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❍❡t❡r♦❣❡♥❡♦✉s ❤❛r❞✇❛r❡ ❆❞❛♣t✐♥❣ t♦ ❛♣♣❧✐❝❛t✐♦♥ ❧♦❛❞ ❉❛t❛❝❡♥t❡r ✐♥ ❛ ❜♦①

❍❛r♥❡ss✐♥❣ ❤❡t❡r♦❣❡♥♦✉s ❛r❝❤✐t❡❝t✉r❡s ❢♦r ❣r❡❡♥ ❝❧♦✉❞ ❞❛t❛❝❡♥t❡rs

• ❡♦r❣❡s ❉❛ ❈♦st❛

❍❡t❡r♦P❛r✬✷✵✶✻

❆✉❣✉st ✷✸r❞✱ ✷✵✶✻

❞❛❝♦st❛❅✐r✐t✳❢r ✶✴✹✺

❍❡t❡r♦❣❡♥❡♦✉s ❤❛r❞✇❛r❡ ❆❞❛♣t✐♥❣ t♦ ❛♣♣❧✐❝❛t✐♦♥ ❧♦❛❞ ❉❛t❛❝❡♥t❡r ✐♥ ❛ ❜♦① ❈♦♥t❡①t ❉❡s✐❣♥❡❞ ❖♣♣♦rt✉♥✐st✐❝

❖✉t❧✐♥❡

✶ ❍❡t❡r♦❣❡♥❡♦✉s ❤❛r❞✇❛r❡

❈♦♥t❡①t ❍❡t❡r♦❣❡♥❡♦✉s❧② ❞❡s✐❣♥❡❞ ❖♣♣♦rt✉♥✐st✐❝❛❧❧② ❤❡t❡r♦❣❡♥❡♦✉s

✷ ❆❞❛♣t✐♥❣ t♦ ❛♣♣❧✐❝❛t✐♦♥ ❧♦❛❞

❈♦♥❝❡♣t ❙t❛t❡❧❡ss ❛♣♣❧✐❝❛t✐♦♥s ❚✐♠✐♥❣ ✐ss✉❡s ❙t❛t❡✲❢✉❧❧ ❛♣♣❧✐❝❛t✐♦♥s

✸ ❉❛t❛❝❡♥t❡r ✐♥ ❛ ❜♦①

❞❛❝♦st❛❅✐r✐t✳❢r ✷✴✹✺

❍❡t❡r♦❣❡♥❡♦✉s ❤❛r❞✇❛r❡ ❆❞❛♣t✐♥❣ t♦ ❛♣♣❧✐❝❛t✐♦♥ ❧♦❛❞ ❉❛t❛❝❡♥t❡r ✐♥ ❛ ❜♦① ❈♦♥t❡①t ❉❡s✐❣♥❡❞ ❖♣♣♦rt✉♥✐st✐❝

■❚ ✐♠♣❛❝t ♦♥ ❡❧❡❝tr✐❝✐t②

❘❡❝❡♥t ❞❛t❛❝❡♥t❡rs✿ ✹✵✵✵✵ s❡r✈❡rs✱ ✺✵✵✵✵✵ s❡r✈✐❝❡s ✭✈✐rt✉❛❧ ♠❛❝❤✐♥❡s✮✳ ●♦♦❣❧❡✱ ❋❛❝❡❜♦♦❦ ❃ ✶ ♠✐❧❧✐♦♥ s❡r✈❡rs ❖♥❡ ♠❛❥♦r ♣♦✇❡r ❝♦♥s✉♠❡r

✷✵✵✵ ✿ ✼✵ ❚❲❤ ✷✵✵✼ ✿ ✸✸✵ ❚❲❤✱ ✷✪ ♦❢ ❈❖✷ ✇♦r❧❞ ♣r♦❞✉❝t✐♦♥ ✷✵✶✶ ✿ ✻t❤ ❡❧❡❝tr✐❝✐t② ❝♦♥s✉♠❡r ✐♥ t❤❡ ✇♦r❧❞ ✷✵✷✵ ✿ ✶✵✵✵ ❚❲❤

❘✐s✐♥❣

✷✵✶✹ t♦ ✷✵✶✻✿ ✾✵✪ ♦❢ ❞❛t❛❝❡♥t❡rs ✇✐❧❧ ♥❡❡❞ ❤❛r❞✇❛r❡ ✉♣❣r❛❞❡s

❞❛❝♦st❛❅✐r✐t✳❢r ✸✴✹✺

❍❡t❡r♦❣❡♥❡♦✉s ❤❛r❞✇❛r❡ ❆❞❛♣t✐♥❣ t♦ ❛♣♣❧✐❝❛t✐♦♥ ❧♦❛❞ ❉❛t❛❝❡♥t❡r ✐♥ ❛ ❜♦① ❈♦♥t❡①t ❉❡s✐❣♥❡❞ ❖♣♣♦rt✉♥✐st✐❝

❍♦✇ t♦ s✉♣♣❧② ❡❧❡❝tr✐❝✐t②❄

❈❤✐♥❛ ❚❡❧❡❝♦♠ ■♥♥❡r ▼♦♥❣♦❧✐❛ ■♥❢♦r♠❛t✐♦♥ P❛r❦

✶✺✵ ▼❲

❚✐❛♥❤❡✲✷

✶✼✳✽▼❲

❞❛❝♦st❛❅✐r✐t✳❢r ✹✴✹✺

❍❡t❡r♦❣❡♥❡♦✉s ❤❛r❞✇❛r❡ ❆❞❛♣t✐♥❣ t♦ ❛♣♣❧✐❝❛t✐♦♥ ❧♦❛❞ ❉❛t❛❝❡♥t❡r ✐♥ ❛ ❜♦① ❈♦♥t❡①t ❉❡s✐❣♥❡❞ ❖♣♣♦rt✉♥✐st✐❝

❲❤② ♣♦✇❡r✴❡♥❡r❣② ✐s ✉♥✐q✉❡

❚❤❡ t❡♠♣♦r❛❧ ♣♦✐♥t ♦❢ ✈✐❡✇

■♥❡rt✐❛ ❞✉❡ t♦ t❡♠♣❡r❛t✉r❡ ❙✇✐t❝❤✐♥❣ ♦♥✴♦✛ s❡r✈❡rs

❖✈❡r✲ ♦r ❯♥❞❡r✲r❡s❡r✈❛t✐♦♥

❈②❝❧❡s ❛r❡ s♦♠❡t✐♠❡ ❣♦♦❞

◆♦♥✲❧✐♥❡❛r✐t✐❡s

❊q✉❛t✐♦♥ ♦❢ ♣♦✇❡r

❋❡❡❞❜❛❝❦ ❧♦♦♣s

❈♦♦❧✐♥❣ s②st❡♠

❱✐♦❧❛✐♥❡ ❡t ❛❧✳✱ ❚❤❡r♠❛❧✲❛✇❛r❡ ❝❧♦✉❞ ♠✐❞❞❧❡✇❛r❡ t♦ r❡❞✉❝❡ ❝♦♦❧✐♥❣ ♥❡❡❞s✱ ❲❊❚■❈❊ ✇♦r❦s❤♦♣✱ ✷✵✶✹ ❞❛❝♦st❛❅✐r✐t✳❢r ✺✴✹✺

❍❡t❡r♦❣❡♥❡♦✉s ❤❛r❞✇❛r❡ ❆❞❛♣t✐♥❣ t♦ ❛♣♣❧✐❝❛t✐♦♥ ❧♦❛❞ ❉❛t❛❝❡♥t❡r ✐♥ ❛ ❜♦① ❈♦♥t❡①t ❉❡s✐❣♥❡❞ ❖♣♣♦rt✉♥✐st✐❝

◆♦ st❛❜✐❧✐t② ♦❢ ❡①♣❡r✐♠❡♥ts

❙✐♠♣❧❡ ❡①♣❡r✐♠❡♥t ♦❢ ❋❛st ❋♦✉r✐❡r ❚r❛♥s❢♦r♠ ✭◆P❇✮ ✶✵✵ ❡①♣❡r✐♠❡♥ts ♦♥ ❡①❛❝t❧② t❤❡ s❛♠❡ ❤❛r❞✇❛r❡ ✭●r✐❞✬✺✵✵✵✮ ▲❛r❣❡ ✈❛r✐❛t✐♦♥s

❚✐♠❡✿ ✶✷s✱ ✼✪ ✭❙t❞✳ ❉❡✈✳ ✸✳✷s✮ ❊♥❡r❣②✿ ✾✳✸❦❏✱ ✺✳✺✪ ✭✸❦❏✮

❋♦r t❤❡ s❛♠❡ t✐♠❡✱ ✶✻✼s

❉✐✛❡r❡♥❝❡ ♦❢ ✹❦❏

❚✐♠❡ = ❊♥❡r❣②

162 164 166 168 170 172 174 164 166 168 170 172 174 176 Temps (s) Energie (kJ) Transformée de fourrier

❞❛❝♦st❛❅✐r✐t✳❢r ✻✴✹✺

❍❡t❡r♦❣❡♥❡♦✉s ❤❛r❞✇❛r❡ ❆❞❛♣t✐♥❣ t♦ ❛♣♣❧✐❝❛t✐♦♥ ❧♦❛❞ ❉❛t❛❝❡♥t❡r ✐♥ ❛ ❜♦① ❈♦♥t❡①t ❉❡s✐❣♥❡❞ ❖♣♣♦rt✉♥✐st✐❝

• ♦❛❧

❍♦✇ t♦ ♦♣t✐♠✐③❡ ❡♥❡r❣② ❛♥❞ ♣❡r❢♦r♠❛♥❝❡ ❛t t❤❡ s❛♠❡ t✐♠❡❄ ❈❧❛ss✐❝❛❧ s❝❤❡❞✉❧✐♥❣ ♦❢ ❤♦♠♦❣❡♥❡♦✉s ❞✐str✐❜✉t❡❞ r❡s♦✉r❝❡s ✐s ❛❧r❡❛❞② ◆P ❝♦♠♣❧❡t❡

❋♦r ♣❡r❢♦r♠❛♥❝❡ ▲❡t✬s ❛❞❞ ❊♥❡r❣②✱ ❘❡s✐❧✐❡♥❝❡✱ ✳✳✳

❋♦r ❍❡t❡r♦❣❡♥❡♦✉s s②st❡♠s ✐t ✐s ❡✈❡♥ ♠♦r❡ ❝♦♠♣❧❡①

❞❛❝♦st❛❅✐r✐t✳❢r ✼✴✹✺

❍❡t❡r♦❣❡♥❡♦✉s ❤❛r❞✇❛r❡ ❆❞❛♣t✐♥❣ t♦ ❛♣♣❧✐❝❛t✐♦♥ ❧♦❛❞ ❉❛t❛❝❡♥t❡r ✐♥ ❛ ❜♦① ❈♦♥t❡①t ❉❡s✐❣♥❡❞ ❖♣♣♦rt✉♥✐st✐❝

❍❡t❡r♦❣❡♥❡♦✉s ❤❡t❡r♦❣❡♥❡♦✉s ❧❛♥❞s❝❛♣❡

❍❛r❞✇❛r❡

❛r❝❤✐t❡❝t✉r❡ ✿ ❛r♠✱ ●P❯✱ ❋P●❆ ❣❡♥❡r❛t✐♦♥ ✿ ✷✵✶✹✱ ✷✵✶✺ ■♥✲❣❡♥❡r❛t✐♦♥ ✿ ■✸ ■✺ ■✼✱ ❳❡♦♥✱ ✳✳✳ ❆♥❞ ❛❧❧ ❡①❝❡♣t ♣r♦❝❡ss♦r ✿ ▼❡♠♦r② t②♣❡ ❛♥❞ ❤✐❡r❛r❝❤②✱ st♦r❛❣❡✱ ♥❡t✇♦r❦✱ ✳✳✳

❘❡❝♦♥✜❣✉r❛t✐♦♥

❉❱❋❙✱ ❆▲❘ ✭❞✈❢s ❢♦r ♥❡t✇♦r❦✮✱ ✳✳✳

❆♣♣❧✐❝❛t✐♦♥

❉✐✛❡r❡♥t ❛♣♣❧✐❝❛t✐♦♥s ❤❛✈❡ ❞✐✛❡r❡♥t ✐♠♣❛❝t✿ ▼❡♠♦r② ❜♦✉♥❞✱ ❝♣✉✲✐♥t❡♥s✐✈❡✱✳✳✳ ❉✐✛❡r❡♥t ✐♠♣❧❡♠❡♥t❛t✐♦♥ ♦❢ t❤❡ s❛♠❡ ❆P■ ❛❧s♦

❞❛❝♦st❛❅✐r✐t✳❢r ✽✴✹✺

❍❡t❡r♦❣❡♥❡♦✉s ❤❛r❞✇❛r❡ ❆❞❛♣t✐♥❣ t♦ ❛♣♣❧✐❝❛t✐♦♥ ❧♦❛❞ ❉❛t❛❝❡♥t❡r ✐♥ ❛ ❜♦① ❈♦♥t❡①t ❉❡s✐❣♥❡❞ ❖♣♣♦rt✉♥✐st✐❝

