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SLIDE 1

❉②♥❛♠✐❝ ❤❛r✈❡st✐♥❣ ♦❢ s♦❝✐❛❧ ❣r❛♣❤s

❏✳ ■✳ ❖r❧✐❝❦✐✶

✶■❚❇❆

❲❉❈❙ ✷✵✵✾✱ ❇✉❡♥♦s ❆✐r❡s✱ ❆r❣❡♥t✐♥❛

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SLIDE 2

▼✐♥✐ ❙❝✐ ❇✐♦

◮ ▲✐tt❧❡ ❜❛❝❦❣r♦✉♥❞ ✐♥ t❤❡♦r❡t✐❝❛❧ ❝♦♠♣✉t❡r s❝✐❡♥❝❡✳ ❘❡✈❡rs✐❜❧❡

❚✉r✐♥❣ ♠❛❝❤✐♥❡s ✭❄✮✳

◮ ▲✐tt❧❡ ❜❛❝❦❣r♦✉♥❞ ✐♥ ❛♣♣❧✐❡❞ s❡❝✉r✐t② r❡s❡❛r❝❤✿ ✐♥❢♦r♠❛t✐♦♥

❣❛t❤❡r✐♥❣ ❛♥❞ ❛tt❛❝❦ s✐♠✉❧❛t✐♦♥✳

◮ ❲♦r❦✐♥❣ ✇✐t❤ P❤❞ ❛❞✈✐s♦rs ❏✳ ■✳ ❆❧✈❛r❡③✲❍❛♠❡❧✐♥ ❛♥❞ P✳ ■✳

❋✐❡r❡♥s ❛t ■❚❇❆ ♦♥ r❡♣✉t❛t✐♦♥ ❛♥❞ ♣r✐✈❛❝② ✐♥ s♦❝✐❛❧ ♥❡t✇♦r❦s✳

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SLIDE 3

❆❣❡♥❞❛

◮ ❲❤❛t❄

◮ ❆♥s✇❡r✿ st✉❞②✐♥❣ s♦❝✐❛❧ ❣r❛♣❤s✴♥❡t✇♦r❦s ❞②♥❛♠✐❝s

◮ ❍♦✇❄

◮ ❆♥s✇❡r✿ ❝♦❧❧❡❝t✐♥❣ ❞②♥❛♠✐❝ s♦❝✐❛❧ ❞❛t❛

◮ ❲❤❡♥❄

◮ ❆♥s✇❡r✿ ✷✵✵✾✲✷✵✶✵✱ ✈❡r② ✐♥t❡r❡st✐♥❣ q✉❡st✐♦♥s ❛r✐s❡✳

◮ ❉❛♥❣❡rs❄

◮ ✏❚❤❡r❡ ❛r❡ ✜❡❧❞s✱ ❡♥❞❧❡ss ✜❡❧❞s✱ ✇❤❡r❡ ❤✉♠❛♥ ❜❡✐♥❣s ❛r❡ ♥♦

❧♦♥❣❡r ❜♦r♥✱ ✇❡ ❛r❡ ❣r♦✇♥✳✑ ▼♦r♣❤❡✉s✱ ▼❛tr✐① ✭✶✾✾✾✮

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SLIDE 4

❚❤❡ ❙♦❝✐❛❧ ●r❛♣❤ ✭❲❤❛t❄✮

◮ ■s ❛ r❡❛❧ ♦❜❥❡❝t✦ ❲❡ ✉s❡ ❣r❛♣❤s ❛s ❛❜str❛❝t✐♦♥s✳ ◮ ✭♥♦t❛t✐♦♥✮ ❙♦❝✐❛❧ ❣r❛♣❤✿ t❤❡ s♦❝✐❛❧ ✐♥t❡r❛❝t✐♦♥s ❜❡t✇❡❡♥ ❤✉♠❛♥

