tr rsss stt rs - - PowerPoint PPT Presentation
s s Prs s rst rts ss r tr rsss
▼❲❊s ❙❖❆ ▲❚❆●s P❛rs✐♥❣ ▼❲❊s ▼❲❊ ❤❡✉r✐st✐❝ ❊①♣❡r✐♠❡♥ts ❈♦♥❝❧✉s✐♦♥s ❇✐❜❧✐♦❣r❛♣❤②
✶✴✹✶
▼❲❊s ❙❖❆ ▲❚❆●s P❛rs✐♥❣ ▼❲❊s ▼❲❊ ❤❡✉r✐st✐❝ ❊①♣❡r✐♠❡♥ts ❈♦♥❝❧✉s✐♦♥s ❇✐❜❧✐♦❣r❛♣❤②
✷✴✹✶
▼❲❊s ❙❖❆ ▲❚❆●s P❛rs✐♥❣ ▼❲❊s ▼❲❊ ❤❡✉r✐st✐❝ ❊①♣❡r✐♠❡♥ts ❈♦♥❝❧✉s✐♦♥s ❇✐❜❧✐♦❣r❛♣❤②
❬◆✐✈r❡ ❛♥❞ ◆✐❧ss♦♥✭✷✵✵✹✮✱ ❋✐♥❦❡❧ ❛♥❞ ▼❛♥♥✐♥❣✭✷✵✵✾✮✱ ❲❡❤r❧✐ ❡t ❛❧✳✭✷✵✶✵✮✱ ❈♦♥st❛♥t ❡t ❛❧✳✭✷✵✶✸✮✱ ◆❛sr ❡t ❛❧✳✭✷✵✶✺✮✱ ❈♦♥st❛♥t ❛♥❞ ◆✐✈r❡✭✷✵✶✻✮❪
❬❲❡❤r❧✐ ❡t ❛❧✳✭✷✵✶✵✮✱ ●r❡❡♥ ❡t ❛❧✳✭✷✵✶✸✮✱ ❱✐♥❝③❡ ❡t ❛❧✳✭✷✵✶✸✮✱ ❈❛♥❞✐t♦ ❛♥❞ ❈♦♥st❛♥t✭✷✵✶✹✮✱ ◆❛sr ❡t ❛❧✳✭✷✵✶✺✮✱ ❈♦♥st❛♥t ❛♥❞ ◆✐✈r❡✭✷✵✶✻✮❪
✸✴✹✶
▼❲❊s ❙❖❆ ▲❚❆●s P❛rs✐♥❣ ▼❲❊s ▼❲❊ ❤❡✉r✐st✐❝ ❊①♣❡r✐♠❡♥ts ❈♦♥❝❧✉s✐♦♥s ❇✐❜❧✐♦❣r❛♣❤②
✹✴✹✶
▼❲❊s ❙❖❆ ▲❚❆●s P❛rs✐♥❣ ▼❲❊s ▼❲❊ ❤❡✉r✐st✐❝ ❊①♣❡r✐♠❡♥ts ❈♦♥❝❧✉s✐♦♥s ❇✐❜❧✐♦❣r❛♣❤②
✺✴✹✶
▼❲❊s ❙❖❆ ▲❚❆●s P❛rs✐♥❣ ▼❲❊s ▼❲❊ ❤❡✉r✐st✐❝ ❊①♣❡r✐♠❡♥ts ❈♦♥❝❧✉s✐♦♥s ❇✐❜❧✐♦❣r❛♣❤②
✻✴✹✶
▼❲❊s ❙❖❆ ▲❚❆●s P❛rs✐♥❣ ▼❲❊s ▼❲❊ ❤❡✉r✐st✐❝ ❊①♣❡r✐♠❡♥ts ❈♦♥❝❧✉s✐♦♥s ❇✐❜❧✐♦❣r❛♣❤②
❬❆❜❡✐❧❧é ❛♥❞ ❙❝❤❛❜❡s✭✶✾✽✾✮❪
✼✴✹✶
▼❲❊s ❙❖❆ ▲❚❆●s P❛rs✐♥❣ ▼❲❊s ▼❲❊ ❤❡✉r✐st✐❝ ❊①♣❡r✐♠❡♥ts ❈♦♥❝❧✉s✐♦♥s ❇✐❜❧✐♦❣r❛♣❤②
P❡rs
✶
◆✉♠
✷
✸
P❡rs
✶
◆✉♠
✷
✸
✽✴✹✶
▼❲❊s ❙❖❆ ▲❚❆●s P❛rs✐♥❣ ▼❲❊s ▼❲❊ ❤❡✉r✐st✐❝ ❊①♣❡r✐♠❡♥ts ❈♦♥❝❧✉s✐♦♥s ❇✐❜❧✐♦❣r❛♣❤②
✾✴✹✶
▼❲❊s ❙❖❆ ▲❚❆●s P❛rs✐♥❣ ▼❲❊s ▼❲❊ ❤❡✉r✐st✐❝ ❊①♣❡r✐♠❡♥ts ❈♦♥❝❧✉s✐♦♥s ❇✐❜❧✐♦❣r❛♣❤②
✭t✶✮ ✭t✷✮ ✭t✸✮ ✭t✹✮ ✭t✺✮ ◆P ◆ ❛❝✐❞ ◆ ◆⋆ ◆ ❛❝✐❞ ◆P ◆ r❛✐♥s ❙ ❱P ❱ r❛✐♥s ◆P↓ ◆P ◆ r❛✐♥s ◆ ❛❝✐❞ ◆P → ◆✵ ◆ → ◆✶ ◆⋆ ◆P → ◆✷ ❙ → ◆P ❱P✸ ◆P → ◆✺ ◆✻ ◆✵ → ❛❝✐❞ ◆✶ → ❛❝✐❞ ◆✷ → r❛✐♥s ❱P✸ → ❱✹ ◆✺ → ❛❝✐❞ ❱✹ → r❛✐♥s ◆✻ → r❛✐♥s
✶✵✴✹✶
▼❲❊s ❙❖❆ ▲❚❆●s P❛rs✐♥❣ ▼❲❊s ▼❲❊ ❤❡✉r✐st✐❝ ❊①♣❡r✐♠❡♥ts ❈♦♥❝❧✉s✐♦♥s ❇✐❜❧✐♦❣r❛♣❤②
✶✶✴✹✶
