phylogenetic models of language diversification...between bengali, persian, and 15 european...
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Submitted on 20 Jan 2012
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Phylogenetic Models of Language DiversificationRobin Ryder
To cite this version:Robin Ryder. Phylogenetic Models of Language Diversification. Applications [stat.AP]. Oxford Uni-versity, 2010. Français. tel-00661866
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P②♦♥t ♦s ♦ ♥
rst♦♥
♦♥ ②r ♥s ♦
♣rs♦r
♦ ♦s
♣rt♠♥t ♦ ttsts
❯♥rst② ♦ ①♦r ❯
ssrtt♦♥ s♠tt ♥ ♣rt ♠♥t
♦ t rqr♠♥ts ♦r t r ♦ ♦t♦r ♦ P♦s♦♣②
♣r
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strt
♥ rst♦♥ s st♦st ♣r♦ss ♣rs♥ts s♠rts t
♣②♦♥t ♦t♦♥ ♥t② tr s ♥ ♥trst ♥ ♠♦♥ ts
♣r♦ss t♦ ♣ s♦ ♣r♦♠s trt♦♥ ♥st ♠t♦s ♥♥♦t
rs♦ ♣r♦♠ ♦ st♠t♥ ♥ q♥t②♥ t ♥rt♥t② ♥ t
♦ t ♠♦st r♥t ♦♠♠♦♥ ♥st♦r ♦ t ♥♦r♦♣♥ ♥s s ♥
①♠♣
❲ ♠♦ ① ♥ ② ♣♦♥t ♣r♦ss ♦♥ ♣②♦♥t tr r
♠♦ s s♣② t♦r t♦ ① t ♥ ♥ ♣rtr trts s♣ts ♦
♥st ♥ r trt♦ ♥♦♥t ♦r ♥ ♦
str♦♥ ♠♣t ♦♥ st♠ts tstr♦♣ rt tr♦♥t② ♥ ♠ss♥
t ❲ ♠♣♦s ♣r♦r strt♦♥ ♦♥ t tr t♦♣♦♦② ♥♦ s ♥ ♦tr
♠♦ ♣r♠trs rrs♦♥s t♦ ♦♠♣t t ♦♦ ♥ st♠t
♣r♠trs ♦♥t② s♥ r♦ ♥ ♦♥t r♦
❲ t ♦r ♠t♦s s♥ ♥ ①t♥s r♦sst♦♥ ♣r♦r
r♦♥strt♥ ♥♦♥ s ♦ ♥tr♥ ♥♦s ❲ ♠ s♦♥ t♦♥
s♥ s②♥tt t ♥ s♦ tt ♠♦ ♠ss♣t♦♥s t♦ ♦rr♦♥
♦ ①♦♥ t♥ ♥s ♥ t ♣rs♥ ♦ ♠♥♥ t♦rs ♥ ①
t ♦ ♥♦t t♦ s②st♠t s
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❲ t ♦r ♠♦ t♦ t♦ t sts ♦ ♥♦r♦♣♥ ♥s ♥ st♠t
t ♦ Pr♦t♦♥♦r♦♣♥ r ♠♥ ♥②ss s st
♣♦str♦r ♣r♦t② ♥st② ♥tr ♦ ②rs ♦r t Prs♥t
♥ ♥ t t s♦ ♥t♦♥ ②♣♦tss ♦r t ①♣♥s♦♥ ♦ t ♥♦
r♦♣♥ ♥s ❲ sss ② r ♥♦t ♦♥r♥ ② t ♠♦s
rts♠s ♦ sttst ♠t♦s ♦r st♦r ♥sts ② rs♥
♥ ❱♦t ❬❪ ❲ s♦ ♣♣② ♦r ♠t♦s t♦ t r♦♥strt♦♥ ♦ t
s♣r ♦ ♥ ts ♥ t♦ t tt♦♥ ♦ ♣♥tt♦♥ rsts ♦
♥ ♥ ♥ t ♥♦r♦♣♥ ♠②
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♥♦♠♥ts
s tss ♦ ♥♦t ♥ ♣♦ss t♦t t ♣ ♦ ♠♥② ♣♦♣
♦t ♦♥② t ♥s ♥tr ♦t♦r r♥♥ ♥tr ♣r♦
♥ ①♥t ♣r♣rt♦♥ t♦ ♦t♦r ♦r t② s♦ ♣r♦ ♥
♣ ♥ ♣rtr r♥ ❨♦rs ♦♠♠t♠♥t t♦ ♣r♦♥ ssst♥ ♥
♦♦♥ ♦r ♥♥ s ♠♣rss
①♠♥rs ♦r ♠② ♠② tr♥sr ♥ ♦♥r♠t♦♥ ♦ stts ♦t♥
♥ ❩♥ ❨♥ s♥ ♥rt ♥ ♥ ❱♥ ♣r♦ ♠ t
♣ ♥sts ♥t♥ t♥s♦♥ ♥ rs ♦tr s♦ ♠
♦♠♠♥ts
② ♦t♦r ②rs ♥ s♦♠ ♦ t ♠♦st ♥♦② ♦ ♠② t♥s
t♦ ♠② ♦♥r ♠② ♥ r♥s ♠ r② rt t♦ ♠② ♣r♥ts ♦r
tr ♦♥t♥ s♣♣♦rt ♥ t ♣rs♥ ♦♥ ♠② s ♦ ♠② ♥é s
Pr♦ss♥s♦♦♥t♦②r s ♥ ♥
♠ ♠③ t ♦ ♠ r ♦ ♦s s ♠♥ t♦ t ♠ ♥
ts ♣st tr ②rs ♣r t♦ ♥ s♣rs ② ♠ ♥
s r② ♠ ♠ss s ♥ ♥ ♦♥rst♦♥ ♥r♥s
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♦♥t♥ts
♥tr♦t♦♥ ♥ r♦♥
♥♦r♦♣♥ ♠② ♦ ♥s
P②♦♥t ♠♦s ♦r ♥st t
P②♦♥ts ♦r tr st♦r② ♥ ♥tr♦♣♦♦②
sr♣t♦♥ ♦ t t ♥ ♦ t ♠♦
sr♣t♦♥ ♦ t t
♦ sr♣t♦♥
Pr♦r strt♦♥ ♦♥ trs
rst♦♥ ♦ ♦♥② sss
rstrt♦♥ ♣r♦ss
P♦♥t ♣r♦ss ♦ rts ♦r rstr ♦♥② sss
♦♦ t♦♥s
P♦str♦r strt♦♥
♠ rrst②
♠♣♠♥tt♦♥
Pr♦♣rt② ♦ t ♣♦str♦r
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♠♣♠♥tt♦♥ ♥ t
r♦ ♥ ♦♥t r♦
♥ tsts
❱t♦♥
♥♠♦ tst♥
tstr♦♣s
ss♥ t
t♦♠♦ tst♥
♦rr♦♥
♥♥ t♦rs
rst②
♦♥strt♦♥ ♦ ♥♦♥ s
♥②ss ♦ ♥♦r♦♣♥ t sts
♥②ss ♦ t ♥ t ❬❪ tst
♥②ss ♦ t ②♥ t ❬❪ t
♦♥s♦♥s ♥ ①t♥s♦♥s
st♥ s♦♠ ①tr♠ ①♠♣s st ② rs♥ ❱♦t
❬❪
♥ ts
P♥tt♦♥ rsts
s st
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♣tr
♥tr♦t♦♥ ♥ r♦♥
♥♦r♦♣♥ ♠② ♦ ♥s
♦st ♥s ♦ r♦♣ ♥ sr ♥s ♦ ♥ r ♠♠rs ♦ t
s♠ ♠② t ♥♦r♦♣♥ ♠②
Prs♦♥s ❬❪ s♦r s♠rts ♥ t ♦rs ♦r s ♥♠rs
t♥ ♥ Prs♥ ♥ r♦♣♥ ♥s ♥ ♥♦t tt ♦♥ t
♦tr ♥ ♥s r ② ♥ rs r② r♥t ♦rs ♦r
♥♠rs ♠ t♦ t ♦♥s♦♥ tt t♦s ♥s r rt ♥
st♠♠ r♦♠ ♦♠♠♦♥ ♥st♦r t ♥ ♦ ♣t s♦♥ ♦ ♦
♦♠ ♦ ts s♠rts r s♦♥ ♥
♠rts t♥ ts ♥s ♥ s♦ ♦♥ ♥ ♠♥② ♦tr ♦rs
♥ ♥ s②♥tt ♥ ♣♦♥t trs rtr♠♦r t r♥s t♥
♥s s♦ r ♣ttr♥s ♠♥ t ♠♣♦ss ♦r ts s♠rts t♦
t♦ ♦♥♥ t s ♥♦ ♣t tt ts ♥s r rt
s♦s t strt♦♥ ♦ t ♥s ♥ t ♥♦r♦♣♥ ♠②
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♥♥ ♥ë ② tr ♥ë♥të♥ tr ♥②♥s ♦♥ t♦ tr ♥♥r ♥ ♦ trs ♥♥rs ♦♥ ♦ tr ♥♦t♥ ♥♦ tr ♥♦Prs♥ ② ♦ s ♥♦ss♥ ♦♥ tr ②ts ♥ t tr ♥♦
♦r♥ ss tr ♥
♥s ② r s♥ r s♥②♠ s♦s tsrs r ü ♦③
♠rs ♥ s♦♠ ♦ t ♥s ♥ Prs♦♥s s♠♣ rst t♥s♦ s♥♥t s♠rts t② r ♠♠rs ♦ t ♥♦r♦♣♥ ♠②♦r ♥s ♦ ♥♦t s t t♥ ♣t s♦ ♥ ♣♣r♦①♠t♣♦♥t tr♥sr♣t♦♥
s t s ♥rst♦♦ ♥♦②s
♥s t ♥♦r♦♣♥ ♠s sr ♥r ♥ st♥s
r♦♣♥ ♥s r ♥ ♠♦r ♦s② rt ♥♠r
♦ ♠♦s ♦ t♦s s♠rts r s♦♦♥ ♣r♦♣♦s ♦r ①♠♣ ♠t
❬❪ ♣r♦♣♦s ♠♦ ♥ ♦r ♥s ♦♣s rt♥
♥♠r ♦ ♥♥♦t♦♥s s♣r t♦ s♦♠ t rr② ♥s ♥
t ♠② s s♦♥ ♥ r♦♣ t♦ ss♥ P♦s
t♥♥ t r♠♥ ♥s r♠♥ s s ♦t
♥ ♠ t rt♥ s ♥♥s r ♦tr ♥s
②♣♦tss s tr♦r tt ♦♥ r♠♥ ♦r t♦ ♥
♦♣ ♥ ♠ s ♥♥ ♥ tt tt ♥♥♦t♦♥ s♣r t♦ ts
♥♦rs t♦t r♥ t ♦tr ♥♦r♦♣♥ ♥s ♥ t
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r ♣ ♦ ♥♦r♦♣♥ ♥s s♦♥ ② ♥s s♥t tr♦♥ rs♦♥ ♦ r②r t ❬❪
♦tr ♥ s♦ r♦♣ t♦ t r♠♥♥ ♥ ♥♦r♥♥
s t♦s ♥s ♥ s r ♦tr ♥s ❬♦r②
❪
♠♦ s ♣♣r♦♣rt ♥ s♠ ♥♠r ♦ ss t ♥ ♥r
♠♦r ♣♣r♦♣rt ♠♦ s ♥t ♦♥ r s str♦♥ tr s♥
♥ ♥st t ❬♦♥ ♥ ♦♥ ❪ ♥ t ♦srt♦♥ ♦
r♥t ♥ ♥ tr♦ rtt♥ t①ts t♥ t♦ t♥ r♥
♥ ♣♥s s♦s tt ♠♦t♦♥ t s♥t ♦♥ts ♦r ♠♦st ♦
t ♥s r ❬❪ s t rst t♦ ♣r♦♣♦s s ♠♦ ♥
♥tr♦ t tr r♣rs♥tt♦♥ ♦rr♦♥ ♦r② r♦♠ ♦♦②
♥tr♦ tr♠s s s ♥s s♣s ♦r rt② t♦ sr ♥
r♦♣♥s ♥ ♠ t rst tt♠♣t t ♥ ♦t♦♥r② tr ♦ ♥♦r♦♣♥
♥s s♠rts t♥ ♥ rst♦♥ ♥ ♦♦
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Indo−Iranian
ArmenianBalto−SlavicGermanic
Italic GreekCeltic
r ♠ts ♠♦ ♦ rt♦♥s♣s t♥ ♥♦r♦♣♥ ♥s ♥ s ♣rt ♦ ♦♥ ♦r sr r♦♣♥s ♠② ♥trst
♦t♦♥ r s♦ ♥♦t ② r♥ ❬❪ ♦r♠t♦♥ ♦ r♥t
♥s ♥ ♦ st♥t s♣s ♥ t ♣r♦♦s tt ♦t ♥ ♦♣
tr♦ r ♣r♦ss r r♦s② ♣r ❲ ♥ ♥ st♥t
♥s str♥ ♦♠♦♦s t♦ ♦♠♠♥t② ♦ s♥t ♥ ♥♦s t♦
s♠r ♣r♦ss ♦ ♦r♠t♦♥ ♥ tr r str♥ s♠rts t♥
t ♣r♦sss ♦ ♦♦ ♦t♦♥ ♥ ♥st rst♦♥ ♥s
t ♦r② ♣♦♥♦♦② ♥ ♠♦r♣♦s②♥t① ♦ ♥s r ♣ss ♦♥ r♦♠
♣r♥ts t♦ r♥ ♥ ♣r♦ss ♦ s♥t t ♠♦t♦♥
❲t tr ♠♦ t♦ qst♦♥s ♥ ♥sr♥ ❲t s t t♦♣♦♦②
♦ t tr ♦ ♦ s t r♦♦t rt♦♥② t t♦♣♦♦② ♦
r♦♥strt ② ♥ ② ♥ ①♣rt ♥st ♦♥ t ♥s ♥r st②
s♥ t ♦♠♣rt ♠t♦ ② ♦♠♣r♥ ♦rs ♦ ♥t ♦r s♠r
♠♥♥s ♥ r♥t ♥s t ♥st ♦ tr② ♥ ♥t② ♦♥ts
♠♥♥ t♦rs ♦r t ♥s rt ♦rs s t♦♥
♥ ♦r ♠♦r ts ♥ ♥ ①♠♣ ♦ ♦♥② sss t
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t s♠ t♠ t② ♦ ♥t② t s②st♠t ♣♦♥t ♦rrs♣♦♥♥s
tr♦ t ♥s ♣ss ② ♦ t♥ r♦♥strt t
t♦♣♦♦② ♦ t tr ♥ t s♦♥ ♥s tt ♦r ♦♠♣rt
♥sts ♦t♥ tr st ♠♦r ♥ rt t♥ s♥
r s ♥♦ rt ② ♦ st♠t♥ t ♦ t r♦♦t s♦ r♦♦
♥ s s ♦r t♥ sss ♥ t s ♦ ♥♦r♦♣♥ ts s
t♦ ♦♥tr♦rs② ❬♠♦♥ ♥ ♦♦ ❪ ♠♥ ②♣♦tss
♠♦♥st ♥sts s ♣♦stt ② ♠ts ♥ ♥♥ ❬❪ ♥ ♦s
tt t ♠♦st r♥t ♦♠♠♦♥ ♥st♦r ♦ ♥♦♥ ♥♦r♦♣♥ ♥s
r♥ ♥♦ rr t♥ ♦t ②rs ♦r t Prs♥t P t
t ①♣♥s♦♥ ♦ t r♥ ♦rs♠♥ ♣♦♣ ♥ ♥ st♣♣s ♥♦rt ♦ t
♣r♦♣♦♥♥ts ♦ t r♥ ②♣♦tss ♦ tt ♦♠stt♦♥
♦ t ♦rs ♥ ♦ t t r♥ s♥♥t ♠tr② ♥t
♦♥ ♥ ♥♦r♠♦s ①♣♥s♦♥ ❬♦r② ❪ ♥ tr♥t ②♣♦tss
ssts tt t s♣r ♥ r♦♥ P ♥ t ♥t♦♥s ♠str
r♠♥ ♥ t r② ♦t ❬♥r ❪ t♥ t r♦♦t ♦ t ♥♦
r♦♣♥ ♥s ♦ tr♦r s t ♦♥ t ♥ts ♦
t ♥♦r♦♣♥ ♠② t♦ s♣r s♦ r s ss s t ♠♥ qst♦♥
♥ ♠ ♦ t ♦r ♣rs♥t ♥ ts tss
rst s②st♠t ♠t♦ ♦r st♠t♥ t r♦♦t ♦tt♦r♦♥♦♦②
s ♦♣ ② ♦rrs s ♥ t s s s st ♦ ♦t
♠♥♥s ♦ ♦r ♦r② tr r♥ t♦ st ♦ ♠♥♥s
r ss♠ t♦ ♦ t ♦♥st♥t s♦ rt ♥ sts ♦ ♦r
♦r② ♦r t♦ ♥s ♦ tr tr ♦rs ♦r
♥ ♠♥♥ r ♦♥t ♣r♥t ♦ ♦♥t ♦rs ♦ t♥
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rt② tr♥st ♥t♦ t t t t t t♦ ♥s s♣t tr♦
t ♦r♠ t = log C
2 log r r C s t ♣r♦♣♦rt♦♥ ♦ sr ♦♥ts ♥
r s t rt♥t♦♥ ♦♥st♥t ss♠ t♦ ♦♥st♥t r♦ss ♥s
❬s ❪ r ♦ st♠t s♥ ♥② ♣r ♦ ♥s ♦r
t ♦ t ♦♠♠♦♥ ♥st♦r s ♥♦♥ rs♥ ♥ ❱♦t ❬❪
② ♦ t♦ ♦tt♦r♦♥♦♦② ♥ t② s ♥♦♥ ts t♦ s♦
tt t rt♥t♦♥ ♦♥st♥t s ♥ t ♥♦t ♦♥st♥t t ts r② r♥t
s ♥ t tr r♦♣s ♦ ♥s t② st ♦rs ♥ ♥
♦r♥ ♥ ♦r♥ ♦r♥ ♥ ♥r♥ ♥ ♥ ♦r♥
r♠♥♥ ♦tt♦r♦♥♦♦② s ♥♦ ♥ srt s♣t rts♠s
♦ t sss rs ② rs♥ ♥ ❱♦t ❬❪ ❬♥♦ ❪ ♥
t s♠s s t♥♥ t♦ ♦♣ t♦ s♠♠rs ♥ ♥ ♥ s♥
♥♠r ♦r tr r sss t rs♥ ♥ ❱♦t ❬❪s ♦r
♥ s♦ ♥ ♣tr tt ♠♦r♥ ♠t♦s r ♥♦t st t♦ t s♠
rts♠s r s tr t ♥st ♦♠♠♥t② r♠♥s ♥♦♥tss
r② s♣t ♦t tt♠♣ts t t♥
P②♦♥t ♠♦s ♦r ♥st t
♥t ♥s ♥ ♣②♦♥ts ♠ t ♣♦ss t♦ t ♠♦s ♦ ♠
rtr ♦♠♣①t② ♥ ♠ ♦sr t♦ rt②
rst tt♠♣ts t tt♥ ♣②♦♥t ♠♦s t♦ ♥st t r
sr ♥ rts ② r② ♥ ♦r♥ ❬❪ ♥ r② ♥ t♥s♦♥ ❬❪
r② ♥ ♦r♥ ❬❪ ♣♣② ♠①♠♠ ♣rs♠♦♥② t♦ tst ♦ ①
t♠s r♦♠ str♦♥s♥ ♥s ♥ ♥ ♥ s♣♣♦rt♥ ♦♥ ♦
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t ♠♥ ②♣♦tss ♦ str♦♥s♥ ①♣♥s♦♥ t s♦ ①♣rsstr♥
②♣♦tss tt str♦♥s s ♦♦♥③ r♣② ② r♠♥ ♣♦♣ ♦t ♦
♥ ② ♦ ♥♦t tt♠♣t t♦ t ♥② ♦ t ♥tr♥ ♥♦s ♦♥
❬❪ s♦ ♣♣② ♠①♠♠ ♣rs♠♦♥② t♦ ♥t ♥ ♥t♦ ♥s
s♣♦♥ ♦t ♦ t r t② ♥ tt t ♠♦st ♣rs♠♦♥♦s tr ♦♦s
t ①♣♥s♦♥ ♦ r♠♥ ♥ sr♥ r ♥t♥ tt t s t
♠str♥ ♦ r♠♥ tt ♦ t ♥t ♣♦♣ t♦ ♦♦♥③ s r
r
r② ♥ t♥s♦♥ ❬❪ ♣♣② t ♣②♦♥t ♠t♦ t♦ ♥♦r♦♣♥
♥ t ♦t ② ②♥ t ❬❪ s♥ t ♥t sts ♠♦
♠♣♠♥t ♥ t r②s ♣ ② s♥ ♥ ♦♥qst ❬❪
rsts ♦t♥ s♥ ♣♥③ ♠①♠♠ ♦♦ r r② ♦s t♦ t
trs ♥ ② ss ♦♠♣rt ♥sts ♠t♦s ② ♠♣♦s ♣rt ♦
t t♦♣♦♦② ♦ t tr ♦tr ♥♦♥str♥ ♥r ② ② tr ♥②ss
♦rrs♣♦♥ t♦ t♦s s② ♣t ② st♦r ♥sts r ♦ t
s♠s t② ♥ s♦ ♦rrs♣♦♥ t♦ t s r② t♦ tr
s s s♠② r♦♣♥ r♠♥ ♦♠♥ ♥ t ♥s tr
♣rts ♦ t tr r ♥rs♦ s s t ♣♦st♦♥ ♦ ♥♥ ❲ tr
rsts ♦ ♥♦t s♦ ♥② ♥ r♦♣♥s t t tt t rsts ♦rrs♣♦♥ t♦
t s ♣t ② ♥sts ♦♣ tt ♣②♦♥ts ♦ sss②
s ♥ ♦tr ss st ♥ ♠s ♦r ♦♥tr♦rs② t②
tt♠♣t t♦ t t ♥tr♥ ♥♦s ♥ r♦♦t ♦ t tr ♥ st♠t t
♦ Pr♦t♦♥♦r♦♣♥ t♦ t♥ P ♥ P ♥ ♥ t
t ♥t♦♥ ②♣♦tss ♦r t ♥t sts ♠♦ t② s s ♥♦t
st t♦ ① t ♥ ♣rtr t ♦s ♦r ♦♠♦♣s② ♦r s♥
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♦♥② ss t♦ ♦r♥ sr t♠s t r♥t ♣♦♥ts ♦ t tr
s ♥♦t ♣♣r♦♣rt s♠ ♠t♦s r ♣♣ t s♠r rsts t♦
♥♦tr t st ♦ ♥♦r♦♣♥ ♥s ② t♥s♦♥ t ❬❪ t
tr s tt ♥ tr♠s ♦ t♦♥ ♦ t ♥♥s
s ♥ ♦ rsr s s♣♥ ♦t ♦ ♥trst ♥♥ ♦ts ♦
s♥t rs ❬❲ ❪ ♥♠r ♦ ♦tr r♦♣s ♣♣ r♦s
♠t♦s r♦♠ ♦♦② t♦ ♥st tsts
①♦ t ❬❪ ♣r♦r♠ ♠①♠♠ ♣rs♠♦♥② ♥②ss ♦ t ②♥
t ❬❪ t ♦ ♥♦r♦♣♥ ① t♠s ② r♦♥strt t
♥♦♥ ♠♦r trs ♦ t ♥♦r♦♣♥ ♠② t tr s ♦t ♦
♥rt♥t② ♦t t t♦♣♦♦② ♦s t♦ t r♦♦t ② ♥♦t tt t s
♦r② ♦ ♥♦r♦♣♥ s str♥② tr r②♥t t ❬❪ ♦♠
t♦ t s♠ ♦♥s♦♥ ♥ tr ♥②ss ♦ t t r♦♠ ②♥ t ❬❪
s♥ ♦rt
♦♥ ♥ ♦♥ ❬❪ s♦ ♣♣② t ♦r♦♥♥ ♠t♦
t♦ ♥♦r♦♣♥ ♥s ♥ ① t♠s ♥r♦♦t tr t②
♦t♥ s♦s t t♥ ♥r ♥r② ♠tt ♦r ♥♦r♦♣♥ ♥s
t ♥♦ r rt♦♥s♣ ♣♣rs t♥ t ♥r
t♥ t ❬❪ s t s♦tr ❬r♠♠♦♥ ♥ ♠t
❪ t♦ st♠t t ♦ t ♠♦st r♥t ♦♠♠♦♥ ♥st♦r t♦ t ♠t
♥s t ♦ ♥♦t t ♥rt♥t② ♦ tr st♠ts
♥♥ t ❬❪ ♣♣② ♠①♠♠ ♣rs♠♦♥② ♥②ss t♦ t strtr
♠♦r♣♦s②♥tt ♥ ♣♦♥♦♦ trs ♦ st ♦ ♥ ♥s
r ♥♦♥ t♦ ♦s② rt t s♠ t♦rs tr ♠♦ ♦♥ t♦
②s♥ ♣②♦♥t ♥②ss s♥ r♦s ♠♦s r♦♠ ♦♦② ❬♥♥
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t ❪ ♥ tr rsts r s♠r t♦ t♦s ♥sts ♦t♥ s♥
t ♦♠♣rt ♠t♦ ② r tt t tr ♠♦ s ttr st
t♦ strtr trs t♥ t♦ ① trts s ♦rr♦♥ ♦ strtr
♦♥② ♣♣♥ ① ♦rr♦♥ s♦ ♦rs rs t ♦♥rs s ♥♦t
tr ❬♦rs ❪ t♦ ♦s ❬❪ ts t ♦♣♣♦st tt
r♠♠t trs ♦ r♣② ♥ r ♠♦r st t♦ r♦♥ ♥♥s
t♥ ① t ♥ t r♦♥strt♦♥ ♦ t ♥ ♠② s ♦♦ t②
①tr♣♦t tr ♠t♦ t♦ ♥♠r ♦ P♣♥ ♥s ♦s st♦r② s
♥♦t ♥♦♥ ② ♦♥ tt t P♣♥ ♥s ♠st tr sr
♦♠♠♦♥ ♥st♦r ♦r tt tr ♠st ♥ ♦♥tt t♥ t P♣♥
♥s ♦r P
❱s r s t♦ tr ♠♦r♣♦s②♥tt ♦r ① t♠s rt♥
♠♦r s♥ r♦♠ ♥s ♥st♦r ♦r ①♠♣ ♦♠s♦♥ ❬❪ ♥♦ts
tt t ♥ ♦ ♥③♥ s ♣♣r♥t② ♦r♥② ♥ t st
♠② ♥ rt♥s ♠ st s ♦r② t tt ts s②♥t① s
♥ ♠♦ ②♦♥ r♦♥t♦♥ tr♦ ♦♥tt t ♥♦r♥ ♥t
♥s s♠ t♦r ♠s tt ts ♦rs ♥ stt♦♥s r
s♣rs ♦ t s♦r ♥ r♥ t r♥ ♥s ♠♣rt②
rs ♦rr♦♥ ♦ ① t ♥♦t ♠♦r♣♦s②♥tt t♠s ♦rs ♥
s♣rs ♦ t r♥ ♥ ♦♣t ♥ t♠s r♦♠ t s♦r ♥
❬♦♠s♦♥ ❪
♥s♥ t ❬❪ ♦♠♣r ① ♥ ♥t t r♦♠ t ♥♦♥s♥
s♥ ♦ ♠ ② ♠ t♦ s♦ tt t ♠♥s ♥s t②
s♠♣ ♦r♠ s ♦ t str♦♥s♥ ♠② t♦ tr r♠♥t s
♥♦t r ♦r ♥trst♥② t② ♥ ♣♦st ♦rrt♦♥ t♥ rt♥t♦♥
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♦ Pr♦t♦str♦♥s♥ ♦♥ts ♥ str♦♥s♥ ❨ r♦♠♦s♦♠ ♥s s
s ♦rrt♦♥ t t st♥ t♦ t ♣ r t s t
♥st♦rs ♦ t ♠♦r♥ ♣♦♣t♦♥s rst r ♦♥ ♠
t♦ s♦♠ ♥rst♦♦ t r rr♦r rs rst♥ r♦♠
sttst ♥②ss ♦ ♦♠♣rt t t♦ s♥ ♦ ♥ss ♥ ts
♠t♦♦♦s t② r t② ♦♥ ♦ ts ♠♥ str♥ts t ♦♠♣rt
♠t♦ s ♣rs♥t② ♦r♠t ♦s ♥♦t st♠ts ♦ ♥rt♥t② ❬P
❪
♥♦tr ♦♠♠♦♥ rts♠ s tt t tr ♠♦ s ♥♦t s st
t♦ ♥s s t s t♦ ♦♦ s♣s ♥ t♦ t ❬❪ ♦♥
②r③t♦♥ ♥ ♦ ♥♠ ♥ ♦ ♣♥t s♣s r ♥ rs♣♦♥s
t♦ ♦♠r ❬❪ ♦ stt tt t tr ♠♦ ♥ssr② ♥♦s
s♠♣t♦♥ ♦ t t st♦r ts ♠♣ ❬❪ ♦♥t♥s tt
st♦r ♥sts ♦ s② t s ♥♦t s♠♣t♦♥ rtr ❬ts ♠t♦s❪
rss rt② ♦♥② ♥rt ♠tr ♦tr ♠t♦s ♥ t♥qs
♣ t♦ ♦♠♣t t ♣tr s s ♥ ♦♣ ♦r tt t q♥ttt
♠t♦s sr t s♣t ♦ ♥ st♦r② t② tt♠♣t t♦
sr rtr t♥ t ♦♠♣t ♣tr ♥ ♥r t tr ♠♦ s
♦♦ t ♦r ♦r ♦r②
♦♠ ♥sts s ♦r ♠♦s ♠♦r s♣② t♦r t♦ ♥st
t ❬r♦t ❪ ♦t♥ t ♥ ♦r ♠♦s s♣ t♦ ♥st t rtr
t♥ ♦rr♦ r♦♠ ♦♦② ❲r♥♦ t ❬❪ ♦♣ ♠♦ ♦r ①
♣♦♥♦♦ ♥ strtr t ♥s s♦♠ ♦ t s♣ts ♦
♥ rst♦♥ ♦r ♣♦♥♦♦ ♥ strtr t ♠tt♦♥
t♦ s♣ t ♦♠♦♣st stt s ♦ ② ss♠ tt ♥
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♦t♦♥ s ♠♥② tr t s♦♠ s t♥ s②♥r♦♥ ♥s
t♦ ♠♦ ♦rr♦♥ ② ss♠ ♦♠♣t rt tr♦♥t② t rts
r r♥t ♦♥ r♥t r♥s ♥ ♦r r♥t rtrs ② ♦
♥♦t t t ♠♦ t ♣r♦ tt t t♦♣♦♦② ♦ t tr s ♥t
♠♦♦ t ♣♠♥t ♦ t r♦♦t ♥ t rt ♣r♠trs s♠ r♦♣
♣r♦♣♦s t♦ ♦♥strt ♣rt ♣②♦♥t ♥t♦rs ❬ t ❪ ②
tr♥s♦r♠♥ ♠①♠♠ ♣rs♠♦♥② tr ♥t♦ ♥t♦r ♥ ♠ t
❬❪ ♥ ♦rôté t ❬❪ ♦♣ ♠♦s ♦r ♣♦♥♦♦ t
♥ s t♠ t♦ ♥t② ♥ ♠s
♦s ♥ r② ❬❪ t ♠♦ s♣② t♦r t♦ ♥st t
s st♦st ①t♥s♦♥ ♦ t ♠♦ sr ② ♦♦ ❬❪ ♥ s
♥ ♦♦ ♦♥t①t ② s♥ ❬❪ ♥ rrs ❬❪ r rsts
s♦ s♣♣♦rt t ♥t♦♥ ②♣♦tss ♥ t② st② ♥♠r ♦ ♠♦
♠ss♣t♦♥s ♦ ♥tr♦ s②st♠t s ♥ ♣rtr
t② ♥♦t tt rr t str♦♥ rt tr♦♥t② ♦ ♥♥
♦♥ t st♠ts s♥ t ♦ r t♦ tt ♥ t t s♠ t♠
r t r ♦♥ ♥②ss s♦ s♦ tt t ② ♠ss♥ t r
♥ ② ♦s ♥ r② ❬❪ s r ♥ t ♦rs t♠ t♦ sr
sr ♥s r♦♠ tr ♥②ss ♣tr ♦ ts tss ①♣♥s t
♠♦ t② ♣r♦♣♦s ❲ ♣♣② t t♦ sr ♥st t sts ♥ ♣tr
♥ trs ♦♥strt t ♣②♦♥t ♠t♦s ♥ s t♦
st② ♦tr s♣ts ♦ ♥ ♥ r♠♥ t ❬❪ st② str♦♥
rs ♥ ♥ ♦r♥ ♥s ♥ t t rt t str♦♥
rs r rr③ t② ♥ tt t rt ♦ rr③t♦♥ ♥s t t
sqr r♦♦t ♦ t s rq♥② r s s t♠s ♠♦r ♦t♥
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t♥ ♥ ♦tr rr③ t t rt rsr ② r♠♥
t ❬❪ s ♠ sr ② t t tt t② ♥ t ♥str② ♦ t
tr ♥s t② r st②♥ P t ❬❪ s t♦ st♠t
rt♦♥ ♥ rts ♦r ♦r② ♥ ts rts r ♠ ♦r t♥ t
rts ♦ rr③t♦♥ ♦ str♦♥ rs t② ♥ t♦ st② ♦♥r t♠
♣r♦ ♥ t② tr♦r ♦s t♦ ♥r rts ♦♥ t ♥tr tr ♦ t ♥♦
r♦♣♥ ♠② ② s ♣♦str♦r s♠♣s s♥ t s♠ ♥t sts ♠♦
