HAL Id: tel-00881242https://tel.archives-ouvertes.fr/tel-00881242v4

Submitted on 9 Dec 2013

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Urban scene modeling from airborne dataYannick Verdie

To cite this version:Yannick Verdie. Urban scene modeling from airborne data. Signal and Image Processing. UniversitéNice Sophia Antipolis, 2013. English. tel-00881242v4

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sss ♥térêts ♣r♠tt♥t ♦t♥r ♥ ♦♠♣ré♥s♦♥ ♣♣r♦♦♥ sè♥

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strts r ♦♣t ♦r t②♣ ♦ r♥ ♠♥ts r ♦ ♥srt♥ ♦t

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strt t r♦st♥ss ♥ st② ♦ ♦r s②st♠s

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r ♣trs ♥ ♦rrs♣♦♥♥ t ♦r tr ts

r t P♦♥t ♦ sst♦♥

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r♥t s③s

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rs ❬❯ ❪ s r♥③t♦♥ rts ♥ ♥rs♥ ♥ ♦r ♥ t♦♠t

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r♥t rs ♦ ♠♣♣♥ srs s s ♦♦ rt ❬♦♦ ❪

♦r r♦s♦t rt rt ❬r♦s♦t ❪ ♠♦♥strts t rr♥t ♥trst ♥

t rt ♣♦t♥t ♦ t♦♠t ♠t♦s t♦ ♥rt t② ♠♣s ♠♥

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stt♦♥s r♥ r♣rs♥tt♦♥ ♥ ssst t♦♥♦♠♦s r♦♦ts ♥t♦♥ ♥

r♦♥ t r♦t ♣♥♥♥

s♣t ts ♣r♦♠s♥ r♥ ♦ ♣♣t♦♥s t rr♥t ♠♦♥ ♦r

s st rstrt t♦ st rs ♦r ♣r♠r② rs♦♥ ♦r ts s t

t② ♦ qr♥ t t ♥ t♦② rqrs ♦t ♦ ♠♥ ♦rt

♣tr ♥tr♦t♦♥

❲t♥ t st ♦r t♦ r♥t t♥qs t♦ t♦♠t② ♦t

r♥ s♥ t ♥ ♣r♦♣♦s ♥ t ♦♥ ♥ sr s♥♥rs s s r

r s t♦ ♣r♦ ♥ rt ♥ ♥s ♣♦♥t ♦ ♦ ♥ r♥ s♥ ♥

t ♦tr ♥ ♠t♣ ♠s ♦ t ts sss② ♥ s t♦tr

♥ ♦rr t♦ s②♥ts③ ♠ss ❲ t s ♦ ts t♦ t♥qs t♦

qr r♣rs♥tt♦♥s ♦ r♥ s♥s ♥ ♦♥sr② ♠♣r♦ ♥ ♥

♥♦ ♥rt r ♥ rt r♣rs♥tt♦♥s ts ♠t♦s ♥rt

q♥tt② ♦ ♥♦r♠t♦♥ t rt s ♦ s ♦t♥ ♥trt Pr♦♥

♠t♦s t♦ ♦♥rt ts ♠♦♥t ♦ t ♥t♦ ♣rt② s r♣rs♥tt♦♥

s ♣r♦♠ ♦ rt ♠♣♦rt♥

❯t♠t② s♣t ♦t ♦ ♦rt ♥ ♥ ♣t ♥t♦ ♥rt♥ ♦♠♣t

r♥ r♦♥strt♦♥s ♥♦ sts②♥ s♦t♦♥ s ②t ♥ r♦t t♦ t t♥

ts ♠♥s st r♣rs♥ts ♥♥ ♣r♦♠

t r♣rs♥tt♦♥

❲ tr r ♠t♣ t t②♣s ♥ r♥ s♥ qst♦♥ s ♦s ♦♥

st t♦ t②♣s ❱ ♠ss ♦t♥ r♦♠ ♠ t ♥ r t

♦t ♦ r s t♥ t ♠t♦s ♣r♦♣♦s ♥ ts tss s t♦ t②♣s

♦ t ♥ tr r t ♠♦st ♦♠♠♦♥② ♦s♥ ♥ s ♥ r♥

s♥ r♦♥strt♦♥ s

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r♦♠ t r♠♦t s♥s♥ ♦♠♠♥t② tr♦ stts qst♦♥ ♦r r♥t

♥s ♥ ♠r s♥s♦rs ♥ s ♠ rrs s s r ♥ Pss

s ♠ qt② ♠ t ② s♣r ♥ ♣② ♠ t

s ♥♦ s② t♦ qr st♦r ♥ s ♥♦t ♦st② s rsts ♥ ♦♥s ♦ ♣trs

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t r♣rs♥tt♦♥

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r t ♦t tt ♦r r r t t ♥s ♥ r ♥t ♣ss

t ♠t♣ rtr♥s

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r ♥♦s ❪ t② ♦ ts s♦r ♦ ♥♦r♠t♦♥ ♠s

