Kimikazu Kato
November 14, 2018
5.8k

# 機械学習に役立つ数学

2018/11/14 みんなのPython勉強会の発表資料です。

## Kimikazu Kato

November 14, 2018

## Transcript

2. ### ࠓ೔ͷ಺༰ • ࣗݾ঺հ • ຊͷએ఻ • ཪ࿩ɾۤ࿑࿩ • ਺ཧ࠷దԽͱͦͷཧղͷͨΊͷ਺ֶ •

ओʹϥάϥϯδϡະఆ৐਺๏ • ຊʹؚ·ΕΔ͜ͱɺؚ·Εͳ͍͜ͱ

5. ### ࣥචͷഎܠ • େਓͷ਺ֶษڧ΍Γ௚͠ϒʔϜ͕དྷͯΔ͔΋͠Εͳ͍ • ͦͷυϥΠϒཁૉͷҰͭͱͳ͍ͬͯΔͷ͕ػցֶशɾਓ޻ ஌ೳ • ݸਓతʹ΋ɺษڧ͍ͨ͠ͷͰͲ͏͢Ε͹ʁͱ͍͏૬ஊ͕͋ͬ ͨΓ •

ػցֶशͷཧ࿦తͳઆ໌͸ɺϕΠζ౷ܭͳͲͷ؍఺͔Βͷ ॻ੶͕ଟ͘ɺ਺ཧ࠷దԽ͔ΒͷΞϓϩʔν͸͋·Γͳ͍
6. ### ํ਑ • Ͱ͖Δ͚ͩʮඞཁͳ͜ͱ͸શͯॻ͍ͯ͋ΔʯΛΊͨ͟͠ • ࣌ؒత੍໿Ͱඞͣ͠΋ୡ੒Ͱ͖ͯͳ͍͕… • ਺ֶ͸ɺʮূ໌ʯΑΓ΋ʮઆ໌ʯΛॏࢹ • ௿࣍ݩͷέʔεΛ؍࡯͠ɺߴ࣍ݩͷ৔߹͸ূ໌ͤͣʹೲಘͯ͠΋Β͏ •

