HAL Id: hal-00937713
https://hal-enac.archives-ouvertes.fr/hal-00937713
Submitted on 29 Apr 2014
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CATS : a complete air traffic simulator
Jean-Marc Alliot, Jean-François Bosc, Nicolas Durand, Lionel Maugis
To cite this version:
Jean-Marc Alliot, Jean-François Bosc, Nicolas Durand, Lionel Maugis. CATS : a complete air traffic simulator. DASC 1997, 16th Digital Avionics Systems Conference, Oct 1997, Irvine, United States.
pp 8.2 - 30-8.2-37 vol.2, �10.1109/DASC.1997.637271�. �hal-00937713�
✍✎✏ ✎ ✑ ✒✒✓✔✕ ✍ ✎✖ ✎ ✗ ✔✘✙ ✚ ✎ ✛ ✜ ✢✣✤ ✥✦ ✧ ✎ ✏ ✣✜★✓✘✩
✪ ✫✬ ✭ ✮ ✯ ✰ ✱ ✲ ✭ ✫✯ ✬
✳✴ ✵✶✷✸ ✹✺✻✼ ✽ ✾✴✵✿ ❀ ✾ ❁❂✾✸✾✴✵ ✵✶✾ ❃❄❅ ❆❇ ✸❈✸✵✾✽ ❉
❅ ✶✾ ✽ ❊✷✴ ✷✹✾❊✸ ❋✾✶✷✴ ✹ ✵✶ ✾ ✹✾✸✷●✴ ✺❍ ❃❄❅ ❆ ❀✾❂✾ ✵✺
✶❊■✾ ❊ ●✾✴ ✾❂❊❏ ❁✼ ❂❁ ✺✸✾ ✸✷✽ ✼❏❊✵✺❂ ❊❋ ❏✾ ✵✺ ❋ ✾ ❊ ✸✵❊❋❏✾
❋❊✸✷✸ ❍✺❂ ✵✶✾ ✹ ✾■✾❏✺❁✽ ✾✴✵ ✺❍ ✺✵✶✾❂ ✽ ✺✹✼❏✾✸✿❂✾❁❂✾✸✾✴✵❑
✷✴● ✹✷▲✾❂✾✴✵ ❏✾■✾❏✸ ✺❍ ❄ ✷❂ ❅❂❊▼ ✻ ❃✺✴✵❂✺❏ ❊✴✹ ❄ ✷❂ ❅❂❊❍❑
◆ ✻ ❖ ❊✴❊●✾✽ ✾✴✵❉
✳✴ ✵✶✾ ◆❂✸✵ ❁ ❊❂✵ ✺❍ ✵✶✷✸ ❁ ❊❁ ✾❂✿ ✵✶✾ ❋❊✸✷✻ ❍❂❊✽ ✾❑
❀✺❂P ❊✴ ✹ ✶❈❁ ✺✵✶✾✸✷✸ ✺❍ ✵✶ ✾ ❃ ❄❅ ❆ ✸✷✽ ✼❏❊✵✺❂ ❊❂✾ ✷✴✵❂✺❑
✹✼✻✾✹ ❉ ❅ ✶✾ ✸✾✻✺✴✹ ❁ ❊❂✵ ✹✾❊❏✸ ❀ ✷✵✶ ✵✶ ✾ ●✾✴✾❂❊❏ ✽ ❊✵✶✾❑
✽ ❊✵✷✻❊❏ ✻✺✴ ✻✾❁✵✸ ❂✾●❊❂✹✷✴● ✻✺✴◗ ✷✻✵ ❂✾✸✺❏✼✵✷✺✴ ❊✴✹ ❊✷❂❑
❋✺❂✴✾ ✻✺❏❏✷✸✷✺✴ ❊■✺✷✹ ❊✴✻✾ ✸❈✸✵✾✽ ✸❉ ❘ ✷▲✾❂✾✴✵ ❂✾✸✼ ❏✵✸
✺❋ ✵❊✷✴ ✾✹ ✸✺ ❍❊❂ ❀ ✷✵✶ ✽ ✺✹✼❏✾✸ ❂✾●❊❂✹✷✴ ● ✻✺✴◗✷✻✵ ❂✾✸❑
✺❏✼✵✷✺✴ ✿ ❊■✺✷✹ ❊✴✻✾✿ ✺❂ ❀ ✺❂P❏✺❊✹ ✿ ❋✼✷❏✵ ✺✴ ✵✺❁ ✺❍ ✵✶✾
❃ ❄❅ ❆ ✸✷✽ ✼❏❊✵✺❂ ❊❂✾ ❁❂✾✸✾✴✵✾✹ ❊✸ ✾❙ ❊✽ ❁❏✾✸ ✷✴ ✵✶✾ ❏❊✸✵
❁❊❂✵❉
❚ ✲ ❯ ✭ ❱ ❱❲ ❱ ✭ ❳ ❨
❩ ❏❊✴✴✷✴●✿ ✺❂ ✽ ❊P✷✴● ✹✾✻✷✸✷✺✴✸ ❍✺❂ ✵✶✾ ✾■✺❏✼✵✷✺✴
✺❍ ✵✶ ✾ ❬✼ ❂✺❁ ✾❊✴ ❄ ✷❂ ❅❂❊▼ ✻ ❖ ❊✴ ❊●✾✽ ✾✴✵ ❆❈✸✵✾✽
❭
❬ ❄❅ ❖ ❆ ❪ ✷✴■✺❏■✾✸ ❊ ✻❊❂✾❍✼❏ ✾■❊❏✼❊✵✷✺✴ ✺❍ ❊❏✵✾❂✴ ❊✵✷■✾
✸✻✾✴ ❊❂✷✺✸❉ ❅ ✶✷✸ ❊✸✸✾✸✸✽ ✾✴✵ ✷✸ ✺❍✵✾✴ ✻❊❂❂✷✾✹ ✺✼✵ ✵✶ ❂✺✼●✶
✾❙❁ ✾❂✷✽ ✾✴✵❊✵✷✺✴✸✿ ✷✴ ❀ ✶✷✻✶ ✽ ✺✹✾❏✷✴ ● ❊✴✹ ✸✷✽ ✼❏❊✵✷✺✴
✻✺✴✵❂✷❋✼✵✾ ✸✷●✴✷◆ ✻❊✴✵❏❈✿ ❋❈ ❂✾✹✼✻✷✴● ✵✶ ✾ ✵✼❂✴❑❊❂✺✼✴ ✹
✵✷✽ ✾ ❋✾✵❀ ✾✾✴ ✵✶✾ ✹✾✸✷●✴ ❊✴✹ ✵✶✾ ✷✽ ❁❏✾✽ ✾✴✵❊✵✷✺✴ ✺❍
❊✹ ■❊✴ ✻✾✹ ✺❁ ✾❂❊✵✷✺✴❊❏ ✻✺✴ ✻✾❁✵✸❉
❄ ❏✵✶✺✼●✶ ✴✼✽ ✾❂✺✼✸ ✽ ❊✵✶✾✽ ❊✵✷✻❊❏ ✽ ✺✹✾❏✸ ❊✴✹ ❍❊✸✵
✵✷✽ ✾ ✸✷✽ ✼❏❊✵✷✺✴ ❍❊✻✷❏✷✵✷✾✸ ❊❂✾ ❊❏❂✾❊✹ ❈ ❋ ✾✷✴ ● ✼ ✸✾✹ ✵✺ ❊✸❑
✸✾✸✸ ✵✶✾ ❁✾❂❍✺❂✽ ❊✴✻✾ ✺❍ ✵✶✾ ❬ ✼❂✺❁ ✾❊✴ ❊✷❂✸❁ ❊✻✾ ✸❈✸❑
✵✾✽
❭❫
❄ ❆❩❄ ❃ ✿ ❬ ❄ ❖ ✿ ❅❄ ❄ ❖ ✿ ❄ ❴ ❃❵❛❛❛✿ ❴ ❄ ❖ ❆ ✿
❆❩ ❬ ❃❅ ❴ ❄ ❪✿ ❂✾✻✾✴✵ ❂✾■✷✾❀ ✸✵✼✹✷✾✸
❭❜
❆✺❍❝❞❊✿ ❆✺❍❝❞❋ ✿
❫
❄ ❆ ❝❞❡❪ ✶✷●✶ ❏✷●✶✵✾✹ ❊❏✸✺ ✵✶✾✷❂ ❏❊✻P ✺❍ ◗ ✾❙✷❋ ✷❏✷✵❈ ✵✺
✻✺❁✾ ❀ ✷✵✶ ✴✾❀ ✻✺✴✻✾❁✵✸✿ ❀ ✷✵✶ ✻✺✽ ❁❏✾❙ ✹❈✴ ❊✽ ✷✻✸ ✺❍
✵✶✾ ❄❅ ❖ ✸❈✸✵✾✽ ✿❀ ✷✵✶ ❏❊❂●✾ ✸✻❊❏✾ ✼ ✴✻✾❂✵❊✷✴✵❈ ❍❊✻✵✺❂✸✿
❊✴ ✹ ❀ ✷✵✶ ✸✷✽ ✼ ❏❊✵✷✺✴ ✸✺❍✵❀ ❊❂✾ ✻✺✽ ❁❏✾❙✷✵❈❉
❢❏✾❙✷❋✷❏✷✵❈ ✷✸ ❊ P✾❈ ❍✾❊✵✼ ❂✾ ✺❍ ✵✶ ✾ ✸✷✽ ✼❏❊✵✺❂ ❊✸ ✴ ✾❀
◆ ❏✵✾❂✸ ❊❂✾ ✾❊✸✷❏❈ ✷✴✵❂✺✹✼ ✻✾✹ ✿ ❊✴ ✹ ✵✼✴✾✹ ✵✺ ✽ ✺✹✾❏ ✸❁ ✾❑
❣❤✐❥❦❧✐♠❦♥❧♦ ♣qrs♠♥t ♥✉✐♠♥❦✈ ✇ ①❦❥✐①♦②③④⑤⑥ ④⑤⑥ ③②⑦ ✐⑧ ④♣
⑨
♦①♥✈②⑩❶❷❸❸ ❹❦❺①❦❺✉♦ ③♦♣♦❻ ❼❧✐✈❽♦②♣❺❧✐✈♣❾ ❧♦❽❿♦❧❽❿♦➀♦✈✐❽➀➁❧
➂
③♦✈♠❧♦ ♣q④♠❺♣♦✉ ♣♦ ①✐ ⑤✐⑧♥➃✐♠♥❦✈ ⑥♦➄❧♥♦✈✈♦②❼❧✐✈❽♦
➅
③⑥❹➆ ✉♠✐✈♣✉ ♦♥♠❿♦❧ ➁❦❧ ③❦ts①♦♠♦ ⑥♥❧ ❹❧✐➇ ❽ ➆♥t❺①✐♠❦❧ ❦❧
✻✷
◆
✻ ❍✾❊✵✼❂✾✸ ✺❍ ❊✴ ✺❁✾❂❊✵✷✺✴❊❏ ✸✻✾✴ ❊❂✷✺ ❉ ❅ ✶✾ ✻✺❂✾ ✺❍
✵✶✾ ✵❂❊▼ ✻ ✸✷✽ ✼ ❏❊✵✺❂ ✷✸ ✸✽ ❊❏❏ ❊✴✹ ✾❊✸❈ ✵✺ ✽ ❊✷✴✵❊✷✴ ❉ ✳✵
✷✸ ❏✾✸✸ ✵✶ ❊✴ ➉ ✿❛❛❛ ❏✷✴ ✾✸ ✺❍ ❖ ➊ ✻✺✹✾➋❉ ✳✵ ❀ ✺❂P✸ ❀ ✷✵✶
✻❏❊✸✸✷✻❊❏ ❊✷❂✻❂❊❍✵ ❁ ✾❂❍✺❂✽ ❊✴✻✾✸✿ ❀ ✷✵✶ ❂✾❊❏ ❊✷❂✸❁❊✻✾ ✹ ✾❑
✸✷●✴✸ ❊✴✹ ✺❁✾❂❊✵✷✺✴❊❏ ✻✺✴ ✸✵❂❊✷✴✵✸❉ ❢✼❂✵✶✾❂✽ ✺❂✾✿ ✷✵
❁❂✺■✷✹ ✾✸ ❊ ❁❂❊✻✵✷✻❊❏ ❍❂❊✽ ✾❀✺❂P ❍✺❂ ✵✶✺❂✺✼ ●✶ ✽ ❊✵✶❑
✾✽ ❊✵✷✻❊❏ ✽ ✺✹ ✾❏ ✹✾■✾❏✺❁ ✽ ✾✴✵✿ ❍✺❂ ❂✺✼✵✾ ✴ ✾✵❀✺❂P ❊✴✹
✸✾✻✵✺❂ ✹ ✾✸✷●✴ ✿ ❊✷❂ ✵❂❊▼ ✻ ❊✸✸✷●✴✽ ✾✴✵✿ ✻✺✴◗✷✻✵ ❂✾✸✺❏✼❑
✵✷✺✴ ❊✴✹ ❊✷❂❋ ✺❂✴ ✾ ✻✺❏❏✷✸✷✺✴ ❊■✺✷✹ ❊✴✻✾✿ ●❂✺✼ ✴✹ ✶✺❏✹✷✴● ❉
➌ ➍➎ ➏ ➐ ➑ ➒ ➓➔→➣↔➣ ➒↕ ➙ ➛ ➜ ➝