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t❱ tr♦ t

t❱ tr♦ ❱ t s s② ♦ t ♦r♠ ♦ ♣♦♥t ♦ ♦r

♠s ♥rt r♦♠ ♦t♦♥ ♦ ♠s s ♠ss r ♦t♥ ② t ♦

♦♥ st♣s strt ♥ ♦r r♦ rst t ♣♦st♦♥ ♦ t ♠r

s r♦r r♦♠ ♠ s st♣ s s② ♦♥ ② trtr r♦♠ ♦

t♦♥ t♥q r s♥t trs r♦♠ ♠ r str t♥

tr s♣ ①tr♥s ♣r♠trs ♦ t ♠rs r r♦♠ t

st ♦ ♦rrs♣♦♥♥s ♥ s♣rs ♣♦♥t ♦ ♦ st s♥t trs ♥

♦t♥ s ♣♣r r♦ ♦r ♠♦r ts ♦♥ t♥q r♦s

♠t♦s ♦r st♠t♥ ♠r ♣r♠trs r sr ♥ ts t♥ ♣♣r ♦

♥ss t ❬♥ss ❪ ♥② ❱ t♥qs ♥rt ♥s ♣♦♥t ♦s

♥ r♣rs♥tt♦♥s ♦ t s♥ s ♠ss st t♦ st♣s ♦♥ ♦r

♣tr ♥tr♦t♦♥

r strt♦♥ ♦ ♠ t t ♦rrs♣♦♥♥ s♥ r♦♥strt♦♥ ♦♣

t ①♠♣s ♦ r ♠ t ♦tt♦♠t ①♠♣s ♦ str♦ r♦♥s

♠ t ♦♣rt ♦♥strt♦♥ ♦ t ♦s♠ ② trtr r♦♠ ♦t♦♥

t♥q t ♠s r♦♠ r ♦tt♦♠rt ♦♥strt♦♥ ♦ t

♦s♠ ② ♣t ♦ t❱ tr♦ ❱ t♥q t ♠s r♦♠ r

♦t ♥ ❱ ♠s ♦rts② ♦ r t ❬r ❪

r♦ ♦t tt t ♠s s ♥rt t trt♦♥ ♠t♦ s s P♦ss♦♥

r♦♥strt♦♥ ❬③♥ ❪

♦♦♥ t t①♦♥♦♠② ♦ t③ t ❬t③ ❪ ❱ t♥qs r

ss ♥t♦ ♦r sss ♦♠tr t ♦r ♦ ♦r♥♥ t

❬♦r♥♥ ❪ ♣t ♠♣ ♠r♥ ♦s t ❬♦s ❪ sr

♦t♦♥ ❩rs t ❬❩rs ❪ ♥ r♦♥r♦♥ r

t ❬r ❪ ♣ t ❬♣ ❪ ttr ♣♣r♦ s ♦s♥ t♦

♥rt ❱ ♠ss ♥ ♦r ♦r ♠t♦s s ♣♣r♦ rst ♦t♥s t

♠r ♣r♠trs t♦ ♥rt qs♥s ♣♦♥t ♦ ② trrs♥ t ♣♣♦r

♥s ♦♥ ♠ ♦♦♥ ♦r ♠t♥ trs ♥② tr♥t♦♥ s

t♥ ♥r♠♥t② ♦♥strt r♦♠ t s♣rs ♣♦♥t ♦ ♥rt t ♠t

♥ trs ♠♥♠♠ st t ♥♦♥ srt st② ♥ sr qt②

①trts ♥ ♥t sr r♣rs♥tt♦♥ ts sr s ♠♦ s t ♥tr

t r♣rs♥tt♦♥

r t♣s ♦r st♥r ♣♣r r♦ ♥ ❱ ♦r r♦ ♥ r

♥♠r ♦ ♠s s tr trs r ①trt t ♥r ♠t♦s s

s rrs ♦r♥r tt♦♥ ♥ r♦♣ ② s♠rt② t rt ♣♦s ♦

♠r s ♦♠♣t trs r ♣r♦t ♥ t s♣ t♦

s♣rs ♣♦♥t ♦ ♥ ♣♦st♦♥ ♦ t ♠rs t rs♣t

♠s r ♦t s② ② ❱ ♥s ♣♦♥t ♦ s ♥rt r♦♠

t ♠s ♥ t rt ♣♦s ♦ ♠r ♠s s ♥rt r♦♠

t ♥s ♣♦♥t ♦

t♥ ♦♠s ♥s ♥ ♦t ♥ ♦♠s ♦ts ♥ ♦t

♥② ts ♥t sr s s s strt♥ s♦t♦♥ ♦r rt♦♥ r♥♠♥t

r♥♠♥t rtr♥s t ♥ sr t②♣② s rtr ♦♠♣①t② t♦

