{"id":"https://openalex.org/W2137259347","doi":"https://doi.org/10.48550/arxiv.1209.0715","title":"The Synthesis and Analysis of Stochastic Switching Circuits","display_name":"The Synthesis and Analysis of Stochastic Switching Circuits","publication_year":2012,"publication_date":"2012-09-04","ids":{"openalex":"https://openalex.org/W2137259347","doi":"https://doi.org/10.48550/arxiv.1209.0715","mag":"2137259347"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:1209.0715","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1209.0715","pdf_url":"https://arxiv.org/pdf/1209.0715","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1209.0715","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5102804953","display_name":"Hongchao Zhou","orcid":"https://orcid.org/0000-0002-9322-0808","observed_orcids":["https://orcid.org/0000-0002-9322-0808","https://orcid.org/0000-0002-9783-0873"]},"institutions":[{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]},{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Zhou, Hongchao","raw_affiliation_strings":["Department of Statistics , University of California , Berkeley , CA 94720","California  Institute of Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics , University of California , Berkeley , CA 94720","institution_ids":["https://openalex.org/I95457486"]},{"raw_affiliation_string":"California  Institute of Technology","institution_ids":["https://openalex.org/I122411786"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5023368186","display_name":"Po\u2010Ling Loh","orcid":"https://orcid.org/0000-0002-6514-7834","observed_orcids":["https://orcid.org/0000-0002-6514-7834"]},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Loh, Po-Ling","raw_affiliation_strings":["Department of Statistics , University of California , Berkeley , CA 94720","University of California, Berkeley"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics , University of California , Berkeley , CA 94720","institution_ids":["https://openalex.org/I95457486"]},{"raw_affiliation_string":"University of California, Berkeley","institution_ids":["https://openalex.org/I95457486"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5043861677","display_name":"Jehoshua Bruck","orcid":"https://orcid.org/0000-0001-8474-0812","observed_orcids":["https://orcid.org/0000-0001-8474-0812"]},"institutions":[{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Bruck, Jehoshua","raw_affiliation_strings":["California  Institute of Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"California  Institute of Technology","institution_ids":["https://openalex.org/I122411786"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":9,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.266400009393692,"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"}},"topics":[{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.266400009393692,"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/T11567","display_name":"semigroups and automata theory","score":0.11429999768733978,"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/T12029","display_name":"DNA and Biological Computing","score":0.08590000122785568,"subfield":{"id":"https://openalex.org/subfields/2614","display_name":"Theoretical Computer Science"},"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/series-parallel-circuits","display_name":"series-parallel circuits","score":0.8270000219345093},{"id":"https://openalex.org/keywords/probability-approximation","display_name":"probability approximation","score":0.9779999852180481},{"id":"https://openalex.org/keywords/local-optimization-algorithms","display_name":"local optimization algorithms","score":0.6930000185966492},{"id":"https://openalex.org/keywords/relay-circuits","display_name":"relay circuits","score":0.4779999852180481}],"concepts":[{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.7348995208740234},{"id":"https://openalex.org/C134146338","wikidata":"https://www.wikidata.org/wiki/Q1815901","display_name":"Electronic circuit","level":2,"score":0.6253637075424194},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.49057430028915405},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.4646014869213104},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.46315258741378784},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.4598866403102875},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.45023664832115173},{"id":"https://openalex.org/C2780971903","wikidata":"https://www.wikidata.org/wiki/Q2933705","display_name":"Stochastic computing","level":3,"score":0.44687822461128235},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41810792684555054},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3680001497268677},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.34388893842697144},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.32691431045532227},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09685170650482178},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.07395920157432556},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"pmh:oai:arXiv.org:1209.0715","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1209.0715","pdf_url":"https://arxiv.org/pdf/1209.0715","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"pmh:oai:CiteSeerX.psu:10.1.1.259.8694","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.259.8694","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.paradise.caltech.edu/hzhou/papers/ISIT2010/stochatic%20circuits.