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Download A Branch and Bound Algorithm for Primary Routes Assignment by Walkowiak K. M. PDF

By Walkowiak K. M.

Problems with computing device community survivability have won a lot recognition lately due to the fact computing device networks performs an incredible position in smooth international. Many firms, associations, businesses use machine networks as a easy software for transmitting many different types of details. provider disruptions in smooth networks are anticipated to be major simply because lack of companies and site visitors in high-speed fiber platforms may cause loads of damages together with fiscal loses, political conflicts, human illnesses. during this paper we specialise in difficulties of survivable connection orientated community layout. a brand new aim functionality LF for basic routes task the local-destination rerouting technique is outlined. subsequent, an optimization challenge of fundamental routes task utilizing the LF functionality is formulated. additionally, a department and sure set of rules for that challenge is proposed. the idea and experimental effects display the facility to use the LF functionality to dynamic and static layout of survivable connection orientated networks.

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S ❁❉❑❵✾❍❚❙✻❩❑✜❏▲❘ ❯ ✍ ✁ ✙✛✚ ✝✠✟☛✡☞✟✍✌ ✁ ✆ ✍ ❯ ✂❬ ✁ ✁ ✞☎✄ ✔✝✆✟✞✡✠☞☛✍✌✎✠☞✠ ☛✍✏✑✠☞✒ ✄ ✠✔✓ ✘✜✼❖❁❉❑❙❁ ✾✽❑▼❁❆❘▼❁❉€✽❁❄❑❵✾❍❞r❏▲❀❂s■✻❩❑▼❚❵✾✽◆❭❚☎s❖❑❙✻❩s■❁❄❑☞❚❵❏◗❁❄❘✂✻❍❡r❚❵✼❇❏▲❘☎❚★✺✔s■❁③✻✽❡✸❀③❫❖❞◗❚❙❏✟✄ ❘❙❋ ✾❍❞▲❁✝❞◗✻ ✎✄ ✄ s✿✾✽❘▼❘✂❑❙❁❉s❖❑❙❁❉❘❙❁❉◆ ✄ ❚❪✾❣❚❵❏▲✻✽◆ ✝ ❯❩❅✏✆✗✾✽❋❪✼✭❏◗❀ ✾✽♣✽❁✬❑▼❁❄s❖❑▼❁❄❘▼❁❄◆❭❚❵❘✬✾✡❃❇❏☞✝ ❁❄❑❙❁❉◆❭❚❛❃❖❁❉♣❩❑❙❁❉❁✪✻✽❡✹❘❙❀❂✻❤✻✽❚❵✼❖❏◗◆❖♣ ✻✽❡✢❚❵✼❖❁✍✻❩❑❙❏◗♣❩❏▲◆❖✾✽❞✜❏▲❀❈✾✽♣❩❁ ✄☎✼❖❏◗❋❪✼✍❑▼❁❄❃❖❫❇❋❄❁❄❘✏◆❖✻❩❏◗❘❙❁✑✾✽◆❖❃✈❚❙❁ ☎❤❚❵❫❖❑▼❁❆❃❇❁❉❚❪✾❍❏▲❞ ❏◗◆ €❍✾✽❑▼❏▲✻❩❫❇❘☎✾✽❀❈✻✽❫❖◆❭❚❵❘❄❅ ❬✔❅☎✠ ❚❈❋ ✾✽◆✲❴ ❁✍❘❙✼❖✻✂✄☎◆ ❚❙✼✿✾❍❚❂❚❵✼❖❁✬✻❩◆❖❞✉✺ ❡ ✾✽❀❂❏▲❞◗✺✡❘❵✾❣❚❵❏▲❘☞❡ ✺❤❏▲◆❖♣ ❚❵✼❖❁✍◆✿✾❍❚❙❫❖❑❵✾✽❞✜❡♦❑▼✻❩◆❭❚ ✄★❁❉◆❖❃✲€❤❏◗❘❙❏▲✻✽◆ ❋❉✻❩◆❖❘▼❚❙❑❵✾✽❏◗◆❭❚❵❘ ✻✽❡✏❞▲❏◗◆❖❁ ✾❍❑❙❏◗❚★✺✽●r❘▼✼❖❏◗❡ ❚ ✄❪●✛❑❙✻❍❚❪✾❍❚❙❏▲✻❩◆ ✄❵●✸✾✽◆❇❃ ❘▼❋ ✾✽❞◗❁❛❏▲◆❭€❍✾✽❑▼❏❥✾✽◆❖❋❉❁❛❏▲❘❆❚❵✼❖❁ ✎✹✾✽❫❖❘▼❘❙❏▲✾✽◆ ❡ ✾✽❀❂❏▲❞✉✺❈✾✽◆❖❃✍✾✽❞▲❞ ❏◗❚❵❘✜s❖✾✽❑▼❚❙❏❥✾✽❞ ❃❖❁❄❑▼❏◗€❍✾❍❚❵❏✉€❩❁❉❘ ✥ ✏✔❯✒✧ ❅ ✍❇❅✙✎✹✾✽❫❖❘▼❘❙❏❥✾❍◆❛❧✿❞◗❚❙❁❄❑❙❏◗◆❖♣ ❘❙❁❉❑▼€✽❁❄❘☎❚❵✻❜❑❙❁❉♣❩❫❖❞❥✾❍❑❙❏☛✡❉❁✂❚❵✼❇❁✢❏▲❀❈✾✽♣❩❁✽●❤❀❈✾✽②♥❏▲◆❖♣ ❘▼❫❖❴❖❘❙❁❉♠♥❫❖❁❄◆❭❚✝❃❇❏☞✝ ❁❄❑❙❁❉◆❭❚❵❏✟✄ ✾❍❚❙❏▲✻❩◆✈✻✽s ❁❉❑❵✾❍❚❙❏▲✻❩◆❖❘✜❀❈✾❍❚❙✼❖❁❄❀❈✾❍❚❵❏◗❋ ✾✽❞◗❞◗✺ ✄✕❁❄❞◗❞✟✄★s■✻❩❘▼❁❄❃ ❅ ✠★◆ ✻❩❫❖❑③❁❄✾✽❑❙❞◗❏▲❁❉❑ ✄✕✻❩❑❙② ✥ ✍❩④✪✧ ✥ ✍❩❨ ✧ ●✆✄✕❁✬s❇❑❙❁❄❘▼❁❄◆❭❚❵❁❉❃ ✾✪❘☞✺❤❘▼❚❵❁❉❀ ❡♦✻❩❑③❘▼❁❄♣❩❀❂❁❄◆❭❚❵✾❍❚❵❏◗✻❩◆ ✻✽❡✙☛✖✥☎✠❆❴❇❑❵✾✽❏◗◆ ❏▲❀❈✾✽♣❩❁❉❘☎❫❖❘❙❏◗◆❖♣❈✻✽◆❖❞◗✺ ❀③❫❇❞◗❚❵❏◗❘❙❋❄✾✽❞▲❁✂❡♦❁❄✾❍❚❵❫❇❑❙❁❄❘❉❅✏✥✏❁❉❘❙❫❖❞✉❚❵❘✏❘❙✼❖✻✂✄✧❚❵✼❇❁❆❏◗❀❈s■✻❩❑▼❚❵✾✽◆❖❋❉❁✢✻✽❡✛❘❙❫❇❋❪✼✖❡♦❁ ✾❍❚❙❫❖❑❙❁❉❘ ❏▲◆ ❃❖❏◗❘❙❋❉❑❙❏▲❀❂❏▲◆❖✾❍❚❵❏◗◆❖♣ ❴■❁❉❚ ✄✕❁❄❁❉◆✖❃❖❏✟✝❦❁❉❑❙❁❄◆❭❚☎❚❵❏◗❘❙❘▼❫❖❁✢❚★✺✔s■❁❄❘❉❅ ✟❖❅ ✷✳✻✽◆❖❘▼❚❙❑❙❫❖❋q❚❵❏▲◆❇♣❈✘✜✼❖❁❆✫✿❁ ✾❍❚❙❫❖❑❙❁✹✐❢✾❍❚❙❚❙❁❄❑▼◆ ✙✌ ❘✢❘❙✼❖✻✂✄☎◆ ❏▲◆ ✫❢❏▲♣❩❫❖❑▼❁ ✟❖● ❫❇❘❙❏▲◆❇♣ ❚❙✼❖❁③❡♦❁ ✾❣❚❵❫❖❑▼❁ ❁ ☎❤❚❵❑❙✾✽❋❉❚❙❏▲✻❩◆ ❀❂❁❉❚❙✼❖✻✔❃❇❘✝❃❖❁❄❘▼❋❄❑▼❏▲❴■❁❄❃ ❏▲◆✪❚❵✼❇❁ ❞❥✾❍❘▼❚✙❘❙❁❄❋q❚❵❏◗✻❩◆❖❘❄●■❁ ✾❍❋❪✼✪€❩✻ ☎✔❁❄❞ ✘ ✄ ✆✟✞ ✠ ✞ ☛✌☞ ●■❏▲❘✏❑❙❁❄s❇❑❙❁❄❘▼❁❄◆❭❚❵❁❉❃ ❴♥✺✍✾❜❡♦❁ ✾❍❚❙❫❖❑❙❁✑€❩❁❄❋q❚❵✻❩❑✗✁ ✄✝✆✟✞ ✠✡✞ ☛✌☞ ❋❄✻❩◆❖❘▼❏▲❘☞❚❵❏▲◆❇♣ ✻✽❡ ✍ s✿✾✽❑❙✾✽❀❈❁q❚❵❁❉❑❙❘ ✝ ❯❩❅✏✫r❏◗❑❙❘☞❚✜✻❩❑❙❃❇❁❄❑✜❡♦❁ ✾❍❚❙❫❖❑❙❁❉❘ ✆ ✾✽◆❇❃ ✍ ✄ ❖❃ ❁❉◆❖✻✽❚❙❁❄❃✖❴❭✺ ✂✝ ✁ ✾✽◆❖❃ ☎✝ ✄ ❑▼❁❄❘▼s ❁❉❋❉❚❵❏✉€❩❁❉❞◗✺❩❅ ❬✔❅☎✘✚❁ ☎❤❚❵❫❇❑❙❁✑❀❈❁❄✾✽❘❙❫❖❑▼❁✝❡♦❁ ✾❍❚❙❫❖❑❙❁❉❘ ✝ ✄✳❁✹❋❄✾✽❞▲❋❉❫❖❞❥✾❍❚❙❁❄❃❛❚❙✼❖❁✹❋❄✻ ✄ ✻✔❋❉❫❖❑❙❑▼❁❄◆❖❋❉❁✑❀❈✾❍❚❙❑❙❏ ☎ ▲❏ ◆✈❡♦✻❩❫❇❑✜❃❖❏▲❑▼❁❄❋✞✄ ❚❙❏▲✻❩◆❖❘ ✄ ✆ ✟ ✟ ✏ ✟ ❲ ✟ ❯ ✍ ✏ ❫❖❘❙❏◗◆❖♣❂✾✽◆✍❏◗◆❭❚❵❁❄❑ ✄★❃❖❏◗❘▼❚❵✾✽◆❖❋❄❁ ✝ ✆③❯❩❅✕✒✔❏▲◆❇❋❄❁ ✄✳❁✑✼✿✾ €❩❁ ✏③♦❡ ❁ ✾❍❚❙❫❖❑❙❁❉❘☎❡♦✻✽❑ ❯✒✡ ❁❄✾✽❋❪✼ ❖❃ ❏◗❑❙❁❉❋❉❚❵❏◗✻❩◆ ❭● ❚❵✼❇❁❄◆ ✕✄ ❁✏✼✿✾ €❩❁✙❚ ✄✕❁❄◆❭❚★✺❂❚❵❁ ☎✔❚❙❫❖❑❙❁✙❀❈❁❄✾✽❘❙❫❇❑❙❁❄❘ ☎✄ ✼❖❏◗❋❪✼ ☎✄ ❏▲❞◗❞✿❴ ❁☎❑▼❁❄s❖❑▼❁❄❘❙❁❉◆❭❚❵❁❄❃ ❴❭✺ ✝ ✞ ❵❚ ✼❖❑▼✻❩❫❖♣❩✼ ✝☎✄ ✞ ❅ ✍❇❅✙☛✍❫❇❞◗❚❵❏◗❘❙❋❄✾✽❞▲❁✈❡♦❁ ✾❣❚❵❫❖❑▼❁❄❘ ✝ ✡ ✁ ❁✪❋❄❑▼❁ ✾❍❚❙❁❄❃✭✾✡✼♥✺❤s■❁❄❑▼❘▼❚❪✾❍❋❪② ✻✽❡✹❘▼❁❉€❩❁❉◆✓❑❙❁❄s❇❞▲❏▲❋❄✾✽❘❂✻✽❡✝❚❵✼❇❁✪❏▲❀❈✾✽♣❩❁ €✽✻❩❞▲❫❖❀❂❁❂✾✽❘✑❃❖❁❄❘▼❋❄❑❙❏◗❴ ❁❉❃ ✾✽■❴ ✻❳€❩❁✽❅✈✘✜✼❇❁❄❘❙❁❈€✽✾❍❞▲❫❖❁❉❘ ✄☎❏◗❞▲❞✸❴■❁❈❑▼❁❄s❖❑▼❁❄❘▼❁❄◆❭❚❵❁❉❃ ❴❭✺ ❁❄❞◗❁❄❀❂❁❄◆❭❚❵❘ ✝☎✄ ❚❙✼❖❑❙✻❩❫❇♣❩✼ ✝ ✞ ☞ Voxel Neighborhood (x,y,z) v First Order Gray Level Parameters µ σ Co−occurrence Matrix ENT COR ASM H CON Original Volume (x,y,z) Filter # 1 v1 Filter # 2 v2 Filter # k vk (x,y,z) (x,y,z) Gaussian Filters Volume Replicas (Hyperstack) Feature Vector X ✫r✠☞✎✹✮✂✥✏✆ ✟ ✁ ✣✚✘ ✙ ✡☛✳✙✢✠ ✣✚✘ ✣ ✙ ✡✆ ✆✗✌✔✙ ✢✆ ✘ ✆✟☛✳✙✛✣ ✱✣ ✆✗✌✏☛ ✘ ✣ ✟✆ ✎✸✄ ✆✗✌✔✙ ✪✆ ✡✌✔✙ ✙✛✆ ✪✘ ❀☛✍✣✚✘ ✠ ✙☎✣ ✆ ✘ ✆ ✢✌✏✎ ✙✛✆ ✖✙ ✪✆ ✑ ✆✟✌ ✢✆ ☎✆ ✖✙ ✢✌✏☛✳✙✛✆✟✞ ✢✣ ✑ ✗✆ ✌✏☛ ✘ ✣ ✖✆✜✎✂✁ ✘ ✆✜✠ ✓ ✣ ✡✣✖✣✖✞ ✌✏✘ ✞ ✑ ✡✎ ✙✛✠ ☛✍✌ ✎✤✆ ✆✗✔✌ ✙ ✢✆ ✣ ✙✛✌✏✠✤✘ ✆✜✞ ✎ ✪✠☞✘ ✓ ✙ ✆ ✘ ✣✕✎ ✑ ✆ ✌✔✙ ✠✤✘ ☛ ✢✆✗✌ ✠✤✘✡✓✕✎ ✎✤✌ ✪✓ ✆ ✒☛✍✌✏✤✎ ✆ ✳✄ ✟☛ ✛✄✒✕ ✆ ☎✄ ✞☛ ✎✠✖✙ ✶✄ ✭☛ ✟☛ ❇☛ ✲✌ ✲✌ ✲✄✒✠ ☛ ☎✄ ✕ ✂✗ ✄ ☎✄ ☛ ✔☛ ✯✠ ✰✌ ✯✕✽✄ ✘❆ ✯✕✽✄ ❂✌ ✛✕✟✄ ☞☛ ✲✄✺✌ ✎✄ ✝☛✾✕✟✄ ☞☛ ✘❆ ✛✄ ✎✙ ✻✙✖✗✏✙ ✡✠ ☞❆ ❁✌ ✄ ❇✕✟✄✯✄ ✯✕✽✄ ✒✠ ✯✠ ✢❆ ✔✕ ☞☛ ✁ ✄ ✞✡✌ ✡✙✢✠ ✘ ✆ ✆✗✌✔✙ ✢✆ ✗✖✆✟✎ ✆✟☛✳✙✢✠✤✣✕✘ ✒✠☞✘ ✓ ✁ ✁☎ ✌✏✘✡✞ ✑ ✆✟✘ ✆ ✙✢✠☞☛ ✎ ✓✕✣ ✪✠ ✙ ✑ ✆ ☛ ✯✕✽✄ ☛ ✲✄ ✯✠ ☛ ✌ ②❍❁❉✺ s❖❑▼✻❩❴❖❞◗❁❄❀ ❏◗◆ ❘▼❚❵✾❍❚❵❏◗❘▼❚❵❏◗❋ ✾✽❞❢s✿✾❍❚▼❚❵❁❄❑▼◆ ❑❙❁❄❋❉✻❩♣❩◆❖❏✉❚❵❏◗✻❩◆ ❏▲❘✝❡♦❁❄✾❍❚❵❫❖❑▼❁ ❘❙❁❉❞▲❁❄❋q❚❵❏◗✻❩◆ ❅ ✫✿❁ ✾❣❚❵❫❖❑▼❁ ❘❙❁❉❞▲❁❉❋❉❚❵❏◗✻❩◆❛❑▼❁❉❡♦❁❄❑▼❘✶❚❵✻ ✾❆s❖❑❙✻❤❋❄❁❉❘❙❘ ✄☎✼❖❁❉❑❙❁❄❴❭✺ ✾❆❃✿✾❍❚❪✾③❘▼s✿✾✽❋❉❁✝❏▲❘✟❚❵❑❵✾❍◆❖❘▼❡♦✻❩❑▼❀❈❁❉❃✈❏▲◆❭❚❵✻③✾❆❡♦❁ ✾❍❚❙❫❖❑❙❁✂❘❙s✿✾✽❋❉❁ ❏▲◆ ❘❙❫❖❋❪✼❜✾ ✄✳✾ ✺ ❚❙✼✿✾❍❚r❚❙✼❖❁✶❃✿✾❣❚❪✾✙❘▼❁❉❚✛❀❈✾ ✺ ❴■❁✳❑▼❁❄s❖❑▼❁❄❘▼❁❄◆❭❚❵❁❉❃❈❴❭✺ ✾✂❑❙❁❉❃❖❫❖❋❄❁❉❃❜◆❤❫❇❀③❴ ❁❉❑✸✻✽❡ ✂✽❁ ✝ ❁❄❋❉❚❙❏◗€✽❁☎✂ ❯④ ❡♦❁ ✾❣❚❵❫❖❑▼❁❄❘✜✾✽◆❇❃ ✺❩❁q❚✜❑❙❁q❚❪✾✽❏◗◆ ❀❂✻❩❘▼❚✕✻✽❡❱❚❵✼❇❁✂❏▲◆❭❚❙❑❙❏▲◆❇❘❙❏▲❋✏❏▲◆✔❡♦✻❩❑❙❀❈✾❍❚❵❏◗✻❩◆❜❋❄✻❩◆❭❚❙❁❄◆❭❚✜✻✽❡❱❚❙✼❖❁✂❃✿✾❣❚❪✾ ❏▲◆ ✻❍❚❵✼❖❁❉❑ ✄✕✻❩❑❙❃❖❘③❚❙✼❖❁❛❃✿✾❣❚❪✾✪❘❙❁q❚ ❫❖◆❖❃❇❁❄❑❙♣✽✻✔❁❉❘❜✾✪❃❖❏▲❀❂❁❄◆❖❘▼❏▲✻❩◆❖✾✽❞▲❏✉❚★✺ ❑❙❁❉❃❖❫❖❋❉❚❙❏▲✻❩◆ ✥ ❯ ✟✪✧ ❅✡✒✔❁❉❞▲❁❄❋q❚❵❏◗◆❖♣ ✾✖❑▼❁❄❃❖❫❖❋❉❁❄❃ ◆♥❫❖❀③❴■❁❄❑✚✻✽❡❖❡♦❁❄✾❍❚❵❫❖❑▼❁❄❘ ✄☎❏▲❞▲❞✽✼✿✾ €❩❁✳❚❙✼❖❁✕❁✞✝❦❁❉❋❉❚r✻✽❡✿❑❙❁❉❃❖❫❖❋❉❏▲◆❖♣✏❚❵✼❖❁✟❋❄✻❩❀❂s❖❫❇❚❵✾❍❚❵❏◗✻❩◆✹❚❵❏▲❀❂❁✛✻✽❡✿❘▼❫❖❴❖❘▼❁❄♠♥❫❖❁❄◆❭❚ ✻❩s■❁❄❑❙✾❍❚❵❏◗✻❩◆❖❘ ✄☎✼❖❁❄◆③✾✽s❖s❖❞◗❏▲❁❄❃✑✻❩◆✑❚❵✼❖❁✕❃✿✾❍❚❪✾☎❘❙❁q❚ ❅✸✘✜✼❇❁✳♣❩✻❭✾❍❞❭❏▲❘✇❚❵✻✂s❇❑❙✢✻ ✙▼❁❉❋❉❚✚❚❵✼❖❁✕❘❙❁❉❚r✻✽❡ ✂ ✂ ✝ ✄ ❃❖❏◗❀❈❁❉◆❖❘❙❏◗✻❩◆✿✾✽❞✔s✿✾❍❚❙❚❙❁❄❑▼◆❖❘✗✻❩◆❭❚❵✻✑✾✽◆ ✠ ✄★❃❖❏◗❀❈❁❉◆❖❘❙❏◗✻❩◆✿✾✽❞✔❘❙s✿✾✽❋❉❁✽● ✄☎✼❖❁❉❑❙❁ ✠ ✝✿❅✸✌✭❞◗❏▲◆❖❁❄✾✽❑✸s❖❑▼✢✻ ✙▼❁❄❋q❚❵❏◗✻❩◆ ❁ ☎✔s❖❑▼❁❄❘▼❘❙❁❄❘✙❚❵✼❖❁ ✠ ◆❖❁ ✄ ❡♦❁❄✾❍❚❵❫❇❑❙❁❄❘✏✾✽❘✏✾ ❞▲❏◗◆❖❁ ✾❍❑✶❋❄✻❩❀ ❴❖❏▲◆✿✾❣❚❵❏▲✻✽◆✈✻✽❡❢❚❙✼❖❁✹✻❩❑❙❏◗♣❩❏▲◆❖✾✽❞ ✝❜❡♦❁ ✾❍❚❙❫❖❑❙❁❉❘ ✁ ✄ ✆✟✞ ✠✡✞ ☛ ☞ ✆✄✂✆☎ ✁ ✄ ✆✟✞ ✠ ✞ ☛✌☞ ❯ ✎ ✝✠✟✖✡✗✟✍✌ ✎ ❯✟ ✟ ✁ ☎✼❖❁❉❑❙❁✝✂✆☎✓❏◗❘✂✾❍◆ ✠ ✂ ✝❛❀❈✾❍❚❵❑▼❏ ☎ ❅✜✞❱❏▲◆❖❁❄✾✽❑☎s❖❑❙✻ ✙▼❁❄❋❉❚❙❏▲✻❩◆✪✾✽❞▲♣❩✻✽❑❙❏◗❚❙✼❖❀❂❘✜✾✽❑❙❁✑❑❙❁❉❞❥✾❍❚❙❏◗€✽❁❄❞◗✺ ❘▼❏▲❀❂s❖❞▲❁✝❚❙✻ ❫❖❘▼❁✽●✕❚❙❁❄◆❖❃ ❚❵✻ s❖❑▼❁❄❘❙❁❉❑▼€✽❁✬❚❙✼❖❁ ❃✿✾❍❚❪✾✔●✳✾✽◆❇❃✲✼✿✾ €✽❁ ✄✕❁❄❞◗❞✟✄★❫❇◆❖❃❖❁❄❑▼❘▼❚❙✻✔✻❤❃ ❀ ✾❍❚❙✼❖❁❄❀❈✾❍❚❙❏▲❋ ✾❍❞✕s❖❑▼✻❩s■❁❄❑▼❚❙❏▲❁❉❘ ✥ ✟ ✪✏ ✧ ❅❂✘✜✼❇❁❂❚★✺❤s■❁❈✻✽❡✕❞▲❏◗◆❖❁ ✾❍❑✝s❖❑❙✻ ✙▼❁❄❋❉❚❙❏▲✻❩◆ ❫❖❘▼❁❄❃ ❏◗◆ s❖❑❵✾✽❋q❚❵❏◗❋❄❁❜❏▲❘✢❏◗◆✟✞✿❫❖❁❉◆❖❋❄❁❉❃ ❴❭✺ ❚❵✼❖❁❂✾ €❍✾✽❏▲❞▲✾✽❴❖❏◗❞▲❏◗❚★✺ ✻✽❡✟❋ ✾❣❚❵❁❄♣✽✻❩❑▼✺✖❏▲◆❇❡♦✻❩❑▼❀ ✾❣❚❵❏▲✻✽◆✖✾✽❴■✻❩❫❇❚✂❚❵✼❖❁③s❖✾❍❚❙❚❙❁❄❑❙◆❇❘❄❅ ✠ ❡✟◆❖✻ ❋❄✾❍❚❵❁❉♣❩✻❩❑▼✺✍❏▲◆✔❡♦✻❩❑❙❀❈✾❍❚❵❏◗✻❩◆✖❏◗❘✝✾ €❍✾✽❏▲❞▲✾✽❴❖❞◗❁✽● ✾✽❘✝❏◗◆✖❚❵✼❇❁③❋ ✾✽❘▼❁ ✻✽❡✗❫❖◆❖❘▼❫❖s■❁❄❑▼€❤❏◗❘❙❁❄❃ ❋❄❞◗❫❖❘▼❚❙❁❄❑▼❏▲◆❖♣❖●■❚❵✼❖❁ ❁❄❏▲♣✽❁❄◆❭€❩❁❉❋❉❚❵✻✽❑✢s❖❑❙✻✢✙▼❁❉❋❉❚❙❏▲✻❩◆ ✾✽❞▲❘▼✻❛❋ ✾❍❞▲❞▲❁❉❃✖❚❵✼❇❁ ①✹✾✽❑❙✼♥❫❖◆❇❁❄◆ ✄★✞✇✻❤❁❉€✽❁✶❀❂❁❉❚❵✼❇✻✔❃ ●❣✻❩❑❢s❖❑❙❏◗◆❖❋❄❏◗s✿✾✽❞❭❋❄✻✽❀❈s■✻❩◆❖❁❉◆♥❚✸✾✽◆✿✾✽❞✉✺❤❘❙❏▲❘ ✐✕✷✳✌ ✁✆✁❱❏▲❘✚❋❄✻❩❀❂❀❈✻✽◆❖❞◗✺✢❫❇❘❙❁❄❃❦❅ ✄ ❯❩❅ ✆✛❏◗♣❩❁❄◆ ✄✗❁❄❋q❚❵✻❩❑☎s❖❑▼✻✢✙▼❁❄❋q❚❵❏▲✻✽◆ ✌✙❘❙❘▼❫❖❀❈❁☎❚❵✼❖✾❍❚✕❚❙✼❖❁✏s✿✾❍❚❙❚❙❁❄❑▼◆ ❀❈✾❍❚❵❑▼❏ ☎ ✻❍❡❦❚❵✼❇❁ ✝ ✄★❃❇❏▲❀❂❁❄◆❖❘▼❏▲✻❩◆✿✾❍❞❇❃✿✾❍❚❵✾✑❘▼❁❉❚ ✁☎✄✝✆✟✞ ✠✡✞ ☛✌☞ ●✔❏◗❘✟♣✽❏◗€❩❁❉◆ ❴❭✺❛❚❵✼❇❁✡✠ ✂ ✝❈❀❈✾❍❚❙❑❙❏ ☎☞☛ ☛ ✆✍✌ ☎✁ ✄ ✁ ✞ ✁ ✞ ✁ ☞ ✓✔✔✔ ✝ ✁✄ ✁ ✞ ✁ ✞ ✁ ☞ ✔✔✔ ✄ ✁ ✁ ✄✞✞☞ ✆ ✔✔✔ ✝ ✁ ✔✕ ✆ ✝ ✆ ✆ ✆ ✆ ✆ ✄✁ ☞ ✞ ☞ ✞ ☞ ☞ ✆ ❯❳❨ ✆ ✆ ✆ ✆ ✆ ☎ ✁ ✄ ☞ ✞ ☞ ✞ ☞ ☞✏✎✒✑ ✆ ✝ ✆✄ ✁ ✞ ✁ ✞ ✁ ☞ ✖✘✗✗✗ ✄✄ ✞ ✁ ✞ ✁ ☞ ✗✗✗ ✆ ✝✆ ✗✗✗ ✗ ✆ ✆ ✆ ✝ ✆✄ ☞ ✞ ☞ ✞ ☞ ☞ ✙ ❯✑✏ ✁ ☎✼❖❁❉❑❙❁✹❁ ✾✽❋❪✼✬❑❙✻✂✄ ❏▲◆ ❏▲❘✜❃❖❁q❧✿◆❖❁❄❃✖✾✽❘ ✄ ☛ ❏▲❘✜✾ s✿✾❣❚❙❚❵❁❉❑❙◆✬✾✽◆❖❃ ✠ ✆ ✂ ✂ ❅✟✘✜✼❇❁ ✝ ✂ ✝❈❋❄✻❳€❍✾✽❑▼❏❥✾✽◆❖❋❉❁✝❀❈✾❍❚❵❑▼❏ ☎ ❯✒✡ ✁ ✆ ✠❯ ☛ ✑ ☛ ✄ ✘✜✼❖❁③❁❉❏▲♣❩❁❉◆❭€❩❁❄❋q❚❵✻❩❑▼❘✝✻✽❡✸❚❙✼❖❁ ❋❉✻❳€✽✾❍❑❙❏❥✾❍◆❖❋❄❁✑❀ ✾❣❚❵❑❙❏ ☎✁ ❃❖q❁ ❧✿◆❖❁③✾❈❞▲❏▲◆❇❁ ✾✽❑☎s❖❑▼✻✢✙▼❁❄❋q❚❵❏▲✻✽◆✍❚❵✼❖✾❍❚✂❑▼❁❄s❖❞▲✾✽❋❄❁❉❘ ❚❵✼❇❁ ❡♦❁ ✾❍❚❙❫❖❑❙❁❉❘✝❏▲◆✍❚❵✼❖❁③❑❙✾ ✄✵❃✿✾❍❚❪✾ ✄☎❏◗❚❵✼✖❫❖◆❖❋❄✻✽❑❙❑❙❁❉❞❥✾❍❚❙❁❄❃✪❡♦❁❄✾❍❚❵❫❖❑▼❁❄❘❉❅✑✒✔❏▲◆❖❋❉❁✂ ❏◗❘✝✾ ✝ ✂ ✝✈s ✻❩❘▼❏◗❚❙❏◗€❩❁ ❃❖❁q❧✿◆❖❏◗❚❙❁✹❀ ✾❍❚❙❑❙❏ ☎❦●✔❏◗❚❙❘✜❁❄❏▲♣✽❁❄◆❭€❍✾✽❞▲❫❖❁❉❘✏✾✽❑❙❁✢❑▼❁ ✾✽❞✇✾✽◆❇❃✬❋❄✾✽◆✬❴ ❁✹❞❥✾❍❴ ❁❉❞▲❁❄❃✈❘▼✻❂❚❙✼✿✾❍❚ ✄ ✁✆☎ ✄ ✄✝☎ ✄ ✄ ✄ ✄ ☎ ✄ ✆✞☎ ✄ ✘✜✼❖❁ ✠ ✂ ✝③❚❙❑❵✾✽◆❖❘☞❡♦✻❩❑❙❀❈✾❍❚❙❏▲✻❩◆❈❀ ✾❍❚❙❑❙❏ ☎ ✾✽❘✜❡♦✻❩❞◗❞▲✻✂✄☎❘ ✂✆☎ ❯④ ❏◗❘✳❃❖❁q❧✿◆❖❁❉❃ ❡♦❑▼✻❩❀ ❚❵✼❖❁✝❋❉✻❩❑❙❑▼❁❄❘▼s ✻❩◆❇❃❖❏▲◆❖♣ ❁❄❏▲♣✽❁❄◆❭€❩❁❉❋❉❚❵✻✽❑❙❘ ✁ ✂☞☎ ✆ ✌ ☛ ✁ ☛ ✄ ✆ ✆ ☛ ☎ ✎✑ ❯❳❨ ☎✼❖❁❉❑❙❁✗❚❵✼❖❁✛❑▼✻ ✄☎❘✚✻✽❡ ✂✆☎ ✾✽❑▼❁✸❚❵✼❖❁✗❁❉❏▲♣❩❁❉◆♥€✽❁❄❋q❚❵✻❩❑▼❘❄❅✸✘✜✼❖❏◗❘❱❀ ✾❣❚❵❑❙❏ ☎✝s❇❑❙✻✢✙▼❁❉❋❉❚❵❘✇❚❵✼❇❁✟s❖✾❍❚❙❚❙❁❄❑❙◆✹❘▼s✿✾✽❋❄❁✟❏▲◆❭❚❙✻ ✾✽◆ ✠ ✄★❃❖❏◗❀❈❁❉◆❖❘❙❏◗✻❩◆✿✾✽❞❢❘❙❫❖❴❇❘❙s✿✾✽❋❉❁ ✄☎✼❖✻✽❘❙❁❈✾ ☎✔❁❄❘❆✾✽❑❙❁ ❚❵✼❇❁❂❃❇❏▲❑❙❁❉❋❉❚❙❏▲✻❩◆❖❘✢✻❍❡✳❚❵✼❇❁❂❞▲✾✽❑❙♣✽❁❄❘▼❚✹❁❉❏▲♣❩❁❉◆❭€✽✾❍❞▲❫❖❁❉❘ ✻✽✟❡ ✁ ✄ ✘✜✼❖❁✑❋❄✻❳€❍✾✽❑❙❏▲✾✽◆❖❋❉❁✢❀ ✓✔✔✔ ✁ ✄ ✁ ✞ ✁ ✞ ✁ ☞ ✖✘✗✗✗ ✔✔✔ ✄ ✁ ✁ ✑ ✗✗✗ ✔✔✔ ✁ ✄ ✞ ✞ ☞ ✑ ✗✗✗ ✠ ☎ ✆ ✔✔ ✔✔✔✕ ✆ ✗✗✗✗✗ ✆ ✁ ✄ ☞ ✞☞ ✞☞ ☞ ✑ ✙ ✓✔✔✔ ✁ ✄ ✁ ✞ ✁ ✞ ✁ ☞ ✖✘✗✗✗ ✔✔✔ ✄ ✁ ✁ ✑ ✗✗✗ ✔✔✔ ✁☎✄ ✞ ✞ ☞ ✑ ✗✗✗ ✆ ✔✔ ✔✔✔✕ ✆ ✗✗✗✗✗ ✂ ☎✑ ✆ ☛ ✂ ☎✑ ✆ ✁☎✄ ☞ ✞ ☞ ✞ ☞ ☞ ✑ ✙ ✾❍❚❙❑❙❏ ☎❛❏◗◆ ❚❙✼❖❁✹◆❖❁ ✄ ❘❙s✿✾❍❋❄❁✽●☛✡ ✙☎ ●✿❏◗❘☎✾ ❃❖❏❥✾✽♣✽✻❩◆✿✾✽❞ ❀❈✾❍❚❙❑❙❏ ☎ ✡ ☎ ✆ ✠ ❯ ✠ ☎✑ ✠ ☎ ✆ ✝ ✄ ✁ ✟ ✄ ✄ ✟ ✆ ✟ ✆ ✟ ✄ ☎ ✁ ✝ ✏ ☎✼❖❏◗❋❪✼ ❏▲❀❂s❖❞▲❏◗❁❄❘✇❚❵✼✿✾❍❚r❚❵✼❖❁ ✾✽❑▼❁✑❫❇◆❖❋❄✻❩❑▼❑❙❁❉❞❥✾❍❚❙❁❄❃ ❅ ✄ ✠ ❯❳❲ ✁ ❬ ✁ ✄ ◆❖❁ ✄✲❡♦❁❄✾❍❚❵❫❇❑❙❁❄❘✛✻✽❴❇❚❪✾✽❏◗◆❖❁❄❃ ❴♥✺③✾✽s❖s❖❞✉✺❤❏▲◆❖♣✏❚❵✼❖❁✜❞◗❏▲◆❖❁❄✾✽❑✚❚❙❑❵✾✽◆❇❘▼❡♦✻❩❑▼❀ ✾❍❚❙❏▲✻❩◆ ❯❳❲ ❬✔❅ ✷✳✼❇✻✔✻❩❘▼❏▲◆❖♣ ❚❙✼❖❁✹◆❤❫❇❀③❴ ❁❉❑☎✻✽❡✸✐✛❑▼❏▲◆❖❋❉❏▲s✿✾✽❞❱✷✳✻❩❀❈s■✻❩◆❖❁❉◆❭❚❵❘ ❤✒ ❁❉€❩❁❉❑❵✾✽❞✜❚❙❁❄❋❪✼❖◆❖❏◗♠♥❫❖❁❄❘❜❡♦✻❩❑❜❋❪✼❖✻❤✻❩❘❙❏◗◆❖♣ ✾✽◆ ✾✽s❖s❖❑▼✻❩s❖❑❙❏▲✾❍❚❵❁❛€❍✾✽❞◗❫❖❁❛❡♦✻❩❑ ✠ ❏◗◆ ✆✗♠❝❅ ❯❳❨ ✁ ✼❖✾❳€✽❁ ❴■❁❄❁❄◆ ❑▼❁❄s■✻❩❑▼❚❙❁❄❃ ✥ ✟ ✏✢✧ ❅✪✘✜✼❖❁❉❘❙❁❛❚❙❁❄❋❪✼❖◆❖❏◗♠♥❫❖❁❄❘❜✾✽❑▼❁❛❴✿✾✽❘▼❁❄❃ ✻❩◆✡❚❵✼❖❁❛❁❉❏▲♣❩❁❉◆❭€✽✾❍❞▲❫❖❁❉❘ ✻✽❡ ✔③❅ ✟❩✾❍❏▲◆ ✥ ✟ ✏✪✧ ❘❙❫❇♣❩♣❩❁❄❘☞❚❵❁❉❃✪✾ ❀❈❁q❚❵✼❖✻❤❃✈❡♦✻❩❑✜❋❪✼❖✻❤✻❩❘❙❏◗◆❖♣ ✠ ❘▼❫❖❋❪✼✍❚❙✼✿✾❍❚☎❚❵✼❖❁✢❡♦✻❩❞◗❞▲✻✂✄☎❏▲◆❇♣③❋❄✻❩◆❇❃❖❏◗❚❙❏▲✻❩◆✈❏◗❘✜❘❵✾❍❚❙❏▲❘▼❧❖❁❄❃ ☎✁ ✁ ✄ ✁ ☎ ✆ ✁ ✁✄ ✁ ✂✁ ❬✔❯ ☎✄ ✂✁ ✁ ☎✼❖❁❉❑❙❁ ✎ ❯❂❏▲❘✹❫❖❘▼❁❄❑ ✄ ❘❙s■❁❄❋❉❏◗❧✿❁❉❃ ❚❵✼❖❑▼❁❄❘▼✼❖✻❩❞▲❃❦❅ ✌✂❘❆✾✽◆✡❁ ☎❇✾✽❀❂s❖❞▲❁❍●✚❘▼❁❉❚▼❚❵❏▲◆❇♣ ✆ ❅❊❲ ✏ ✄✕✻❩❫❖❞◗❃ ✾✽❘▼❘❙❫❖❀❂❁✑❚❙✼✿✾❍❚✙❲ ✏ ✻✽❡❢❚❙✼❖❁✹€✽✾❍❑❙❏❥✾❍◆❖❋❄❁✢❏◗❘✏❑▼❁❉❚❵✾✽❏▲◆❖❁❉❃✍❏◗◆✈❚❵✼❖❁✑◆❖❁ ✄ ❘❙s✿✾✽❋❉❁✂✥ ✟ ✏✪✧ ❅✟✘✜✼❖❁❄❘▼❁❆❚❵❁❉❋❪✼❖◆❖❏◗♠❤❫❇❁❄❘ ✾✽❑▼❁✑❴❖✾✽❘❙❁❉❃✍✻❩◆✬✼❖❁❉❫❖❑❙❏◗❘▼❚❵❏◗❋❄❘☎✾✽◆❇❃✍❑▼❁❄♠♥❫❖❏▲❑▼❁❄❘☎❘❙✻✽❀❈❁✹❫❖❘▼❁❄❑ ✄ ❏▲◆❭❚❵❁❉❑▼€✽❁❄◆❭❚❵❏◗✻❩◆ ❅ ✄ ✄ ✄ ✝✆ ✠★◆ ❚❵✼❖❏◗❘✑❘▼❁❄❋q❚❵❏▲✻✽◆ ● ✄✕❁ ✄☎❏▲❞▲❞r❃❖❁❉€✽❁❄❞▲✻✽s ✾ ◆❖❁ ✄ ❚❵❁❄❋❪✼❇◆❖❏▲♠♥❫❖❁❂❡♦✻❩❑✢❋❪✼❖✻❤✻❩❘❙❏◗◆❖♣✬❚❙✼❖❁❂◆❤❫❇❀③❴ ❁❉❑✹✻✽❡✶s❖❑▼❏▲◆❖❋❉❏✟✄ ✿s ✾✽❞❢❋❄✻❩❀❂s■✻❩◆❖❁❄◆❭❚❙❘✂❴❭✺✪❀❈✾ ☎✔❏▲❀❂❏☛✡❉❏▲◆❖♣❂✾✽◆✪✻✽❴ ✙▼❁❄❋q❚❵❏◗€✽❁③❡♦❫❖◆❖❋q❚❵❏▲✻✽◆✪❫❖❘❙❏◗◆❖♣❛♣❩❁❉◆❖❁❉❚❙❏▲❋ ✾✽❞▲♣❩✻✽❑❙❏◗❚❙✼❖❀❂❘❄❅✏✘✜✼❖❁ ✻❩❴ ✙▼❁❉❋❉❚❙❏◗€❩❁❈❡♦❫❖◆❖❋❉❚❙❏▲✻❩◆✡❏▲❘✑❡♦✻❩❑❙❀③❫❇❞❥✾❍❚❙❁❄❃ ❏▲◆ ❘▼❫❖❋❪✼ ✾ ✄✳✾ ✺✡❚❙✼✿✾❍❚③❫❇❘❙❏▲◆❇♣✍❚❵✼❇❁❛❀❈❏◗◆❖❏▲❀ ❫❖❀ ◆♥❫❖❀③❴■❁❄❑❆✻✽❡ s❖❑▼❏▲◆❖❋❉❏▲s✿✾✽❞❢❋❄✻❩❀❂s■✻❩◆❖❁❄◆❭❚❙❘✝❚❵✼❖❁ ❁❉❑❙❑❙✻✽❑✢❴ ❁q❚ ✄✳❁❉❁❄◆✡❚❙✼❖❁ ✻❩❑▼❏▲♣❩❏◗◆✿✾✽❞✇❃✿✾❍❚❵✾ ❘▼❁❉❚✑✾✽◆❇❃ ❚❙✼❖❁ ❑❙❁❉❋❄✻❩◆❇❘▼❚❵❑▼❫❖❋❉❚❙❁❄❃ ❘❙❁q❚ ●♥❫❖❘▼❏▲◆❖♣✑✾✢❑❙❁❉❃❖❫❖❋❄❁❉❃❈◆♥❫❖❀ ❴ ❁❉❑✟✻❍❡ s❇❑❙❏▲◆❇❋❄❏▲s❖✾✽❞❇❋❉✻❩❀❈s■✻❩◆❖❁❉◆❭❚❵❘❄●♥❏◗❘✛❀❈❏◗◆❖❏▲❀③❫❇❀✍❅❱✠★◆❜❚❵✼❖❏◗❘✸❘❙❁❉❋❉❚❙❏▲✻❩◆ ● ✄✕❁ ✄☎❏▲❞◗❞❭❃❖❁❉€✽❁❄❞◗✻❩s③❚❵✼❖❁✕✻❩❴ ✙▼❁❉❋❉❚❵❏✉€❩❁✳❡♦❫❇◆❖❋❉❚❙❏▲✻❩◆ ✄☎✼❖❏▲❋❪✼ ✄☎❏◗❞▲❞♥❴■❁✳❀❈✾ ☎✔❏▲❀❂❏☛✡❄❁❉❃✹❫❖❘❙❏◗◆❖♣✢✾✙♣✽❁❄◆❖❁q❚❵❏▲❋✳✾✽❞▲♣✽✻❩❑❙❏✉❚❵✼❖❀✬❅ ✘✜✼❖❁✑✻❩❫❇❚❙❞▲❏▲◆❇❁✝✻✽❡✚❚❵✼❖❁✹❀❂❁❉❚❵✼❇✻✔❃ ❏▲❘✜s❇❑❙❁❄❘▼❁❄◆❭❚❵❁❉❃✪❏▲◆ ✫❢❏▲♣❩❫❖❑▼❁✆✏ ✞❱❁❉❚ ✝ ✄ ❑❙❁❉s❖❑❙❁❉❘❙❁❉◆♥❚❆❚❵✼❖❁❜s❖❑▼✻✢✙▼❁❄❋q❚❵❏◗✻❩◆ ✻✽❡✶❃✿✾❣❚❪✾❛€❩❁❉❋❉❚❵✻✽❑ ✁ ✄ ✆✟✞ ✠ ✞ ☛✌☞ ❏▲◆ ❚❵✼❖❁ ✁ ❵❚ ✼ s❖❑▼❏▲◆❖❋❉❏▲s✿✾✽❞❢❃❖❏▲❑▼❁❄❋q❚❵❏▲✻✽◆ s❇❑❙❏▲◆❇❋❄❏▲s❖✾✽❞❦❋❉✻❩❀❈s■✻❩◆❖❁❉◆❭❚ ✁ ✝ ✄ ✆ ☛ ✄✑ ✁ ✄✝✆✟✞ ✠✡✞ ☛✌☞ ✄ ❬❩❬ ✁ ✘✜✼❖❁✝✻✽❑❙❏▲♣✽❏▲◆✿✾✽❞✿❃❖✾❍❚❪✾❆€✽❁❄❋q❚❵✻❩❑ ✁☎✄ ✆✟✞ ✠✡✞ ☛ ☞ ❋❄✾✽◆✈❴■❁✂❑❙❁❉❋❄✻❩◆❇❘▼❚❵❑▼❫❖❋❉❚❙❁❄❃ ❁ ☎❇✾✽❋q❚❵❞✉✺❈❡♦❑▼✻❩❀ ❏◗❚❙❘✳s❖❑▼❏▲◆❖❋❉❏▲s✿✾✽❞❝❋❉✻❩❀✆✄ s■✻❩◆❖❁❄◆❭❚❙❘ ✓ ✝ ✄ ✝ ✁ ✆✦❯ ✟ ❬ ✟ ✄ ✄ ✄ ✟ ✝ ✘❆✾✽❘✜❡♦✻❩❞◗❞▲✻✂✄☎❘ ✆ ✁ ✄✝✆✟✞ ✠✡✞ ☛✌☞ ✆ ✄✠ ✁ ✞✁ ❬ ✝ ✄☛✄✄ ❬✍ ✁ (x,y,z) (x,y,z)’ (x,y,z) X X PCA Y Fitness Fm m GA ✫r✠☞✎✹✮✂✥✏✆ ✏ ✗ ✆✟✎✤✆✟☛✳✙✢✠✤✘✡✓ ✙✯✠ ✆ ✣✎✆ ✙✢✠ ✑ ✌✏✎ ✘✿✕ ✑ ✒✆✟✎ ✆✜☛✳✙✛✠✤✣✕✘✝✠ ✡✌ ✒✆✟✞ ✣✕✘ ✑ ✌ ✠ ✑ ✠ ✠✤✘✡✓ ✌✏✘ ✑ ✠ ✠☞✘ ✓ ✙ ✡✆ ✣ ✒✆✟☛✳✙✢✠ ✘ ✆ ✘✡☛✳✙✢✠ ✣✚✘ ✆✟✘ ✪✆ ✞ ✌✔✙✛✌ ✒✆ ✙ ✁ ✄ ✆✟✞ ✠ ✞ ☛✌☞ ✌✏✘✡✞★✙ ✡✆ ✢✆✟☛✍✣✚✘ ✙ ✡☛✳✙✛✆✟✞ ✆ ✂✣ ✪✠✤✘ ☛ ✠ ✌ ✎ ☛✍✣ ✑ ✣✕✘✡✆✟✘✚✙ ✠ ✑ ✠☞✘✡✠ ✑ ☛ ❇☛✵✙ ✭☛ ❆ ✯✠ ✲✙✖✼ ✌ ✕ ✟☛✾✕✽✄ ☞☛ ☛ ✙ ☎✄ ✲✌ ✛✠ ✆✞✄ ❃✆ ✄ ✆ ✟☛ ✛✄✒✕ ✛☛✩★ ❇☛ ✆ ✦✣ ✪✠☞✘✡☛ ✠ ✡✌✏✎ ☛✍✣ ✑ ✣✕✘ ✆✟✘✚✙ ✳✄ ✖ ✡✆ ✣ ✒✆✟☛✳✙✢✠ ✘ ✆ ✘✡☛✳✙✢✠ ✣✚✘ ✠✤✘✡✓ ✑✂ ☎✄ ✓ ✌ ✠ ✙ ✡✌✔✙ ✙ ✆ ✆ ✢✣ ✆ ✙ ✆✗✆✟✘ ✙ ✆ ✣ ✪✠ ✓✕✠☞✘ ✌✏✎ ✒✆ ✙ ✁ ✄✝✆✟✞ ✠✡✞ ☛✌☞ ✍ ✒✠☞✘ ✓ ✙ ✡✆ ✑ ✠✤✘✡✠ ✑ ✑ ✘ ✑ ✑ ✄ ✙ ☎✄ ✲✌✹✆✟✄ ✎✙✖✼ ❇✆ ✆ ✌ ✕ ✛✠ ✯✠ ☎✄✒✄ ✲✄ ☛ ✯☛ ✑✠ ❁✕✟☛ ✙ ★✳✕✞☛ ✪ ✯✠ ✢❆ ✯✠ ✂✥ ✕ ✎✄ ✖✕ ✥ ✕ ✙✮ ❘▼❏▲◆❖♣✬✻❩◆❖❞✉✺✪❚❵✼❇❁❈❋❉✻❩❀❈s■✻❩◆❖❁❉◆❭❚❵❘✹❋❄✻❩❑▼❑❙❁❉❘❙s■✻❩◆❖❃❖❏◗◆❖♣✍❚❙✻✬❚❙✼❖❁ ✠ ❞❥✾✽❑▼♣❩❁❄❘☞❚✑❁❄❏▲♣✽❁❄◆❭€❍✾✽❞▲❫❖❁❉❘❄● ✄✳❁❂❋ ❍✾ ◆ ✾✽s ✄ s❖❑▼✻✂☎✔❏◗❀ ✾❍❚❙❁ ❚❵✼❇❁ ❃✿✾❍❚❪✾❛€✽❁❄❋❉❚❙✻❩❑ ✁ ❴♥✺✖❚❵❑❙❫❇◆❖❋ ✾❍❚❙❏▲◆❖♣✈❚❙✼❖❁ ❁ ☎✔s✿✾✽◆❇❘❙❏▲✻✽◆ ✻❍❡✶✆✛♠❝❅ ❬ ✍ ✁✝✾❍❡ ❚❙❁❄❑ ✠ ❵❚ ❁❉❑❙❀❂❘ ✾✽❘✜❡♦✻❩❞◗❞▲✂✻ ✄☎❘ ☎ ✁ ✄✝✆✟✞ ✠✡✞ ☛✌☞ ✆ ✝ ✄✠ ✁ ✞✁ ✄☛✄✄ ❬✟ ✘✜✼❖❁❆❞❥✾✽❑▼♣❩❁❄❑✜❚❵✼❇❁❆€❍✾✽❞▲❫❇❁❆✻✽❡ ✠ ●■❚❙✼❖❁ ❋❉❞▲✻❩❘▼❁❄❑✏❏▲❘ ✁ ✄✝✆✟✞ ✠✡✞ ☛✌☞ ❚❵✻ ✁ ✄✝✆✟✞ ✠✡✞ ☛✌☞ ❅✏✘✜✼❇❁ ✻❳€❩❁❉❑❵✾✽❞◗❞❢❀❂❁ ✾✽◆✍❘❙♠♥❫✿✾✽❑▼❁ ❁❄❑▼❑❙✻❩✂❑ ✁✦❴■❁❉❚ ✄✕❁❄❁❉◆❛❚❵✼❖❁✙✻❩❑❙❏◗♣❩❏▲◆❖✾✽❞❖❃✿✾❍❚❵✾❆❘▼❁❉❚✜✾❍◆❖❃❈❚❙✼❖❁✂✻❩◆❇❁✂❑❙❁❉❋❄✻❩◆❇❘▼❚❵❑▼❫❖❋❉❚❙❁❄❃✈❫❖❘▼❏▲◆❖♣ ✠ ❋❄✻✽❀❈s■✻❩◆❖❁❉◆♥❚❙❘ ❏▲❘✜♣✽❏◗€❩❁❉◆✍❴❭✺ ✁ ✁ ❯ ☞ ☞ ☞ ✆ ✞ ✠ ✁✠ ✁✠ ✆☞ ✠☞ ☛☞ ❯ ✁ ✁ ✁ ✁ ✞ ✁ ✁ ✆ ✞ ✠ ✁✠ ✁✠ ✆ ✠ ☛ ✁ ✁ ✄ ✆✟✞ ✠✡✞ ☛ ☞ ✁ ✄ ✆✟✄✞ ✠ ✞ ☛✌☞ ✁ ✄✝✆✟✞ ✠✡✞ ☛✌☞ ✄ ✆ ✄ ☎☎✄ ✁ ✝ ✄ ☛ ✄ ✄ ✁ ✄ ✆✟✞ ✠ ✞ ☛✌☞ ✄ ☎ ✞ ✞ ✁ ✄ ✞ ❬✏ ✁ ❬✡ ✁ ✞ ✁ ✁ ✞ ✞ ✘✜✼❖❁✑✻❩❴ ✙▼❁❉❋❉❚❵❏✉€❩❁✢❡♦❫❖◆❖❋q❚❵❏◗✻❩◆✝✆ ✭ ☎ ❋❄✾✽◆✍❴■❁✢❚❵✼❖❁❉❑❙❁q❡♦✻❩❑❙❁✢❡♦✻❩❑▼❀③❫❖❞❥✾❣❚❵❁❄❃ ✾❍❘ ✆ ☎ ✆✞✁ ✁ ✟ ☞ ✁ ✄ ✟ ❬✔❯ ☎✼❖❁❉❑❙❁ ✁ ✁ ❏▲❘✜♣❩❏✉€❩❁❉◆✍❴❭✺ ✄ ✁ ✁ ✦ ✆ ❯❃☎ ✁ ✆✦❯ ✞ ✠ ✁ ✠ ✁ ✠ ✆ ✠ ☛ ❃☎ ✾❍◆❖❃✝✁ ✄ ✆ ❬ ☎✆ ❅ ❯ ☞ ☞ ☞ ✁ ✁ ✞ ✁ ✁ ✆ ✄ ☎☎ ✄ ✁ ✝ ✄ ☛ ✄ ✁ ✁ ✁ ✄ ✆✟✞ ✠ ✞ ☛✌☞ ✁ ✄ ✞ ✄ ❬❩④ ✁ ♠☎ ✌✂❘✑❘❙✼❇✻ ✄☎◆✡❏▲◆✡✆✛♠■❅ ❬ ✡ ✁q●❱❚❵✼❖❁❂✻❩❴ ✙▼❁❉❋❉❚❙❏◗€❩❁❜❡♦❫❖◆❖❋q❚❵❏◗✻❩◆✡✼❖✾✽❘✑❚ ✄✕✻ ❚❵❁❄❑▼❀❈❘❉❅ ✘✜✼❖❁❜❧✿❑▼❘▼❚❆❋❄✻❩❀❂s ✻✽◆❖❁❄◆❭❚ ● ✁ ✁ ✁q● ❏◗❘ ❀ ✾ ☎❇❏◗❀❈❏☞✡❄❁❉❃✝❴❭✺✢❘❙❁❉❞▲❁❄❋q❚❵❏◗◆❖♣☎✾✜❞❥✾✽❑▼♣❩❁❢€❍✾✽❞◗❫❖❁✸❡♦✻❩❑ ✠ ❅✚✘✜✼❖❁✗❘❙❁❉❋❄✻❩◆❖❃✹❚❵❁❉❑❙❀✬● ✁ ✄ ● ❏▲❘❦❀ ✾ ☎✔❏◗❀❈❏☞✡❄❁❄❃ ❴❭✺ ❋❪✼❖✻❤✻❩❘❙❏◗◆❖♣✬✾❛❘❙❀❈✾✽❞▲❞✚€❍✾✽❞▲❫❖❁❆❡♦✻❩❑ ✠ ❅③✘✚✻✬❀❈✾ ☎✔❏▲❀❂❏☛✡❉❁ ✆✒☎ ❏▲◆ ✆✛♠❝❅ ❬ ✡ ✁ ● ✄✳❁❂✾✽s❖s❇❞▲❏▲❁❉❃ ✾✈♣❩❁❄◆❖❁q❚❵❏◗❋ ✾✽❞◗♣❩✻❩❑❙❏✉❚❵✼❖❀ ❚❵✻✝❘▼❁❄❞◗❁❄❋❉❚❢❚❵✼❖❁✕✻❩s❇❚❙❏▲❀③❫❖❀✧◆♥❫❖❀ ❴ ❁❉❑r✻✽❡✿s❇❑❙❏▲◆❇❋❄❏▲s❖✾✽❞♥❋❄✻❩❀❂s ✻✽◆❖❁❄◆❭❚❵❘❉❅r✠★◆ ❚❙✼❖❁✳◆❇❁ ☎❤❚✛❘❙❁❉❋❉❚❙❏▲✻❩◆ ● ✄✕❁ ✄☎❏▲❞▲❞☎s❖❑▼❁❄❘▼❁❄◆❭❚✬✾ ❴❖❑▼❏▲❁❉❡✹✻❳€✽❁❄❑▼€❤❏◗❁ ✄ ✻✽❡✹♣❩❁❄◆❇❁❉❚❵❏◗❋✪✾✽❞◗♣❩✻❩❑▼❏◗❚❵✼❇❀❈❘❂✾✽◆❖❃✭✻✽❫❖❑ ❏◗❀❈s❖❞◗❁❄❀❂❁❄◆❭❚❪✾❣❚❵❏▲✻✽◆ ❚❙✻ ❀❈✾ ☎✔❏▲❀❂❏☛✡❄❁ ✆ ☎✙❅ ✎ ✄ ✑ ✆✟✘ ✆✗✙✛✠☞☛✒✞ ✙✢✠ ✑ ✠ ✌✜✙✢✠✤✣✕✘ ✆ ✎ ❁❄◆❇❁❉❚❵❏◗❋✹✾✽❞▲♣✽✻❩❑❙❏✉❚❵✼❖❀❂❘❄● ✄☎✼❖❏▲❋❪✼ ✄✳❁❉❑❙❁✑s❖❏▲✻✽◆❖❁❄❁❉❑❙❁❄❃✬❴❭✺✍✎✹✻✽❞▲❃❖❴■❁❄❑▼♣ ✥ ✏✽❨✪✧ ●❝✾✽❑▼❁✑✾✽❃✿✾✽s❇❚❙❏◗€✽❁✽●✿❃❖✻ ✄ ✢ ❀❈✾✽❏▲◆❆❏▲◆❖❃❖❁❉s ❁❉◆❖❃❖❁❉◆♥❚✸❘❙❁ ✾❍❑❙❋❪✼❜s❖❑❙✻❤❋❄❁❉❃❖❫❖❑▼❁❄❘✸❃❖❁❉❑❙❏✉€❩❁❄❃③❡♦❑▼✻❩❀✧❚❵✼❖❁✳s❖❑❙❏◗◆❖❋❄❏◗s❖❞▲❁❉❘❢✻✽❡❝◆❖✾❍❚❵❫❖❑❙✾✽❞❤s ✻❩s❇❫❖❞❥✾❍❚❙❏▲✻❩◆ ♣❩❁❉◆❖❁❉❚❙❏▲❋❄❘❉❅✕✎✹✌✙❘✏❑▼❁❄s❖❑▼❁❄❘▼❁❄◆❭❚✝s■✻✽❚❵❁❉◆❭❚❵❏❥✾❍❞ ❘❙✻❩❞◗❫❇❚❵❏◗✻❩◆❖❘✶✻❍❡r❚❵✼❇❁✑✻✽s❇❚❵❏◗❀❈❏☞✡ ✾❍❚❙❏▲✻❩◆❂❚❪✾✽❘▼②✈✾✽❘☎❞▲❏◗◆❖❁ ✾✽❑✳❘▼❚❵❑▼❏▲◆❖♣✽❘ ✻✽❡☎❋❉✻✔❃❖❁❈❋❪✼✿✾✽❑❙✾✽❋❉❚❙❁❄❑❙❘❉❅ ✤✝❫❖❑❙❏◗◆❖♣✖❁❄✾✽❋❪✼ ❘▼❚❵✾✽♣❩❁ ✻❍❡✜❚❵✼❖❁ ✎✢✌ ✻✽s❇❚❵❏◗❀❈❏☞✡ ✾❍❚❙❏▲✻❩◆ ●✇✾✍s ✻❤✻❩❞✟✻✽❡☎s ✻❍❚❵❁❄◆❭❚❙❏❥✾✽❞ ❘❙✻✽❞▲❫❇❚❙❏▲✻❩◆❖❘❢❏▲❘❢❁❉€❍✾✽❞▲❫❖✾❍❚❵❁❉❃ ❅✛✒✔❫❇❋❪✼❈✾✙s ✻❤✻❩❞❤✻✽❡❝s ✻✽❘❙❘❙❏◗❴❖❞▲❁✕❘❙✻❩❞◗❫❇❚❵❏◗✻❩◆❖❘❢❏▲❘r❋❄✾✽❞▲❞◗❁❄❃❆s ✻❩s❇❫❖❞❥✾❍❚❙❏▲✻❩◆❆✻✽❡❝❘▼❚❙❑❙❏◗◆❖♣❩❘❄❅ ✎✢✌✂❘✙❚❙❁❄❘☞❚✝❀❈✾✽◆❭✺ s ✻❩s❇❫❖❞❥✾❍❚❙❏▲✻❩◆❇❘ ✾✽❞▲❘▼✻ ❋❄✾✽❞▲❞◗❁❄❃✬♣❩❁❄◆❖❁❉❑❵✾❍❚❙❏▲✻❩◆❇❘ ✁✏✻❍❡✛❘▼❚❙❑❙❏▲◆❇♣❩❘✂✾❍◆❖❃✖❚❵✼❇❁ ◆❖❁ ✄✦s■✻❩s❖❫❇❞❥✾ ✄ ❚❵❏◗✻❩◆ ❏▲❘✑✾✽❞ ✄✳✾ ✺❤❘❆❃❖❁❉❑❙❏✉€❩❁❄❃ ❡♦❑❙✻❩❀ ❚❙✼❖❁❂s❖❑❙❁q€✔❏◗✻❩❫❖❘✑✻❩◆❖❁❍❅✈✱✕✺ ❡♦✻❩❞◗❞▲✂✻ ✄☎❏▲◆❖♣❛❚❙✼❖❁❂s❖❑❙❏◗◆❖❋❄❏◗s❖❞▲❁ ✻✽❡✳◆✿✾❍❚❙❫❖❑❵✾✽❞ ❁❉€✽✻❩❞▲❫✔❚❵❏▲✻✽◆ ●✸✎✢✌✂❘✑❏▲❀❂s❖❑▼✻ €✽❁ ❚❵✼❖❁❈❀❈❁❄✾✽◆✡♠♥❫✿✾❍❞▲❏◗❚★✺✪✻✽❡✶❚❵✼❇❁❈s■✻❩s❖❫❖❞▲✾❍❚❵❏◗✻❩◆❖❘✢✻✽❡✶❘▼❚❵❑▼❏▲◆❖♣✽❘✹❡♦❑▼✻❩❀ ♣❩❁❉◆❖❁❄❑ ✄ ✾❍❚❙❏▲✻❩◆✖❚❙✻❛♣❩❁❉◆❖❁❄❑❙✾❍❚❵❏◗✻❩◆ ❅✑✒✔❫❖❑☞€❤❏◗€❍✾✽❞r✻❍❡✟❚❙✼❖❁ ❧❖❚▼❚❵❁❉❘▼❚✹❏▲❘✏❚❵✼❖❁ ❀❈✾✽❏◗◆✖❘▼❚❙❑❵✾❍❚❙❁❄♣✽✺✍✻✽❡✗❚❵✼❇❏▲❘✂✻✽s❇❚❵❏◗❀❈❏☞✡ ✾❍❚❙❏▲✻❩◆ ❚❵❁❉❋❪✼❖◆❖❏◗♠❤❫❇❁✙✾❍◆❖❃③❚❵✼❖❁✶❧❖◆✿✾✽❞❖✻❩s✔❚❵❏▲❀❈✾✽❞❤❘❙✻❩❞◗❫❇❚❵❏◗✻❩◆③❏◗❘✸❑❙❁❉s❖❑❙❁❉❘❙❁❄◆❭❚❙❁❄❃ ❴❭✺❆❚❵✼❖❁✶❧❖❚▼❚❵❁❉❘▼❚✗❘▼❚❙❑❙❏◗◆❖♣✢❏▲◆③❚❙✼❖❁✶❧✿◆✿✾✽❞ s■✻❩s❖❫❖❞▲✾❍❚❵❏◗✻❩◆ ✥ ❲ ✧ ❅ ❬❩❬ ✫r❏✉€❩❁✝❋❉✻❩❀❈s■✻❩◆❖❁❉◆❭❚❵❘✜✾✽❑▼❁✝❑❙❁❉♠♥❫❖❏▲❑▼❁❄❃✈❚❵✻ ✾❍s❖s❖❞◗✺ ✾③♣❩❁❉◆❖❁❉❚❙❏▲❋✢✾✽❞◗♣❩✻❩❑▼❏◗❚❵✼❇❀ ❚❵✻❜✾✽◆❭✺ s❖❑❵✾✽❋q❚❵❏◗❋ ✾✽❞■s❖❑❙✻✽❴❖❞▲❁❉❀ ✝ ✾ ✁☞✌✣❘▼❚❵❑▼❫❖❋❉❚❙❫❖❑❵✾❍❞ ❋❪✼❖❑❙✻❩❀❂✻❩❘▼✻❩❀ ✾❍❞ ✁✳❑❙❁❉s❖❑❙❁❉❘❙❁❉◆♥❚❵✾❍❚❵❏◗✻❩◆✪✻✽❡r❘❙✻❩❞◗❫❇❚❵❏◗✻❩◆❖❘✜❚❵✻❂❚❵✼❖❁❆s❖❑❙✻✽❴❖❞▲❁❉❀✍❅✶✠★◆☎✄ ❃❖❏✉€✔❏◗❃❖❫✿✾✽❞◗❘ s■✻❩❏▲◆❭❚❙❘ ✁☎✾✽❑❙❁✹❚★✺❤s❖❏▲❋❄✾✽❞▲❞✉✺❛❑❙❁❉s❖❑❙❁❉❘❙❁❉◆♥❚❙❁❄❃ ❴❭✺✬❴❖❏▲◆✿✾❍❑▼✺✈◆❖✻❍❚❪✾❍❚❙❏▲✻❩◆ ❚❵✻❂s❖❑❙✻✽❀❈✻✽❚❙❁❆❁✩✫❂❋❄❏▲❁❉◆❖❋❉✺ ✾✽◆❖❃ ✾✽s❇s❖❞▲❏◗❋ ✾❍❚❙❏▲✻❩◆✪❏◗◆❖❃❖❁❉s ❁❉◆❖❃❖❁❄◆❇❋❄❁❂❏▲◆ ❚❵✼❖❁ ♣✽❁❄◆❖❁q❚❵❏▲❋❜✻❩s■❁❄❑❙✾❍❚❵❏◗✻❩◆❖❘❉❅③✆✗✾✽❋❪✼ ❋❪✼❖❑❙✻❩❀❂✻❩❘▼✻❩❀❈❁ ❋❉✻❩◆❖❘▼❏▲❘▼❚❙❘ ✻✽❡✗✾❜❧ ☎✔❁❄❃✪◆♥❫❖❀ ❴ ❁❉❑✙✻✽❡✸❴❖❏◗❚❙❘❄❅☎✆✗✾✽❋❪✼✪❴❖❏✉❚✏❑❙❁❄s❇❑❙❁❄❘▼❁❄◆❭❚❵❘✢✻✽◆❖❁❆s❇❑❙❏▲◆❇❋❄❏▲s❖✾✽❞❱❋❄✻❩❀❂s■✻❩◆❖❁❄◆❭❚✂✾✽◆❖❃✪✼❖✾✽❘✏❚ ✄✕✻ ❘▼❚❵✾❍❚❵❁❉❘ ✝✉❯✍✻✽❑ ● ✄☎✼❖❁❄❑▼❁ ❯✈❃❖❁❄◆❖✻❍❚❵❁❄❘ ❚❙✼✿✾❍❚ ❚❵✼❇❏▲❘③s✿✾❍❑▼❚❵❏◗❋❄❫❖❞▲✾✽❑ ❋❉✻❩❀❂s ✻❩◆❇❁❄◆❭❚❜❏▲❘③❴■❁❄❏◗◆❖♣ ❫❖❘▼❁❄❃✲✾✽◆❖❃ ✻✽❚❙✼❖❁❄❑ ✄☎❏▲❘❙❁❍❅ ❴ ✁☞✌✂◆ ❁q€✽✾❍❞▲❫✿✾❍❚❙❏▲✻❩◆ ✻❩❴ ✙▼❁❄❋❉❚❙❏◗€✽❁✹❡♦❫❇◆❖❋❉❚❙❏▲✻❩◆ ✁✟✻✽❡✚❏▲◆❖❃❖❏✉€❤❏▲❃❖❫✿✾❍❞▲❘✟❏▲◆❛❚❵❁❉❑❙❀ ✻✽❡✇❚❵✼❖❁❉❏▲❑✳❧❖❚❙◆❖❁❄❘▼❘❄❅✟✠★◆ ✻❩❫❖❑✜s❇❑❙✻❩❴❖❞◗❁❄❀✬●❖✘✜✼❖❁✹✻❩❴ ✙▼❁❉❋❉❚❙❏◗€❩❁✹❡♦❫❖◆❖❋q❚❵❏◗✻❩◆ ❏▲❘✜♣❩❏✉€❩❁❄◆✬❏▲◆✬✆✛♠♥◆ ❅ ❬ ✡ ✁ ❅ ❋ ✁☞✌✣❀❈❁q❚❵✼❖✻❤❃ ❚❵✻ ❏◗◆❖❏◗❚❙❏❥✾✽❞◗❏☛✡❉❁✂✾❂s ✻❩s❇❫❖❞❥✾❍❚❙❏▲✻❩◆ ✻✽❡r❋ ✾✽◆❇❃❖❏▲❃✿✾❣❚❵❁✑❘❙✻❩❞◗❫❇❚❵❏◗✻❩◆❖❘❄❅✳✮✙❘▼❫✿✾✽❞▲❞✉✺❛❚❵✼❇❁❆❏◗◆❖❏✟✄ ❚❵❏▲✾✽❞ ❘▼❁❄❁❄❃✍s ✻✽s❖❫❖❞❥✾❣❚❵❏▲✻✽◆❛❡♦❑❙✻❩❀ ✄☎✼❇❏▲❋❪✼✍❚❙✼❖❁✹♣❩❁❄◆❇❁❉❚❵❏◗❋✹s❖❑❙✻❤❋❄❁❉❘❙❘✂❴■❁❄♣✽❏▲◆❖❘✜❏◗❘✏❋❪✼❇✻❩❘❙❁❉◆✪❑❵✾✽◆❇❃❖✻❩❀❂❞◗✺❈✻❩❑☎✻❩◆ ❚❵✼❇❁✑❴❖✾✽❘❙❏◗❘✏✻❍❡r✼❖❁❉❫❖❑❙❏◗❘▼❚❙❏▲❋❄❘❉❅ ❃ ✁❙✎✢❁❄◆❖❁q❚❵❏▲❋✍✻❩s■❁❄❑❵✾❣❚❵✻❩❑▼❘ ✄☎✼❖❏◗❋❪✼✭s❖❑❙✻❤❃❖❫❖❋❉❁✪◆❖❁ ✄ ❘▼❁❉❚❙❘❛✻✽❡✢❏◗◆❖❃❖❏◗€❤❏◗❃❖❫✿✾✽❞◗❘❄❅ ✙❁ ✄ ❏◗◆❖❃❖❏✉€✔❏◗❃❖❫ ✄ ✾✽❞◗❘✙✾❍❑❙❁✑❋❄❑❙❁❄✾❍❚❵❁❉❃✖❫❖❘▼❏▲◆❖♣❜❚ ✄✕✻❛❀ ✾❍❏▲◆ ♣❩❁❄◆❇❁❉❚❵❏◗❋✹❑❙❁❄❋❉✻❩❀③❴❖❏◗◆✿✾❍❚❙❏▲✻❩◆ ✻❩s■❁❄❑❙✾❍❚❵❏◗✻❩◆❖❘☎②♥◆❖✻✂✄☎◆ ✾✽❘✏❋❄❑❙✻✽❘❙❘❙✻❳€✽❁❄❑ ✾✽◆❖❃✖❀③❫❇❚❪✾❣❚❵❏▲✻✽◆ ❅✙✘✜✼❇❁❄❘❙❁ ✻❩s ❁❉❑❵✾❍❚❙❏▲✻❩◆❇❘✂❁❄◆❖✾✽❴❖❞▲❁③✎✹✌✙❘✙❚❙✻❛❫❖❘❙❁ ❑❙❁❄❞▲✾❍❚❵❏✉€❩❁❉❞◗✺✈❡♦❁ ✄✵❘❙✾✽❀❂s❖❞▲❁❉❘✙❚❵✻ ❘❙❁ ✾❍❑❙❋❪✼ ❞❥✾❍❑❙♣❩❁ ❘❙s❖✾✽❋❄❁❉❘❄❅ ✷✳❑❙✻❩❘▼❘❙✻❳€❩❁❉❑✈❏▲❘❜❚❵✼❖❁✬❀❈✻✽❘▼❚❈❏▲❀❂s ✻❩❑☞❚❪✾✽◆❭❚❜✻❩s■❁❄❑❙✾❍❚❵❏◗✻❩◆ ❏▲◆✲❚❙✼❖❁ ✎✢✌ ✻❩s❇❚❙❏▲❀❂❏☛✡ ✾❣❚❵❏▲✻✽◆ ❅ ✥✏✾✽◆❖❃❖✻❩❀❂❞◗✺❂❘▼❁❄❞▲❁❉❋❉❚❙❁❄❃ s✿✾✽❏◗❑❙❘✶✻✽❡✇❘☞❚❵❑▼❏▲◆❖♣❩❘✶❡♦❑▼✻❩❀ ❚❵✼❖❁✝❋❉❫❖❑❙❑▼❁❄◆❭❚✏s ✻✽s❖❫❖❞❥✾❣❚❵❏▲✻✽◆❛✾✽❑▼❁✝❀ ✾❣❚❵❁❄❃✈❫❇❘❙❏▲◆❇♣ ❑❵✾✽◆ ✄ ❃❖✻❩❀❂❞◗✺③❏▲❃❖❁❉◆♥❚❙❏◗❧✿❁❉❃ ❋❉❑❙✻❩❘▼❘❙✻❳€❩❁❉❑✶s ✻✽❘❙❏◗❚❙❏▲✻❩◆❇❘ ✥ ✏ ✳✟ ✧ ❅✸✠★◆✈✾✹✻❩◆❖❁✙s ✻✽❏▲◆❭❚✟❋❄❑❙✻✽❘❙❘❙✻❳€✽❁❄❑❄●❇❘❙✼❖✂✻ ✄☎◆✈❏▲◆❈✫r❏◗♣❩❫❖❑❙❁ ✡❇● ◆❖❁ ✄✭❘▼❚❙❑❙❏▲◆❇♣❩❘✟✾✽❑❙❁☎s❖❑▼✻✔❃❖❫❇❋❄❁❄❃❈❴❭✺❜❘ ✄✳✾✽s❖s❖❏◗◆❖♣❆✻✽s❖s ✻✽❘❙❏◗❚❙❁☎s ✻❩❑☞❚❵❏◗✻❩◆❖❘✛✻✽❡ ❚❵✼❖❁✜❚ ✄✕✻ ❘▼❚❙❑❙❏◗◆❖♣❩❘❄❅✛☛✍❫❇❚❪✾❣❚❵❏▲✻✽◆ ❏▲❘❆❚❵✼❖❁❛✻❤❋❄❋❄✾✽❘❙❏◗✻❩◆✿✾✽❞ ✄☎❏✉❚❵✼ €✽❁❄❑▼✺ ❘❙❀❈✾✽❞▲❞✟s❖❑❙✻✽❴✿✾✽❴❖❏◗❞▲❏◗❚★✺ ✁✢❑❵✾✽◆❇❃❖✻❩❀ ✾✽❞◗❚❙❁❄❑❵✾❣❚❵❏▲✻✽◆ ✻✽❡☎❚❵✼❇❁ €❍✾✽❞▲❫❖❁ ✻✽❡✏✾ ❘▼❚❙❑❙❏◗◆❖♣ s ✻✽❘❙❏◗❚❙❏▲✻❩◆❦❅✛✤✝❫❖❁✝❚❵✻③❚❙✼❖❁✹❑❵✾✽◆❇❃❖✻❩❀ ◆❖✾❍❚❵❫❖❑▼❁✢✻✽❡✚❚❵✼❖❁✢❋❉❑❙✻❩❘▼❘✏✻❳€✽❁❄❑✏✾✽◆❖❃ ❑❙❁❉s❖❑❙✻❤❃❖❫❖❋q❚❵❏◗✻❩◆ ✻❩s ❁❉❑❵✾ ✄ ❚❵❏◗✻❩◆❖❘❉● ❘▼✻❩❀❈❁❆❋❄✻❤❃❖❁ ❋❪✼❖✾✽❑❵✾✽❋q❚❵❁❉❑❙❘✢❀❈✾❳✺ ◆❇✻✽❚✝❴■❁③✾✽s❇s ❁❄✾✽❑❙❏◗◆❖♣ ❏◗◆✍❚❵✼❇❁③◆❖❁ ✄✣s■✻❩s❖❫❖❞▲✾❍❚❵❏◗✻❩◆✬❘❙❏▲◆❇❋❄❁❆❚❙✼❖❁❉✺ ❬✍ ✕❁❄❑❙❁✢❞◗✻❩❘▼❚✳❏▲◆❂❚❵✼❖❁✝s❇❑❙❁❉€❤❏◗✻❩❫❖❘✶♣❩❁❉◆❖❁❄❑❙✾❍❚❵❏◗✻❩◆❖❘❉❅✛✘✜✼❖❁✝❀③❫❇❚❵✾❍❚❵❏◗✻❩◆ ✻✽s ❁❉❑❵✾❍❚❙❏▲✻❩◆❈❘❙❁❄❑☞€❩❁❉❑❙❘✜❚❵✼❖❁✂s❖❫❖❑❙s■✻❩❘▼❁✝✻✽❡ ❑❙❁❉❏▲◆❭❚❵❑▼✻✔❃❇❫❖❋❄❏◗◆❖♣✍❘▼❫❖❋❪✼ ❋❄✻❤❃❖❁❈❋❪✼✿✾✽❑❵✾❍❋❉❚❵❁❉❑❙❘❆❏▲◆ ❘☞❚❵❑▼❏▲◆❖♣❩❘✑✻✽❡✕❚❵✼❖❁❈s ✻❩s❇❫❖❞❥✾❍❚❙❏▲✻❩◆❦❅ ☛✍❫❇❚❵✾❍❚❵❏◗✻❩◆✡s❇❑❙✻✽❚❙❁❄❋❉❚❙❘ ❚❵✼❇❁ ✎✢✌✧s❖❑▼✻✔❋❉❁❄❘❙❘✙✾✽♣❭✾❍❏▲◆❖❘☞❚☎❏▲❑❙❑▼❁❄❋❉✻ €✽❁❄❑❙✾✽❴❖❞▲❁✢❞◗✻❩❘❙❘☎✻✽❡❢♣❩✻❤✻✔❃✈❘▼✻❩❞▲❫✔❚❵❏▲✻✽◆❛❡♦❁ ✾❍❚❙❫❖❑❙❁❉❘❄❅ ✄ ❁ ✁☞✌ ❚❙❁❄❑▼❀❈❏◗◆✿✾❍❚❵❏◗✻❩◆✬❋❄❑❙❏✉❚❵❁❉❑❙❏❥✾❂❡♦✻❩❑✙❚❙✼❖❁③♣❩❁❉◆❖❁❉❚❙❏▲❋ ✾✽❞◗♣❩✻❩❑▼❏◗❚❵✼❇❀✍❅✏✘❢❁❉❑❙❀❂❏▲◆✿✾❣❚❵❏▲✻✽◆✖❀❈✾❳✺✍❴■❁ ❚❵❑▼❏▲♣ ✄ ♣❩❁❉❑❙❁❄❃✈❴❭✺❈❧✿◆❖❃❖❏◗◆❖♣❜✾✽◆ ✾✽❋❉❋❄❁❄s✔❚❪✾✽❴❖❞◗❁✢✾✽s❖s❇❑❙✻ ☎✔❏▲❀❈✾❍❚❵❁✙❘❙✻❩❞◗❫❇❚❵❏◗✻❩◆ ✻❩❑✳❴♥✺❈✻❩❴❖❘▼❁❄❑☞€✔❏◗◆❖♣❜◆❖✻③s■❁❄❑☞❡♦✻❩❑❙❀❈✾✽◆❖❋❉❁ ❏▲❀❂s❖❑▼✻ €✽❁❄❀❂❁❄◆❭❚❵❘☎✻❳€❩❁❉❑✏✾❂❋❉❁❄❑▼❚❵✾✽❏▲◆ ◆♥❫❖❀③❴■❁❄❑☎✻✽❡❢♣❩❁❉◆❖❁❄❑❙✾❍❚❵❏◗✻❩◆❖❘❄❅ Crossover site Genes after Crossover Genes before Crossover ✁ ✌✏✘✡✞✡✣ ✑ ✎ ✒✆✟✎✤✆✟☛✳✙✛✆✟✞ ✡✌✏✠ ✣ ✙ ✪✠✤✘✡✓ ✢✣ ✑ ✫r✠☞✎✹✮✂✥✏✆ ✡ ✁ ✠✤✘✡☛ ✠ ✎✤✆ ✣ ☛ ✪✣ ✣ ✘ ✆ ✂ ✙ ❀ ✆ ☛ ✢✆✜✘✕✙ ✣ ✡✎✤✌✔✙✛✠✤✣✕✘ ✌ ✪✆ ✑ ✔✌ ✙ ✆✜✞ ✒✠☞✘ ✓ ✢✌✏✘✡✞ ✣ ✑ ✎ ✠✤✞✡✆✟✘✚✙✛✠ ✆✟✞ ☛ ✢✣ ✒✣ ✘ ✆ ✣ ✠ ✙✢✠ ✣✚✘ ✳✄ ✄ ✯✠ ✘✕✽✄✯✄ ☛ ✟☛ ✆ ❇✆ ✎✆✞✕ ✲✌ ✶✄ ✎☛✾☛ ✄ ☎✄☞✣ ✂✗ ✻✕✞☛ ✄ ☛ ❈✆ ❃✗ ❃✄✒☛ ❃✴ ✲✌ ☛ ✛✄ ✶✄ ✎☛✾☛ ✎☛ ✌ ✄ ☎✄ ✆ ✝✥ ❯❩❅ ✷✳✻✽◆♥€✽❁❄❑▼♣❩❁❄◆❖❋❉❁③✻✽❡✚❚❵✼❖❁❆✎✢❁❄◆❖❁q❚❵❏◗❋✢✌✂❞▲♣✽✻❩❑❙❏✉❚❵✼❖❀ ✘✚✻✈❫❖◆❖❃❇❁❄❑❙❘☞❚❪✾✽◆❇❃✡✼❖✻✂✄✰✎✹✌✙❘✹✾✽❑❙❁ ❘❙❫❖❋❉❋❄❁❄❘▼❘▼❡♦❫❖❞✗❏◗◆ ✻❩❴❇❚❪✾❍❏▲◆❖❏◗◆❖♣❈❚❙✼❖❁ ✻❩s❇❚❙❏▲❀❈✾✽❞❢❘▼✻❩❞▲❫✔❚❵❏▲✻✽◆ ● ✄✕❁ ◆❖❁❉❁❄❃ ❚❙✻ ❃❖❁q❧✿◆❖❁✝❘▼✻❩❀❈❁☎❚❵❁❉❑❙❀❂❘ ✥ ✏✽✪❨ ✧ ❅✛✘✜✼❖❁✏❧✿❑❙❘☞❚✳❚❵❁❉❑❙❀ ❏▲❘✗❚❵✼❇❁✂❘❙❋❪✼❇❁❄❀❈✾❍❚❪✾❇● ✞ ● ✄☎✼❖❏▲❋❪✼ ❏▲❘✕✾❆❘❙❏◗❀❈❏◗❞❥✾✽❑ ✄ ❏◗❚★✺❆❚❵❁❉❀❈s❖❞▲✾❍❚❵❁✳❃❖❁❄❘▼❋❄❑❙❏◗❴❖❏▲◆❇♣❆✾✢❘▼❫❖❴❖❘❙❁q❚✳✻❍❡❦❘☞❚❵❑❙❏◗◆❖♣❩✆❘ ✄☎❏✉❚❵✼❜❘❙❏◗❀❈❏◗❞❥✾✽❑▼❏◗❚❵❏◗❁❄❘✚✾❍❚✗❋❉❁❄❑▼❚❵✾✽❏▲◆❜❘☞❚❵❑❙❏◗◆❖♣✢s■✻❩❘❙❏✉❚❵❏▲✻✽◆❖❘❄❅ ✠★◆ ♣❩❁❄◆❖❁❉❑❵✾✽❞✶❡♦✻✽❑ ❘▼❚❵❑▼❏▲◆❖♣ ✻✽❡✂❞▲❁❉◆❖♣✽❚❵✼ ✟ ✾❍◆❖❃ ✞ ✾✽❞◗s❖✼✿✾✽❴■❁❉❚ ❚❙✼❖❁❄❑▼❁✬✾✽❑❙❁ ✞ ☞✓❯ ✁ ❘▼❋❪✼❖❁❄❀❈✾❍❚❵✾❇❅ ✘✜✼❖❁ ❘❙❁❉❋❄✻❩◆❇❃ ❚❙❁❄❑▼❀ ❏◗❘✙❚❵✼❇❁ ✻❩❑▼❃❖❁❄❑✝✻❍❡✗❘❙❋❪✼❖❁❉❀ ✾❍❚❵✾❇✂● ✁ ✞ ✁ ● ✄☎✼❇❏▲❋❪✼ ❏▲❘✏❚❵✼❖❁ ◆❤❫❇❀③❴ ❁❉❑✝✻✽❡✛❧ ☎✔❁❉❃ s ✻❩❘▼❏◗❚❙❏▲✻❩◆❖❘ s❖❑▼❁❄❘❙❁❉◆❭❚✕❏◗◆③❚❵✼❖❁✶❚❙❁❄❀❂s❖❞❥✾❣❚❵❁✽❅r✫r❏▲◆❖✾✽❞▲❞✉✺✢❚❵✼❖❁✜❞◗❁❄◆❖♣✽❚❙✼ ✻✽❡ ✾✢❘❙❋❪✼❖❁❉❀ ✾❍❚❵✾❇● ✝ ✞ ✁ ✞● ✄☎✼❖❏◗❋❪✼❂❏◗❘✸❚❵✼❖❁✜❃❇❏▲❘▼❚❵✾✽◆❖❋❉❁ ❬✟ ❴■❁❉❚ ✄✕❁❄❁❄◆✍❚❵✼❖❁✢❧✿❑▼❘▼❚✙✾✽◆❖❃ ❞❥✾❍❘▼❚☎❘❙s■❁❄❋❉❏◗❧✿❋✹❘☞❚❵❑❙❏◗◆❖♣❜s ✻✽❘❙❏◗❚❙❏▲✻❩◆✈❏◗◆✈❚❵✼❖❁✢❚❵❁❉❀❈s❇❞❥✾❍❚❙❁✽❅ ✒✔❫❖s❇s ✻❩❘▼❁☎✾❍❚✛❚❵❏◗❀❈❁ ●❭❏▲◆ ✾✝s■✻❩s❖❫❇❞❥✾❍❚❙❏▲✻❩◆✂✁ ✁ ✄✕❁☎✼✿✾ €❩❁ ✠ ❁ ☎❇✾✽❀❂s❖❞▲❁❉❘✛✻✽❡ ✾✝s✿✾✽❑☞❚❵❏▲❋❉❫❖❞❥✾❍❑❢❘▼❋❪✼❖❁❄❀❈✾❍❚❪✾✔● ✞ ● ✄✳❁✹❋ ✾❍❞▲❞❦❏✉❚ ✠☎✄ ✞ ✁q❅✸✌✧❘☞❚❵❑❙❏◗◆❖♣✆✁ ✁ ❏◗❘✶❘❙❁❉❞▲❁❉❋❉❚❵❁❉❃✖✾❍❋❄❋❄✻✽❑❙❃❖❏◗◆❖♣③❚❵✻❜✾ s❖❑▼✻❩❴✿✾✽❴❖❏◗❞▲❏✉❚★✺❩●✞✝ ✁ ●❖❃❇❁❉❧✿◆❖❁❉❃✖✾❍❘ ✟✁✁✄ ✟ ✝✁✆ ❬✽❨ ✁ ✒✔✻❜❏◗❡r✾ ◆❖✻❩◆✬✻❳€❩❁❄❑▼❞❥✾✽s❇s❖❏▲◆❖♣❜s■✻❩s❖❫❖❞▲✾❍❚❵❏◗✻❩◆❛✻✽❡❢❘❙❏☞✡❄❁✡✠ ❏▲❘✜❘▼❁❄❞▲❁❉❋❉❚❙❁❄❃✍❚❙✼❖❁❄◆☛✄✕❁❆❁ ☎❇s■❁❄❋q❚☎❚❵✻❂✼✿✾ €❩❁ ✥ ✏✽❨✢✧ ✞ ✁ ☎✄ ✄ ✁ ✞ ✁ ✆ ☎ ✠ ✄ ✞ ☛ ✁ ✠☞✟ ✟✁ ✄☎✼❖❁❉❑❙❁ ✟ ✞ ✁✟❏▲❘✜❚❵✼❖❁✑✾ €❩❁❉❑❵✾✽♣✽❁✹❧❇❚❵◆❖❁❉❘❙❘✏✻✽❡ ✠☎✄ ✞ ✁q❅✗✞❱❁q❚ ✁ ✆ ✟ ✟✞✌ ✠ ❬✽❲ ✁ ✍ ✁ ✍❇❯ ✁ ✠ ❚❵✼❇❁❄◆ ✞ ☎✄ ✄ ✁ ✞ ✁ ✆ ☎ ✠ ✄ ✞ ✁ ✟ ✟✍✌ ✠ ✁ ✌✵❘❙❋❪✼❖❁❉❀ ✾❣❚❪✾✟✞ ❏◗❘✜❃❖❁❄❘☞❚❵❑▼✻ ✺✽❁❄❃✪❴❭✺✈❋❉❑❙✻❩❘▼❘❙✻❳€❩❁❉❑ ☎✄ ❏✉❚❵✼ s❖❑❙✻✽❴✿✾✽❴❖❏◗❞▲❏◗❚★✺✡✝ ✆ ❃❖❁❉❧❖◆❖❁❄❃✖✾✽❘ ✝ ✝✆ ✆ ✟ ☎ ✞ ❯ ✁ ✍❭❬ ✁ ✍✍ ✁ ✍✟ ✁ ✁ ✻❩❑✜❏✉❚☎❘❙❫❖❑☞€✔❏✉€❩❁❉❘ ☎✄ ❏✉❚❵✼✆✝✏✎ ✣ ✆ ❯ ✑✝ ✆ ❅✗✠ ❡❢❋❄❑▼✻❩❘❙❘▼✻ €✽❁❄❑✙❏▲❘✜❑❵✾❍◆❖❃❖✻❩❀ ☎✄ ❏✉❚❵✼ s❖❑▼✻❩❴✿✾✽❴❖❏◗❞▲❏✉❚★✺✒✝✔✓❪●❖❚❵✼❖❁❉◆ ❃☎ ✝✏✎ ☎ ❯ ✑✝✕✓ ✝ ✟ ✭✞ ❯ ✁ ✁ ❃☎ ☎ ❘❙✻❈✾❍❡ ❚❙❁❄❑✜❋❄❑▼✻❩❘❙❘▼✻❳€❩❁❄❑✂✾✽◆❖❃ ❀③❫❇❚❵✾❍❚❵❏◗✻❩◆ ✕✄ ❁❆❁ ☎❇s■❁❄❋q❚ ☎✄ ✄ ✁ ✞ ✠ ✁ ☎ ☎✄ ✞ ✁ ✟ ✞ ✠ ✟✞✌ ✁ ❯ ✑✝✔✓ ✝ ✟ ✞ ❯ ✁ ✁ ✸☎ ☎ ☎ ✁ ✞ ✖✁ ✝ ☎ ✁ ☎✼❖❁❉❑❙❁✑✝ ☎ ▲❏ ❘✬❚❵✼❖❁ ❀③❫❇❚❪✾❣❚❵❏▲✻✽◆ s❖❑▼✻❩❴✿✾✽❴❖❏◗❞▲❏✉❚★✺❩❅ ✘✜✼❖❁❄❑▼❁❉❡♦✻❩❑▼❁✽●✑❚❵✼❖❁ s❇❑❙✻❩❴✿✾❍❴❖❏▲❞◗❏◗❚★✺ ❚❙✼✿✾❍❚ ✾✲❋❄❁❄❑☞❚❪✾✽❏◗◆ ❘❙❋❪✼❇❁❄❀❈✾❍❚❪✾ ✄☎▲❏ ❞▲❞❇❘❙❫❖❑☞€✔❏✉€❩❁✙❏▲❘✛❃❖❁q❚❵❁❄❑▼❀❈❏◗◆❖❁❄❃❈❴❭✺ ❚❵✼❖❁☎❧❖❚❵◆❇❁❄❘❙❘✕✻✽❡❦❚❙✼❖❁✏❏▲◆❖❃❖❏✉€❤❏▲❃❖❫✿✾❍❞▲❘✸❏◗◆❜❚❙✼❖❏▲❘✗❘▼❋❪✼❖❁❄❀❈✾❍❚❪✾✔❅ ✄ ❬✏ ✠ ❡✢❚❵✼❇❏▲❘❜❧❖❚❵◆❖❁❉❘❙❘❛❏◗❘ ✼❖❏◗♣❩✼ ● ✄☎✼❇❏▲❋❪✼ ❀❂❁ ✾✽◆❇❘ ❏◗❚❈❋❄✻✽◆♥❚❵✾✽❏▲◆❇❘❈♣❩✻❤✻❤❃ ❘❙✻✽❞▲❫❇❚❙❏▲✻❩◆ ❚❵✻ ❚❙✼❖❁✖s❇❑❙✻❩❴❖❞◗❁❄❀✬●✳❚❵✼❇❁ s❖❑▼✻❩❴✿✾✽❴❖❏◗❞▲❏✉❚★✺ ✻✽❡✹❘❙❫❖❑☞€❤❏◗€❤❏▲◆❖♣ ❏◗❘❛✼❖❏◗♣❩✼ ❅✧✌✂❞◗❘❙✻ ❏✉❡✢❚❵✼❖❁✖❞▲❁❄◆❇♣✽❚❵✼✭✻✽❡✢❚❙✼❖❁ ❘❙❋❪✼❇❁❄❀❈✾❍❚❪✾ ❏◗❘ ❘❙❀❈✾✽❞◗❞ ●✶❚❵✼❇❁ s❖❑▼✻❩❴✿✾✽❴❖❏◗❞▲❏✉❚★✺ ✻✽❡✏❘❙❫❖❑☞€✔❏✉€❤❏▲◆❖♣✪❏◗❘③✼❖❏◗♣❩✼❖❁❄❑❉❅ ✘✜✼❖❁✈✻❳€❩❁❉❑❵✾✽❞◗❞✳◆❖❁q❚ ❁ ✝ ❁❄❋q❚❜✻✽❡☎❚❵✼❖❁❛❏✉❚❵❁❉❑❵✾❍❚❙❏◗€❩❁❈s❖❑❙✻❤❋❄❁❉❘❙❘ ❏◗❘ ✾✽◆✪❫❇s ✄✳✾✽❑▼❃ ❘❙✼❖❏✉❡ ❚✂❏◗◆✍❚❵✼❇❁ s■✻❩s❖❫❖❞▲✾❍❚❵❏◗✻❩◆ ✛ ❘✂✾ €❩❁❉❑❵✾✽♣✽❁❆❧❖❚❙◆❖❁❄❘▼❘❄❅✹✒✔❏◗◆❖❋❄❁✑❚❵✼❖❁❆✻❳€❩❁❄❑❙✾✽❞▲❞❢✾ €❩❁❉❑❵✾✽♣❩❁ ❀❈✻❳€❩❁❉❘ ❫❖s ✄✳✾✽❑❙❃ ✻❳€❩❁❉❑ ❚❵❏◗❀❈❁❍●r❚❵✼❖❁ ♣❩❁❄◆❖❁q❚❵❏◗❋❛✾✽❞◗♣❩✻❩❑❙❏✉❚❵✼❖❀ ❏◗❘③✾✖♣✽❞▲✻❩❴✿✾❍❞✗❡♦✻✽❑❙❋❄❁ ✄☎✼❖❏▲❋❪✼ ❘▼✼❖❏◗❡ ❚❙❘③✾❍❚▼❚❵❁❄◆❭❚❙❏▲✻❩◆ ❚❙✻ s❖❑▼✻✔❃❖❫❇❋❉❚❵❏✉€❩❁❆❑❙❁❄♣✽❏▲✻❩◆❖❘✏❏▲◆✬❚❵✼❖❁❆❘❙❁❄✾✽❑❙❋❪✼✪❘▼s✿✾✽❋❉❁✽❅✝✩✏✂✻ ✄✳❁q€❩❁❄❑❉● ❘❙❏◗◆❖❋❄❁✑❚❵✼❖❁❆s ✻✽s❖❫❖❞❥✾❣❚❵❏▲✻✽◆✬❏◗❘✙❃❇❏▲❘▼❚❙❑❙❏◗❴❖❫❇❚❵❁❉❃ ❚❵✼❇❑❙✻❩❫❖♣✽✼❖✻❩❫❇❚✙❚❵✼❖❁③❘▼❁ ✾✽❑▼❋❪✼ ❘❙s✿✾❍❋❄❁✽●❦♣❩❁❄◆❖❁q❚❵❏◗❋③✾✽❞◗♣❩✻❩❑❙❏✉❚❵✼❖❀❂❘☎❁ ✝ ❁❄❋q❚❵❏◗€✽❁❄❞✉✺✖❀❂❏▲◆❖❏◗❀❈❏☞✡❄❁✝❚❙✼❖❁ s❖❑▼✻❩❴❖❞◗❁❄❀ ✻✽❡ ❋❄✻✽◆♥€✽❁❄❑▼♣❩❏▲◆❖♣❜❚❵✻❜❞◗✻✔❋❄✾✽❞ ❀❈✾ ☎✔❏▲❀❈✾ ✥ ✡ ✟ ✧ ❅ ✌ ✄ ✆✗✌✔✙ ✪✆ ✗✖✆✟✎ ✆✜☛✳✙✛✠✤✣✕✘ ✎ ✓ ✣ ✠ ✙ ✑ ✯✕✽✄ ✲✄ ✯✠ ❢✫ ❏▲♣❩❫❖❑▼❁ ④ s❖❑▼❁❄❘▼❁❄◆❭❚❵❘✹❚❵✼❖❁ ❃❇❏☞✝ ❁❄❑❙❁❉◆❭❚✹❘▼❚❵❁❉s❖❘✝❡♦✻❩❑✂❡♦❁❄✾❍❚❵❫❇❑❙❁ ❘❙❁❉❞▲❁❉❋❉❚❵❏◗✻❩◆ ❫❖❘▼❏▲◆❖♣✈❚❵✼❇❁ ✐✟✷✳✌ ✾❍◆❖❃ ✎✢✌ ❅✛✌✂◆✲❏▲◆❖❏✉❚❵❏▲✾✽❞✳s■✻❩s❖❫❖❞▲✾❍❚❵❏◗✻❩◆ ✻✽❡✢❘▼❏☛✡❉❁✁ ✣●✜❑❙❁❄s❇❑❙❁❄❘▼❁❄◆❭❚❵❏◗◆❖♣ ❃❇❏☞✝ ❁❄❑❙❁❉◆❭❚ ◆♥❫❖❀③❴■❁❄❑❂✻✽❡✙❡♦❁ ✾❍❚❙❫❖❑❙❁❉❘❄●✶❏◗❘ ❘❙❁❉❞▲❁❉❋❉❚❵❁❉❃③✾❍❚✇❑❙✾✽◆❖❃❖✻✽❀✍❅❢✐✟✷✳✌ ❏◗❘❱❚❵✼❖❁❉◆❆s■❁❄❑☞❡♦✻❩❑❙❀❂❁❄❃✹❫❖❘▼❏▲◆❖♣☎❚❵✼❖❁✗❘▼❁❄❞▲❁❉❋❉❚❙❁❄❃ ◆♥❫❖❀ ❴ ❁❉❑✚✻❍❡✔❡♦❁❄✾❍❚❵❫❖❑▼❁❄❘❉❅✛✎✢✌ ❚❵✼❇❁❄◆✬❫❖❘❙❁❉❘✙❏✉❚❵❘✜❋❄❑▼✻❩❘❙❘▼✻❳€❩❁❄❑✂✾✽◆❖❃✬❀③❫❇❚❵✾❍❚❵❏◗✻❩◆✈✻❩s■❁❄❑❵✾❣❚❵❏▲✻✽◆❖❘✳❚❵✻❂❀❈✾ ☎✔❏▲❀❂❏☛✡❄❁✏❚❵✼❖❁✹✻❩❴ ✙▼❁❄❋❉❚❙❏◗€✽❁✹❡♦❫❇◆❖❋❉❚❙❏▲✻❩◆ ❅ ✄ ✑ ✎ ✆ ✑ ✆✟✘✚✙✛✌✔✙✛✠✤✣✕✘ ✆ ✘✜✼❇❁❛✾✽❞◗♣❩✻❩❑❙❏✉❚❵✼❖❀ ❃❖❁❄❘▼❋❄❑▼❏▲❴■❁❄❃ ✾✽❴■✻❳€❩❁ ✄✳✾✽❘③❏◗❀❈s❇❞▲❁❄❀❂❁❄◆❭❚❙❁❄❃ ✻❩◆ ✾ ❯✒✡ ✄★s❇❑❙✻❤❋❄❁❄❘▼❘❙✻❩❑▼❘③✥✹❯ ✒✔❏◗❞▲❏▲❋❉✻❩◆ ♣❩❑❵✾❍s❖✼❖❏▲❋❉❘ ✄✕✻❩❑❙②♥❘☞❚❪✾❍❚❙❏▲✻❩◆ ❅✙✆✗✾✽❋❪✼✪♣❩❁❉◆❖❁ ❋❉✻❩◆❖❘▼❏▲❘▼❚❙❁❄❃ ✻✽❡ ✏❂❴❖❏✉❚❵❘✂❑▼❁❄s❖❑▼❁❄❘▼❁❄◆❭❚❵❏◗◆❖♣ ❚❵✼❇❁ ✻❩❑▼❏▲♣❩❏◗◆✿✾✽❞ ❃❖❏◗❀❈❁❉◆❖❘❙❏◗✻❩◆✭✻✽❡✑❚❵✼❖❁✪❡♦❁❄✾❍❚❵❫❖❑▼❁ €❩❁❄❋q❚❵✻❩❑❉❅ ✘✜✼❖❁ ❏▲◆❖❏✉❚❵❏▲✾✽❞✙s■✻❩s❖❫❇❞❥✾❍❚❙❏▲✻❩◆ ❘▼❏☛✡❉❁ ✄✶✾✽❘ ❘▼❁❉❚ ❚❵✻✓❯ ❅ ✘✜✼❖❁ ✾ €❩❁❉❑❵✾✽♣❩❁✙❑❙❫❖◆❈❚❵❏▲❀❂❁✜❡♦✻❩❑✕✾③❬ ✏ ✡ ☎✿❬ ✏ ✡ ☎❇❲ €❩✻❩❞◗❫❖❀❈❁✏❏▲❘✕✾✽❑▼✻❩❫❖◆❖❃ ✍❆❀❂❏▲◆ ❅❢✘✜✼❖❏▲❘✕s❖❑❙✻❤❋❄❁❉❘❙❘❄●✔✼❖✻✂✄✳❁q€❩❁❉❑❄●❖❏◗❘ ✻❩◆❖❞✉✺✑s ❁❉❑▼❡♦✻❩❑▼❀❈❁❉❃③✻❩◆❖❋❉❁✳❡♦✻❩❑✸✾✙❋❄❁❄❑☞❚❪✾✽❏◗◆③❀❈✾✽❋❪✼❖❏▲◆❇❁✶❘❙❏◗◆❖❋❄❁✟❚❵✼❖❁✶❃❖✾❍❚❪✾✝s❖❑▼✻✔❃❇❫❖❋❄❁❉❃ ✄✳✻❩❫❇❞▲❃③✼✿✾ €✽❁✜❘❙❏▲❀❂❏▲❞▲✾✽❑ ♣❩❑❙✾❳✺✑❞◗❁❉€❩❁❉❞✔❃❇❏▲❘▼❚❙❑❙❏◗❴❖❫❇❚❵❏◗✻❩◆ ❅❢✒✔❏◗◆❖❋❄❁✟❚❵✼❖❁✳✾✽❞▲♣❩✻✽❑❙❏◗❚❙✼❖❀ ❏◗❘❢s❖✾✽❑❵✾✽❞◗❞▲❁❉❞❭❏▲◆ ◆❖✾❍❚❵❫❖❑▼❁✽●❍s ❁❉❑▼❡♦✻❩❑▼❀ ✾✽◆❇❋❄❁✳❋❉✻❩❫❖❞◗❃ ❴■❁ ❁❄◆❇✼✿✾✽◆❖❋❉❁❄❃ ❴❭✺❆✾✽❘❙❘▼❏▲♣❩◆❖❏◗◆❖♣✝✾✏s❖❑❙✻❤❋❄❁❉❘❙❘▼✻❩❑❢❡♦✻❩❑✚❁ ✾❍❋❪✼③❘❙❁❉❁❄❃ ❏▲◆✑❚❵✼❖❁✕s ✻✽s❖❫❖❞❥✾❣❚❵❏▲✻✽◆ ❅❱✌ ❀❈✾✽❘▼❚❙❁❄❑✚s❖❑❙✻❤❋❄❁❉❘❙❘▼✻❩❑ ✄✕✻❩❫❖❞▲❃❂❚❵✼❖❁❉◆❛s■❁❄❑▼❡♦✻✽❑❙❀ ❋❄❑▼✻❩❘❙❘▼✻ €✽❁❄❑✜✾❍◆❖❃❛❀③❫❇❚❵✾❍❚❵❏◗✻❩◆❜❴✿✾✽❘▼❁❄❃✈✻❩◆❂❚❵✼❖❁✙❏▲◆❇❡♦✻❩❑▼❀ ✾❣❚❵❏▲✻✽◆③❚❵✼✿✾❍❚✕❏◗❚✟❑▼❁❄❋❄❁❉❏◗€✽❁❄❘ ❬✡ Feature Selection Algorithm Construct Feature Vector X.

Select and encode initial Population P(t) of size M do { For m = 0 to M { Perform PCA using selected number of reduced features. Reconstruct the original set X’ Calculate fitness Fm } t=t+1 Perform Crossover and mutation and reproduce P(t) } Unitil Termination Criterion is reached.

Select and encode initial Population P(t) of size M do { For m = 0 to M { Perform PCA using selected number of reduced features. Reconstruct the original set X’ Calculate fitness Fm } t=t+1 Perform Crossover and mutation and reproduce P(t) } Unitil Termination Criterion is reached.

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