❅ ✶✾ ✻✺❂✾ ✺❍ ✵✶✾ ❃❄ ❅ ❆ ✸❈✸✵✾✽ ✷✸ ❊✴ ✾✴❑❂✺✼✵✾ ✵❂❊❍❑
◆
✻ ✸✷✽ ✼❏❊✵✷✺✴ ✾✴ ●✷✴✾❉ ✳✵ ✷✸ ❋ ❊✸✾✹ ✺✴ ❊ ✹✷✸✻❂✾✵✾✿
◆
❙✾✹
✵✷✽ ✾ ✸❏✷✻✾ ✾❙✾✻✼✵✷✺✴ ✽ ✺✹✾❏➞ ✵✶ ✾ ❁✺✸✷✵✷✺✴ ❊✴ ✹ ■✾❏✺✻✷✵✷✾✸
✺❍ ❊✷❂✻❂❊❍✵ ❊❂✾ ✻✺✽ ❁✼✵✾✹ ❊✵
◆
❙✾✹ ✵✷✽ ✾ ✸✵✾❁✸✿ ✼✸✼ ❊❏❏❈
✾■✾❂❈ ➟✿ ➠❛ ✺❂ ➠➟ ✸✾✻✺✴ ✹✸❉
❄ ✷❂✻❂❊❍✵ ❁ ✾❂❍✺❂✽ ❊✴✻✾✸ ❊❂✾ ✷✴ ✵❊❋✼ ❏❊✵✾✹ ❍✺❂✽ ✹ ✾❑
✸✻❂✷❋ ✷✴● ●❂✺✼✴ ✹ ✸❁✾✾✹ ✿ ■✾❂✵✷✻❊❏ ✸❁✾✾✹ ✿ ❊✴ ✹ ❍✼✾❏ ❋✼❂✴
❊✸ ❊ ❍✼ ✴✻✵✷✺✴ ✺❍ ❊❏✵✷✵✼✹✾✿ ❊✷❂✻❂❊❍✵ ✵❈❁ ✾ ❊✴✹ ◗✷●✶✵ ✸✾●❑
✽ ✾✴✵
❭
✻❂✼✷✸✾✿ ✻❏✷✽ ❋ ✺❂ ✹✾✸✻✾✴✵❉❪ ❅ ❀ ✺ ✽ ❊✷✴ ✹❊✵❊✸✾✵✸
❍✺❂ ❊✷❂✻❂❊❍✵ ◗ ✷●✶✵ ❁ ✾❂❍✺❂✽ ❊✴ ✻✾ ❊❂✾ ✼✸✾✹ ➞
➡
❃ ❄➢ ❅ ❴ ❄ ➤ ❬
❫
❄ ❃➥ ❊✷❂✻❂❊❍✵ ❁ ✾❂❍✺❂✽ ❊✴ ✻✾ ✵❊❋❏✾✸✿
✾❙✵❂❊✻✵✾✹ ❍❂✺✽ ✵✶✾ ❢❂✾✴✻✶ ◗✷●✶✵ ✹ ❊✵❊ ❁❂✺✻✾✸✸✷✴●
✸❈✸✵✾✽ ➦
➡ ➧
❊✸✾ ✺❍ ❊✷❂✻❂❊❍✵ ✹ ❊✵❊
❭
➧
❄ ❘ ❄ ❪ ❁ ✾❂❍✺❂✽ ❊✴✻✾ ✸✼ ✽ ❑
✽ ❊❂❈ ✵❊❋❏✾✸ ✹✾❂✷■✾✹ ❍❂✺✽ ✵✶✾ ✵✺✵❊❏ ✾✴✾❂●❈ ✽ ✺✹ ✾❏
✺❍ ❬➢ ❴➨ ❃ ➨
❫
❅ ❴ ➨ ➊ ❉ ❞❝ ✹✷▲✾❂✾✴✵ ❊✷❂✻❂❊❍✵ ✵❈❁ ✾✸
❊❂✾ ✹✾✸✻❂✷❋✾✹ ❉ ❆❈✴✺✴❈✽ ❊✷❂✻❂❊❍✵ ❊❂✾ ✼✸✾✹ ✵✺
✽ ✺✹✾❏ ✵✶ ✾ ❂✾✸✵ ✺❍ ✵✶ ✾ ◗✾✾✵❉ ❅ ✶✾ ❄ ✷❂❋ ✼✸ ❄ ➉❵❛
❭
❬ ❄ ➉❵❪ ✷✸ ✼✸✾✹ ❊✸ ✹✾❍❊✼❏✵ ❊✷❂✻❂❊❍✵❉
❄ ✷❂✻❂❊❍✵ ✼✸✾ ✹✷▲✾❂✾✴✵ ✴ ❊■✷●❊✵✷✺✴ ✽ ✺✹✾✸➞ ✵✶✾❈ ✻❊✴
◗❈ ✹✷❂✾✻✵ ❂✺✼✵✾✸ ✵✺ ✵✶✾✷❂ ✹✾✸✵✷✴ ❊✵✷✺✴ ✿ ✺❂ ❍✺❏❏✺❀ ✵✶✾ ✸✾❑
➩
✼✾✴✻✾ ✺❍ ✴ ❊■✷●❊✵✷✺✴ ❊✷✹✸ ✹ ✾✸✻❂✷❋✾✹ ✷✴ ✵✶✾✷❂ ◗ ✷●✶✵ ❁❏❊✴ ❉
❄ ❏✵✶✺✼●✶ ✵✶✾❂✾ ✷✸ ✴✺ ❂✺✼ ✵✾ ✺❂✷✾✴✵❊✵✷✺✴ ✸✻✶✾✽ ✾ ✾❙❁❏✷✻❑
✷✵❏❈ ✹✾◆ ✴✾✹ ❍✺❂ ✵✶ ✾ ❊✷❂ ✵❂❊▼ ✻ ✴ ✾✵❀✺❂P ✿ ❊✷❂✻❂❊❍✵ ✽ ❊❈ ✼ ✸✾
✺✴✾ ❏✾■✾❏ ✺✼ ✵ ✺❍ ✵❀✺ ❋❊✸✾✹ ✺✴ ✷✵✸ ✶ ✾❊✹✷✴ ●
❭
✴✺❂✵✶ ➤✸✺✼ ✵✶
✺❂ ✾❊✸✵➤❀ ✾✸✵ ❂✺✼✵✾ ✺❂✷✾✴✵❊✵✷✺✴❪❉ ❬■✾❂❈ ❍✺✼❂ ❏✾■✾❏✸ ✻❊✴
❋ ✾ ❊❏✸✺ ✼✸✾✹ ❋ ❊✸✾✹ ✺✴ ✵✶ ✾
❭❫
❬ ✿❆❬ ✿❆➫
✿❫
➫ ❪ ❊✷❂✻❂❊❍✵➭✸
✺❂✷✾✴✵❊✵✷✺✴
❭
➩
✼❊✹ ❂✼ ❁❏✾ ❊❏✵✾❂✴❊✵✾❪❉
➯
③⑥➈ ❤ ♥✉ ✐ s❦①➲t ❦❧s❿♥❽②✉♠❧❦✈➃ ♠➲s♦♣ ➳♥♠❿ ♥✈➁♦❧♦✈❽♦ ♠➲s♥✈➃
①✐✈➃❺✐➃♦
➵
➢ ✴✻✾❂✵❊✷✴✵✷✾✸ ✺✴ ✸❁ ✾✾✹
❭
✾✷✵✶✾❂ ■✾❂✵✷✻❊❏ ✺❂ ✶✺❂✷➸✺✴❑
✵❊❏❪ ✻❊✴ ❋✾ ✽ ✺✹✷◆ ✾✹ ✿ ❊✴ ✹ ❊ ✻✺✴■✾❙ ✻✺✴◗ ✷✻✵ ✹ ✾✵✾✻✵✷✺✴
❭
✹✾✵❊✷❏✾✹ ✷✴ ❁ ❊❂✵ ➉❉➠❪ ✷✸ ✼✸✾✹ ❉
➌ ➍➌ ➺ ➻ ➓➑ ➻➓➣ ➒ ↕ ➙ ➛ ➜ ➝
❅ ✶✾ ✸✷✽ ✼❏❊✵✷✺✴ ✸❈✸✵✾✽ ❂✾✻✺❂✹✸ ❊✴✹ ✻✺✽ ❁✼ ✵✾✸ ✵✶ ✾
❍✺❏❏✺❀ ✷✴● ✺✼ ✵❁ ✼✵ ■❊❂✷❊❋❏✾✸➞
➡
✷✴✸✵❊✴✵❊✴✾✺✼✸ ❊✷❂✻❂❊❍✵ ✻✺✼✴✵ ❁ ✾❂ ✸✾✻✵✺❂➦
➡
❊✷❂✻❂❊❍✵ ◗ ✺❀ ❂❊✵✾✸ ✵✶❂✺✼●✶ ✸✾✻✵✺❂✸➦
➡
✻✺✴◗✷✻✵ ✸✵❊✵✷✸✵✷✻✸
❭
●✾✺✽ ✾✵❂❈✿ ❊✷❂✻❂❊❍✵ ✽ ❊✴ ✾✼■✾❂✸✿
✹✼❂❊✵✷✺✴ ✿ ✾✵✻❪➦
➡
✻✺✴◗✷✻✵ ❂✾✸✺❏✼✵✷✺✴ ✸✵❊✵✷✸✵✷✻✸
❭
✴✼ ✽ ❋ ✾❂ ✺❍ ✽ ❊✴ ✾✼❑
■✾❂✸✿ ✴✼✽ ❋ ✾❂ ✺❍ ✻❏✼✸✵✾❂✸✿ ✻❏✼ ✸✵✾❂✸ ✸✷➸✾✸✿ ✽ ❊✴ ✾✼❑
■✾❂✸ ✹✼❂❊✵✷✺✴ ✿ ✹✾❏❊❈✸ ✹✼ ✾ ✵✺ ✽ ❊✴✾✼■✾❂✸✿ ✵❈❁✾ ✺❍
✽ ❊✴✾✼■✾❂✸❪
➡
❊✷❂❋ ✺❂✴ ✾ ✸✾❁ ❊❂❊✵✷✺✴ ❊✴ ✹ ✻✺❏❏✷✸✷✺✴ ❊■✺✷✹ ❊✴✻✾ ✸❈✸❑
✵✾✽ ✸✵❊✵✷✸✵✷✻✸
❭
✴✼✽ ❋ ✾❂✿ ✹✼❂❊✵✷✺✴ ✿ ✵❈❁ ✾ ✺❍ ✽ ❊✴ ✾✼❑
■✾❂✸❪➦
➡
✸✵❊✵✷✸✵✷✻✸ ❍❂✺✽ ✺✵✶✾❂
◆
❏✵✾❂✸ ✸✼ ✻✶ ❊✸ ●❂✺✼✴✹ ✹✾❏❊❈✸✿
❂✼ ✴❀❊❈ ✻❊❁❊✻✷✵❈ ✼✵✷❏✷➸❊✵✷✺✴ ❊❂✾ ❊❏✸✺ ❊■❊✷❏❊❋ ❏✾❉
➼ ✲ ✯ ✬ ➽ ➾ ✫✲ ✭ ❱ ✯ ➾➚ ❳ ✮ ❨ ✯ ✰ ❳ ➾ ✫✬ ➪
❄ ✽ ✺✴ ● ✵✶✾ ❁ ❂✺❋❏✾✽ ✸ ✵✶❊✵ ✻❊✴ ❋✾ ✵✾✸✵✾✹ ✺✴ ❂✾❊❏ ✵❂❊❍❑
◆ ✻ ❀ ✷✵✶ ❃❄❅ ❆ ✿ ✵❀✺ ❊❁ ❁❂✺✻✶✾✸ ✺❍ ❊✼✵✺✽ ❊✵✷✻ ✻✺✴◗✷✻✵
❂✾✸✺❏✼✵✷✺✴ ❊❂✾ ✹✾✵❊✷❏✾✹ ❊✸ ✾❙❊✽ ❁❏✾✸ ✷✴ ✵✶ ✷✸ ❁ ❊❂✵❉ ❅ ✶ ✾
◆ ❂✸✵ ✺✴✾ ✹✾❊❏✸ ❀ ✷✵✶ ❊ ✻✾✴✵❂❊❏✷➸✾✹ ✻✺✴✵❂✺❏ ✸❈✸✵✾✽ ❍✺❂
✶✷●✶ ✹✾✴✸✷✵❈ ❊❂✾❊✸ ❊✴✹ ✽ ✾✹✷✼ ✽ ✵✾❂✽
❭
➠❛ ✵✺ ➠➟ ✽ ✷✴❑
✼✵✾✸ ❊✶✾❊✹ ❪ ✻✺✴✵❂✺❏❉ ❅ ✶✾ ✸✾✻✺✴✹ ✺✴ ✾ ✹✾❊❏✸ ❀✷✵✶ ❊✴
✺✴ ❋ ✺❊❂✹ ❂✾❊✻✵✷■✾ ✸✶✺❂✵ ✵✾❂✽
❭
➉ ✵✺ ➠❛ ✽ ✷✴✼✵✾✸ ❊✶✾❊✹ ❪
❊✼ ✵✺✽ ❊✵✷✻ ✻✺✴◗ ✷✻✵ ✸✺❏■✾❂❉
❄ ✸ ❋ ✺✵✶ ✸✺❏■✾❂✸ ✼✸✾ ❊ ✻✺✴◗ ✷✻✵ ✹ ✾✵✾✻✵✷✺✴ ✵✶ ❊✵ ✷✸ ❂✺❑
❋✼✸✵ ✵✺ ✼✴ ✻✾❂✵❊✷✴✵✷✾✸✿ ❊ ✻✺✴■✾❙ ✽ ✺✹ ✾❏✷✴● ✺❍ ✼✴✻✾❂✵❊✷✴❑
✵✷✾✸ ✷✸
◆
❂✸✵ ✷✴✵❂✺✹✼✻✾✹ ❉
➶ ➍➎ ➙ ➒ ➹ ➘→➴ ➷ ➒ ➬ →➮↔➹ ➱ ➒↕ ➻ ➹ ✃→❐➓❒ ↔➹ ➓↔→➣
➫ ✾ ❊✸✸✼✽ ✾ ✵✶ ❊✵ ✵✶✾❂✾ ✷✸ ❊✴ ✾❂❂✺❂ ❊❋ ✺✼ ✵ ✵✶ ✾ ❊✷❂❑
✻❂❊❍✵➭✸ ❍✼✵✼❂✾ ❏✺✻❊✵✷✺✴ ❋ ✾✻❊✼ ✸✾ ✺❍ ●❂✺✼✴✹ ✸❁ ✾✾✹ ❁ ❂✾❑
✹✷✻✵✷✺✴ ✼✴ ✻✾❂✵❊✷✴✵✷✾✸❮❉ ❅ ✶ ✾ ✼✴✻✾❂✵❊✷✴✵✷✾✸ ✺✴ ✻❏✷✽ ❋✷✴ ●
❊✴ ✹ ✹✾✸✻✾✴ ✹✷✴ ● ❂❊✵✾✸ ❊❂✾ ✾■✾✴ ✽ ✺❂✾ ✷✽ ❁✺❂✵❊✴✵❉ ❄ ✸ ✵✶ ✾
