❙t❛t❡ ❙♣❛❝❡ ❊①♣❧♦s✐♦♥ ♦r✿ ❍♦✇ ❚♦ ❋✐❣❤t ❆♥ ❯♣❤✐❧❧ ❇❛tt❧❡ ❆ ♣r❛❝t✐t✐♦♥❡rs ❣✉✐❞❡ t♦ ♠♦❞❡❧ ❝❤❡❝❦✐♥❣ ✇✐t❤ ❚▲❈ ▼❛r❦✉s ❆✳ ❑✉♣♣❡ ▼✐❝r♦s♦❢t ❊♥❣✐♥❡❡r ❚▲❆ ✰ ❖ ☞ ✉✐♥❝❡❛➠❡r❛ ✲ ❏✉❧② ✶✽✱ ✷✵✶✽ ✶ ✴ ✺✽
◆❡✇ ❚▲❆ ✰ ❚♦♦❧s ❛♥❞ ❚♦♦❧❜♦① ❘❡❧❡❛s❡ ◮ ❚✉t♦r✐❛❧ ❛✐♠❡❞ ❛t ❚▲❆ ✰ ❚♦♦❧❜♦① ✶✳✺✳✼ ❛♥❞ ❚▲❈ ✷✳✶✸ r❡❧❡❛s❡ ❛s ♦❢ ❏✉❧② ✶✽✱ ✷✵✶✽ ✭❝❤❛♥❣❡❧♦❣✮ ✷ ✴ ✺✽
❙t❛t❡ ❙♣❛❝❡ ❊①♣❧♦s✐♦♥ Pr♦❜❧❡♠ ♦❢ ✭❡①♣❧✐❝✐t st❛t❡✮ ♠♦❞❡❧ ❝❤❡❝❦✐♥❣✿ ▲✐♥❡❛r ✐♥❝r❡❛s❡ ✐♥ s✐③❡ ♦❢ s♣❡❝✐✜❝❛t✐♦♥ ♦r ♣r♦♣❡rt✐❡s ❝❛♥ ❧❡❛❞ ✉♣ t♦ ❡①♣♦♥❡♥t✐❛❧ ❣r♦✇t❤ ♦❢ st❛t❡ s♣❛❝❡ ✸ ✴ ✺✽
❙t❛t❡ ❙♣❛❝❡ ❊①♣❧♦s✐♦♥ ✹ ♣r♦❝ ✶ qs♣✐♥❧♦❝❦ ✶ ♣r♦❝❡ss ✷ ♣r♦❝ ✸ ♣r♦❝ ∼ ✶✵ ✹ ∼ ✸ . ✻ × ✶✵ ✼ > ✶ . ✷ × ✶✵ ✶✵ ❉✐st✐♥❝t ❙t❛t❡s ✼ ❘✉♥✲t✐♠❡ ✶ s ∼ ✸✵ s ∼ ✻ ♠ ❉❛②s ✶ ❙②♠♠❡tr② ✫ ✸✷ ❝♦r❡ ♠❛❝❤✐♥❡ ✹ ✴ ✺✽
❚▲❈ ◮ ❙❛❢❡t② ❝❤❡❝❦✐♥❣ ❝♦rr❡s♣♦♥❞s t♦ ❇r❡❛❞t❤✲❋✐rst s❡❛r❝❤ ♦✈❡r ♦♥✲t❤❡✲✢② ❣❡♥❡r❛t❡❞ st❛t❡ ❣r❛♣❤ ◮ ▲✐✈❡♥❡ss ❝❤❡❝❦✐♥❣ ❝♦rr❡s♣♦♥❞s t♦ ❉❡♣t❤✲❋✐rst s❡❛r❝❤ ♦✈❡r ✭♣❛rt✐❛❧✮ ❜❡❤❛✈✐♦r ❣r❛♣❤ ❬s❡❡ ▼❛♥♥❛ ❛♥❞ P♥✉❡❧✐✱ ✶✾✾✺✱ ❢♦r ❛❧❣♦r✐t❤♠❪ ◮ ❇❡❤❛✈✐♦r ❣r❛♣❤ ✐s ❝r♦ss✲♣r♦❞✉❝t ♦❢ st❛t❡ ❣r❛♣❤ ❛♥❞ ❧✐✈❡♥❡ss t❛❜❧❡❛✉ ❣r❛♣❤ ✭✐❢ ❛♥②✮ ✺ ✴ ✺✽
