{"id":"https://openalex.org/W4399441144","doi":"https://doi.org/10.1137/22m1489071","title":"Brillouin Zones of Integer Lattices and Their Perturbations","display_name":"Brillouin Zones of Integer Lattices and Their Perturbations","publication_year":2024,"publication_date":"2024-06-07","ids":{"openalex":"https://openalex.org/W4399441144","doi":"https://doi.org/10.1137/22m1489071"},"language":"en","primary_location":{"id":"doi:10.1137/22m1489071","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1489071","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal.science/hal-04628684/document","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5069999967","display_name":"Herbert Edelsbrunner","orcid":"https://orcid.org/0000-0002-9823-6833"},"institutions":[{"id":"https://openalex.org/I157556583","display_name":"Institute of Science and Technology Austria","ror":"https://ror.org/03gnh5541","country_code":"AT","type":"education","lineage":["https://openalex.org/I157556583"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"Herbert Edelsbrunner","raw_affiliation_strings":["IST Austria (Institute of Science and Technology Austria), Klosterneuburg, 3400, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IST Austria (Institute of Science and Technology Austria), Klosterneuburg, 3400, Austria","institution_ids":["https://openalex.org/I157556583"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5019670101","display_name":"Alexey Garber","orcid":"https://orcid.org/0000-0002-9474-2077"},"institutions":[{"id":"https://openalex.org/I2802326326","display_name":"The University of Texas Rio Grande Valley","ror":"https://ror.org/02p5xjf12","country_code":"US","type":"education","lineage":["https://openalex.org/I2802326326"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Alexey Garber","raw_affiliation_strings":["School of Mathematical and Statistical Sciences, University of Texas Rio Grande Valley, Brownsville, TX 78520 USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical and Statistical Sciences, University of Texas Rio Grande Valley, Brownsville, TX 78520 USA","institution_ids":["https://openalex.org/I2802326326"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018574593","display_name":"Mohadese Ghafari","orcid":null},"institutions":[{"id":"https://openalex.org/I12912129","display_name":"Northeastern University","ror":"https://ror.org/04t5xt781","country_code":"US","type":"education","lineage":["https://openalex.org/I12912129"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Mohadese Ghafari","raw_affiliation_strings":["Khoury College of Computer Sciences, Northeastern University, Boston, MA 02115 USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Khoury College of Computer Sciences, Northeastern University, Boston, MA 02115 USA","institution_ids":["https://openalex.org/I12912129"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004873270","display_name":"Teresa Heiss","orcid":"https://orcid.org/0000-0002-1780-2689"},"institutions":[{"id":"https://openalex.org/I157556583","display_name":"Institute of Science and Technology Austria","ror":"https://ror.org/03gnh5541","country_code":"AT","type":"education","lineage":["https://openalex.org/I157556583"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Teresa Heiss","raw_affiliation_strings":["IST Austria (Institute of Science and Technology Austria), Klosterneuburg, 3400, Austria"],"raw_orcid":"https://orcid.org/0000-0002-1780-2689","affiliations":[{"raw_affiliation_string":"IST Austria (Institute of Science and Technology Austria), Klosterneuburg, 3400, Austria","institution_ids":["https://openalex.org/I157556583"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038928621","display_name":"Morteza Saghafian","orcid":"https://orcid.org/0000-0002-4201-5775"},"institutions":[{"id":"https://openalex.org/I157556583","display_name":"Institute of Science and Technology Austria","ror":"https://ror.org/03gnh5541","country_code":"AT","type":"education","lineage":["https://openalex.org/I157556583"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Morteza Saghafian","raw_affiliation_strings":["IST Austria (Institute of Science and Technology Austria), Klosterneuburg, 3400, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IST Austria (Institute of Science and Technology Austria), Klosterneuburg, 3400, Austria","institution_ids":["https://openalex.org/I157556583"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5003460394","display_name":"Mathijs Wintraecken","orcid":"https://orcid.org/0000-0002-7472-2220"},"institutions":[{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en