s r② ♥ t♥s♦♥ ❬❪ ♥ ♦♠♣r t rts ♦r ♠♥♥ t♦r②
t♦ t rq♥② ♦ s ♥ ♦r ♠♦r♥ ♥♦r♦♣♥ ♥s ♥s
♣♥s ss♥ ♥ r t② ♥ s♥♥t ♥t ♦rrt♦♥
t♥ rq♥② ♦ s ♥ rst♦♥ rt ② r t♦ ①♣♥
♦ t rt♦♥ ♥ t rts ♦ ♦t♦♥ t t♦ ♣s ♦ ♥♦r♠t♦♥
rq♥② ♦ ♦r s ♥ ♣rt ♦ s♣ r ♥♦♥ ♥♠r P ♥
❬❪ ♣♣② s♠r ♠t♦s t♦ t ♥t ♠②
♠r② t♥s♦♥ t ❬❪ s P t ❬❪s s♦tr
②sP②♦♥s t♦ trs ♦r t ♥♦r♦♣♥ ♥t ♥ str♦♥s♥
♥s ② ♦♥ tt ♠♦r ♥s ♦r ♦♥ ♣ts t ♠♦r
r♥♥ ♥ ♦♥ tt t♥ ♥ ♦ ♥ ♥
♣♣♥s ♥ ♣♥tt♦♥ rsts ♥ t♦ ♥s r t t
r♠♥r ♦ ♥ ♥ ♣♣♥♥ ♦♥t♥② tr♦ t♠ ❲ rst
ts ss ♥ ♣tr
r s♦ ♥ s♦♠ ♦rts t♦ tt ♦♥ts t♦♠t② rtr
t♥ ② s♥ t ♠♥ts ♦ ①♣rt ♥sts ❬② ♥ ♦♥r ❪
t ts r s st r② ♠ ♥r♦♣
s ♦♣♣♦s t♦ t s♦♥ s♥ ♥ ♠♥② ♦ t rts t ♦ tr
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s♦ s♠s t♦ t♥♥② ♠♦♥st s♦♠ ♥♦♥s♣st s♥tsts t♦ ♦♥sr
♣②♦♥t ♥②ss ♦ ♥st t s ♥ s② ♥ ♥ ♣r♦♠ ♥ t♦
♥♠r ♦ ♣t♦♥s t tt ♦r ♥♦ ♥st ♦r sttst r♦♥♥
r ♥ Ptr♦♥ ❬❪ ♥♦t tt t ♦♠♣rt ♠t♦ ♥ ♦♥②
♣♣ t♦ ♥s ♥ ①t♥s② st ② ♥sts ♥ t②
♠ tt t sst♦♥ ♥t♦ ♦♥t sss s t♦ stt②
s♦ ♦ tr t♥ r②♥ ♦♥ t ♠♥ts ♦ ♥sts t②
s t s♣♥s ♦ ♦rs ♦♥ t s st ♦r ♥♦r♦♣♥ ♥s
♦♠♣t t ♥st♥ st♥ t♥ ♣r ♦ ♦rs ♥ ♣♣② t
❯P♠t♦ t♦ t t t② ♦t t② ♦♣ t♦ ♣♣② t s♠ ♠t♦s
t♦ ss st ♥ ♠s ♥t♥t♦♥ s ♦♦ t tr ♠t♦♦♦②
s ♥♦rt♥t② ♥ t② r ♥ t ♥s s t
st r♥t ♣ts t② tr♥sr ts ♥s ♥t♦ t t♥
♣t r r ♠♥② ②s ♦ ♦♥ ts s♦ t ♦tt② t② r ♦♥
♦r s ♥r qst♦♥ ❯♥sr♣rs♥② t ♥s ♥ tr r♦♥strt
tr r r♦♣ ② ♣t ♥♥ s r♦♣ t t ♦tr ♥s
s♥ t t♥ ♣t ♣♦st♦♥ ♥♦ ♥st ♦ t♦
♦rrt rs r ♥ r♠♥♥ s ♣ts ♦ tr ♦♥ r
t ♦tr♦♣s r♠♥ t t ♥ ♥♦r♥♥ sr♦♣s r
♦rrt② r♦♥strt t t ts ♦ ts r♦♣s s r② r r♦♠ t
♥♦♥ ♥st trt t ♣♦st♦♥ ♦ ♥s ♥ P♦s ♥② tr
♦r♠ ♦r t♥ s s♠♣st rs ♦♥ ♦♥② t♦ ♥♦♥ ts t♦ ♠♥②
♦trs r ♥ t② ♦ ♥♦t ♥ tt♠♣t t♦ ♠sr t ♥rt♥t②
♦ tr rsts ♠t♦ ♦ ♣r♦② st② ♠♣r♦ ② r②♥ ♦♥
♣♦♥t tr♥sr♣t♦♥ rtr t♥ t s♣♥ ♦ t ♦rs ♥ tr t ♥
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② ♥♥ ♥♦♥♥r② st♥ s♦ tt s♠r ♣♦♥♠s r ♠ ♦sr
t♥ r② st♥t ♣♦♥♠s ♥ ♠ t ❬❪
♦rstr ♥ ♦t ❬❪ st② t ♥ ♦♠♥ ♥s t t②
r s t tr t ♦t♦♥ ♥ ♥ ♣rtr t t ♦♥②
♠♥ts tr t♥ s ♦♥② ♠♥ts ♠ ② ①♣rt ♥sts
t② r♦♣ t♦tr ♦rs ♦♦ s♦♠t s♠r ♥ t② r ♥♦♥
② ♥sts t♦ ♦♠ r♦♠ r♥t ♦r♥s ♥ s♣rt ♦tr ♦rs r
♥♦♥ t♦ ♦♥ts s ♥s t ❬❪ ♦r ♥ ①t♥s rts♠ ♦rstr
♥ ♦t ❬❪ t t ①♣♥s♦♥ ♦ t t♦ ± P ② ♥
s♥ ♥ r t♦ tr st ♦ t ♥ ♦♠♥ ♥s t②
st♠t t ♦ Pr♦t♦♥♦r♦♣♥ t ± P ♥ ♥r②♥
ss♠♣t♦♥ ♦ tr st♠t s tt r s ♥ ♦tr♦♣ ♦ t ♥♦r♦♣♥
♠② s r r♦♠ rt♥
t s ♦rt ♥♦t♥ tt ♥♦♥ ♦ ts ♦rs ♥♦r ♦rs tt♠♣ts t♦ s♦r
♥ ♥ ♠s tr ♥ st ♦ ♥s r② ♥♦♥ t♦
rt st♠t ts ♥tr♥ strtr ♥ ts
P②♦♥ts ♦r tr st♦r② ♥ ♥tr♦♣♦♦②
♥♠r ♦ tr s♣ts rs② ♥ ② s♠r t♦ ♥s ❬ ♥
♦♥ r♥ ♥ ②♠♥ s♦ t ❪ s s tr
♥ ♠♥② r♥t tt♠♣ts t♦ ♣♣② ♣②♦♥t ♠t♦s t♦ tr
t sts s sst ② P ❬❪ ♥ ♥r s♦tr ♦♣ ♦r
♦♦ t s ♥ s t♦t qst♦♥♥ t ss♠♣t♦♥s ♠ ②
t ♠♦s t s ♦t♥ r t♦ s② tt tr trts r ♦sr t♦ ♥st t♥
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♦♦ trts s♦ s rsr ♦ rt② ♥t r♦♠ ♠♦r ♦♣
♥ ttr ♣③ s♦tr ♦r ♥st rst♦♥ ①♠♣s ♥
t sts ♦♥ P♦♥♥ ♣♦♥ts ❬r♥ t ❪ r♦♣♥ ♥♦t
♣♦ttr② ❬♦r ♥ ♥♥♥ ❪ t ♠r♥ sts ❬♦r♥ ♥
♥♥♥ ❪ ♥ st r♥ ♥s♣ ♥ ♠rr trt♦♥s ❬r
t ❪ t♦♥ ❬❪ ①♠♥s r♥s ♥ ②s ♦ rt♥ ♥r
♦♥ ♣♦ttr② t♦ r♦♥strt t st♦r② ♦ t ♥
tr ♦t♦♥ ♥ rr t♦ ♥②s t s r ♦ t♦ s♣t
♥st t ♥t♦ st ♦ trts ♥♥ s st ♦ trts ♥ s②st♠t
♥ ♥s ② ♦r tr t s ♥♦t s s② ♥♦tr ss s tt ♦
t①♦♥ ♦♥strt♦♥ s t sr t♦ tr t♦ ♥♠s r ♠♠rs ♦
t s♠ s♣s t♥ t♦ tr t♦ ♣♦♣ s♣ t♦ r♥ts ♦ t
s♠ ♥ ♦r t♦ st♥t t ♦s② rt ♥s t s ♥ rr
t♦ ♥ t ♦♥sttts s♥ ♥ tr ♦ tr ♦t♦♥ ❬r♥
t ❪
r② t ❬❪ sst tr♠♥s♦♥ s♣ t♦ ♣ ♦♦s tr
tsts tr ♠♦ ♦ st st ② ♣r♦♣♦s t♦ ♦♦ ♦r tr
trts ♠♥♠③ t rt ♦ ♥ ♥ rt tr♥s♠ss♦♥ ♥ t rt
♦ ♦r③♦♥t tr♥s♠ss♦♥ ♥ ♠①♠③ t ①t♥t t♦ r♥t
s♣ts ♦ tr r ♦♣ t♦tr t t ♠t♦s t♦ ♠sr ts
rtrsts r s♦♠t ♥r
r s s♦ ♥ ♥trst ♥ ♦♠♣r♥ ♦t♦♥r② trs ♦t♥ r♦♠
♥t t t t♦s tt ♦♠ ♦t ♦ ♥st ♦r tr t sts ❬♦♥s
❪ s ♥ ♦ rsr s ♥tt ② ♦r③ t ❬❪ ♦
♥♦r♣♦rt ♥t t r♦♠ ♣♦♣t♦♥s ♥ t ♦r ♥ ♥st
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t r♦♠ ♥ ♠s ♥ ♠ t♦ ♥ ♦♥sr ♣rs♠
t♥ ♥t ♥ ♥st ♦t♦♥ ♦r t ♥st r♦♣♥s
t② s ♥ t s♣r♠s ♦ r♥r ❬❪ r ②
♦♥tr♦rs
♦♥ ♥ ❬❪ ss♠ tt ♥ trs r ♦♦ ♠♦ ♦
tr ♦t♦♥ s ♥ ♦rr t♦ tst tr s♣r ♦ tt s ♦rrt
t ♠tr♥② ♥ ♥t ♣♦♣t♦♥s t② ♣♦t trts ♦♥ ♦r ♠tr♥②
♦r ♣tr♥② ♥ ♦r ♣♦ssss♦♥ ♦ tt ♦♥ ♣②♦♥t tr ♦ ♥
rst♦♥ ss♠♥ tt t tr trts ♦ ♦♥ t s♠
tr t② s♦ tt ♠tr♥ s♦ts ♠ ♣tr♥ tr t② qr
♦♠st tt ♠r② ♦rt♥t♦ t ❬❪ s ♣②♦♥t tr ♦
♥♦r♦♣♥ ♥s sst ♦ t ②♥ t ❬❪ t st
♥②s ♥ tr ♣trs t♦ st♠t tt ♦r② s ② t♦ r② ①st ♥
t Pr♦t♦♥♦r♦♣♥ s♦t②
♣♥r t ❬❪ ♣r♦r♠ s♠t♦♥ st② r t tr tr s
♥♦♥ t② s♠t ♦♣②♥ ♦ ♠♥sr♣ts ② s♥ ♠♦r♥ srs
t♦ ♦♣② ♣♦♠ r♦♠ ♣r♦s ♦♣② ② s ♦r ♦♥♥
♥ ♠①♠♠ ♣rs♠♦♥② t♦ r♦♥strt t ♦t♦♥r② tr ♦t ♠t♦s
② rsts r ♦s t♦ t tr tr s ♣♦st rsts r
s♥ s t♦♥ ♦ t ♦r ② rr♦♦ t ❬❪ ♦ ♣♣② ♥
♥s♦s ♣②♦♥t ♠t♦ ♣rs♠② ♠①♠♠ ♣rs♠♦♥② t♦ r♦s
♠♥sr♣ts ♦ ❲ ♦ ts Pr♦♦ r♦♠ ♥trr② s ♥
s♦ tt s♦♠ ♠♥sr♣ts ♥ ♥♦r ② s♦rs r t②
♥ ♠tr♥ s♦t② r♦♣ ♠♠rs♣ s ♥rt r♦♠ ♥ ♥s ♠♦trrtr t♥ r♦♠ tr tr
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t ♦sst t♦ rs ♦r♥ ♣♥r t ❬❪ s♦ ♠①♠♠
♣rs♠♦♥② tr s♥ t ♦rr ♥ t ♥trr② s r rtt♥ ♥
sst ♦ t ♠♥sr♣ts
❲ tr s ♦t ♦ ♥trst ♦r ♣♣②♥ ♣②♦♥t ♠t♦s t♦
♥st ♥ tr t tr r sr♣rs♥② ♠♦s s♣②
t♦r t♦ ts ♠♥♥ tt ♠♦st ♦ t rsr s ♦♥t s♥ ♠♦s
♦rr♦ r♦♠ ♦♦② s rt♥② r♦ t st♠ts s♥
♠♦s ♥ s♣ts ♦ ♥ ♥ ♦ ♠♦r r
♥ ss ♣r♦♥ t♦ rsst♥ ② ♥sts
♥ ts tss ♦s ♦♥ tr ♠♦ ♦r ① t
st♦st ♦♦ ♠♦ tr ♦♦ ❬❪ ♦ rst ♣r♦♣♦s ♠♦ r
t ♦ss ♦ trt s rrrs ♦♥ s♣s s ♦st trt t ♥♥♦t
r♦ tt s♠ trt s ♣r♥♣ tr ♦♦s s t♦t
t♦ ♠♦st ♥rs ♦r ♦♠♣① ♠♦r♣♦♦ trts ♥ ♦♦② t♦
①♣t♦♥s ♥ ♦♥ ❬P ❪ ♥ t ♠♦ sr ♥ ♣tr
trt ♥ ♦♥② ♦r♥ ♦♥ ♦♥ tr ♥ ♦tr ♦rs trt s s♣②
t t♦ s ♦ t tr ts t♦ ♥st♥s ♦ t trt ♠st ♦♠♦♦♦s
ts ♦rrs♣♦♥s t♦ ♦ ①♣t ① ♥ t♦ ♦r s ♠♦ s
s♠r t♦ ♠♦s ♦♣ ♦r ♦♦ trt t ② s♦♥ ♥ t ❬❪
♥ s②♥♦ t ❬❪ ♥ t ♠♥♦r st♠♥ts ♦r ♠♦ ♦
♣r♦② ♣♣ t♦ rt♥ ♦♦ t sts
♥t ♠♣r♦♠♥ts ♥ ♦♠♣tt♦♥ ♣♦r ♦ ②s♥
♥r♥ t♦ ♦♠ ♣r♠♥♥t ♥ ♣②♦♥ts ♦♦♥ ❨♥ ♥ ♥♥
❬❪ ♥ ♣rtr ♠♥② t♥qs ♦r st♠t♦♥ r♦ ♥
♦♥t r♦ ♥ ♦♣ ❬rt ♥ ♠♦♥ ❪ ♥ ♦r ♦♥t①t
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②s♥ ♥r♥ ♣rs♥ts t♦ ♠♥ ♥ts rst t ♦s s t♦ st♠t
♥rt♥ts ♥ ♥tr ② ♦♥ t ♦s s t♦ ①♣t ♦r ♣r♦r s
♦♥ ② ♣r♠trs ♥ r ♠♦st② ♥trst ♥ t♥ t r♦♦t ♦ t
♥♦r♦♣♥ ♠② sr ♥ ♣tr ♦ t♦ ♠♣♦s ♥♦r♠ ♣r♦r
♦♥ ts sttst
sss ♦ t♥ ♦♥ ♣②♦♥t trs ♥ rsr ①t♥s② ♦r
♠♦r ♣②♦♥ts ♦r♥ t ❬❪ st② ♠♦ ♦ ♦t♦♥ ♦
t rt ♦ ♠♦r ♦t♦♥ ♥ ♣r♦♣♦s ♠t♦s t♦ st♠t ts ♦♥
♣②♦♥t tr ♥ t ②♣♦tss ♦ ♦♥st♥t ♠♦r ♦ ♦s ♥♦t
♦ ♦r♥ ♥ s♥♦ ❬❪ st② t tt♦♥ ♦ ♦rrt♦♥s ♥ t
♦t♦♥ ♦ rts ❨♥ ♥ ♥♥ ❬❪ ①♠♥ sss t rt♦♥
t s♣② t ♥♥ ♦ s♦t ♦♥s ♦ t s♦r
♥♦♥ ♥str ♥♦s t♦ ♦ts ♦ ♦♥str♥t ♥♥ ♥ ❨♥ ❬❪
♥ ♥♦ t ❬❪ sss t ♠♣t ♦ t ♣r♦r ♥ ♦ t s③ ♦ t t
♦♥ t ♥rt♥t② ♥ ♣♦str♦r st♠ts ♦ ts rsr s r♥t t♦
♣②♦♥t t♥ qst♦♥s ♥ ♥sts
♦♠ ♥sts r② ♠r t ♦ ♣♣②♥ ♣②♦♥t
♠t♦s t♦ ♥st t ❬t ❪ t ♦trs r r② ♦♣♣♦s t♦
t ♦♥♣t ❬♦♠ rrs ❪ ♦ts tt ♥ ①♣rss
♥♦t ♥ t ② rts ♥♦r ♥st t ♦r ①♠♣
❬♥s t ❪ rt③ ♦rstr ♥ ♦t ❬❪ qt str♥② t s♦
♥t tt ts ♠t♦♦♦② s t♠ t♦ r② ♦ ♠♥② ♦tr
♣②♦♥t ♥②ss ♦ ♥st t ♥♥ ♥②ss ♦ ♥♦t
s ♦♦s s s ♦ t ♦tt♦r♦♥♦♦② s♦ t♥ ♠t♦s
r ♠t t ♥ ♠♦r s♣ts♠ ❬♦♥ ♥ ♦♥ ❪ s s
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♣rtr tt♥t♦♥ ♠st ♥ t♦ t t♦♥ ♦ t ♠t♦s t
♠♥ ♥ ❬❪ ♦♥♥♥ r ♣rts ♦ ts tss
♦s ♦♥ s ♦♥♥♥
♥ ♣tr ♣rs♥t ♠♦ t♦r t♦ ① ♥ ❲ ts
♦♥ ♦ ♠♣♠♥t t t ♦ t ♠♦ ♥ ♣tr ❲ ♣r♦ ♥♠r
♦ t♦♥ s ♥ ♣tr ♥ ♥②s t♦ t sts ♦ ♥♦r♦♣♥
♥s ♥ ♣tr ♥ ♣tr sss ♦tr ♣♦ss ♣♣t♦♥s
♦ ♦r ♠t♦s
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♣tr
sr♣t♦♥ ♦ t t ♥ ♦ t
♠♦
sr♣t♦♥ ♦ t t
r ♥t ♦s s ♦♥ t♦ t sts ♦ ♦r② ♦r ♥♦r♦♣♥ ♥s
♦♥ ♦t ② ♥ t ❬❪ ♥ t ♦tr ② ②♥ t ❬❪ ♥
t ❬❪ ♦t t r♦♠ ♠♥♥ t♦rs ♦r ♠♦st② ♥♥t
♥s ♥ ♦ t t ♥ ♦♠♦♦② sss ②♥ t ❬❪
♦t t ♦r ♠♦r♥ ♥s ♥ ♠♥♥ t♦rs r② ♥
t♥s♦♥ ❬❪ ♥♥t ♥s ttt ♦r♥ ♥ ♦r♥
t♦ t st r♥♥ t ♣ t♦ ♥s ♥ ♦♠♦♦② sss r
s tt ♦r♣ t♥ t sts ♦ ♥s ♥ t t♦ t sts
♦t tsts ♦r t ♦r ♦r② ♠♥♥s s s ♥♠
ss ♦♠♣t st s ♥ ♥ ♣♣♥① s ♠♥♥ t♦rs
r ♥ ♥ ♥ ♥ r ①♣t t♦ ①st ♥ ♥s ①♣rt
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♥sts sts ♦rs sr ♦♠♠♦♥ ♥st♦r ♦ ♦rs ♥ t
s♠ ♠♥♥ t♦r② ♥ s♦♥ t♦ s♥ r♦♠ ♦♠♠♦♥
♥st♦r tr♦ s②st♠t ♣♦♥♦♦ ♥s r ♦♥ts s
q♥ rt♦♥s♣ sss ♦rs ♥t♦ ♦♥② sss ♦r ①♠♣
♦r t ♠♥♥ t t♥ tst ♥ t r♥ têt ♦♥ t♦ t
s♠ ♦♥② ss t ♥s ♥ t s ♦♥
t♦ ♥♦tr ♦♥② ss ♥ ♠♥t ♦ ♦♥② ss s ts ♦r ♥
♣rtr ♥ ♦r② ♦ s♥ ♥ s r♣rs♥t s
st ♦ st♥t ♦♥ts ♥ s♦♠ ss ♦♥② sss ♥ r② r t♦
tt t♦ t ♠♦♥t ♦ ♣♦♥t ♥s
tr r N st♥t ♦♥② sss ♥ t ♦r L ♥s t♥ t
at ss Ma ⊆ 1, 2, ..., L s st ♦ t ♥s ♦ ♥s ♣♦ssss
♦♥t ♥ tt ss t r ♦t♥ ♦ s ♥r② ♠tr① D r♦
♦rrs♣♦♥s t♦ ♥ ♥ ♦♠♥ t♦ ♦♥② ss s♦ tt Di,a = 1
t at ♦♥② ss s ♥ ♥st♥ ♥ t it ♥ ♥ Di,a = 0
♦trs ♦r ♥ ①♠♣ s ♦♥ ♦s ♥ t♦
sr ♦rs ♦r ♦♥ ♠♥♥ s s r♠♥ strt ♥
t♦t ♦r s ♥ ♥st♥ ♦ ♣♦②♠♦r♣s♠ ♦r ♥♦ ♦r t s
t♦♥ ♦r sss♦♥ ♦ sss ts rss ss♥ ♠tr① ♠♥ts
♠♦st② rs s t r♦♥strt ♦rs ♦ s♦♠ ♥♥t ♥s
r ♥♦♠♣t ♦r s♦♠ ♠♦r♥ ♥s s♠ ♠♦♥ts ♦ t r s♦
♠ss♥ ts ♠② s t ♥sts r ♥sr s t♦ tr ♦r
♦♥s t♦ ♦♥t ss r ♥ t♦ ♥sr t qst♦♥ ♦s
♦r ♥st♥ t ♥s ♥ t r κυκλoς ♥ ② r ♦♥t ♦t♦♠ r♦♠ t Pr♦t♦♥♦r♦♣♥ ♦r r♦♥strt s ♦s t ts s rt♥②♥♦t ♦♦s t♦ t ♥tr♥ ♦srr
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♥s strþ r♠♥ strt t♦t
st♥ ♠rt r ♦♥ ♠rt
t♥ ♠♦rtrs♥
♥s r♠♥
st♥ r ♦♥
t♥ s♥
(a) (b)
♥ ①♠♣ ♦ t ♦♥ t ♦r s ♥ s①♥♥t ♥♦r♦♣♥ ♥s t ♦♥ ♦ ts t s ♥r②♠tr① t s ♦r ♠ss♥ t rst ♦♥② ss s M ∈ Ω t Ω = ♥s r♠♥, ♥s r♠♥ s♥
♥ i ♣♦ssss ♦♥t ♥ ♦♥② ss a t♥ st Di,a =?
❲ ♥ ♥♦tt♦♥ ♦r ♦t ♠tr① ♥ st r♣rs♥tt♦♥s t ♠ss♥
t ♥♦t ② Ba ♦♠♥ a ♦ L × N ♠tr① B ♦r a = 1, 2, ..., N t Da
t st ♦ ♦♠♥ t♦rs d∗ ♦ ② t t Da ♥ ♦♠♥ a ♦ D
Da =
d∗ ∈ 0, 1L : Di,a ∈ 0, 1 ⇒ d∗a = Di,a, i = 1, 2, ..., L
.
♦r d∗ ∈ Da t m(d∗) = i : d∗i = 1 ♥♦t ② Ωa t st ♦ ♦♥② sss
♦♥sst♥t t t t Da s♦ tt
Ωa = ω ⊆ 1, 2, . . . , N : ω = m(d∗), d∗ ∈ Da.
t D r t♥ q♥t② Ω = (Ω1, Ω2, ..., ΩN) Ωa♥♦tt♦♥
♥r③s t Ma♥♦tt♦♥ t♦ ♥ ♠ss♥ t
♥ t ❬❪ st ♠♦st② ♥♥t ♥s ♦r ♦ ts
♥s t♥ ♦r♥ t♥ ♦rs t t r ♥♦♥ ♦r
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t ♦trs t ♣r♦♣♦rt♦♥ ♦ ♠ss♥ ♥trs rs t♥ ♦r rs
♥ ♦r ②♥ ♥ ♥♥t ♥ ♦ ♥t♦ t ♥s
st ② ②♥ t ❬❪ ♥♦ ♠ss♥ t ♦st ♦tr ♥s
r② ♠ss♥ t ♣♦♥ts t ♣r♦♣♦rt♦♥ ♦ ♠ss♥ ♥trs rs
t♥ ♦r ♦♥♥ ♥ ♦r ♦r♥
♦t tt t r s② ♠ss♥ ♥ s♠ ♦s ♦rrs♣♦♥♥ t♦ t
♦♥② sss ♦r ♥ ♠♥♥ t♦r② s ♥ ❲ ♦ ♥♦t ♠♦
ts s♣t ♦ t ♠ss♥ t s s rt t♦ t ♠♦rr♦r ♦s ♥
r② ❬❪ ❵t ♠♣t② ♣♣r♦①♠t♦♥ ♥r ♦♥② sss
♥ t s♠ ♠♥♥ t♦r② r ss♠ t♦ ♦ ♥♣♥♥t② t♦♥
♦r ♥ ♥②ss ♦ ♣♦ss s②st♠t s ts ♦ ♥t
r s sst♦♥ ♦ t t ② ♥ t ❬❪ rstrt
t♦ ♠♥♥ t♦rs sts t ♦r ♥s r♦ss ♦♥②
sss r r ♦s r r♦s ♥ r ♦rrs♣♦♥♥ t♦
♦♥② sss ♥ ♦ r♦ ♦rrs♣♦♥s t♦ ♥ ♥ ♦♠♥ t♦
♦♥② ss s♠ sqr ♦rrs♣♦♥s t♦ ♥ t t t
sqr ♦rrs♣♦♥s t♦ ♥ t t ♥ r② sqr ♦rrs♣♦♥s t♦
s r s♦s ♦ t trs ♦ t t ♠♦st ♦ t t r s
♠♦st ♦♥② sss r ♦♥② s♣② t r② s♠ ♥♠r ♦ ♥s
♦r t ♣♣r t ♠♦st ♥s ♥ t r ♠ss♥ ♥
♦s
t s s♦ ♦rt ♥♦t♥ tt r t rst t♦ ♣r♦♣♦s ♠♦ t♦r
t♦ ♥ rst♦♥ ♦rrt② ♥s ♠ss♥ t ♥ ♣r♦s
rsr ♠ss♥ t r ♥r② ss♠ t♦ s♥t s r r♣
t s ♦s ♥ r② ❬❪ s♦ t♦ sr ♥s r♦♠ tr
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r ❱s③t♦♥ ♦ t ♥ t ❬❪ t ♦r ♥ ♥r♦ ♦♥② ss ♦♠♥ ♥ ♣rs♥t s♥t t ♦r tt ♣♦♥t ♥ ♠ss♥ r②
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st② s t② ♦♥t♥ t♦♦ ♠♥② ♠ss♥ t rs r t♦
♥ ♥s ♥ ♦r ♥②ss r ♥sts ①♣rss rrt
t t ♦ ♦rrt ♥♥ ♦ ♠ss♥ t ♥♥ t♦♥ ❬❪ ♥
♥♥ ♣rs ♦♠♠
♦r ts ♥♦r♦♣♥ ♣②♦♥s s♦♠ strs r ♥♦♥ ♦r
①♠♣ t t ♥s r ♥♦♥ t♦ ♦r♠ str ♥ t② r ♥♦♥
t♦ r tr t ♦ ♥ ❬r② t ❪ ♠r②
s♦♠ ♥♦ ♦ t ts t ♥str ♥s r s♣♦♥
ts t t ♦r♠ ♦ ♦r ♥ ♥ ♣♣r ♦♥ ♦♥ t str r♦♦t ❲
s♦ ♦♥str♥ts ♦♥ t ♦ ♥♦♥♦♥t♠♣♦rr② s s♥ ♥♦
♥ ts ①t♥t ♥s r ♥ s ♦♥s r s t♦ rt
♠♦ ♣r♠trs ♥ t♦ ♥r ts ♦r ♦tr ♥♦s sts t
♦♥str♥ts s ♥ ♦r ♥②ss ♦ t ②♥ t ❬❪ t ♠♣♥
t♦ ♦r rsts r s s♠♣ r♦♠ t ♣♦str♦r strt♦♥
♥ ♦r ♣②♦♥s ♥ ♦r ♥②ss ♦ t ♥ t ❬❪ t rt♦♥
♦♥str♥ts r r♣rs♥t ② t rs r♦ss ♥♦s ♥ ts tr
♦ sr♣t♦♥
❲ s♣② st ♣r♦r ♦r ♣②♦♥s r♣rs♥t♥ stt ♦ ♥♦
♦ ♥trst t♦ s ❲ ♠♦ ♦r② rst♦♥ ♦♥ ♥ ♦t♦♥r②
tr r r♣rs♥ts ♥ ♥ ♦r t
♠tr ♥ ts sst♦♥ ♦♦s ♦s ♥ r② ❬❪ t
sr ①t♥s♦♥s tstr♦♣ rt tr♦♥t② ♦rrt ♥♥
♦ ♠ss♥ t ♥ ♠♦r rstrt♦♥ ♣r♦sss
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♥ ① t ∞
r②t♦♥ t
r♥r♥ r♠♥ t♦
∞♥ ∞
♥♦r♥♥ ∞r♥♥ ∞r ∞
♦r ttt
♦r♥ ♦r♥
♦♥str♥ts ♦r t ②♥ t ❬❪ t st rst s ②r② ♥ t♥s♦♥ ❬❪ rst t r♦s r s ♦r ♥♦ ♦t t ♦ t r♦♦t t st tr r ♥♥t ♥s ♦r ♥♦ ♥ t② ①st
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r s♠♣ ♦s t♦ t ♠①♠♠ ♦ t ♣♦str♦r ♦r t ♥②ss ♦t ♥ t ❬❪ t t ♦♥str♥ts ♦♥ t ♥♦ s r s♦♥ ♦♥str♥ts ♦r t t ♥♦r♥♥ ♥ r♥♥ r♦♣s ♦ ♥♦t ♥ ♣♣r ♦♥ ts s ♥♦t ② t s♥ ♦ t ♦♥ t s ♦ t♦♥
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Pr♦r strt♦♥ ♦♥ trs
t g r♦♦t tr t 2L ♥♦s L s L−2 ♥tr♥ ♥♦s r♦♦t ♥♦
r = 2L−1 ♥ ♥ ♠ ♥♦ A = 2L s ♥ t♦ r ② ♦ ♥♥t
♥t ♥♦ i = 1, 2, . . . , 2L s ss♥ ♥ ti ♥ t = (t1, t2, ..., tA)
t ♥ts ♦ r ②rs ♦r t ♣rs♥t ♦r t ♠ ♥♦ tA = +∞
t♥ ♣r♥t ♥♦ j ♥ ♥♦ i s rt r♥ 〈i, j〉
♦ t ♣②♦♥② t t ♦rr♥ ti < tj t E t st ♦ s
♥♥ t 〈r, A〉 t V t st ♦ ♥♦s ♥ t VL = 1, 2, ..., L
t st ♦ ♥♦s
❲ r ♥t② ♥trst ♥ t st Γ ♦ r♦♦t rt ♥r② trs
g = (E, V, t) t st♥s s i = 1, 2, . . . , L ❲t ts ♥♦tt♦♥
(E, V ) s t t♦♣♦♦② ♦ r♦♦t rt ♥r② tr t σ(t) t ♦rr
♦ t ♥tr♥ s ti ♦r i = L+1, . . . , 2L− 2 ♥ t tr♣t (E, V, σ(t)) s
t st♦r② ♦ t tr ♥ ♥r sr st♦rs ♦rrs♣♦♥
t♦ ♦♥ t♦♣♦♦②
❲ rstrt t st ♦ ♦ trs Γ ② ♠♣♦s♥ C rt♦♥
♦♥str♥ts ♦♥ t t♦♣♦♦② ♥ ♦♥ rt♥ ♥♦ s s r sr
t t ♥ ♦ t♦♥ ♦♥str♥t c rstrts Γ t♦ t st ♦ trs Γ(c)
♥ rt♥ st ♦ s ♦r♠ str ♦r ♦♠ ♦♥str♥ts
s♦ ♠♣♦s ♦r ♥♦r ♣♣r ♦♥ ♦ t r♦♦t ♦ t ♥ s♦♠
ss t ♠♣♦s ♦♥t♥s ♦♥② ♦♥ s♦ tt t ♦♥str♥t s ♦♥②
♠♣♦s♥ r♥ ♦♥ t ♦ t ts s s ♦r ♥♥t ♥s ❲
t♦ ts ♦♥str♥ts ♥ ♣♣r ♦♥ ♦♥ t r♦♦t t♠ t s♦♠ T > 0
♥ ♠♦st ♦ ♦r ♥②ss ♦ ♥♦r♦♣♥ t s T = 16, 000 s
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♠ rtr t♥ ♥② ♣♦ss r♦♦t ♦♥sr ♣s ② ♥sts t
Γ(0) = (E, V, t) ∈ Γ : tr ≤ T s♣ ♦ rt ♣②♦♥s s t♥
ΓC =C⋂
c=0
Γ(c).