❊✈❡♥ ♠♦❞❡❧s ❛r❡ ❤❡t❡r♦❣❡♥❡♦✉s

❊❧❡❝tr✐❝❛❧ ♣♦✇❡r ♠♦❞❡❧s ❢♦r ❛ s✐♥❣❧❡ s❡r✈❡r✿ ❈❧❛ss✐❝❛❧ ✿ ❧✐♥❡❛r ✭❡rr♦r ❊∼✶✵✲✶✺✪✮ ❋✐♥❡r ✿ Pr♦❝❡ss♦r ✈♦❧t❛❣❡✴❢r❡q✉❡♥❝② ✭❊ ✺✲✾✪✮ ❊✈❡♥ ✜♥❡r✿ Pr♦❝❡ss♦r t❡♠♣❡r❛t✉r❡ ✭❊ ✹✲✼✪✮ ❉♦ ♥♦t ❢♦r❣❡t ❛❜♦✉t ❜✐❛s✿ ♣♦✇❡r s✉♣♣❧② ✉♥✐t ❊ ✷✲✸✪✱ ❝♦♦❧✐♥❣✱ ✳✳✳ ▲❡❛r♥✐♥❣ ♠❡t❤♦❞s ✭♥❡✉r❛❧ ♥❡t✇♦r❦s✱ ❊ ✷✪✮ P♦✇❡r = P♠✐♥ + ▲♦❛❞ × (P♠❛① − P♠✐♥)

❞❛❝♦st❛❅✐r✐t✳❢r ✾✴✹✺

❍❡t❡r♦❣❡♥❡♦✉s ❤❛r❞✇❛r❡ ❆❞❛♣t✐♥❣ t♦ ❛♣♣❧✐❝❛t✐♦♥ ❧♦❛❞ ❉❛t❛❝❡♥t❡r ✐♥ ❛ ❜♦① ❈♦♥t❡①t ❉❡s✐❣♥❡❞ ❖♣♣♦rt✉♥✐st✐❝

❊✈❡♥ ♠♦❞❡❧s ❛r❡ ❤❡t❡r♦❣❡♥❡♦✉s

❊❧❡❝tr✐❝❛❧ ♣♦✇❡r ♠♦❞❡❧s ❢♦r ❛ s✐♥❣❧❡ s❡r✈❡r✿ ❈❧❛ss✐❝❛❧ ✿ ❧✐♥❡❛r ✭❡rr♦r ❊∼✶✵✲✶✺✪✮ ❋✐♥❡r ✿ Pr♦❝❡ss♦r ✈♦❧t❛❣❡✴❢r❡q✉❡♥❝② ✭❊∼✺✲✾✪✮ ❊✈❡♥ ✜♥❡r✿ Pr♦❝❡ss♦r t❡♠♣❡r❛t✉r❡ ✭❊ ✹✲✼✪✮ ❉♦ ♥♦t ❢♦r❣❡t ❛❜♦✉t ❜✐❛s✿ ♣♦✇❡r s✉♣♣❧② ✉♥✐t ❊ ✷✲✸✪✱ ❝♦♦❧✐♥❣✱ ✳✳✳ ▲❡❛r♥✐♥❣ ♠❡t❤♦❞s ✭♥❡✉r❛❧ ♥❡t✇♦r❦s✱ ❊ ✷✪✮ P♦✇❡r = P♠✐♥ + ▲♦❛❞ × α❱♦❧t❛❣❡✷❋r❡q✉❡♥❝②

❞❛❝♦st❛❅✐r✐t✳❢r ✾✴✹✺

❍❡t❡r♦❣❡♥❡♦✉s ❤❛r❞✇❛r❡ ❆❞❛♣t✐♥❣ t♦ ❛♣♣❧✐❝❛t✐♦♥ ❧♦❛❞ ❉❛t❛❝❡♥t❡r ✐♥ ❛ ❜♦① ❈♦♥t❡①t ❉❡s✐❣♥❡❞ ❖♣♣♦rt✉♥✐st✐❝

❊✈❡♥ ♠♦❞❡❧s ❛r❡ ❤❡t❡r♦❣❡♥❡♦✉s

❊❧❡❝tr✐❝❛❧ ♣♦✇❡r ♠♦❞❡❧s ❢♦r ❛ s✐♥❣❧❡ s❡r✈❡r✿ ❈❧❛ss✐❝❛❧ ✿ ❧✐♥❡❛r ✭❡rr♦r ❊∼✶✵✲✶✺✪✮ ❋✐♥❡r ✿ Pr♦❝❡ss♦r ✈♦❧t❛❣❡✴❢r❡q✉❡♥❝② ✭❊∼✺✲✾✪✮ ❊✈❡♥ ✜♥❡r✿ Pr♦❝❡ss♦r t❡♠♣❡r❛t✉r❡ ✭❊∼✹✲✼✪✮ ❉♦ ♥♦t ❢♦r❣❡t ❛❜♦✉t ❜✐❛s✿ ♣♦✇❡r s✉♣♣❧② ✉♥✐t ❊ ✷✲✸✪✱ ❝♦♦❧✐♥❣✱ ✳✳✳ ▲❡❛r♥✐♥❣ ♠❡t❤♦❞s ✭♥❡✉r❛❧ ♥❡t✇♦r❦s✱ ❊ ✷✪✮ P♦✇❡r = P♠✐♥+▲♦❛❞×α❱♦❧t❛❣❡✷❋r❡q✉❡♥❝②+λ❚❡♠♣❡r❛t✉r❡

5 10 15 20 25 30 35 40 45 50 200 400 600 800 1000 Puissance (W) Temps (s) Applications Courant de fuite Puissance a vide Total

❞❛❝♦st❛❅✐r✐t✳❢r ✾✴✹✺

❍❡t❡r♦❣❡♥❡♦✉s ❤❛r❞✇❛r❡ ❆❞❛♣t✐♥❣ t♦ ❛♣♣❧✐❝❛t✐♦♥ ❧♦❛❞ ❉❛t❛❝❡♥t❡r ✐♥ ❛ ❜♦① ❈♦♥t❡①t ❉❡s✐❣♥❡❞ ❖♣♣♦rt✉♥✐st✐❝

❊✈❡♥ ♠♦❞❡❧s ❛r❡ ❤❡t❡r♦❣❡♥❡♦✉s

❊❧❡❝tr✐❝❛❧ ♣♦✇❡r ♠♦❞❡❧s ❢♦r ❛ s✐♥❣❧❡ s❡r✈❡r✿ ❈❧❛ss✐❝❛❧ ✿ ❧✐♥❡❛r ✭❡rr♦r ❊∼✶✵✲✶✺✪✮ ❋✐♥❡r ✿ Pr♦❝❡ss♦r ✈♦❧t❛❣❡✴❢r❡q✉❡♥❝② ✭❊∼✺✲✾✪✮ ❊✈❡♥ ✜♥❡r✿ Pr♦❝❡ss♦r t❡♠♣❡r❛t✉r❡ ✭❊∼✹✲✼✪✮ ❉♦ ♥♦t ❢♦r❣❡t ❛❜♦✉t ❜✐❛s✿ ♣♦✇❡r s✉♣♣❧② ✉♥✐t ❊∼✷✲✸✪✱ ❝♦♦❧✐♥❣✱ ✳✳✳ ▲❡❛r♥✐♥❣ ♠❡t❤♦❞s ✭♥❡✉r❛❧ ♥❡t✇♦r❦s✱ ❊ ✷✪✮ P♦✇❡r❉❈ = ω✵ + ω✶P♦✇❡r❆❈ + ω✷P♦✇❡r✸

❆❈

200 400 600 800 1000 20 40 60 80 100

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• ● ●
• DC Power (W)

Efficiency (%)

❞❛❝♦st❛❅✐r✐t✳❢r ✾✴✹✺

❍❡t❡r♦❣❡♥❡♦✉s ❤❛r❞✇❛r❡ ❆❞❛♣t✐♥❣ t♦ ❛♣♣❧✐❝❛t✐♦♥ ❧♦❛❞ ❉❛t❛❝❡♥t❡r ✐♥ ❛ ❜♦① ❈♦♥t❡①t ❉❡s✐❣♥❡❞ ❖♣♣♦rt✉♥✐st✐❝

❊✈❡♥ ♠♦❞❡❧s ❛r❡ ❤❡t❡r♦❣❡♥❡♦✉s

❊❧❡❝tr✐❝❛❧ ♣♦✇❡r ♠♦❞❡❧s ❢♦r ❛ s✐♥❣❧❡ s❡r✈❡r✿ ❈❧❛ss✐❝❛❧ ✿ ❧✐♥❡❛r ✭❡rr♦r ❊∼✶✵✲✶✺✪✮ ❋✐♥❡r ✿ Pr♦❝❡ss♦r ✈♦❧t❛❣❡✴❢r❡q✉❡♥❝② ✭❊∼✺✲✾✪✮ ❊✈❡♥ ✜♥❡r✿ Pr♦❝❡ss♦r t❡♠♣❡r❛t✉r❡ ✭❊∼✹✲✼✪✮ ❉♦ ♥♦t ❢♦r❣❡t ❛❜♦✉t ❜✐❛s✿ ♣♦✇❡r s✉♣♣❧② ✉♥✐t ❊∼✷✲✸✪✱ ❝♦♦❧✐♥❣✱ ✳✳✳ ▲❡❛r♥✐♥❣ ♠❡t❤♦❞s ✭♥❡✉r❛❧ ♥❡t✇♦r❦s✱ ❊∼✷✪✮ ∗

∗

▲❡❛♥❞r♦ ❡t ❛❧✳✱ ❚♦✇❛r❞s ❛ ❣❡♥❡r✐❝ ♣♦✇❡r ❡st✐♠❛t♦r✱ ❈❙❘❉ ❥♦✉r♥❛❧✱ ✷✵✶✺

...

input layer

...

• utput layer

hidden layers ❞❛❝♦st❛❅✐r✐t✳❢r ✾✴✹✺

❍❡t❡r♦❣❡♥❡♦✉s ❤❛r❞✇❛r❡ ❆❞❛♣t✐♥❣ t♦ ❛♣♣❧✐❝❛t✐♦♥ ❧♦❛❞ ❉❛t❛❝❡♥t❡r ✐♥ ❛ ❜♦① ❈♦♥t❡①t ❉❡s✐❣♥❡❞ ❖♣♣♦rt✉♥✐st✐❝

▼♦❞❡❧✐♥❣ ❛ ❞❛t❛❝❡♥t❡r ✐s ❛ ❝♦♠♣❧❡① t❛s❦

▲❛r❣❡ ♥✉♠❜❡r ♦❢ ❡❧❡♠❡♥ts

❆♣♣❧✐❝❛t✐♦♥s

Pr♦❝❡ss✿ ❚r❛❝❡s✱ ❤✐❣❤✲❧❡✈❡❧ ♠♦♥✐t♦r✐♥❣ t❤❡♥ ❛❜str❛❝t✐♦♥

❙❡r✈❡rs ■♥❢r❛str✉❝t✉r❡

❆♥❞ t❤❡✐r ✐♥t❡r❛❝t✐♦♥s

❚❤❡r♠❛❧ ✭❉✲▼❛tr✐①✮ ❇❡t✇❡❡♥ ❛♣♣❧✐❝❛t✐♦♥s

❞❛❝♦st❛❅✐r✐t✳❢r ✶✵✴✹✺

❍❡t❡r♦❣❡♥❡♦✉s ❤❛r❞✇❛r❡ ❆❞❛♣t✐♥❣ t♦ ❛♣♣❧✐❝❛t✐♦♥ ❧♦❛❞ ❉❛t❛❝❡♥t❡r ✐♥ ❛ ❜♦① ❈♦♥t❡①t ❉❡s✐❣♥❡❞ ❖♣♣♦rt✉♥✐st✐❝

▼♦❞❡❧✐♥❣ ❛ ❞❛t❛❝❡♥t❡r ✐s ❛ ❝♦♠♣❧❡① t❛s❦

▲❛r❣❡ ♥✉♠❜❡r ♦❢ ❡❧❡♠❡♥ts

❆♣♣❧✐❝❛t✐♦♥s

Pr♦❝❡ss✿ ❚r❛❝❡s✱ ❤✐❣❤✲❧❡✈❡❧ ♠♦♥✐t♦r✐♥❣ t❤❡♥ ❛❜str❛❝t✐♦♥

❙❡r✈❡rs ■♥❢r❛str✉❝t✉r❡

❆♥❞ t❤❡✐r ✐♥t❡r❛❝t✐♦♥s

❚❤❡r♠❛❧ ✭❉✲▼❛tr✐①✮ ❇❡t✇❡❡♥ ❛♣♣❧✐❝❛t✐♦♥s

❞❛❝♦st❛❅✐r✐t✳❢r ✶✵✴✹✺

❍❡t❡r♦❣❡♥❡♦✉s ❤❛r❞✇❛r❡ ❆❞❛♣t✐♥❣ t♦ ❛♣♣❧✐❝❛t✐♦♥ ❧♦❛❞ ❉❛t❛❝❡♥t❡r ✐♥ ❛ ❜♦① ❈♦♥t❡①t ❉❡s✐❣♥❡❞ ❖♣♣♦rt✉♥✐st✐❝

