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"Augustana", "College,", "Rock", "Island,", "USA;", "Talha", "Hassan,", "talhahassan18@augustana.edu,", "Augustana", "College,", "Rock", "Island,", "USA;", "Andrew", "Sward,", "andrewsward@augustana.edu,", "Augustana", "College,", "Rock", "Island,", "USA;", "Tauheed", "Khan", "Mohd,", "tauheedkhanmohd@augustana.edu,", "Augustana", "College,", "Rock", "Island,", "USA." ] }
2301.00001v1.pdf_2
null
ArxivOCR_part_1
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2301.00001v1.pdf_3
null
ArxivOCR_part_1
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2301.00001v1.pdf_4
null
ArxivOCR_part_1
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2301.00001v1.pdf_5
null
ArxivOCR_part_1
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2301.00001v1.pdf_6
null
ArxivOCR_part_1
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2301.00001v1.pdf_7
null
ArxivOCR_part_1
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"cards", "that", "they", "currently", "own,", "and", "see", "options", "for", "combining", "them", "using", "either", "multiplication", "or", "division.", "Figure", "1", "displays", "the", "layout", "of", "the", "screen", "where", "user", "selected", "cards", "are", "shown", "on", "the", "left,", "and", "potential", "results", "are", "shown", "on", "the", "right.", "The", "page", "utilizes", "Bootstrap5", "capabilities", "to", "format", "effectivel", "to", "differe", "screen", "sizes", "and", "resolutions.", "It", "connects", "with", "a", "back", "end", "script", "to", "the", "smart", "contract.", "This", "provides", "functionality", "to", "the", "buttons", "and", "easy", "generation", "of", "possible", "NFT", "results.", "Below", "shows", "the", "probabilities", "of", "generated", "NFT", "outcomes", "based", "on", "the", "selected", "input", "cards.", "5.6.3", "Marketplace", "and", "MyCards.", "Marketplace", "and", "MyCards", "are", "similar", "pages,", "as", "they", "connect", "to", 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2301.00001v1.pdf_8
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ArxivOCR_part_1
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2301.00001v1.pdf_9
null
ArxivOCR_part_1
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2301.00001v1.pdf_10
null
ArxivOCR_part_1
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{ "word": [ "Jordan", "Thompson,", "Ryan", "Benac,", "Kidus", "Olana,", "Talha", "Hassan,", "Andrew", "Sward,", "and", "Tauheed", "Khan", "Mohd", "10", "Polygon", "testnet", "and", "can", "be", "interacted", "with", "using", "test", "Matic.", "Each", "web", "page", "has", "functionality", "to", "display", "the", "user’s", "owned", "NFTs", "as", "well", "as", "the", "NFTs", "they", "have", "put", "for", "sale", "on", "the", "marketplace.", "Using", "NextJS", "will", "also", "allow", "the", "Combination", "page", "to", "have", "functionality", "and", "smart", "contract", "use.", "It", "is", "also", "worth", "noting", "that", "the", "created", "web", "page", "is", "not", "required", "to", "interact", "with", "the", "NFTrig", "smart", "contracts.", "8", "RECOMMENDATIONS", "FOR", "FUTURE", "WORK", "The", "goal", "for", "this", "project", "was", "a", "working", "Beta", "demo", "that", "shows", "application", "functionality,", "and", "correct", "smart", "contract", "execution.", "There", "are", "many", "other", "features", "planned", "for", "the", "continued", "work", "of", "this", "project.", "The", "first", "as", "earlie", "explained", "is", "a", "gam", "optio", "which", "challenge", "the", "user", "with", "trigonometr", "trivia", "and", "math", "problems.", "Answering", "these", "questions", "successfully", "will", "increase", "the", "experience", "points", "of", "a", "user.", "The", "user", "can", "then", "use", "these", "experience", "points", "to", "purchase", "individual", "or", "packs", "of", "NFTrig", "cards,", "or", "they", "can", "be", "used", "to", "combine", "cards.", "REFERENCES", "[1]", "Rana", "M", "Amir", "Latif,", "Khalid", "Hussain,", "NZ", "Jhanjhi,", "Anand", "Nayyar,", "and", "Osama", "Rizwan.", "2020.", "A", "remix", "IDE:", "smart", "contract-based", "framework", "for", "the", "healthcare", "sector", "by", "using", "Blockchain", "technology.", "Multimedia", "Tools", "and", "Applications", "(2020),", "1–24.", "[2]", "Mohsen", "Attaran", "and", "Angappa", "Gunasekaran.", "2019.", "Blockchain", "for", "Gaming.", "In", "Applications", "of", "Blockchain", "Technology", "in", "Business.", "Springer,", "85–88.", "[3]", "Rocsana", "Bucea-Manea-T,", "Oliva", "Martins,", "Radu", "Bucea-Manea-T,", "Cătălin", "Gheorghit,ă,", "Valentin", "Kuleto,", "Milena", "P", "Ilić,", "and", "Violeta-Elena", "Simion.", "2021.", "Blockchain", "Technology", "Enhances", "Sustainable", "Higher", "Education.", "Sustainability", "13,", "22", "(2021),", "12347.", "[4]", "Juan", "José", "Bullón,", "Ascensión", "Hernández", "Encinas,", "M.", "Jesús", "Santos", "Sánchez,", "and", "Víctor", "Gayoso", "Martínez.", "2018.", "Analysis", "of", "student", "feedback", "when", "using", "gamificatio", "tools", "in", "math", "subjects", "In", "2018", "IEE", "Global", "Engineerin", "Educatio", "Conference", "(EDUCON).", "1818–1823.", "https://doi.org/10.1109/EDUCON.2018.8363455", "[5]", "Guang", "Chen,", "Bing", "Xu,", "Manli", "Lu,", "and", "Nian-Shing", "Chen.", "2018.", "Exploring", "blockchain", "technology", "and", "its", "potential", "applications", "for", "education.", "Smart", "Learning", "Environments", "5,", "1", "(2018),", "1–10.", "[6]", "Luisanna", "Cocco,", "Andrea", "Pinna,", "and", "Michele", "Marchesi.", "2017.", "Banking", "on", "blockchain:", "Costs", "savings", "thanks", "to", "the", "blockchain", "technology.", "Future", "internet", "9,", "3", "(2017),", "25.", "[7]", "Marco", "Conoscenti,", "Antonio", "Vetro,", "and", "Juan", "Carlos", "De", "Martin.", "2016.", "Blockchain", "for", "the", "Internet", "of", "Things:", "A", "systematic", "literature", "review.", "In", "2016", "IEEE/ACS", "13th", "International", "Conference", "of", "Computer", "Systems", "and", "Applications", "(AICCSA).", "IEEE,", "1–6.", "[8]", "Oscar", "Delgado-Mohatar,", "Ruben", "Tolosana,", "Julian", "Fierrez,", "and", "Aythami", "Morales.", "2020.", "Blockchain", "in", "the", "Internet", "of", "Things:", "Architectures", "and", "Implementation.", "In", "2020", "IEEE", "44th", "Annual", "Computers,", "Software,", "and", "Applications", "Conference", "(COMPSAC).", "1072–1077.", "https://doi.org/10.1109/COMPSAC48688.2020.0-131", "[9]", "A", "Elmessiry,", "M", "Elmessiry,", "and", "L", "Bridgesmith.", "2021.", "NFT", "STUDENT", "TEACHER", "INCENTIVE", "SYSTEM", "(NFT-STIS).", "In", "Proceedings", "of", "EDULEARN21", "Conference,", "Vol.", "5.", "6th.", "[10]", "Usef", "Faghihi,", "Albert", "Brautigam,", "Kris", "Jorgenson,", "David", "Martin,", "Angela", "Brown,", "Elizabeth", "Measures,", "and", "Sioui", "Maldonado-", "Bouchard.", "2014.", "How", "Gamificatio", "Applies", "for", "Educationa", "Purpos", "Speciall", "with", "College", "Algebra.", "Procedi", "Compute", "0.1016/j.procs.2014.11.102", "5th", "Annual", "International", "Conference", "on", "Science", "41", "(2014),", "182–187.", "Biologically", "Inspired", "Cognitive", "Architectures,", "2014", "BICA.", "[11]", "Julian", "Alberto", "Garcia-Garcia,", "Nicolás", "Sánchez-Gómez,", "David", "Lizcano,", "María", "José", "Escalona,", "and", "Tomás", "Wojdyński.", "2020.", "Using", "blockchain", "to", "improve", "collaborative", "business", "process", "management:", "Systematic", "literature", "review.", "IEEE", "Access", "8", "(2020),", "142312–142336.", "[12]", "Susan", "Gass,", "Koen", "Van", "Gorp,", "and", "Paula", "Winke.", "2019.", "Using", "differen", "carrots", "How", "incentivizatio", "affec", "proficie", "testing", "outcomes.", "Foreign", "Language", "Annals", "52,", "2", "(2019),", "216–236.", "[13]", "Ammar", "Yanuar", "Ghulam.", "2021.", "Konseptual", "Desain", "Website", "Aplikasi", "Penyedia", "Jasa", "Kursus", "Mengemudi", "Mobil", "Di", "Purwokerto", "Menggunakan", "Framework", "Bootstrap", "5.", "(2021).", "[14]", "Alexander", "Grech", "and", "Anthony", "F", "Camilleri.", "2017.", "Blockchain", "in", "education.", "Luxembourg:", "Publications", "Offi", "of", "the", "European", "Union.", "[15]", "Marijn", "Haverbeke.", "2018.", "Eloquent", "javascript:", "A", "modern", "introduction", "to", "programming.", "No", "Starch", "Press.", "[16]", "Marko", "Hölbl,", "Marko", "Kompara,", "Aida", "Kamišalić,", "and", "Lili", "Nemec", "Zlatolas.", "2018.", "A", "systematic", "review", "of", "the", "use", "of", "blockchain", "in", "healthcare.", "Symmetry", "10,", "10", "(2018),", "470." ] }
2301.00002v1.pdf_1
null
ArxivOCR_part_1
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2301.00002v1.pdf_2
null
ArxivOCR_part_1
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2301.00002v1.pdf_3
null
ArxivOCR_part_1
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2301.00002v1.pdf_4
null
ArxivOCR_part_1
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2301.00002v1.pdf_5
null
ArxivOCR_part_1
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2301.00002v1.pdf_6
null
ArxivOCR_part_1
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2301.00002v1.pdf_7
null
ArxivOCR_part_1
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2301.00002v1.pdf_8
null
ArxivOCR_part_1
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2301.00002v1.pdf_9
null
ArxivOCR_part_1
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2301.00002v1.pdf_10
null
ArxivOCR_part_1
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2301.00003v1.pdf_1
null
ArxivOCR_part_1
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2301.00003v1.pdf_2
null
