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࿦จ঺հ Audience Size Forecasting Fast and Smart Budget Planning for Media Buyers Shi, Yeming, et al. "Audience Size Forecasting: Fast and Smart Budget Planning for Media Buyers." Proceedings of the 24th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining. 2018. https://dl.acm.org/doi/abs/10.1145/3219819.3219893 %4࿦จಡΈձ! ੢ྛ޹ 5BLBTIJ/JTIJCBZBTIJIBHJOP 1

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֓ཁ w ,%%࠾୒ w %41Ͱ޿ࠂΩϟϯϖʔϯͷ*NQϘϦϡʔϜਪఆػೳΛ࡞ͬͨ w Ωϟϯϖʔϯͷηάϝϯτఆٛͱ༧ࢉɾೖࡳֹ͔ۚΒ*NQϘϦϡʔϜ Λਪఆ͢ΔػೳΛϚʔέολʔʹఏڙͨ͠ w ഑৴৚݅ͷ૊Έ͋ΘͤΛબΜͩͱ͖ʹඵͰਪఆϘϦϡʔϜ͕ฦͤ ΔΑ͏ʹͳͬͨ )JWFΫΤϦͰ෼͔͔ͬͨͷ͕  w ,FZXPSE"VEJFODF4J[F'PSFDBTUJOH w %TUJMMFSZࣾͷ%41ʹ͓͚Δ։ൃ੒Ռ ೥ʹ%41DMPTFͯ͠Δʜʜ

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*OUSPEVDUJPO

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޿ࠂΩϟϯϖʔϯͷޮՌͱ഑৴৚݅ w ޿ࠂΩϟϯϖʔϯͷ഑৴৚݅ w %FWJDF 1MBUGPSN 04WFS -PDBUJPO 7JFXBCJMJUZ "VEJFODF 4FHNFOU $POUFYU ࣌ؒଳ NFEJBDBUFHPSZ ౳ w ڐՄϧʔϧͱڋ൱ϧʔϧͷ૊Έ͋Θͤ w ચ࿅͞ΕͨλʔήςΟϯάઃఆΛ࠾༻͢Δͱ޿ࠂΩϟϯϖʔϯͷύϑΥʔ Ϛϯε͸্͕Δ w ͔͠͠৚݅ΛߜΓ͗͢Δͱ*NQϘϦϡʔϜ͕ग़ͳ͍ w ༧ࢉʹదͨ͠*NQϘϦϡʔϜ͕֫ಘͰ͖Δ഑৴৚͕݅஌Γ͍ͨ w ͋Δ഑৴৚݅ΛબΜͩͱ͖ͷ*NQϘϦϡʔϜ͕஌Γ͍ͨ

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"VEJFODF4J[F'PSFDBTUJOH w ഑৴৚݅ͷ૊Έ͋Θ͔ͤΒਪఆ*NQ਺ΛಘΔ w *ODMVEFPSFYDMVEFSVMF w %FWJDF "E5ZQF (FPHSBQIJDBMBSFB 7JFXBCJMJUZ w /BJWFʹ࣮૷͢ΔͳΒ#JE3FRVFTUϩάΛΫΤϦ͢Δ42-Λྲྀ͢ w ਪఆ֫ಘ*NQ3FRVFTU7PMVNFºਪఆউ཰ w ͨͩ͠#JE3FRVFTUϩά͸๲େ ஶऀΒ͸ ԯSFREBZ  w αϯϓϦϯάͰϨίʔυݮΒͨ͠ͱͯ͠΋)JWFΫΤϦͰ෼ w 1PPSVTFSFYQFSJFODF

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"VEJFODF4J[F'PSFDBTUJOH ଓ w ௿ϨΠςϯγͰ*NQϘϦϡʔϜਪఆΛ࣮ݱ͍ͨ͠ w NBKPSDIBMMFOHFJOUIFJOEVTUSZ w Ͳ͜ͷ%41Ͱ΋ཉ͘͠ͳΔػೳͷͻͱͭ w ݸʑͷ഑৴৚͕݅ಠཱͳΒ؆୯͕࣮ͩࡍ͸ w ళฮ"ʹ๚Εͨਓηάϝϯτͱళฮ#ʹ๚Εͨਓηάϝϯτͷཁ ૉ ਓ ͕ॏෳ͍ͯ͠Δ w େ఍͸૬ؔ΍ཁૉͷPWFSXSBQ͕͋Δ͔Βݸʑͷ ܭࢉ݁ՌΛ࢖ָͬͯͰ͖ͳ͍