♥ r ♥trst ♥ t r♦♦t ♦♦s ♣r♦r ♦♥ trs ♦r
t ♠r♥ ♣r♦r ♦♥ t r♦♦t tr s ♥♦r♠ ♦r ♥ ♥tr tL ≤ tr ≤ T
♥♦r♠ ♣r♦r ♦♥ Γ ♣ts ♠♦r t ♦♥ rtr s ♦ tr s
i r s♦r♦♥♦s t ti = 0 ♥ tr r ♥♦ rt♦♥ ♦♥str♥ts t♥
♦s ♥ r② ❬❪ s♦ tt t ♣r♦r f(g|T ) ∝ t2−Lr Itr≤T s t sr
♥♦r♠ ♠r♥ ♣r♦r ♦♥ tr ♦r t ♥s♦♥ ♦ rt♦♥ ♦♥str♥ts
♦♠♣ts ♠ttrs
♦r ♥♦ i ∈ V t t+i = supg∈ΓC ti ♥ t−i = infg∈ΓC ti t rtst ♥
st ♠ss s ♦r ♥♦ i ♥ t S = i ∈ V : t+i = T s♦ tt S s
t st ♦ ♥♦s ♥ s ♥♦t ♦♥ ♦ ② rt♦♥ tr r
s ♥♦s ♥ r ♦r ①♠♣ t ♠♦st r♥t ♦♠♠♦♥ ♥st♦r t♦
t♥ ❯♠r♥ ♥ s♥ ♦s ♥ r② ❬❪ s♦ t s♠t♦♥
sts tt t ♣r♦r ♣r♦t② strt♦♥ t ♥st②
fG(g|T ) ∝∏
i∈S
(tr − t−i )−1
s ♠r♥ ♥st② ♦r tr s ♣♣r♦①♠t② ♥♦r♠ ♥ tL < tr <
T ♥ t♦♥ T ≫ maxi∈V \S t+i s s t ♣r♦r s ♦s ♥
r② ❬❪ ♦ ♥♦t ♦♠♠♥t ♦♥ t strt♦♥ tr♠♥ ② fG ♦r tr
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t♦♣♦♦s ❲ ♦♥sr t♦ ♣r♦rs ♦♥ t♦♣♦♦s ♥♦r♠ strt♦♥ ♦♥
st♦rs ♦rrs♣♦♥♥ t♦ t strt♦♥ ♦r t ❨ ❬❪ ♠♦
♦rs ♥ t♦♣♦♦s ❬❱s♦ ❪ ♥ ♥♦r♠ strt♦♥ ♦♥
t♦♣♦♦s ♦rs s♠ ♥ r s ♥st ♠♠s③ s
❬♦♦♦ ♥ P♦ ❪ ♥ ♦t ss t ♠r♥ ♣r♦r s ♥ ♦r Γ
rtr t♥ ΓC t♦♥ ♦ ♦♥str♥ts ♠♦s ts ♣r♦r ♥ t♦ ②s
t♦♣♦♦ ♦♥str♥ts r ♦t rt♥ t♦♣♦♦s stt♥ t ♣r♦r ♣r♦t②
t♦ ♦♥str♥ts ♠♦② t ♦♠ t♦ t♦♣♦♦② s♦ tt
♦r ♣r♦rs r ♥ t ♥♦t ①t② ♥♦r♠ ♦r st♦rs ♦r t♦♣♦♦s
♦r ΓC ♦r t t♦♥ ♥②ss ♣rs♥t ♥ ♣tr s ♦♥② t
♥♦r♠ ♣r♦r ♦♥ st♦rs s ♦t ♣r♦rs ♦r ♦r ♥②ss ♦ r
t ♣rs♥t ♥ ♣tr
t♦♥ ♦ tstr♦♣s sr ♥ t♦♥ s ♥♦ ♠♣t ♦♥
t ♠r♥ ♣r♦r ♥st② ♦r tr ♥♦r ♦♥ t ♠r♥ ♣r♦r strt♦♥ ♦♥
t♦♣♦♦s r s♦s s♠♣ r♦♠ t ♣r♦r ♦ t r♦♦t t t
♦♥str♥ts r♦♠ t ♥ t ❬❪ t ♣r♦r s r♦② ♥♦r♠
t♥ ♥ P ♦rs ♦r r♦♥ ♦ ♥trst t ♣r♦r ♦s
♥♦t ♦rrs♣♦♥ t♦ ♥② rs♦♥ ♣r♦r ♦r P t ts ♦s
♥♦t ♠ttr s♥ ts r♦♥ s r ♦t ② t ♦♦
♣r♦r ♦♥ t s ♦ ♥tr♥ ♥♦s ♥ s ♣♥s ♦♥ t
♦♥str♥ts ♦r ①♠♣ t ♦r♥ t s ♦♥str♥ t♦
t♥ ♥ P ♥ ts ♣r♥t t ♦♠♠♦♥ ♥st♦r t
♦r♥ s ♦♥str♥ t♦ t♥ ♥ P rst ♦
t tr ①rts tt ♥♥ ♦♥ t ♣r♦r ♦♥ t ♦ ♦r♥ ♥ s♦
tt ♣r♦r s ♣♣r♦①♠t② ♥♦r♠ ♦r t ♦ r♥ s s♦♥ ② t
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r ♠♣ r♦♠ t ♣r♦r strt♦♥ ♦♥ t r♦♦t ♣r♦r s♣♣r♦①♠t② t ♦r t r♦♥ ♦ ♥trst t♥ ♥ P
s♠♣ r♦♠ t ♣r♦r ♥ r ♦r ♦tr ♥♦s r ♦♥str♥
t♦ t♥ ♥ ♣♣r ♥ ♦r ♦♥ t ♣r♦r s ♥♦t ♥ssr② ①t②
♥♦r♠ t s♠t♦♥s r♦♠ t ♣r♦r s♦ tt t s ②s r② ♦s t♦
♥♦r♠ ♣rs♠② s t t♦r③ r♥ s ②s qt s♠ s
s ♥♦t tr ♦r ♦ ♥♦s ♥♦ ♣♣r ♦♥ ♦♥ t r
s♦s s♠♣ r♦♠ t ♣r♦r ♦r t ♠♦st r♥t ♦♠♠♦♥ ♥st♦r t♦ t
t ♥s s ♦♥② ♦♥str♥ t♦ ♦r t♥ P ♣r♦r
s str♦♥② s t♦rs ②♦♥r s s ♥sr♣rs♥ s♥ ②♦♥r
s ♠♦r ♦♠ ♦r t ♥♦s ♦ t t ♥
♥r r ♥♦t ♥trst ♥ t♥ ♥tr♥ ♥♦s s♦ ts s ♥♦t ♥ ss
♠r♥ ♣r♦r ♦♥ t ♦ ts ♥♦ s ♥ t ♦♠♣r t♦ ♣r♦rs
♦t♥ s♥ s♦t ♦♥s ♥ ♠♦r ♣②♦♥ts ❨♥ ♥ ♥♥
❬❪ ❲ ♥♦ rtr ♥♦r♠t♦♥ ♦♥ t ♣r♦r ♥sts ♦♥
t strt♦♥ ♦ ♣s s ♦r ♥♥t ♥♦s r t ♦ ♥trst♥
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1250 1300 1350 1400 1450 15000
10
20
30
40
50
60
70
80
90
r ♠♣ r♦♠ t ♣r♦r strt♦♥ ♦♥ ♦r♥
t♦ ♥ t s ♥♦r♠t♦♥ ♠
rst♦♥ ♦ ♦♥② sss
♥ ts sst♦♥ ①t♥ t st♦st ♦♦ ♠♦ ♦ ♦s ♥ r②
❬❪ t♦ ♥♦r♣♦rt rt tr♦♥t② ♥ t♠ ♥ s♣ tstr♦♣
♣r♦ss
t♦ ts ♠♦ s ♦♣ t ♥s ♥ ♠♥ t ♥ s♦
♣♣ t♦ ♦tr ♥s ♦ trt t s s s♦♠ ♦ t t sts ♠♥t♦♥ ♥
t♦♥ ♦r t ♠♦r♣♦♦ t sts ♦ ♥♥r t ❬❪ s②♥♦
t ❬❪ ①t♥ ♦tr s♣ts ♦ t ♠♦ t♦ ♣♣t♦♥s ♥ ♥ts
♦♥② sss r ♦r♥ ♥ ♦♥ t tr s s♦♥ ♥ r
♦♥② ss s ♦r♥ ♥ ♥ ♦r ♣♣rs ♥ ♥ s ♦♥t
t ♥♦ ♦tr ♦r ♥ t ♣r♦ss rt ♥t ♦rs ♥ ♦♠♣t②
♥ ♦r ♣♣rs t s♦ ♥ ♦r s ♦rr♦ r♦♠ ♥ ♦ts
t st② ♦r ♥ ♥ ①st♥ ♦r ♥s ♠♥♥ ♦♥t s ♥
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r ♠♣ r♦♠ t ♣r♦r strt♦♥ ♦♥ t ♦ t ♠♦st r♥t♦♠♠♦♥ ♥st♦r t♦ t t ♥s
♥ ♥ ♥ t s ♥♦ ♦♥r s ♦r t ♠♥♥ t s ss♥ t♦
t ♠② ♦♠♣t② s t♦ s ♦r t ♠② ♥ ♠♥♥
♦♥ts ♦♥ ♥ s♥ ♥ i.e. ♦♥ s♥ r♥ ♦
♥ ♣②♦♥② r ♦r♥ ♥♣♥♥t② t rt λ ♥♣♥♥t②
t ♣r ♣t rt µ ♥ r st t♦ ♣♦♥t tstr♦♣s t②
♥♦♥tr t rt ρ ♦♥ r♥ t tstr♦♣ ♦♥t s
♥♣♥♥t② t ♣r♦t② κ ♥ P♦ss♦♥ ♥♠r ♦ ♦♥ts t
♠♥ ν r ♦r♥ tstr♦♣ ♦rrs♣♦♥s t♦ rt ♥t ♠t
♦r ①♠♣ ♠rt♦♥ ♥ ♣♠ ♦r r rt♦♥ ♥ ♣♦♣t♦♥ s
t♦s sr ② ♥♥♥ ♥ ♥♦r♦ ❬❪ ♥ r♥② ♥ r♦♥
❬❪ t r♥♥ ♥t ♦ t ♣②♦♥② t st ♦ ♦♥ts r♣rs♥t♥
t r♥♥ ♦r② s ♦♣ ♥t♦ ♦ t tr ♥s
r
♣r♦ss sr s ♥♦t rrs ♥ ts rt② ♦♠♣ts
t ♥②ss ❲ s♦ ♥ t♦♥ tt ♥ssr② ♥ s♥t ♦♥t♦♥
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1,2
−2
+12,13
−1
+9,10−8,9
+11
+14
−2
+6 −12
−12
+5−1
+3
−3
+8
+7
1
1,3,14
10,11
5
5
1,6,7,13
1,6,13
1,13
r sr♣t♦♥ ♦ t ♠♦ rts ♥ ts ♦ ♦♥② sss r♠r ♦ts ♦rrs♣♦♥ t♦ tstr♦♣s t ♠t♣ rts ♥ts ♠② ♦r s♠t♥♦s② ♦♥t sts ts ♥rts t s rs♦♥ ♦♥ t rt ♥r t♠ ♦s r♦♠ t t♦ rt ♥ t rsti ♥ t t①t ♥rs r♦♠ rt t♦ t r♦♦t s r♣rs♥t ② t sqr♦♥ t t
♦r t ♣r♦ss t♦ t♠rrs s ν = κλ/µ s s rs♦♥
♠♦♥ ss♠♣t♦♥ t ♥♥ ♣r♦ss t♦t tstr♦♣s s t♦
♥♠r ♦ ♦♥② sss t ♥② ♥ ♣♦♥t s P♦ss♦♥strt
t ♠♥ λ/µ t ν = κλ/µ t♥ t qr♠ t strt♦♥
♦ t ♥♠r ♦ ♦♥② sss s ♥♥ ② ♥ t tstr♦♣
♣r♦ss ❯♥r ts ♦♥t♦♥ ♥ tstr♦♣ t♦ ♥ s q♥t
qr♠ s ♥ r s♥ ♥ ♥♥t ♠♦♥t ♦ t♠ ♣ss ♦♥ t ♠r♦♦t
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t♦ ♥t♥♥ tt ② TC(κ, µ) = − log(1 − κ)/µ ②rs s ♦♦s
s t ♥♠r ♦ ♦♥ts ♥rt ② t ♥♥ ♣rt ♦ t ♣r♦ss
♥ ♥ ♥tr ♦ ♥t TC s P♦ss♦♥ strt t ♠♥ λµ(1−e−µTC ) q
t♦ κλ/µ ♥ t ♣r♦t② tt ♦♥t ♥tr♥ ♥ ♥tr ♦ ♥t TC
s r♥ tt ♥tr s 1 − e−µTC qs κ
s tstr♦♣ s♠♣② ①t♥s ts ② ♦ ♦ rt t♠
t ♦♦ ♣♥s ♦♥② ♦♥ t ♥♠r ♦ tstr♦♣s ♦♥ ♥ ♥ ♥♦t
tr ♦t♦♥ ♥ t♠ t ki t ♥♠r ♦ tstr♦♣s ♦♥ 〈i, j〉 ♥
k = (k1, . . . , k2L−2) t tstr♦♣ stt t♦r ❲ r♦r ♥♦ tstr♦♣s
♦♥ t 〈r, A〉 ts ♥t s r② ♥♥t tr g = (V, E, t, k) s
s♣ ② ts t♦♣♦♦② ♥♦ s ♥ tstr♦♣ stt rt tr
s♣ ①t♥ ♦r tstr♦♣s s
ΓCK = (V, E, t, k) : (V, E, t) ∈ ΓC , k ∈ N
2L−20 .
❲ r♦♣ t tstr♦♣ ♣r♦ss r♦♠ t t♦♥ ♥ t♦♥ t s
strt♦rr t♦ rst♦r t ♥ ♦ ts ♥ t ①♣rss♦♥ ♦r t ♣♦str♦r
strt♦♥ ♥ t♦♥
rstrt♦♥ ♣r♦ss
❲♥ ♥sts ♦t ① t s♦♠ t r ♠ss♥ ♦r r ♦trs
sr tr♦ t rstrt♦♥ ♣r♦ss sr ♥ ts st♦♥
t i t ♣♦♥t s ♠ss♥ t ♣r♦t② ξi ss♠ ts
♣r♦t② ♣♥s ♦♥② ♦♥ t ♥ i ♥ ♥♦t ♦♥ t ♦♥② ss t
r s② ♠ss♥ ♥ ♥♥t ♥s r ♦♥② ♣rt② r♦♥strt
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❬ ❪ ❬ ❪ ❬ ⑦ ❪ ❬ ❪ ❬ ❪
r strt♦♥ ♦ t ♦r② r③ ♥ r s♣♣♦s♥ ♠s♥ ♠tr① I∗ s ♦ D∗ s t ♥♦sr t t ♦♠♥ ♦r ♦♥② ss ♥ r♦ ♦r ♥ ♦ r ts ♦♥t s♣rs♥t ♥ r♦s ♥ ③r♦s ♥ t ♠s♥ ♠tr① I∗ ♥t ♠ss♥♠tr① ♠♥ts ♦♠ ♦♥② sss r t♥ t♥♥ ♥ ts ①♠♣ trstrt♦♥ r ♣s ♦♥② sss t ♥st♥s s♣② ♥ ♦♥ ♦r ♠♦r♥ t♦ t rstr t D
t s♦ ♦sr s♠ ♠♦♥ts ♦ ♠ss♥ t ♥ s♦♠ ♠♦r♥ ♥s
t D∗ ♥♦t ♥♦t♦♥ r♥♦♠ ♥r② t ♠tr① r♣rs♥t♥ t
♦t♦♠ ♦ t rst♦♥ ♣r♦ss ♦ t♦♥ ♥♠r ♦ ♦♠♥s
♥ D∗ s r♥♦♠ ♥ q t♦ N∗ ♦r t r③t♦♥ ♣t ♥ r
D∗ = D∗ t D∗ s♣② ♥ r
♦♠♥ ♦ D∗ ♦rrs♣♦♥s t♦ ♦♥② ss s tr ♣rs♥t
t t r♦♦t ♦r s ♦r♥ ♦ t ♥♥ s♦♠ ♦♥② sss
♦t ♦♠♣t② ♥♠r ♦ ♦♠♥s N∗ ♦♦s Poisson(|g| + kT · TC)
strt♦♥ r |g| s t t♦t ♥t ♦ t tr kT s t t♦t ♥♠r
♦ tstr♦♣s ♦♥ t tr ♥ TC s t ♠♦♥t ♦ t♠ q♥t t♦ ♦♥
tstr♦♣
♦sr t D r tr♥r② ♠tr① ♦ s s ♥ s t N
♦♠♥s N ≤ N∗ ❲ t ♠♣♣♥ ♦ t ♥♥♦♥ ♦♠♣t t D∗
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t♦ t ♦sr t D t rstrt♦♥ ♣r♦ss s ♣r♦ss ♦rs ♥ t♦
st♣s rst s♦♠ t ♦ ♠ss♥ s♦♥ s♦♠ ♦♥② sss r r♠♦
r♦♠ t t
t I∗ r♥♦♠ L × N∗ ♥t♦r ♠tr① ♦ ♥♣♥♥t r♥♦
r♥♦♠ rs ♦r ♦sr ♠♥ts s tt ♦r i = 1 . . . , L ♥ a =
1, . . . , N∗ P [I∗i,a = 1] = ξi s♦ tt ξi s t ♣r♦t② tt ♥ ♥sr
t qst♦♥ ♦s ♥ i s♣② ♥ ♥st♥ ♦ ♦♥② ss a
t ♥ ♥sr t s ss♠ ♦rrt ♥ I∗i,a = 1 ♦ ♥♦t t ♥ ♥sr
t♥ I∗i,a = 0 t ③r♦s ♦ I
∗ ♥t t ♣♦♥ts r ♠ss♥ t
ξ = (ξ1, . . . , ξL) ♥ ♥♦t ② I∗ r③t♦♥ ♦ I∗
♦ t D = D(D∗, I∗) t ♠s rs♦♥ ♦ t r♥♦♠ t
♠tr① I∗i,a = 1 t♥ Di,a = D∗
i,a ♥ I∗i,a = 0 t♥ Di,a =? ♠♣♣♥
♦ D∗ t♦ D ♦rrs♣♦♥s t♦ t rst st♣ ♦ t rstrt♦♥ ♣r♦ss
♥ t s♦♥ st♣ s♦♠ ♦♠♥s r r♠♦ r♦♠ D ♦r ①♠♣ t
s♦♥ ♥ tr ♦♠♥s ♦ D ♦♥sst ♥tr② ♦ s ♥ s t ♦rrs♣♦♥♥
♦♥② sss r ♥r ♦sr t ♥② ♦♥② sss r
♥♦t ♥ ♥ t rstr t tr t②♣s ♦ ♦♠♥s ♠② s♦
r♠♦ r♦♠ t t s t② r ♠ ♥r ♥♦t ② R t
rstrt♦♥ r D = R(D) ♠♣♣♥ t t t♦ rstr t t Y
♥ Q ♥t♦♥s ♦ t ♦♠♥s ♦ D∗ ♥ I∗ ♦♥t♥ t s s ♥
s rs♣t②
Y (D∗a, I
∗a) =
L∑
i=1
I∗i,aD
∗i,a,
Q(I∗a) =L
∑
i=1
(1 − I∗i,a).
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♥ a = 1, 2, ..., N∗ t Ya = Y (D∗a, I
∗a) ♥ Qa = Q(I∗a)
❲ ♥ ♥t ♦rt♠ ♦r ♦♠♣t♥ t ♦♦ ♦r rs ♦r♠
② ♦♠♣♦♥♥ t ♦♦♥ ♠♥tr② t♥♥♥ ♦♣rt♦♥s
R1(D) = (Da : Ya > 0) sr sss t ♥♦ ♥st♥s t t s
R2(D) = (Da : Ya > 1) sr sss s♥t♦♥s ♦sr t s♥
R3(D) = (Da : Ya < L) sr sss r ♦sr t s
R4(D) = (Da : Ya < L − 1) sr sss r ♦sr t
s ♦r t s t ♦♥
R5(D) = (Da : Ya + Qa < L) sr sss r ♣♦t♥t②
♣rs♥t t s
R6(D) = (Da : Ya + Qa < L − 1) sr sss r ♣♦t♥t②
♣rs♥t t s ♦r t s t ♦♥
❲ ss♠ t ♦s♥ r ♥s ♦♥t♦♥ r D = R(D) t
R(D) = R6R2(D) ♦ts ♣rs♠♦♥② ♥♦r♠t ♦♥② sss ♦♥qst
t ❬❪ t ♦♦ ♦r t ♥tsts trt ♦t♦♥ ♠♦ ♦ s
❬❪ ♦r rstrt♦♥ rs st♦♥ ♦ ♦♠♥s s s♦♠t♥
♥ ♥r ♥♦ ♦♥tr♦ ♦r t ♦♠♥ st♦♥ r s♠♣② srs
t ♣♣♥ t rstrt♦♥ s ♥ ♥ ♥ ② t ♥st ♦t♥
t t ♥ t ①♠♣ ♥ r ♥ ♥ ♦r ♥②ss ♦ t ♥ t
❬❪ t t t rstr t R(D) = R1(D) ♥ s♦ s r
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R2 t♦ t ♦r rsts ②♥ t ❬❪ t s rstrt♦♥ r
R(D) = R2(D)
♥② ♦tr rstrt♦♥ rs ♦ t♦t ♦ ♥ t ♦♦
t♦♥s ♦ r ♦rrt ♦r rt② ♦ rs ♦r ♦♥② rqr♠♥t
s tt t ♥t tt ss s rstr s ♥♣♥♥t ♦ ♥ts ♥
♦tr ♦♥② sss ❲ rrs♦♥s ♦r rs s♥ ts r ②
t♦ t ♠♦st rq♥t② s
t♥♥♥ D = R(D) ♦rrs♣♦♥s t♦ t s♦♥ st♣ ♦ t rstrt♦♥
♣r♦ss ♥ s rs t♦ t ♦sr t t I L×N ♠tr① ♦♥t♥♥
t♦s ♦♠♥s ♦ I∗ sr t t♥♥♥ ❲ ♦sr t r③t♦♥ I
♦ I
♦♠♥ ♥s a = 1, 2, ..., N∗ r ①♥ t s ♦♥♥♥t t♦
r♥♠r t ♦♠♥s ♦ D∗ I∗ ♥ D tr rstrt♦♥ s♦ tt Da = Da
♥ I∗a = Ia ♦r a = 1, 2, ..., N ♥♦r♠t♦♥ ♥ t♦ t Ya
♥ Qa s ♥ t ♦♠♥ Da ♥ st Ωa r♣rs♥tt♦♥s ❲ rt
Y (Da) = Y (Ωa) = Ya ♥ Q(Da) = Q(Ωa) = Qa
P♦♥t ♣r♦ss ♦ rts ♦r rstr ♦♥② sss
① tstr♦♣r ♣②♦♥② g ∈ ΓCK t k = (0, 0, ..., 0) ♥ t ♥
〈i, j〉 ♥ t♠ τ ∈ [ti, tj) ♥ ♥♦t ② [g] t st ♦ ♣♦♥ts (τ, i)
♦♥ t ♣②♦♥② ♥♥ ♣♦♥ts (τ, r) t τ ≥ tr ♥ t 〈r, A〉
♦t♦♥s zD = z1, z2, ..., zN ♦ t rt ♥ts ♦ t N rstr ♦♥②
sss r r③t♦♥ ♦ ♥ ♥♦♠♦♥♦s P♦ss♦♥ ♣♦♥t ♣r♦ss ZD ♦♥ [g]
t Z ∈ [g] t rt ♦t♦♥ ♦ ♥r ♦♥② ss M ⊆ 1, 2, ..., L
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♦rrs♣♦♥♥ t♦ ♦♠♥ ♦ D t Y ♦sr 1s ♥ Q ?s ♥ t EZ
t ♥t tt ts ss ♥rts ♦♠♥ ♦ t rstr t
♣♦♥t ♣r♦ss ZD ♦ rt ♦t♦♥s ♦ rstr ♦♥② sss s
♥t♥st②
λ(z) = λ Pr(EZ |g, µ, λ, ξ, Z = z)
t z ∈ [g] ♥ ♣r♦t② ♥st②
fZD(zD) =
1
N !e−Λ([g])
N∏
a=1
λ(za)
t rs♣t t♦ t ♠♥t ♦ ♦♠ dzD = dz1dz2...dzN ♥ [g]N r
Λ([g]) =
∫
[g]
λ(z)dz
=∑
〈i,j〉∈E
∫ tj
ti
λ((τ, i))dτ.
♥♠r N ♦ rstr ♦♥② sss s N ∼ P♦ss♦♥(Λ([g]))
♦♦ t♦♥s
❲ t ♦♦ ♦r g µ λ κ ρ ♥ ξ ♥ t t ♦♥ t ♥
♥t ♦rt♠ t♦ ♦♠♣t t s♠ ♦r ♠ss♥ t
❲ ♥ t♦ ♦♠♣t P [D|g, µ, λ, ξ, R(D)] t ♦♦ ♦ t ♦sr
t ♥ t tr g t rt ♥ t rts ♥ λ ♥ µ t ♦srt♦♥
♠♦ ♣r♠trs ξ ♥ t ♥t tt t trts ♦♥sr ♥
rstr ❲ rst♦r t rt ♦t♦♥s ♥ s♦ ♦♠t λ r♦♠ t ♦♥t♦♥♥
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♥ t♦r③ s♥ t ♦♥t ♥♣♥♥ ♦ Da, a = 1, 2, ..., N ♥r t
♥ ♦♥t♦♥s
P [D=D|g, µ, λ, ξ,D=R(D)]
=
∫
fZD(zD)P [D=D|g, µ, ξ, ZD =zD,D=R(D)] dzD
=e−Λ([g])
N !
N∏
a=1
∫
[g]
λ(za)P [Da =Da|g, µ, ξ, Za =za, EZa] dza
=e−Λ([g])
N !
N∏
a=1
∫
[g]
λP [EZa|g, µ, ξ, Za =za]P [Da =Da|g, µ, ξ, Za =za, EZa
] dza
=e−Λ([g])
N !
N∏
a=1
λ
∫
[g]
P [Da =Da, EZa|g, µ, ξ, Za =za] dza.
=e−Λ([g])
N !
N∏
a=1
λ
∫
[g]
P [Da =Da|g, µ, ξ, Za =za] dza.
st ♥ ♦♦s s trts ♥ t t ♥ rstr ♥
t ♥t Da =Da s sst ♦ t ♥t EZa ♦♦ ♣♥s ♦♥
t r ♦♥t♦♥ D = R(D) ♦♥② tr♦ t ♠♥ ♥♠r λ([g]) ♦
rstr ♦♥② sss t♦♥ s s♦ r ①t♥ ♦s ♥
r② ❬❪ t♦ t ♦♦ ♦r rtr rt② ♦ ♦♠♥ t♥♥♥ rs
❲ ♥♦ t ♠ss♥ ♠♥t ♦♠♣♦♥♥t ♦ t rstrt♦♥ ♣r♦ss
❲ s♠ ♦r ♣♦ss s ♦ t ♠ss♥ ♠tr① ♠♥ts ♥ t rstr
t ♦tr ♠♥ts ♥ D t st ♦ ♣♦ss s ♦r D ♥ D
♥ P [Da = Da|g, µ, λ, ξ, Za = za] s ♥♦t ♦♥t♦♥ ♦♥ t rqr♠♥t tt
t ♦♠♥ Da ts rstr t ♥trs ♦ t ♦rrs♣♦♥♥ ♦♠♥ Ia r
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tr♠♥ ② t ♥♦♥t♦♥ r♥♦ ♣r♦ss ♥
P [Da = Da|g, µ, ξ, Za = za] =∑
d∗∈Da
P [I∗a,D∗a = d∗|g, µ, ξ, Za = za]
=L
∏
i=1
ξIa,i
i (1 − ξi)1−Ia,i
∑
d∗∈Da
P [D∗a = d∗|g, µ, ξ, Za = za].
♦♦ s
P [D = D|g, µ, λ, ξ,D = R(D)] =
e−Λ([g])
N !
N∏
a=1
(L
∏
i=1
ξIa,i
i (1 − ξi)1−Ia,i)λ
∫
[g]
∑
ω∈Ωa
P [M = ω|g, µ, ξ, Z = za]dza,
r st r♦♠ s♠♠♥ d∗ ∈ Da t♦ t q♥t st
r♣rs♥tt♦♥ ω ∈ Ωa
♦r t t♦ ♥trt q♥tts ♥ qt♦♥ trt
rrs ♦r♠ ❲ r s♥ ♣r♥♥ ♣r♦r ♥ t♦ s♥st♥
❬❪ ❲ ♥ t Λ([g])
❲ ♠ t rs♦♥ ss♠♣t♦♥ tt t rstrt♦♥ r ♥s t
st ♦♥t♦♥ R1 r♦♠ t♦♥ t ♦♦s tt ♦♥② ss ♦r♥ t
Z = (τ, i) ♥ [g] ♠st sr ♦♥ t♦ t ♥♦ ♦ t Z = (ti, i) ♥ ♦rr
t♦ rstr ♥ s♦
P [EZ |Z = (τ, i), g, µ, ξ] = P [EZ |Z = (ti, i), g, µ, ξ]e−µ(τ−ti).
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❲ ♥ ssttt ts ♥t♦ t ①♣rss♦♥ ♦r Λ([g]) ♥ ♥trt t♦ t
Λ([g]) =λ
µ
∑
〈i,j〉∈E
P [EZ |Z = (ti, i), g, µ, ξ](
1 − e−µ(tj−ti))
.
♥ ♥♦ i t V(i)L t st ♦ ♥♦s s♥ r♦♠ i ♥♥
i ts i s t si = r(V(i)L ) ♥♦t ② u
(n)i = P [Y = n|Z =
(ti, i), g, µ, ξ] ♥ v(n)i = P [Y + Q = n|Z = (ti, i), g, µ, ξ] ❲ ♥ ♦♠♣t
Λ([g]) ♦r rs ♠ ♣ ♦ ♦♠♥t♦♥s ♦ ♦♥t♦♥ R1 t ♥② ♦♠♥t♦♥
♦ ♦♥t♦♥s R2R6 r♦♠ u(0)i u
(1)i u
(si−1)i u
(si)i v
(si−1)i ♥ v
(si)i ♦r
①♠♣
P [EZ |Z = (ti, i), g, µ, ξ] =
1 − u(0)i R = R1,
1 − u(0)i − u
(1)i R = R2,
1 − u(0)i − u
(1)i − u
(L−1)i − u
(L)i R = R4 R2.
♦t tt u(n)i = 0 ♥ss si ≥ n s♦ ♦r ①♠♣ u
(L)i s ♥♦♥③r♦ t i = r t
r♦♦t ♥♦ ♦♥②
♦r ♥♦s i ♥ j t δi,j = e−µ(tj−ti) t ♣r♦t② ♦r ♦♥t ss
♣rs♥t t (tj, j) t♦ sr ♦♥ t♦ (ti, i) ♦♥sr ♣r ♦ s 〈c1, i〉
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〈c2, i〉 ♥ E ♥
u(0)i =
(
(1 − δi,c1) + δi,c1u(0)c1
) (
(1 − δi,c2) + δi,c2u(0)c2
)
u(1)i = δi,c1(1 − δi,c2)u
(1)c1
+ δi,c2(1 − δi,c1)u(1)c2
+ δi,c1δi,c2(u(1)c1
u(0)c2
+ u(0)c1
u(1)c2
)
u(si)i = δi,c1u
(sc1 )c1 δi,c2u
(sc2 )c2
u(si−1)i =
(
δi,c1u(sc1−1)c1 + Isc1=1(1 − δi,c1)
)
δi,c2u(sc2 )c2
+δi,c1u(sc1 )c1
(
δi,c2usc2−1c2 + Isc2=1(1 − δi,c2)
)
v(0)i =
δi,c1v(0)c1
+ (1 − δi,c1)∏
j∈Vc1L
ξj
δi,c2v(0)c2
+ (1 − δi,c2)∏
j∈Vc2L
ξj
v(si)i =
δi,c1v(sc1 )c1 + (1 − δi,c1)
∏
j∈Vc1L
(1 − ξj)
δi,c2v(sc2 )c2 + (1 − δi,c2)
∏
j∈Vc2L
(1 − ξj)
v(si−1)i =
δi,c1v(sc1−1)c1 + (1 − δi,c1)
∑
j∈Vc1L
ξj
∏
k 6=j
(1 − ξk)
δi,c2v(sc2 )c2 + (1 − δi,c2)
∏
j∈Vc2L
(1 − ξj)
+
δi,c1v(sc1 )c1 + (1 − δi,c1)
∏
j∈Vc1L
(1 − ξj)
δi,c2v(sc2−1)c2 + (1 − δi,c2)
∑
j∈Vc2L
ξj
∏
k 6=j
(1 − ξk)
rrs♦♥ s t r♦♠ t s i ∈ VL t
u(0)i = u
(si−1)i = 1 − ξi
u(1)i = u
(si)i = ξi
v(0)i = v
(si−1)i = 0
v(si)i = 1
❲ ♥♦ t q♥t rrs♦♥s ♦r λ∫
[g]
∑
ω∈ΩaP [M = ωa|Z =
za, g, µ] dza ♦♥sr t st ma =⋂
ω∈Ωaω ♦ s ♥♦♥ t♦ ♦♥t
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♥ t at rstr ♦♥② ss ma s t st ♦ s i s tt Di,a = 1
t Ea t st ♦ r♥s ♦♥ t ♣t r♦♠ t ♠♦st r♥t ♦♠♠♦♥
♥st♦r ♦ t s ♥ ma ♣ t♦ t ♠♥♦ A ♦ t r♦♦t ♦♥②
ss a ♠st ♥ ♦r♥ ♦♥ ♥ ♥ Ea ♦r a = 1, 2, ..., N ss Ma
s ♥♦♥♠♣t② s♦ a ♠st sr r♦♠ ts rt ♣♦♥t ♦♥ t♦ t ♥♦
♦ ❲ ♥ st t rt ♦t♦♥ t♦ t ♥♦ ♦ ♥ ♦♥rt t
♥tr t♦ s♠
λ
∫
[g]
∑
ω∈Ωa
P [M = ω|Z = za, g, µ] dza =λ
µ
∑
〈i,j〉∈Ea
∑
ω∈Ωa
P [M = ω|Z = (ti, i), g, µ](1−δi,j).
♦r a = 1, 2, ..., N ♥ ω ∈ Ωa t ω(i) = ω ∩ V(i)L ♥
Ω(i)a = ω(i) : ω(i) = ω ∩ V
(i)L , ω ∈ Ωa
♥♦t t st ♦ ssts ω(i) ♦ t s V(i)L r ♦♥② sss
♦♥sst♥t t t t ♦r t♦s s ♦♥sr t♦ r♥s
〈c1, i〉 ♥ 〈c2, i〉 t ♥♦ i ♥ Ωa = Ω(c1)a ×Ω
(c2)a ♥ ss♠ tt
♥ts r ♥♣♥♥t ♦♥ t t♦ r♥s
∑
ω∈Ωa
P [M = ω|Z = (ti, i), g, µ, ξ] =∑
ω(c1)∈Ω(c1)a
P [M = ω(c1)|Z = (ti, c1), g, µ]
×∑
ω(c2)∈Ω(c2)a
P [M = ω(c2)|Z = (ti, c2), g, µ].
♥ ♠♦ t rt ♥t t (ti, i) t♦ (ti, c1) ♥ (ti, c2) ♦ t ♥♦ ♥
♦♥t♦ ts s ♥♦ ♠♦ t rt ♥t t (ti, c) t♦ (tc, c) ♦r c = c1, c2
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♦♥ ♥ s ♦♦s
∑
ω∈Ω(c)a
P [M = ω|Z = (ti, c), g, µ] =
δi,c ×∑
ω∈Ω(c)a
P [M = ω|Z = (tc, c), g, µ] Y (Ω(c)a ) ≥ 1
(1 − δi,c) + δi,c ×∑
ω∈Ω(c)a
P [M = ω|Z = (tc, c), g, µ] Y (Ω(c)a ) = 0 ♥ Q(Ω
(c)a ) ≥ 1
(1 − δi,c) + δi,cv(0)c Y (Ω
(c)a ) + Q(Ω
(c)a ) = 0
Ω(c)a = ∅
rrs♦♥ s t r♦♠ t s c s t♥
∑
ω∈Ω(c)a
P [M = ω|Z = (tc, c), g, µ] =
1 Ω(c)a = c, ∅ ♦r c Dc,a ∈ ?, 1
0 Ω(c)a = ∅ Dc,a = 0.