❚▲❈ ❋P❙ ❋✐♥❣❡r♣r✐♥t ❙❡t ✭❝♦♥t❛✐♥s ❛ ❤❛s❤ ♦❢ ❛❧❧ ❛❧r❡❛❞② ❡①♣❧♦r❡❞ st❛t❡s✮ ❙◗ ❙t❛t❡ ◗✉❡✉❡ ✭❝♦♥t❛✐♥s ❛❧❧ ✉♥❡①♣❧♦r❡❞ st❛t❡s✮ ❚ ❚r❛❝❡ ✭♣❛t❤s ❢r♦♠ ✐♥✐t✐❛❧ st❛t❡s t♦ ❛♥② st❛t❡ ✭❢♦r❡st✮✮ ❲❖❘❑❊❘ ❙❡t ♦❢ ✇♦r❦❡r ♥♦❞❡s ✭♥♦❞❡s✴❝♦r❡s ❡①❡❝✉t✐♥❣ ✐♥✐t ❛♥❞ ♥❡①t✲st❛t❡ r❡❧❛t✐♦♥s✮ φ ❙❛❢❡t② ✫ ▲✐✈❡♥❡ss ♣r♦♣❡rt✐❡s ✭❛s ❞❡✜♥❡❞ ❜② t❤❡ ♠♦❞❡❧✮ ✻ ✴ ✺✽
■❖✲❜♦✉♥❞ ▼♦❞❡❧ ❈❤❡❝❦✐♥❣ ✼ ✴ ✺✽
▲♦✇ ❍❛♥❣✐♥❣ ❋r✉✐ts ✶✳ ❉✐s❛❜❧❡ ❝❤❡❝❦♣♦✐♥ts ✈✐❛ ✏ ✲❝❤❡❝❦♣♦✐♥t ✵ ✑ ✷ ✷✳ ❘❡❞✉❝❡ ❝♦✈❡r❛❣❡ r❡♣♦rt✐♥❣ ✈✐❛ ✏ ✲❝♦✈❡r❛❣❡ ✾✾✾✾✾✑ ✷ ▼❛♥✉❛❧❧② tr✐❣❣❡r ❝❤❡❝❦♣♦✐♥t✐♥❣ ✈✐❛ ❏▼❳✳ ✽ ✴ ✺✽
P♦st♣♦♥❡ ▲✐✈❡♥❡ss ❈❤❡❝❦✐♥❣ ✸ ◮ ❚▲❈ ✲ ❜② ❞❡❢❛✉❧t ✲ ♣❡r✐♦❞✐❝❛❧❧② ❝❤❡❝❦s ❧✐✈❡♥❡ss ♦♥ ♣❛rt✐❛❧ st❛t❡ ❣r❛♣❤ ◮ ▲✐✈❡♥❡ss ❝❤❡❝❦✐♥❣ ♥♦t ❞♦♥❡ ✐♥❝r❡♠❡♥t❛❧❧② ◮ ❊✳❣✳ ✏♣❡r✐♦❞✐❝✑ ❛❞❞s ✹✵ ♠✐♥s t♦ ❛ ∼ ✷❤ r✉♥ ◮ ❚▲❈ ♣❛r❛♠❡t❡r✿ ✏✲❧♥❝❤❡❝❦ ✜♥❛❧✑ ✸ ▼❛♥✉❛❧❧② tr✐❣❣❡r ❧✐✈❡♥❡ss ❝❤❡❝❦✐♥❣ ✈✐❛ ❏▼❳✳ ✾ ✴ ✺✽
❏▼❳ ❢r♦♥t✲❡♥❞ ◮ ❈♦♥♥❡❝t t♦ ❧♦❝❛❧ ♦r r❡♠♦t❡ ❚▲❈ ♣r♦❝❡ss ✇✐t❤ ❡✳❣✳ ❏❛✈❛ ▼✐ss✐♦♥ ❈♦♥tr♦❧ ✭✐♥❝❧✉❞❡❞ ✐♥ ❏❉❑✮ ◮ ▲❛r❣❡ ❛♠♦✉♥ts ♦❢ t❡❧❡♠❡tr② ❞❛t❛ ◮ ◆❡①t✲❙t❛t❡ ✏■♥s♣❡❝t✐♦♥ ❍❛t❝❤✑ ◮ ❚▲❈ ♦♣❡r❛t✐♦♥s ◮ ▲✐✈❡♥❡ss ❝❤❡❝❦✐♥❣ ◮ ❈❤❡❝❦♣♦✐♥t✐♥❣ ✶✵ ✴ ✺✽
