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Evolutionary neural network learning

2003
Several gradient-based methods have been developed for Artificial Neural Network (ANN) training. Still, in some situations, such procedures may lead to local minima, making Evolutionary Algorithms (EAs) a promising alternative. In this work, EAs using direct representations are applied to several classification and regressionANN learning tasks. Furthermore, EAs are also combined with local optimization, under the Lamarckian framework. Both strategies are compared with conventional training methods....Read more
✂✁☎✄✝✆✟✞✡✠☞☛✌✄☎✍✏✎✒✑☞✓✕✔✗✖✘✞✏✑✙✎✚✆✛✔✗✖✜✠✣✢✤✄✥✑✙✦★✧✛✖✩✎✒✑✪✍✫☛✬✍✏✭ ✫✮ ✯✱✰✳✲✵✴✬✶✸✷✩✹✻✺✽✼✿✾❁❀❃❂✵❄✙✾❅✲✵✶❆✹❈❇❉✹✳❊●❋❍✴✬■❑❏▲❂▼✾❖◆✿P✡◗✳✹✳❘❚✴❱❙ ❯✩✴✬❲✳✴✟❘❳❀ ❨❬❩✜❭❍❪✻❫✬❴❛❵●❫✬❜✒❭✽❝▲❵❡❞❣❢❅❭✐❤❥❝❅❦❧❞✟❴❡❜♥❫✌♠ ❵❡♦q♣❳❫✘rts✉❝✳♦✇✈❑❭❍❴❡①❛♦✇❢❁❫❑❢❅❭✐❢✳❞✒②☎♦✇❝✳③❁❞ ❫✟❜✒❪✳⑤❁①✪❢✳❭✐⑥✉⑤✻❫✟⑦⑧❵●❫✌❴❳⑨✻⑩▲❶▲❷❳❸✌r❥❸❑❹❑❶✒❺❻❴●❫✬❼❃❫❣r❻❽❿❾✉➀t➁☞s✜⑥✜➂✉➃ ➄❈❩✜❭✽❪❁❫✬❴❛❵●④ ❫✟❜✒❭❍❝❖❵❡❞✘❢✳❭➆➅❖♦q①➇❵❡❭✽❜✚❫✟①✪❢❅❭✐❤❥❝✳❦❆❞✟❴❡❜✚❫❁♣❑➈ ❫✟➉ ❞❣rts❉❝❁♦q✈❃❭❍❴❡①❛♦✇❢❁❫✟❢✳❭✐❢❅❞✚②☎♦q❝❁③✳❞ ④ ❫✟❜✒❪✳⑤❁①✪❢❅❭✐➂❉➊✽⑤❅❴❅❭✽♠ ❜❬⑨❅⑩❃➋✟❸❑❸✬r➌❸❑❹✟➋✥⑥✉⑤❁♦q❜✚❫✬❴❳❫✬➉ ❭✽①✙r❻❽❿❾✉➀t➁☞s✐⑥✜➂❉➃ ➍❅➎❖➏▲➐✌➑❅➒✟➓❑➔❅→↔➣➙↕✌➍❚→✌➛❃➑❅➏↔➣➙➜▲➝➞➜✳➐❑➏✟➎❃➝❃➟❑➠▲➓❑➔❅➡❑→↔➣➙↕✬➍❚→❳➛❃➑❅➏✣➣➙➜❃➝➤➢✬➛❖➟✟➥▲➟❖➡✟➓❑➔❖→↔➣➙↕✬➍❚→❳➛❃➑❅➏✣➣➙➜❃➝ ✚➦ ➧➩➨✽➫✽➭✌➯✻➲✟➫❑➳ ➺ ➅❖❭✽✈❃❭❍❴●❫✬⑦✳❼✬❴●➺❛❫❑❒❰❢✳♦q❮❧❭✽➸ ❝▲❵❛r➙➵✻❫✬①❛❵❛❭❳❴●❢❣❫✟♦q❜✒❝✳♦✇❭❍❝✳❵❡❼✳③✳Ð❻❞❖❢✳➅▲①➩❵❡♦✇③❁⑦q⑦➪❫✌⑨✸✈❑♦q❭✙❝Ñ➵❚①❛❭✽❞❑❭✽❜✒❝✒❭✥❢❅❭✽①❛✈❃♦q❵❡❭✽⑤❁⑦q❞❑❫✬❪❚❵❡♦q❭✽❞❑❢✘❝✳①✽❦❧❞✬⑨✸❴✪①❛⑤❁➸➻♣●➺➽③ ➼ ❪❅➾➪➚ ❴❡➶❻❞▲➹❍♣✽➚➴❭❳➘❑❢✳➷t⑤❅➬✩❴❡❭✽➮➽①✐➱ ❜✚➘❑➷❻❫✽ÒÓ➬✩⑦q➮➽❭❳➾➪❫❑✃❻❢❈❐ ❵❡❞☎⑦q❞▲♣❳➬❉❫✬➬☞⑦❻❜✒Ï ♦q❝❁♦q❜✚❫❖⑨✵❜✚❫✟Ô❖♦q❝❁❼☎Õ✙Ö ❐❑➷ ➱❖➾➪➚➴❐✬×❚➘ ➺●Ø✝➸ ➷ Ù❃❐ ➺ ➚❧➾❆Ú❖Û✘Ü ❮❆Õ❻➸ ❫✒❪✳❴❡❞✟❜✒♦q①❛♦✇❝✳❼✚❫✟⑦⑧❵❡❭❍❴❡❝❁❫✬❵❡♦q✈❃❭❑Ð❁❤❥❝❬❵❡③❁♦q①✪Ý☞❞✬❴❡Ô✵⑨❚Õ❿➸ ⑤✳①❛♦✇❝✳❼✚❢✳♦⑧❴❡❭✽♣❍❵➻❴❡❭✽❪❅❴❡❭✽①❛❭✽❝✳r ❵●❫✌❵❡♦✇❞✟Ü➙❝❁Ï ①➻❫✬❴❡❭✜❫✟❪❁❪✳⑦q♦✇❭✽❢✥❵❡❞❣①❛❭❍✈❃❭❍❴●❫✟⑦ ➹✽➷q➘✟Ü❡Ü❡➚ ➶❻➹●➘✬➾➪➚➴❐✟× ❫✬❝✻❢Ó➺ ➮➴Ü Ù ➺ ➮➽Ü❡Ü❡➚➴❐✟× ➸ ➬❉➬ ⑦q❭❳❫✬❴❡❝✳♦q❝❁❼ ❵●❫✬①❛Ô❅①✽Ð❁Þ❁⑤❅❴❛❵❡③❁❭❍❴❡❜✒❞✬❴❡❭❑⑨❁Õ❿➸ Ü ❫✌❴❡❭✩❫✟⑦q①❛❞✒♣✽❞✟❜❣➵❁♦q❝✳❭❳❢✚Ý✪♦⑧❵❡③❬⑦q❞▲♣❳❫✬⑦↔❞✟❪✳❵❡♦q❜✒♦q➊❳❫✬❵❡♦q❞❑❝▼⑨❁⑤✳❝✳r ❢❅❭❍❴✪❵❡③❁❭➆ß ➺ ❒ ❦❆❴●❫✬❜✒❭❍Ý☞❞✬❴❡Ô✵Ð❁❺❿❞✬❵❡③❬①➇❵❛❴●❫✬❵❡❭✽❼✟♦q❭✽①✜❫✌❴❡❭✐♣✽❞❑❜✒❪❁❫✬❴❡❭❳❢✝Ý✪♦⑧❵❡③❬♣❍❞❑❝✳r ✈❃❭❍❝❖❵❡♦q❞✟❝✻❫✟⑦✳➘✟❵❛Û❱❴●❫✟➘ ♦q❝❁➹♦q❝❁➚➪❼✩➘✟❜✒× ❭❍❵❡③✳❞❖❢✳①✽Ð❃➁☞③❁❭✪❴❡❭✽①❛⑤❁⑦⑧❵❡①❻❴❡❭❍✈❃❭❳❫✟⑦✻❫✟❝✒❭✽❝✳③✻❫✟❝✳♣✽❭❳❢❱❪❚❭❍❴❛❦❆❞✟❴❡❜✚❫✬❝❁♣✽❭ ➵▲Ò✝❫❣❜✚❫✟♣➽❴❡❞✟r➙❜❣⑤❅❵●❫✬❵❡♦q❞❑❝✥➵✻❫✬①❛❭❳❢Óß ➘✟Û❱➘ ➺ ➹ ❒ ➚➪➘✟× ❫✟❪✳❪✳❴❡❞❃❫✬♣➽③▼Ð