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ػցֶशͷத਎Λ ཧղ͢Δ 2018/12/5ˏϦΫϧʔτελοϑΟϯά Ճ౻ެҰ

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ࣗݾ঺հ Ճ౻ެҰʢ͔ͱ͏͖Έ͔ͣʣ ॴଐɿγϧόʔΤοάɾςΫϊϩδʔʢגʣ ത࢜ʢ৘ใཧ޻ֶʣ ʢम࢜·Ͱ͸਺ֶʣ झຯɿےτϨ Twitter: @hamukazu ࢓ࣄɿϨίϝϯσʔγϣϯγεςϜʹؔ͢Δݚڀ։ൃ ஶॻ

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ࠓ೔ͷ࿩ • ຊͷએ఻ • ػցֶशͱ਺ֶͷؔ܎ʹ͍ͭͯ • ਺ֶͷجຊ • ઢܗ୅਺ • ඍੵ෼ • ਺ཧ࠷దԽʹ͍ͭͯ • ػցֶशͷΞϧΰϦζϜʢαϙʔτϕΫλϚγϯʣ • ࠓޙԿΛษڧ͢΂͖͔

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ࠓ೔ͷ໨ඪɿ αϙʔτϕΫλϚγϯͷத਎ Λཧղ͢Δ

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એ఻ ಛ௃ɿ ɾπʔϧͷ࢖͍ํͰ͸ͳ͘ػցֶशΞϧΰϦζϜͷ࢓૊ΈΛղઆͨ͠ຊ ɾPythonͷجຊ΍ɺΞϧΰϦζϜͷཧղʹඞཁͳ਺ֶ͔Βղઆ http://bit.ly/mlessence ʢؒҧ͍͕ଟͯ͘͝ΊΜͳ͍͞ɻਖ਼ޡද͸αϙʔτϖʔδࢀরɻʣ

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ࣥචͷഎܠ • େਓͷ਺ֶษڧ΍Γ௚͠ϒʔϜ͕དྷͯΔ͔΋͠Εͳ͍ • ͦͷυϥΠϒཁૉͷҰͭͱͳ͍ͬͯΔͷ͕ػցֶशɾਓ޻ ஌ೳ • ݸਓతʹ΋ɺษڧ͍ͨ͠ͷͰͲ͏͢Ε͹ʁͱ͍͏૬ஊ͕͋ͬ ͨΓ • ػցֶशͷཧ࿦తͳઆ໌͸ɺϕΠζ౷ܭͳͲͷ؍఺͔Βͷ ॻ੶͕ଟ͘ɺ਺ཧ࠷దԽ͔ΒͷΞϓϩʔν͸͋·Γͳ͍

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ํ਑ • Ͱ͖Δ͚ͩʮඞཁͳ͜ͱ͸શͯॻ͍ͯ͋ΔʯΛΊͨ͟͠ • ࣌ؒత੍໿Ͱඞͣ͠΋ୡ੒Ͱ͖ͯͳ͍͕… • ਺ֶ͸ɺʮূ໌ʯΑΓ΋ʮઆ໌ʯΛॏࢹ • ௿࣍ݩͷέʔεΛ؍࡯͠ɺߴ࣍ݩͷ৔߹͸ূ໌ͤͣʹೲಘͯ͠΋Β͏ • ূ໌͠ͳͯ͘΋ɺఆཧͷओு͸ਖ਼֬ʹ • σΟʔϓϥʔχϯάͷઆ໌͸͠ͳ͍ • ਺ֶͱ਺஋ܭࢉͷઆ໌Λ׬શʹ෼཭ • ͢΂ͯʹαϯϓϧίʔυΛ͚ͭΔ

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ۤ࿑࿩ • ͳ͔ͳ͔ಈ͔ͳ͍αϯϓϧίʔυʢΪϦΪϦ·Ͱσόοάʣ • ਺ࣜͷσόοάͷ೉͠͞ • ਺ࣜʹ׳Εͯͳ͍ฤूऀ • ਤͷ४උͷେม͞

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ۤ࿑ͷࠟ੻

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਺ֶ͸σʔλαΠΤϯςΟετ ͷඞਢ஌ࣝʁ • ଟ෼No! • ͔͠͠਺ֶ͕Ͱ͖Δ͜ͱ͸ࠩผԽʹ͸ͳΔ • ෳ਺ͷબ୒ࢶͷதͰ໘ന͍ͱࢥ͏͜ͱΛ༏ઌͯ͠΍Δͷ͸ Α͍ΩϟϦΞΞοϓઓུ

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த਎Λ෼Δ͜ͱͷϝϦοτ • ࠷৽ͷݚڀ࿦จʹΩϟονΞοϓͰ͖Δ • طଘͷΞϧΰϦζϜΛमਖ਼ͨ͠ಠࣗͷΞϧΰϦζϜΛ࣮૷ Ͱ͖Δ • ϋΠύʔύϥϝʔλͷҙຯΛཧղͯ͠ޮ཰ͷྑ͍νϡʔχ ϯά͕Ͱ͖Δ • ͭ·Γࢼߦࡨޡͷ෯͕޿͕Δ

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ػցֶशʹඞཁͳ਺ֶ • ֶशϑΣʔζͰ͸਺ཧܭը๏͕Α͘࢖ΘΕΔ • ਺ཧܭը๏ͷཧղͷϕʔεͱͳΔͷ͕ɺઢܗ୅਺ͱඍੵ෼ • σʔλͷղऍ΍Ճ޻Ͱ΋ศརͳͷ͕ઢܗ୅਺

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਺ཧ࠷దԽʁ Bishop, “Pattern Recognition and Machine Learning” ͰͷSVMͷઆ໌ ͜ͷΑ͏ʹɺػցֶशͰͷύϥϝʔλܾఆ͸ɺ ͋Δؔ਺Λ࠷େԽʢ࠷খԽʣ͢Δม਺Λݟ͚ͭΔ ͱ͍͏໰୊ʹؼண͞ΕΔ͜ͱ͕ଟ͍

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Α͋͘Δύλʔϯ Α͠ʂػցֶशษڧ͢Δͧʂ ԿΛಡΉͷ͕͍͍͔ͳʁ༗໊͔ͩΒPRMLಡΜͲ͔͘ ਺ࣜΛݟܸͯ௜

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Α͋͘ΔϋϚΓϙΠϯτ ·ͨPRMLͷSVMͷઆ໌ ͜Ε͕ ͜͏ͳΔͱॻ͍ͯΔ ʁʁʁʁ ࠓ೔͸͜ͷ࿩Λ͠·͢ʂ

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ͱ͜ΖͰɺ ࢲͷීஈͷ࢓ࣄͰ͕͢ • ࿦จΛಡΈͳ͕Β࣮૷ͱ͍͏͜ͱ͕ଟ͍Ͱ͢ • طଘͷϥΠϒϥϦ͕͋Δ৔߹Ͱ΋͋͑ͯ࠶࣮૷ͯ͠೿ੜΞ ϧΰϦζϜΛߟ͑Δ͜ͱ΋ • ʮػցֶशͷΤοηϯεʯ͸ීஈͷ࢓ࣄͷ͔ͨ͠Λ༗໊Ξ ϧΰϦζϜΛ࢖ͬͯ࠶ݱͨ͠ͱ΋͍͑·͢

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਺ཧ࠷దԽͱ͸ ༩͑ΒΕ੍ͨ໿ͷ΋ͱɺ༩͑ΒΕͨؔ਺Λ࠷খԽʢ·ͨ͸࠷େԽʣ ͢Δͱ͍͏໰୊ x2 + xy + y2 + 2x + 4y AAAB+XicbZDLSgMxFIbP1Futt1GXuggWQSiUmSLosujGZQv2Au1YMmnahmYyQ5IpHYa+iRsXirh143O4c+ejmF4W2nog5OP/zyEnvx9xprTjfFmZtfWNza3sdm5nd2//wD48qqswloTWSMhD2fSxopwJWtNMc9qMJMWBz2nDH95O/caISsVCca+TiHoB7gvWYwRrI3Vse/xQKoyTQmKu0rhwmXTsvFN0ZoVWwV1Avnz6Uf0GgErH/mx3QxIHVGjCsVIt14m0l2KpGeF0kmvHikaYDHGftgwKHFDlpbPNJ+jcKF3UC6U5QqOZ+nsixYFSSeCbzgDrgVr2puJ/XivWvWsvZSKKNRVk/lAv5kiHaBoD6jJJieaJAUwkM7siMsASE23CypkQ3OUvr0K9VHQNV00aNzCvLJzAGVyAC1dQhjuoQA0IjOARnuHFSq0n69V6m7dmrMXMMfwp6/0HpHeUkQ== AAAB+XicbZDLSgMxFIbPeK31NupSkWARhEKZKYIui25ctmAv0I4lk2ba0MyFJFM6DF36Fm5cKOLWTZ/Dnc/gS5heFtp6IOTj/88hJ78bcSaVZX0ZK6tr6xubma3s9s7u3r55cFiTYSwIrZKQh6LhYkk5C2hVMcVpIxIU+y6ndbd/O/HrAyokC4N7lUTU8XE3YB4jWGmpbZrDh2J+mOQTfRWH+cukbeasgjUttAz2HHKlk3Hl+/F0XG6bn61OSGKfBopwLGXTtiLlpFgoRjgdZVuxpBEmfdylTY0B9ql00unmI3SulQ7yQqFPoNBU/T2RYl/KxHd1p49VTy56E/E/rxkr79pJWRDFigZk9pAXc6RCNIkBdZigRPFEAyaC6V0R6WGBidJhZXUI9uKXl6FWLNiaKzqNG5hVBo7hDC7AhisowR2UoQoEBvAEL/BqpMaz8Wa8z1pXjPnMEfwp4+MHgryV9w== AAAB+XicbZDLSgMxFIbPeK31NupSkWARhEKZKYIui25ctmAv0I4lk2ba0MyFJFM6DF36Fm5cKOLWTZ/Dnc/gS5heFtp6IOTj/88hJ78bcSaVZX0ZK6tr6xubma3s9s7u3r55cFiTYSwIrZKQh6LhYkk5C2hVMcVpIxIU+y6ndbd/O/HrAyokC4N7lUTU8XE3YB4jWGmpbZrDh2J+mOQTfRWH+cukbeasgjUttAz2HHKlk3Hl+/F0XG6bn61OSGKfBopwLGXTtiLlpFgoRjgdZVuxpBEmfdylTY0B9ql00unmI3SulQ7yQqFPoNBU/T2RYl/KxHd1p49VTy56E/E/rxkr79pJWRDFigZk9pAXc6RCNIkBdZigRPFEAyaC6V0R6WGBidJhZXUI9uKXl6FWLNiaKzqNG5hVBo7hDC7AhisowR2UoQoEBvAEL/BqpMaz8Wa8z1pXjPnMEfwp4+MHgryV9w== AAAB+XicbZDLSgMxFIbP1Futt1GXboJFEAplpgi6LLpxWcFeoB1LJs20oZnMkGRKh6Fv4saFIm59E3e+jWk7C209EPLx/+eQk9+POVPacb6twsbm1vZOcbe0t39weGQfn7RUlEhCmyTikez4WFHOBG1qpjntxJLi0Oe07Y/v5n57QqVikXjUaUy9EA8FCxjB2kh9254+1SrTtJKaqzatXKV9u+xUnUWhdXBzKENejb791RtEJAmp0IRjpbquE2svw1Izwums1EsUjTEZ4yHtGhQ4pMrLFpvP0IVRBiiIpDlCo4X6eyLDoVJp6JvOEOuRWvXm4n9eN9HBjZcxESeaCrJ8KEg40hGax4AGTFKieWoAE8nMroiMsMREm7BKJgR39cvr0KpVXcMPTrl+m8dRhDM4h0tw4RrqcA8NaAKBCTzDK7xZmfVivVsfy9aClc+cwp+yPn8AlH2STA== x + y = 0 AAAB7HicbZDLSgMxFIbPeK31VnWpi2ARBKHMuNGNUHTjsgWnLbRDyaSZNjTJDElGHIY+gxsXirj1GXwOd+58FNPLQlt/CHz85xxyzh8mnGnjul/O0vLK6tp6YaO4ubW9s1va22/oOFWE+iTmsWqFWFPOJPUNM5y2EkWxCDlthsObcb15T5VmsbwzWUIDgfuSRYxgYy3/4Sy7crulsltxJ0KL4M2gXD36qH8DQK1b+uz0YpIKKg3hWOu25yYmyLEyjHA6KnZSTRNMhrhP2xYlFlQH+WTZETqxTg9FsbJPGjRxf0/kWGididB2CmwGer42Nv+rtVMTXQY5k0lqqCTTj6KUIxOj8eWoxxQlhmcWMFHM7orIACtMjM2naEPw5k9ehMZ5xbNct2lcw1QFOIRjOAUPLqAKt1ADHwgweIRneHGk8+S8Om/T1iVnNnMAf+S8/wAqEpB2 AAAB7HicbZDLSsNAFIZP6q3WW9WlIoNFEISSuNGNUHTjsgXTFtpQJtNJO3QyCTMTMYQuXbtxoYhbn6HP4c5n8CWcXhba+sPAx3/OYc75/ZgzpW37y8otLa+sruXXCxubW9s7xd29uooSSahLIh7Jpo8V5UxQVzPNaTOWFIc+pw1/cDOuN+6pVCwSdzqNqRfinmABI1gby304S6/sTrFkl+2J0CI4MyhVDke178ejUbVT/Gx3I5KEVGjCsVItx461l2GpGeF0WGgnisaYDHCPtgwKHFLlZZNlh+jEOF0URNI8odHE/T2R4VCpNPRNZ4h1X83XxuZ/tVaig0svYyJONBVk+lGQcKQjNL4cdZmkRPPUACaSmV0R6WOJiTb5FEwIzvzJi1A/LzuGayaNa5gqDwdwDKfgwAVU4Baq4AIBBk/wAq+WsJ6tN+t92pqzZjP78EfWxw8IV5Hc AAAB7HicbZDLSsNAFIZP6q3WW9WlIoNFEISSuNGNUHTjsgXTFtpQJtNJO3QyCTMTMYQuXbtxoYhbn6HP4c5n8CWcXhba+sPAx3/OYc75/ZgzpW37y8otLa+sruXXCxubW9s7xd29uooSSahLIh7Jpo8V5UxQVzPNaTOWFIc+pw1/cDOuN+6pVCwSdzqNqRfinmABI1gby304S6/sTrFkl+2J0CI4MyhVDke178ejUbVT/Gx3I5KEVGjCsVItx461l2GpGeF0WGgnisaYDHCPtgwKHFLlZZNlh+jEOF0URNI8odHE/T2R4VCpNPRNZ4h1X83XxuZ/tVaig0svYyJONBVk+lGQcKQjNL4cdZmkRPPUACaSmV0R6WOJiTb5FEwIzvzJi1A/LzuGayaNa5gqDwdwDKfgwAVU4Baq4AIBBk/wAq+WsJ6tN+t92pqzZjP78EfWxw8IV5Hc AAAB7HicbZBNS8NAEIYn9avWr6pHL4tFEISSeNGLUPTisYKphTaUzXbTLt1swu5EDKW/wYsHRbz6g7z5b9y2OWjrCwsP78ywM2+YSmHQdb+d0srq2vpGebOytb2zu1fdP2iZJNOM+yyRiW6H1HApFPdRoOTtVHMah5I/hKObaf3hkWsjEnWPecqDmA6UiASjaC3/6Sy/cnvVmlt3ZyLL4BVQg0LNXvWr209YFnOFTFJjOp6bYjCmGgWTfFLpZoanlI3ogHcsKhpzE4xny07IiXX6JEq0fQrJzP09MaaxMXkc2s6Y4tAs1qbmf7VOhtFlMBYqzZArNv8oyiTBhEwvJ32hOUOZW6BMC7srYUOqKUObT8WG4C2evAyt87pn+c6tNa6LOMpwBMdwCh5cQANuoQk+MBDwDK/w5ijnxXl3PuatJaeYOYQ/cj5/ABoYjjE= Minimize Subject to ྫɿ ←໨తؔ਺ ←੍໿ࣜ

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ػցֶशΞϧΰϦζϜͱ ਺ཧ࠷దԽ • ઢܗճؼ →2࣍ܭը๏ • ϥοιճؼ →࠲ඪ߱Լ๏ • ϩδεςΟοΫճؼ →χϡʔτϯ๏ • SVM →ϥάϥϯδϡະఆ৐਺๏ɺ2࣍ܭը๏

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ػցֶशͰ࢖ΘΕΔ ਺ཧ࠷దԽʹ͍ͭͯͷ஫ҙ • ػցֶशͷΞϧΰϦζϜ͸ɺ਺ཧ࠷దԽʹؼண͞ΕΔ͜ͱ ͕ଟ͍ • ݫີͳ࠷దղΛಘΑ͏͢Δ͜ͱΑΓʮ࠷దղʹۙͮ͘ʯ ͜ͱ͕େࣄͳ͜ͱ΋

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਺ཧ࠷దԽͷཧղͰ ඞཁͳ਺ֶ • ઢܗ୅਺ • ඍੵ෼

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ઢܗ୅਺ • ߦྻͱϕΫτϧ • ػցֶशͷཧղͷ্Ͱ͸ɺઢܗۭؒͷΠϝʔδΛ࣋ͭ͜ͱ ͕େࣄ • ຊൃදͰ͸SVMͰ࢖ΘΕΔڑ཭ͷެ͚ࣜͩઆ໌͢Δ

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b AAACCXicbZDLSsNAFIYnXmu9pbp0M1gEVyURQZdFNy4r2As0ocxMJ+3QmWSYmSgl5Al8Bre6didufQqXvomTNgvb+sOBj/+cwzn8WHKmjed9O2vrG5tb25Wd6u7e/sGhWzvq6CRVhLZJwhPVw0hTzmLaNsxw2pOKIoE57eLJbdHvPlKlWRI/mKmkoUCjmEWMIGOtgVsLsMhQHkiqZIE4H7h1r+HNBFfBL6EOSrUG7k8wTEgqaGwIR1r3fU+aMEPKMMJpXg1STSUiEzSifYsxElSH2ez1HJ5ZZwijRNmKDZy5fzcyJLSeCmwnBTJjvdwrzP96/dRE12HGYpkaGpP5oSjl0CSwyAEOmaLE8KkFRBSzv0IyRgoRY9NauIJFkYm/nMAqdC4avuX7y3rzpkynAk7AKTgHPrgCTXAHWqANCHgCL+AVvDnPzrvz4XzOR9eccucYLMj5+gUCLJsH AAACCXicbZDLSsNAFIYnXmu9pbp0M1gEVyURQZdFNy4r2As0ocxMJ+3QmWSYmSgl5Al8Bre6didufQqXvomTNgvb+sOBj/+cwzn8WHKmjed9O2vrG5tb25Wd6u7e/sGhWzvq6CRVhLZJwhPVw0hTzmLaNsxw2pOKIoE57eLJbdHvPlKlWRI/mKmkoUCjmEWMIGOtgVsLsMhQHkiqZIE4H7h1r+HNBFfBL6EOSrUG7k8wTEgqaGwIR1r3fU+aMEPKMMJpXg1STSUiEzSifYsxElSH2ez1HJ5ZZwijRNmKDZy5fzcyJLSeCmwnBTJjvdwrzP96/dRE12HGYpkaGpP5oSjl0CSwyAEOmaLE8KkFRBSzv0IyRgoRY9NauIJFkYm/nMAqdC4avuX7y3rzpkynAk7AKTgHPrgCTXAHWqANCHgCL+AVvDnPzrvz4XzOR9eccucYLMj5+gUCLJsH AAACCXicbZDLSsNAFIYnXmu9pbp0M1gEVyURQZdFNy4r2As0ocxMJ+3QmWSYmSgl5Al8Bre6didufQqXvomTNgvb+sOBj/+cwzn8WHKmjed9O2vrG5tb25Wd6u7e/sGhWzvq6CRVhLZJwhPVw0hTzmLaNsxw2pOKIoE57eLJbdHvPlKlWRI/mKmkoUCjmEWMIGOtgVsLsMhQHkiqZIE4H7h1r+HNBFfBL6EOSrUG7k8wTEgqaGwIR1r3fU+aMEPKMMJpXg1STSUiEzSifYsxElSH2ez1HJ5ZZwijRNmKDZy5fzcyJLSeCmwnBTJjvdwrzP96/dRE12HGYpkaGpP5oSjl0CSwyAEOmaLE8KkFRBSzv0IyRgoRY9NauIJFkYm/nMAqdC4avuX7y3rzpkynAk7AKTgHPrgCTXAHWqANCHgCL+AVvDnPzrvz4XzOR9eccucYLMj5+gUCLJsH AAACCXicbZDLSsNAFIYnXmu9pbp0M1gEVyURQZdFNy4r2As0ocxMJ+3QmWSYmSgl5Al8Bre6didufQqXvomTNgvb+sOBj/+cwzn8WHKmjed9O2vrG5tb25Wd6u7e/sGhWzvq6CRVhLZJwhPVw0hTzmLaNsxw2pOKIoE57eLJbdHvPlKlWRI/mKmkoUCjmEWMIGOtgVsLsMhQHkiqZIE4H7h1r+HNBFfBL6EOSrUG7k8wTEgqaGwIR1r3fU+aMEPKMMJpXg1STSUiEzSifYsxElSH2ez1HJ5ZZwijRNmKDZy5fzcyJLSeCmwnBTJjvdwrzP96/dRE12HGYpkaGpP5oSjl0CSwyAEOmaLE8KkFRBSzv0IyRgoRY9NauIJFkYm/nMAqdC4avuX7y3rzpkynAk7AKTgHPrgCTXAHWqANCHgCL+AVvDnPzrvz4XzOR9eccucYLMj5+gUCLJsH aT b = a1b1 + a2b2 + · · · + anbn AAACJ3icbVDNSgMxGMz6W+tf1aOXYBGEgu4WQS9C0YvHCm0V2rp8SbMaTLJLkhXKso/hQ/gMXvXsTfTYNzHb9qDWgZBh5hu+ZEgiuLG+/+XNzS8sLi2XVsqra+sbm5Wt7Y6JU01Zm8Yi1jcEDBNcsbblVrCbRDOQRLBr8nBR+NePTBseq5YdJqwv4U7xiFOwTgorRz0iM8hvW8VN8jMIAxIGNQjrmIT1Gu7RQWwNrmEIlVNcouof+mPgWRJMSRVN0Qwro94gpqlkylIBxnQDP7H9DLTlVLC83EsNS4A+wB3rOqpAMtPPxh/L8b5TBjiKtTvK4rH6M5GBNGYoiZuUYO/NX68Q//O6qY1O+xlXSWqZopNFUSqwjXHREh5wzagVQ0eAau7eiuk9aKDWdflrC5G56yT428As6dQPA8evjquN82k7JbSL9tABCtAJaqBL1ERtRNETekGv6M179t69D+9zMjrnTTM76Be80TczFKTO AAACJ3icbVDNSgMxGMz6W+tf1aOXYBGEgu4WQS9C0YvHCm0V2rp8SbMaTLJLkhXKso/hQ/gMXvXsTfTYNzHb9qDWgZBh5hu+ZEgiuLG+/+XNzS8sLi2XVsqra+sbm5Wt7Y6JU01Zm8Yi1jcEDBNcsbblVrCbRDOQRLBr8nBR+NePTBseq5YdJqwv4U7xiFOwTgorRz0iM8hvW8VN8jMIAxIGNQjrmIT1Gu7RQWwNrmEIlVNcouof+mPgWRJMSRVN0Qwro94gpqlkylIBxnQDP7H9DLTlVLC83EsNS4A+wB3rOqpAMtPPxh/L8b5TBjiKtTvK4rH6M5GBNGYoiZuUYO/NX68Q//O6qY1O+xlXSWqZopNFUSqwjXHREh5wzagVQ0eAau7eiuk9aKDWdflrC5G56yT428As6dQPA8evjquN82k7JbSL9tABCtAJaqBL1ERtRNETekGv6M179t69D+9zMjrnTTM76Be80TczFKTO AAACJ3icbVDNSgMxGMz6W+tf1aOXYBGEgu4WQS9C0YvHCm0V2rp8SbMaTLJLkhXKso/hQ/gMXvXsTfTYNzHb9qDWgZBh5hu+ZEgiuLG+/+XNzS8sLi2XVsqra+sbm5Wt7Y6JU01Zm8Yi1jcEDBNcsbblVrCbRDOQRLBr8nBR+NePTBseq5YdJqwv4U7xiFOwTgorRz0iM8hvW8VN8jMIAxIGNQjrmIT1Gu7RQWwNrmEIlVNcouof+mPgWRJMSRVN0Qwro94gpqlkylIBxnQDP7H9DLTlVLC83EsNS4A+wB3rOqpAMtPPxh/L8b5TBjiKtTvK4rH6M5GBNGYoiZuUYO/NX68Q//O6qY1O+xlXSWqZopNFUSqwjXHREh5wzagVQ0eAau7eiuk9aKDWdflrC5G56yT428As6dQPA8evjquN82k7JbSL9tABCtAJaqBL1ERtRNETekGv6M179t69D+9zMjrnTTM76Be80TczFKTO AAACJ3icbVDNSgMxGMz6W+tf1aOXYBGEgu4WQS9C0YvHCm0V2rp8SbMaTLJLkhXKso/hQ/gMXvXsTfTYNzHb9qDWgZBh5hu+ZEgiuLG+/+XNzS8sLi2XVsqra+sbm5Wt7Y6JU01Zm8Yi1jcEDBNcsbblVrCbRDOQRLBr8nBR+NePTBseq5YdJqwv4U7xiFOwTgorRz0iM8hvW8VN8jMIAxIGNQjrmIT1Gu7RQWwNrmEIlVNcouof+mPgWRJMSRVN0Qwro94gpqlkylIBxnQDP7H9DLTlVLC83EsNS4A+wB3rOqpAMtPPxh/L8b5TBjiKtTvK4rH6M5GBNGYoiZuUYO/NX68Q//O6qY1O+xlXSWqZopNFUSqwjXHREh5wzagVQ0eAau7eiuk9aKDWdflrC5G56yT428As6dQPA8evjquN82k7JbSL9tABCtAJaqBL1ERtRNETekGv6M179t69D+9zMjrnTTM76Be80TczFKTO ੒෼ͷੵͷ࿨Ͱఆٛ͞ΕΔ A B O H aT b = ! OH ⇥ ! 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Slide 24