ArxivOCR_part_1
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2301.00003v1.pdf_3
null
ArxivOCR_part_1
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{ "word": [ "Emotion", "in", "Cognitive", "Architecture:", "Emergent", "Properties", "from", "Interactions", "with", "Human", "Emotion", "CHAI", "’22,", "December", "5,", "2022,", "Christchurch,", "New", "Zealand", "REFERENCES", "(Biopolis,", "Singapore)", "(HAI", "’16).", "341–344.", "[11]", "Junya", "Morita,", "Thanakit", "Pitakchokchai,", "Giri", "Basanta", "Raj,", "Yusuke", "Yamamoto,", "[1]", "John", "R", "Anderson.", "2007.", "How", "Can", "the", "Human", "Mind", "Occur", "in", "the", "Physical", "Universe.", "Hiroyasu", "Yuhashi,", "and", "Teppei", "Koguchi.", "2022.", "Regulating", "Ruminative", "Web", "Brows-", "Oxford", "University", "Press,", "New", "York.", "ing", "Based", "on", "the", "Counterbalance", "Modeling", "Approach.", "Frontiers", "in", "Artificia", "[2]", "Simon", "Baron-Cohen.", "2020.", "The", "pattern", "seekers:", "How", "autism", "drives", "human", "invention.", "[12]", "Kazuma", "Nagashima,", "Junya", "Morita,", "and", "Yugo", "Takeuchi.", "2020.", "Modeling", "intrin-", "Basic", "Books.", "Intelligence", "5", "(2022).", "[3]", "Lisa", "Feldman", "Barrett.", "2017.", "How", "emotions", "are", "made:", "The", "secret", "life", "of", "the", "brain.", "sic", "motivation", "in", "ACT-R", "Focusing", "on", "the", "relation", "between", "pattern", "matching", "Pan", "Macmillan.", "and", "intellectual", "curiosity.", "In", "Proceedings", "of", "the", "18th", "International", "Conference", "on", "[4]", "Antonio", "Damasio.", "1994.", "Descartes’", "Error.", "Random", "House,", "New", "York.", "Cognitive", "Modelling.", "Applied", "Cognitive", "Science", "Lab,", "167–173.", "[5]", "Christopher", "L", "Dancy,", "Frank", "E", "Ritter,", "Keith", "A", "Berry,", "and", "Laura", "C", "Klein.", "2015.", "Using", "a", "cognitive", "architecture", "with", "a", "physiological", "substrate", "to", "represent", "ef-", "[13]", "Kazuma", "Nagashima,", "Junya", "Morita,", "and", "Yugo", "Takeuchi.", "2021.", "Curiosity", "as", "pattern", "matching:", "Simulating", "the", "effect", "of", "intrinsi", "reward", "on", "the", "level", "of", "processing", "fects", "of", "a", "psychological", "stressor", "on", "cognition.", "Computational", "and", "Mathematical", "In", "Proceedings", "of", "the", "19th", "International", "Conference", "on", "Cognitive", "Modelling.", "197–", "Organization", "Theory", "21,", "1", "(2015),", "90–114.", "203.", "[6]", "K.", "Itabashi,", "J.", "Morita,", "T.", "Hirayama,", "K.", "Mase,", "and", "Yamada", "K.", "2020.", "Interactive", "Model-based", "Reminiscence", "Using", "a", "Cognitive", "Model", "and", "Physiological", "Indices.", "[14]", "K", "Nagashima,", "J", "Nishikawa,", "R", "Yoneda,", "J", "Morita,", "and", "T", "Terada.", "2022.", "Model-", "ing", "optimal", "arousal", "by", "integrating", "basic", "cognitive", "components.", "In", "International", "In", "Proceedings", "of", "the", "18th", "International", "Conference", "on", "Cognitive", "Modeling.", "Conference", "on", "Cognitive", "Modeling", "2022.", "[7]", "Raph", "Koster.", "2013.", "Theory", "of", "Fun", "for", "Game", "Design.", "O’Reilly", "Media,", "Sebastopol.", "[15]", "F.", "E.", "Ritter.", "2009.", "Two", "cognitive", "modeling", "frontiers", "Emotions", "and", "usability.", "[8]", "D.", "M.", "Landers.", "1980.", "The", "arousal-performance", "relationship", "revisited.", "Research", "Transactions", "of", "the", "Japanese", "Society", "for", "Artificia", "Intelligenc", "24,", "2", "(2009)", "241-", "Quarterly", "for", "Exercise", "and", "Sport", "51,", "1", "(1980),", "77–90.", "249.", "[9]", "Joseph", "LeDoux.", "2020.", "The", "deep", "history", "of", "ourselves:", "The", "four-billion-year", "story", "of", "[16]", "James", "A", "Russell.", "2003.", "Core", "affec", "and", "the", "psychologica", "constructio", "of", "emotion", "how", "we", "got", "conscious", "brains.", "Penguin.", "Psychological", "Review", "110,", "1", "(2003),", "145.", "[10]", "Junya", "Morita,", "Takatsugu", "Hirayama,", "Kenji", "Mase,", "and", "Kazunori", "Yamada.", "2016.", "Model-Based", "Reminiscence:", "Guiding", "Mental", "Time", "Travel", "by", "Cognitive", "Modeling.", " [17]", "Gary", "R", "VandenBos.", "2007.", "APA", "dictionary", "of", "psychology.", "American", "Psychological", "Association.", "In", "Proceedings", "of", "the", "Fourth", "International", "Conference", "on", "Human", "Agent", "Interaction" ] }
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ArxivOCR_part_1
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2301.00008v1.pdf_3
null
ArxivOCR_part_1
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2301.00008v1.pdf_4
null
ArxivOCR_part_1
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2301.00008v1.pdf_5
null
ArxivOCR_part_1
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2301.00008v1.pdf_6
null
ArxivOCR_part_1
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null
ArxivOCR_part_1
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"target", "function", "are", "the", "same", "for", "both", "the", "manifolds.", "This", "ensures", "that", "the", "domains", "of", "both", "the", "problems", "have", "length", "close", "to", "6.28.", "Further", "experimental", "details", "are", "in", "Appendix", "H.", "The", "results,", "averaged", "over", "20", "runs,", "are", "presented", "in", "Figures", "4", "and", "5.", "We", "note", "that", "C", "M", "is", "smaller", "for", "Sphere", "(based", "on", "Figure", "4)", "and", "the", "curvature", "is", "positive", "whilst", "C", "M", "is", "larger", "for", "tractrix", "and", "the", "curvature", "is", "negative.", "Both", "of", "these", "constants", "(curvature", "and", "C", "M", ")", "contribute", "to", "the", "lower", "bound", "7" ] }
2301.00008v1.pdf_8
null
ArxivOCR_part_1
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2301.00008v1.pdf_9
null
ArxivOCR_part_1
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2301.00008v1.pdf_10
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ArxivOCR_part_1
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{ "word": [ "2015,", "Schmidt-Hieber,", "2019].", "We", "incorporate", "the", "idea", "of", "data", "geometry", "into", "measuring", "the", "effective", "approximation", "capacity", "of", "DNNs,", "deriving", "average", "bounds", "on", "the", "density", "of", "boundary", "regions", "and", "distance", "from", "the", "boundary", "when", "the", "data", "is", "sampled", "from", "a", "low", "dimensional", "manifold.", "Our", "experimental", "results", "corroborate", "our", "theoretical", "results.", "We", "also", "present", "insights", "into", "expressivity", "of", "DNNs", "on", "low", "dimensional", "manfiolds", "for", "the", "case", "of", "high", "dimensional", "datasets.", "Estimating", "the", "geometry,", "dimensionality", "and", "curvature,", "of", "these", "image", "manifolds", "accurately", "is", "a", "problem", "that", "remains", "largely", "unsolved", "[Brehmer", "and", "Cranmer,", "2020,", "Perraul-Joncas", "and", "Meila,", "2013],", "which", "limits", "our", "inferences", "on", "high", "dimensional", "dataset", "to", "observations", "that", "guide", "future", "research.", "We", "note", "that", "proving", "a", "lower", "bound", "on", "the", "number", "of", "linear", "regions,", "as", "done", "by", "Hanin", "and", "Rolnick", "[2019a],", "for", "the", "manifold", "setting", "remains", "open.", "Our", "work", "opens", "up", "avenues", "for", "further", "research", "that", "combines", "model", "geometry", "and", "data", "geometry", "and", "can", "lead", "to", "empirical", "research", "geared", "towards", "developing", "DNN", "architectures", "for", "high", "dimensional", "datasets", "that", "lie", "on", "low", "dimensional", "manifold.", "6", "Acknowledgements", "This", "work", "was", "funded", "by", "L2M", "(DARPA", "Lifelong", "Learning", "Machines", "program", "under", "grant", "number", "FA8750-18-2-0117),", "the", "Penn", "MURI", "(ONR", "under", "the", "PERISCOPE", "MURI", "Contract", "N00014-", "17-", "1-2699),", "and", "the", "ONR", "Swarm", "(the", "ONR", "under", "grant", "number", "N00014-21-1-2200).", "This", "research", "was", "conducted", "using", "computational", "resources", "and", "services", "at", "the", "Center", "for", "Computation", "and", "Visualization,", "Brown", "University.", "We", "would", "like", "to", "thank", "Sam", "Lobel,", "Rafael", "Rodriguez", "Sanchez,", "and", "Akhil", "Bagaria", "for", "refining", "our", "work,", "multiple", "technical", "discussions,", "and", "their", "helpful", "feedback", "on", "the", "implementation", "details.", "We", "also", "thank", "Tejas", "Kotwal", "for", "assistance", "on", "deriving", "the", "mathematical", "details", "related", "to", "the", "1D", "Tractrix", "and", "sources", "for", "various", "citations.", "We", "thank", "Professor", "Pedro", "Lopes", "de", "Almeida,", "Nihal", "Nayak,", "Cameron", "Allen", "and", "Aarushi", "Kalra", "for", "their", "valuable", "comments", "on", "writing", "and", "presentation", "of", "our", "work.", "We", "thank", "all", "the", "members", "of", "the", "Brown", "robotics", "lab", "for", "their", "guidance", "and", "support", "at", "various", "stages", "of", "our", "work.", "Finally,", "we", "are", "indebted", "to,", "and", "graciously", "thank,", "the", "numerous", "anonymous", "reviewers", "for", "their", "time", "and", "labor", "as", "their", "valuable", "feedback", "and", "thoughtful", "engagement", "have", "shaped", "and", "vastly", "refine", "our", "work.", "References", "Zeyuan", "Allen-Zhu,", "Y.", "Li,", "and", "Zhao", "Song.", "A", "convergence", "theory", "for", "deep", "learning", "