à á❁â➻ã❚ä✵å✐æ✘ç➆è↔ã✵é❡å➻â ❛ê ◆➤ë✫ì❚íqî➌ï✱ð❻ñ▲ò❅ó✬ô❈õ✐ó✌ô❍ö❍ó❛÷↔î❥ô➽ø❖ù✵úüû❥ë✡ðtõ❉ú➇ý▲❂☞✹❅◆✵✴✡✹❖þ✐❋❍✼✵✴✡ÿ❬✹❁❘❡❋✁✿✹✂✵✲✵✶❧✾❖❊☎✄✘ô❳î➌ï ✆✉ö✌ï➙ñ❖í✞✝✝ó✌ì❚ô➽ñ❖í ✝✥ó✬✠î ➻✟ ø❖☛ô ✡❰☞û ✄✌✝✍✝✐ý✚✾❖❊✽✺✽✼✵✯✇❋❍✴✟✺✌❋➽✲✵❊❍✴✟❘✟❂❻ù✣ó✌ì❚ô❍ø▲ù✵ú➆✾❅❊➽✴✝✰❅❊❍✹❅✎✲ ↔✴✟PÑ✯✱◆ í✱ñ▲ò❅ó✬ô✽ú❣✾❅◆▼PÑ✹✳◆✵✑✶ ✏✓✒✌ø❖✔ô ✟➻ñ▲☛ô ✕ ö❍ø❖ù▼ù✣ó❍ö✬î❥ï➙ø▲ù✵ú❉✗✴ ✖❚✯❆❘●✙❋ ✘ ✚✜✛✣✢✥✜✤ ✼✵✴❱✯❆◆✳❋❍✴✬❊❍✴✟❘●❋✉✯❆◆Ñë✡ð❻õ❉✧ú ✦✜✾❅❘✉❘❡❋❍✯✱ÿ✝✲✵✶❧✾▲❋➽✴❑✩P ★✪❬✏ ❋❍✼✵✴✒✾❅P❚❲✳✴✬◆❁❋❉✹❅þt❋➽✼▼✴ ✫➆ñ✳✬ö ✡✽÷↔ô➽ø✽÷✵✮ñ ✭✳ñ❖î➌ï➙ø❖ù ✾❅✶✱✰✳✹❅❊❍✯✇❋❍✼✵ÿ ✾❅◆▼P✏❘●✯❆◆▼✺✌✴❣❋❍✼✵✴✬◆Ñ❘➽✴✬❲✳✴✬❊✽✾❖✶✣❲▲✾❖❊❍✯❆✾❅◆✳❋✽❘✉✼▼✾❃❲❅✯✴ ★↔✴✬✴✬◆✰✵❊❍✱✹ ↔✹✳❘➽✴✟P✸❂ ❘●✲▼✺✽✼✫✾✳❘✜❋➽✼✵✁✴ ✲➆✳õ ✲✵✴➻✶õ ✘✸✷✹✛✺✢✥✻✪✴✬❋✟❂✿❋➽✼✵✴❑❘●✴✒✰✳❊❍✾✳P❚✯✱✴✟◆❁✽❋ ✼✺★▼✾❅❘➽✴✟✾P ✵❊❍✹✻✺✬✴✟P❚✲▼❊➽✴❑❘✐✾❖❊❍✴❣◆▼✹❖❋✩þ➴❊❍✴✬✴❱þ➴❊❍✹❅ÿ ✰❅✴✌❋➽❋➽✯❆◆✵✰✡❋➽❊✽✿✾ ✎↔✴✟Pü✯✱◆❁❋➽✹✡✶✱✹❚✺✟✾❖✶☞ÿ❬✯✱◆✵✯❆ÿÓ✾✩✐✦ ✼▼✴✬◆Ñ❋❍✼✵✴☎✴✬❊❍❊➽✹✳❊✘❘➽✲✵❊●þ➙✾✳✺✌✴✝✯❆❘❣❊❍✲✵✰❅✰✳✴✟P➩❀❂ ★✿✴✟✯✱◆▼✰ ✾❅✶❆❘➽✹ ❘●✴✟◆▼❘●✯✱❋➽✯❆❲❅✴❣❋❍✹❬❋➽✼✵✴✟✯✱❁❊ ▼✾❅❊❍✾❅ÿ❬✴✌❋➽✴✟❊✐❘●✴✬❋●❋➽✯❆◆✵✰❁❘✩✾❖◆▼P ❋➽✹☎❋❍✼✵✴✒◆✵✴✌❂❋ ✦✉✹❅✬❊ ❃❈✯❆◆✵✯✱❋➽✯❧✾❖✶❄✦✉✴✬✯❆✰❅✼❁❋❍✮❘ ✢ ❅ ◆ ✾❖✶✱❋➽✴✟❊➽◆▼✾❖❋➽✯❆❲❅✴ ✿✾ ❆✵❊➽✹❁✾❅✺✽✼ ✺✌✹✳ÿ☎✴❑❘ þ➴❊➽✹✳ÿ ❋❍✼✵✴➞✲▼❘➽✴ ✹❖þ✩❇❉▲❈ ø▲íqì❚î❥ï➙ø▲ù✣ñ▲ô❳ò❊✄✘í ✭❁ø▲ô❳ï➪●î ❋✪✝❍ ú ●û ❇■✄❣ú➇ý▲■❂ ✐✦ ✼✵✴✟❊➽✴Ñ✾ ◆✻✲✵✵ÿ ★✿✴✟❊❈✹❖✙þ ↔✹❖❋❍✴✬◆❁❋➽✯❧✾❖✶❣❘●✹✳✶✱✲❚❋❍✯✱✹✳◆▼❘❬❋❍✹➞✾❏✵❊❍✱✹ ★✵✶❆✴✬ÿ ÿ❬✱✾ ❃❅✴❑❘❈✾❖◆ ✴✬❲✳✹❅✶❆❑❲ ✼ ✯✱◆✵▲✰ ✿✹✂✵✲✵✶❧✾▲❋➽✯❆✹❅▼ ◆ ✘ ◆❚☛❂ ❖✿✛✺✢❉❇P✄❣úÓ✾❖❊❍✴Ñ✿✾ ❆✿✴❑✾❖✶❆✯✱◆✵✰ þ➴✹✳◗❊ ✄✌✝❘✝ ❋➽❊✽✾❖✯❆◆✵✯❆◆✵✰➞❘●✯❆◆▼✺✬❙✴ ✘ ❚✿✛✣❯✉✾ ✰❅✶❆✱✹ ★▼✾❅✶ ÿ✥✲✵✶✱❋➽✑✯ ✼✣↔✹❅✯❆◆❁❋✉❘➽✴✟✾❅❊❍✺✽✼☎✯❆✧❘ ✵❊❍✹▲❲✻✯❆P❚✴❑❄P ❱❖◆✵✹✥✰❅❊✽✾❅P❚✯❆✴✬◆❁❋✪✯❆◆❚þ➴✹❅❊❍ÿÓ✾▲❋➽✯❆✹❅◆Ó✯❧❘✪❊❍✴✮❲❁✲✵✯❆❊❍✴✟❄P ❱❅✾❅◆▼P☎❋➽✼▼❳✴ ✏Ó✾❖❊❍✴ ✰❅✴✬◆▼✴✬❊✽✾❖❑✶ ✵✲✵✬❊ ✿✹❁❘●✴✜ÿ❬✴✌❋❍✼✵✹❚P✵❁❘ ❨➪❋❍✼✵✴✐❘➽✾❅ÿ☎✴✌❇P✄✛ÿÓ❩✾ ✏✙★✿✴✜✲▼❘➽✴✟P✝✯❆◆☎P❚✑✯ ❬✣✴✬❊❍✴✬◆❁❋☞❋❂✏❑↔✴✟❘☞✹❅❭þ ✄✌✝❘✝❱✽ú ❪✔✢ ❫✵✹❅✶❆✶❆✜✹ ✦✐✯✱◆✵✰✏❋❍✼✵✯❧❘✒❋➽❊❍✴✬◆✿P➩❂✸❋❍✼✵✯❆✵❘ ✉✦ ✹❅✬❊ ❃ü✾❖✯❆ÿÓ❘✥✾▲❋✝✴✗✖✥✵✶❆✹❅❊❍✯✱◆✵✰✏❋❍✼✵✴❈✲▼❘➽✴❈✹❅þ✍❇■✄❣ú❱þ➴✹❅❊Óë✡ð❻õ ❋➽❊✽✾❖✯❆◆✵✯✱◆▼✰▼✥❂ ✦✐✼✵✴✟◆✏✱✾ ✎✵✶❆✯✱✴❑P❈❋❍✹üö✌í❆ñ❃ú✽ú❳ï ✆❉ö✽ñ▲î❥ï➙ø▲ù ✾❅◆▼P♥ô➽✺ó ✭❖ô➽ó✌ú✽ú❳ï➙ø▲ù❬❋❍✾✳✽❘ ❃❚❘✮✢ ❴ ❵◗❛❁❜✙✸❝ ä▼é☛❞❡❝❻â➻✥ã ❢✳❣☎❤❉❝➩ã✵ç✌❜ ❘➽✴✌❋❱✹❖þ➻❋➽✴✬✐◆ ★↔✴✬◆▼✺✽✼✵ÿÓ✾❅☛❊ ❃❚❘❘ ✦✉✾✳❘❣✺✬✹❅◆▼❘➽✯❧P❚✴✬❊❍✴✟P✫✯❆◆♥❋➽✼✵✯❧❘❥✦❉✹✳☛❊ ❃❏❨☞❿✤ ✾✿★▼✶✱◗✴ ❦✹❪✌❂➩✴✬◆▼P❚✹✳❊❍❘➽✯❆◆✵✰❈❂❋ ✦✉✹ ÿ❬✾❅✯✱◆✥❋❂✏✪✿✴❑❘❁❨➙✺✌✹✳✶✱✲▼ÿ☎◆✁❧♠❪❻✹❖❀þ ✵❊➽✹✂★✵✶❆✴✬ÿÓ❘❳❯❀♥☞í✱ñ❃ú✽ú❳ï ✆❉ö✽ñ❖î➌ï➙ø❖ù♥û♦↔♥ ý❉✾❖◆✿P✵➆✲ ó✺✭❅ô➽ó✌ú❍ú❳ï➙ø❖ùÑû●✲✉ý✙❋❍✾✳✽❘ ❃❚❘✮✢ ♣ q✯ ✖✏❊❍✴✟✾❖✑✶ ✼✺✦❉✹✳❊➽✶❧☎ P ✵❊❍✱✹ ★▼✶✱✴✟ÿ❬❘r✦✉✴✬❊❍✴✚✺✽✼✵✹❁❘●✴✟◆✡þ➴❊❍✹❅ÿ ❋➽✼✵❙✴ s✧♥✉t✉ÿÓ✾❅✺✽✼✵✯❆◆✵✴✒✶❆✴✟✾❖❊❍◆✵✯❆◆✵✰Ó❊❍❳✴ ↔✹✳❘➽✯✇❋❍✹❅✬❊ ✏ ✘ ✈✿✛✣✢✎✤✜✼✵✴✥✳õ ✲❘✄ ✯❧❁❘ ★▼✾✳❘●✴❑P❈✹✳◆ ✾☎❊❍✴✟✾❖✶❆✯❧❘❡❋❍✯❆✺❱❘➽✯✱ÿ✝✲✵✶❆✾❖❋➽✯❆✹❅◆✡✹❖þt❋❍✼✵✴✚P✥✏✻◆▼✾❅ÿ☎✯❧✺✬❘✜✹❅þ❿✾☎❊❍✱✹ ★↔✹❖❋✩✾❖❊❍✰ ÿ ✢ ❅ ✤✜✼✵✴✘✾❅❊●❋❍✯ ✿✺✬✯❆✾❅✶▼❋✽✾❅❘☛❃❚❘✪✯❆◆▼✺✌✶❆✲▼P❚✴✘❋➽✼✵✴➆þ➙✾❖ÿ❬✹❅✲✿❘❉✝▼✩✫ ï➪î❿õ✐ñ▲ô❳ï➪î❥ò✵✘✸✷✹➇✛ ❂✳❋➽✼✵✴ P♥r♥ ✦✐✼▼✯❆✺✽✼ ✺✬✹❅◆▼❘➽✯❧❘❡❋✽❘ ✹❅◆ ✾✳❘➽❘➽✯✱✰✳◆✵✯❆◆✵✰✒✹❅◆✵✴✘✹❖þ➩❋❍✼✵❊➽✴✟✴➆✺✌✹✳✶✱✹✳❊❍❘✪❋➽✹✚✴❑✾❅✺✽✓ ✼ ★✵✶❆✹❚✺♦❃❬✹❖þt✾ ✈✿✖✥✈✿✖✎✈❱✰❅❊❍✯❆P❈✺✬✲✎★↔✴✘✾❖◆✿P❬❋➽✼✵✴ ✿❂ ✾✝❊❍✴✬✰✳❊➽✴❑❘➽❘➽✯❆✹❅◆Ó❋✽✾❅❘☛❃☎✐✦ ✼✵✴✬❊❍✴❱❋➽✼▼✴✒✹❅✲❚❋✬✵✲❚❋✩✯❧❘✜✰❅✯❆❲❅✴✬◆◗★✪✏❭❯ P❨✠❚ ❀❪ P❨ ❭❪✔✢ ✁ ✄✂ ✆☎✝✂✞☎ ✠✟☛✡✌☞✎✍✑✏ ✪✩ ✙ ➯❁➧ ✦✥ ✛✚✢✜✤✣ ✜ ✙✬✫ ✧ ✹✪✺ ✘✗✓✒ ✎✭✢✮ ★✧ ✪✭✢✯✠✰ ✱ ✼✻ ❅ ❇❆ ❉ ✥☛❊ ✪❋ ❅ ✎❀ ✕❆ ✎❆ ▲✽ ❍✑✧■❏ ✶❆❈❆✾❅ ❃ ✺ P❀✖❀✾❀✿❆ ❖◆ ▲❆ ◗❅ ❉ ❂ ❁❀ ❈❆ ●✽ ✿✽ ✧■❍❑❏ ▼ ✲✴✳✶✵✸✷ ✽ ✾✽✿✽ ❂❄❃✝❃ ✧■❊ ❘❅ ❊ ✧ ✕✔✄☞✖✍✑✏ ❁➳ ➁☞③✳❭ ☎ß ✫⑦q❭❳❫✬❴❡❝✳♦q❝❁❼✒➵❚❭✽❝✳♣➽③✳❜✚❫✬❴❡Ô❖①✽Ð ✻➯ ➨ ❅➨❳➲❑➭ ↔➫ ✬⑩ ❷ ⑩ ④ ➅❅♦ ☎❺❿♦⑧❵❉❽➩❫✬❴❡♦⑧❵❥Ò ✟❶ ➋ ❹ ④ ➁☞③✳❴❡❭❍❭ ④ ❞✟⑦q❞✟❴ ④ ⑤❁➵❚❭ ❷❳❸✬⑩ ✟❸ ❷ ❃❶ ④ ➅❅❞✟❝✻❫✌❴ ✻➀➻❞▲♣➽Ô❖①✙✈❖①➻②☎♦q❝❁❭✽① ✟❸✟❸ ❶ ❶ ❷ ✬⑩ ④ ❽✸♦✇❜✚❫✘❤❥❝✻❢❅♦✇❫✟❝❁①✙❩✉♦✱❫✬➵❚❭❍❵❡❭✽① ❷✌❹✬❸ ⑩ ✟❶ ④ ❤➌❴❡♦q①➻❽✸⑦✱❫✬❝▲❵❉❩✜❫✬❵●❫✟➵❁❫✟①❛❭ ❷ ✬⑩ ④ ♦q①❛♣✽❞✟❝❁①❛♦q❝❈❺❻❴❡❭❳❫✬①➇❵ ④ ❫✬❝❁♣✽❭❍❴ ⑩ ➀➞➅❅♦q❝Ó➁☞♦q❜✒❭✽①❉➅❖♦✇❝ ➋✟❸ ❷ ➋ ❷ ✟❹ ✪➸ ➀ ❽✸⑤❁❜✚❫❑❢❖Ò❅❝✝➀➻❞❑➵❚❞✬❵✉➂✪❴❡❜ ❷ ✬➋ ➋ ➋ ❷ ➋❖❷ ➀ ➀➻♦✇①❛❭✩➁☞♦q❜✒❭➆➅❖❭❍❴❡✈❃❞❑❜✒❭❍♣➽③❁❫✟❝❁♦q①❛❜ ❷ ❑❶ ⑩ ⑩✤❷ ✟❹ ➀ ❽➩❴❡❞❑❼❑❝✳❞❑①➇❵❡♦q♣✘❺❻❴❡❭❳❫✟①➇❵ ④ ❫✟❝✳♣✽❭❍❴ ❷ ✟➋ ⑩✤❷➆❷ ❑❶ ✙ ❉ ✓✒ ✺ ❂ ✪✽ ❉ ◗❅ ✪❀ ❙❆❁❅ ❃ ✪❆ ➻✾❅✺✽✼ ✵❊➽✹✂★✵✶❆✴✬ÿ ✦✐✯❆✶✱✶✳★↔✴❬ÿ☎✹❚P❚✴✟✶✱✴❑P ★✪✏Ñ✾ þ➴✲✵✶❆✶✑✏ü✺✬✹❅◆✵◆▼✴✟✺❳❋❍✴✟P✛ë✡ðtõ✉❂❄✦✐✯✱❋➽✼❰✹❅◆✵✴☎✼✵✯❧P✵P❚✴✟◆ ✶❆✾❩✏✳✴✬❊✐✾❖◆▼P ✬ï➙ñ❃ú✐✺✌✹✳◆✵◆✵✴✟✺✌❋➽✯❆✹❅◆▼❘✟❂✥★↔✴✬✯❆◆✵✰❬❋➽✼✵✴❱❋❍✹✱↔✹❅✶❆✹❅✂✰ ✏❈✰❅✯❆❲❅✴✟◆✡✯❆◆ ✤❻✾✱★✵✶✱✴ ❦✳❂✎✦✐✼✵✴✬❊❍✴✒✺✌✹✳✶✱✲✵ÿ❬◆▼❘ ▲❂ ✾❖◆▼P P❚✴✟◆✵✹❖❋❍✴✐❋➽✼✵✴✐◆✻✲✵ÿ✵★✿✴✟❊✪✹❖þ✣✯❆◆✎✵✲❚❋❑❂❅✼✵✯❧P✵P❚✴✟◆❈✾❖◆▼P☎✹❅✲✵❋☛✵✲❚❋❉◆✵✹❚P❚✴✟❘✟❂✿✦✐✼✵✯❆✶✱✴✩✺✬✹❅✶❆✲✵ÿ❬◆ ❘●✼▼✜✹ ✦✩❘❣❋➽✼✵✴Ó◆✻✲✵✵ÿ ★✿✴✟❊✒✹❖þ✐✺✌✹❅◆▼◆✵✴✟✺✌❋➽✯❆✹❅◆▼✮❘ ✢❻❇❉✶❆✾✳❘➽❘➽✯ ✿✺✬✾❖❋➽✯❆✹❅◆Ñ❋✽✾❅❘☛❃❚❘❱ÿ❬✾✱❃❅✴☎✲▼❘➽✴Ó✹❖þ✉✾✫❘➽✯❆◆✵✰❅✶❆✴ ★✵✯✱◆✿✾❖❊✬✏✫✹❅✲❚✬❋ ✵✲❚❋✩❨➴✯✱þ✉❋❂✦❉✹✫✺✌✶❧✾❅❘❍❘➽✴✟❘❱✾❖❊❍✵✴ ▼❊➽✴❑❘●✴✟◆✳✔❋ ❪✘✹❅❊❱✹❅◆✵✴ ★↔✹✻✹❅✶❆✴✟✾❖◆♥❲▲✾❖✶❆✲✵✴ ✿✴✟❊✒✴✟✾❅✺✽✼ ✺✌✶❧✾❅❘❍✮❘ ✢ ê❛◆ ô❍ó✣✭❅ô➽ó✌ú✽ú✽ï➙ø❖ù ✵❊❍✹✱★✵✶❆✴✬ÿÓ❘❱✹✳◆✵✴Ó❊➽✴❑✾❖✶✑✼❥❲▲✾❅✶✱✲✵✴❑Pü✹✳✲❚❋☛▼✲❚❋✥✴✬◆✿✺✌✹❚P❚✴✟❘✒❋➽✼✵✴ ✕✳ó➇÷▼ó✌ù❭✕❅ó✬ù▼î❉❲❃✾❅❊➽✯❧✾✿★▼✶✱✂✴ ✢ ✤✜✼✵✴Ó❘❡❋✽✾❖◆▼P✵✾❅❊❍Pü✶✱✹✳✰❅✯❧❘❡❋❍✯❆✺✝✾❅✺✌❋➽✯❆❲❃✾❖❋➽✯❆✹❅◆♥þ➴✲✵◆▼✺✌❋➽✯❆✹❅◆ ❨ ❀ ❪✍✦✜✾❅❘✘✲▼❘➽✴✟P♥✯✱◆ ✾❖✶❆✶➆ö✬í✱ñ❃ú✽ú❳ï ✆❉ö✽ñ▲î❥ï➙ø▲ù ❋❍✾❅❘☛❃❚❘❳✢ ❅ P✵✯q❬✣✴✬❊❍✴✬◆❁❋✙❘❡❋❍❊❍✾❖❋➽✴✬✰✂✏❘✦✜✾❅❘❻✾❅P❚✹✂❚❋➽✴❑P❱þ➴✹❅❊❻❋➽✼▼❀ ✴➆ô➽ó✺✭❅ô➽ó❳ú✽ú❳ï➙ø▲ù❥✵❊❍✹✱★✵✶❆✴✬ÿÓ❘✟❂❑❘➽✯❆◆▼✺✌✴❉✹❅✲❚❋✬✵✲❚❋❍❘ ÿ❬✾❩✏❬✶❆✯✱✴❱✹✳✲❚❋✉✹❅þ✸❋➽✼▼✴❣✺✬✹✿✼❛P❚✹❅ÿÓ✾❖✯❆◆ ❨☛✘ ❳❦✗✛●❪✔✢✥✤✜✼✻✲▼❘✟❂❁❋➽✼✵✴☎í✱ø✬✭❖ï❧ú❳î❥ï➙ö✉þ➴✲✵◆▼✺✌❋➽✯❆✹❅◆✩✜✦ ✾❅❘✜✾✳P❚✹✱❚❋❍✴✟PÓ✹✳◆ ❋➽✼✵✴❈✼▼✯❆P✵P✵✴✬◆ ◆✵✹❚P❚✴✟❘✟❂✉✐✦ ✼✵✯❆✶❆✴Ó❋➽✼✵✴Ó✹✳✲❚❋☛▼✲❚❋✥✹❅◆▼✴✟❘✒✲▼❘➽✴✟P ❘➽✼✵✹❅❊➽❋❍✺✬✲❚❋✥✺✌✹✳◆✵◆✵✴❑✺❳❋➽✯❆✹❅◆✿❘✒✾❖◆▼P íqï➪ù✣ó❍ñ❖ô þ➴✲✵◆▼✺❳❋❍✯✱✹✳◆▼❘✟❂✳❋❍✹☎❘❍✺✬✾❅✶✱✴✩❋➽✼✵✴❣❊❍✾❅◆✵✰❅✴✘✹❖þ➩❋❍✼✵✴✘✹✳✲❚❋☛▼✲❚❋❍❘✮✢✥❫✵✹❅❊✜✾❖✶❆✶↔❋➽❊✽✾❖✯❆◆✵✯❆◆✵✰✥ÿ❬✴✌❋❍✼✵✹❚P✵❘✟❂✳❋❍✼✵✴❣✯✱◆✵✯✱❋➽✯❧✾❖✶ ✦❉✴✟✯✱✰✳✼✳❋✽❘✒✾❖❊❍✴❬❊❍✾❅◆▼P❚✹❅ÿ❬✶ ✏♥✾✳❘➽❘➽✯✱✰✳◆✵✴✟P ✦✐✯✱❋➽✼✵✯❆◆❰❋➽✼✵✴❈❊✽✾❖◆▼✰❅✴ ✘ ✙❦✂❱❳❦❳✛❥❂❄★↔✴✬✯❆◆✵✰✏❋➽✼▼✴ ✾❅✺✟✺✌✲✵❊✽✾❅❳✺ ✏✫✹❖þ ✴✟✾❅✺✽✼♥ë✡ðtõ✛ÿ❬✴✟✾✳❘●✲✵❊❍✴✟P✡✯❆◆✡❋❍✴✬❊❍ÿÓ❘✜✹❖þ❿❋➽✼✵✴♠✲✘ø✟ø❖î✪ëüó✽ñ▲ù ✌ì▼ñ❖ô➽ó♦✕✵✉❇ ô❳ô❍ø▲ôÓû●❣✲ ë ✥❇❻ý✜✢ ❚ ❱❯ ❲ ❨❳ ❬❩ ❭ ❪ ❴❫❛❵❝❜❨❞ ❡❣❢ ✁❤ ❖☎✛✐ ✤☎ ❵ ❛❁❜✙❝✸ä▼é☛❞❡❝❻â➻ã ◗ é❡ã ❵ ➻■å ❣➽ç✐ã✵é❡å❉â✌❢☞ä ❣ ➻å✪ä▼é❛ã ❘❞ ê❛◆ ❋❍✼✵✯❧❘ ❘●❋➽✲▼P✥✏✳❂❥✕❖ï➪ô➽ó✽ö✌î✩✴✟◆▼✺✌✹❚P❚✯❆◆✵✰ ✯❧❘Ó✴✬ÿ✵✵★ ❊✽✾❅✺✌✴❑P ❨➙✹❅◆✵✴ü✰❅✴✬◆▼✴◗↔✴✬❊ ✺✌✹✳◆✵◆✵✴✟✺✌❋➽✯❆✹❅◆❊✦❉✴✟✯✱✰✳✼❁❋♦❳❪ ❂ ✾❖◆ü✾❅✶✇❋❍✴✬❊❍◆▼✾▲❋❍✯✱❲✳✴✥✺✌✶❆✹✳❘➽✴✬❊➆❋➽✹❈❋❍✼✵✁✴ ✵✼✵✴✬◆▼✹❖❋❂✏✪✿✴✳❂↔✾❅✶✱✶❆✹✜✦✐✯❆◆✵✰Ó❋➽✼▼✴☎P❚✴ ▼◆✵✯✱❋➽✯❆✹❅◆♥✹❖þ✪❊❍✯❆✺✽✼✵✴✟❊➆✰✳✴✬◆✵✴✬❋➽✯❧✺ ✹✱↔✴✬❊✽✾▲❋➽✹✳❊❍✯❘ ✘ ◆❩✛✺✢✎✤r✦❉✹❬ÿ✝✲❚❋❍✾❖❋➽✯❆✹❅◆ ✹✱↔✴✬❊✽✾▲❋➽✹✳❊❍❘❉✦✉✴✬❊❍✴❱✲▼❘●✴❑P➩❂❚◆▼✾❅ÿ☎✴✟✶✑✏❭❯ ✲➆ñ❖ù❀✕❅ø✿❍ ë✫ì❚î❛ñ▲î❥ï➙ø▲ù▼❂✪✐✦ ✼✵✯❧✺✽✼ ❊➽✴✮✵✶❆✾✳✺✌✴❑❘➻✹✳◆✵✍✴ ✦✉✴✬✯❆✰❅✼❁❋r★❑✏❈✾✝◆✵✮✴ ✦ ❊❍✾❅◆▼P❚✹✳ÿ☎✶ ✏❬✰❅✴✟◆✵✴✬❊✽✾▲❋❍✴✟P ❲▲✾❖✶❆✲✵✴❅✎❂ ✦✐✯✱❋➽✼▼✯✱◆ ❋➽✼▼✴✒❊❍✾❅◆✵✰❅✴ ✘ ✙❦ ❳❦❳✛✣❱✵✾❅◆▼P ñ▲ì✻ú✽ú❳ï➙ñ▲ùÓë✫ì❚î❛ñ▲î❥ï➙ø▲ù▼❩❂ ✦✐✼✵✯❧✺✽✼✥✾✳P✵P✵❘t❋➽✹✘✾➆✰❅✯❆❲❅✴✟◆✚✰❅✴✟◆✵✴❉✾➆❲❃✾❅✶✱✲▼✴✪❋❍✾✱❃❅✴✟◆✒þ➴❊➽✹✳ÿ ✾✩✰✳✾❅✲▼❘❍❘●✯❧✾❖◆ P❚✯❧❘❡❋❍❊➽✯ ★✵✲❚❋❍✯✱✹✳◆✸❂✎✦✐✯✱❋➽✼✫✾☎■✬✴✬❊❍✹❬ÿ❬✴✟✾❖◆✏✾❖◆✿P ✚✂✥◆ ❘●❋❍✾❅◆▼P✵✾❅❊❍P✡P❚✴✬❲✻✯❧✾▲❋➽✯❆✹❅◆❏✘ ❖✿✛✺✢ ê❛◆✾★↔✹❖❋❍✼✡✺✬✾✳❘●✴❑❘✬❂❚✾✥❊❍✾❅◆▼P❚✹❅ÿ ◆✻✲✵✵ÿ ★✿✴✟❊✜✹❖þt✰✳✴✬◆✵✴❑❘❉✯❧❘✜✺✽✼▼✾❖◆▼✰❅✴✟P✸✂❂ ★↔✴✌❂❋ ✦✉✴✬✴✟◆ ❦ ❋➽✹✓✚ ✹❅þt❋➽✼▼✴ ◆❁✲▼ÿ♠★↔✴✬❊✐✹❖þ■✄✌✝❘✝ ✦❉✴✟✯✱✰✳✼✳❋✽❘❳✢✥✜✤ ✼✵✴❱þ➴✹✳✶✱✶❆✜✹ ✦✐✯❆◆✵✰Ó✺✌❊❍✹✳❘❍❘●✹▲❲✳✴✬❊➻✂✹ ✿✴✟❊❍✾❖❋➽✹✳❊❍❘✧✦❉✴✟❊➽✴✒✾❅✶❆❘➽✹☎❋➽✴✟❘●❋➽✴❑P❄❯ ❥ ❧❦♥♠ ❧♦ q♣ ✠r▲s ✉t ❧♦ ✶❦ ✎ ✈ ✁❤ ❨❢ ✈✾✇ q❡❣① P② ✓❡③② ✂ ✟➻✁ø ➌õ✐ø❖ï➪ù▼î❥❂✌s❻ù✿ï ✒✌ø▲✔ô ❍☎❂❀✄✘ô❳ï➪î●❋✪❍Óó✌î❥ï➙ö✽ñ▲í✵✾❖◆✿❖ P ☎↔✥ì ❍✝❂✵❘●❋❍✾❅◆▼P✵✾❖❊✽P ❇P✄ ✹✱↔✴✬❊✽✾▲❋❍✹❅❊✽❘❘ ✘ ◆❩✛✺❱ t ❳ ❖ ù ↔ ÷ ❚ ì ☞ î ❖ ✾ ▼ ◆ ✶ P ✉ ✴ ❚ ì ✇ î ↔ ÷ ❚ ì ☞ î ✌ ✺ ✳ ✹ ✵ ◆ ✵ ◆ ❑ ✴ ❳ ✺ ➽ ❋ ❆ ✯ ❅ ✹ ✿ ◆ ✬ ❘ ✣ ❂ ● ❘ ❆ ✯ ❬ ÿ ✱ ✯ ❧ ✶ ❖ ✾ ❊✘❋➽✹✏✾ ø▲ù↔ó✂❆÷▼ø▲ï➪ù▼î✙✺✬❊➽✹❁❘➽❘➽✹▲❲❅✴✟❊✩✴✗✖✵✺✌✴✮❚❋❣❋➽✼▼✾❖❋ ✈ ❋➽✼✵✴✘❘●✴✬❋✪✹❖þ➩✯✱◆❆✵✲❚❋❘❨➙✹❅✲❚❋✬✵✲❚❋♦❪➻✺✌✹✳◆✵◆✵✴✟✺✌❋➽✯❆✹❅◆▼❘❿❋❍✹✥✾❱◆✵✹❚P❚✴✩✺✟✾❖◆❬◆✵✹❖❋✧★✿✴✩P❚✯❧❘➽❊➽✲✎✵❋➽✴✟P ✘ ✗✜✛✺❱❅✾❅◆▼P ✴ ✵❊❍✴✬❲✻✯❆✹❅✲▼❘❿❋❂✉✦ ✹✘✹✂✿✴✟❊❍✾❖❋➽✹✳❊❍❘✮❱❃✯✠✢ ✴✱✢❆❂❅✾❖✶❆✶✵✺✌✹✳◆✵◆✵✴❑✺❳❋➽✯❆✹❅◆✿❘ ✈ ✄✒ï☞✕✂✕❅ó✬ù✚◆✵✹❚P❚✴✟❘✟❂❃❋➽✼✿✾▲❋➻✺✌✹✳ÿ♠★✵✯❆◆✵✴❑❘t❋❍✼✵❁ ❋➽✆✹ ☎❑þ➴❊❍✹❅ÿ ✾☎✼✵✯❧P✵P❚✴✟◆ ◆▼✹✻P✵✴✚✺✬✾❖◆ ◆✵✹❅❋r↔★ ✴✚❘➽✴❳▼✾❅❊❍✾❖❋➽✴✟P✉✢ ✤✜✼✵✴❁❇■✄❣ú✉↔✹✱✵✲✵✶❧✾▲❋❍✯✱✹✳◆✝❘➽✯✱■✟✴✧✦✜✾❅❘❿❘➽✴✌❋❿❋➽✹✯✈ ❡✵❂✹↔★ ✴✬✯❆◆✵✰❣❋➽✼✵✴✘ú✬ó✌í✱ó✽ö✬î➌ï➙ø❖ù✒P❚✹❅◆✵✴❉★✪✏✚✺✌✹✳◆❁❲✳✴✬❊➽❋➽✯❆◆✵✰ ❋➽✼✵✴☛✵❋❍◆✵✴✟❘❍❘❱❲▲✾❖✶❆✲✵✴ ❨✠✲❱q ë ☎✎❇✳❣❪ ✯❆◆✳❋❍✹✏✯✇❋✽❘✒❊❍✾❅✎◆ ❃✻✯✱◆▼✰▼❂➩✾❖◆▼P♥❋❍✼✵✴✬◆ ✾✿❆✵✶✑✏✻✯❆◆✵✰✫✾ ❊➽✹✳✲✵✶✱✴✬❋●❋❍✴✁✦✐✼▼✴✬✴✬✶ ❘➽✺✽✼✵✴✟ÿ❬✴❅❂❆★↔✴✬✯❆◆✵✰❈✲✿❘●✴❑P✫✾Ó❘●✎✲ ★✿❘❡❋❍✯✇❋❍✲❚❋➽✯❆✹❅◆Ñ❊✽✾▲❋❍✴✒✹❖þ■✓◆ ❡ ② ✾❅◆▼P ❋➽✼✵✴✏ó✌í✇ï➪î➌ï❧ú✔❍ ❲❃✾❅✶✱✲▼✴✚❘●✴✬❋✩❋➽✹❈✹✳◆✵✴✱✢ ❅ ✶❆✶▼❋❍✴✟❘●❋❍P❘ ✦✉✴✬❊❍✴✩✺✌✹✳◆▼P❚✲▼✺✌❋➽✴❑P❬✲▼❘●✯❆◆✵✰✒❋❍✼✵✞✴ ✝❚ñ✿❈❃ñ✩✶❆✾❅◆✵✰❅✲▼✾❅✰❅✴✳❂▲❊➽✲✵◆▼◆✵✯✱◆▼✰✚✹❅◆❈✾✝õ✩ó✌ù✿î➌ï➪✥ì ❍ t✽t☛✠t ✟☛✡☛✡ ë ✄✠✌❱õ❥♥✞✢❆✤✜✼✵✴❱❋➽✴✟❊➽ÿ❬✯❆◆▼✾▲❋❍✯✱✹✳◆ ✺✬❊➽✯✱❋➽✴✟❊➽✯❧✾✁✉✦ ✾✳❘✜❘●✴✬❋✌★❑✏✏❇✉❄✎✍ ❋➽✯❆ÿ❬✴☎❨❂❁❦ ❡ ❡☎❘●✴❑✺✌✹❅◆✿P✵❘✬❪✗✢ ☞ ✤✜✼✵✴❱❊➽✴❑❘●✲✵✶✱❋❍❘✐✾❅❊➽✴❱✺✌✹✳ÿ ✵✯✱✶❆✴✟P✡✯❆◆✰✤❿✾✿★▼✶✱✴ ✚❚❂✥✦✐✼▼✯❆✺✽✼✏❘●✼▼✜✹ ✦✩❘➻❋❍✼✵✴ ❲❁✲▼✾❖✶❆✯✱❋❂✑ ✏ ✏✓✒✚❂▼ÿ☎✴❑✾❅❘➽✲✵❊❍✴✟P ★❑✏✛✼✵✹✜✦ þ➙✾❅❊ ❨➴✯❆◆ ✿✴✟❊❍✺✬✴✬◆❁❋❍✾❅✰❅✴✹❪✥✯✱❋❍❘Ó✴✟❊➽❊❍✹❅❊ ✕❨ ✔✓✖✘✗✚✙✛✒✛✜ ✢❍❂✙❋❍✼✵✴✫ÿ❬✴✟✾❖◆ ✹❖þ❣❋➽✼▼✯✱❊➽❋❂✏➞❊❍✲✵◆▼❘❬þ➴✹✳❊ ❋➽✼✵✴✡ÿ☎✹❚P❚✴✟✎✶ ✣ ✾❖◆▼P ❋✽✾❅❘☛✥ ❃ ✤✽✚❪ ✯❆❘✚þ➴❊➽✹✳ÿ ❋❍✼✵✴✩★↔✴✟❘●❋✥❊❍✴✟❘➽✲✵✶✇◗ ❋ ✕❨ ✦✧✢✽❪❳❂❿✰❅✯❆❲❅✴✬◆ ★✪✏❭★❯ ✏✓✒❇✡ ✖❦ ❡ ❡ ✔ ✪❨ ✩ ✢✬✫☛✭✯✮✱✰✳✲✵✴✷✶✹✸ ✺ ❤ ❦✹❪✞✦✐✼✵✴✟❊➽✧ ✴ ✦ ✢ ✡✼✣q✍✑✏✾✽ ✫ ✿❨ ✔✓✖✘✗✚✙✛✽ ✜ ✢ ❪❳❂✻✾❖◆✿P✳❀ ✾❖◆▼☞ P ✖ P❚✴✟◆✵✹❖❋❍✴✩❋➽✼▼✴ ❘●✴✬❋✝✹❖þ✐✶❆✴✟✾❅❊➽◆✵✻ ✯❆✺ ◆✵✰➞î❛ñ❃ú☛✡▲ú❱✾❅◆▼P ❍Óø✮✕✳ó✌íq♦ú ✢☞ê❛◆ ❋❍✼✵❬ ✴ ✰ ▼❊✽❘●❋✝❊❍✜✹ ✦✒❂✸✹❅◆✵✶ ✏♥❋➽✼✵✴✡ÿ✥✲❚❋✽✾▲❋➽✯❆✹❅◆✛✹✱↔✴✬❊✽✾▲❋➽✹✳❊ ✯❆❘❣✾✿✎▼✶✱✯❆✴✟P❄✢❄❫▼✹❅❊✘❋➽✼✵✴☎✹❖❋❍✼✵✴✬❊✽❘✬❂↔✴✟✾✳✺✽✼✫✱✹ ↔✴✬❊✽✾▲❋❍✹❅❊✍★▼❊➽✴✟✴✟P✵❘✯✓◆ ❡ ② ✹❅þ✙❋➽✼✵✴☎✹✿❬➩❘☛✵❊➽✯❆◆✵✰ ✢❀✤✜✼✵✴✁↔★ ✴✟❘●❋ ✿✴✟❊●þ➴✹✳❊➽ÿÓ✾❖◆✿✺✌✴✉✯❆❘☞✾❅✺✽✼▼✯✱✴✟❲❅✴✟P♠★✪✏♠✭✳ñ❖ì✻ú❍ú❳ï➙ñ❖ù❣ÿ✝✲❚❋❍✾❖❋➽✯❆✹❅◆✸❂✜★↔✴✬✯❆◆✵✰❱◆✵✹❣✰✳✾❅✯✱◆✝✯✱◆☎✲▼❘➽✯✱◆✵✰❱✾❣✺✌❊❍✹✳❘❍❘●✹▲❲✳✴✬❊ ✹✱↔✴✬❊✽✾▲❋➽✹✳❊✟❂✵❋➽✼✻✲▼❘➆þ➙✾❃❲❅✹❅❊❍✯❆◆✵✾ ✰ ❇❉❈▲ø▲íqì❚î❥ï➙ø▲ù✣ñ▲ô❳ò õ✉ô➽ø✬✭❖ô❍ñ✜❍✁❍✝ï➪ù✪✭✩✘ ❖✿✛✺✢❀✤✜✼▼✯❆❘✘ÿÓ✾❩✏✾★↔✴☎P✵✲✵✴✚❋❍✹❈❋➽✼▼✴ ÷✵ó✬ô✔❍✝ì❚î❛ñ▲î❥ï➙ø▲ù✓▼❊➽✹✂★✵✶✱✴✟ÿ✰❱❚✠✯ ✢ ✴✱✢❆❂▼❘➽✴✬❲❅✴✟❊❍✾❅✶✣✰❅✴✬◆▼✹❅ÿ❬✴✟❘✉ÿÓ✾❩✏❈✴✬◆✿✺✌✹❚P❚✴❣❋➽✼✵✴✚❘❍✾❖ÿ❬✴♠✄✌✝❘✝ ✘ ❚✿✛✣✢ ✈ ✙ ❛ ➯❁➧✛✚✢✜❂❁✵➳ ➁☞③✳❭✜❞✌✈❃❭❍❴●❫✬⑦✇⑦✣Õ❿➸✳❃ Ü ❴❡❭✽①❛⑤❁⑦⑧❵❡①✙❦❧❞✬❴➻❭❳❫✟♣●③❬❜✒❞❖❢✳❭❍⑦❅❄❇❆❉❈✛❊✛✈❑❫✬⑦q⑤❁❭✽●① ❋➽Ð ✱➆❘➭ ❚✯ ➨❳➨ ✯☛❍✠✜❅➭ ■✥➯❑❏✣➨❳➨✪✭✱➯ ✰▼▲◆✿ ❏ ➫✽➯❁➫✪✭❪✯✠✰P❖✒➯ ✰✷◗ ✯❙❘❚▲◆❏↔➫❍➯❁➫✪✭✢✯ ✰ ❷✽⑩❃➋❖Ð ❅❲❱ ❁▼➳ ✣✵❯ ➬✩❐✬×✵➮ ➼ ✧ ❖ ❀ Ð ❳ ➋ ❱ ❷✽P⑩ ❆❖Ð ✽❳❱ ❂ ✃❻❐ ❐✟➚❧×✳➾ ❷✽❸❅Ð ❆❳❱ ❷✽⑩P❆❖Ð ⑩✁❱ ❨ ×✳➚ ❩✽❐ ➺ Û ➸➻➺ ➚❆➾❆Ú❖Û✚➮➽➾➪➚➴➹❡➘❑➷ ❅✌⑩✳Ð ❆❳❱ ❷✽⑩P❖✽ Ð ❸❳❱ ❶✌⑩✳Ð ✁⑩ ❱ ❶✟➋❖Ð ❆❲❱ ❉ ➱❖Û ❍ ❲× ❬✻➱❖➾ ❀❖Ð ❆❳❱ ❷✽P⑩ ❖❆ Ð ❲❶ ❱ ❶▲Ð ❳➋ ❱ ❷✽P⑩ ❖❆ Ð ❲❹ ❱ ❭ ➱❖❪➾ ❬✻➱❖➾ ❀❖Ð ❲❹ ❱ ❷✽P⑩ ❆❖Ð ❲❹ ❱ ❫ ❵➚ ❴❳❴▲➮➽× ❵◗❛❁❜✙❝✸ä▼é☛❞❡❝❻â➻ã❧❦♥♠ é❡ã❧♦❝❜♠❢✞❞ ❢☞ä▼❅è ❞✜é✽✙❢ â❢❡❏➆❜ ã✵é✽❞✤é❤❣❄❢❿ã✵é❡å➻â ✤✜✼✵✴✩❇P✄❣ú✍↔✴✬❊➽þ➴✹❅❊❍ÿÓ✾❖◆▼✺✬✴☎✺✟✾❖◆ ★✿✴❬✯❆ÿ✁▼❊➽✹▲❲✳✴✟P ★✪✏✫❋❍✼✵✴❬✲▼❘➽✴☎✹❅þ✪❋➽✼▼✴✡ðtñ✿❍❬ñ❖ô➽ö✬✡❖ï➙ñ▲ù ↔✹❅✯❆◆❁❋✒✹❖þ ❁❲ ✯❆✴❳✦ ✘q❦❳✛✣❯✣✯❆◆Ñ❋➽✼▼✯❆✯❘ ✦✉✹❅❊✬❃✫✾❖◆▼Pü✯✱◆♥✴✬❲❅✴✟❊☛✏✏✰✳✴✬◆✵✴✟❊❍✾❖❋➽✯❆✹❅◆✸❂↔✴✟✾✳✺✽✼Ñ✯✱◆✿P❚✯✱❲✻✯❧P❚✲▼✾❅✶❿✯❧❘✒❘➽✲✎★✆✐❡✴✟✺✌❋✘❋❍✹✰◆ ❡ ✴❳↔✹✻✺✽✼✿❘✘✹❅þ➻❋❍✼✵✴ ✲✘õ✳✲✵✴✪õ ✾❖✶❆✰❅✹✳❊➽✯✱❋➽✼✵ÿ ✘✸✷✹✛➇❂❭★✿✴✟✯✱◆▼✰ ❋❍✼✵✴❬◆✵❳✴ ✦❡✦❉✴✟✯✱✰✳✼✳❋✽❘➆✴✟◆▼✺✌✹❚P❚✴❑P ★✿✾❅♦✺ ❃✏✯✱◆❁❋❍✹ ❋➽✼✵✴✒✺✽✼✵❊❍✹❅ÿ❬✹✳❘➽✹❅ÿ❬✁✴ ❨☞❫❿✯✱✰✳✲✵❊❍✴✵❦❩❪✔✢✩✤r✦✉✹☎P✵✯❆❘●❋➽✯❆◆▼✺❳❋✘ð❻ñ✜Ó ❍ ñ▲ô➽ö♦✡❖ï➙ñ▲ù ❇P❣✄ ú☎û➴ð ❇P❣✄ ú➇ý✍✦✉✴✬❊❍✴✘❋➽✴✟❘●❋➽✴❑P ❨☞✤❿✾✿★✵✶❆✴❉✈❑❪❳❂✹✦✐✯✇❋❍✼✁✚ ❡✩✯❆◆▼P❚✯❆❲❁✯❧P❚✲▼✾❅✶❆❘❿✾❖◆✿P✚✹❅◆▼✴➻ÿ✥✲✵❋❍✾▲❋❍✯✱✹✳◆✚✹✱↔✴✬❊✽✾▲❋❍✹❅❊❑✹❂ ✭❁ñ▲ì✻ú✽ú❳ï➙ñ▲ù ❨➙✺✬✹❅✶❆✲✵ÿ❬◆✳❥❧❦✧❪ ✹❅❊❱ô➽ñ▲ù❭❅✕ ø✿❍ ❨➙✺✬✹❅✶❆✲✵ÿ❬❧ ◆ ♠✑❦✧❪❳❂✿❘●✯❆◆▼✺✌✴❣❋❍✼✵✴✒✺✌❊❍✹✳❘❍❘●✹▲❲✳✴✬❊✽❘✪❊❍✴✬❲❅✴❑✾❖✶❆✴✟✓ P ↔✹✻✹❅❁❊ ↔✴✬❊➽þ➴✹❅❊❍ÿÓ✾❖◆▼✺✬✴✟❘✮✢♦➆♥ ✴✬❊❍✴ ❋➽✼✵✴✐✺✌✹✳ÿ ▼✾❖❊❍✯❆❘➽✹❅◆❱þ➙✾❃❲✳✹❅❊✽❘➩❋❍✼✵✴✜✶❆✾❖❋●❋➽✴✟❊✧❍Óñ❅ö✬ô➽ø♣ ❍✝ì❚î❛ñ▲î❥ï➙ø▲ù✿❂✜✦✐✼✵✯❆✺✽✼✝ÿÓ❩✾ ✏❱✾❅✶✱✶❆✜✹ ✦ ✯❆◆▼P❚✯❆❲❁✯❧P❚✲▼✾❅✶❆❘❻❋❍✹ Population Lamarckian Mutation ✝✆✆ ✝✝✆ ... Selection ☎ ✄✁ ✁✂ ✁ ✄ ✄☎✄ Encode Decode Learning ... ... ✞ ✠✭ ✟↔➳ ✣✻➳ ➂❉❝✝♦q⑦✇⑦q⑤✳①➇❵❛❴●❫✬❵❡♦q❞❑❝Ó❞✬❦➩❵❡③❁❭✐➃✿❫✟❜✚❫✬❴❡♣●Ô❖♦✇❫✟❝☎①➇❵❛❴●❫✌❵❡❭✽❼✟Ò✝❞✟❦✸♦q❝✳③❁❭❍❴❡♦⑧❵●❫✟❝✳♣✽❭❑Ð ✐❡✲✵ÿ ✩★↔✴✌❂❋ ✦✉✴✬✴✬◆Ó✶❆✹❚✺✬✾❅✶▼ÿ❬✯✱◆▼✯✱ÿÓ✾✵❑❂ ✦✐✼✵✯❆✶✱✴➆❋➽✼✵✴✯✭✳ñ❖ì✻ú✽ú✽ï➙ñ❖ù✥ÿ✝✲❚❋❍✾❖❋➽✯❆✹❅◆❈✴❳❬↔✴❑✺❳❋❉ÿÓ✾❩✏✁★✿✴✘❊➽✴✟❲❅✴✟❊❍❘➽✴✟P ❑★ ✏❈❋➽✼✵♠✴ ✲➆õP✲♠✴➻õ❉✢ ✤❻✾✱★✵✶✱✴✌✈✒✾❅✶❆❘➽✹✚✺✌✹✳ÿ ▼✾❖❊❍✴✟❘❿❋❍✼✵✴✌★↔✴✟❘●r❋ ❇P✄❣ú✞✦✐✯✱❋➽✼Ó✰❅❊✽✾❅P✵✯✱✴✟◆✳❋☛✼✣★✿✾❅❘➽✴✟P✝ÿ☎✴✬❋➽✼✵✹❚P✵❘✍❨➴❲▲✾❖✶❆✲✵✴✟❘❉✾❖❊❍✴ ✵❊➽✴❑❘●✴✟◆❁❋➽✴✟P✛✯✱◆ ❋➽✴✟❊➽ÿÓ❘☎✹❖þ✘❋➽✼✵✴ ÿ❬✴✟✾❅◆ ✹❅þ✩❋➽✼✵✯❆❊➽❋❂✏➞❊➽✲▼◆▼✬❘ ❪✗✢✳✤✜✼✵✴ ✝✥ó✬ì❚ô➽ñ▲í➻õ✐ø✽÷↔ì❚í✱ñ❖î➌ï➙ø❖ù û●✝✘õ❻ý ÿ☎✹❚P❚✴✟✶✳✦✉✾✳❘✒✾❅P✵P✵✴✟P➩❂❄✦✐✼✵✴✟❊➽✴✓✚✓❡♥ë✡ðtõ☛✡ ú❘✦✐✯❆✶✱✶P★↔✴☎❋➽❊✽✾❖✯❆◆✵✴✟P♥❲✻✯❆✾✡❋❍✼✵✴✩➆✲ õ✳✲✵➻✴ õ➤✾❅✶✱✰✳✹❅❊❍✯✇❋❍✼✵ÿ✏❂ ✯✱◆✫✹✳❊❍P❚✴✟❊✜❋➽✹❈✾✳✺✽✼✵✯✱✴✟❲❅✴✒✾☎þ➙✾❖✯❆❊➆✺✬✹❅ÿ ▼✾❖❊❍✯❧❘●✹✳◆✡✾❖ÿ❬✹✳◆✵✰✝÷✵ø✽÷↔ì❚í✱ñ❖î➌ï➙ø❖ù✡✾❖◆✿P♥ù✣ø▲ù ❆÷✵ø✽÷↔ì❚í✱ñ❖î➌ï➙ø❖ù✡✾✿✎✼ ✵❊➽✹❁✾❅✺✽✼✵✴❑❘❳✢✂✤✜✼✵✴✯✫✘ñ❅ö♦✡✟õ✜ô➽ø❍÷▼ñ❳❁✭ ñ▲î❥ï➙ø▲ù û●✉✫ õ❻ý✐✯❧❘➻✹✳✲❚❋☛↔✴✬❊➽þ➴✹❅❊❍ÿ❬✴✟P ★✪✏☎❋➽✼✵✴✯✳✭ ñ❖ì✻ú❍ú❳ï➙ñ❖ù✥ÿ✥✲✵❋❍✾▲❋❍✯✱✹✳◆ ❇P✄ ✯✱◆ þ➴✹✳✲✵❊✌↔★ ✴✬◆▼✺✽✼✵ÿÓ✾❅❊☛❃❚❘✟✥❂ ✦✐✼✵✯✱✶❆✴❱❋➽✼▼✴♠✲➆õ✳✲✵➻✴ õ û●✲➆õ❻ý✘✾❅✶✑✦✜✾❩❚✏ ❘✉❘➽✲✵❊✬▼✾❅❘❍❘➽✴✟❘✉❋➽✼▼✵✴ ❇P✄✯✢❆✤✜✼▼✴ ✝✘õ✰★↔✴✬✼✿✾❃❲❅✴✟❘ ★↔✴✌❋●❋❍✴✬❊❑❂▲✾❖✶✱❋➽✼✵✹✳✲✵✰❅✼✒❋❍✼✵✌✴ ✲➆ð❬✴❳✖✵✺✌✴✬✶❧❘☞✾❖✶❆✶✳ÿ❬✴✬❋➽✼✵✹❚P✵❘✟❂❖❘❡❋❍❊➽✴❑❘➽❘➽✯❆◆✵✰✐❋➽✼▼✴✉✯❆ÿ ✿✹✳❊●❋✽✾❖◆▼✺✬✴ ✹❖þ❿❋➽✼✵✴✒❊✽✾❖◆▼P✵✹❅ÿ ÿ✥✲✵❋❍✾▲❋❍✯✱✹✳◆✫✾❖◆▼P ❘●✴✟✶✱✴❑✺❳❋❍✯✱✹✳◆✡✹✂✿✴✟❊❍✾❖❋➽✹❅❊✽❘✮✢ ❅ ❋➽✴✟ÿ✁↔✹❅❊✽✾❖✶❘✿✴✟❊❍❘☛↔✴✟✺❳❋❍✯✱❲✳✴Ñ✯❧❘ ✰✳✯✱❲✳✴✬◆ ✯✱◆ ❫❻✯❆✰❅✲▼❊➽✴ ✚ þ➴✹❅❊❈❋❍✼✵✴ ✂■♥r♥ ❋❍✾✳❘✽❃✣❂❉❊➽✴✌☞▼✴✟✺✌❋➽✯❆◆✵✰ ✴✟✾❅✺✽✼✡ÿ❬✴✌❋➽✼▼✹✻P▼✌❘ ❚✍ ❋❍❊❍✾❅✯✇❋✽❘❳❁❯ ❋❍✼✵✴✵❇P✄ ✾❖◆▼P ✫✉õ➞❘➽✼✵✹✜✦ ❘➽✶❆✹✜✦ ✶✱✴❑✾❖❊❍◆✵✯❆◆✵✰✝❊✽✾▲❋❍✴✟✮❘ ❱❁❋➽✼✵✴ ✲➆õ➞✰❅✴✬❋❍❘✉❋➽✼▼✴ þ➙✾❅❘●❋➽✴✟❘●❋✥✺✌✹✳◆✻❲❅✴✬❊❍✰❅✴✟◆▼✺✌✴✳❭❂ ✵★ ✲❚❋✥✯✱❋✵❁❲ ✲✵✯❧✺♦❁❃ ✶ ✏♥❘●❋❍✾❅✰❅◆▼✾❖❋➽✴❑❘❳❱❄★↔✹❖❋❍✼ ❋➽✼✵✴Ó❊✽✾❖◆▼P✵✹❅ÿ ÿ✝✲❚❋❍✾❖❋➽✯❆✹❅◆✛ð ❇■✄ ✾❖◆▼P ✝✘õ ❊➽✴✟❲❅✴❑✾❖✞✶ ★✿✴✬❋●❋❍✴✬❊✒✶❆✹❅◆✵✰ ❋➽✴✟❊➽ÿ ✿✴✟❊●þ➴✹✳❊➽ÿÓ✾❖◆✿✺✌✴✟❘✟❂✣✾❖✶ ★✿✴✟✯✇❋✒❋❍✼✵✴☎þ➴✹❅❊❍ÿ☎✴✟❊❱ÿ☎✴✬❋➽✼✵✹❚P❰✰✳✾❅✯✱◆✿❘ ✾❖◆✏✾❅P❚❲▲✾❖◆❁❋✽✾❖✰❅✂✴ ✢ ④ ❞✟❜✒❪✻❫✬❴❡♦q①❛❞✟❝❬➵❚❭❍❵❥Ý❿❭✽❭✽❝Ó❢❅✒♦ ✑✵❭❍❴❡❭✽❝▲❵✙❵❛❴●❫✟♦q❝❁♦q❝✳❼✒❫✟❪✳❪✳❴❡❞❃❫✬♣➽③✳❭✽✛① ❆✔✓✖✕✘✗✚✙➤✈✟❫✟⑦q⑤❁❭✽●① ❋➽Ð ✛❉➦ ■✢✜ ❖✣✜ ✤✦✥ ❖✣✥ ✧★✥ ✙ ➯✻➨✪✩ ❸❖Ðq❷✽⑩❃➋ ❸❅Ð ❸❃❶✬➋ ✩ ➳ ✩ ✎✫✪ ❸❖Ð ❸❑❶✟❸ ❸❅Ð ❅✬❁⑩ ❆ ❸❅Ð ❆❁✬✽ ⑩ ✹✪✺ ✧ ❸❖Ð ❅❖✪❷ ✽ ❸❅Ðq❷❑❷ ❆ ✩ ➳ ✩ ✪✫✬ ❸❖Ð✇❷✽❸❅❷ ❸❅Ðq✪❷ ❀✬⑩ ❸❅Ð ❅✟❸❖❷ ❂❄❃✝❃ ❸❖Ðq❷✌✖❹ ❆ ✩ ➳ ✩✫✩✫✩ ✩ ➳ ✩✫✩✫✩ ✩ ➳ ✩✫✩✫✩ ❸❅Ð ❁❸ ❑✽ ❶ ❸❅Ð ❸✟⑩❃❹ ❉ ✥☛❊ ✧■❍❑❏ ❸❖Ð ❅✖✽P❅ ❸❅Ðq❷✽⑩✟⑩ ✩ ➳ ✣✮✭✯✎ ❸❖Ð✇❷❳❹❖❷ ❸❅Ðq❷✌❶✟❹ ❸❅Ðq✪❷ ✽✬⑩ ❍✑✧■❏ ❸❖Ð ❸❑➋❅❷ ❸❅Ð ❸✟⑩❃❹ ✩ ➳ ✩ ✎ ✩ ❸❖Ð ❸✬⑩❃❸ ❸❅Ð ❁❸ ✬✽ ⑩ ❸❅Ð ❸❑➋✟➋ ❸❖Ðq✪❷ ❆❅❷ ✩ ➳ ✩ ✬✰✭ ✩ ➳ ✩ ✬✰✭ ❸❖Ð ✖❸ ❀❁❀ ❸❅Ðq❷❳❸❑❶ ❸❅Ðq❷❳❸✬⑩ ▼ ✺ ❃ ❸❖Ð ❆P❅✖❀ ❸❅Ð ❁❸ ❑❀ ❹ ✩ ➳ ✩✯✱✳✲ ❸❖Ð✇❷✽❁❸ ❀ ❸❅Ð ❁❸ ❑❀ ❹ ❸❅Ð ❅✖❀✖❀ ❉ ❂ ❉ ✧■❊✪➸ ❷✟Ðq✪❷ ❀❑❸ ❸❅Ð ⑩ ❅✬❸ ✩ ✠➳ ✎✫✬ ✩ ❸❖Ð P⑩ ✟❅ ❸ ❸❅Ð ⑩❑⑩❑❸ ❷❑Ð ❶✟➋✟❸ ❊ ❂ ❉ ❸❖Ð ❹❑❶❖❷ ❸❅Ð ❅✖✽✖✽ ✩ ➳ ❁✰✭❙❁ ❸❖Ð ❅✟❹✬⑩ ❸❅Ð ❆❑➋❖❷ ❸❅Ð ❁❹ ❅✎❆ ✧ ✺ ❃ ❅✖✽❅Ðq❷ ✪❷ ❀❖Ð ➋ ❅▲❷❑Ð ❹ ❅❖❷✟Ð ❀ ❆❑➋❖Ð ✽ ✣✴✬✵➳ ✩ ✙ ➯✳➧✛✚✢✜✏✎▼➳ ♥å❉â➆❄è ❣●✦ç ❦✻é❡å➻â✦❦ ✷✐✴✟❘➽✲✵✶✱❋❍❘✸✹✂★❚❋❍✾❅✯✱◆▼✴✟P✯★✪✏✍✵✲▼❊➽✴❉❇■❣✄ ú➩❘❡❋❍❊➽✴❑❘➽❘✣❋❍✼✵✴✪✯❆ÿ ✿✹✳❊●❋✽✾❖◆▼✺✬✴✙✹❖þ✻❋➽✼✵✴➻✰✳✾❖✲✿❘➽❘➽✯❆✾❅◆✘ÿ✝✲❚❋❍✾❖❋➽✯❆✹❅◆✚✾❅◆▼P ❋➽✼✵✴❬P❚✯ Ó✺✬✲✵✶✱❂❋ ✏ ✯❆◆Ñ❋❍✼✵✴❬P❚✴✟❘➽✯✱✰✳◆Ñ✹❖þ➻✺✬❊➽✹❁❘➽❘➽✹▲❲❅✴✟❊✐✹✱↔✴✬❊✽✾▲❋❍✹❅❊✽❳❘ ✢ ❅ ✶✇❋❍✼✵✹❅✲▼✰❅✼ü✹❅❋➽✼✵✴✟❊➆ÿ❬✴✌❋❍✼✵✹❚P✵❘❱✾❖❊❍✴ ÿ☎✹✳❊➽✴✉✗✴ ❬✣✴✟✺✌❋➽✯❆❲❅✴✜✯❆◆☎❘➽✎✲ ↔✴✬❊❍❲❁✯❧❘➽✴✟P✒❋✽✾❅☛❘ ❃❚❘✬❂❑❋➽✼▼✯❆❘✙✱✾ ✎✵❊❍✹✳✾❅✺✽✼✝✺✬✾❖◆✁↔★ ✴r❁❲ ✲✵✯✱❋➽✴✜✲▼❘➽✴✌þ➴✲▼✶✻þ➴✹❅❊✜ô➽ó✽ö✌ì❚ô❳ô❍ó✌ù✿î ù↔ó✬ì❚ô➽ñ▲í✸ù✣ó✌✣î ✟➻ø▲☛ô ✡▲ú❉✹✳❊❱ô➽ó✌ï➪✹ù ✒✌ø▲ô➽ö✽❳ó ❍❬ó✬ù▼î✉í✱ó✽ñ▲ô❳ù✿ï➪❑ù ✭✱✢ ❫▼✹❅❊✥ö✬í✱ñ❃ú✽ú❳ï ✆❉ö✽ñ▲î❥ï➙ø▲ù✡✾❖◆▼P♥ô➽ó✺✭❖ô❍ó❳ú✽ú❳ï➙ø▲ù✿❂✵❋➽✼▼✴ ✗✴ ✖✥✿✴✟❊➽✯❆ÿ❬✴✬◆❁❋❍❘❻✺✬✾❅❊➽❊❍✯✱✴❑P❣✹❅✲❚❋❿✼▼✾❃❲❅✴✪❘➽✼✵✜✹ ✦✐◆❣❋➽✼▼✾❖❋t❋❍✼✵✴❉✲➆Põ ✲♠✴➻õ ✾❅✶✱✰✳✹❅❊❍✯✇❋❍✼✵ÿ✂✯❧❘➩❋❍✼✵✴■★↔✴✟❘●❋❿✺✽✼✵✹✳✯❆✺✬✴ ✦✐✼✵✴✬◆ þ➴✴❳✂ ✦ ✺✬✹❅ÿ ✵✲❚❋✽✾▲❋➽✯❆✹❅◆✿✾❖✶✣❊➽✴❑❘●✹✳✲✵❊✽✺✌✴✟❘❉✾❖❊❍✴➆✾❃❲▲✾❖✯❆✶❆✱✾ ★✵✶❆✱✴ ✢❑♥✩✜✹ ✦✉✴✬❲❅✴✟❊✟❂❁✾♠↔★ ✴✌❋➽❋➽✴✟❉❊ ↔✴✬❊➽þ➴✹❅❊❍ÿÓ✾❖◆▼✺✬✴ ✯❆❘☞✾❅✺✽✼▼✯✱✴✟❲❅✴✟P ★❑✏✚❋➽✼✵✴✉✲▼❘➽✴✉✹❅þ✿✾✒ðt✿ñ ❍❬ñ❖ô➽ö✬✡❖ï➙ñ▲ù✚✾✱✎✵❊❍✹✳✾✳✺✽✼✸❳❂ ★↔✴✬✯❆◆✵✰✒❘●✼▼✜✹ ✦✐◆✒❋➽✼▼✾❖❋✙✯✱◆▼✺✬✹❅✬❊ ✿✹✳❊❍✾❖❋➽✯❆◆✵✰ ✾✝ÿÓ✾✳✺✌❊❍✿✹ ✼➇ÿ✥✲❚❋✽✾▲❋➽✯❆✹❅◆✡✯❆❘✜✴❑❘➽❘➽✴✬◆❁❋❍✯❆✾❅✶✣❋➽✹Ó✱✹ ★✵❋❍✾❖✯❆◆ ✯✱ÿ ✵❊❍✹▲❲❅✴❑☎P ↔✴✬❊➽þ➴✹❅❊❍ÿ❬✾❅◆▼✺✌✴❑❳❘ ✢ ❝ ✬❝tä✎❝tâ➆❭è ❝ ❦ ❷✟Ð✜➀✩Ð❃❺❻❭✽⑦q❭❍Ý✐⑨ ✳Ð❃②☎♣✽❤➌❝❁❭❍❴❡❝✳❭❍Ò▲⑨✟❫✟❝✻❢ ✘Ð❑➅❅♣●③✳❴●❫✬⑤✻❢❅❞❑⑦q❪❁③▼Ð ✸✈❃❞✟⑦✇✈❖♦q❝❁❼ ✉❭❍❵➌Ý☞❞✟❴❡Ô❖① ❋✟s✉①❛♦q❝❁❼➻❵❡③❁❭✪⑥✉❭❍❝❁❭❍❵❡♦q♣ ➂➻⑦✇❼✟❞✟❴❡♦⑧❵❡③❁❜✒①✙Ý✪♦⑧❵❡③ ④ ❞✟❝❁❝❁❭❍♣❍❵❡♦q❞❑❝❁♦q①➇❵✉➃✿❭❳❫✌❴❡❝❁♦q❝❁❼❅Ð ④ ➅ ❰➁☞➀ ④ ❨➅ ❀✟❸✬r❡❷✌❶✌⑩✳⑨❚s ④ ➅❅❩❣⑨✵❷ ❀❁❀❑❸❖Ð ❅▲Ð ④ Ð✻❺❿♦q①❛③❁❞❑❪▼Ð ➬➆➮➽➱ ➺ ➘✟➷✵➬✩➮➽➾➪✃❿❐ ➺❡❒ ✾Ü ❩✽❐ ➺✴✧ ➘✟➾➪➾➌➮ ➺ × ❊ ➮❛➹❡❐❡Ù✟×❁➚❧➾➪➚➪❐✟× Ð☞❾✴✻❖❦❧❞✟❴●❢✥s✉❝✳♦✇✈❚Ð✳❽➩❴❡❭✽①❛①✽⑨↔❷ ❀❁❀❃❹▲Ð ⑩❅❆❖ÐÐ✐➃✸④ Ð Ð✻✳❺❿Ð❁⑦✇❫✟Þ❁Ô❃❞✟❭✩❼❑❭✽❫✬⑦➪❝✻Ð❄❢ ❍ ×❁④ ➾➌➮❍Ð❚➷❧②☎➷ ➚qÙ▲❭❍➮➽❴❡×❚➊❑➹●Ðt➮ s ❂ ④ Ú ❤❻➺ ❐✟➀❉➱❑❭❍Ù✌❪❚Ú ❞❑❉①❛♦⑧➚❧❵❡Û❣❞✟❴❛➱❅Ò✝➷q➘✟❞✟➾➌❦❻➮ ❴ ②❬Õ☞❫✬Ö ♣➽❐❑③✳➷ ♦✇➱❖❝✳➾➪❭✩➚➴❐✟➃✿× ❭❳❫✌↔❴❡❝❁❐ ➺♦q❝❁➾ Ø ❼❣❩✐➮❛❫✬➘ ❵●➺ ❫✬Ü➆➵✻❐✪❫✟❩ ①❛❭❍Õ☞①✽⑨↔Ö ❐❑✪❷ ➷❀✖➱❖❀❑➾➪➋❖➚➴❐✟Ð ×✻➘ ➺●Ø ❹▲Ð ✧☞✣Ð✉➺ ❐❡②☎Ù ➺ ♦✇➘✟♣●Û❣③✻❫✬Û✘⑦q❭❍➚❧Ý✪×❖Ù ♦q♣✽Ð ➊❑❑Ð ❞❑③✳❝ ➮➽◆ ×✵➮➽♦q➾➪⑦q➚➴❭❍➹ Ò▲⑨ ➸ ✉➷ Ù❃❭❍Ý❐ ➺ ➚❧❻➾❆Ú❖❞✟Û✘❴❡Ô❚Ü ⑨✵❷✪❀✖❀❁❏ ❅❀ Ð ➘✟➾➙➘ ❉ ➾ ➺ ➱✳➹❍➾➪➱ ➺ ➮➽Ü Õ✙Ö ❐❑➷ ➱❖➾➪➚➴❐✬× ✧✙➺ ❐❡Ù ➺ ➘✟Û✘Ü Ð ➅❖❪✳❴❡♦q❝❁❼✟❭❍❴❛r ❻❭❍❴❡⑦✇❫✬❼✳⑨✳s✐➅✳➂✩⑨❖❵❡③❁♦⑧❴●❢✝❭❳❢❅♦⑧❵❡♦✇❞✟❝✿⑨✿❷✪❀❁❀✖✽❅Ð ✽❖Ð✜❩❣Ð✪②☎❞❑❝▲❵●❫✟❝❁❫ü❫✬❝✻❢➞➃tÐ☞❩✐❫❳✈❅♦q①✽Ð ➁✿❴●❫✬♦✇❝✳♦q❝❁❼Ñ❦❧❭✽❭❳❢❖❦❧❞✬❴❛Ý✙❫✬❴●❢➞❝❁❭❍⑤✳❴●❫✟⑦✉❝❁❭❍❵➌Ý☞❞✟❴❡Ô❖①✝⑤❁①❛♦q❝❁❼Ñ❼❑❭❍❝❁❭❍❵❡♦q♣ ❶▲Ð✩❫✬②✡⑦✇❼✟Ð❖❞✟➀➻❴❡♦⑧♦q❵❡❭❳③❁❢✳❜✒❜✒①✽♦q⑦qÐt⑦q❭❍❤➌❴❳❝ Ð↔✧☞➅❅⑤❁➺ ❐❳❪❚➹ ❭➽❴❡✈❅♦q✬①❛➾❆❭❳Ú ❢✒❍ ➃▼❭❳❃ ❫✬➸ ❴❡❝✳❍●♦q⑨❅❝❁❪✻❼➆❫✬♦✇❼❑❝✝❭✽①✉②☎✖❶ ⑤✳✽❁⑦q❅ ❵❡❅♦q⑦✇✎❶ ❫✽✽❃Ò▲❶▲❭❍Ð▼❴✪②☎❽✣❭➽❞✟❴❡❴❡♣✽❼❑❭✽❫✟❪✳❝ ❵❛❴❡✩❞✟❝❁❫✟①t⑤❅❦❧r✣❜✚❦❆❴❡❫✬❞✟❝❁❜ ❝✿⑨✵❺☞❷ ❫✬❀❑♣➽❁➋ Ô❖❀❖❪✳Ð ❴❡❞✟❪✻❫✬❼❃❫✬r ➋❖Ð ❵❡➆♦q❞❑Ð ❝✝❿❵❡❫✟❞✒❞❅Ð ➂✉t❢✳✈❃❫✟❞✟❪✳⑦q❵❡✈❅♦q♦q✈❃❝✳❭✜❼✒➃✿➂➻❭❳❴❛❫✌❵❡❴❡♦ ❝❁✻♦q♣❍❝❁♦✱❼✒❫✬⑦ ➁✿❉❭✽♣➽❭✽③✳⑤✳❝❁❴●❫✬♦ ▲⑦ ⑤❁❉❭✽❭❍①✜❵❥Ý❿Ð ❞✟❃ ❴❡❐✬Ô❖Û ①✽Ð■❬ ✧✙➺❉ ❐❳➾➙➹ ➘✬×✆❍➇❴ ÕttÕt➘✟Õ✙✆× ❴ ⑨✳➋❃❍ ❶♣×❁❆ ➾➌❀❳➮ ❋➺ ❩✽❋q❷✽➘❃⑩P➹●❅✖➮➽Ü❆✌⑨✣r●❷❍❷ ⑩❑✽❅⑩❃⑨↔❶❖❷ ⑨✸❀❁✪❷❀✬❀✖⑩✳❀❁Ð ❀❅Ð ✁ ✝✆ ✟✞ ✡✠ ☞☛ ✌✠ ✍☛ ✎✞ ✕✔ ✑✏✓✒ ✖✞ ✚✙ ✍✠ ✘✗ ✜✛ ✣✢ ✣✤ ✦✥ ★✧✝✩✪✩ ✬✫ ✮✭ ✲✱ ✴✳ ✍✗ ✝☛ ✶✵ ✷✠ ✰✯ ✓✧ ✷✠ ✟✧ ★✧ 0.6 EA BP RP LEA NNP 0.55 0.5 0.45 0.4 Error (RMSE) ☎ ✄✂ 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 20 ✭ ↔➳ ❁▼➳ ✟ ✞ 40 60 ➁☞③✳❭✐❭❍❴❛❴❡❞✟❴➻❭✽✈❑❞❑⑦q⑤✳❵❡♦q❞❑❝✝❦❧❞✟❴➻❵❡③❁❭ 80 Time (seconds) ❂❄❃✝❃ ❵●❫✟①❛Ô❚Ð 100