❜❡✐♥❣s✳

◮ ✭♥♦t❛t✐♦♥✮ ❙♦❝✐❛❧ ♥❡t✇♦r❦ ✭s❡r✈✐❝❡✮✿ ❛ ❝♦♠♠✉♥✐❝❛t✐♦♥ s②st❡♠

❞❡s✐❣♥❡❞ ❢♦r ✉s✐♥❣ ❛♥❞ ❡①♣❛♥❞✐♥❣ t❤❡ s♦❝✐❛❧ ❣r❛♣❤✳ ❤tt♣✿✴✴❜✐t✳❧②✴♦r❦✉t✲❦✲❝♦r❡s✲❜✐❣

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SLIDE 5

❙♦❝✐❛❧ ◆❡t✇♦r❦ ❙❡r✈✐❝❡s ✭❲❤❛t❄✮

✶✳ Pr♦✈✐❞❡ ❛❜str❛❝t✐♦♥ ♦❢ ✉s❡r ♣r♦✜❧❡ ❛♥❞ s♦❝✐❛❧ ❝♦♥t❛❝ts✳ ✷✳ Pr♦✈✐❞❡ ❝♦♠♠✉♥✐❝❛t✐♦♥ ✇✐t❤ s♦❝✐❛❧ ❝♦♥t❛❝ts✳ ✸✳ Pr♦✈✐❞❡ ✇❛②s t♦ st❛② ✐♥ t♦✉❝❤ ✇✐t❤ ❝♦♥t❛❝ts✳ ✹✳ Pr♦✈✐❞❡ ♥❛✈✐❣❛t✐♦♥ ❛♥❞ r❡❝♦♠♠✳ ♦❢ ♥❡✇ ❝♦♥t❛❝ts✳

parameter Cyworld Flickr LiveJournal Orkut #nodes 12,048,186 1,846,198 5,284,457 3,072,441 %nodes 100% 26.9% 95.4% 11.3% #links 190,589,667 22,613,981 77,402,652 223,534,301 %simmetric links 100% 62.0% 73.5% 100.0%

  • ave. deg ❦

31.6 12.24 16.97 106.1 in/out α

  • 1.74 / 1.78

1.59 / 1.65 1.50 / 1.50 clustering ❈ 0.16 0.31 0.33 0.17 assortativity r

  • 0.13

0.20 0.18 0.07

  • ave. distance

3.2 5.67 5.88 4.25 diameter

  • 27

6 9

❛♥❛❧②s✐s ❢r♦♠ ❬▼✐s❧♦✈❡ ❡t ❛❧✳✱ ✷✵✵✼❪ ❛♥❞ ❬❆❤♥ ❡t ❛❧✳✱ ✷✵✵✼❪

slide-6
SLIDE 6

❙♦❝✐❛❧ ◆❡t✇♦r❦ ❙❡r✈✐❝❡s✱ ❝♦♥t✳ ✭❲❤❛t❄✮

◮ ▼✐❝r♦✴♥❛♥♦✲❜❧♦❣❣✐♥❣✿ ♥❡t✇♦r❦ s✐♠♣❧✐❝✐t②✱ s❤♦rt ♠❡ss❛❣❡s✱

r❛♣✐❞ ❞✐✛✉s✐♦♥✳

◮ ❉②♥❛♠✐❝s✿ ✇❡✐❣❤t❡❞ ♠❡♥t✐♦♥ ♥❡t✇♦r❦s ❬❙❤❛♠♠❛ ❡t ❛❧✳✱ ✷✵✵✾❪

❛♥❞ r❡t✇❡❡t✐♥❣ ❞②♥❛♠✐❝s ✭♠❡ss❛❣❡ ❢♦r✇❛r❞✐♥❣✮✳ ❊①❛♠♣❧❡✿ ❚✇✐tt❡r✱ ❏❛✐❦✉✱ ❡t❝✳

slide-7
SLIDE 7

❖♣❡♥♥❡ss ✈❡rs✉s Pr✐✈❛❝② ✭❲❤❛t❄✮

◮ ❙♦❝✐❛❧ ♥❡t✇♦r❦s ❛r❡ ♠❡❛♥s ♦❢ ❝♦♠♠✉♥✐❝❛t✐♦♥✱ s♦ ❛r❡ ✉s❡❢✉❧✳ ◮ ❚❡♥s✐♦♥ ❜❡t✇❡❡♥ t❤♦s❡ ✇❤♦ ❧✐❦❡ ♣r✐✈❛❝② ❛♥❞ t❤♦s❡ ✇❤♦ ❧✐❦❡