♥ ♦rr t♦ rst♦r tstr♦♣s t♦ ts t♦♥ ♥ ♥ g ∈ ΓK t
ki tstr♦♣s ♦♥ 〈i, j〉 ∈ E r♣ tj − ti t tj − ti + kiTC(κ, µ) ♥
♦♥t♦♥s ♦♥ µ t ♦♥t♦♥s ♦♥ µ, κ tr♦♦t
P♦str♦r strt♦♥
r ♣r♦r strt♦♥ ♦♥ t tstr♦♣ t ♣r♦t② κ ♥ ♦♥ ♦
t ♠ss♥ t ♣r♠trs ξi, i = 1 . . . L s ♥♦r♠ strt♦♥ ♦♥ t
♥tr [0, 1] ♦r t rt ♣r♠trs µ λ ♥ ρ ♠♣♦s ♥ ♠♣r♦♣r
♣r♦r strt♦♥ p(µ, λ, ρ) ∝ 1µλρ
s ♣r♦r s s♥r♥t s
t t♠s t ② t♦r η t′ = ηt t♥ t s♥ (µ′, λ′, ρ′) = (µ/η, λ/η, ρ/η)
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s t ♦♦ ♥♥ t s tr♦r rs♦♥ t♦ ♣t t s♠ ♣r♦r
t ♦r rt ♣r♠tr ♦♥ ♥ ♥tr [a, b] s ♦♥ t ♥tr [a/η, b/η]
♥ s♦♠ ♥②ss s Γ(1.5, 0.0002) ♣r♦r ♦♥ ρ st
♣r♦t② ♥st② ♥tr ♦r ts strt♦♥ ♦rrs♣♦♥s t♦ tstr♦♣s
♦r♥ t♥ r② ②rs ♥ r② ②rs ♥♥ t ♣r♦r
♥♦t t ♦r rsts r ♣r♦r ♦♥ t tr g s sr ♥ t♦♥
❲ t ♥♦r♠ ♣r♦r ♦r [0, 1] ♦r t t ♣r♦t② t tstr♦♣
κ ♥ ♠ss♥ t ♣r♠tr ξi
sttt♥ s♥ qt♦♥s ♥t♦ qt♦♥ ♥ ♠t♣②♥
② t ♣r♦r fG(g|T )p(λ, µ, ρ) ♦t♥ t ♣♦str♦r strt♦♥
p(g, µ, λ, κ, ρ, ξ|D = D)
=1
N !
(
λ
µ
)N
exp
−λ
µ
∑
〈i,j〉∈E
P [EZ |Z = (ti, i), g, µ, κ, ξ](1 − e−µ(tj−ti+kiTC))
×N∏
a=1
∑
〈i,j〉∈Ea
∑
ω∈Ωa
P [M = ω|Z = (ti, i), g, µ](1 − e−µ(tj−ti+kiTC))
×1
µλp(ρ)fG(g|T )
e−ρ|g|(ρ|g|)kT
kT !
L∏
i=1
(1 − ξi)QiξN−Qi
i
♦r ♣r♠trs µ, λ, ρ > 0 0 ≤ κ, ξi ≤ 1 ♥ trs g ∈ Γ(C)K
❲t t ♣r♦r p(ρ) ∝ 1/ρ t ♣♦str♦r s ♠♣r♦♣r t♦t ♦♥s ♦♥
ρ s♥ kT = 0 s ♦ ❲ ♣ r② ♦♥srt ♦♥s ♦♥ ρ sts
r ♥♦t s♥st t♦ ts ♦ ❲ sss t ♣r♦♣rt② ♦ t ♣♦str♦r ♥
t♦♥
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♠ rrst②
♥ ts st♦♥ s♦ tt t ♣r♦ss s t♠rrs ♥ ♦♥② ν =
κλ/µ s ♠ ♥ st♦♥ ♦r ts ♦♦ t t tr♥st♦♥ rts ri,j
r♦♠ t stt t i ♦♥② sss ♥ ♥ t♦ t stt t j ♦♥②
sss s tr♥st♦♥ rts r t s♠ ♦ t tr♥st♦♥ rts ♦r t
♥♥ ♣r♦ss ♦s tr♥st♦♥s r♦♠ i t♦ i + 1 ♥ i − 1 ♥ t
tr♥st♦♥ rts ♦r t tstr♦♣ ♣r♦ss ♦s tr♥st♦♥s r♦♠ ♥②
i t♦ ♥② j
♦r |i− j| 6= 1 t tr♥st♦♥ r♦♠ i t♦ j s t♦ ♦ tr♦ tstr♦♣
ts ♦r t rt ρ ♦r tstr♦♣ ♦rr♥ t t♠ τ s② tt t
ts ♣♣♥ t τ ♥ t rts ♣♣♥ s♦rt② tr t τ − ǫ t k t
♥♠r ♦ ♦♥② sss ①st♥ tr t ts ♦rr t ♦r
t rts ♥② ts ♦rr t♦ ♦ r♦♠ i t♦ k s♦ k ≤ i ♥ ♦♥② rts
♦r t♦ ♦ r♦♠ k t♦ j s♦ k ≤ j k ♥ t ♥② t♥ ♥ min(i, j)
♠♠♥ ♦r ts s t
ri,j = ρ
k=min(i,j)∑
k=0
Bin(k; i, 1 − κ) × Poi(j − k; ν)
strt♥ t i ♦♥② sss k ♦♥② sss t♦ sr t t♥♥♥
♣r♦ss t sr ♣r♦t② 1−κ t♥ t r♠♥♥ j−k ♦♥② sss
r ♦r♥ tr♦ t Poi(ν) ♣r♦ss s ♦♠s
ri,j = ρκie−ννji! 2F0
(
−i,−j;1 − κ
νκ
)
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r
2F0(−i,−j; θ) =
k=min(i,j)∑
k=0
θk 1
k!(i − k)!(j − k)!
s ♥r③ ②♣r♦♠tr ♥t♦♥ ❬r♠♦t③ ♥ t♥ ❪ ♦t
tt 2F0(−i,−j; θ) = 2F0(−j,−i; θ)
♦r j = i + 1 t tr♥st♦♥ rts r
ri,j = λ + ρe−ν νjκj−1
j!2F0
(
−i,−j;1 − κ
νκ
)
rj,i = µj + ρe−ν νj−1κj
(j − 1)!2F0
(
−j,−i;1 − κ
νκ
)
.
rst ss♠ tt ν = κλ/µ ❲ ♣r♦♥ ♥ t♦♥ tt t
qr♠ t ♣r♦t② ♦r ♥② ♣♦♥t ♦♥ t tr t♦ s♣② ①t② i
♦♥t sss s πi = e−νκ νi/(i!κi) |i − j| 6= 1 t s strt♦rr t♦
tt πiri,j = πjrj,i j = i + 1 t♥
πjrj,i
πiri,j
=λ
µ
1
j×
µj + ρe−ν νj−1κj
(j−1)! 2F0
(
−j,−i; 1−κνκ
)
λ + ρe−ν νjκj−1
j! 2F0
(
−i,−j; 1−κνκ
)
=λ
µ×
µ + ρe−ν νj−1κj
j! 2F0
(
−j,−i; 1−κνκ
)
λ + ρe−ν νjκj−1
j! 2F0
(
−i,−j; 1−κνκ
)
=
λµµ + ν
κρe−ν νj−1κj
j! 2F0
(
−j,−i; 1−κνκ
)
λ + ρe−ν νjκj−1
j! 2F0
(
−i,−j; 1−κνκ
)
= 1.
♦r i ♥ j πiri,j = πjrj,i ♥ s♦ t ♣r♦ss s t♠rrs
♣♣♦s ♦♥rs② tt t ♣r♦ss s t♠rrs i ≥ 2 ♥ t
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j = i + 1 ♥
πi =π0r0,i
ri,0
② t♠rrst②
=νi
κi
π0
i!② qt♦♥
πj =νj
κj
π0
j!
♥ πi/πj = (i + 1)κ/ν qt♦♥s ♥
rj,i
ri,j
=µ(i + 1) + ρe−ννiκi+1
i! 2F0
(
−i,−j; 1−κνκ
)
λ + ρe−ννi+1κi
(i+1)! 2F0
(
−j,−i; 1−κνκ
)
♥ t ♣r♦ss s t♠ rrs πi
πj=
rj,i
ri,j
(i + 1)κ
ν=
µ(i + 1) + ρe−ννiκi+1
i! 2F0
(
−i,−j; 1−κνκ
)
λ + ρe−ννi+1κi
(i+1)! 2F0
(
−i,−j; 1−κνκ
)
♥ t ♥♠rt♦r ♦ ♦t ss ② (i + 1)κ ♥ t ♥♦♠♥t♦r ♦ ♦t
ss ② ν s
1 =
µ
κ+ ρe−ννiκi
(i+1)! 2F0
(
−i,−j; 1−κνκ
)
λν
+ ρe−ννiκi
(i+1)! 2F0
(
−i,−j; 1−κνκ
) .
t ♦♦s tt µ/κ = λ/ν
s s♦s tt t ♣r♦ss s t♠ rrs ♥ ♦♥② ν = λκ/µ
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♣tr
♠♣♠♥tt♦♥
s ♣tr s t ♣♦str♦r ♣r♦t② strt♦♥ s ♣r♦♣r sts ♦t
t r♦ ♥ ♦♥t r♦ ♦rt♠ ①♣♥s ♦ t s ♠♣♠♥t
srs ♥ s ♥ r② sts ♦tr s♣ts ♦ t s♦tr
rt ♥ ♦ ♦s ❲ ♥ ts t♦r ♠♣♠♥t
t st♦st ♦♦ ♠♦ sr ♥ ♣tr
Pr♦♣rt② ♦ t ♣♦str♦r
tt ♦r ♣r♦r ♦♥ t rt ♣r♠tr λ ♥ t t ♣r♠tr µ s
p(λ, µ) ∝ 1λµ s ♠♣r♦♣r t s tr♦r ♣♦ss tt t ♣♦str♦r
strt♦♥ s ♠♣r♦♣r qt♦♥ s t ♣♦str♦r strt♦♥ ♦ t
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tr ♥ ♣r♠trs ♥ t t s
p(g, µ, λ, κ, ρ, ξ|D = D)
=1
N !
(
λ
µ
)N
exp
−λ
µ
∑
〈i,j〉∈E
P [EZ |Z = (ti, i), g, µ, κ, ξ](1 − e−µ(tj−ti+kiTC))
×N∏
a=1
∑
〈i,j〉∈Ea
∑
ω∈Ωa
P [M = ω|Z = (ti, i), g, µ](1 − e−µ(tj−ti+kiTC))
×1
µλp(ρ)fG(g|T )
e−ρ|g|(ρ|g|)kT
kT !
L∏
i=1
(1 − ξi)QiξN−Qi
i
♦r ♣r♠trs µ, λ, ρ > 0 0 ≤ κ, ξi ≤ 1 ♥ trs g ∈ Γ(C)K
❲ ♦♥t♦♥s ♥r t ♣♦str♦r ♥ s♦♥ t♦ ♣r♦♣r
r strt② s t♦ rst ♥trt ♦t λ ♥ t♥ ♥ ♥ ♣♣r ♦♥ ♦♥
t ♥tr ♦ t ♣♦str♦r ♥ µ → ∞ ♥ µ → 0 ♦r s♣②
s ♥ µ0 ♥ µ1 s tt tr s ♦♥ ♦r t ♥tr ♦♥ [µ0,∞)
♥ ♦♥ ♦♥ t ♥tr ♦♥ [0, µ1] ♥tr ♦♥ [µ1, µ0] s t ♥tr
♦ ♦♥ ♥t♦♥ ♦r ♦♠♣t st ♥ s tr♦r ♥t ♦r s
♦ rt② t θ = (g, κ, ρ, ξ) ♥ dθ = dκdρdξ∏
i dti t ♦♥t♥
♠sr ♦♥ t♦♣♦♦s
♠r♥ ♦r λ s ♠♠strt λ|µ, θ, D ∼ Γ(N, β) r
β =µ
∑
〈i,j〉∈E P [EZ |Z = (ti, i), θ, µ](1 − e−µ(tj−ti+kiTC))
♥ t ♣r♦t② ♥st② ♥t♦♥ ♦ Γ(α, β) s f(x) = xα−1e−βxβα
Γ(α)
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❲♥ ♥trt ♦t λ ♣ ♣ t t♦rs ♥♦r♠③♥ ts strt♦♥
p(µ, θ|D) ∝
∑
〈i,j〉∈E
P [EZ |Z = (ti, i), θ, µ](1 − e−µ(tj−ti+kiTC))
−N
×N∏
a=1
∑
〈i,j〉∈Ea
∑
ω∈Ωa
P [M = ω|Z = (ti, i), g, µ](1 − e−µ(tj−ti+kiTC))
×1
N !
1
µp(ρ)fG(g|T )
e−ρ|g|(ρ|g|)kT
kT !
L∏
i=1
(1 − ξi)QiξN−Qi
i
♥ ts s ♥ t t ♦r♠ s ♥ t ♠♣♠♥tt♦♥ sr tr
♥ ts ♣tr
❲ rst ①♠♥ t s②♠♣t♦t ♦r ♥ µ → +∞ ♥ ♦rr t♦
♣r♦ tt t ♣♦str♦r s ♣r♦♣r ss♠ t t ♥s trt
s♣② ♥ t♦ s ♥ r♥t s trt ♠st sr ♦r
♥t t♠ ♥ t s s ♠♣♦ss t µ → ∞
❲ rrt qt♦♥
p(µ, θ|D) ∝C
µ
N∏
a=1
∑
〈i,j〉∈Ea
∑
ω∈ΩaP [M = ω|Z = (ti, i), θ, µ](1 − e−µ(tj−ti+kiTC))
∑
〈i,j〉∈E P [EZ |Z = (ti, i), θ, µ](1 − e−µ(tj−ti+kiTC))
r C =QL
i=1(1−ξi)Qiξ
N−Qii
N !p(ρ)fG(g|T ) e−ρ|g|(ρ|g|)kT
kT !
♥♠rt♦r s ♦♥ s♦ t ♦♥ ♦r t t ♥
♥ ♥ ♦r ♦♥ ♦r t ♥♦♠♥t♦r ♥ ♦r ω ∈ Ωa t
♥t Ma = ω|Z = (ti, i) s ♦♥t♥ ♥ t ♥t EZ |Z = (ti, i) ♥ s♥
Ea ⊆ E t tr♠s ♥ ts ♣r♦t r ss t♥ t ts ♣♣r ♦♥ s
♥♦t qt ♥♦ t♦ s♦ tt t ♥tr ♦r µ s ♣r♦♣r
t s ♥♦ ♦♥sr t s r t rstrt♦♥ ♦♥t♦♥ s Y (a) > 0
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i2
i1
i0
a0,...
a0,...
r ♥ ①♠♣ tr ♦r q r ♦♥t ss a0 s s♣②♦♥② t s i1 ♥ i2 t rs♣t② k1 = 1 ♥ k2 = 3 tstr♦♣s ♦t♠
sr ♦♥② sss r ♥r ♦sr ts ♦♥t♦♥ R1
♥ t♦♥ ♣♣♦s tr s ♦♥② ss a0 s tt a0 s s♣②
t ①t② t♦ s i1 ♥ i2 ♦r ♥♦ ss♠ tt i1 ♥ i2 r s♥s
s ♥ r t i0 tr ♦♠♠♦♥ ♣r♥t ♥♦ ♥ t k1 ♥ k2
t ♥♠r ♦ tstr♦♣s ♦♥ t r♥s 〈i1, i0〉 ♥ 〈i2, i0〉 rs♣t②
s r ❲ ♥ t♥ ♦t♥ ♦r ♦♥ ♦♥ t ♥♦♠♥t♦r ♦
qt♦♥
∑
〈i,j〉∈E
P [EZ |Z = (ti, i), θ, µ](1 − e−µ(tj−ti+kiTC))
=∑
〈i,j〉∈E
P [Y (a) > 0|Z = (ti, i), θ, µ](1 − e−µ(tj−ti+kiTC))
≥ P [Y (a) > 0|Z = (ti1 , i1), θ, µ](1 − e−µ(ti0−ti1+k1TC))
≥ ξ1 × (1 − e−µ(ti0−ti1+k1TC))
≥ ξ1(1 − e−µ(ti0−ti1 ))
❲ ♥♦ ♥ ♥ ♣♣r ♦♥ ♦♥ t ♥♠rt♦r ♦ qt♦♥
♦ s♠∑
〈i,j〉∈Ea0
∑
ω∈Ωa0P [M = ω|Z = (ti, i), θ, µ](1 − e−µ(tj−ti+kiTC))
♥ ♦tr ♦rs Ωa0= i1, i2 ♥ ts s t ♦ s♠ ♦r Ea ♥ Ωa
tr♦r ♦♥② s♠ ♦r Ea s♥ tr r ♥♦ ♠ss♥ t ♦r ts ♦♥② ss
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♦♥t♥s t ♠♦st L − 2 tr♠s ♥ 1 − e−µ(tj−ti+kiTC) ≤ 1 ♥ s♥
t ♠①♠ ♦r i ♦ t tr♠s P [M = ω|Z = (ti, i), θ, µ] r②
♦rrs♣♦♥s t♦ rt t t ♠♦st r♥t ♦♠♠♦♥ ♥st♦r i0
∑
〈i,j〉∈Ea0
∑
ω∈Ωa0
P [M = ω|Z = (ti, i), θ, µ](1 − e−µ(tj−ti+kiTC))
≤ (L − 2)P [M = i1, i2|Z = (ti0 , i0), θ, µ]
≤ (L − 2)ξi1ξi2e−µ(ti0−ti1+k1TC)e−µ(ti0−ti2+k2TC).
② s♥ ts ♣♣r ♦♥ ♦r t tr♠ a0 ♥ t t tt t tr♠s
♥ t ♣r♦t ♦r a 6= a0 r ss t♥ 1 t tt
p(µ, θ|D) ≤ C(L − 2)ξi1ξi2
e−µ(2ti0−ti1−ti2+(k1+k2)TC)
µ(1 − e−µ(ti0−ti1 ))
s♠r rst ♥ ♦t♥ i1 ♥ i2 r ♥♦t s♥s
❲ ♥ ♥♦ s tt ♦r µ ≥ 1
e−µ(2ti0−ti1−ti2+(k1+k2)TC)
µ≤ e−µ(2ti0−ti1−ti2+(k1+k2)TC) ≤ e−µ(2ti0−ti1−ti2 ).
r♦r
p(µ, θ|D) ≤ C(L − 2)ξi1ξi2
e−µ(2ti0−ti1−ti2 )eµ(ti0−ti1 )
eµ(ti0−ti1 ) − 1
≤ C(L − 2)ξi1ξi2
e−µ(ti0−ti2 )
eti0−ti1 − 1
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❲ ♥ ♥trt µ ♦t ♦ [1,∞) ♥ ♦t♥
p(θ|D)dθ ≤ C(L − 2)ξi1ξi2
e−(ti0−ti2 )
(ti0 − ti2)e(ti0−ti1 ) − 1
dθ
s ♦♥ s ♥ ♣t ♦r ♦♥ ♦♥ ti0 − ti1 ♥ ti0 − ti2 ts
♣r♦♣r ss♠♥ tt i1 ♥ i2 r ♠♦r♥ s s♦ tt tr s
♦♥str♥ t♦ s ♦r ♦♥ ♥ ♦t♥ tr s ♦r
♦♥ ♦♥ ti0 ♦♥str♥t ♦♥ t r♦♦t ♦ ♦♥t♥♥
i1 t ♥♦t i2 ♥tr s tr♦r ♣r♦♣r ♦r µ ∈ [1,∞[ t st ♦♥
♦♥② ss s s♣② ♥ ①t② t♦ ♥s ♥ t♦ r♥t s ♦r
①♠♣ ♥ r ♦♥② ss s♣② ♥ t♥ ♥ ❲s ♦
sts② ts ♦♥t♦♥
s rst ♥ ①t♥ t♦ t s r a0 s s♣② t ♠♦r t♥
s ♥ r t t r ♠ss♥ t s♦♠ s ♥ ♥r t
rstrt♦♥ ♦♥t♦♥ ts t ♦r♠ Y (a) > d ♦r s♦♠ ♦ d t ♥
①t♥ t♦ t s r tr ①sts ♦♥② ss a0 s♣② t t st
d + 2 s ♥ t♦ r♥t s ❲ ss♣t tt ts ♦♥t♦♥ ♦
♠ ss str♥♥t t t s r② sts ② ♦r t t rstrt♦♥
♦♥t♦♥ ♥s ♦♥ ♦ ♦♥t♦♥s R3R6 ♦ st♦♥ Y (a) < L
sr ♥② ♦♥② ss s♣② t r② t t♦♥ st ♦s
s ♦♥ s i0 s ss t♥ L s♥♥ts ♦r L−1 ♣♥♥ ♦♥ t ♦♥t♦♥
s s µ → ∞ s ♦r
t s strt♦rr t♦ s♦ tt ♥r rstrt♦♥ ♦♥t♦♥ R1 t
♣♦str♦r strt♦♥ ♦r t ♥ ♦♥② sss r s♣② t
st ♦♥ s ♠♣r♦♣r ❲ ♦ ♥♦t ♥♦ t t ♣r♦♣rt② ♦ t ♥tr
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s ♥ ♦♥② sss r s♣② t ♠♦r t♥ d + 1 s t t
t s ♥ t s♠ ss♣t t s ♠♣r♦♣r
❲ ♥♦ ♦♥sr t s µ → 0 ❲t tstr♦♣s ♥ t ♣♦str♦r
s ♠♣r♦♣r ♥ ♦r tr t ♦♥ tstr♦♣ ♦♥ r♥ ♥ t
① κ t ♦♦ ♦s ♥♦t ♦ t♦ ♥ µ → 0 s♥ s tr s
q♥t t♦ tr ♥ r♥s q ♥t TC = − log(1 −
κ)/µ ❲ s♦ tt ♦r tr t♦t tstr♦♣s ♥ ♥r rs♦♥
♦♥t♦♥s ♦♥ t t t ♣♦str♦r s ♣r♦♣r ♥ µ → 0 s t♠ t
② s t♦ ss♠ ♦♥② ss ♠st t st ♦♥ t ♦♥ t
tr ♥② ♦♥② ss s ♥♦t ♠♦♥♦♣②t s ts rtr♦♥ ❲
♥♦ ♥ θ = (g, ξ) ♥ ♦♦ ♦♥② t tstr♦♣r trs
ss♠ tt t rstrt♦♥ ♦♥t♦♥ s ♦ t ♦r♠ Y (a) > d ♦r s♦♠ d
❲ s s t♦ ♣r♦♣rts ♦ t ①♣♦♥♥t ♥t♦♥
∀x ∈ R, 1 − e−x ≤ x
∀x ∈ [0, 1], 1 − e−x ≥x
2
s tr♥st ♥t♦
∀µ ∈ R+,∀〈i, j〉 ∈ E, 1 − e−µ(tj−ti) ≤ µ(tj − ti)
∀µ ≤ 1/T,∀〈i, j〉 6= 〈r, A〉, 1 − e−µ(tj−ti) ≥µ(tj − ti)
2
tt 〈r, A〉 s t ♦♦t♠ r♥ ♥ T s t ♣♣r ♦♥ ♦♥
t r♦♦t s♦♥ qt♦♥ ♦s s ∀〈i, j〉 6= 〈r, A〉, tj − ti ≤ T
♥ µ(tj − ti) ≤ 1
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s♦ ♥♦t tt
∀〈i, j〉 ∈ E, 1 ≥ P [EZ |Z = (ti, i), θ, µ] ≥ e−µ[(d+1)T ]
t st tr♠ ♦rrs♣♦♥s t♦ ♦♥② ss ♣rs♥t t t r♦♦t ♥ sr♥
♦♥ d + 1 ♣ts ♦ ♥t T s ♦♥ ② ♦ ♥ t ♥t EZ ♦r
qt♦♥s ♥ ♦r ♦♥ ♦♥ t ♥♦♠♥t♦r ♦
∑
〈i,j〉∈E
P [EZ |Z = (ti, i), θ, µ](1 − e−µ(tj−ti)) ≥ e−µ[(d+1)T ] ·µ
2
∑
〈i,j〉6=〈r,A〉
(tj − ti)
≥ e−µ[(d+1)T ]µ
2tr
r tr s t r♦♦t
♥ tr g ♥ ♦♥② ss a s② tt t ♦♥② ss a s
♠♦♥♦♣②t ♥ ♦♥② tr s str h ♦ g s tt a s ♣♦t♥t②
s♣② t t s ♦ h ♥ ♥♦r s ♦ s♣♣♦s tt t st
♦♥ ♦♥② ss am s② ♦r♥ t (ti, i) s ♥♦t ♠♦♥♦♣②t ♥ t st
♦♥ t ♠st ♦rr ♥ t str ♦ (ti, i) ♥t ♦ tt
str s t ♠♦st tr · L s♦ ♦r ♥② ω ∈ Ωam
P [M = ω|Z = (ti, i), θ, µ] ≤ 1 − e−µtrL ≤ µtrL
s s tr ♦r ♣♦ss s ♦ i ♦r 〈i, j〉 ∈ Eam ♦ tr r t
♠♦st L− 1 ♥ ♦r ♣♦ss s ♦ ω ∈ Ωam ♦ tr r t ♠♦st
♦r s ♥ t str t t ♥ ♦r ? ♦r s ♦ts t str t t♥ ♦r ?
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2L−3 ♥ s♥ qt♦♥
∑
〈i,j〉∈Eam
∑
ω∈Ωam
P [M = ω|Z = (ti, i), θ, µ](1 − e−µ(tj−ti))
≤∑
〈i,j〉∈Eam
∑
ω∈Ωam
P [M = ω|Z = (ti, i), θ, µ]µ(tj − ti)
≤ µ(trL) · µT · (L − 1) · 2L−3
♦♠♥ t♦ t ♣r♦t ♥ t t ♥ ♦ qt♦♥ t
tr♠ ♦r am ♥ t ♣r♦t ♥ ♦♥
∑
〈i,j〉∈Eam
∑
ω∈ΩamP [M = ω|Z = (ti, i), θ, µ](1 − e−µ(tj−ti))
∑
〈i,j〉∈E P [EZ |Z = (ti, i), θ, µ](1 − e−µ(tj−ti))≤
µ(trL) · µT · (L − 1) · 2L−3
e−µ[(d+1)T ] µ
2tr
s ♣r♦s② r② ♦tr tr♠ ♦ ts ♣r♦t s ♦♥ ② ♥
qt♦♥ ♦♠s ♦r s♦♠ ♦♥st♥t C ′
p(θ, µ|D) ≤ C ′µ(L) · T · (L − 1) · 2L−3
e−µ[(d+1)T ] 12
1
µt2−Lr fG(g|T )
s ♣r♦♣r ♦r µ ∈ [0, 1/T ]
♣♣♦s ♥♦ tt tr r t♦ rstrt♦♥ ♦♥t♦♥s Y (a) > d ♥
Y (a) < L − d′ ♦r ①♠♣ ♥ s♥ t ♥♦tt♦♥ r♦♠ t♦♥ R =
R3 R2 t B t st ♦ s t st L − d′ s♥♥ts
ts r s ♦s t♦ t r♦♦t ♦ t tr ♥qt② ♦s ♥♦t ♦
♥②♠♦r ♦r t s ♥ B
♣♣♦s tt tr s g′ s tt
• r r ss t♥ L − d′ s ♥ g′
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• ❲ ♥ ♣t ♦r ♦♥ T ′ ♦♥ t r♦♦t ♦ g′ ts ♥ ♦♥
tr♦ t ♦♥str♥ts ♥♦ ♦r rt♥ ♥str ♥♦s
t E ′ t st ♦ s ♥ g′ ♥qt② st ♦s ♦r t ♠♥ts
♦ E ′ ♥qt② ♦♠s
∑
〈i,j〉∈E
P [EZ |Z = (ti, i), g, µ](1 − e−µ(tj−ti)) ≥∑
〈i,j〉∈E′
P [EZ |Z = (ti, i), g, µ](1 − e−µ(tj−ti))
≥ e−µ[(d+1)T ] ·µ
2
∑
〈i,j〉∈E′
(tj − ti)
≥ e−µ[(d+1)T ]µ
2T ′
st② ♠♦ rs♦♥ ♦ ♥qt② s♦s tt t ♥tr s
st ♣r♦♣r
r② s♠r r♠♥t ♦s ♦r t s r t rstrt♦♥ ♦♥t♦♥
s ♦ t ♦r♠ Y (a) + Q(a) < L − d′ s µ → 0 s ♦r
♥ t ♦tr ♥ t ♦♥② sss r ♠♦♥♦♣②t t s r
tt t ♣♦str♦r strt♦♥ s ♠♣r♦♣r ♥ µ → 0
♦ s♠ ♣ ♥r t ♣r♦r p(µ, λ) ∝ 1µλ t tstr♦♣s ① ♥
t t rstrt♦♥ ♦♥t♦♥ d < Y (a) < L−d′ t ♦♦♥ ♦♥t♦♥s r
s♥t ♦r t ♣♦str♦r t♦ ♣r♦♣r
tr ①sts ♦♥② ss a0 s tt a0 s s♣② t t st d + 2
r♥t s ♥ r♥t s
tr ①sts ♥♦♥♠♦♥♦♣②t ♦♥② ss am
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tr ①sts g′ s tt tr r ss t♥ L − d′ s ♥ g
♥ ♥ ♣t ♦r ♦♥ T ′ ♦♥ t r♦♦t ♦ g′
s ♦♥t♦♥s r ♠t ② ♥② rst t ♦r ①♠♣ ♥ t ♥
t ❬❪ t ♦r R = R1 0 < Y (a) ♦rrs♣♦♥♥ t♦ d = 0
t♥ ♠♦rtr ♥ t r ♦♥ ♠rt ♦t ♠♥♥
s r ♦♥t ♥ ♥ r♥t s
s ♦♥② ss s ♥♦t ♠♦♥♦♣②t s♥ Prss♥ s ♦♥str♥
t♦ ♥ t t♦ t r ♦♥ t t♦t
t♥ ♥ tr s ♥♦ ♥st♥ ♦ ts ss ♥ Prss♥ t ♦♥②
Prss♥ tr♠ ♦r s s t s ♥ r♥t ♦♥②
ss
r r s sts② t st ♦♥t♦♥ ♦r ①♠♣ t
r♠♥
❲t tstr♦♣s ♥ t ♣♦str♦r s ♠♣r♦♣r ♥ µ → 0 s
t♥ TC → ∞ t t ♥t ♥ ♦ t♦ ♥♥t② t ♥s
♣♣♥♥ ♦♥ tstr♦♣s ♥ ♥♦ ♥ ♦rr♥ tr♦ t ♥♥
♣r♦ss s s ♠♦st s② rs♦ ② ♠♣♦s♥ ♦r ♦♥ ♦♥ µ t
♦ s♦ rs♦ ② ♠♣♦s♥ ♦♥t♦♥s ♦♥ t tstr♦♣s ♦r
ts s ♥♦t ♥ssr② ♥ ♣rt s♥ ♥r ♦sr µ → 0 ♥ ♦r ♥②ss
♠♣♠♥tt♦♥ ♥ t
st♦st ♦♦ ♠♦ sr ♥ ♣tr s ♠♣♠♥t ♥ t
② ♦ ♦s ❲ ♥ ts t♦r rst♥ ♥ ♣ ♦
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♣♦♠♥ s♦tr ♥♠ rt tr tstr♦♣s ♥ ♠♦
♣r♠trs r st♠t ♦♥t② r♦ ♥ ♦♥t r♦ s sr
♥ t♦♥
rt ts s ♥ ①s ♦r♠t t ♥②ss t t ♥r t
st♦st ♦♦ ♠♦ t ♦♣t♦♥s t♦ ♥ s♦♠ ♦r t ♦♥str♥ts
♥ t ①s s s t♦ ① s♣ trts ♦r ♥s ♥s♦♥
♦ tstr♦♣s s ♦♣t♦♥ ♥ t sr ♠② ♦♦s t♦ ♥ ♠ss♥ t
♦rrt② ♦r t♦ trt ♠ss♥ t s s♥t r♣♥ s t s
t ♠② s②♥tt③ r♦♠ t ♠♦ rt② r♦♠ t r♣ ❯sr
♥tr ❯ ♦st ♦ t t②♣s ♦ ♦t♦♠♦ t sr ♥ ♣tr
♠② s♦ s②♥tt③ rt② r♦♠ t ❯ ♥♥ t t ♦rr♦♥
♥ t ♠ss♥ ♥ ♦s
♥②ss ♣rt ♦ t ❯ s t♦♦s t♦ ♦♥r♥ ♥ ♠①♥
♦ t t t♦♦rrt♦♥s ♣♦ts ♦r s① sttsts t r♦♦t tr t
t rt µ t tstr♦♣ ♣r♠trs ρ ♥ κ t ♦♦♦ ♥ t
♣r♦r r t♦♦s ♦r ♥②ss ♦ t t r ♥ ♥♥ t t②
t♦ ♦♥strt ♦♥s♥ss trs ♦r tstr♦♣ ♠♦s s sr ♥ ♣tr
♥ ♦♣t♦♥ ♦s t♦ s rsts t♦ ♦r♠t ♦r s ♦ sr♥
r♦ ♥ ♦♥t r♦
❲ s r♦ ♥ ♦♥t r♦ t♦ s♠♣ t ♣♦str♦r
strt♦♥ ♥ st♠t s♠♠r② sttsts ❲ ♦ ♥♦t st♠t λ
♥trt ♦t ♦♦♥ qt♦♥ stt s t♥ x =
((E, V, t, k), µ, κ, ρ, ξ)
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♥ ♣r♦r strt♦♥ p ♥ ♦♦ ♥t♦♥ L(·|D) t strt②
♥ r♦ ♥ ♦♥t r♦ s t♦ r♦ ♥ ♦s stt♦♥r②
strt♦♥ s t ♣♦str♦r strt♦♥ s t♦ s♠♣ r♦♠ t xn
t stt ♦ t r♦ ♥ t st♣ n t stt xn+1 s ♦♥strt s ♦♦s
Pr♦♣♦s t♦ ♠♦ r♦♠ xn t♦ x′ r x′ s r♥ r♦♠ ♣r♦♣♦s
strt♦♥ q(x′|xn)
♦♠♣t
α = min
(
1,p(x′)L(x′|D)q(xn|x
′)
p(xn)L(xn|D)q(x′|xn)
)
.