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Ͳ͏΍Δ͔ w %BUBCBTFͰ#JE3FRVFTUϩάΛΫΤϦ͢Δͷ͸஗͗ͯ͢ແཧ w Ξϓϩʔν w ΧʔσΟφϦςΟਪఆ DBSEJOBMJUZFTUJNBUJPO ͕Ͱ͖Δσʔλ ѹॖΞϧΰϦζϜΛ࢖ͬͨ w ͜Ε͸༷ʑͳϏδωε্ͷΧʔσΟφϦςΟਪఆ໰୊ʹରԠՄೳ w ηάϝϯτಉ࢜ͷڞ௨෦෼͸ϚʔέςΟϯάʹੜ͔ͤΔ

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$BSEJOBMJUZFTUJNBUJPO w ू߹ͷཁૉ਺DPVOU EJTUJODU9 ͷਪఆ w Ԡ༻ w ෳ਺ͷू߹ͷڞ௨෦෼Λਪఆ͢Δ w σʔλϕʔεʹ͓͚ΔΫΤϦϓϥϯબ୒ w ͭͷςʔϒϧͷڞ௨෦෼ KPJOޙͷߦ਺ ͕Θ͔Δͱద੾ͳ݁ ߹ΞϧΰϦζϜ͕બ΂Δ w ৄࡉ͸અ

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1SPCMFN4FUVQ #VTJOFTT3FRVJSFNFOUT

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"WBJMGPSFDBTUJOH ஫l"WBJMz͸ஶऀΒͷ଄ޠͬΆ͍ w ༩͑ΒΕͨ഑৴৚݅ͷݩͰ޿ࠂΩϟϯϖʔϯͷ*NQΩϟύγςΟͷ ༧ଌΛఏڙ͢Δͷ͕ૂ͍ w ϒϥϯυҊ݅ w Ϛʔέολʔ͕഑৴৚݅ͷ૊߹ͤΛબͿ w ৚݅͸আ֎৚݅΋͋Δɺطଘސ٬ηάϝϯτͱϦλʔήςΟϯάη άϝϯτଧͪফ͋ͬͯ͠͠·͏ࣄ͕͋Δɻ w ՝ۚݟࠐ౓߹͍ͷߴ͍ηάϝϯτΛͦͷ··࢖͏ͱ$73͕ܹݮ ͨ͠Γ͢Δɺطଘސ٬σϦλή͸ॏཁ  w 6OEFSEFMJWFSZ͸ආ͚͍ͨ ͓ͦΒ͘༧ࢉ͕༨ͬͯ͠·͏͔Β

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"VEJFODFଐੑ w $POUFYU w 8FCPS"QQ EFWJDFUZQF 41 UBCMFU 1$ "E4MPUUZQF w (FPHSBQIJDBMBSFB w "OZDPNCJOBUJPOPGTUBUFT PSBOZDPNCJOBUJPOPGQPTUBM DPEFT w 7JFXBCJMJUZ w ࠷খ஋Λࢦఆ FHWJFXBCJMJUZҎ্ͷJOWFOUPSZͷΈങ͏

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#JE1SJDF w *NQΩϟύγςΟʹӨڹΛ༩͑Δ࠷ޙͷύϥϝʔλ w ೖࡳΤϯδϯ͸ݸʑͷೖࡳֹۚΛ࠷దԽ͢Δ͕ w Ϛʔέλʔ͸ฏۉ΋͘͠͸্ݶೖࡳֹۚΛઃఆ͢Δ

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#JEEJOH1SPDFTT

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ೖࡳϓϩηεͷཁૉ w 2VBMJUZ"TTFTTNFOU w #JE3FRVFTUͷΛ͜͜Ͱམͱ͍ͯ͠Δ ϒϥϯυҊ݅ϝΠϯ͔ͩΒݫ͠Ί  w ΞμϧταΠτ GSBVE IFBEFSCJEEJOHͷ͍͕ٙ͋ΔJOWFOUPSZ w "E$BNQBJHO4FMFDUJPO w ࿮αΠζ w 7BMVF&TUJNBUJPOBOE1SJDF"EKVTUNFOU w 'SFRVFODZ΍ཤྺʹج͍ͮͨ$53ɾ$73༧ଌΛ༻͍Δ w ͜ΕΒͷϑΟϧλ΍Ձ஋ධՁΛߟྀ͢Δඞཁ͕͋Δ

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1SPCMFN'PSNVMBUJPO $IBMMFOHFT  BOE$PODFQUVBM"QQSPBDI

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ఆࣜԽ w Ωϟϯϖʔϯ഑৴৚݅ͷ૊Έ͋ΘͤΛ  w ʹର͢Δ*NQΩϟύγςΟ "WBJM Λ  w #JE3FRVFTU਺Λ  w ഑৴৚݅Λ ͱͨ͠ͱ͖ͷ*NQൃੜ֬཰Λ ͱ͢Δͱ w  w C C A(C) NBRQ C pi (C)

