{"id":"https://openalex.org/W4416497929","doi":"https://doi.org/10.48550/arxiv.2506.22172","title":"Bridging Chaos Game Representations and $k$-mer Frequencies of DNA Sequences","display_name":"Bridging Chaos Game Representations and $k$-mer Frequencies of DNA Sequences","publication_year":2025,"publication_date":"2025-06-27","ids":{"openalex":"https://openalex.org/W4416497929","doi":"https://doi.org/10.48550/arxiv.2506.22172"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2506.22172","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2506.22172","pdf_url":"https://arxiv.org/pdf/2506.22172","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"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2506.22172","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5111363039","display_name":"Haoze He","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"He, Haoze","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5041517753","display_name":"Lila Kari","orcid":"https://orcid.org/0000-0001-5700-5353"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kari, Lila","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5035876835","display_name":"Pablo Millan Arias","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Arias, Pablo Millan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"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":2,"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/T12946","display_name":"Fractal and DNA sequence analysis","score":0.9710000157356262,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},"topics":[{"id":"https://openalex.org/T12946","display_name":"Fractal and DNA sequence analysis","score":0.9710000157356262,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T13664","display_name":"Genome Rearrangement Algorithms","score":0.004100000020116568,"subfield":{"id":"https://openalex.org/subfields/1311","display_name":"Genetics"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T10015","display_name":"Genomics and Phylogenetic Studies","score":0.0034000000450760126,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/de-bruijn-sequence","display_name":"De Bruijn sequence","score":0.6406000256538391},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6025999784469604},{"id":"https://openalex.org/keywords/eulerian-path","display_name":"Eulerian path","score":0.5525000095367432},{"id":"https://openalex.org/keywords/complementary-sequences","display_name":"Complementary sequences","score":0.4237000048160553},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.37880000472068787},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.36419999599456787},{"id":"https://openalex.org/keywords/vectorization","display_name":"Vectorization (mathematics)","score":0.35359999537467957},{"id":"https://openalex.org/keywords/dna-sequencing","display_name":"DNA sequencing","score":0.33149999380111694}],"concepts":[{"id":"https://openalex.org/C170320093","wikidata":"https://www.wikidata.org/wiki/Q1953457","display_name":"De Bruijn sequence","level":2,"score":0.6406000256538391},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6025999784469604},{"id":"https://openalex.org/C43058520","wikidata":"https://www.wikidata.org/wiki/Q624580","display_name":"Eulerian path","level":3,"score":0.5525000095367432},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.5001000165939331},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.49470001459121704},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4763999879360199},{"id":"https://openalex.org/C32795469","wikidata":"https://www.wikidata.org/wiki/Q5156430","display_name":"Complementary sequences","level":2,"score":0.4237000048160553},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3986000120639801},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.37880000472068787},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.36419999599456787},{"id":"https://openalex.org/C41681595","wikidata":"https://www.wikidata.org/wiki/Q7917855","display_name":"Vectorization (mathematics)","level":2,"score":0.35359999537467957},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3529999852180481},{"id":"https://openalex.org/C51679486","wikidata":"https://www.wikidata.org/wiki/Q380546","display_name":"DNA sequencing","level":3,"score":0.33149999380111694},{"id":"https://openalex.org/C20218877","wikidata":"https://www.wikidata.org/wiki/Q3066095","display_name":"De Bruijn graph","level":3,"score":0.32839998602867126},{"id":"https://openalex.org/C68859911","wikidata":"https://www.wikidata.org/wiki/Q1503724","display_name":"Pattern matching","level":2,"score":0.3264000117778778},{"id":"https://openalex.org/C138268822","wikidata":"https://www.wikidata.org/wiki/Q1051925","display_name":"Resolution (logic)","level":2,"score":0.32170000672340393},{"id":"https://openalex.org/C39368324","wikidata":"https://www.wikidata.org/wiki/Q5024959","display_name":"Hyperspace","level":2,"score":0.3158999979496002},{"id":"https://openalex.org/C160920958","wikidata":"https://www.wikidata.org/wiki/Q7662746","display_name":"Synthetic data","level":2,"score":0.30979999899864197},{"id":"https://openalex.org/C35527583","wikidata":"https://www.wikidata.org/wiki/Q189156","display_name":"Cellular automaton","level":2,"score":0.27559998631477356},{"id":"https://openalex.org/C2779374083","wikidata":"https://www.wikidata.org/wiki/Q5011038","display_name":"CHAOS (operating system)","level":2,"score":0.27480000257492065},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.2563000023365021},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.2549999952316284}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2506.22172","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2506.22172","pdf_url":"https://arxiv.org/pdf/2506.22172","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"},{"id":"doi:10.48550/arxiv.2506.22172","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2506.22172","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2506.22172","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2506.22172","pdf_url":"https://arxiv.org/pdf/2506.22172","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":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"This":[0,95],"paper":[1],"establishes":[2],"formal":[3],"mathematical":[4],"foundations":[5],"linking":[6],"Chaos":[7],"Game":[8],"Representations":[9],"(CGR)":[10],"of":[11,26,35,50,59,98,111,126,134],"DNA":[12,81,127],"sequences":[13,82,99],"to":[14,32,46,63],"their":[15],"underlying":[16],"$k$-mer":[17,48,85,102,159],"frequencies.":[18],"We":[19],"prove":[20],"that":[21,78,155],"the":[22,47,51,68,109,132,151],"Frequency":[23],"CGR":[24,36,60,113,157],"(FCGR)":[25],"order":[27],"$k$":[28],"is":[29,150],"mathematically":[30],"equivalent":[31],"a":[33],"discretization":[34],"at":[37],"resolution":[38],"$2^k":[39],"\\times":[40],"2^k$,":[41],"and":[42,142,161,170],"its":[43],"vectorization":[44],"corresponds":[45],"frequencies":[49],"sequence.":[52],"Additionally,":[53],"we":[54,74],"characterize":[55],"how":[56],"symmetry":[57],"transformations":[58],"images":[61,114],"correspond":[62],"specific":[64],"nucleotide":[65],"permutations":[66],"in":[67],"originating":[69],"sequences.":[70,128],"Leveraging":[71],"these":[72],"insights,":[73],"introduce":[75],"an":[76],"algorithm":[77],"generates":[79],"synthetic":[80,112],"from":[83],"prescribed":[84],"distributions":[86],"by":[87],"constructing":[88],"Eulerian":[89],"paths":[90],"on":[91],"De":[92],"Bruijn":[93],"multigraphs.":[94],"enables":[96],"reconstruction":[97],"matching":[100],"target":[101],"profiles":[103],"with":[104],"arbitrarily":[105],"high":[106],"precision,":[107],"facilitating":[108],"creation":[110],"for":[115,121,167],"applications":[116],"such":[117],"as":[118],"data":[119,141],"augmentation":[120],"machine":[122],"learning-based":[123],"taxonomic":[124],"classification":[125],"Numerical":[129],"experiments":[130],"validate":[131],"effectiveness":[133],"our":[135,147],"method":[136],"across":[137],"both":[138],"real":[139],"genomic":[140,168],"artificially":[143],"sampled":[144],"distributions.":[145],"To":[146],"knowledge,":[148],"this":[149],"first":[152],"comprehensive":[153],"framework":[154],"unifies":[156],"geometry,":[158],"statistics,":[160],"sequence":[162],"reconstruction,":[163],"offering":[164],"new":[165],"tools":[166],"analysis":[169],"visualization.":[171]},"counts_by_year":[{"year":2025,"cited_by_count":2}],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2025-10-10T00:00:00"}