▼♦❞❡❧✐♥❣ ❛ ❞❛t❛❝❡♥t❡r ✐s ❛ ❝♦♠♣❧❡① t❛s❦

▲❛r❣❡ ♥✉♠❜❡r ♦❢ ❡❧❡♠❡♥ts

❆♣♣❧✐❝❛t✐♦♥s

Pr♦❝❡ss✿ ❚r❛❝❡s✱ ❤✐❣❤✲❧❡✈❡❧ ♠♦♥✐t♦r✐♥❣ t❤❡♥ ❛❜str❛❝t✐♦♥

❙❡r✈❡rs ■♥❢r❛str✉❝t✉r❡

❆♥❞ t❤❡✐r ✐♥t❡r❛❝t✐♦♥s

❚❤❡r♠❛❧ ✭❉✲▼❛tr✐①✮ ❇❡t✇❡❡♥ ❛♣♣❧✐❝❛t✐♦♥s

❞❛❝♦st❛❅✐r✐t✳❢r ✶✵✴✹✺

❍❡t❡r♦❣❡♥❡♦✉s ❤❛r❞✇❛r❡ ❆❞❛♣t✐♥❣ t♦ ❛♣♣❧✐❝❛t✐♦♥ ❧♦❛❞ ❉❛t❛❝❡♥t❡r ✐♥ ❛ ❜♦① ❈♦♥t❡①t ❉❡s✐❣♥❡❞ ❖♣♣♦rt✉♥✐st✐❝

▼♦❞❡❧✐♥❣ ❛ ❞❛t❛❝❡♥t❡r ✐s ❛ ❝♦♠♣❧❡① t❛s❦

▲❛r❣❡ ♥✉♠❜❡r ♦❢ ❡❧❡♠❡♥ts

❆♣♣❧✐❝❛t✐♦♥s

Pr♦❝❡ss✿ ❚r❛❝❡s✱ ❤✐❣❤✲❧❡✈❡❧ ♠♦♥✐t♦r✐♥❣ t❤❡♥ ❛❜str❛❝t✐♦♥

❙❡r✈❡rs ■♥❢r❛str✉❝t✉r❡

❆♥❞ t❤❡✐r ✐♥t❡r❛❝t✐♦♥s

❚❤❡r♠❛❧ ✭❉✲▼❛tr✐①✮∗ ❇❡t✇❡❡♥ ❛♣♣❧✐❝❛t✐♦♥s

∗ ❍♦♥❣ ❨❛♥❣ ❡t ❛❧✳✱❊♥❡r❣②✲❡✣❝✐❡♥t ❛♥❞ t❤❡r♠❛❧✲❛✇❛r❡ r❡s♦✉r❝❡ ♠❛♥❛❣❡♠❡♥t ❢♦r ❤❡t❡r♦❣❡♥❡♦✉s ❞❛t❛❝❡♥t❡rs✱ ❙❯❙❈❖▼ ❥♦✉r♥❛❧✱ ✷✵✶✹✳

❞❛❝♦st❛❅✐r✐t✳❢r ✶✵✴✹✺

❍❡t❡r♦❣❡♥❡♦✉s ❤❛r❞✇❛r❡ ❆❞❛♣t✐♥❣ t♦ ❛♣♣❧✐❝❛t✐♦♥ ❧♦❛❞ ❉❛t❛❝❡♥t❡r ✐♥ ❛ ❜♦① ❈♦♥t❡①t ❉❡s✐❣♥❡❞ ❖♣♣♦rt✉♥✐st✐❝

❆ ❝♦♠♣❧❡① ❧❛♥❞s❝❛♣❡

❍P❈

■♠♣r♦✈❡ ♣❡r❢♦r♠❛♥❝❡✱ t❤r♦✉❣❤♣✉t ❙t❡❛❞② ❛♥❞ ❦♥♦✇♥ ✇♦r❦❧♦❛❞

❈❧♦✉❞ s②st❡♠s

■♠♣r♦✈❡ ❝♦st ❡✣❝✐❡♥❝② ❱❛r②✐♥❣ ✇♦r❦❧♦❛❞✱ ❞✐✣❝✉❧t t♦ ♣r❡❞✐❝t

❚✇♦ ♠❛✐♥ q✉❡st✐♦♥s ✿

❍♦✇ t♦ ♣r♦❣r❛♠∗t❤❡♠ ❛t ❧❛r❣❡ s❝❛❧❡❄ ❍♦✇ t♦ ♠❛♥❛❣❡ t❤❡♠ ❛t r✉♥t✐♠❡❄

∗ ●❡♦r❣❡s ❡t ❛❧✳ ❊①❛s❝❛❧❡ ♠❛❝❤✐♥❡s r❡q✉✐r❡ ♥❡✇ ♣r♦❣r❛♠♠✐♥❣ ♣❛r❛❞✐❣♠s ❛♥❞ r✉♥t✐♠❡s✱ ❙❋■ ❥♦✉r♥❛❧✱ ✷✵✶✺

❞❛❝♦st❛❅✐r✐t✳❢r ✶✶✴✹✺

❍❡t❡r♦❣❡♥❡♦✉s ❤❛r❞✇❛r❡ ❆❞❛♣t✐♥❣ t♦ ❛♣♣❧✐❝❛t✐♦♥ ❧♦❛❞ ❉❛t❛❝❡♥t❡r ✐♥ ❛ ❜♦① ❈♦♥t❡①t ❉❡s✐❣♥❡❞ ❖♣♣♦rt✉♥✐st✐❝

❉❡❞✐❝❛t❡❞ ❤❛r❞✇❛r❡

❍P❈ ❛♣♣❧✐❝❛t✐♦♥s

❖❧❞ ♠❡t❤♦❞✿ ❈♦♠♠✉♥✐❝❛t✐♦♥ ❛♥❞ ❝♦♠♣✉t❛t✐♦♥ ♦✈❡r❧❛♣ ◆❡✇ ♠❡t❤♦❞✿ ❈♦♠♠✉♥✐❝❛t✐♦♥✱ ❝♦♠♣❧❡① ❝♦♠♣✉t❛t✐♦♥✱ ❤✐❣❤❧② ♣❛r❛❧❧❡❧ ❝♦♠♣✉t❛t✐♦♥✱✳✳✳

❉❡❞✐❝❛t❡❞ ❤❛r❞✇❛r❡

❉❡❞✐❝❛t❡❞ ❤❛r❞✇❛r❡ ❢♦r ❡❛❝❤ s✉❜✲t❛s❦ t♦ ✐♠♣r♦✈❡ ♦✈❡r❧❛♣

POTRF TRSM TRSM TRSM SYRK POTRF TRSM TRSM SYRK POTRF TRSM SYRK POTRF GEMM GEMM SYRK GEMM SYRK SYRK GEMM

❞❛❝♦st❛❅✐r✐t✳❢r ✶✷✴✹✺

❍❡t❡r♦❣❡♥❡♦✉s ❤❛r❞✇❛r❡ ❆❞❛♣t✐♥❣ t♦ ❛♣♣❧✐❝❛t✐♦♥ ❧♦❛❞ ❉❛t❛❝❡♥t❡r ✐♥ ❛ ❜♦① ❈♦♥t❡①t ❉❡s✐❣♥❡❞ ❖♣♣♦rt✉♥✐st✐❝

❙♦♠❡ ❡①❛♠♣❧❡s ♦❢ ❞❡❞✐❝❛t❡❞ ❤❛r❞✇❛r❡

❚♦♣✺✵✵

❚✐❛♥❤❡✲✷ ✿ ✶✻✱✵✵✵ ♥♦❞❡s✱ ❡❛❝❤ ❜✉✐❧❞ ♦❢ t✇♦ ■♥t❡❧ ■✈② ❇r✐❞❣❡ ❳❡♦♥ ❛♥❞ t❤r❡❡ ❳❡♦♥ P❤✐ ❝♦♣r♦❝❡ss♦rs

❊✉r♦♣❡❛♥ ♣r♦❥❡❝t ▼♦♥t❇❧❛♥❝

✷✶✻✵ ❆❘▼ ❈♦rt❡①✲❆✶✺ ❅ ✶✳✼ ●❍③ ❞✉❛❧ ❝♦r❡ ❈P❯ ❛♥❞ ✶✵✽✵ ❆❘▼ ▼❛❧✐ ❚✲✻✵✹ ●P❯

❍P ▼♦♦♥❙❤♦t ♣r♦❥❡❝t

❈P❯s✱ ❆P❯s✱ ●P❯s✱ ❉❙Ps✱ ❛♥❞ ❋P●❆s

❚❛s❦ ❞❡❞✐❝❛t❡❞ ❤❛r❞✇❛r❡

❉❡❡♣ ▲❡❛r♥✐♥❣ ✭◆❱■❉■❆ ❉●❳✲✶✱ ■♥t❡❧ ❳❡♦♥ P❤✐ ❑♥✐❣❤ts ▼✐❧❧✮

❞❛❝♦st❛❅✐r✐t✳❢r ✶✸✴✹✺

❍❡t❡r♦❣❡♥❡♦✉s ❤❛r❞✇❛r❡ ❆❞❛♣t✐♥❣ t♦ ❛♣♣❧✐❝❛t✐♦♥ ❧♦❛❞ ❉❛t❛❝❡♥t❡r ✐♥ ❛ ❜♦① ❈♦♥t❡①t ❉❡s✐❣♥❡❞ ❖♣♣♦rt✉♥✐st✐❝

❉❡❞✐❝❛t❡❞ ❤❡t❡r♦❣❡♥❡✐t② ✐s ❛t ❛❧❧ s❝❛❧❡

❉❛r❦ ❙✐❧✐❝♦♥

❖♥❣♦✐♥❣ r❡s❡❛r❝❤ ▼♦st❧② ♦♥ ♣r♦❝❡ss♦r ❙✇✐t❝❤ ♦✛ ✉♥✉s❡❞ ♣r♦❝❡ss♦rs ✉♥✐ts

❍❡t❡r♦❣❡♥❡♦✉s ♦♥✲❞✐❡ ❝♦r❡s

❇✐❣✳▲■❚❚▲❊ ❆❘▼ ✿ ❈♦rt❡① ❆✼ ✰ ❈♦rt❡① ❆✶✺✱ ✷✵µs ♠✐❣r❛t✐♦♥ ◆❱■❉■❆ ❖♣t✐♠✉s ✿ ❈P❯✲✐♥t❡❣r❛t❡❞ ●P❯ ✰ ❋✉❧❧✲✢❡❣❡❞ ●P❯✱ ✶✴✺t❤ ❢r❛♠❡ ♠✐❣r❛t✐♦♥

❙❛♠❡ ♣r♦❜❧❡♠s

▼♦t❤❡r❜♦❛r❞ ❢❛❝✐❧✐t✐❡s ✭❜✉s✱ ♥❡t✇♦r❦✱✳✳✳✮ ❛❧✇❛②s ♦♥ ❛♥❞ ❧❡ss ❞②♥❛♠✐❝ ❇❛s❡❧✐♥❡ ❡♥❡r❣②✲❝♦sts ❛r❡ ❤✐❣❤

❞❛❝♦st❛❅✐r✐t✳❢r ✶✹✴✹✺

❍❡t❡r♦❣❡♥❡♦✉s ❤❛r❞✇❛r❡ ❆❞❛♣t✐♥❣ t♦ ❛♣♣❧✐❝❛t✐♦♥ ❧♦❛❞ ❉❛t❛❝❡♥t❡r ✐♥ ❛ ❜♦① ❈♦♥t❡①t ❉❡s✐❣♥❡❞ ❖♣♣♦rt✉♥✐st✐❝

❊①❛♠♣❧❡ ♦❢ ❧♦♥❣✲t❡r♠ ♦r❣❛♥✐❝ ❣r♦✇

◆✉♠❜❡r ♦❢ ♣r♦❝❡ss♦rs ❢♦r ❡❛❝❤ t②♣❡ ♦♥ ●r✐❞✬✺✵✵✵ ✭t♦t❛❧ ✷✶✶✻✮ ❆▼❉ ❖♣t❡r♦♥ ✷✷✶✽ ✶✵✵ ■♥t❡❧ ❳❡♦♥ ❊✺✲✷✻✷✵ ✽ ■♥t❡❧ ❳❡♦♥ ❊✺✹✷✵ ✻✽ ❆▼❉ ❖♣t❡r♦♥ ✷✺✵ ✶✺✽ ■♥t❡❧ ❳❡♦♥ ❊✺✲✷✻✷✵ ✈✸ ✶✷ ■♥t❡❧ ❳❡♦♥ ❊✺✹✹✵ ✾✷ ❆▼❉ ❖♣t❡r♦♥ ✻✶✻✹ ❍❊ ✶✻✽ ■♥t❡❧ ❳❡♦♥ ❊✺✲✷✻✸✵ ✹✵ ■♥t❡❧ ❳❡♦♥ ❊✺✺✷✵ ✷✺✹ ■♥t❡❧ ❳❡♦♥ ❊✺✲✷✻✸✵ ✈✸ ✸✺✵ ■♥t❡❧ ❳❡♦♥ ❊✺✻✷✵ ✺✻ ■♥t❡❧ ❳❡♦♥ ❊✺✲✷✻✸✵▲ ✸✷ ■♥t❡❧ ❳❡♦♥ ❊✼✹✺✵ ✺✷ ■♥t❡❧ ❳❡♦♥ ❊✺✲✷✻✺✵ ✽ ■♥t❡❧ ❳❡♦♥ ▲✺✸✸✺ ✹✹ ■♥t❡❧ ❳❡♦♥ ❊✺✲✷✻✻✵ ✹✹ ■♥t❡❧ ❳❡♦♥ ▲✺✹✷✵ ✸✸✷ ■♥t❡❧ ❳❡♦♥ ❊✺✲✷✻✻✵ ✈✷ ✶✻ ■♥t❡❧ ❳❡♦♥ ❳✸✹✹✵ ✶✹✹ ■♥t❡❧ ❳❡♦♥ ❳✺✺✼✵ ✺✵ ■♥t❡❧ ❳❡♦♥ ❳✺✻✼✵ ✽✽