Slide 24 text

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AAAB/HicbZDLSgMxFIbP1Futt6pLN8EiuCozItRl0Y3LCvYC7VAyaaaNTTJDkhHLUJ/Bra7diVvfxaVvYqadhW39IfDxn3M4J38Qc6aN6347hbX1jc2t4nZpZ3dv/6B8eNTSUaIIbZKIR6oTYE05k7RpmOG0EyuKRcBpOxjfZPX2I1WaRfLeTGLqCzyULGQEG2u1eoFIn6b9csWtujOhVfByqECuRr/80xtEJBFUGsKx1l3PjY2fYmUY4XRa6iWaxpiM8ZB2LUosqPbT2bVTdGadAQojZZ80aOb+nUix0HoiAtspsBnp5Vpm/lfrJia88lMm48RQSeaLwoQjE6Hs62jAFCWGTyxgopi9FZERVpgYG9DClkBkmXjLCaxC66LqWb67rNSv83SKcAKncA4e1KAOt9CAJhB4gBd4hTfn2Xl3PpzPeWvByWeOYUHO1y+nfJXn AAAB/HicbZDLSgMxFIbP1Futt6pLN8EiuCozItRl0Y3LCvYC7VAyaaaNTTJDkhHLUJ/Bra7diVvfxaVvYqadhW39IfDxn3M4J38Qc6aN6347hbX1jc2t4nZpZ3dv/6B8eNTSUaIIbZKIR6oTYE05k7RpmOG0EyuKRcBpOxjfZPX2I1WaRfLeTGLqCzyULGQEG2u1eoFIn6b9csWtujOhVfByqECuRr/80xtEJBFUGsKx1l3PjY2fYmUY4XRa6iWaxpiM8ZB2LUosqPbT2bVTdGadAQojZZ80aOb+nUix0HoiAtspsBnp5Vpm/lfrJia88lMm48RQSeaLwoQjE6Hs62jAFCWGTyxgopi9FZERVpgYG9DClkBkmXjLCaxC66LqWb67rNSv83SKcAKncA4e1KAOt9CAJhB4gBd4hTfn2Xl3PpzPeWvByWeOYUHO1y+nfJXn x AAAB/HicbZDLSgMxFIbP1Futt6pLN8EiuCozItRl0Y3LCvYC7VAyaaaNTTJDkhHLUJ/Bra7diVvfxaVvYqadhW39IfDxn3M4J38Qc6aN6347hbX1jc2t4nZpZ3dv/6B8eNTSUaIIbZKIR6oTYE05k7RpmOG0EyuKRcBpOxjfZPX2I1WaRfLeTGLqCzyULGQEG2u1eoFIn6b9csWtujOhVfByqECuRr/80xtEJBFUGsKx1l3PjY2fYmUY4XRa6iWaxpiM8ZB2LUosqPbT2bVTdGadAQojZZ80aOb+nUix0HoiAtspsBnp5Vpm/lfrJia88lMm48RQSeaLwoQjE6Hs62jAFCWGTyxgopi9FZERVpgYG9DClkBkmXjLCaxC66LqWb67rNSv83SKcAKncA4e1KAOt9CAJhB4gBd4hTfn2Xl3PpzPeWvByWeOYUHO1y+nfJXn AAAB/HicbZDLSgMxFIbP1Futt6pLN8EiuCozItRl0Y3LCvYC7VAyaaaNTTJDkhHLUJ/Bra7diVvfxaVvYqadhW39IfDxn3M4J38Qc6aN6347hbX1jc2t4nZpZ3dv/6B8eNTSUaIIbZKIR6oTYE05k7RpmOG0EyuKRcBpOxjfZPX2I1WaRfLeTGLqCzyULGQEG2u1eoFIn6b9csWtujOhVfByqECuRr/80xtEJBFUGsKx1l3PjY2fYmUY4XRa6iWaxpiM8ZB2LUosqPbT2bVTdGadAQojZZ80aOb+nUix0HoiAtspsBnp5Vpm/lfrJia88lMm48RQSeaLwoQjE6Hs62jAFCWGTyxgopi9FZERVpgYG9DClkBkmXjLCaxC66LqWb67rNSv83SKcAKncA4e1KAOt9CAJhB4gBd4hTfn2Xl3PpzPeWvByWeOYUHO1y+nfJXn AAAB/HicbZDLSgMxFIbP1Futt6pLN8EiuCozItRl0Y3LCvYC7VAyaaaNTTJDkhHLUJ/Bra7diVvfxaVvYqadhW39IfDxn3M4J38Qc6aN6347hbX1jc2t4nZpZ3dv/6B8eNTSUaIIbZKIR6oTYE05k7RpmOG0EyuKRcBpOxjfZPX2I1WaRfLeTGLqCzyULGQEG2u1eoFIn6b9csWtujOhVfByqECuRr/80xtEJBFUGsKx1l3PjY2fYmUY4XRa6iWaxpiM8ZB2LUosqPbT2bVTdGadAQojZZ80aOb+nUix0HoiAtspsBnp5Vpm/lfrJia88lMm48RQSeaLwoQjE6Hs62jAFCWGTyxgopi9FZERVpgYG9DClkBkmXjLCaxC66LqWb67rNSv83SKcAKncA4e1KAOt9CAJhB4gBd4hTfn2Xl3PpzPeWvByWeOYUHO1y+nfJXn AAAB/HicbZDLSgMxFIbP1Futt6pLN8EiuCozItRl0Y3LCvYC7VAyaaaNTTJDkhHLUJ/Bra7diVvfxaVvYqadhW39IfDxn3M4J38Qc6aN6347hbX1jc2t4nZpZ3dv/6B8eNTSUaIIbZKIR6oTYE05k7RpmOG0EyuKRcBpOxjfZPX2I1WaRfLeTGLqCzyULGQEG2u1eoFIn6b9csWtujOhVfByqECuRr/80xtEJBFUGsKx1l3PjY2fYmUY4XRa6iWaxpiM8ZB2LUosqPbT2bVTdGadAQojZZ80aOb+nUix0HoiAtspsBnp5Vpm/lfrJia88lMm48RQSeaLwoQjE6Hs62jAFCWGTyxgopi9FZERVpgYG9DClkBkmXjLCaxC66LqWb67rNSv83SKcAKncA4e1KAOt9CAJhB4gBd4hTfn2Xl3PpzPeWvByWeOYUHO1y+nfJXn ฏ໘ͷํఔࣜ ฏ໘͕ݪ఺Λ௨Δ৔߹ ฏ໘͕఺ɹɹΛ௨Δ৔߹ ͱ͓͘ͱ aT x + b = 0 AAACCnicbZDLSgMxFIYz9VbrbaxLN8EiCEKZEUE3QtGNywq9QTuWTJppQ5PMkGSkZZg38Bnc6tqduPUlXPomZtpZ2NYDIR//fw7n8PsRo0o7zrdVWFvf2Nwqbpd2dvf2D+zDckuFscSkiUMWyo6PFGFUkKammpFOJAniPiNtf3yX+e0nIhUNRUNPI+JxNBQ0oBhpI/Xtcs/nCUofG9k/Sc/9G6dvV5yqMyu4Cm4OFZBXvW//9AYhjjkRGjOkVNd1Iu0lSGqKGUlLvViRCOExGpKuQYE4UV4yuz2Fp0YZwCCU5gkNZ+rfiQRxpabcN50c6ZFa9jLxP68b6+DaS6iIYk0Eni8KYgZ1CLMg4IBKgjWbGkBYUnMrxCMkEdYmroUtPk9NJu5yAqvQuqi6hh8uK7XbPJ0iOAYn4Ay44ArUwD2ogybAYAJewCt4s56td+vD+py3Fqx85ggslPX1C604msA= AAACCnicbZDLSgMxFIYz9VbrbaxLN8EiCEKZEUE3QtGNywq9QTuWTJppQ5PMkGSkZZg38Bnc6tqduPUlXPomZtpZ2NYDIR//fw7n8PsRo0o7zrdVWFvf2Nwqbpd2dvf2D+zDckuFscSkiUMWyo6PFGFUkKammpFOJAniPiNtf3yX+e0nIhUNRUNPI+JxNBQ0oBhpI/Xtcs/nCUofG9k/Sc/9G6dvV5yqMyu4Cm4OFZBXvW//9AYhjjkRGjOkVNd1Iu0lSGqKGUlLvViRCOExGpKuQYE4UV4yuz2Fp0YZwCCU5gkNZ+rfiQRxpabcN50c6ZFa9jLxP68b6+DaS6iIYk0Eni8KYgZ1CLMg4IBKgjWbGkBYUnMrxCMkEdYmroUtPk9NJu5yAqvQuqi6hh8uK7XbPJ0iOAYn4Ay44ArUwD2ogybAYAJewCt4s56td+vD+py3Fqx85ggslPX1C604msA= AAACCnicbZDLSgMxFIYz9VbrbaxLN8EiCEKZEUE3QtGNywq9QTuWTJppQ5PMkGSkZZg38Bnc6tqduPUlXPomZtpZ2NYDIR//fw7n8PsRo0o7zrdVWFvf2Nwqbpd2dvf2D+zDckuFscSkiUMWyo6PFGFUkKammpFOJAniPiNtf3yX+e0nIhUNRUNPI+JxNBQ0oBhpI/Xtcs/nCUofG9k/Sc/9G6dvV5yqMyu4Cm4OFZBXvW//9AYhjjkRGjOkVNd1Iu0lSGqKGUlLvViRCOExGpKuQYE4UV4yuz2Fp0YZwCCU5gkNZ+rfiQRxpabcN50c6ZFa9jLxP68b6+DaS6iIYk0Eni8KYgZ1CLMg4IBKgjWbGkBYUnMrxCMkEdYmroUtPk9NJu5yAqvQuqi6hh8uK7XbPJ0iOAYn4Ay44ArUwD2ogybAYAJewCt4s56td+vD+py3Fqx85ggslPX1C604msA= AAACCnicbZDLSgMxFIYz9VbrbaxLN8EiCEKZEUE3QtGNywq9QTuWTJppQ5PMkGSkZZg38Bnc6tqduPUlXPomZtpZ2NYDIR//fw7n8PsRo0o7zrdVWFvf2Nwqbpd2dvf2D+zDckuFscSkiUMWyo6PFGFUkKammpFOJAniPiNtf3yX+e0nIhUNRUNPI+JxNBQ0oBhpI/Xtcs/nCUofG9k/Sc/9G6dvV5yqMyu4Cm4OFZBXvW//9AYhjjkRGjOkVNd1Iu0lSGqKGUlLvViRCOExGpKuQYE4UV4yuz2Fp0YZwCCU5gkNZ+rfiQRxpabcN50c6ZFa9jLxP68b6+DaS6iIYk0Eni8KYgZ1CLMg4IBKgjWbGkBYUnMrxCMkEdYmroUtPk9NJu5yAqvQuqi6hh8uK7XbPJ0iOAYn4Ay44ArUwD2ogybAYAJewCt4s56td+vD+py3Fqx85ggslPX1C604msA= aT p = b AAACCXicbZDLSgMxFIYzXmu9TXXpJlgEN5YZEXQjFN24rNAbtGNJ0kwbmmSGJKOUYZ7AZ3Cra3fi1qdw6ZuYabuwrQdCPv7/HM7hxzFn2njet7Oyura+sVnYKm7v7O7tu6WDpo4SRWiDRDxSbYw05UzShmGG03asKBKY0xYe3eZ+65EqzSJZN+OYBgINJAsZQcZKPbd01sUiRdlDPf/j7Br33LJX8SYFl8GfQRnMqtZzf7r9iCSCSkM40rrje7EJUqQMI5xmxW6iaYzICA1ox6JEguognZyewROr9GEYKfukgRP170SKhNZjgW2nQGaoF71c/M/rJCa8ClIm48RQSaaLwoRDE8E8B9hnihLDxxYQUczeCskQKUSMTWtuCxaZzcRfTGAZmucV3/L9Rbl6M0unAI7AMTgFPrgEVXAHaqABCHgCL+AVvDnPzrvz4XxOW1ec2cwhmCvn6xco1ZqA AAACCXicbZDLSgMxFIYzXmu9TXXpJlgEN5YZEXQjFN24rNAbtGNJ0kwbmmSGJKOUYZ7AZ3Cra3fi1qdw6ZuYabuwrQdCPv7/HM7hxzFn2njet7Oyura+sVnYKm7v7O7tu6WDpo4SRWiDRDxSbYw05UzShmGG03asKBKY0xYe3eZ+65EqzSJZN+OYBgINJAsZQcZKPbd01sUiRdlDPf/j7Br33LJX8SYFl8GfQRnMqtZzf7r9iCSCSkM40rrje7EJUqQMI5xmxW6iaYzICA1ox6JEguognZyewROr9GEYKfukgRP170SKhNZjgW2nQGaoF71c/M/rJCa8ClIm48RQSaaLwoRDE8E8B9hnihLDxxYQUczeCskQKUSMTWtuCxaZzcRfTGAZmucV3/L9Rbl6M0unAI7AMTgFPrgEVXAHaqABCHgCL+AVvDnPzrvz4XxOW1ec2cwhmCvn6xco1ZqA AAACCXicbZDLSgMxFIYzXmu9TXXpJlgEN5YZEXQjFN24rNAbtGNJ0kwbmmSGJKOUYZ7AZ3Cra3fi1qdw6ZuYabuwrQdCPv7/HM7hxzFn2njet7Oyura+sVnYKm7v7O7tu6WDpo4SRWiDRDxSbYw05UzShmGG03asKBKY0xYe3eZ+65EqzSJZN+OYBgINJAsZQcZKPbd01sUiRdlDPf/j7Br33LJX8SYFl8GfQRnMqtZzf7r9iCSCSkM40rrje7EJUqQMI5xmxW6iaYzICA1ox6JEguognZyewROr9GEYKfukgRP170SKhNZjgW2nQGaoF71c/M/rJCa8ClIm48RQSaaLwoRDE8E8B9hnihLDxxYQUczeCskQKUSMTWtuCxaZzcRfTGAZmucV3/L9Rbl6M0unAI7AMTgFPrgEVXAHaqABCHgCL+AVvDnPzrvz4XxOW1ec2cwhmCvn6xco1ZqA AAACCXicbZDLSgMxFIYzXmu9TXXpJlgEN5YZEXQjFN24rNAbtGNJ0kwbmmSGJKOUYZ7AZ3Cra3fi1qdw6ZuYabuwrQdCPv7/HM7hxzFn2njet7Oyura+sVnYKm7v7O7tu6WDpo4SRWiDRDxSbYw05UzShmGG03asKBKY0xYe3eZ+65EqzSJZN+OYBgINJAsZQcZKPbd01sUiRdlDPf/j7Br33LJX8SYFl8GfQRnMqtZzf7r9iCSCSkM40rrje7EJUqQMI5xmxW6iaYzICA1ox6JEguognZyewROr9GEYKfukgRP170SKhNZjgW2nQGaoF71c/M/rJCa8ClIm48RQSaaLwoRDE8E8B9hnihLDxxYQUczeCskQKUSMTWtuCxaZzcRfTGAZmucV3/L9Rbl6M0unAI7AMTgFPrgEVXAHaqABCHgCL+AVvDnPzrvz4XxOW1ec2cwhmCvn6xco1ZqA p AAAB/HicbZDLSgMxFIbP1Futt1GXboJFcFVmRNBl0Y3LCvYC7VAyaaaNTTJDkhHKUJ/Bra7diVvfxaVvYqadhW39IfDxn3M4J3+YcKaN5307pbX1jc2t8nZlZ3dv/8A9PGrpOFWENknMY9UJsaacSdo0zHDaSRTFIuS0HY5v83r7iSrNYvlgJgkNBB5KFjGCjbVavVBkybTvVr2aNxNaBb+AKhRq9N2f3iAmqaDSEI617vpeYoIMK8MIp9NKL9U0wWSMh7RrUWJBdZDNrp2iM+sMUBQr+6RBM/fvRIaF1hMR2k6BzUgv13Lzv1o3NdF1kDGZpIZKMl8UpRyZGOVfRwOmKDF8YgETxeytiIywwsTYgBa2hCLPxF9OYBVaFzXf8v1ltX5TpFOGEziFc/DhCupwBw1oAoFHeIFXeHOenXfnw/mct5acYuYYFuR8/QKa3JXf AAAB/HicbZDLSgMxFIbP1Futt1GXboJFcFVmRNBl0Y3LCvYC7VAyaaaNTTJDkhHKUJ/Bra7diVvfxaVvYqadhW39IfDxn3M4J3+YcKaN5307pbX1jc2t8nZlZ3dv/8A9PGrpOFWENknMY9UJsaacSdo0zHDaSRTFIuS0HY5v83r7iSrNYvlgJgkNBB5KFjGCjbVavVBkybTvVr2aNxNaBb+AKhRq9N2f3iAmqaDSEI617vpeYoIMK8MIp9NKL9U0wWSMh7RrUWJBdZDNrp2iM+sMUBQr+6RBM/fvRIaF1hMR2k6BzUgv13Lzv1o3NdF1kDGZpIZKMl8UpRyZGOVfRwOmKDF8YgETxeytiIywwsTYgBa2hCLPxF9OYBVaFzXf8v1ltX5TpFOGEziFc/DhCupwBw1oAoFHeIFXeHOenXfnw/mct5acYuYYFuR8/QKa3JXf AAAB/HicbZDLSgMxFIbP1Futt1GXboJFcFVmRNBl0Y3LCvYC7VAyaaaNTTJDkhHKUJ/Bra7diVvfxaVvYqadhW39IfDxn3M4J3+YcKaN5307pbX1jc2t8nZlZ3dv/8A9PGrpOFWENknMY9UJsaacSdo0zHDaSRTFIuS0HY5v83r7iSrNYvlgJgkNBB5KFjGCjbVavVBkybTvVr2aNxNaBb+AKhRq9N2f3iAmqaDSEI617vpeYoIMK8MIp9NKL9U0wWSMh7RrUWJBdZDNrp2iM+sMUBQr+6RBM/fvRIaF1hMR2k6BzUgv13Lzv1o3NdF1kDGZpIZKMl8UpRyZGOVfRwOmKDF8YgETxeytiIywwsTYgBa2hCLPxF9OYBVaFzXf8v1ltX5TpFOGEziFc/DhCupwBw1oAoFHeIFXeHOenXfnw/mct5acYuYYFuR8/QKa3JXf AAAB/HicbZDLSgMxFIbP1Futt1GXboJFcFVmRNBl0Y3LCvYC7VAyaaaNTTJDkhHKUJ/Bra7diVvfxaVvYqadhW39IfDxn3M4J3+YcKaN5307pbX1jc2t8nZlZ3dv/8A9PGrpOFWENknMY9UJsaacSdo0zHDaSRTFIuS0HY5v83r7iSrNYvlgJgkNBB5KFjGCjbVavVBkybTvVr2aNxNaBb+AKhRq9N2f3iAmqaDSEI617vpeYoIMK8MIp9NKL9U0wWSMh7RrUWJBdZDNrp2iM+sMUBQr+6RBM/fvRIaF1hMR2k6BzUgv13Lzv1o3NdF1kDGZpIZKMl8UpRyZGOVfRwOmKDF8YgETxeytiIywwsTYgBa2hCLPxF9OYBVaFzXf8v1ltX5TpFOGEziFc/DhCupwBw1oAoFHeIFXeHOenXfnw/mct5acYuYYFuR8/QKa3JXf aT (x p) = 0 AAACEXicbZDLSgMxFIYz9VbrbdSVuAkWoS4sMyLoRii6cVmhN2jHkkkzbWiSGZKMWIbBh/AZ3Oranbj1CVz6JmbaLmzrgZCP/z+Hk/x+xKjSjvNt5ZaWV1bX8uuFjc2t7R17d6+hwlhiUschC2XLR4owKkhdU81IK5IEcZ+Rpj+8yfzmA5GKhqKmRxHxOOoLGlCMtJG69kHH5wlK72ulDB7T0+yK0pMrp2sXnbIzLrgI7hSKYFrVrv3T6YU45kRozJBSbdeJtJcgqSlmJC10YkUihIeoT9oGBeJEecn4Cyk8NkoPBqE0R2g4Vv9OJIgrNeK+6eRID9S8l4n/ee1YB5deQkUUayLwZFEQM6hDmOUBe1QSrNnIAMKSmrdCPEASYW1Sm9ni89Rk4s4nsAiNs7Jr+O68WLmeppMHh+AIlIALLkAF3IIqqAMMnsALeAVv1rP1bn1Yn5PWnDWd2QczZX39At7dnYo= AAACEXicbZDLSgMxFIYz9VbrbdSVuAkWoS4sMyLoRii6cVmhN2jHkkkzbWiSGZKMWIbBh/AZ3Oranbj1CVz6JmbaLmzrgZCP/z+Hk/x+xKjSjvNt5ZaWV1bX8uuFjc2t7R17d6+hwlhiUschC2XLR4owKkhdU81IK5IEcZ+Rpj+8yfzmA5GKhqKmRxHxOOoLGlCMtJG69kHH5wlK72ulDB7T0+yK0pMrp2sXnbIzLrgI7hSKYFrVrv3T6YU45kRozJBSbdeJtJcgqSlmJC10YkUihIeoT9oGBeJEecn4Cyk8NkoPBqE0R2g4Vv9OJIgrNeK+6eRID9S8l4n/ee1YB5deQkUUayLwZFEQM6hDmOUBe1QSrNnIAMKSmrdCPEASYW1Sm9ni89Rk4s4nsAiNs7Jr+O68WLmeppMHh+AIlIALLkAF3IIqqAMMnsALeAVv1rP1bn1Yn5PWnDWd2QczZX39At7dnYo= AAACEXicbZDLSgMxFIYz9VbrbdSVuAkWoS4sMyLoRii6cVmhN2jHkkkzbWiSGZKMWIbBh/AZ3Oranbj1CVz6JmbaLmzrgZCP/z+Hk/x+xKjSjvNt5ZaWV1bX8uuFjc2t7R17d6+hwlhiUschC2XLR4owKkhdU81IK5IEcZ+Rpj+8yfzmA5GKhqKmRxHxOOoLGlCMtJG69kHH5wlK72ulDB7T0+yK0pMrp2sXnbIzLrgI7hSKYFrVrv3T6YU45kRozJBSbdeJtJcgqSlmJC10YkUihIeoT9oGBeJEecn4Cyk8NkoPBqE0R2g4Vv9OJIgrNeK+6eRID9S8l4n/ee1YB5deQkUUayLwZFEQM6hDmOUBe1QSrNnIAMKSmrdCPEASYW1Sm9ni89Rk4s4nsAiNs7Jr+O68WLmeppMHh+AIlIALLkAF3IIqqAMMnsALeAVv1rP1bn1Yn5PWnDWd2QczZX39At7dnYo= AAACEXicbZDLSgMxFIYz9VbrbdSVuAkWoS4sMyLoRii6cVmhN2jHkkkzbWiSGZKMWIbBh/AZ3Oranbj1CVz6JmbaLmzrgZCP/z+Hk/x+xKjSjvNt5ZaWV1bX8uuFjc2t7R17d6+hwlhiUschC2XLR4owKkhdU81IK5IEcZ+Rpj+8yfzmA5GKhqKmRxHxOOoLGlCMtJG69kHH5wlK72ulDB7T0+yK0pMrp2sXnbIzLrgI7hSKYFrVrv3T6YU45kRozJBSbdeJtJcgqSlmJC10YkUihIeoT9oGBeJEecn4Cyk8NkoPBqE0R2g4Vv9OJIgrNeK+6eRID9S8l4n/ee1YB5deQkUUayLwZFEQM6hDmOUBe1QSrNnIAMKSmrdCPEASYW1Sm9ni89Rk4s4nsAiNs7Jr+O68WLmeppMHh+AIlIALLkAF3IIqqAMMnsALeAVv1rP1bn1Yn5PWnDWd2QczZX39At7dnYo= p AAAB/HicbZDLSgMxFIbP1Futt1GXboJFcFVmRNBl0Y3LCvYC7VAyaaaNTTJDkhHKUJ/Bra7diVvfxaVvYqadhW39IfDxn3M4J3+YcKaN5307pbX1jc2t8nZlZ3dv/8A9PGrpOFWENknMY9UJsaacSdo0zHDaSRTFIuS0HY5v83r7iSrNYvlgJgkNBB5KFjGCjbVavVBkybTvVr2aNxNaBb+AKhRq9N2f3iAmqaDSEI617vpeYoIMK8MIp9NKL9U0wWSMh7RrUWJBdZDNrp2iM+sMUBQr+6RBM/fvRIaF1hMR2k6BzUgv13Lzv1o3NdF1kDGZpIZKMl8UpRyZGOVfRwOmKDF8YgETxeytiIywwsTYgBa2hCLPxF9OYBVaFzXf8v1ltX5TpFOGEziFc/DhCupwBw1oAoFHeIFXeHOenXfnw/mct5acYuYYFuR8/QKa3JXf AAAB/HicbZDLSgMxFIbP1Futt1GXboJFcFVmRNBl0Y3LCvYC7VAyaaaNTTJDkhHKUJ/Bra7diVvfxaVvYqadhW39IfDxn3M4J3+YcKaN5307pbX1jc2t8nZlZ3dv/8A9PGrpOFWENknMY9UJsaacSdo0zHDaSRTFIuS0HY5v83r7iSrNYvlgJgkNBB5KFjGCjbVavVBkybTvVr2aNxNaBb+AKhRq9N2f3iAmqaDSEI617vpeYoIMK8MIp9NKL9U0wWSMh7RrUWJBdZDNrp2iM+sMUBQr+6RBM/fvRIaF1hMR2k6BzUgv13Lzv1o3NdF1kDGZpIZKMl8UpRyZGOVfRwOmKDF8YgETxeytiIywwsTYgBa2hCLPxF9OYBVaFzXf8v1ltX5TpFOGEziFc/DhCupwBw1oAoFHeIFXeHOenXfnw/mct5acYuYYFuR8/QKa3JXf AAAB/HicbZDLSgMxFIbP1Futt1GXboJFcFVmRNBl0Y3LCvYC7VAyaaaNTTJDkhHKUJ/Bra7diVvfxaVvYqadhW39IfDxn3M4J3+YcKaN5307pbX1jc2t8nZlZ3dv/8A9PGrpOFWENknMY9UJsaacSdo0zHDaSRTFIuS0HY5v83r7iSrNYvlgJgkNBB5KFjGCjbVavVBkybTvVr2aNxNaBb+AKhRq9N2f3iAmqaDSEI617vpeYoIMK8MIp9NKL9U0wWSMh7RrUWJBdZDNrp2iM+sMUBQr+6RBM/fvRIaF1hMR2k6BzUgv13Lzv1o3NdF1kDGZpIZKMl8UpRyZGOVfRwOmKDF8YgETxeytiIywwsTYgBa2hCLPxF9OYBVaFzXf8v1ltX5TpFOGEziFc/DhCupwBw1oAoFHeIFXeHOenXfnw/mct5acYuYYFuR8/QKa3JXf AAAB/HicbZDLSgMxFIbP1Futt1GXboJFcFVmRNBl0Y3LCvYC7VAyaaaNTTJDkhHKUJ/Bra7diVvfxaVvYqadhW39IfDxn3M4J3+YcKaN5307pbX1jc2t8nZlZ3dv/8A9PGrpOFWENknMY9UJsaacSdo0zHDaSRTFIuS0HY5v83r7iSrNYvlgJgkNBB5KFjGCjbVavVBkybTvVr2aNxNaBb+AKhRq9N2f3iAmqaDSEI617vpeYoIMK8MIp9NKL9U0wWSMh7RrUWJBdZDNrp2iM+sMUBQr+6RBM/fvRIaF1hMR2k6BzUgv13Lzv1o3NdF1kDGZpIZKMl8UpRyZGOVfRwOmKDF8YgETxeytiIywwsTYgBa2hCLPxF9OYBVaFzXf8v1ltX5TpFOGEziFc/DhCupwBw1oAoFHeIFXeHOenXfnw/mct5acYuYYFuR8/QKa3JXf

Slide 25

Slide 25 text

ڑ཭ͷެࣜ ฏ໘ ͱ఺ ͷڑ཭͸ ͳͥ͜͏ͳΔͷ͔ʁ aT x + b = 0 AAACCnicbZDLSgMxFIYz9VbrbaxLN8EiCEKZEUE3QtGNywq9QTuWTJppQ5PMkGSkZZg38Bnc6tqduPUlXPomZtpZ2NYDIR//fw7n8PsRo0o7zrdVWFvf2Nwqbpd2dvf2D+zDckuFscSkiUMWyo6PFGFUkKammpFOJAniPiNtf3yX+e0nIhUNRUNPI+JxNBQ0oBhpI/Xtcs/nCUofG9k/Sc/9G6dvV5yqMyu4Cm4OFZBXvW//9AYhjjkRGjOkVNd1Iu0lSGqKGUlLvViRCOExGpKuQYE4UV4yuz2Fp0YZwCCU5gkNZ+rfiQRxpabcN50c6ZFa9jLxP68b6+DaS6iIYk0Eni8KYgZ1CLMg4IBKgjWbGkBYUnMrxCMkEdYmroUtPk9NJu5yAqvQuqi6hh8uK7XbPJ0iOAYn4Ay44ArUwD2ogybAYAJewCt4s56td+vD+py3Fqx85ggslPX1C604msA= AAACCnicbZDLSgMxFIYz9VbrbaxLN8EiCEKZEUE3QtGNywq9QTuWTJppQ5PMkGSkZZg38Bnc6tqduPUlXPomZtpZ2NYDIR//fw7n8PsRo0o7zrdVWFvf2Nwqbpd2dvf2D+zDckuFscSkiUMWyo6PFGFUkKammpFOJAniPiNtf3yX+e0nIhUNRUNPI+JxNBQ0oBhpI/Xtcs/nCUofG9k/Sc/9G6dvV5yqMyu4Cm4OFZBXvW//9AYhjjkRGjOkVNd1Iu0lSGqKGUlLvViRCOExGpKuQYE4UV4yuz2Fp0YZwCCU5gkNZ+rfiQRxpabcN50c6ZFa9jLxP68b6+DaS6iIYk0Eni8KYgZ1CLMg4IBKgjWbGkBYUnMrxCMkEdYmroUtPk9NJu5yAqvQuqi6hh8uK7XbPJ0iOAYn4Ay44ArUwD2ogybAYAJewCt4s56td+vD+py3Fqx85ggslPX1C604msA= AAACCnicbZDLSgMxFIYz9VbrbaxLN8EiCEKZEUE3QtGNywq9QTuWTJppQ5PMkGSkZZg38Bnc6tqduPUlXPomZtpZ2NYDIR//fw7n8PsRo0o7zrdVWFvf2Nwqbpd2dvf2D+zDckuFscSkiUMWyo6PFGFUkKammpFOJAniPiNtf3yX+e0nIhUNRUNPI+JxNBQ0oBhpI/Xtcs/nCUofG9k/Sc/9G6dvV5yqMyu4Cm4OFZBXvW//9AYhjjkRGjOkVNd1Iu0lSGqKGUlLvViRCOExGpKuQYE4UV4yuz2Fp0YZwCCU5gkNZ+rfiQRxpabcN50c6ZFa9jLxP68b6+DaS6iIYk0Eni8KYgZ1CLMg4IBKgjWbGkBYUnMrxCMkEdYmroUtPk9NJu5yAqvQuqi6hh8uK7XbPJ0iOAYn4Ay44ArUwD2ogybAYAJewCt4s56td+vD+py3Fqx85ggslPX1C604msA= AAACCnicbZDLSgMxFIYz9VbrbaxLN8EiCEKZEUE3QtGNywq9QTuWTJppQ5PMkGSkZZg38Bnc6tqduPUlXPomZtpZ2NYDIR//fw7n8PsRo0o7zrdVWFvf2Nwqbpd2dvf2D+zDckuFscSkiUMWyo6PFGFUkKammpFOJAniPiNtf3yX+e0nIhUNRUNPI+JxNBQ0oBhpI/Xtcs/nCUofG9k/Sc/9G6dvV5yqMyu4Cm4OFZBXvW//9AYhjjkRGjOkVNd1Iu0lSGqKGUlLvViRCOExGpKuQYE4UV4yuz2Fp0YZwCCU5gkNZ+rfiQRxpabcN50c6ZFa9jLxP68b6+DaS6iIYk0Eni8KYgZ1CLMg4IBKgjWbGkBYUnMrxCMkEdYmroUtPk9NJu5yAqvQuqi6hh8uK7XbPJ0iOAYn4Ay44ArUwD2ogybAYAJewCt4s56td+vD+py3Fqx85ggslPX1C604msA= aT x + b = 0 AAACCnicbZDLSgMxFIYz9VbrbaxLN8EiCEKZEUE3QtGNywq9QTuWTJppQ5PMkGSkZZg38Bnc6tqduPUlXPomZtpZ2NYDIR//fw7n8PsRo0o7zrdVWFvf2Nwqbpd2dvf2D+zDckuFscSkiUMWyo6PFGFUkKammpFOJAniPiNtf3yX+e0nIhUNRUNPI+JxNBQ0oBhpI/Xtcs/nCUofG9k/Sc/9G6dvV5yqMyu4Cm4OFZBXvW//9AYhjjkRGjOkVNd1Iu0lSGqKGUlLvViRCOExGpKuQYE4UV4yuz2Fp0YZwCCU5gkNZ+rfiQRxpabcN50c6ZFa9jLxP68b6+DaS6iIYk0Eni8KYgZ1CLMg4IBKgjWbGkBYUnMrxCMkEdYmroUtPk9NJu5yAqvQuqi6hh8uK7XbPJ0iOAYn4Ay44ArUwD2ogybAYAJewCt4s56td+vD+py3Fqx85ggslPX1C604msA= AAACCnicbZDLSgMxFIYz9VbrbaxLN8EiCEKZEUE3QtGNywq9QTuWTJppQ5PMkGSkZZg38Bnc6tqduPUlXPomZtpZ2NYDIR//fw7n8PsRo0o7zrdVWFvf2Nwqbpd2dvf2D+zDckuFscSkiUMWyo6PFGFUkKammpFOJAniPiNtf3yX+e0nIhUNRUNPI+JxNBQ0oBhpI/Xtcs/nCUofG9k/Sc/9G6dvV5yqMyu4Cm4OFZBXvW//9AYhjjkRGjOkVNd1Iu0lSGqKGUlLvViRCOExGpKuQYE4UV4yuz2Fp0YZwCCU5gkNZ+rfiQRxpabcN50c6ZFa9jLxP68b6+DaS6iIYk0Eni8KYgZ1CLMg4IBKgjWbGkBYUnMrxCMkEdYmroUtPk9NJu5yAqvQuqi6hh8uK7XbPJ0iOAYn4Ay44ArUwD2ogybAYAJewCt4s56td+vD+py3Fqx85ggslPX1C604msA= 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AAAB/HicbZDLSgMxFIbP1Futt6pLN8EiuCozIuiy6MZlBXuBdiiZNNPGJplpkhHKUJ/Bra7diVvfxaVvYqadhW39IfDxn3M4J38Qc6aN6347hbX1jc2t4nZpZ3dv/6B8eNTUUaIIbZCIR6odYE05k7RhmOG0HSuKRcBpKxjdZvXWE1WaRfLBTGLqCzyQLGQEG2s1u4FIx9NeueJW3ZnQKng5VCBXvVf+6fYjkggqDeFY647nxsZPsTKMcDotdRNNY0xGeEA7FiUWVPvp7NopOrNOH4WRsk8aNHP/TqRYaD0Rge0U2Az1ci0z/6t1EhNe+ymTcWKoJPNFYcKRiVD2ddRnihLDJxYwUczeisgQK0yMDWhhSyCyTLzlBFaheVH1LN9fVmo3eTpFOIFTOAcPrqAGd1CHBhB4hBd4hTfn2Xl3PpzPeWvByWeOYUHO1y+ccJXg AAAB/HicbZDLSgMxFIbP1Futt6pLN8EiuCozIuiy6MZlBXuBdiiZNNPGJplpkhHKUJ/Bra7diVvfxaVvYqadhW39IfDxn3M4J38Qc6aN6347hbX1jc2t4nZpZ3dv/6B8eNTUUaIIbZCIR6odYE05k7RhmOG0HSuKRcBpKxjdZvXWE1WaRfLBTGLqCzyQLGQEG2s1u4FIx9NeueJW3ZnQKng5VCBXvVf+6fYjkggqDeFY647nxsZPsTKMcDotdRNNY0xGeEA7FiUWVPvp7NopOrNOH4WRsk8aNHP/TqRYaD0Rge0U2Az1ci0z/6t1EhNe+ymTcWKoJPNFYcKRiVD2ddRnihLDJxYwUczeisgQK0yMDWhhSyCyTLzlBFaheVH1LN9fVmo3eTpFOIFTOAcPrqAGd1CHBhB4hBd4hTfn2Xl3PpzPeWvByWeOYUHO1y+ccJXg 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Slide 26

Slide 26 text

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AAAB/HicbZDLSgMxFIbP1Futt1GXboJFcFVmRNBl0Y3LCvYC7VAyaaaNTTJDkhHKUJ/Bra7diVvfxaVvYqadhW39IfDxn3M4J3+YcKaN5307pbX1jc2t8nZlZ3dv/8A9PGrpOFWENknMY9UJsaacSdo0zHDaSRTFIuS0HY5v83r7iSrNYvlgJgkNBB5KFjGCjbVavVBkatp3q17Nmwmtgl9AFQo1+u5PbxCTVFBpCMdad30vMUGGlWGE02mll2qaYDLGQ9q1KLGgOshm107RmXUGKIqVfdKgmft3IsNC64kIbafAZqSXa7n5X62bmug6yJhMUkMlmS+KUo5MjPKvowFTlBg+sYCJYvZWREZYYWJsQAtbQpFn4i8nsAqti5pv+f6yWr8p0inDCZzCOfhwBXW4gwY0gcAjvMArvDnPzrvz4XzOW0tOMXMMC3K+fgGeBJXh AAAB/HicbZDLSgMxFIbP1Futt1GXboJFcFVmRNBl0Y3LCvYC7VAyaaaNTTJDkhHKUJ/Bra7diVvfxaVvYqadhW39IfDxn3M4J3+YcKaN5307pbX1jc2t8nZlZ3dv/8A9PGrpOFWENknMY9UJsaacSdo0zHDaSRTFIuS0HY5v83r7iSrNYvlgJgkNBB5KFjGCjbVavVBkatp3q17Nmwmtgl9AFQo1+u5PbxCTVFBpCMdad30vMUGGlWGE02mll2qaYDLGQ9q1KLGgOshm107RmXUGKIqVfdKgmft3IsNC64kIbafAZqSXa7n5X62bmug6yJhMUkMlmS+KUo5MjPKvowFTlBg+sYCJYvZWREZYYWJsQAtbQpFn4i8nsAqti5pv+f6yWr8p0inDCZzCOfhwBXW4gwY0gcAjvMArvDnPzrvz4XzOW0tOMXMMC3K+fgGeBJXh AAAB/HicbZDLSgMxFIbP1Futt1GXboJFcFVmRNBl0Y3LCvYC7VAyaaaNTTJDkhHKUJ/Bra7diVvfxaVvYqadhW39IfDxn3M4J3+YcKaN5307pbX1jc2t8nZlZ3dv/8A9PGrpOFWENknMY9UJsaacSdo0zHDaSRTFIuS0HY5v83r7iSrNYvlgJgkNBB5KFjGCjbVavVBkatp3q17Nmwmtgl9AFQo1+u5PbxCTVFBpCMdad30vMUGGlWGE02mll2qaYDLGQ9q1KLGgOshm107RmXUGKIqVfdKgmft3IsNC64kIbafAZqSXa7n5X62bmug6yJhMUkMlmS+KUo5MjPKvowFTlBg+sYCJYvZWREZYYWJsQAtbQpFn4i8nsAqti5pv+f6yWr8p0inDCZzCOfhwBXW4gwY0gcAjvMArvDnPzrvz4XzOW0tOMXMMC3K+fgGeBJXh AAAB/HicbZDLSgMxFIbP1Futt1GXboJFcFVmRNBl0Y3LCvYC7VAyaaaNTTJDkhHKUJ/Bra7diVvfxaVvYqadhW39IfDxn3M4J3+YcKaN5307pbX1jc2t8nZlZ3dv/8A9PGrpOFWENknMY9UJsaacSdo0zHDaSRTFIuS0HY5v83r7iSrNYvlgJgkNBB5KFjGCjbVavVBkatp3q17Nmwmtgl9AFQo1+u5PbxCTVFBpCMdad30vMUGGlWGE02mll2qaYDLGQ9q1KLGgOshm107RmXUGKIqVfdKgmft3IsNC64kIbafAZqSXa7n5X62bmug6yJhMUkMlmS+KUo5MjPKvowFTlBg+sYCJYvZWREZYYWJsQAtbQpFn4i8nsAqti5pv+f6yWr8p0inDCZzCOfhwBXW4gwY0gcAjvMArvDnPzrvz4XzOW0tOMXMMC3K+fgGeBJXh a AAAB/HicbZDLSgMxFIbP1Futt1GXboJFcFVmRNBl0Y3LCvYC7VAyaaaNTTJDkhHKUJ/Bra7diVvfxaVvYqadhW39IfDxn3M4J3+YcKaN5307pbX1jc2t8nZlZ3dv/8A9PGrpOFWENknMY9UJsaacSdo0zHDaSRTFIuS0HY5v83r7iSrNYvlgJgkNBB5KFjGCjbVavVBkeNp3q17Nmwmtgl9AFQo1+u5PbxCTVFBpCMdad30vMUGGlWGE02mll2qaYDLGQ9q1KLGgOshm107RmXUGKIqVfdKgmft3IsNC64kIbafAZqSXa7n5X62bmug6yJhMUkMlmS+KUo5MjPKvowFTlBg+sYCJYvZWREZYYWJsQAtbQpFn4i8nsAqti5pv+f6yWr8p0inDCZzCOfhwBXW4gwY0gcAjvMArvDnPzrvz4XzOW0tOMXMMC3K+fgGDMJXQ AAAB/HicbZDLSgMxFIbP1Futt1GXboJFcFVmRNBl0Y3LCvYC7VAyaaaNTTJDkhHKUJ/Bra7diVvfxaVvYqadhW39IfDxn3M4J3+YcKaN5307pbX1jc2t8nZlZ3dv/8A9PGrpOFWENknMY9UJsaacSdo0zHDaSRTFIuS0HY5v83r7iSrNYvlgJgkNBB5KFjGCjbVavVBkeNp3q17Nmwmtgl9AFQo1+u5PbxCTVFBpCMdad30vMUGGlWGE02mll2qaYDLGQ9q1KLGgOshm107RmXUGKIqVfdKgmft3IsNC64kIbafAZqSXa7n5X62bmug6yJhMUkMlmS+KUo5MjPKvowFTlBg+sYCJYvZWREZYYWJsQAtbQpFn4i8nsAqti5pv+f6yWr8p0inDCZzCOfhwBXW4gwY0gcAjvMArvDnPzrvz4XzOW0tOMXMMC3K+fgGDMJXQ AAAB/HicbZDLSgMxFIbP1Futt1GXboJFcFVmRNBl0Y3LCvYC7VAyaaaNTTJDkhHKUJ/Bra7diVvfxaVvYqadhW39IfDxn3M4J3+YcKaN5307pbX1jc2t8nZlZ3dv/8A9PGrpOFWENknMY9UJsaacSdo0zHDaSRTFIuS0HY5v83r7iSrNYvlgJgkNBB5KFjGCjbVavVBkeNp3q17Nmwmtgl9AFQo1+u5PbxCTVFBpCMdad30vMUGGlWGE02mll2qaYDLGQ9q1KLGgOshm107RmXUGKIqVfdKgmft3IsNC64kIbafAZqSXa7n5X62bmug6yJhMUkMlmS+KUo5MjPKvowFTlBg+sYCJYvZWREZYYWJsQAtbQpFn4i8nsAqti5pv+f6yWr8p0inDCZzCOfhwBXW4gwY0gcAjvMArvDnPzrvz4XzOW0tOMXMMC3K+fgGDMJXQ AAAB/HicbZDLSgMxFIbP1Futt1GXboJFcFVmRNBl0Y3LCvYC7VAyaaaNTTJDkhHKUJ/Bra7diVvfxaVvYqadhW39IfDxn3M4J3+YcKaN5307pbX1jc2t8nZlZ3dv/8A9PGrpOFWENknMY9UJsaacSdo0zHDaSRTFIuS0HY5v83r7iSrNYvlgJgkNBB5KFjGCjbVavVBkeNp3q17Nmwmtgl9AFQo1+u5PbxCTVFBpCMdad30vMUGGlWGE02mll2qaYDLGQ9q1KLGgOshm107RmXUGKIqVfdKgmft3IsNC64kIbafAZqSXa7n5X62bmug6yJhMUkMlmS+KUo5MjPKvowFTlBg+sYCJYvZWREZYYWJsQAtbQpFn4i8nsAqti5pv+f6yWr8p0inDCZzCOfhwBXW4gwY0gcAjvMArvDnPzrvz4XzOW0tOMXMMC3K+fgGDMJXQ ͭ·Γ Αͬͯ ͕ฏ໘্ʹ͋Δͱ͍͏৚݅ʹΑΓ r q AAACA3icbZDLSgMxFIbP1Futt6pLN8EiuLHMiKDLohuXFewF2qFk0kwbmmSmSUYoQ5c+g1tduxO3PohL38RMOwvbeiDk4//P4Rz+IOZMG9f9dgpr6xubW8Xt0s7u3v5B+fCoqaNEEdogEY9UO8CaciZpwzDDaTtWFIuA01Ywusv81hNVmkXy0Uxi6gs8kCxkBBsr+d1ApGp6kX3jaa9ccavurNAqeDlUIK96r/zT7UckEVQawrHWHc+NjZ9iZRjhdFrqJprGmIzwgHYsSiyo9tPZ0VN0ZpU+CiNlnzRopv6dSLHQeiIC2ymwGeplLxP/8zqJCW/8lMk4MVSS+aIw4chEKEsA9ZmixPCJBUwUs7ciMsQKE2NzWtgSiCwTbzmBVWheVj3LD1eV2m2eThFO4BTOwYNrqME91KEBBMbwAq/w5jw7786H8zlvLTj5zDEslPP1CxBpmOg= AAACA3icbZDLSgMxFIbP1Futt6pLN8EiuLHMiKDLohuXFewF2qFk0kwbmmSmSUYoQ5c+g1tduxO3PohL38RMOwvbeiDk4//P4Rz+IOZMG9f9dgpr6xubW8Xt0s7u3v5B+fCoqaNEEdogEY9UO8CaciZpwzDDaTtWFIuA01Ywusv81hNVmkXy0Uxi6gs8kCxkBBsr+d1ApGp6kX3jaa9ccavurNAqeDlUIK96r/zT7UckEVQawrHWHc+NjZ9iZRjhdFrqJprGmIzwgHYsSiyo9tPZ0VN0ZpU+CiNlnzRopv6dSLHQeiIC2ymwGeplLxP/8zqJCW/8lMk4MVSS+aIw4chEKEsA9ZmixPCJBUwUs7ciMsQKE2NzWtgSiCwTbzmBVWheVj3LD1eV2m2eThFO4BTOwYNrqME91KEBBMbwAq/w5jw7786H8zlvLTj5zDEslPP1CxBpmOg= AAACA3icbZDLSgMxFIbP1Futt6pLN8EiuLHMiKDLohuXFewF2qFk0kwbmmSmSUYoQ5c+g1tduxO3PohL38RMOwvbeiDk4//P4Rz+IOZMG9f9dgpr6xubW8Xt0s7u3v5B+fCoqaNEEdogEY9UO8CaciZpwzDDaTtWFIuA01Ywusv81hNVmkXy0Uxi6gs8kCxkBBsr+d1ApGp6kX3jaa9ccavurNAqeDlUIK96r/zT7UckEVQawrHWHc+NjZ9iZRjhdFrqJprGmIzwgHYsSiyo9tPZ0VN0ZpU+CiNlnzRopv6dSLHQeiIC2ymwGeplLxP/8zqJCW/8lMk4MVSS+aIw4chEKEsA9ZmixPCJBUwUs7ciMsQKE2NzWtgSiCwTbzmBVWheVj3LD1eV2m2eThFO4BTOwYNrqME91KEBBMbwAq/w5jw7786H8zlvLTj5zDEslPP1CxBpmOg= AAACA3icbZDLSgMxFIbP1Futt6pLN8EiuLHMiKDLohuXFewF2qFk0kwbmmSmSUYoQ5c+g1tduxO3PohL38RMOwvbeiDk4//P4Rz+IOZMG9f9dgpr6xubW8Xt0s7u3v5B+fCoqaNEEdogEY9UO8CaciZpwzDDaTtWFIuA01Ywusv81hNVmkXy0Uxi6gs8kCxkBBsr+d1ApGp6kX3jaa9ccavurNAqeDlUIK96r/zT7UckEVQawrHWHc+NjZ9iZRjhdFrqJprGmIzwgHYsSiyo9tPZ0VN0ZpU+CiNlnzRopv6dSLHQeiIC2ymwGeplLxP/8zqJCW/8lMk4MVSS+aIw4chEKEsA9ZmixPCJBUwUs7ciMsQKE2NzWtgSiCwTbzmBVWheVj3LD1eV2m2eThFO4BTOwYNrqME91KEBBMbwAq/w5jw7786H8zlvLTj5zDEslPP1CxBpmOg= r q = ka AAACDXicbVDLSsNAFL3xWesrKq7cBIvgxpKIoBuh6MZlBfuANpTJdNIOnZnEmYlQQr7Bb3Cra3fi1m9w6Z84abOwrQcu93DOvdzLCWJGlXbdb2tpeWV1bb20Ud7c2t7Ztff2mypKJCYNHLFItgOkCKOCNDTVjLRjSRAPGGkFo9vcbz0RqWgkHvQ4Jj5HA0FDipE2Us8+7AY8ldlZ3h6z61HeUdazK27VncBZJF5BKlCg3rN/uv0IJ5wIjRlSquO5sfZTJDXFjGTlbqJIjPAIDUjHUIE4UX46eT9zTozSd8JImhLamah/N1LElRrzwExypIdq3svF/7xOosMrP6UiTjQReHooTJijIyfPwulTSbBmY0MQltT86uAhkghrk9jMlYDnmXjzCSyS5nnVM/z+olK7KdIpwREcwyl4cAk1uIM6NABDCi/wCm/Ws/VufVif09Elq9g5gBlYX7/mppyV AAACDXicbVDLSsNAFL3xWesrKq7cBIvgxpKIoBuh6MZlBfuANpTJdNIOnZnEmYlQQr7Bb3Cra3fi1m9w6Z84abOwrQcu93DOvdzLCWJGlXbdb2tpeWV1bb20Ud7c2t7Ztff2mypKJCYNHLFItgOkCKOCNDTVjLRjSRAPGGkFo9vcbz0RqWgkHvQ4Jj5HA0FDipE2Us8+7AY8ldlZ3h6z61HeUdazK27VncBZJF5BKlCg3rN/uv0IJ5wIjRlSquO5sfZTJDXFjGTlbqJIjPAIDUjHUIE4UX46eT9zTozSd8JImhLamah/N1LElRrzwExypIdq3svF/7xOosMrP6UiTjQReHooTJijIyfPwulTSbBmY0MQltT86uAhkghrk9jMlYDnmXjzCSyS5nnVM/z+olK7KdIpwREcwyl4cAk1uIM6NABDCi/wCm/Ws/VufVif09Elq9g5gBlYX7/mppyV AAACDXicbVDLSsNAFL3xWesrKq7cBIvgxpKIoBuh6MZlBfuANpTJdNIOnZnEmYlQQr7Bb3Cra3fi1m9w6Z84abOwrQcu93DOvdzLCWJGlXbdb2tpeWV1bb20Ud7c2t7Ztff2mypKJCYNHLFItgOkCKOCNDTVjLRjSRAPGGkFo9vcbz0RqWgkHvQ4Jj5HA0FDipE2Us8+7AY8ldlZ3h6z61HeUdazK27VncBZJF5BKlCg3rN/uv0IJ5wIjRlSquO5sfZTJDXFjGTlbqJIjPAIDUjHUIE4UX46eT9zTozSd8JImhLamah/N1LElRrzwExypIdq3svF/7xOosMrP6UiTjQReHooTJijIyfPwulTSbBmY0MQltT86uAhkghrk9jMlYDnmXjzCSyS5nnVM/z+olK7KdIpwREcwyl4cAk1uIM6NABDCi/wCm/Ws/VufVif09Elq9g5gBlYX7/mppyV AAACDXicbVDLSsNAFL3xWesrKq7cBIvgxpKIoBuh6MZlBfuANpTJdNIOnZnEmYlQQr7Bb3Cra3fi1m9w6Z84abOwrQcu93DOvdzLCWJGlXbdb2tpeWV1bb20Ud7c2t7Ztff2mypKJCYNHLFItgOkCKOCNDTVjLRjSRAPGGkFo9vcbz0RqWgkHvQ4Jj5HA0FDipE2Us8+7AY8ldlZ3h6z61HeUdazK27VncBZJF5BKlCg3rN/uv0IJ5wIjRlSquO5sfZTJDXFjGTlbqJIjPAIDUjHUIE4UX46eT9zTozSd8JImhLamah/N1LElRrzwExypIdq3svF/7xOosMrP6UiTjQReHooTJijIyfPwulTSbBmY0MQltT86uAhkghrk9jMlYDnmXjzCSyS5nnVM/z+olK7KdIpwREcwyl4cAk1uIM6NABDCi/wCm/Ws/VufVif09Elq9g5gBlYX7/mppyV r = ka + q AAACDXicbVDLSsNAFL3xWesrKq7cBIsgCCURQTdC0Y3LCvYBbSiT6aQdOjOJMxOhhHyD3+BW1+7Erd/g0j9x0mZhWw9c7uGce7mXE8SMKu2639bS8srq2nppo7y5tb2za+/tN1WUSEwaOGKRbAdIEUYFaWiqGWnHkiAeMNIKRre533oiUtFIPOhxTHyOBoKGFCNtpJ592A14KrPrUd5Rdpa3x6xnV9yqO4GzSLyCVKBAvWf/dPsRTjgRGjOkVMdzY+2nSGqKGcnK3USRGOERGpCOoQJxovx08n7mnBil74SRNCW0M1H/bqSIKzXmgZnkSA/VvJeL/3mdRIdXfkpFnGgi8PRQmDBHR06ehdOnkmDNxoYgLKn51cFDJBHWJrGZKwHPM/HmE1gkzfOqZ/j9RaV2U6RTgiM4hlPw4BJqcAd1aACGFF7gFd6sZ+vd+rA+p6NLVrFzADOwvn4B46Cckw== AAACDXicbVDLSsNAFL3xWesrKq7cBIsgCCURQTdC0Y3LCvYBbSiT6aQdOjOJMxOhhHyD3+BW1+7Erd/g0j9x0mZhWw9c7uGce7mXE8SMKu2639bS8srq2nppo7y5tb2za+/tN1WUSEwaOGKRbAdIEUYFaWiqGWnHkiAeMNIKRre533oiUtFIPOhxTHyOBoKGFCNtpJ592A14KrPrUd5Rdpa3x6xnV9yqO4GzSLyCVKBAvWf/dPsRTjgRGjOkVMdzY+2nSGqKGcnK3USRGOERGpCOoQJxovx08n7mnBil74SRNCW0M1H/bqSIKzXmgZnkSA/VvJeL/3mdRIdXfkpFnGgi8PRQmDBHR06ehdOnkmDNxoYgLKn51cFDJBHWJrGZKwHPM/HmE1gkzfOqZ/j9RaV2U6RTgiM4hlPw4BJqcAd1aACGFF7gFd6sZ+vd+rA+p6NLVrFzADOwvn4B46Cckw== AAACDXicbVDLSsNAFL3xWesrKq7cBIsgCCURQTdC0Y3LCvYBbSiT6aQdOjOJMxOhhHyD3+BW1+7Erd/g0j9x0mZhWw9c7uGce7mXE8SMKu2639bS8srq2nppo7y5tb2za+/tN1WUSEwaOGKRbAdIEUYFaWiqGWnHkiAeMNIKRre533oiUtFIPOhxTHyOBoKGFCNtpJ592A14KrPrUd5Rdpa3x6xnV9yqO4GzSLyCVKBAvWf/dPsRTjgRGjOkVMdzY+2nSGqKGcnK3USRGOERGpCOoQJxovx08n7mnBil74SRNCW0M1H/bqSIKzXmgZnkSA/VvJeL/3mdRIdXfkpFnGgi8PRQmDBHR06ehdOnkmDNxoYgLKn51cFDJBHWJrGZKwHPM/HmE1gkzfOqZ/j9RaV2U6RTgiM4hlPw4BJqcAd1aACGFF7gFd6sZ+vd+rA+p6NLVrFzADOwvn4B46Cckw== AAACDXicbVDLSsNAFL3xWesrKq7cBIsgCCURQTdC0Y3LCvYBbSiT6aQdOjOJMxOhhHyD3+BW1+7Erd/g0j9x0mZhWw9c7uGce7mXE8SMKu2639bS8srq2nppo7y5tb2za+/tN1WUSEwaOGKRbAdIEUYFaWiqGWnHkiAeMNIKRre533oiUtFIPOhxTHyOBoKGFCNtpJ592A14KrPrUd5Rdpa3x6xnV9yqO4GzSLyCVKBAvWf/dPsRTjgRGjOkVMdzY+2nSGqKGcnK3USRGOERGpCOoQJxovx08n7mnBil74SRNCW0M1H/bqSIKzXmgZnkSA/VvJeL/3mdRIdXfkpFnGgi8PRQmDBHR06ehdOnkmDNxoYgLKn51cFDJBHWJrGZKwHPM/HmE1gkzfOqZ/j9RaV2U6RTgiM4hlPw4BJqcAd1aACGFF7gFd6sZ+vd+rA+p6NLVrFzADOwvn4B46Cckw== aT (ka + q) + b = 0 AAACFHicbZDLSgMxFIYzXmu9jbrUxWARKoUyI4JuhKIblxV6g3YsSZq2oUlmTDJCGWbjQ/gMbnXtTty6d+mbmGlnYVsPhHz8/zmc5Echo0q77re1tLyyurae28hvbm3v7Np7+w0VRBKTOg5YIFsIKsKoIHVNNSOtUBLIESNNNLpJ/eYjkYoGoqbHIfE5HAjapxhqI3Xtow7iMUzua8XRlErp9ZCcltCV27ULbtmdlLMIXgYFkFW1a/90egGOOBEaM6hU23ND7cdQaooZSfKdSJEQ4hEckLZBATlRfjz5ReKcGKXn9ANpjtDORP07EUOu1Jgj08mhHqp5LxX/89qR7l/6MRVhpInA00X9iDk6cNJInB6VBGs2NgCxpOatDh5CCbE2wc1sQTwxmXjzCSxC46zsGb47L1Sus3Ry4BAcgyLwwAWogFtQBXWAwRN4Aa/gzXq23q0P63PaumRlMwdgpqyvX8wZnog= AAACFHicbZDLSgMxFIYzXmu9jbrUxWARKoUyI4JuhKIblxV6g3YsSZq2oUlmTDJCGWbjQ/gMbnXtTty6d+mbmGlnYVsPhHz8/zmc5Echo0q77re1tLyyurae28hvbm3v7Np7+w0VRBKTOg5YIFsIKsKoIHVNNSOtUBLIESNNNLpJ/eYjkYoGoqbHIfE5HAjapxhqI3Xtow7iMUzua8XRlErp9ZCcltCV27ULbtmdlLMIXgYFkFW1a/90egGOOBEaM6hU23ND7cdQaooZSfKdSJEQ4hEckLZBATlRfjz5ReKcGKXn9ANpjtDORP07EUOu1Jgj08mhHqp5LxX/89qR7l/6MRVhpInA00X9iDk6cNJInB6VBGs2NgCxpOatDh5CCbE2wc1sQTwxmXjzCSxC46zsGb47L1Sus3Ry4BAcgyLwwAWogFtQBXWAwRN4Aa/gzXq23q0P63PaumRlMwdgpqyvX8wZnog= AAACFHicbZDLSgMxFIYzXmu9jbrUxWARKoUyI4JuhKIblxV6g3YsSZq2oUlmTDJCGWbjQ/gMbnXtTty6d+mbmGlnYVsPhHz8/zmc5Echo0q77re1tLyyurae28hvbm3v7Np7+w0VRBKTOg5YIFsIKsKoIHVNNSOtUBLIESNNNLpJ/eYjkYoGoqbHIfE5HAjapxhqI3Xtow7iMUzua8XRlErp9ZCcltCV27ULbtmdlLMIXgYFkFW1a/90egGOOBEaM6hU23ND7cdQaooZSfKdSJEQ4hEckLZBATlRfjz5ReKcGKXn9ANpjtDORP07EUOu1Jgj08mhHqp5LxX/89qR7l/6MRVhpInA00X9iDk6cNJInB6VBGs2NgCxpOatDh5CCbE2wc1sQTwxmXjzCSxC46zsGb47L1Sus3Ry4BAcgyLwwAWogFtQBXWAwRN4Aa/gzXq23q0P63PaumRlMwdgpqyvX8wZnog= AAACFHicbZDLSgMxFIYzXmu9jbrUxWARKoUyI4JuhKIblxV6g3YsSZq2oUlmTDJCGWbjQ/gMbnXtTty6d+mbmGlnYVsPhHz8/zmc5Echo0q77re1tLyyurae28hvbm3v7Np7+w0VRBKTOg5YIFsIKsKoIHVNNSOtUBLIESNNNLpJ/eYjkYoGoqbHIfE5HAjapxhqI3Xtow7iMUzua8XRlErp9ZCcltCV27ULbtmdlLMIXgYFkFW1a/90egGOOBEaM6hU23ND7cdQaooZSfKdSJEQ4hEckLZBATlRfjz5ReKcGKXn9ANpjtDORP07EUOu1Jgj08mhHqp5LxX/89qR7l/6MRVhpInA00X9iDk6cNJInB6VBGs2NgCxpOatDh5CCbE2wc1sQTwxmXjzCSxC46zsGb47L1Sus3Ry4BAcgyLwwAWogFtQBXWAwRN4Aa/gzXq23q0P63PaumRlMwdgpqyvX8wZnog= k = aT q + b kak2 AAACLHicbZBNS8MwGMdTX+d8q3r0EhyCII52DPQiDL14nLA3WLuRZukWlrQ1SYVR+kX8EH4Gr3r2IuLBi5/DdOvBbT4Q+OX/fx6e5O9FjEplWR/Gyura+sZmYau4vbO7t28eHLZkGAtMmjhkoeh4SBJGA9JUVDHSiQRB3GOk7Y1vM7/9SISkYdBQk4i4HA0D6lOMlJb6ZnV8fQEdXyCcOB5PUNprwAwe0nMvTRzWIkLBmQMdkd16lbRvlqyyNS24DHYOJZBXvW9+O4MQx5wECjMkZde2IuUmSCiKGUmLTixJhPAYDUlXY4A4kW4y/V0KT7UygH4o9AkUnKp/JxLEpZxwT3dypEZy0cvE/7xurPwrN6FBFCsS4NkiP2ZQhTCLCg6oIFixiQaEBdVvhXiEdFRKBzq3xeNZJvZiAsvQqpRtzffVUu0mT6cAjsEJOAM2uAQ1cAfqoAkweAIv4BW8Gc/Gu/FpfM1aV4x85gjMlfHzC1AhqMk= AAACLHicbZBNS8MwGMdTX+d8q3r0EhyCII52DPQiDL14nLA3WLuRZukWlrQ1SYVR+kX8EH4Gr3r2IuLBi5/DdOvBbT4Q+OX/fx6e5O9FjEplWR/Gyura+sZmYau4vbO7t28eHLZkGAtMmjhkoeh4SBJGA9JUVDHSiQRB3GOk7Y1vM7/9SISkYdBQk4i4HA0D6lOMlJb6ZnV8fQEdXyCcOB5PUNprwAwe0nMvTRzWIkLBmQMdkd16lbRvlqyyNS24DHYOJZBXvW9+O4MQx5wECjMkZde2IuUmSCiKGUmLTixJhPAYDUlXY4A4kW4y/V0KT7UygH4o9AkUnKp/JxLEpZxwT3dypEZy0cvE/7xurPwrN6FBFCsS4NkiP2ZQhTCLCg6oIFixiQaEBdVvhXiEdFRKBzq3xeNZJvZiAsvQqpRtzffVUu0mT6cAjsEJOAM2uAQ1cAfqoAkweAIv4BW8Gc/Gu/FpfM1aV4x85gjMlfHzC1AhqMk= AAACLHicbZBNS8MwGMdTX+d8q3r0EhyCII52DPQiDL14nLA3WLuRZukWlrQ1SYVR+kX8EH4Gr3r2IuLBi5/DdOvBbT4Q+OX/fx6e5O9FjEplWR/Gyura+sZmYau4vbO7t28eHLZkGAtMmjhkoeh4SBJGA9JUVDHSiQRB3GOk7Y1vM7/9SISkYdBQk4i4HA0D6lOMlJb6ZnV8fQEdXyCcOB5PUNprwAwe0nMvTRzWIkLBmQMdkd16lbRvlqyyNS24DHYOJZBXvW9+O4MQx5wECjMkZde2IuUmSCiKGUmLTixJhPAYDUlXY4A4kW4y/V0KT7UygH4o9AkUnKp/JxLEpZxwT3dypEZy0cvE/7xurPwrN6FBFCsS4NkiP2ZQhTCLCg6oIFixiQaEBdVvhXiEdFRKBzq3xeNZJvZiAsvQqpRtzffVUu0mT6cAjsEJOAM2uAQ1cAfqoAkweAIv4BW8Gc/Gu/FpfM1aV4x85gjMlfHzC1AhqMk= AAACLHicbZBNS8MwGMdTX+d8q3r0EhyCII52DPQiDL14nLA3WLuRZukWlrQ1SYVR+kX8EH4Gr3r2IuLBi5/DdOvBbT4Q+OX/fx6e5O9FjEplWR/Gyura+sZmYau4vbO7t28eHLZkGAtMmjhkoeh4SBJGA9JUVDHSiQRB3GOk7Y1vM7/9SISkYdBQk4i4HA0D6lOMlJb6ZnV8fQEdXyCcOB5PUNprwAwe0nMvTRzWIkLBmQMdkd16lbRvlqyyNS24DHYOJZBXvW9+O4MQx5wECjMkZde2IuUmSCiKGUmLTixJhPAYDUlXY4A4kW4y/V0KT7UygH4o9AkUnKp/JxLEpZxwT3dypEZy0cvE/7xurPwrN6FBFCsS4NkiP2ZQhTCLCg6oIFixiQaEBdVvhXiEdFRKBzq3xeNZJvZiAsvQqpRtzffVUu0mT6cAjsEJOAM2uAQ1cAfqoAkweAIv4BW8Gc/Gu/FpfM1aV4x85gjMlfHzC1AhqMk= Αͬͯ kr qk = kkak = |k|kak = |aT q + b| kak2 · kak = |aT q + b| kak 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 AAAC9nictVJNS8MwGE7r9/yaevQSHA5BlFYEvQiiF48Kbg6WOdI0nWFJW5NUHKV/wKuevYlX/45H/4iYdhXc9OoLgYfned73DU/ixZwp7Tjvlj0xOTU9MztXmV9YXFqurqw2VZRIQhsk4pFseVhRzkLa0Exz2oolxcLj9Mrrn+b61R2VikXhpR7EtCNwL2QBI1gbqlv9RLxJpYbIE6nM4E4BbjOIZE7Xj0q5n9P4m0aoUj+CiN8VkiEL8GPSqBMFEpO0tA/l68vvRdvQG/Zn6V8DrvcyRPzon6Zn3WrN2XWKgr+BW4IaKOu8W/1AfkQSQUNNOFaq7Tqx7qRYakY4zSooUTTGpI97tG1giAVVnbR4pwxuGsaHQSTNCTUs2J8dKRZKDYRnnALrGzWu5eRfWjvRwWEnZWGcaBqS4aIg4VBHMH906DNJieYDAzCRzNwVkhtsctPma4xs8USeiTuewG/Q3Nt1Db7Yrx2flOnMgnWwAbaACw7AMTgD56ABiOVbD9aj9WTf28/2i/06tNpW2bMGRsp++wI2qfGU 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 ڑ཭͸