t xn+1 = x′ t ♣r♦t② α ♥ xn+1 = xn t ♣r♦t② 1 − α
❯♥r ♦♥t♦♥s ts r♦ ♥ ♦♥rs t♦ t ♣♦str♦r strt♦♥
♦r t ♣r♦♣♦s strt♦♥ s t ♠♦s sr ②
r♠♠♦♥ t ❬❪ ♥ ♦s ♥ r② ❬❪ t♦ ♠♦s
t♦ t ♥t♦ ♦♥t ♦r t♦♥ ♣r♠trs r ♦♠♣t st ♦
♠♦s s s ♦♦s str ♥♦ts ♠♦s ② t ♣rs♥t t♦r
• ♦s ♦♥ t t♦♣♦♦②
①♥ t ♣♦st♦♥s ♦ t♦ ♦s ♥♦s ♥♦ ♥ ts ♥
t ♦ ts s♥
①♥ t ♣♦st♦♥s ♦ ♥② t♦ ♥♦s
♦ str t♦ ♦s ♣♦st♦♥
♦ str t♦ ♥② ♦tr ♣♦st♦♥ ♥ t tr
• ♦s ♦♥ t s
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♥ t ♦ ♥ ♥tr♥ ♥♦
♥ t ♦ ♥♦♥♠♦r♥
s t ♦ tr
s str
s t t♦♣ ♦ t tr
• ♦s ♦♥ tstr♦♣s
♥ tstr♦♣
t tstr♦♣
♦ tstr♦♣ t♦ ♥♦r♥
• ♦s ♦♥ t ♣r♠trs
♥♦♠ ♦ s ♦ t t rt µ
♥♦♠ ♦ s ♦ t tstr♦♣ rt ρ
♥♦♠ ♦♥ [0, 1] ♦r t tstr♦♣ t ♣r♦t② κ
s t ♠ss♥ t ♣r♠tr ξi ♦r s♥ i
s t ♥tr t♦r ♦ ♠ss♥ t ♣r♠trs ξ
♣r♦t② 0 < ξi < 1 ♦r ♥ ♠♥t ♦ t rstr t ♠tr① t♦
♦sr s ♦r ♠♥② s ♦s t♦ ♦♥ s♦ ♣t t♦s ♣r♠trs
② s♥ 1 − ξi ❲ s♦ ♥ ♠♦ ss ξi i = 1 . . . L
s♠t♥♦s② ② r♦♠ ② t♦r ♦ η r η ∼ U([1/2, 2]) ♥ ts
s t ♦♥ ♦r t tr♥s♦r♠t♦♥ r♦♠ (ξ1, . . . , ξL, η) t♦ (1 − η(1 −
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r ♥ ①♠♣ ♦ ♠♦ ♠♦♥ tstr♦♣ r♦♠ ♥ t♦ ♦♥ ♦ ts ♥♦rs
ξ1), . . . , 1 − η(1 − ξL), 1/η) s ηL−2 s♦ t ♣t♥ ♣r♦t② s
α(x′|x) = min
(
1,p(x′|D)
p(x|D)ηL−2
)
♦r t t♦♥ ♥ t♦♥ ♦ tstr♦♣s ♦ ♥♦t ♥ t♦ s
rrs ♠♣ r♦ ♥ ♦♥t r♦ s t stt t♦r s♣s t
♥♠rs ♥ ♥♦t t ♦t♦♥s ♦ tstr♦♣s ♦♥ s
❲ ♦♠t t ts ♦ ts ♠♦s t s ♥ ①♠♣ t ♣t
tt ♠♦s tstr♦♣ r♦♠ ♥ t♦ ♣r♥t ♦r s♥
t kT =∑2L−2
i=1 ki t t♦t ♥♠r ♦ tstr♦♣s ♥ stt
x = (g, µ, κ, ρ, ξ) t g = (V, E, t, k) ♣ 〈i, j〉 ∈ E t ♣r♦t②
ki/kT t E〈i,j〉 t st ♦ s ♥♦r♥ 〈i, j〉 s♥ ♥
♣r♥t s t ①♥ t 〈r, A〉 s♥ ♣t ♥♦ tstr♦♣s ♦♥
ts ♦ ♥♥t ♥t ♥ t qi = r(E〈i,j〉) ❲ ♥ ♥r qi = 4
♦r ♦r i t ♥① ♦ ♥♦ qi = 2 ♣r♥t s♥ ♥♦ r♥
j s t r♦♦t ♥ i s ♥♦♥ t♥ qi = 3 s♥ r♥ ♥ j s t
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r♦♦t ♥ i s qi = 1 s♥ ♦♦s ♥♦r♥
〈i, j〉 ♥♦r♠② t r♥♦♠ r♦♠ E〈i,j〉 ♥ ♠♦ ♦♥ tstr♦♣ r♦♠ 〈i, j〉 t♦
〈i, j〉 ♥t stt s x′ = ((V, E, t, k′), µ, κ, ρ) t k′i = ki − 1 ♥
k′i= ki + 1 ♥ k′
l = kl ♦r l 6= i, i s ♠♦ s ♣t t ♣r♦t②
α(x′|x) = min
(
1,qi k
′ip(x′|D)
qi ki p(x|D)
)
.
r♦ ♥ ♦♥t r♦ ♣rs♥ts t♦ sss t ♥ s♠♣s r♦♠ t
♣♦str♦r strt♦♥ ♦♥② ♦♥ t s r qr♠ ♥ t s♠♣s
t ♦t♣ts r ♥♦t ♥♣♥♥t ❲ ssss ♦♥r♥ t t s②♠♣t♦t
♦r ♦ t t♦♦rrt♦♥ ♦r t ♣r♠trs µ κ ρ ♥ tr ♥ t
♦♦♦ s sst ② ②r ❬❪ ♥ r♦ ♥ (Xn) r♦♠
r♥ ♦ ♥t Nsamp ♥ ♥ sttst S t t♦♦rrt♦♥
♥t♦♥ rS ♥ t ♥trt t♦♦rrt♦♥ t♠ τS r ♥ s
rS(t) =cov (S(Xn), S(Xn+t))
var(S)
τS =+∞∑
t=−∞
rS(t).
❲ st♠t τS ② rstrt♥ t s♠ t♥ −M ♥ M ♦r s♦♠ M
1 ≪ M ≪ Nsamp ♥ Nsamp/τ s t t s♠♣ s③ ♠sr ♦
t s③ ♦ ♥ ♥♣♥♥t s♠♣ ♦ ♣r♦ t s♠ r♥ ♦
t s♠♣ ♠♥ s t s♠♣ ♦t♣t ② t s ♠t♦ ♥ts
tt ♥ s r♥s ♦ ♦t ♠♦♥ s♠♣s t♥♥ ♦♥ t♦
s♠♣s s♦ t t r♥ ♦r ♠♦♥ s♠♣s ♥ tt
t ♦♠♣t sttsts ♥♦t r② s ♥ ①♠♣ ♥ r
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0 20 40 60 80 100−0.2
0
0.2
0.4
0.6
0.8
1
1.2
ROOT TIME τf=7.8414 M=8 N=901
auto
corr
elat
ion
lag0 200 400 600 800
6500
7000
7500
8000
8500
9000
9500
10000
10500
11000
11500MCMC output trace
MCMC updates
r ♦♠ ♦ t ♦t♣t s t♦ ssss ♦♥r♥ ♦r t rsts s♦♥♥ t♦♥ s t♦ ♣♦ts ♣ t♦ s③ sttst S r t r♦♦t tr r♥ ♦ ♠♦♥ s♠♣s s t♥♥ ♦♥ t♦ Nsamp = 1000 s♠♣s ♦ t rst r sr s r♥♥ ♦r t r♠♥♥ s♠♣st t ♣♦t s♦s t t♦♦rrt♦♥s rS(t) ♥st t t♦ ♦tt r ♥s♠t r ♥tr ♦r t ♦rrt♦♥ ♦ ♥♣♥♥t s♠♣s s♦tt ♦♥ t t♦♦rrt♦♥ s t♥ ts t♦ ♥s t ♦t♣ts♠♣s r q♥t t♦ ♥♣♥♥t s♠♣s rt ♣♦t s♦s t tr♦ t r♦♦t ♥ t ♦t♣t
♣rt ♦ t ♦t♣t s t♦ ssss ♦♥r♥ ♦r t rsts s♦♥ ♥
t♦♥
♥ tsts
❲ ♠ ♥♠r ♦ ♥ s ♦♥ ♦r ♦ ❲ ♥②s ♥ ♠♣t②
t ♥ st t ♦♦♦ t♦ t♥ tt t ♣♦str♦r
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strt♦♥s ♦r t t ♣r♠tr µ t tstr♦♣ ♣r♠trs ρ ♥
κ ♥ t r♦♦t tr r ♥t t♦ t ♣r♦r strt♦♥s ♥ s♠ trs
t s♠ t sts t ♦♦ ♥ ♦♠♣t ② ♥ t
rsts r♦♠ ♦r ♦ ♥st ♠♥ t♦♥s ♦r t sts t
♦r trts ♦♥ tr t s
♥ tr t s ♥rt ♣♦ss rstr t sts t
♥♦♥③r♦ ♣r♦t② ♥♥ ♣♦ss ♣ttr♥s ♦ ♠ss♥ t ♦♦♥
rstrt♦♥ r R1 r♦♠ t♦♥ ❲ ♦s t rt s♦ tt
t ♦♦ ♦ t sts ♥ ♦r ♠♦r trts sr s ♥
❲t ♣r♠trs ① tt t ♦♦s ♦ t sts
s♠♠ t♦ s s r② strt rqr♠♥t ♥② t♦ sts tr
r s ♦r ♣♦♥t♣r♦ss ♦ t ♥ ♠♦♥ ♦r t ❲ r♣t ts
t rstrt♦♥ r R2 s ♣r♦s ♦ t ♠t♠t rt♦♥
s s ♦ t ♦
♥②ss ♦ s②♥tt t r ♣rs♥t ♥ ♣tr
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♣tr
❱t♦♥
♥ ts ♣tr ♣rs♥t rsts s♦♥ t t② ♦ ♦r ♠t♦s s♥
s②♥tt t s s r♦sst♦♥ ♦♥ t r t st ♦t ② ♥
t ❬❪
♥ ♥②ss t s♠♣ r♦♠ t ♣♦str♦r strt♦♥ ♦♥ trs s
s♠♠r③ t ♦♥s♥ss tr s♦s s♣ts t t st
s♣♣♦rt ♥ t ♣♦str♦r s♠♣ ❲♥ t s♣♣♦rt ♦r s♣t s t♥
♥ t s♣t s ♥ s♣ts r t st s♣♣♦rt
♥ t ♣♦str♦r s♣② ♥t ♦ r♥ s t r ♥t ♦
tt r♥ ♥ t ♣♦str♦r ♦♥t♦♥ ♦♥ tt r♥ ①st♥ ts ♠♥s
tt t t♠ ♣ts s♦♥ ♦♥ ♦♥s♥ss trs ♥ ♦s♦♥② ♦♥s♥
s♣② ♥ tr s ♥rt♥t② ♥ t t♦♣♦♦② ♥♠r ♦
tstr♦♣s s♣② ♦♥ r♥ s t r ♥♠r ♦ tstr♦♣s ♦♥
tt r♥ ♥ t ♣♦str♦r s♠♣ ♦♥t♦♥ ♦♥ tt r♥ ①st♥ ♥
r♦♥ t♦ t ♥rst ♥tr s♠♣s r♦♠ t ♣♦str♦r strt♦♥
♦r t ♣r♠trs ♦ t ♠♦ r s♠♠r③ t tr st♦r♠s r♦♠
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t ♣♦str♦r ♦r st Pr♦t② ♥st② P ♥trs
♥♠♦ tst♥
❲♠ ♥♠r ♦ tsts s♥ s②♥tt t tt♥ t ♠♦ t♦ s②♥tt
t s♠t ♦r♥ t♦ t ♦♦ P (D = D|g, µ, λ, ρ, κ, ξ,D =
R(D)) ♥♠♦ t s♦s s st ♦ ♥♦r♠t t t s ♦r t
t♦♣♦♦② ♥♦ s tstr♦♣ ♣♠♥t ♥ ♣r♠tr s s s
♠♥ ♦♥ ♦r ♠♣♠♥tt♦♥
♦r rt② rst ♦♦ t t s♠t ♦♥ trs t tstr♦♣s t
r ♥♦ t ♦ ♠ss♥ t♥ t t s♠t ♦♥ trs t ♥♦ tstr♦♣s
t r s♦♠ t ♦ ♠ss♥ rsts st ♦ ♥ ♦t sss r
♦♠♥
tstr♦♣s
❲ s♠t t ♥r ♦r ♠♦ ♦r r♥t s ♦ λ µ κ ♥ ρ ♥
♦rr t♦ ①♣♦r t r♥t ♣♦ss s♥r♦s ♦ rt tr♦♥t② s s
r tstr♦♣s ♦r ♠♥② s♠ tstr♦♣s ❲ s②♥ts③ t ♦r
♥s t ♦♥ r λ/µ = 100 trts ♣r ♥ ♥
♦♥str♥ts t r t sts ♥②s ♥ ♣tr ♠♦r trts t♥
ts ❲ st µ = 2 · 10−5 ts②r s♥ t st♠ts ♦r tt ♣r♠tr
♥ ♣tr r r♦♥ tt ❲ st s♠ κ = 0.1 ♠♠ κ =
0.2 ♥ r κ = 0.5 tstr♦♣s ♦rrs♣♦♥♥ t♦ tstr♦♣s q♥t
t♦ ②rs ②rs ♥ ②rs ♦ ♥ rs♣t② ❲ st
s ♦ t tstr♦♣ rt ρ ♦rrs♣♦♥♥ t♦ rr tstr♦♣s t♥
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♥ tstr♦♣s ♦♥ tr t r♥s ♦s♦♥ tstr♦♣s
r♦♥ tstr♦♣s ♦♥ t tr ♥ r② rq♥t tstr♦♣s ♣ t♦
tstr♦♣s ♦♥ t tr ♦r ♦t ♣r r♥ ♦♥ r s♦
st ♣r♠tr s t♥ r♦♠ t ♣♦str♦r strt♦♥ ♦r ♦r ♥②ss
♦ t ♥ t ❬❪ t sr ♥ ♣tr ❲ s♦ t②♣ rsts
♥ rs ♥ tr t♦♣♦♦② s ♠♦st ♣rt② r♦♥strt
♥ r② s t ♣♦st♦♥ ♦ tstr♦♣s s ♣rt② r♦♥strt t
♣♦str♦r t♦♥s ♦ t ♣r♠trs r ♦s t♦ t tr s s
r♠♥s tr ♦r rt② ♦ ♣r♠tr s
❲♥ tstr♦♣s r ♣rs♥t ♥ t tr tr t s♥ ♦r t♠ s str♦♥
❲ s t♦ t ♥♥ ♦ tstr♦♣s ♦♥ ♦r r♦♥strt♦♥s s♦
tr tt♥ ♠♦ t♦t tstr♦♣s t♦ t ♥ t ♦
t tstr♦♣s r s t②♣ ♦ ♥♦t ♥ tstr♦♣s ♥
t ♠♦ ♦r r♦♥strt ♣r♠trs r♦♦t ♥ t rt µ r r②
r r♦♠ t tr s r♦♥strt t♦♣♦♦② s s♦ ♠ rtr r♦♠
t trt t♥ ♥ t t ♠♦ t tstr♦♣s
♦t tt ts rsts s♦ s♦ tt ♦r ♠t♦s r ♥♦t st t♦
t rts♠s ♦ st ❬❪ ♦ ♠ tt sss ♦ rt tr♦♥t②
♠♥t tt ①♦sttsts ♦s♥t ♦r tt t t♦♣♦♦② ♦ t tr
♥♥♦t r♦♥strt tr♦ sttst ♠♦♥ ♠♥ ss rs
② st ❬❪ s t② ♦♥ r♥ ttrt♦♥ ♦ s ♥♦tt♦♥ s
r♥t s ♦♥r♥ t trs s s t ♦♥ s♦♥ ♥ r ❲♥
tr s ♥♦ rt tr♦♥t② t ♠② ♣♣r tt ♥ s ♦sr t♦
♥s ♥ t♥ t♦ ♥ ts tr s♥ ♥ tt ♥
tr♦r ♥ ♣ tr s② r♦♣ t ♥ ♦r s② s
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(a) (b)
(c) (d)
r ♠t♦♥s ♦ s②♥tt t s♦ t r♦st♥ss ♦ t ♠♦ ♥ tr trs ♥ r♦♥strt ♦♥s♥ss trs ♦♥s♥sstrs r r② ♦s t♦ t tr trs ♥ t r♦♥strt tstr♦♣s r ♦♥t ♦rrt r♥s
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(a) (b)
(c) (d)
r ♠t♦♥s ♦ s②♥tt t s♦ t r♦st♥ss ♦ t ♠♦s♠♣s r♦♠ t ♣♦str♦r ♦r t r♦♦t tr t t rt µ tt ♣r♦t② t tstr♦♣ κ ♥ t tstr♦♣ rt ρ r ♦st♦ t tr s s♦♥ r ♥ r
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1
2
3
4
56
7
8
9
1011
12
1314
1516
17
18
1920
True tree
0 5 1015202530354045 (a) (b)
20
19
5
4
3
2
1
18
17
11
6
910
13
12
14
16
15
87
80
90
8181
52
92
0 2 4 6 8 1012 (c) (d)
(e)
r ♠♣♦rt♥ ♦ ♥♥ t tstr♦♣s ♥ t s②♥ts③♥r tr tr t tstr♦♣s s r♦♥strt ② ♠♦t tstr♦♣s s s♦♥ ♥ t ♦♥s♥ss tr tr t♦ t ♠♦t♦t tstr♦♣s t♦♣♦♦② s♦♦♥ ♥ t ♦♥s♥ss tr r♦♦t tr ♥ t rt µ r ② r♦♥strt
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A
B
C
D
r ♦r ♥ s ♣♣♥ ♦♥ t r♥s ♥ t♦ ♥ t♥ ♦♥ t r♥s ♥ t♦ ♥ st ❬❪ s ♦♥r♥ tt sstt♦♥s t♦ sr♦♣ s♣tt♥
♥ s♦t st ❬❪ s ts sr♦♣ s♣tt♥ r♦♥strt♦♥s
♦ s♦ tt rt tr♦♥t② ♥ tt ♥ ♥ ♥♦t t♦ s
r♦♣♥s ♦rst tt ♥ ♣♣♥ s tt t♦♦ ♠ ♥ ♦rs tr
♥rt♥t② ♥ t r♦♥strt♦♥ t ts s ♦ ♦rs tr ♦ ♥②
♠t♦ ♦r ①♠♣ ♥ r t str ♦♥t♥♥ ♥s
♥ rs♠s r ♥ s ♦rrt② r♦♥strt s ♥rt♥
♥ r ♥ t ♦tr ♥ ♥ r t str ♦♥t♥♥
♥s ♥ s ♥♦rrt② ♥ ♦♥♥t② r♦♥strt
♥ r ♥ tstr♦♣s r ♥♦t t♥ ♥t♦ ♦♥t
ss♥ t
t s ♥ ts st♦♥ r s②♥tt③ s♥ t ♠♦ sr
♥ ♣tr t ♥♦ tstr♦♣s ♥ t s ♠ss♥ t
♣r♠trs ξi i = 1 . . . 20 r r♥ r♦♠ Beta(3, 1) strt♦♥ rstrt
t♦ t r♥ [0.05, 1] s♥ ts ♦rrs♣♦♥s r♦② t♦ t ♣r♦♣♦rt♦♥s ♦
♠ss♥ t ♦sr ♥ r t sts
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3
4
8
19
20
16
5
1415
1
910
2
7
13
17
18
6
1112
0 500 10001500200025003000
9
10
2
13
18
17
7
6
11
12
1
14
15
8
16
20
19
5
3
4
0 500 1000150020002500
r r ♥ ♦♥s♥ss tr ♦r s②♥tt t t s♦♠ t ♠ss♥t t s
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r tr s ♦ t ♣r♠trs ξi i = 1 . . . 20 P♥trs r♦♠ t ♣♦str♦r strt♦♥
r s♦s t tr tr s t♦ s②♥tt③ t t ♥ t
♦♥s♥ss tr r♦♠ ♦r ♥②ss t♦♣♦♦② s ♠♦st ♣rt② r♦♥strt
t ♦♥② ss ♥ tt t t♦♣♦♦② ♦ t str t s ♥
s ♥ r s♦s t tr s ♦ t ξi i = 1 . . . 20 ♥
P ♥trs r♦♠ t ♣♦str♦r s♠♣s t ♣r♠trs r
♦r ② t P ♥tr ♥ ♦♥ s ♥♦t r s♦s tt t r♦♦t
t♠ ♥ t ♣r♠tr µ r s♦ r♦♥strt
s ♥②ss ♦♥ ♥♠♦ s②♥tt t s♦ tt t s♠t
♦♦♥ ♦r ♠♦ ♥ ♦ t s③ tt t②♣② ♦sr ♥ r t sts
♦♥t♥ rt ♦ s ♥♦r♠t♦♥ ♦t t t♦♣♦♦② tstr♦♣
♣♠♥t ♥ ♠♦ ♣r♠trs t st ♦r t ♣r♠tr r♦♥s
♦♥sr
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2600 2800 3000 3200 3400 3600
ROOT TIME
1.9 2 2.1 2.2 2.3 2.4 2.5
MU
r tr s ♦ t r♦♦t t♠ t ♥ ♦ t t ♣r♠trµ st♦r♠s r♦♠ t ♣♦str♦r s♠♣ s s ♥♦t st①♠♣ t s s♠♣② t rst ♦♥ ♥rt
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t♦♠♦ tst♥
❲ t ♦t♦♠♦ t s♦ s r s②♥tt t s♠t ♥r ②
♠♦♦t♦♥ s♥r♦s ♥ r s t♦ ♥t② s♦rs ♦ s②st♠t s
♦rr♦♥
♦rr♦♥ t♥ ♥s s rq♥t ♣♥♦♠♥♦♥ ♦ ♥♦t
♥ ♥ ♦r ♠♦ ♥ t♦ t s ♦ ♦rr♦♥ ♦r ♦r ♦r②
r ♠ ♦r t♥ ♦r ♥r ♦r② ❬♠t♦♥ ❪ sr ♦r
♣♦t♥t s②st♠t s ❲ s♠t t t r♥t s ♦ ♦rr♦♥
♥r t♦ r♥t ♠♦s ♦ ♦rr♦♥ ♦ ♥ ♦ ♠♦ ♦
♦rr♦♥ s s s ♦♦s ♦rr♦♥ ♥ts ♦r t rt bµ ♥
♥ ♦r s♦♠ ♦ ♦rr♦♥ b t ♦rr♦♥ ♥t t t♠ t ♥
♥ l1 ♥ l2 s ♦s♥ ♥♦r♠② t r♥♦♠ ♦♥ trt s ♦s♥
♥♦r♠② t r♥♦♠ ♠♦♥st t♦s ♣rs♥t ♥ ♥ l1 t t♠ t ♥ t
s ♦♣ ♥t♦ l2 t trt s r② ♣rs♥t ♥ l2 t♥ tr s ♥♦ t
❯♥r t ♦ ♠♦ ♦rr♦♥ ♥ ♦r t♥ ♥② t♦ ♥s
❯♥r t ♦ ♠♦ t ♥ ♦r ♦♥② t♥ ♥s s♣t ss
t♥ Tb ②rs ♣r♦s② s Tb = 1000 ②rs ts s r ♣r♦①② ♦r
♦r♣ ♣r♦①♠t② s ♠♦ ♦ ♦rr♦♥ s s♣ ② ♦s ♥
r② ❬❪ ♦ s♦ ♦rr♦♥ ♦r s♠♣ ♠♦ t ❲ ♦♦
t ♦ s b = 0.1 ♥ s b = 0.5 ♦ ♦rr♦♥ ❲ ♥♦t
♦♥sr tstr♦♣ ♦rr♦♥ ♥ ♦♥ ♥ ♦ ♦rr♦ ♠♥②
♦rs r♦♠ ♥♦tr ♥ ♥ s♦rt ♠♦♥t ♦ t♠ s ❲r♥♦ t
❬❪ rsts ♣rs♥t r r ♦r t ♦ ♠♦ rsts ♦r t ♦
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♠♦ r r② s♠r
♠r sts s♥ ts ①t ♠♦ ♥ ♣r♦r♠ ② r♥
t ❬❪ ♦ s♦ ♦♥ tt t s ♦ ♦rr♦♥ ♦ ①♣t
♥ ♦r ♦r② r ♥② t♦ ♥tr♦ s♥♥t s②st♠t s ♥
♥ t♦♣♦♦② st♠ts ♥♥ t ❬❪ s♦ ♥ ♥ ♦ s
♥ r♦♥strt♦♥s ♦r t t s ♦ ♦rr♦♥
♦r b = 0.1 t t♦♣♦♦② s r♦♥strt t ♦♥② ♠♥♦r r♥s
t♥ t tr tr ♥ t ♦t♣t r ts
tstr♦♣s ♥ ♣r♠trs r s♦ ♦rrt② r♦♥strt s s t②♣
s♦ t t ♦ ♦ s ♦ ♦rr♦♥ s ♥ ♥r ♦t ♦ ♥
♦ ♠♦s ♦ ♦rr♦♥ ♦r b = 0.5 t t♦♣♦♦② s sr♣rs♥②
r♦♥strt ♥ t ①♠♣s ♦♦ t ♥ t ♠♦♥t ♦ ♥♦s
♥ t t r ♦r ♦♥ tt ♦r b = 0.5
s②st♠t② ♥rst♠t t r♦♦t ♥ ♦rst♠t t rt
♣r♠trs ② ♣ t♦ r s s ♦ tt ♦♥r♥ t♦ s
s♥ rs♦♥ t♦ tt ♥♦ s s ♦ ♦rr♦♥ ♦rr
♥ t t r ♥②s♥ ♦r ①♠♣ ♥s s ♦t♥ t s ♥
♦rr♦ ♦t ♦ ts ①♦♥ t s st♠t tt ♦ ts ①♦♥ s
♦rr♦ r♦♠ ♦♠♥ ♥s ♠♥② r♥ ♥ t♥ t ♦r t
♦♥② ♦♥t♥s t ♦r ♦r② ♥② ♦ t ♦r ♦r② ♦ ♥s
♦♠s r♦♠ ♦rr♦♥ ❬♠t♦♥ ❪ rtr♠♦r ts ♦rr♦♥s r
s② t♦ tt tr♦ ♣♦♥♦♦ rrrts ♥ r r♠♦ r♦♠ t
t
♥ t ♦tr ♥ r② s ♦ ♦r③♦♥t tr♥s♠ss♦♥ ♥
①♣t ♥ rt♥ tr t sts s s t s♣r ♦ ♦rstr
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(a) (b)
(c) (d)
(e) (f)
r ♥♥ ♦ ♦rr♦♥ ♦ s ♦ ♦rr♦♥ ♥ ts ♦♥ t t♦♣♦♦② ♥ t ♣r♠tr st♠ts s ♦ ♦rr♦♥ st ♦ t♦ r♦♥strt ♠♦st ♦ t t♦♣♦♦②t t r♦♦t ♥ ♣r♠tr st♠ts s♦♥ r ♦r b = 0.5 r s
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♥ ♠r ❬♦ ❪ ♦r ♦ trts ss♦t t s♠ ♥ st r
❬♥s♠♥r ❪ ❲ ♦ tr♦r ①♣t ♦r ♠t♦s t♦ ♣r♦r♠ ♣♦♦r②
♦♥ s tsts
s rsts t qst♦♥ ♦ ♦ tt t sts t
s ♦ ♦rr♦♥ t♦ ♦ ♥♦t ♣rs ♠sr t♦ sst
t strt♦♥ ♦ t ♥♠r ♦ ♥s ♣r ♦♥② ss s♠s ♣
❲ s②♥tt③ t t ♦rr♦♥ b = 0, 0.1, 0.5 ♥ ♦♥ tr s♠♣
r♦♠ t ♣♦str♦r ♦r ♦r ♥②ss ♦ t ♥ t ❬❪ t ♥s
t ♣r♠trs s♦ t♥ r♦♠ t ♣♦str♦r r s t ♠t
strt♦♥ ♦ t ♥♠r ♦ ♥s t ♦♥② ss ♣♣rs
s♦ ♥ t strt♦♥ ♦r t ♥ t ❬❪ t s ♦♥ ♦
①♣t r s ♦ ♦rr♦♥ ♠ ♦♥② sss ♣♣r t ♠♦r s
r s r r♥ t♥ t r♦s r♣s ♥ ♦ s t♦
tt t t ♦rr♦♥ r♣ ♦r ♥ t ❬❪ t s r② ♦s
t♦ t r♣s ♦r s②♥tt t tt ♦r ♥♦ ♦rr♦♥ ♥ ♥ t ♥sts
st♠ts ♦ ♦rr♦♥ ♥ t ♥♦r♦♣♥ ♦r ♦r② ❬♠t♦♥ ❪
t s♦ ♥♦t tt t strt♦♥ ♦ t ♥♠r ♦ ♥s ♣r
♦♥② ss ♣♥s ♥♦t ♦♥② ♦♥ t ♦ ♦rr♦♥ t s♦ ♦♥ t
t♦♣♦♦② ♥ ♦tr ♠♦ ♣r♠trs ♥ ♦rr t♦ tt ♦rr♦♥ ♥ t
st tr♦r sst t♦ rst ♥②s t t t♥ ♦♥strt s②♥tt
t sts s♥ tr ♥ ♣r♠tr s r♦♠ t ♣♦str♦r ♥ t r♦s
rs ♦ ♦rr♦♥
t ② ♥♥ t ❬❪
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2 4 6 8 10 12 14 16 18 20 22 240.4
0.5
0.6
0.7
0.8
0.9
1
Ringe 100
b=0
b=0.1
b=0.5
b=1
r ♠t ♣r♦♣♦rt♦♥ ♦ t ♥♠r ♦ ♥s t ♦♥② ss s s♣② ♦r s②♥tt t t r♦s s ♦ t♦rr♦♥ ♣r♠tr b ♥ ♦r t r t r♦♠ ♥ t ❬❪
♥♥ t♦rs
r ♠♦ ♥♦rs t t tt t t r r♦♣ ♥ ♠♥♥ t♦rs
s s t♦ sr sss
❲ trt ♦♥t sss s ♥ ♥♣♥♥t r♦♠ ♦tr
♦r t s ② tt ♦♥t sss t♥ ♦♥ ♠♥♥ t♦r②
r ♥♦t ♥♣♥♥t ♥ ♣rtr t ♣r♦t② ♦r ♦r t♦ ♦t
s ♣rs♠② r s②♥♦♥②♠ ①sts ♥ t ♥
r ♠♦ ♦s ♦r ♥ t♦ ♥♦t ♥② ♦r ♥ ♥ ♠♥♥
t♦r② s ♥② t♦ ♣♣♥ s♥ r ♥ t ♦r
♦r②
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❲ ss♠ tt t ♦ ♠ss♥ ♥♦r♠② t r♥♦♠ t② t②
♦ ♠ss♥ ♥ ♦s ♥ s qst♦♥ ♠r ♦r ♥
♦♥t ss t s② ♠♥s tt ♦ ♥♦t ♥♦ t ♦rs ♦r
tt ♠♥♥ t♦r② ♥ tt ♥ ♥ t ♥ s②
s♦ qst♦♥ ♠rs ♦r ♦tr ♦♥t sss ♥ tt ♠♥♥
t♦r②
❲ ♥♦t tst ♦r s②st♠t s rs♥ r♦♠ t ss♠♣t♦♥ tt
♠♥♥ t♦rs r ♥♣♥♥t ♦ tst ♦r s②st♠t s rs♥
r♦♠ t ss♠♣t♦♥ tt ♦♥② sss t♥ ♠♥♥ t♦r② r
♥♣♥♥t s♠t s②♥tt t t♥ ♥t♦ ♦♥t t ♠♥♥
t♦r② strtr ♥ tt♠♣t t♦ r♦♥strt t ♣r♠trs ♥ tr
ts ①♣♥s ♦♥ ♥ ♥②ss ② ♦s ♥ r② ❬❪
r ♠♦ ♦r rst♦♥ t ♠♥♥ t♦rs s s♠r t♦ t
♠♦ sr ♥ ♣tr t t♦ ♠♦t♦♥s rst ♥
♠♥♥ t♦rs ❲♥ ♦r ♥ ♥ s t♦ tr t
s t st ♦r ♥ tt ♥ ♦r tt ♠♥♥ t♦r② t s s♠♣②
♥♦r t t ♥t s ♠♥s tt t ♥② ♣♦♥t ♦♥ t tr tr s t
st ♦♥ ♦r ♣r ♠♥♥ t♦r② t s♦ ♠♥s tt t t t rt
s ♦r t♥ t t rt ♥ s♦ s♦ ♥♦t ①♣t ♦r st♠t
♦ t ♣r♠tr µ t♦ ♦rrt ♦♥ s♠t t ♠ss♥ ♥ ♦s
♥ i ♥ ♠♥♥ t♦r② t ♦r tt ♠♥♥ t♦r② t
tt ♦ ♠ss♥ s♠t♥♦s② t ♣r♦t② ξi ♥ t ♦r tt
♠♥♥ t♦r② t tt r ♦rrt② rstr t ♣r♦t② 1 − ξi
ts rs t♦ t ♠♦ t s♥ tr ss♠ tt t r♥t ♦♥②
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45
3
6
17
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7
8
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1314
12
0 500 100015002000250030003500
r r tr ♥ ♦♥s♥ss tr ♦r s②♥tt t t ♠♥♥t♦rs ♠♣♦s
sss ♥ t s♠ ♠♥♥ t♦r② ♦ ♠ss♥ ♥♣♥♥t② ♦ ♦tr
♦t tt st ①♣t t♦ s rs♦♥ st♠ts ♦ ξ ❲ s♠t t
♦♥ tr t s ♦♥str♥ts ♥♦ tstr♦♣s ♥ t µ = 2.2·10−4
t♥ r♦♠ t ♣♦str♦r strt♦♥ ♦ t ♥②ss ♦ t ②♥ t ❬❪
♣rs♥t ♥ ♣tr
r s♦s t tr tr s t♦ s②♥tt③ t s s t
♦♥s♥ss tr r♦♥strt♦♥ s ♦♦ t t♦ sss strtr
♦ t str ♠ ♦ s ♥ s ♥rt♥ t r♦♥ ♥
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♠♦st ♦ t ♣♦str♦r s♠♣s t ♦rrt strtr ♣♣rs ♥ ♦ t
♣♦str♦r s♠♣s ♣♦st♦♥ ♦ s ♥ rt t♦ tt str
s ♥ t ♦rrt strtr ♣♣rs ♥ ♦ t ♣♦str♦r s♠♣s
♥ ♦t ss ts s ♣rs♠② s t tr tr ♦♥t♥s r② s♦rt
r♥ ♦♥ tt ♦r ♥♦ ♥ ♦rr s ①♣t t t rt µ s
♥♦t r♦♥strt t t r♦♦t tr ♥ t ♠ss♥ t ♣r♠trs ξ r
st ♦rrt② st♠t rs ♥ r ts r♦♥strt♦♥s
t ♦t♦♠♦ t r r② ♣♦st
❲ r t♦ ♦rrt② st♠t t r♦♦t ♥ ♦tr ♥tr♥ ♥♦
t♠s s♣t ♦r st♠t ♦ t t rt µ s t ♠♦ ♠s
s♣t♦♥ s ♥♦r♠ ♦r t tr t t t rt s st ♦♥st♥t
♦r t ♥tr tr t s t t t rt tt r♦♥strt ♥ r
rst②
♥ ♦r ♠♦ ♠♣♦s t rrst② ♦♥t♦♥ ν = κλ/µ ♥ ♦rr
t♦ ♦r s②st♠t s rs♥ r♦♠ ts ♦♥t♦♥ s♠t t
t r♥t s ♦ ν ♥ st♠t ♣r♠trs ♥r t rrst②
♦♥t♦♥ r ♥ ♦ ♥♦t ①♣t t♦ t♦ ♦rrt② st♠t
♣r♠trs t ♦♣ tt ♥♦ s②st♠t s ♥tr♦ ♥ t
st♠ts ♦ t t♦♣♦♦② ♥ ♦ t r♦♦t t s♠t s
t ♣r♠tr s µ = 2.23 · 10−4 κ = 0.2 λ = 4.46 · 10−2 ♥ st
ν = 2κλ/µ ♥ ν = κλ/2µ t r s♠t ♦♥ tr t
♥s ♥ ♥tr♥ ♦♥str♥ts
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r ♥②ss s♥ s②♥tt t t ♠♥♥ t♦rs ♠♣♦s tr s ♦ t r♦♦t t♠ tr t ♥ ♦ t t ♣r♠tr µ rt st♦r♠s r♦♠ t ♣♦str♦r s♠♣
r ♦♥strt♦♥ ♦ t ♠ss♥ t ♣r♠trs ξi i = 1 . . . 20 ♦rs②♥tt t t ♠♥♥ t♦rs ♠♣♦s
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1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
0 10002000300040005000600070008000
2
3
4
13
14
6
1
7
12
11
17
18
5
9
8
19
10
20
16
15
79
53
0 10002000300040005000600070008000
r ♥♥ ♦ t rrst② ♦♥t♦♥ t tr tr ♥r t r s♠t ♥r t ♦♥t♦♥ ν = κλ/2µ rt r♦♥strt♦♥s♥ss tr
r♦♥strt♦♥ ♦ t t♦♣♦♦② s ♥♦t t t t♦♣♦♦② s st
♠♦st ♣rt② r♦♥strt s s♦♥ ♥ r ♦r t ♣♦st♦♥
♦ tstr♦♣s s ♠ ♠♦r ♥rt♥ ♥♦ tstr♦♣s r s♣♣♦rt ♥ ♠♦r
t♥ ♦ t ♣♦str♦r trs s♦♥ r ♦r ν = κλ/2µ t stt♦♥
s s♠r ♦r ν = 2κλ/µ
♣r♠trs µ ♥ κ r ♥♦t r♦♥strt s s♦♥ ♥ r
t ♣♦str♦r strt♦♥ s ② ♥♥♦r♠t ♦ κ ♥ t t rt µ s
s②st♠t② ♦rst♠t ♦r t r♦♦t s t ♣r♠tr
♦ ♥trst s r♦♥strt ♦r ν = κλ/2µ t tr r♦♦t s P
♥ t P s P ♦r ν = 2κλ/µ t tr r♦♦t s P
♥ t P s P ♥ ♦t ss t P ♦rs t
tr
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6500 7000 7500 8000 8500 9000 95000
20
40
60
80
100
120
140ROOT TIME
2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8
x 10−4
0
20
40
60
80
100
120
140MU
0 0.2 0.4 0.6 0.8 10
20
40
60
80
100
120
140
160
180KAPPA
6000 6500 7000 7500 8000 85000
20
40
60
80
100
120
140ROOT TIME
2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8
x 10−4
0
20
40
60
80
100
120MU
0 0.2 0.4 0.6 0.8 10
20
40
60
80
100
120KAPPA
r ♥♥ ♦ t rrst② ♦♥t♦♥ ♦♣ t s♠t ♥rt ♦♥t♦♥ ν = κλ/2µ ♦tt♦♠ t s♠t ♥r t ♦♥t♦♥ ν =2κλ/µ ♣♦str♦r s♠♣ r♦♠ t r♦♥strt♦♥ ♥r t rrst②♦♥t♦♥ ν = κλ/µ r tr ♦ t r♦♦t t rt µ ♥ ♣r♦t②♦ t t tstr♦♣ κ
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♦♥strt♦♥ ♦ ♥♦♥ s
rt♦♥ ♦♥str♥ts sr ♥ t♦♥ ♠♣♦s ♦♥str♥ts
♦♥ s♦♠ ♥tr♥ ♥♦s ♥ s♦♠ s ♥ ts st♦♥ ♣r♦r♠ r♦ss
t♦♥ tst ♦♥ ♦♥str♥ts ♥ t ♥ t ❬❪ t
❲ r♠♦ rt♦♥ ♦♥str♥t ♥ tr♥ ♥ tt♠♣t t♦ r♦♥strt
ts r♦♠ t t ♥ t ♦tr rt♦♥ ♦♥str♥ts ♥ t r♠♥
♠② tr ♦♥str♥ts ♠♦♥ ♦♥② ♦♥ ♦ ts ♦♥str♥ts
♦ sr tt ♣r♣♦s s♥ t ♦ t ♦rrs♣♦♥♥ ♥♦ ♦
t② st ♦♥str♥ ② t t♦ ♦tr ♦♥str♥ts ♥ s♦ ♦
①♣t t♦ ♦rrt② r♦♥strt t ♥♦ ♥ ♥② s ❲ tr♦r r♠♦
ts tr ♦♥str♥ts s♠t♥♦s② ♥ st♠t t ♦rrs♣♦♥♥ ♥♦
s ♦♥t②
r sss t ts ①rs ♦♦ ♥t♦r t♦ ♦ ♠ ♥
trst t st♠ts ♦r ♥♦s ♦r tr r ♥♦ ♦♥str♥ts ♥♥
t r♦♦t t♦♣♦♦ ♦♥str♥ts r ♣rt② r♦♥strt
♦tt♦♠ ♦ r s t ♦♥str♥t ♦r ♥♦ s s
P ♥tr r♦♠ t ♣♦str♦r s♠♣ ♦r tt ♥♦ ♥ ♦t ♦
tsts t P ♦r♣s t ♦♥str♥ ♥tr
♦♠ ♦ t P ♥trs r r② r ♥ ♦♥② r② ♦r t
♦♥str♥t ♦r ①♠♣ t ♦♥ ♦r ttt ♦ q♥t② ♦♦♥ss ♦ t ♥
♥ ♣rtr t♦ st♠t t ♣r♦t② ♦r s t♦ ♠ t②♣ rr♦r s
②s t♦rs ♥st ♦ ♣s ♥ rt♦♥ c c ∈ 1 . . . C t
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ΓC−c =C⋂
c′=0c′ 6=c
Γ(c′).