via", "over-", "parameterization.", "ArXiv,", "abs/1811.03962,", "2019.", "M.", "Anthony", "and", "P.", "Bartlett.", "Neural", "network", "learning", "theoretical", "foundations.", "In", "Neural", "Network", "Learning", "-", "Theoretical", "Foundations,", "1999.", "Sanjeev", "Arora,", "Rong", "Ge,", "Behnam", "Neyshabur,", "and", "Yi", "Zhang.", "Stronger", "generalization", "bounds", "for", "deep", "nets", "via", "a", "compression", "approach.", "ArXiv,", "abs/1802.05296,", "2018.", "Sanjeev", "Arora,", "Nadav", "Cohen,", "Noah", "Golowich,", "and", "Wei", "Hu.", "A", "convergence", "analysis", "of", "gradient", "descent", "for", "deep", "linear", "neural", "networks.", "ArXiv,", "abs/1810.02281,", "2019a.", "Sanjeev", "Arora,", "Nadav", "Cohen,", "Wei", "Hu,", "and", "Yuping", "Luo.", "Implicit", "regularization", "in", "deep", "matrix", "factorization.", "In", "NeurIPS,", "2019b.", "D.", "Arpit,", "Stanislaw", "Jastrzebski,", "Nicolas", "Ballas,", "David", "Krueger,", "Emmanuel", "Bengio,", "Maxinder", "s.", "Kanwal,", "Tegan", "Maharaj,", "Asja", "Fischer,", "Aaron", "C.", "Courville,", "Yoshua", "Bengio,", "and", "S.", "Lacoste-Julien.", "A", "closer", "look", "at", "memorization", "in", "deep", "networks.", "ArXiv,", "abs/1706.05394,", "2017.", "Peter", "L.", "Bartlett,", "Vitaly", "Maiorov,", "and", "Ron", "Meir.", "Almost", "linear", "vc-dimension", "bounds", "for", "piecewise", "polynomial", "networks.", "Neural", "Computation,", "10:2159–2173,", "1998.", "P.", "P.", "Brahma,", "Dapeng", "Oliver", "Wu,", "and", "Y.", "She.", "Why", "deep", "learning", "works:", "A", "manifold", "disentanglement", "perspective.", "IEEE", "Transactions", "on", "Neural", "Networks", "and", "Learning", "Systems,", "27:1997–2008,", "2016.", "Johann", "Brehmer", "and", "Kyle", "Cranmer.", "Flows", "for", "simultaneous", "manifold", "learning", "and", "density", "estimation.", "ArXiv,", "abs/2003.13913,", "2020.", "10" ] }
2301.00009v1.pdf_1
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ArxivOCR_part_1
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2301.00009v1.pdf_2
null
ArxivOCR_part_1
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ArxivOCR_part_1
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2301.00009v1.pdf_4
null
ArxivOCR_part_1
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2301.00009v1.pdf_5
null
ArxivOCR_part_1
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2301.00009v1.pdf_6
null
ArxivOCR_part_1
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2301.00009v1.pdf_7
null
ArxivOCR_part_1
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2301.00009v1.pdf_8
null
ArxivOCR_part_1
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2301.00009v1.pdf_9
null
ArxivOCR_part_1
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2301.00009v1.pdf_10
null
ArxivOCR_part_1
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"2016.", "10" ] }
2301.00011v1.pdf_1
null
ArxivOCR_part_1
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2301.00011v1.pdf_2
null
ArxivOCR_part_1
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2301.00011v1.pdf_3
null
ArxivOCR_part_1
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2301.00011v1.pdf_4
null
ArxivOCR_part_1
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2301.00011v1.pdf_5
null
ArxivOCR_part_1
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2301.00011v1.pdf_6
null
ArxivOCR_part_1
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2301.00011v1.pdf_7
null
ArxivOCR_part_1
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2301.00011v1.pdf_8
null
ArxivOCR_part_1
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"2022.", "Learning", "discrete", "structured", "variational", "auto-", "face", "attributes", "in", "the", "wild.", "In", "ICCV.", "Rainforth,", "T.;", "Bauer,", "s.;", "encoder", "using", "natural", "evolution", "strategies.", "In", "ICLR.", "Locatello,", "F.;", "Abbati,", "G.;", "Bowman,", "S.", "R.;", "Vilnis,", "L.;", "Vinyals,", "O.;", "Dai,", "A.", "M.;", "Jozefow-", "Sch¨olkopf,", "B.;", "and", "Bachem,", "O.", "2019.", "On", "the", "fairness", "of", "icz,", "R.;", "and", "Bengio,", "S.", "2016.", "Generating", "sentences", "from", "disentangled", "representations.", "In", "NeurIPS.", "continuous", "space.", "In", "CONLL.", "Marcinkiewicz,", "M.", "A.", "1994.", "Building", "a", "large", "annotated", "cor-", "Bozkurt,", "A.;", "Esmaeili,", "B.;", "Tristan,", "J.-B.;", "Brooks,", "D.", "H.;", "Dy,", "pus", "of", "English:", "The", "penn", "treebank.", "Using", "Large", "Corpora.", "J.", "G.;", "and", "van", "de", "Meent,", "J.-W.", "2021.", "Rate-regularization", "and", "Mita,", "G.;", "Filippone,", "M.;", "and", "Michiardi,", "P.", "2021.", "An", "identifi-", "generalization", "in", "VAEs.", "AISTATS.", "able", "double", "VAE", "for", "disentangled", "representations.", "In", "ICML.", "Burda,", "Y.;", "Grosse,", "R.;", "and", "Salakhutdinov,", "R.", "2016.", "Impor-", "Nalisnick,", "E.;", "Matsukawa,", "A.;", "Teh,", "Y.", "W.;", "Gorur,", "D.;", "and", "tance", "weighted", "autoencoders.", "In", "ICLR.", "Lakshminarayanan,", "B.", "2019.", "Do", "deep", "generative", "models", "Burgess,", "C.", "P.;", "Higgins,", "I.;", "Pal,", "A.;", "Matthey,", "L.;", "Watters,", "N.;", "know", "what", "they", "don’t", "know?", "In", "ICLR.", "Desjardins,", "G.;", "and", "Lerchner,", "A.", "2018.", "Understanding", "dis-", "Ran,", "X.;", "Xu,", "M.;", "Mei,", "L.;", "Xu,", "Q.;", "and", "Liu,", "Q.", "2022.", "Detect-", "entangling", "in", "β-VAE.", "In", "NeurIPS.", "ing", "out-of-distribution", "samples", "via", "variational", "autoencoder", "Deb,", "K.;", "and", "Beyer,", "H.-G.", "2001.", "Self-adaptive", "genetic", "algo-", "with", "reliable", "uncertainty", "estimation.", "Neural", "Networks.", "rithms", "with", "simulated", "binary", "crossover.", "Evolutionary", "Com-", "Razavi,", "A.;", "Van", "den", "Oord,", "A.;", "and", "Vinyals,", "o.", "2019.", "Gen-", "erating", "diverse", "high-fidelity", "images", "with", "VQ-VAE-2.", "In", "putation,", "9(2):", "197–221.", "Domke,", "J.;", "and", "Sheldon,", "D.", "R.", "2019.", "Divide", "and", "couple:", "Us-", "NeurIPS.", "Ruiz,", "F.", "J.;", "Titsias,", "M.", "K.;", "Cemgil,", "T.;", "and", "Doucet,", "A.", "2021.", "ing", "monte", "carlo", "variational", "objectives", "for", "posterior", "approxi-", "Unbiased", "gradient", "estimation", "for", "variational", "autoencoders", "mation.", "In", "NeurIPS.", "Esmaeili,", "B.;", "Wu,", "H.;", "Jain,", "S.;", "Bozkurt,", "A.;", "Siddharth,", "N.;", "using", "coupled", "markov", "chains.", "In", "UAI.", "A.;", "Liu,", "S.;", "Liu,", "D.;", "Paige,", "B.;", "Brooks,", "D.", "H.;", "Dy,", "J.;", "and", "Meent,", "J.-W.", "2019.", "Shao,", "H.;", "Yao,", "sS.;", "Sun,", "D.;", "Zhang,", "Controlvae:", "Controllable", "Structured", "disentangled", "representations.", "In", "AISTATS.", "Wang,", "J.;", "and", "Abdelzaher,", "T.", "2020.", "variational", "autoencoder.", "In", "ICML.", "Fortuin,", "V.;", "H¨user,", "M.;", "Locatello,", "F.;", "Strathmann,", "H.;", "and", "Shi,", "Y.;", "Paige,", "B.;", "Torr,", "P.;", "et", "al.", "2019.", "Variational", "mixture-", "R¨atsch,", "G.", "2019.", "Som-vae:", "Interpretable", "discrete", "represen-", "of-experts", "autoencoders", "for", "multi-modal", "deep", "generative", "tation", "learning", "on", "time", "series.", "In", "ICLR.", "models.", "In", "NeurIPS.", "Fu,", "H.;", "Li,", "C.;", "Liu,", "X.;", "Gao,", "J.;", "Celikyilmaz,", "A.;", "and", "Carin,", "Sohn,", "K.;", "Lee,", "H.;", "and", "Yan,", "X.", "2015.", "Learning", "struc-", "L.", "2019.", "Cyclical", "annealing", "schedule:", "A", "simple", "approach", "to", "tured", "output", "representation", "using", "deep", "conditional", "genera-", "mitigating", "KL", "vanishing.", "In", "NAACL.", "tive", "models.", "In", "NeurIPS.", "Ghosh,", "P.;", "Sajjadi,", "M.", "S.;", "Vergari,", "A.;", "Black,", "M.;", "and", "Sutter,", "T.", "M.;", "Daunhawer,", "I.;", "and", "Vogt,", "J.", "E.", "2021.", "General-", "Sch¨olkopf,", "B.", "2019.", "From", "variational", "to", "deterministic", "au-", "ized", "multimodal", "ELBO.", "arXiv.", "toencoders.", "In", "ICLR.", "Tolstikhin,", "I.;", "Bousquet,", "O.;", "Gelly,", "S.;", "and", "Schoelkopf,", "B.", "Havtorn,", "J.", "D.", "D.;", "Frellsen,", "J.;", "Hauberg,", "S.;", "and", "Maaløe,", "L.", "2017.", "Wasserstein", "autoencoders.", "arXiv.", "2021.", "Hierarchical", "VAEs", "know", "what", "they", "don’t", "know.", "In", "Tomczak,", "J.;", "and", "Welling,", "M.", "2018.", "VAE", "with", "vampprior.", "ICML.", "In", "AISTATS.", "Higgins,", "I.;", "Matthey,", "L.;", "Pal,", "A.;", "Burgess,", "C.;", "Glorot,", "X.;", "Wang,", "P.", "Z.;", "and", "Wang,", "W.", "Y.", "2019.", "Neural", "gaussian", "copula", "Botvinick,", "M.;", "Mohamed,", "S.;", "and", "Lerchner,", "A.", "2017.", "B-", "for", "variational", "autoencoder.", "In", "EMNLP.", "VAE:", "Learning", "basic", "visual", "concepts", "with", "constrained", "Wu,", "D.;", "Wang,", "L.;", "and", "Zhang,", "P.", "2019.", "Solving", "statistical", "variational", "framework.", "In", "ICLR.", "mechanics", "using", "variational", "autoregressive", "networks.", "Phys-", "Jankowiak,", "M.;", "and", "Phan,", "D.", "2022.", "Surrogate", "likelihoods", "ical", "Review", "Letters,", "122(8):", "080602.", "for", "variational", "annealed", "importance", "sampling.", "In", "ICML.", "Xiao,", "Z.;", "Yan,", "Q.;", "and", "Amit,", "Y.", "2020.", "Likelihood", "regret:", "Kamata,", "H.;", "Mukuta,", "Y.;", "and", "Harada,", "T.", "2022.", "Fully", "spiking", "An", "out-of-distribution", "detection", "score", "for", "variational", "auto-", "encoder.", "NeurIPS.", "variational", "autoencoder.", "AAAI.", "Khemakhem,", "I.;", "Kingma,", "D.;", "Monti,", "R.;", "and", "Hyvarinen,", "A.", "Zhang,", "Y.;", "Wang,", "Y.;", "Zhang,", "L.;", "Zhang,", "Z.;", "and", "Gai,", "K.", "2020.", "Variational", "autoencoders", "and", "nonlinear", "ICA:", "A", "unify-", "2019.", "Improve", "diverse", "text", "generation", "by", "self", "labeling", "con-", "ditional", "variational", "auto", "encoder.", "In", "ICASSP.", "ing", "framework.", "In", "AISTATS.", "Kingma,", "D.", "P.;", "and", "Welling,", "M.", "2013.", "Auto-encoding", "varia-", "Zhao,", "S.;", "Song,", "J.;", "and", "Ermon,", "S.", "2019.", "InfoVAE:", "Balancing", "learning", "and", "inference", "in", "variational", "autoencoders.", "In", "AAAI.", "tional", "bayes.", "arXiv." ] }