♣t t♦ sr♣ rss ♥ s ♥ s♠♦♦t ♥ s♣rs ♦♥ t rs

rt♦♥ r♥♠♥t s♦ rss t ♦ ♥♦s ♥ ♦rrts s♦♥t♥ts

♦♥ t ♦r♥ sr ♦r ts ♥ ts ♦♥ ts ♠t♦ r ♥ ♥ t

♣♣r ♦ ♣ t ❬♣ ❪

❱ ♠ss ♥rt r♦♠ ♣ t ❬♣ ❪ r s♦♥ t♦ ♠♦r

rt ♥ ♦♠♣t t♥ ♣r♦s stt♦trt ♠t♦s ♥ ❱ t♥qs t tt

t♠ Prtr② t rt ♠①tr t♥ ♣♦t♦♦♥sst♥② ♥ rr③t♦♥

♣tr ♥tr♦t♦♥

r ❱ ♠ss ♥♣t t r ♥s ♠ss ♣♣r♦① ts ♣r ♠

♥rt ② t❱ tr♦ s②st♠ r♦♠ r ♠s ② r s♠♥tr

♥ ♦♥t♥ ♦♠tr ♥ t♦♣♦♦ ts s s ♦s s♥trst♥ ts

r♦♥ ♥s tt ♠r r♥ ♦♠♣♦♥♥ts ♥ ② r s♣t str

t♦♥s ♦ rts ♥ ts s ♦s♣s ss ♦rts② ♦ ♥trtst

s t♦ s♠♦♦t t rt r♦♥strt♦♥ ♦ t s♥ ♥ t♦♥ t ♠s s

t♦♠t② st t♦ ♠ rs♦t♦♥ ♥ ♣rsrs sr♣ ♥ s♠ ts ♦

t ♦ts ♦♠♣r♥ t r t sr ♥ t ♦♦♥ t♦♥

❱ t s ♦r t♠tr r② t ♠♦r ♦♠♦♥♦s ♣♥♠tr s

trt♦♥ ♥ t♦♥ t ♥♦r♦♦ rt♦♥s♣ t♥ t ♣♦♥ts s ♥

♥ r♦♠tr ♥♦r♠t♦♥ ♦♥t♥ ♥ t ♠s ♥ s♣♣♦rt t s♠♥t③t♦♥

♦ t s♥ s ♣tr

❱ ♠ss r ♦r ♥♦t ♦♣t♠ ♦r rt♥ ♣♣t♦♥s s s r♥

♣♥♥♥ rss ♣r♦♣t♦♥ s♠t♦♥ ♦r ♥t♦♥ ♦r ♠♦s

♠st tr ♦♠♣t ♦r ♦♥t♥ s♠♥t ♥♦r♠t♦♥ ♦♥ t ♥tt♦♥

♦ r♥ ♦ts t♥ t s♥ ♦r♦r ♦♠tr ♥ t♦♣♦♦ ts

①st ♥ t ♠ss t ♠♥ ♣r♦♠s ♦♠ r♦♠ t ♠ss♥ t ♦s ♥ s

♥trst♥ ts t s♣t tr♦♥♦s strt♦♥s ♦ rts ♥ ts

t ♦ss ♦ r② ♥ ♣rs♥ ♦ rt♥ srs s s ss ♥ t ♠r♥

♦ r♥t r♥ ♦♠♣♦♥♥ts s s trs t s s ts ♠♦st②

t r♣rs♥tt♦♥

♥rt ② t rt♦♥ ♣♣r♦ ♦ ♣ t ❬♣ ❪ r strt ♥

♦t tt t ♠ss s t♥ ts tss ♥ ♥② ♣r♦

tr♦ t ♦rts② ♦ ♥trtst r♥ t s♠♥t③t♦♥ ♦ t

♠ss s♦t♦♥ t♦ ♥rt t s♠♥ts ♦ t r♥ s♥ r♦♠ ❱ ♠ss s

♣r♦♣♦s ♥ ♣tr t♦♥ ♥♦r♠t♦♥ ♥ r ♦r ♦ ♠t♦s s♥

trtr r♦♠ ♦t♦♥ ♥ t❱ tr♦ t♥qs s ♥ ♥ t♦♥

r t

♥r sr♣t♦♥

r t rs ♣rs ♥ qs♥s ♣♦♥t ♦s st ♦r r♥ r

♦♥strt♦♥ r st♥♥ ♦r t tt♦♥ ♥ ♥♥ s t♥♦♦②

s♥ ♥ t s♥s♦r t♦ ♠sr st♥s t♥♦♦② s s ♦♥ t t♠

♦t ♣r♥♣ r sr ♠ts t ♣ttr♥ ♥ t rt t s

♥②③ r t♥♦♦② rs ♦♥ t♦ ♠♥ rtrsts rst t rt♦♥

♦ t ♣ttr♥ s♦ sttr t s ♥ ♥t♥st② ♣♥♥ ♦♥ t

s③ ♦ t ♦t s s ts ♥tr♥s rt♥ ♣r♦♣rt② s t rt♥