Slide 27

Slide 27 text

ิ଍ aT x + b AAACCHicbZDLSgMxFIYz9VbrbdSlm2ARBKHMiKDLohuXFXqDdixJmrahSWZIMsUyzAv4DG517U7c+hYufRMz7Sxs64GQj/8/h3P4ccSZNp737RTW1jc2t4rbpZ3dvf0D9/CoqcNYEdogIQ9VGyNNOZO0YZjhtB0pigTmtIXHd5nfmlClWSjrZhrRQKChZANGkLFSz3W7WCQofaxn/1N6gXtu2at4s4Kr4OdQBnnVeu5Ptx+SWFBpCEdad3wvMkGClGGE07TUjTWNEBmjIe1YlEhQHSSzy1N4ZpU+HITKPmngTP07kSCh9VRg2ymQGellLxP/8zqxGdwECZNRbKgk80WDmEMTwiwG2GeKEsOnFhBRzN4KyQgpRIwNa2ELFqnNxF9OYBWalxXf8sNVuXqbp1MEJ+AUnAMfXIMquAc10AAETMALeAVvzrPz7nw4n/PWgpPPHIOFcr5+Aao3mj8= AAACCHicbZDLSgMxFIYz9VbrbdSlm2ARBKHMiKDLohuXFXqDdixJmrahSWZIMsUyzAv4DG517U7c+hYufRMz7Sxs64GQj/8/h3P4ccSZNp737RTW1jc2t4rbpZ3dvf0D9/CoqcNYEdogIQ9VGyNNOZO0YZjhtB0pigTmtIXHd5nfmlClWSjrZhrRQKChZANGkLFSz3W7WCQofaxn/1N6gXtu2at4s4Kr4OdQBnnVeu5Ptx+SWFBpCEdad3wvMkGClGGE07TUjTWNEBmjIe1YlEhQHSSzy1N4ZpU+HITKPmngTP07kSCh9VRg2ymQGellLxP/8zqxGdwECZNRbKgk80WDmEMTwiwG2GeKEsOnFhBRzN4KyQgpRIwNa2ELFqnNxF9OYBWalxXf8sNVuXqbp1MEJ+AUnAMfXIMquAc10AAETMALeAVvzrPz7nw4n/PWgpPPHIOFcr5+Aao3mj8= AAACCHicbZDLSgMxFIYz9VbrbdSlm2ARBKHMiKDLohuXFXqDdixJmrahSWZIMsUyzAv4DG517U7c+hYufRMz7Sxs64GQj/8/h3P4ccSZNp737RTW1jc2t4rbpZ3dvf0D9/CoqcNYEdogIQ9VGyNNOZO0YZjhtB0pigTmtIXHd5nfmlClWSjrZhrRQKChZANGkLFSz3W7WCQofaxn/1N6gXtu2at4s4Kr4OdQBnnVeu5Ptx+SWFBpCEdad3wvMkGClGGE07TUjTWNEBmjIe1YlEhQHSSzy1N4ZpU+HITKPmngTP07kSCh9VRg2ymQGellLxP/8zqxGdwECZNRbKgk80WDmEMTwiwG2GeKEsOnFhBRzN4KyQgpRIwNa2ELFqnNxF9OYBWalxXf8sNVuXqbp1MEJ+AUnAMfXIMquAc10AAETMALeAVvzrPz7nw4n/PWgpPPHIOFcr5+Aao3mj8= AAACCHicbZDLSgMxFIYz9VbrbdSlm2ARBKHMiKDLohuXFXqDdixJmrahSWZIMsUyzAv4DG517U7c+hYufRMz7Sxs64GQj/8/h3P4ccSZNp737RTW1jc2t4rbpZ3dvf0D9/CoqcNYEdogIQ9VGyNNOZO0YZjhtB0pigTmtIXHd5nfmlClWSjrZhrRQKChZANGkLFSz3W7WCQofaxn/1N6gXtu2at4s4Kr4OdQBnnVeu5Ptx+SWFBpCEdad3wvMkGClGGE07TUjTWNEBmjIe1YlEhQHSSzy1N4ZpU+HITKPmngTP07kSCh9VRg2ymQGellLxP/8zqxGdwECZNRbKgk80WDmEMTwiwG2GeKEsOnFhBRzN4KyQgpRIwNa2ELFqnNxF9OYBWalxXf8sNVuXqbp1MEJ+AUnAMfXIMquAc10AAETMALeAVvzrPz7nw4n/PWgpPPHIOFcr5+Aao3mj8= ͷූ߸͸ʮ఺͕ฏ໘ͷͲͪΒଆʹ͋Δ͔ʯΛද͢ aT x + b = 0 AAACCnicbZDLSgMxFIYz9VbrbaxLN8EiCEKZEUE3QtGNywq9QTuWTJppQ5PMkGSkZZg38Bnc6tqduPUlXPomZtpZ2NYDIR//fw7n8PsRo0o7zrdVWFvf2Nwqbpd2dvf2D+zDckuFscSkiUMWyo6PFGFUkKammpFOJAniPiNtf3yX+e0nIhUNRUNPI+JxNBQ0oBhpI/Xtcs/nCUofG9k/Sc/9G6dvV5yqMyu4Cm4OFZBXvW//9AYhjjkRGjOkVNd1Iu0lSGqKGUlLvViRCOExGpKuQYE4UV4yuz2Fp0YZwCCU5gkNZ+rfiQRxpabcN50c6ZFa9jLxP68b6+DaS6iIYk0Eni8KYgZ1CLMg4IBKgjWbGkBYUnMrxCMkEdYmroUtPk9NJu5yAqvQuqi6hh8uK7XbPJ0iOAYn4Ay44ArUwD2ogybAYAJewCt4s56td+vD+py3Fqx85ggslPX1C604msA= AAACCnicbZDLSgMxFIYz9VbrbaxLN8EiCEKZEUE3QtGNywq9QTuWTJppQ5PMkGSkZZg38Bnc6tqduPUlXPomZtpZ2NYDIR//fw7n8PsRo0o7zrdVWFvf2Nwqbpd2dvf2D+zDckuFscSkiUMWyo6PFGFUkKammpFOJAniPiNtf3yX+e0nIhUNRUNPI+JxNBQ0oBhpI/Xtcs/nCUofG9k/Sc/9G6dvV5yqMyu4Cm4OFZBXvW//9AYhjjkRGjOkVNd1Iu0lSGqKGUlLvViRCOExGpKuQYE4UV4yuz2Fp0YZwCCU5gkNZ+rfiQRxpabcN50c6ZFa9jLxP68b6+DaS6iIYk0Eni8KYgZ1CLMg4IBKgjWbGkBYUnMrxCMkEdYmroUtPk9NJu5yAqvQuqi6hh8uK7XbPJ0iOAYn4Ay44ArUwD2ogybAYAJewCt4s56td+vD+py3Fqx85ggslPX1C604msA= AAACCnicbZDLSgMxFIYz9VbrbaxLN8EiCEKZEUE3QtGNywq9QTuWTJppQ5PMkGSkZZg38Bnc6tqduPUlXPomZtpZ2NYDIR//fw7n8PsRo0o7zrdVWFvf2Nwqbpd2dvf2D+zDckuFscSkiUMWyo6PFGFUkKammpFOJAniPiNtf3yX+e0nIhUNRUNPI+JxNBQ0oBhpI/Xtcs/nCUofG9k/Sc/9G6dvV5yqMyu4Cm4OFZBXvW//9AYhjjkRGjOkVNd1Iu0lSGqKGUlLvViRCOExGpKuQYE4UV4yuz2Fp0YZwCCU5gkNZ+rfiQRxpabcN50c6ZFa9jLxP68b6+DaS6iIYk0Eni8KYgZ1CLMg4IBKgjWbGkBYUnMrxCMkEdYmroUtPk9NJu5yAqvQuqi6hh8uK7XbPJ0iOAYn4Ay44ArUwD2ogybAYAJewCt4s56td+vD+py3Fqx85ggslPX1C604msA= AAACCnicbZDLSgMxFIYz9VbrbaxLN8EiCEKZEUE3QtGNywq9QTuWTJppQ5PMkGSkZZg38Bnc6tqduPUlXPomZtpZ2NYDIR//fw7n8PsRo0o7zrdVWFvf2Nwqbpd2dvf2D+zDckuFscSkiUMWyo6PFGFUkKammpFOJAniPiNtf3yX+e0nIhUNRUNPI+JxNBQ0oBhpI/Xtcs/nCUofG9k/Sc/9G6dvV5yqMyu4Cm4OFZBXvW//9AYhjjkRGjOkVNd1Iu0lSGqKGUlLvViRCOExGpKuQYE4UV4yuz2Fp0YZwCCU5gkNZ+rfiQRxpabcN50c6ZFa9jLxP68b6+DaS6iIYk0Eni8KYgZ1CLMg4IBKgjWbGkBYUnMrxCMkEdYmroUtPk9NJu5yAqvQuqi6hh8uK7XbPJ0iOAYn4Ay44ArUwD2ogybAYAJewCt4s56td+vD+py3Fqx85ggslPX1C604msA= aT x + b > 0 AAACCnicbZDLSgMxFIYz9VbrbaxLN8EiCEKZEUFXUnTjskJv0I4lk2ba0CQzJBlpGeYNfAa3unYnbn0Jl76JmXYWtvVAyMf/n8M5/H7EqNKO820V1tY3NreK26Wd3b39A/uw3FJhLDFp4pCFsuMjRRgVpKmpZqQTSYK4z0jbH99lfvuJSEVD0dDTiHgcDQUNKEbaSH273PN5gtLHRvZP0nP/xunbFafqzAqugptDBeRV79s/vUGIY06Exgwp1XWdSHsJkppiRtJSL1YkQniMhqRrUCBOlJfMbk/hqVEGMAileULDmfp3IkFcqSn3TSdHeqSWvUz8z+vGOrj2EiqiWBOB54uCmEEdwiwIOKCSYM2mBhCW1NwK8QhJhLWJa2GLz1OTibucwCq0Lqqu4YfLSu02T6cIjsEJOAMuuAI1cA/qoAkwmIAX8ArerGfr3fqwPuetBSufOQILZX39Aq7MmsE= AAACCnicbZDLSgMxFIYz9VbrbaxLN8EiCEKZEUFXUnTjskJv0I4lk2ba0CQzJBlpGeYNfAa3unYnbn0Jl76JmXYWtvVAyMf/n8M5/H7EqNKO820V1tY3NreK26Wd3b39A/uw3FJhLDFp4pCFsuMjRRgVpKmpZqQTSYK4z0jbH99lfvuJSEVD0dDTiHgcDQUNKEbaSH273PN5gtLHRvZP0nP/xunbFafqzAqugptDBeRV79s/vUGIY06Exgwp1XWdSHsJkppiRtJSL1YkQniMhqRrUCBOlJfMbk/hqVEGMAileULDmfp3IkFcqSn3TSdHeqSWvUz8z+vGOrj2EiqiWBOB54uCmEEdwiwIOKCSYM2mBhCW1NwK8QhJhLWJa2GLz1OTibucwCq0Lqqu4YfLSu02T6cIjsEJOAMuuAI1cA/qoAkwmIAX8ArerGfr3fqwPuetBSufOQILZX39Aq7MmsE= AAACCnicbZDLSgMxFIYz9VbrbaxLN8EiCEKZEUFXUnTjskJv0I4lk2ba0CQzJBlpGeYNfAa3unYnbn0Jl76JmXYWtvVAyMf/n8M5/H7EqNKO820V1tY3NreK26Wd3b39A/uw3FJhLDFp4pCFsuMjRRgVpKmpZqQTSYK4z0jbH99lfvuJSEVD0dDTiHgcDQUNKEbaSH273PN5gtLHRvZP0nP/xunbFafqzAqugptDBeRV79s/vUGIY06Exgwp1XWdSHsJkppiRtJSL1YkQniMhqRrUCBOlJfMbk/hqVEGMAileULDmfp3IkFcqSn3TSdHeqSWvUz8z+vGOrj2EiqiWBOB54uCmEEdwiwIOKCSYM2mBhCW1NwK8QhJhLWJa2GLz1OTibucwCq0Lqqu4YfLSu02T6cIjsEJOAMuuAI1cA/qoAkwmIAX8ArerGfr3fqwPuetBSufOQILZX39Aq7MmsE= AAACCnicbZDLSgMxFIYz9VbrbaxLN8EiCEKZEUFXUnTjskJv0I4lk2ba0CQzJBlpGeYNfAa3unYnbn0Jl76JmXYWtvVAyMf/n8M5/H7EqNKO820V1tY3NreK26Wd3b39A/uw3FJhLDFp4pCFsuMjRRgVpKmpZqQTSYK4z0jbH99lfvuJSEVD0dDTiHgcDQUNKEbaSH273PN5gtLHRvZP0nP/xunbFafqzAqugptDBeRV79s/vUGIY06Exgwp1XWdSHsJkppiRtJSL1YkQniMhqRrUCBOlJfMbk/hqVEGMAileULDmfp3IkFcqSn3TSdHeqSWvUz8z+vGOrj2EiqiWBOB54uCmEEdwiwIOKCSYM2mBhCW1NwK8QhJhLWJa2GLz1OTibucwCq0Lqqu4YfLSu02T6cIjsEJOAMuuAI1cA/qoAkwmIAX8ArerGfr3fqwPuetBSufOQILZX39Aq7MmsE= aT x + b < 0 AAACCnicbZDLSgMxFIYz9VbrbaxLN8EiCEKZEUEXLopuXFboDdqxZNJMG5pkhiQjLcO8gc/gVtfuxK0v4dI3MdPOwrYeCPn4/3M4h9+PGFXacb6twtr6xuZWcbu0s7u3f2AfllsqjCUmTRyyUHZ8pAijgjQ11Yx0IkkQ9xlp++O7zG8/EaloKBp6GhGPo6GgAcVIG6lvl3s+T1D62Mj+SXru3zh9u+JUnVnBVXBzqIC86n37pzcIccyJ0JghpbquE2kvQVJTzEha6sWKRAiP0ZB0DQrEifKS2e0pPDXKAAahNE9oOFP/TiSIKzXlvunkSI/UspeJ/3ndWAfXXkJFFGsi8HxREDOoQ5gFAQdUEqzZ1ADCkppbIR4hibA2cS1s8XlqMnGXE1iF1kXVNfxwWand5ukUwTE4AWfABVegBu5BHTQBBhPwAl7Bm/VsvVsf1ue8tWDlM0dgoayvX6ukmr8= AAACCnicbZDLSgMxFIYz9VbrbaxLN8EiCEKZEUEXLopuXFboDdqxZNJMG5pkhiQjLcO8gc/gVtfuxK0v4dI3MdPOwrYeCPn4/3M4h9+PGFXacb6twtr6xuZWcbu0s7u3f2AfllsqjCUmTRyyUHZ8pAijgjQ11Yx0IkkQ9xlp++O7zG8/EaloKBp6GhGPo6GgAcVIG6lvl3s+T1D62Mj+SXru3zh9u+JUnVnBVXBzqIC86n37pzcIccyJ0JghpbquE2kvQVJTzEha6sWKRAiP0ZB0DQrEifKS2e0pPDXKAAahNE9oOFP/TiSIKzXlvunkSI/UspeJ/3ndWAfXXkJFFGsi8HxREDOoQ5gFAQdUEqzZ1ADCkppbIR4hibA2cS1s8XlqMnGXE1iF1kXVNfxwWand5ukUwTE4AWfABVegBu5BHTQBBhPwAl7Bm/VsvVsf1ue8tWDlM0dgoayvX6ukmr8= AAACCnicbZDLSgMxFIYz9VbrbaxLN8EiCEKZEUEXLopuXFboDdqxZNJMG5pkhiQjLcO8gc/gVtfuxK0v4dI3MdPOwrYeCPn4/3M4h9+PGFXacb6twtr6xuZWcbu0s7u3f2AfllsqjCUmTRyyUHZ8pAijgjQ11Yx0IkkQ9xlp++O7zG8/EaloKBp6GhGPo6GgAcVIG6lvl3s+T1D62Mj+SXru3zh9u+JUnVnBVXBzqIC86n37pzcIccyJ0JghpbquE2kvQVJTzEha6sWKRAiP0ZB0DQrEifKS2e0pPDXKAAahNE9oOFP/TiSIKzXlvunkSI/UspeJ/3ndWAfXXkJFFGsi8HxREDOoQ5gFAQdUEqzZ1ADCkppbIR4hibA2cS1s8XlqMnGXE1iF1kXVNfxwWand5ukUwTE4AWfABVegBu5BHTQBBhPwAl7Bm/VsvVsf1ue8tWDlM0dgoayvX6ukmr8= AAACCnicbZDLSgMxFIYz9VbrbaxLN8EiCEKZEUEXLopuXFboDdqxZNJMG5pkhiQjLcO8gc/gVtfuxK0v4dI3MdPOwrYeCPn4/3M4h9+PGFXacb6twtr6xuZWcbu0s7u3f2AfllsqjCUmTRyyUHZ8pAijgjQ11Yx0IkkQ9xlp++O7zG8/EaloKBp6GhGPo6GgAcVIG6lvl3s+T1D62Mj+SXru3zh9u+JUnVnBVXBzqIC86n37pzcIccyJ0JghpbquE2kvQVJTzEha6sWKRAiP0ZB0DQrEifKS2e0pPDXKAAahNE9oOFP/TiSIKzXlvunkSI/UspeJ/3ndWAfXXkJFFGsi8HxREDOoQ5gFAQdUEqzZ1ADCkppbIR4hibA2cS1s8XlqMnGXE1iF1kXVNfxwWand5ukUwTE4AWfABVegBu5BHTQBBhPwAl7Bm/VsvVsf1ue8tWDlM0dgoayvX6ukmr8= ڑ཭ͷެ͔ࣜΒઈର஋Λͱͬͨ΋ͷ ͸ɺཪද৘ใ෇͖ͷڑ཭ͱߟ͑Δ͜ͱ΋Ͱ͖Δ aT x + b kak AAACIHicbZDLSgMxFIYzXmu9jbp0EyxCQSgzIuiy6MZlhd6gM5YkzbShycyQZMQyzCv4ED6DW127E5e6803MtLOwrQdCPv7/HE7y45gzpR3ny1pZXVvf2Cxtlbd3dvf27YPDtooSSWiLRDySXYwU5SykLc00p91YUiQwpx08vsn9zgOVikVhU09i6gs0DFnACNJG6ttVL5CIpB4WKcrum/n9mJ3hLPV4m0oNEfRkDlnfrjg1Z1pwGdwCKqCoRt/+8QYRSQQNNeFIqZ7rxNpPkdSMcJqVvUTRGJExGtKewRAJqvx0+qMMnhplAINImhNqOFX/TqRIKDUR2HQKpEdq0cvF/7xeooMrP2VhnGgaktmiIOFQRzCPBw6YpETziQFEJDNvhWSETETahDi3BYs8E3cxgWVon9dcw3cXlfp1kU4JHIMTUAUuuAR1cAsaoAUIeAIv4BW8Wc/Wu/Vhfc5aV6xi5gjMlfX9C/SKpJA= AAACIHicbZDLSgMxFIYzXmu9jbp0EyxCQSgzIuiy6MZlhd6gM5YkzbShycyQZMQyzCv4ED6DW127E5e6803MtLOwrQdCPv7/HE7y45gzpR3ny1pZXVvf2Cxtlbd3dvf27YPDtooSSWiLRDySXYwU5SykLc00p91YUiQwpx08vsn9zgOVikVhU09i6gs0DFnACNJG6ttVL5CIpB4WKcrum/n9mJ3hLPV4m0oNEfRkDlnfrjg1Z1pwGdwCKqCoRt/+8QYRSQQNNeFIqZ7rxNpPkdSMcJqVvUTRGJExGtKewRAJqvx0+qMMnhplAINImhNqOFX/TqRIKDUR2HQKpEdq0cvF/7xeooMrP2VhnGgaktmiIOFQRzCPBw6YpETziQFEJDNvhWSETETahDi3BYs8E3cxgWVon9dcw3cXlfp1kU4JHIMTUAUuuAR1cAsaoAUIeAIv4BW8Wc/Wu/Vhfc5aV6xi5gjMlfX9C/SKpJA= AAACIHicbZDLSgMxFIYzXmu9jbp0EyxCQSgzIuiy6MZlhd6gM5YkzbShycyQZMQyzCv4ED6DW127E5e6803MtLOwrQdCPv7/HE7y45gzpR3ny1pZXVvf2Cxtlbd3dvf27YPDtooSSWiLRDySXYwU5SykLc00p91YUiQwpx08vsn9zgOVikVhU09i6gs0DFnACNJG6ttVL5CIpB4WKcrum/n9mJ3hLPV4m0oNEfRkDlnfrjg1Z1pwGdwCKqCoRt/+8QYRSQQNNeFIqZ7rxNpPkdSMcJqVvUTRGJExGtKewRAJqvx0+qMMnhplAINImhNqOFX/TqRIKDUR2HQKpEdq0cvF/7xeooMrP2VhnGgaktmiIOFQRzCPBw6YpETziQFEJDNvhWSETETahDi3BYs8E3cxgWVon9dcw3cXlfp1kU4JHIMTUAUuuAR1cAsaoAUIeAIv4BW8Wc/Wu/Vhfc5aV6xi5gjMlfX9C/SKpJA= AAACIHicbZDLSgMxFIYzXmu9jbp0EyxCQSgzIuiy6MZlhd6gM5YkzbShycyQZMQyzCv4ED6DW127E5e6803MtLOwrQdCPv7/HE7y45gzpR3ny1pZXVvf2Cxtlbd3dvf27YPDtooSSWiLRDySXYwU5SykLc00p91YUiQwpx08vsn9zgOVikVhU09i6gs0DFnACNJG6ttVL5CIpB4WKcrum/n9mJ3hLPV4m0oNEfRkDlnfrjg1Z1pwGdwCKqCoRt/+8QYRSQQNNeFIqZ7rxNpPkdSMcJqVvUTRGJExGtKewRAJqvx0+qMMnhplAINImhNqOFX/TqRIKDUR2HQKpEdq0cvF/7xeooMrP2VhnGgaktmiIOFQRzCPBw6YpETziQFEJDNvhWSETETahDi3BYs8E3cxgWVon9dcw3cXlfp1kU4JHIMTUAUuuAR1cAsaoAUIeAIv4BW8Wc/Wu/Vhfc5aV6xi5gjMlfX9C/SKpJA=