sciences et technologies du num\u00e9rique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"government","lineage":["https://openalex.org/I1326498283"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Mathijs Wintraecken","raw_affiliation_strings":["Inria centre Universit\u00e9 C\u00f4te d\u2019Azur, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Inria centre Universit\u00e9 C\u00f4te d\u2019Azur, France","institution_ids":["https://openalex.org/I1326498283"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5069999967"],"corresponding_institution_ids":["https://openalex.org/I157556583"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.13093203,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"38","issue":"2","first_page":"1784","last_page":"1807"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9160000085830688,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9160000085830688,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T11429","display_name":"Semiconductor Lasers and Optical Devices","score":0.9049999713897705,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9009000062942505,"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/brillouin-zone","display_name":"Brillouin zone","score":0.6780155897140503},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.670110285282135},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6695161461830139},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5520171523094177},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.41827964782714844},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.19609588384628296},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.169048011302948},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.13074013590812683}],"concepts":[{"id":"https://openalex.org/C16291881","wikidata":"https://www.wikidata.org/wiki/Q917246","display_name":"Brillouin zone","level":2,"score":0.6780155897140503},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.670110285282135},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6695161461830139},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5520171523094177},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41827964782714844},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.19609588384628296},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.169048011302948},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.13074013590812683},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/22m1489071","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1489071","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-04628684v1","is_oa":true,"landing_page_url":"https://hal.science/hal-04628684","pdf_url":"https://hal.science/hal-04628684/document","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"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":"SIAM Journal on Discrete Mathematics, 2024, 38 (2), pp.1784-1807. &#x27E8;10.1137/22M1489071&#x27E9;","raw_type":"Journal articles"},{"id":"pmh:oai:scholarworks.utrgv.edu:mss_fac-1555","is_oa":false,"landing_page_url":"https://scholarworks.utrgv.edu/mss_fac/555","pdf_url":null,"source":{"id":"https://openalex.org/S4306402611","display_name":"ScholarWorks @ UTRGV (The University of Texas Rio Grande Valley)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2802326326","host_organization_name":"The University of Texas Rio Grande Valley","host_organization_lineage":["https://openalex.org/I2802326326"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"School of Mathematical & Statistical Sciences Faculty Publications and Presentations","raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-04628684v1","is_oa":true,"landing_page_url":"https://hal.science/hal-04628684","pdf_url":"https://hal.science/hal-04628684/document","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"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":"SIAM Journal on Discrete Mathematics, 2024, 38 (2), pp.1784-1807. &#x27E8;10.1137/22M1489071&#x27E9;","raw_type":"Journal articles"},"sustainable_development_goals":[{"display_name":"Climate action","id":"https://metadata.un.org/sdg/13","score":0.8500000238418579}],"awards":[{"id":"https://openalex.org/G2829023891","display_name":"Mathematics, Computer Science","funder_award_id":"Z 342","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G3622264694","display_name":"Alpha Shape Theory Extended","funder_award_id":"788183","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G4101941094","display_name":"ISTplus - Postdoctoral Fellowships","funder_award_id":"754411","funder_id":"https://openalex.org/F4320338337","funder_display_name":"H2020 Marie Sk\u0142odowska-Curie Actions"},{"id":"https://openalex.org/G4470488369","display_name":null,"funder_award_id":"754411","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G5705358137","display_name":null,"funder_award_id":"M-3073","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G6773318802","display_name":null,"funder_award_id":"TRR 109","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G6843533210","display_name":null,"funder_award_id":"342-N31","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G7139889009","display_name":null,"funder_award_id":"Z 342-N31","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G7236747564","display_name":null,"funder_award_id":"I 02979-N35","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G7401564395","display_name":null,"funder_award_id":"02979-N35","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G8184282109","display_name":null,"funder_award_id":"788183","funder_id":"https://openalex.org/F4320334678","funder_display_name":"European Research Council"}],"funders":[{"id":"https://openalex.org/F4320307517","display_name":"American Friends of the Alexander von Humboldt Foundation","ror":"https://ror.org/00c33a344"},{"id":"https://openalex.org/F4320308269","display_name":"Alexander von Humboldt-Stiftung","ror":"https://ror.org/012kf4317"},{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"},{"id":"https://openalex.org/F4320334678","display_name":"European Research Council","ror":"https://ror.org/0472cxd90"},{"id":"https://openalex.org/F4320338337","display_name":"H2020 Marie Sk\u0142odowska-Curie Actions","ror":null}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4399441144.pdf"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W565214016","https://openalex.org/W1847031659","https://openalex.org/W1964143376","https://openalex.org/W1979843794","https://openalex.org/W1992930621","https://openalex.org/W2035774625","https://openalex.org/W2046782253","https://openalex.org/W2053678829","https://openalex.org/W2054680493","https://openalex.org/W2080802055","https://openalex.org/W2094035703","https://openalex.org/W2094683955","https://openalex.org/W2149757010","https://openalex.org/W2157053574","https://openalex.org/W2158375645","https://openalex.org/W2261545547","https://openalex.org/W2279589090","https://openalex.org/W2785135064","https://openalex.org/W2795257408","https://openalex.org/W3105953210","https://openalex.org/W4300640952","https://openalex.org/W4388288416"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2036113194","https://openalex.org/W1979597421","https://openalex.org/W4388155470","https://openalex.org/W2046979465","https://openalex.org/W2007980826","https://openalex.org/W2017848950","https://openalex.org/W2394164816","https://openalex.org/W2061531152","https://openalex.org/W3002753104"],"abstract_inverted_index":{"For":[0],"a":[1,43,105,110,120,135],"locally":[2],"finite":[3],"set,":[4],"\ud835\udc34\u2286\u211d\ud835\udc51":[5],",":[6,71,126],"the":[7,15,24,29,35,45,51,67,79,93,102,115,128,131,140],"\ud835\udc58":[8,25,46,70],"th":[9,26,47],"Brillouin":[10,48,89,106],"zone":[11,107,121],"of":[12,17,50,57,69,88,104,117,130,134],"\ud835\udc4e\u2208\ud835\udc34":[13],"is":[14,23,42],"region":[16],"points":[18,36,52],"\ud835\udc65\u2208\u211d\ud835\udc51":[19],"for":[20,122,139],"which":[21],"\u2016\ud835\udc65\u2212\ud835\udc4e\u2016":[22],"smallest":[27],"among":[28],"Euclidean":[30],"distances":[31],"between":[32],"\ud835\udc65":[33],"and":[34,60,85,96,127],"in":[37,53,78,119,124],"\ud835\udc34":[38,41,54],".":[39],"If":[40],"lattice,":[44],"zones":[49],"are":[55],"translates":[56],"each":[58],"other,":[59],"together":[61],"they":[62,72],"tile":[63],"space.":[64],"Depending":[65],"on":[66,92,114],"value":[68],"express":[73],"medium-":[74],"or":[75],"long-range":[76],"order":[77],"set.":[80],"We":[81],"study":[82],"fundamental":[83],"geometric":[84],"combinatorial":[86],"properties":[87],"zones,":[90],"focusing":[91],"integer":[94,141],"lattice":[95],"its":[97],"perturbations.":[98],"Our":[99],"results":[100],"include":[101],"stability":[103],"under":[108],"perturbations,":[109],"linear":[111],"upper":[112],"bound":[113],"number":[116],"chambers":[118],"lattices":[123],"\u211d2":[125],"convergence":[129],"maximum":[132],"volume":[133],"chamber":[136],"to":[137],"zero":[138],"lattice.":[142]},"counts_by_year":[],"updated_date":"2026-05-13T08:25:38.343686","created_date":"2025-10-10T00:00:00"}