♣r♦♣rt② ♦ t ♠♥ts s ♥♦♥ r♦♠ t rtr♥ s♥ ♦♥ t t♠ ♦r

t t ♣ttr♥ t♦ tr ♥ ♦rt s rt② ♣r♦♣♦rt♦♥ t♦ t st♥

r♦♠ t s♥♥r t♦ t ♦t ♥ tr♦r ♣rs ♠sr ♦ t st♥

s ♦t♥ s t♥♦♦② s ♥t② s ♦r ♠t♦r♦♦② t t s q②

♥ ♥t t♦ rt ♣♦t♥t ♦r r s ♠sr♠♥ts r s ♥

♠♣♦② ♥ ♥♠r♦s ♣r♦ts t♦ sst t ♥s♣ t♦♣♦♦② s s ♦♥ ♦♦rs

♦rst ♥♦♣s r♥ s♥rs ♥ ♠♦♥t♥s ♣r♦♣rts st ♦ ①♣♥

s♦♠ rs♦♥s ♦r t sss ♦ r

❱rstt② r♥t ❵s♥s ♥ s♥t ♣♥♥ ♦♥ t stt♦♥ ♦

♣♥trt t tr ♥rr♦ ♥t ♥ t②♣② ♥♥♦♠tr

♠ s s r ♥ s s ♦r st♥r ♠sr♠♥t

♥♥♦♠tr ♠

♦♠♣t♥ss ♠sr♠♥t s ①tr♠② ♥s t r♦♥

t♦ ♠sr♠♥ts ♣r s♦♥ r♣rs♥t♥ r♦♥ t rs♣t②

♣tr ♥tr♦t♦♥

trt② ♣♦♥ts ♣r sqr ♠tr ♦r r♦r♥ r t rs♣t② trrstr

r t

r② ♠sr♠♥t s ①tr♠② ♣rs t s♠♣♥ rr♦r ♦

♥t♠trs rs♣t② ♠♠trs ♦r r♦r♥ r t rs♣t②

trrstr r t

♦♠♣r t♦ ♠s ❱ t r ♠sr♠♥ts r r② rt ♠♥

ts t♥♦♦② st ♦r r② t r♦♥strt♦♥ ♦ ♥s ♥ s

♥ t♦♥ r♦r♥ r s♥♥rs ♥ s② s♥ r② r s♥s ♥♦tr

♠♣♦rt♥t ♥t ♦ ts t♥♦♦② ♦r ♦♥♥t♦♥ ♠rs s ts rt

♠♠♥t② r♦♠ t♥ ♥ ♥ rt♦♥ t♦tr r t s ♣rtr②

♣♣r♦♣rt ♦r r♥ r♦♥strt♦♥ ♦r r♦s t♦rs t t ♥t

♦ s♥ s t♥♦♦② ♦ ♥ t ts t♥♦♦② s st ♥♦♠♠♦♥ t

s♥♥r rqr t♦ ♦t t t s ①tr♠② ①♣♥s ♥ r② ♦rt♦rs

♥ ♦r ♦♥ rtr♠♦r r t s rr♥ s ♥♦♠♣t s♠♥s ♣♦♥t

♦s ♥ t ♣♦t♦♠tr ♥♦r♠t♦♥ s ♦t♥ ♠ss♥ ♣♦♥t ♦s

♠ss♥ ♠sr♠♥ts ♦r t♦ ♠♥ rs♦♥s rst② ts t♥♦♦② s str♦♥②

♣♥♥t ♦♥ t ♠tr ♣r♦♣rt② ♦ t ♦ts ♦r srs s♥♥ ♥ t♦

♣♦♦r qt② ♦r ♠ss♥ ♠sr♠♥ts ♦r ♥♦♥♦♣q ♠trs tr♥s♣r♥t

♦ts s s ♥♦s ♦ ♥♦t rs♣♦♥ ♦♣q ♦ts ♦♥② ♦s ♥

s♦♥t♥ts r ♦♥ t♥ t ♠sr♠♥ts t♦ t ♥♦st ♣r♦♣rt②

♦ stt s♥♥r ♦♥ t s♥♥r ♦r s♥ ♠t♣ s♥♥rs r s♠♣ t

t ②s t♦ ♠t ts ♣r♦♠ t♦ ts ♦s ♥♦t ♦♠♣t② s♣♣rss t

s strts r ♦♠♠♦♥② ♦s♥ ♥ t trtr tr ♠t♦s t♦ t

♠ss♥ t ♥ s②♥ts③♥ ♣♦♥ts ♣s♠♣♥ r t t♥qs

t ♦r ♦ ❲♥ t ❬❲♥ ❪ ♦r s♥ ♦s srs ♦r t ♠ss

t ♦r ♦ ♠ t ❬♠ ❪ ts ts ♣♦♦r ♠sr♠♥ts

♠ss♥ t ♥ ♦s♦♥s ♥ s♥♥t② ♠♣r t qt② ♦ t r t

s