2301.00011v1.pdf_9
null
ArxivOCR_part_1
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{ "word": [ "References", "Klushyn,", "A.;", "Chen,", "N.;", "Kurle,", "R.;", "Cseke,", "B.;", "and", "van", "der", "Alemi,", "A.;", "Poole,", "B.;", "Fischer,", "I.;", "Dillon,", "J.;", "Saurous,", "R.", "A.;", "Smagt,", "P.", "2019.", "Learning", "hierarchical", "priors", "in", "VAEs.", "In", "and", "Murphy,", "K.", "2018.", "Fixing", "a", "broken", "ELBO.", "In", "ICML.", "NeurIPS.", "Alemi,", "A.", "A.;", "Fischer,", "I.;", "Dillon,", "J.", "V.;", "and", "Murphy,", "K.", "2017.", "Kviman,", "O.;", "Melin,", "H.;", "Koptagel,", "H.;", "Elvira,", "V.;", "and", "Lager-", "gren,", "J.", "2022.", "Multiple", "importance", "sampling", "ELBO", "and", "Deep", "variational", "information", "bottleneck.", "In", "ICLR.", "deep", "ensembles", "of", "variational", "approximations.", "In", "AISTATS.", "Berliner,", "A.;", "Rotman,", "G.;", "Adi,", "Y.;", "Reichart,", "R.;", "and", "Hazan,", "Liu,", "Z.;", "Luo,", "P.;", "Wang,", "X.;", "and", "Tang,", "X.", "2015.", "Deep", "learning", "T.", "2022.", "Learning", "discrete", "structured", "variational", "auto-", "face", "attributes", "in", "the", "wild.", "In", "ICCV.", "Rainforth,", "T.;", "Bauer,", "s.;", "encoder", "using", "natural", "evolution", "strategies.", "In", "ICLR.", "Locatello,", "F.;", "Abbati,", "G.;", "Bowman,", "S.", "R.;", "Vilnis,", "L.;", "Vinyals,", "O.;", "Dai,", "A.", "M.;", "Jozefow-", "Sch¨olkopf,", "B.;", "and", "Bachem,", "o.", "2019.", "On", "the", "fairness", "of", "icz,", "R.;", "and", "Bengio,", "S.", "2016.", "Generating", "sentences", "from", "disentangled", "representations.", "In", "NeurIPS.", "continuous", "space.", "In", "CONLL.", "Marcinkiewicz,", "M.", "A.", "1994.", "Building", "a", "large", "annotated", "cor-", "Bozkurt,", "A.;", "Esmaeili,", "B.;", "Tristan,", "J.-B.;", "Brooks,", "D.", "H.;", "Dy,", "pus", "of", "English:", "The", "penn", "treebank.", "Using", "Large", "Corpora.", "J.", "G.;", "and", "van", "de", "Meent,", "J.-W.", "2021.", "Rate-regularization", "and", "Mita,", "G.;", "Filippone,", "M.;", "and", "Michiardi,", "P.", "2021.", "An", "identifi-", "generalization", "in", "VAEs.", "AISTATS.", "able", "double", "VAE", "for", "disentangled", "representations.", "In", "ICML.", "Burda,", "Y.;", "Grosse,", "R.;", "and", "Salakhutdinov,", "R.", "2016.", "Impor-", "Nalisnick,", "E.;", "Matsukawa,", "A.;", "Teh,", "Y.", "W.;", "Gorur,", "D.;", "and", "tance", "weighted", "autoencoders.", "In", "ICLR.", "Lakshminarayanan,", "B.", "2019.", "Do", "deep", "generative", "models", "Burgess,", "C.", "P.;", "Higgins,", "I.;", "Pal,", "A.;", "Matthey,", "L.;", "Watters,", "N.;", "know", "what", "they", "don’t", "know?", "In", "ICLR.", "Desjardins,", "G.;", "and", "Lerchner,", "A.", "2018.", "Understanding", "dis-", "Ran,", "X.;", "Xu,", "M.;", "Mei,", "L.;", "Xu,", "Q.;", "and", "Liu,", "Q.", "2022.", "Detect-", "entangling", "in", "β-VAE.", "In", "NeurIPS.", "ing", "out-of-distribution", "samples", "via", "variational", "autoencoder", "Deb,", "K.;", "and", "Beyer,", "H.-G.", "2001.", "Self-adaptive", "genetic", "algo-", "with", "reliable", "uncertainty", "estimation.", "Neural", "Networks.", "rithms", "with", "simulated", "binary", "crossover.", "Evolutionary", "Com-", "Razavi,", "A.;", "Van", "den", "Oord,", "A.;", "and", "Vinyals,", "O.", "2019.", "Gen-", "putation,", "9(2):", "197–221.", "erating", "diverse", "high-fidelity", "images", "with", "VQ-VAE-2.", "In", "NeurIPS.", "Domke,", "J.;", "and", "Sheldon,", "D.", "R.", "2019.", "Divide", "and", "couple:", "Us-", "ing", "monte", "carlo", "variational", "objectives", "for", "posterior", "approxi-", "Ruiz,", "F.", "J.;", "Titsias,", "M.", "K.;", "Cemgil,", "T.;", "and", "Doucet,", "A.", "2021.", "Unbiased", "gradient", "estimation", "for", "variational", "autoencoders", "mation.", "In", "NeurIPS.", "Esmaeili,", "B.;", "Wu,", "H.;", "Jain,", "S.;", "Bozkurt,", "A.;", "Siddharth,", "N.;", "using", "coupled", "markov", "chains.", "In", "UAI.", "Paige,", "B.;", "Brooks,", "D.", "H.;", "Dy,", "J.;", "and", "Meent,", "J.-W.", "2019.", "Shao,", "H.;", "Yao,", "s.;", "Sun,", "D.;", "Zhang,", "A.;", "Liu,", "S.;", "Liu,", "D.;", "Structured", "disentangled", "representations.", "In", "AISTATS.", "Wang,", "J.;", "and", "Abdelzaher,", "T.", "2020.", "Controlvae:", "Controllable", "variational", "autoencoder.", "In", "ICML.", "Fortuin,", "V.;", "H¨user,", "M.;", "Locatello,", "F.;", "Strathmann,", "H.;", "and", "R¨atsch,", "G.", "2019.", "Som-vae:", "Interpretable", "discrete", "represen-", "Shi,", "Y.;", "Paige,", "B.;", "Torr,", "P.;", "et", "al.", "2019.", "Variational", "mixture-", "of-experts", "autoencoders", "for", "multi-modal", "deep", "generative", "tation", "learning", "on", "time", "series.", "In", "ICLR.", "models.", "In", "NeurIPS.", "Fu,", "H.;", "Li,", "C.;", "Liu,", "X.;", "Gao,", "J.;", "Celikyilmaz,", "A.;", "and", "Carin,", "Sohn,", "K.;", "Lee,", "H.;", "and", "Yan,", "X.", "2015.", "Learning", "struc-", "L.", "2019.", "Cyclical", "annealing", "schedule:", "A", "simple", "approach", "to", "tured", "output", "representation", "using", "deep", "conditional", "genera-", "mitigating", "KL", "vanishing.", "In", "NAACL.", "Ghosh,", "P.;", "Sajjadi,", "M.", "S.;", "Vergari,", "A.;", "Black,", "M.;", "and", "tive", "models.", "In", "NeurIPS.", "Sch¨olkopf,", "B.", "2019.", "From", "variational", "to", "deterministic", "au-", "ized", "multimodal", "ELBO.", "arXiv.", "Vogt,", "J.", "E.", "2021.", "General-", "Sutter,", "T.", "M.;", "Daunhawer,", "I.;", "and", "toencoders.", "In", "ICLR.", "Havtorn,", "J.", "D.", "D.;", "Frellsen,", "J.;", "Hauberg,", "S.;", "and", "Maaløe,", "L.", "2017.", "Wasserstein", "autoencoders.", "arXiv.", "and", "Schoelkopf,", "B.", "2021.", "Hierarchical", "VAEs", "know", "what", "they", "don’t", "know.", "In", "Tomczak,", "J.;", "and", "Welling,", "M.", "2018.", "VAE", "with", "vampprior.", "Tolstikhin,", "I.;", "Bousquet,", "o.;", "Gelly,", "S.;", "ICML.", "In", "AISTATS.", "Higgins,", "I.;", "Matthey,", 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"score", "for", "variational", "auto-", "variational", "autoencoder.", "AAAI.", "encoder.", "NeurIPS.", "Khemakhem,", "I.;", "Kingma,", "D.;", "Monti,", "R.;", "and", "Hyvarinen,", "A.", "Zhang,", "Y.;", "Wang,", "Y.;", "Zhang,", "L.;", "Zhang,", "Z.;", "and", "Gai,", "K.", "2020.", "Variational", "autoencoders", "and", "nonlinear", "ICA:", "A", "unify-", "2019.", "Improve", "diverse", "text", "generation", "by", "self", "labeling", "con-", "ing", "framework.", "In", "AISTATS.", "ditional", "variational", "auto", "encoder.", "In", "ICASSP.", "Kingma,", "D.", "P.;", "and", "Welling,", "M.", "2013.", "Auto-encoding", "varia-", "Zhao,", "S.;", "Song,", "J.;", "and", "Ermon,", "S.", "2019.", "InfoVAE:", "Balancing", "tional", "bayes.", "arXiv.", "learning", "and", "inference", "in", "variational", "autoencoders.", "In", "AAAI." ] }
2301.00011v1.pdf_10
null
ArxivOCR_part_1
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2301.00013v1.pdf_1
null
ArxivOCR_part_1
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2301.00013v1.pdf_2
null
ArxivOCR_part_1
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2301.00013v1.pdf_3
null
ArxivOCR_part_1
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2301.00013v1.pdf_4
null
ArxivOCR_part_1
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2301.00014v1.pdf_1
null
ArxivOCR_part_1
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{ "word": [ "Time", "series", "Forecasting", "to", "detect", "anomalous", "behaviours", "in", "Multiphase", "Flow", "Meters", "T.", "Barbariol,", "Università", "degli", "Studi", "di", "Padova", "D.", "Masiero,", "Università", "degli", "Studi", "di", "Padova", "E.", "Feltresi,", "Pietro", "Fiorentini", "G.A.", "Susto,", "Università", "degli", "Studi", "di", "Padova", "INTRODUCTION", "Multiphase", "flow", "meters", "(MPFM)", "are", "inline", "metering", "tools,", "able", "to", "measure", "the", "individual", "flow", "rates", "of", "a", "multiphase", "flow.", "These", "instruments", "measure", "multiple", "properties", "of", "the", "fluid", "and", "then", "compute", "the", "water,", "oil", "and", "gas", "flow", "rates.", "These", "derived", "quantities", "are", "then", "fed", "into", "reservoir", "models", "in", "order", "to", "make", "predictions", "on", "the", "future", "production,", "or", "to", "allocate", "revenues", "and", "taxes.", "The", "main", "fluid", "properties", "measured", "by", "the", "MPFM", "are", "the", "electrical", "impedance,", "the", "gamma-ray", "absorption,", "and", "the", "velocity", "of", "the", "flow.", "These", "are", "sampled", "by", "means", "of", "three", "modules:", "electrical", "probes,", "gamma-ray", "densitometer", "and", "Venturi", "tube.", "The", "reliability", "of", "these", "modules", "is", "of", "primary", "importance:", "if", "one", "of", "them", "experiences", "a", "fault,", "the", "provided", "flow", "measurements", "will", "be", "incorrect.", "This", "might", "affect", "in", "cascade", "all", "the", "following", "steps,", "leading", "to", "wrong", "decisions", "about", "the", "reservoir", "[1].", "Without", "proper", "supervision,", "one", "module", "might", "fail", "without", "anyone", "noticing", "it", "and", "without", "expert", "human", "intervention.", "In", "order", "to", "prevent", "these", "situations,", "a", "system", "able", "to", "detect", "anomalous", "behaviours", "is", "needed:", "this", "system", "has", "to", "work", "autonomously,", "and", "to", "adapt", "to", "different", "working", "conditions", "without", "losing", "its", "efficacy.", "These", "intelligent", "modules", "go", "under", "the", "name", "of", "Anomaly", "Detection", "(AD),", "or,", "more", "in", "general,", "Fault", "Detection", "(FD)", "systems.", "They", "are", "applied", "to", "multiple", "objects", "that", "have", "strong", "reliability", "requirements,", "such", "as:", "smart", "grids", "[2],", "medical", "devices", "[3],", "autonomous", "vehicles", "[4].", "Depending", "on", "the", "approach,", "AD/FD", "technologies", "can", "be", "divided", "into", "two", "categories:", "model-driven", "or", "data-driven", "approaches.", "Due", "to", "its", "high", "flexibility", "and", "effectiveness", "in", "this", "work", "we", "described", "the", "adoption", "of", "data-driven", "approaches", "in", "the", "field", "of", "MPFM.", "This", "is", "one", "of", "the", "first", "works", "that", "addresses", "the", "fault", "detection", "problem", "in", "Multiphase", "Flow", "Meters,", "employing", "time-series", "forecasting", "tools.", "Moreover,", "this", "is", "one", "of", "the", "earliest", "applications", "of", "the", "Temporal", "Convolutional", "Network", "to", "time-series", "anomaly", "detection.", "This", "paper", "is", "structured", "as", "follows:", "in", "Section", "2", "the", "MPFM", "fault", "detection", "problem", "addressed", "in", "this", "paper", "will", "be", "described", "in", "more", "detail,", "together", "with", "the", "algorithmic", "tools", "employed", "in", "this", "analysis.", "Then", "in", "Section", "3", "these", "tools", "will", "be", "applied", "to", "real", "faults.", "In", "the", "last", "Section", "the", "conclusions", "of", "this", "paper", "will", "be", "discussed.", "2", "MATERIALS", "AND", "METHODS:", "MPFM", "and", "ML", "2.1", "Multiphase", "flow", "meters", "As", "already", "mentioned", "in", "the", "introduction,", "the", "MPFM", "is", "a", "complex", "metrology", "instrument,", "able", "to", "quantify", "the", "individual", "flow", "rates", "of", "a", "mixture.", "It", "is", "placed", "on", "1" ] }
2301.00014v1.pdf_2
null
ArxivOCR_part_1
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2301.00014v1.pdf_3
null
ArxivOCR_part_1
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{ "word": [ "time-aligned", "version", "of", "another,", "correlated", "signal.", "If", "y", "and", "x", "are", "misaligned", "by", "m", "time", "steps,", "then", "the", "forecast", "will", "be", "y(t+1)=x(t+1-m).", "Residue", "analysis", "and", "fault", "alarm", "Once", "the", "forecast", "has", "been", "obtained,", "the", "next", "step", "is", "the", "analysis", "of", "the", "residue", "between", "the", "forecast", "and", "the", "actual", "value.", "Obviously,", "the", "higher", "this", "difference", "is,", "the", "higher", "will", "be", "the", "probability", "that", "the", "actual", "value", "is", "indeed", "anomalous.", "A", "threshold", "on", "the", "residue", "is", "needed", "in", "order", "to", "discriminate", "if", "one", "value", "has", "to", "be", "flagged", "as", "anomalous", "or", "not.", "This", "threshold", "can", "be", "learned", "in", "advance,", "by", "looking", "at", "some", "statistical", "properties", "of", "the", "past", "residues.", "More", "specifically,", "the", "procedure", "followed", "in", "this", "paper", "is", "the", "following.", "Since", "the", "residue", "has", "a", "quite", "strong", "fluctuation,", "a", "time-window", "has", "been", "defined", "and", "the", "instantaneous", "residue", "has", "been", "substituted", "by", "two", "derived", "quantities:", "the", "absolute", "rolling", "mean", "(mean)", "and", "the", "absolute", "rolling", "standard", "deviation", "(std).", "The", "thresholds", "for", "these", "quantities", "have", "been", "learnt", "in", "advance,", "when", "the", "MPFM", "was", "working", "in", "controlled", "conditions.", "Each", "threshold", "corresponds", "to", "the", "maximum", "value", "assumed", "by", "its", "corresponding", "quantity", "in", "this", "specific", "time", "interval.", "When", "the", "mean", "or", "the", "std", "exceeds", "its", "threshold,", "the", "fault", "is", "detected", "and", "an", "alarm", "is", "raised.", "3", "RESULTS", "In", "this", "Section,", "the", "results", "of", "the", "simulations", "will", "be", "described,", "starting", "from", "the", "forecast,", "passing", "through", "the", "residue", "analysis,", "and", "ending", "with", "real", "and", "synthetic", "fault", "tests", "that", "will", "prove", "the", "effectiveness", "of", "the", "proposed", "method.", "Two", "signals", "have", "been", "collected:", "the", "electric", "impedance", "of", "the", "flow", "C,", "and", "the", "gamma-ray", "attenuation", "G.", "For", "simplicity", "the", "target", "signal", "will", "be", "G,", "but", "for", "construction", "an", "anomaly", "on", "G", "will", "trigger", "an", "anomaly", "C", "too", "and", "vice", "versa.", "3.1", "Forecast", "The", "metric", "that", "shows", "the", "general", "goodness", "of", "the", "forecast", "is", "depicted", "in", "Figure", "1.", "It", "is", "the", "mean", "squared", "error", "(mse),", "a", "metric", "commonly", "used", "in", "ML", "to", "assess", "the", "performance", "of", "a", "model.", "Lower", "it", "is,", "the", "better", "the", "model", "is", "performing.", "What", "is", "important", "is", "the", "mse", "value", "of", "forecasting", "models,", "compared", "to", "the", "Naive", "forecasting", "(the", "baseline).", "3" ] }
2301.00014v1.pdf_4
null
ArxivOCR_part_1
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2301.00014v1.pdf_5
null
ArxivOCR_part_1
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2301.00014v1.pdf_6
null
ArxivOCR_part_1
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2301.00014v1.pdf_7
null
ArxivOCR_part_1
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2301.00014v1.pdf_8
null
ArxivOCR_part_1
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2301.00014v1.pdf_9
null
ArxivOCR_part_1
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{ "word": [ "4", "3", "2", "1", "pi", "0", "g", "-1", "-2", "actual", "G", "-3", "predicted", "G", "-4", "7000", "0", "1000", "2000", "6000", "3000", "4000", "5000", "Time", "(arb.", "unit)", "4", "3", "2", "1", "pi", "0", "goi", "-1", "abs", "rolling", "std", "----", "std-threshold", "residue", "-3", "abs", "rolling", "mean", "mean-th", "-4", "6000", "7000", "0", "1000", "2000", "5000", "3000", "4000", "Time", "(arb.", "unit)", "Figure", "9:", "Unplugged", "communication", "cable.", "4", "CONCLUSIONS", "In", "this", "paper", "an", "approach", "to", "the", "fault", "detection", "of", "Multiphase", "Flow", "Meters", "has", "been", "proposed.", "It", "applies", "to", "its", "sensors", "and", "specifically", "to", "its", "time-series", "measures.", "It", "consists", "of", "three", "steps:", "forecast,", "residual", "analysis", "and", "fault", "alarm.", "In", "the", "forecasting", "step,", "care", "has", "been", "taken", "not", "only", "to", "the", "prediction", "accuracy,", "but", "also", "to", "the", "robustness", "of", "the", "method.", "After", "the", "development,", "it", "was", "applied", "to", "real", "faults", "and", "it", "proved", "its", "ability", "to", "easily", "detect", "the", "generated", "faults.", "The", "authors", "see", "two", "natural", "research", "directions", "for", "future", "works:", "to", "test", "new", "prediction", "models", "trying", "to", "improve", "the", "predictive", "performances,", "and", "to", "make", "long-term", "forecasts", "in", "order", "to", "lessen", "the", "computational", "burden", "of", "the", "method.", "5", "REFERENCES", "[1]", "L.S", "HANSEN,", "S.", "PEDERSEN,", "P.", "DURDEVIC.", "\"Multi-phase", "flow", "metering", "in", "offshore", "oil", "and", "gas", "transportation", "pipelines:", "Trends", "and", "perspectives.\"", "Sensors", "19.9", "(2019):", "2184.", "[2]", "C.A.", "ANDRESEN,", "B.N.", "TORSAETER,", "H.", "HAUGDAL,", "K.", "UHLEN.", "\"Fault", "detection", "and", "prediction", "in", "smart", "grids.\"", "2018", "IEEE", "9th", "International", "Workshop", "on", "Applied", "Measurements", "for", "Power", "Systems", "(AMPS).", "IEEE,", "2018.", "\"", "[3]", "L.", "MENEGHETTI,", "M.", "TERZI,", "S.", "DEL", "FAVERO,", "G.A.", "SUSTO,", "C.", "COBELLI", "Data-driven", "anomaly", "recognition", "for", "unsupervised", "model-free", "fault", "detection", "in", "artificial", "pancreas.\"", "IEEE", "Transactions", "on", "Control", "Systems", "Technology", "28.2,", "pag.", "33-47", "(2020).", "J.", "REN,", "R.", "REN,", "M.", "GREEN,", "X.", "HUANG.", "\"A", "deep", "learning", "method", "for", "fault", "[4]", "detection", "of", "autonomous", "vehicles.\"", "2019", "14th", "International", "Conference", "on", "Computer", "Science", "&", "Education", "(ICCSE).", "IEEE,", "2019.", "9" ] }
2301.00014v1.pdf_10
null
ArxivOCR_part_1