✻✺✴◗✷✻✵ ✹✾✵✾✻✵✷✺✴ ✽ ✼ ✸✵ ❋✾ ❂✺❋ ✼✸✵ ❂✾●❊❂✹✷✴● ✵✶ ✾✸✾ ❊✴ ✹
❰Ï
✈❽♦❧♠✐♥✈♠♥♦✉ ❦✈ ➃❧❦❺✈♣ ♠❧✐❽Ð ➳♥①① ✈❦♠ ❥♦ ❽❦✈✉♥♣♦❧♦♣② ✐✉
♠❿♦➲ ♣❦ ✈❦♠ ♥✈❽❧♦✐✉♦ ➳♥♠❿ ♠♥t ♦ ✐✈♣ ➳♥①① ❥♦ ❺✉❺✐①①➲ ♥✈❽①❺♣♦♣ ♥✈
HORIZONTAL PLANE
VERTICAL PLANE t=2
t=1 t=3 t=4
t=5 t=6
t=7
t=8
t=9
t=10
❢ ✷●✼❂✾ ➠➞ ❖ ✺✹✾❏✷✴● ✺❍ ✸❁✾✾✹ ✼ ✴✻✾❂✵❊✷✴✵✷✾✸❉
✽ ❊✴❈ ✺✵✶✾❂ ✼✴✻✾❂✵❊✷✴✵✷✾✸✿ ❊✴ ❊✷❂✻❂❊❍✵ ✷✸ ❂✾❁❂✾✸✾✴✵✾✹ ❋❈
❊ ❁ ✺✷✴✵ ❊✵ ✵✶✾ ✷✴ ✷✵✷❊❏ ✵✷✽ ✾❉ ❅ ✶ ✾ ❁ ✺✷✴✵ ❋ ✾✻✺✽ ✾✸ ❊ ❏✷✴ ✾
✸✾●✽ ✾✴✵ ✷✴ ✵✶✾ ✼ ✴✻✾❂✵❊✷✴✵❈ ✹✷❂✾✻✵✷✺✴
❭
◆ ●✼ ❂✾ ➠❪❉ ➫ ✶✾✴
✻✶ ❊✴●✷✴● ✹ ✷❂✾✻✵✷✺✴ ❋✾✻❊✼✸✾ ✺❍ ❊ ✽ ❊✴ ✾✼■✾❂ ✺❂✹✾❂ ✺❂ ❊
❋ ✾❊✻✺✴
❭Ñ Ò Ó
❪✿ ✵✶✾ ✸✾●✽ ✾✴✵ ❋ ✾✻✺✽ ✾✸ ❊ ❁ ❊❂❊❏❏✾❏✺●❂❊✽
✵✶❊✵ ✷✴ ✻❂✾❊✸✾✸ ✷✴ ✵✶✾ ✸❁ ✾✾✹ ✹✷❂✾✻✵✷✺✴ ❉ ➫ ✶ ✾✴ ✻✶ ❊✴ ●❑
✷✴ ● ❊ ✸✾✻✺✴ ✹ ✵✷✽ ✾ ✹✷❂✾✻✵✷✺✴
❭Ñ Ò Ô
❪✿ ✵✶ ✾ ❁ ❊❂❊❏❏✾❏✺●❂❊✽
❋ ✾✻✺✽ ✾✸ ❊✴ ✶ ✾❙❊●✺✴ ✵✶ ❊✵ ✷✴✻❂✾❊✸✾✸ ✷✴ ✵✶✾ ✴ ✾❀ ✸❁✾✾✹
✹✷❂✾✻✵✷✺✴ ✿ ❊✴✹ ✸✺ ✺✴ ❉ ❅✺ ✻✶ ✾✻P ❊ ✻✺✴◗ ✷✻✵ ❊✵ ✵✷✽ ✾ Ñ
✿
✵✶✾ ✹✷✸✵❊✴ ✻✾ ❋✾✵❀ ✾✾✴ ✵✶✾ ✵❀ ✺ ❁✺❏❈●✺✴ ✸ ✽ ✺✹✾❏✷✴ ● ✵✶✾
❊✷❂✻❂❊❍✵ ❁ ✺✸✷✵✷✺✴✸ ✷✸ ✻✺✽ ❁ ❊❂✾✹ ✵✺ ✵✶✾ ✸✾❁ ❊❂❊✵✷✺✴ ✸✵❊✴❑
✹❊❂✹ ❉
✳✴ ✵✶✾ ■✾❂✵✷✻❊❏ ❁❏❊✴ ✾✿ ❊ ✻❈❏✷✴✹❂✷✻❊❏ ✽ ✺✹ ✾❏✷✴● ✷✸ ✼✸✾✹
❭
◆ ●✼❂✾ ➠❪❉ ❬ ❊✻✶ ❊✷❂✻❂❊❍✵ ✶ ❊✸ ❊ ✽ ❊❙✷✽ ❊❏ ❊❏✵✷✵✼ ✹✾ ❊✴✹
❊ ✽ ✷✴✷✽ ❊❏ ❊❏✵✷✵✼✹ ✾❉ ❅✺ ✻✶ ✾✻P ✷❍ ✵❀✺ ❊✷❂✻❂❊❍✵ ❊❂✾ ✷✴
✻✺✴◗ ✷✻✵✿ ✵✶ ✾ ✽ ✷✴✷✽ ❊❏ ❊❏✵✷✵✼✹✾ ✺❍ ✵✶✾ ✶✷●✶ ✾❂ ❊✷❂✻❂❊❍✵ ✷✸
✻✺✽ ❁❊❂✾✹ ✵✺ ✵✶✾ ✽ ❊❙✷✽ ❊❏ ❊❏✵✷✵✼✹✾ ✺❍ ✵✶ ✾ ❏✺❀✾❂ ❊✷❂❑
✻❂❊❍✵❉
❅ ✶✷✸ ✽ ✺✹✾❏ ●✼❊❂❊✴✵✾✾✸ ✵✶ ❊✵ ✷❍ ❊✷❂✻❂❊❍✵ ✻❊✴ ✶❊✴✹❏✾
✸✼✻✶ ✼ ✴✻✾❂✵❊✷✴✵✷✾✸ ✵✶ ❊✴ ✵✶✾❈ ❀ ✷❏❏ ❊❏❀ ❊❈✸ ◗ ❈ ✷✴ ✵✶ ✾✷❂
❋ ✺❙✾✸❉ ❅ ✶✾ ✼✴ ✻✾❂✵❊✷✴✵❈ ❂❊✵✾ ✻❊✴ ❋ ✾ ✹✷▲✾❂✾✴✵ ❍✺❂ ✾■✾❂❈
❊✷❂✻❂❊❍✵❉
➶ ➍➌ ➙ → ➹➓❐❒ ➮↔Õ →➬ ➑ ❐➒Ö ➮→ ➷ ➣➒➮➘ →❐
❅ ✶✾ ✻✾✴✵❂❊❏✷➸✾✹ ❁❂✺❋❏✾✽ ✸✺❏■✾❂ ✹✾■✾❏✺❁ ❁✾✹ ❋❈ ❘ ✼❑
❂❊✴ ✹
❜
❘ ✼❂❝❞❡ ✻❊✴ ✶ ❊✴✹❏✾ ✻✺✴◗✷✻✵✸ ✷✴■✺❏■✷✴● ✽ ✺❂✾ ✵✶ ❊✴
❵ ❊✷❂✻❂❊❍✵❉ ❅ ✶✾✸✾ ✻✺✴◗ ✷✻✵✸ ❊❂✾ ✻❊❏❏✾✹ ✻❏✼✸✵✾❂✸ ❊✸ ✵✶✾❈
❊❂✾ ✺❋ ✵❊✷✴ ✾✹ ❋❈ ✽ ✾❂●✷✴● ➠❑✵✺❑➠ ✻✺✴◗✷✻✵✸ ✷✴■✺❏■✷✴●
✻✺✽ ✽ ✺✴ ❊✷❂✻❂❊❍✵ ✹✼ ❂✷✴● ✵✶✾ ✴✾❙✵ ×Ø ✽ ✷✴✼✵✾✸
❭
×Ø ✷✸
✻❊❏❏✾✹ ✵✶✾ ✵✷✽ ✾ ❀ ✷✴✹ ✺❀ ✿❍✺❂ ✵✶✾ ❊❁ ❁❏✷✻❊✵✷✺✴✸✿ ×Ø Ò
➠❵
✽ ✴ ❪❉
ÙÚÛ ÚÜ ÝÞ ßàáâ àãäáåæ ç
❅ ✶✾ ✽ ❊✷✴ ✷✹✾❊ ●✼ ✷✹✷✴ ● ✵✶✾ ✹✾✸✷●✴ ✺❍ ✵✶✾ ✸✺❏■✾❂✿ ✷✸ ✵✺
❋✾ ❊✸ ✻❏✺✸✾ ❊✸ ❁✺✸✸✷❋❏✾ ✵✺ ✵✶✾ ✻✼ ❂❂✾✴✵ ❄❅ ❃ ✸❈✸✵✾✽ ➞
➡
❃✺✴◗ ✷✻✵ ❍❂✾✾ ✵❂❊è✾✻✵✺❂✷✾✸ ✽ ✼✸✵ ❂✾✸❁ ✾✻✵ ❋✺✵✶ ❊✷❂❑
✻❂❊❍✵ ❊✴ ✹ ❁✷❏✺✵ ❁ ✾❂❍✺❂✽ ❊✴✻✾✸❉ ❃✺✴✸✷✹✾❂✷✴● ✵✶ ✾
✾■✺❏✼✵✷✺✴ ✺❍ ❄❅ ❃ ✵✺❀❊❂✹ ❊✼✵✺✽ ❊✵✷✺✴
❜❘
❄ ❖ ❝➉❡✿
✵❂❊è✾✻✵✺❂✷✾✸ ✽ ✼✸✵ ❂✾✽ ❊✷✴ ✸✷✽ ❁ ❏✾ ❍✺❂ ✻✺✴✵❂✺❏❏✾❂✸ ✵✺
✹✾✸✻❂✷❋✾ ❊✸ ❀✾❏❏ ❊✸ ❍✺❂ ❁✷❏✺✵✸ ✵✺ ✼✴✹ ✾❂✸✵❊✴✹ ❊✴ ✹
❍✺❏❏✺❀ ❉
➡
❖ ❊✴✾✼■✾❂ ✺❂✹ ✾❂✸ ✽ ✼✸✵ ❋ ✾ ●✷■✾✴ ❀ ✷✵✶ ❊✴ ❊✹■❊✴✻✾
✴✺✵✷✻✾ ✵✺ ✵✶✾ ❁✷❏✺✵❉ ➫ ✶ ✾✴ ❊ ✽ ❊✴ ✾✼■✾❂ ✶ ❊✸ ❋ ✾●✼✴ ✿
✷✵ ✽ ✼ ✸✵ ✴✺✵ ❋ ✾ ✻❊❏❏✾✹ ✷✴✵✺
➩
✼✾✸✵✷✺✴ ❉
❅ ✶✾ ❍✼✴ ✻✵✷✺✴ ✵✺ ✺❁✵✷✽ ✷➸✾ ✷✸ ✹✾✻❂✷❋ ✾✹ ✷✴ ❁ ❊❂✵ ➉❉❵❉❞❉
ÙÚÛ ÚÛ é åêßëáæ ì
❅ ✶✾ ✻✼❂❂✾✴✵ ❊✷❂✻❂❊❍✵ ❁✺✸✷✵✷✺✴✸ ❊✴✹ ◗ ✷●✶✵ ❁ ❏❊✴✸ ❊❂✾ ✸✾✴✵
❋❈ ❃ ❄❅ ❆ ✵✺ ❊ ❁ ❂✺✻✾✸✸ ❘ ❃
❭
❘ ✾✵✾✻✵✷✺✴ ❃❏✼ ✸✵✾❂✷✴●❪ ✵✶ ❊✵
❋✼✷❏✹✸ ✵❂❊è✾✻✵✺❂✷✾✸ ❍✺❂✾✻❊✸✵ ❍✺❂ ×
Ø
✽ ✷✴✼✵✾✸✿ ✹ ✺✾✸ ✻✺✴❑
◗ ✷✻✵ ✹ ✾✵✾✻✵✷✺✴ ❋❈ ❁❊✷❂✸ ❊✴✹ ✵❂❊✴✸❍✺❂✽ ✸ ➠❑✵✺❑➠ ✻✺✴◗✷✻✵✸
✷✴ ✴❑❊✷❂✻❂❊❍✵ ✻✺✴◗✷✻✵ ✻❊❏❏✾✹ ✻❏✼✸✵✾❂✸❉ ❅ ✶ ✾✴ ✿ ✵✶✾ ❁❂✺❋❑
❏✾✽ ✸✺❏■✾❂ ✸✺❏■✾✸ ✷✴ ❁❊❂❊❏❏✾❏ ✾❊✻✶ ✻❏✼✸✵✾❂✿ ❊✸ ❊✷❂✻❂❊❍✵ ✷✴
✾❊✻✶ ✻❏✼ ✸✵✾❂ ❊❂✾ ✷✴✹ ✾❁ ✾✴ ✹✾✴✵ ❍❂✺✽ ❊✷❂✻❂❊❍✵ ✷✴ ✵✶✾ ✺✵✶ ✾❂
✻❏✼✸✵✾❂✸❉ ❅ ✶✾ ❁❂✺❋❏✾✽ ✸✺❏■✾❂ ✸✾✴ ✹✸ ✵✺ ❘ ❃ ✴✾❀ ✺❂✹ ✾❂✸
❊✴ ✹ ❘ ❃ ❋✼ ✷❏✹ ✸ ✴✾❀ ✵❂❊è✾✻✵✺❂✷✾✸ ❍✺❂✾✻❊✸✵ ❋ ❊✸✾✹ ✺✴ ✵✶✾✸✾
✺❂✹✾❂✸❉ ➨ ✴✻✾ ❊●❊✷✴ ❘ ❃ ❂✼✴✸ ❊ ✻✺✴◗✷✻✵ ✹✾✵✾✻✵✷✺✴ ❁ ❂✺❑
✻✾✸✸ ✵✺ ✻✶ ✾✻P ✵✶ ❊✵ ✽ ✺✹✷◆ ✾✹ ✵❂❊è✾✻✵✺❂✷✾✸ ❍✺❂ ❊✷❂✻❂❊❍✵ ✹✺
✴✺✵ ✷✴✵✾❂❍✾❂✾ ❀✷✵✶ ❊✷❂✻❂❊❍✵ ✷✴ ❊✴✺✵✶✾❂ ✻❏✼✸✵✾❂✿ ✺❂ ❀ ✷✵✶
✴✾❀ ❊✷❂✻❂❊❍✵❉ ✳❍ ✴✺ ✷✴✵✾❂❍✾❂✾✴✻✾ ✷✸ ❍✺✼✴✹ ✿ ✴✾❀ ◗ ✷●✶✵
✺❂✹✾❂✸ ❊❂✾ ✸✾✴✵ ✵✺ ❃❄❅ ❆ ❉ ✳❍ ✵✶✾❂✾ ❊❂✾ ✷✴✵✾❂❍✾❂✾✴✻✾✸✿