▼❲❊s ❙❖❆ ▲❚❆●s P❛rs✐♥❣ ▼❲❊s ▼❲❊ ❤❡✉r✐st✐❝ ❊①♣❡r✐♠❡♥ts ❈♦♥❝❧✉s✐♦♥s ❇✐❜❧✐♦❣r❛♣❤②
(N5 → •acid, 0, 0)0, 1 (N0 → •acid, 0, 0)0, 1.5 (N5 → acid•, 0, 1)0, 1 (NP → •N5N6, 0, 0)0, 1 (N6 → •rains, 1, 1)0, 1 (N0 → acid•, 0, 1)0, 1.5 (NP → •N0, 0, 0)0, 1.5 (V4 → •rains, 1, 1)0, 1.5 (NP → N5 • N6, 0, 1)0, 1 (N6 → rains•, 1, 2)0, 1 (S → •NP VP3, 0, 0)0, 1.5 (NP → N0•, 0, 1)1, 0.5 (V4 → rains•, 1, 2)0, 1.5 (VP3 → •V4, 1, 1)0, 1.5 (NP → N5N6•, 0, 2)1, 0 (S → NP • VP3, 0, 1)1, 1 (VP3 → V4•, 1, 2)0, 1.5 (S → NP • V P3, 0, 2)1, 0 (S → NP VP3•, 0, 2)2, 0
✶✷✴✹✶
▼❲❊s ❙❖❆ ▲❚❆●s P❛rs✐♥❣ ▼❲❊s ▼❲❊ ❤❡✉r✐st✐❝ ❊①♣❡r✐♠❡♥ts ❈♦♥❝❧✉s✐♦♥s ❇✐❜❧✐♦❣r❛♣❤②
✶✸✴✹✶
▼❲❊s ❙❖❆ ▲❚❆●s P❛rs✐♥❣ ▼❲❊s ▼❲❊ ❤❡✉r✐st✐❝ ❊①♣❡r✐♠❡♥ts ❈♦♥❝❧✉s✐♦♥s ❇✐❜❧✐♦❣r❛♣❤②
✶✹✴✹✶
▼❲❊s ❙❖❆ ▲❚❆●s P❛rs✐♥❣ ▼❲❊s ▼❲❊ ❤❡✉r✐st✐❝ ❊①♣❡r✐♠❡♥ts ❈♦♥❝❧✉s✐♦♥s ❇✐❜❧✐♦❣r❛♣❤②
✶✺✴✹✶
▼❲❊s ❙❖❆ ▲❚❆●s P❛rs✐♥❣ ▼❲❊s ▼❲❊ ❤❡✉r✐st✐❝ ❊①♣❡r✐♠❡♥ts ❈♦♥❝❧✉s✐♦♥s ❇✐❜❧✐♦❣r❛♣❤②
❊♥❝♦❞❡❞ ▼❲❊s✿ ❛❝✐❞ r❛✐♥s✱ ♣❛✐♥ ✐♥ t❤❡ ♥❡❝❦✱ ❞❡❛❞ ❢r♦♠ t❤❡ ♥❡❝❦ ✉♣ ♠✐♥✇(acid) = ♠✐♥✇(rains) = ✵.✺✱ ♠✐♥✇(pain) = ♠✐♥✇(in) = ✵.✷✺✱ ♠✐♥✇(the) = ♠✐♥✇(neck) = ✵.✷✱ ✳ ✳ ✳
✶✻✴✹✶
▼❲❊s ❙❖❆ ▲❚❆●s P❛rs✐♥❣ ▼❲❊s ▼❲❊ ❤❡✉r✐st✐❝ ❊①♣❡r✐♠❡♥ts ❈♦♥❝❧✉s✐♦♥s ❇✐❜❧✐♦❣r❛♣❤②
✶✼✴✹✶
▼❲❊s ❙❖❆ ▲❚❆●s P❛rs✐♥❣ ▼❲❊s ▼❲❊ ❤❡✉r✐st✐❝ ❊①♣❡r✐♠❡♥ts ❈♦♥❝❧✉s✐♦♥s ❇✐❜❧✐♦❣r❛♣❤②
I = (N✺ → acid•, ✵, ✶) tree(r) = t✺ Rest(I) = {(rains, ✶), (in, ✷), (Ghana, ✶), (are, ✶), (a, ✶), (pain, ✶), (the, ✶), (neck, ✶)} Req(I) = {(rains, ✶)} Rest(I) \ Req(I) = {(in, ✷), (Ghana, ✶), (are, ✶), (a, ✶), (pain, ✶), (the, ✶), (neck, ✶)} ♠✐♥✇(Ghana) = ♠✐♥✇(are) = ♠✐♥✇(a) = ✶✱ ♠✐♥✇(pain) = ♠✐♥✇(in) = ✵.✷✺✱ ♠✐♥✇(the) = ♠✐♥✇(neck) = ✵.✷ h(I) = W (t✺)+h✵(I) = ✶+✵.✷✺×✷+✶+✶+✶+✵.✷✺+✵.✷+✵.✷ = ✶+✹.✶✺ = ✺✳✶✺ β(I) = ✵