♦♣❡♥♥❡ss✳

◮ ▲✐♠✐t❡❞ ✈✐s✐❜✐❧✐t② ✉s✉❛❧❧② ✈✐❛ ❧✐♠✐t❡❞ ❧♦♦❦❛❤❡❛❞ ✭t❤❡ ✐♥❢❛♠♦✉s

❖♥❧② ❋r✐❡♥❞s ✈s✳ ❋r✐❡♥❞s ♦❢ ❋r✐❡♥❞s ❢❡❛t✉r❡s ✐♥ ❋❛❝❡❜♦♦❦✮✳

◮ ❊①❛♠♣❧❡ ♦❢ ♣r✐✈❛❝②✿ ▲✐♥❦❡❞■♥ ✇❡❜s✐t❡✱ ♣r✐✈❛t❡ ❞❛t❛ ❛♥❞ ❧✐♠✐t❡❞

❧♦♦❦❛❤❡❛❞ ✭❞✐st❛♥❝❡ ✸✮✳

◮ ❊①❛♠♣❧❡ ♦❢ ♦♣❡♥♥❡ss✿ ●♦♦❣❧❡ ❙♦❝✐❛❧●r❛♣❤ ❬❋✐t③♣❛tr✐❝❦✱ ✷✵✵✼❪✱

♣✉❜❧✐❝ ✐♥t❡r❢❛❝❡✳

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SLIDE 8

❚♦♦❧s ❢♦r ❞②♥❛♠✐❝ ❤❛r✈❡st✐♥❣ ✭❍♦✇❄✮

◮ ❊①♦♠✐♥❞ ❬❏■❖✱ ✷✵✵✽❪ ✭❤tt♣✿✴✴❜✐t✳❧②✴❡①♦♠✐♥❞✮✿ s✉♣♣♦rt❡❞

❜② ❈♦r❡ ❙❚✱ ♠♦st❧② ❢♦❝✉s❡❞ ✐♥ st❛t✐❝ ❖❙■◆❚ ❛♥❞ s♦❝✐❛❧

✐♥✜❧tr❛t✐♦♥✳ ■♥❝❧✉❞❡s ❞②♥❛♠✐❝ ✉♣❞❛t❡s ◆♦r♠❛❧✐③❡❞ ●♦♦❣❧❡

❉✐st❛♥❝❡ ✭◆●❉✮ ❛♥❞ ♦t❤❡r s❡❛r❝❤ ❡♥❣✐♥❡ ♠✐♥✐♥❣ ✐♥❢♦r♠❛t✐♦♥✳

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SLIDE 9

❚♦♦❧s ❢♦r ❞②♥❛♠✐❝ ❤❛r✈❡st✐♥❣✱ ❝♦♥t✳ ✭❍♦✇❄✮

◮ ❚✉♣❧❡ts ❬❏■❖✱ ✷✵✵✾❪ ✭❤tt♣✿✴✴t✉♣❧❡ts✳❛♣♣s♣♦t✳❝♦♠✮✿ ❛♥

❡①♣❡r✐♠❡♥t❛❧ ❝❧♦✉❞ s❤❡❧❧ ❢♦r s♦❝✐❛❧ ♥❡t✇♦r❦ ❝r❛✇❧✐♥❣ ❛♥❞