♦t tt t♦ t ♠♥♠♠ ♥♦r♠t♦♥ ♣r♦ ② r t s t

st♥ t♦ t ♦ts t♦♥ ♥♦r♠t♦♥ s s♦♠t♠ ♣r♦ s s

t r♣rs♥tt♦♥

r ♦♣t rrstr sr ♥♥r t r♦♠ t ♣♦♥t ♦ t

s♥♥r r t ♠sr♠♥t s♠s ♥s ♦♣rt ♠ t s③

r♦♠ t s ♦ t ♥♦st ♦ t s♥♥r ♦t t ♦s ♥ t str♦♥

s♦♥t♥ts r rs ♥ t ♥st② ♦ t ♠sr♠♥t ♠s r

♦rts② ♦ ❬t♦ ❪ ♦tt♦♠t r♦r♥ r t ♦t ♥ t

♣sss ♦tt♦♠t ♦t tt t rt strtrs r ♥♦t ②s s♥♥

r ♦① ♥ tt t ♦r♣♣♥ st t rts str♦♥ rt♦♥ ♥ t

♣♦♥t ♦ ♥st② r♥ ♦① t t♥ r♦♠ ❬♣♥t♦♣♦r♣② ❪

♥♠r ♦ rtr♥ ♣ttr♥s ♦r ♥♠r ♦ ♦s ♠♣t ♦ t rtr♥

s♥s ♥ rst ♥ st ♦ s ♥♦r♠t♦♥ s ♥ts ♦♥ t ♠tr

♣r♦♣rts ♦ t ♦ts ♥ ♥ s ♦r st♥s♥ t♠ r♦♠ ♦tr

s t sst♦♥ ♠t♦ sr ♥ ♣tr ♦r ♠♦r ♥♦r♠t♦♥ ♦♥

t ♥♦ ♦r♠ ♦ t r t ♥ ② t♦ t③ t ♦♥ ♥ ♦♥st t

♦r ♦ t t ❬t ❪ ② s r P♦♥t Pr♦ss PP t♦

♠♦ t sttr s♥s s ♠①tr ♦ ss♥s

♣tr ♥tr♦t♦♥

♦♦♥ st♦♥s sr ♠♦r ts ♦ t r t♥♦♦② ♥ ♥

♣rtr t♦ st♦rs r trrstr r ♥ r♦r♥ r

rrstr r

rrstr sr ♥♥rs r ♦♥ ② t♦ qr r t

r♥ ♦ ②s t♦ rt② ♦ t♥ s♦t♦♥s ♦ s♣♣♦rt♥ ♣t♦r♠s s

s rs tr♣♦s ♦r ♣s ♦♥t ♦♥ r t s s ♦r s♥♥♥

s ♦ ♥s s ♠♥t♦♥ ♥ t ♦r ♦ r t ❬r ❪ ♥ t

s♠ ② t ❬ ❪ s t trt♣♣r ♠♦ sr s♥♥♥

s②st♠ tt ♣trs 360 ♠sr♠♥t ♦ t strt ♥ tr stt♥ t s②st♠

s ♦r r s♥♥rs t ♥ r② ♦ ♠♠ ♦t tt t P❯

♥♦r♠t♦♥ s s s②♥ts③ ♠♦ ♦ t t② s s t♦ rstr ♥

♣r♦♣r② ♥ r s♥ t♦ ♦tr

♥t② s ♥ ♠♦♥t ♦♥ ♣ ♦r ♥♦♦r s♥ r♦♥strt♦♥

❬ ❪ ♠ s♥s♦rs ♥ r rt t♦ ♦tr t♦ ♦t♥ ♥ rt

r♦♥strt♦♥ ♦ ♥♦♦r ♥r♦♥♠♥ts ♠ trs r s t♦ ♣r♦♣r② ♦♠♣t

♠♦s ♦ ♠s ♥ t♥ ①trt ♣♥ ♣s t ♠♣♣♥ ♦ t t①trs t♦

t sr s♥ ♥ ♥r t ♠sr♠♥t r♦♠ stts s ♥ ♥♦♠♣t

s♠♥s ♣♦♥t ♦ s t♦♣ r♦

r♦r♥ r

r♦r♥ r t s qr r♦♠ r♦r♥ sr ♥♥rs ♠♦♥t

♦♥ r s s s ♣♥s r♦♥s ♦♣trs t s♥♥r rs ♦♥

❯ ♥♦r♠t♦♥ t♦ ♣r♦♣r② rstr t t ❲t♥ t st

s♥♥t q♥tt② ♦ r♦r♥ r t ♥ ♦t r♦♠ ♣♥s ② t

♠r♥ t♦♥ ♥tr ♦r r♦r♥ sr ♣♣♥ ❬ ❪ ♥ ♠

♦r ♣r♦ts ♦r r♥t② ♥♠r♦s ♣r♦ts ♦st ♠♦st② ♥

t ❯ ♠ tr r t s♦ ♦r rsr ♣r♣♦ss ❬❯