❏▼❳ ❢r♦♥t✲❡♥❞ ❉❡♠♦ t✐♠❡ ✶✶ ✴ ✺✽
P❛r❛❧❧❡❧ ❚▲❈ ◮ ◆✉♠❜❡r ♦❢ ✇♦r❦❡rs ❞❡❢❛✉❧ts t♦ ✶✴✷ ♠❛❝❤✐♥❡✬s ❝♦r❡ ❝♦✉♥t ◮ ❜❡❝❛✉s❡ ❚▲❈ ✐s ❛ss✉♠❡❞ t♦ r✉♥ ♦♥ ②♦✉r ✇♦r❦st❛t✐♦♥ ◮ ❉r❛✇❜❛❝❦ ◮ ◆♦ str✐❝t ❇r❡❛❞t❤✲❋✐rst s❡❛r❝❤ ◮ ∼ > ❆♣♣r♦①✐♠❛t❡s s❤♦rt❡st ❡rr♦r tr❛❝❡ ✶✷ ✴ ✺✽
P❛r❛❧❧❡❧ ❚▲❈ Pr♦t♦t②♣❡ r❡❞✉❝❡s ✇♦r❦❡r ❝♦♥t❡♥t✐♦♥ ✈✐❛✿ ✶✳ P❛rt✐t✐♦♥❡❞✴❙❤❛r❞❡❞ ❋P❙ ✷✳ ❚r❛❝❡ ❚ ♣❡r ✇♦r❦❡r ✸✳ ❙❤❛r❡❞✲◆♦t❤✐♥❣ ❙t❛t❡ ◗✉❡✉❡ ❙◗ ✸✳✶ ▼♦r❡ ❞❛t❛ t♦ ✈❛❧✐❞❛t❡ ✉♥❞❡r❧②✐♥❣ ❛ss✉♠♣t✐♦♥s ❛❜♦✉t ❛✈❡r❛❣❡ s❤❛♣❡✴♣r♦♣❡rt✐❡s ♦❢ st❛t❡ ❣r❛♣❤s✦ ✶✸ ✴ ✺✽
P❛r❛❧❧❡❧ ❚▲❈ Dataset: 2017−02−21_x32 & 2017−02−22_x32 TLC ● ● ● ● ● ● 35 ● ● ● ● Spin ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 30 ● ● ● ● ● ● ● ● ● ◮ ❚▲❈ ♣r♦t♦t②♣❡ ● ● ● ● ● 25 ● ● ● ◮ ❚▲❈ ❜❡❛ts ● ● ● ● s❝❛❧❛❜✐❧✐t② ♦❢ ❙P■◆ Speedup Z ● ● 20 ❍♦❧③♠❛♥♥ ❬✷✵✵✶❪ ◮ ❇❛❦❡r② s♣❡❝ 15 ● ● ● ◮ ✭❙P■◆ ♦✉t♣❡r❢♦r♠s 10 t❤r♦✉❣❤♣✉t ♦❢ ● ● ● ❚▲❈✮ 5 ● ● ● ● ● ● ● ● ● 0 0 50 100 150 N ✶✹ ✴ ✺✽
