HAL Id: tel-00661866https://tel.archives-ouvertes.fr/tel-00661866

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

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

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

❲ 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

♥♦♠♥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

♦♥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

♠♣♠♥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

♣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

♥♥ ♥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

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♦♥ ♥ ♦♦

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

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♥

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♥ ♦♥ ♦

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♥

♦♥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 ❬♥♥

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♦♥

♦ 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 ♥

♦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♥

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

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 ♥

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♥

♦♦ 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

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

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

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

♣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

♣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

♥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

♥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

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

r ❱s③t♦♥ ♦ t ♥ t ❬❪ t ♦r ♥ ♥r♦ ♦♥② ss ♦♠♥ ♥ ♣rs♥t s♥t t ♦r tt ♣♦♥t ♥ ♠ss♥ r②

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

♥ 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

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♦♥

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

♠ 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

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

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♥

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 ♥

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♦♥

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

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

❬ ❪ ❬ ❪ ❬ 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∗

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).

♥ 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

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

♦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♦♥♥

♥ 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

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).

❲ ♥ 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〉

〈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

♥ 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

♦♥ ♥ 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)

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♦♥

♠ 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

)

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

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

♣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

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)

❲♥ ♥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

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

♦♥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

❲ ♥ ♥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

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

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 ?

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′

• ❲ ♥ ♣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

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♥ ♥ ♣ ♦

♣♦♠♥ 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)

♥ ♣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

♥ 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 −

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

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

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

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

♣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♦♠

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♥

♥ 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

(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

(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

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

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

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

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

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

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 ♦

♠♦ 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

(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

♥ ♠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 ❬❪

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

❲ 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

45

3

6

17

18

7

8

15

16

12

19

20

10

11

9

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♦♥ ♥

♠♦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

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

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

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

♦♥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

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♠♦

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 ❪

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♦♣

♣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♠

♦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 ♦♥

hittite

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tocharian_a

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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

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 ♥

armenian

albanian

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luvian

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tocharian_b

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latin

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62

78

66

85

58

0 10002000300040005000600070008000

r ♦♥s♥ss tr ♦r t ♥ t ❬❪ tst ♦ts s♦tstr♦♣s s♣♣♦rt t ♣r♦t② ♦ ♦♥

♥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

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

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

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

♥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♦♠

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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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

♣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

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

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

♠♦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♦

♥♦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

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

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 ❬❪

♥ 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♦♥ ♦

♦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

♥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♦♠

♦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

♥ ♥ ♥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

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

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♦♥

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

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

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

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

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♥

♣♣♥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

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♥

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♦

♦ ♥♦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

♦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

♦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

♦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

♦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

♦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

♥ 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

♥♥ 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

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

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♦♥

❲ 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

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

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

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