ূ໌͠ͳͯ͘΋ɺఆཧͷओு͸ਖ਼֬ʹ • ਺ֶͱ਺஋ܭࢉͷઆ໌Λ׬શʹ෼཭ • ͢΂ͯʹαϯϓϧίʔυΛ͚ͭΔ

8. None

10. ### ਺ཧ࠷దԽͱ͸ ༩͑ΒΕ੍ͨ໿ͷ΋ͱͷ༩͑ΒΕͨؔ਺Λ࠷খԽʢ·ͨ͸࠷ େԽʣ͢Δͱ͍͏໰୊ x2 + xy + y2 + 2x

+ 4y <latexit sha1_base64="G4C6fxrFwI495oKxSmWNZiJhiHQ=">AAAB+XicbZDLSgMxFIbP1Futt1GXuggWQSiUmSLosujGZQv2Au1YMmnahmYyQ5IpHYa+iRsXirh143O4c+ejmF4W2nog5OP/zyEnvx9xprTjfFmZtfWNza3sdm5nd2//wD48qqswloTWSMhD2fSxopwJWtNMc9qMJMWBz2nDH95O/caISsVCca+TiHoB7gvWYwRrI3Vse/xQKoyTQmKu0rhwmXTsvFN0ZoVWwV1Avnz6Uf0GgErH/mx3QxIHVGjCsVIt14m0l2KpGeF0kmvHikaYDHGftgwKHFDlpbPNJ+jcKF3UC6U5QqOZ+nsixYFSSeCbzgDrgVr2puJ/XivWvWsvZSKKNRVk/lAv5kiHaBoD6jJJieaJAUwkM7siMsASE23CypkQ3OUvr0K9VHQNV00aNzCvLJzAGVyAC1dQhjuoQA0IjOARnuHFSq0n69V6m7dmrMXMMfwp6/0HpHeUkQ==</latexit> <latexit sha1_base64="0VLOn/OcbEm4Bc1VZd2AwfGlSO8=">AAAB+XicbZDLSgMxFIbPeK31NupSkWARhEKZKYIui25ctmAv0I4lk2ba0MyFJFM6DF36Fm5cKOLWTZ/Dnc/gS5heFtp6IOTj/88hJ78bcSaVZX0ZK6tr6xubma3s9s7u3r55cFiTYSwIrZKQh6LhYkk5C2hVMcVpIxIU+y6ndbd/O/HrAyokC4N7lUTU8XE3YB4jWGmpbZrDh2J+mOQTfRWH+cukbeasgjUttAz2HHKlk3Hl+/F0XG6bn61OSGKfBopwLGXTtiLlpFgoRjgdZVuxpBEmfdylTY0B9ql00unmI3SulQ7yQqFPoNBU/T2RYl/KxHd1p49VTy56E/E/rxkr79pJWRDFigZk9pAXc6RCNIkBdZigRPFEAyaC6V0R6WGBidJhZXUI9uKXl6FWLNiaKzqNG5hVBo7hDC7AhisowR2UoQoEBvAEL/BqpMaz8Wa8z1pXjPnMEfwp4+MHgryV9w==</latexit> <latexit sha1_base64="0VLOn/OcbEm4Bc1VZd2AwfGlSO8=">AAAB+XicbZDLSgMxFIbPeK31NupSkWARhEKZKYIui25ctmAv0I4lk2ba0MyFJFM6DF36Fm5cKOLWTZ/Dnc/gS5heFtp6IOTj/88hJ78bcSaVZX0ZK6tr6xubma3s9s7u3r55cFiTYSwIrZKQh6LhYkk5C2hVMcVpIxIU+y6ndbd/O/HrAyokC4N7lUTU8XE3YB4jWGmpbZrDh2J+mOQTfRWH+cukbeasgjUttAz2HHKlk3Hl+/F0XG6bn61OSGKfBopwLGXTtiLlpFgoRjgdZVuxpBEmfdylTY0B9ql00unmI3SulQ7yQqFPoNBU/T2RYl/KxHd1p49VTy56E/E/rxkr79pJWRDFigZk9pAXc6RCNIkBdZigRPFEAyaC6V0R6WGBidJhZXUI9uKXl6FWLNiaKzqNG5hVBo7hDC7AhisowR2UoQoEBvAEL/BqpMaz8Wa8z1pXjPnMEfwp4+MHgryV9w==</latexit> <latexit sha1_base64="3YwNdNiYMFSWdPltxu7RfpfdQUY=">AAAB+XicbZDLSgMxFIbP1Futt1GXboJFEAplpgi6LLpxWcFeoB1LJs20oZnMkGRKh6Fv4saFIm59E3e+jWk7C209EPLx/+eQk9+POVPacb6twsbm1vZOcbe0t39weGQfn7RUlEhCmyTikez4WFHOBG1qpjntxJLi0Oe07Y/v5n57QqVikXjUaUy9EA8FCxjB2kh9254+1SrTtJKaqzatXKV9u+xUnUWhdXBzKENejb791RtEJAmp0IRjpbquE2svw1Izwums1EsUjTEZ4yHtGhQ4pMrLFpvP0IVRBiiIpDlCo4X6eyLDoVJp6JvOEOuRWvXm4n9eN9HBjZcxESeaCrJ8KEg40hGax4AGTFKieWoAE8nMroiMsMREm7BKJgR39cvr0KpVXcMPTrl+m8dRhDM4h0tw4RrqcA8NaAKBCTzDK7xZmfVivVsfy9aClc+cwp+yPn8AlH2STA==</latexit> x + y = 0 <latexit sha1_base64="7/EnbG619G+dyndXMk7ryXe7N50=">AAAB7HicbZDLSgMxFIbPeK31VnWpi2ARBKHMuNGNUHTjsgWnLbRDyaSZNjTJDElGHIY+gxsXirj1GXwOd+58FNPLQlt/CHz85xxyzh8mnGnjul/O0vLK6tp6YaO4ubW9s1va22/oOFWE+iTmsWqFWFPOJPUNM5y2EkWxCDlthsObcb15T5VmsbwzWUIDgfuSRYxgYy3/4Sy7crulsltxJ0KL4M2gXD36qH8DQK1b+uz0YpIKKg3hWOu25yYmyLEyjHA6KnZSTRNMhrhP2xYlFlQH+WTZETqxTg9FsbJPGjRxf0/kWGididB2CmwGer42Nv+rtVMTXQY5k0lqqCTTj6KUIxOj8eWoxxQlhmcWMFHM7orIACtMjM2naEPw5k9ehMZ5xbNct2lcw1QFOIRjOAUPLqAKt1ADHwgweIRneHGk8+S8Om/T1iVnNnMAf+S8/wAqEpB2</latexit> <latexit sha1_base64="d50r2+C94qjmMxhh95DV8I3TZnM=">AAAB7HicbZDLSsNAFIZP6q3WW9WlIoNFEISSuNGNUHTjsgXTFtpQJtNJO3QyCTMTMYQuXbtxoYhbn6HP4c5n8CWcXhba+sPAx3/OYc75/ZgzpW37y8otLa+sruXXCxubW9s7xd29uooSSahLIh7Jpo8V5UxQVzPNaTOWFIc+pw1/cDOuN+6pVCwSdzqNqRfinmABI1gby304S6/sTrFkl+2J0CI4MyhVDke178ejUbVT/Gx3I5KEVGjCsVItx461l2GpGeF0WGgnisaYDHCPtgwKHFLlZZNlh+jEOF0URNI8odHE/T2R4VCpNPRNZ4h1X83XxuZ/tVaig0svYyJONBVk+lGQcKQjNL4cdZmkRPPUACaSmV0R6WOJiTb5FEwIzvzJi1A/LzuGayaNa5gqDwdwDKfgwAVU4Baq4AIBBk/wAq+WsJ6tN+t92pqzZjP78EfWxw8IV5Hc</latexit> <latexit sha1_base64="d50r2+C94qjmMxhh95DV8I3TZnM=">AAAB7HicbZDLSsNAFIZP6q3WW9WlIoNFEISSuNGNUHTjsgXTFtpQJtNJO3QyCTMTMYQuXbtxoYhbn6HP4c5n8CWcXhba+sPAx3/OYc75/ZgzpW37y8otLa+sruXXCxubW9s7xd29uooSSahLIh7Jpo8V5UxQVzPNaTOWFIc+pw1/cDOuN+6pVCwSdzqNqRfinmABI1gby304S6/sTrFkl+2J0CI4MyhVDke178ejUbVT/Gx3I5KEVGjCsVItx461l2GpGeF0WGgnisaYDHCPtgwKHFLlZZNlh+jEOF0URNI8odHE/T2R4VCpNPRNZ4h1X83XxuZ/tVaig0svYyJONBVk+lGQcKQjNL4cdZmkRPPUACaSmV0R6WOJiTb5FEwIzvzJi1A/LzuGayaNa5gqDwdwDKfgwAVU4Baq4AIBBk/wAq+WsJ6tN+t92pqzZjP78EfWxw8IV5Hc</latexit> <latexit sha1_base64="IjsygNkVUs3wQ0OAiraJ0gLonbA=">AAAB7HicbZBNS8NAEIYn9avWr6pHL4tFEISSeNGLUPTisYKphTaUzXbTLt1swu5EDKW/wYsHRbz6g7z5b9y2OWjrCwsP78ywM2+YSmHQdb+d0srq2vpGebOytb2zu1fdP2iZJNOM+yyRiW6H1HApFPdRoOTtVHMah5I/hKObaf3hkWsjEnWPecqDmA6UiASjaC3/6Sy/cnvVmlt3ZyLL4BVQg0LNXvWr209YFnOFTFJjOp6bYjCmGgWTfFLpZoanlI3ogHcsKhpzE4xny07IiXX6JEq0fQrJzP09MaaxMXkc2s6Y4tAs1qbmf7VOhtFlMBYqzZArNv8oyiTBhEwvJ32hOUOZW6BMC7srYUOqKUObT8WG4C2evAyt87pn+c6tNa6LOMpwBMdwCh5cQANuoQk+MBDwDK/w5ijnxXl3PuatJaeYOYQ/cj5/ABoYjjE=</latexit> Minimize Subject to ྫɿ ←໨తؔ਺ ←੍໿ࣜ