❞❛❝♦st❛❅✐r✐t✳❢r ✶✺✴✹✺

❍❡t❡r♦❣❡♥❡♦✉s ❤❛r❞✇❛r❡ ❆❞❛♣t✐♥❣ t♦ ❛♣♣❧✐❝❛t✐♦♥ ❧♦❛❞ ❉❛t❛❝❡♥t❡r ✐♥ ❛ ❜♦① ❈♦♥t❡①t ❉❡s✐❣♥❡❞ ❖♣♣♦rt✉♥✐st✐❝

■❚ ❞❡♣❛rt♠❡♥ts ❡✈♦❧✈❡

▲❛r❣❡ ✐♥st✐t✉t✐♦♥s ❛r❡ ❜✉✐❧❞ ♦✈❡r ②❡❛rs ❙♠❛❧❧❡st ♦♥❡ ❞♦ ♥♦t ♥❡❝❡ss❛r② ❝❤❛♥❣❡ ❤❛r❞✇❛r❡✱ ♦♥❧② ❜✉② ♥❡✇ ♦♥❡ ❚r✉❡ ❛❧s♦ ❢♦r s❝✐❡♥t✐sts

❑❡❡♣ ♦❧❞ ❤❛❜✐ts ❙♦♠❡t✐♠❡ ✉s❡ ❛❧❧ s❡r✈❡rs ❡✈❡♥ ♦❧❞❡st ♦♥❡

❚r✉❡ ❛❧s♦ ❢♦r s✐③❡

❙♠❛❧❧ ❞❡❞✐❝❛t❡❞ ❝❧✉st❡rs ❢♦r ♣❛rt✐❝✉❧❛r t❛s❦s

❞❛❝♦st❛❅✐r✐t✳❢r ✶✻✴✹✺

❍❡t❡r♦❣❡♥❡♦✉s ❤❛r❞✇❛r❡ ❆❞❛♣t✐♥❣ t♦ ❛♣♣❧✐❝❛t✐♦♥ ❧♦❛❞ ❉❛t❛❝❡♥t❡r ✐♥ ❛ ❜♦① ❈♦♥❝❡♣t ❙t❛t❡❧❡ss ❛♣♣❧✐❝❛t✐♦♥s ❚✐♠✐♥❣ ✐ss✉❡s ❙t❛t❡✲❢✉❧❧

❖✉t❧✐♥❡

✶ ❍❡t❡r♦❣❡♥❡♦✉s ❤❛r❞✇❛r❡

❈♦♥t❡①t ❍❡t❡r♦❣❡♥❡♦✉s❧② ❞❡s✐❣♥❡❞ ❖♣♣♦rt✉♥✐st✐❝❛❧❧② ❤❡t❡r♦❣❡♥❡♦✉s

✷ ❆❞❛♣t✐♥❣ t♦ ❛♣♣❧✐❝❛t✐♦♥ ❧♦❛❞

❈♦♥❝❡♣t ❙t❛t❡❧❡ss ❛♣♣❧✐❝❛t✐♦♥s ❚✐♠✐♥❣ ✐ss✉❡s ❙t❛t❡✲❢✉❧❧ ❛♣♣❧✐❝❛t✐♦♥s

✸ ❉❛t❛❝❡♥t❡r ✐♥ ❛ ❜♦①

❞❛❝♦st❛❅✐r✐t✳❢r ✶✼✴✹✺

❍❡t❡r♦❣❡♥❡♦✉s ❤❛r❞✇❛r❡ ❆❞❛♣t✐♥❣ t♦ ❛♣♣❧✐❝❛t✐♦♥ ❧♦❛❞ ❉❛t❛❝❡♥t❡r ✐♥ ❛ ❜♦① ❈♦♥❝❡♣t ❙t❛t❡❧❡ss ❛♣♣❧✐❝❛t✐♦♥s ❚✐♠✐♥❣ ✐ss✉❡s ❙t❛t❡✲❢✉❧❧

❍❛r♥❡ss✐♥❣ ❤❡t❡r♦❣❡♥❡✐t②

❍P❈

❯s❡ ❛❧❧ t❤❡ ♣❧❛t❢♦r♠ ❢♦r ♠❛①✐♠✉♠ ♣❡r❢♦r♠❛♥❝❡

❈❧♦✉❞

❈♦♥s♦❧✐❞❛t✐♦♥ ♦❢ ♠✉❧t✐♣❧❡ ❛♣♣❧✐❝❛t✐♦♥s ✭✈✐rt✉❛❧ ♠❛❝❤✐♥❡s✮

❈♦♠♠♦♥

❆❧❧♦❝❛t❡ t❛s❦s✴❱✐rt✉❛❧ ♠❛❝❤✐♥❡s ♦♥ t❤❡ ♠♦st ❛❞❛♣t❡❞ ❤❛r❞✇❛r❡ ❯s❡ t❤❡ ❜❡st st❛t❡ ✭❢r❡q✉❡♥❝②✱ ❞❛t❛ ♠♦✈❡♠❡♥t✱✳✳✳✮

❞❛❝♦st❛❅✐r✐t✳❢r ✶✽✴✹✺

❍❡t❡r♦❣❡♥❡♦✉s ❤❛r❞✇❛r❡ ❆❞❛♣t✐♥❣ t♦ ❛♣♣❧✐❝❛t✐♦♥ ❧♦❛❞ ❉❛t❛❝❡♥t❡r ✐♥ ❛ ❜♦① ❈♦♥❝❡♣t ❙t❛t❡❧❡ss ❛♣♣❧✐❝❛t✐♦♥s ❚✐♠✐♥❣ ✐ss✉❡s ❙t❛t❡✲❢✉❧❧

❙♠❛❧❧ ✐s ❜❡❛✉t✐❢✉❧

❲❤❛t ✐s t❤❡ st❛t✉s ♦❢ ❡♥❡r❣②✲❡✣❝✐❡♥❝② ✐♥ ❞❛t❛✲❝❡♥t❡rs❄ ❈✉rr❡♥t❧②✱ ❧♦ts ♦❢ ✇♦r❦ ✐s ❞♦♥❡ ♦♥ ❝♦♥s♦❧✐❞❛t✐♦♥ ▼❡tr✐❝ ❛r❡ ❡✈❛❧✉❛t❡❞ ❛t ❢✉❧❧ ❝❤❛r❣❡ ❋♦r ❛❧❧ ✉s❛❣❡s ❄ ◆♦t ❢♦r✿

■rr❡❣✉❧❛r ✇♦r❦❧♦❛❞ ▲♦✇ ✇♦r❦❧♦❛❞

❲❤② ✐s ✐t ✐♠♣♦rt❛♥t ❄

❇❡❝❛✉s❡ ✇❡ ❛r❡ ♥♦t ✐♥ ❛ ❧✐♥❡❛r ✇♦r❧❞ ✦ ❊✈❡♥ ❢♦r r❡❛❧❧② ❡✣❝✐❡♥t s②st❡♠s ✭❛t ❢✉❧❧ ❝❤❛r❣❡✮

❞❛❝♦st❛❅✐r✐t✳❢r ✶✾✴✹✺

❍❡t❡r♦❣❡♥❡♦✉s ❤❛r❞✇❛r❡ ❆❞❛♣t✐♥❣ t♦ ❛♣♣❧✐❝❛t✐♦♥ ❧♦❛❞ ❉❛t❛❝❡♥t❡r ✐♥ ❛ ❜♦① ❈♦♥❝❡♣t ❙t❛t❡❧❡ss ❛♣♣❧✐❝❛t✐♦♥s ❚✐♠✐♥❣ ✐ss✉❡s ❙t❛t❡✲❢✉❧❧

▲♦✇ ✉t✐❧✐③❛t✐♦♥ ❂ ❤✐❣❤ ❡❧❡❝tr✐❝❛❧ ✇❛st❡

■♥ ❧❛r❣❡ ♦r❣❛♥✐③❛t✐♦♥s✱ ❝♦♠♣✉t❡rs ❛r❡ ✉s✉❛❧❧② ✇♦r❦✐♥❣ ❜❡t✇❡❡♥ ✶✵ t♦ ✺✵✪ ❧♦❛❞ ■❞❧❡ ♣♦✇❡r ✐s ❤❛❧❢ ♦❢ ♠❛① ♣♦✇❡r Pr♦❜❧❡♠✿ ❖♥ ❧♦✇ ❧♦❛❞✱ ❲❛tt✴❘❡q✉❡st ✐s ❜❛❞

❇❛rr♦s♦ ✷✵✵✼

❞❛❝♦st❛❅✐r✐t✳❢r ✷✵✴✹✺

❍❡t❡r♦❣❡♥❡♦✉s ❤❛r❞✇❛r❡ ❆❞❛♣t✐♥❣ t♦ ❛♣♣❧✐❝❛t✐♦♥ ❧♦❛❞ ❉❛t❛❝❡♥t❡r ✐♥ ❛ ❜♦① ❈♦♥❝❡♣t ❙t❛t❡❧❡ss ❛♣♣❧✐❝❛t✐♦♥s ❚✐♠✐♥❣ ✐ss✉❡s ❙t❛t❡✲❢✉❧❧

▲♦✇ ✉t✐❧✐③❛t✐♦♥ ❂ ❤✐❣❤ ❡❧❡❝tr✐❝❛❧ ✇❛st❡

■♥ ❧❛r❣❡ ♦r❣❛♥✐③❛t✐♦♥s✱ ❝♦♠♣✉t❡rs ❛r❡ ✉s✉❛❧❧② ✇♦r❦✐♥❣ ❜❡t✇❡❡♥ ✶✵ t♦ ✺✵✪ ❧♦❛❞ ■❞❧❡ ♣♦✇❡r ✐s ❤❛❧❢ ♦❢ ♠❛① ♣♦✇❡r Pr♦❜❧❡♠✿ ❖♥ ❧♦✇ ❧♦❛❞✱ ❲❛tt✴❘❡q✉❡st ✐s ❜❛❞

0.1 1 10 100 200 300 400 500 600 700 Energy per request (Joules) Requests per second Proportional hardware Intel I7

❞❛❝♦st❛❅✐r✐t✳❢r ✷✵✴✹✺

❍❡t❡r♦❣❡♥❡♦✉s ❤❛r❞✇❛r❡ ❆❞❛♣t✐♥❣ t♦ ❛♣♣❧✐❝❛t✐♦♥ ❧♦❛❞ ❉❛t❛❝❡♥t❡r ✐♥ ❛ ❜♦① ❈♦♥❝❡♣t ❙t❛t❡❧❡ss ❛♣♣❧✐❝❛t✐♦♥s ❚✐♠✐♥❣ ✐ss✉❡s ❙t❛t❡✲❢✉❧❧

❈✉rr❡♥t ♠❡t❤♦❞s

❈✉rr❡♥t ♠❡t❤♦❞s✿

❖♥ ❤✐❣❤ ❧♦❛❞✱ ❝♦♥s♦❧✐❞❛t✐♦♥✳ ❖♥ ❤✐❣❤ ♥✉♠❜❡r ♦❢ r❡q✉❡sts✱ ♦✈❡r❤❡❛❞ ✐s s♣r❡❛❞ ♦♥ ❧♦ts ♦❢ ♥♦❞❡s ❇✉t ✇❛st❡❞ ❲❛tts ❝♦♥t✐♥✉❡ t♦ ❛❞❞✲✉♣

❲❤❛t ❞♦ ✇❡ ✇❛♥t ❄

♣r♦♣♦rt✐♦♥❛❧ ❝♦♠♣✉t✐♥❣ ✐❞❧❡ ❧♦❛❞ ❂ ✵❲

❞❛❝♦st❛❅✐r✐t✳❢r ✷✶✴✹✺

❍❡t❡r♦❣❡♥❡♦✉s ❤❛r❞✇❛r❡ ❆❞❛♣t✐♥❣ t♦ ❛♣♣❧✐❝❛t✐♦♥ ❧♦❛❞ ❉❛t❛❝❡♥t❡r ✐♥ ❛ ❜♦① ❈♦♥❝❡♣t ❙t❛t❡❧❡ss ❛♣♣❧✐❝❛t✐♦♥s ❚✐♠✐♥❣ ✐ss✉❡s ❙t❛t❡✲❢✉❧❧