Slide 28

Slide 28 text

ิ଍2 Ҏ্Ͱ͸3࣍ݩͷ৔߹ʹ͕ࣔͨ͠ɺ͜Ε͸Ұൠͷ࣍ݩͰ੒Γཱͭ aT x + b = 0 AAACCnicbZDLSgMxFIYz9VbrbaxLN8EiCEKZEUE3QtGNywq9QTuWTJppQ5PMkGSkZZg38Bnc6tqduPUlXPomZtpZ2NYDIR//fw7n8PsRo0o7zrdVWFvf2Nwqbpd2dvf2D+zDckuFscSkiUMWyo6PFGFUkKammpFOJAniPiNtf3yX+e0nIhUNRUNPI+JxNBQ0oBhpI/Xtcs/nCUofG9k/Sc/9G6dvV5yqMyu4Cm4OFZBXvW//9AYhjjkRGjOkVNd1Iu0lSGqKGUlLvViRCOExGpKuQYE4UV4yuz2Fp0YZwCCU5gkNZ+rfiQRxpabcN50c6ZFa9jLxP68b6+DaS6iIYk0Eni8KYgZ1CLMg4IBKgjWbGkBYUnMrxCMkEdYmroUtPk9NJu5yAqvQuqi6hh8uK7XbPJ0iOAYn4Ay44ArUwD2ogybAYAJewCt4s56td+vD+py3Fqx85ggslPX1C604msA= AAACCnicbZDLSgMxFIYz9VbrbaxLN8EiCEKZEUE3QtGNywq9QTuWTJppQ5PMkGSkZZg38Bnc6tqduPUlXPomZtpZ2NYDIR//fw7n8PsRo0o7zrdVWFvf2Nwqbpd2dvf2D+zDckuFscSkiUMWyo6PFGFUkKammpFOJAniPiNtf3yX+e0nIhUNRUNPI+JxNBQ0oBhpI/Xtcs/nCUofG9k/Sc/9G6dvV5yqMyu4Cm4OFZBXvW//9AYhjjkRGjOkVNd1Iu0lSGqKGUlLvViRCOExGpKuQYE4UV4yuz2Fp0YZwCCU5gkNZ+rfiQRxpabcN50c6ZFa9jLxP68b6+DaS6iIYk0Eni8KYgZ1CLMg4IBKgjWbGkBYUnMrxCMkEdYmroUtPk9NJu5yAqvQuqi6hh8uK7XbPJ0iOAYn4Ay44ArUwD2ogybAYAJewCt4s56td+vD+py3Fqx85ggslPX1C604msA= AAACCnicbZDLSgMxFIYz9VbrbaxLN8EiCEKZEUE3QtGNywq9QTuWTJppQ5PMkGSkZZg38Bnc6tqduPUlXPomZtpZ2NYDIR//fw7n8PsRo0o7zrdVWFvf2Nwqbpd2dvf2D+zDckuFscSkiUMWyo6PFGFUkKammpFOJAniPiNtf3yX+e0nIhUNRUNPI+JxNBQ0oBhpI/Xtcs/nCUofG9k/Sc/9G6dvV5yqMyu4Cm4OFZBXvW//9AYhjjkRGjOkVNd1Iu0lSGqKGUlLvViRCOExGpKuQYE4UV4yuz2Fp0YZwCCU5gkNZ+rfiQRxpabcN50c6ZFa9jLxP68b6+DaS6iIYk0Eni8KYgZ1CLMg4IBKgjWbGkBYUnMrxCMkEdYmroUtPk9NJu5yAqvQuqi6hh8uK7XbPJ0iOAYn4Ay44ArUwD2ogybAYAJewCt4s56td+vD+py3Fqx85ggslPX1C604msA= AAACCnicbZDLSgMxFIYz9VbrbaxLN8EiCEKZEUE3QtGNywq9QTuWTJppQ5PMkGSkZZg38Bnc6tqduPUlXPomZtpZ2NYDIR//fw7n8PsRo0o7zrdVWFvf2Nwqbpd2dvf2D+zDckuFscSkiUMWyo6PFGFUkKammpFOJAniPiNtf3yX+e0nIhUNRUNPI+JxNBQ0oBhpI/Xtcs/nCUofG9k/Sc/9G6dvV5yqMyu4Cm4OFZBXvW//9AYhjjkRGjOkVNd1Iu0lSGqKGUlLvViRCOExGpKuQYE4UV4yuz2Fp0YZwCCU5gkNZ+rfiQRxpabcN50c6ZFa9jLxP68b6+DaS6iIYk0Eni8KYgZ1CLMg4IBKgjWbGkBYUnMrxCMkEdYmroUtPk9NJu5yAqvQuqi6hh8uK7XbPJ0iOAYn4Ay44ArUwD2ogybAYAJewCt4s56td+vD+py3Fqx85ggslPX1C604msA= ௒ฏ໘ ͱ఺ ͷڑ཭͸ aT x + b = 0 AAACCnicbZDLSgMxFIYz9VbrbaxLN8EiCEKZEUE3QtGNywq9QTuWTJppQ5PMkGSkZZg38Bnc6tqduPUlXPomZtpZ2NYDIR//fw7n8PsRo0o7zrdVWFvf2Nwqbpd2dvf2D+zDckuFscSkiUMWyo6PFGFUkKammpFOJAniPiNtf3yX+e0nIhUNRUNPI+JxNBQ0oBhpI/Xtcs/nCUofG9k/Sc/9G6dvV5yqMyu4Cm4OFZBXvW//9AYhjjkRGjOkVNd1Iu0lSGqKGUlLvViRCOExGpKuQYE4UV4yuz2Fp0YZwCCU5gkNZ+rfiQRxpabcN50c6ZFa9jLxP68b6+DaS6iIYk0Eni8KYgZ1CLMg4IBKgjWbGkBYUnMrxCMkEdYmroUtPk9NJu5yAqvQuqi6hh8uK7XbPJ0iOAYn4Ay44ArUwD2ogybAYAJewCt4s56td+vD+py3Fqx85ggslPX1C604msA= AAACCnicbZDLSgMxFIYz9VbrbaxLN8EiCEKZEUE3QtGNywq9QTuWTJppQ5PMkGSkZZg38Bnc6tqduPUlXPomZtpZ2NYDIR//fw7n8PsRo0o7zrdVWFvf2Nwqbpd2dvf2D+zDckuFscSkiUMWyo6PFGFUkKammpFOJAniPiNtf3yX+e0nIhUNRUNPI+JxNBQ0oBhpI/Xtcs/nCUofG9k/Sc/9G6dvV5yqMyu4Cm4OFZBXvW//9AYhjjkRGjOkVNd1Iu0lSGqKGUlLvViRCOExGpKuQYE4UV4yuz2Fp0YZwCCU5gkNZ+rfiQRxpabcN50c6ZFa9jLxP68b6+DaS6iIYk0Eni8KYgZ1CLMg4IBKgjWbGkBYUnMrxCMkEdYmroUtPk9NJu5yAqvQuqi6hh8uK7XbPJ0iOAYn4Ay44ArUwD2ogybAYAJewCt4s56td+vD+py3Fqx85ggslPX1C604msA= AAACCnicbZDLSgMxFIYz9VbrbaxLN8EiCEKZEUE3QtGNywq9QTuWTJppQ5PMkGSkZZg38Bnc6tqduPUlXPomZtpZ2NYDIR//fw7n8PsRo0o7zrdVWFvf2Nwqbpd2dvf2D+zDckuFscSkiUMWyo6PFGFUkKammpFOJAniPiNtf3yX+e0nIhUNRUNPI+JxNBQ0oBhpI/Xtcs/nCUofG9k/Sc/9G6dvV5yqMyu4Cm4OFZBXvW//9AYhjjkRGjOkVNd1Iu0lSGqKGUlLvViRCOExGpKuQYE4UV4yuz2Fp0YZwCCU5gkNZ+rfiQRxpabcN50c6ZFa9jLxP68b6+DaS6iIYk0Eni8KYgZ1CLMg4IBKgjWbGkBYUnMrxCMkEdYmroUtPk9NJu5yAqvQuqi6hh8uK7XbPJ0iOAYn4Ay44ArUwD2ogybAYAJewCt4s56td+vD+py3Fqx85ggslPX1C604msA= AAACCnicbZDLSgMxFIYz9VbrbaxLN8EiCEKZEUE3QtGNywq9QTuWTJppQ5PMkGSkZZg38Bnc6tqduPUlXPomZtpZ2NYDIR//fw7n8PsRo0o7zrdVWFvf2Nwqbpd2dvf2D+zDckuFscSkiUMWyo6PFGFUkKammpFOJAniPiNtf3yX+e0nIhUNRUNPI+JxNBQ0oBhpI/Xtcs/nCUofG9k/Sc/9G6dvV5yqMyu4Cm4OFZBXvW//9AYhjjkRGjOkVNd1Iu0lSGqKGUlLvViRCOExGpKuQYE4UV4yuz2Fp0YZwCCU5gkNZ+rfiQRxpabcN50c6ZFa9jLxP68b6+DaS6iIYk0Eni8KYgZ1CLMg4IBKgjWbGkBYUnMrxCMkEdYmroUtPk9NJu5yAqvQuqi6hh8uK7XbPJ0iOAYn4Ay44ArUwD2ogybAYAJewCt4s56td+vD+py3Fqx85ggslPX1C604msA= q AAAB/HicbZDLSgMxFIbP1Futt6pLN8EiuCozIuiy6MZlBXuBdiiZNNPGJplpkhHKUJ/Bra7diVvfxaVvYqadhW39IfDxn3M4J38Qc6aN6347hbX1jc2t4nZpZ3dv/6B8eNTUUaIIbZCIR6odYE05k7RhmOG0HSuKRcBpKxjdZvXWE1WaRfLBTGLqCzyQLGQEG2s1u4FIx9NeueJW3ZnQKng5VCBXvVf+6fYjkggqDeFY647nxsZPsTKMcDotdRNNY0xGeEA7FiUWVPvp7NopOrNOH4WRsk8aNHP/TqRYaD0Rge0U2Az1ci0z/6t1EhNe+ymTcWKoJPNFYcKRiVD2ddRnihLDJxYwUczeisgQK0yMDWhhSyCyTLzlBFaheVH1LN9fVmo3eTpFOIFTOAcPrqAGd1CHBhB4hBd4hTfn2Xl3PpzPeWvByWeOYUHO1y+ccJXg AAAB/HicbZDLSgMxFIbP1Futt6pLN8EiuCozIuiy6MZlBXuBdiiZNNPGJplpkhHKUJ/Bra7diVvfxaVvYqadhW39IfDxn3M4J38Qc6aN6347hbX1jc2t4nZpZ3dv/6B8eNTUUaIIbZCIR6odYE05k7RhmOG0HSuKRcBpKxjdZvXWE1WaRfLBTGLqCzyQLGQEG2s1u4FIx9NeueJW3ZnQKng5VCBXvVf+6fYjkggqDeFY647nxsZPsTKMcDotdRNNY0xGeEA7FiUWVPvp7NopOrNOH4WRsk8aNHP/TqRYaD0Rge0U2Az1ci0z/6t1EhNe+ymTcWKoJPNFYcKRiVD2ddRnihLDJxYwUczeisgQK0yMDWhhSyCyTLzlBFaheVH1LN9fVmo3eTpFOIFTOAcPrqAGd1CHBhB4hBd4hTfn2Xl3PpzPeWvByWeOYUHO1y+ccJXg AAAB/HicbZDLSgMxFIbP1Futt6pLN8EiuCozIuiy6MZlBXuBdiiZNNPGJplpkhHKUJ/Bra7diVvfxaVvYqadhW39IfDxn3M4J38Qc6aN6347hbX1jc2t4nZpZ3dv/6B8eNTUUaIIbZCIR6odYE05k7RhmOG0HSuKRcBpKxjdZvXWE1WaRfLBTGLqCzyQLGQEG2s1u4FIx9NeueJW3ZnQKng5VCBXvVf+6fYjkggqDeFY647nxsZPsTKMcDotdRNNY0xGeEA7FiUWVPvp7NopOrNOH4WRsk8aNHP/TqRYaD0Rge0U2Az1ci0z/6t1EhNe+ymTcWKoJPNFYcKRiVD2ddRnihLDJxYwUczeisgQK0yMDWhhSyCyTLzlBFaheVH1LN9fVmo3eTpFOIFTOAcPrqAGd1CHBhB4hBd4hTfn2Xl3PpzPeWvByWeOYUHO1y+ccJXg AAAB/HicbZDLSgMxFIbP1Futt6pLN8EiuCozIuiy6MZlBXuBdiiZNNPGJplpkhHKUJ/Bra7diVvfxaVvYqadhW39IfDxn3M4J38Qc6aN6347hbX1jc2t4nZpZ3dv/6B8eNTUUaIIbZCIR6odYE05k7RhmOG0HSuKRcBpKxjdZvXWE1WaRfLBTGLqCzyQLGQEG2s1u4FIx9NeueJW3ZnQKng5VCBXvVf+6fYjkggqDeFY647nxsZPsTKMcDotdRNNY0xGeEA7FiUWVPvp7NopOrNOH4WRsk8aNHP/TqRYaD0Rge0U2Az1ci0z/6t1EhNe+ymTcWKoJPNFYcKRiVD2ddRnihLDJxYwUczeisgQK0yMDWhhSyCyTLzlBFaheVH1LN9fVmo3eTpFOIFTOAcPrqAGd1CHBhB4hBd4hTfn2Xl3PpzPeWvByWeOYUHO1y+ccJXg |aT q + b| kak AAACNXicbVBPS8MwHE3nvzn/VT16CQ5BEEYrgl6EoRePE/YP1jrSLN3CkrYmqTBKP40fws/gVU8ePAji1a9g2hV0mw8CL++9H7/keRGjUlnWm1FaWl5ZXSuvVzY2t7Z3zN29tgxjgUkLhywUXQ9JwmhAWooqRrqRIIh7jHS88XXmdx6IkDQMmmoSEZejYUB9ipHSUt+8dHyBcOIwHVLQ8XiC0rtmTu5TeOJBR2ROqhPt34RWs1vaN6tWzcoBF4ldkCoo0OibH84gxDEngcIMSdmzrUi5CRKKYkbSihNLEiE8RkPS0zRAnEg3yb+ZwiOtDKAfCn0CBXP170SCuJQT7ukkR2ok571M/M/rxcq/cBMaRLEiAZ4u8mMGVQizzuCACoIVm2iCsKD6rRCPkO5N6WZntng868Seb2CRtE9rtua3Z9X6VdFOGRyAQ3AMbHAO6uAGNEALYPAInsELeDWejHfj0/iaRktGMbMPZmB8/wCuxq0W AAACNXicbVBPS8MwHE3nvzn/VT16CQ5BEEYrgl6EoRePE/YP1jrSLN3CkrYmqTBKP40fws/gVU8ePAji1a9g2hV0mw8CL++9H7/keRGjUlnWm1FaWl5ZXSuvVzY2t7Z3zN29tgxjgUkLhywUXQ9JwmhAWooqRrqRIIh7jHS88XXmdx6IkDQMmmoSEZejYUB9ipHSUt+8dHyBcOIwHVLQ8XiC0rtmTu5TeOJBR2ROqhPt34RWs1vaN6tWzcoBF4ldkCoo0OibH84gxDEngcIMSdmzrUi5CRKKYkbSihNLEiE8RkPS0zRAnEg3yb+ZwiOtDKAfCn0CBXP170SCuJQT7ukkR2ok571M/M/rxcq/cBMaRLEiAZ4u8mMGVQizzuCACoIVm2iCsKD6rRCPkO5N6WZntng868Seb2CRtE9rtua3Z9X6VdFOGRyAQ3AMbHAO6uAGNEALYPAInsELeDWejHfj0/iaRktGMbMPZmB8/wCuxq0W AAACNXicbVBPS8MwHE3nvzn/VT16CQ5BEEYrgl6EoRePE/YP1jrSLN3CkrYmqTBKP40fws/gVU8ePAji1a9g2hV0mw8CL++9H7/keRGjUlnWm1FaWl5ZXSuvVzY2t7Z3zN29tgxjgUkLhywUXQ9JwmhAWooqRrqRIIh7jHS88XXmdx6IkDQMmmoSEZejYUB9ipHSUt+8dHyBcOIwHVLQ8XiC0rtmTu5TeOJBR2ROqhPt34RWs1vaN6tWzcoBF4ldkCoo0OibH84gxDEngcIMSdmzrUi5CRKKYkbSihNLEiE8RkPS0zRAnEg3yb+ZwiOtDKAfCn0CBXP170SCuJQT7ukkR2ok571M/M/rxcq/cBMaRLEiAZ4u8mMGVQizzuCACoIVm2iCsKD6rRCPkO5N6WZntng868Seb2CRtE9rtua3Z9X6VdFOGRyAQ3AMbHAO6uAGNEALYPAInsELeDWejHfj0/iaRktGMbMPZmB8/wCuxq0W AAACNXicbVBPS8MwHE3nvzn/VT16CQ5BEEYrgl6EoRePE/YP1jrSLN3CkrYmqTBKP40fws/gVU8ePAji1a9g2hV0mw8CL++9H7/keRGjUlnWm1FaWl5ZXSuvVzY2t7Z3zN29tgxjgUkLhywUXQ9JwmhAWooqRrqRIIh7jHS88XXmdx6IkDQMmmoSEZejYUB9ipHSUt+8dHyBcOIwHVLQ8XiC0rtmTu5TeOJBR2ROqhPt34RWs1vaN6tWzcoBF4ldkCoo0OibH84gxDEngcIMSdmzrUi5CRKKYkbSihNLEiE8RkPS0zRAnEg3yb+ZwiOtDKAfCn0CBXP170SCuJQT7ukkR2ok571M/M/rxcq/cBMaRLEiAZ4u8mMGVQizzuCACoIVm2iCsKD6rRCPkO5N6WZntng868Seb2CRtE9rtua3Z9X6VdFOGRyAQ3AMbHAO6uAGNEALYPAInsELeDWejHfj0/iaRktGMbMPZmB8/wCuxq0W ͸Ұൠʹ͸ʮ௒ฏ໘ʯͱݺ͹ΕΔ ಛʹ2࣍ݩͷ৔߹ɿ ௚ઢ ͱ఺ ͷڑ཭͸ aT x + b = 0 AAACCnicbZDLSgMxFIYz9VbrbaxLN8EiCEKZEUE3QtGNywq9QTuWTJppQ5PMkGSkZZg38Bnc6tqduPUlXPomZtpZ2NYDIR//fw7n8PsRo0o7zrdVWFvf2Nwqbpd2dvf2D+zDckuFscSkiUMWyo6PFGFUkKammpFOJAniPiNtf3yX+e0nIhUNRUNPI+JxNBQ0oBhpI/Xtcs/nCUofG9k/Sc/9G6dvV5yqMyu4Cm4OFZBXvW//9AYhjjkRGjOkVNd1Iu0lSGqKGUlLvViRCOExGpKuQYE4UV4yuz2Fp0YZwCCU5gkNZ+rfiQRxpabcN50c6ZFa9jLxP68b6+DaS6iIYk0Eni8KYgZ1CLMg4IBKgjWbGkBYUnMrxCMkEdYmroUtPk9NJu5yAqvQuqi6hh8uK7XbPJ0iOAYn4Ay44ArUwD2ogybAYAJewCt4s56td+vD+py3Fqx85ggslPX1C604msA= AAACCnicbZDLSgMxFIYz9VbrbaxLN8EiCEKZEUE3QtGNywq9QTuWTJppQ5PMkGSkZZg38Bnc6tqduPUlXPomZtpZ2NYDIR//fw7n8PsRo0o7zrdVWFvf2Nwqbpd2dvf2D+zDckuFscSkiUMWyo6PFGFUkKammpFOJAniPiNtf3yX+e0nIhUNRUNPI+JxNBQ0oBhpI/Xtcs/nCUofG9k/Sc/9G6dvV5yqMyu4Cm4OFZBXvW//9AYhjjkRGjOkVNd1Iu0lSGqKGUlLvViRCOExGpKuQYE4UV4yuz2Fp0YZwCCU5gkNZ+rfiQRxpabcN50c6ZFa9jLxP68b6+DaS6iIYk0Eni8KYgZ1CLMg4IBKgjWbGkBYUnMrxCMkEdYmroUtPk9NJu5yAqvQuqi6hh8uK7XbPJ0iOAYn4Ay44ArUwD2ogybAYAJewCt4s56td+vD+py3Fqx85ggslPX1C604msA= 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AAAB/HicbZDLSgMxFIbP1Futt6pLN8EiuCozIuiy6MZlBXuBdiiZNNPGJplpkhHKUJ/Bra7diVvfxaVvYqadhW39IfDxn3M4J38Qc6aN6347hbX1jc2t4nZpZ3dv/6B8eNTUUaIIbZCIR6odYE05k7RhmOG0HSuKRcBpKxjdZvXWE1WaRfLBTGLqCzyQLGQEG2s1u4FIx9NeueJW3ZnQKng5VCBXvVf+6fYjkggqDeFY647nxsZPsTKMcDotdRNNY0xGeEA7FiUWVPvp7NopOrNOH4WRsk8aNHP/TqRYaD0Rge0U2Az1ci0z/6t1EhNe+ymTcWKoJPNFYcKRiVD2ddRnihLDJxYwUczeisgQK0yMDWhhSyCyTLzlBFaheVH1LN9fVmo3eTpFOIFTOAcPrqAGd1CHBhB4hBd4hTfn2Xl3PpzPeWvByWeOYUHO1y+ccJXg AAAB/HicbZDLSgMxFIbP1Futt6pLN8EiuCozIuiy6MZlBXuBdiiZNNPGJplpkhHKUJ/Bra7diVvfxaVvYqadhW39IfDxn3M4J38Qc6aN6347hbX1jc2t4nZpZ3dv/6B8eNTUUaIIbZCIR6odYE05k7RhmOG0HSuKRcBpKxjdZvXWE1WaRfLBTGLqCzyQLGQEG2s1u4FIx9NeueJW3ZnQKng5VCBXvVf+6fYjkggqDeFY647nxsZPsTKMcDotdRNNY0xGeEA7FiUWVPvp7NopOrNOH4WRsk8aNHP/TqRYaD0Rge0U2Az1ci0z/6t1EhNe+ymTcWKoJPNFYcKRiVD2ddRnihLDJxYwUczeisgQK0yMDWhhSyCyTLzlBFaheVH1LN9fVmo3eTpFOIFTOAcPrqAGd1CHBhB4hBd4hTfn2Xl3PpzPeWvByWeOYUHO1y+ccJXg 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B B B @ a1 a2 . . . ad 1 C C C A AAACMXicbVDLSsNAFJ3UV42vqEs3wSK4KkkR1IVQdOOygn1AE8JkctsOnUzCzKRYQr/Fj/Ab3Oq6O3XrTzh9ILb1wlzOPfdc7p0TpoxK5Thjo7C2vrG5Vdw2d3b39g+sw6OGTDJBoE4SlohWiCUwyqGuqGLQSgXgOGTQDPt3k35zAELShD+qYQp+jLucdijBSlOBdY1vTC+ELuV5GmMl6NPIxIHreTpXdPYGUaLktIxMD3j0KwusklN2pmGvAncOSmgetcD69KKEZDFwRRiWsu06qfJzLBQlDEaml0lIMenjLrQ15DgG6efTL47sM81EdicR+nFlT9m/EzmOpRzGoVbq+3pyuTch/+u1M9W58nPK00wBJ7NFnYzZKrEnftkRFUAUG2qAiaD6Vpv0sMBEaVcXtoTxxBN32YFV0KiUXY0fLkrV27k7RXSCTtE5ctElqqJ7VEN1RNAzekVv6N14McbGh/E1kxaM+cwxWgjj+wfpqan+ 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AAACMXicbVBNS8NAEN3Urxq/oh69BIvgqSRFUA9C0YvHCrYVmlA2m2m7dLMJu5vSEvpb/BH+Bq967k29+ifctEVs68AOb968YWZfkDAqleNMjMLa+sbmVnHb3Nnd2z+wDo8aMk4FgTqJWSyeAiyBUQ51RRWDp0QAjgIGzaB/l/ebAxCSxvxRjRLwI9zltEMJVppqW9fDG9MLoEt5lkRYCTocm8O263k6V3T2BmGs5LQMTQ94+CtrWyWn7EzDXgXuHJTQPGpt69MLY5JGwBVhWMqW6yTKz7BQlDAYm14qIcGkj7vQ0pDjCKSfTb84ts80E9qdWOjHlT1l/05kOJJyFAVaqe/ryeVeTv7Xa6Wqc+VnlCepAk5mizops1Vs537ZIRVAFBtpgImg+lab9LDARGlXF7YEUe6Ju+zAKmhUyq7GDxel6u3cnSI6QafoHLnoElXRPaqhOiLoGb2iN/RuvBgT48P4mkkLxnzmGC2E8f0DhyCqWg== 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AAAB6HicbZC7SwNBEMbnfMbzFbW0WQyCVbiz0UYM2lgmYB6QhLC3mUvW7O0du3tiOAL2NhaK2PrP2Nv537h5FJr4wcKP75thZyZIBNfG876dpeWV1bX13Ia7ubW9s5vf26/pOFUMqywWsWoEVKPgEquGG4GNRCGNAoH1YHA9zuv3qDSP5a0ZJtiOaE/ykDNqrFV56OQLXtGbiCyCP4PC5ad78QgA5U7+q9WNWRqhNExQrZu+l5h2RpXhTODIbaUaE8oGtIdNi5JGqNvZZNARObZOl4Sxsk8aMnF/d2Q00noYBbYyoqav57Ox+V/WTE143s64TFKDkk0/ClNBTEzGW5MuV8iMGFqgTHE7K2F9qigz9jauPYI/v/Ii1E6LvuWKVyhdwVQ5OIQjOAEfzqAEN1CGKjBAeIIXeHXunGfnzXmfli45s54D+CPn4wdUQo7F AAAB6HicbZC7SgNBFIbPxltcb1FLm8UgWIVdG23EoI1lAuYCyRJmJ2eTMbOzy8ysGJY8gY2FIrb6MPY24ts4uRSa+MPAx/+fw5xzgoQzpV3328otLa+sruXX7Y3Nre2dwu5eXcWppFijMY9lMyAKORNY00xzbCYSSRRwbASDq3HeuEOpWCxu9DBBPyI9wUJGiTZW9b5TKLoldyJnEbwZFC8+7PPk/cuudAqf7W5M0wiFppwo1fLcRPsZkZpRjiO7nSpMCB2QHrYMChKh8rPJoCPnyDhdJ4yleUI7E/d3R0YipYZRYCojovtqPhub/2WtVIdnfsZEkmoUdPpRmHJHx854a6fLJFLNhwYIlczM6tA+kYRqcxvbHMGbX3kR6iclz3DVLZYvYao8HMAhHIMHp1CGa6hADSggPMATPFu31qP1Yr1OS3PWrGcf/sh6+wFF0ZA5 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AAAB7HicbZBNSwMxEIZn/az1q+rRS2gRK0LZ9aLHohePFdy20C4lm862odnskmTFUvobvHhQRPDkD/LmvzH9OGjrC4GHd2bIzBumgmvjut/Oyura+sZmbiu/vbO7t184OKzrJFMMfZaIRDVDqlFwib7hRmAzVUjjUGAjHNxM6o0HVJon8t4MUwxi2pM84owaa/nRafnxrFMouRV3KrIM3hxK1WL7/AMAap3CV7ubsCxGaZigWrc8NzXBiCrDmcBxvp1pTCkb0B62LEoaow5G02XH5MQ6XRIlyj5pyNT9PTGisdbDOLSdMTV9vVibmP/VWpmJroIRl2lmULLZR1EmiEnI5HLS5QqZEUMLlCludyWsTxVlxuaTtyF4iycvQ/2i4lm+s2lcw0w5OIYilMGDS6jCLdTABwYcnuAFXh3pPDtvzvusdcWZzxzBHzmfP96Bj4c= AAAB7HicbZDLSsNAFIZP6q3WW9Slm6FFrAglcaPLohuXFUxbaEOZTCft0MkkzEzEEPoMbrpQxK0P5K5v4/Sy0NYfBj7+cw5zzh8knCntOFOrsLG5tb1T3C3t7R8cHtnHJ00Vp5JQj8Q8lu0AK8qZoJ5mmtN2IimOAk5bweh+Vm89U6lYLJ50llA/wgPBQkawNpYXXlRfLnt2xak5c6F1cJdQqZe7V5NpPWv07O9uPyZpRIUmHCvVcZ1E+zmWmhFOx6VuqmiCyQgPaMegwBFVfj5fdozOjdNHYSzNExrN3d8TOY6UyqLAdEZYD9VqbWb+V+ukOrz1cyaSVFNBFh+FKUc6RrPLUZ9JSjTPDGAimdkVkSGWmGiTT8mE4K6evA7N65pr+NGkcQcLFeEMylAFF26gDg/QAA8IMHiFN3i3hDWxPqzPRWvBWs6cwh9ZXz/n65EN AAAB7HicbZDLSsNAFIZP6q3WW9Slm6FFrAglcaPLohuXFUxbaEOZTCft0MkkzEzEEPoMbrpQxK0P5K5v4/Sy0NYfBj7+cw5zzh8knCntOFOrsLG5tb1T3C3t7R8cHtnHJ00Vp5JQj8Q8lu0AK8qZoJ5mmtN2IimOAk5bweh+Vm89U6lYLJ50llA/wgPBQkawNpYXXlRfLnt2xak5c6F1cJdQqZe7V5NpPWv07O9uPyZpRIUmHCvVcZ1E+zmWmhFOx6VuqmiCyQgPaMegwBFVfj5fdozOjdNHYSzNExrN3d8TOY6UyqLAdEZYD9VqbWb+V+ukOrz1cyaSVFNBFh+FKUc6RrPLUZ9JSjTPDGAimdkVkSGWmGiTT8mE4K6evA7N65pr+NGkcQcLFeEMylAFF26gDg/QAA8IMHiFN3i3hDWxPqzPRWvBWs6cwh9ZXz/n65EN AAAB7HicbZA9TwJBEIbn8AvxC7W02UiM2JA7Gy2JNpaYeEACF7K37MGGvb3L7pyREH6DjYXG2PqD7Pw3LnCFgm+yyZN3ZrIzb5hKYdB1v53C2vrG5lZxu7Szu7d/UD48apok04z7LJGJbofUcCkU91Gg5O1UcxqHkrfC0e2s3nrk2ohEPeA45UFMB0pEglG0lh+dV58ueuWKW3PnIqvg5VCBXI1e+avbT1gWc4VMUmM6nptiMKEaBZN8WupmhqeUjeiAdywqGnMTTObLTsmZdfokSrR9Csnc/T0xobEx4zi0nTHFoVmuzcz/ap0Mo+tgIlSaIVds8VGUSYIJmV1O+kJzhnJsgTIt7K6EDammDG0+JRuCt3zyKjQva57le7dSv8njKMIJnEIVPLiCOtxBA3xgIOAZXuHNUc6L8+58LFoLTj5zDH/kfP4AzAKN/g== ͸ฏۉมԽ཰ͷۃݶͭ·Γ f0(x) = lim h!0 f(x + h) f(x) h AAACEnicbVDLSgMxFL1TX7W+qi7dBIvYIpYZNwoiFF3osoJ9QKeUTJrphGYeJBlpGQb8Azf+hWs3LhRx68qdf2P6WGj1QMjhnHtJznEizqQyzS8jMze/sLiUXc6trK6tb+Q3t+oyjAWhNRLyUDQdLClnAa0ppjhtRoJi3+G04fQvRn7jlgrJwuBGDSPa9nEvYC4jWGmpky+5+8VB6czmzO8knq1CZKbIdgUmiVscHHilQ32V0sRLO/mCWTbHQH+JNSWFyunl4x0AVDv5T7sbktingSIcS9myzEi1EywUI5ymOTuWNMKkj3u0pWmAfSrbyThSiva00kVuKPQJFBqrPzcS7Es59B096WPlyVlvJP7ntWLlnrQTFkSxogGZPOTGHOnko35QlwlKFB9qgolg+q+IeFj3oXSLOV2CNRv5L6kflS3Nr3Ub5zBBFnZgF4pgwTFU4AqqUAMC9/AEL/BqPBjPxpvxPhnNGNOdbfgF4+MbbeeeOw== 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 AAACEnicbVA7T8MwGHTKq5RXgJHFokK0QlQJCyxIFSyMRaIPqYkix3Uaq3YS2Q5qFeU3sPBXWBhAiJWJjX+D22aAwkmWT3ffJ/vOTxiVyrK+jNLS8srqWnm9srG5tb1j7u51ZJwKTNo4ZrHo+UgSRiPSVlQx0ksEQdxnpOuPrqd+954ISePoTk0S4nI0jGhAMVJa8sx6cFwb1y8dRrmXhY6KoZVDJxAIZ0FtfBLWT/VVz7Mw98yq1bBmgH+JXZAqKNDyzE9nEOOUk0hhhqTs21ai3AwJRTEjecVJJUkQHqEh6WsaIU6km80i5fBIKwMYxEKfSMGZ+nMjQ1zKCff1JEcqlIveVPzP66cquHAzGiWpIhGePxSkDOrk037ggAqCFZtogrCg+q8Qh0j3oXSLFV2CvRj5L+mcNWzNb61q86qoowwOwCGoARucgya4AS3QBhg8gCfwAl6NR+PZeDPe56Mlo9jZB79gfHwD1FicTg== f0(x) = 0 AAAB7nicbZDLSgMxFIbP1Futt6pLN6FFrAhlxo1uhKIblxXsBdqhZNIzbWgmMyQZsZQ+hBsXiujS53Hn25heFtr6Q+DjP+eQc/4gEVwb1/12Miura+sb2c3c1vbO7l5+/6Cu41QxrLFYxKoZUI2CS6wZbgQ2E4U0CgQ2gsHNpN54QKV5LO/NMEE/oj3JQ86osVYjPCk9nl65nXzRLbtTkWXw5lCsFNpnHwBQ7eS/2t2YpRFKwwTVuuW5ifFHVBnOBI5z7VRjQtmA9rBlUdIItT+arjsmx9bpkjBW9klDpu7viRGNtB5Gge2MqOnrxdrE/K/WSk146Y+4TFKDks0+ClNBTEwmt5MuV8iMGFqgTHG7K2F9qigzNqGcDcFbPHkZ6udlz/KdTeMaZsrCERSgBB5cQAVuoQo1YDCAJ3iBVydxnp03533WmnHmM4fwR87nD9CHkAg= AAAB7nicbZDLSgMxFIZPvNZ6q7p0E1rEilBm3OhGKLpxWcFeoB1KJs20oZnMkGTEYehDCOJCEbc+j7u+jelloa0/BD7+cw455/djwbVxnDFaWV1b39jMbeW3d3b39gsHhw0dJYqyOo1EpFo+0UxwyeqGG8FasWIk9AVr+sPbSb35yJTmkXwwacy8kPQlDzglxlrN4LT8dHbtdAslp+JMhZfBnUOpWuycv4yraa1b+O70IpqETBoqiNZt14mNlxFlOBVslO8kmsWEDkmftS1KEjLtZdN1R/jEOj0cRMo+afDU/T2RkVDrNPRtZ0jMQC/WJuZ/tXZigisv4zJODJN09lGQCGwiPLkd97hi1IjUAqGK210xHRBFqLEJ5W0I7uLJy9C4qLiW720aNzBTDo6hCGVw4RKqcAc1qAOFITzDG7yjGL2iD/Q5a11B85kj+CP09QPZ8ZGO AAAB7nicbZDLSgMxFIZPvNZ6q7p0E1rEilBm3OhGKLpxWcFeoB1KJs20oZnMkGTEYehDCOJCEbc+j7u+jelloa0/BD7+cw455/djwbVxnDFaWV1b39jMbeW3d3b39gsHhw0dJYqyOo1EpFo+0UxwyeqGG8FasWIk9AVr+sPbSb35yJTmkXwwacy8kPQlDzglxlrN4LT8dHbtdAslp+JMhZfBnUOpWuycv4yraa1b+O70IpqETBoqiNZt14mNlxFlOBVslO8kmsWEDkmftS1KEjLtZdN1R/jEOj0cRMo+afDU/T2RkVDrNPRtZ0jMQC/WJuZ/tXZigisv4zJODJN09lGQCGwiPLkd97hi1IjUAqGK210xHRBFqLEJ5W0I7uLJy9C4qLiW720aNzBTDo6hCGVw4RKqcAc1qAOFITzDG7yjGL2iD/Q5a11B85kj+CP09QPZ8ZGO AAAB7nicbZA9SwNBEIbn/IzxK2ppsxjE2IQ7G22EoI1lBPMByRH2NnPJkr29Y3dPDEd+hI2FIrb+Hjv/jZvkCk18YeHhnRl25g0SwbVx3W9nZXVtfWOzsFXc3tnd2y8dHDZ1nCqGDRaLWLUDqlFwiQ3DjcB2opBGgcBWMLqd1luPqDSP5YMZJ+hHdCB5yBk11mqFZ5Wn82u3Vyq7VXcmsgxeDmXIVe+Vvrr9mKURSsME1brjuYnxM6oMZwInxW6qMaFsRAfYsShphNrPZutOyKl1+iSMlX3SkJn7eyKjkdbjKLCdETVDvVibmv/VOqkJr/yMyyQ1KNn8ozAVxMRkejvpc4XMiLEFyhS3uxI2pIoyYxMq2hC8xZOXoXlR9Szfu+XaTR5HAY7hBCrgwSXU4A7q0AAGI3iGV3hzEufFeXc+5q0rTj5zBH/kfP4AvgiOfw== Λղ͚͹ۃ஋ʢۃେ஋orۃখ஋ʣΛٻΊΒΕΔʢ͔΋͠Εͳ͍ʣ x + h AAAB6nicbZDLSgMxFIbP1Ftbb1WXboJFEIQy40aXRTcuK9oLtEPNpJk2NJMZkjNiGfoIblwoxa1P5M63Mb0stPWHwMd/ziHn/EEihUHX/XZya+sbm1v5QnF7Z3dvv3Rw2DBxqhmvs1jGuhVQw6VQvI4CJW8lmtMokLwZDG+m9eYT10bE6gFHCfcj2lciFIyite6fzwfdUtmtuDORVfAWUK4WkskjANS6pa9OL2ZpxBUySY1pe26CfkY1Cib5uNhJDU8oG9I+b1tUNOLGz2arjsmpdXokjLV9CsnM/T2R0ciYURTYzojiwCzXpuZ/tXaK4ZWfCZWkyBWbfxSmkmBMpneTntCcoRxZoEwLuythA6opQ5tO0YbgLZ+8Co2Limf5zqZxDXPl4RhO4Aw8uIQq3EIN6sCgDy/wBu+OdF6difMxb805i5kj+CPn8wdYrI9R AAAB6nicbZC7SgNBFIbPek3iLWppMxgEQQi7NloGbSwjmgsmS5idzCZDZmeXmbOSEPIINhZKsLX3Xex8Gp1cCk38YeDjP+cw5/xBIoVB1/1yVlbX1jc2M9nc1vbO7l5+/6Bq4lQzXmGxjHU9oIZLoXgFBUpeTzSnUSB5LehdT+q1R66NiNU9DhLuR7SjRCgYRWvd9c+6rXzBLbpTkWXw5lAoZZPxw0f/u9zKfzbbMUsjrpBJakzDcxP0h1SjYJKPcs3U8ISyHu3whkVFI2784XTVETmxTpuEsbZPIZm6vyeGNDJmEAW2M6LYNYu1iflfrZFieOkPhUpS5IrNPgpTSTAmk7tJW2jOUA4sUKaF3ZWwLtWUoU0nZ0PwFk9ehup50bN8a9O4gpkycATHcAoeXEAJbqAMFWDQgSd4gVdHOs/O2Hmbta4485lD+CPn/QcvPZFx AAAB6nicbZC7SgNBFIbPek3iLWppMxgEQQi7NloGbSwjmgsmS5idzCZDZmeXmbOSEPIINhZKsLX3Xex8Gp1cCk38YeDjP+cw5/xBIoVB1/1yVlbX1jc2M9nc1vbO7l5+/6Bq4lQzXmGxjHU9oIZLoXgFBUpeTzSnUSB5LehdT+q1R66NiNU9DhLuR7SjRCgYRWvd9c+6rXzBLbpTkWXw5lAoZZPxw0f/u9zKfzbbMUsjrpBJakzDcxP0h1SjYJKPcs3U8ISyHu3whkVFI2784XTVETmxTpuEsbZPIZm6vyeGNDJmEAW2M6LYNYu1iflfrZFieOkPhUpS5IrNPgpTSTAmk7tJW2jOUA4sUKaF3ZWwLtWUoU0nZ0PwFk9ehup50bN8a9O4gpkycATHcAoeXEAJbqAMFWDQgSd4gVdHOs/O2Hmbta4485lD+CPn/QcvPZFx AAAB6nicbZBNS8NAEIYn9avWr6pHL4tFEISSeKnHohePFe0HtKFstpN26WYTdjdiCf0JXjwo4tVf5M1/47bNQVtfWHh4Z4adeYNEcG1c99sprK1vbG4Vt0s7u3v7B+XDo5aOU8WwyWIRq05ANQousWm4EdhJFNIoENgOxjezevsRleaxfDCTBP2IDiUPOaPGWvdPF6N+ueJW3bnIKng5VCBXo1/+6g1ilkYoDRNU667nJsbPqDKcCZyWeqnGhLIxHWLXoqQRaj+brzolZ9YZkDBW9klD5u7viYxGWk+iwHZG1Iz0cm1m/lfrpia88jMuk9SgZIuPwlQQE5PZ3WTAFTIjJhYoU9zuStiIKsqMTadkQ/CWT16F1mXVs3znVurXeRxFOIFTOAcPalCHW2hAExgM4Rle4c0Rzovz7nwsWgtOPnMMf+R8/gAOyo2f df dx (x) AAAB+XicbZC7TsMwFIZPyq2UW4CRxaJCKkuVsNCxgoWxSPQitVHlOE5r1XEi26laRXkTFgYQYuVFEBsTr4J7GaDllyx9+s85Ose/n3CmtON8WYWNza3tneJuaW//4PDIPj5pqTiVhDZJzGPZ8bGinAna1Exz2kkkxZHPadsf3c7q7TGVisXiQU8T6kV4IFjICNbG6tt2L5SYZEGYZ8Ekr0wu+3bZqTpzoXVwl1Cu174/EAA0+vZnL4hJGlGhCcdKdV0n0V6GpWaE07zUSxVNMBnhAe0aFDiiysvml+fowjgBCmNpntBo7v6eyHCk1DTyTWeE9VCt1mbmf7VuqsOalzGRpJoKslgUphzpGM1iQAGTlGg+NYCJZOZWRIbYRKFNWCUTgrv65XVoXVVdw/cmjRtYqAhncA4VcOEa6nAHDWgCgTE8wjO8WJn1ZL1ab4vWgrWcOYU/st5/ALLpleU= AAAB+XicbZDLSsNAFIZP6q3WW9SFiJtgEeqmJG7ssujGZQV7gTaUyWTSDp1MwsyktIS8iRsXirj1RcSdbtz6GE4vC239YeDjP+dwzvxezKhUtv1h5FZW19Y38puFre2d3T1z/6Aho0RgUscRi0TLQ5IwykldUcVIKxYEhR4jTW9wPak3h0RIGvE7NY6JG6IepwHFSGmra5qdQCCc+kGW+qOsNDrvmkW7bE9lLYMzh2K18vV29Pl9XOua7x0/wklIuMIMSdl27Fi5KRKKYkayQieRJEZ4gHqkrZGjkEg3nV6eWWfa8a0gEvpxZU3d3xMpCqUch57uDJHqy8XaxPyv1k5UUHFTyuNEEY5ni4KEWSqyJjFYPhUEKzbWgLCg+lYL95GOQumwCjoEZ/HLy9C4KDuab3UaVzBTHk7gFErgwCVU4QZqUAcMQ7iHR3gyUuPBeDZeZq05Yz5zCH9kvP4AIlGXtw== AAAB+XicbZDLSsNAFIZP6q3WW9SFiJtgEeqmJG7ssujGZQV7gTaUyWTSDp1MwsyktIS8iRsXirj1RcSdbtz6GE4vC239YeDjP+dwzvxezKhUtv1h5FZW19Y38puFre2d3T1z/6Aho0RgUscRi0TLQ5IwykldUcVIKxYEhR4jTW9wPak3h0RIGvE7NY6JG6IepwHFSGmra5qdQCCc+kGW+qOsNDrvmkW7bE9lLYMzh2K18vV29Pl9XOua7x0/wklIuMIMSdl27Fi5KRKKYkayQieRJEZ4gHqkrZGjkEg3nV6eWWfa8a0gEvpxZU3d3xMpCqUch57uDJHqy8XaxPyv1k5UUHFTyuNEEY5ni4KEWSqyJjFYPhUEKzbWgLCg+lYL95GOQumwCjoEZ/HLy9C4KDuab3UaVzBTHk7gFErgwCVU4QZqUAcMQ7iHR3gyUuPBeDZeZq05Yz5zCH9kvP4AIlGXtw== AAAB+XicbZC7TsMwFIZPyq2UW4CRxaJCKkuVsJSxgoWxSPQitVHlOE5r1XEi26laRXkTFgYQYuVN2Hgb3DYDtPySpU//OUfn+PcTzpR2nG+rtLW9s7tX3q8cHB4dn9inZx0Vp5LQNol5LHs+VpQzQduaaU57iaQ48jnt+pP7Rb07pVKxWDzpeUK9CI8ECxnB2lhD2x6EEpMsCPMsmOW12fXQrjp1Zym0CW4BVSjUGtpfgyAmaUSFJhwr1XedRHsZlpoRTvPKIFU0wWSCR7RvUOCIKi9bXp6jK+MEKIyleUKjpft7IsORUvPIN50R1mO1XluY/9X6qQ5vvYyJJNVUkNWiMOVIx2gRAwqYpETzuQFMJDO3IjLGJgptwqqYENz1L29C56buGn50qs27Io4yXMAl1MCFBjThAVrQBgJTeIZXeLMy68V6tz5WrSWrmDmHP7I+fwCfHpOe ·ͨ͸