14. ### (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 <latexit sha1_base64="v2A8WjmdhF4yb8Koqa2ouC/k9wg=">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</latexit> <latexit sha1_base64="v2A8WjmdhF4yb8Koqa2ouC/k9wg=">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</latexit> <latexit sha1_base64="v2A8WjmdhF4yb8Koqa2ouC/k9wg=">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</latexit> <latexit sha1_base64="v2A8WjmdhF4yb8Koqa2ouC/k9wg=">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</latexit> x5 + 3x3 4x2 0 = x5 0 + 3 x3 0 4 x2 0 = 5x4 + 3 ⇥ 3x2 4 ⇥ 2x = 5x4 + 9x2 8x <latexit sha1_base64="VdBVctCD+AZR5U1nYJvNrSKSI+U=">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</latexit> <latexit sha1_base64="VdBVctCD+AZR5U1nYJvNrSKSI+U=">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</latexit> <latexit sha1_base64="VdBVctCD+AZR5U1nYJvNrSKSI+U=">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</latexit> <latexit sha1_base64="VdBVctCD+AZR5U1nYJvNrSKSI+U=">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</latexit> ॏཁެࣜ ܭࢉྫ

16. ### ޯ഑ rf = 0 B B B B @ @f

@x1 @f @x2 . . . @f @xn 1 C C C C A <latexit sha1_base64="hC1lFOa7kcTq/yfZde0vM408z4g=">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</latexit> <latexit sha1_base64="LJSyuN+lgRu5CL2m4nWlo9jmyBc=">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</latexit> <latexit sha1_base64="LJSyuN+lgRu5CL2m4nWlo9jmyBc=">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</latexit> <latexit sha1_base64="f4YMgJx/+UhxtJVbH1guIFy0GUY=">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</latexit> Λޯ഑ͱݺͿ rf = 0 <latexit sha1_base64="i6wBboO4NG7nVj5mfWggrqQGqKg=">AAAB8XicbZC7SgNBFIbPxluMt6ilFoNBsAq7NtoIQRvLBMwFkyWcncwmQ2Znl5lZISx5CxsLRWx9AZ/Dzs5HcXIpNPGHgY//nMOc8weJ4Nq47peTW1ldW9/Ibxa2tnd294r7Bw0dp4qyOo1FrFoBaia4ZHXDjWCtRDGMAsGawfBmUm8+MKV5LO/MKGF+hH3JQ07RWOu+IzEQSMIrt1ssuWV3KrIM3hxKleOP2jcAVLvFz04vpmnEpKECtW57bmL8DJXhVLBxoZNqliAdYp+1LUqMmPaz6cZjcmqdHgljZZ80ZOr+nsgw0noUBbYzQjPQi7WJ+V+tnZrw0s+4TFLDJJ19FKaCmJhMzic9rhg1YmQBqeJ2V0IHqJAaG1LBhuAtnrwMjfOyZ7lm07iGmfJwBCdwBh5cQAVuoQp1oCDhEZ7hxdHOk/PqvM1ac8585hD+yHn/AZ0Xkmw=</latexit> <latexit sha1_base64="EBcZz4Qhcz2fIBuwKjfgLbxt5lw=">AAAB8XicbZBLSgNBEIZr4ivGV9SlIo1BcBVm3OhGCLpxmYBJxGQINZ2epElPz9DdI4SQpTdw40IRt14g53DnGbyEncdCE39o+Piriq76g0RwbVz3y8ksLa+srmXXcxubW9s7+d29mo5TRVmVxiJWdwFqJrhkVcONYHeJYhgFgtWD3vW4Xn9gSvNY3pp+wvwIO5KHnKKx1n1TYiCQhJduK19wi+5EZBG8GRRKh6PK9+PRqNzKfzbbMU0jJg0VqHXDcxPjD1AZTgUb5pqpZgnSHnZYw6LEiGl/MNl4SE6s0yZhrOyThkzc3xMDjLTuR4HtjNB09XxtbP5Xa6QmvPAHXCapYZJOPwpTQUxMxueTNleMGtG3gFRxuyuhXVRIjQ0pZ0Pw5k9ehNpZ0bNcsWlcwVRZOIBjOAUPzqEEN1CGKlCQ8AQv8Opo59l5c96nrRlnNrMPf+R8/AB7XJPS</latexit> <latexit