♣♥t♦♣♦r♣② ❪

♣r♥♣ ♥t ♦ s ts t② t♦ ♣r♦r♠ q qst♦♥s s♥

t r ♦rs r r♦♥ ♥ s♦rt ♣r♦ ♦ t♠ ♦r t

t r♣rs♥tt♦♥

r ♦♣t ♠ ♦ rrstr sr ♥♥r ❱❩ ♠♦♥t

♦♥ tr♣♦ ♥ ♦♣rt ② Pr♦ss♦r ♦q♥ ❲♥ ♥ st♥t r♥②s ♠r③

r♦♠ t ❯♥rst② ♦ Prt♦ ♦ t ②③ ♦♣rt t rst♥ r t

♥ ♠♦♥ ♠s r ♦rts② ♦ t ❯❱ ♣r♦t ❬❯❱ ❪

♦tt♦♠t ♠ ♦ trt♣♣r ♠♦ sr s♥♥♥ s②st♠ ♦tt♦♠rt

t rst♥ r t ♠s ♦rts② ♦ ❬ ❪

♣r♥♣ r ♦ trrstr r t ♥♦st ss s ♥tt

t r s s♥ t s♥♥r s rtr ②s r♦♠ t ♦ts ♥ s

♦r♥t ♦♥rs s ♦♥sq♥ ♠♦st ♦ t rt strtrs s

s t r ♠ss♥ r♦♠ t ♠sr♠♥t ♥ r ♦① ♦♥ ♥

s tt ♠♦st ♦ t rt s ♦ t ♥s r ♠ss♥ t s♦♠ ♣rts

r ♥♦♥tss ♣rt② ♣tr t♦ t ♦q ♥♦st ♦ t s♥♥r

♣rt② ♦r♥ t♠ s ♠s t sst♦♥ ♦ t ♣♦♥ts ♥ ♠♦r

t s♥ ♦♥ ♥♥♦t ♥♦r ♥② str♦♥ ♣r♦rs ♦♥ t t s s ss♠♥

tt ♥♦ ♣♦♥t ♦♥s t♦ rt strtr

♣tr ♥tr♦t♦♥

r strt♦♥ ♦ r♦r♥ sr ♥♥r ♥ r♦r♥ r t

t ♦♠♥ qst♦♥ ♦r r♦r♥ r ♠sr♠♥t t ♦♠♥

r♦r♥ r t t ♦♦r ♦rrs♣♦♥♥ t♦ t r♥t ♠♣ts ♦ t

sttr s♥ ♠s ♦rts② ♦ ❬♦♥♦r♠ts ❪

♥ t♦ ts t♦ t②♣s ♦ t ♥ qr r♦♠ trrstr ♦r r♦r♥

s♥s♦rs ♥♦t tt ♥ ♣rt r t s ♣tr tr♦ r s♥♥rs

❱ t s ♥r② s②♥ts③ r♦♠ r♦♥s ♠s t♥ ♥t ♦

t q♥tt② ♦ ♣trs t♥ ② t♦rsts ♥ r② strt ♦♥♥ ♥t②

♥ tr♥ ♥ ♦sr ♥ ♣♦♥t ♦ t s s ♦r ♥♦♦r r♦♥str

t♦♥ ❬ s ❪ s t♥♥② s ♠♦st② t♦ t r♥t t②

♦ ♦♦st r♥ s♥♥rs s s t r♦s♦t ♥t ♣r♦ ♥s t

♥♦s② ♠sr♠♥t t♥ st♥ ♦ ♦♥ t♦ ♠trs ❬③ ❩♦ ❪

s ♣♣r♦s r ♦♥② ♥ t r② ♦♣♠♥t ♣s ♥ ♦t ♦ t s♦♣ ♦

ts tss

♥ t ♦♦♥ st♦♥s r ♦♥ ♥r ♣♣r♦s s♥ ♠

t r t ♦r ♦t t♦ r♦♥strt r♥ s♥s

trtr r ♦♥ r♥ r♦♥strt♦♥

trtr r ♦♥ r♥ r♦♥strt♦♥

r r ♠t♣ ♣♣r♦s ♦r r♦♥strt♥ ♠♦s ♦ r♥ s♥r②

♥ s♠r ♠♥♥r s ss t ❬ss ❪ st♥s t♥

♣♣r♦s rqr♥ sr ♥♣t s♥ ♠♦♥ ♠t♦s ♥ ② t♦♠t

♣♣r♦s s♥ r♦♥strt♦♥ ♠t♦s ♥ ♠♦♥ rqrs sr

♥trt♦♥s t♦ ♦♥tr♦ t ♣r♦ss r ♦ ♥trt♦♥ ♣♥s ♦♥ t qt②

rqr ② t sr ♠♦r ♥trt♦♥ ♥ t♦ ♠♦r ♣rs r♦♥strt♦♥ t t