✐♥t❡r❛❝t✐♦♥ ✭❲❡❜ ✹✳✵❄✮✳

◮ ◆❛♥♦✲❜❧♦❣❣✐♥❣ ✇❡✐❣❤t❡❞ ♠❡♥t✐♦♥ ❧✐♥❦s✿

❃✗❃✗❃✗❃ t✇✐tt❡r ❅❛s❞❢❛s❞❢ ❳ ❄ ②❡s t✇✐tt❡r ❅❛s❞❢❛s❞❢ ❅q✇❡rq✇❡r✶ ✭✸✸✳✾ ✪✮ t✇✐tt❡r ❅❛s❞❢❛s❞❢ ❅q✇❡rq✇❡r✷ ✭✶✵✳✼ ✪✮ t✇✐tt❡r ❅❛s❞❢❛s❞❢ ❅q✇❡rq✇❡r✸ ✭✽✳✾ ✪✮ t✇✐tt❡r ❅❛s❞❢❛s❞❢ ❅q✇❡rq✇❡r✹ ✭✼✳✶ ✪✮ t✇✐tt❡r ❅❛s❞❢❛s❞❢ ❅q✇❡rq✇❡r✺ ✭✼✳✶ ✪✮ t✇✐tt❡r ❅❛s❞❢❛s❞❢ ❅q✇❡rq✇❡r✻ ✭✺✳✹ ✪✮ t✇✐tt❡r ❅❛s❞❢❛s❞❢ ❅q✇❡rq✇❡r✼ ✭✺✳✹ ✪✮ ✳✳✳ ❃✗❃✗❃✗❃ s♦❝✐❛❧❣r❛♣❤ ❛s❞❢❛s❞❢✳❜❧♦❣s♣♦t✳❝♦♠ ❳ ❄ ✳✳✳ ❃✗❃✗❃✗❃ ❛❧♣❤❛ ✏❛r❣❡♥t✐♥❛ ❡①t❡r♥❛❧ ❞❡❜t✑ ❳ ❄ ✳✳✳ ❃✗❃✗❃✗❃ ❛❧♣❤❛ ✏❛r❣❡♥t✐♥❛ ♣❛t❡♥ts✑ ❳ ❄ ✳✳✳ ❃✗❃✗❃✗❃ ❛❧♣❤❛ ✧t❤❡ ♠❡❛♥✐♥❣ ♦❢ ❧✐❢❡ t❤❡ ✉♥✐✈❡rs❡ ❛♥❞ ❡✈❡r②t❤✐♥❣✧

slide-10
SLIDE 10

❚♦♣✐❝s✿ ◆❡✇s ❈②❝❧❡ ✭❲❤❡♥❄✮

◮ ◆❡✇s ❞✐✛✉s✐♦♥ ❜② ♥❡✇s s♦✉r❝❡s ❬▲❡s❦♦✈❡❝ ❡t ❛❧✳✱ ✷✵✵✾❪✳ ◮ ❙t✉❞② ♦❢ ♠❡♠❡s✴♣❤r❛s❡s ✐♥ ❜❧♦❣ ❛♥❞ tr❛❞✐t✐♦♥❛❧ ♥❡✇s ♠❡❞✐❛✳ ◮ ❆♥❛❧②s✐s ♦❢ ✾✵ ♠✐❧❧✐♦♥ ❛rt✐❝❧❡s t♦ ❡①tr❛❝t ✶✶✷ ♠✐❧❧✐♦♥ q✉♦t❡s ❛♥❞