sha1_base64="EBcZz4Qhcz2fIBuwKjfgLbxt5lw=">AAAB8XicbZBLSgNBEIZr4ivGV9SlIo1BcBVm3OhGCLpxmYBJxGQINZ2epElPz9DdI4SQpTdw40IRt14g53DnGbyEncdCE39o+Piriq76g0RwbVz3y8ksLa+srmXXcxubW9s7+d29mo5TRVmVxiJWdwFqJrhkVcONYHeJYhgFgtWD3vW4Xn9gSvNY3pp+wvwIO5KHnKKx1n1TYiCQhJduK19wi+5EZBG8GRRKh6PK9+PRqNzKfzbbMU0jJg0VqHXDcxPjD1AZTgUb5pqpZgnSHnZYw6LEiGl/MNl4SE6s0yZhrOyThkzc3xMDjLTuR4HtjNB09XxtbP5Xa6QmvPAHXCapYZJOPwpTQUxMxueTNleMGtG3gFRxuyuhXVRIjQ0pZ0Pw5k9ehNpZ0bNcsWlcwVRZOIBjOAUPzqEEN1CGKlCQ8AQv8Opo59l5c96nrRlnNrMPf+R8/AB7XJPS</latexit> <latexit sha1_base64="2jek3adgZlMoxExh2C8HvCm+H1s=">AAAB8XicbZBNS8NAEIYn9avWr6hHL4tF8FQSL3oRil48VrAf2IYy2W7apZtN2N0IJfRfePGgiFf/jTf/jds2B219YeHhnRl25g1TwbXxvG+ntLa+sblV3q7s7O7tH7iHRy2dZIqyJk1Eojohaia4ZE3DjWCdVDGMQ8Ha4fh2Vm8/MaV5Ih/MJGVBjEPJI07RWOuxJzEUSKJrr+9WvZo3F1kFv4AqFGr03a/eIKFZzKShArXu+l5qghyV4VSwaaWXaZYiHeOQdS1KjJkO8vnGU3JmnQGJEmWfNGTu/p7IMdZ6Eoe2M0Yz0su1mflfrZuZ6CrIuUwzwyRdfBRlgpiEzM4nA64YNWJiAanidldCR6iQGhtSxYbgL5+8Cq2Lmm/53qvWb4o4ynACp3AOPlxCHe6gAU2gIOEZXuHN0c6L8+58LFpLTjFzDH/kfP4AjR2QJw==</latexit> ͱ͓͘ͱɺۃ஋ΛٻΊΒΕΔʢ͔΋͠Εͳ͍ʣ
17. ### ޯ഑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)
18. ### ޯ഑߱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
19. ### ϥάϥϯδϡະఆ৐਺๏ f(x, y) <latexit sha1_base64="9eJ9KPRF7PwM5mM5fqqiuW86LXQ=">AAAB7XicbZDLSgMxFIbP1Futt6pLN8EiVJAyI4Iui25cVrAXaIeSSTNtbCYZkow4DH0HNy4Ucev7uPNtTNtZaOsPgY//nEPO+YOYM21c99sprKyurW8UN0tb2zu7e+X9g5aWiSK0SSSXqhNgTTkTtGmY4bQTK4qjgNN2ML6Z1tuPVGkmxb1JY+pHeChYyAg21mqF1aez9LRfrrg1dya0DF4OFcjV6Je/egNJkogKQzjWuuu5sfEzrAwjnE5KvUTTGJMxHtKuRYEjqv1stu0EnVhngEKp7BMGzdzfExmOtE6jwHZG2Iz0Ym1q/lfrJia88jMm4sRQQeYfhQlHRqLp6WjAFCWGpxYwUczuisgIK0yMDahkQ/AWT16G1nnNs3x3Ualf53EU4QiOoQoeXEIdbqEBTSDwAM/wCm+OdF6cd+dj3lpw8plD+CPn8wezN46K</latexit> <latexit sha1_base64="9eJ9KPRF7PwM5mM5fqqiuW86LXQ=">AAAB7XicbZDLSgMxFIbP1Futt6pLN8EiVJAyI4Iui25cVrAXaIeSSTNtbCYZkow4DH0HNy4Ucev7uPNtTNtZaOsPgY//nEPO+YOYM21c99sprKyurW8UN0tb2zu7e+X9g5aWiSK0SSSXqhNgTTkTtGmY4bQTK4qjgNN2ML6Z1tuPVGkmxb1JY+pHeChYyAg21mqF1aez9LRfrrg1dya0DF4OFcjV6Je/egNJkogKQzjWuuu5sfEzrAwjnE5KvUTTGJMxHtKuRYEjqv1stu0EnVhngEKp7BMGzdzfExmOtE6jwHZG2Iz0Ym1q/lfrJia88jMm4sRQQeYfhQlHRqLp6WjAFCWGpxYwUczuisgIK0yMDahkQ/AWT16G1nnNs3x3Ualf53EU4QiOoQoeXEIdbqEBTSDwAM/wCm+OdF6cd+dj3lpw8plD+CPn8wezN46K</latexit> <latexit sha1_base64="9eJ9KPRF7PwM5mM5fqqiuW86LXQ=">AAAB7XicbZDLSgMxFIbP1Futt6pLN8EiVJAyI4Iui25cVrAXaIeSSTNtbCYZkow4DH0HNy4Ucev7uPNtTNtZaOsPgY//nEPO+YOYM21c99sprKyurW8UN0tb2zu7e+X9g5aWiSK0SSSXqhNgTTkTtGmY4bQTK4qjgNN2ML6Z1tuPVGkmxb1JY+pHeChYyAg21mqF1aez9LRfrrg1dya0DF4OFcjV6Je/egNJkogKQzjWuuu5sfEzrAwjnE5KvUTTGJMxHtKuRYEjqv1stu0EnVhngEKp7BMGzdzfExmOtE6jwHZG2Iz0Ym1q/lfrJia88jMm4sRQQeYfhQlHRqLp6WjAFCWGpxYwUczuisgIK0yMDahkQ/AWT16G1nnNs3x3Ualf53EU4QiOoQoeXEIdbqEBTSDwAM/wCm+OdF6cd+dj3lpw8plD+CPn8wezN46K</latexit> <latexit

