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❊rr♦r ❊st✐♠❛t✐♦♥ ❢♦r ◆♦♥❧✐♥❡❛r ❘❡❞✉❝❡❞ ❇❛s✐s ▼❡t❤♦❞s ❜❛s❡❞ ♦♥ ❊♠♣✐r✐❝❛❧ ❖♣❡r❛t♦r ■♥t❡r♣♦❧❛t✐♦♥ ▼✳ ❉r♦❤♠❛♥♥ ✶ ❇✳ ❍❛❛s❞♦♥❦ ✷ ▼✳ ❖❤❧❜❡r❣❡r ✸ ✶ ❙❛♥❞✐❛ ◆❛t✐♦♥❛❧ ▲❛❜♦r❛t♦r✐❡s✱ ▲✐✈❡r♠♦r❡✱ ❈❆✱ ✭ ♠❞r♦❤♠❛❅s❛♥❞✐❛✳❣♦✈ ✮ ✷ ■♥st✐t✉t❡ ❢♦r ❆♣♣❧✐❡❞ ❆♥❛❧②s✐s ❛♥❞ ◆✉♠❡r✐❝❛❧ ❙✐♠✉❧❛t✐♦♥✱ ❙t✉tt❣❛rt✱ ●❡r♠❛♥② ✸ ■♥st✐t✉t❡ ♦❢ ◆✉♠❡r✐❝❛❧ ❛♥❞ ❆♣♣❧✐❡❞ ▼❛t❤❡t❤❡♠❛t✐❝s✱ ▼ü♥st❡r✱ ●❡r♠❛♥② ❙■❆▼ ❈❙❊ ✷✵✶✷✱ ❇♦st♦♥✱ ▼❆✱ ✵✷✴✷✼✴✷✵✶✸ ❙❛♥❞✐❛ ◆❛t✐♦♥❛❧ ▲❛❜♦r❛t♦r✐❡s ✐s ❛ ♠✉❧t✐✲♣r♦❣r❛♠ ❧❛❜♦r❛t♦r② ♠❛♥❛❣❡❞ ❛♥❞ ♦♣❡r❛t❡❞ ❜② ❙❛♥❞✐❛ ❈♦r♣♦r❛t✐♦♥✱ ❛ ✇❤♦❧❧② ♦✇♥❡❞ s✉❜s✐❞✐❛r② ♦❢ ▲♦❝❦❤❡❡❞ ▼❛rt✐♥ ❈♦r♣♦r❛t✐♦♥✱ ❢♦r t❤❡ ❯✳❙✳ ❉❡♣❛rt♠❡♥t ♦❢ ❊♥❡r❣②✬s ◆❛t✐♦♥❛❧ ◆✉❝❧❡❛r ❙❡❝✉r✐t② ❆❞♠✐♥✐str❛t✐♦♥ ✉♥❞❡r ❝♦♥tr❛❝t ❉❊✲❆❈✵✹✲✾✹❆▲✽✺✵✵✵

❖❢t❡♥ t❤❡r❡ ✐s ❛ tr❛❞❡✲♦✛ ❜❡t✇❡❡♥ ❡✣❝✐❡♥❝② ❛♥❞ r✐❣♦r ✴ ❡✛❡❝t✐✈✐t② ✳ ❊rr♦r ❡st✐♠❛t❡s ❢♦r ♠♦❞❡❧ ♦r❞❡r r❡❞✉❝t✐♦♥ ♠❡t❤♦❞s ▼♦❞❡❧ r❡❞✉❝t✐♦♥ ✐♠♣❧✐❡s ❡rr♦r t♦ ❤✐❣❤ ✜❞❡❧✐t② ♠♦❞❡❧✿ ❡ := ✉ ❤ − ✉ r❡❞ ✳ ❊rr♦r ❜♦✉♥❞s ❊rr♦r ❜♦✉♥❞s η s❤♦✉❧❞ ❜❡ r✐❣♦r♦✉s ✿ η ≥ � ❡ � ✱ ❡✛❡❝t✐✈❡ ✿ � ❡ � ≤ ❈ ❡✛ ♦r ✏♥♦t t♦♦ ❜✐❣✑ η ❛♥❞ ❡✣❝✐❡♥t ✱ ✐✳❡✳ q✉✐❝❦❧② ❝♦♠♣✉t❛❜❧❡ ✭❛s ❢❛st ❛s r❡❞✉❝❡❞ ♠♦❞❡❧✮ ▼✳ ❉r♦❤♠❛♥♥ ✭♠❞r♦❤♠❛❅s❛♥❞✐❛✳❣♦✈✮ ✵✷✴✷✼✴✷✵✶✸ ✷ ✴ ✷✺