❣❡♥❡r❛t❡ ✸✺✱✽✵✵ ♣❤r❛s❡ ❝❧✉st❡rs✳ ❤tt♣✿✴✴♠❡♠❡tr❛❝❦❡r✳♦r❣✴

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SLIDE 11

❚♦♣✐❝s✿ ◆❡✇s ❈②❝❧❡✱ ❝♦♥t✳ ✭❲❤❡♥❄✮

❙♦♠❡ ❝✉r✐♦✉s ♣r♦♣❡rt✐❡s t❤❡② ❢♦✉♥❞✿

slide-12
SLIDE 12

❚♦♣✐❝s✿ ◆❡✇s ❈②❝❧❡✱ ❝♦♥t✳ ✭❲❤❡♥❄✮

◮ P❡❛❦ ✈♦❧✉♠❡ ♦❢ ♠❡♠❡s✴♣❤r❛s❡ ❛♥❞ ❞❡❝❛②✿ ②(t) ∼ ❛❧♦❣(t) ◮ ▼♦❞❡❧✿ ♣❡r✐♦❞s t = ✶,✷,...✱❚✱ ✇✐t❤ ◆ ♠❡❞✐❛ s♦✉r❝❡s r❡♣♦rt✐♥❣

♦♥❡ t❤r❡❛❞ ♣❡r ♣❡r✐♦❞✱ ♦♥❡ ♥❡✇ t❤r❡❛❞ ✐s ❣❡♥❡r❛t❡❞ ❡❛❝❤ ♣❡r✐♦❞ ❛♥❞ ❛❧❧ s♦✉r❝❡ r❡♣♦rt ❞✐✛❡r❡♥t t❤r❡❛❞s ❛t t = ✵✳

◮ ❙✐♠♣❧❡ ♣r❡❢✳ ❛tt❛❝❤♠❡♥t✿

Pr(❥,t) = ❢ (♥❥)δ(t −t❥) ✇❤❡r❡ ♥❥ ✐s t❤❡ t♦t❛❧ ♣r❡✈✐♦✉s st♦r✐❡s ❛❜♦✉t t❤r❡❛❞ ❥ ❛♥❞ t❥ ✐s ✇❤❡♥ t❤r❡❛❞✴❤✐st♦r② ❥ ✇❛s ✜rst ♣r♦❞✉❝❡ ✳

◮ ❢ (·) ♠♦♥♦✳ ✐♥❝r❡❛s✐♥❣ ♦♥ ♥❥ ✭✐♠✐t❛t✐♦♥ ❡✛❡❝t✮ ◮ δ(·) ♠♦♥♦✳ ❞❡❝r❡❛s✐♥❣ ✐♥ t −t❥ ✭r❡❝❡♥❝② ❡✛❡❝t✮✳

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SLIDE 13

❚♦♣✐❝s✿ ◆❡✇s ❈②❝❧❡✱ ❝♦♥t✳ ✭❲❤❡♥❄✮

■♥ ❛ ♥❛♥♦✲❜❧♦❣❣✐♥❣ ❡♥✈✐r♦♥♠❡♥t ❚r❡♥❞✐st✐❝ ✭❜② ❋❧❛♣t♦r✮✱ ❝♦❧❧❡❝t ❛♥❞ s❤♦✇ s✐♠✐❧❛r ♠❡♠❡✴♣❤r❛s❡ ♣❡❛❦ ❜❡❤❛✈✐♦r ✭❤tt♣✿✴✴tr❡♥❞✐st✐❝✳❝♦♠✮✳ ❊①❛♠♣❧❡✿ ❢❛❝❡❜♦♦❦ ♣r✐✈❛❝② ✭❧❛st ✸✵ ❞❛②s✮