❘❡❛❝❤✐♥❣ ❡♥❡r❣②✲♣r♦♣♦rt✐♦♥❛❧✐t② ✉s✐♥❣ ❤❡t✲ ❡r♦❣❡♥❡♦✉s ❤❛r❞✇❛r❡

❯s❡ ♥♦❞❡s ❞❡♣❡♥❞✐♥❣ ♦♥ t❤❡ r❡❛❧ ❧♦❛❞ ✭✇❡❜ s❡r✈❡r ❛s ❡①❛♠♣❧❡✮✱ ♥♦t t❤❡ ♣❡❛❦ ❧♦❛❞ ❊①❛♠♣❧❡✿ Pr♦❝❡ss♦r ❲❛tt r❛♥❣❡ ▼❛① r❡q✉❡st✴s ❊✣❝✐❡♥❝② ✭❲✴r✮ ■♥t❡❧ ■✼ ✶✶ ✲ ✹✷ ✸✺✸ ✳✶✷ ■♥t❡❧ ❆t♦♠ ✽ ✲ ✾ ✸✹ ✳✷✻ ❘❛s♣❜❡rr② P✐ ✷✳✺✻ ✲ ✷✳✽✶ ✺✳✻ ✳✺✵ ■♥t✉✐t✐♦♥✿ ❙❡✈❡r❛❧ s♠❛❧❧ ♥♦❞❡ ❛♥❞ ✐♥t❡r♠❡❞✐❛r② ♥♦❞❡s t♦ ❤❛✈❡ ❛ ♠✉❧t✐✲s❝❛❧❡ s♠♦♦t❤ ❝✉r✈❡

❞❛❝♦st❛❅✐r✐t✳❢r ✷✷✴✹✺

❍❡t❡r♦❣❡♥❡♦✉s ❤❛r❞✇❛r❡ ❆❞❛♣t✐♥❣ t♦ ❛♣♣❧✐❝❛t✐♦♥ ❧♦❛❞ ❉❛t❛❝❡♥t❡r ✐♥ ❛ ❜♦① ❈♦♥❝❡♣t ❙t❛t❡❧❡ss ❛♣♣❧✐❝❛t✐♦♥s ❚✐♠✐♥❣ ✐ss✉❡s ❙t❛t❡✲❢✉❧❧

❩♦♦♠ ♦♥ ■♥t❡❧ ■✼

5 10 15 20 25 30 35 40 45 50 100 150 200 250 300 T

• tal Watt/Requests per second/Latency

Number of clients Power consumption (W) Latency (1/100th of second) 10 Requests per second

❞❛❝♦st❛❅✐r✐t✳❢r ✷✸✴✹✺

❍❡t❡r♦❣❡♥❡♦✉s ❤❛r❞✇❛r❡ ❆❞❛♣t✐♥❣ t♦ ❛♣♣❧✐❝❛t✐♦♥ ❧♦❛❞ ❉❛t❛❝❡♥t❡r ✐♥ ❛ ❜♦① ❈♦♥❝❡♣t ❙t❛t❡❧❡ss ❛♣♣❧✐❝❛t✐♦♥s ❚✐♠✐♥❣ ✐ss✉❡s ❙t❛t❡✲❢✉❧❧

❩♦♦♠ ♦♥ ■♥t❡❧ ❆t♦♠

2 4 6 8 10 12 10 20 30 40 50 60 T

• tal Watt/Requests per second/Latency

Number of clients Power consumption (W) Latency (1/10th of second) 10 Requests per second

❞❛❝♦st❛❅✐r✐t✳❢r ✷✹✴✹✺

❍❡t❡r♦❣❡♥❡♦✉s ❤❛r❞✇❛r❡ ❆❞❛♣t✐♥❣ t♦ ❛♣♣❧✐❝❛t✐♦♥ ❧♦❛❞ ❉❛t❛❝❡♥t❡r ✐♥ ❛ ❜♦① ❈♦♥❝❡♣t ❙t❛t❡❧❡ss ❛♣♣❧✐❝❛t✐♦♥s ❚✐♠✐♥❣ ✐ss✉❡s ❙t❛t❡✲❢✉❧❧

❈♦♠♣❛r✐s♦♥

2 4 6 8 10 12 14 16 5 10 15 20 25 30 35 40 45 50 T

• tal Watt

Requests per second Intel I7 Intel Atom Raspberry Pi 2 Raspberry Pi 3 Raspberry Pi

❞❛❝♦st❛❅✐r✐t✳❢r ✷✺✴✹✺

❍❡t❡r♦❣❡♥❡♦✉s ❤❛r❞✇❛r❡ ❆❞❛♣t✐♥❣ t♦ ❛♣♣❧✐❝❛t✐♦♥ ❧♦❛❞ ❉❛t❛❝❡♥t❡r ✐♥ ❛ ❜♦① ❈♦♥❝❡♣t ❙t❛t❡❧❡ss ❛♣♣❧✐❝❛t✐♦♥s ❚✐♠✐♥❣ ✐ss✉❡s ❙t❛t❡✲❢✉❧❧

❆ ♥❡❛r✲❧✐♥❡❛r ❜❡❤❛✈✐♦r

❚❛❦❡ t❤❡ ♠♦st ❡✣❝✐❡♥t ❤❛r❞✇❛r❡ ❛s ❢✉♥❝t✐♦♥ ♦❢ ✇♦r❦❧♦❛❞✿ ✵→✺ r❡q✴s ✶ ❘❛s♣❜❡rr② P✐ ✺→✶✵ r❡q✴s ✷ ❘❛s♣❜❡rr② P✐ ✶✵→✸✺ r❡q✴s ✶ ■♥t❡❧ ❆t♦♠ ✸✺→✹✵ r❡q✴s ✶ ■♥t❡❧ ❆t♦♠ ✰ ✶ ❘❛s♣❜❡rr② P✐ ✹✵→✸✺✵ r❡q✴s ✶ ■♥t❡❧ ■✼ ❋♦r ♦✈❡r ✸✺✵r❡q✴s✱ ✉s❡ ♠♦❞✉❧♦ ✸✺✵✱ ❛♥❞ ✉s❡ ❛s ♠❛♥② ■✼ ❛s ♥❡❝❡ss❛r②

❞❛❝♦st❛❅✐r✐t✳❢r ✷✻✴✹✺

❍❡t❡r♦❣❡♥❡♦✉s ❤❛r❞✇❛r❡ ❆❞❛♣t✐♥❣ t♦ ❛♣♣❧✐❝❛t✐♦♥ ❧♦❛❞ ❉❛t❛❝❡♥t❡r ✐♥ ❛ ❜♦① ❈♦♥❝❡♣t ❙t❛t❡❧❡ss ❛♣♣❧✐❝❛t✐♦♥s ❚✐♠✐♥❣ ✐ss✉❡s ❙t❛t❡✲❢✉❧❧

❙t✐❧❧ ❢❛r ❢❛r ❛✇❛②✳✳✳

5 10 15 20 25 30 35 40 45 50 100 150 200 250 300 350 T

• tal Watt

Requests per second Proportional hardware Intel I7 Heterogeneous hardware

❞❛❝♦st❛❅✐r✐t✳❢r ✷✼✴✹✺

❍❡t❡r♦❣❡♥❡♦✉s ❤❛r❞✇❛r❡ ❆❞❛♣t✐♥❣ t♦ ❛♣♣❧✐❝❛t✐♦♥ ❧♦❛❞ ❉❛t❛❝❡♥t❡r ✐♥ ❛ ❜♦① ❈♦♥❝❡♣t ❙t❛t❡❧❡ss ❛♣♣❧✐❝❛t✐♦♥s ❚✐♠✐♥❣ ✐ss✉❡s ❙t❛t❡✲❢✉❧❧

◆♦t s♦ ❢❛r✱ ❡✣❝✐❡♥❝② ✈✐❡✇ ✦

1 2 3 4 5 6 7 8 50 100 150 200 250 300 350 Energy per request (Joules) Requests per second Proportional hardware Heterogeneous hardware Intel I7

❞❛❝♦st❛❅✐r✐t✳❢r ✷✽✴✹✺

❍❡t❡r♦❣❡♥❡♦✉s ❤❛r❞✇❛r❡ ❆❞❛♣t✐♥❣ t♦ ❛♣♣❧✐❝❛t✐♦♥ ❧♦❛❞ ❉❛t❛❝❡♥t❡r ✐♥ ❛ ❜♦① ❈♦♥❝❡♣t ❙t❛t❡❧❡ss ❛♣♣❧✐❝❛t✐♦♥s ❚✐♠✐♥❣ ✐ss✉❡s ❙t❛t❡✲❢✉❧❧

✾✽ ❋♦♦t❜❛❧❧ ❲♦r❧❞ ❈✉♣

❆✈❛✐❧❛❜❧❡ ❞❛t❛ ✾✷ ❞❛②s ♦❢ ✇❡❜ s❡r✈❡r ❛❝❝❡ss ❧♦❣s ❲♦r❦❧♦❛❞ ♣r❡❝✐s❡ ❛t t❤❡ s❡❝♦♥❞ ❧❡✈❡❧ ❋♦✉r ❣❡♦❣r❛♣❤✐❝ ❧♦❝❛t✐♦♥s✱ t❤r❡❡ ✐♥ ❯❙✱ ♦♥❡ ✐♥ ❋r❛♥❝❡ ❙❡✈❡r❛❧ ♣❤❛s❡s

▲♦✇ ♣❤❛s❡s✱ ✜rst ✹✵ ❞❛②s ❛♥❞ ❧❛st ✶✵ ❞❛②s ❍✐❣❤ ♣❤❛s❡✱ ❞✉r✐♥❣ t❤❡ ❝♦♠♣❡t✐t✐♦♥

❞❛❝♦st❛❅✐r✐t✳❢r ✷✾✴✹✺

❍❡t❡r♦❣❡♥❡♦✉s ❤❛r❞✇❛r❡ ❆❞❛♣t✐♥❣ t♦ ❛♣♣❧✐❝❛t✐♦♥ ❧♦❛❞ ❉❛t❛❝❡♥t❡r ✐♥ ❛ ❜♦① ❈♦♥❝❡♣t ❙t❛t❡❧❡ss ❛♣♣❧✐❝❛t✐♦♥s ❚✐♠✐♥❣ ✐ss✉❡s ❙t❛t❡✲❢✉❧❧

100 200 300 400 500 600 700 10 20 30 40 50 60 70 80 90 100 Mean number of requests/second Time (day) ALL 98 World cup web sites Santa Clara servers Plano servers Herndon servers Paris servers

❞❛❝♦st❛❅✐r✐t✳❢r ✸✵✴✹✺

❍❡t❡r♦❣❡♥❡♦✉s ❤❛r❞✇❛r❡ ❆❞❛♣t✐♥❣ t♦ ❛♣♣❧✐❝❛t✐♦♥ ❧♦❛❞ ❉❛t❛❝❡♥t❡r ✐♥ ❛ ❜♦① ❈♦♥❝❡♣t ❙t❛t❡❧❡ss ❛♣♣❧✐❝❛t✐♦♥s ❚✐♠✐♥❣ ✐ss✉❡s ❙t❛t❡✲❢✉❧❧

❈♦♠♣❛r✐s♦♥ ✐❢ ✉s✐♥❣ ♦♥❡ s✐♥❣❧❡ ❞❛t❛✲❝❡♥t❡r

2e+06 4e+06 6e+06 8e+06 1e+07 1.2e+07 1.4e+07 1.6e+07 1.8e+07 2e+07 10 20 30 40 50 60 70 80 90 100 Energy (J) Time (day) Proportional hardware Heterogeneous hardware Intel I7 Intel Atom Raspberry Pi

❞❛❝♦st❛❅✐r✐t✳❢r ✸✶✴✹✺

❍❡t❡r♦❣❡♥❡♦✉s ❤❛r❞✇❛r❡ ❆❞❛♣t✐♥❣ t♦ ❛♣♣❧✐❝❛t✐♦♥ ❧♦❛❞ ❉❛t❛❝❡♥t❡r ✐♥ ❛ ❜♦① ❈♦♥❝❡♣t ❙t❛t❡❧❡ss ❛♣♣❧✐❝❛t✐♦♥s ❚✐♠✐♥❣ ✐ss✉❡s ❙t❛t❡✲❢✉❧❧

❩♦♦♠ ♦♥ t❤❡ ♠♦st ❡✣❝✐❡♥t ♠❡t❤♦❞s

1e+06 2e+06 3e+06 4e+06 5e+06 6e+06 10 20 30 40 50 60 70 80 90 100 Energy (J) Time (day) Proportional hardware Heterogeneous hardware Intel I7

❞❛❝♦st❛❅✐r✐t✳❢r ✸✷✴✹✺

❍❡t❡r♦❣❡♥❡♦✉s ❤❛r❞✇❛r❡ ❆❞❛♣t✐♥❣ t♦ ❛♣♣❧✐❝❛t✐♦♥ ❧♦❛❞ ❉❛t❛❝❡♥t❡r ✐♥ ❛ ❜♦① ❈♦♥❝❡♣t ❙t❛t❡❧❡ss ❛♣♣❧✐❝❛t✐♦♥s ❚✐♠✐♥❣ ✐ss✉❡s ❙t❛t❡✲❢✉❧❧

❋❛r r❡❛❝❤❡❞ ❣♦❛❧✿ ♣r♦♣♦rt✐♦♥❛❧ ❝♦♠♣✉t✲ ✐♥❣

1 10 100 10 20 30 40 50 60 70 80 90 100 Energy Inefficiency (Proportional=1) Time (day) Proportional hardware Heterogeneous hardware Intel I7 Intel Atom Raspberry Pi