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ఆࣜԽ w ΦʔσΟΤϯεηάϝϯτ͸แؚηάϝϯτͱআ֎ηάϝϯτͷ ࠩ w  w ηάϝϯτ͸Φʔόʔϥοϓ͢ΔͷͰ03ԋࢉࢠͰ࿈݁ w 

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$IBMMFOHFT w ηάϝϯτ͕ ݸ͋ͬͨΒ ݸͷ૊Έ͋Θ͕ͤଘࡏ͢ΔͨΊɺ ༧Ί૊߹ͤʹରԠ͢Δ݁ՌΛ֨ೲ͢Δͷ͸ݱ࣮తͰ͸ͳ͍ w ϨεϙϯελΠϜΛॏࢹ͢ΔͷͰ%#ΛΫΤϦ͢Δͷ΋͕͔͔࣌ؒ Γ͗͢ΔɻඵҎ಺ʹ݁Ռ͕ಘΒΕΔ࢓૊ΈͰ࣮ݱ͠ͳ͚Ε͹͍͚ ͳ͍ w ઢܗϞσϧͷ༷ͳ΋ͷͰηάϝϯτಛ௃ྔΛݩʹܭࢉͰ͖Δ͔  w แؚηάϝϯτͷ߹ܭ͔Βআ֎ηάϝϯτͷ߹ܭΛҾ͘ͱϚΠφ εʹͳͬͯ͠·͏ˠͭ·ΓͰ͖ͳ͍ w ͸ ͷΈͰදݱͰ͖ͳ͍ΦʔΫγϣϯͷউ཰ͷӨڹ΋ड͚Δ N 2N − 1 A(C) C

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$PODFQUVBM"QQSPBDI w ৚݅෇͖ಠཱΛԾఆͯ͠ܭࢉྔΛݮΒ͢ ߟྀ͕ඞཁͳ૊Έ͋ΘͤΛݮΒ͢ w ΧʔσΟφϦςΟͷখ͍͞&OW5ZQF 8&#PS"QQ %FW$MBTT "E5ZQFΛ $POUFYUͱͯ͠·ͱΊΔͱࣜ  ϑΟϧλ௨ա཰ 83J಺෦ΦʔΫγϣϯͷউ཰ 83F֎෦ΦʔΫγϣϯͷউ཰ ΞϓϦ໘ͱ8FC໘Ͱ7JFXBCJMJUZͷ ෼෍͕ಉ͡ͱԾఆ͢ΔͳΜͯͦΜͳ ཚ๫ͳɺͱ͍͏ؾ࣋ͪΛ͙ͬͱת͑ ͯઌʹਐΈ·͢

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ഉଞతͳ৚݅ͷѻ͍ w ഑৴৚݅ʹ8FC໘ͱ"QQ໘ͷ྆ํΛબΜͩ৔߹ɺPWFSXSBQ͕ແ͍ ͷͰ୯ʹ଍ͤ͹ྑ͍ w Q &OW5ZQF\8&# "QQ^ Q &OW5ZQF8&#  Q &OW5ZQF"QQ  w (FP-PDBUJPO΋ಉ͡

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͜͏ͳΔ w ͱ ͸&OW5ZQFʹͷΈґଘ͢Δൺྫఆ਺ͱͯ͠௥͍ग़͢ NBRQ PF(EnvType) w ྆ลର਺Λͱͬͯਖ਼ଇԽઢܗϞσϧͱͯ͠pUͨ͠΋ͷΛ࢖͏ &OW5ZQFຖͷ੾ย ͕ਪఆͨ֬͠཰Q ɾ ɺ ͸ઢܗϞσϧΛpUֶͯ͠शͨ͠܎਺ xk βk ࣜΛͦͷ··࢖Θͳ͍ͷ͸Կނ  ͓ͦΒ֬͘཰Q ɾ ͷਪఆ஋ͷޡΓΛ ܎਺ЌͰิਖ਼͢ΔࣄͰϩόετͳϞσ ϧΛಘ͍ͯΔ

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&TUJNBUJPOT

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$POUFYUͱ(FP-PDBUJPO w Q $POUFYU ͸&OW5ZQF %FWJDF$MBTT "E5ZQF͝ͱʹूܭ͓ͯ͠ ͚͹Α͍ w $POUFYUͷΧʔσΟφϦςΟ͸ w ूܭͯ͠อଘ͓͚ͯ͠͹Α͍ w Q (FPc&OW5ZQF ΋ಉ͡ w &OW5ZQF͸஋ w (FP͸भ΍༣ศ൪߸ͰΧʔσΟφϦςΟ͕  w Q (FPc&OW5ZQF ͸º  ߦͷσʔλ