✷✴✵✾❂❍✾❂✷✴ ● ✻❏✼ ✸✵✾❂✸ ❊❂✾ è✺✷✴✾✹ ❊✴✹ ✵✶✾ ❁❂✺❋ ❏✾✽ ✸✺❏■✾❂
✷✸ ✼✸✾✹ ❊●❊✷✴ ✺✴ ✵✶❊✵
❭
✵✶ ✾✸✾❪ ✻❏✼✸✵✾❂
❭
✸❪❉ ❅ ✶ ✾ ❁❂✺✻✾✸✸
✷✸ ✷✵✾❂❊✵✾✹ ✼✴✵✷❏ ✴✺ ✷✴✵✾❂❍✾❂✾✴ ✻✾ ❋ ✾✵❀✾✾✴ ✻❏✼ ✸✵✾❂✸ ❂✾❑
✽ ❊✷✴✸✿ ✺❂ ✴ ✺ ✴ ✾❀ ❊✷❂✻❂❊❍✵ ✷✸ ✻✺✴✻✾❂✴✾✹ ❋❈ ✽ ✺✹✷◆ ✾✹
✵❂❊è✾✻✵✺❂✷✾✸❉ ❅ ✶✾ ✴ ✾❀ ✺❂✹ ✾❂✸ ❊❂✾ ✸✾✴✵ ❋ ❊✻P ✵✺ ✵✶✾ ✵❂❊❍❑
◆ ✻ ✸✷✽ ✼ ❏❊✵✺❂❉
❅ ✶✾ ❊❋✺■✾ ❁❂✺✻✾✸✸ ✷✸ ✷✵✾❂❊✵✾✹ ❊✴✹ ❊❏❏ ✵❂❊è✾✻✵✺❂✷✾✸
❊❂✾ ✺❁✵✷✽ ✷➸✾✹ ✾❊✻✶ í ✽ ✷✴✼✵✾✸❉ î ✺❀ ✾■✾❂✿ ✹✼ ❂✷✴● ✵✶✾
✻✺✽ ❁✼✵❊✵✷✺✴ ✵✷✽ ✾✿ ❊✷❂✻❂❊❍✵ ❊❂✾ ◗ ❈✷✴● ❊✴✹ ✽ ✼✸✵ P✴✺❀
✷❍ ✵✶✾❈ ✽ ✼✸✵ ✻✶ ❊✴●✾ ✵✶✾✷❂ ❂✺✼✵✾ ✺❂ ✴✺✵❉ í ✸✶✺✼ ❏✹ ❋✾
❏❊❂●✾ ✾✴✺✼●✶ ✵✺ ✻✺✽ ❁✼✵✾ ❊ ✸✺❏✼✵✷✺✴ ✿ ✸✾✴✹ ✷✵ ✵✺ ✵✶✾
❁✷❏✺✵ ❊✴✹ ❏✾✵ ✶ ✷✽ ✵✷✽ ✾ ✾✴✺✼●✶ ✵✺ ❋ ✾●✷✴ ✵✶✾ ✽ ❊✴✾✼■✾❂❉
❃ ✺✴✸✾
➩
✼✾✴✵❏❈✿❍✺❂ ✾❊✻✶ ❊✷❂✻❂❊❍✵✿❊✵ ✵✶✾ ❋ ✾●✷✴ ✴✷✴● ✺❍ ✵✶✾
✻✼ ❂❂✾✴✵ ✺❁✵✷✽ ✷➸❊✵✷✺✴ ✿ ✵❂❊è✾✻✵✺❂✷✾✸ ❊❂✾ ✹✾✵✾❂✽ ✷✴✾✹ ❋❈
✵✶✾ ❁ ❂✾■✷✺✼✸ ❂✼✴ ✺❍ ✵✶✾ ❁❂✺❋❏✾✽ ✸✺❏■✾❂ ❊✴ ✹ ✻❊✴✴✺✵ ❋✾
✻✶❊✴●✾✹ ❍✺❂ ✵✶ ✾ ✴✾❙✵ í ✽ ✴
❭
➉ ✽ ✴ ✷✴ ✵✶ ✾ ❊❁❁❏✷✻❊✵✷✺✴✸❪❉
ÙÚÛ ÚÙ ï ëð çäßñáæ ì
❄ ❍✵✾❂ ❁❊✷❂ ✹✾✵✾✻✵✷✺✴ ✿ ❘ ❃ ❁ ❂✺✻✾✸✸ ✹✺✾✸ ❊ ✻❏✼✸✵✾❂✷✴●
❀ ✶✷✻✶ ✷✸ ❊ ✵❂❊✴✸✷✵✷■✾ ✻❏✺✸✷✴● ✺✴ ❊❏❏ ❁❊✷❂✸❉ ❬ ❊✻✶ ✾ ✼ ✷■❑
Turning Point Model
t=0 t
s
0 t 1
❢✷●✼❂✾ ❵➞ î ✺❂✷➸✺✴✵❊❏ ✽ ❊✴ ✾✼■✾❂ ✽ ✺✹✾❏✷✴●❉
❊❏✾✴ ✻✾ ✻❏❊✸✸ ❍✺❂ ✵✶✾ ❂✾❏❊✵✷✺✴ ò✷✸ ✷✴ ✻✺✴◗✷✻✵ ❀ ✷✵✶ó✿ ✷✸ ❊
✻❏✼✸✵✾❂❉
❅ ✶✾ ❁ ❂✺✻✾✸✸ ❀ ✷❏❏❊❏❀ ❊❈✸ ✻✺✴■✾❂●✾➞ ✷✴ ✵✶ ✾ ❀✺❂✸✵ ✻❊✸✾✿
✵✶✾ ❁❂✺❋❏✾✽ ✸✺❏■✾❂ ❀ ✷❏❏ ✶❊■✾ ✵✺ ✸✺❏■✾ ❊ ■✾❂❈ ❏❊❂●✾ ✻❏✼✸❑
✵✾❂ ✷✴✻❏✼✹ ✷✴● ❊❏❏ ❊✷❂✻❂❊❍✵ ❁❂✾✸✾✴✵ ✷✴ ✵✶ ✾ ✴✾❙✵ ×Ø ✽ ✷✴❑
✼✵✾✸❉ î ✺❀ ✾■✾❂✿ ✵✶✷✸ ✵✾✻✶ ✴✷
➩
✼✾ ✷✸ ✼✸✼ ❊❏❏❈ ✾▼ ✻✷✾✴✵ ❊✸
❊ ■✾❂❈ ❏❊❂●✾ ✴✼✽ ❋✾❂ ✺❍ ✻❏✼✸✵✾❂✸ ✻❊✴ ❋ ✾ ✸✺❏■✾✹ ■✾❂❈
➩
✼✷✻P❏❈ ✷✴ ❁❊❂❊❏❏✾❏❉
ÙÚÛÚô ï åõ Þ ëßöáä÷ åø äù ß Þ ñåú ëßõ
❅ ✶✾ ✻✺✽ ❁❏✾❙✷✵❈ ✺❍ ✵✶✾ ❁ ❂✺❋❏✾✽ ✷✸ ✾❙❁ ✺✸✾✹ ❋❈ ❖ ✾✹ ✷✺✴✷✿
❘ ✼ ❂❊✴✹ ❊✴ ✹ ❄ ❏❏✷✺✵ ✷✴
❜❘
✼ ❂❝❞❡❉ ➊✾✵➭✸ ✻✺✴✸✷✹✾❂ ❊ ✻✺✴❑
◗✷✻✵ ❋ ✾✵❀ ✾✾✴ ✵❀ ✺ ❊✷❂✻❂❊❍✵❉ ➫ ✾ ✻❊✴ ✾❊✸✷❏❈ ❁❂✺■✾ ✵✶❊✵
✵✶✾ ✽ ✷✴✷✽ ✷➸✾✹ ❍✼ ✴✻✵✷✺✴ ✷✸ ✻✺✴■✾❙ ✿ ❋✼✵ ✵✶ ✾ ✸✾✵ ✺❍ ✻✺✴❑
◗✷✻✵ ❍❂✾✾ ✵❂❊è✾✻✵✺❂✷✾✸ ✷✸ ✴✺✵❉ ✳✵ ✷✸ ✴✺✵ ✾■✾✴ ✻✺✴ ✴✾✻✵✾✹ ❉
✳❍ ✵❂❊è✾✻✵✺❂✷✾✸ ✹✺✴ ➭✵ ❏✺✺❁ ✿✵✶✾ ✸✾✵ ✺❍ ✻✺✴◗✷✻✵ ❍❂✾✾ ✵❂❊è✾✻❑
✵✺❂✷✾✸ ✶❊✸ ✵❀✺ ✻✺✴✴✾✻✵✾✹ ✻✺✽ ❁✺✴✾✴✵✸❉ ❢✺❂ ❊ ✻✺✴◗ ✷✻✵
✷✴■✺❏■✷✴● û ❊✷❂✻❂❊❍✵✿ ✵✶✾❂✾ ✽ ❊❈ ❋ ✾ ❵ üýüþÿ
✁
✻✺✴ ✴✾✻✵✾✹
✻✺✽ ❁ ✺✴✾✴✵✸ ✷✴ ✵✶✾ ❍❂✾✾ ✵❂❊è✾✻✵✺❂❈ ✸❁ ❊✻✾ ❀ ✶✷✻✶ ✸✵❂✺✴●❏❈
✸✼●●✾✸✵✸ ✵✶ ❊✵ ❊✴❈ ✽ ✾✵✶✺✹ ❀ ✶✷✻✶ ❂✾
➩
✼✷❂✾✸ ✾❙❁❏✺❂✷✴ ● ✾■❑
✾❂❈ ✻✺✴✴✾✻✵✾✹ ✻✺✽ ❁✺✴✾✴✵ ✷✸
❫
❩ ✂❉ ✳✵ ✷✸ ✷✽ ❁ ✺❂✵❊✴✵ ✵✺
✴✺✵✾ ✵✶ ❊✵ ✵✶✷✸ ✻✺✽ ❁❏✾❙✷✵❈ ✷✸ ✷✴ ✹✾❁✾✴✹✾✴✵ ✺❍ ✵✶✾ ✽ ✺✹❑
✾❏✷✴● ✻✶✺✸✾✴
❭
✸✾✾
❜
❘ ✼❂❝❞❡❪❉
ÙÚÛÚ✄ é ãæ ßð☎ßñ õ åêßëáæ ì
✳✴ ✵✶✾ ✶ ✺❂✷➸✺✴✵❊❏ ❁ ❏❊✴ ✾✿ ❊✷❂✻❂❊❍✵ ❊❂✾ ●✷■✾✴ ✵✼❂✴✷✴ ●
❁ ✺✷✴✵ ✽ ❊✴✾✼ ■✾❂✸
❭
◆●✼❂✾ ❵❪❉ ❅ ✶✾ ✵✼ ❂✴ ✷✴● ❁ ✺✷✴✵ ❊✴●❏✾✸
❊❂✾ ➠❛✿ ❵❛ ✺❂ ➉❛ ✹ ✾●❂✾✾✸❉
❄ ✽ ❊✴✾✼■✾❂ ✷✸ ✹ ✾✵✾❂✽ ✷✴ ✾✹ ❋❈ ✵✶ ✾ ✽ ❊✴ ✾✼■✾❂ ✸✵❊❂✵✷✴ ●
✵✷✽ ✾ Ñ✆
✿ ✵✶ ✾ ✵✼ ❂✴ ✷✴● ❁✺✷✴✵ ✵✷✽ ✾ Ñ
❇
❊✴✹ ✵✶✾ ✹✾■✷❊✵✷✺✴
❊✴●❏✾ ✝❉
✳✴ ✵✶✾ ■✾❂✵✷✻❊❏ ❁❏❊✴✾✿ ❊✷❂✻❂❊❍✵ ✵❂❊è✾✻✵✺❂✷✾✸ ❊❂✾ ✹✷❑
■✷✹✾✹ ✷✴ Ó
❁ ✾❂✷✺✹ ✸
❭
◆ ●✼❂✾ ➉❪❉ ❘ ✼❂✷✴● ✵✶✾ ✻❏✷✽ ❋✷✴ ●
❁ ✾❂✷✺✹ ✿ ❊✷❂✻❂❊❍✵ ✻❊✴ ❋ ✾ ❏✾■✾❏✾✹ ❊✵ ❊ ❏✺❀ ✾❂ ✵✶❊✴ ❂✾❑
➩
✼✾✸✵✾✹ ◗✷●✶✵ ❏✾■✾❏ ✹✼ ❂✷✴● ❊ ✽ ✺✽ ✾✴✵ ✵✺ ❂✾✸✺❏■✾ ❊ ✻✺✴❑
◗✷✻✵❉ ➫ ✶✾✴ ❊✷❂✻❂❊❍✵ ✶ ❊■✾ ❂✾❊✻✶✾✹ ✵✶✾✷❂ ✹✾✸✷❂✾✹ ◗ ✷●✶✵
❏✾■✾❏✿ ✵✶✾❈ ✽ ❊❈ ❋ ✾ ✽ ✺■✾✹ ✵✺ ✵✶✾ ✴ ✾❊❂✾✸✵ ❏✺❀✾❂ ❏✾■✾❏ ✵✺
❂✾✸✺❏■✾ ❊ ✻✺✴◗✷✻✵❉ ➫ ✶ ✾✴ ❊✷❂✻❂❊❍✵ ❊❂✾ ❊❋ ✺✼✵ ➟❛ ✴ ❊✼ ✵✷✻
✽ ✷❏✾✸ ❍❂✺✽ ❋✾●✷✴✴✷✴ ● ✵✶✾✷❂ ✹✾✸✻✾✴✵ ✵✺ ✹✾✸✵✷✴❊✵✷✺✴ ✿✵✶✾❈
✞
⑥ ⑤❦✈ ♣♦♠♦❧t♥✈♥✉♠♥❽ ✟❦①➲✈❦t ♥✐① ✠⑤✟✡ s❧❦❥①♦t ❥♦①❦✈➃✉ ♠❦
✐ ❽①✐✉✉ ❦➁ s❧❦❥①♦t ➁❦❧ ➳❿♥❽❿ ♠❿♦❧♦ ✐❧♦ ✈❦ s❦①➲✈❦t ♥✐①☛♠♥t ♦ ✐①➃❦☛
❧♥♠❿t Ð✈❦➳✈ ♠❦ ✉❦①⑧♦ ♠❿♦ s❧❦❥①♦t ➀
Climbing Cruising End of Cruising
Descending
period period period
t t
t t t
t
0
0 0
1
1