❖✉t❧✐♥❡ ▲❡ts ❝❡❧❡❜r❛t❡✦ Pr♦❜❧❡♠ ❉❡s❝r✐♣t✐♦♥ Pr❡q✉❡❧ ❈♦♥st❛♥t ❖✈❡r❤❡❛❞ ❚✉♥✐♥❣ ♥❡①t✲st❛t❡ r❡❧❛t✐♦♥ ❊✈❛❧✉❛t✐♦♥ ▼♦❞✉❧❡ ❖✈❡r✇r✐t❡s ❙❝❛❧✐♥❣ ♥❡①t✲st❛t❡ r❡❧❛t✐♦♥ ❉✐str✐❜✉t❡❞ ❚▲❈ ❈❧♦✉❞ ❚▲❈ ❙t❛t❡ ❙♣❛❝❡ ❘❡❞✉❝t✐♦♥ ❱✐❡✇s ❙②♠♠❡tr② ❘❡❞✉❝t✐♦♥ ❘❛♥❞♦♠✐③❛t✐♦♥ ❈♦♥❝❧✉s✐♦♥ ✶✺ ✴ ✺✽
❖r❞❡r ♦❢ ❊①♣r❡ss✐♦♥s ❱❆❘■❆❇▲❊❙ ① , ② ∆ ❡①♣❡♥s✐✈❡❖♣ ( ♥ ) = ❈❍❖❖❙❊ ❡ ∈ ❙❯❇❙❊❚ ( ✶ . . ♥ ) : tr✉❡ ∆ ■♥✐t = ① = ✵ ∧ ② = ✵ ◆❡①t❆✱ ◆❡①t❇ ♦r ✧❚❤✐s ✐s ♠❛t❤ s♦ ✇❤♦ ❝❛r❡s✦✧ ❄ ∆ ◆❡①t❆ = ∧ ① = ✵ ∧ ② = ✵ ∧ ① ′ ∈ ✶ . . ✶✵✵✵✵ ∧ ② ′ = ❡①♣❡♥s✐✈❡❖♣ ( ✶✽ ) ∆ ◆❡①t❇ = ∧ ① = ✵ ∧ ② = ✵ ∧ ② ′ = ❡①♣❡♥s✐✈❡❖♣ ( ✶✽ ) ∧ ① ′ ∈ ✶ . . ✶✵✵✵✵ ✶✻ ✴ ✺✽
❖r❞❡r ♦❢ ❊①♣r❡ss✐♦♥s ❆❙❙❯▼❊ ( ❚▲❈❙❡t ( ✹✷ , � ✏❡①♣❡♥s✐✈❡❖♣✑ , ✵ � ) ∆ ❡①♣❡♥s✐✈❡❖♣ ( ♥ ) = ❈❍❖❖❙❊ ❡ ∈ ❙❯❇❙❊❚ ( ✶ . . ♥ ) : tr✉❡ ∧ ❚▲❈❙❡t ( ✹✷ , [ ❚▲❈●❡t ( ✹✷ ) ❡①❝❡♣t ✦ [ ✷ ] = @ + ✶ ]) ∆ ◆❡①t = ∧ . . . ∧ Pr✐♥t❚ ( ❚▲❈●❡t ( ✹✷ )) ◆❡①t❆✿ ◆❡①t❇✿ ❁✗❁✧❡①♣❡♥s✐✈❡❖♣✧✱ ✶❃✗❃ ❁✗❁✧❡①♣❡♥s✐✈❡❖♣✧✱ ✶❃✗❃ ❁✗❁✧❡①♣❡♥s✐✈❡❖♣✧✱ ✷❃✗❃ ❁✗❁✧❡①♣❡♥s✐✈❡❖♣✧✱ ✶❃✗❃ ❁✗❁✧❡①♣❡♥s✐✈❡❖♣✧✱ ✸❃✗❃ ❁✗❁✧❡①♣❡♥s✐✈❡❖♣✧✱ ✶❃✗❃ ✳✳✳ ✳✳✳ ✶✼ ✴ ✺✽
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