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"VEJFODF4FHNFOU w Q "VE4FHc&OW5ZQF ͷਪఆ w ϦΫΤετ਺%FWJDF͸ηάϝϯτʹΑΒͣҰఆͱԾఆ͢Δͱ w ϦΫΤετ਺ͷ୅ΘΓʹσόΠε਺Λߟ͑Ε͹ྑ͘ͳΔ Q "VE4FH   w ϦΫΤετ਺͕ ԯEBZͳͷʹରͯ͠ϢχʔΫσόΠε਺͸ ԯEBZͳͷͰ໰୊ͷαΠζΛஶ͘͠ݮΒ͢ࣄ͕Ͱ͖Δ PGEFWJDFJOTFHNFOU PGUPUBMEFWJDF

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4LFUDI w ΦʔσΟΤϯεηάϝϯτͷશͯͷ૊Έ͋Θͤʹ͍ͭͯΧʔσΟφ ϦςΟΛࣄલʹܭࢉ͢Δͷ͸ݱ࣮తͰ͸ͳ͍ w ू߹શମͷ୅ΘΓʹू߹ͷѹॖදݱ 4LFUDI Λ࢖͏ w 4LFUDI͔Βू߹ͷαΠζͷਪఆ͕Ͱ͖Δ w #MPPN'JMUFSͱ.JO)BTIΛݕ౼ͨ͠ w ˠ4LFUDIJOHBMHPSJUINͰௐ΂Δͱ͍Ζ͍Ζग़͖ͯ·͢ w ࢀߟ IUUQXXXDTVDGFEVTUSJOHCJPUBMLTUBMLQEG

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#MPPN'JMUFSͰΧʔσΟφϦςΟਪఆ αΠζ ͷϏοτ഑ྻΛ༻ҙͨ͠ͱ͖ʹཱ͕͍ͬͯΔϏοτͷ਺͕  ݸ͋ΔͱΧʔσΟφϦςΟ ͷਪఆ஋͸ m X n CJUXJTF03ΛऔΔ͜ͱͰ࿨ू߹ͷαΠζ ΛಘΔࣄ͕Ͱ͖Δɻੵ ू߹ͱࠩ͸௚઀ܭࢉͰ͖ͳ͍͕࣍ͷ௨ΓܭࢉͰ͖Δɻ |A ∪ B| ཱ͕ͨͩͭ͠Ϗοτͷ਺͕૿͑Δͱਪఆਫ਼౓͕Լ͕Δ͠ɺηάϝϯτ͕ ԯҎ্ʹͳΔ͜ͱΛߟ͑ΔͱσΟεΫ༰ྔతʹ࠾༻Λݟૹͬͨ

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.JO)BTIͰΧʔσΟφϦςΟਪఆ w #MPPN'JMUFSΑΓ΋ඞཁͳ༰ྔ͕খ͍͞ w ཁૉΛϋογϡԽ͢Δ͕อ࣋͢Δͷ͸࠷খͷQݸͷϋογϡͷΈ w อ࣋ͨ͠ϋογϡ͕Rݸ R㱡Q ͷ੔਺ΛؚΈ࠷େͷ΋ͷ͕.Ͱ͋ Δ৔߹઎༗Ϗοτͷີ౓͸ R .Ͱࣜʹ͋ͯ͸ΊΔͱ w ඞཁͳ༰ྔ͕খ͍͞ͷͰNΛେ͖͘ͱΔ͜ͱ͕Ͱ͖ΔɻஶऀΒ͸ Qͷ.JO)BTITLFUDIΛ࠾༻ɻ͢΂ͯͷΦʔσΟΤϯεηάϝϯτ ͕#MPPN'JMUFSͰ(#ʹͳͬͨͷ͕.JO)BTIͰ͸.#ͰࡁΜͩɻ

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.JO)BTIͰΧʔσΟφϦςΟਪఆ ଓ w ࣮ࡍͷηάϝϯτΛ࢖ͬͯਪఆ ਫ਼౓ͷ࣮ݧΛͨ͠ w ඇৗʹྑ͍ਪఆ͕ಘΒΕ͍ͯ Δɻ w ϋογϡ஋ಉ࢜ΛVOJPOͯ͠࠶ ͼQݸͷ࠷খϋογϡΛऔΕ͹ ࿨ू߹ͷΧʔσΟφϦςΟ͕ܭ ࢉͰ͖Δɻ w ૊Έ͋Θͤʹ͍ͭͯ΋࣮ݧͨ͠ ͕ͷޡࠩ