1
❢ ✷●✼❂✾ ➉ ➞ ☞✾❂✵✷✻❊❏ ✽ ❊✴✾✼ ■✾❂ ✽ ✺✹ ✾❏✷✴● ❉
✽ ❊❈ ❋✾ ✽ ✺■✾✹ ✵✺ ❊ ❏✺❀✾❂ ❏✾■✾❏ ✵✺ ❂✾✸✺❏■✾ ❊ ✻✺✴◗✷✻✵❉
❘ ✼ ❂✷✴● ✵✶✾ ✹✾✸✻✾✴✵ ✴✺ ■✾❂✵✷✻❊❏ ✽ ❊✴ ✾✼■✾❂ ✷✸ ❁ ✺✸✸✷❋❏✾❉
❫
✺ ✽ ❊✴✾✼■✾❂ ✷✸ ✸✷✽ ✼❏✵❊✴✾✺✼ ✸❏❈ ✹✺✴✾ ✷✴ ✵✶ ✾ ✶ ✺❂✷❑
➸✺✴✵❊❏ ❊✴✹ ■✾❂✵✷✻❊❏ ❁❏❊✴ ✾❉ ❅ ✶✷✸ ✽ ✺✹✾❏ ✶❊✸ ✵✶✾ ●❂✾❊✵
❊✹ ■❊✴✵❊●✾ ✺❍ ❂✾✹ ✼✻✷✴● ✵✶✾ ✸✷➸✾ ✺❍ ✵✶✾ ❁❂✺❋ ❏✾✽ ❉ ✳✴ ✺❂❑
✹✾❂ ✵✺ ✸✺❏■✾ ✻✺✴◗✷✻✵ ✹✼ ✾ ✵✺ ❊✷❂✻❂❊❍✵ ✵❊P✷✴ ● ✺▲ ✺❂ ✾✴✵✾❂❑
✷✴● ✵✶ ✾ ❊✷❂✸❁❊✻✾ ✸✷✽ ✼ ❏✵❊✴ ✾✺✼✸❏❈ ❊✵ ✵✶✾ ✸❊✽ ✾ ❁ ✺✷✴✵✿ ❊
■❊❂✷❊❋❏✾ ✺❍ ✹✾❏❊❈ Ñ✌
✷✸ ✷✴✵❂✺✹✼✻✾✹ ❉
❢✺❂ ❊ ✻✺✴◗ ✷✻✵ ✷✴■✺❏■✷✴● û ❊✷❂✻❂❊❍✵✿✵✶✾ ✹✷✽ ✾✴✸✷✺✴ ✺❍
✵✶✾ ✸✾❊❂✻✶ ✸❁❊✻✾ ✷✸ Ó
û❉ ❅ ✶✷✸ ❀ ✷❏❏ ❊❏❏✺❀ ✼✸ ✵✺ ✸✺❏■✾ ■✾❂❈
✹✷▼ ✻✼ ❏✵ ✻✺✴◗✷✻✵✸ ❀ ✷✵✶ ✽ ❊✴❈ ❊✷❂✻❂❊❍✵ ❀ ✷✵✶✺✼✵ ✷✴■✾✸✵✷❑
●❊✵✷✴● ❊ ❏❊❂●✾ ✸✺❏✼✵✷✺✴ ✸❁❊✻✾❉
ÙÚÛ Ú✍ ✎ ù ß øðæ àäáåæ äå åÞ äáõ á✏ß
➨ ✴ ✾ ✺❍ ✵✶✾ ❁ ❂✷✴✻✷❁❊❏ ❊❏●✺❂✷✵✶ ✽ ✹✾✸✷●✴ ✻✶ ❊❏❏✾✴ ●✾✸ ✷✸ ✵✺
✹✾
◆
✴✾ ❊ ✸✼✷✵❊❋❏✾ ❍✼✴✻✵✷✺✴ ✵✺ ✺❁ ✵✷✽ ✷➸✾❉ ❄ ✽ ✼ ❏✵✷❁❏✾❑
✻❂✷✵✾❂✷❊ ❍✼✴ ✻✵✷✺✴ ✷✸ ❂✾
➩
✼✷❂✾✹ ✵✶ ❊✵ ✸✷✽ ✼❏✵❊✴✾✺✼✸❏❈ ❊✵❑
✵✾✽ ❁✵✸ ✵✺➞
➡
✽ ✷✴✷✽ ✷➸✾ ✵✶✾ ✹✾❏❊❈ ✹✼✾ ✵✺ ✹✾■✷❊✵✷✺✴✸ ✷✽ ❁ ✺✸✾✹ ✺✴
❊✷❂✻❂❊❍✵❉
➡
✽ ✷✴✷✽ ✷➸✾ ✵✶✾ ✵✺✵❊❏ ✴✼✽ ❋✾❂ ✺❍ ❂✾✸✺❏✼✵✷✺✴ ✽ ❊✴ ✾✼❑
■✾❂✸ ❂✾
➩
✼✷❂✾✹ ❊✴✹ ✵✶✾ ✵✺✵❊❏✴✼✽ ❋ ✾❂ ✺❍ ❊✷❂✻❂❊❍✵ ✵✶ ❊✵
❀✷❏❏ ❋✾ ✽ ✺■✾✹ ✑❉
➡
✽ ✷✴✷✽ ✷➸✾ ✵✶✾ ✽ ❊✴✾✼ ■✾❂ ✹✼❂❊✵✷✺✴ ✸✺ ✵✶ ❊✵ ❊✷❂✻❂❊❍✵
❊❂✾ ❍❂✾✾✹ ❊✸ ✸✺✺✴ ❊✸ ❁ ✺✸✸✷❋ ❏✾ ❍✺❂ ✽ ❊✴✾✼ ■✾❂✸ ✵✶ ❊✵
✽ ❊❈ ❋ ✾ ✴✾✻✾✸✸❊❂❈ ✸✼❋ ✸✾
➩
✼✾✴✵❏❈❉
➡
✾✴❍✺❂✻✾ ❊❏❏ ✸✾❁ ❊❂❊✵✷✺✴ ✻✺✴✸✵❂❊✷✴✵✸ ❋ ✾✵❀✾✾✴ ❊✷❂❑
✻❂❊❍✵❉
ÙÚÛ Ú✒ ✓ Þ äáõ á✏ãäáåæ äååë
➢ ✸✾ ✺❍ ❏✺✻❊❏ ✽ ✾✵✶ ✺✹ ✸✿✸✼✻✶ ❊✸ ●❂❊✹ ✷✾✴✵ ❍✺❂ ✾❙❊✽ ❁❏✾✿✷✸
✼✸✾❏✾✸✸ ✶✾❂✾✿ ❋✾✻❊✼✸✾ ✵✶ ✾✸✾ ✽ ✾✵✶ ✺✹✸ ❂✾❏❈ ✺✴ ✵✶✾ ❊❂❋✷❑
✵❂❊❂❈ ✻✶✺✷✻✾ ✺❍ ❊ ✸✵❊❂✵✷✴● ❁ ✺✷✴✵❉ ❬ ❊✻✶ ✻✺✴✴✾✻✵✾✹ ✻✺✽ ❑
❁✺✴✾✴✵ ✽ ❊❈ ✻✺✴✵❊✷✴ ✺✴✾ ✺❂ ✸✾■✾❂❊❏ ❏✺✻❊❏ ✺❁✵✷✽ ❊✿ ❊✴ ✹
✔
❹❿❺✉②♥✈✉♠♦✐♣ ❦➁ ✉❿✐❧♥✈➃ ♠❿♦ ➃①❦❥✐①♣♦①✐➲ ❦✈ ✐①①♠❿♦ ✐♥❧❽❧✐➁♠②
✉❦t ♦ ✐♥❧❽❧✐➁♠ ➳♥①① ✉❺ss❦❧♠ ✐ s✐❧♠ ❦➁ ♠❿♦ ♣♦①✐➲ ✐✈♣ ❦♠❿♦❧✉ ➳♥①①
❀✾ ✻❊✴ ✾❊✸✷❏❈ ✼ ✴✹✾❂✸✵❊✴✹ ✵✶ ❊✵ ✵✶✾ ✻✶✺✷✻✾ ✺❍ ✵✶ ✾ ✸✵❊❂✵❑
✷✴ ● ❁✺✷✴✵ ✷✴ ✺✴✾ ✺❍ ✵✶✾✸✾ ✻✺✽ ❁ ✺✴✾✴✵✸ ✻❊✴ ✴✺✵ ❏✾❊✹ ❋❈
❊ ❏✺✻❊❏ ✽ ✾✵✶✺✹ ✵✺ ❊✴ ✺❁✵✷✽ ✼ ✽ ✷✴ ❊✴✺✵✶ ✾❂ ✻✺✽ ❁✺✴✾✴✵❉
➫ ✾ ✻❊✴ ✵✶✼✸ ✾❙❁ ✾✻✵ ✺✴❏❈ ❊ ❏✺✻❊❏ ✺❁ ✵✷✽ ✼ ✽ ❉
❅ ✶✾ ❁❂✺❋ ❏✾✽ ✸✺❏■✾❂ ✼✸✾✸ ✕ ✾✴✾✵✷✻ ❄ ❏●✺❂✷✵✶ ✽ ✸
❭
✕ ❄ ✸❪
✵✺
◆
✴ ✹ ✵✶ ✸✾✵ ✺❍ ■❊❂✷❊❋❏✾✸
❭Ñ✌✖Ñ✆✖Ñ
❇
✖
✝❪ ✵✶ ❊✵ ✺❁✵✷✽ ✷➸✾✸
✵✶✾ ❊❋✺■✾ ✻❂✷✵✾❂✷❊❉ ✕ ❄ ✸ ❊❂✾ ●❏✺❋ ❊❏ ✸✵✺✻✶ ❊✸✵✷✻ ✺❁✵✷❑
✽ ✷➸❊✵✷✺✴ ✵✾✻✶✴ ✷✻✸ ✵✶ ❊✵ ✽ ✷✽ ✷✻ ✴ ❊✵✼❂❊❏ ✾■✺❏✼✵✷✺✴ ❉ ❅✶ ✾❈
❀✾❂✾ ✷✴✷✵✷❊❏❏❈ ✹✾■✾❏✺❁ ✾✹ ❋❈ ✗✺✶ ✴ î ✺❏❏❊✴✹
❜î
✺❏ Ô
➟❡ ✷✴
✵✶✾ ✸✷❙✵✷✾✸❉ ❅ ✶✾ ✸✼❋è✾✻✵ ✺❍ ✵✶✷✸ ❁❊❁✾❂ ✷✸ ✴✺✵ ✕ ❄ ✸ ❊✴✹
✵✶✾ ✷✴✵✾❂✾✸✵✾✹ ❂✾❊✹✾❂ ✸✶✺✼❏✹ ❂✾❊✹ ✵✶✾ ❊❁❁❂✺❁❂✷❊✵✾ ❏✷✵❑
✾❂❊✵✼❂✾ ✺✴ ✵✶✾ ✸✼❋è✾✻✵
❜
✕ ✺❏✘❝❡❉
✕ ✾✴ ✾✵✷✻ ❊❏●✺❂✷✵✶✽ ✸ ❊❂✾ ❊ ■✾❂❈ ❁✺❀ ✾❂❍✼❏ ✵✺✺❏✿ ❋✾❑
✻❊✼✸✾ ✵✶✾❈ ✹✺ ✴✺✵ ❂✾
➩
✼✷❂✾ ✽ ✼✻✶ ✷✴❍✺❂✽ ❊✵✷✺✴ ❊✴✹ ❊❂✾
❊❋❏✾ ✵✺
◆
✴✹ ✽ ❊✴❈ ✹ ✷▲✾❂✾✴✵ ✺❁ ✵✷✽ ❊ ✵✶ ❊✵ ✻❊✴ ❋✾ ❁ ❂✾❑
✸✾✴✵✾✹ ✵✺ ❊ ✶✼✽ ❊✴ ✺❁ ✾❂❊✵✺❂❉
❖ ✺❂✾✺■✾❂✿ ❀✾ P✴✺❀ ✽ ✼ ✻✶ ❊❋ ✺✼ ✵ ✵✶✾ ❍✼ ✴✻✵✷✺✴ ✵✺
✺❁✵✷✽ ✷➸✾ ❊✴ ✹ ✵✶✷✸ ✷✴❍✺❂✽ ❊✵✷✺✴ ✻❊✴ ❋✾ ✼✸✾✹ ✵✺ ✻❂✾❊✵✾
❊✹❊❁ ✵✾✹ ✻❂✺✸✸✺■✾❂
❜
❘ ❄
❫
❝❞❡ ❊✴✹ ✽ ✼ ✵❊✵✷✺✴ ✺❁✾❂❊✵✺❂✸✿
❊✴ ✺✵✶✾❂ ❊✹■❊✴✵❊●✾ ✺❍ ✕ ❄ ✸ ✺■✾❂ ✺✵✶✾❂ ✺❁✵✷✽ ✷➸❊✵✷✺✴
✵✾✻✶ ✴✷✻✸❉
➶ ➍➶ ➺ ➹ Ö ➒❒❐➬ ✃➒ ➹✙ ↔✃➓ ➣➒ ➮➘→❐
❴ ✾❊✻✵✷■✾ ❂✾✸✺❏✼✵✷✺✴ ✽ ✾✵✶✺✹✸ ✸✷✽ ✷❏❊❂ ✵✺ ✵✶ ✺✸✾ ✹✾■✾❏❑
✺❁✾✹ ❋❈ ✚ ❊❂✷✽ ✛✾●✶ ❊❏
❭❜
✛✾●❝➉✿ ✛✾●❝ Ó
❡❪ ❊❂✾ ✼✸✾✹ ✷✴
✵✶✷✸ ❁ ❊❂✵❉ ❅ ✶✾✷❂ ✽ ❊✷✴ ❊✹ ■❊✴✵❊●✾ ✷✸ ✸✷✽ ❁❏✷✻✷✵❈ ✺❍ ✹✾■✾❏❑
✺❁✽ ✾✴✵ ❊✴ ✹ ✼ ✸✾✿ ✸✷✴✻✾ ✴✺ ✾❙✵❂❊❁✺❏❊✵✷✺✴ ✺❍ ✵❂❊è✾✻✵✺❂✷✾✸
✷✸ ✴✾✻✾✸✸❊❂❈❉ ❅ ✶✾ ✽ ✷✴✷✽ ❊❏ ✸✾✵ ✺❍ ✷✴❍✺❂✽ ❊✵✷✺✴ ✻✺✴ ✻✾❂✴❑
✷✴ ● ❊✴ ✷✴✵❂✼✹ ✾❂ ❊✷❂✻❂❊❍✵ ✷✸ ✹ ✷✸✵❊✴✻✾✿ ❊❏✵✷✵✼ ✹✾✿ ❊➸✷✽ ✼ ✵✶ ✿
❂✾❏❊✵✷■✾ ✸❁✾✾✹ ✿ ❊✴✹ ✵✶✾ ✷✴✵❂✼✹✾❂➭✸ ✵❈❁✾ ✺❍ ❋✾✶❊■✷✺✼❂
❭