Slide 31

Slide 31 text

(f(x) + g(x))0 = f0(x) + g0(x) (kf(x))0 = kf0(x) (f(x)g(x))0 = f0(x)g(x) + f(x)g0(x) (xn)0 = nxn 1 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 AAACeHicbVFNSwMxEM2u3/Wr6tFLsGpbxLIrgl4E0YtHBatCt5ZsmrSh2eySzErL0t/gf/PmD/Hiyey2oFUHMjzeezNJZsJECgOe9+64c/MLi0vLK6XVtfWNzfLW9oOJU01Zk8Yy1k8hMUwKxZogQLKnRDMShZI9hoPrXH98YdqIWN3DKGHtiPSU4IISsFSn/BpIxqHGa8P6Uc+mQIteH+rVwwteLbg8B0FpYhvwGcuAz6i5+E+PnDoqtBn38Fl9GxUePmfq2B93yhWv4RWB/wJ/CipoGred8lvQjWkaMQVUEmNavpdAOyMaBJVsXApSwxJCB6THWhYqEjHTzorBjfGBZbqYx9oeBbhgf1ZkJDJmFIXWGRHom99aTv6ntVLg5+1MqCQFpujkIp5KDDHOt4C7QjMKcmQBoVrYt2LaJ5pQsLsq2SH4v7/8FzycNHyL704rl1fTcSyjXbSHashHZ+gS3aBb1EQUfTi7zr5z4Hy62K269YnVdaY1O2gm3JMvNHu3vQ== 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 x5 + 3x3 4x2 0 = x5 0 + 3 x3 0 4 x2 0 = 5x4 + 3 ⇥ 3x2 4 ⇥ 2x = 5x4 + 9x2 8x 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 ॏཁެࣜ ܭࢉྫ

Slide 32

Slide 32 text

ภඍ෼ f(x1, x2, . . . , xn) AAAB/nicbZDLSsNAFIZP6q3WW1RcuQktQsVSkm50WXTjsoK9QBPCZDpph04mYWYiLaHgo+jGhSJufQ53vo3Ty0Jbfxj4+M85nDN/kDAqlW1/G7m19Y3Nrfx2YWd3b//APDxqyTgVmDRxzGLRCZAkjHLSVFQx0kkEQVHASDsY3kzr7QciJI35vRonxItQn9OQYqS05ZsnYXnkO5WRX6u4rBcrqZGf+2bJrtozWavgLKBUL7oXTwDQ8M0vtxfjNCJcYYak7Dp2orwMCUUxI5OCm0qSIDxEfdLVyFFEpJfNzp9YZ9rpWWEs9OPKmrm/JzIUSTmOAt0ZITWQy7Wp+V+tm6rwyssoT1JFOJ4vClNmqdiaZmH1qCBYsbEGhAXVt1p4gATCSidW0CE4y19ehVat6mi+02lcw1x5OIUilMGBS6jDLTSgCRgyeIZXeDMejRfj3fiYt+aMxcwx/JHx+QObrZYV AAAB/nicbZDLSsNAFIYn9VbrLSqu3AwtQsVSkm50WXTjsoK9QBPCZDJph04mYWYiDaHgQ/gCblwo4tbncNe3cXpZaPWHgY//nMM58/sJo1JZ1tQorK1vbG4Vt0s7u3v7B+bhUUfGqcCkjWMWi56PJGGUk7aiipFeIgiKfEa6/uhmVu8+ECFpzO9VlhA3QgNOQ4qR0pZnnoTVsWfXxl6j5rAgVlIjP/fMilW35oJ/wV5CpVl2Lp6mzazlmV9OEOM0IlxhhqTs21ai3BwJRTEjk5KTSpIgPEID0tfIUUSkm8/Pn8Az7QQwjIV+XMG5+3MiR5GUWeTrzgipoVytzcz/av1UhVduTnmSKsLxYlGYMqhiOMsCBlQQrFimAWFB9a0QD5FAWOnESjoEe/XLf6HTqNua73Qa12ChIjgFZVAFNrgETXALWqANMMjBM3gFb8aj8WK8Gx+L1oKxnDkGv2R8fgOlF5eb AAAB/nicbZDLSsNAFIYn9VbrLSqu3AwtQsVSkm50WXTjsoK9QBPCZDJph04mYWYiDaHgQ/gCblwo4tbncNe3cXpZaPWHgY//nMM58/sJo1JZ1tQorK1vbG4Vt0s7u3v7B+bhUUfGqcCkjWMWi56PJGGUk7aiipFeIgiKfEa6/uhmVu8+ECFpzO9VlhA3QgNOQ4qR0pZnnoTVsWfXxl6j5rAgVlIjP/fMilW35oJ/wV5CpVl2Lp6mzazlmV9OEOM0IlxhhqTs21ai3BwJRTEjk5KTSpIgPEID0tfIUUSkm8/Pn8Az7QQwjIV+XMG5+3MiR5GUWeTrzgipoVytzcz/av1UhVduTnmSKsLxYlGYMqhiOMsCBlQQrFimAWFB9a0QD5FAWOnESjoEe/XLf6HTqNua73Qa12ChIjgFZVAFNrgETXALWqANMMjBM3gFb8aj8WK8Gx+L1oKxnDkGv2R8fgOlF5eb AAAB/nicbZDLSsNAFIYnXmu9RcWVm8EiVCgl6UaXRTcuK9gLtCFMppN26GQSZk6kJRR8FTcuFHHrc7jzbZy2WWjrDwMf/zmHc+YPEsE1OM63tba+sbm1Xdgp7u7tHxzaR8ctHaeKsiaNRaw6AdFMcMmawEGwTqIYiQLB2sHodlZvPzKleSwfYJIwLyIDyUNOCRjLt0/D8th3K2O/VumJfgzaoLz07ZJTdebCq+DmUEK5Gr791evHNI2YBCqI1l3XScDLiAJOBZsWe6lmCaEjMmBdg5JETHvZ/PwpvjBOH4exMk8Cnru/JzISaT2JAtMZERjq5drM/K/WTSG89jIukxSYpItFYSowxHiWBe5zxSiIiQFCFTe3YjokilAwiRVNCO7yl1ehVau6hu+dUv0mj6OAztA5KiMXXaE6ukMN1EQUZegZvaI368l6sd6tj0XrmpXPnKA/sj5/AIkulIw= xi AAAB6nicbZC7SgNBFIbPxluMt6hgYzMYBKuwa6Nl0MYyQXOBZImzk7PJkNnZZWZWDEsewcZCEVufyM7GZ3FyKTTxh4GP/5zDnPMHieDauO6Xk1tZXVvfyG8WtrZ3dveK+wcNHaeKYZ3FIlatgGoUXGLdcCOwlSikUSCwGQyvJ/XmAyrNY3lnRgn6Ee1LHnJGjbVuH7u8Wyy5ZXcqsgzeHEqVo9r3PQBUu8XPTi9maYTSMEG1bntuYvyMKsOZwHGhk2pMKBvSPrYtShqh9rPpqmNyap0eCWNlnzRk6v6eyGik9SgKbGdEzUAv1ibmf7V2asJLP+MySQ1KNvsoTAUxMZncTXpcITNiZIEyxe2uhA2ooszYdAo2BG/x5GVonJc9yzWbxhXMlIdjOIEz8OACKnADVagDgz48wQu8OsJ5dt6c91lrzpnPHMIfOR8/7eqPuQ== AAAB6nicbZC7SgNBFIbPxluMt6hgYzMYBKuwa6NliI1lguYCSQizk7PJkNnZZWZWDEsewcZCEVtb38InsLPxWZxcCk38YeDjP+cw5/x+LLg2rvvlZFZW19Y3spu5re2d3b38/kFdR4liWGORiFTTpxoFl1gz3Ahsxgpp6Ats+MOrSb1xh0rzSN6aUYydkPYlDzijxlo3913ezRfcojsVWQZvDoXSUfWbv5c/Kt38Z7sXsSREaZigWrc8NzadlCrDmcBxrp1ojCkb0j62LEoaou6k01XH5NQ6PRJEyj5pyNT9PZHSUOtR6NvOkJqBXqxNzP9qrcQEl52UyzgxKNnsoyARxERkcjfpcYXMiJEFyhS3uxI2oIoyY9PJ2RC8xZOXoX5e9CxXbRplmCkLx3ACZ+DBBZTgGipQAwZ9eIAneHaE8+i8OK+z1owznzmEP3LefgA/OpF1 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AAACCHicbZDLSsNAFIZPvNZ6i7p04WARXJVEBF1JURCXFewFmhAm00k7dHJhZiKWkKUbn8K9GxeKuPUR3Pk2TtqC2vrDwMd/zpmZ8/sJZ1JZ1pcxN7+wuLRcWimvrq1vbJpb200Zp4LQBol5LNo+lpSziDYUU5y2E0Fx6HPa8gcXRb11S4VkcXSjhgl1Q9yLWMAIVtryzD0nEJhkToKFYpijIP/hO4/lnlmxqtZIaBbsCVRqZ5fHjwBQ98xPpxuTNKSRIhxL2bGtRLlZcSXhNC87qaQJJgPcox2NEQ6pdLPRIjk60E4XBbHQJ1Jo5P6eyHAo5TD0dWeIVV9O1wrzv1onVcGpm7EoSRWNyPihIOVIxahIBXWZoETxoQZMBNN/RaSPdTJKZ1fWIdjTK89C86hqa77WaZzDWCXYhX04BBtOoAZXUIcGELiHJ3iBV+PBeDbejPdx65wxmdmBPzI+vgGi3JvV AAACCHicbZBNS8MwGMfT+TbnW9WjB4ND8DRaEfQkU0HE0wT3AmspaZZuYWlaklQcpUcvfgE/hBcPyvDqR/DmtzHdBurmHwI//s/zJHn+fsyoVJb1ZRTm5hcWl4rLpZXVtfUNc3OrIaNEYFLHEYtEy0eSMMpJXVHFSCsWBIU+I02/f5HXm3dESBrxWzWIiRuiLqcBxUhpyzN3nUAgnDoxEooiBoPsh+89mnlm2apYI8FZsCdQrp5eHj0Nz65rnvnpdCKchIQrzJCUbduKlZvmV2JGspKTSBIj3Edd0tbIUUikm44WyeC+djowiIQ+XMGR+3siRaGUg9DXnSFSPTldy83/au1EBSduSnmcKMLx+KEgYVBFME8FdqggWLGBBoQF1X+FuId0MkpnV9Ih2NMrz0LjsGJrvtFpnIOximAH7IEDYINjUAVXoAbqAIMH8AxewZvxaLwYQ+N93FowJjPb4I+Mj29Fe50O AAACCHicbZBNS8MwGMfT+TbnW9WjB4ND8DRaEfQkU0HE0wT3AmspaZZuYWlaklQcpUcvfgE/hBcPyvDqR/DmtzHdBurmHwI//s/zJHn+fsyoVJb1ZRTm5hcWl4rLpZXVtfUNc3OrIaNEYFLHEYtEy0eSMMpJXVHFSCsWBIU+I02/f5HXm3dESBrxWzWIiRuiLqcBxUhpyzN3nUAgnDoxEooiBoPsh+89mnlm2apYI8FZsCdQrp5eHj0Nz65rnvnpdCKchIQrzJCUbduKlZvmV2JGspKTSBIj3Edd0tbIUUikm44WyeC+djowiIQ+XMGR+3siRaGUg9DXnSFSPTldy83/au1EBSduSnmcKMLx+KEgYVBFME8FdqggWLGBBoQF1X+FuId0MkpnV9Ih2NMrz0LjsGJrvtFpnIOximAH7IEDYINjUAVXoAbqAIMH8AxewZvxaLwYQ+N93FowJjPb4I+Mj29Fe50O AAACCHicbZC7TsMwFIZPuJZyCzAyYFEhMVUJC4wVLIxFohepiSLHdVqrjhPZDqKKOrLwKiwMIMTKI7DxNjhtJKDllyx9+s85ts8fppwp7Thf1tLyyuraemWjurm1vbNr7+23VZJJQlsk4YnshlhRzgRtaaY57aaS4jjktBOOrop6545KxRJxq8cp9WM8ECxiBGtjBfaRF0lMci/FUjPMUTT54fuATQK75tSdqdAiuCXUoFQzsD+9fkKymApNOFaq5zqp9vPiSsLppOpliqaYjPCA9gwKHFPl59NFJujEOH0UJdIcodHU/T2R41ipcRyazhjroZqvFeZ/tV6mows/ZyLNNBVk9lCUcaQTVKSC+kxSovnYACaSmb8iMsQmGW2yq5oQ3PmVF6F9VncN3zi1xmUZRwUO4RhOwYVzaMA1NKEFBB7gCV7g1Xq0nq03633WumSVMwfwR9bHN3wEmj0= ଟม਺ؔ਺ ͰɺɹɹҎ֎ͷม਺Λ͢΂ͯఆ਺ͩͱࢥͬͯ Ͱඍ෼ͨ͠΋ͷΛ xi AAAB6nicbZC7SgNBFIbPxluMt6hgYzMYBKuwa6Nl0MYyQXOBZImzk7PJkNnZZWZWDEsewcZCEVufyM7GZ3FyKTTxh4GP/5zDnPMHieDauO6Xk1tZXVvfyG8WtrZ3dveK+wcNHaeKYZ3FIlatgGoUXGLdcCOwlSikUSCwGQyvJ/XmAyrNY3lnRgn6Ee1LHnJGjbVuH7u8Wyy5ZXcqsgzeHEqVo9r3PQBUu8XPTi9maYTSMEG1bntuYvyMKsOZwHGhk2pMKBvSPrYtShqh9rPpqmNyap0eCWNlnzRk6v6eyGik9SgKbGdEzUAv1ibmf7V2asJLP+MySQ1KNvsoTAUxMZncTXpcITNiZIEyxe2uhA2ooszYdAo2BG/x5GVonJc9yzWbxhXMlIdjOIEz8OACKnADVagDgz48wQu8OsJ5dt6c91lrzpnPHMIfOR8/7eqPuQ== AAAB6nicbZC7SgNBFIbPxluMt6hgYzMYBKuwa6NliI1lguYCSQizk7PJkNnZZWZWDEsewcZCEVtb38InsLPxWZxcCk38YeDjP+cw5/x+LLg2rvvlZFZW19Y3spu5re2d3b38/kFdR4liWGORiFTTpxoFl1gz3Ahsxgpp6Ats+MOrSb1xh0rzSN6aUYydkPYlDzijxlo3913ezRfcojsVWQZvDoXSUfWbv5c/Kt38Z7sXsSREaZigWrc8NzadlCrDmcBxrp1ojCkb0j62LEoaou6k01XH5NQ6PRJEyj5pyNT9PZHSUOtR6NvOkJqBXqxNzP9qrcQEl52UyzgxKNnsoyARxERkcjfpcYXMiJEFyhS3uxI2oIoyY9PJ2RC8xZOXoX5e9CxXbRplmCkLx3ACZ+DBBZTgGipQAwZ9eIAneHaE8+i8OK+z1owznzmEP3LefgA/OpF1 AAAB6nicbZC7SgNBFIbPxluMt6hgYzMYBKuwa6NliI1lguYCSQizk7PJkNnZZWZWDEsewcZCEVtb38InsLPxWZxcCk38YeDjP+cw5/x+LLg2rvvlZFZW19Y3spu5re2d3b38/kFdR4liWGORiFTTpxoFl1gz3Ahsxgpp6Ats+MOrSb1xh0rzSN6aUYydkPYlDzijxlo3913ezRfcojsVWQZvDoXSUfWbv5c/Kt38Z7sXsSREaZigWrc8NzadlCrDmcBxrp1ojCkb0j62LEoaou6k01XH5NQ6PRJEyj5pyNT9PZHSUOtR6NvOkJqBXqxNzP9qrcQEl52UyzgxKNnsoyARxERkcjfpcYXMiJEFyhS3uxI2oIoyY9PJ2RC8xZOXoX5e9CxXbRplmCkLx3ACZ+DBBZTgGipQAwZ9eIAneHaE8+i8OK+z1owznzmEP3LefgA/OpF1 AAAB6nicbZBNT8JAEIan+IX4hXr0spGYeCKtFz0SvXjEaIEEGrJdtrBhu212p0bS8BO8eNAYr/4ib/4bF+hBwTfZ5Mk7M9mZN0ylMOi6305pbX1jc6u8XdnZ3ds/qB4etUySacZ9lshEd0JquBSK+yhQ8k6qOY1Dydvh+GZWbz9ybUSiHnCS8iCmQyUiwSha6/6pL/rVmlt35yKr4BVQg0LNfvWrN0hYFnOFTFJjup6bYpBTjYJJPq30MsNTysZ0yLsWFY25CfL5qlNyZp0BiRJtn0Iyd39P5DQ2ZhKHtjOmODLLtZn5X62bYXQV5EKlGXLFFh9FmSSYkNndZCA0ZygnFijTwu5K2IhqytCmU7EheMsnr0Lrou5ZvnNrjesijjKcwCmcgweX0IBbaIIPDIbwDK/w5kjnxXl3PhatJaeYOYY/cj5/AF9SjdQ= ͱॻ͘ f(x, y) = x2 + xy + y3 + 3y AAAB/XicbZDLSsNAFIYn9VbrLV52bgaLUKmUpBV0IxTduKxgL9CmZTKdtEMnkzAzkcZQfBU3LhRx63u4822ctllo9YeBj/+cwznzuyGjUlnWl5FZWl5ZXcuu5zY2t7Z3zN29hgwigUkdBywQLRdJwigndUUVI61QEOS7jDTd0fW03rwnQtKA36k4JI6PBpx6FCOlrZ554BXGp/HJ5bhbLo7jYtytFCtxz8xbJWsm+BfsFPIgVa1nfnb6AY58whVmSMq2bYXKSZBQFDMyyXUiSUKER2hA2ho58ol0ktn1E3isnT70AqEfV3Dm/pxIkC9l7Lu600dqKBdrU/O/WjtS3oWTUB5GinA8X+RFDKoATqOAfSoIVizWgLCg+laIh0ggrHRgOR2Cvfjlv9Aol2zNt2f56lUaRxYcgiNQADY4B1VwA2qgDjB4AE/gBbwaj8az8Wa8z1szRjqzD37J+PgGHeWTtA== AAAB/XicbZDLSsNAFIYn9VbrLV52bgaLUKmUpBV0IxTduKxgL9CmZTKdtEMnkzAzkcZQfBU3LhRx63u4822ctllo9YeBj/+cwznzuyGjUlnWl5FZWl5ZXcuu5zY2t7Z3zN29hgwigUkdBywQLRdJwigndUUVI61QEOS7jDTd0fW03rwnQtKA36k4JI6PBpx6FCOlrZ554BXGp/HJ5bhbLo7jYtytFCtxz8xbJWsm+BfsFPIgVa1nfnb6AY58whVmSMq2bYXKSZBQFDMyyXUiSUKER2hA2ho58ol0ktn1E3isnT70AqEfV3Dm/pxIkC9l7Lu600dqKBdrU/O/WjtS3oWTUB5GinA8X+RFDKoATqOAfSoIVizWgLCg+laIh0ggrHRgOR2Cvfjlv9Aol2zNt2f56lUaRxYcgiNQADY4B1VwA2qgDjB4AE/gBbwaj8az8Wa8z1szRjqzD37J+PgGHeWTtA== AAAB/XicbZDLSsNAFIYn9VbrLV52bgaLUKmUpBV0IxTduKxgL9CmZTKdtEMnkzAzkcZQfBU3LhRx63u4822ctllo9YeBj/+cwznzuyGjUlnWl5FZWl5ZXcuu5zY2t7Z3zN29hgwigUkdBywQLRdJwigndUUVI61QEOS7jDTd0fW03rwnQtKA36k4JI6PBpx6FCOlrZ554BXGp/HJ5bhbLo7jYtytFCtxz8xbJWsm+BfsFPIgVa1nfnb6AY58whVmSMq2bYXKSZBQFDMyyXUiSUKER2hA2ho58ol0ktn1E3isnT70AqEfV3Dm/pxIkC9l7Lu600dqKBdrU/O/WjtS3oWTUB5GinA8X+RFDKoATqOAfSoIVizWgLCg+laIh0ggrHRgOR2Cvfjlv9Aol2zNt2f56lUaRxYcgiNQADY4B1VwA2qgDjB4AE/gBbwaj8az8Wa8z1szRjqzD37J+PgGHeWTtA== AAAB/XicbZDLSsNAFIYn9VbrLV52bgaLUKmUpBV0IxTduKxgL9CmZTKdtEMnkzAzkcZQfBU3LhRx63u4822ctllo9YeBj/+cwznzuyGjUlnWl5FZWl5ZXcuu5zY2t7Z3zN29hgwigUkdBywQLRdJwigndUUVI61QEOS7jDTd0fW03rwnQtKA36k4JI6PBpx6FCOlrZ554BXGp/HJ5bhbLo7jYtytFCtxz8xbJWsm+BfsFPIgVa1nfnb6AY58whVmSMq2bYXKSZBQFDMyyXUiSUKER2hA2ho58ol0ktn1E3isnT70AqEfV3Dm/pxIkC9l7Lu600dqKBdrU/O/WjtS3oWTUB5GinA8X+RFDKoATqOAfSoIVizWgLCg+laIh0ggrHRgOR2Cvfjlv9Aol2zNt2f56lUaRxYcgiNQADY4B1VwA2qgDjB4AE/gBbwaj8az8Wa8z1szRjqzD37J+PgGHeWTtA== @f @x = 2x + y AAACDXicbZBNS8MwGMfT+TbnW9Wjl+AUBGG0Q9CLMPTicYJ7gbWMNEu3sDQtSSorpV/Ai1/FiwdFvHr35rcx3Qrq5h8CP/7P8yR5/l7EqFSW9WWUlpZXVtfK65WNza3tHXN3ry3DWGDSwiELRddDkjDKSUtRxUg3EgQFHiMdb3yd1zv3REga8juVRMQN0JBTn2KktNU3jxxfIJw6ERKKIgb97IcnGbyE9clp0jerVs2aCi6CXUAVFGr2zU9nEOI4IFxhhqTs2Vak3DS/FzOSVZxYkgjhMRqSnkaOAiLddLpNBo+1M4B+KPThCk7d3xMpCqRMAk93BkiN5HwtN/+r9WLlX7gp5VGsCMezh/yYQRXCPBo4oIJgxRINCAuq/wrxCOl4lA6wokOw51dehHa9Zmu+Pas2roo4yuAAHIITYINz0AA3oAlaAIMH8ARewKvxaDwbb8b7rLVkFDP74I+Mj2/+Kpt2 AAACDXicbZBNS8MwGMfT+TbnW9Wjl+AUBGG0Q9CLMPTicYJ7gbWMNEu3sDQtSSorpV/Ai1/FiwdFvHr35rcx3Qrq5h8CP/7P8yR5/l7EqFSW9WWUlpZXVtfK65WNza3tHXN3ry3DWGDSwiELRddDkjDKSUtRxUg3EgQFHiMdb3yd1zv3REga8juVRMQN0JBTn2KktNU3jxxfIJw6ERKKIgb97IcnGbyE9clp0jerVs2aCi6CXUAVFGr2zU9nEOI4IFxhhqTs2Vak3DS/FzOSVZxYkgjhMRqSnkaOAiLddLpNBo+1M4B+KPThCk7d3xMpCqRMAk93BkiN5HwtN/+r9WLlX7gp5VGsCMezh/yYQRXCPBo4oIJgxRINCAuq/wrxCOl4lA6wokOw51dehHa9Zmu+Pas2roo4yuAAHIITYINz0AA3oAlaAIMH8ARewKvxaDwbb8b7rLVkFDP74I+Mj2/+Kpt2 AAACDXicbZBNS8MwGMfT+TbnW9Wjl+AUBGG0Q9CLMPTicYJ7gbWMNEu3sDQtSSorpV/Ai1/FiwdFvHr35rcx3Qrq5h8CP/7P8yR5/l7EqFSW9WWUlpZXVtfK65WNza3tHXN3ry3DWGDSwiELRddDkjDKSUtRxUg3EgQFHiMdb3yd1zv3REga8juVRMQN0JBTn2KktNU3jxxfIJw6ERKKIgb97IcnGbyE9clp0jerVs2aCi6CXUAVFGr2zU9nEOI4IFxhhqTs2Vak3DS/FzOSVZxYkgjhMRqSnkaOAiLddLpNBo+1M4B+KPThCk7d3xMpCqRMAk93BkiN5HwtN/+r9WLlX7gp5VGsCMezh/yYQRXCPBo4oIJgxRINCAuq/wrxCOl4lA6wokOw51dehHa9Zmu+Pas2roo4yuAAHIITYINz0AA3oAlaAIMH8ARewKvxaDwbb8b7rLVkFDP74I+Mj2/+Kpt2 AAACDXicbZBNS8MwGMfT+TbnW9Wjl+AUBGG0Q9CLMPTicYJ7gbWMNEu3sDQtSSorpV/Ai1/FiwdFvHr35rcx3Qrq5h8CP/7P8yR5/l7EqFSW9WWUlpZXVtfK65WNza3tHXN3ry3DWGDSwiELRddDkjDKSUtRxUg3EgQFHiMdb3yd1zv3REga8juVRMQN0JBTn2KktNU3jxxfIJw6ERKKIgb97IcnGbyE9clp0jerVs2aCi6CXUAVFGr2zU9nEOI4IFxhhqTs2Vak3DS/FzOSVZxYkgjhMRqSnkaOAiLddLpNBo+1M4B+KPThCk7d3xMpCqRMAk93BkiN5HwtN/+r9WLlX7gp5VGsCMezh/yYQRXCPBo4oIJgxRINCAuq/wrxCOl4lA6wokOw51dehHa9Zmu+Pas2roo4yuAAHIITYINz0AA3oAlaAIMH8ARewKvxaDwbb8b7rLVkFDP74I+Mj2/+Kpt2 @f @y = x + 3y2 + 3 AAACEXicbZBNS8MwGMdTX+d8q3r0EhzCYDDaTdCLMPTicYJ7ga2ONEu3sDQtSSqW0q/gxa/ixYMiXr1589uYbgV18w+BH//neZI8fzdkVCrL+jKWlldW19YLG8XNre2dXXNvvy2DSGDSwgELRNdFkjDKSUtRxUg3FAT5LiMdd3KZ1Tt3REga8BsVh8Tx0YhTj2KktDUwy31PIJz0QyQURQx66Q/HKTyH95V6fFur1AdmyapaU8FFsHMogVzNgfnZHwY48glXmCEpe7YVKifJ7saMpMV+JEmI8ASNSE8jRz6RTjLdKIXH2hlCLxD6cAWn7u+JBPlSxr6rO32kxnK+lpn/1XqR8s6chPIwUoTj2UNexKAKYBYPHFJBsGKxBoQF1X+FeIx0REqHWNQh2PMrL0K7VrU1X5+UGhd5HAVwCI5AGdjgFDTAFWiCFsDgATyBF/BqPBrPxpvxPmtdMvKZA/BHxsc3Nsycjg== AAACEXicbZBNS8MwGMdTX+d8q3r0EhzCYDDaTdCLMPTicYJ7ga2ONEu3sDQtSSqW0q/gxa/ixYMiXr1589uYbgV18w+BH//neZI8fzdkVCrL+jKWlldW19YLG8XNre2dXXNvvy2DSGDSwgELRNdFkjDKSUtRxUg3FAT5LiMdd3KZ1Tt3REga8BsVh8Tx0YhTj2KktDUwy31PIJz0QyQURQx66Q/HKTyH95V6fFur1AdmyapaU8FFsHMogVzNgfnZHwY48glXmCEpe7YVKifJ7saMpMV+JEmI8ASNSE8jRz6RTjLdKIXH2hlCLxD6cAWn7u+JBPlSxr6rO32kxnK+lpn/1XqR8s6chPIwUoTj2UNexKAKYBYPHFJBsGKxBoQF1X+FeIx0REqHWNQh2PMrL0K7VrU1X5+UGhd5HAVwCI5AGdjgFDTAFWiCFsDgATyBF/BqPBrPxpvxPmtdMvKZA/BHxsc3Nsycjg== AAACEXicbZBNS8MwGMdTX+d8q3r0EhzCYDDaTdCLMPTicYJ7ga2ONEu3sDQtSSqW0q/gxa/ixYMiXr1589uYbgV18w+BH//neZI8fzdkVCrL+jKWlldW19YLG8XNre2dXXNvvy2DSGDSwgELRNdFkjDKSUtRxUg3FAT5LiMdd3KZ1Tt3REga8BsVh8Tx0YhTj2KktDUwy31PIJz0QyQURQx66Q/HKTyH95V6fFur1AdmyapaU8FFsHMogVzNgfnZHwY48glXmCEpe7YVKifJ7saMpMV+JEmI8ASNSE8jRz6RTjLdKIXH2hlCLxD6cAWn7u+JBPlSxr6rO32kxnK+lpn/1XqR8s6chPIwUoTj2UNexKAKYBYPHFJBsGKxBoQF1X+FeIx0REqHWNQh2PMrL0K7VrU1X5+UGhd5HAVwCI5AGdjgFDTAFWiCFsDgATyBF/BqPBrPxpvxPmtdMvKZA/BHxsc3Nsycjg== AAACEXicbZBNS8MwGMdTX+d8q3r0EhzCYDDaTdCLMPTicYJ7ga2ONEu3sDQtSSqW0q/gxa/ixYMiXr1589uYbgV18w+BH//neZI8fzdkVCrL+jKWlldW19YLG8XNre2dXXNvvy2DSGDSwgELRNdFkjDKSUtRxUg3FAT5LiMdd3KZ1Tt3REga8BsVh8Tx0YhTj2KktDUwy31PIJz0QyQURQx66Q/HKTyH95V6fFur1AdmyapaU8FFsHMogVzNgfnZHwY48glXmCEpe7YVKifJ7saMpMV+JEmI8ASNSE8jRz6RTjLdKIXH2hlCLxD6cAWn7u+JBPlSxr6rO32kxnK+lpn/1XqR8s6chPIwUoTj2UNexKAKYBYPHFJBsGKxBoQF1X+FeIx0REqHWNQh2PMrL0K7VrU1X5+UGhd5HAVwCI5AGdjgFDTAFWiCFsDgATyBF/BqPBrPxpvxPmtdMvKZA/BHxsc3Nsycjg== ܭࢉྫɿ ͷͱ͖

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ޯ഑ rf = 0 B B B B @ @f @x1 @f @x2 . . . @f @xn 1 C C C C A 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 AAACfnichVHLSgMxFM2M7/qqunQTLYoo1pludCMU3bhUsLbQKeVO5k4NzWSGJCOWoZ/hj7nzW9yY1uKrohcCh3NPcm7ODTPBtfG8F8edmZ2bX1hcKi2vrK6tlzc273SaK4YNlopUtULQKLjEhuFGYCtTCEkosBn2L0f95gMqzVN5awYZdhLoSR5zBsZS3fJTICEUQGN6XgpC7HFZZAkYxR+HpSBWwIogA2U4CBoPP/Fj1x8Gwd+K2ljxEKVG/yeV1gxl9GHdLVe8qjcuOg38CaiQSV13y89BlLI8QWmYAK3bvpeZTjEyYALt67nGDFgfeti2UEKCulOM4xvSPctENE6VPdLQMfv1RgGJ1oMktEo7373+2RuRv/XauYnPOgWXWW5QsnejOBfUpHS0CxpxhcyIgQXAFLezUnYPNidjN1ayIfg/vzwN7mpV3+Ibr1K/mMSxSLbJLjkgPjkldXJFrkmDMPLq7DiHzpFL3H332D15l7rO5M4W+Vbu2RufGsNS Λޯ഑ͱݺͿ rf = 0 AAAB8XicbZC7SgNBFIbPxluMt6ilFoNBsAq7NtoIQRvLBMwFkyWcncwmQ2Znl5lZISx5CxsLRWx9AZ/Dzs5HcXIpNPGHgY//nMOc8weJ4Nq47peTW1ldW9/Ibxa2tnd294r7Bw0dp4qyOo1FrFoBaia4ZHXDjWCtRDGMAsGawfBmUm8+MKV5LO/MKGF+hH3JQ07RWOu+IzEQSMIrt1ssuWV3KrIM3hxKleOP2jcAVLvFz04vpmnEpKECtW57bmL8DJXhVLBxoZNqliAdYp+1LUqMmPaz6cZjcmqdHgljZZ80ZOr+nsgw0noUBbYzQjPQi7WJ+V+tnZrw0s+4TFLDJJ19FKaCmJhMzic9rhg1YmQBqeJ2V0IHqJAaG1LBhuAtnrwMjfOyZ7lm07iGmfJwBCdwBh5cQAVuoQp1oCDhEZ7hxdHOk/PqvM1ac8585hD+yHn/AZ0Xkmw= AAAB8XicbZBLSgNBEIZr4ivGV9SlIo1BcBVm3OhGCLpxmYBJxGQINZ2epElPz9DdI4SQpTdw40IRt14g53DnGbyEncdCE39o+Piriq76g0RwbVz3y8ksLa+srmXXcxubW9s7+d29mo5TRVmVxiJWdwFqJrhkVcONYHeJYhgFgtWD3vW4Xn9gSvNY3pp+wvwIO5KHnKKx1n1TYiCQhJduK19wi+5EZBG8GRRKh6PK9+PRqNzKfzbbMU0jJg0VqHXDcxPjD1AZTgUb5pqpZgnSHnZYw6LEiGl/MNl4SE6s0yZhrOyThkzc3xMDjLTuR4HtjNB09XxtbP5Xa6QmvPAHXCapYZJOPwpTQUxMxueTNleMGtG3gFRxuyuhXVRIjQ0pZ0Pw5k9ehNpZ0bNcsWlcwVRZOIBjOAUPzqEEN1CGKlCQ8AQv8Opo59l5c96nrRlnNrMPf+R8/AB7XJPS AAAB8XicbZBLSgNBEIZr4ivGV9SlIo1BcBVm3OhGCLpxmYBJxGQINZ2epElPz9DdI4SQpTdw40IRt14g53DnGbyEncdCE39o+Piriq76g0RwbVz3y8ksLa+srmXXcxubW9s7+d29mo5TRVmVxiJWdwFqJrhkVcONYHeJYhgFgtWD3vW4Xn9gSvNY3pp+wvwIO5KHnKKx1n1TYiCQhJduK19wi+5EZBG8GRRKh6PK9+PRqNzKfzbbMU0jJg0VqHXDcxPjD1AZTgUb5pqpZgnSHnZYw6LEiGl/MNl4SE6s0yZhrOyThkzc3xMDjLTuR4HtjNB09XxtbP5Xa6QmvPAHXCapYZJOPwpTQUxMxueTNleMGtG3gFRxuyuhXVRIjQ0pZ0Pw5k9ehNpZ0bNcsWlcwVRZOIBjOAUPzqEEN1CGKlCQ8AQv8Opo59l5c96nrRlnNrMPf+R8/AB7XJPS AAAB8XicbZBNS8NAEIYn9avWr6hHL4tF8FQSL3oRil48VrAf2IYy2W7apZtN2N0IJfRfePGgiFf/jTf/jds2B219YeHhnRl25g1TwbXxvG+ntLa+sblV3q7s7O7tH7iHRy2dZIqyJk1Eojohaia4ZE3DjWCdVDGMQ8Ha4fh2Vm8/MaV5Ih/MJGVBjEPJI07RWOuxJzEUSKJrr+9WvZo3F1kFv4AqFGr03a/eIKFZzKShArXu+l5qghyV4VSwaaWXaZYiHeOQdS1KjJkO8vnGU3JmnQGJEmWfNGTu/p7IMdZ6Eoe2M0Yz0su1mflfrZuZ6CrIuUwzwyRdfBRlgpiEzM4nA64YNWJiAanidldCR6iQGhtSxYbgL5+8Cq2Lmm/53qvWb4o4ynACp3AOPlxCHe6gAU2gIOEZXuHN0c6L8+58LFpLTjFzDH/kfP4AjR2QJw== ͱ͓͘ͱɺۃ஋ΛٻΊΒΕΔʢ͔΋͠Εͳ͍ʣ