sha1_base64="ck8pdC+ekZH4nUmSP+ZG7r8lEyk=">AAAB2XicbZDNSgMxFIXv1L86Vq1rN8EiuCozbnQpuHFZwbZCO5RM5k4bmskMyR2hDH0BF25EfC93vo3pz0JbDwQ+zknIvSculLQUBN9ebWd3b/+gfugfNfzjk9Nmo2fz0gjsilzl5jnmFpXU2CVJCp8LgzyLFfbj6f0i77+gsTLXTzQrMMr4WMtUCk7O6oyaraAdLMW2IVxDC9YaNb+GSS7KDDUJxa0dhEFBUcUNSaFw7g9LiwUXUz7GgUPNM7RRtRxzzi6dk7A0N+5oYkv394uKZ9bOstjdzDhN7Ga2MP/LBiWlt1EldVESarH6KC0Vo5wtdmaJNChIzRxwYaSblYkJN1yQa8Z3HYSbG29D77odOn4MoA7ncAFXEMIN3MEDdKALAhJ4hXdv4r15H6uuat66tDP4I+/zBzjGijg=</latexit> <latexit sha1_base64="4QsSB70Qi04m97dQBnmQWme8VIM=">AAAB4nicbZBLSwMxFIXv1FetVatbN8EiVJAy40aXghuXFewD2qFk0jttbCYZkow4lP4HNy4U8Ue589+YPhbaeiDwcU5C7j1RKrixvv/tFTY2t7Z3irulvfL+wWHlqNwyKtMMm0wJpTsRNSi4xKblVmAn1UiTSGA7Gt/O8vYTasOVfLB5imFCh5LHnFHrrFZce77Iz/uVql/35yLrECyhCks1+pWv3kCxLEFpmaDGdAM/teGEasuZwGmplxlMKRvTIXYdSpqgCSfzaafkzDkDEivtjrRk7v5+MaGJMXkSuZsJtSOzms3M/7JuZuPrcMJlmlmUbPFRnAliFZmtTgZcI7Mid0CZ5m5WwkZUU2ZdQSVXQrC68jq0LuuB43sfinACp1CDAK7gBu6gAU1g8Agv8AbvnvJevY9FXQVv2dsx/JH3+QOOXY0y</latexit> <latexit sha1_base64="4QsSB70Qi04m97dQBnmQWme8VIM=">AAAB4nicbZBLSwMxFIXv1FetVatbN8EiVJAy40aXghuXFewD2qFk0jttbCYZkow4lP4HNy4U8Ue589+YPhbaeiDwcU5C7j1RKrixvv/tFTY2t7Z3irulvfL+wWHlqNwyKtMMm0wJpTsRNSi4xKblVmAn1UiTSGA7Gt/O8vYTasOVfLB5imFCh5LHnFHrrFZce77Iz/uVql/35yLrECyhCks1+pWv3kCxLEFpmaDGdAM/teGEasuZwGmplxlMKRvTIXYdSpqgCSfzaafkzDkDEivtjrRk7v5+MaGJMXkSuZsJtSOzms3M/7JuZuPrcMJlmlmUbPFRnAliFZmtTgZcI7Mid0CZ5m5WwkZUU2ZdQSVXQrC68jq0LuuB43sfinACp1CDAK7gBu6gAU1g8Agv8AbvnvJevY9FXQVv2dsx/JH3+QOOXY0y</latexit> <latexit sha1_base64="MRUYAfazeX61kQ75Tpd5BxgO8xc=">AAAB7XicbZDLSgMxFIbP1Futt6pLN8EiVJAy040ui25cVrAXaIeSSTNtbCYZkow4DH0HNy4Ucev7uPNtTNtZaOsPgY//nEPO+YOYM21c99sprK1vbG4Vt0s7u3v7B+XDo7aWiSK0RSSXqhtgTTkTtGWY4bQbK4qjgNNOMLmZ1TuPVGkmxb1JY+pHeCRYyAg21mqH1aeL9HxQrrg1dy60Cl4OFcjVHJS/+kNJkogKQzjWuue5sfEzrAwjnE5L/UTTGJMJHtGeRYEjqv1svu0UnVlniEKp7BMGzd3fExmOtE6jwHZG2Iz1cm1m/lfrJSa88jMm4sRQQRYfhQlHRqLZ6WjIFCWGpxYwUczuisgYK0yMDahkQ/CWT16Fdr3mWb5zK43rPI4inMApVMGDS2jALTShBQQe4Ble4c2Rzovz7nwsWgtOPnMMf+R8/gCx946G</latexit> <latexit sha1_base64="9eJ9KPRF7PwM5mM5fqqiuW86LXQ=">AAAB7XicbZDLSgMxFIbP1Futt6pLN8EiVJAyI4Iui25cVrAXaIeSSTNtbCYZkow4DH0HNy4Ucev7uPNtTNtZaOsPgY//nEPO+YOYM21c99sprKyurW8UN0tb2zu7e+X9g5aWiSK0SSSXqhNgTTkTtGmY4bQTK4qjgNN2ML6Z1tuPVGkmxb1JY+pHeChYyAg21mqF1aez9LRfrrg1dya0DF4OFcjV6Je/egNJkogKQzjWuuu5sfEzrAwjnE5KvUTTGJMxHtKuRYEjqv1stu0EnVhngEKp7BMGzdzfExmOtE6jwHZG2Iz0Ym1q/lfrJia88jMm4sRQQeYfhQlHRqLp6WjAFCWGpxYwUczuisgIK0yMDahkQ/AWT16G1nnNs3x3Ualf53EU4QiOoQoeXEIdbqEBTSDwAM/wCm+OdF6cd+dj3lpw8plD+CPn8wezN46K</latexit> <latexit sha1_base64="9eJ9KPRF7PwM5mM5fqqiuW86LXQ=">AAAB7XicbZDLSgMxFIbP1Futt6pLN8EiVJAyI4Iui25cVrAXaIeSSTNtbCYZkow4DH0HNy4Ucev7uPNtTNtZaOsPgY//nEPO+YOYM21c99sprKyurW8UN0tb2zu7e+X9g5aWiSK0SSSXqhNgTTkTtGmY4bQTK4qjgNN2ML6Z1tuPVGkmxb1JY+pHeChYyAg21mqF1aez9LRfrrg1dya0DF4OFcjV6Je/egNJkogKQzjWuuu5sfEzrAwjnE5KvUTTGJMxHtKuRYEjqv1stu0EnVhngEKp7BMGzdzfExmOtE6jwHZG2Iz0Ym1q/lfrJia88jMm4sRQQeYfhQlHRqLp6WjAFCWGpxYwUczuisgIK0yMDahkQ/AWT16G1nnNs3x3Ualf53EU4QiOoQoeXEIdbqEBTSDwAM/wCm+OdF6cd+dj3lpw8plD+CPn8wezN46K</latexit> <latexit