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{ "word": [ "[5]", "S.", "AHMAD,", "S.", "PURDY.", "\"Real-time", "anomaly", "detection", "for", "streaming", "analytics.\"", "arXiv", "preprint", "arXiv:1607.02480", "(2016).", "[6]", "K.", "HUNDMAN,", "V.", "CONSTANTINOU,", "C.", "LAPORTE,", "I", "COLWELL,", "T.", "SODERSTROM.", "\"Detecting", "spacecraft", "anomalies", "using", "lstms", "and", "nonparametric", "dynamic", "thresholding.\"", "Proceedings", "of", "the", "24th", "ACM", "SIGKDD", "international", "conference", "on", "knowledge", "discovery", "&", "data", "mining.", "2018.", "[7]", "S.", "BAI,", "J.Z.", "KOLTER,", "V.", "KOLTUN.", "\"An", "empirical", "evaluation", "of", "generic", "convolutional", "and", "recurrent", "networks", "for", "sequence", "modeling.\"", "arXiv", "preprint", "arXiv:1803.01271", "(2018).", "[8]", "Y.", "JINING,", "M.", "LIN,", "L.", "WANG,", "R.", "RAJIV,", "A.Y.", "ZOMAYA.", "\"Temporal", "Convolutional", "Networks", "for", "the", "Advance", "Prediction", "of", "ENSO.\"", "Scientific", "Reports", "(Nature", "Publisher", "Group)", "10.1", "(2020).", "T.", "BARBARIOL,", "E.", "FELTRESI,", "G.A.", "SUSTO.", "\"Self-Diagnosis", "of", "Multiphase", "[9]", "Flow", "Meters", "through", "Machine", "Learning-Based", "Anomaly", "Detection.\"", "Energies", "13.12", "(2020):", "3136.", "10" ] }
2301.00016v1.pdf_1
null
ArxivOCR_part_1
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2301.00016v1.pdf_2
null
ArxivOCR_part_1
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2301.00016v1.pdf_3
null
ArxivOCR_part_1
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2301.00016v1.pdf_4
null
ArxivOCR_part_1
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2301.00016v1.pdf_5
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ArxivOCR_part_1
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{ "word": [ "References", "1.Kraus,", "s.,", "Azaria,", "A.,", "Fiosina,", "J.,", "Greve,", "M.,", "Hazon,", "N.,", "Kolbe,", "L.,", "Lembcke,", "T.B.,", "Muller,", "J.P.,", "Schleibaum,", "s.", "and", "Vollrath,", "M.,", "2020,", "April.", "AI", "for", "explaining", "decisions", "in", "multi-", "agent", "environments.", "In", "Proceedings", "of", "the", "AAAI", "Conference", "on", "Artificial", "Intelligence", "(Vol.", "34,", "No.", "09,", "pp.", "13534-13538).", "2.Shrotri,", "A.A.,", "Narodytska,", "N.,", "Ignatiev,", "A.,", "Meel,", "K.,", "Marques-Silva,", "J.", "and", "Vardi,", "M.,", "2022.", "Constraint-Driven", "Explanations", "of", "Black-Box", "ML", "Models.", "AAAI.", "3.Kleinerman,", "A.,", "Rosenfeld,", "A.", "and", "Kraus,", "s.,", "2018,", "September.", "Providing", "explanations", "for", "recommendations", "in", "reciprocal", "environments.", "In", "Proceedings", "of", "the", "12th", "ACM", "conference", "on", "recommender", "systems", "(pp.", "22-30).", "4.Ribeiro,", "M.T.,", "Singh,", "S.", "and", "Guestrin,", "C.,", "2016,", "August.", ",,", "Why", "should", "i", "trust", "you?”", "Explaining", "the", "predictions", "of", "any", "classifier.", "In", "Proceedings", "of", "the", "22nd", "ACM", "SIGKDD", "international", "conference", "on", "knowledge", "discovery", "and", "data", "mining", "(pp.", "1135-1144).", "5.Lundberg,", "S.M.", "and", "Lee,", "S.I.,", "2017.", "A", "unified", "approach", "to", "interpreting", "model", "predictions.", "Advances", "in", "neural", "information", "processing", "systems,", "30.", "6.Ribeiro,", "M.T.,", "Singh,", "s.", "and", "Guestrin,", "c.,", "2018,", "April.", "Anchors:", "High-precision", "model-agnostic", "explanations.", "In", "Pro-", "ceedings", "of", "the", "AAAI", "conference", "on", "artificial", "intelligence", "(Vol.", "32,", "No.", "1).", "7.Pascanu,", "R.,", "Mikolov,", "T.", "and", "Bengio,", "Y.,", "2013,", "May.", "On", "the", "difficulty", "of", "training", "recurrent", "neural", "networks.", "In", "International", "conference", "on", "machine", "learning", "(pp.", "1310-1318).", "PMLR.", "APPENDIX" ] }
2301.00020v1.pdf_1
null
ArxivOCR_part_1
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"explaining", "the", "thermalization", "of", "the", "quantum", "many-", "the", "quantum", "revival", "of", "the", "states", "in", "the", "PXP", "model:", "periodic", "body", "system.", "Recently,", "beyond", "the", "quantum", "thermalization,", "driving.", "In", "most", "of", "the", "cases,", "periodic", "driving", "induces", "ther-", "the", "system", "which", "strongly", "violates", "the", "ETH", "has", "been", "actively", "malization", "of", "the", "scar", "states,", "and", "thus", "destructs", "the", "fidelity", "re-", "vival.", "However,", "recent", "experimental", "and", "theoretical", "studies", "studied,", "such", "as", "integrable", "systems", "and", "many-body", "localiza-", "show10,15", "that", "periodic", "driving", "with", "certain", "amplitudes", "sur-", "tion.", "Here,", "the", "”strong", "violation”", "of", "the", "ETH", "means", "ev-", "ery", "eigenstate", "breaks", "the", "ergodicity", "and", "never", "get", "thermal-", "prisingly", "enhances", "the", "fidelity", "revival.", "Furthermore,", "it", "has", "ized.", "There", "are", "also", "the", "systems", "which", "”weakly", "violate”", "the", "also", "been", "observed", "that", "the", "subharmonic", "response", "of", "fidelity", "Loe", "ETH,", "implying", "only", "small", "portion", "of", "the", "eigenstates", "violates", "revival", "exists", "with", "doubled", "period", "compared", "to", "the", "driving", "the", "ergodicity", "while", "all", "the", "other", "states", "get", "thermalized.", "In", "mode.", "This", "kind", "of", "subharmonic", "response", "breaks", "the", "discrete", "particular,", "quantum", "many-body", "scarring(QMBS)", "systems", "are", "time", "translational", "symmetry", "of", "the", "driving", "mode,", "and", "hence", "the", "examples", "which", "weakly", "violates", "ETH,", "containing", "a", "small", "get", "attention", "as", "a", "time-version", "of", "crystalline", "order,", "called", "a", "number", "of", "highly", "excited", "non-thermal", "eigenstates,", "called", "scar", "discrete", "time-crystal", "(DTC)", "which", "is", "also", "a", "recently", "studied", "eigenstates5,6.", "Such", "scar", "eigenstates", "show", "exotic", "physical", "be-", "subject16,17.", "Although", "earlier", "research", "had", "demonstrated", "this", "Gnh", "havior", "compared", "to", "the", "thermal", "Gibbs", "state.", "For", "example,", "subharmonic", "fidelity", "revival", "in", "the", "limit", "of", "large", "driving", "am-", "while", "the", "thermal", "Gibbs", "state", "predicts", "the", "entanglement", "en-", "plitude", "and", "high", "frequency18,", "the", "general", "mechanism", "of", "such", "tropy", "proportional", "to", "the", "volume", "of", "subsystem", "in", "the", "middle", "subharmonic", "revival", "has", "not", "been", "explored", "well.", "of", "the", "spectrum,", "the", "entanglement", "entropy", "of", "the", "scar", "eigen-", "state", "scales", "proportionally", "to", "the", "area", "of", "the", "subsystem.", "Be-", "cause", "the", "QMBS", "often", "appear", "in", "a", "tower", "of", "scar", "states", "where", "a", "set", "of", "states", "with", "equidistant", "energy", "spacing", "exists7,", "if", "the", "initial", "product", "state", "is", "superposition", "of", "the", "scar", "states,", "then", "In", "this", "paper,", "we", "study", "the", "periodically", "driven", "PXP", "model,", "the", "system", "exhibits", "the", "perfect", "revival.", "Conversely,", "it", "has", "been", "focusing", "on", "the", "subharmonic", "fidelity", "revivals.", "In", "Section", "II,", "also", "shown", "that", "the", "persistent", "revival", "of", "product", "state", "implies", "we", "introduce", "the", "PXP", "model", "with", "square", "pulse", "driving", "modes.", "QMBS8.", "Hence,", "is", "important", "to", "observe", "the", "fidelity", "revival", "By", "calculating", "the", "average", "fidelity", "and", "the", "Fourier", "compo-", "as", "evidence", "for", "the", "QMBS", "in", "experiments.", "nents", "of", "the", "fidelity", "signal,", "we", "study", "the", "conditions", "under", "In", "recent", "experiments", "of", "Rydberg", "atom", "simulator,", "it", "has", "which", "the", "fidelity", "is", "enhanced", "and", "subharmonic", "response", "oc-", "been", "observed", "that", "certain", "product", "states", "show", "persistent,", "curs.", "Then,", "based", "on", "the", "similarity", "of", "the", "Hamiltonian", "ad-", "though", "imperfect", "revival", "under", "van", "der", "Waals", "interaction.", "jacent", "graph", "between", "PXP", "model", "and", "free", "spin", "model19,", "we", "This", "indicates", "the", "presence", "of", "a", "QMBS", "in", "the", "system9–11.", "Tak-", "show", "that", "they", "can", "be", "explained", "by", "the", "free", "spin-1/2", "model", "ing", "the", "extreme", "limit", "of", "strong", "van", "der", "Waals", "interaction", "in", "with", "the", "same", "driving", "which", "is", "exactly", "solvable.", "In", "Section", "III,", "the", "Rydberg", "blockade", "of", "the", "Rydberg", "atom", "chain", "gives", "rise", "we", "introduce", "an", "analytic", "approach", "for", "the", "driven", "PXP", "model.", "Within", "perturbative", "analysis,", "we", "derive", "the", "driving", "conditions", "to", "the", "so-called", "PXP", "model,", "which", "has", "a", "Hilbert", "space", "pro-", "jected", "onto", "the", "states", "with", "no", "neighboring", "excited", "states.", "The", "for", "subharmonic", "responses", "in", "the", "driven", "PXP", "model", "and", "dis-", "QMBS", "structure", "of", "the", "PXP", "model", "has", "been", "actively", "stud-", "cuss", "their", "applications.", "In", "Section", "IV,", "we", "summarize", "our", "ied", "theoretically,", "including", "the", "report", "that", "it", "also", "shows", "the", "works", "and", "suggest", "interesting", "future", "directions." ] }
2301.00020v1.pdf_2
null
ArxivOCR_part_1
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2301.00020v1.pdf_3
null
ArxivOCR_part_1
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2301.00020v1.pdf_4
null
ArxivOCR_part_1