(N5 → •acid, 0, 0)0, 5.15 (N5 → acid•, 0, 1)0, 5.15
✶✽✴✹✶
▼❲❊s ❙❖❆ ▲❚❆●s P❛rs✐♥❣ ▼❲❊s ▼❲❊ ❤❡✉r✐st✐❝ ❊①♣❡r✐♠❡♥ts ❈♦♥❝❧✉s✐♦♥s ❇✐❜❧✐♦❣r❛♣❤②
I = (N✵ → acid•, ✵, ✶) tree(r) = t✶ Rest(I) = {(rains, ✶), (in, ✷), (Ghana, ✶), (are, ✶), (a, ✶), (pain, ✶), (the, ✶), (neck, ✶)} Req(I) = ∅ ♠✐♥✇(rains) = ✵.✺ h(I) = W (t✶) + h✵(I) = ✶ + ✶ + ✹.✶✺ = ✺✳✻✺ β(I) = ✵
(N0 → •acid, 0, 0)0, 5.65 (N0 → acid•, 0, 1)0, 5.65
✶✾✴✹✶
▼❲❊s ❙❖❆ ▲❚❆●s P❛rs✐♥❣ ▼❲❊s ▼❲❊ ❤❡✉r✐st✐❝ ❊①♣❡r✐♠❡♥ts ❈♦♥❝❧✉s✐♦♥s ❇✐❜❧✐♦❣r❛♣❤②
I = (NP → N✺ • N✻, ✵, ✶) tree(r) = t✺ Rest(I) = {(rains, ✶), (in, ✷), (Ghana, ✶), (are, ✶), (a, ✶), (pain, ✶), (the, ✶), (neck, ✶)} Req(I) = {(rains, ✶)} Rest(I) \ Req(I) = {(in, ✷), (Ghana, ✶), (are, ✶), (a, ✶), (pain, ✶), (the, ✶), (neck, ✶)} h(I) = W (t✺) + h✵(I) = ✶ + ✹.✶✺ = ✺✳✶✺ β(I) = ✵
(N5 → •acid, 0, 0)0, 5.15 (N5 → acid•, 0, 1)0, 5.15 (NP → •N5N6, 0, 0)0, 5.15 (NP → N5 • N6, 0, 1)0, 5.15
✷✵✴✹✶
▼❲❊s ❙❖❆ ▲❚❆●s P❛rs✐♥❣ ▼❲❊s ▼❲❊ ❤❡✉r✐st✐❝ ❊①♣❡r✐♠❡♥ts ❈♦♥❝❧✉s✐♦♥s ❇✐❜❧✐♦❣r❛♣❤②
I = (NP → N✺N✻•, ✵, ✷) tree(r) = t✺ Rest(I) = {(in, ✷), (Ghana, ✶), (are, ✶), (a, ✶), (pain, ✶), (the, ✶), (neck, ✶)} Req(I) = ∅ ♠✐♥✇(Ghana) = ♠✐♥✇(are) = ♠✐♥✇(a) = ✶✱ ♠✐♥✇(pain) = ♠✐♥✇(in) = ✵.✷✺✱ ♠✐♥✇(the) = ♠✐♥✇(neck) = ✵.✷ h(I) = h✵(I) = ✹✳✶✺ β(I) = W (t✺) = ✶
(N5 → •acid, 0, 0)0, 5.15 (N5 → acid•, 0, 1)0, 5.15 (NP → •N5N6, 0, 0)0, 5.15 (N6 → •rains, 1, 1)0, 5.15 (NP → N5 • N6, 0, 1)0, 5.15 (N6 → rains•, 1, 2)0, 5.15 (NP → N5N6•, 0, 2)1, 4.15
✷✶✴✹✶
▼❲❊s ❙❖❆ ▲❚❆●s P❛rs✐♥❣ ▼❲❊s ▼❲❊ ❤❡✉r✐st✐❝ ❊①♣❡r✐♠❡♥ts ❈♦♥❝❧✉s✐♦♥s ❇✐❜❧✐♦❣r❛♣❤②
✷✷✴✹✶
▼❲❊s ❙❖❆ ▲❚❆●s P❛rs✐♥❣ ▼❲❊s ▼❲❊ ❤❡✉r✐st✐❝ ❊①♣❡r✐♠❡♥ts ❈♦♥❝❧✉s✐♦♥s ❇✐❜❧✐♦❣r❛♣❤②