❊■✺✷✹ ❊✴✻✾ ❀ ✷✵✶ ❊✴ ✷✹✾✴✵✷✻❊❏ ✺❂ ✹✷▲✾❂✾✴✵ ✽ ✾✵✶ ✺✹ ✿ ✷✴❑
✵✾❂✻✾❁✵✷✺✴❪❉ ❆✺✽ ✾ ❊✹✹ ✷✵✷✺✴❊❏ ✷✴❍✺❂✽ ❊✵✷✺✴ ✿ ✷✴ ❁❊❂✵✷✻✼❑
❏❊❂ ❁❏❊✴✴✾✹ ✻✶ ❊✴●✾✸ ✷✴ ✻✺✼❂✸✾ ✺❂ ■✾❂✵✷✻❊❏ ✸❁✾✾✹ ✿ ✻❊✴ ❋✾
✶✾❏❁❍✼❏❉
➊✷✽ ✷✵❊✵✷✺✴✸ ✶❊■✾ ❋✾✾✴ ❁ ✼✵ ✺✴ ❊✷❂✻❂❊❍✵ ✽ ❊✴✾✼ ■✾❂✸❉
❫
✺ ✸❁ ✾✾✹ ✻✶ ❊✴●✾ ✷✸ ❊❏❏✺❀ ✾✹ ❊✴✹ ✺✴❏❈ ❏❊✵✾❂❊❏ ✽ ❊✴✾✼ ■✾❂✸
❊❂✾ ●✷■✾✴ ❉ ❅✺ ✷✽ ❁❂✺■✾ ✻✺✴◗ ✷✻✵ ❂✾✸✺❏✼✵✷✺✴ ❋ ✾✵❀✾✾✴ ❊✷❂❑
✻❂❊❍✵ ❍✺❏❏✺❀ ✷✴●
➩
✼❊✸✷❑❁❊❂❊❏❏✾❏ ✵❂❊✻P✸
❭
❁ ❊✸✸❑✺■✾❂ ✺❂ ✻✺✴❑
■✾❂●✾✴✻✾ ❀✷✵✶ ❊ ✸✽ ❊❏❏ ❊✴●❏✾❪✿ ❊ ❂✾❁ ✼❏✸✷■✾ ✻✺✽ ❁ ✺✴✾✴✵
✶❊✸ ❋✾✾✴ ❊✹✹✾✹ ✵✺ ✵✶✾ ❍✺❂✻✾ ■✾✻✵✺❂❉ ❅ ✶✾ ❂✾❁❊❂✵✷✵✷✺✴
❋ ✾✵❀ ✾✾✴ ✵✶✾ ✵❀✺ ✻✺✽ ❁ ✺✴✾✴✵✸ ✹✾❁✾✴✹✸ ✺✴ ✵✶ ✾ ✻✺✴◗ ✷✻✵
●✾✺✽ ✾✵❂❈❉ ❅ ✶✾ ❂✾✸✼ ❏✵✷✴● ❍✺❂✻✾ ✷✸ ❁✼❂✾❏❈ ✵❊✴●✾✴✵✷❊❏ ✷❍
❋ ✺✵✶ ❊✷❂✻❂❊❍✵ ❊❂✾ ✺✴ ❊ ✻✺❏❏✷✹✷✴ ● ✻✺✼❂✸✾ ❊✴✹ ❁✼ ❂✾❏❈ ❂✾❑
❁✼ ❏✸✷■✾ ✷❍ ✵✶✾❈ ◗❈ ✺✴ ❁ ❊❂❊❏❏✾❏ ✵❂❊✻P✸❉
❅ ✶✾ ✷✴✵✾✴ ✸✷✵❈ ✺❍ ✵✶✾ ❊■✺✷✹❊✴✻✾ ❍✺❂✻✾ ✷✸ ❁❂✺❁✺❂✵✷✺✴ ❊❏
✵✺ ✵✶✾ ✷✴■✾❂✸✾ ✺❍ ✵✶✾ ✵✷✽ ✾ ❂✾✽ ❊✷✴ ✷✴● ✼✴✵✷❏ ✴ ✺❂✽ ❊❏ ✸✾❁ ❊❑
❂❊✵✷✺✴ ❀ ✷❏❏❋ ✾ ❏✺✸✵❉ ❄ ✴ ❊✵✵❂❊✻✵✷✺✴ ✵✺❀❊❂✹ ✸ ✵✶✾ ❊✷❂✻❂❊❍✵➭✸
✹✾✸✵✷✴❊✵✷✺✴ ✷✸ ❊✹✹✾✹ ✵✺ ✵✶✾ ✵✺✵❊❏ ❍✺❂✻✾❑■✾✻✵✺❂
❭
✵✶✾ ✻✼❂❑
❂✾✴✵ ✷✽ ❁❏✾✽ ✾✴✵❊✵✷✺✴ ✺✴❏❈ ❊❏❏✺❀✸ ✸✵❂❊✷●✶✵ ❂✺✼✵✾ ✴❊■✷❑
●❊✵✷✺✴❪❉ ❅✶ ✾ ❊✷❂✻❂❊❍✵ ✵✶✾✴ ✵❂✷✾✸ ✵✺ ❂✾❊✻✶ ✵✶ ✾ ❂✾✸✼❏✵✷✴ ●
✹✷❂✾✻✵✷✺✴ ✿ ❀ ✷✵✶ ❊ ❏✷✽ ✷✵ ✺❍ ➉✜✢✝ ✺✴ ✵✶✾ ✵✼ ❂✴ ✷✴● ❂❊✵✾❉
●✾✴✾❂❊✵✾✸ ✸✽ ✺✺✵✶ ✵❂❊è✾✻✵✺❂✷✾✸
❭
❀ ✶ ✷✻✶ ✶ ✺❀✾■✾❂ ❊❂✾ ✴ ✺✵
◗ ❈❊❋❏✾ ❋❈ ❊ ✶✼✽ ❊✴ ❁✷❏✺✵ ✸✷✴✻✾ ✹✼ ❂✷✴● ✽ ❊✴✾✼■✾❂✸ ✶ ✾❊✹❑
✷✴● ✻✶ ❊✴●✾✸ ✸❏✷●✶✵❏❈ ❊✵ ✾■✾❂❈ ✸✵✾❁ ✺❍ ✻✺✽ ❁✼✵❊✵✷✺✴ ❪❉
❆✺✽ ✾ ❁❂✺❋❏✾✽ ✸ ✸✵✷❏❏ ✺✻✻✼ ❂ ✷✴ ✻❊✸✾✸ ❀ ✶✾❂✾ ✵✶✾ ❊✴●❏✾
❋✾✵❀ ✾✾✴ ✵✶✾ ✵❀ ✺ ✵❂❊è✾✻✵✺❂✷✾✸ ✷✸ ✸✽ ❊❏❏ ❊✴ ✹ ✵✶✾ ❂❊✵✷✺ ✺❍
✵✶✾ ✸❁ ✾✾✹✸ ✷✸ ✻❏✺✸✾ ✵✺ ➠✣❉
❅ ❀✺ ✹✷▲✾❂✾✴✵ ✷✽ ❁❏✾✽ ✾✴✵❊✵✷✺✴✸ ✶❊■✾ ❋ ✾✾✴ ✵✾✸✵✾✹ ❉
➨ ✴ ✾ ✷✸ ✵❂✼ ❏❈ ❂✾❊✻✵✷■✾✿ ❊❏❏ ✷✴✵❂✼ ✹✾❂ ❊✷❂✻❂❊❍✵ ❊❂✾ ✵❊P✾✴
✷✴✵✺ ❊✻✻✺✼✴✵✿ ❀ ✶ ✷✻✶ ✷✴ ✻❏✼ ✹✾✸ ✽ ❊✴❈ ❊✷❂✻❂❊❍✵ ✵✶❊✵ ✹✺✴ ➭✵
❂✾❊❏❏❈ ✻✺✴✸✵✷✵✼ ✵✾ ❊ ✵✶❂✾❊✵❉ ❅ ✶✾ ✺✴❏❈ ❁ ❊❂❊✽ ✾✵✾❂✸ ✼✸✾✹
✵✺ ✹✷✸✵✷✴●✼ ✷✸✶ ❊✷❂✻❂❊❍✵ ✵✶❊✵ ✽ ❊❈ ●✾✴✾❂❊✵✾ ❊ ✻✺✴◗✷✻✵ ❊❂✾
✹✷✸✵❊✴ ✻✾ ❊✴ ✹ ✻❏✺✸✷✴● ✸❁ ✾✾✹ ✿ ✵✶✾❂✾❍✺❂✾ ✵✶ ✾ ✸✾❏✾✻✵✷✺✴ ❁ ❂✺❑
✻✾✸✸ ✷✸ ✴✺✵ ■✾❂❈ ✾▼ ✻✷✾✴✵❉
✳✴ ✵✶✾ ✺✵✶ ✾❂ ■✾❂✸✷✺✴ ✿ ❊✷❂✻❂❊❍✵ ✵❂❊è✾✻✵✺❂✷✾✸ ❊❂✾
◆
❂✸✵
✸✷✽ ✼ ❏❊✵✾✹
❭
❀ ✷✵✶✺✼✵ ❂✾✸✺❏✼✵✷✺✴ ✿ ✷✾ ❊✷❂✻❂❊❍✵ ◗ ❈ ✸✵❂❊✷●✶✵
✵✺ ✵✶ ✾✷❂ ✹✾✸✵✷✴ ❊✵✷✺✴ ❪ ✵✺ ✹ ✾✵✾✻✵ ❍✼✵✼❂✾ ✻✺✴◗✷✻✵✸❉ ❅ ❈❁✷❑
✻❊❏❏❈ ✵✶✾ ✸✷✽ ✼❏❊✵✷✺✴ ✺✻✻✼ ❂✸ ✾■✾❂❈ ➠ ✵✺ ➟ ✽ ✷✴✼✵✾✸✿ ❊✴ ✹
✸❁❊✴ ✸ ✺■✾❂ ✵✶✾ ✴✾❙✵ ➟ ✵✺ ❵❛ ✽ ✷✴✼ ✵✾✸❉ ❄ ✴ ✷✴✻❂✾❊✸✾✹
✶✺❂✷➸✺✴✵❊❏ ✸✾❁❊❂❊✵✷✺✴
❭
✼ ✸✼ ❊❏❏❈ ✵❀ ✷✻✾ ✵✶✾ ✴✺❂✽ ❊❏ ✸✾❁ ❊❑
❂❊✵✷✺✴❪ ❊✴✹ ✵✶✾ ✼✴ ✻✾❂✵❊✷✴✵❈ ❊❁❁❂✺❙✷✽ ❊✵✷✺✴ ✹✾✸✻❂✷❋✾✹
✷✴ ❁❊❂✵ ➉❉➠ ❊❂✾ ✼ ✸✾✹ ✵✺ ❋ ✼✷❏✹ ✻❏✼✸✵✾❂✸❉ ❅ ✶✾ ✻✺✽ ❁✼✵❊❑
✵✷✺✴ ✺❍ ❂✾❊✻✵✷■✾ ❍✺❂✻✾✸ ✷✸ ✵✶✾✴ ✺✴ ❏❈ ❊❁ ❁❏✷✾✹ ✵✺ ❊✷❂✻❂❊❍✵
✺❍ ✵✶✾ ✸❊✽ ✾ ✻❏✼✸✵✾❂✸❉ ❅ ✶✾ ✵✷✽ ✾ ✺❍ ✻✺✽ ❁✼ ✵❊✵✷✺✴ ✷✸ ❊❁❑
❁❂✺❙✷✽ ❊✵✾❏❈ ✹✷■✷✹ ✾✹ ❋❈ ❞ ❉
✤ ✮ ❳ ❱ ✱ ➾ ✭ ❱
❅ ✶✾ ❂✾✸✼❏✵✸ ❁❂✾✸✾✴✵✾✹ ❋ ✾❏✺❀ ❊❂✾ ✸✷✽ ✼ ❏❊✵✷✺✴ ✸ ✼✸❑
✷✴● ✹ ✷▲✾❂✾✴✵ ✽ ✺✹✼ ❏✾✸ ❂✾●❊❂✹✷✴● ✵✶✾ ✻✾✴✵❂❊❏✷➸✾✹ ❁❂✺❋❑
❏✾✽ ✸✺❏■✾❂ ❊✴✹ ✵✶✾ ✺✴ ❋ ✺❊❂✹ ✻✺✴◗ ✷✻✵ ✸✺❏■✾❂ ❁❂✾✸✾✴✵✾✹
❊❋ ✺■✾✿ ❊✴✹ ✵✶✾ ✷✽ ❁ ❊✻✵ ✺❍ ❂✾✹✼✻✾✹ ■✾❂✵✷✻❊❏ ✸✾❁❊❂❊✵✷✺✴
✽ ✷✴✷✽ ❊
❭
❴☞ ❆ ❖ ❪ ✺✴ ✻✺✴◗✷✻✵ ❀✺❂P❏✺❊✹ ✿ ❋✼✷❏✵ ✺✴ ✵✺❁ ✺❍
✵✶✾ ❃ ❄❅ ❆ ✸✷✽ ✼ ❏❊✵✺❂❉ ❅ ✶✾✸✾ ✸✷✽ ✼❏❊✵✷✺✴ ❊❂✾ ✴✺✵ ✾❙❑
✶❊✼✸✵✷■✾ ❊✴✹ ❊❂✾ ✾❙ ❊✽ ❁❏✾✸ ✺❍ ✵✶✾ ❁ ✺✸✸✷❋ ✷❏✷✵✷✾✸ ✺▲✾❂✾✹
❋❈ ❃❄ ❅ ❆ ❉
✥ ➍➎ ➙ → ➹➓❐❒➮↔Õ→➬ ➑ ❐➒ Ö ➮→ ➷ ➣➒➮➘ →❐
❄ ✻✺✽ ❁ ❏✾✵✾ ✾❙❁ ✾❂✷✽ ✾✴✵ ✹✺✴✾ ❀ ✷✵✶ ✼✴❂✾●✼ ❏❊✵✾✹
◗ ✷●✶✵ ❁❏❊✴✸ ✺❍ ✵✶ ✾ ❵➠✵✶ ✺❍ ✗✼ ✴✾ ➠❝❝❞ ✷✸ ✹✾✸✻❂✷❋✾✹ ✶ ✾❂✾❉
✳✵ ✷✴■✺❏■✾✸ ❞➉✘✘ ❊✷❂✻❂❊❍✵ ✺■✾❂ ❢❂❊✴ ✻✾❉ ➢ ✴✻✾❂✵❊✷✴✵✷✾✸ ✺✴
✻❏✷✽ ❋ ✷✴● ❂❊✵✾ ❊✴✹ ●❂✺✼ ✴✹ ✸❁ ✾✾✹ ❊❂✾ ❂✾✸❁ ✾✻✵✷■✾❏❈ ✸✾✵ ✵✺
❵❛✦ ❊✴✹ ➟✦ ✿❊✴✹ ✸✵❊✴ ✹❊❂✹ ✸✾❁❊❂❊✵✷✺✴✸ ❊❂✾ ✸✾✵ ✵✺ ❞ ✴ ✽
❊✴ ✹ ➠❛❛❛ ❍✾✾✵❉ ❅ ✶✾ ✾❙❁✾❂✷✽ ✾✴✵ ✷✸ ❂✼✴ ✼ ✴✹✾❂ ✵✶✾ ❘ ✷❂✾✻✵