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2301.00020v1.pdf_5
null
ArxivOCR_part_1
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2301.00020v1.pdf_6
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ArxivOCR_part_1
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2301.00020v1.pdf_7
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ArxivOCR_part_1
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ArxivOCR_part_1
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{ "word": [ "Anyon", "statistics", "through", "conductance", "measurements", "of", "time-domain", "interferometry", "Noam", "Schiller1,", "Yotam", "Shapira2,", "Ady", "Stern1,", "and", "Yuval", "Oreg1", "1Department", "of", "Condensed", "Matter", "Physics", "2Department", "of", "Physics", "of", "Complex", "Systems", "Weizmann", "Institute", "of", "Science,", "Rehovot", "7610001,", "Israel", "We", "propose", "method", "to", "extract", "the", "mutual", "exchange", "statistics", "of", "the", "anyonic", "excitations", "of", "a", "general", "Abelian", "fractional", "quantum", "Hall", "state,", "by", "comparing", "the", "tunneling", "characteristics", "of", "a", "quantum", "point", "contact", "in", "two", "different", "experimental", "conditions.", "In", "the", "first,", "the", "tunneling", "current", "between", "two", "edges", "at", "different", "chemical", "potentials", "is", "measured.", "In", "the", "second,", "one", "of", "these", "edges", "is", "2020", "strongly", "diluted", "by", "an", "earlier", "point", "contact.", "We", "describe", "the", "case", "of", "the", "dilute", "beam", "in", "terms", "of", "a", "time-domain", "interferometer", "between", "the", "anyons", "flowing", "along", "the", "edge", "and", "quasiparticle-quasihole", "excitations", "created", "at", "the", "tunneling", "quantum", "point", "contact.", "In", "both", "cases,", "temperature", "is", "kept", "large,", "such", "that", "the", "measured", "current", "is", "given", "to", "linear", "response.", "Remarkably,", "our", "proposal", "does", "Soe", "not", "require", "the", "measurement", "of", "current", "correlations,", "and", "allows", "us", "to", "carefully", "separate", "effects", "of", "the", "fractional", "charge", "and", "statistics", "from", "effects", "of", "intra-", "and", "inter-edge", "interactions.", "Introduction.—", "It", "has", "been", "almost", "four", "decades", "since", "injected", "quasiparticle", "charge,", "8", "is", "the", "tunneling", "quasi-", "the", "initial", "proposal", "that", "the", "elementary", "quasiparticles", "particle", "scaling", "dimension,", "θ12", "is", "the", "mutual", "statistics", "of", "fractional", "quantum", "Hall", "(FQH)", "systems", "obey", "anyonic", "phase", "between", "the", "injected", "and", "tunneling", "quasiparticles,", "statistics", "[1].", "Despite", "the", "apparent", "maturity", "of", "the", "field,", "T", "is", "temperature,", "and", "G", "direct", "is", "a", "residual", "conductance", "the", "pursuit", "to", "definitively", "observe", "the", "physical", "quanti-", "corresponding", "to", "direct", "tunneling", "[24–26]", "through", "both", "ties", "and", "quantum", "numbers", "characterizing", "anyons", "[2,", "3]", "is", "QPCs.", "The", "full", "crossover", "between", "these", "two", "limits", "is", "constantly", "being", "reinvigorated", "[4–20].", "In", "particular,", "early", "shown", "schematically", "in", "Fig.", "1(b).", "2020", "saw", "two", "major", "experimental", "steps", "forward:", "the", "ob-", "The", "mechanism", "leading", "to", "this", "result", "is", "a", "time-domain", "servation", "of", "anyonic", "braiding", "in", "a", "Fabry-Perot", "interfer-", "interferometer", "at", "the", "tunneling", "QPC", "which", "is", "created", "by", "ometer", "[21],", "and", "demonstration", "of", "a", "so-called", "“anyon", "col-", "the", "dilute", "incident", "beam.", "The", "interference", "is", "between", "two", "lider”", "[22,", "23]", "using", "cross-correlation", "measurements.", "processes,", "in", "which", "a", "quasiparticle-quasihole", "excitation", "Here", "we", "show", "that", "anyonic", "statistics", "can", "be", "inferred", "di-", "occurs", "at", "the", "tunneling", "QPC", "either", "before", "or", "after", "the", "rectly", "from", "conductance", "measurements,", "without", "requir-", "arrival", "of", "an", "injected", "quasiparticle", "(see", "Fig.", "2).", "A", "similar", "Goe", "ing", "current", "correlation", "measurements", "or", "explicitly", "build-", "physical", "picture", "has", "been", "shown", "in", "Refs.", "[25,", "27,", "28].", "We", "ing", "an", "interferometer.", "The", "configuration", "we", "propose", "to", "further", "find", "that", "this", "interference", "is", "sensitive", "to", "the", "mu-", "obtain", "this", "result", "consists", "of", "quantum", "point", "contact", "tual", "statistics", "phase", "between", "the", "injected", "and", "the", "tunnel-", "(QPC)", "between", "two", "edges", "of", "a", "general", "Abelian", "FQH", "state", "ing", "quasiparticles,", "0", "12", ".", "We", "emphasize", "that", "these", "quasi-", "which", "are", "driven", "out", "of", "equilibrium.", "The", "edges", "may", "be", "particles", "are", "not", "necessarily", "of", "the", "same", "type,", "although", "Ganh", "driven", "off-equilibrium", "by", "one", "of", "three", "methods:", "inject-", "they", "must", "be", "supported", "by", "the", "same", "FQH", "liquid.", "ing", "a", "single", "quasiparticle", "into", "one", "of", "the", "edges;", "injecting", "Since", "our", "focus", "is", "the", "interference", "of", "two", "amplitudes", "a", "Poissonian,", "dilute", "beam", "of", "quasiparticles", "into", "one", "of", "which", "differ", "from", "one", "another", "by", "the", "orderings", "of", "events,", "the", "edges;", "and", "placing", "a", "finite", "bias", "voltage", "between", "the", "the", "key", "point", "of", "our", "analysis", "is", "the", "identification", "of", "the", "edges.", "phase", "differences", "between", "the", "two", "orderings.", "We", "find", "Our", "proposed", "setup,", "shown", "in", "Fig.", "1(a),", "allows", "a", "phase", "differences", "that", "are", "determined", "by", "the", "quasiparti-", "smooth", "transition", "between", "the", "dilute", "Poissonian", "beam", "cle", "charge", "e*", "which", "is", "a", "fraction", "of", "the", "electron", "charge", "and", "a", "full", "beam", "at", "finite", "bias", "voltage.", "This", "is", "ob-", "for", "non-integer", "values", "of", "v", "[4–6];", "the", "scaling", "dimension", "δ,", "tained", "by", "tuning", "second,", "injection", "QPC", "from", "fully", "open", "which", "defines", "the", "zero-temperature", "time", "correlations", "of", "inj,", "the", "quasiparticle", "via", "the", "relation", "t(T)4(0)", "5", "ti", "T", "S", "h", "(a", "differential", "conductance,", "G", "inj", "28", "dI", "j/dV", "satisfying", "G", "Tinj", "/o", "xy", "0)", "to", "fully", "closed", "(G", "in", "/o", "xy", "1).", "We", "hence-", "[29–32];", "and", "the", "exchange", "statistics", "phase", "θ,", "which", "for", "forth", "refer", "to", "these", "as", "the", "dilute", "and", "full", "limits,", "respec-", "anyons", "take", "special", "values", "beyond", "the", "fermionic", "�", "and", "tively.", "the", "bosonic", "2π", "[1–3].", "We", "propose", "sweeping", "G", "inj", "through", "this", "range,", "and", "We", "are", "interested", "here", "in", "isolating", "the", "effect", "of", "o", "from", "measuring", "the", "ratio", "I/I", "inj", "where", "I", "is", "the", "measured", "cur-", "the", "other", "two", "effects.", "In", "particular,", "we", "would", "like", "to", "rent", "after", "the", "tunneling", "QPC,", "and", "I", "inj", "is", "the", "injected", "inci-", "separate", "it", "from", "the", "effect", "of", "d.", "For", "non-interacting", "dent", "current,", "as", "defined", "in", "Fig.", "1(a).", "Comparing", "the", "val-", "edges,", "in", "which", "all", "the", "modes", "propagate", "in", "the", "same", "di-", "out", "non-universal", "rection,", "2πδ", "=", "0;", "however,", "in", "general", "8", "is", "affected", "by", "non-universal", "factors,", "such", "as", "intra-edge", "and", "inter-edge", "G", "direct", ".", "(1)", "interactions,", "1/f", "noise", "or", "neutral", "modes", "[33–38].", "This", "in", "+", "=", "sin", "20", "12", "I", "inj", "(T", "full", "G", "inj", "stark", "contrast", "to", "the", "charge,", "exchange", "statistics", "phase,", "I", "inj", "(T", "2πe∗", "1e∗", "dilute", "or", "filling", "factor,", "which", "are", "universal.", "*", "is", "the", "tunneling", "quasiparticle", "charge,", "e", "the", "We", "separate", "the", "effect", "of", "o", "from", "that", "of", "8", "by", "tuning", "Here,", "e", "1" ] }
2301.00021v1.pdf_2
null
ArxivOCR_part_1
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2301.00021v1.pdf_3
null
ArxivOCR_part_1
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2301.00021v1.pdf_4
null
ArxivOCR_part_1
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null
ArxivOCR_part_1