✷✸✴✹✶
▼❲❊s ❙❖❆ ▲❚❆●s P❛rs✐♥❣ ▼❲❊s ▼❲❊ ❤❡✉r✐st✐❝ ❊①♣❡r✐♠❡♥ts ❈♦♥❝❧✉s✐♦♥s ❇✐❜❧✐♦❣r❛♣❤②
✷✹✴✹✶
▼❲❊s ❙❖❆ ▲❚❆●s P❛rs✐♥❣ ▼❲❊s ▼❲❊ ❤❡✉r✐st✐❝ ❊①♣❡r✐♠❡♥ts ❈♦♥❝❧✉s✐♦♥s ❇✐❜❧✐♦❣r❛♣❤②
✷✺✴✹✶
▼❲❊s ❙❖❆ ▲❚❆●s P❛rs✐♥❣ ▼❲❊s ▼❲❊ ❤❡✉r✐st✐❝ ❊①♣❡r✐♠❡♥ts ❈♦♥❝❧✉s✐♦♥s ❇✐❜❧✐♦❣r❛♣❤②
✷✻✴✹✶
▼❲❊s ❙❖❆ ▲❚❆●s P❛rs✐♥❣ ▼❲❊s ▼❲❊ ❤❡✉r✐st✐❝ ❊①♣❡r✐♠❡♥ts ❈♦♥❝❧✉s✐♦♥s ❇✐❜❧✐♦❣r❛♣❤②
✷✼✴✹✶
▼❲❊s ❙❖❆ ▲❚❆●s P❛rs✐♥❣ ▼❲❊s ▼❲❊ ❤❡✉r✐st✐❝ ❊①♣❡r✐♠❡♥ts ❈♦♥❝❧✉s✐♦♥s ❇✐❜❧✐♦❣r❛♣❤②
✷✽✴✹✶
▼❲❊s ❙❖❆ ▲❚❆●s P❛rs✐♥❣ ▼❲❊s ▼❲❊ ❤❡✉r✐st✐❝ ❊①♣❡r✐♠❡♥ts ❈♦♥❝❧✉s✐♦♥s ❇✐❜❧✐♦❣r❛♣❤②
✷✾✴✹✶
▼❲❊s ❙❖❆ ▲❚❆●s P❛rs✐♥❣ ▼❲❊s ▼❲❊ ❤❡✉r✐st✐❝ ❊①♣❡r✐♠❡♥ts ❈♦♥❝❧✉s✐♦♥s ❇✐❜❧✐♦❣r❛♣❤②
❛◆♦t❡ t❤❛t ✐t ❝❛♥ ❝♦♥t❛✐♥ s♦♠❡ s✉❜✲♦♣t✐♠❛❧ ✐♥t❡r♣r❡t❛t✐♦♥s t♦♦
✸✵✴✹✶
▼❲❊s ❙❖❆ ▲❚❆●s P❛rs✐♥❣ ▼❲❊s ▼❲❊ ❤❡✉r✐st✐❝ ❊①♣❡r✐♠❡♥ts ❈♦♥❝❧✉s✐♦♥s ❇✐❜❧✐♦❣r❛♣❤②
✸✶✴✹✶
▼❲❊s ❙❖❆ ▲❚❆●s P❛rs✐♥❣ ▼❲❊s ▼❲❊ ❤❡✉r✐st✐❝ ❊①♣❡r✐♠❡♥ts ❈♦♥❝❧✉s✐♦♥s ❇✐❜❧✐♦❣r❛♣❤②
5 10 15 20 1000 3000 5000 sentence length # of hyperarcs
Baseline+PM ST ST+PM
✸✷✴✹✶
▼❲❊s ❙❖❆ ▲❚❆●s P❛rs✐♥❣ ▼❲❊s ▼❲❊ ❤❡✉r✐st✐❝ ❊①♣❡r✐♠❡♥ts ❈♦♥❝❧✉s✐♦♥s ❇✐❜❧✐♦❣r❛♣❤②
0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.2 0.4 0.6 0.8 1.0 |MWE derivation| / |Compositional deriv.| % of hyperarcs (ST+PM vs. ST) All MWEs
✸✸✴✹✶
▼❲❊s ❙❖❆ ▲❚❆●s P❛rs✐♥❣ ▼❲❊s ▼❲❊ ❤❡✉r✐st✐❝ ❊①♣❡r✐♠❡♥ts ❈♦♥❝❧✉s✐♦♥s ❇✐❜❧✐♦❣r❛♣❤②
0.5 0.6 0.7 0.8 0.9 0.2 0.4 0.6 0.8 1.0 |MWE derivation| / |Compositional deriv.| % of hyperarcs (ST+PM vs. ST)
Walenty
✸✹✴✹✶
▼❲❊s ❙❖❆ ▲❚❆●s P❛rs✐♥❣ ▼❲❊s ▼❲❊ ❤❡✉r✐st✐❝ ❊①♣❡r✐♠❡♥ts ❈♦♥❝❧✉s✐♦♥s ❇✐❜❧✐♦❣r❛♣❤②
✸✺✴✹✶
▼❲❊s ❙❖❆ ▲❚❆●s P❛rs✐♥❣ ▼❲❊s ▼❲❊ ❤❡✉r✐st✐❝ ❊①♣❡r✐♠❡♥ts ❈♦♥❝❧✉s✐♦♥s ❇✐❜❧✐♦❣r❛♣❤②
✸✻✴✹✶