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ޯ഑ͷزԿతੑ࣭ f(x, y) (x0, y0) f(x0, y0) = a rf(x0, y0) f(x, y) = a ͳΊΒ͔ͳ2ม਺ؔ਺ ʹ͓͍ͯ ͱ͢Δɻ (x0, y0) ఺ ʹ͓͚Δޯ഑ ͸ɺۂઢ ͷ f(x, y) = a ఺ ʹ͓͚Δ઀ઢͱਨ௚Ͱ͋Γɺ͔ͭ f(x, y)͕େ͖͘ ͳΔํ޲Λ޲͍͍ͯΔ rf(x0, y0) f(x, y) খ f(x, y) େ ͜ͷɹɹɹɹɹΛ఺ɹɹɹʹ͓͚Δ๏ઢϕΫτϧͱݺͿ (x0, y0) rf(x0, y0)

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ޯ഑߱Լ๏ xk+1 = xk ↵rf(xk) rf(xk) ߋ৽ࣜɿ rf ɹɹͷํ޲ʹগ͠ਐΉͱؔ਺ͷ஋͸ খ͘͞ͳΔͩΖ͏ͱ͍͏ߟ͑ํ ྫɿ f(x, y) = 5x2 6xy + 3y2 + 6x 6y Λ࠷খԽ ͜ͷ఺ઢ͕౳ߴઢʢf=Ұఆͷઢʣ ౳ߴઢʹ͍ͭͯߟ͑Δ͜ͱ͕ɺ͜ΕҎ߱ͱͯ΋େࣄʂ

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ޯ഑߱Լ๏ͷऩଋ xk+1 = xk ↵rf(xk) ͷ஋ʹΑͬͯৼΔ෣͍͕શ͘ҧ͏ ͋Β͔͡ΊΑ͍ɹ ͷ஋Λ༧ଌ͢Δͷ͸ࠔ೉ͳ͜ͱ΋ଟ͍ɻ ↵ AAAB/HicbZA9SwNBEIbn4leMX1FLm8UgWIU7EbQM2lhGMB+QHGFus5es2ds7dveEcMTfYKu1ndj6Xyz9J26SK0ziCwsP78wws2+QCK6N6347hbX1jc2t4nZpZ3dv/6B8eNTUcaooa9BYxKodoGaCS9Yw3AjWThTDKBCsFYxup/XWE1Oax/LBjBPmRziQPOQUjbWaXRTJEHvlilt1ZyKr4OVQgVz1Xvmn249pGjFpqECtO56bGD9DZTgVbFLqppolSEc4YB2LEiOm/Wx27YScWadPwljZJw2ZuX8nMoy0HkeB7YzQDPVybWr+V+ukJrz2My6T1DBJ54vCVBATk+nXSZ8rRo0YW0CquL2V0CEqpMYGtLAliCY2E285gVVoXlQ9y/eXldpNnk4RTuAUzsGDK6jBHdShARQe4QVe4c15dt6dD+dz3lpw8pljWJDz9QtNlJWu AAAB/HicbZA9SwNBEIbn4leMX1FLm8UgWIU7EbQM2lhGMB+QHGFus5es2ds7dveEcMTfYKu1ndj6Xyz9J26SK0ziCwsP78wws2+QCK6N6347hbX1jc2t4nZpZ3dv/6B8eNTUcaooa9BYxKodoGaCS9Yw3AjWThTDKBCsFYxup/XWE1Oax/LBjBPmRziQPOQUjbWaXRTJEHvlilt1ZyKr4OVQgVz1Xvmn249pGjFpqECtO56bGD9DZTgVbFLqppolSEc4YB2LEiOm/Wx27YScWadPwljZJw2ZuX8nMoy0HkeB7YzQDPVybWr+V+ukJrz2My6T1DBJ54vCVBATk+nXSZ8rRo0YW0CquL2V0CEqpMYGtLAliCY2E285gVVoXlQ9y/eXldpNnk4RTuAUzsGDK6jBHdShARQe4QVe4c15dt6dD+dz3lpw8pljWJDz9QtNlJWu AAAB/HicbZA9SwNBEIbn4leMX1FLm8UgWIU7EbQM2lhGMB+QHGFus5es2ds7dveEcMTfYKu1ndj6Xyz9J26SK0ziCwsP78wws2+QCK6N6347hbX1jc2t4nZpZ3dv/6B8eNTUcaooa9BYxKodoGaCS9Yw3AjWThTDKBCsFYxup/XWE1Oax/LBjBPmRziQPOQUjbWaXRTJEHvlilt1ZyKr4OVQgVz1Xvmn249pGjFpqECtO56bGD9DZTgVbFLqppolSEc4YB2LEiOm/Wx27YScWadPwljZJw2ZuX8nMoy0HkeB7YzQDPVybWr+V+ukJrz2My6T1DBJ54vCVBATk+nXSZ8rRo0YW0CquL2V0CEqpMYGtLAliCY2E285gVVoXlQ9y/eXldpNnk4RTuAUzsGDK6jBHdShARQe4QVe4c15dt6dD+dz3lpw8pljWJDz9QtNlJWu AAAB/HicbZA9SwNBEIbn4leMX1FLm8UgWIU7EbQM2lhGMB+QHGFus5es2ds7dveEcMTfYKu1ndj6Xyz9J26SK0ziCwsP78wws2+QCK6N6347hbX1jc2t4nZpZ3dv/6B8eNTUcaooa9BYxKodoGaCS9Yw3AjWThTDKBCsFYxup/XWE1Oax/LBjBPmRziQPOQUjbWaXRTJEHvlilt1ZyKr4OVQgVz1Xvmn249pGjFpqECtO56bGD9DZTgVbFLqppolSEc4YB2LEiOm/Wx27YScWadPwljZJw2ZuX8nMoy0HkeB7YzQDPVybWr+V+ukJrz2My6T1DBJ54vCVBATk+nXSZ8rRo0YW0CquL2V0CEqpMYGtLAliCY2E285gVVoXlQ9y/eXldpNnk4RTuAUzsGDK6jBHdShARQe4QVe4c15dt6dD+dz3lpw8pljWJDz9QtNlJWu ↵ AAAB/HicbZA9SwNBEIbn4leMX1FLm8UgWIU7EbQM2lhGMB+QHGFus5es2ds7dveEcMTfYKu1ndj6Xyz9J26SK0ziCwsP78wws2+QCK6N6347hbX1jc2t4nZpZ3dv/6B8eNTUcaooa9BYxKodoGaCS9Yw3AjWThTDKBCsFYxup/XWE1Oax/LBjBPmRziQPOQUjbWaXRTJEHvlilt1ZyKr4OVQgVz1Xvmn249pGjFpqECtO56bGD9DZTgVbFLqppolSEc4YB2LEiOm/Wx27YScWadPwljZJw2ZuX8nMoy0HkeB7YzQDPVybWr+V+ukJrz2My6T1DBJ54vCVBATk+nXSZ8rRo0YW0CquL2V0CEqpMYGtLAliCY2E285gVVoXlQ9y/eXldpNnk4RTuAUzsGDK6jBHdShARQe4QVe4c15dt6dD+dz3lpw8pljWJDz9QtNlJWu AAAB/HicbZA9SwNBEIbn4leMX1FLm8UgWIU7EbQM2lhGMB+QHGFus5es2ds7dveEcMTfYKu1ndj6Xyz9J26SK0ziCwsP78wws2+QCK6N6347hbX1jc2t4nZpZ3dv/6B8eNTUcaooa9BYxKodoGaCS9Yw3AjWThTDKBCsFYxup/XWE1Oax/LBjBPmRziQPOQUjbWaXRTJEHvlilt1ZyKr4OVQgVz1Xvmn249pGjFpqECtO56bGD9DZTgVbFLqppolSEc4YB2LEiOm/Wx27YScWadPwljZJw2ZuX8nMoy0HkeB7YzQDPVybWr+V+ukJrz2My6T1DBJ54vCVBATk+nXSZ8rRo0YW0CquL2V0CEqpMYGtLAliCY2E285gVVoXlQ9y/eXldpNnk4RTuAUzsGDK6jBHdShARQe4QVe4c15dt6dD+dz3lpw8pljWJDz9QtNlJWu AAAB/HicbZA9SwNBEIbn4leMX1FLm8UgWIU7EbQM2lhGMB+QHGFus5es2ds7dveEcMTfYKu1ndj6Xyz9J26SK0ziCwsP78wws2+QCK6N6347hbX1jc2t4nZpZ3dv/6B8eNTUcaooa9BYxKodoGaCS9Yw3AjWThTDKBCsFYxup/XWE1Oax/LBjBPmRziQPOQUjbWaXRTJEHvlilt1ZyKr4OVQgVz1Xvmn249pGjFpqECtO56bGD9DZTgVbFLqppolSEc4YB2LEiOm/Wx27YScWadPwljZJw2ZuX8nMoy0HkeB7YzQDPVybWr+V+ukJrz2My6T1DBJ54vCVBATk+nXSZ8rRo0YW0CquL2V0CEqpMYGtLAliCY2E285gVVoXlQ9y/eXldpNnk4RTuAUzsGDK6jBHdShARQe4QVe4c15dt6dD+dz3lpw8pljWJDz9QtNlJWu AAAB/HicbZA9SwNBEIbn4leMX1FLm8UgWIU7EbQM2lhGMB+QHGFus5es2ds7dveEcMTfYKu1ndj6Xyz9J26SK0ziCwsP78wws2+QCK6N6347hbX1jc2t4nZpZ3dv/6B8eNTUcaooa9BYxKodoGaCS9Yw3AjWThTDKBCsFYxup/XWE1Oax/LBjBPmRziQPOQUjbWaXRTJEHvlilt1ZyKr4OVQgVz1Xvmn249pGjFpqECtO56bGD9DZTgVbFLqppolSEc4YB2LEiOm/Wx27YScWadPwljZJw2ZuX8nMoy0HkeB7YzQDPVybWr+V+ukJrz2My6T1DBJ54vCVBATk+nXSZ8rRo0YW0CquL2V0CEqpMYGtLAliCY2E285gVVoXlQ9y/eXldpNnk4RTuAUzsGDK6jBHdShARQe4QVe4c15dt6dD+dz3lpw8pljWJDz9QtNlJWu ࣮ݧʹΑܾͬͯఆ͢Δ

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ʢͪΐͬͱ୤ઢʣ χϡʔϥϧωοτϫʔΫͷ ΞϧΰϦζϜ ޯ഑߱Լ๏ͷߟ͑ํΛར༻ʢޯ഑߱Լ๏ͦͷ΋ͷͰ͸ͳ͍ʣ ޯ഑߱Լ๏ɿ1ͭͷ໨తؔ਺ͷޯ഑ํ޲ʹਐΉ χϡʔϥϧωοτϫʔΫɿnݸͷ໨తؔ਺Λ1ͭͣͭݟͳ͕ΒͦΕͧΕͷޯ഑ํ޲ʹਐΉ nݸͷ໨తؔ਺ͷྫɿnݸͷը૾͕ਖ਼͘͠෼ྨͰ͖͍ͯΔ͔Λࣔ͢਺஋ i൪໨ͷը૾ͷ෼ྨ༧ଌͱਖ਼͍͠෼ྨͷࠩҟΛ໨తؔ਺ͱ͢Δ ʢॻ੶Ͱ͸શ͘৮Εͳ͔ͬͨ࿩ʣ

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vj = f X k w(1) kj xk ! 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Slide 39

Slide 39 text

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AAAB4nicbZBLSwMxFIXv1FetVatbN8EiVJAy40aXghuXFewD2qFk0jttbCYZkow4lP4HNy4U8Ue589+YPhbaeiDwcU5C7j1RKrixvv/tFTY2t7Z3irulvfL+wWHlqNwyKtMMm0wJpTsRNSi4xKblVmAn1UiTSGA7Gt/O8vYTasOVfLB5imFCh5LHnFHrrFZce77Iz/uVql/35yLrECyhCks1+pWv3kCxLEFpmaDGdAM/teGEasuZwGmplxlMKRvTIXYdSpqgCSfzaafkzDkDEivtjrRk7v5+MaGJMXkSuZsJtSOzms3M/7JuZuPrcMJlmlmUbPFRnAliFZmtTgZcI7Mid0CZ5m5WwkZUU2ZdQSVXQrC68jq0LuuB43sfinACp1CDAK7gBu6gAU1g8Agv8AbvnvJevY9FXQVv2dsx/JH3+QOOXY0y AAAB4nicbZBLSwMxFIXv1FetVatbN8EiVJAy40aXghuXFewD2qFk0jttbCYZkow4lP4HNy4U8Ue589+YPhbaeiDwcU5C7j1RKrixvv/tFTY2t7Z3irulvfL+wWHlqNwyKtMMm0wJpTsRNSi4xKblVmAn1UiTSGA7Gt/O8vYTasOVfLB5imFCh5LHnFHrrFZce77Iz/uVql/35yLrECyhCks1+pWv3kCxLEFpmaDGdAM/teGEasuZwGmplxlMKRvTIXYdSpqgCSfzaafkzDkDEivtjrRk7v5+MaGJMXkSuZsJtSOzms3M/7JuZuPrcMJlmlmUbPFRnAliFZmtTgZcI7Mid0CZ5m5WwkZUU2ZdQSVXQrC68jq0LuuB43sfinACp1CDAK7gBu6gAU1g8Agv8AbvnvJevY9FXQVv2dsx/JH3+QOOXY0y AAAB7XicbZDLSgMxFIbP1Futt6pLN8EiVJAy040ui25cVrAXaIeSSTNtbCYZkow4DH0HNy4Ucev7uPNtTNtZaOsPgY//nEPO+YOYM21c99sprK1vbG4Vt0s7u3v7B+XDo7aWiSK0RSSXqhtgTTkTtGWY4bQbK4qjgNNOMLmZ1TuPVGkmxb1JY+pHeCRYyAg21mqH1aeL9HxQrrg1dy60Cl4OFcjVHJS/+kNJkogKQzjWuue5sfEzrAwjnE5L/UTTGJMJHtGeRYEjqv1svu0UnVlniEKp7BMGzd3fExmOtE6jwHZG2Iz1cm1m/lfrJSa88jMm4sRQQRYfhQlHRqLZ6WjIFCWGpxYwUczuisgYK0yMDahkQ/CWT16Fdr3mWb5zK43rPI4inMApVMGDS2jALTShBQQe4Ble4c2Rzovz7nwsWgtOPnMMf+R8/gCx946G AAAB7XicbZDLSgMxFIbP1Futt6pLN8EiVJAyI4Iui25cVrAXaIeSSTNtbCYZkow4DH0HNy4Ucev7uPNtTNtZaOsPgY//nEPO+YOYM21c99sprKyurW8UN0tb2zu7e+X9g5aWiSK0SSSXqhNgTTkTtGmY4bQTK4qjgNN2ML6Z1tuPVGkmxb1JY+pHeChYyAg21mqF1aez9LRfrrg1dya0DF4OFcjV6Je/egNJkogKQzjWuuu5sfEzrAwjnE5KvUTTGJMxHtKuRYEjqv1stu0EnVhngEKp7BMGzdzfExmOtE6jwHZG2Iz0Ym1q/lfrJia88jMm4sRQQeYfhQlHRqLp6WjAFCWGpxYwUczuisgIK0yMDahkQ/AWT16G1nnNs3x3Ualf53EU4QiOoQoeXEIdbqEBTSDwAM/wCm+OdF6cd+dj3lpw8plD+CPn8wezN46K AAAB7XicbZDLSgMxFIbP1Futt6pLN8EiVJAyI4Iui25cVrAXaIeSSTNtbCYZkow4DH0HNy4Ucev7uPNtTNtZaOsPgY//nEPO+YOYM21c99sprKyurW8UN0tb2zu7e+X9g5aWiSK0SSSXqhNgTTkTtGmY4bQTK4qjgNN2ML6Z1tuPVGkmxb1JY+pHeChYyAg21mqF1aez9LRfrrg1dya0DF4OFcjV6Je/egNJkogKQzjWuuu5sfEzrAwjnE5KvUTTGJMxHtKuRYEjqv1stu0EnVhngEKp7BMGzdzfExmOtE6jwHZG2Iz0Ym1q/lfrJia88jMm4sRQQeYfhQlHRqLp6WjAFCWGpxYwUczuisgIK0yMDahkQ/AWT16G1nnNs3x3Ualf53EU4QiOoQoeXEIdbqEBTSDwAM/wCm+OdF6cd+dj3lpw8plD+CPn8wezN46K AAAB7XicbZDLSgMxFIbP1Futt6pLN8EiVJAyI4Iui25cVrAXaIeSSTNtbCYZkow4DH0HNy4Ucev7uPNtTNtZaOsPgY//nEPO+YOYM21c99sprKyurW8UN0tb2zu7e+X9g5aWiSK0SSSXqhNgTTkTtGmY4bQTK4qjgNN2ML6Z1tuPVGkmxb1JY+pHeChYyAg21mqF1aez9LRfrrg1dya0DF4OFcjV6Je/egNJkogKQzjWuuu5sfEzrAwjnE5KvUTTGJMxHtKuRYEjqv1stu0EnVhngEKp7BMGzdzfExmOtE6jwHZG2Iz0Ym1q/lfrJia88jMm4sRQQeYfhQlHRqLp6WjAFCWGpxYwUczuisgIK0yMDahkQ/AWT16G1nnNs3x3Ualf53EU4QiOoQoeXEIdbqEBTSDwAM/wCm+OdF6cd+dj3lpw8plD+CPn8wezN46K AAAB7XicbZDLSgMxFIbP1Futt6pLN8EiVJAyI4Iui25cVrAXaIeSSTNtbCYZkow4DH0HNy4Ucev7uPNtTNtZaOsPgY//nEPO+YOYM21c99sprKyurW8UN0tb2zu7e+X9g5aWiSK0SSSXqhNgTTkTtGmY4bQTK4qjgNN2ML6Z1tuPVGkmxb1JY+pHeChYyAg21mqF1aez9LRfrrg1dya0DF4OFcjV6Je/egNJkogKQzjWuuu5sfEzrAwjnE5KvUTTGJMxHtKuRYEjqv1stu0EnVhngEKp7BMGzdzfExmOtE6jwHZG2Iz0Ym1q/lfrJia88jMm4sRQQeYfhQlHRqLp6WjAFCWGpxYwUczuisgIK0yMDahkQ/AWT16G1nnNs3x3Ualf53EU4QiOoQoeXEIdbqEBTSDwAM/wCm+OdF6cd+dj3lpw8plD+CPn8wezN46K AAAB7XicbZDLSgMxFIbP1Futt6pLN8EiVJAyI4Iui25cVrAXaIeSSTNtbCYZkow4DH0HNy4Ucev7uPNtTNtZaOsPgY//nEPO+YOYM21c99sprKyurW8UN0tb2zu7e+X9g5aWiSK0SSSXqhNgTTkTtGmY4bQTK4qjgNN2ML6Z1tuPVGkmxb1JY+pHeChYyAg21mqF1aez9LRfrrg1dya0DF4OFcjV6Je/egNJkogKQzjWuuu5sfEzrAwjnE5KvUTTGJMxHtKuRYEjqv1stu0EnVhngEKp7BMGzdzfExmOtE6jwHZG2Iz0Ym1q/lfrJia88jMm4sRQQeYfhQlHRqLp6WjAFCWGpxYwUczuisgIK0yMDahkQ/AWT16G1nnNs3x3Ualf53EU4QiOoQoeXEIdbqEBTSDwAM/wCm+OdF6cd+dj3lpw8plD+CPn8wezN46K AAAB7XicbZDLSgMxFIbP1Futt6pLN8EiVJAyI4Iui25cVrAXaIeSSTNtbCYZkow4DH0HNy4Ucev7uPNtTNtZaOsPgY//nEPO+YOYM21c99sprKyurW8UN0tb2zu7e+X9g5aWiSK0SSSXqhNgTTkTtGmY4bQTK4qjgNN2ML6Z1tuPVGkmxb1JY+pHeChYyAg21mqF1aez9LRfrrg1dya0DF4OFcjV6Je/egNJkogKQzjWuuu5sfEzrAwjnE5KvUTTGJMxHtKuRYEjqv1stu0EnVhngEKp7BMGzdzfExmOtE6jwHZG2Iz0Ym1q/lfrJia88jMm4sRQQeYfhQlHRqLp6WjAFCWGpxYwUczuisgIK0yMDahkQ/AWT16G1nnNs3x3Ualf53EU4QiOoQoeXEIdbqEBTSDwAM/wCm+OdF6cd+dj3lpw8plD+CPn8wezN46K g(x, y) = 0 AAAB73icbZDLSgMxFIZPvNZ6q7p0EyxCBSkzIuhGKLpxWcFeoB1KJs20oZnMmGTEYehLuHGhiFtfx51vY9rOQlt/CHz85xxyzu/HgmvjON9oaXlldW29sFHc3Nre2S3t7Td1lCjKGjQSkWr7RDPBJWsYbgRrx4qR0Bes5Y9uJvXWI1OaR/LepDHzQjKQPOCUGGu1B5Wn0/TkyumVyk7VmQovgptDGXLVe6Wvbj+iScikoYJo3XGd2HgZUYZTwcbFbqJZTOiIDFjHoiQh01423XeMj63Tx0Gk7JMGT93fExkJtU5D33aGxAz1fG1i/lfrJCa49DIu48QwSWcfBYnAJsKT43GfK0aNSC0QqrjdFdMhUYQaG1HRhuDOn7wIzbOqa/nuvFy7zuMowCEcQQVcuIAa3EIdGkBBwDO8wht6QC/oHX3MWpdQPnMAf4Q+fwCnyI8M AAAB73icbZDLSgMxFIZPvNZ6q7p0EyxCBSkzIuhGKLpxWcFeoB1KJs20oZnMmGTEYehLuHGhiFtfx51vY9rOQlt/CHz85xxyzu/HgmvjON9oaXlldW29sFHc3Nre2S3t7Td1lCjKGjQSkWr7RDPBJWsYbgRrx4qR0Bes5Y9uJvXWI1OaR/LepDHzQjKQPOCUGGu1B5Wn0/TkyumVyk7VmQovgptDGXLVe6Wvbj+iScikoYJo3XGd2HgZUYZTwcbFbqJZTOiIDFjHoiQh01423XeMj63Tx0Gk7JMGT93fExkJtU5D33aGxAz1fG1i/lfrJCa49DIu48QwSWcfBYnAJsKT43GfK0aNSC0QqrjdFdMhUYQaG1HRhuDOn7wIzbOqa/nuvFy7zuMowCEcQQVcuIAa3EIdGkBBwDO8wht6QC/oHX3MWpdQPnMAf4Q+fwCnyI8M AAAB73icbZDLSgMxFIZPvNZ6q7p0EyxCBSkzIuhGKLpxWcFeoB1KJs20oZnMmGTEYehLuHGhiFtfx51vY9rOQlt/CHz85xxyzu/HgmvjON9oaXlldW29sFHc3Nre2S3t7Td1lCjKGjQSkWr7RDPBJWsYbgRrx4qR0Bes5Y9uJvXWI1OaR/LepDHzQjKQPOCUGGu1B5Wn0/TkyumVyk7VmQovgptDGXLVe6Wvbj+iScikoYJo3XGd2HgZUYZTwcbFbqJZTOiIDFjHoiQh01423XeMj63Tx0Gk7JMGT93fExkJtU5D33aGxAz1fG1i/lfrJCa49DIu48QwSWcfBYnAJsKT43GfK0aNSC0QqrjdFdMhUYQaG1HRhuDOn7wIzbOqa/nuvFy7zuMowCEcQQVcuIAa3EIdGkBBwDO8wht6QC/oHX3MWpdQPnMAf4Q+fwCnyI8M AAAB73icbZDLSgMxFIZPvNZ6q7p0EyxCBSkzIuhGKLpxWcFeoB1KJs20oZnMmGTEYehLuHGhiFtfx51vY9rOQlt/CHz85xxyzu/HgmvjON9oaXlldW29sFHc3Nre2S3t7Td1lCjKGjQSkWr7RDPBJWsYbgRrx4qR0Bes5Y9uJvXWI1OaR/LepDHzQjKQPOCUGGu1B5Wn0/TkyumVyk7VmQovgptDGXLVe6Wvbj+iScikoYJo3XGd2HgZUYZTwcbFbqJZTOiIDFjHoiQh01423XeMj63Tx0Gk7JMGT93fExkJtU5D33aGxAz1fG1i/lfrJCa49DIu48QwSWcfBYnAJsKT43GfK0aNSC0QqrjdFdMhUYQaG1HRhuDOn7wIzbOqa/nuvFy7zuMowCEcQQVcuIAa3EIdGkBBwDO8wht6QC/oHX3MWpdQPnMAf4Q+fwCnyI8M L(x, y, ) = f(x, y) + g(x, y) AAACEHicbVDNS8MwHE39nPOr6tFLcIgbjtGKoBdh6MWDhwnuA7Yy0izdwtK0JKlYyv4EL/4rXjwo4tWjN/8b064H3XwQeHnv90h+zw0Zlcqyvo2FxaXlldXCWnF9Y3Nr29zZbckgEpg0ccAC0XGRJIxy0lRUMdIJBUG+y0jbHV+lfvueCEkDfqfikDg+GnLqUYyUlvrm0U35oRpXe0xHBqgCL6CXCpVjmEtwmN37ZsmqWRngPLFzUgI5Gn3zqzcIcOQTrjBDUnZtK1ROgoSimJFJsRdJEiI8RkPS1ZQjn0gnyRaawEOtDKAXCH24gpn6O5EgX8rYd/Wkj9RIznqp+J/XjZR37iSUh5EiHE8f8iIGVQDTduCACoIVizVBWFD9V4hHSCCsdIdFXYI9u/I8aZ3UbM1vT0v1y7yOAtgHB6AMbHAG6uAaNEATYPAInsEreDOejBfj3fiYji4YeWYP/IHx+QMoupoi AAACEHicbVDNS8MwHE39nPOr6tFLcIgbjtGKoBdh6MWDhwnuA7Yy0izdwtK0JKlYyv4EL/4rXjwo4tWjN/8b064H3XwQeHnv90h+zw0Zlcqyvo2FxaXlldXCWnF9Y3Nr29zZbckgEpg0ccAC0XGRJIxy0lRUMdIJBUG+y0jbHV+lfvueCEkDfqfikDg+GnLqUYyUlvrm0U35oRpXe0xHBqgCL6CXCpVjmEtwmN37ZsmqWRngPLFzUgI5Gn3zqzcIcOQTrjBDUnZtK1ROgoSimJFJsRdJEiI8RkPS1ZQjn0gnyRaawEOtDKAXCH24gpn6O5EgX8rYd/Wkj9RIznqp+J/XjZR37iSUh5EiHE8f8iIGVQDTduCACoIVizVBWFD9V4hHSCCsdIdFXYI9u/I8aZ3UbM1vT0v1y7yOAtgHB6AMbHAG6uAaNEATYPAInsEreDOejBfj3fiYji4YeWYP/IHx+QMoupoi AAACEHicbVDNS8MwHE39nPOr6tFLcIgbjtGKoBdh6MWDhwnuA7Yy0izdwtK0JKlYyv4EL/4rXjwo4tWjN/8b064H3XwQeHnv90h+zw0Zlcqyvo2FxaXlldXCWnF9Y3Nr29zZbckgEpg0ccAC0XGRJIxy0lRUMdIJBUG+y0jbHV+lfvueCEkDfqfikDg+GnLqUYyUlvrm0U35oRpXe0xHBqgCL6CXCpVjmEtwmN37ZsmqWRngPLFzUgI5Gn3zqzcIcOQTrjBDUnZtK1ROgoSimJFJsRdJEiI8RkPS1ZQjn0gnyRaawEOtDKAXCH24gpn6O5EgX8rYd/Wkj9RIznqp+J/XjZR37iSUh5EiHE8f8iIGVQDTduCACoIVizVBWFD9V4hHSCCsdIdFXYI9u/I8aZ3UbM1vT0v1y7yOAtgHB6AMbHAG6uAaNEATYPAInsEreDOejBfj3fiYji4YeWYP/IHx+QMoupoi AAACEHicbVDNS8MwHE39nPOr6tFLcIgbjtGKoBdh6MWDhwnuA7Yy0izdwtK0JKlYyv4EL/4rXjwo4tWjN/8b064H3XwQeHnv90h+zw0Zlcqyvo2FxaXlldXCWnF9Y3Nr29zZbckgEpg0ccAC0XGRJIxy0lRUMdIJBUG+y0jbHV+lfvueCEkDfqfikDg+GnLqUYyUlvrm0U35oRpXe0xHBqgCL6CXCpVjmEtwmN37ZsmqWRngPLFzUgI5Gn3zqzcIcOQTrjBDUnZtK1ROgoSimJFJsRdJEiI8RkPS1ZQjn0gnyRaawEOtDKAXCH24gpn6O5EgX8rYd/Wkj9RIznqp+J/XjZR37iSUh5EiHE8f8iIGVQDTduCACoIVizVBWFD9V4hHSCCsdIdFXYI9u/I8aZ3UbM1vT0v1y7yOAtgHB6AMbHAG6uAaNEATYPAInsEreDOejBfj3fiYji4YeWYP/IHx+QMoupoi Minimize Subject to ͜ΕΛղ͘ʹ͸ ͱ͓͍ͯ Λղ͚͹Α͍ rL = 0 AAAB8XicbZA9SwNBEIbn4leMX1FLm8UgWIU7EbQRgjYWFhHMByZHmNvsJUv29o7dPSEc+Rc2ForY+m/s/Ddukis08YWFh3dm2Jk3SATXxnW/ncLK6tr6RnGztLW9s7tX3j9o6jhVlDVoLGLVDlAzwSVrGG4EayeKYRQI1gpGN9N664kpzWP5YMYJ8yMcSB5yisZaj12JgUByd+X2yhW36s5ElsHLoQK56r3yV7cf0zRi0lCBWnc8NzF+hspwKtik1E01S5COcMA6FiVGTPvZbOMJObFOn4Sxsk8aMnN/T2QYaT2OAtsZoRnqxdrU/K/WSU146WdcJqlhks4/ClNBTEym55M+V4waMbaAVHG7K6FDVEiNDalkQ/AWT16G5lnVs3x/Xqld53EU4QiO4RQ8uIAa3EIdGkBBwjO8wpujnRfn3fmYtxacfOYQ/sj5/AFmwZAR AAAB8XicbZA9SwNBEIbn4leMX1FLm8UgWIU7EbQRgjYWFhHMByZHmNvsJUv29o7dPSEc+Rc2ForY+m/s/Ddukis08YWFh3dm2Jk3SATXxnW/ncLK6tr6RnGztLW9s7tX3j9o6jhVlDVoLGLVDlAzwSVrGG4EayeKYRQI1gpGN9N664kpzWP5YMYJ8yMcSB5yisZaj12JgUByd+X2yhW36s5ElsHLoQK56r3yV7cf0zRi0lCBWnc8NzF+hspwKtik1E01S5COcMA6FiVGTPvZbOMJObFOn4Sxsk8aMnN/T2QYaT2OAtsZoRnqxdrU/K/WSU146WdcJqlhks4/ClNBTEym55M+V4waMbaAVHG7K6FDVEiNDalkQ/AWT16G5lnVs3x/Xqld53EU4QiO4RQ8uIAa3EIdGkBBwjO8wpujnRfn3fmYtxacfOYQ/sj5/AFmwZAR AAAB8XicbZA9SwNBEIbn4leMX1FLm8UgWIU7EbQRgjYWFhHMByZHmNvsJUv29o7dPSEc+Rc2ForY+m/s/Ddukis08YWFh3dm2Jk3SATXxnW/ncLK6tr6RnGztLW9s7tX3j9o6jhVlDVoLGLVDlAzwSVrGG4EayeKYRQI1gpGN9N664kpzWP5YMYJ8yMcSB5yisZaj12JgUByd+X2yhW36s5ElsHLoQK56r3yV7cf0zRi0lCBWnc8NzF+hspwKtik1E01S5COcMA6FiVGTPvZbOMJObFOn4Sxsk8aMnN/T2QYaT2OAtsZoRnqxdrU/K/WSU146WdcJqlhks4/ClNBTEym55M+V4waMbaAVHG7K6FDVEiNDalkQ/AWT16G5lnVs3x/Xqld53EU4QiO4RQ8uIAa3EIdGkBBwjO8wpujnRfn3fmYtxacfOYQ/sj5/AFmwZAR AAAB8XicbZA9SwNBEIbn4leMX1FLm8UgWIU7EbQRgjYWFhHMByZHmNvsJUv29o7dPSEc+Rc2ForY+m/s/Ddukis08YWFh3dm2Jk3SATXxnW/ncLK6tr6RnGztLW9s7tX3j9o6jhVlDVoLGLVDlAzwSVrGG4EayeKYRQI1gpGN9N664kpzWP5YMYJ8yMcSB5yisZaj12JgUByd+X2yhW36s5ElsHLoQK56r3yV7cf0zRi0lCBWnc8NzF+hspwKtik1E01S5COcMA6FiVGTPvZbOMJObFOn4Sxsk8aMnN/T2QYaT2OAtsZoRnqxdrU/K/WSU146WdcJqlhks4/ClNBTEym55M+V4waMbaAVHG7K6FDVEiNDalkQ/AWT16G5lnVs3x/Xqld53EU4QiO4RQ8uIAa3EIdGkBBwjO8wpujnRfn3fmYtxacfOYQ/sj5/AFmwZAR