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SLIDE 14

❚♦♣✐❝s✿ ◆❛♥♦✲❜❧♦❣❣✐♥❣ ❡❝♦♥♦♠②✱ ❝♦♥t✳ ✭❲❤❡♥❄✮

◮ ❲❤✉✣❡❇❛♥❦ ✭❤tt♣✿✴✴✇❤✉✣❡❜❛♥❦✳♦r❣✮ ❞✐s❝✉ss✐♦♥✿

✐♥❢♦r♠❛t✐♦♥ r❡♣❧✐❝❛t✐♦♥ ❂ ♠♦♥❡② ❂ r❡♣✉t❛t✐♦♥ ✭❄✮✳

◮ ❊❛❝❤ r❡t✇❡❡t ✐s ❛ r❡♣❧✐❝❛t✐♦♥ ♦❢ ❛ ♠❡ss❛❣❡ ❜② ❛♥♦t❤❡r

♥♦❞❡✴✉s❡r✳ ▲♦❝❛❧ ❞❡❝✐s✐♦♥✿ ✰✶ ✇❤✉✣❡ t♦ ❅✉s❡r❆ ❛❝❝♦✉♥t ✐❢ ❅✉s❡r❳ r❡t✇❡❡ts ❅✉s❡r❆✳

◮ ❈r✐t✐❝✐s♠❄ ❈♦rr❡❧❛t✐♦♥ ✇✐t❤ ❦✐♥ ❄ ❆ ❢❛❦❡ ❉❡❡♣❛❦ ❈❤♦♣r❛

✐s ★✶✷ ❄✦

◮ ■♥ ❊❣❣✲❖✲▼❛t✐❝ ♣r♦t♦t②♣❡ ❬❏■❖ ❡t ❛❧✳✱ ✷✵✵✾❪ s♠❛❧❧✲s❝❛❧❡

❡①♣❡r✐♠❡♥ts ✇❤❡r❡ P❛❣❡❘❛♥❦ ✇✐t❤ ❞❛t❛s❡ts ♦❢ ♣❤♦t♦❣r❛♣❤✐❝ ❛♥❞ ✈✐❞❡♦ s♦❝✐❛❧ ♥❡t✇♦r❦s✱ ❣♦♦❞ ❢❛❝❡t❡❞ r❡s✉❧ts✳

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SLIDE 15

❈♦♥❝❧✉s✐♦♥s

◮ P❧❡❛s❡ ❛♥❛❧②③❡ r❡❧❛t✐♦♥ ♦❢ ✐♥❢♦r♠❛t✐♦♥ ❞✐✛✉s✐♦♥ ✇✐t❤

❡♣✐❞❡♠✐❝s✳

◮ ❈❛♥ ✇❡ ❤❛r✈❡st ❛♥❞ ✐♥t❡r❛❝t ✇✐t❤ t❤❡ s♦❝✐❛❧ ♥❛♥♦✲❜❧♦❣❣✐♥❣

s②st❡♠s ✐♥ ❛ ✇❛② t♦ ❣❡♥❡r❛t❡ ✉s❡❢✉❧ ❛❞✲❤♦❝ ❡❝♦♥♦♠✐❡s❄

◮ ❈❛♥ ✇❡ ✐❞❡♥t✐❢② tr❡♥❞② ♣❡♦♣❧❡ ♦r ♣❡♦♣❧❡ ❣❡♥❡r❛t✐♥❣ t❤❡

tr❡♥❞❄

◮ ❈❛♥ ✇❡ ❞✐s❝r✐♠✐♥❛t❡ ❡♣❤❡♠❡r❛❧ ❢r♦♠ ♣❡rs✐st❡♥t tr❡♥❞s❄ ◮ ❙❤❛❧❧ ✇❡ ♣r❡❢❡r ❛♥ ✐♠♣❧✐❝✐t r❡♣✉t❛t✐♦♥ s②st❡♠s ✐♥❝❧✉❞✐♥❣

❡✐❣❡♥✈❡❝t♦r ❝❡♥tr❛❧✐t② ✭s✉❝❤ ❛s P❛❣❡❘❛♥❦✮ t♦ ♠♦r❡ ❡①♣❧✐❝✐t✴❛❞✲❤♦❝ ♠♦♥❡② ❡❝♦♥♦♠✐❡s❄