❴ ✺✼ ✵✾ ✶❈❁ ✺✵✶✾✸✷✸
❭
❊✷❂✻❂❊❍✵ ❊❂✾ ❊❏❏✺❀✾✹ ✵✺ ●✺ ✹✷❂✾✻✵❏❈
✵✺ ✵✶✾✷❂ ✹✾✸✵✷✴❊✵✷✺✴ ❪❉ ➫ ✾ ✺✴❏❈ ✹✾✵✾✻✵ ❊✴ ✹ ✸✺❏■✾ ✻✺✴❑
◗ ✷✻✵✸ ❊❋✺■✾ ➠❛❛❛❛ ❍✾✾✵✿ ❊✸ ❀ ✾ ❊❂✾ ✺✴❏❈ ✷✴✵✾❂✾✸✵✾✹ ✷✴ ❬ ✴
❴ ✺✼ ✵✾ ✻✺✴◗ ✷✻✵✸❉ ❄ ✷❂✻❂❊❍✵ ✾✴✵✾❂✷✴● ❩❊❂✷✸ ❅ ❖ ❄ ✻✺✴✵❂✺❏
✧
❹❿♦✉♦ ❽✐✉♦✉ ✐❧♦ Ð✈❦➳✈ ♠❦ ❥♦ ♠❿♦ t ❦✉♠ ♣♥➇ ❽❺①♠ ♠❦
➩
✻✺✴✵❂✺❏ ✷✸ ✹ ✺✴✾ ✷✴ ✸✷✹✾ ✵✶✾ ❅ ❖ ❄ ❉ ❅ ✶✾ ✸✷✽ ✼ ❏❊✵✷✺✴ ❀ ❊✸
❁ ✾❂❍✺❂✽ ✾✹ ✷✴ ❂✾❊❏ ✵✷✽ ✾ ✺✴ ➟ ❁ ✾✴✵✷✼✽ ❵❛❛ ❉
➫ ✶ ✾✴ ❂✼✴ ✴✷✴● ✵✶✷✸ ✺✴✾ ✹ ❊❈ ✵✾✸✵ ❀ ✷✵✶ ❊ ■✾❂❈ ❋❊✸✷✻
✻✺✴◗ ✷✻✵ ✹✾✵✾✻✵✷✺✴ ❊❏●✺❂✷✵✶✽
❭
✺✴❏❈ ❊✻✵✼ ❊❏ ✻✺✴◗✷✻✵✸ ❊❂✾
✹✾✵✾✻✵✾✹ ✿ ❀ ✷✵✶ ✴✺ ✼✴✻✾❂✵❊✷✴✵❈ ✺✴ ✸❁✾✾✹ ❪ ❊✴✹ ❀ ✷✵✶ ✴ ✺
✻✺✴◗ ✷✻✵ ❂✾✸✺❏✼✵✷✺✴ ✿ ➠❞ Ó
❝ ✻✺✴◗ ✷✻✵✸ ❊❂✾ ✹ ✾✵✾✻✵✾✹ ❉
➫ ✶ ✾✴ ❂✼✴✴ ✷✴● ✵✶✾ ✻✺✽ ❁ ❏✾✵✾ ✸✷✽ ✼❏❊✵✷✺✴ ❀ ✷✵✶ ✹ ✾✵✾✻❑
✵✷✺✴ ❊✴✹ ❂✾✸✺❏✼ ✵✷✺✴ ✿✵✶ ✾ ❘ ❃ ❁❂✺✻✾✸✸ ✹✾✵✾✻✵✸ ➟❛❞ Ó
➠❑✵✺❑➠
✹✷▲✾❂✾✴✵ ✻✺✴◗ ✷✻✵✸
❭
❅ ✶✷✸ ✽ ✾❊✴✸ ✵✶❊✵ ❊ ✹✾✵✾✻✵✾✹ ✻✺✴◗ ✷✻✵
✶❊✸
❇✑❮✭
✂
✆
✑❮ Ò
➉❵✮❞✦ ✻✶ ❊✴✻✾ ✵✺ ❂✾❊❏❏❈ ✺✻✻✼❂❉ ❅ ✶✾ ❁❂✺❋❏✾✽
✸✺❏■✾❂ ❂✾✸✺❏■✾✸ ❝➠➉❛ ✻❏✼✸✵✾❂✸ ✺❍ ✹✷▲✾❂✾✴✵ ✸✷➸✾✸
❭
❍❂✺✽ ❵
✵✺ ➉❵ ❊✷❂✻❂❊❍✵❪❉ ❅ ✶✾❂✾ ❊❂✾ Ó
➠➟➟ ✻❏✼ ✸✵✾❂✸ ✷✴ ✻❏✼ ✹✷✴ ● ✹✷❍❑
❍✾❂✾✴✵ ✸✾✵✸ ✺❍ ❊✷❂✻❂❊❍✵❉ ❅ ✶✾❂✾ ✷✸ ✴✺ ✼✴✸✺❏■✾✹ ✻❏✼✸✵✾❂
❊✴✹ ✻✺✴✸✾
➩
✼✾✴✵❏❈ ✴ ✺ ✻✺✴◗ ✷✻✵ ❂✾✽ ❊✷✴ ✸❉
➨ ✴ ❏❈ ➠❞✘ Ô
❊✷❂✻❂❊❍✵ ❊❂✾ ●✷■✾✴ ❵❵❛❛ ✽ ❊✴ ✾✼■✾❂✸ ❀ ✶✷✻✶
❂✾❁❂✾✸✾✴✵✸ ➠✮➉ ✽ ❊✴✾✼ ■✾❂ ❁ ✾❂ ❊✷❂✻❂❊❍✵❉ ❅ ✶✾ ✽ ✾❊✴ ✹ ✼❂❊❑
✵✷✺✴ ✺❍ ❊ ✽ ❊✴✾✼ ■✾❂ ✷✸ ❵✯ û❵➉✝❉
➠➉➉ Ô
❊✷❂✻❂❊❍✵ ❊❂✾ ✹✾❏❊❈✾✹ ❋ ✾❍✺❂✾ ✵❊P✷✴● ✺▲ ✺❂ ✾✴✵✾❂❑
✷✴ ● ✵✶✾ ❢❂✾✴ ✻✶ ❊✷❂✸❁❊✻✾❉ ❢✺❂ ✵✶✾✸✾ ❊✷❂✻❂❊❍✵✿ ✵✶✾ ✽ ✾❊✴
✵❊P✾ ✺▲ ✺❂ ✾✴✵✾❂✷✴● ✹✾❏❊❈ ✷✸ ❵✯ û➟❞✝
❭
✽ ❊❙✷✽ ✼✽ ❞✯ û❪❉
❅ ✶✾ ●❏✺❋ ❊❏ ✽ ✾❊✴ ✵❊P✾ ✺▲ ✺❂ ✾✴✵✾❂✷✴● ✹✾❏❊❈ ✷✸ ➉ Ô
✝❉
❅ ✶✾ ✽ ✾❊✴ ✽ ❊✴✾✼■✾❂ ✹✼ ❂❊✵✷✺✴ ✾❙❁✾✻✵❊✵✷✺✴ ❁ ✾❂ ❊✷❂❑
✻❂❊❍✵ ✷✸ Ó
❝✝ ❀✶ ✷✻✶ ❂✾❁ ❂✾✸✾✴✵✸ ➠✮ Ô
❝✦ ✺❍ ✵✶✾ ◗ ✷●✶✵ ✹ ✼❂❊❑
✵✷✺✴ ❉
❅ ✶✾ ✽ ✾❊✴ ◗ ✷●✶✵ ✹✼❂❊✵✷✺✴ ✷✸ Ó
➟✯ û➟
Ó
✝ ❋ ✾❍✺❂✾ ❂✾✸✺❑
❏✼ ✵✷✺✴ ❊✴✹ Ó
➟✯ û➟✘✝ ❊❍✵✾❂ ❂✾✸✺❏✼✵✷✺✴ ❉ ❅ ✶✾ ✽ ✾❊✴ ✹ ✾❑
❏❊❈ ✻❊✼ ✸✾✹ ❋❈ ✽ ❊✴✾✼■✾❂✸ ✷✸ Ó
✝❉ ➨ ✴ ❏❈ ❝➉
Ó
❊✷❂✻❂❊❍✵ ❊❂✾
✹✾❏❊❈✾✹ ❋✾✻❊✼✸✾ ✺❍ ✽ ❊✴ ✾✼■✾❂✸
❭
✽ ✺✸✵ ✺❍ ✵✶✾ ❊✷❂✻❂❊❍✵
✽ ✺■✾✹ ✷✴ ✵✶✾ ■✾❂✵✷✻❊❏ ❁❏❊✴✾ ❊❂✾ ✴✺✵ ✹ ✾❏❊❈✾✹❪❉ ❅✶ ✾
✽ ❊❙✷✽ ✼✽ ✹✾❏❊❈ ✷✸ Ó
✯ û ❊✴ ✹ ✵✶✾ ✽ ✾❊✴ ✹✾❏❊❈
❭
❍✺❂ ❊✷❂❑
✻❂❊❍✵ ✹ ✾❏❊❈✾✹❪ ✷✸ ❵❝✝❉
❅ ✶✷✸ ✸✷✽ ✼❏❊✵✷✺✴ ●✷■✾✸ ❊ ●✺✺✹ ✷✹✾❊ ✺❍ ✵✶ ✾ ❊❋✷❏✷✵❈ ✺❍
✵✶✾ ❁❂✺❋❏✾✽ ✸✺❏■✾❂ ✵✺ ✸✺❏■✾ ✾✴ ❂✺✼✵✾ ✻✺✴◗ ✷✻✵✸ ❀ ✷✵✶ ❊✻❑
✵✼❊❏ ✵❂❊▼ ✻❉ ❖ ✺❂✾ ✹ ✾✵❊✷❏✸ ✻❊✴ ❋ ✾ ❍✺✼✴✹ ✷✴
❜❘
❄ ❝
Ô
❡❉
✥ ➍➌ ➺ ➹ Ö ➒❒❐➬ ✃➒ ➹✙ ↔✃➓ ➣➒ ➮➘→❐
➫ ✶ ✾✴ ✼✸✷✴● ✵✶✾ ✺✴ ❋✺❊❂✹ ✻✺✴◗✷✻✵ ✸✺❏■✾❂ ✺✴ ✸✷✽ ✷❏❊❂
✹❊✵❊✸✿ ❋ ✺✵✶ ■✾❂✸✷✺✴✸
❭
✷❉✾❉✿ ❀ ✷✵✶ ❊✴ ✹ ❀ ✷✵✶ ✺✼✵ ✻✺✴◗ ✷✻✵
❁❂✾❑✹✾✵✾✻✵✷✺✴❪ ●✷■✾ ✸✷✽ ✷❏❊❂ ❂✾✸✼❏✵✸ ❂✾●❊❂✹✷✴ ● ✵✶✾ ✴✼✽ ❑
❋ ✾❂ ✺❍ ✼✴✸✺❏■✾✹ ✻✺✴◗✷✻✵✸❉ ❅ ✶✾ P✴✺❀ ❏✾✹●✾ ✺❍ ❍✼ ✵✼ ❂✾
✵❂❊è✾✻✵✺❂✷✾✸ ❂✾✹✼ ✻✾✸ ✵✶✾ ❊✽ ✺✼✴✵ ✺❍ ❁❂✺✻✾✸✸✷✴●
❭
❋✼✵ ✵✶✾
■✺❏✼ ✽ ✾ ✺❍ ✹ ❊✵❊ ✵✺ ✵❂❊✴✸✽ ✷✵ ✷✸ ✷✴ ✻❂✾❊✸✾✹ ❪✿ ❊✴✹ ❊❏✸✺ ✵✶✾
✴✼✽ ❋✾❂ ✺❍ ✼✸✾❏✾✸✸ ❊■✺✷✹ ❊✴✻✾ ✽ ❊✴ ✾✼ ■✾❂✸❉ ❅✶ ✾ ❊■✾❂❊●✾
✷✴ ✻❂✾❊✸✾ ✷✴ ◗✷●✶✵ ✵✷✽ ✾ ✷✴✹✼ ✻✾✹ ❋❈ ✽ ❊✴✾✼ ■✾❂✸ ✷✸ ❛❉➉✦
❭
✻✺✽ ❁❊❂✾✹ ✵✺ ➠❉➟✦ ❀ ✷✵✶ ✵✶ ✾ ❁✼❂✾❏❈ ❂✾❊✻✵✷■✾ ■✾❂✸✷✺✴❪❉
❅ ✶✾ ✽ ❊✴✾✼■✾❂✷✴ ● ✵✷✽ ✾ ✷✸ ❊❁ ❁❂✺❙✷✽ ❊✵✾❏❈ ➠❛✦ ❉
0 500 1000 1500 2000 2500 3000 3500 4000 4500
1 2 3 4 5 6 7
Conflicts
Density
No resolution 2 sep, 5 mn 2 sep, 1 mn 1 sep, 5 mn
❢ ✷●✼❂✾ Ó
➞
❫
✼✽ ❋ ✾❂ ✺❍ ✸✾❁❊❂❊✵✷✺✴ ❏✺✸✸✾✸ ■✸ ✹ ✾✴✸✷✵❈
0 20 40 60 80 100 120 140 160 180
1 2 3 4 5 6 7
%
Density
2 sep, 5 mn 2 sep, 1 mn 1 sep, 5 mn
❢✷●✼ ❂✾ ➟➞ ❩ ✾❂✻✾✴✵❊●✾ ✺❍ ✼✴ ✸✺❏■✾✹ ✻✺✴◗✷✻✵✸ ■✸ ✹✾✴ ✸✷✵❈
ôÚÛ ÚÜ ✰ ß çð ëäç ✱ áäù ✲æ å✱ ëß êìß åø øðäð ñß äñã✳ß à✴
äåñáßç
❢ ✷●✼ ❂✾ Ó
✸✶✺❀✸ ✵✶✾ ✾■✺❏✼✵✷✺✴ ✺❍ ✵✶✾ ✴✼ ✽ ❋ ✾❂ ✺❍ ✸✾❁ ❊❑
❂❊✵✷✺✴ ❏✺✸✸✾✸ ■✾❂✸✼ ✸ ✵❂❊▼ ✻ ✹✾✴ ✸✷✵❈✿ ❋ ✺✵✶ ❀ ✷✵✶✺✼✵
❭
❊❏❑