♥♦t t ♥r tr s♣ t t ct ♦♥str♥t r♠♦ t ♦tr
♦♥str♥ts ♠♣♦s t ΓC−cK t ♥r tr s♣ ①t♥ t♦ ♥
tstr♦♣s s ♥ t♦♥ ❲ t♥ ♣r♦r♠ ♠♦ ♦♠♣rs♦♥
t♥ t ♥ ♠♦ t t ♦♥str♥ts MC : g ∈ ΓCK ♥ t
tr♥t ♠♦ MC−c : g ∈ ΓC−cK t t ♦♥str♥t r♠♦
②s t♦r BC,C−c ♦r t ♠♦ ♦♠♣rs♦♥ s t rt♦ ♦ t ♣♦str♦r
♣r♦ts ♦r ts ♠♦s t q ♣r♦r ♣r♦t② ♦♥ t t♦ ♠♦s
P (MC−c) = P (MC) = 0.5
BC,C−c =P (D|g ∈ ΓC
K)
P (D|g ∈ ΓC−cK )
=P (D|g ∈ ΓC
K , g ∈ ΓC−cK )
P (D|g ∈ ΓC−cK )
(since ΓCK ⊂ ΓC−c
K )
=P (g ∈ ΓC
K , g ∈ ΓC−cK |D)P (D)
P (g ∈ ΓCK , g ∈ ΓC−c
K )×
P (g ∈ ΓC−cK )
P (g ∈ ΓC−cK |D)P (D)
=P (g ∈ ΓC
K |g ∈ ΓC−cK , D)P (g ∈ ΓC−c
K |D)
P (g ∈ ΓCK)
×P (g ∈ ΓC−c
K )
P (g ∈ ΓC−cK , D)
=P (g ∈ ΓC
K |g ∈ ΓC−cK , D)
P (g ∈ ΓCK |g ∈ ΓC−c
K )
♥ t st rt♦♥ t ♥♠rt♦r P (g ∈ ΓCK |g ∈ ΓC−c
K , D) s t ♣♦str♦r
♣r♦t② ♦ ♦♥str♥t c ♥ rs♣t ♥ t t ♥r t tr♥t
♠♦ MC−c t ♥♦♠♥t♦r P (g ∈ ΓCK |g ∈ ΓC−c
K ) s t ♣r♦r ♣r♦t② ♦
t s♠ ♥t ❲ st♠t ts ♣r♦ts ② s♠t♥ t ♣r♦r ♥
♣♦str♦r strt♦♥ ♥r t tr♥t ♠♦ t ♦♥str♥t c r♠♦
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st♠ts ♦r t ②s t♦rs r ♣♦tt ♥ t t♦♣ ♦ r
r♥ ♦ ts st♠t♦rs s ♥
st ♥ t r♦sst♦♥ ♦rrs♣♦♥s t♦ str♦♥ ♥ ♥st t
♦♥str♥t ♦♦♥ tr② ❬❪ t ②s t♦r ①♥
2 log(BC,C−c) & 5 s str♦♥ ♥ ♥st t ♦♥str♥t ❲
♦♥t ♦r tr ♦ t trt② ♦♥str♥ts t s ♦ t♦ s rs ♥
st♥ ♥ t ♦ ♦♥ t♦ s ♦r ♥②ss ♥ ♣tr
s♦s tr s ♣♦str♦r ♣r♦t② tt tstr♦♣ ♥t ♦rr
♦♥ t r♥ t♥ rs ♥ ❲s ♥ ♥♦tr t♥ Prs♥
♥ st♥ ♥ ♦r rt tr♦♥t② ♥ rst ♦ t tr s s♦ st
tt ♥ tr② t♦ ♣rt ts rt♦♥s r ♣rt♥ t②♣ ♥ts
♦t tt ♦r ♥♥ ♦ ♠ss♥ t s ♥str♠♥t ♥ ♠♣r♦♥
♦r ♣rt♦♥s rt♦♥ ♥tr ♦r t ttt ♦r② ♥ ts
t s P ♥♦r ♠ss♥ t s♦ r♣ s t s ♦r
♣rt♦♥ ♦r t ♦ ttt s P ♦ts ♦ t ♦♥str♥ts
❲t ♠ss♥ t ♥ ♥ t ♠♦ t P ♥tr ♦r t
♦ ttt ♥ ♦r ♠♦ s P st ♦r♣s t ♦♥str♥t ♥
s r ♠♥ s♦ r ♥♦t ♦♥② tt♥ rtr ♥rt♥t② t s♦
♠♣r♦♥ t t ②s t♦r s ♦s ss t♥ ♥st s♦ t
♥ ♥st t ♦♥str♥t s r② ♦rt ♠♥t♦♥♥ ❬tr② ❪
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8000
6000
4000
2000
0
−100
−10
−5
−2
0
2
5
10
100
HI TA TB LU LY OI UM OS LA GK AR GO ON OE OG OS PR AV PE VE CE IT GE WG NW BS BA IR II TG
r ♦♥strt♦♥ ♦ ♥♦♥ ♥♦ s t♦♣ ♦rt♠ ♦ ②st♦rs log(BC,C−c) ♦r c = 1, 2, ..., C ♦tt♦♠ t♥ ♥s s♦ ♦♥str♥ts♦r r♥t ♥♦s t ♥s s♦ ♣♦str♦r P ♥tr ♦r tr♦♥strt ts ♥ t ♦♥str♥t s r♠♦ ttt ♦r♥ ♦r♥ ❯ ♥ ❨ ②♥ rs ❯ ❯♠r♥ s♥ t♥ r r♠♥♥ ♦t ♦rs ♥s r♠♥ r ♦♥P Prss♥ ❱ st♥ P Prs♥ ❱ ❱ t r♦♣ t r♦♣ r♠♥ r♦♣ ❲ ❲st r♠♥ r♦♣ ❲ ♦rt❲st r♠♥ r♦♣ t♦ r♦♣ t r♦♣ r♥♥r♦♣ ♥♦r♥♥ r♦♣ ♦r♥ r♦♣
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♣tr
♥②ss ♦ ♥♦r♦♣♥ t
sts
♥ ts ♣tr ♥②s t♦ ① t sts ♦ ♥♦r♦♣♥ ♥s
♥ st♠t t ♦ Pr♦t♦♥♦r♦♣♥ s♥ t ♠♦ ♣rs♥t ♥
♣tr ♥ t t ♠♣♠♥t♦♥ sr ♥ ♣tr
♦♥s♥ss trs s♣② ♥ ts ♣tr r t s♥ t s♠
♠t♦ s ♥ ♣tr ♥ tr ♥ ♦rrs♣♦♥s t♦ s♣t ♣rtt♦♥♥
t s ♥t♦ t♦ sts ♦♥s♥ss tr s♣②s st t♦s s♣ts ♣rs♥t ♥ t
st ♦ t ♣♦str♦r s♠♣ ♣ts r ss t♥ s♣♣♦rt
r ❲r ♥♦ s♣t s ♣rs♥t ♥ ♦ t ♣♦str♦r s♠♣ t
♦♥s♥ss tr s ♠trt♥ ♥t s♦♥ ♦r ♥ s t r
♣♦str♦r ♥t ♥ t ①st♥ ♦ t s♣t s♠r② t ♥♠r ♦
tstr♦♣s s♦♥ ♦♥ ♥ s t r ♣♦str♦r ♥♠r ♦ tstr♦♣s
♦♥ tt ♥ t ①st♥ ♦ t s♣t r♦♥ t♦ t ♥rst ♥tr
♥ t ♣r♠trs ♠r♥ ♣♦str♦r strt♦♥ ♦s t♦ ♥♦r♠
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♦r st♠ts s st ♣r♦t② ♥st② ♥trs ♥ t
♥♦r♠ ♣♣r♦①♠t♦♥ s♥ t ♠♥ ♥ t t st♥r t♦♥ ♥ t
♣♦str♦r s♠♣ ♦r t r♦♦t st ♣r♦t② ♥st②
♥trs
♥②ss ♦ t ♥ t ❬❪ tst
s ♠♥t♦♥ ♥ t♦♥ sr t♦♣♦♦ ♥ ♦♥str♥ts r
♠♣♦s ♦♥ t trs r♦♥strt ♦♥ t r♥ ♦ s ♦r ♥str
♥♦s ♥ ♥♥t ♥s tr ♥ r s♦s t ♦♥s♥ss
tr r♦♠ r♦♥strt♦♥ ♥♦rs ts ♦♥str♥ts ♥ ♥ tt♠♣t t♦
r♦♥strt ts ♥♦♥ t♦♣♦♦ ts ❲t♦t ♥② ♥tr♥ ♦♥str♥ts
tr s ♥♦ ♥♦r♠t♦♥ ♦t t rt ♣r♠trs ♥ t st♠ts r
♠♥♥ss ♥ ts ♥②ss t ♦♦ ♦ ♥♥ ② ♠t♣②♥
r♥ ♥ts ② ♥ rtrr② t♦r ν ♥ ♥ t rts ② ν
♠r② t s♥ ♦ ♦♥str♥ts ♠♣s tt tr s ♥♦ s♥ ♦r
tstr♦♣s ♥ s♦ ♥♦ r♥ rs tstr♦♣s ♥ ♠♦r t♥ ♦ t
s♠♣ trs r r tr♦r ♥♦ tstr♦♣s ♥ r ♥ ♦ ♥♦t
s♦ ♥② t♠ s ♦r t r♦♥strt♦♥ ♦ t t♦♣♦♦② s ♥trst♥
♥♥ ♦ t t♥ ♥♦♥ t♦♣♦♦ trs r s♣♣♦rt t ♣r♦t② t
st ♥ t ♣♦str♦r strt♦♥ ♦♥② ①♣t♦♥ s t ♦rt❲st
r♠♥ ♦r♠ ② ♥s r♠♥ ♥ ♦rs
♣♣rs ♥ ♦ t ♣♦str♦r s♠♣
❲ s♦ ♦♥s♥ss tr ♥ r ♦r t ♦♠♣t t ♥②s t
♦♥str♥ts ♥ ♦r t rsts sr r ♦r ♣r♦r ♦♥
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hittite
vedic
luvian
umbrian
armenian
oldenglish
latvian
welsh
albanian
lithuanian
oldnorse
oldprussian
oldirish
gothic
tocharian_a
oldcslavonic
oldhighgerman
greek
avestan
oldpersian
tocharian_b
latin
lycian
oscan
52
65
74
60
57
r ♦♣ ♦♥s♥ss tr ♦r t ♥ t ❬❪ tst t♦t ♥②♥tr♥ ♦♥str♥ts ts r ♠♥♥ss ♥ r tr♦r ♥♦t s♦♥t t t♦♣♦♦② s r♦♥strt ♦tt♦♠ s♠♣ tr s♦♥ t t♦♣♦♦ ♦♥str♥ts ♥ t rs ♦♥ ♥tr♥ ♥♦s r t♦♣♦♦♦♥str♥ts
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r ♦♥strt s ♦ t ♠ss♥ t ♣r♠trs 1 − ξi ♦r t♥ t ❬❪ t st ♣r♦t② ♥st② ♥trs t ♥ ♣r♦♣♦rt♦♥ ♦ ♠ss♥ t ♦r t ♥
t♦♣♦♦s s ♥♦r♠ ♦♥ st♦rs ♥ t ♣r♦r ♦♥ t tstr♦♣ rt
ρ s Γ(1.5, 0.0002) t s♠r rsts t ♥♦r♠ ♣r♦r ♦♥ t♦♣♦♦s
♥ ♣r♦r ♦♥ t tstr♦♣ rt p(ρ) ∝ 1/ρ ♣r♦r ♦♥ ♦tr ♣r♠trs
♦ t ♠♦ s sr ♥ ♣tr r st♠ts ♦r t ♣r♠trs
r s ♦♦s µ = 1.86 · 10−4 ± 3.94 · 10−5 ts②r κ = 0.361 ± 0.11
ρ = 1.3 · 10−4 ± 3.3 · 10−5 tstr♦♣s②r ♦rrs♣♦♥♥ t♦ r t rr
tstr♦♣s ♦t tstr♦♣ r② ②rs ♦r ♥ r ♦ ♦♥
t tr t tstr♦♣ ♦rrs♣♦♥♥ t♦ ②rs ♦ ♥
①♣t♥② ♦ ♦♥② ss ♦♥ r♥ s t♥ 1/(µ+κρ) = 4800 ②rs
s s rtr t♥ t r r♥ ♥t ♦ ②rs s♦ ①♣t ♥
①♣♦s♦♥ ♦ t ♥♠r ♦ ♥s rstr ♦♥② ss ♣♣rs t
r st♠ts ♦ t ♠ss♥ t ♣r♠trs ξi r s♦♥ ♥ r ♦r
♥② ♥ i t ♣♦str♦r strt♦♥ ♦ ξi s qt tt ♥ ♦s t♦ t
♣r♦♣♦rt♦♥ ♦ ♠ss♥ t ♥ tt ♥
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armenian
albanian
oldirish
welsh
luvian
oldnorse
oldenglish
oldhighgerman
gothic
lycian
oldcslavonic
latvian
lithuanian
oldprussian
tocharian_a
tocharian_b
hittite
greek
vedic
avestan
oldpersian
latin
umbrian
oscan
62
78
66
85
58
0 10002000300040005000600070008000
r ♦♥s♥ss tr ♦r t ♥ t ❬❪ tst ♦ts s♦tstr♦♣s s♣♣♦rt t ♣r♦t② ♦ ♦♥
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♥②ss r♦♥strts s♦♠ ♥♦♥ trs ♦ t ♥♦r♦♣♥
tr r ♥♦t ♣rt ♦ ♦r ♦♥str♥ts ♥sts ♥r② r tt
t r♠♥ t ♥ t ♠s ♦r♠ str t♦ t rt
♣♦st♦♥s ♦ t tr ♠s ♥ ts str s st t♦ t r
♥②ss r♦♥strts ts str t ♥♦ ♣rtr ♦♥rt♦♥ ♦ t
rt ♣♦st♦♥s s ♦r ♥♦Prs♥ r♦♣ ♥ ♦ts t
t♦ r♦♣ t t rt ♣♦st♦♥ ♦ ts t♦ s ♥rt♥
♣ t♦♣♦♦② ♦ t tr s t qt ♥rt♥ ② ts t s♣② t
♣♦st♦♥ ♦ ♥♥ ❲ ♥ ♥ ♦r tstr♦♣ rt tr♦♥t② ♥
tr ♣♦st♦♥s ♦♥ t s ♥ t♦ rs Prs♥ ♥ ♥ t
❯♠r♥s♥
r ♣♦str♦r st ♣r♦t② ♥st② P ♥tr ♦r t r♦♦t
♦ t ♥♦r♦♣♥ ♠② s ②rs P ♣♦str♦r
strt♦♥ ♦ ts ② sttst s ♦s t♦ ♥♦r♠
rstrt♦♥ r s ② ♥ t ❬❪ ♥ ♦t♥ tr t
s r R1 r♦♠ t♦♥ t r ♦sr t t st ♦♥
r r♦r ♦ t ♦r rsts r♠♦ s♥t♦♥s trts
r ♦sr t ①t② ♦♥ ♥ t t ♦
♥ ♦t♥ rstrt♦♥ r R2 ♥ ♦♦ ♦♥s♥ss tr s
s♣② ♥ r
♥ ♥r t r♦♥strt♦♥ ♦ t t♦♣♦♦② s s♠r t♦ ♦r ♣r♦s
♥②ss P ♥tr ♦r t r♦♦t s P ♦♥sst♥t
t ♦r ♣r♦s ♥②ss ♣r♠tr st♠ts r s ♦♦s µ =
1.56 ·10−4±2.8 ·10−5 ts②r κ = 0.19±0.11 ρ = 1.01 ·10−4±8.72 ·10−5
♦rrs♣♦♥♥ ♦♥ tstr♦♣ r② ②rs ♦r ♥ r ♦ ♦♥ t
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tr t tstr♦♣ q♥t t♦ TC = 1350 ②rs ♦ ♥
①♣t♥② ♦ rstr ♦r s ②rs ♦♥② ♥♦t♦rt② r♥
s t ♣♦st♦♥ ♦ tstr♦♣s r ♥ r② r♥t ♣s t ♦♥②
♦♥sr tstr♦♣ s t ♦♥ ♦♥ t r♥ ♥ t♦ rs s
s ♥♦t sr♣rs♥ ♥ r t tstr♦♣s r ♦s t♦ t s
Prs♠② t s♥ ♦r ts tstr♦♣s ♦♠s ♥ r ♣rt r♦♠ ♥
♥s ♥♠r ♦ s♥t♦♥s t t♦s s s st ①♣♥ ②
tstr♦♣ ♥t ❲t s♥t♦♥s r♠♦ t s♥ s ♠ r
s ♦♥sq♥ t r♦♥strt tstr♦♣s r s♠r ♥ r ♣
♥ ♣♦st♦♥s r tr s rt tr♦♥t② t ♥♦t s str♦♥ s t rt
tr♦♥t② tt ♥ r s tstr♦♣s r ♣rs♥t ♥ s♦♠
♦ t ♣♦str♦r s♠♣s ♦r t ♥②ss t s♥t♦♥s ♥ t t②
♣♣r ♥ ss t♥ t s♠♣s ♥ r tr♦r ♥♦t s♣② ♥ t
♦♥s♥ss tr ♦ r
♥♦tr t♦♥ ♠t♦ ♦ ♦r rsts s t♦ ① ♣rt ♦ t t
tr ② r♠♦♥ s♦♠ ♦♥② sss ♦r ② r♠♦♥ s♦♠ ♥s
rsts ♦r ts ♥②ss r ♥ ♥ t t♦s ♦r t ♦♠♣t t ♦♥ t
♦♥ ♥ r♠♦♥ s♦♠ ♦♥② sss ♠s ♥♦ s♥♥t r♥ ♥ t
r♦♥strt t♦♣♦♦② ♥ st② ♥rss t r♥ ♦ t r♦♥strt
s ♦♥ t ♦tr ♥ r♠♦♥ s♦♠ ♥s ♥rss t ♥rt♥t②
♦ t t♦♣♦♦② ♥ ♦ t r♦♥strt s s ♥ ①♠♣ r
♣rs♥ts ♦♥s♥ss tr t t ♥s ♥ t ♦♥② sss
① ① trts r ♦s♥ t r♥♦♠ t ① ♥s
r ♦s♥ ♥ ② tt ♥srs tt ♠♦st s♠s r r♣rs♥t
t♦ t t ♠② s ♥♦t r♣rs♥t ② ♥② ♥ ♥ ts ♥②ss
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tocharian_atocharian_b
oldirish
welsh
luvian
oldprussian
lithuanianlatvian
oldcslavonic
albanian
hittite
oldnorse
oldenglish
oldhighgerman
gothic
greek
lycianarmenian
vedic
oldpersianavestan
umbrian
latin
oscan
95
56
59
5958
0 10002000300040005000600070008000
r ♦♥s♥ss tr ♦r t ♥②ss ♦ t ♥ t ❬❪ t ts♥t♦♥s ①
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armenian
oldpersian
hittite
oldprussian
albanian
latin
oldenglish
tocharian_a
tocharian_b
oldcslavonic
greek
welsh
95
87
60
59
59
77
0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000
r ♦♥s♥ss tr ♦r sst ♦ t ♥ t ❬❪ t
t s ♦rt ♥♦t♥ tt ♥ t ♥ ♠♦r t♥ ♦ t ♦♥② sss r
sr s♥ s♦♠ ♦ t r♠♥♥ sss r ♦♥② ♦sr t s
r ① r♦♠ t t
❲t ts r t st tr s ♥♦ s♥ ♦r tstr♦♣s ♥ t ♠♦
♦r t tstr♦♣ t ♣r♦t② κ s t② t ❯♥sr♣rs♥② t
r♥ ♦ r♦♥strt sttsts s r② t P ♥tr ♦r
t r♦♦t s P t t ♠♦ ♦r ts sttst s ♦s t♦ t
♠♦ ♥ ♥②ss t t ♦♠♣t t ♠r② t t ♣r♠tr µ
s r♦♥strt s 1.35 · 10−4 ± 9.2 · 10−5 ♠ rtr r♥ t♥ ♥
♣r♦s ♥②ss rsts r s♠r ♥ ♦♥② ♦♥② sss ♦r ♦♥②
♥s r ① t♦ t r♥ s ♥♦t s r
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♥②ss ♦ t ②♥ t ❬❪ t
r ♣rs♥ts ♦♥s♥ss tr ♦r t ♥②ss ♦ t ②♥ t ❬❪
t ♥r ♦r st♦st♦♦ ♠♦ r st♠ts ♦r t ♣r♠trs r
s ♦♦s µ = 2.37 · 10−4 ± 2.16 · 10−5 ts②r κ = 0.121 ± 0.096
ρ = 2.17 · 10−4 ± 1.2 · 10−4 tstr♦♣s②r ♦rrs♣♦♥♥ t♦ s♠r t
♠♦r ♦♠♠♦♥ tstr♦♣s t♥ ♦r t ♥ t ❬❪ t ♦t
tstr♦♣ r② ②rs ♦r ♥ r ♦ ♦♥ t tr t
tstr♦♣ ♦rrs♣♦♥♥ t♦ ②rs ♦ ♥ ①♣t♥② ♦
rstr ♦r s ②rs ♥ rtr t♥ t r r♥ ♥t ♦
②rs
♥②ss ♦ t ②♥ t ❬❪ t str♦♥② s♣♣♦rts ♥♦r♥♥
s ♥ ♦tr♦♣ t s♦ s♣♣♦rts t r♠♥ ♥ t s♠s ♥
s♥s t t s t ♥①t ♦sst ♦s♥ t♦ t ♦♥rt♦♥s
r♠♥t ♥ tt r s♦ ♣rs♥t ♥ t ♣♦str♦r t ♦t
♣♦str♦r ♣r♦t② ♥ t ♦tr ♥ t ♥②ss ♦ t
♥ t ❬❪ t ♦s ♥♦t s♣♣♦rt ♥② ♣rtr ♦tr♦♣ ♥ t
s♦s ♣rr♥ ♦r r♠♥t sr♦♣♥ r ♥ t ♦tr
♦♥rt♦♥s s♦ ♣♣r ♥ t ♣♦str♦r s♠♣ ♥ ♥♦♥♥ rq♥s
♥ ♦t ss t ♣♦st♦♥ ♦ ♥♥ s r② ♥r r s r♠♥t
t♥ t ♥②ss ♦r t ♦tr t♦♣♦♦ trs ts s♦ ♦rrs♣♦♥
t♦ t rsts ♥sts ♦t♥ tr♦ t ♦♠♣rt ♠t♦
r s rt tr♦♥t② ♥ ♥♠r ♦ ♣♦st♦♥s ♣r②
s♦♠ ♦ ts ♣♦st♦♥s ♦ ①♣t ♦r ①♠♣ r♥ r♦s
P♥♥s②♥ t ♥ t ②♣s② ♥ ♦ r ♥t tr♦ s♦♠
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rt tr♦♥t② ♦ ♥ t♦ t r ♦r♣ st♥
r♦♠ tr ♣r♥t ♥ ❲ ♦ ♥♦t ♥ ①♣♥t♦♥ ♦r t ♦tr
tstr♦♣s t♦ t② r str♦♥② s♣♣♦rt ♥ ♦r ♥②ss ❲ ♥♥♦t
♦♠♣r t ♣♦st♦♥ ♦ tstr♦♣s ♥ rs ♥ s t
tstr♦♣s ♥ r ♦r ♦s t♦ t s ♥ t ♥s
s ♥ t t♦ ♥②ss r r♥t ♦r tr s ♦♥ tstr♦♣ ♣
♥ t tr ♥ ♦r ♥②ss ♦ t ♥ t ❬❪ t t s♥t♦♥s
r♠♦ r ♦♥ t r♥ ♥ t♦ t str ♦♥t♥♥ t
r♠♥ t ♥ t ♥s ♥trst♥② ts s s♦ ♦♥ ♦ ♦♥②
t♦ tstr♦♣s ♣ ♥ t tr ♥ ♦r ♥②ss ♦ t ②♥ t ❬❪ t
♥②ss ♦ t ②♥ t ❬❪ t s st ♣r♦t②
♥st② ♥tr ♦r t r♦♦t ♦ P t s♥♥t ♦r♣ ♦
♦r st♠ts s♥ t ♥ t ❬❪ t
②♥ t ❬❪s t r rstr ② r② ♥ t♥s♦♥ ❬❪
♦♦♥ rstrt♦♥ r R2 t② sr s♥t♦♥s s♦ t s ♥♦t
♣♦ss t♦ t ♦r rsts ② ♥②s♥ t t ♥r r♥t
rstrt♦♥ r ♦r s ♣r♦s② t ♦r rsts ② s♥
♦♥② ssts ♦ ♦r t ♥ s ♣r♦s② ts t♦ s♠r rsts s t
t ♦♠♣t t ♦♥② t rtr ♥rt♥t②
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Persian_List
Waziri
WakhiBaluchi
Tadzik
AfghanOssetic
Khaskura
MarathiBengaliNepali_List
Gujarati
Panjabi_ST
KashmiriGypsy_GkSinghalese
Lahnda
Hindi
LatvianLithuanian_STLithuanian_O
Czech
Byelorussian
Slovenian
Lusatian_L
Czech_E
UkrainianRussian
Slovak
SerbocroatianMacedonian
Lusatian_U
Polish
Bulgarian
Albanian_TopAlbanian_G
Albanian_T
Albanian_KAlbanian_C
Swedish_List
FaroeseIcelandic_ST
Swedish_UpSwedish_VL
RiksmalDanish
English_STTakitaki
Frisian
Penn_Dutch
Afrikaans
German_ST
Flemish
Dutch_List
Armenian_ModArmenian_List
Sardinian_C
Romanian_List
Sardinian_LVlach
Sardinian_N
Brazilian
Walloon
Ladin
French_Creole_D
Portuguese_STProvencal
French
CatalanSpanish
French_Creole_C
Italian
Breton_SE
Welsh_C
Breton_List
Breton_ST
Welsh_N
Irish_BIrish_A
Greek_ModGreek_ML
Greek_D
Greek_MD
Greek_K
TOCHARIAN_BTOCHARIAN_AHITTITE
76
81
94
94
72
67
72
95
84
93
61
77
77
0 10002000300040005000600070008000
r ♦♥s♥ss tr ♦r t ②♥ t ❬❪ t st
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♣tr
♦♥s♦♥s ♥ ①t♥s♦♥s
r tt♠♣ts t t♥ Pr♦t♦♥♦r♦♣♥ s♥ sttst ♠t♦s
♥ ♠ ♣r♦s② s ♠♥t♦♥ ♥ ♣tr ♦r s♦♠ ♦
t ♠♦s s r r② ♥♦t ♣t t♦ ① t ♥ ♥♦♥ ♦ ts
♠♦s ♥ ② t ♠♦ sr ♥ ♣tr
♥ ♠♣♠♥t s s ♥ ♣tr s s♣② t♦r t♦ ①
t Ps s♦rs ♦r s②st♠t s r tr ♥♦r♣♦rt ♥ t ♠♦
♦r ♥ tst ♦r s♥ s②♥tt t tr ② s ♥ ♣tr ♦r ♥
♣r♦s ♦r ♦st s♥♥t② s♦ tt ♦rr♦♥ t t s
tt ①♣t ♥ ♦r t ♦s ♥♦t s ♦r st♠ts
r♦♥strt♦♥ ♦ ♥♦♥ s ♣rs♥t ♥ t♦♥ rtr ts
♦r t② t♦ ♣rt t♠ ♣ts tr sr ♥②ss ♦ t♦ t sts
♣tr ♦r rsts r t t ♥t♦♥ ②♣♦tss tt t s♣r
♦ t ♥♦r♦♣♥ ♠② strt r♦♥ P ♦♥ ♦ ♦r ♥②ss
r t t r♥ t♦r② tt t s♣r strt t♥ ♥
P
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rsts ♣rs♥t ♥ ts tss s♦ ♦ ♣r♦♠s♥ sttst ♠♦s
♦ ♥ rst♦♥ r t♦ ♠ ♦ t ♦rt s♦ r s ♥
♥ ♦♣♥ ♠♦s ♦ ① t t ♦ q② ♥trst♥ t♦
t♦ ♦rrt② ♥ t r② rs s♣ts ♦ ♥st t ♠♦s
♦ r♠♠t ♥ ♣♦♥♦♦ t s s ♠♦s ♦ ♦♥tt♥
♥ rtr t♥ s♥t t ♠♦t♦♥ ♦ r② s t♦ ♣
rtr ♦r ♥rst♥♥ ♦ ♥ st♦r②
s ♠♦s r② ①st ♥ ♥ ♠♥t♦♥ ♥ t♦♥
t ♦ ♦ ♣rtr ♥trst t♦ t♦ r♦♥ t r♦s s♣ts ♦
♥ ♥ s♣t t r♥t ♠♥s♠s t ♣② ts s♣ts r
♥♦t ♥♣♥♥t ♦ ♦tr ♥ ♠st st s♠t♥♦s②
r t♦ ♥rst♥ t ♦ ♣tr ♦ ♥ rst♦♥
s ♠♦s ♦r ①t♥s♦♥s ♦ ts ♠♦s ♦ s♦ s t♦ ♥
♥♦ ♦♥ t ♥str ♥s t♠ss ♥ t♦ t ♥♦s
♦♥ t trs r♦♥strt ♦ ♥♦t ♦rrs♣♦♥ ①t② t♦ ♥② ♥s ♦
♥trst t② r ♦s② rt t♦ s ♥s ♦♥strt♥ ♥str
sq♥s s ♥ t st ♦ ♠ rsr ♥ ♠♦r ♣②♦♥ts
❬t ❨♥ t ❪ ♥ ♣rtr ♠♥② ♥sts r ♥trst ♥