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಺෦ΦʔΫγϣϯͷউ཰༧ଌ w ஶऀΒͷϓϥοτϑΥʔϜʹ͓͚Δ಺෦ΦʔΫγϣϯͷฏۉ͸ w খചɾ)FBMUI$BSF͕ߴ͍ɺཱྀߦɾඇӦར͕௿͍ w ۀछ͕༧ଌʹޮ͔͘Βಛ௃ྔʹ࢖͍ͬͯΔ w ͱॻ͍ͯ͋Δ͕ۀछຖͷฏۉΛ࢖͍ͬͯΔ͚ͩ

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֎෦ΦʔΫγϣϯͷউ཰༧ଌ w ஶऀΒͷউ཰ͷฏۉ͸ w Q XJOcೖࡳֹۚ ΛٻΊΔ w %JTQMBZ ڪΒ͘CBOOFSͷҙ  ͱ7JEFPͰউ཰ۂઢ͕ҟͳΔ ͷͰ෼ֶ͚ͯश͍ͯ͠Δɻ $POUFYUຖʹύϥϝʔλЍ В ͷ஋Λֶशͨ͘͠ͳΓͦ͏ͩ ͕ɺ͍ͯ͠ͳ͍ ೖࡳֹۚ

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.PEFM#VJMEJOHBOE &WBMVBUJPO

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.PEFMpUUJOH Ϟσϧ͸ࣜ  ͷઢܗϞσϧ -ਖ਼ଇԽɺ ͸*NQΩϟύγςΟ A(C) w ֶशσʔλͱͳΔઆ໌ม਺ ͱ໨తม਺ ͷϖΞ͕ཉ͍͠ w ͸഑৴࣮੷ͱ ͔Βܭࢉ ষͷ಺༰ xk A(C) xk C

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σʔλऩू ໨తม਺ w ͷऩू w ͨͩ͠Ωϟϯϖʔϯͷ৚݅͢΂ͯͷ૊߹ͤͰूΊΔͷ͸ෆՄೳ w ਪఆ͢Δͷ͸༧ࢉ͕ແ੍ݶͩͬͨͱ͖ͷ*NQΩϟύγςΟͳͷͰɺ஋ͦͷ΋ͷ͸ ௚઀ूΊΒΕͳ͍ w ͳͷͰஶऀΒͷϓϥοτϑΥʔϜͰ഑৴தͷΩϟϯϖʔϯΛ࢖ͬͨ w ࣮ࡍͷ഑৴Ͱ͸೔ͷ༧ࢉΛݩʹϖʔγϯά͍ͯ͠ΔͷͰɺ಺෦ΦʔΫγϣϯԠࡳ ཰Λ Λ࢖ͬͯ ͕ಘΒΕΔɻͨͩ͠ ͕ඇৗʹ௿͍΋ͷ͸আ֎ A(C) tpr ∈ [0,1] A(C) tpr

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σʔλऩू આ໌ม਺ w ࡢ೔ͷ#JE3FRVFTUͷ$POUFYUٴͼ(FP-PDBUJPO͝ͱͷूܭ w ࡢ೔ͷ"VEJFODF4FHNFOUͷ.JO)BTI w աڈिؒͷΦʔΫγϣϯͷউ཰ w ࡢ೔ͷΩϟϯϖʔϯຖͷ*NQ਺ w ͜ΕΒ͔ΒNPEFMGFBUVSF Λܭࢉ͢Δ xk

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#VEHFU1BDJOH w %41ͷඪ४ػೳ w ೔ͷ༧ࢉΛ͔͚࣌ؒͯফԽ͢Δ w ஶऀΒͷ༧ࢉফԽϖʔγϯά͸ΩϟϯϖʔϯͷதͰޮՌͷྑ͍ TQFOE DBNQBJHOͷԼҐͷ୯Ґ ͷԠࡳ཰Λ্͛ΔΑ͏ʹͳͬͯ ͍Δɻ w ޮՌͷྑ͍ͱ͜ΖʹࢿۚΛدͤΔ

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ΦϑϥΠϯ࣮ݧ w ਅͷ ͱਪఆ஋ͷࠩͷฏۉ͸ w ഒͷζϨ w ࣮༻͢Δͷʹ͸े෼ w ࢼ͠ʹ.JO)BTI࢖Θͳ͔ͬͨΒ w 3ܾఆ܎਺มΘΒͣʜʜ log10 (A(C)) 100.35 = 2.2

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