❊rr♦r ❡st✐♠❛t❡s ❢♦r ♠♦❞❡❧ ♦r❞❡r r❡❞✉❝t✐♦♥ ♠❡t❤♦❞s ▼♦❞❡❧ r❡❞✉❝t✐♦♥ ✐♠♣❧✐❡s ❡rr♦r t♦ ❤✐❣❤ ✜❞❡❧✐t② ♠♦❞❡❧✿ ❡ := ✉ ❤ − ✉ r❡❞ ✳ ❊rr♦r ❜♦✉♥❞s ❊rr♦r ❜♦✉♥❞s η s❤♦✉❧❞ ❜❡ r✐❣♦r♦✉s ✿ η ≥ � ❡ � ✱ ❡✛❡❝t✐✈❡ ✿ � ❡ � ≤ ❈ ❡✛ ♦r ✏♥♦t t♦♦ ❜✐❣✑ η ❛♥❞ ❡✣❝✐❡♥t ✱ ✐✳❡✳ q✉✐❝❦❧② ❝♦♠♣✉t❛❜❧❡ ✭❛s ❢❛st ❛s r❡❞✉❝❡❞ ♠♦❞❡❧✮ ❖❢t❡♥ t❤❡r❡ ✐s ❛ tr❛❞❡✲♦✛ ❜❡t✇❡❡♥ ❡✣❝✐❡♥❝② ❛♥❞ r✐❣♦r ✴ ❡✛❡❝t✐✈✐t② ✳ ▼✳ ❉r♦❤♠❛♥♥ ✭♠❞r♦❤♠❛❅s❛♥❞✐❛✳❣♦✈✮ ✵✷✴✷✼✴✷✵✶✸ ✷ ✴ ✷✺

❖✉t❧✐♥❡ ✶ ❘❡❞✉❝❡❞ ❜❛s✐s ♠❡t❤♦❞ ❢♦r ♥♦♥✕❧✐♥❡❛r ♣r♦❜❧❡♠s ✷ ❆ ♣♦st❡r✐♦r✐ ❡rr♦r ❡st✐♠❛t♦rs ✸ ◆✉♠❡r✐❝❛❧ ❡①♣❡r✐♠❡♥ts ✹ ❙✉♠♠❛r② ❛♥❞ ❢✉t✉r❡ ✇♦r❦ ▼✳ ❉r♦❤♠❛♥♥ ✭♠❞r♦❤♠❛❅s❛♥❞✐❛✳❣♦✈✮ ✵✷✴✷✼✴✷✵✶✸ ✸ ✴ ✷✺

❖✉t❧✐♥❡ ✶ ❘❡❞✉❝❡❞ ❜❛s✐s ♠❡t❤♦❞ ❢♦r ♥♦♥✕❧✐♥❡❛r ♣r♦❜❧❡♠s ✷ ❆ ♣♦st❡r✐♦r✐ ❡rr♦r ❡st✐♠❛t♦rs ✸ ◆✉♠❡r✐❝❛❧ ❡①♣❡r✐♠❡♥ts ✹ ❙✉♠♠❛r② ❛♥❞ ❢✉t✉r❡ ✇♦r❦ ▼✳ ❉r♦❤♠❛♥♥ ✭♠❞r♦❤♠❛❅s❛♥❞✐❛✳❣♦✈✮ ✵✷✴✷✼✴✷✵✶✸ ✹ ✴ ✷✺

❘❡❞✉❝❡❞ ❇❛s✐s ▼❡t❤♦❞ ❘❇ ❙❝❡♥❛r✐♦✿ P❛r❛♠❡tr✐③❡❞ P❉❊s ✭❡✳❣✳ ❡✈♦❧✉t✐♦♥ ♣r♦❜❧❡♠ ✏ ∂ t ✉ ( µ ) − L ( µ )[ ✉ ] = ✵ , ✉ ( ✵ ; µ ) = ✉ ✵ ( µ ) ✑✮ t✐♠❡✲❝r✐t✐❝❛❧ ❛♣♣❧✐❝❛t✐♦♥s ♠❛♥②✲q✉❡r② ❛♣♣❧✐❝❛t✐♦♥s ●♦❛❧s✿ ❖✤✐♥❡✲ ✴❖♥❧✐♥❡ ❞❡❝♦♠♣♦s✐t✐♦♥ ❊✣❝✐❡♥t r❡❞✉❝❡❞ s✐♠✉❧❛t✐♦♥s ❆ ♣♦st❡r✐♦r✐ ❡rr♦r ❝♦♥tr♦❧ ❘❡❢❡r❡♥❝❡s✿ ❬P❛t❡r❛✫❘♦③③❛✱ ✷✵✵✻❪✱ ❬❍❛❛s❞♦♥❦ ❡t ❛❧✳✱ ✷✵✵✽❪ ▼✳ ❉r♦❤♠❛♥♥ ✭♠❞r♦❤♠❛❅s❛♥❞✐❛✳❣♦✈✮ ✵✷✴✷✼✴✷✵✶✸ ✺ ✴ ✷✺