▼❲❊s ❙❖❆ ▲❚❆●s P❛rs✐♥❣ ▼❲❊s ▼❲❊ ❤❡✉r✐st✐❝ ❊①♣❡r✐♠❡♥ts ❈♦♥❝❧✉s✐♦♥s ❇✐❜❧✐♦❣r❛♣❤②
❆❜❡✐❧❧é✱ ❆✳ ❛♥❞ ❙❝❤❛❜❡s✱ ❨✳ ✭✶✾✽✾✮✳ P❛rs✐♥❣ ✐❞✐♦♠s ✐♥ ❧❡①✐❝❛❧✐③❡❞ t❛❣s✳ ■♥ ❍✳ ▲✳ ❙♦♠❡rs ❛♥❞ ▼✳ ▼✳ ❲♦♦❞✱ ❡❞s✳✱ Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ✹t❤ ❈♦♥❢❡r❡♥❝❡ ♦❢ t❤❡ ❊✉r♦♣❡❛♥ ❈❤❛♣t❡r ♦❢ t❤❡ ❆❈▲✱ ❊❆❈▲✬✽✾✱ ▼❛♥❝❤❡st❡r✱ ♣♣✳ ✶✕✾✳ ❚❤❡ ❆ss♦❝✐❛t✐♦♥ ❢♦r ❈♦♠♣✉t❡r ▲✐♥❣✉✐st✐❝s✳ ❆❧♦♥s♦✱ ▼✳✱ ❈❛❜r❡r♦✱ ❉✳✱ ❞❡ ❧❛ ❈❧❡r❣❡r✐❡✱ ❊✳ ❱✳✱ ❛♥❞ ❋❡rr♦✱ ▼✳ ❱✳ ✭✶✾✾✾✮✳ ❚❛❜✉❧❛r ❛❧❣♦r✐t❤♠s ❢♦r ❚❆● ♣❛rs✐♥❣✳ ■♥ ❊❆❈▲ ✶✾✾✾✱ ♣♣✳ ✶✺✵✕✶✺✼✳ ❈❛♥❞✐t♦✱ ▼✳ ❛♥❞ ❈♦♥st❛♥t✱ ▼✳ ✭✷✵✶✹✮✳ ❙tr❛t❡❣✐❡s ❢♦r ❈♦♥t✐❣✉♦✉s ▼✉❧t✐✇♦r❞ ❊①♣r❡ss✐♦♥ ❆♥❛❧②s✐s ❛♥❞ ❉❡♣❡♥❞❡♥❝② P❛rs✐♥❣✳ ■♥ Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ✺✷♥❞ ❆♥♥✉❛❧ ▼❡❡t✐♥❣ ♦❢ t❤❡ ❆ss♦❝✐❛t✐♦♥ ❢♦r ❈♦♠♣✉t❛t✐♦♥❛❧ ▲✐♥❣✉✐st✐❝s✱ ❆❈▲ ✷✵✶✹✱ ❏✉♥❡ ✷✷✲✷✼✱ ✷✵✶✹✱ ❇❛❧t✐♠♦r❡✱ ▼❉✱ ❯❙❆✱ ❱♦❧✉♠❡ ✶✿ ▲♦♥❣ P❛♣❡rs✱ ♣♣✳ ✼✹✸✕✼✺✸✳ ❈❤❡♥✱ ❏✳ ❛♥❞ ❙❤❛♥❦❡r✱ ❱✳ ❑✳ ✭✷✵✵✹✮✳ ❆✉t♦♠❛t❡❞ ❊①tr❛❝t✐♦♥ ♦❢ ❚❛❣s ❢r♦♠ t❤❡ P❡♥♥ ❚r❡❡❜❛♥❦✳ ■♥ ❍✳ ❇✉♥t✱ ❏✳ ❈❛rr♦❧❧✱ ❛♥❞ ●✳ ❙❛tt❛✱ ❡❞s✳✱ ◆❡✇ ❉❡✈❡❧♦♣♠❡♥ts ✐♥ P❛rs✐♥❣ ❚❡❝❤♥♦❧♦❣②✱ ♣♣✳ ✼✸✕✽✾✳ ❑❧✉✇❡r ❆❝❛❞❡♠✐❝ P✉❜❧✐s❤❡rs✱ ◆♦r✇❡❧❧✱ ▼❆✱ ❯❙❆✳ ❈♦♥st❛♥t✱ ▼✳ ❛♥❞ ◆✐✈r❡✱ ❏✳ ✭✷✵✶✻✮✳ ❆ tr❛♥s✐t✐♦♥✲❜❛s❡❞ s②st❡♠ ❢♦r ❥♦✐♥t ❧❡①✐❝❛❧ ❛♥❞ s②♥t❛❝t✐❝ ❛♥❛❧②s✐s✳ ■♥ Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ✺✹t❤ ❆♥♥✉❛❧ ▼❡❡t✐♥❣ ♦❢ t❤❡ ❆ss♦❝✐❛t✐♦♥ ❢♦r ❈♦♠♣✉t❛t✐♦♥❛❧ ▲✐♥❣✉✐st✐❝s✱ ♣♣✳ ✶✻✶✕✶✼✶✳ ✸✼✴✹✶
▼❲❊s ❙❖❆ ▲❚❆●s P❛rs✐♥❣ ▼❲❊s ▼❲❊ ❤❡✉r✐st✐❝ ❊①♣❡r✐♠❡♥ts ❈♦♥❝❧✉s✐♦♥s ❇✐❜❧✐♦❣r❛♣❤②
❈♦♥st❛♥t✱ ▼✳✱ ❙✐❣♦❣♥❡✱ ❆✳✱ ❛♥❞ ❲❛tr✐♥✱ P✳ ✭✷✵✶✷✮✳ ❉✐s❝r✐♠✐♥❛t✐✈❡ str❛t❡❣✐❡s t♦ ✐♥t❡❣r❛t❡ ♠✉❧t✐✇♦r❞ ❡①♣r❡ss✐♦♥ r❡❝♦❣♥✐t✐♦♥ ❛♥❞ ♣❛rs✐♥❣✳ ■♥ Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ✺✵t❤ ❆♥♥✉❛❧ ▼❡❡t✐♥❣ ♦❢ t❤❡ ❆ss♦❝✐❛t✐♦♥ ❢♦r ❈♦♠♣✉t❛t✐♦♥❛❧ ▲✐♥❣✉✐st✐❝s✿ ▲♦♥❣ P❛♣❡rs ✲ ❱♦❧✉♠❡ ✶✱ ♣♣✳ ✷✵✹✕✷✶✷✱ ❙tr♦✉❞s❜✉r❣✱ P❆✱ ❯❙❆✳ ❆ss♦❝✐❛t✐♦♥ ❢♦r ❈♦♠♣✉t❛t✐♦♥❛❧ ▲✐♥❣✉✐st✐❝s✳ ❈♦♥st❛♥t✱ ▼✳✱ ❘♦✉①✱ ❏✳ ▲✳✱ ❛♥❞ ❙✐❣♦❣♥❡✱ ❆✳ ✭✷✵✶✸✮✳ ❈♦♠❜✐♥✐♥❣ ❝♦♠♣♦✉♥❞ r❡❝♦❣♥✐t✐♦♥ ❛♥❞ P❈❋●✲▲❆ ♣❛rs✐♥❣ ✇✐t❤ ✇♦r❞ ❧❛tt✐❝❡s ❛♥❞ ❝♦♥❞✐t✐♦♥❛❧ r❛♥❞♦♠ ✜❡❧❞s✳ ❆❈▼ ❚r❛♥s✳ ❙♣❡❡❝❤ ▲❛♥❣✳ Pr♦❝❡ss✳✱ ✶✵✭✸✮✱ ✽✿✶✕✽✿✷✹✳ ❈③❡r❡♣♦✇✐❝❦❛✱ ▼✳ ❛♥❞ ❙❛✈❛r②✱ ❆✳ ✭✷✵✶✺✮✳ ❙❊❏❋ ✲ ❛ ●r❛♠♠❛t✐❝❛❧ ▲❡①✐❝♦♥ ♦❢ P♦❧✐s❤ ▼✉❧t✐✲❲♦r❞ ❊①♣r❡ss✐♦♥✳ ■♥ Pr♦❝❡❡❞✐♥❣s ♦❢ ▲❛♥❣✉❛❣❡ ❛♥❞ ❚❡❝❤♥♦❧♦❣② ❈♦♥❢❡r❡♥❝❡ ✭▲❚❈✬✶✺✮✱ P♦③♥❛➠✱ P♦❧❛♥❞✳ ❲②❞❛✇♥✐❝t✇♦ P♦③♥❛➠s❦✐❡✳ ❊❧ ▼❛❛r♦✉❢✱ ■✳ ❛♥❞ ❖❛❦❡s✱ ▼✳ ✭✷✵✶✺✮✳ ❙t❛t✐st✐❝❛❧ ▼❡❛s✉r❡s ❢♦r ❈❤❛r❛❝t❡r✐s✐♥❣ ▼❲❊s✳ ■♥ ■❈✶✷✵✼ ❈❖❙❚ P❆❘❙❊▼❊ ✺t❤ ❣❡♥❡r❛❧ ♠❡❡t✐♥❣✳ ❋✐♥❦❡❧✱ ❏✳ ❘✳ ❛♥❞ ▼❛♥♥✐♥❣✱ ❈✳ ❉✳ ✭✷✵✵✾✮✳ ❏♦✐♥t P❛rs✐♥❣ ❛♥❞ ◆❛♠❡❞ ❊♥t✐t② ❘❡❝♦❣♥✐t✐♦♥✳ ■♥ ❍▲❚✲◆❆❆❈▲✱ ♣♣✳ ✸✷✻✕✸✸✹✳ ❚❤❡ ❆ss♦❝✐❛t✐♦♥ ❢♦r ❈♦♠♣✉t❛t✐♦♥❛❧ ▲✐♥❣✉✐st✐❝s✳
❉✐r❡❝t❡❞ ❤②♣❡r❣r❛♣❤s ❛♥❞ ❛♣♣❧✐❝❛t✐♦♥s✳ ❉✐s❝r❡t❡ ❆♣♣❧✳ ▼❛t❤✳✱ ✹✷✭✷✲✸✮✱ ✶✼✼✕✷✵✶✳ ✸✽✴✹✶
▼❲❊s ❙❖❆ ▲❚❆●s P❛rs✐♥❣ ▼❲❊s ▼❲❊ ❤❡✉r✐st✐❝ ❊①♣❡r✐♠❡♥ts ❈♦♥❝❧✉s✐♦♥s ❇✐❜❧✐♦❣r❛♣❤②
P❛rs✐♥❣ ▼♦❞❡❧s ❢♦r ■❞❡♥t✐❢②✐♥❣ ▼✉❧t✐✇♦r❞ ❊①♣r❡ss✐♦♥s✳ ❈♦♠♣✉t❛t✐♦♥❛❧ ▲✐♥❣✉✐st✐❝s✱ ✸✾✭✶✮✱ ✶✾✺✕✷✷✼✳ ❑❧❡✐♥✱ ❉✳ ❛♥❞ ▼❛♥♥✐♥❣✱ ❈✳ ❉✳ ✭✷✵✵✶✮✳ P❛rs✐♥❣ ❛♥❞ ❤②♣❡r❣r❛♣❤s✳ ■♥ Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ❙❡✈❡♥t❤ ■♥t❡r♥❛t✐♦♥❛❧ ❲♦r❦s❤♦♣ ♦♥ P❛rs✐♥❣ ❚❡❝❤♥♦❧♦❣✐❡s ✭■❲P❚✲✷✵✵✶✮✱ ✶✼✲✶✾ ❖❝t♦❜❡r ✷✵✵✶✱ ❇❡✐❥✐♥❣✱ ❈❤✐♥❛✳ ❚s✐♥❣❤✉❛ ❯♥✐✈❡rs✐t② Pr❡ss✳ ❑❧❡✐♥✱ ❉✳ ❛♥❞ ▼❛♥♥✐♥❣✱ ❈✳ ❉✳ ✭✷✵✵✸✮✳ ❆✯ ♣❛rs✐♥❣✿ ❋❛st ❡①❛❝t ✈✐t❡r❜✐ ♣❛rs❡ s❡❧❡❝t✐♦♥✳ ■♥ Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ✷✵✵✸ ❍✉♠❛♥ ▲❛♥❣✉❛❣❡ ❚❡❝❤♥♦❧♦❣② ❈♦♥❢❡r❡♥❝❡ ♦❢ t❤❡ ◆♦rt❤ ❆♠❡r✐❝❛♥ ❈❤❛♣t❡r ♦❢ t❤❡ ❆ss♦❝✐❛t✐♦♥ ❢♦r ❈♦♠♣✉t❛t✐♦♥❛❧ ▲✐♥❣✉✐st✐❝s✳ ❑r❛s♥♦✇s❦❛✱ ❑✳ ✭✷✵✶✸✮✳ ❚♦✇❛r❞s ❛ ♣♦❧✐s❤ ▲❚❆● ❣r❛♠♠❛r✳ ■♥ ▼✳ ❆✳ ❑❧♦♣♦t❡❦✱ ❏✳ ❑♦r♦♥❛❝❦✐✱ ▼✳ ▼❛r❝✐♥✐❛❦✱ ❆✳ ▼②❦♦✇✐❡❝❦❛✱ ❛♥❞ ❙✳ ❚✳ ❲✐❡r③❝❤♦♥✱ ❡❞s✳✱ ▲❛♥❣✉❛❣❡ Pr♦❝❡ss✐♥❣ ❛♥❞ ■♥t❡❧❧✐❣❡♥t ■♥❢♦r♠❛t✐♦♥ ❙②st❡♠s ✲ ✷✵t❤ ■♥t❡r♥❛t✐♦♥❛❧ ❈♦♥❢❡r❡♥❝❡✱ ■■❙ ✷✵✶✸✱ ❲❛rs❛✇✱ P♦❧❛♥❞✱ ❏✉♥❡ ✶✼✲✶✽✱ ✷✵✶✸✳ Pr♦❝❡❡❞✐♥❣s✱ ♣♣✳ ✶✻✕✷✶✳ ❙♣r✐♥❣❡r✳ ▼❝❙❤❛♥❡❛✱ ▼✳✱ ◆✐r❡♥❜✉r❣✱ ❙✳✱ ❛♥❞ ❇❡❛❧❡✱ ❙✳ ✭✷✵✶✺✮✳ ❚❤❡ ❖♥t♦❧♦❣✐❝❛❧ ❙❡♠❛♥t✐❝ tr❡❛t♠❡♥t ♦❢ ♠✉❧t✐✇♦r❞ ❡①♣r❡ss✐♦♥s✳ ▲✐♥❣✈✐st✐❝æ ■♥✈❡st✐❣❛t✐♦♥❡s✱ ✸✽✭✶✮✱ ✼✸✕✶✶✵✳ ◆❛sr✱ ❆✳✱ ❘❛♠✐s❝❤✱ ❈✳✱ ❉❡✉❧♦❢❡✉✱ ❏✳✱ ❛♥❞ ❆♥❞ré✱ ❱✳ ✭✷✵✶✺✮✳ ❏♦✐♥t ❉❡♣❡♥❞❡♥❝② P❛rs✐♥❣ ❛♥❞ ▼✉❧t✐✇♦r❞ ❊①♣r❡ss✐♦♥ ❚♦❦❡♥✐s❛t✐♦♥✳ ■♥ Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ❆♥♥✉❛❧ ▼❡❡t✐♥❣ ♦❢ t❤❡ ❆ss♦❝✐❛t✐♦♥ ❢♦r ❈♦♠♣✉t❛t✐♦♥❛❧ ▲✐♥❣✉✐st✐❝s ✭❆❈▲✬✶✺✮✳ ✸✾✴✹✶
▼❲❊s ❙❖❆ ▲❚❆●s P❛rs✐♥❣ ▼❲❊s ▼❲❊ ❤❡✉r✐st✐❝ ❊①♣❡r✐♠❡♥ts ❈♦♥❝❧✉s✐♦♥s ❇✐❜❧✐♦❣r❛♣❤②
◆✐✈r❡✱ ❏✳ ❛♥❞ ◆✐❧ss♦♥✱ ❏✳ ✭✷✵✵✹✮✳ ▼✉❧t✐✇♦r❞ ✉♥✐ts ✐♥ s②♥t❛❝t✐❝ ♣❛rs✐♥❣✳ ■♥ Pr♦❝❡❡❞✐♥❣s ♦❢ ▼❊▼❯❘❆ ✷✵✵✹ ✕ ▼❡t❤♦❞♦❧♦❣✐❡s ❛♥❞ ❊✈❛❧✉❛t✐♦♥ ♦❢ ▼✉❧t✐✇♦r❞ ❯♥✐ts ✐♥ ❘❡❛❧✲❲♦r❧❞ ❆♣♣❧✐❝❛t✐♦♥s✱ ❲♦r❦s❤♦♣ ❛t ▲❘❊❈ ✷✵✵✹✱ ▼❛② ✷✺✱ ✷✵✵✹✱ ▲✐s❜♦♥✱ P♦rt✉❣❛❧✱ ♣♣✳ ✸✾✕✹✻✱ ▲✐s❜♦♥✱ P♦rt✉❣❛❧✳ Pr③❡♣✐ór❦♦✇s❦✐✱ ❆✳✱ ❍❛❥♥✐❝③✱ ❊✳✱ P❛t❡❥✉❦✱ ❆✳✱ ❛♥❞ ❲♦❧✐➠s❦✐✱ ▼✳ ✭✷✵✶✹✮✳ ❊①t❡♥❞❡❞ ♣❤r❛s❡♦❧♦❣✐❝❛❧ ✐♥❢♦r♠❛t✐♦♥ ✐♥ ❛ ✈❛❧❡♥❝❡ ❞✐❝t✐♦♥❛r② ❢♦r ◆▲P ❛♣♣❧✐❝❛t✐♦♥s✳ ■♥ Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ❲♦r❦s❤♦♣ ♦♥ ▲❡①✐❝❛❧ ❛♥❞ ●r❛♠♠❛t✐❝❛❧ ❘❡s♦✉r❝❡s ❢♦r ▲❛♥❣✉❛❣❡ Pr♦❝❡ss✐♥❣ ✭▲●✲▲P ✷✵✶✹✮✱ ♣♣✳ ✽✸✕✾✶✱ ❉✉❜❧✐♥✱ ■r❡❧❛♥❞✳ ❆ss♦❝✐❛t✐♦♥ ❢♦r ❈♦♠♣✉t❛t✐♦♥❛❧ ▲✐♥❣✉✐st✐❝s ❛♥❞ ❉✉❜❧✐♥ ❈✐t② ❯♥✐✈❡rs✐t②✳ ❙❛✈❛r②✱ ❆✳✱ ❲❛s③❝③✉❦✱ ❏✳✱ ❛♥❞ Pr③❡♣✐ór❦♦✇s❦✐✱ ❆✳ ✭✷✵✶✵✮✳ ❚♦✇❛r❞s t❤❡ ❛♥♥♦t❛t✐♦♥ ♦❢ ♥❛♠❡❞ ❡♥t✐t✐❡s ✐♥ t❤❡ ♥❛t✐♦♥❛❧ ❝♦r♣✉s ♦❢ ♣♦❧✐s❤✳ ■♥ ◆✳ ❈✳ ❈✳ ❈❤❛✐r✮✱ ❑✳ ❈❤♦✉❦r✐✱ ❇✳ ▼❛❡❣❛❛r❞✱ ❏✳ ▼❛r✐❛♥✐✱ ❏✳ ❖❞✐❥❦✱ ❙✳ P✐♣❡r✐❞✐s✱ ▼✳ ❘♦s♥❡r✱ ❛♥❞ ❉✳ ❚❛♣✐❛s✱ ❡❞s✳✱ Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ❙❡✈❡♥t❤ ■♥t❡r♥❛t✐♦♥❛❧ ❈♦♥❢❡r❡♥❝❡ ♦♥ ▲❛♥❣✉❛❣❡ ❘❡s♦✉r❝❡s ❛♥❞ ❊✈❛❧✉❛t✐♦♥ ✭▲❘❊❈✬✶✵✮✱ ❱❛❧❧❡tt❛✱ ▼❛❧t❛✳ ❊✉r♦♣❡❛♥ ▲❛♥❣✉❛❣❡ ❘❡s♦✉r❝❡s ❆ss♦❝✐❛t✐♦♥ ✭❊▲❘❆✮✳ ❙❤✐❡❜❡r✱ ❙✳ ▼✳✱ ❙❝❤❛❜❡s✱ ❨✳✱ ❛♥❞ P❡r❡✐r❛✱ ❋✳ ❈✳ ✭✶✾✾✺✮✳ Pr✐♥❝✐♣❧❡s ❛♥❞ ✐♠♣❧❡♠❡♥t❛t✐♦♥ ♦❢ ❞❡❞✉❝t✐✈❡ ♣❛rs✐♥❣✳ ❚❤❡ ❏♦✉r♥❛❧ ♦❢ ❧♦❣✐❝ ♣r♦❣r❛♠♠✐♥❣✱ ✷✹✭✶✮✱ ✸✕✸✻✳ ❱✐♥❝③❡✱ ❱✳✱ ◆❛❣② ❚✳✱ ■✳✱ ❛♥❞ ❩s✐❜r✐t❛✱ ❏✳ ✭✷✵✶✸✮✳ ▲❡❛r♥✐♥❣ t♦ ❞❡t❡❝t ❡♥❣❧✐s❤ ❛♥❞ ❤✉♥❣❛r✐❛♥ ❧✐❣❤t ✈❡r❜ ❝♦♥str✉❝t✐♦♥s✳ ❆❈▼ ❚r❛♥s✳ ❙♣❡❡❝❤ ▲❛♥❣✳ Pr♦❝❡ss✳✱ ✶✵✭✷✮✱ ✻✿✶✕✻✿✷✺✳ ✹✵✴✹✶
▼❲❊s ❙❖❆ ▲❚❆●s P❛rs✐♥❣ ▼❲❊s ▼❲❊ ❤❡✉r✐st✐❝ ❊①♣❡r✐♠❡♥ts ❈♦♥❝❧✉s✐♦♥s ❇✐❜❧✐♦❣r❛♣❤②
❲❛s③❝③✉❦✱ ❏✳✱ ❙❛✈❛r②✱ ❆✳✱ ❛♥❞ P❛r♠❡♥t✐❡r✱ ❨✳ ✭✷✵✶✻✮✳ ❊♥❤❛♥❝✐♥❣ ♣r❛❝t✐❝❛❧ ❚❆● ♣❛rs✐♥❣ ❡✣❝✐❡♥❝② ❜② ❝❛♣t✉r✐♥❣ r❡❞✉♥❞❛♥❝②✳ ■♥ ✷✶st ■♥t❡r♥❛t✐♦♥❛❧ ❈♦♥❢❡r❡♥❝❡ ♦♥ ■♠♣❧❡♠❡♥t❛t✐♦♥ ❛♥❞ ❆♣♣❧✐❝❛t✐♦♥ ♦❢ ❆✉t♦♠❛t❛ ✭❈■❆❆ ✷✵✶✻✮✱ ❙é♦✉❧✱ ❙♦✉t❤ ❑♦r❡❛✳ ❲❡❤r❧✐✱ ❊✳✱ ❙❡r❡t❛♥✱ ❱✳✱ ❛♥❞ ◆❡r✐♠❛✱ ▲✳ ✭✷✵✶✵✮✳ ❙❡♥t❡♥❝❡ ❛♥❛❧②s✐s ❛♥❞ ❝♦❧❧♦❝❛t✐♦♥ ✐❞❡♥t✐✜❝❛t✐♦♥✳ ■♥ Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ❲♦r❦s❤♦♣ ♦♥ ▼✉❧t✐✇♦r❞ ❊①♣r❡ss✐♦♥s✿ ❢r♦♠ ❚❤❡♦r② t♦ ❆♣♣❧✐❝❛t✐♦♥s ✭▼❲❊ ✷✵✶✵✮✱ ♣♣✳ ✷✼✕✸✺✱ ❇❡✐❥✐♥❣✱ ❈❤✐♥❛✳ ❆ss♦❝✐❛t✐♦♥ ❢♦r ❈♦♠♣✉t❛t✐♦♥❛❧ ▲✐♥❣✉✐st✐❝s✳ ➅✇✐❞③✐➠s❦✐✱ ▼✳ ❛♥❞ ❲♦❧✐➠s❦✐✱ ▼✳ ✭✷✵✶✵✮✳ ❚♦✇❛r❞s ❛ ❜❛♥❦ ♦❢ ❝♦♥st✐t✉❡♥t ♣❛rs❡ tr❡❡s ❢♦r P♦❧✐s❤✳ ■♥ P✳ ❙♦❥❦❛✱ ❆✳ ❍♦rá❦✱ ■✳ ❑♦♣❡↔❡❦✱ ❛♥❞ ❑✳ P❛❧❛✱ ❡❞s✳✱ ❚❡①t✱ ❙♣❡❡❝❤ ❛♥❞ ❉✐❛❧♦❣✉❡✿ ✶✸t❤ ■♥t❡r♥❛t✐♦♥❛❧ ❈♦♥❢❡r❡♥❝❡✱ ❚❙❉ ✷✵✶✵✱ ❇r♥♦✱ ❈③❡❝❤ ❘❡♣✉❜❧✐❝✱ ♣♣✳ ✶✾✼✕✷✵✹✱ ❍❡✐❞❡❧❜❡r❣✳ ❙♣r✐♥❣❡r✲❱❡r❧❛❣✳ ✹✶✴✹✶