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{ "word": [ "5", "For", "general", "temperatures,", "the", "current", "can", "no", "longer", "be", "of", "a", "single", "quantum", "Hall", "droplet", "with", "two", "QPCs,", "which", "treated", "as", "a", "linear", "response", "to", "the", "drive", "of", "the", "full", "or", "di-", "effectively", "create", "a", "time-domain", "interferometer,", "as", "can", "lute", "beams.", "We", "hence", "obtain", "the", "typical", "power", "laws", "char-", "be", "identified", "from", "current", "measurements.", "We", "thus", "avoid", "acterizing", "tunneling", "in", "Luttinger", "liquids", "[2,", "34,", "42,", "43].", "both", "current", "correlation", "(or", "noise)", "measurements,", "and", "Comparing", "measurements", "of", "the", "full", "and", "dilute", "limits", "at", "the", "need", "for", "a", "real", "space", "interferometer,", "making", "the", "iden-", "the", "low", "temperature", "limit", "T", "e", "*V,", "inj", "can", "still", "give", "a", "tification", "of", "the", "exchange", 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"quasiparticle,", "do", "not", "by", "the", "product", "of", "the", "transparencies", "of", "the", "two", "QPCs", "appear", "in", "our", "derivation.", "Rather,", "it", "is", "the", "two", "particles’", "mutual", "statistics,", "θ12", "that", "affect", "the", "modified", "correlation", "along", "the", "electron’s", "path,", "regardless", "of", "whether", "they", "are", "functions,", "and", "hence,", "the", "physical", "observables.", "Likewise,", "close", "to", "full", "transmission", "or", "full", "reflection.", "This", "requires", "accounting", "for", "the", "direct", "tunneling", "term", "in", "Eq.", "(1),", "which", "the", "scaling", "dimension", "and", "electric", "charge", "which", "directly", "We", "do", "this", "by", "accounting", "for", "the", "finite", "width", "of", "the", "particle,", "and", "e", "(properties", "of", "the", "injected", "quasiparti-", "soliton.", "This", "leads", "to", "the", "required,", "Landauer-Buttiker-", "cles", "may", "implicitly", "enter", "through", "the", "injection", "rate).", "ex-", "Imry", "consistent", "result", "of", "Idilute", "=", "422¢2I", "inj", "j.", "The", "phys-", "quasiparticles", "are", "identical,", "l", "l1", "=", "l", "2", ",", "do", "we", "obtain", "re-", "ical", "intuition", "behind", "the", "requirement", "of", "a", "finite", "soliton", "change", "statistics", "for", "a", "single", "quasiparticle", "type.", "We", "quasi-", "effect", "observables", "are", "only", "those", "of", "the", "tunneling", "tunneling", "Only", "in", "the", "case", "where", "the", "injected", "and", "o*", "i", "now", "becomes", "the", "leading", "contribution.", "width", "is", "that", "tunneling", "without", "time-domain", "interferom-", "mark", "that", "this", "is", "indeed", "the", "case", "in", "the", "experiment", "of", "etry,", "dubbed", "the", "direct", "tunneling", "process", "in", "[24,", "25],", "is", "dominated", "by", "short", "times.", "Performing", "these", "calculations", "Ref.", "[22],", "where", "all", "quasiparticles", "are", "Laughlin", "e", "=", "e/3", "anyons,", "and", "subsequent", "recreations", "for", "the", "=", "1/3", "and", "explicitly", "in", "App.", "B,", "we", "show", "that", "the", "ratio", "between", "v", "=", "2/5", "cases", "[26,", "46,", "47].", "Interestingly,", "a", "recent", "ex-", "the", "first", "term", "in", "Eq.", "(1)", "and", "G", "direct", "is", "shown", "[24,", "25]", "quasiparticle", "was", "a", "e/3", "anyon", "and", "the", "tunneling", "quasi-", "where", "T", "is", "the", "soliton", "width.", "It", "has", "been", "ensure", "G", "direct", "is", "particle", "was", "an", "electron,", "observed", "Andreev-like", "reflection", "that", "T", "Ts", "max", "o", "eV,", "k", "B", "T", "};", "as", "such,", "to", "(T1", "s", ")481", "2,", "periment", "employing", "a", "similar", "setup,", "where", "the", "injected", "ee", "sub-dominant,", "the", "dilute", "limit", "must", "be", "measured", "when", "[48].", "This", "is", "consistent", "with", "a", "mutual", "statistics", "phase", "of", "k", "B", "T", "(", "id", "28)", "eV", "<", "2.", "0", "12", "=", "π,", "for", "which", "Eq.", "(1)", "gives", "no", "time-domain", "interfer-", "Several", "contemporary", "experimental", "setups", "use", "the", "ometry", "signal.", "equivalent", "of", "non-interacting", "fermionic", "formulae", "to", "rea-", "Acknowledgements.—", "We", "thank", "Tomer", "Alkalay,", "Moty", "sonable", "success", "[45],", "corresponding", "to", "the", "limiting", "value", "Heiblum,", "Changki", "Hong,", "June-Young", "Lee", "and", "H.-S.", "of", "28", "1", "=", "1.", "In", "this", "case,", "the", "second", "term", "of", "Eq.", "(1)", "is", "Sim", "for", "insightful", "discussions", "and", "comments", "on", "the", "a", "numerical", "coefficient", "of", "order", "one,", "which", "may", "depend", "manuscript.", "This", "work", "was", "partially", "supported", "by", "grants", "solely", "on", "e", "and", "0", "12", "For", "non-interacting", "fermions,", "from", "the", "ERC", "under", "the", "European", "Union’s", "Horizon", "2020", "this", "coefficient", "is", "easily", "found", "by", "comparing", "to", "known", "research", "and", "innovation", "programme", "(grant", "agreements", "Landauer-Buttiker-Imry", "scattering", "theory", "[44],", "but", "it", "is", "LEGOTOP", "No.", "788715", "and", "HQMAT", "No.", "817799),", "the", "straightforward", "to", "generalize.", "We", "discuss", "this", "coefficient", "DFG", "(CRC/Transregio", "183,", "EI", "519/7-1),", "the", "BSF", "and", "further", "in", "App.", "B.", "NSF", "(2018643),", "the", "ISF", "Quantum", "Science", "and", "Technol-", "Discussion.—", "We", "propose", "a", "simple", "method", "to", "extract", "ogy", "(2074/19).", "N.S.", "was", "supported", "by", "the", "Clore", "Scholars", "anyonic", "exchange", "statistics.", "Our", "system", "consists", "only", "Programme.", " [1]", "D.", "Arovas,", "J.", "R.", "Schrieffer,", "and", "F.", "Wilczek,", "Fractional", "[4]", "R.", "B.", "Laughlin,", "Anomalous", "Quantum", "Hall", "Effect:", "An", "In-", "Statistics", "and", "the", "Quantum", "Hall", "Effect,", "Physical", "Review", "compressible", "Quantum", "Fluid", "with", "Fractionally", "Charged", "Letters", "53,", "722", "(1984),", "publisher:", "American", "Physical", "So-", "Excitations,", "Physical", "Review", "Letters", "50,", "1395", "(1983),", "ciety.", "publisher:", "American", "Physical", "Society.", "[2]", "X.", "Wen,", "Quantum", "Field", "Theory", " of", "Many-Body", "Sys-", "[5]", "R.", "de", "Picciotto,", "M.", "Reznikov,", "M.", "Heiblum,", "V.", "Uman-", "tems:From", "the", "Origin", "of", "Sound", "to", "an", "Origin", "of", "Light", "sky,", "G.", "Bunin,", "and", "D.", "Mahalu,", "Direct", "observation", "of", "a", "and", "Electrons:", "From", "the", "Origin", " of", "Sound", "to", "an", "Origin", "fractional", "charge,", "Nature", "389,", "162", "(1997).", " of", "Light", "and", "Electrons,", "Oxford", "Graduate", "Texts", "(OUP", "[6]", "L.", "Saminadayar,", "D.", "C.", "Glattli,", "Y.", "Jin,", "and", "B.", "Etienne,", "Oxford,", "2004).", "Observation", "of", "the", "e/3", "Fractionally", "Charged", "Laughlin", "[3]", "A.", "Stern,", "Anyons", "and", "the", "quantum", "Hall", "effect", "-", "a", "peda-", "Quasiparticle,", "Physical", "Review", "Letters", "79,", "2526", "(1997).", "gogical", "review,", "Annals", "of", "Physics", "323,", "204", "(2008),", "arXiv:", "[7]", "C.", "L.", "Kane", "and", "M.", "P.", "A.", "Fisher,", "Nonequilibrium", "noise", "0711.4697.", "and", "fractional", "charge", "in", "the", "quantum", "Hall", "effect,", "Physical" ] }
2301.00021v1.pdf_6
null
ArxivOCR_part_1
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ArxivOCR_part_1
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2301.00021v1.pdf_8
null
ArxivOCR_part_1
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2301.00021v1.pdf_9
null
ArxivOCR_part_1
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2301.00021v1.pdf_10
null
ArxivOCR_part_1
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2301.00026v2.pdf_1
null
ArxivOCR_part_1
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2301.00026v2.pdf_2
null
ArxivOCR_part_1
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2301.00026v2.pdf_3
null
ArxivOCR_part_1
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2301.00026v2.pdf_4
null
ArxivOCR_part_1
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2301.00026v2.pdf_5
null
ArxivOCR_part_1
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2301.00026v2.pdf_6
null
ArxivOCR_part_1
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2301.00026v2.pdf_7
null
ArxivOCR_part_1
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2301.00026v2.pdf_8
null
ArxivOCR_part_1
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2301.00026v2.pdf_9
null
ArxivOCR_part_1
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2301.00026v2.pdf_10
null
ArxivOCR_part_1
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2301.00027v2.pdf_1
null
ArxivOCR_part_1
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"Institute,", "162", "5th", "Avenue,", "New", "York,", "nY,", "10010,", "USA", "25Department", "of", "Physics,", "196", "Auditorium", "Road,", "Unit", "3046,", "University", "of", "Connecticut,", "Storrs,", "CT", "06269,", "USA", "FL", "26MMT/Steward", "Observatory,", "University", "of", "Arizona,", "933", "N.", "Cherry", "Ave.,", "Tucson,", "AZ", "85721,", "USA", "27Astronomy", "Centre,", "University", "of", "Sussex,", "Falmer,", "Brighton", "BN1", "9QH,", "UK", "28Institute", "of", "Space", "Sciences", "and", "Astronomy,", "University", "of", "Malta,", "Msida", "MSD", "2080,", "Malta", "29National", "Astronomical", "Observatory", "of", "Japan,", "2-21-1", "Osawa,", "Mitaka,", "Tokyo", "181-8588,", "Japan", "ABSTRACT", "We", "present", "results", "from", "the", "Cosmic", "Evolution", "Early", "Release", "Survey", "(CEERS)", "on", "the", "stellar-population", "pa-", "rameters", "for", "28", "galaxies", "with", "redshifts", "4", "<", "z", "<", "9", "using", "imaging", "data", "from", "the", "James", "Webb", "Space", "Telescope", "(JWST)", "Mid-Infrared", "Instrument", "(MIRI)", "combined", "with", "data", "from", "the", "Hubble", "Space", "Telescope", "and", "the", "Spitzer", "Space", "Telescope.", "The", "JWST/MIRI", "5.6", "and", "7.7", "µm", "data", "extend", "the", "coverage", "of", "the", "rest-frame", "spectral-energy", "Corresponding", "author:", "Casey", "Papovich", "papovich@tamu.edu" ] }