❘❡❞✉❝❡❞ ❇❛s✐s ▼❡t❤♦❞ ❘❇ ❙❝❡♥❛r✐♦✿ P❛r❛♠❡tr✐③❡❞ P❉❊s ✭❡✳❣✳ ❡✈♦❧✉t✐♦♥ ♣r♦❜❧❡♠ ✏ ∂ t ✉ ( µ ) − L ( µ )[ ✉ ] = ✵ , ✉ ( ✵ ; µ ) = ✉ ✵ ( µ ) ✑✮ t✐♠❡✲❝r✐t✐❝❛❧ ❛♣♣❧✐❝❛t✐♦♥s ♠❛♥②✲q✉❡r② ❛♣♣❧✐❝❛t✐♦♥s ●♦❛❧s✿ ❖✤✐♥❡✲ ✴❖♥❧✐♥❡ ❞❡❝♦♠♣♦s✐t✐♦♥ ❊✣❝✐❡♥t r❡❞✉❝❡❞ s✐♠✉❧❛t✐♦♥s ❆ ♣♦st❡r✐♦r✐ ❡rr♦r ❝♦♥tr♦❧ ❘❡❢❡r❡♥❝❡s✿ ❬P❛t❡r❛✫❘♦③③❛✱ ✷✵✵✻❪✱ ❬❍❛❛s❞♦♥❦ ❡t ❛❧✳✱ ✷✵✵✽❪ ▼✳ ❉r♦❤♠❛♥♥ ✭♠❞r♦❤♠❛❅s❛♥❞✐❛✳❣♦✈✮ ✵✷✴✷✼✴✷✵✶✸ ✺ ✴ ✷✺

❘❡❞✉❝❡❞ ❇❛s✐s ▼❡t❤♦❞ ❘❇ ❙❝❡♥❛r✐♦✿ P❛r❛♠❡tr✐③❡❞ P❉❊s ✭❡✳❣✳ ❡✈♦❧✉t✐♦♥ ♣r♦❜❧❡♠ ✏ ∂ t ✉ ( µ ) − L ( µ )[ ✉ ] = ✵ , ✉ ( ✵ ; µ ) = ✉ ✵ ( µ ) ✑✮ t✐♠❡✲❝r✐t✐❝❛❧ ❛♣♣❧✐❝❛t✐♦♥s ♠❛♥②✲q✉❡r② ❛♣♣❧✐❝❛t✐♦♥s ●♦❛❧s✿ ❖✤✐♥❡✲✴ ❖♥❧✐♥❡ ❞❡❝♦♠♣♦s✐t✐♦♥ ❊✣❝✐❡♥t r❡❞✉❝❡❞ s✐♠✉❧❛t✐♦♥s ❆ ♣♦st❡r✐♦r✐ ❡rr♦r ❝♦♥tr♦❧ ❘❡❢❡r❡♥❝❡s✿ ❬P❛t❡r❛✫❘♦③③❛✱ ✷✵✵✻❪✱ ❬❍❛❛s❞♦♥❦ ❡t ❛❧✳✱ ✷✵✵✽❪ ▼✳ ❉r♦❤♠❛♥♥ ✭♠❞r♦❤♠❛❅s❛♥❞✐❛✳❣♦✈✮ ✵✷✴✷✼✴✷✵✶✸ ✺ ✴ ✷✺

❍✐❣❤✕❞✐♠❡♥s✐♦♥❛❧ ♠♦❞❡❧ L ❤ ✶✶ ✶✷ ✶ t ❤ ✉ ❤ = ✶✵ ✷ ( ∂ t ✉ ❤ )+ ❜ ❤ ❍ ✾ ✸ ✽ ✹ ✼ ✺ ✻ ❍ ▼✳ ❉r♦❤♠❛♥♥ ✭♠❞r♦❤♠❛❅s❛♥❞✐❛✳❣♦✈✮ ✵✷✴✷✼✴✷✵✶✸ ✻ ✴ ✷✺