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.760.9190","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.760.9190","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1209.0715.pdf","raw_type":"text"},{"id":"pmh:oai:authors.library.caltech.edu:64187","doi":null,"is_oa":false,"landing_page_url":"https://resolver.caltech.edu/CaltechAUTHORS:20160203-092316194","pdf_url":null,"source":{"id":"https://openalex.org/S4306402161","display_name":"CaltechAUTHORS (California Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I122411786","host_organization_name":"California Institute of Technology","host_organization_lineage":["https://openalex.org/I122411786"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Report or Paper"},{"id":"doi:10.48550/arxiv.1209.0715","doi":"https://doi.org/10.48550/arxiv.1209.0715","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1209.0715","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1209.0715","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1209.0715","pdf_url":"https://arxiv.org/pdf/1209.0715","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G4841326577","display_name":"Collaborative Research: The Molecular Programming Project","funder_award_id":"0832824","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2137259347.pdf","grobid_xml":"https://content.openalex.org/works/W2137259347.grobid-xml"},"referenced_works_count":15,"referenced_works":["https://openalex.org/W1621944155","https://openalex.org/W1983575666","https://openalex.org/W1987683681","https://openalex.org/W2000617148","https://openalex.org/W2000804241","https://openalex.org/W2013098447","https://openalex.org/W2019906979","https://openalex.org/W2030020312","https://openalex.org/W2053619330","https://openalex.org/W2114723472","https://openalex.org/W2116676915","https://openalex.org/W2143075476","https://openalex.org/W2150477349","https://openalex.org/W2162346812","https://openalex.org/W2996041333"],"related_works":["https://openalex.org/W2108896030","https://openalex.org/W2169544988","https://openalex.org/W2019906979","https://openalex.org/W2026284009","https://openalex.org/W1975491074","https://openalex.org/W2021307999","https://openalex.org/W2070952247","https://openalex.org/W1988630495","https://openalex.org/W2128168148","https://openalex.org/W2040189269"],"abstract_inverted_index":{"Stochastic":[0],"switching":[1,17,40,129,157,235],"circuits":[2,5,18,79,89],"are":[3,80,90],"relay":[4],"that":[6,76,165,182,229],"consist":[7],"of":[8,15,25,38,61,99,109,116,119,127,171,204,233],"stochastic":[9,16,39,68,128,156],"switches":[10],"called":[11],"pswitches.":[12],"The":[13,226],"study":[14,50,124],"has":[19],"widespread":[20],"applications":[21],"in":[22,66],"many":[23],"fields":[24],"computer":[26],"science,":[27],"neuroscience,":[28],"and":[29,45,74,135,163],"biochemistry.":[30],"In":[31,210],"this":[32,211],"paper,":[33],"we":[34,49,123,141,213],"discuss":[35],"several":[36],"properties":[37],"circuits,":[41],"including":[42],"robustness,":[43,52],"expressibility,":[44],"probability":[46,145],"approximation.":[47],"First,":[48],"the":[51,54,93,117,120,125,175,192,230],"namely,":[53],"effect":[55],"caused":[56],"by":[57,97,105],"introducing":[58],"an":[59,132,205,215,240],"error":[60,84,95,232],"size":[62,100,118],"\u03b5to":[63],"each":[64],"pswitch":[65,137,207],"a":[67,106,111,136,153,169,186,201,234],"circuit.":[69,121],"We":[70,159,179],"analyze":[71],"two":[72],"constructions":[73],"prove":[75,164],"simple":[77,112,154],"series-parallel":[78,88,113,155],"robust":[81],"to":[82,221],"small":[83],"perturbations,":[85],"while":[86],"general":[87,202],"not.":[91],"Specifically,":[92],"total":[94],"introduced":[96],"perturbations":[98],"less":[101],"than":[102,190],"\u03b5is":[103],"bounded":[104],"constant":[107],"multiple":[108,170],"\u03b5in":[110],"circuit,":[114],"independent":[115],"Next,":[122],"expressibility":[126],"circuits:":[130],"Given":[131],"integer":[133],"q":[134,167,184],"set":[138,208],"S=\\{\\frac{1}{q},\\frac{2}{q},...,\\frac{q-1}{q}\\},":[139],"can":[140],"synthesize":[142],"any":[143,223],"rational":[144],"with":[146,152,239],"denominator":[147],"q^n":[148],"(for":[149],"arbitrary":[150,206],"n)":[151],"circuit?":[158],"generalize":[160],"previous":[161],"results":[162],"when":[166,183],"is":[168,177,185,194,198],"2":[172],"or":[173],"3,":[174,191],"answer":[176,193],"yes.":[178],"also":[180],"show":[181],"prime":[187],"number":[188],"larger":[189],"no.":[195],"Probability":[196],"approximation":[197,231],"studied":[199],"for":[200],"case":[203],"S=\\{s_1,s_2,...,s_{|S|}\\}.":[209],"case,":[212],"propose":[214],"algorithm":[216],"based":[217],"on":[218],"local":[219],"optimization":[220],"approximate":[222],"desired":[224],"probability.":[225],"analysis":[227],"reveals":[228],"circuit":[236,242],"decreases":[237],"exponentially":[238],"increasing":[241],"size.":[243]},"counts_by_year":[{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-11-05T12:25:35.769452","created_date":"2016-06-24T00:00:00"}