sha1_base64="9eJ9KPRF7PwM5mM5fqqiuW86LXQ=">AAAB7XicbZDLSgMxFIbP1Futt6pLN8EiVJAyI4Iui25cVrAXaIeSSTNtbCYZkow4DH0HNy4Ucev7uPNtTNtZaOsPgY//nEPO+YOYM21c99sprKyurW8UN0tb2zu7e+X9g5aWiSK0SSSXqhNgTTkTtGmY4bQTK4qjgNN2ML6Z1tuPVGkmxb1JY+pHeChYyAg21mqF1aez9LRfrrg1dya0DF4OFcjV6Je/egNJkogKQzjWuuu5sfEzrAwjnE5KvUTTGJMxHtKuRYEjqv1stu0EnVhngEKp7BMGzdzfExmOtE6jwHZG2Iz0Ym1q/lfrJia88jMm4sRQQeYfhQlHRqLp6WjAFCWGpxYwUczuisgIK0yMDahkQ/AWT16G1nnNs3x3Ualf53EU4QiOoQoeXEIdbqEBTSDwAM/wCm+OdF6cd+dj3lpw8plD+CPn8wezN46K</latexit> <latexit sha1_base64="9eJ9KPRF7PwM5mM5fqqiuW86LXQ=">AAAB7XicbZDLSgMxFIbP1Futt6pLN8EiVJAyI4Iui25cVrAXaIeSSTNtbCYZkow4DH0HNy4Ucev7uPNtTNtZaOsPgY//nEPO+YOYM21c99sprKyurW8UN0tb2zu7e+X9g5aWiSK0SSSXqhNgTTkTtGmY4bQTK4qjgNN2ML6Z1tuPVGkmxb1JY+pHeChYyAg21mqF1aez9LRfrrg1dya0DF4OFcjV6Je/egNJkogKQzjWuuu5sfEzrAwjnE5KvUTTGJMxHtKuRYEjqv1stu0EnVhngEKp7BMGzdzfExmOtE6jwHZG2Iz0Ym1q/lfrJia88jMm4sRQQeYfhQlHRqLp6WjAFCWGpxYwUczuisgIK0yMDahkQ/AWT16G1nnNs3x3Ualf53EU4QiOoQoeXEIdbqEBTSDwAM/wCm+OdF6cd+dj3lpw8plD+CPn8wezN46K</latexit> <latexit sha1_base64="9eJ9KPRF7PwM5mM5fqqiuW86LXQ=">AAAB7XicbZDLSgMxFIbP1Futt6pLN8EiVJAyI4Iui25cVrAXaIeSSTNtbCYZkow4DH0HNy4Ucev7uPNtTNtZaOsPgY//nEPO+YOYM21c99sprKyurW8UN0tb2zu7e+X9g5aWiSK0SSSXqhNgTTkTtGmY4bQTK4qjgNN2ML6Z1tuPVGkmxb1JY+pHeChYyAg21mqF1aez9LRfrrg1dya0DF4OFcjV6Je/egNJkogKQzjWuuu5sfEzrAwjnE5KvUTTGJMxHtKuRYEjqv1stu0EnVhngEKp7BMGzdzfExmOtE6jwHZG2Iz0Ym1q/lfrJia88jMm4sRQQeYfhQlHRqLp6WjAFCWGpxYwUczuisgIK0yMDahkQ/AWT16G1nnNs3x3Ualf53EU4QiOoQoeXEIdbqEBTSDwAM/wCm+OdF6cd+dj3lpw8plD+CPn8wezN46K</latexit> <latexit sha1_base64="9eJ9KPRF7PwM5mM5fqqiuW86LXQ=">AAAB7XicbZDLSgMxFIbP1Futt6pLN8EiVJAyI4Iui25cVrAXaIeSSTNtbCYZkow4DH0HNy4Ucev7uPNtTNtZaOsPgY//nEPO+YOYM21c99sprKyurW8UN0tb2zu7e+X9g5aWiSK0SSSXqhNgTTkTtGmY4bQTK4qjgNN2ML6Z1tuPVGkmxb1JY+pHeChYyAg21mqF1aez9LRfrrg1dya0DF4OFcjV6Je/egNJkogKQzjWuuu5sfEzrAwjnE5KvUTTGJMxHtKuRYEjqv1stu0EnVhngEKp7BMGzdzfExmOtE6jwHZG2Iz0Ym1q/lfrJia88jMm4sRQQeYfhQlHRqLp6WjAFCWGpxYwUczuisgIK0yMDahkQ/AWT16G1nnNs3x3Ualf53EU4QiOoQoeXEIdbqEBTSDwAM/wCm+OdF6cd+dj3lpw8plD+CPn8wezN46K</latexit> g(x, y) = 0 <latexit sha1_base64="P8AV/tm+teqXGKUJIXmiPWcoTu8=">AAAB73icbZDLSgMxFIZPvNZ6q7p0EyxCBSkzIuhGKLpxWcFeoB1KJs20oZnMmGTEYehLuHGhiFtfx51vY9rOQlt/CHz85xxyzu/HgmvjON9oaXlldW29sFHc3Nre2S3t7Td1lCjKGjQSkWr7RDPBJWsYbgRrx4qR0Bes5Y9uJvXWI1OaR/LepDHzQjKQPOCUGGu1B5Wn0/TkyumVyk7VmQovgptDGXLVe6Wvbj+iScikoYJo3XGd2HgZUYZTwcbFbqJZTOiIDFjHoiQh01423XeMj63Tx0Gk7JMGT93fExkJtU5D33aGxAz1fG1i/lfrJCa49DIu48QwSWcfBYnAJsKT43GfK0aNSC0QqrjdFdMhUYQaG1HRhuDOn7wIzbOqa/nuvFy7zuMowCEcQQVcuIAa3EIdGkBBwDO8wht6QC/oHX3MWpdQPnMAf4Q+fwCnyI8M</latexit> <latexit