Slide 40

Slide 40 text

rf = rg AAACBXicbVDLSsNAFJ3UV62vqEtdDBbBjSURQTdC0Y3LCvYBTSg3k0k7dDIJMxOhhG7c+CtuXCji1n9w5984bbPQ1gMDh3Pu4c49QcqZ0o7zbZWWlldW18rrlY3Nre0de3evpZJMEtokCU9kJwBFORO0qZnmtJNKCnHAaTsY3kz89gOViiXiXo9S6sfQFyxiBLSRevahJyDggCN8dYo9boIh4ELr9+yqU3OmwIvELUgVFWj07C8vTEgWU6EJB6W6rpNqPwepGeF0XPEyRVMgQ+jTrqECYqr8fHrFGB8bJcRRIs0TGk/V34kcYqVGcWAmY9ADNe9NxP+8bqajSz9nIs00FWS2KMo41gmeVIJDJinRfGQIEMnMXzEZgASiTXEVU4I7f/IiaZ3VXMPvzqv166KOMjpAR+gEuegC1dEtaqAmIugRPaNX9GY9WS/Wu/UxGy1ZRWYf/YH1+QMfA5cL AAACBXicbVDLSsNAFJ3UV62vqEtdDBbBjSURQTdC0Y3LCvYBTSg3k0k7dDIJMxOhhG7c+CtuXCji1n9w5984bbPQ1gMDh3Pu4c49QcqZ0o7zbZWWlldW18rrlY3Nre0de3evpZJMEtokCU9kJwBFORO0qZnmtJNKCnHAaTsY3kz89gOViiXiXo9S6sfQFyxiBLSRevahJyDggCN8dYo9boIh4ELr9+yqU3OmwIvELUgVFWj07C8vTEgWU6EJB6W6rpNqPwepGeF0XPEyRVMgQ+jTrqECYqr8fHrFGB8bJcRRIs0TGk/V34kcYqVGcWAmY9ADNe9NxP+8bqajSz9nIs00FWS2KMo41gmeVIJDJinRfGQIEMnMXzEZgASiTXEVU4I7f/IiaZ3VXMPvzqv166KOMjpAR+gEuegC1dEtaqAmIugRPaNX9GY9WS/Wu/UxGy1ZRWYf/YH1+QMfA5cL AAACBXicbVDLSsNAFJ3UV62vqEtdDBbBjSURQTdC0Y3LCvYBTSg3k0k7dDIJMxOhhG7c+CtuXCji1n9w5984bbPQ1gMDh3Pu4c49QcqZ0o7zbZWWlldW18rrlY3Nre0de3evpZJMEtokCU9kJwBFORO0qZnmtJNKCnHAaTsY3kz89gOViiXiXo9S6sfQFyxiBLSRevahJyDggCN8dYo9boIh4ELr9+yqU3OmwIvELUgVFWj07C8vTEgWU6EJB6W6rpNqPwepGeF0XPEyRVMgQ+jTrqECYqr8fHrFGB8bJcRRIs0TGk/V34kcYqVGcWAmY9ADNe9NxP+8bqajSz9nIs00FWS2KMo41gmeVIJDJinRfGQIEMnMXzEZgASiTXEVU4I7f/IiaZ3VXMPvzqv166KOMjpAR+gEuegC1dEtaqAmIugRPaNX9GY9WS/Wu/UxGy1ZRWYf/YH1+QMfA5cL AAACBXicbVDLSsNAFJ3UV62vqEtdDBbBjSURQTdC0Y3LCvYBTSg3k0k7dDIJMxOhhG7c+CtuXCji1n9w5984bbPQ1gMDh3Pu4c49QcqZ0o7zbZWWlldW18rrlY3Nre0de3evpZJMEtokCU9kJwBFORO0qZnmtJNKCnHAaTsY3kz89gOViiXiXo9S6sfQFyxiBLSRevahJyDggCN8dYo9boIh4ELr9+yqU3OmwIvELUgVFWj07C8vTEgWU6EJB6W6rpNqPwepGeF0XPEyRVMgQ+jTrqECYqr8fHrFGB8bJcRRIs0TGk/V34kcYqVGcWAmY9ADNe9NxP+8bqajSz9nIs00FWS2KMo41gmeVIJDJinRfGQIEMnMXzEZgASiTXEVU4I7f/IiaZ3VXMPvzqv166KOMjpAR+gEuegC1dEtaqAmIugRPaNX9GY9WS/Wu/UxGy1ZRWYf/YH1+QMfA5cL g = 0 AAAB6nicbZBNS8NAEIYn9avWr6pHL4tF8FQSEfQiFL14rGhtoQ1ls92kSzebsDsRSuhP8OJBEa/+Im/+G7dtDtr6wsLDOzPszBukUhh03W+ntLK6tr5R3qxsbe/s7lX3Dx5NkmnGWyyRie4E1HApFG+hQMk7qeY0DiRvB6Obab39xLURiXrAccr9mEZKhIJRtNZ9dOX2qzW37s5ElsEroAaFmv3qV2+QsCzmCpmkxnQ9N0U/pxoFk3xS6WWGp5SNaMS7FhWNufHz2aoTcmKdAQkTbZ9CMnN/T+Q0NmYcB7Yzpjg0i7Wp+V+tm2F46edCpRlyxeYfhZkkmJDp3WQgNGcoxxYo08LuStiQasrQplOxIXiLJy/D41nds3x3XmtcF3GU4QiO4RQ8uIAG3EITWsAggmd4hTdHOi/Ou/Mxby05xcwh/JHz+QO8j41s AAAB6nicbZBNS8NAEIYn9avWr6pHL4tF8FQSEfQiFL14rGhtoQ1ls92kSzebsDsRSuhP8OJBEa/+Im/+G7dtDtr6wsLDOzPszBukUhh03W+ntLK6tr5R3qxsbe/s7lX3Dx5NkmnGWyyRie4E1HApFG+hQMk7qeY0DiRvB6Obab39xLURiXrAccr9mEZKhIJRtNZ9dOX2qzW37s5ElsEroAaFmv3qV2+QsCzmCpmkxnQ9N0U/pxoFk3xS6WWGp5SNaMS7FhWNufHz2aoTcmKdAQkTbZ9CMnN/T+Q0NmYcB7Yzpjg0i7Wp+V+tm2F46edCpRlyxeYfhZkkmJDp3WQgNGcoxxYo08LuStiQasrQplOxIXiLJy/D41nds3x3XmtcF3GU4QiO4RQ8uIAG3EITWsAggmd4hTdHOi/Ou/Mxby05xcwh/JHz+QO8j41s 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AAAB6nicbZBNS8NAEIYn9avWr6pHL4tF8CAlEUGPRS8eK9oPaEPZbCft0s0m7G7EEvoTvHhQxKu/yJv/xm2bg7a+sPDwzgw78waJ4Nq47rdTWFldW98obpa2tnd298r7B00dp4phg8UiVu2AahRcYsNwI7CdKKRRILAVjG6m9dYjKs1j+WDGCfoRHUgeckaNte6fzsa9csWtujORZfByqECueq/81e3HLI1QGiao1h3PTYyfUWU4EzgpdVONCWUjOsCORUkj1H42W3VCTqzTJ2Gs7JOGzNzfExmNtB5Hge2MqBnqxdrU/K/WSU145WdcJqlByeYfhakgJibTu0mfK2RGjC1QprjdlbAhVZQZm07JhuAtnrwMzfOqZ/nuolK7zuMowhEcwyl4cAk1uIU6NIDBAJ7hFd4c4bw4787HvLXg5DOH8EfO5w8rU421 AAAB6nicbZBNS8NAEIYn9avWr6pHL4tF8CAlEUGPRS8eK9oPaEPZbCft0s0m7G7EEvoTvHhQxKu/yJv/xm2bg7a+sPDwzgw78waJ4Nq47rdTWFldW98obpa2tnd298r7B00dp4phg8UiVu2AahRcYsNwI7CdKKRRILAVjG6m9dYjKs1j+WDGCfoRHUgeckaNte6fzsa9csWtujORZfByqECueq/81e3HLI1QGiao1h3PTYyfUWU4EzgpdVONCWUjOsCORUkj1H42W3VCTqzTJ2Gs7JOGzNzfExmNtB5Hge2MqBnqxdrU/K/WSU145WdcJqlByeYfhakgJibTu0mfK2RGjC1QprjdlbAhVZQZm07JhuAtnrwMzfOqZ/nuolK7zuMowhEcwyl4cAk1uIU6NIDBAJ7hFd4c4bw4787HvLXg5DOH8EfO5w8rU421 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AAAB7nicbVDLSsNAFL2pr1pfVZduBovgqiQi1GXRjcsK9gFtKDeTSTt0MgkzE6GEfoQbF4q49Xvc+TdO2yy09cDA4ZxzmXtPkAqujet+O6WNza3tnfJuZW//4PCoenzS0UmmKGvTRCSqF6BmgkvWNtwI1ksVwzgQrBtM7uZ+94kpzRP5aKYp82McSR5xisZK3YGw0RCH1Zpbdxcg68QrSA0KtIbVr0GY0Cxm0lCBWvc9NzV+jspwKtisMsg0S5FOcMT6lkqMmfbzxbozcmGVkESJsk8aslB/T+QYaz2NA5uM0Yz1qjcX//P6mYlu/JzLNDNM0uVHUSaIScj8dhJyxagRU0uQKm53JXSMCqmxDVVsCd7qyeukc1X3LH+4rjVvizrKcAbncAkeNKAJ99CCNlCYwDO8wpuTOi/Ou/OxjJacYuYU/sD5/AE8x499 AAAB7nicbVDLSsNAFL2pr1pfVZduBovgqiQi1GXRjcsK9gFtKDeTSTt0MgkzE6GEfoQbF4q49Xvc+TdO2yy09cDA4ZxzmXtPkAqujet+O6WNza3tnfJuZW//4PCoenzS0UmmKGvTRCSqF6BmgkvWNtwI1ksVwzgQrBtM7uZ+94kpzRP5aKYp82McSR5xisZK3YGw0RCH1Zpbdxcg68QrSA0KtIbVr0GY0Cxm0lCBWvc9NzV+jspwKtisMsg0S5FOcMT6lkqMmfbzxbozcmGVkESJsk8aslB/T+QYaz2NA5uM0Yz1qjcX//P6mYlu/JzLNDNM0uVHUSaIScj8dhJyxagRU0uQKm53JXSMCqmxDVVsCd7qyeukc1X3LH+4rjVvizrKcAbncAkeNKAJ99CCNlCYwDO8wpuTOi/Ou/OxjJacYuYU/sD5/AE8x499 ɹʹ͍ͭͯͷภඍ෼ΑΓ ɹʹ͍ͭͯͷภඍ෼ΑΓ L(x, y, ) = f(x, y) + g(x, y) AAACEHicbVDNS8MwHE39nPOr6tFLcIgbjtGKoBdh6MWDhwnuA7Yy0izdwtK0JKlYyv4EL/4rXjwo4tWjN/8b064H3XwQeHnv90h+zw0Zlcqyvo2FxaXlldXCWnF9Y3Nr29zZbckgEpg0ccAC0XGRJIxy0lRUMdIJBUG+y0jbHV+lfvueCEkDfqfikDg+GnLqUYyUlvrm0U35oRpXe0xHBqgCL6CXCpVjmEtwmN37ZsmqWRngPLFzUgI5Gn3zqzcIcOQTrjBDUnZtK1ROgoSimJFJsRdJEiI8RkPS1ZQjn0gnyRaawEOtDKAXCH24gpn6O5EgX8rYd/Wkj9RIznqp+J/XjZR37iSUh5EiHE8f8iIGVQDTduCACoIVizVBWFD9V4hHSCCsdIdFXYI9u/I8aZ3UbM1vT0v1y7yOAtgHB6AMbHAG6uAaNEATYPAInsEreDOejBfj3fiYji4YeWYP/IHx+QMoupoi AAACEHicbVDNS8MwHE39nPOr6tFLcIgbjtGKoBdh6MWDhwnuA7Yy0izdwtK0JKlYyv4EL/4rXjwo4tWjN/8b064H3XwQeHnv90h+zw0Zlcqyvo2FxaXlldXCWnF9Y3Nr29zZbckgEpg0ccAC0XGRJIxy0lRUMdIJBUG+y0jbHV+lfvueCEkDfqfikDg+GnLqUYyUlvrm0U35oRpXe0xHBqgCL6CXCpVjmEtwmN37ZsmqWRngPLFzUgI5Gn3zqzcIcOQTrjBDUnZtK1ROgoSimJFJsRdJEiI8RkPS1ZQjn0gnyRaawEOtDKAXCH24gpn6O5EgX8rYd/Wkj9RIznqp+J/XjZR37iSUh5EiHE8f8iIGVQDTduCACoIVizVBWFD9V4hHSCCsdIdFXYI9u/I8aZ3UbM1vT0v1y7yOAtgHB6AMbHAG6uAaNEATYPAInsEreDOejBfj3fiYji4YeWYP/IHx+QMoupoi AAACEHicbVDNS8MwHE39nPOr6tFLcIgbjtGKoBdh6MWDhwnuA7Yy0izdwtK0JKlYyv4EL/4rXjwo4tWjN/8b064H3XwQeHnv90h+zw0Zlcqyvo2FxaXlldXCWnF9Y3Nr29zZbckgEpg0ccAC0XGRJIxy0lRUMdIJBUG+y0jbHV+lfvueCEkDfqfikDg+GnLqUYyUlvrm0U35oRpXe0xHBqgCL6CXCpVjmEtwmN37ZsmqWRngPLFzUgI5Gn3zqzcIcOQTrjBDUnZtK1ROgoSimJFJsRdJEiI8RkPS1ZQjn0gnyRaawEOtDKAXCH24gpn6O5EgX8rYd/Wkj9RIznqp+J/XjZR37iSUh5EiHE8f8iIGVQDTduCACoIVizVBWFD9V4hHSCCsdIdFXYI9u/I8aZ3UbM1vT0v1y7yOAtgHB6AMbHAG6uAaNEATYPAInsEreDOejBfj3fiYji4YeWYP/IHx+QMoupoi AAACEHicbVDNS8MwHE39nPOr6tFLcIgbjtGKoBdh6MWDhwnuA7Yy0izdwtK0JKlYyv4EL/4rXjwo4tWjN/8b064H3XwQeHnv90h+zw0Zlcqyvo2FxaXlldXCWnF9Y3Nr29zZbckgEpg0ccAC0XGRJIxy0lRUMdIJBUG+y0jbHV+lfvueCEkDfqfikDg+GnLqUYyUlvrm0U35oRpXe0xHBqgCL6CXCpVjmEtwmN37ZsmqWRngPLFzUgI5Gn3zqzcIcOQTrjBDUnZtK1ROgoSimJFJsRdJEiI8RkPS1ZQjn0gnyRaawEOtDKAXCH24gpn6O5EgX8rYd/Wkj9RIznqp+J/XjZR37iSUh5EiHE8f8iIGVQDTduCACoIVizVBWFD9V4hHSCCsdIdFXYI9u/I8aZ3UbM1vT0v1y7yOAtgHB6AMbHAG6uAaNEATYPAInsEreDOejBfj3fiYji4YeWYP/IHx+QMoupoi ੍໿ࣜͷ๏ઢͱ౳ߴઢͷ๏ઢ͕ฏߦͱ͍͏৚݅ ݩͷ੍໿ f(x, y) = 5x2 + 6xy + 5y2 26x 26y g(x, y) = x2 + y2 4 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 ྫɿ

Slide 41

Slide 41 text

ϥάϥϯδϡະఆ৐਺๏ ʢෆ౳੍ࣜ໿ʣ f(x, y) AAAB7XicbZDLSgMxFIbP1Futt6pLN8EiVJAyI4Iui25cVrAXaIeSSTNtbCYZkow4DH0HNy4Ucev7uPNtTNtZaOsPgY//nEPO+YOYM21c99sprKyurW8UN0tb2zu7e+X9g5aWiSK0SSSXqhNgTTkTtGmY4bQTK4qjgNN2ML6Z1tuPVGkmxb1JY+pHeChYyAg21mqF1aez9LRfrrg1dya0DF4OFcjV6Je/egNJkogKQzjWuuu5sfEzrAwjnE5KvUTTGJMxHtKuRYEjqv1stu0EnVhngEKp7BMGzdzfExmOtE6jwHZG2Iz0Ym1q/lfrJia88jMm4sRQQeYfhQlHRqLp6WjAFCWGpxYwUczuisgIK0yMDahkQ/AWT16G1nnNs3x3Ualf53EU4QiOoQoeXEIdbqEBTSDwAM/wCm+OdF6cd+dj3lpw8plD+CPn8wezN46K AAAB7XicbZDLSgMxFIbP1Futt6pLN8EiVJAyI4Iui25cVrAXaIeSSTNtbCYZkow4DH0HNy4Ucev7uPNtTNtZaOsPgY//nEPO+YOYM21c99sprKyurW8UN0tb2zu7e+X9g5aWiSK0SSSXqhNgTTkTtGmY4bQTK4qjgNN2ML6Z1tuPVGkmxb1JY+pHeChYyAg21mqF1aez9LRfrrg1dya0DF4OFcjV6Je/egNJkogKQzjWuuu5sfEzrAwjnE5KvUTTGJMxHtKuRYEjqv1stu0EnVhngEKp7BMGzdzfExmOtE6jwHZG2Iz0Ym1q/lfrJia88jMm4sRQQeYfhQlHRqLp6WjAFCWGpxYwUczuisgIK0yMDahkQ/AWT16G1nnNs3x3Ualf53EU4QiOoQoeXEIdbqEBTSDwAM/wCm+OdF6cd+dj3lpw8plD+CPn8wezN46K 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AAAB7XicbZDLSgMxFIbP1Futt6pLN8EiVJAyI4Iui25cVrAXaIeSSTNtbCYZkow4DH0HNy4Ucev7uPNtTNtZaOsPgY//nEPO+YOYM21c99sprKyurW8UN0tb2zu7e+X9g5aWiSK0SSSXqhNgTTkTtGmY4bQTK4qjgNN2ML6Z1tuPVGkmxb1JY+pHeChYyAg21mqF1aez9LRfrrg1dya0DF4OFcjV6Je/egNJkogKQzjWuuu5sfEzrAwjnE5KvUTTGJMxHtKuRYEjqv1stu0EnVhngEKp7BMGzdzfExmOtE6jwHZG2Iz0Ym1q/lfrJia88jMm4sRQQeYfhQlHRqLp6WjAFCWGpxYwUczuisgIK0yMDahkQ/AWT16G1nnNs3x3Ualf53EU4QiOoQoeXEIdbqEBTSDwAM/wCm+OdF6cd+dj3lpw8plD+CPn8wezN46K L(x, y, ) = f(x, y) + g(x, y) AAACEHicbVDNS8MwHE39nPOr6tFLcIgbjtGKoBdh6MWDhwnuA7Yy0izdwtK0JKlYyv4EL/4rXjwo4tWjN/8b064H3XwQeHnv90h+zw0Zlcqyvo2FxaXlldXCWnF9Y3Nr29zZbckgEpg0ccAC0XGRJIxy0lRUMdIJBUG+y0jbHV+lfvueCEkDfqfikDg+GnLqUYyUlvrm0U35oRpXe0xHBqgCL6CXCpVjmEtwmN37ZsmqWRngPLFzUgI5Gn3zqzcIcOQTrjBDUnZtK1ROgoSimJFJsRdJEiI8RkPS1ZQjn0gnyRaawEOtDKAXCH24gpn6O5EgX8rYd/Wkj9RIznqp+J/XjZR37iSUh5EiHE8f8iIGVQDTduCACoIVizVBWFD9V4hHSCCsdIdFXYI9u/I8aZ3UbM1vT0v1y7yOAtgHB6AMbHAG6uAaNEATYPAInsEreDOejBfj3fiYji4YeWYP/IHx+QMoupoi AAACEHicbVDNS8MwHE39nPOr6tFLcIgbjtGKoBdh6MWDhwnuA7Yy0izdwtK0JKlYyv4EL/4rXjwo4tWjN/8b064H3XwQeHnv90h+zw0Zlcqyvo2FxaXlldXCWnF9Y3Nr29zZbckgEpg0ccAC0XGRJIxy0lRUMdIJBUG+y0jbHV+lfvueCEkDfqfikDg+GnLqUYyUlvrm0U35oRpXe0xHBqgCL6CXCpVjmEtwmN37ZsmqWRngPLFzUgI5Gn3zqzcIcOQTrjBDUnZtK1ROgoSimJFJsRdJEiI8RkPS1ZQjn0gnyRaawEOtDKAXCH24gpn6O5EgX8rYd/Wkj9RIznqp+J/XjZR37iSUh5EiHE8f8iIGVQDTduCACoIVizVBWFD9V4hHSCCsdIdFXYI9u/I8aZ3UbM1vT0v1y7yOAtgHB6AMbHAG6uAaNEATYPAInsEreDOejBfj3fiYji4YeWYP/IHx+QMoupoi AAACEHicbVDNS8MwHE39nPOr6tFLcIgbjtGKoBdh6MWDhwnuA7Yy0izdwtK0JKlYyv4EL/4rXjwo4tWjN/8b064H3XwQeHnv90h+zw0Zlcqyvo2FxaXlldXCWnF9Y3Nr29zZbckgEpg0ccAC0XGRJIxy0lRUMdIJBUG+y0jbHV+lfvueCEkDfqfikDg+GnLqUYyUlvrm0U35oRpXe0xHBqgCL6CXCpVjmEtwmN37ZsmqWRngPLFzUgI5Gn3zqzcIcOQTrjBDUnZtK1ROgoSimJFJsRdJEiI8RkPS1ZQjn0gnyRaawEOtDKAXCH24gpn6O5EgX8rYd/Wkj9RIznqp+J/XjZR37iSUh5EiHE8f8iIGVQDTduCACoIVizVBWFD9V4hHSCCsdIdFXYI9u/I8aZ3UbM1vT0v1y7yOAtgHB6AMbHAG6uAaNEATYPAInsEreDOejBfj3fiYji4YeWYP/IHx+QMoupoi AAACEHicbVDNS8MwHE39nPOr6tFLcIgbjtGKoBdh6MWDhwnuA7Yy0izdwtK0JKlYyv4EL/4rXjwo4tWjN/8b064H3XwQeHnv90h+zw0Zlcqyvo2FxaXlldXCWnF9Y3Nr29zZbckgEpg0ccAC0XGRJIxy0lRUMdIJBUG+y0jbHV+lfvueCEkDfqfikDg+GnLqUYyUlvrm0U35oRpXe0xHBqgCL6CXCpVjmEtwmN37ZsmqWRngPLFzUgI5Gn3zqzcIcOQTrjBDUnZtK1ROgoSimJFJsRdJEiI8RkPS1ZQjn0gnyRaawEOtDKAXCH24gpn6O5EgX8rYd/Wkj9RIznqp+J/XjZR37iSUh5EiHE8f8iIGVQDTduCACoIVizVBWFD9V4hHSCCsdIdFXYI9u/I8aZ3UbM1vT0v1y7yOAtgHB6AMbHAG6uAaNEATYPAInsEreDOejBfj3fiYji4YeWYP/IHx+QMoupoi Minimize Subject to ͜ΕΛղ͘ʹ͸ ͱ͓͍ͯ Λղ͚͹Α͍ g(x, y)  0 AAAB83icbZDLSgNBEEVr4ivGV9Slm8YgRJAwI4Iug25cRjAPyAyhp1OTNOl52N0jhiG/4caFIm79GXf+jZ1kFpp4oeFwq4qqvn4iuNK2/W0VVlbX1jeKm6Wt7Z3dvfL+QUvFqWTYZLGIZcenCgWPsKm5FthJJNLQF9j2RzfTevsRpeJxdK/HCXohHUQ84IxqY7mD6tPZ+NQV+EDsXrli1+yZyDI4OVQgV6NX/nL7MUtDjDQTVKmuYyfay6jUnAmclNxUYULZiA6wazCiISovm908ISfG6ZMgluZFmszc3xMZDZUah77pDKkeqsXa1Pyv1k11cOVlPEpSjRGbLwpSQXRMpgGQPpfItBgboExycythQyop0yamkgnBWfzyMrTOa47hu4tK/TqPowhHcAxVcOAS6nALDWgCgwSe4RXerNR6sd6tj3lrwcpnDuGPrM8fkBGQtQ== AAAB83icbZDLSgNBEEVr4ivGV9Slm8YgRJAwI4Iug25cRjAPyAyhp1OTNOl52N0jhiG/4caFIm79GXf+jZ1kFpp4oeFwq4qqvn4iuNK2/W0VVlbX1jeKm6Wt7Z3dvfL+QUvFqWTYZLGIZcenCgWPsKm5FthJJNLQF9j2RzfTevsRpeJxdK/HCXohHUQ84IxqY7mD6tPZ+NQV+EDsXrli1+yZyDI4OVQgV6NX/nL7MUtDjDQTVKmuYyfay6jUnAmclNxUYULZiA6wazCiISovm908ISfG6ZMgluZFmszc3xMZDZUah77pDKkeqsXa1Pyv1k11cOVlPEpSjRGbLwpSQXRMpgGQPpfItBgboExycythQyop0yamkgnBWfzyMrTOa47hu4tK/TqPowhHcAxVcOAS6nALDWgCgwSe4RXerNR6sd6tj3lrwcpnDuGPrM8fkBGQtQ== AAAB83icbZDLSgNBEEVr4ivGV9Slm8YgRJAwI4Iug25cRjAPyAyhp1OTNOl52N0jhiG/4caFIm79GXf+jZ1kFpp4oeFwq4qqvn4iuNK2/W0VVlbX1jeKm6Wt7Z3dvfL+QUvFqWTYZLGIZcenCgWPsKm5FthJJNLQF9j2RzfTevsRpeJxdK/HCXohHUQ84IxqY7mD6tPZ+NQV+EDsXrli1+yZyDI4OVQgV6NX/nL7MUtDjDQTVKmuYyfay6jUnAmclNxUYULZiA6wazCiISovm908ISfG6ZMgluZFmszc3xMZDZUah77pDKkeqsXa1Pyv1k11cOVlPEpSjRGbLwpSQXRMpgGQPpfItBgboExycythQyop0yamkgnBWfzyMrTOa47hu4tK/TqPowhHcAxVcOAS6nALDWgCgwSe4RXerNR6sd6tj3lrwcpnDuGPrM8fkBGQtQ== AAAB83icbZDLSgNBEEVr4ivGV9Slm8YgRJAwI4Iug25cRjAPyAyhp1OTNOl52N0jhiG/4caFIm79GXf+jZ1kFpp4oeFwq4qqvn4iuNK2/W0VVlbX1jeKm6Wt7Z3dvfL+QUvFqWTYZLGIZcenCgWPsKm5FthJJNLQF9j2RzfTevsRpeJxdK/HCXohHUQ84IxqY7mD6tPZ+NQV+EDsXrli1+yZyDI4OVQgV6NX/nL7MUtDjDQTVKmuYyfay6jUnAmclNxUYULZiA6wazCiISovm908ISfG6ZMgluZFmszc3xMZDZUah77pDKkeqsXa1Pyv1k11cOVlPEpSjRGbLwpSQXRMpgGQPpfItBgboExycythQyop0yamkgnBWfzyMrTOa47hu4tK/TqPowhHcAxVcOAS6nALDWgCgwSe4RXerNR6sd6tj3lrwcpnDuGPrM8fkBGQtQ== KKT৚݅ͱݺ͹ΕΔ rL(x, y, ) = 0 g(x, y) = 0 0 g(x, y)  0 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

Slide 42

Slide 42 text

f(x, y) = 5x2 + 6xy + 5y2 26x 26y g(x, y) = x2 + y2 4 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Slide 43

Slide 43 text

ϥάϥϯδϡະఆ৐਺๏ ʢҰൠͷ৔߹ʣ Minimize f(x) Subject to g1(x) = 0 g2(x) = 0 . . . gl(x) = 0 h1(x)  0 h2(x)  0 . . . hm(x)  0 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 L(x, , µ) =f(x) + 1g1(x) + 2g2(x) + · · · + lgl(x) + µ1h1(x) + µ2h2(x) + · · · + µ1h1(x) AAACtXicbZHfSuQwFMbTqqt23XXUS2+Cw4riIu0g6I0geqPghf9GhWkpaZrOBJOmJKk4lD6aD+Klb+KZsYIz44HSr7/vOyflJCkEN9b33xx3bn7h1+LSsvd75c/f1dba+r1RpaasS5VQ+jEhhgmes67lVrDHQjMiE8Eekqezkf/wzLThKr+zw4JFkvRznnFKLKC49Xq5Eyayeqn/j16hgM6UNB+yrHePt72sSezueY0fB7gfB7O4A7jzDdNUWePtfdkCbPFlh6G3DRFZwrDBxDBAHUA/DZpOx622v++PC8+KoBFt1NRV3HoPU0VLyXJLBTGmF/iFjSqiLaeC1V5YGlYQ+kT6rAcyJ5KZqBqvucb/gKQ4Uxqe3OIx/d5REWnMUCaQlMQOzLQ3gj95vdJmR1HF86K0LKefB2WlwFbh0Z3hlGtGrRiCIFRz+FdMB0QTauFmJ05JZA07CaY3MCvuO/sB6OuD9slps50ltIm20A4K0CE6QefoCnURddrOhXPj3LqHbuSmbvYZdZ2mZwNNlKs+AHr60J4= 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 rL(x, , µ) = 0, µ1h1(x) = 0, µ2h2(x) = 0, . . . , µlhl(x) = 0, µ1 0, µ2 0, . . . , µl 0, h1(x)  0, h2(x)  0, . . . , hm(x)  0 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 ໰୊ ϥάϥϯδϡؔ਺ ৚݅ ʢؔ਺͸͢΂ͯͳΊΒ͔ͱԾఆʣ

Slide 44

Slide 44 text

αϙʔτϕΫλϚγϯ ʢSVMʣ ͜͜Ͱѻ͏ͷ͸௚ઢͰ׬શʹ෼ྨՄೳͳ৔߹ʢͦΕҎ֎ͷέʔε͸ॻ੶ࢀরʣ ༩͑ΒΕͨ2छྨͷ఺ྻΛ෼ྨ͍ͨ͠ ʢڭࢣ͋Γֶशʣ ೖྗσʔλ X = 0 B B B @ xT 1 xT 2 . . . xT n 1 C C C A 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 y = 0 B B B @ y1 y2 . . . yn 1 C C C A 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 ఺ྻ ϥϕϧ yi = 1 or 1 AAACDHicbZDLSsNAFIYn9VbrLV52bgaL4MaSiKAboejGZQV7gTaEyXTSDp1cmDkRY8gr+Axude1O3PoOLn0Tp20WtvWsPv7/HP7D78WCK7Csb6O0tLyyulZer2xsbm3vmLt7LRUlkrImjUQkOx5RTPCQNYGDYJ1YMhJ4grW90c3Ybz8wqXgU3kMaMycgg5D7nBLQkmsepC6/OrVxD9gjZDiSOMe2a1atmjUZvAh2AVVUTMM1f3r9iCYBC4EKolTXtmJwMiKBU8HySi9RLCZ0RAasqzEkAVNONvk+x8da6WNfR/tRCHii/r3ISKBUGnh6MyAwVPPeWPzP6ybgXzoZD+MEWEinQX4iMER4XAXuc8koiFQDoZLrXzEdEkko6MJmUrwg153Y8w0sQuusZmu+O6/Wr4t2yugQHaETZKMLVEe3qIGaiKIn9IJe0ZvxbLwbH8bndLVkFDf7aGaMr1+PLpqQ AAACDHicbZDLSsNAFIYn9VbrLV52bgaL4MaSiKAboejGZQV7gTaEyXTSDp1cmDkRY8gr+Axude1O3PoOLn0Tp20WtvWsPv7/HP7D78WCK7Csb6O0tLyyulZer2xsbm3vmLt7LRUlkrImjUQkOx5RTPCQNYGDYJ1YMhJ4grW90c3Ybz8wqXgU3kMaMycgg5D7nBLQkmsepC6/OrVxD9gjZDiSOMe2a1atmjUZvAh2AVVUTMM1f3r9iCYBC4EKolTXtmJwMiKBU8HySi9RLCZ0RAasqzEkAVNONvk+x8da6WNfR/tRCHii/r3ISKBUGnh6MyAwVPPeWPzP6ybgXzoZD+MEWEinQX4iMER4XAXuc8koiFQDoZLrXzEdEkko6MJmUrwg153Y8w0sQuusZmu+O6/Wr4t2yugQHaETZKMLVEe3qIGaiKIn9IJe0ZvxbLwbH8bndLVkFDf7aGaMr1+PLpqQ AAACDHicbZDLSsNAFIYn9VbrLV52bgaL4MaSiKAboejGZQV7gTaEyXTSDp1cmDkRY8gr+Axude1O3PoOLn0Tp20WtvWsPv7/HP7D78WCK7Csb6O0tLyyulZer2xsbm3vmLt7LRUlkrImjUQkOx5RTPCQNYGDYJ1YMhJ4grW90c3Ybz8wqXgU3kMaMycgg5D7nBLQkmsepC6/OrVxD9gjZDiSOMe2a1atmjUZvAh2AVVUTMM1f3r9iCYBC4EKolTXtmJwMiKBU8HySi9RLCZ0RAasqzEkAVNONvk+x8da6WNfR/tRCHii/r3ISKBUGnh6MyAwVPPeWPzP6ybgXzoZD+MEWEinQX4iMER4XAXuc8koiFQDoZLrXzEdEkko6MJmUrwg153Y8w0sQuusZmu+O6/Wr4t2yugQHaETZKMLVEe3qIGaiKIn9IJe0ZvxbLwbH8bndLVkFDf7aGaMr1+PLpqQ AAACDHicbZDLSsNAFIYn9VbrLV52bgaL4MaSiKAboejGZQV7gTaEyXTSDp1cmDkRY8gr+Axude1O3PoOLn0Tp20WtvWsPv7/HP7D78WCK7Csb6O0tLyyulZer2xsbm3vmLt7LRUlkrImjUQkOx5RTPCQNYGDYJ1YMhJ4grW90c3Ybz8wqXgU3kMaMycgg5D7nBLQkmsepC6/OrVxD9gjZDiSOMe2a1atmjUZvAh2AVVUTMM1f3r9iCYBC4EKolTXtmJwMiKBU8HySi9RLCZ0RAasqzEkAVNONvk+x8da6WNfR/tRCHii/r3ISKBUGnh6MyAwVPPeWPzP6ybgXzoZD+MEWEinQX4iMER4XAXuc8koiFQDoZLrXzEdEkko6MJmUrwg153Y8w0sQuusZmu+O6/Wr4t2yugQHaETZKMLVEe3qIGaiKIn9IJe0ZvxbLwbH8bndLVkFDf7aGaMr1+PLpqQ ͨͩ͠