♦st ♦ st② ♥ s♥ r♦♥strt♦♥ t♦♠t ♣♣♥ ♦ t♦♥s s

♣r♦r♠ t♦ r♦♥strt t s♥ t♦t ♥② ♥ ♦r sr ♥trt♦♥

♥trt s♥♠ s ♠t♦s

♥♠ s♥ ♠♦♥ ♠t♦s s ♥ ♠ s rr♥ ♦r t

sr s ♣r♦s t s t♦ ♠♥② ♥♥♦tt ♥♦r♠t♦♥ s s ♥s♥

♣♦♥ts ♣♥r strs t t♦ ♦♠♣♥st t ♣t ♥♦r♠t♦♥ ♥tr♥s②

♠ss♥ ♥ ♠s ♥♠ s♥ ♠♦♥ s ♦ ♥trst ②rs

♦ ♦r ①♠♣ t ❬ ❪ rqr sr ♥♥♦tt♦♥s ♦ t

♠♥ s ♦ t ♥s t♦ ♥r t ♣r♦♣rts ♦ t s♥ ♣♦ t

❬♣♦ ❪ ♣r♦♣♦s P♦t♦r ♠t♦ s♥ ♥rt ♠s ♥

♦♠♥t♦♥ t sr ♥trt♦♥s t♦ r♦♥strt t①tr ♥s ♥t②

♥ t ❬♥ ❪ ①♣♦t s②♠♠trs ♥ ♥♦r♠t♦♥ ♣r♦ ② t

sr t♦ ♣r♦♣r② r♦♥strt ♦♠♣① ♥s ♠tt♦♥ ♦ t s♥♠

s♥ ♠♦♥ ♣♣r♦ s ts str♦♥ ♣♥♥② ♦♥ ♥♦r♠t♦♥ ♣r♦ ② t

sr ♠♥ t s②st♠ ♥♦♠♣t t ♥ t♦♠t ①t♦♥ s rt②

rstr♥s t s ♦ s ♠t♦s t♦ s♥ ♥ r♦♥strt♦♥ ♦r♦r t

♦♥② ♦♥ ♠ t♦♦ ♠♥② rs ♦ r♦♠ r t rst♥ ♥ ♠ts

♣tr ♥tr♦t♦♥

♥trt ♥ t♦♠t ♠t♣♠ s ♠t♦s

t♣♠ s♥ ♠♦♥ ♥ r♦♥strt♦♥ ♠t♦s ❬

♦s r ❪ r ♠♦r r♦st s♦t♦♥s ❲ st♥s t♦ ♠♥

sss ♦ t♥qs

trtr r♦♠ ♠♦t♦♥

trtr r♦♠ ♠♦t♦♥ ♥t② ♦♥sst ♦ st♠t♥ t ♠r

♦t♦♥ ♥ ♠ t♥ r♦♠ t♠♣♦r ♥♣t sq♥ ② tt♥

r♥t tr ♣♦♥ts ♥ st ♦ ♣trs s s s♠rts t♥

t♠ss ♦♥ ♥ ♦t♥ ② rt ♠r ♣r♠trs ♥ s♣rs

♣♦♥t ♦ ♦ t s♥ r♥t ♣♣r♦s s♥ ♥ ♣r♦♣♦s

♥ t trtr ❬♥ ♥ ♦r♥s r ❪ ♥

t ❬♥ ❪ t sr♥ ♠♦s t♦ ♣♦♥t ♦ ♥rt ②

trt♥ r♦♠ ♥ ♥t t ♣r♦ ② t sr ♦s ♦r ♣♥s r trt②

r♥ t♦ ♠ t♠ t ♣r♦♣r② ♥ ♣r♦t ♥t♦ t ♣trs ♥ t

❬♥ ❪ s t♥q ♦r t ♠♦♥ ♥ sr ♥trt♦♥s r♥

t t①tr ♠♣♣♥ ❱♥s♥ rt♦♥s r rt② ♦♠♣t t♦ ssst t

st♥ r♦♠ ts rs ♣♥s t①tr ② s♥ ♥r② ♦♣t♠③t♦♥

♥ P♦ss♦♥ ♥♥ r ♦♠♣t ♥t② r♠r t♦♠t ♠t♦s

r ♣s ❬♦s r ❪ ♦s♥ ♦ ♣trs ①trt r♦♠

s srs r r s t♦ r♦♥strt ♦♠♣t r♥ strts ♥

ts ♠t♦s t ♠♥ ♥ s ♥ t ♦r♠♥ q♥tt② ♦ ♠s

♥t♦ t s②st♠ ♣r s♠ s ♣r♦♣♦s t♦ ♥t② tt t s♠rts

t♥ ♣trs ♦♦ ② r② ♥t ♦♣t♠③t♦♥ ♠t♦ ♦r ①tr♠②

r ♥♦♥♥r st sqrs ♣r♦♠s

t❱ tr♦

t❱ tr♦ ❱ ♠t♦s ♥rt ♥s strtr ♣♦♥ts ♦r

♣ts r♦♠ ♥ ♥s♦rt st ♦ ♠s strtrs r ♦♠♣t s♥ t

trtr r ♦♥ r♥ r♦♥strt♦♥