sha1_base64="P8AV/tm+teqXGKUJIXmiPWcoTu8=">AAAB73icbZDLSgMxFIZPvNZ6q7p0EyxCBSkzIuhGKLpxWcFeoB1KJs20oZnMmGTEYehLuHGhiFtfx51vY9rOQlt/CHz85xxyzu/HgmvjON9oaXlldW29sFHc3Nre2S3t7Td1lCjKGjQSkWr7RDPBJWsYbgRrx4qR0Bes5Y9uJvXWI1OaR/LepDHzQjKQPOCUGGu1B5Wn0/TkyumVyk7VmQovgptDGXLVe6Wvbj+iScikoYJo3XGd2HgZUYZTwcbFbqJZTOiIDFjHoiQh01423XeMj63Tx0Gk7JMGT93fExkJtU5D33aGxAz1fG1i/lfrJCa49DIu48QwSWcfBYnAJsKT43GfK0aNSC0QqrjdFdMhUYQaG1HRhuDOn7wIzbOqa/nuvFy7zuMowCEcQQVcuIAa3EIdGkBBwDO8wht6QC/oHX3MWpdQPnMAf4Q+fwCnyI8M</latexit> <latexit sha1_base64="P8AV/tm+teqXGKUJIXmiPWcoTu8=">AAAB73icbZDLSgMxFIZPvNZ6q7p0EyxCBSkzIuhGKLpxWcFeoB1KJs20oZnMmGTEYehLuHGhiFtfx51vY9rOQlt/CHz85xxyzu/HgmvjON9oaXlldW29sFHc3Nre2S3t7Td1lCjKGjQSkWr7RDPBJWsYbgRrx4qR0Bes5Y9uJvXWI1OaR/LepDHzQjKQPOCUGGu1B5Wn0/TkyumVyk7VmQovgptDGXLVe6Wvbj+iScikoYJo3XGd2HgZUYZTwcbFbqJZTOiIDFjHoiQh01423XeMj63Tx0Gk7JMGT93fExkJtU5D33aGxAz1fG1i/lfrJCa49DIu48QwSWcfBYnAJsKT43GfK0aNSC0QqrjdFdMhUYQaG1HRhuDOn7wIzbOqa/nuvFy7zuMowCEcQQVcuIAa3EIdGkBBwDO8wht6QC/oHX3MWpdQPnMAf4Q+fwCnyI8M</latexit> <latexit sha1_base64="P8AV/tm+teqXGKUJIXmiPWcoTu8=">AAAB73icbZDLSgMxFIZPvNZ6q7p0EyxCBSkzIuhGKLpxWcFeoB1KJs20oZnMmGTEYehLuHGhiFtfx51vY9rOQlt/CHz85xxyzu/HgmvjON9oaXlldW29sFHc3Nre2S3t7Td1lCjKGjQSkWr7RDPBJWsYbgRrx4qR0Bes5Y9uJvXWI1OaR/LepDHzQjKQPOCUGGu1B5Wn0/TkyumVyk7VmQovgptDGXLVe6Wvbj+iScikoYJo3XGd2HgZUYZTwcbFbqJZTOiIDFjHoiQh01423XeMj63Tx0Gk7JMGT93fExkJtU5D33aGxAz1fG1i/lfrJCa49DIu48QwSWcfBYnAJsKT43GfK0aNSC0QqrjdFdMhUYQaG1HRhuDOn7wIzbOqa/nuvFy7zuMowCEcQQVcuIAa3EIdGkBBwDO8wht6QC/oHX3MWpdQPnMAf4Q+fwCnyI8M</latexit> L(x, y, ) = f(x, y) + g(x, y) <latexit sha1_base64="rCgmpYHoyGRkVEcY7fEWIPQgUN4=">AAACEHicbVDNS8MwHE39nPOr6tFLcIgbjtGKoBdh6MWDhwnuA7Yy0izdwtK0JKlYyv4EL/4rXjwo4tWjN/8b064H3XwQeHnv90h+zw0Zlcqyvo2FxaXlldXCWnF9Y3Nr29zZbckgEpg0ccAC0XGRJIxy0lRUMdIJBUG+y0jbHV+lfvueCEkDfqfikDg+GnLqUYyUlvrm0U35oRpXe0xHBqgCL6CXCpVjmEtwmN37ZsmqWRngPLFzUgI5Gn3zqzcIcOQTrjBDUnZtK1ROgoSimJFJsRdJEiI8RkPS1ZQjn0gnyRaawEOtDKAXCH24gpn6O5EgX8rYd/Wkj9RIznqp+J/XjZR37iSUh5EiHE8f8iIGVQDTduCACoIVizVBWFD9V4hHSCCsdIdFXYI9u/I8aZ3UbM1vT0v1y7yOAtgHB6AMbHAG6uAaNEATYPAInsEreDOejBfj3fiYji4YeWYP/IHx+QMoupoi</latexit> <latexit sha1_base64="rCgmpYHoyGRkVEcY7fEWIPQgUN4=">AAACEHicbVDNS8MwHE39nPOr6tFLcIgbjtGKoBdh6MWDhwnuA7Yy0izdwtK0JKlYyv4EL/4rXjwo4tWjN/8b064H3XwQeHnv90h+zw0Zlcqyvo2FxaXlldXCWnF9Y3Nr29zZbckgEpg0ccAC0XGRJIxy0lRUMdIJBUG+y0jbHV+lfvueCEkDfqfikDg+GnLqUYyUlvrm0U35oRpXe0xHBqgCL6CXCpVjmEtwmN37ZsmqWRngPLFzUgI5Gn3zqzcIcOQTrjBDUnZtK1ROgoSimJFJsRdJEiI8RkPS1ZQjn0gnyRaawEOtDKAXCH24gpn6O5EgX8rYd/Wkj9RIznqp+J/XjZR37iSUh5EiHE8f8iIGVQDTduCACoIVizVBWFD9V4hHSCCsdIdFXYI9u/I8aZ3UbM1vT0v1y7yOAtgHB6AMbHAG6uAaNEATYPAInsEreDOejBfj3fiYji4YeWYP/IHx+QMoupoi</latexit> <latexit sha1_base64="rCgmpYHoyGRkVEcY7fEWIPQgUN4=">AAACEHicbVDNS8MwHE39nPOr6tFLcIgbjtGKoBdh6MWDhwnuA7Yy0izdwtK0JKlYyv4EL/4rXjwo4tWjN/8b064H3XwQeHnv90h+zw0Zlcqyvo2FxaXlldXCWnF9Y3Nr29zZbckgEpg0ccAC0XGRJIxy0lRUMdIJBUG+y0jbHV+lfvueCEkDfqfikDg+GnLqUYyUlvrm0U35oRpXe0xHBqgCL6CXCpVjmEtwmN37ZsmqWRngPLFzUgI5Gn3zqzcIcOQTrjBDUnZtK1ROgoSimJFJsRdJEiI8RkPS1ZQjn0gnyRaawEOtDKAXCH24gpn6O5EgX8rYd/Wkj9RIznqp+J/XjZR37iSUh5EiHE8f8iIGVQDTduCACoIVizVBWFD9V4hHSCCsdIdFXYI9u/I8aZ3UbM1vT0v1y7yOAtgHB6AMbHAG6uAaNEATYPAInsEreDOejBfj3fiYji4YeWYP/IHx+QMoupoi</latexit> <latexit