],"play":[139,181],"an":[140,182],"important":[141,183],"role":[142,184],"in":[143,176,179],"classification":[145],"classes.":[148],"so-called":[150],"polymatroidal":[151],"functions,":[154],"most":[155],"interesting":[156],"for":[157,185,191],"applications,":[158],"related":[160],"to":[161],"unimodular":[163],"system":[164],"An:=":[165],"{±ei,":[166],"ei−":[167],"ej}.":[168],"demonstrate":[170],"that":[171],"naturally":[174],"appear":[175],"mathematical":[177],"economics,":[178],"combinatorics,":[180],"solution":[186],"Horn":[189],"problem,":[190],"describing":[192],"submodule":[193],"invariants":[194],"over":[195],"valuation":[197],"rings,":[198],"etc.":[199]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}