❞❛❝♦st❛❅✐r✐t✳❢r ✸✸✴✹✺

❍❡t❡r♦❣❡♥❡♦✉s ❤❛r❞✇❛r❡ ❆❞❛♣t✐♥❣ t♦ ❛♣♣❧✐❝❛t✐♦♥ ❧♦❛❞ ❉❛t❛❝❡♥t❡r ✐♥ ❛ ❜♦① ❈♦♥❝❡♣t ❙t❛t❡❧❡ss ❛♣♣❧✐❝❛t✐♦♥s ❚✐♠✐♥❣ ✐ss✉❡s ❙t❛t❡✲❢✉❧❧

❈♦♠♣❛r✐s♦♥ ✐❢ ✉s✐♥❣ ♠✉❧t✐♣❧❡ ❞❛t❛✲❝❡♥t❡rs

5e+07 1e+08 1.5e+08 2e+08 Santa Clara Plano Herndon Paris Joules One Single Data-center Proportional hardware Heterogeneous hardware Intel I7

❞❛❝♦st❛❅✐r✐t✳❢r ✸✹✴✹✺

❍❡t❡r♦❣❡♥❡♦✉s ❤❛r❞✇❛r❡ ❆❞❛♣t✐♥❣ t♦ ❛♣♣❧✐❝❛t✐♦♥ ❧♦❛❞ ❉❛t❛❝❡♥t❡r ✐♥ ❛ ❜♦① ❈♦♥❝❡♣t ❙t❛t❡❧❡ss ❛♣♣❧✐❝❛t✐♦♥s ❚✐♠✐♥❣ ✐ss✉❡s ❙t❛t❡✲❢✉❧❧

❆❞❞✐♥❣ ♠❛♥❛❣❡♠❡♥t ❤❡t❡r♦❣❡♥❡✐t②

❙✇✐t❝❤✐♥❣ ♦♥✴♦✛ ♥♦❞❡s t❛❦❡ t✐♠❡ ❙✇✐t❝❤✐♥❣ ♦♥✴♦✛ ♥♦❞❡s ❝♦♥s✉♠❡s ❡♥❡r❣②

❋♦r ❛♣♣❧✐❝❛t✐♦♥ r❡❝♦♥✜❣✉r❛t✐♦♥ ❋♦r s✇✐t❝❤✐♥❣ ♦♥✴♦✛ t❤❡ s❡r✈❡r

▲❡❢❡✈r❡ ❛♥❞ ❛❧✳✱ ❙✉♣❡r❝♦♠♣✉t✐♥❣ ✷✵✵✽ ❞❛❝♦st❛❅✐r✐t✳❢r ✸✺✴✹✺

❍❡t❡r♦❣❡♥❡♦✉s ❤❛r❞✇❛r❡ ❆❞❛♣t✐♥❣ t♦ ❛♣♣❧✐❝❛t✐♦♥ ❧♦❛❞ ❉❛t❛❝❡♥t❡r ✐♥ ❛ ❜♦① ❈♦♥❝❡♣t ❙t❛t❡❧❡ss ❛♣♣❧✐❝❛t✐♦♥s ❚✐♠✐♥❣ ✐ss✉❡s ❙t❛t❡✲❢✉❧❧

❙❡✈❡r❛❧ ♠❡t❤♦❞s t♦ ♠❛♥❛❣❡ s❡r✈❡rs

❊①❛❝t ❛♣♣r♦❛❝❤✱ ❧✐♥❡❛r ♣r♦❣r❛♠♠✐♥❣ ❍❡✉r✐st✐❝s

❘❡❛❝t✐✈❡

❲❤❡♥ ♦✈❡r❧♦❛❞❡❞✱ st❛rt ♥❡✇ s❡r✈❡rs✱ ✇❤❡♥ ✉♥❞❡r✲❧♦❛❞❡❞ st♦♣ s♦♠❡

Pr♦✲❛❝t✐✈❡

Pr❡❞✐❝t t❤❡ ❢✉t✉r❡ ❛♥❞ ❞❡❝✐❞❡ ✇❤✐❝❤ s❡r✈❡r t♦ ✉s❡

t0 shortWin_i tOn_j tOn_k shortWin_k shortWin_j tOn_i tOn_k + 1 tOn_i + 1 tOn_j + 1

❱✐♦❧❛✐♥❡ ❛♥❞ ❛❧✳✱ ❙❇❆❈✲P❆❉ ✷✵✶✻ ❞❛❝♦st❛❅✐r✐t✳❢r ✸✻✴✹✺

❍❡t❡r♦❣❡♥❡♦✉s ❤❛r❞✇❛r❡ ❆❞❛♣t✐♥❣ t♦ ❛♣♣❧✐❝❛t✐♦♥ ❧♦❛❞ ❉❛t❛❝❡♥t❡r ✐♥ ❛ ❜♦① ❈♦♥❝❡♣t ❙t❛t❡❧❡ss ❛♣♣❧✐❝❛t✐♦♥s ❚✐♠✐♥❣ ✐ss✉❡s ❙t❛t❡✲❢✉❧❧

▲✐♥❡❛r ♣r♦❣r❛♠♠✐♥❣

❉❡s❝r✐❜❡ ❛❧❧ ❝♦♥str❛✐♥ts ✇✐t❤ ❧✐♥❡❛r ❡q✉❛t✐♦♥s ❉❡s❝r✐❜❡ t❤❡ ♦❜❥❡❝t✐✈❡ ❛s ❛ ❢✉♥❝t✐♦♥ t♦ ♠✐♥✐♠✐③❡ ❋♦r♠❛❧✐③❡ ❧❡✈❡r❛❣❡s ❛♥❞ t❤❡✐r ✐♠♣❛❝t ❆♣♣r♦①✐♠❛t✐♦♥ ♦❢ r❡❛❧ ✇♦r❧❞ ✭q✉❛❞r❛t✐❝ ♣❤❡♥♦♠❡♥❛✮ ❊①❛❝t r❡s♦❧✉t✐♦♥ ❢♦r s♠❛❧❧ ❝❛s❡s ❊①❛♠♣❧❡ ✿ ❆ t❛s❦ ✐s ♦♥ ❛ ✉♥✐q✉❡ s❡r✈❡r ▲❡t ❡❥❤ t❤❡ ❢❛❝t t❤❛t t❛s❦ ❥ r✉♥s ♦♥ s❡r✈❡r ❤ ❡❥❤ = ✶ ✐✐❢ t❛s❦ ❥ ✐s ♦♥ s❡r✈❡r ❤ ∀❥, ❤ ❡❥❤ ∈ {✵, ✶}✱ ∀❥

• ❤ ❡❥❤ = ✶

❞❛❝♦st❛❅✐r✐t✳❢r ✸✼✴✹✺

❍❡t❡r♦❣❡♥❡♦✉s ❤❛r❞✇❛r❡ ❆❞❛♣t✐♥❣ t♦ ❛♣♣❧✐❝❛t✐♦♥ ❧♦❛❞ ❉❛t❛❝❡♥t❡r ✐♥ ❛ ❜♦① ❈♦♥❝❡♣t ❙t❛t❡❧❡ss ❛♣♣❧✐❝❛t✐♦♥s ❚✐♠✐♥❣ ✐ss✉❡s ❙t❛t❡✲❢✉❧❧

▲✐♥❡❛r ♣r♦❣r❛♠♠✐♥❣

❉❡s❝r✐❜❡ ❛❧❧ ❝♦♥str❛✐♥ts ✇✐t❤ ❧✐♥❡❛r ❡q✉❛t✐♦♥s ❉❡s❝r✐❜❡ t❤❡ ♦❜❥❡❝t✐✈❡ ❛s ❛ ❢✉♥❝t✐♦♥ t♦ ♠✐♥✐♠✐③❡ ❋♦r♠❛❧✐③❡ ❧❡✈❡r❛❣❡s ❛♥❞ t❤❡✐r ✐♠♣❛❝t ❆♣♣r♦①✐♠❛t✐♦♥ ♦❢ r❡❛❧ ✇♦r❧❞ ✭q✉❛❞r❛t✐❝ ♣❤❡♥♦♠❡♥❛✮ ❊①❛❝t r❡s♦❧✉t✐♦♥ ❢♦r s♠❛❧❧ ❝❛s❡s ❊①❛♠♣❧❡ ✿ ▼✐♥✐♠✐③❡ t❤❡ t♦t❛❧ ♣♦✇❡r ❝♦♥s✉♠❡❞ Pst❛t

❤

❡t P❞②♥

❤

✿ st❛t✐❝ ❛♥❞ ❞②♥❛♠✐❝ ♣♦✇❡r ♦❢ s❡r✈❡r ❤ ✭❧✐♥❡❛r ♠♦❞❡❧✮ ▲❡t α❥❤ t❤❡ ♣r♦❝❡ss♦r ❢r❛❝t✐♦♥ ♦❢ t❛s❦ ❥ ♦♥ s❡r✈❡r ❤ ♠✐♥

❤ (Pst❛t ❤

+

❥ α❥❤P❞②♥ ❤

)

❞❛❝♦st❛❅✐r✐t✳❢r ✸✼✴✹✺

❍❡t❡r♦❣❡♥❡♦✉s ❤❛r❞✇❛r❡ ❆❞❛♣t✐♥❣ t♦ ❛♣♣❧✐❝❛t✐♦♥ ❧♦❛❞ ❉❛t❛❝❡♥t❡r ✐♥ ❛ ❜♦① ❈♦♥❝❡♣t ❙t❛t❡❧❡ss ❛♣♣❧✐❝❛t✐♦♥s ❚✐♠✐♥❣ ✐ss✉❡s ❙t❛t❡✲❢✉❧❧

▲✐♥❡❛r ♣r♦❣r❛♠♠✐♥❣

❉❡s❝r✐❜❡ ❛❧❧ ❝♦♥str❛✐♥ts ✇✐t❤ ❧✐♥❡❛r ❡q✉❛t✐♦♥s ❉❡s❝r✐❜❡ t❤❡ ♦❜❥❡❝t✐✈❡ ❛s ❛ ❢✉♥❝t✐♦♥ t♦ ♠✐♥✐♠✐③❡ ❋♦r♠❛❧✐③❡ ❧❡✈❡r❛❣❡s ❛♥❞ t❤❡✐r ✐♠♣❛❝t ❆♣♣r♦①✐♠❛t✐♦♥ ♦❢ r❡❛❧ ✇♦r❧❞ ✭q✉❛❞r❛t✐❝ ♣❤❡♥♦♠❡♥❛✮ ❊①❛❝t r❡s♦❧✉t✐♦♥ ❢♦r s♠❛❧❧ ❝❛s❡s

❈♦♥str❛✐♥ts ✿ ∀❤ ♣❤ ∈ {✵, ✶} ∀❥

• ❤ ❡❥❤ = ✶,

∀❥, ❤ ❡❥❤ ∈ {✵, ✶}, α❥❤ ≤ ❡❥❤, ♠❥❤ ≤ ❡❥❤ ∀❥ ✈❥ ∈ {✵, ✶}, ∀❤

• ❥ α❥❤ ≤ ✈❥ ,

❥ ♠❥❤ ≤ ✈❥

∀❥, ❤ ♣❤ ≤ (✶ − ❡❥❤) + ✈❥ ∀❥, ❤ ✈❥ ≤ (✶ − ❡❥❤) + ♣❤ ∀❤

• ❥ α❥❤/r❥ ≤ ✈❥

∀❥

• ❤ ♠❥❤ ≤ ✈❥

▼✐♥✐♠✐③❡ ♣♦✇❡r ✉♥❞❡r ♣❡r❢♦r♠❛♥❝❡ ❝♦♥str❛✐♥ts✿ ∀❥

• ❤ α❥❤/r❥ > ❚❤r❡s❤♦❧❞

♠✐♥(

❤ (P♠✐♥ ❤

+

❥ α❥❤ × (P♠❛① ❤

− P♠✐♥

❤

)) ❉❛♠✐❡♥ ❡t ❛❧✳✱ ❊♥❡r❣②✲❆✇❛r❡ ❙❡r✈✐❝❡ ❆❧❧♦❝❛t✐♦♥✱ ❋●❈❙ ❥♦✉r♥❛❧✱ ✷✵✶✶ ❞❛❝♦st❛❅✐r✐t✳❢r ✸✼✴✹✺

❍❡t❡r♦❣❡♥❡♦✉s ❤❛r❞✇❛r❡ ❆❞❛♣t✐♥❣ t♦ ❛♣♣❧✐❝❛t✐♦♥ ❧♦❛❞ ❉❛t❛❝❡♥t❡r ✐♥ ❛ ❜♦① ❈♦♥❝❡♣t ❙t❛t❡❧❡ss ❛♣♣❧✐❝❛t✐♦♥s ❚✐♠✐♥❣ ✐ss✉❡s ❙t❛t❡✲❢✉❧❧