sha1_base64="rCgmpYHoyGRkVEcY7fEWIPQgUN4=">AAACEHicbVDNS8MwHE39nPOr6tFLcIgbjtGKoBdh6MWDhwnuA7Yy0izdwtK0JKlYyv4EL/4rXjwo4tWjN/8b064H3XwQeHnv90h+zw0Zlcqyvo2FxaXlldXCWnF9Y3Nr29zZbckgEpg0ccAC0XGRJIxy0lRUMdIJBUG+y0jbHV+lfvueCEkDfqfikDg+GnLqUYyUlvrm0U35oRpXe0xHBqgCL6CXCpVjmEtwmN37ZsmqWRngPLFzUgI5Gn3zqzcIcOQTrjBDUnZtK1ROgoSimJFJsRdJEiI8RkPS1ZQjn0gnyRaawEOtDKAXCH24gpn6O5EgX8rYd/Wkj9RIznqp+J/XjZR37iSUh5EiHE8f8iIGVQDTduCACoIVizVBWFD9V4hHSCCsdIdFXYI9u/I8aZ3UbM1vT0v1y7yOAtgHB6AMbHAG6uAaNEATYPAInsEreDOejBfj3fiYji4YeWYP/IHx+QMoupoi</latexit> Minimize Subject to ͜ΕΛղ͘ʹ͸ ͱ͓͍ͯ Λղ͚͹Α͍ rL = 0 <latexit sha1_base64="JV7LyuUXTnS2vmk5qCUA1wbg5B0=">AAAB8XicbZA9SwNBEIbn4leMX1FLm8UgWIU7EbQRgjYWFhHMByZHmNvsJUv29o7dPSEc+Rc2ForY+m/s/Ddukis08YWFh3dm2Jk3SATXxnW/ncLK6tr6RnGztLW9s7tX3j9o6jhVlDVoLGLVDlAzwSVrGG4EayeKYRQI1gpGN9N664kpzWP5YMYJ8yMcSB5yisZaj12JgUByd+X2yhW36s5ElsHLoQK56r3yV7cf0zRi0lCBWnc8NzF+hspwKtik1E01S5COcMA6FiVGTPvZbOMJObFOn4Sxsk8aMnN/T2QYaT2OAtsZoRnqxdrU/K/WSU146WdcJqlhks4/ClNBTEym55M+V4waMbaAVHG7K6FDVEiNDalkQ/AWT16G5lnVs3x/Xqld53EU4QiO4RQ8uIAa3EIdGkBBwjO8wpujnRfn3fmYtxacfOYQ/sj5/AFmwZAR</latexit> <latexit sha1_base64="JV7LyuUXTnS2vmk5qCUA1wbg5B0=">AAAB8XicbZA9SwNBEIbn4leMX1FLm8UgWIU7EbQRgjYWFhHMByZHmNvsJUv29o7dPSEc+Rc2ForY+m/s/Ddukis08YWFh3dm2Jk3SATXxnW/ncLK6tr6RnGztLW9s7tX3j9o6jhVlDVoLGLVDlAzwSVrGG4EayeKYRQI1gpGN9N664kpzWP5YMYJ8yMcSB5yisZaj12JgUByd+X2yhW36s5ElsHLoQK56r3yV7cf0zRi0lCBWnc8NzF+hspwKtik1E01S5COcMA6FiVGTPvZbOMJObFOn4Sxsk8aMnN/T2QYaT2OAtsZoRnqxdrU/K/WSU146WdcJqlhks4/ClNBTEym55M+V4waMbaAVHG7K6FDVEiNDalkQ/AWT16G5lnVs3x/Xqld53EU4QiO4RQ8uIAa3EIdGkBBwjO8wpujnRfn3fmYtxacfOYQ/sj5/AFmwZAR</latexit> <latexit sha1_base64="JV7LyuUXTnS2vmk5qCUA1wbg5B0=">AAAB8XicbZA9SwNBEIbn4leMX1FLm8UgWIU7EbQRgjYWFhHMByZHmNvsJUv29o7dPSEc+Rc2ForY+m/s/Ddukis08YWFh3dm2Jk3SATXxnW/ncLK6tr6RnGztLW9s7tX3j9o6jhVlDVoLGLVDlAzwSVrGG4EayeKYRQI1gpGN9N664kpzWP5YMYJ8yMcSB5yisZaj12JgUByd+X2yhW36s5ElsHLoQK56r3yV7cf0zRi0lCBWnc8NzF+hspwKtik1E01S5COcMA6FiVGTPvZbOMJObFOn4Sxsk8aMnN/T2QYaT2OAtsZoRnqxdrU/K/WSU146WdcJqlhks4/ClNBTEym55M+V4waMbaAVHG7K6FDVEiNDalkQ/AWT16G5lnVs3x/Xqld53EU4QiO4RQ8uIAa3EIdGkBBwjO8wpujnRfn3fmYtxacfOYQ/sj5/AFmwZAR</latexit> <latexit sha1_base64="JV7LyuUXTnS2vmk5qCUA1wbg5B0=">AAAB8XicbZA9SwNBEIbn4leMX1FLm8UgWIU7EbQRgjYWFhHMByZHmNvsJUv29o7dPSEc+Rc2ForY+m/s/Ddukis08YWFh3dm2Jk3SATXxnW/ncLK6tr6RnGztLW9s7tX3j9o6jhVlDVoLGLVDlAzwSVrGG4EayeKYRQI1gpGN9N664kpzWP5YMYJ8yMcSB5yisZaj12JgUByd+X2yhW36s5ElsHLoQK56r3yV7cf0zRi0lCBWnc8NzF+hspwKtik1E01S5COcMA6FiVGTPvZbOMJObFOn4Sxsk8aMnN/T2QYaT2OAtsZoRnqxdrU/K/WSU146WdcJqlhks4/ClNBTEym55M+V4waMbaAVHG7K6FDVEiNDalkQ/AWT16G5lnVs3x/Xqld53EU4QiO4RQ8uIAa3EIdGkBBwjO8wpujnRfn3fmYtxacfOYQ/sj5/AFmwZAR</latexit>