Slide 45

Slide 45 text

min i yi(w0 + wT xi) AAACGnicbZDLSgMxFIYzXmu9jbp0E1qEilBmRNBl0Y3LCr1Bpw6ZNG1Dk8yQZKzDMHsfwmdwq2t34taNS9/E9LKwrT8EPv5zDufkDyJGlXacb2tldW19YzO3ld/e2d3btw8OGyqMJSZ1HLJQtgKkCKOC1DXVjLQiSRAPGGkGw5txvflApKKhqOkkIh2O+oL2KEbaWL5d8DgVPs0nPoWlke+ceQFPR9l9DY7hMfPpqW8XnbIzEVwGdwZFMFPVt3+8bohjToTGDCnVdp1Id1IkNcWMZHkvViRCeIj6pG1QIE5UJ538JYMnxunCXijNExpO3L8TKeJKJTwwnRzpgVqsjc3/au1Y9646KRVRrInA00W9mEEdwnEwsEslwZolBhCW1NwK8QBJhLWJb25LwDOTibuYwDI0zsuu4buLYuV6lk4OHIMCKAEXXIIKuAVVUAcYPIEX8ArerGfr3fqwPqetK9Zs5gjMyfr6BfRSoLk= AAACGnicbZDLSgMxFIYzXmu9jbp0E1qEilBmRNBl0Y3LCr1Bpw6ZNG1Dk8yQZKzDMHsfwmdwq2t34taNS9/E9LKwrT8EPv5zDufkDyJGlXacb2tldW19YzO3ld/e2d3btw8OGyqMJSZ1HLJQtgKkCKOC1DXVjLQiSRAPGGkGw5txvflApKKhqOkkIh2O+oL2KEbaWL5d8DgVPs0nPoWlke+ceQFPR9l9DY7hMfPpqW8XnbIzEVwGdwZFMFPVt3+8bohjToTGDCnVdp1Id1IkNcWMZHkvViRCeIj6pG1QIE5UJ538JYMnxunCXijNExpO3L8TKeJKJTwwnRzpgVqsjc3/au1Y9646KRVRrInA00W9mEEdwnEwsEslwZolBhCW1NwK8QBJhLWJb25LwDOTibuYwDI0zsuu4buLYuV6lk4OHIMCKAEXXIIKuAVVUAcYPIEX8ArerGfr3fqwPqetK9Zs5gjMyfr6BfRSoLk= AAACGnicbZDLSgMxFIYzXmu9jbp0E1qEilBmRNBl0Y3LCr1Bpw6ZNG1Dk8yQZKzDMHsfwmdwq2t34taNS9/E9LKwrT8EPv5zDufkDyJGlXacb2tldW19YzO3ld/e2d3btw8OGyqMJSZ1HLJQtgKkCKOC1DXVjLQiSRAPGGkGw5txvflApKKhqOkkIh2O+oL2KEbaWL5d8DgVPs0nPoWlke+ceQFPR9l9DY7hMfPpqW8XnbIzEVwGdwZFMFPVt3+8bohjToTGDCnVdp1Id1IkNcWMZHkvViRCeIj6pG1QIE5UJ538JYMnxunCXijNExpO3L8TKeJKJTwwnRzpgVqsjc3/au1Y9646KRVRrInA00W9mEEdwnEwsEslwZolBhCW1NwK8QBJhLWJb25LwDOTibuYwDI0zsuu4buLYuV6lk4OHIMCKAEXXIIKuAVVUAcYPIEX8ArerGfr3fqwPqetK9Zs5gjMyfr6BfRSoLk= AAACGnicbZDLSgMxFIYzXmu9jbp0E1qEilBmRNBl0Y3LCr1Bpw6ZNG1Dk8yQZKzDMHsfwmdwq2t34taNS9/E9LKwrT8EPv5zDufkDyJGlXacb2tldW19YzO3ld/e2d3btw8OGyqMJSZ1HLJQtgKkCKOC1DXVjLQiSRAPGGkGw5txvflApKKhqOkkIh2O+oL2KEbaWL5d8DgVPs0nPoWlke+ceQFPR9l9DY7hMfPpqW8XnbIzEVwGdwZFMFPVt3+8bohjToTGDCnVdp1Id1IkNcWMZHkvViRCeIj6pG1QIE5UJ538JYMnxunCXijNExpO3L8TKeJKJTwwnRzpgVqsjc3/au1Y9646KRVRrInA00W9mEEdwnEwsEslwZolBhCW1NwK8QBJhLWJb25LwDOTibuYwDI0zsuu4buLYuV6lk4OHIMCKAEXXIIKuAVVUAcYPIEX8ArerGfr3fqwPqetK9Zs5gjMyfr6BfRSoLk= w0, w AAACAXicbZDLSgMxFIbP1Futt6pLN8EiuJAyI4Iui25cVrAXaIeSSTNtaJIZkoylDF35DG517U7c+iQufRMz7Sxs6w+Bj/+cwzn5g5gzbVz32ymsrW9sbhW3Szu7e/sH5cOjpo4SRWiDRDxS7QBrypmkDcMMp+1YUSwCTlvB6C6rt56o0iySj2YSU1/ggWQhI9hYqzPuuReoG4h0PO2VK27VnQmtgpdDBXLVe+Wfbj8iiaDSEI617nhubPwUK8MIp9NSN9E0xmSEB7RjUWJBtZ/OTp6iM+v0URgp+6RBM/fvRIqF1hMR2E6BzVAv1zLzv1onMeGNnzIZJ4ZKMl8UJhyZCGX/R32mKDF8YgETxeytiAyxwsTYlBa2BCLLxFtOYBWal1XP8sNVpXabp1OEEziFc/DgGmpwD3VoAIEIXuAV3pxn5935cD7nrQUnnzmGBTlfv36hl2o= AAACAXicbZDLSgMxFIbP1Futt6pLN8EiuJAyI4Iui25cVrAXaIeSSTNtaJIZkoylDF35DG517U7c+iQufRMz7Sxs6w+Bj/+cwzn5g5gzbVz32ymsrW9sbhW3Szu7e/sH5cOjpo4SRWiDRDxS7QBrypmkDcMMp+1YUSwCTlvB6C6rt56o0iySj2YSU1/ggWQhI9hYqzPuuReoG4h0PO2VK27VnQmtgpdDBXLVe+Wfbj8iiaDSEI617nhubPwUK8MIp9NSN9E0xmSEB7RjUWJBtZ/OTp6iM+v0URgp+6RBM/fvRIqF1hMR2E6BzVAv1zLzv1onMeGNnzIZJ4ZKMl8UJhyZCGX/R32mKDF8YgETxeytiAyxwsTYlBa2BCLLxFtOYBWal1XP8sNVpXabp1OEEziFc/DgGmpwD3VoAIEIXuAV3pxn5935cD7nrQUnnzmGBTlfv36hl2o= AAACAXicbZDLSgMxFIbP1Futt6pLN8EiuJAyI4Iui25cVrAXaIeSSTNtaJIZkoylDF35DG517U7c+iQufRMz7Sxs6w+Bj/+cwzn5g5gzbVz32ymsrW9sbhW3Szu7e/sH5cOjpo4SRWiDRDxS7QBrypmkDcMMp+1YUSwCTlvB6C6rt56o0iySj2YSU1/ggWQhI9hYqzPuuReoG4h0PO2VK27VnQmtgpdDBXLVe+Wfbj8iiaDSEI617nhubPwUK8MIp9NSN9E0xmSEB7RjUWJBtZ/OTp6iM+v0URgp+6RBM/fvRIqF1hMR2E6BzVAv1zLzv1onMeGNnzIZJ4ZKMl8UJhyZCGX/R32mKDF8YgETxeytiAyxwsTYlBa2BCLLxFtOYBWal1XP8sNVpXabp1OEEziFc/DgGmpwD3VoAIEIXuAV3pxn5935cD7nrQUnnzmGBTlfv36hl2o= AAACAXicbZDLSgMxFIbP1Futt6pLN8EiuJAyI4Iui25cVrAXaIeSSTNtaJIZkoylDF35DG517U7c+iQufRMz7Sxs6w+Bj/+cwzn5g5gzbVz32ymsrW9sbhW3Szu7e/sH5cOjpo4SRWiDRDxS7QBrypmkDcMMp+1YUSwCTlvB6C6rt56o0iySj2YSU1/ggWQhI9hYqzPuuReoG4h0PO2VK27VnQmtgpdDBXLVe+Wfbj8iiaDSEI617nhubPwUK8MIp9NSN9E0xmSEB7RjUWJBtZ/OTp6iM+v0URgp+6RBM/fvRIqF1hMR2E6BzVAv1zLzv1onMeGNnzIZJ4ZKMl8UJhyZCGX/R32mKDF8YgETxeytiAyxwsTYlBa2BCLLxFtOYBWal1XP8sNVpXabp1OEEziFc/DgGmpwD3VoAIEIXuAV3pxn5935cD7nrQUnnzmGBTlfv36hl2o=  AAAB/HicbZDLSgMxFIbP1Futt6pLN8EiuCozIuiy6MZlBXuBdiiZNNPGJpmQZIQy1Gdwq2t34tZ3cembmLazsK0/BD7+cw7n5I8UZ8b6/rdXWFvf2Nwqbpd2dvf2D8qHR02TpJrQBkl4otsRNpQzSRuWWU7bSlMsIk5b0eh2Wm89UW1YIh/sWNFQ4IFkMSPYOqvZHWGlcK9c8av+TGgVghwqkKveK/90+wlJBZWWcGxMJ/CVDTOsLSOcTkrd1FCFyQgPaMehxIKaMJtdO0FnzumjONHuSYtm7t+JDAtjxiJynQLboVmuTc3/ap3UxtdhxqRKLZVkvihOObIJmn4d9ZmmxPKxA0w0c7ciMsQaE+sCWtgSiYnLJFhOYBWaF9XA8f1lpXaTp1OEEziFcwjgCmpwB3VoAIFHeIFXePOevXfvw/uctxa8fOYYFuR9/QJYqJW1 AAAB/HicbZDLSgMxFIbP1Futt6pLN8EiuCozIuiy6MZlBXuBdiiZNNPGJpmQZIQy1Gdwq2t34tZ3cembmLazsK0/BD7+cw7n5I8UZ8b6/rdXWFvf2Nwqbpd2dvf2D8qHR02TpJrQBkl4otsRNpQzSRuWWU7bSlMsIk5b0eh2Wm89UW1YIh/sWNFQ4IFkMSPYOqvZHWGlcK9c8av+TGgVghwqkKveK/90+wlJBZWWcGxMJ/CVDTOsLSOcTkrd1FCFyQgPaMehxIKaMJtdO0FnzumjONHuSYtm7t+JDAtjxiJynQLboVmuTc3/ap3UxtdhxqRKLZVkvihOObIJmn4d9ZmmxPKxA0w0c7ciMsQaE+sCWtgSiYnLJFhOYBWaF9XA8f1lpXaTp1OEEziFcwjgCmpwB3VoAIFHeIFXePOevXfvw/uctxa8fOYYFuR9/QJYqJW1 AAAB/HicbZDLSgMxFIbP1Futt6pLN8EiuCozIuiy6MZlBXuBdiiZNNPGJpmQZIQy1Gdwq2t34tZ3cembmLazsK0/BD7+cw7n5I8UZ8b6/rdXWFvf2Nwqbpd2dvf2D8qHR02TpJrQBkl4otsRNpQzSRuWWU7bSlMsIk5b0eh2Wm89UW1YIh/sWNFQ4IFkMSPYOqvZHWGlcK9c8av+TGgVghwqkKveK/90+wlJBZWWcGxMJ/CVDTOsLSOcTkrd1FCFyQgPaMehxIKaMJtdO0FnzumjONHuSYtm7t+JDAtjxiJynQLboVmuTc3/ap3UxtdhxqRKLZVkvihOObIJmn4d9ZmmxPKxA0w0c7ciMsQaE+sCWtgSiYnLJFhOYBWaF9XA8f1lpXaTp1OEEziFcwjgCmpwB3VoAIFHeIFXePOevXfvw/uctxa8fOYYFuR9/QJYqJW1 AAAB/HicbZDLSgMxFIbP1Futt6pLN8EiuCozIuiy6MZlBXuBdiiZNNPGJpmQZIQy1Gdwq2t34tZ3cembmLazsK0/BD7+cw7n5I8UZ8b6/rdXWFvf2Nwqbpd2dvf2D8qHR02TpJrQBkl4otsRNpQzSRuWWU7bSlMsIk5b0eh2Wm89UW1YIh/sWNFQ4IFkMSPYOqvZHWGlcK9c8av+TGgVghwqkKveK/90+wlJBZWWcGxMJ/CVDTOsLSOcTkrd1FCFyQgPaMehxIKaMJtdO0FnzumjONHuSYtm7t+JDAtjxiJynQLboVmuTc3/ap3UxtdhxqRKLZVkvihOObIJmn4d9ZmmxPKxA0w0c7ciMsQaE+sCWtgSiYnLJFhOYBWaF9XA8f1lpXaTp1OEEziFcwjgCmpwB3VoAIFHeIFXePOevXfvw/uctxa8fOYYFuR9/QJYqJW1 Λ ഒ͢Δͱ໨తؔ਺ ͸ AAAB/HicbZDLSgMxFIbP1Futt6pLN8EiuCozIuiy6MZlBXuBdiiZNNPGJpmQZIQy1Gdwq2t34tZ3cembmLazsK0/BD7+cw7n5I8UZ8b6/rdXWFvf2Nwqbpd2dvf2D8qHR02TpJrQBkl4otsRNpQzSRuWWU7bSlMsIk5b0eh2Wm89UW1YIh/sWNFQ4IFkMSPYOqvZHWGlcK9c8av+TGgVghwqkKveK/90+wlJBZWWcGxMJ/CVDTOsLSOcTkrd1FCFyQgPaMehxIKaMJtdO0FnzumjONHuSYtm7t+JDAtjxiJynQLboVmuTc3/ap3UxtdhxqRKLZVkvihOObIJmn4d9ZmmxPKxA0w0c7ciMsQaE+sCWtgSiYnLJFhOYBWaF9XA8f1lpXaTp1OEEziFcwjgCmpwB3VoAIFHeIFXePOevXfvw/uctxa8fOYYFuR9/QJYqJW1 AAAB/HicbZDLSgMxFIbP1Futt6pLN8EiuCozIuiy6MZlBXuBdiiZNNPGJpmQZIQy1Gdwq2t34tZ3cembmLazsK0/BD7+cw7n5I8UZ8b6/rdXWFvf2Nwqbpd2dvf2D8qHR02TpJrQBkl4otsRNpQzSRuWWU7bSlMsIk5b0eh2Wm89UW1YIh/sWNFQ4IFkMSPYOqvZHWGlcK9c8av+TGgVghwqkKveK/90+wlJBZWWcGxMJ/CVDTOsLSOcTkrd1FCFyQgPaMehxIKaMJtdO0FnzumjONHuSYtm7t+JDAtjxiJynQLboVmuTc3/ap3UxtdhxqRKLZVkvihOObIJmn4d9ZmmxPKxA0w0c7ciMsQaE+sCWtgSiYnLJFhOYBWaF9XA8f1lpXaTp1OEEziFcwjgCmpwB3VoAIFHeIFXePOevXfvw/uctxa8fOYYFuR9/QJYqJW1 AAAB/HicbZDLSgMxFIbP1Futt6pLN8EiuCozIuiy6MZlBXuBdiiZNNPGJpmQZIQy1Gdwq2t34tZ3cembmLazsK0/BD7+cw7n5I8UZ8b6/rdXWFvf2Nwqbpd2dvf2D8qHR02TpJrQBkl4otsRNpQzSRuWWU7bSlMsIk5b0eh2Wm89UW1YIh/sWNFQ4IFkMSPYOqvZHWGlcK9c8av+TGgVghwqkKveK/90+wlJBZWWcGxMJ/CVDTOsLSOcTkrd1FCFyQgPaMehxIKaMJtdO0FnzumjONHuSYtm7t+JDAtjxiJynQLboVmuTc3/ap3UxtdhxqRKLZVkvihOObIJmn4d9ZmmxPKxA0w0c7ciMsQaE+sCWtgSiYnLJFhOYBWaF9XA8f1lpXaTp1OEEziFcwjgCmpwB3VoAIFHeIFXePOevXfvw/uctxa8fOYYFuR9/QJYqJW1 AAAB/HicbZDLSgMxFIbP1Futt6pLN8EiuCozIuiy6MZlBXuBdiiZNNPGJpmQZIQy1Gdwq2t34tZ3cembmLazsK0/BD7+cw7n5I8UZ8b6/rdXWFvf2Nwqbpd2dvf2D8qHR02TpJrQBkl4otsRNpQzSRuWWU7bSlMsIk5b0eh2Wm89UW1YIh/sWNFQ4IFkMSPYOqvZHWGlcK9c8av+TGgVghwqkKveK/90+wlJBZWWcGxMJ/CVDTOsLSOcTkrd1FCFyQgPaMehxIKaMJtdO0FnzumjONHuSYtm7t+JDAtjxiJynQLboVmuTc3/ap3UxtdhxqRKLZVkvihOObIJmn4d9ZmmxPKxA0w0c7ciMsQaE+sCWtgSiYnLJFhOYBWaF9XA8f1lpXaTp1OEEziFcwjgCmpwB3VoAIFHeIFXePOevXfvw/uctxa8fOYYFuR9/QJYqJW1 ഒʹͳΔ Minimize w0,w 1 2 kwk2 Subject to yi(w0 + wT xi) 1 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 ͷ஋͸มΘΒͳ͍ 1 kwk min i yi(w0 + wT xi) 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 min i yi(w0 + wT xi) AAACGnicbZDLSgMxFIYzXmu9jbp0E1qEilBmRNBl0Y3LCr1Bpw6ZNG1Dk8yQZKzDMHsfwmdwq2t34taNS9/E9LKwrT8EPv5zDufkDyJGlXacb2tldW19YzO3ld/e2d3btw8OGyqMJSZ1HLJQtgKkCKOC1DXVjLQiSRAPGGkGw5txvflApKKhqOkkIh2O+oL2KEbaWL5d8DgVPs0nPoWlke+ceQFPR9l9DY7hMfPpqW8XnbIzEVwGdwZFMFPVt3+8bohjToTGDCnVdp1Id1IkNcWMZHkvViRCeIj6pG1QIE5UJ538JYMnxunCXijNExpO3L8TKeJKJTwwnRzpgVqsjc3/au1Y9646KRVRrInA00W9mEEdwnEwsEslwZolBhCW1NwK8QBJhLWJb25LwDOTibuYwDI0zsuu4buLYuV6lk4OHIMCKAEXXIIKuAVVUAcYPIEX8ArerGfr3fqwPqetK9Zs5gjMyfr6BfRSoLk= AAACGnicbZDLSgMxFIYzXmu9jbp0E1qEilBmRNBl0Y3LCr1Bpw6ZNG1Dk8yQZKzDMHsfwmdwq2t34taNS9/E9LKwrT8EPv5zDufkDyJGlXacb2tldW19YzO3ld/e2d3btw8OGyqMJSZ1HLJQtgKkCKOC1DXVjLQiSRAPGGkGw5txvflApKKhqOkkIh2O+oL2KEbaWL5d8DgVPs0nPoWlke+ceQFPR9l9DY7hMfPpqW8XnbIzEVwGdwZFMFPVt3+8bohjToTGDCnVdp1Id1IkNcWMZHkvViRCeIj6pG1QIE5UJ538JYMnxunCXijNExpO3L8TKeJKJTwwnRzpgVqsjc3/au1Y9646KRVRrInA00W9mEEdwnEwsEslwZolBhCW1NwK8QBJhLWJb25LwDOTibuYwDI0zsuu4buLYuV6lk4OHIMCKAEXXIIKuAVVUAcYPIEX8ArerGfr3fqwPqetK9Zs5gjMyfr6BfRSoLk= AAACGnicbZDLSgMxFIYzXmu9jbp0E1qEilBmRNBl0Y3LCr1Bpw6ZNG1Dk8yQZKzDMHsfwmdwq2t34taNS9/E9LKwrT8EPv5zDufkDyJGlXacb2tldW19YzO3ld/e2d3btw8OGyqMJSZ1HLJQtgKkCKOC1DXVjLQiSRAPGGkGw5txvflApKKhqOkkIh2O+oL2KEbaWL5d8DgVPs0nPoWlke+ceQFPR9l9DY7hMfPpqW8XnbIzEVwGdwZFMFPVt3+8bohjToTGDCnVdp1Id1IkNcWMZHkvViRCeIj6pG1QIE5UJ538JYMnxunCXijNExpO3L8TKeJKJTwwnRzpgVqsjc3/au1Y9646KRVRrInA00W9mEEdwnEwsEslwZolBhCW1NwK8QBJhLWJb25LwDOTibuYwDI0zsuu4buLYuV6lk4OHIMCKAEXXIIKuAVVUAcYPIEX8ArerGfr3fqwPqetK9Zs5gjMyfr6BfRSoLk= AAACGnicbZDLSgMxFIYzXmu9jbp0E1qEilBmRNBl0Y3LCr1Bpw6ZNG1Dk8yQZKzDMHsfwmdwq2t34taNS9/E9LKwrT8EPv5zDufkDyJGlXacb2tldW19YzO3ld/e2d3btw8OGyqMJSZ1HLJQtgKkCKOC1DXVjLQiSRAPGGkGw5txvflApKKhqOkkIh2O+oL2KEbaWL5d8DgVPs0nPoWlke+ceQFPR9l9DY7hMfPpqW8XnbIzEVwGdwZFMFPVt3+8bohjToTGDCnVdp1Id1IkNcWMZHkvViRCeIj6pG1QIE5UJ538JYMnxunCXijNExpO3L8TKeJKJTwwnRzpgVqsjc3/au1Y9646KRVRrInA00W9mEEdwnEwsEslwZolBhCW1NwK8QBJhLWJb25LwDOTibuYwDI0zsuu4buLYuV6lk4OHIMCKAEXXIIKuAVVUAcYPIEX8ArerGfr3fqwPqetK9Zs5gjMyfr6BfRSoLk= ͷ஋͸޷͖ͳΑ͏ʹௐ੔ՄೳͰ͋Δ͜ͱΛҙຯ͢Δ ͜Ε͸ͭ·Γ ͷͰ͜ΕΛ1ͱ͢Δ ݁ہ͜ͷ໰୊Λղ͚͹Α͍ɿ Maximize w0,w min i yi(w0 + wT xi) kwk = Maximize w0,w 1 kwk min i yi(w0 + wT xi) 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 AAAB6HicbZBLSwMxFIXv1FetVevaTbAIrsqMG10KblxWsA9oh5LJ3GlD8xiSjFKG/gG3rt2J/8ml/8T0sbDWA4GPcxLuzUlywa0Lw6+gsrO7t39QPawd1WvHJ6eNetfqwjDsMC206SfUouAKO447gf3cIJWJwF4yvV/kvWc0lmv15GY5xpKOFc84o85b7VGjGbbCpcg2RGtowlqjxvcw1ayQqBwT1NpBFOYuLqlxnAmc14aFxZyyKR3jwKOiEm1cLteck0vvpCTTxh/lyNL9/aKk0tqZTPxNSd3E/s0W5n/ZoHDZbVxylRcOFVsNygpBnCaLP5OUG2ROzDxQZrjflbAJNZQ538zGlETOfSXR3wK2oXvdijw/hlCFc7iAK4jgBu7gAdrQAQYpvMJb8BK8Bx+r6irBusMz2FDw+QN9JZC/ 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 AAAC0nicjVFNb9QwEHXCVwkf3cKRi8WKqghUJVzggrRqL1yQirS7rbReIsc7aa3aTmRPaLdWDhVX/iDc+Cc4uznQFhAjWXqemec3flPUSjpM0+9RfOv2nbv3Nu4nDx4+erw52HoydVVjBUxEpSp7VHAHShqYoEQFR7UFrgsFh8Xpflc//ALWycqMcVnDXPNjI0spOIZUPvixzRqzCA2A/ixPX7NC+7O29UxzPLHaf+TnUssLaFvKtDS5TFhpufDLXNKdQHi1Jnwe0w6ct7l8GchqChbpukSZ7W4tY8n2++S/1Xqd7C+vJf00/5gjHwzT3XQV9CbIejAkfRzkg59sUYlGg0GhuHOzLK1x7rlFKRQEycZBzcUpP4ZZgIZrcHO/2kFLX4TMgpaVDccgXWV/Z3iunVvqInR2n3XXa13yT7VZg+W7uZembhCMWAuVjaJY0W6hdCEtCFTLALiwMsxKxQkP3mHw+YpKodvgSXbdgZtg+mY3C/hTOhzt9e5skGfkOdkhGXlLRuQDOSATIqJRVEZVVMfj+CK+jL+uW+Oo5zwlVyL+9guyD+Vm 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 Ϛʔδϯ࠷େԽΛࣜͰද͢ͱ

Slide 46

Slide 46 text

Minimize w0,w 1 2 kwk2 Subject to yi(w0 + wT xi) 1 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 L(w0, w, a) = 1 2 kwk2 n X i=1 ai yi(w0 + wT xi) 1 AAACa3icbVHLahsxFNVMX477cppd2sWlJpDQJsyYQLsJhHaTRRcpxE7AsgeNrLFFJM0g3WlqxHxolv2AfkOrsb1okh4QOjrnXl1xlFdKOkyS2yh+9PjJ02edre7zFy9fve5tvxm5srZcDHmpSnuVMyeUNGKIEpW4qqxgOlfiMr/+2vqXP4R1sjQXuKzERLO5kYXkDIOU9dy3/Zss+Uhz7W+a1caaAzgBWljGfdr4QUPVSFiEdQlQ256mAzgE6mqdeXmSNlMDLJNdqkSB1C8zCe2tH9Yt0wv4mcmDw5RaOV8gbbJePzlKVoCHJN2QPtngPOv9orOS11oY5Io5N06TCieeWZRciaZLaycqxq/ZXIwDNUwLN/GrcBrYC8oMitKGZRBW6r8dnmnnljoPlZrhwt33WvF/3rjG4vPES1PVKAxfDypqBVhCmzTMpBUc1TIQxq0MbwW+YCFWDP9xZ0qu20zS+wk8JKPBURr49+P+6ZdNOh3ylrwn+yQln8gpOSPnZEg4uSV/ok60Ff2Od+Ld+N26NI42PTvkDuK9v0yqunE= 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 ai 0 yi(w0 + wT xi) 1 0 ai yi(w0 + wT xi) 1 = 0 AAACYnicfZFNaxsxEIblTdo67kc29TE5iJgGl1KzWwrtpWDSS44JxHHAchetPGsrkXa30mxds+x/zDXHQn5DronW8SFfdEDw6J15GfEqzpW0GASXDW9t/cXLV82N1us3b99t+lvvT2xWGAEDkanMnMbcgpIpDFCigtPcANexgmF8/rPuD/+AsTJLj3GRw1jzaSoTKTg6KfLPeCTpHpvCbxow1lq4W3ceBZ9YrMt59euY1vC3iuTHz+G9udrFFCTIyv9bmJHTGbJq70cQ+Z2gFyyLPoVwBR2yqsPI/8cmmSg0pCgUt3YUBjmOS25QCgVVixUWci7O+RRGDlOuwY7LZSYV/eCUCU0y406KdKned5RcW7vQsZvUHGf2ca8Wn+uNCky+j0uZ5gVCKu4WJYWimNE6YDqRBgSqhQMujHRvpWLGDRfovuHBllhXLpPwcQJP4eRLL3R89LXT31+l0yTbZJd0SUi+kT45IIdkQAS5INfkpkEaV17L2/Lad6NeY+Vpkwfl7dwC3FG1wg== 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 ϥάϥϯδϡؔ਺ KKT৚݅

Slide 47

Slide 47 text

Λܭࢉ͠ rL = 0 AAACAHicbZA9SwNBEIbn4leMX1FLm8UgWIU7EbQRgjYWFhHMByZHmNvsJUv29o7dPSGENP4GW63txNZ/Yuk/cZNcYRJfWHh4Z4aZfYNEcG1c99vJrayurW/kNwtb2zu7e8X9g7qOU0VZjcYiVs0ANRNcsprhRrBmohhGgWCNYHAzqTeemNI8lg9mmDA/wp7kIadorPXYlhgIJHdXbqdYcsvuVGQZvAxKkKnaKf60uzFNIyYNFah1y3MT449QGU4FGxfaqWYJ0gH2WMuixIhpfzS9eExOrNMlYazsk4ZM3b8TI4y0HkaB7YzQ9PVibWL+V2ulJrz0R1wmqWGSzhaFqSAmJpPvky5XjBoxtIBUcXsroX1USI0NaW5LEI1tJt5iAstQPyt7lu/PS5XrLJ08HMExnIIHF1CBW6hCDShIeIFXeHOenXfnw/mcteacbOYQ5uR8/QI1TZan AAACAHicbZA9SwNBEIbn4leMX1FLm8UgWIU7EbQRgjYWFhHMByZHmNvsJUv29o7dPSGENP4GW63txNZ/Yuk/cZNcYRJfWHh4Z4aZfYNEcG1c99vJrayurW/kNwtb2zu7e8X9g7qOU0VZjcYiVs0ANRNcsprhRrBmohhGgWCNYHAzqTeemNI8lg9mmDA/wp7kIadorPXYlhgIJHdXbqdYcsvuVGQZvAxKkKnaKf60uzFNIyYNFah1y3MT449QGU4FGxfaqWYJ0gH2WMuixIhpfzS9eExOrNMlYazsk4ZM3b8TI4y0HkaB7YzQ9PVibWL+V2ulJrz0R1wmqWGSzhaFqSAmJpPvky5XjBoxtIBUcXsroX1USI0NaW5LEI1tJt5iAstQPyt7lu/PS5XrLJ08HMExnIIHF1CBW6hCDShIeIFXeHOenXfnw/mcteacbOYQ5uR8/QI1TZan AAACAHicbZA9SwNBEIbn4leMX1FLm8UgWIU7EbQRgjYWFhHMByZHmNvsJUv29o7dPSGENP4GW63txNZ/Yuk/cZNcYRJfWHh4Z4aZfYNEcG1c99vJrayurW/kNwtb2zu7e8X9g7qOU0VZjcYiVs0ANRNcsprhRrBmohhGgWCNYHAzqTeemNI8lg9mmDA/wp7kIadorPXYlhgIJHdXbqdYcsvuVGQZvAxKkKnaKf60uzFNIyYNFah1y3MT449QGU4FGxfaqWYJ0gH2WMuixIhpfzS9eExOrNMlYazsk4ZM3b8TI4y0HkaB7YzQ9PVibWL+V2ulJrz0R1wmqWGSzhaFqSAmJpPvky5XjBoxtIBUcXsroX1USI0NaW5LEI1tJt5iAstQPyt7lu/PS5XrLJ08HMExnIIHF1CBW6hCDShIeIFXeHOenXfnw/mcteacbOYQ5uR8/QI1TZan AAACAHicbZA9SwNBEIbn4leMX1FLm8UgWIU7EbQRgjYWFhHMByZHmNvsJUv29o7dPSGENP4GW63txNZ/Yuk/cZNcYRJfWHh4Z4aZfYNEcG1c99vJrayurW/kNwtb2zu7e8X9g7qOU0VZjcYiVs0ANRNcsprhRrBmohhGgWCNYHAzqTeemNI8lg9mmDA/wp7kIadorPXYlhgIJHdXbqdYcsvuVGQZvAxKkKnaKf60uzFNIyYNFah1y3MT449QGU4FGxfaqWYJ0gH2WMuixIhpfzS9eExOrNMlYazsk4ZM3b8TI4y0HkaB7YzQ9PVibWL+V2ulJrz0R1wmqWGSzhaFqSAmJpPvky5XjBoxtIBUcXsroX1USI0NaW5LEI1tJt5iAstQPyt7lu/PS5XrLJ08HMExnIIHF1CBW6hCDShIeIFXeHOenXfnw/mcteacbOYQ5uR8/QI1TZan L = n X k=1 ak 1 2 n X k=1 n X l=1 akalykylxT k xl 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 ʢܭࢉաఔͷৄࡉʹ͍ͭͯ͸ॻ੶ࢀরʣ n X i=1 aiyi = 0 AAACDnicbZDLSsNAFIYn9VbrLSq4cTNYBFclEUE3haIblxXsBdoYJtNJO3RmEmYmQoh5B5/Bra7diVtfwaVv4rTNwrb+cODjP+dwDn8QM6q043xbpZXVtfWN8mZla3tnd8/eP2irKJGYtHDEItkNkCKMCtLSVDPSjSVBPGCkE4xvJv3OI5GKRuJepzHxOBoKGlKMtLF8+6ivEu5ntO7mDwIin8LUp3XHt6tOzZkKLoNbQBUUavr2T38Q4YQToTFDSvVcJ9ZehqSmmJG80k8UiREeoyHpGRSIE+Vl0/9zeGqcAQwjaUpoOHX/bmSIK5XywExypEdqsTcx/+v1Eh1eeRkVcaKJwLNDYcKgjuAkDDigkmDNUgMIS2p+hXiEJMLaRDZ3JeC5ycRdTGAZ2uc11/DdRbVxXaRTBsfgBJwBF1yCBrgFTdACGDyBF/AK3qxn6936sD5noyWr2DkEc7K+fgHgj5vf AAACDnicbZDLSsNAFIYn9VbrLSq4cTNYBFclEUE3haIblxXsBdoYJtNJO3RmEmYmQoh5B5/Bra7diVtfwaVv4rTNwrb+cODjP+dwDn8QM6q043xbpZXVtfWN8mZla3tnd8/eP2irKJGYtHDEItkNkCKMCtLSVDPSjSVBPGCkE4xvJv3OI5GKRuJepzHxOBoKGlKMtLF8+6ivEu5ntO7mDwIin8LUp3XHt6tOzZkKLoNbQBUUavr2T38Q4YQToTFDSvVcJ9ZehqSmmJG80k8UiREeoyHpGRSIE+Vl0/9zeGqcAQwjaUpoOHX/bmSIK5XywExypEdqsTcx/+v1Eh1eeRkVcaKJwLNDYcKgjuAkDDigkmDNUgMIS2p+hXiEJMLaRDZ3JeC5ycRdTGAZ2uc11/DdRbVxXaRTBsfgBJwBF1yCBrgFTdACGDyBF/AK3qxn6936sD5noyWr2DkEc7K+fgHgj5vf AAACDnicbZDLSsNAFIYn9VbrLSq4cTNYBFclEUE3haIblxXsBdoYJtNJO3RmEmYmQoh5B5/Bra7diVtfwaVv4rTNwrb+cODjP+dwDn8QM6q043xbpZXVtfWN8mZla3tnd8/eP2irKJGYtHDEItkNkCKMCtLSVDPSjSVBPGCkE4xvJv3OI5GKRuJepzHxOBoKGlKMtLF8+6ivEu5ntO7mDwIin8LUp3XHt6tOzZkKLoNbQBUUavr2T38Q4YQToTFDSvVcJ9ZehqSmmJG80k8UiREeoyHpGRSIE+Vl0/9zeGqcAQwjaUpoOHX/bmSIK5XywExypEdqsTcx/+v1Eh1eeRkVcaKJwLNDYcKgjuAkDDigkmDNUgMIS2p+hXiEJMLaRDZ3JeC5ycRdTGAZ2uc11/DdRbVxXaRTBsfgBJwBF1yCBrgFTdACGDyBF/AK3qxn6936sD5noyWr2DkEc7K+fgHgj5vf AAACDnicbZDLSsNAFIYn9VbrLSq4cTNYBFclEUE3haIblxXsBdoYJtNJO3RmEmYmQoh5B5/Bra7diVtfwaVv4rTNwrb+cODjP+dwDn8QM6q043xbpZXVtfWN8mZla3tnd8/eP2irKJGYtHDEItkNkCKMCtLSVDPSjSVBPGCkE4xvJv3OI5GKRuJepzHxOBoKGlKMtLF8+6ivEu5ntO7mDwIin8LUp3XHt6tOzZkKLoNbQBUUavr2T38Q4YQToTFDSvVcJ9ZehqSmmJG80k8UiREeoyHpGRSIE+Vl0/9zeGqcAQwjaUpoOHX/bmSIK5XywExypEdqsTcx/+v1Eh1eeRkVcaKJwLNDYcKgjuAkDDigkmDNUgMIS2p+hXiEJMLaRDZ3JeC5ycRdTGAZ2uc11/DdRbVxXaRTBsfgBJwBF1yCBrgFTdACGDyBF/AK3qxn6936sD5noyWr2DkEc7K+fgHgj5vf ͕ಋ͔ΕΔ ͱ Maximize f(a) = n X k=1 ak 1 2 n X k=1 n X l=1 akalykylxT k xl Subject to n X i=1 aiyi = 0 ai 0 ai yi(w0 + wT xi) 1 = 0 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 ͭ·Γ࣍Λղ͚͹͍͍͜ͱʹͳΔ ͜Ε͸ೋ࣍ܭը໰୊

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Maximize f(a) = n X k=1 ak 1 2 n X k=1 n X l=1 akalykylxT k xl Subject to n X i=1 aiyi = 0 ai 0 ai yi(w0 + wT xi) 1 = 0 AAAC23icbVFNb9QwEHXCVwlfCxy5WKyotkKtkgqJXlaq4AIHpCK6baV1GjleZ9eNnaS2QxOinLghrvw4jog/wmSzfGzLSI7fzLzRc97EhRTG+v53x712/cbNWxu3vTt3791/MHj46MjkpWZ8wnKZ65OYGi5FxidWWMlPCs2piiU/jtPXXf/4I9dG5NmhrQseKjrPRCIYtVCKBj+J5ZVt3tFKKPGJtwRvJiMSq4a2W2NiShU16ThoTzNMo9Tb9kiiKWuCttltvbV2n8g/XDgS13DXcFdRenoIX+kR4vWKH8r4jDOLbd5p9tPi97SAKTH2gbzZZWTOz/HfTPLEkqaj4NFF5D/vnnvRgkAHqjYSW9sBJlrMF5a0eOxHg6G/4y8DXwXBCgzRKg6iwQ8yy1mpeGaZpMZMA7+wYUO1FUxy+PHS8IKylM75FGBGFTdhs1xGi59BZYaTXMPJLF5W/51oqDKmVjEwFbULc7nXFf/Xm5Y22QsbkRWl5RnrhZJSgoO42yyeCQ2GyhoAZVrAWzFbUFiXhf2vqcSqBU+Cyw5cBUe7OwHg9y+G+69W7mygJ+gpGqEAvUT76A06QBPEnLdO7lRO7YbuZ/eL+7Wnus5q5jFaC/fbLxYF4fI= 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 AAAC23icbVFNb9QwEHXCVwlfCxy5WKyotkKtkgqJXlaq4AIHpCK6baV1GjleZ9eNnaS2QxOinLghrvw4jog/wmSzfGzLSI7fzLzRc97EhRTG+v53x712/cbNWxu3vTt3791/MHj46MjkpWZ8wnKZ65OYGi5FxidWWMlPCs2piiU/jtPXXf/4I9dG5NmhrQseKjrPRCIYtVCKBj+J5ZVt3tFKKPGJtwRvJiMSq4a2W2NiShU16ThoTzNMo9Tb9kiiKWuCttltvbV2n8g/XDgS13DXcFdRenoIX+kR4vWKH8r4jDOLbd5p9tPi97SAKTH2gbzZZWTOz/HfTPLEkqaj4NFF5D/vnnvRgkAHqjYSW9sBJlrMF5a0eOxHg6G/4y8DXwXBCgzRKg6iwQ8yy1mpeGaZpMZMA7+wYUO1FUxy+PHS8IKylM75FGBGFTdhs1xGi59BZYaTXMPJLF5W/51oqDKmVjEwFbULc7nXFf/Xm5Y22QsbkRWl5RnrhZJSgoO42yyeCQ2GyhoAZVrAWzFbUFiXhf2vqcSqBU+Cyw5cBUe7OwHg9y+G+69W7mygJ+gpGqEAvUT76A06QBPEnLdO7lRO7YbuZ/eL+7Wnus5q5jFaC/fbLxYF4fI= ͜ͷղ͖ํɿ Ұൠͷೋ࣍ܭը໰୊ͷղ์Ͱ͸ͳ͘ɺ͜ͷ໰୊ಛ༗ͷੑ࣭Λར༻ ΞϧΰϦζϜ֓ཁɿ ҎԼΛ܁Γฦ͢ ɾ໨తؔ਺ͷվળʹد༩͢ΔʮΑ͍ʯ Λબ୒ ɾ Λߋ৽ i, j AAAB+XicbZC7SgNBFIbPxluMt6ilzWAQLCTsiqBl0MYyorlAsoTZyWwyZi7LzKwQljyCrdZ2YuvTWPomTpItTPSHgY//nMM580cJZ8b6/pdXWFldW98obpa2tnd298r7B02jUk1ogyiudDvChnImacMyy2k70RSLiNNWNLqZ1ltPVBum5IMdJzQUeCBZzAi2zrpnZ4+9csWv+jOhvxDkUIFc9V75u9tXJBVUWsKxMZ3AT2yYYW0Z4XRS6qaGJpiM8IB2HEosqAmz2akTdOKcPoqVdk9aNHN/T2RYGDMWkesU2A7Ncm1q/lfrpDa+CjMmk9RSSeaL4pQjq9D036jPNCWWjx1gopm7FZEh1phYl87ClkhMXCbBcgJ/oXleDRzfXVRq13k6RTiCYziFAC6hBrdQhwYQGMAzvMCrl3lv3rv3MW8tePnMISzI+/wBqsWULQ== AAAB+XicbZC7SgNBFIbPxluMt6ilzWAQLCTsiqBl0MYyorlAsoTZyWwyZi7LzKwQljyCrdZ2YuvTWPomTpItTPSHgY//nMM580cJZ8b6/pdXWFldW98obpa2tnd298r7B02jUk1ogyiudDvChnImacMyy2k70RSLiNNWNLqZ1ltPVBum5IMdJzQUeCBZzAi2zrpnZ4+9csWv+jOhvxDkUIFc9V75u9tXJBVUWsKxMZ3AT2yYYW0Z4XRS6qaGJpiM8IB2HEosqAmz2akTdOKcPoqVdk9aNHN/T2RYGDMWkesU2A7Ncm1q/lfrpDa+CjMmk9RSSeaL4pQjq9D036jPNCWWjx1gopm7FZEh1phYl87ClkhMXCbBcgJ/oXleDRzfXVRq13k6RTiCYziFAC6hBrdQhwYQGMAzvMCrl3lv3rv3MW8tePnMISzI+/wBqsWULQ== AAAB+XicbZC7SgNBFIbPxluMt6ilzWAQLCTsiqBl0MYyorlAsoTZyWwyZi7LzKwQljyCrdZ2YuvTWPomTpItTPSHgY//nMM580cJZ8b6/pdXWFldW98obpa2tnd298r7B02jUk1ogyiudDvChnImacMyy2k70RSLiNNWNLqZ1ltPVBum5IMdJzQUeCBZzAi2zrpnZ4+9csWv+jOhvxDkUIFc9V75u9tXJBVUWsKxMZ3AT2yYYW0Z4XRS6qaGJpiM8IB2HEosqAmz2akTdOKcPoqVdk9aNHN/T2RYGDMWkesU2A7Ncm1q/lfrpDa+CjMmk9RSSeaL4pQjq9D036jPNCWWjx1gopm7FZEh1phYl87ClkhMXCbBcgJ/oXleDRzfXVRq13k6RTiCYziFAC6hBrdQhwYQGMAzvMCrl3lv3rv3MW8tePnMISzI+/wBqsWULQ== AAAB+XicbZC7SgNBFIbPxluMt6ilzWAQLCTsiqBl0MYyorlAsoTZyWwyZi7LzKwQljyCrdZ2YuvTWPomTpItTPSHgY//nMM580cJZ8b6/pdXWFldW98obpa2tnd298r7B02jUk1ogyiudDvChnImacMyy2k70RSLiNNWNLqZ1ltPVBum5IMdJzQUeCBZzAi2zrpnZ4+9csWv+jOhvxDkUIFc9V75u9tXJBVUWsKxMZ3AT2yYYW0Z4XRS6qaGJpiM8IB2HEosqAmz2akTdOKcPoqVdk9aNHN/T2RYGDMWkesU2A7Ncm1q/lfrpDa+CjMmk9RSSeaL4pQjq9D036jPNCWWjx1gopm7FZEh1phYl87ClkhMXCbBcgJ/oXleDRzfXVRq13k6RTiCYziFAC6hBrdQhwYQGMAzvMCrl3lv3rv3MW8tePnMISzI+/wBqsWULQ== ai, aj AAAB/nicbZA9SwNBEIbn/IzxK2ppsxgECwl3ImgZtLGMYD4gOY65zV6yZvfu2N0TQgj4G2y1thNb/4ql/8RNcoVJfGHh4Z0ZZvYNU8G1cd1vZ2V1bX1js7BV3N7Z3dsvHRw2dJIpyuo0EYlqhaiZ4DGrG24Ea6WKoQwFa4aD20m9+cSU5kn8YIYp8yX2Yh5xisZaLQz4OcHgMSiV3Yo7FVkGL4cy5KoFpZ9ON6GZZLGhArVue25q/BEqw6lg42In0yxFOsAea1uMUTLtj6b3jsmpdbokSpR9sSFT9+/ECKXWQxnaTommrxdrE/O/Wjsz0bU/4nGaGRbT2aIoE8QkZPJ50uWKUSOGFpAqbm8ltI8KqbERzW0J5dhm4i0msAyNi4pn+f6yXL3J0ynAMZzAGXhwBVW4gxrUgYKAF3iFN+fZeXc+nM9Z64qTzxzBnJyvX/ralf8= AAAB/nicbZA9SwNBEIbn/IzxK2ppsxgECwl3ImgZtLGMYD4gOY65zV6yZvfu2N0TQgj4G2y1thNb/4ql/8RNcoVJfGHh4Z0ZZvYNU8G1cd1vZ2V1bX1js7BV3N7Z3dsvHRw2dJIpyuo0EYlqhaiZ4DGrG24Ea6WKoQwFa4aD20m9+cSU5kn8YIYp8yX2Yh5xisZaLQz4OcHgMSiV3Yo7FVkGL4cy5KoFpZ9ON6GZZLGhArVue25q/BEqw6lg42In0yxFOsAea1uMUTLtj6b3jsmpdbokSpR9sSFT9+/ECKXWQxnaTommrxdrE/O/Wjsz0bU/4nGaGRbT2aIoE8QkZPJ50uWKUSOGFpAqbm8ltI8KqbERzW0J5dhm4i0msAyNi4pn+f6yXL3J0ynAMZzAGXhwBVW4gxrUgYKAF3iFN+fZeXc+nM9Z64qTzxzBnJyvX/ralf8= AAAB/nicbZA9SwNBEIbn/IzxK2ppsxgECwl3ImgZtLGMYD4gOY65zV6yZvfu2N0TQgj4G2y1thNb/4ql/8RNcoVJfGHh4Z0ZZvYNU8G1cd1vZ2V1bX1js7BV3N7Z3dsvHRw2dJIpyuo0EYlqhaiZ4DGrG24Ea6WKoQwFa4aD20m9+cSU5kn8YIYp8yX2Yh5xisZaLQz4OcHgMSiV3Yo7FVkGL4cy5KoFpZ9ON6GZZLGhArVue25q/BEqw6lg42In0yxFOsAea1uMUTLtj6b3jsmpdbokSpR9sSFT9+/ECKXWQxnaTommrxdrE/O/Wjsz0bU/4nGaGRbT2aIoE8QkZPJ50uWKUSOGFpAqbm8ltI8KqbERzW0J5dhm4i0msAyNi4pn+f6yXL3J0ynAMZzAGXhwBVW4gxrUgYKAF3iFN+fZeXc+nM9Z64qTzxzBnJyvX/ralf8= AAAB/nicbZA9SwNBEIbn/IzxK2ppsxgECwl3ImgZtLGMYD4gOY65zV6yZvfu2N0TQgj4G2y1thNb/4ql/8RNcoVJfGHh4Z0ZZvYNU8G1cd1vZ2V1bX1js7BV3N7Z3dsvHRw2dJIpyuo0EYlqhaiZ4DGrG24Ea6WKoQwFa4aD20m9+cSU5kn8YIYp8yX2Yh5xisZaLQz4OcHgMSiV3Yo7FVkGL4cy5KoFpZ9ON6GZZLGhArVue25q/BEqw6lg42In0yxFOsAea1uMUTLtj6b3jsmpdbokSpR9sSFT9+/ECKXWQxnaTommrxdrE/O/Wjsz0bU/4nGaGRbT2aIoE8QkZPJ50uWKUSOGFpAqbm8ltI8KqbERzW0J5dhm4i0msAyNi4pn+f6yXL3J0ynAMZzAGXhwBVW4gxrUgYKAF3iFN+fZeXc+nM9Z64qTzxzBnJyvX/ralf8=

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·ͱΊ • ਺ֶ͸σʔλαΠΤϯςΟετͷඞਢ஌ࣝͰ͸ͳ͍ • ͔͠͠ػցֶशͷத਎ΛΘ͔͍ͬͯΔ͜ͱ͸ࠩผԽʹͳ Δ • ໘ന͍ͱࢥ͏ͳΒ΍ͬͯΈΔՁ஋͸͋Δ ʢ͔͠͠ਂ෵ʹ͸·Δͱਓੜ͕ఀ଺͢Δ͔΋͠Εͳ͍…ʣ

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ػցֶशͷͨΊͷ ਺ֶษڧ๏ͷఏҊ • ಛʹઢܗ୅਺͸ͪΌΜͱͨ͠ڭՊॻͰֶΜͩ΄͏͕͍͍Ͱ͢ʢʮػ ցֶशͷΤοηϯεʯ͸ೖΓޱͱͯ͠ʣ • ڭՊॻΛ௨ಡ͢Δඞཁͳ͍ͷͰɺඞཁʹԠͯ͡ಡΈ௚͢ͷ͕͍͍ ͷͰ͸ʢඞཁͳ͍෦෼΋ଟ͍ʣ • ίϯϐϡʔλΛ࢖Θͣʹखܭࢉ͢Δͷ΋܇࿅ͱͯ͠ඞཁ • ઢܗ୅਺ʹ͍ͭͯ͸ओཁఆཧͷূ໌΋࣮༻త • ඍੵ෼ʹ͍ͭͯ͸ূ໌ͷཧղ͸ෆཁͰɺܭࢉ໰୊͕େମղ͚Δఔ ౓Ͱ͖Ε͹͍͍ͷͰ͸ɻ

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ਪનਤॻ ʮࣗ෼͕ੲಡΜ͔ͩΒʯͱ͍͏Ҏ֎ʹͱ͘ʹਪનཧ༝͸ͳ͍ͷͰɺଞʹ͍͍ຊ͸ͨ͘͞Μ ͋Δͱࢥ͍·͢ɻେֶ1, 2೥ੜ޲͚ͷڭՊॻͰ͍Ζ͍Ζͱ୳ͯ͠Έ·͠ΐ͏ɻ

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Good News! https://www.microsoft.com/en-us/research/people/cmbishop/#!prml-book ͋ͷPRMLʢӳޠ൛ʣ͕ແྉͰಡΊΔΑ͏ʹͳΓ·ͨ͠ʂ