❙❝❛❧✐♥❣ ♦❢ ❧✐♥❡❛r ♣r♦❣r❛♠♠✐♥❣

❊①❛❝t ♠❡t❤♦❞✿ t✐♠❡ ❝♦♠♣❧❡①✐t② ❡①♣♦♥❡♥t✐❛❧ ✐♥ ❢✉♥❝t✐♦♥ ♦❢ ✐♥t❡❣❡r ✈❛r✐❛❜❧❡s

✻ s❡r✈❡rs✱ ✶✻ t❛s❦s ✿ ✸ ♠✐♥✉t❡s ✭●▲P❑✮

▼❡t❤♦❞s ♦❢ ❝♦♥st❛♥t ✈❛r✐❛❜❧❡s

❋✐① s♦♠❡ ✈❛r✐❛❜❧❡s✱ s♦❧✈❡✱ ❝❤❛♥❣❡ t❤❡ ✜①❡❞ ✈❛r✐❛❜❧❡s ❛♥❞ ✐t❡r❛t❡ ❲♦rs❡ t❤❛♥ t❤❡ ♦♣t✐♠❛❧ ❜✉t ❝❛♥ ❜❡ ✈❡r② ❢❛st

❘❡❧❛① t❤❡ ✐♥t❡❣❡r ❝♦♥str❛✐♥t

✏❇❡tt❡r✑ t❤❛♥ ♦♣t✐♠❛❧ ✭❛ t❛s❦ ❤❛❧❢ ♦♥ ❛ s❡r✈❡r ❛♥❞ ❛♥❞ ❤❛❧❢ ♦♥ ❛♥♦t❤❡r ♦♥❡✮

❯s✐♥❣ ❜♦t❤ ✐t ✐s ♣♦ss✐❜❧❡ t♦ ❤❛✈❡ ❛ ✐♥t❡r✈❛❧

❞❛❝♦st❛❅✐r✐t✳❢r ✸✽✴✹✺

❍❡t❡r♦❣❡♥❡♦✉s ❤❛r❞✇❛r❡ ❆❞❛♣t✐♥❣ t♦ ❛♣♣❧✐❝❛t✐♦♥ ❧♦❛❞ ❉❛t❛❝❡♥t❡r ✐♥ ❛ ❜♦① ❈♦♥❝❡♣t ❙t❛t❡❧❡ss ❛♣♣❧✐❝❛t✐♦♥s ❚✐♠✐♥❣ ✐ss✉❡s ❙t❛t❡✲❢✉❧❧

❙❝❛❧✐♥❣ ♦❢ ❧✐♥❡❛r ♣r♦❣r❛♠♠✐♥❣

❊①❛❝t ♠❡t❤♦❞✿ t✐♠❡ ❝♦♠♣❧❡①✐t② ❡①♣♦♥❡♥t✐❛❧ ✐♥ ❢✉♥❝t✐♦♥ ♦❢ ✐♥t❡❣❡r ✈❛r✐❛❜❧❡s

✻ s❡r✈❡rs✱ ✶✻ t❛s❦s ✿ ✸ ♠✐♥✉t❡s ✭●▲P❑✮

▼❡t❤♦❞s ♦❢ ❝♦♥st❛♥t ✈❛r✐❛❜❧❡s

❋✐① s♦♠❡ ✈❛r✐❛❜❧❡s✱ s♦❧✈❡✱ ❝❤❛♥❣❡ t❤❡ ✜①❡❞ ✈❛r✐❛❜❧❡s ❛♥❞ ✐t❡r❛t❡ ❲♦rs❡ t❤❛♥ t❤❡ ♦♣t✐♠❛❧ ❜✉t ❝❛♥ ❜❡ ✈❡r② ❢❛st

❘❡❧❛① t❤❡ ✐♥t❡❣❡r ❝♦♥str❛✐♥t

✏❇❡tt❡r✑ t❤❛♥ ♦♣t✐♠❛❧ ✭❛ t❛s❦ ❤❛❧❢ ♦♥ ❛ s❡r✈❡r ❛♥❞ ❛♥❞ ❤❛❧❢ ♦♥ ❛♥♦t❤❡r ♦♥❡✮

❯s✐♥❣ ❜♦t❤ ✐t ✐s ♣♦ss✐❜❧❡ t♦ ❤❛✈❡ ❛ ✐♥t❡r✈❛❧

❞❛❝♦st❛❅✐r✐t✳❢r ✸✽✴✹✺

❍❡t❡r♦❣❡♥❡♦✉s ❤❛r❞✇❛r❡ ❆❞❛♣t✐♥❣ t♦ ❛♣♣❧✐❝❛t✐♦♥ ❧♦❛❞ ❉❛t❛❝❡♥t❡r ✐♥ ❛ ❜♦① ❈♦♥❝❡♣t ❙t❛t❡❧❡ss ❛♣♣❧✐❝❛t✐♦♥s ❚✐♠✐♥❣ ✐ss✉❡s ❙t❛t❡✲❢✉❧❧

❙❝❛❧✐♥❣ ♦❢ ❧✐♥❡❛r ♣r♦❣r❛♠♠✐♥❣

❊①❛❝t ♠❡t❤♦❞✿ t✐♠❡ ❝♦♠♣❧❡①✐t② ❡①♣♦♥❡♥t✐❛❧ ✐♥ ❢✉♥❝t✐♦♥ ♦❢ ✐♥t❡❣❡r ✈❛r✐❛❜❧❡s

✻ s❡r✈❡rs✱ ✶✻ t❛s❦s ✿ ✸ ♠✐♥✉t❡s ✭●▲P❑✮

▼❡t❤♦❞s ♦❢ ❝♦♥st❛♥t ✈❛r✐❛❜❧❡s

❋✐① s♦♠❡ ✈❛r✐❛❜❧❡s✱ s♦❧✈❡✱ ❝❤❛♥❣❡ t❤❡ ✜①❡❞ ✈❛r✐❛❜❧❡s ❛♥❞ ✐t❡r❛t❡ ❲♦rs❡ t❤❛♥ t❤❡ ♦♣t✐♠❛❧ ❜✉t ❝❛♥ ❜❡ ✈❡r② ❢❛st

❘❡❧❛① t❤❡ ✐♥t❡❣❡r ❝♦♥str❛✐♥t

✏❇❡tt❡r✑ t❤❛♥ ♦♣t✐♠❛❧ ✭❛ t❛s❦ ❤❛❧❢ ♦♥ ❛ s❡r✈❡r ❛♥❞ ❛♥❞ ❤❛❧❢ ♦♥ ❛♥♦t❤❡r ♦♥❡✮

❯s✐♥❣ ❜♦t❤ ✐t ✐s ♣♦ss✐❜❧❡ t♦ ❤❛✈❡ ❛ ✐♥t❡r✈❛❧

❞❛❝♦st❛❅✐r✐t✳❢r ✸✽✴✹✺

❍❡t❡r♦❣❡♥❡♦✉s ❤❛r❞✇❛r❡ ❆❞❛♣t✐♥❣ t♦ ❛♣♣❧✐❝❛t✐♦♥ ❧♦❛❞ ❉❛t❛❝❡♥t❡r ✐♥ ❛ ❜♦① ❈♦♥❝❡♣t ❙t❛t❡❧❡ss ❛♣♣❧✐❝❛t✐♦♥s ❚✐♠✐♥❣ ✐ss✉❡s ❙t❛t❡✲❢✉❧❧

❙❝❛❧✐♥❣ ♦❢ ❧✐♥❡❛r ♣r♦❣r❛♠♠✐♥❣

❊①❛❝t ♠❡t❤♦❞✿ t✐♠❡ ❝♦♠♣❧❡①✐t② ❡①♣♦♥❡♥t✐❛❧ ✐♥ ❢✉♥❝t✐♦♥ ♦❢ ✐♥t❡❣❡r ✈❛r✐❛❜❧❡s

✻ s❡r✈❡rs✱ ✶✻ t❛s❦s ✿ ✸ ♠✐♥✉t❡s ✭●▲P❑✮

▼❡t❤♦❞s ♦❢ ❝♦♥st❛♥t ✈❛r✐❛❜❧❡s

❋✐① s♦♠❡ ✈❛r✐❛❜❧❡s✱ s♦❧✈❡✱ ❝❤❛♥❣❡ t❤❡ ✜①❡❞ ✈❛r✐❛❜❧❡s ❛♥❞ ✐t❡r❛t❡ ❲♦rs❡ t❤❛♥ t❤❡ ♦♣t✐♠❛❧ ❜✉t ❝❛♥ ❜❡ ✈❡r② ❢❛st

❘❡❧❛① t❤❡ ✐♥t❡❣❡r ❝♦♥str❛✐♥t

✏❇❡tt❡r✑ t❤❛♥ ♦♣t✐♠❛❧ ✭❛ t❛s❦ ❤❛❧❢ ♦♥ ❛ s❡r✈❡r ❛♥❞ ❛♥❞ ❤❛❧❢ ♦♥ ❛♥♦t❤❡r ♦♥❡✮

❯s✐♥❣ ❜♦t❤ ✐t ✐s ♣♦ss✐❜❧❡ t♦ ❤❛✈❡ ❛ ✐♥t❡r✈❛❧

❞❛❝♦st❛❅✐r✐t✳❢r ✸✽✴✹✺

❍❡t❡r♦❣❡♥❡♦✉s ❤❛r❞✇❛r❡ ❆❞❛♣t✐♥❣ t♦ ❛♣♣❧✐❝❛t✐♦♥ ❧♦❛❞ ❉❛t❛❝❡♥t❡r ✐♥ ❛ ❜♦① ❈♦♥❝❡♣t ❙t❛t❡❧❡ss ❛♣♣❧✐❝❛t✐♦♥s ❚✐♠✐♥❣ ✐ss✉❡s ❙t❛t❡✲❢✉❧❧

Pr♦✲❛❝t✐✈❡ ❍❡✉r✐st✐❝s

Pr❡❞✐❝t ❧♦❛❞ ❛♥❞ s✇✐t❝❤ ♦♥ ♥♦❞❡s t♦ ❣✉❛r❛♥t② ◗♦❙ ❙✇✐t❝❤✐♥❣ ♦♥ ❝❛♥ ❜❡ ❢♦❧❧♦✇❡❞ ❜② s✇✐t❝❤✐♥❣ ♦✛ ❲❤❡♥ ❧♦❛❞ ❞❡❝r❡❛s❡✱ s✇✐t❝❤ ♦✛ s❡r✈❡rs ❛❝❝♦r❞✐♥❣❧② ❙t❛② ♥❡❛r t❤❡ ♦♣t✐♠❛❧ r❡♣❛rt✐t✐♦♥

❞❛❝♦st❛❅✐r✐t✳❢r ✸✾✴✹✺

❍❡t❡r♦❣❡♥❡♦✉s ❤❛r❞✇❛r❡ ❆❞❛♣t✐♥❣ t♦ ❛♣♣❧✐❝❛t✐♦♥ ❧♦❛❞ ❉❛t❛❝❡♥t❡r ✐♥ ❛ ❜♦① ❈♦♥❝❡♣t ❙t❛t❡❧❡ss ❛♣♣❧✐❝❛t✐♦♥s ❚✐♠✐♥❣ ✐ss✉❡s ❙t❛t❡✲❢✉❧❧

Pr♦✲❛❝t✐✈❡ ❍❡✉r✐st✐❝s

Pr❡❞✐❝t ❧♦❛❞ ❛♥❞ s✇✐t❝❤ ♦♥ ♥♦❞❡s t♦ ❣✉❛r❛♥t② ◗♦❙ ❙✇✐t❝❤✐♥❣ ♦♥ ❝❛♥ ❜❡ ❢♦❧❧♦✇❡❞ ❜② s✇✐t❝❤✐♥❣ ♦✛ ❲❤❡♥ ❧♦❛❞ ❞❡❝r❡❛s❡✱ s✇✐t❝❤ ♦✛ s❡r✈❡rs ❛❝❝♦r❞✐♥❣❧② ❙t❛② ♥❡❛r t❤❡ ♦♣t✐♠❛❧ r❡♣❛rt✐t✐♦♥

❞❛❝♦st❛❅✐r✐t✳❢r ✸✾✴✹✺

❍❡t❡r♦❣❡♥❡♦✉s ❤❛r❞✇❛r❡ ❆❞❛♣t✐♥❣ t♦ ❛♣♣❧✐❝❛t✐♦♥ ❧♦❛❞ ❉❛t❛❝❡♥t❡r ✐♥ ❛ ❜♦① ❈♦♥❝❡♣t ❙t❛t❡❧❡ss ❛♣♣❧✐❝❛t✐♦♥s ❚✐♠✐♥❣ ✐ss✉❡s ❙t❛t❡✲❢✉❧❧

Pr♦✲❛❝t✐✈❡ ❍❡✉r✐st✐❝s

Pr❡❞✐❝t ❧♦❛❞ ❛♥❞ s✇✐t❝❤ ♦♥ ♥♦❞❡s t♦ ❣✉❛r❛♥t② ◗♦❙ ❙✇✐t❝❤✐♥❣ ♦♥ ❝❛♥ ❜❡ ❢♦❧❧♦✇❡❞ ❜② s✇✐t❝❤✐♥❣ ♦✛ ❲❤❡♥ ❧♦❛❞ ❞❡❝r❡❛s❡✱ s✇✐t❝❤ ♦✛ s❡r✈❡rs ❛❝❝♦r❞✐♥❣❧② ❙t❛② ♥❡❛r t❤❡ ♦♣t✐♠❛❧ r❡♣❛rt✐t✐♦♥