◮ ❍♦✇ ♣r✐✈❛❝② r❡str✐❝t✐♦♥s ❛✛❡❝t ✐♥❢♦r♠❛t✐♦♥ ❞✐✛✉s✐♦♥❄

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SLIDE 16

❇✐❜❧✐♦❣r❛♣❤②

❬▼✐s❧♦✈❡ ❡t ❛❧✳✱ ✷✵✵✼❪ ▼✐s❧♦✈❡✱ ▼❛r❝♦♥✱ ●✉♠♠❛❞✐✱ ❉r✉s❝❤❡❧ ❛♥❞ ❇❤❛tt❛❝❤❛r❥❡❡✱ ✏▼❡❛s✉r❡♠❡♥t ❛♥❞ ❛♥❛❧②s✐s ♦❢ ♦♥❧✐♥❡ s♦❝✐❛❧ ♥❡t✇♦r❦s✑✳ ❤tt♣✿✴✴✇✇✇✳✐♠❝♦♥❢✳♥❡t✴✐♠❝✲✷✵✵✼✴♣❛♣❡rs✴✐♠❝✶✼✵✳♣❞❢ ❬❆❤♥ ❡t ❛❧✳✱ ✷✵✵✼❪ ❆❤♥✱ ❍❛♥✱ ❑✇❛❦✱ ▼♦♦♥ ❛♥❞ ❏❡♦♥❣✱ ✏❆♥❛❧②s✐s ♦❢ t♦♣♦❧♦❣✐❝❛❧ ❝❤❛r❛❝t❡r✐st✐❝s ♦❢ ❤✉❣❡ ♦♥❧✐♥❡ s♦❝✐❛❧ ♥❡t✇♦r❦✐♥❣ s❡r✈✐❝❡s✑✳ ❤tt♣✿✴✴✇✇✇✷✵✵✼✳♦r❣✴♣❛♣❡rs✴♣❛♣❡r✻✼✻✳♣❞❢ ❬❙❤❛♠♠❛ ❡t ❛❧✳✱ ✷✵✵✾❪ ❙❤❛♠♠❛✱ ❑❡♥♥❡❞② ❛♥❞ ❈❤✉r❝❤✐❧❧✱ ✏❚✇❡❡t t❤❡ ❉❡❜❛t❡s✑✳ ❤tt♣✿✴✴r❡s❡❛r❝❤✳②❛❤♦♦✳❝♦♠✴❢✐❧❡s✴✇s♠✵✶❛✲s❤❛♠♠❛✳♣❞❢ ❬❋✐t③♣❛tr✐❝❦✱ ✷✵✵✼❪ ❋✐t③♣❛tr✐❝❦✱ ✏❚❤♦✉❣❤ts ♦♥ t❤❡ ❙♦❝✐❛❧ ●r❛♣❤✑✳ ❤tt♣✿✴✴✇✇✇✳❜r❛❞❢✐t③✳❝♦♠✴s♦❝✐❛❧✲❣r❛♣❤✲♣r♦❜❧❡♠✴ ❬▲❡s❦♦✈❡❝ ❡t ❛❧✳✱ ✷✵✵✾❪ ▲❡s❦♦✈❡❝✱ ❇❛❝❦str♦♠ ❛♥❞ ❑❧❡✐♥❜❡r❣✱✏▼❡♠❡✲tr❛❝❦✐♥❣ ❛♥❞ t❤❡ ❉②♥❛♠✐❝s ♦❢ t❤❡ ◆❡✇s ❈②❝❧❡✑✳ ❤tt♣✿✴✴✇✇✇✳❝s✳❝♦r♥❡❧❧✳❡❞✉✴❤♦♠❡✴❦❧❡✐♥❜❡r✴❦❞❞✵✾✲q✉♦t❡s✳♣❞❢ ❬❏■❖ ❡t ❛❧✳✱ ✷✵✵✾❪ ❖r❧✐❝❦✐✱ ❆❧✈❛r❡③✲❍❛♠❡❧✐♥ ❛♥❞ ❋✐❡r❡♥s✱ ✏❋❛❝❡t❡❞ ❘❛♥❦✐♥❣ ♦❢ ❊❣♦s ✐♥ ❈♦❧❧❛❜♦r❛t✐✈❡ ❚❛❣❣✐♥❣ ❙②st❡♠s✑✳ ❤tt♣✿✴✴❛r①✐✈✳♦r❣✴♣❞❢✴✵✽✵✾✳✹✻✻✽