✐♥t❡r♣♦❧❛t✐♦♥ ♣♦✐♥ts ❳ ① ✶ ① ▼ ❛♥❞ ❢✉♥❝t✐♦♥s ▼ ✱ ✶ ❖❢❢❧✐♥❡ ♣❤❛s❡ ❋✐♥❞ r❡❞✉❝❡❞ ❜❛s✐s ❢✉♥❝t✐♦♥s Φ := { ϕ ✶ , . . . , ϕ ◆ } ✱ s✉❝❤ t❤❛t Φ ✉ ❤ ❛♥❞ ❍ ❛ ≈ L ❤ Φ L r❡❞ := Φ ❚ ◆ ◆ ❍ ❍ ◆ ▼✳ ❉r♦❤♠❛♥♥ ✭♠❞r♦❤♠❛❅s❛♥❞✐❛✳❣♦✈✮ ✵✷✴✷✼✴✷✵✶✸ ✼ ✴ ✷✺

❖❢❢❧✐♥❡ ♣❤❛s❡ ❋✐♥❞ r❡❞✉❝❡❞ ❜❛s✐s ❢✉♥❝t✐♦♥s Φ := { ϕ ✶ , . . . , ϕ ◆ } ✱ ✐♥t❡r♣♦❧❛t✐♦♥ ♣♦✐♥ts ❳ := { ① ✶ , . . . , ① ▼ } ❛♥❞ ❢✉♥❝t✐♦♥s Ξ := { ξ ✶ , . . . , ξ ▼ } ✱ s✉❝❤ t❤❛t L ❤ | ❳ ✉ ❤ ≈ Φ ✉ ❤ L ❤ Ξ ❛♥❞ ❍ ❛ ≈ ✉ ❤ | ❳ ▼ L ❤ | ❳ Ξ L r❡❞ := Φ ❚ ◆ ▼ ❍ ▼ ▼✳ ❉r♦❤♠❛♥♥ ✭♠❞r♦❤♠❛❅s❛♥❞✐❛✳❣♦✈✮ ✵✷✴✷✼✴✷✵✶✸ ✼ ✴ ✷✺

❖❢❢❧✐♥❡ ♣❤❛s❡ ❋✐♥❞ r❡❞✉❝❡❞ ❜❛s✐s ❢✉♥❝t✐♦♥s Φ := { ϕ ✶ , . . . , ϕ ◆ } ✱ ✐♥t❡r♣♦❧❛t✐♦♥ ♣♦✐♥ts ❳ := { ① ✶ , . . . , ① ▼ } ❛♥❞ ❢✉♥❝t✐♦♥s Ξ := { ξ ✶ , . . . , ξ ▼ } ✱ s✉❝❤ t❤❛t L ❤ | ❳ ✉ ❤ ≈ Φ ✉ ❤ L ❤ Ξ ❛♥❞ ❍ ❛ ≈ ✉ ❤ | ❳ ▼ L ❤ | ❳ Ξ ✶✶✶✷ ✶ t ♦✛ L r❡❞ := ✶✵ ✷ Φ ❚ ◆ ✾ ✸ ✽ ✹ ✼ ✺ ✻ ▼ ❍ ▼ ▼✳ ❉r♦❤♠❛♥♥ ✭♠❞r♦❤♠❛❅s❛♥❞✐❛✳❣♦✈✮ ✵✷✴✷✼✴✷✵✶✸ ✼ ✴ ✷✺

❘❡❞✉❝❡❞ ❜❛s✐s ♠♦❞❡❧ ✶✶ ✶✷ t r❡❞ ✶ ✶✵ ✷ Φ | ❳ ❛ = ( ∂ t ✉ r❡❞ +) ✾ ✸ L r❡❞ ❜ r❡❞ ◆ ✽ ✹ ✼ ✺ ✻ ▼ ◆ ❊rr♦r✿ ❡ := ✉ ❤ − ✉ r❡❞ ✇✐t❤ ✉ r❡❞ := Φ ❛ ▼✳ ❉r♦❤♠❛♥♥ ✭♠❞r♦❤♠❛❅s❛♥❞✐❛✳❣♦✈✮ ✵✷✴✷✼✴✷✵✶✸ ✽ ✴ ✷✺