❞❛❝♦st❛❅✐r✐t✳❢r ✸✾✴✹✺

❍❡t❡r♦❣❡♥❡♦✉s ❤❛r❞✇❛r❡ ❆❞❛♣t✐♥❣ t♦ ❛♣♣❧✐❝❛t✐♦♥ ❧♦❛❞ ❉❛t❛❝❡♥t❡r ✐♥ ❛ ❜♦① ❈♦♥❝❡♣t ❙t❛t❡❧❡ss ❛♣♣❧✐❝❛t✐♦♥s ❚✐♠✐♥❣ ✐ss✉❡s ❙t❛t❡✲❢✉❧❧

Pr♦✲❛❝t✐✈❡ ❍❡✉r✐st✐❝s

Pr❡❞✐❝t ❧♦❛❞ ❛♥❞ s✇✐t❝❤ ♦♥ ♥♦❞❡s t♦ ❣✉❛r❛♥t② ◗♦❙ ❙✇✐t❝❤✐♥❣ ♦♥ ❝❛♥ ❜❡ ❢♦❧❧♦✇❡❞ ❜② s✇✐t❝❤✐♥❣ ♦✛ ❲❤❡♥ ❧♦❛❞ ❞❡❝r❡❛s❡✱ s✇✐t❝❤ ♦✛ s❡r✈❡rs ❛❝❝♦r❞✐♥❣❧② ❙t❛② ♥❡❛r t❤❡ ♦♣t✐♠❛❧ r❡♣❛rt✐t✐♦♥

❞❛❝♦st❛❅✐r✐t✳❢r ✸✾✴✹✺

❍❡t❡r♦❣❡♥❡♦✉s ❤❛r❞✇❛r❡ ❆❞❛♣t✐♥❣ t♦ ❛♣♣❧✐❝❛t✐♦♥ ❧♦❛❞ ❉❛t❛❝❡♥t❡r ✐♥ ❛ ❜♦① ❈♦♥❝❡♣t ❙t❛t❡❧❡ss ❛♣♣❧✐❝❛t✐♦♥s ❚✐♠✐♥❣ ✐ss✉❡s ❙t❛t❡✲❢✉❧❧

Pr♦✲❛❝t✐✈❡ ❍❡✉r✐st✐❝s

Pr❡❞✐❝t ❧♦❛❞ ❛♥❞ s✇✐t❝❤ ♦♥ ♥♦❞❡s t♦ ❣✉❛r❛♥t② ◗♦❙ ❙✇✐t❝❤✐♥❣ ♦♥ ❝❛♥ ❜❡ ❢♦❧❧♦✇❡❞ ❜② s✇✐t❝❤✐♥❣ ♦✛ ❲❤❡♥ ❧♦❛❞ ❞❡❝r❡❛s❡✱ s✇✐t❝❤ ♦✛ s❡r✈❡rs ❛❝❝♦r❞✐♥❣❧② ❙t❛② ♥❡❛r t❤❡ ♦♣t✐♠❛❧ r❡♣❛rt✐t✐♦♥

❞❛❝♦st❛❅✐r✐t✳❢r ✸✾✴✹✺

❍❡t❡r♦❣❡♥❡♦✉s ❤❛r❞✇❛r❡ ❆❞❛♣t✐♥❣ t♦ ❛♣♣❧✐❝❛t✐♦♥ ❧♦❛❞ ❉❛t❛❝❡♥t❡r ✐♥ ❛ ❜♦① ❈♦♥❝❡♣t ❙t❛t❡❧❡ss ❛♣♣❧✐❝❛t✐♦♥s ❚✐♠✐♥❣ ✐ss✉❡s ❙t❛t❡✲❢✉❧❧

❙t❛t❡✲❢✉❧❧ ❞✐str✐❜✉t❡❞ ❛♣♣❧✐❝❛t✐♦♥s

❈❧❛ss✐❝❛❧ ❛♣♣❧✐❝❛t✐♦♥s ❛r❡ ♥♦t ♠❛❧❡❛❜❧❡

❉✐str✐❜✉t❡❞ ❞❛t❛❜❛s❡s ❖♣❡♥▼P ♦r ▼P■ ❛♣♣❧✐❝❛t✐♦♥s

■♠♣♦ss✐❜❧❡ t♦ ❝❤❛♥❣❡ t❤❡ ♥✉♠❜❡r ♦❢ ❛♣♣❧✐❝❛t✐♦♥ ✐♥st❛♥❝❡ ❆❞❞ ♠✐❣r❛t✐♦♥ t✐♠❡✴❡♥❡r❣② t♦ ❙✇✐t❝❤ ♦♥✴♦✛

❞❛❝♦st❛❅✐r✐t✳❢r ✹✵✴✹✺

❍❡t❡r♦❣❡♥❡♦✉s ❤❛r❞✇❛r❡ ❆❞❛♣t✐♥❣ t♦ ❛♣♣❧✐❝❛t✐♦♥ ❧♦❛❞ ❉❛t❛❝❡♥t❡r ✐♥ ❛ ❜♦① ❈♦♥❝❡♣t ❙t❛t❡❧❡ss ❛♣♣❧✐❝❛t✐♦♥s ❚✐♠✐♥❣ ✐ss✉❡s ❙t❛t❡✲❢✉❧❧

❍❡t❡r♦❣❡♥❡♦✉s ♠✐❝r♦✲❛r❝❤✐t❡❝t✉r❡s

■♥st❛♥❝❡ ❝❛♥ ❜❡ ♠✐❣r❛t❡❞ ❜❡t✇❡❡♥ ❛r❝❤✐t❡❝t✉r❡s P❡r❢♦r♠❛♥❝❡ ❞❡♣❡♥❞s ♦♥ ❛r❝❤✐t❡❝t✉r❡ ♦❢ ❱▼ ❛♥❞ s❡r✈❡r

Host ARM

ARM Virtualization Ext.

VM x86

x86 ARM → translation

EMULATION

Host x86

x86 Virtualization Ext.

VM x86

Host ARM

ARM Virtualization Ext.

VM ARM

Host x86

x86 Virtualization Ext.

VM ARM

ARM x86 → translation

EMULATION

❚r❛♥s❧❛t✐♦♥ s❧♦✇❞♦✇♥ r❛t✐♦✿ ✽

❱✐♦❧❛✐♥❡ ❛♥❞ ❛❧✳ PP▲ ✷✵✵✺

▲♦✇ ❧♦❛❞ ♦♥ ❆❘▼✱ ❤✐❣❤ ❧♦❛❞ ♦♥ ①✽✻✱ ①✽✻ ❱▼

❞❛❝♦st❛❅✐r✐t✳❢r ✹✶✴✹✺

❍❡t❡r♦❣❡♥❡♦✉s ❤❛r❞✇❛r❡ ❆❞❛♣t✐♥❣ t♦ ❛♣♣❧✐❝❛t✐♦♥ ❧♦❛❞ ❉❛t❛❝❡♥t❡r ✐♥ ❛ ❜♦①

❖✉t❧✐♥❡

✶ ❍❡t❡r♦❣❡♥❡♦✉s ❤❛r❞✇❛r❡

❈♦♥t❡①t ❍❡t❡r♦❣❡♥❡♦✉s❧② ❞❡s✐❣♥❡❞ ❖♣♣♦rt✉♥✐st✐❝❛❧❧② ❤❡t❡r♦❣❡♥❡♦✉s

✷ ❆❞❛♣t✐♥❣ t♦ ❛♣♣❧✐❝❛t✐♦♥ ❧♦❛❞

❈♦♥❝❡♣t ❙t❛t❡❧❡ss ❛♣♣❧✐❝❛t✐♦♥s ❚✐♠✐♥❣ ✐ss✉❡s ❙t❛t❡✲❢✉❧❧ ❛♣♣❧✐❝❛t✐♦♥s

✸ ❉❛t❛❝❡♥t❡r ✐♥ ❛ ❜♦①

❞❛❝♦st❛❅✐r✐t✳❢r ✹✷✴✹✺

❍❡t❡r♦❣❡♥❡♦✉s ❤❛r❞✇❛r❡ ❆❞❛♣t✐♥❣ t♦ ❛♣♣❧✐❝❛t✐♦♥ ❧♦❛❞ ❉❛t❛❝❡♥t❡r ✐♥ ❛ ❜♦①

❲❤② ❞❛t❛❝❡♥t❡rs ❡①✐st❄

❙❝❛❧✐♥❣

❇❡✐♥❣ ❛❜❧❡ t♦ r✉♥ ❧❛r❣❡ ❛♣♣❧✐❝❛t✐♦♥s✴s❡r✈✐❝❡s

▼❛♥❛❣❡♠❡♥t ❛♥❞ r❡s♦✉r❝❡s s❤❛r✐♥❣

❈♦♦❧✐♥❣✱ ❤❛r❞✇❛r❡ r❡♣❧❛❝❡♠❡♥t✱ ❡❧❡❝tr✐❝❛❧ r❡❞♦♥❞❛♥❝② ❈♦♥s♦❧✐❞❛t✐♦♥✱ ❈♦♠♠✉♥✐❝❛t✐♦♥ ❛♥❞ ❝♦♠♣✉t❛t✐♦♥ ♦✈❡r❧❛♣

■♥t❡r♥❛❧ ❞❛t❛❝❡♥t❡rs

■♥❢♦r♠❛t✐♦♥ ✐s ❦❡② ❈r✐t✐❝❛❧ ✇♦r❦❧♦❛❞

❞❛❝♦st❛❅✐r✐t✳❢r ✹✸✴✹✺

❍❡t❡r♦❣❡♥❡♦✉s ❤❛r❞✇❛r❡ ❆❞❛♣t✐♥❣ t♦ ❛♣♣❧✐❝❛t✐♦♥ ❧♦❛❞ ❉❛t❛❝❡♥t❡r ✐♥ ❛ ❜♦①

❉❛t❛❝❡♥t❡r ✐♥ ❛ ❜♦①

❖♥❡ st❡♣ ❢✉rt❤❡r t❤❛♥ ❜✐❣✳▲■❚❚▲❊ ❛r❝❤✐t❡❝t✉r❡

▲✐♠✐t❡❞ ❜② ♥♦♥✲♣r♦❝❡ss♦r ❤❛r❞✇❛r❡✿ ▼♦t❤❡r❜♦❛r❞✱ ▼❡♠♦r②✱ ❙t♦r❛❣❡✱ ◆❡t✇♦r❦✱✳✳✳

❉❛t❛❝❡♥t❡r ✐♥ ❛ ❜♦①

❙❡✈❡r❛❧ ❝♦r❡s ✭❛♥❞ ❛r❝❤✐t❡❝t✉r❡s✮ ❯s❡ t❤❡ r✐❣❤t ❝♦♠❜✐♥❛t✐♦♥ ♦❢ ❝♦♠♣♦♥❡♥ts ❞❡♣❡♥❞✐♥❣ ♦♥ t❤❡ ❧♦❛❞ Pr♦♣♦rt✐♦♥❛❧ ♣♦✇❡r ❝♦♥s✉♠♣t✐♦♥

❆❧r❡❛❞② ❛ tr❡♥❞

❆✈❛✐❧❛❜❧❡ ❢♦r s♠❛rt♣❤♦♥❡s✱ ❧❛♣t♦♣s

❞❛❝♦st❛❅✐r✐t✳❢r ✹✹✴✹✺

❍❡t❡r♦❣❡♥❡♦✉s ❤❛r❞✇❛r❡ ❆❞❛♣t✐♥❣ t♦ ❛♣♣❧✐❝❛t✐♦♥ ❧♦❛❞ ❉❛t❛❝❡♥t❡r ✐♥ ❛ ❜♦①

❖♣❡♥ r❡s❡❛r❝❤ q✉❡st✐♦♥s

Pr♦❣r❛♠♠✐♥❣ ♣❛r❛❞✐❣♠s

❆❜✐❧✐t② t♦ ❞❡s❝r✐❜❡ ♣❛r❛❧❧❡❧✐s♠ ✐♥t✉✐t✐✈❡❧② ❘❡♠♦✈❡ t❤❡ ❜✉r❞❡♥ ❢r♦♠ ❞❡✈❡❧♦♣❡r

❘✉♥t✐♠❡s

❈❛♣❛❜✐❧✐t② t♦ ❛❞❛♣t t♦ ♣❛rt✐❝✉❧❛r ♣r♦✜❧❡s ❛♥❞ t❤❡✐r ✐♥t❡r❛❝t✐♦♥s ❆❜✐❧✐t② t♦ ❝❤❛♥❣❡ ❦❡r♥❡❧s ✐♥ ❢✉♥❝t✐♦♥ ♦❢ ❝♦♥t❡①t

❈♦♠♠✉♥✐❝❛t✐♦♥ ❜❡t✇❡❡♥ t❤❡s❡ t✇♦ ❧❡✈❡❧s ❈♦♦♣❡r❛t✐♦♥ ❜❡t✇❡❡♥ ♦♣❡r❛t♦rs

❈❧♦✉❞ ❢❡❞❡r❛t✐♦♥ ❈❧♦✉❞ ❛♥❞ ❍P❈ s②st❡♠s

❞❛❝♦st❛❅✐r✐t✳❢r ✹✺✴✹✺