{"id":"https://openalex.org/W7162404380","doi":"https://doi.org/10.48550/arxiv.2605.25533","title":"Projected multi-reference alignment","display_name":"Projected multi-reference alignment","publication_year":2026,"publication_date":"2026-05-25","ids":{"openalex":"https://openalex.org/W7162404380","doi":"https://doi.org/10.48550/arxiv.2605.25533"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.25533","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.25533","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":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2605.25533","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5137064658","display_name":"Amnon Balanov","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Balanov, Amnon","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5137015964","display_name":"Josh Katz","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Katz, Josh","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5137034334","display_name":"Tamir Bendory","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bendory, Tamir","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5137029008","display_name":"Dan Edidin","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Edidin, Dan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"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/T10044","display_name":"Protein Structure and Dynamics","score":0.08320000022649765,"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/T10044","display_name":"Protein Structure and Dynamics","score":0.08320000022649765,"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/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.066600002348423,"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/T10885","display_name":"Gene expression and cancer classification","score":0.060100000351667404,"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/moment","display_name":"Moment (physics)","score":0.7056999802589417},{"id":"https://openalex.org/keywords/dihedral-angle","display_name":"Dihedral angle","score":0.6780999898910522},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.45399999618530273},{"id":"https://openalex.org/keywords/population","display_name":"Population","score":0.3634999990463257},{"id":"https://openalex.org/keywords/second-moment-of-area","display_name":"Second moment of area","score":0.3490000069141388},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.33500000834465027},{"id":"https://openalex.org/keywords/orientation","display_name":"Orientation (vector space)","score":0.33250001072883606}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7069000005722046},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.7056999802589417},{"id":"https://openalex.org/C89025888","wikidata":"https://www.wikidata.org/wiki/Q911907","display_name":"Dihedral angle","level":4,"score":0.6780999898910522},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.45399999618530273},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4309999942779541},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.3634999990463257},{"id":"https://openalex.org/C61062188","wikidata":"https://www.wikidata.org/wiki/Q835065","display_name":"Second moment of area","level":2,"score":0.3490000069141388},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.33500000834465027},{"id":"https://openalex.org/C16345878","wikidata":"https://www.wikidata.org/wiki/Q107472979","display_name":"Orientation (vector space)","level":2,"score":0.33250001072883606},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.3073999881744385},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2946999967098236},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.2915000021457672},{"id":"https://openalex.org/C112313634","wikidata":"https://www.wikidata.org/wiki/Q7886648","display_name":"Complement (music)","level":5,"score":0.2888000011444092},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.28700000047683716},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.28369998931884766},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.28349998593330383},{"id":"https://openalex.org/C194226119","wikidata":"https://www.wikidata.org/wiki/Q161779","display_name":"Spatial reference system","level":2,"score":0.2752000093460083},{"id":"https://openalex.org/C178009071","wikidata":"https://www.wikidata.org/wiki/Q93344","display_name":"Trigonometric functions","level":2,"score":0.25060001015663147}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.25533","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.25533","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":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2605.25533","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.25533","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":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Motivated":[0],"by":[1,25,32],"structural":[2],"biology":[3],"applications,":[4],"we":[5],"study":[6],"the":[7,51,55,61,64,69,84,91,103,105,109,112,116,124,130,149,171,183,194,201],"projected":[8,70,88],"multi-reference":[9],"alignment":[10],"(MRA)":[11],"model,":[12],"in":[13,60,129,170],"which":[14],"an":[15],"unknown":[16],"signal":[17],"is":[18,48,80,193,200],"observed":[19],"through":[20],"noisy":[21],"samples,":[22],"each":[23],"generated":[24],"applying":[26],"a":[27,33,73,81,137],"random":[28],"cyclic":[29],"shift":[30],"followed":[31],"fixed":[34],"projection.":[35],"The":[36,46,77,166],"projection":[37],"merges":[38],"reflection-symmetric":[39],"index":[40],"pairs,":[41],"thereby":[42],"discarding":[43],"orientation":[44],"information.":[45],"goal":[47],"to":[49,90,102,136,144],"recover":[50],"dihedral":[52,75,96,131],"orbit":[53],"of":[54,68,95,196],"signal.":[56],"We":[57,147],"prove":[58],"that":[59],"high-noise":[62,172],"regime,":[63,173],"first":[65,106],"three":[66],"moments":[67,122,142],"observations":[71,197],"determine":[72],"generic":[74],"orbit.":[76],"main":[78],"mechanism":[79],"reduction,":[82],"at":[83],"moment":[85,107,114,159,164,178],"level,":[86],"from":[87,141],"MRA":[89],"reflection-invariant":[92],"phase-coupling":[93,126],"structure":[94],"MRA.":[97],"In":[98],"Fourier-cosine":[99,163],"coordinates":[100],"adapted":[101],"projection,":[104],"determines":[108,115],"mean":[110],"component,":[111],"second":[113],"Fourier":[117],"magnitudes,":[118],"and":[119,161,176,198],"selected":[120],"third":[121],"yield":[123],"cosine":[125],"relations":[127,134],"appearing":[128],"bispectrum.":[132],"These":[133],"lead":[135],"constructive":[138],"recovery":[139],"scheme":[140],"up":[143],"order":[145],"three.":[146],"complement":[148],"population":[150],"theory":[151],"with":[152,182],"finite-sample":[153],"experiments":[154],"comparing":[155],"expectation--maximization":[156],"(EM),":[157],"direct":[158,162,177],"optimization,":[160],"optimization.":[165],"results":[167],"show":[168],"that,":[169],"both":[174],"EM":[175],"optimization":[179],"are":[180],"consistent":[181],"predicted":[184],"third-moment":[185],"sample-complexity":[186],"scaling":[187],"$n":[188],"\\gtrsim":[189],"\u03c3^6$,":[190],"where":[191],"$n$":[192],"number":[195],"$\u03c3^2$":[199],"noise":[202],"variance.":[203]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-05-27T00:00:00"}