✽ ✺✸✵ ✸✵❂❊✷●✶✵ ❏✷✴✾✵❪ ❊✴ ✹ ❀✷✵✶ ➉ ✺✵✶ ✾❂ ✻✺✴◗✷✻✵ ❂✾✸✺❏✼❑
✵✷✺✴ ❉ ❴✾✸✺❏✼✵✷✺✴ ✷✸ ❁ ✾❂❍✺❂✽ ✾✹ ❀✷✵✶ ❁❂✾❑✹✾✵✾✻✵✷✺✴ ✺❍
✻✺✴◗✷✻✵✸✿ ❀ ✷✵✶ ✹✷▲✾❂✾✴✵ ✻✺✴ ✹✷✵✷✺✴✸ ❍✺❂ ✾❊✻✶ ✻✼❂■✾ ➞ ❂✾❑
✸❁✾✻✵✷■✾❏❈ ✾■✾❂❈ ➟ ✽ ✴ ❀ ✷✵✶ ✵❀ ✷✻✾ ✵✶✾ ✴✺❂✽ ❊❏ ✸✾❁❊❂❊❑
✵✷✺✴ ✿ ✾■✾❂❈ ✽ ✷✴✼✵✾ ❀ ✷✵✶ ✵❀ ✷✻✾ ✵✶✾ ✴ ✺❂✽ ❊❏ ✸✾❁ ❊❂❊✵✷✺✴ ✿
❊✴ ✹ ✾■✾❂❈ ➟ ✽ ✴ ❀✷✵✶ ✺✴✾ ✴✺❂✽ ❊❏ ✸✾❁ ❊❂❊✵✷✺✴ ❉ ❢ ✷●✼ ❂✾
➟ ✸✶ ✺❀ ✸ ✵✶✾ ❁ ✾❂✻✾✴✵❊●✾ ✺❍ ✼✴✸✺❏■✾✹ ✻✺✴◗ ✷✻✵✸ ❂✾❏❊✵✷■✾
✵✺ ✵✶✾ ✴✼✽ ❋ ✾❂ ✺❍ ✸✾❁ ❊❂❊✵✷✺✴ ❏✺✸✸✾✸ ✺❋✸✾❂■✾✹ ❀✷✵✶ ✺✼ ✵
❂✾✸✺❏✼✵✷✺✴ ❉
✶
❹❿♦ ❧♦✉❺①♠✉ ❿♦❧♦ ✐❧♦ ❦❥✉♦❧⑧♦♣ ❦✈ ♠❿♦ ➁❺①① ♠❧✐➇ ❽ ✉✐t s①♦
✠❶ ♣✐➲✡② ➳❿♥❽❿ ♦❻s①✐♥✈✉ ♠❿♦ ①♥✈♦✐❧ ✉❿✐s♦ ❦➁ ♠❿♦ ❽❦✈✷♥❽♠ ✈❺t☛
❥♦❧ ➳♥♠❿❦❺♠ ❧♦✉❦①❺♠♥❦✈➀ ✸➁ ♠❧✐➇ ❽ ➳✐✉ ✉♠✐❥①♦ ♣❺❧♥✈➃ ♠❿♦ ➳❿❦①♦
✺æ ✻ ð ßæ àß åø äñã✼ à ê ßæ çáä÷ ✽ ➫ ✶ ✾✴ ✹ ✾✴✸✷✵❈ ✷✸ ✷✴❑
✻❂✾❊✸✾✹ ✿ ✵✶✾ ✻✼❂■✾ ✻❏✾❊❂❏❈ ✸✶ ✺❀ ✸ ✵✶✾ ✸❊✵✼❂❊✵✷✺✴ ✺❍ ✵✶✾
❂✾✸✺❏✼✵✷✺✴ ✽ ✾✵✶✺✹ ❉ î ✺❀ ✾■✾❂✿ ✷✵ ❊❁ ❁✾❊❂✸ ❏❊✵✾❂ ✵✶ ❊✴
❀ ✷✵✶ ✵✶ ✾ ❁✼❂✾❏❈ ❂✾❊✻✵✷■✾ ✽ ✾✵✶ ✺✹
❭
✴ ✺ ❁❂✾✹✷✻✵✷✺✴ ✺❍ ✻✺✴❑
◗✷✻✵✸❪❉ ❅ ✶✾ ❁ ✾❂✻✾✴✵❊●✾ ✺❍ ✼✴ ✸✺❏■✾✹ ✻✺✴◗ ✷✻✵✸ ✷✸ ❁❂✾✵✵❈
●✺✺✹ ✼❁ ✵✺ ✹✾✴ ✸✷✵❈ ❵❉➟
❭
➠ Ô
✦ ✼✴✸✺❏■✾✹ ✿ ✻✺✽ ❁ ❊❂✾✹ ✵✺
❵➟✦ ❀ ✷✵✶ ✵✶✾ ❁✼❂✾❏❈ ❂✾❊✻✵✷■✾ ✽ ✾✵✶ ✺✹❪✿❋✼✵ ✷✵ ✷✴✻❂✾❊✸✾✸
✹❂❊✽ ❊✵✷✻❊❏❏❈ ❀✶ ✾✴ ✹✾✴ ✸✷✵❈ ✾❙✻✾✾✹✸ ➉
❭Ô
❛✦ ✼✴✸✺❏■✾✹
❍✺❂ ✹ ✾✴✸✷✵❈ Ó
✿ ✻✺✽ ❁ ❊❂✾✹ ✵✺ ➟❛✦ ❀ ✷✵✶✺✼✵ ✻✺✴◗ ✷✻✵ ❁ ❂✾❑
✹✷✻✵✷✺✴❪❉ ❅ ✶✾❂✾ ✷✸ ❊❏✸✺ ❊ ❂❊❁✷✹ ✷✴✻❂✾❊✸✾ ✺❍ ✵✶✾ ✴✼✽ ❋✾❂
✺❍ ✼✴❁ ❂✾✹✷✻✵✾✹ ✻✺✴◗ ✷✻✵✸❉
✳✵ ✷✸ ❁✺✸✸✷❋❏✾ ✵✺ ✹✾❏❊❈ ✸❊✵✼❂❊✵✷✺✴ ❀ ✶✾✴ ✹ ✾✴✸✷✵❈ ✷✴❑
✻❂✾❊✸✾✸❉ ❅ ✶✾ ❁❂✾■✷✺✼ ✸ ❂✾✸✼ ❏✵✸ ❀✾❂✾ ✺❋ ✵❊✷✴ ✾✹ ❀ ✷✵✶ ✻✺✴❑
◗✷✻✵ ❁❂✾❑✹✾✵✾✻✵✷✺✴ ❁✾❂❍✺❂✽ ✾✹ ✾■✾❂❈ ➟ ✽ ✴ ✺✴ ❊ ➠➟ ✽ ✴
❁ ✾❂✷✺✹ ❉ ➫ ✷✵✶ ❊ ❍❂✾
➩
✼✾✴✻❈ ✺❍ ✺✴ ✻✾ ✾■✾❂❈ ✽ ✴ ❊✴✹ ❊ ❁✾❑
❂✷✺✹ ✺❍ ➟ ✽ ✴ ✿❁ ✾❂❍✺❂✽ ❊✴✻✾ ❂✾✽ ❊✷✴✸ ✸✷✽ ✷❏❊❂ ❊✵ ❏✺❀ ✹✾✴❑
✸✷✵❈✿ ❋✼ ✵ ✸❊✵✼❂❊✵✷✺✴ ❊❁❁✾❊❂✸ ✺✴ ❏❈ ❊✵ ✹✾✴✸✷✵✷✾✸ ✶ ✷●✶✾❂
✵✶❊✴ ➟❉
❄ ✴✺✵✶✾❂ ❁ ✺✸✸✷❋ ✷❏✷✵❈ ✷✸ ✵✺ ✼ ✸✾ ❊ ✸✽ ❊❏❏✾❂ ✶✺❂✷➸✺✴✵❊❏
✸✾❁ ❊❂❊✵✷✺✴ ❍✺❂ ❁ ❂✾❑✹✾✵✾✻✵✷✺✴ ❉ ➨ ✴ ❋ ✺✵✶
◆
●✼❂✾✸✿ ✻✼❂■✾✸
ò➠ ✸✾❁ó ❊❂✾ ✺❋✵❊✷✴✾✹ ❀✷✵✶ ❁❂✾❑✹✾✵✾✻✵✷✺✴ ✾■✾❂❈ ➟ ✽ ✴ ✿
✼✸✷✴ ● ✵✶✾ ✴ ✺❂✽ ❊❏ ✶✺❂✷➸✺✴✵❊❏ ✸✾❁ ❊❂❊✵✷✺✴ ❉ ❅ ✶ ✷✸ ❏✷✽ ✷✵✸
✵✶✾ ✴✼ ✽ ❋ ✾❂ ✺❍ ❊✷❂✻❂❊❍✵ ❁ ❊✷❂✸ ✵✶ ❊✵ ❊❂✾ ✵❂✾❊✵✾✹ ✸✷✽ ✼ ❏❑
✵❊✴ ✾✺✼✸❏❈✿ ❀✶ ✷✻✶ ✷✸ ✵✶✾ ✻❊✼✸✾ ✺❍ ✸❊✵✼❂❊✵✷✺✴ ❉ ❄ ✵ ✸✺✽ ✾
❁ ✺✷✴✵ ✵✶✾ ✵❂❊è✾✻✵✺❂✷✾✸ ✺❍ ❊✷❂✻❂❊❍✵ ✸✼ ❋✽ ✷✵✵✾✹ ✵✺ ✽ ✼❏✵✷❑
❁❏✾ ❍✺❂✻✾✸ ❋✾✻✺✽ ✾ ✸✺ ✷❂❂✾●✼❏❊❂ ✵✶❊✵ ✽ ✺❂✾ ✻✺✴◗✷✻✵✸ ❊❂✾
●✾✴✾❂❊✵✾✹ ✵✶❊✴ ✸✺❏■✾✹
❭
❀ ✶✷✻✶ ✹✺✾✸✴ ➭✵ ✽ ✾❊✴ ✵✶❊✵ ✴ ✺
✻✺✴◗ ✷✻✵❑❍❂✾✾ ✵❂❊è✾✻✵✺❂✷✾✸ ✾❙✷✸✵❪❉ ❅✶ ✾ ✻✼❂■✾✸ ✸✶✺❀ ✵✶❊✵
✸❊✵✼❂❊✵✷✺✴ ❊❁❁ ✾❊❂✸ ✽ ✼✻✶ ❏❊✵✾❂❉ î ✺❀ ✾■✾❂ ❁✾❂❍✺❂✽ ❊✴✻✾
✷✸ ✸❏✷●✶✵❏❈ ❀✺❂✸✾ ❊✵ ❏✺❀ ✹✾✴ ✸✷✵❈
❭
✽ ✺❂✾ ✵✶ ❊✴ ✵❀ ✷✻✾ ❊✸
✽ ❊✴❈ ✻✺✴◗✷✻✵✸ ❂✾✽ ❊✷✴ ✼✴✸✺❏■✾✹ ❪❉ ❅ ✶ ✷✸ ✷✸ ❋✾✻❊✼✸✾ ❀ ✷✵✶
❊ ❂✾✹ ✼✻✾✹ ✸✾❁ ❊❂❊✵✷✺✴ ❍✺❂ ❁❂✾❑✹✾✵✾✻✵✷✺✴ ✿ ✽ ❊✴✾✼ ■✾❂✷✴●
❊✷❂✻❂❊❍✵ ✽ ❊❈ ✻❂✾❊✵✾ ✴✾❀ ✻✺✴◗ ✷✻✵✸ ❀✷✵✶ ✸✼❂❂✺✼✴ ✹✷✴ ●
❊✷❂✻❂❊❍✵ ✴ ✺✵ ✷✴✷✵✷❊❏❏❈ ✷✴■✺❏■✾✹ ❉ ❅✶ ✺✸✾ ✻✺✴◗ ✷✻✵✸ ❀ ✺✴ ➭✵
❋ ✾ ✵❂✾❊✵✾✹ ✼ ✴✵✷❏ ✵✶ ✾ ✴✾❙✵ ❁ ❂✾❑✹✾✵✾✻✵✷✺✴ ✸✵✾❁ ✿ ❀ ✶✷✻✶ ✺❍
✻✺✼❂✸✾ ✷✸ ✼✴❊✻✻✾❁✵❊❋❏✾ ✷✴ ❊ ❂✾❊❏ ✸❈✸✵✾✽ ❉ ❖ ✺❂✾ ✹✾✵❊✷❏✸
✻❊✴ ❋ ✾ ❍✺✼✴✹ ✷✴
❜❄
➧
❫
➊ ❝ Ô
❡❉
✥ ➍➶ ➛ ➣➣→➣➣➷ →➹ ➓ ➒ ↕ ✾✿ ➝ ❀ ➑ ❐➒ ✃→➬ ➻ ❐→➣
❅ ✶✷✸ ✸✾✻✵✷✺✴ ✹✾✸✻❂✷❋ ✾✸ ❁❂✾❏✷✽ ✷✴ ❊❂❈ ❂✾✸✼❏✵✸ ❍✺❂ ❊✸❑
✸✾✸✸✷✴● ✵✶✾ ✷✴✵❂✺✹✼ ✻✵✷✺✴ ✺❍ ❂✾✹✼✻✾✹ ■✾❂✵✷✻❊❏ ✸✾❁ ❊❂❊✵✷✺✴
✽ ✷✴ ✷✽ ❊ ❁ ❂✺✻✾✹ ✼❂✾✸
❭❜
✳✴✵❝❵❡❪ ✷✴ ✻✺✴✵✷✴✾✴✵❊❏ ❊✷❂✸❁ ❊✻✾
❊❋✺■✾ ◗✷●✶✵ ❏✾■✾❏ ❢ ➊❵❝❛❉ ➫ ✾ ✼ ✸✾ ✵✶✾ ❃❄❅ ❆ ✸✷✽ ✼❏❊✵✷✺✴
❋❊✸✾✹ ❁❏❊✴✴ ✾❂ ✵✺ ✸✵✼ ✹❈ ✵✶ ❂✾✾ ✽ ❊✷✴ ❴☞ ❆❖ ❊✷❂✸❁ ❊✻✾ ✺❂❑
●❊✴✷➸❊✵✷✺✴ ✸✿ ❀ ✷✵✶ ✵✶ ✾ ❁❂✷✽ ❊❂❈ ✺❋è✾✻✵✷■✾ ✺❍ ✾✸✵✷✽ ❊✵✷✴●
❁ ✺✵✾✴✵✷❊❏ ❋ ✾✴ ✾◆✵✸ ✺✴ ✻✺✴◗ ✷✻✵ ❀ ✺❂P ❏✺❊✹ ✿ ❊✴✹ ❊ ✸✾✻❑
✺✴✹❊❂❈ ✺❋è✾✻✵✷■✾ ✺❍ ✻✺✽ ❁ ❊❂✷✴● ✵✶✾✸✾ ❊❏✵✾❂✴ ❊✵✷■✾ ✺❂●❊❑
✴✷➸❊✵✷✺✴ ✸ ❊✻✻✺❂✹ ✷✴● ✵✺ ✵✶ ✾ ✹✾✴✸✷✵❈ ✺❍ ❁ ✺✵✾✴✵✷❊❏ ✻✺✴❑
◗✷✻✵✸❉