r♦♥strt♥ trs ♦ t ♥ s♣♦♥ ② t Pr♦t♦♥♦r♦♣♥s
❬r ❪ st♠t♥ ♦♥ts r ♣rs♥t t t r♦♦t ♦ t
trs s♠♣ ♦ ♣r♦ ♥♦r♠t♦♥ ♦t ts Pr♦t♦♥ ♥ t
♦ ♦ rt ♥trst t♦ ♦♠♣r ts r♦♥strt♦♥s t♦ t♦s ♦t♥ ②
♥sts s♥ t ♦♠♣rt ♠t♦ ❬s ❪
rsts ♣rs♥t ♥ ♣tr ♥t tt ♦r ♠♦♥ ♦ tstr♦♣
rt tr♦♥t② s stst♦r② ♥ t stt♥ st ♦ ♣♣② t t♦ ♦tr
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stt♥s ♦r t ♠② ♥ssr② t♦ ①♣♥ ♦♥ t ♦r ①♠♣ t ♠②
♥trst♥ t♦ ♠♣♦s tt tstr♦♣ ♦r s♠t♥♦s② ♦♥ r♥s
t t s♠ t♠ ♦rrs♣♦♥♥ t♦ ♥ ♥t tt ♠♣ts ♥s t ♠②
s♦ ♦rt② t♦ ♦ ♥t tstr♦♣s ♦r ♣r♦s ♦ t♠ r♥
♥♦ ♥ ♦rs ♠♦st ♦♦s ①t♥s♦♥ s t♦ ♦ tstr♦♣s
t♦ r♥t s③s ♦♠ ♦ t ♦r ♥ ♠♦r ♣②♦♥ts ♠♥t♦♥
♥ t♦♥ ♠② r♥t
♥ t ♦♦♥ st♦♥s tr ♣♦ss ①t♥s♦♥s ♦ ♦r ♠t♦s
sss t ♦t♦♥s ♠♦s② rs ② rs♥ ♥ ❱♦t ❬❪ ♥st
♦tt♦r♦♥♦♦② r♦♥strt t s♣r ♦ ♥ ts ♥ ①♠♥ t
②♣♦tss tt ♣♥tt♦♥ rsts t ♥ s♣tt♥ ♥ts ♦♥t
♦r r ♠♦♥t ♦ ♥st ♥ rtr ♦r s ♥ t♦ ttr
♥rst♥ ♥ t t s ♣rs♥t ♥ ts ♣tr
st♥ s♦♠ ①tr♠ ①♠♣s st ②
rs♥ ❱♦t ❬❪
s ❬❪ ♦♣ ♠t♦ ♥♦♥ s ♦tt♦r♦♥♦♦②
♠ ♦ s t♦ t t ♠♦st r♥t ♦♠♠♦♥ ♥st♦r ♦ ♥② t♦
rt ♥s ② t♥ t ♣r♥t ♦ sr ♦♥ts ♥ t
♦r ♦r② s s t rst tt♠♣t t t♥ ♥♥t ♥s t
♠t♠t ♠t♦s s ❬❪ ss♠ tt t ♦r ♦r②
♦ t ♦♥st♥t rt t t♥ ♦♦s ♠♠t② tt C s t
♣r♥t ♦ sr ♦♥ts ♥ r t rt♥t♦♥ rt t♥ t ♦ t
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♠♦st r♥t ♦♠♠♦♥ ♥st♦r s t = log C
2 log r ♦♥st♥t r s st♠t s♥
♣r ♦ ♥s ♦r t ♦ t ♠♦st r♥t ♦♠♠♦♥ ♥st♦r s
♥♦♥ ♦tt♦r♦♥♦♦② ♠♥② s♦rt♦♠♥s r♦♠ sttst ♣♦♥t ♦
t ♠♥ sss r tt tr s ♥r ♥② tt♠♣t t♦ t t
♥rt♥t② ♦ t st♠t♦rs ♥ tt r ♠♦♥ts ♦ t r ♥♦t s
rs♥ ♥ ❱♦t ❬❪ str♦♥② rt③ ♦tt♦r♦♥♦♦② ♥ tr
rsr s t t ♦r♥ ♦ t str♦♥ s ♠♦♥st ♥sts ♦ ♥②
sttst ♠t♦ ♦r t♥ ♥♥t ♥s rs♥ ♥ ❱♦t ❬❪
s tr sts ♦ rt ♥s ♥ ♥ tr ♦r♥ ts
t② ♦♠♣r t♦ sr rs♦♥s ♦ t ♦♠♠♦♥ ♥st♦r ♦rs
♦r♥ ♦r♥ ♦r♥ ♥ ♥r♥ tr rt♥ ♥s
♥ ♥ ♦r♥ r♠♥♥ ② st♠t t rt♥t♦♥ rt r ♦r
st ♥ ♦t♥ r② r♥t s s s t♥ t♦ s♦ tt tr s
♥♦ ♥rs ♦♥st♥t rt♥t♦♥ rt ♥ tt tt♠♣ts t t♥ r tr♦r
♣♦♥tss
♠t♦s sr ♥ ts tss ♥ ♥ ♦tr r♥t ♦rs ♦♥
t♥ ♥♥t ♥s ♣rs♥t sr ♥ts ♥ ♦♠♣r t♦
♦tt♦r♦♥♦♦②
t s t r② ♥tr ♦ ②s♥ st♠t♦♥ t♦ ♦♠♣t ♥rt♥ts
P②♦♥t ♠t♦s ♦ s t♦ ♥ t r♦♠ ♠♥② ♥s
rtr t♥ ♦♥② t♦
♠t♦ sr ② s ❬❪ ♥ s ② rs♥ ♥
❱♦t ❬❪ ♦♥② ♦ ♦♥ ♦♥② ss ♣r ♠♥♥ t♦r② ❲r
tr s ♣♦②♠♦r♣s♠ s♦♠ ♥ ♦s♦♥② ♠♦st ♦ t t t♦
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♥♦r
rsr ② rs♥ ♥ ❱♦t ❬❪ s st ② ♠♥② ♥sts
s ♥ ss tt ♥♦ t♥ ♠t♦ s♦ r s ♠♥ t♦ r♠♥t ♦r
①♠♣ t ❬❪ stt tt ♥♦♥ ♦ ❬rs♥ ♥ ❱♦ts❪
♦t♦♥s ♥ t② ♠t ② r♥t ♦r
♣♦♥ts ♠ ② rs♥ ♥ ❱♦t ❬❪ ♣ rt ♥
♣tt♥ ♦rr t s ♦ ♦tt♦r♦♥♦♦② t tr ♠t♦s s♦ sr
r♦♠ rs ♠ tr ♣♦♥t ss ♦r ♥ ts ♣tr s♦
tt ♠♦st ♦ t sss rs ② rs♥ ♥ ❱♦t ❬❪ ♦ ♥♦t ♣♣② t♦
♦r ♠t♦s ❲ t ts ♦r t Prs♥t P ② ♣rs♥t
♠♥ t t♠ t t t r r♦r s ♥ t ♣♣r♦①♠t②
rst st ♦ ♥s ♥②s ② rs♥ ♥ ❱♦t ❬❪ ♥s
♦r♥ ♥ ♦r♥ s♠ ♥ t ♦r♥ ts ♦ st
♥ ♥♥s s s rs♦♥s ♦ ♦rs t t t ♥ t
♥tr② ♦rs ♥ ♦rs ❲ ♥♦r ♦rs ♥ ts
♥②ss s t ♦ ts ♥ s ♥♦t r ♥♦♥ t♦♣♦♦②
♦ t ♦tr ♥s s s♦♥ ♥ r ♦t tt ♥ t ♥♥t
♥s ♥ ♦tr ♣trs ♦ ts tss t rs♦♥s ♦ ♦rs r ♥♦t
s ♥♦r r t② t ♠♦st r♥t ♦♠♠♦♥ ♥st♦r ♦ st ♦ ♥s
tr t② r ss♠ t♦ ♦♥ t ♠♦♦t r♥ s s q♥t
t♦ ♦♥ ts ♥s s s t t r♥ ♦ t♠ ♥ ♥t
s ♥ r ♥ t t ♥tr② ♦rs s r② ♦s t♦ t ♠♦st
r♥t ♦♠♠♦♥ ♥str ♦ ♦r♥ ♥ s♠ st ♥ ♥♥s
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Icelandic
Riksmal
Sandnes
Gjestal
X XI XII XIII
r ♥♦♥ t♦♣♦♦② ♦ t t st ♥s ♦ t ♦rs ♠②❳ ❳ ❳ ❳ t t t ♥ t ♥tr② ♦rs
OldNorse10
OldNorse11
OldNorse12
OldNorse13
Icelandic
Riksmal
Gjestal
Sandnes
0 200 400 600 800 1000
r ♣rs♥tt♦♥ ♥ rt ♦ t ♥♦♥ t♦♣♦♦② ♦ t ♦rs♠② ♦t tt t r♥s ♥ t♦ t ♥str ♥s ♥t
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rs♥ ♥ ❱♦t ❬❪ ♠ tt ♥ s st t♦ ♠♦st ♥♦
♥ t♥ t t ♥ t ♥trs ♥ ♣rtr t② ♠ tt
♥ t t r rstrt t♦ t s♦rtr s st ♥ ♥ ♣♣♥①
t st ♦ ♦♥② sss ♦sr ♥ ♦r♥ ♥ s ①t② t st
♦sr ♥ t ♥tr② ♦rs s s tr ♦r t t t② ♦t
t ♦♥② s tr ♦r st ♦r ♦r♥ ♥ ♥s ♦rs
t② sr s rr ♥ trr② ♥ r ♥ t ♥♦t s ♥②♠♦r
♥ s♣♦♥ ♥ s ♦s ♥st st ♣rt ♥ ♥st t ♦t♦♥
❬s ❪ ♥ ♦r ♥②ss ♦rs ♦♥② ①st ♥ trr② ♥ r
trt s s♥t ♥ tt ♥ ❲ s♦ ① trr② ♦rs ♥ t ♦tr
♠♦r♥ ♥s t ts r ♠ ss rq♥t ♣rs♠② s ts
♥s ss ♦ trr② trt♦♥
♦tt♦r♦♥♦♦② s ♦♣ ② s ❬❪ ♥ s ② rs♥
♥ ❱♦t ❬❪ ♥♦t ♦ ♦r ♣♦②♠♦r♣s♠ sr ♦rs ♦r ♦♥
♠♥♥ s②♥♦♥②♠s r ♥ s ♥ ♥ rs♥ ♥ ❱♦t ❬❪
♦♦ ②♠s ❬❪s t♦ t♦ss ♦♥ t♦ ♦♦s ♦♥ t♦ ♣ ♥
t♦ rs♥ ♥ ❱♦t ❬❪ r ♥♦t t♦ ♥ ♣♦②♠♦r♣s♠ t②
st st ♦rs ♦r ♥ ♠♥♥ t♦r② ♥ r② ♥ ♥ tr
♦r sts ❲♥ ♦ ♣ t t ♥ ♥r② ♦r♠t r tr♦r
t♦ ♥ ♦rs ♥ ♥ ♠♥♥ t♦r② ♦r r② ♥ ❲rr
rs♥ ♥ ❱♦t ❬❪ ①♣rss ♦t ♦♥ t ♣rs♥ ♦ ♦♥② ss
♥ ♥ st tt t ♣♦♥t s ♠ss♥ ❲ ① ♥♦♥
♦rr♦♥s ♥ trt ♦rr♦ ♦rs s s♥t ♥ ♦♥ ts ♦♦
t♦ t st ♦ ♦r t② t st♥r ♣r♦r ♦r rstrt♦♥ t s ②
♥ t ❬❪
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♥ t ts t ① s♦ ①♣t ♥ t♦
①♣r♥ ss ♥ t♥ r ♥ tr s st♦♥ s ♥
t t ♥②s ② rs♥ ♥ ❱♦t ❬❪ t ♥s t② st
r ♦s♥ s t② r ①♣t t♦ ①♣t♦♥s t♦ s ❬❪s
rt♥t♦♥ ♦♥st♥t ts st♦♥ s s r② ♥ ♣♦♥t ♦t ② ♥♦
❬❪ ♠♣♦rt♥t qst♦♥ s tr ts rt tr♦♥t② s s♦ str♦♥
s t♦ ♣r♥t s r♦♠ ♦rrt② st♠t♥ t ♦ ♥tr♥ ♥♦s
♥ t ♥②ss ♣rs♥t ♥ ts st♦♥ ♥♦t ♥ tstr♦♣
rt tr♦♥t②
r ♠♥ ♥trst ♥ ♣tr s ♥ t♥ ♥str ♥♦s ♠♥
qst♦♥ t ts t s tr♦r tr r t♦ r♦♥strt t
♥♦♥ s ♦ ♥♥t ♥s ♥ t r♥t rs♦♥s ♦ ♦rs r
♥ ♦s sss♦♥ r♠♦♥ t ♦♥str♥t ♦♥ ♦♥ ♥ ♥ tr②♥
t♦ r♦♥strt ts s ♥ t♦♥ ♦r t ♥ t ❬❪
t srs tt ♣r♣♦s t r♦♥strt♦♥ ②s ♦r t ♦♥str♥t
s tr r ♦♥str♥ts ♦♥ t ♦tr ♥s t② st
♦♥str♥ t ♥s ♠♦♥ ♦♥str♥ts t t s♠ t♠ s
♦r t r♠♥ ♥ ts ss ♥ t♦♥ s ♥♦t ♣♦ss
s♥ ♦ t♥ ♥♦ ♦♥str♥ts t ♥ tr♦r ♥♦ ♠♥s ♦
st♠t♥ t ♣r♠trs ♥ s ♥st ♥②s t st rstrt
t♦ ♦♥② t ♥tr② ♦rs ♥ t ♠♦r♥ ♥s ♥ ① µ =
1.86 · 10−4 t ♠♥ r♦♠ ♦r ♠♥ ♥②ss ♦ t ♥ t ❬❪
t ♣rs♥t ♥ ♣tr ttr t♦ ss ♣rt ♣♣r♦ ♦
♥ t♦ r s♠♣s r♦♠ t ♣♦str♦r strt♦♥ ♦r µ
s♠♣ ♥ t♦♥ ts ♦ ♥rs t st♥r t♦♥ ♦
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♦r st♠t ♦ t ♦ ♦rs ❲ ♥♦r t ♥♦♥ ♦♥str♥t
♦♥ ♦rs ♥ tt♠♣t t♦ r♦♥strt t ♦ ts ♥♥t ♥
♦♥str♥t s P ss♠♥ t t r ♦t ♥
♥ t P ♥tr ♦r t r♦♥strt s P ♦♠♣t②
♦r♥ t ♦♥str♥t s s♦s tt ♥ ♦♥ ♥ ♥s t
r② r♥t rt t ♣rs♥ ♦ sr ♥s st ♦s s t♦ ♦rrt②
r♦♥strt t ♦ ♥♥t ♥s tr t♥ s ♦ µ t♥
r♦♠ t ♣♦str♦r s♠♣ ♦ ♥♦tr ♥②ss t ♦ ♥trst♥ t♦ t ♥
♦♥str♥t ♦r ♥♦tr ♥tr♥ ♥♦ ♦ t tr s s t ♠♦st r♥t
♦♠♠♦♥ ♥st♦r t♦ s♠ ♥♥s ♥ st ♥ s ts ♦♥str♥t
t♦ ♦♥t② st♠t µ ♥ r♦♥strt t ♦ ♦rs ♥♦rt♥t②
♥♦ s t♠♣♦r ♥♦r♠t♦♥ t ♦r s♣♦s
rs♥ ♥ ❱♦t ❬❪s ♣♦♥t r♠♥s ♥ tr② t♦ r♦♥strt
t ♦ r♥ t♥ t ♥tr② ♦rs ♥ ♦r♥
♥ s♦ ♦ ♥t t♥ ♥ ②rs ❲ ♥②s t t
t s♠ ♥♥s ♥ st ♦♥str♥ t♦ ♠♦r♥ s ♥ t
t ♥tr② t♠ ♦♥str♥ts ♦♥ t r♥ts ♦rs ♦ ♦rs t
♦ t ♦ ♥ t♦ r② P ♥tr ♦r t ♥t ♦
t r♥ t♥ t ♥tr② ♦rs ♥ ♦r♥ ♥ s
②rs r r♦♠ t ♦rrt r♥ tr t♦ ♣rt t ♦ ♥
♦ ♥ ts s♣t t ♥♥s ♦ rs♥ ♥ ❱♦t ❬❪
r ♦♥r♠ ♥ ♥ t r② ♦ rt ♦♥tss ts ♦
rt ♦♥ ♦♥ r♥ ♦s ♥♦t ♠♣t s♥♥t② ♦r st♠ts ♦ ♦r s
♥ ♣r♠trs t st♠t♦♥ s ①♣♦s t♦ rr♦r ♦♥ t r♥
rs t r♦♦t s ♠♦r r♦st
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♥② ♥②s t ♦♠♣t t t ♦♥str♥ts ♥
♥ t t♦♣♦♦② ♥ t ♥♦ s r ♥♦♥ t ♦♥② ♣r♠tr ♦
♥trst s t t rt µ st♠t t µ = 2.47 · 10−4 ± 4.0 · 10−5
ts②r s s ♥ ♥ t t st♠ts ♦r t ♥ t ❬❪ ♥
②♥ t ❬❪ t sts ♣rs♥t ♥ ♣tr ♠♥ s µ = 1.86·10−4
♥ µ = 2.37 · 10−4 rs♣t② ♠♠r tt ♥ ♥ ♦rs
r ♦s♥ ② rs♥ ♥ ❱♦t ❬❪ s t② r t ♠♦st ①tr♠
①♠♣ t② ♦ ♥ ②t ♦r st♠t ♦ µ s ♥ t s♠ r♥ s ♦r ♦tr
t sts ♥ r t♦ r♦♥strt t ♦ t ♥tr② ♦rs
s s ♦♦ ①♠♣ ♦ t ♠♥ ♥t ♦ ♠♦r♥ ♣②♦♥t ♠t♦s
♥st ♦tt♦r♦♥♦♦② t t② t♦ ♥ ♠♥② ♥s ♥ ♥ ♥②ss
♠♥s tt t ♥tr r♥ ♥ rts ts r ♦t ♥ ♥ st
♦♠♣t st♠ts
s♦♥ t st st ② rs♥ ♥ ❱♦t ❬❪ ♦♠♣rss
♦r♥ t ♥tr② ♦r♥ ♦r♥ ♥ ♥r♥ ♥ s♣♦♥
♥ ❲st ♦r ♦r♥ ♦r♥ s ss♠ t♦ s♥ rt② r♦♠
♦r♥ ♦ ts ♠♦st r♥t ♦♠♠♦♥ ♥st♦r t ♥r♥ s ♥♦t
♥♦♥ t t ♣r♦② s t♦ ♣ ♥ t st ♠♥♠ ♦r♥
t♦ rs♥ ♥ ❱♦t ❬❪ ♥ ♥②② ♦r t t ♥tr② ❨t
♥ t② s ♦tt♦r♦♥♦♦② ♦♥ t ♣r ♦r♥ ♦r♥♥r♥
rs♥ ♥ ❱♦t ❬❪ r♦♥strt ♥ ♦ ♦t P ♥ t
t ♥tr② t② ♠ t♦♦ ②♦♥
♥ ts s t s s② t♦ s ② t r♦♥strt s ♦ t ♠r
tr♦ s t♦r♠♥t st♦r② ♥r♥ s ♦rr♦ ♠♥② ♦rs r♦♠
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♦r♥ s s s② t s ts ♦rs ♥ tt t♥s t♦
tr rrr ♣♦♥♦♦ rtrsts ♣② rs♥ ♥ ❱♦t
❬❪ s♣② ♦rs ♥ ♦rr♦ t t② ♦ ♥♦t sr
t♠ r♦♠ tr t s♦ r t♦ rstr t t s♥ t s♠
st♥r ♣r♦r s ♥ t ❬❪ ①♥ ♦rr♦♥s r♦♠ ♦r t
r♠♥t ♦r ①♥ ♦rr♦ ♦rs s qt r ♥ ♥r♥
♦rr♦ ♦r r♦♠ ♦r♥ t ♦r♥ ♦r ♠st r② ♦t
♥ ♥r♥ trt♥ ♦rr♦ ♦rs s ♣rs♥t ♥ t t ♦ tr♦r
s②st♠t② ♥rst♠t t t rt µ ❲ ♦♥ ♥ ① t t
♣r♠tr µ t♦ t ♠♥ r♦♠ ♦r ♥②ss ♦ t ♥ t ❬❪ t
µ = 1.86·10−4 P ♥tr ♦r t ♦ t ♠♦st r♥t ♦♠♠♦♥
♥st♦r t♦ ♦r♥ ♥ ♥r♥ s P ♦♥s ♠♦st
①t② t t st ♠♥♠
❲ r ♥♦t t♦ s t tr st ♦ ♥s st ② rs♥
♥ ❱♦t ❬❪ s t ♦♣ r♠♥♥ ♥ ♦r♥ r♠♥♥
s t ♦r sts r ♥♦t r ♥♦ t♦ tr♥sr ♥t♦ ♥r②
t rs♥ ♥ ❱♦t ❬❪ ♠ tt ts ♥♦tr s r ♥s
♥ t rt s♦r t♥ s ♦r t r♠♥t ♦r ♥♥
♠♥② ♥s rtr t♥ ♦♥② t♦ st ♦s ♥ t ♦ ♥trst♥
t♦ s tr tr rsts r ♥t t ♦tr rt ♥s ♥ t
s♠ ♥②ss
❲ rt♥② ♦ ♥♦t sr t rs♥ ♥ ❱♦t ❬❪ tt tr
s rt② ♥ t ♥♠r ♦ ♥s tt ♦r ♣r ♠♥♠ ♥ r♥t
♥s ♦r ts rt② s t♥ ♥t♦ ♦♥t ② st♦st ♠♦s
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♥ ♥ ♥r t ♦s ♥♦t ♥r ♦r t② t♦ t ♥str ♥s ♦r t♦
r♦♥strt t ♠♦ ♣r♠trs t ①♣♦ss s ♠♦r t♦ rr♦rs ♦♥ s
t tt s ♥♦t ♥ st♠t♦♥ ♣r♦♠ ♦ rt ♥trst t♦ s
♥ tr ♦♥s♦♥s rs♥ ♥ ❱♦t ❬❪ ♠ tt t rt
tr♦♥t② t② ①t ♣r♥ts sttst ♠t♦s r♦♠ ♦rrt②
st♠t♥ ts ♥ tt t ♦♦s tt t t♦♣♦♦② ♥♥♦t ♦rrt②
r♦♥strt tr s ♣s①ts♠ s ♥ t r r♦♠ ♦♦s ♥ t
r t s tt ♦r ♠t♦s ♦ ♥♦t ♦rrt② st♠t ts t② ♠②
t♦ r♦♥strt t t♦♣♦♦② st ♥rt♥t② ♥ t t♦♣♦♦②
♦s ♥♦t ♠♣② tt ♥♥♦t r♦♥strt ts ♥ t ♥sts s♦
r t♥ t♦ ♣t t ♠♦r s tt sttst ♠t♦s r t♦ ♥r
t♦♣♦♦s t♥ ts ❬♦♥ ♥ ♦♥ ❪
♥ ts
s st♦♥ ♣rs♥ts ♥②ss ♦ t st ♦ ♥st trs ♦
♥ ts s♣♦♥ ♥ ♥❲ürt♠r ♥ r t
r ♥t② ♦t ② ♦♥ ❬❪ ♦♥ ♠♣s r t♥
tr♥sr ♥t♦ ♥r② t ② ♦tr ❬♣rs ♦♠♠❪ t ♦r ①
r♠♠t ♥ ♣♦♥♦♦ trs ♥ r ♥t♦ t♦rs
♠♥ ♦② ♦♠♠♥t② ♥ ♦t♥ r♠♥ tr ♥ ♥
♦r ♦♦ ♦s♦r t♠ ♥ rs tt ♥ ♣ts r♦♣s ♦♦♦r
♥ tr♥s♣♦rtt♦♥ ① ♦ q♥tts s♦rt ♦s ♦♥ ♦s
♥ ♣t♦♥s ♣♦s ♦♥s♦♥♥ts ♦tr ♦♥s♦♥♥ts ♣♦♥♦♦ r
♦r♠s ♥♦♥ ♥ rt ♦r♠s ♣r♦♥♦♥ ♥ t ♦r♠s ♥ s②♥t①
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r♠♠t
t♠♣♦r ♥ ♦r♣ ss ♦ ts t r ♠ s♠r t♥
♦r t ♥♦r♦♣♥ ♠② s s ♠t ①♣t r ♠♦♥ts ♦
♦rr♦♥ ♥ tr ♠♦ ♣r♦② ♥♦t ♣tr t ♥tr ♥st
st♦r② ♦ ts ts ♦♥tss t s rt♥② ♥trst♥ t♦ s tr
r♦♥strt trs ♦♥ ts t s♥ ♦r ♠♦ ♦rrs♣♦♥s t♦ ♥♦♥
st♦r ts
r♦ ♦r♣ ♣♦st♦♥ ♦ t ts ♥ r ♥
s s♦♥ ♥ r rr s♦ s♦♥ ♥ r s str♦♥
♣②s ♦♥r② ♥ s ①♣t t♦ s♣t t ts ♥t♦ t♦ sr♦♣s ♦♥
tr s ♦ t ♦r♥ t♦ ♦tr ❬♣rs ♦♠♠❪ s♦ ①♣t t♦ s
t♦ strs ♦rrs♣♦♥♥ t♦ t t♦ ss ♦ t rr ♥ ♦t ss t
♥s ♣r♦rss r♦♠ ♦rt t♦ ♦t s♦ s♦ s♦ ♦♣ t♦ s ts
♥ t r♦♥strt trs
r s♦s ♦♥s♥ss tr ♦r ♥ ♥②ss ♦ t ♦s♦ ①♦♥
t ♦♥② ♦♥str♥t ♠♣♦s s tt t r♦♦t t♥ ♥
P ♦♥s♥ss tr ♦rrs♣♦♥s ♦s② t♦ t ♦r♣ trs
♦sr r st❲st t ♥ ♦♥ ♦t ss ♣r♦rss♦♥ r♦♠ ♦rt
t♦ ♦t s ♦rrs♣♦♥s t♦ t ♣t ♦♥ t s t ♥s
♦♦♥③ t r♦♥ t♦ t s s♦ ♣♦ss tt t t ♦♥t♥
s♥ ♦r ts t♦♣♦♦② s ① t♠s r ♦rr♦ ♦♥ ts ♣t
♥② tstr♦♣s r ♦♥ ♦♥ t r♥ ♥ t♦ t str♥♥ t
str♥♥ s ♥♦♥ t♦ ♣r♦♠t s t t ♠② ♥♦t ♦rrt②
rt ts t
r ♠♦ s ♦♣ t ① t ♥ ♠♥ ♥ ♣rtr t
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Ries
Ostfranken
Nordbaiern
Ostlech
Nord
Ostlech
Süd
Ammersee
Ost
Lechrain
Ostallgau
Süd
Kemptener
Raum
Memminger
RaumOstallgau
Nord
Ulmer
Raum
Stauden
Dillinger
Wertingen
r ♦ ♦r♣ ♣♦st♦♥ ♦ ♥ ts t ♥ r♣rs♥ts t rr str♦♥ ♣②s ♦♥r② t♥ t st ♥❲st ♦ ts r♦♥
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Ostfranken
Nordbaiern
Ostlech_Sued
Ries
Ulmer_Raum
Ostlech_Nord
Ostallgaeu_Nord
Stauden
Lechrain
Ostallgaeu_Sued
Kemptener_Raum
Ammersee_Ost
Memminger_Raum
Dillingen_Wertingen
94
85
72
89
66
90
85
0 500 10001500
r ♦♥s♥ss tr ♦r ♥ ♥②ss ♦ t ♦s♦ ①♦♥ t ♦♥ ts
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tr tt ♦r ♥ ♦♥② ♦r♥ ♦♥ ♦♥ t tr ♦s ♥♦t ♣♣② t♦
s②♥tt ♦r ♣♦♥♦♦ t r ♥t st ♣♣r♦ s s t ♦♥
sr ② s ❬❪ ♠② ♣♣r♦♣rt s ♠♥t♦♥ ♥ ♣tr t s
s♦ t tr tr ♠♦ s ♣♣r♦♣rt ♦r s t ♥ ♦r
♥②ss ♦ ♣♦♥♦♦ ♥ s②♥tt t ♣r♦ ♠ ss ♦♥♥♥
rsts s t ① t
P♥tt♦♥ rsts
tstr♦♣s r ♥t② ♥tr♦ ♥ ♦r ♠♦ t♦ t ♥t♦ ♦♥t
♣♦ss tstr♦♣ rt tr♦♥t② ♦r ♥♦tr ♣♦ss s ♦
ts tr s t♦ ♥②s t t♥s♦♥ t ❬❪ ♣♥tt♦♥ rsts
t♥s♦♥ t ❬❪ s t♦ tst t ②♣♦tss tt ♥s rs②
t t♦ rts s s♦ rt ♦♥ t ♥tr tr t ♥♥ ♣r♦ss
♥ str rt ♥r t♦ ♥s s♣t ♣♥tt♦♥ rsts r
r sr ♣s ①♣♥t♦♥s ♦r ♣♥tt♦♥ rsts ❲♥ ♥
s ♦♥ ② t ♠rt♦♥ ♦ s♠ sst ♦ ♣♦♣t♦♥ t ♦♥r
t s t♦ st ♥ ♦r s♦rt ♣r♦ ♦ t♠ ♥ s♣tt♥ s
s♦ ss♦t t ♦tr ♥ts ♥ t♦ st ♥ s s r
t♥s♦♥ t ❬❪ st② tr ♥ ♠s ♥♦r♦♣♥
sst ♦ t ②♥ t ❬❪ t str♦♥s♥ ♥ ♥t ♥ ♦rr t♦
tst ♦r ♣♥tt♦♥ rsts t② ♦♥strt ♥ trs ♦r ♠②
s♥ t s♦tr ②srts ❬P t ❪ ♦r t ♥
t s r ♠♦r♥ i.e. s♦r♦♥♦s t② t♥ ♣♦t t ♥♠r ♦ ♥s
t♥ ♥ t r♦♦t ♦ t tr ♥st t ♥♠r ♦ ♥tr♥ ♥♦s
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t♥ t ♥ t r♦♦t ♥ ♥ ♣♦st ♦rrt♦♥ s s♥
♦r t ①st♥ ♦ ♣♥tt♦♥ rsts ② t tt ♣♥tt♦♥
rsts ♦♥t ♦r ♦ ♥s ♥ t st♦r② ♦ t ♥♦r♦♣♥ ♠②
♠♦r rt ② t♦ tst ♦r ♣♥tt♦♥ rsts s t♦ ♥ t♠
rt② ♥ t ♠♦ ♥ ♣♥tt♦♥ rsts ♦r ♦♥ t tr
t② r q♥t t♦ tstr♦♣ ♥t ♦r♥ tr r② s♣tt♥ ♥t
♦r tt t ♣♦st♦♥ ♦ tstr♦♣ ♦♥ r♥ ♦s ♥♦t ♠ttr
♦ ♥ ♣♥tt♦♥ rsts ♥ ♦r ♠♦ tr♦r s♠♣② ♥ t♦
♠♣♦s t ♣rs♥ ♦ ①t② ♦♥ tstr♦♣ ♦♥ r♥ s s♦♥ ♥
r ❲t L ♥s tr 2L− 2 tstr♦♣s ♦♥ t tr g
♦rrs♣♦♥♥ t♦ ♥ t ♥t TC t t♦t ♥t ♦ t tr s
♥♦t ② |g| t ♣r♦♣♦rt♦♥ ♦ ♥ ttrt t♦ ♣♥tt♦♥ rsts
s (2L−2)TC
|g|+(2L−2)TC
❲ s ts ♠♦ t♦ ♥②s t ♥ t ❬❪ t s s t
s♠ sst ♦ t ②♥ t ❬❪ t s t♥s♦♥ t ❬❪ rs♦♥
♦r t♥ ♦♥② sst ♦ t t s tt s♦♠ ♦ t ♥s st ② ②♥
t ❬❪ ♦ ♠ t♦♦ ♦s ♦r tr r♥ t♦ tr② rr
s ♥ s♣tt♥ ♥t r♦r ♥s r r♠♦ r♦♠ t
t t s ♦rt r♠♠r♥ r♦♠ t♦♥ tt t ♦♥ tstr♦♣
♦♥ r② r♥ ♥ t t ♠♣r♦♣r ♣r♦r strt♦♥ ♦♥ t t rt
p(µ) ∝ 1/µ t ♣♦str♦r strt♦♥ ♥ s♦ ♠♣r♦♣r ♥ µ → 0 s
s ♥♦t ♥ ss ♥ ts s s t ♦♦ s r② s♠ ♦r s♠ s ♦ µ
♥ s♦ t ♥r sts ts ♣rt ♦ t stts♣ s♦ ♥ ♠♣♦s
r② ♦♥srt t♦ r♥r♥ t ♣♦str♦r strt♦♥ ♣r♦♣r t♦t
tr♥ t
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r rsts r str② r♥t t♦ t♦s ♦t♥ ② t♥s♦♥ t ❬❪
♥ ♦r ♥②ss t ♣r♦t② ♦ t t tstr♦♣ κ s r② ♦s t♦
♠♣②♥ tt ♣♥tt♦♥ rsts ♦s t♦ ♥♦ t ♦r t ♥
t ❬❪ t ♦r ♠♦ ttrts ♦ ♥s t♦ ♣♥tt♦♥
rsts ♦r t ②♥ t ❬❪ t ♦ ♥s r ttrt t♦
♣♥tt♦♥ rsts
rtr ♦r s ♥ t♦ ♥rst♥ t sr♣♥② t♥ ♦r rsts
♥ t♦s ♦ t♥s♦♥ t ❬❪ t♥s♦♥ t ❬❪ s♦ tr♦
s♠t♦♥ sts tt t ♣rs♥ ♦ ♦rr♦♥ ♥ t t ♦s ♥♦t ♠♣t
tr ♠♦ ♦ ♣♥tt♦♥ rsts t ♦ ♦r ♥trst♥ t♦ s
tr t ♣rs♥ ♦ tstr♦♣ rt tr♦♥t② ♦r tr s
s♥ ♥ t t s s♦♥ ♥ t♦♥ ♥ ♥tr♦s s ♦r ♦r
♥st ♣♥tt♦♥ rsts ♥ tr ♠t♦♦♦② ♦t s♦ tt ♦r ♠t♦
ss♠s qs③ tstr♦♣s ♦♥ r♥s ♥ tt ♥ t♥s♦♥
t ❬❪ ♦r ♠♦ ♦ ♥ ♥ s ♦ ts ♠t ①♣♥ t
sr♣♥②
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albanian
greek
armenian
tocharian_atocharian_b
oldpersianavestan
vedic
latin
oscanumbrian
oldirish
welsh
gothic
oldhighgerman
oldenglish
oldnorse
oldcslavonic
oldprussian
lithuanianlatvian
hittitelycian
luvian
0 10002000300040005000600070008000
r ①♠♣ tr t ♣♥tt♦♥ rsts ♦♥ tstr♦♣ ♦♥ r♥
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♣♣♥①
s st
s ♣♣♥① s ♠♥♥ t♦rs ♥ t st♥r s st
s ② ♥ t ❬❪ ②♥ t ❬❪ ♥ rs♥ ♥ ❱♦t ❬❪
r ♥ ♥♠r ♦ ♠♥♦r st♠♥ts sst ♦r ts st
♠♦r r♥♠♥t s ♥ s s♦rt♥ t st t♦ ♠♥♥
t♦rs ♠♥♥s r s♦ ♥ ♥ t s♦rtr st r
♥t ♥ ♦
♥
♥♠
ss
t
r
s
②
r
t
♦♦
♦
♦♥
rst
rt
r♥
♦
♦
♦♠
♦♥t
t
②
rt②
♦
r♥
r②
st
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r
rt
t
②
r
t
tr
r
tr
t
r
s
♦t
♦
♦r
②
♦
♦♦t
♦r
r③
♦♦
rss
r♥
ts
r
♥
r
rt
②
r
t
♦
♦r♥
♦
♥t
s♥
♥
♥
♥♦
t
r
♦♥
♦s
♠♥
♠♥②
♠t
♠♦♦♥
♠♦tr
♠♦♥t♥
♠♦t
♥♠
♥rr♦
♥r
♥
♥
♥t
♥♦s
♥♦t
♦
♦♥
♦tr
♣rs♦♥
♣②
♣
♣s
r♥
r
rt♦rrt
rt s
rr
r♦
r♦♦t
r♦♣
r♦tt♥
r♦♥
r
st
s♥
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s②
srt
s
s
s
s
sr♣
s♦rt
s♥
st
s♥
s②
s♣
s♠
s♠
s♠♦
s♠♦♦t
s♥
s♥♦
s♦♠
s♣t
s♣t
sq③
st
st♥
str
st
st♦♥
strt
s
s♥
s
s♠
t
t♥
tt
tr
t②
t
t♥
t♥
ts
t♦
tr
tr♦
t
t♦♥
t♦♦t
tr
tr♥
t♦
♦♠t
r♠
s
tr
t
t
♥
r
t
♦
♥
♥
♣
t
♦♠♥
♦♦s
♦r♠
②
②r
②♦
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♦ ♥♦tt♦♥s
♦♦♥ t s r sr♣t♦♥ ♦ t ♥♦tt♦♥s s ♥ tstss s s t ♣ r t ♥♦tt♦♥ s ♥tr♦ t♦ t ♠ts③ ♦ t ♣ts s♦♠ ♥♦tt♦♥s sr ♠♥♥s t t ♦♥t①t②s ♣r♥ts ♥② ♦♥s♦♥
♦tt♦♥ ②♣ sr♣t♦♥ P
A ♥♦ t ♠ ♥♦ ♦ tr ♥ ② r♥ ♦♥♥t ♥t t♦ t r♦♦t
a ♥tr ♥① ♦ ♦♥② ss ♦r ♦♠♥ ♦ D 1 ≤ a ≤N
B ♠tr① ♥② ♠tr① ♥ ♣rt ♦♥ ♦ D D∗ I B st ♦ s t st ♦ s t t st L − d′ s♥♥ts
BC,C−c r ②s t♦r b r t ♦ ♦rr♦♥ t rt ♦ ♦rr♦♥ s
bµ
C ♥tr t ♥♠r ♦ ♦♥str♥ts C r ♥t ♦♥st♥t C r t ♣r♦♣♦rt♦♥ ♦ sr ♦♥ts t♥ t♦
♥s
c ♦♥str♥t ♦♥str♥t ♦♥ t tr c1, c2 ♥♦ t r♥ ♥♦s ♦ ♥♦ i D L × N
♠tr①t ♥trs ♥ ♦r
D∗ L × N∗
r♥♦♠♠tr①
♥♦t♦♥ r♥♦♠ ♥r② t ♠tr①
D∗ L × N∗
♠tr①r③t♦♥ ♦ D
∗
Da st ♦t♦rs
st ♦ t♦rs d∗ ♦ ♥ ♦♠♥ a
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♦tt♦♥ ②♣ sr♣t♦♥ P
D L × N♠tr①
♠s rs♦♥ ♦ D∗ ♦rrs♣♦♥s t♦ D∗ ts♦♠ ♥trs r♣ t ♥ t♦ D t ①tr♥rstr ♦♠♥s
d, d′ ♥trs ♥trs ♥♦ ♥ t rstrt♦♥ ♦♥t♦♥ss② q t♦ ♦r
d∗ ♥r②t♦r
♦♠♥ ♦ ② t t
E st ♦ s t st ♦ s ♥ tr E ♥t t ♥t tt ♦♥② ss s rstr
E〈i,j〉 st ♦ s t st ♦ s ♥♦r♥ 〈i, j〉
2F0 ♥t♦♥ ♥r③ ②♣r♦♠tr ♥t♦♥ f ♥t♦♥ ♣r♦r strt♦♥fG ♥t♦♥ t ♣r♦r strt♦♥ ♦♥ trs g tr ♥r② r♦♦t tr I∗ L × N∗
r♥♦♠♠tr①
r♥♦♠ ♥t♦r ♠tr① ♦ ♦srt♦♥s
I∗ L × N∗
♠tr①r③t♦♥ ♦ I
∗
i ♥tr ♥① ♦ ♥ ♦r ♥♦ ♦ tr ♦r r♦ ♦t t D 1 ≤ i ≤ L
j ♥♦ ♥♦ ♦ tr ♦t♥ t ♣r♥t ♦ ♥♦ ik t♦r ♦
♥trst♦r ♦ ♥♠r ♦ tstr♦♣s
ki ♥tr t ♥♠r ♦ tstr♦♣s ♦♥ i, j L ♥tr ♥♠r ♦ ♥s
L(x) ♥t♦♥ t ♦♦ ♥t♦♥M st ♦
♥trs ♦♥② ss M ⊆ 1, 2, ..., L
MC ♠♦ t ♥ ♠♦ t ♦♥str♥ts ♥ MC−c ♠♦ t ♠♦ t ♦♥str♥t c r♠♦
m st ♦♥trs
st ♦ ♥s s♣②♥ ♦♥② ss ♥ t♥♦sr ♦♠♣t t
ma st ♦s
st ♦ s ♥♦♥ t♦ s♣② ♦♥② ss a
N ♥tr ♥♠r ♦ ♦♥② sss N∗ ♥tr ♥♠r ♦ ♦♥② sss ♦r♥ ♦♥ t tr
♥♥ ♥rstr sss
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♦tt♦♥ ②♣ sr♣t♦♥ P
Nsamp ♥tr t ♥♠r ♦ s♠♣s ♥ r♥ p ♥t♦♥ ♣r♦r strt♦♥Q ♥t♦♥ ♥t♦♥ ♦♥t♥ t ♥♠r ♦ s ♥ ♦♠♥ Qa ♥tr ♥♠r ♦ ♥s ♦r t t ♦r
♦♥t a s
q ♥t♦♥ ♣r♦♣♦s strt♦♥ qi ♥tr t ♥♠r ♦ s ♥♦r♥ 〈i, j〉 R ♥t♦♥ rstrt♦♥ r r ♥♦ t r♦♦t ♦ tr r r ss rt♥t♦♥ rt
ri,j r tr♥st♦♥ rt rS ♥t♦♥ t t♦♦rrt♦♥ ♥t♦♥ ♦ sttst S ♦
r♦ ♥
S st ♦♥♦s
t st ♦ ♥♦s ♥ s ♥♦t ♦♥ ♦ ② ♦♥str♥t
si ♥tr t ♥♠r ♦ s s♥ r♦♠ ♥♦ i T r ♣♣r ♦♥ ♦♥ t ♦ t r♦♦t Tb r t t♠ tr ♦ ♦rr♦♥ s ♥♦ ♦♥r
♦
TC r ♠♦♥t ♦ t♠ q♥t t♦ tstr♦♣ ti r t ♦ ♥♦ ♦r i tr r t ♦ t r♦♦t r t t♦r ♦
rst t♦r ♦ s ♦ ♥♦s ♥ tr t =(t1, t2, ..., tA)
u(n)i r t ♣r♦t② ♦r ♦♥t ss ♣rs♥t t ♥♦
i t♦ rstr t ①t② n s ♦ i
V st ♦♥♦s
t st ♦ ♥♦s ♦ tr
VL st ♦s
t st ♦ s ♦ tr VL ⊂ V
V(i)L st ♦
st st ♦ s s♥ r♦♠ ♥♦ i
v(n)i r t ♣r♦t② ♦r ♦♥t ss ♣rs♥t t ♥♦
i t♦ rstr ♦r ♠ss♥ t ①t② n s♦ i
(Xn) r♥♦♠♣r♦ss
r♦ ♥
x stt stt
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♦tt♦♥ ②♣ sr♣t♦♥ P
Y ♥t♦♥ ♥t♦♥ ♦♥t♥ t ♥♠r ♦ s ♥ ♦♠♥ Ya ♥tr ♥♠r ♦ ♥s ♦r t t ♦r
♦♥t a s
ZD ♣♦♥t♣r♦ss
t ♣♦♥t ♣r♦ss ♦ rt ♦t♦♥s ♦♥ t tr
z ♥♦t♠♦♣
♣♦♥t ♦♥ t tr
α r ♣tt♦♥ ♣r♦t② α, β rs t ♣r♠trs ♦ ♠♠ strt♦♥ Γ st ♦ trs t st ♦ r♦♦t ♥r② trs t L
st♥s s
Γ(c) st ♦ trs t st ♦ trs ♦②♥ ♦♥str♥t c ΓC st ♦ trs t st ♦ trs ♦②♥ ♦♥str♥ts δi,j r t ♣r♦t② ♦r ♦♥② ss t♦ sr ♦♥
〈i, j〉
ǫ r t ♥t ♦ t♠ t♥ ts ♥ rts t tstr♦♣ r② ♦s t♦
η r ♥ rtrr② t♦r θ st ♦
♣r♠trs♦♥♥s ♥♦tt♦♥ ♦r st ♦ ♣r♠trs ♦r①♠♣ θ = (g, κ, ρ, ξ)
κ r ♣r♦t② ♦ t ♦ ♦♥t t tstr♦♣
Λ([g]) r ♥♦r♠③♥ ♦♥st♥t Λ([g]) =∫
[g]λ(z) dz
λ r rt rt ♦ ♦♥② sss ♦ts ♦ tstr♦♣s
λ ♥t♦♥ t rt rt ♦ ♦♥② sss t ♣♦♥t ♦♥t tr
µ r t rt ♦ ♦♥② sss ♦ts ♦tstr♦♣s
ν r ♠♥ ♥♠r ♦ rts t tstr♦♣ ξi r ♣r♦t② ♦r ♦♥t ss t♦ ♠ss♥ t
i
ξ t♦r ♦rs
t t♦r (ξ1, . . . , ξL
πi r t qr♠ ♣r♦t② ♦ s♣②♥ i ♦♥②sss
ρ r rt ♦ ♦rr♥ ♦ tstr♦♣s σ(t) ♣r♠tt♦♥ ♦rr ♦ t ♥tr♥ s t τ r t♠ ♦♥ ♥ ♦ t tr
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♦tt♦♥ ②♣ sr♣t♦♥ P
τS r t t♦♦rrt♦♥ t♠ ♦ sttst S Ωa st ♦ sts
♦ ♥trsst ♦ ♦♥② sss ♦♥sst♥t t t t ♦r♦♥② ss a
Ω st ♦ sts♦ sts ♦♥trs
t t♦r (Ω1, Ω2, ..., ΩN)
ω st ♦♥trs
♣♦ss ♦r t st ♦ ♥s t ♦♥② ss s s♣②
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♦r♣②
r♠♦t③ ♥ t♥ ♥♦♦ ♦ t♠t ♥t♦♥s t♦r♠s r♣s ♥ t♠t s ♦r ❨♦r ♥♥t ♦r♣r♥t♥ t♥t ♣♦ ♣r♥t♥ t♦♥
s②♥♦ ♥ r ❲♥r ♥ ♦♦ t♦stt ② ♦♠♣♦s♥ ♦ Prs♠♦♥♦s ♦♦s ②st♠t ♦♦②
t♥s♦♥ ♦s ❲ ♥ r② r♦♠ ♦rs t♦ tstr ♥t♦ ♥ ♠t♠ ♦r ♣②♦♥t ♥r♥ r♥st♦♥s ♦t P♦♦ ♦t②
t♥s♦♥ ❱♥tt r♥ ♥ P ♥s♦ ♥ ♣♥tt♦♥ rsts ♥
rr♦♦ ♦ ♥ P ♦♥s♦♥ ♣②♦♥② ♦ t♥trr② s tr
s ♦♠♣rt ♥♦r♦♣♥ ♥sts ♥ ♥tr♦t♦♥♠str♠ ♥♠♥s
♥ ♠ P r ♥ ❱é ♥ st ♦♥strt♦♥ ♦♥st rs tr♦ ❱♦ t ♦r♥ ♦ ♥ttt ♥sts
rs♥ ♥ ❱♦t ♥ t t② ♦ ♦tt♦r♦♥♦♦② rr♥t♥tr♦♣♦♦②
st ❲② ①♦sttsts ♦s♥t ♦r t ♥rs ♦♥st♥t ②♣♦tss♥ t str♦♥s♥ ♥s ♠ ♣t ♥ st♦r ♥sts
♦rôté P ♥ rts ♥ ♥ Pr♦st♣♣r♦ t♦ r♦♥ P♦♥♦♦② ♠♣r t♦s ♥ tr
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♥ Pr♦ss♥ ♥ ♦♠♣tt♦♥ tr ♥ r♥♥P♦
r②♥t ♠♦♥ ♥ r② ❯♥t♥♥ ♦r ♣st ♥s trss♣ts ♥ ♥t♦rs ♦t♦♥ ♦ tr rst② P②♦♥t♣♣r♦ ♣s
♠♣ ♥s ♥ ♥s ♥ ♦♦rt♦♥ s♦♠ ♣rt ♠ttrs♥ ♥ ♥ ♥s ♥ ♥trs♣♥r② ♦♥r♥ ❯♥rst② ♦♦r♥ ♥t rr ♣s
♦r③ P③③ P ♥♦③③ ♥ ♦♥t♥ ♦♥strt♦♥ ♦♠♥ ♦t♦♥ r♥♥ t♦tr ♥t r♦♦ ♥ ♥stt Pr♦♥s ♦ t t♦♥ ♠② ♦ ♥s
♦r ♥ ♥♥♥ t♥♦♥ss rss ♣②♦♥ss ♥ ♣rst♦rtr ♥ s st② s♥ r♦♣♥ ♥♦t ♣♦ttr② ♥ ♦♦♣②♦♥t t♥qs r♦♥ts ♥ t ♣♦♣t♦♥♣rst♦r② ♦ r♦♣ ♠r ♦♥ ♥sttt ♦r r♦♦sr ♣ ♣s
♦♠r P♦st♦♥ ♣♣r ♦r t ♥s ♥ ♥s ♦♥r♥ t ❯♣t♠r
❲ r♦t ♦t♦♥r② ♥sts ♥♥ ♦ ♥tr♦♣♦♦②
r♥ s♥t ♦ ♥ ♥ t♦♥ ♥ t♦♥ t♦ ①
♠♦♥ ♥ P ♦♦ r♠rs ♥ tr ♥s t rst①♣♥s♦♥s ♥
♦♦ s ♦s é♦t♦♥ t♥ ♦été é♦♦ Pé♦♥t♦♦ t ②r♦♦ r♥st ♥ ♦ ❬❪
r♠♠♦♥ ♥ ♠t ②s♥ ♦t♦♥r② ♥②ss ②s♠♣♥ trs ♦t♦♥r② ♦♦②
r♠♠♦♥ ♦s ♦r♦ ♥ ❲ ♦♦♠♦♥ st♠t♥tt♦♥ Pr♠trs P♦♣t♦♥ st♦r② ♥ ♥♦② ♠t♥♦s②r♦♠ ♠♣♦r② ♣ q♥ t ♥ts
r②r s♣♠t ♥ ♦♠r ❲♦r ts ♦ ♥trtrs
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♥♥ rr s♥ ♦② ♥ ♥s♦♥ trtr♣②♦♥ts ♥ t r♦♥strt♦♥ ♦ ♥♥t ♥ st♦r②
♥♥ ♥s♦♥ ♥strö♠ s♥ ♥ rr trtr♣②♦♥② ♥ st♦r ♥sts ♠t♦♦♦ ①♣♦rt♦♥s ♣♣ ♥s♥ ♥s ♥
②♥ rs ♥ t r♦♠tt♣♥tt♦♥♥s① ♥r② t r♦♠ tt♣♣s②♥♥③♣s②rsrssstt♠
♠t♦♥ ttsts ♥ st♦r ♥sts r♦♠②r
♥s♠♥r r♥st♦♥ ♦sts ♥ s♠ ①♣♥♥ ♦♥rs♦♥ ♥ r♦r♥ ♦ ♥sttt♦♥ ♥ ♦rt ♦♥♦♠s
♥s ♥ ♥ ❲r♥♦ ♥r♥ ♦ r♥ t♠s s sttst ♥rs ♣r♦♠ P②♦♥t t♦s ♥ t Prst♦r② ♦♥s ♦♥ ♥sttt ♦♥♦r♣s ♣s
rrs P②♦♥t ♥②ss ❯♥r ♦♦s ②st♠t ❩♦♦♦②
s♥st♥ ♥rr♥ ♣②♦♥s ♥r ss♦ts ♥r♥ ss❯
❲ t ♦r ♥♥ t ♦rs ♦ ♦t♦♥ ♠♥♠♠ ♥ ♦r s♣ tr t♦♣♦♦② ②st♠t ③♦♦♦②
❲ t ♥sts♥ ♥s ♥ tr
P ♦rstr ♥ ♦t ♦r ♣②♦♥t r♦♥♦♦② ♦ ♥♥ts t ♥ ♥♦r♦♣♥ Pr♦♥s ♦ t t♦♥ ♠②♦ ♥s
♦rt♥t♦ ♦♥ ♥ r♦♠ rt t♦ ♦r② ②s♥ st♠t♦♥ ♦ ♥str tts ♦ rr r♥srs ♥ ♥♦r♦♣♥ r♦♣s ♠♥ tr
♠♥ ♥ t ♥②ss s♥ rrss♦♥ ♥♠trr ♠♦s ♠r ❯♥rst② Prss ❨♦r
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②r Prt ♠r♦ ♥ ♠♦♥t r♦ ttst ♥
♠ts ♥ ♥♥ ♣rst♦r② ♦ str♥ r♦♣ P♦②s♠
♥♥r ♥s♥ ør♥s♥ ♦♥qst s♥ ♥ ❲rs ②s♥ ♥r♥ ♦ t t③♦♥ P②♦♥② ♦♠♥♦r ♥ ♦r♣♦♦ ♣♣r♦ rr♥t ♦♦②
P ♦♦♦ ♥ P♦ Prs♠♦♥② ♥ ②s♥ ♣②♦♥ts Prs♠♦♥②P②♦♥② ♥ ♥♦♠s ♣s
♦ ♦♦ ♦♥ ♦♦s rrrst② ♥ t stts ♦ ♦t♦♥r②s ♦r♥ ♦ t st♦r② ♦ ♦♦②
r② ♥ t♥s♦♥ ♥tr r♥ t♠s s♣♣♦rt t♥t♦♥ t♦r② ♦ ♥♦r♦♣♥ ♦r♥ tr
r② ♥ ♦r♥ ♥ trs s♣♣♦rt t ①♣rsstr♥ sq♥ ♦str♦♥s♥ ①♣♥s♦♥ tr
r② r♥ ♥ ♦ss ♣srs ♥ ♣rs ♦ r♥③♥tr t ♣②♦♥s ♦♦ ♦r②
r♥r ♥ ♥ t ♠rs t♥♦r ❯♥rst② Prss
r♥ rr ♥ r② ♦s ♦r③♦♥t tr♥s♠ss♦♥ ♥ttr ♣②♦♥s Pr♦♥s ♦ t ♦② ♦t②
♦♥ ♥t ♥ trs rt t s♣r ♦ r♠♥ r♦ss sr♥ r ♠①♠♠♣rs♠♦♥② ♥②ss Pr♦♥s ♦ t ♦②♦t② ♦♦ ♥s
♦♥ ♥ ♣r ♦ tt t♦ t ♦ss ♦ ♠tr♥ s♥t♥ r ♦♦t♦♥r② ♥②ss Pr♦♥s ♦♦ ♥s
♦♠ ♥ r♦rt♠ ♦ ♥♦r♦♣♥ ïtrsï ♥ ♥♦rt♠s r t ♣②♦♥② ♥ ♥ ♣rst♦r② ♦ ♥♦r♦♣♥♦r♥ ♦ ♥ttt ♥sts
s♥ ♥ ♦♥qst ❨ ②s♥ ♥r♥ ♦♣②♦♥t trs
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s♦♥ ♥ t P②♦♥t trs s ♦♥ ♥ ♦♥t♥t♦♥♦r♠ts
②♠s ①♦sttsts s♦ r rr♥t ♥tr♦♣♦♦②
♥♦ P ♦♥♦ ♥ ❩ ❨♥ ♠♣t ♦ t r♣rs♥tt♦♥ ♦ ♦ssrt♦♥s ♦♥ ②s♥ st♠t♦♥ ♦ s♣s r♥ t♠s ②st ♦
♦♥s ♥s♣ ♥ ♣ st♦r② ①♣♦r♥ ♦♥♥t♦♥s t♥ trrs ♥s ♥ ♥s ♠r♥ ♥tr♦♣♦♦st
P ♦r♥ ♥ ♥♥♥ tr tr♥s♠ss♦♥ ♥ ♥ str②trt♦♥s ♠♦♥st t ♦r♥ ♥♥s ♦r♥ ♦ ♥tr♦♣♦♦r♦♦②
t♥ rt ss ♥ ♥ ②s♥ ♣②♦♥t♥②ss ♦ ♠t ♥s ♥ts ♥ r② r♦♥③ ♦r♥ ♦ ♠t♥ t r st Pr♦♥s ♦ t ♦② ♦t②
❲ ♦♥ ♣rts ♦♥ ②rs♥
♥s♥ ♦① ♦♥② r ♠r rtP ♦rqst ♦♥r ♦②♦ ❲t♥s t ♦♦t♦♥ ♦♥s ♥ ♥s ♦♥ t s♥ ♦ ♠ str♥ ♥♦♥s Pr♦♥s♦ t t♦♥ ♠② ♦ ♥s
rt ♥ ♠♦♥ r♦ ♥ ♦♥t r♦ ♦rt♠s ♦r t②s♥ ♥②ss ♦ ♣②♦♥t trs ♦r ♦♦② ♥ ♦t♦♥
❲ s♥ rtr ts s ♦♥ t ❯♥q② r rtr♦♥♣t ②st♠t ❩♦♦♦②
P s ♦♦ ♣♣r♦ t♦ st♠t♥ P②♦♥② r♦♠ srt♦r♣♦♦ rtr t ②st♠t ♦♦②
r♠♥ s♦♥ ♥ ♥ ♦ ♥t②♥ t♦t♦♥r② ②♥♠s ♦ ♥ tr
♥ ♦♥ ♣②♦♥t ♣♣r♦ t♦ tr ♦t♦♥ r♥s♥ ♦♦② ♦t♦♥
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❲ ② ♥ ♦♥r ♦♠♣t♥ ♦r s♠rt② ♥ ♥t②♥♦♥ts t Pr ♥ r♦ ♦s ♥ Pr♦♥s ♦ t t♦♥r♥ ♦♥ ♦♠♣tt♦♥ tr ♥ r♥♥ ♦ ♣s
t ②r③t♦♥ s ♥ ♥s♦♥ ♦ t ♥♦♠ r♥s ♥ ♦♦② ♦t♦♥
♦r② ♥ sr ♦ t ♥♦r♦♣♥s ♥ r♦♦② ♥ ♠②t♠s ♥ s♦♥
rrs ♥ rrr tr
♦♥ ♥ ♦♥ ♥ sst♦♥ ② ♠rs ①♦r♥sts
♦♥ ♥ ♦♥ ❲② ♥sts ♦♥ït ♦ ts ♥r♦♠ ♥♦r♦♣♥ ♥ str♥ ♥s P②♦♥t t♦s ♥t Prst♦r② ♦ ♥s ♣
s♦ ❲t♥ ♥ ♥ rrs♦♥ Prs♣t s ♠♥tr ♦t♦♥ r♥♥ ♥ r r♦♠ t ♣rs♣t ♦ r♥ ♦ ♣s ♦t♦♥
♦rs ♥ ♦♥tt ❯♥rss ♦ ♠♥ ♥
r ♦rr♠r s♠♥ ♥ rt♦♥ st② ♦ str♥ ♥s♣ ♥ ♠rr s♥ ♣②♦♥t② s ♦♠♣rt♠t♦ ♠r♥ ♥tr♦♣♦♦st ♣s
♥ ♥ ❲r♥♦ Prt ♣②♦♥t ♥t♦rs ♥ ♠t♦♦♦② ♦r r♦♥strt♥ t ♦t♦♥r② st♦r② ♦ ♥tr♥s ♥
♦s ♥ r② t ♥str trs r♦♠ ♥r② trt t ♥tr ♣♣t♦♥ t♦ t rst♦♥ ♦ ♥s ♦r♥ ♦ t ♦②ttst ♦t② rs ttst t♦♦♦②
♦s ♥st rst② ♥ ♣ ♥ ♠ ❯♥rst② ♦ ♦Prss
♥♥ r ♥ ♥② ♦♠♣rt ♠t♦s ♦r st②♥tr trt ♦t♦♥ s♠t♦♥ st② r♦sstr sr
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r♥ ♥ ②♠♥ ♦t♦♥r② r♦♦② rr♥t stts ♥ tr♣r♦s♣ts ♦t♦♥r② ♥tr♦♣♦♦②
r♥ r♥t ♥ ②♠♥ sts s s ♦r r♦♥strt♥r♦♦ ♣②♦♥s P♦♥♥ ♣♦♥ts r♦♠ t s♦tstr♥❯♥t tts ♦r♥ ♦ r♦♦ ♥
r♥ ②♠♥ ❨ r♥t ♥ ♦r ♦sss ♥ r♦♦ ♣②♦♥ts t①♦♥ ♦♥strt♦♥ ♥ ♦tr♦♣st♦♥ ♦r♥ ♦ t♦rt ♦♦②
P ♠t♦ ♦r t ♥②ss ♦ ♦♠♣rt t ♦r♥ ♦♦rt ♦♦②
P ttst ♥②ss ♦ ♦♠♣rt t r♥s ♥ ♦♦② ♥♦t♦♥
P ♠♣ts r ♦♦s r♥s ♥ ♦♦② ♦t♦♥
P ♥ st♠t♥ rts ♦ ① r♣♠♥t ♦♥♣②♦♥t trs ♦ ♥s ♥ P②♦♥t t♦s ♥ t Prst♦r②♦ ♥s ♦♠ ♣ ♦♥ ♥sttt ♦r r♦♦sr
P ♥ rr ②s♥ st♠t♦♥ ♦ ♥str rtrstts ♦♥ ♣②♦♥s ②st♠t ♦♦②
P t♥s♦♥ ♥ rq♥② ♦ ♦rs ♣rts rts♦ ① ♦t♦♥ tr♦♦t ♥♦r♦♣♥ st♦r② tr
Prs♦♥s ♠♥s ♦ ♣t ♥ st♦r ♥qrs ♥t♦ t ♥t②♥ ♦r♥s ♦ t r♦♣♥ ♥s
tr② ②♣♦tss tst♥ ♥ ♠♦ st♦♥ ♥ ❲ s rs♦♥♥ ♣tr t♦rs r♦ ♥ ♦♥t r♦ ♥ Prt♣♠♥
♥♥ ♥ ❩ ❨♥ ♥rr♥ s♣t♦♥ t♠s ♥r ♥ ♣s♦ ♠♦r♦ ②st♠t ♦♦②
♥r r♦♦② ♥ ♥ P③③ ♦ ♥♦r♦♣♥ r♥srr♥t ♥tr♦♣♦♦②
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①♦ r②♥t ♥ ❩r③② st ♥②ss ♦ ♥s ♥♦r♦♣♥ sst♦♥ s ♦♥ ①♦sttst t sts
♥ ❲r♥♦ ♥ ②♦r ♥♦r♦♣♥ ♥ ♦♠♣tt♦♥sts r♥st♦♥s ♦ t P♦♦ ♦t②
♦ ♥♥ ♥ t ♦rs ❯♥rst② ♦ ♦♠ Prss
♦♥qst s♥ ♥ P ♥ r r r②s ♥♦♦ ♦ ♦♠♣tt♦♥ ♥ ♦r tt ❯♥rst②
♥♦ ♥ t rt ♦ r♣♠♥t ♦ ♦r♠♥♥ rt♦♥s♣s♥ ♣s
r ♥sts ❯♥trs♥♥ ♣r♥ r♦♣s♥ s②st♠tsr Ürst ♦♥♥ ö♥
r ♥ ♥ ♥♦r♠♥sr rs♣r tr ③r r♥♥ ♣r♦rs♥ ♠ t r rs♥ts♥ ♥ ss♥ ♣r♥
♠t ❱r♥tstsrït♥ss r ♥♦r♠♥s♥♣r♥ ♦♥♥
r ♥ Ptr♦♥ ♥♦r♦♣♥ ♥s tr ② ♥st♥st♥ Pr♦♣②ss ttrs
♥♥♥ ♥ ♥♦r♦ Prst♦r ♣♦♣t♦♥ st♦r② r♦♠ tt t♦ t t ♦t ♥ ♥tr ♥ ♦rtr♥ r♦♣ ♦r♥♦ r♦♦ ♥
t♦♥ t♦s ♦ ❯s♥ P②♦♥t ②st♠ts t♦ ♦♥strt tst♦r② ♦ t ♥r r♣t r♦♠tr②
s ①♦sttsts ② r♦♠ t r♠r ♥♥ ♣♦♣ ♣r♦♣s♥ ♣r♦♠s r♥st♦♥s ♦ t P♦♦ ♦t②
♣♥r ♦r♦ ❲♥ rr♦♦ ♦♦♥② P ♦♥s♦♥ ❲r♥♦ ♥ ♦ ♥②③♥ t ♦rr ♦ t♠s ♥ ♠♥sr♣ts ♦ ♥trr② s ♦♠♣trs ♥ t ♠♥ts
♣♥r s♦♥ rr♦♦ ♥ ♦ P②♦♥ts ♦ rt♠♥sr♣ts ♦r♥ ♦ t♦rt ♦♦②
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s ①♦sttst t♥ ♦ ♣rst♦r t♥ ♦♥tts t s♣rr♥ t♦ ♦rt ♠r♥ ♥♥s ♥ s♠♦s Pr♦♥s ♦ t♠r♥ ♣♦s♦♣ s♦t② ♣s
♦♠s♦♥ ♥ t ♥♣rtt② ♦ ♦♥tt ts ♦♦♥stts
♦♠s♦♥ ♦♥tt♥ t②♣♦♦ ♥ ♥ t②♣♦♦② ♥♥ ♥rss ♥ ♥tr♥t♦♥ ♥♦♦ ♣s
♦r♥ ♥ s♥♦ r♥ t♠ ♥ ♦t♦♥r② rt st♠t♦♥t ♠t♦s t ②st♠t ♦♦②
♦r♥ s♥♦ ♥ P♥tr st♠t♥ t rt ♦ ♦t♦♥ ♦ trt ♦ ♠♦r ♦t♦♥ ♦r ♦♦② ♥ ♦t♦♥
r♥② ♥ r♦♥ tstr♦♣ r② ♦♦♥ s rs ♠♥♠rt♦♥ ♥ t ♦t tr♥st♦♥ ♥ r♦♣ tr♥r② ♥s
❱s♦ ♣r♦r ♣r♦ts ♦ ♣②♦♥t trs ♦♦② ♥P♦s♦♣②
❲ ♦♦ ♦r t ♦♦ts ♦ ♥ ❨♦r ♠s
❲r♥♦ ♥s ♥ ♥ t♦st♠♦ ♦ ♥ ♦t♦♥ tt ♥♦r♣♦rts ♦♠♦♣s② ♥ ♦rr♦♥P②♦♥t t♦s ♥ t Prst♦r② ♦ ♥s
❩ ❨♥ ♥ ♥♥ ②s♥ ♣②♦♥t ♥r♥ s♥ sq♥s r♦ ♥ ♦♥t r♦ ♠t♦ ♦r ♦♦② ♥♦t♦♥
❩ ❨♥ ♥ ♥♥ ②s♥ st♠t♦♥ ♦ s♣s r♥ t♠s♥r ♠♦r ♦ s♥ ♠t♣ ♦ss rt♦♥s t s♦t ♦♥s♦r ♦♦② ♥ ♦t♦♥
❩ ❨♥ ♠r ♥ ♥ ♠t♦ ♦ ♥r♥ ♦ ♥str♥♦t ♥ ♠♥♦ sq♥s ♥ts
❨ ♠t♠t t♦r② ♦ ♦t♦♥ s ♦♥ t ♦♥s♦♥s ♦ r ❲s P♦s♦♣ r♥st♦♥s ♦ t ♦② ♦t② ♦ ♦♥♦♥rs ♦♥t♥♥ P♣rs ♦ ♦♦ rtr