♥♦♥ ♠r ♦t♦♥s t tr rs♣t ♠s ♦t♦♥ ♦ t ♠rs

♥ ♦t♥ s♥ t♥q ♥t② ❱ ♠t♦s r ♦♥ t

♦♥♣t ♦ ♣♥rs♣♥ t♦ ♥r t strtrs ❬♦♥s ❪ ♦r

t ♠t♦s rst② ♦ t♥ t st ②rs ♦r ♠♦r ts

rr t rr t♦ t ①♥t sr② ♦♥ ❱ ② t③ t ❬t③ ❪

♦r ①♠♣ ♥ t ❬♥ ❪ ♠♣r♦ t ❱ ♠t♦ s♥ st♥

♥♦ tt ♣r♦♣r② ♥s ♦s♦♥s ♣ t ❬♣ ❪ ♣r♦♣♦s r♦st

t♦♠t ❱ ♠t♦ r②♥ ♦♥ r♣ ♦♣t♠③t♦♥ s ♠t♦ ♥rts

qt② r♥ ♠ss r ♥♦rt♥t② t♦t ♥② s♠♥ts ♥ ♣tr

♣r♦♣♦s ♠t♦ t♦ t ♠ss♥ s♠♥ts ♥ t♦ s♠♣② ♠ss

♥rt t ts ♣♣r♦ ♥② ♥♦s t ❬♥♦s ❪ ♠♣r♦

❱ ♦r ②s♣♣♦rt srs ♥ t ♦♠♣tt♦♥ s ♣r♦♣♦s ♦r

♣r♦♣r② ♥ ♥s♦ts ♥② ttrr③t♦♥ s t♦ t

♠s r♦♥strt♦♥ s ♠t♦s ♣r♦ r s♥ r♦♥strt♦♥s t t

rst♥ ♠ss ♦♠tr ts ♥tr s♠♥ts ♥♦r ♥② ♥rst♥♥

♦ t s♥ ♦r♦r t♦ ♣rsr s♠ ts ♦ t s♥ ♥s ♠ss

r ♥rt ♥ ♥ t rs r t ♦ ♥♦t ♥ssr② ♥ r

r♦♥strt♦♥s s s rt ts s t ts

♥trt sr s ♠t♦s

srs s♥ ♠♦♥ ♥ r♦♥strt♦♥ ♠t♦s s t r♦♠ sr

s♥♥rs t♦ s②♥ts③ r♥ s♥s ♣♦♥t ♦ ♦ t s♥ s s② ♦

t♥ r♦♠ ♣t ♠♣s s ♦r r♦s♦t ♥t ♦r rt② r♦♠ t s♥♥rs

s ♦r r t s ①♣♥ ♦r srs t ♥ s♣② r

t tt s rtr ♥s ♥ qt s♠rr s ♣rt② st ♦r r♥ ♠♦

♥ ♦r ♥♦s ♥ ♦trs ♦t♥ ♦rr♣t t ♠sr♠♥t rqr♥ sr

♥trt♦♥ t♦ r♦♥strt t r♥ s♥s ♥ t ❬♥ ❪ ♣r♦♣♦s ♥ ♥

trt tt♥ ♦ ♦①s ♦♥ ♥♦♠♣t r t ♦r r♦♥strt♦♥ s♥ t

♥ ♦♥t①t ♦♥srt♦♥s srt ♦♣t♠③t♦♥ s s t♦ ss♠ ♦①s ②

♥♥ s♥♣♣♥ ♦rs ttt♥ tr♠ ♥ ♦♥t①t tr♠ ♥s t♦

♣tr ♥tr♦t♦♥

♠♥ t♥ r♥s ♥♦ ♦t t s♠♥t ♦ t s♥s

rt ♠♦s r ♥rt ♥ s♣t ♦ ♠ss♥ ♦r ♥rt t ♥ t

♦tr ♥ t ❬ ❪ s ♦♦st ♣t ♠rs s s r♦s♦t ♥t

♥ sr ♥trt♦♥s ♦r ♥trt ♥♦♦r ♠♦♥ ♥ tr ♦r ♦♥♥ sr

♥trt♦♥s ♠♣r♦ t rt♠ ♠♦♥ ♦r ①♠♣ ♣ t t ♦♦♣

♦sr ♣r♦♠ ❬trst ❪ ♥s♦ts ♥ ♥ ♥♦♦r ♠♣♣♥

t♦♠t sr s ♠t♦s

❲ ♥trt ♠t♦s ♣r♦ stst♦r② rsts t② ♦♣rt ♣♣r♦♣r

t② ♦♥② ♦r ♥ ♥s ❲♥ t ♦♠s t♦ r s♥ r♦♥strt♦♥ t

♠♥ ♦♣rt♦♥s t♥ t ♥trt ♠t♦s ♦♠ t♦s s t♦♠t

r s♥ r♦♥strt♦♥ ❬❩♦ P♦s ❩♦ r ❪ s♠s

t♦ t ♥①t ♦ st♣ t♦ ♥ r ♥ t r♥ s♥s ♥ t s

♥ ♥ ♦♦t♣r♥ts ♥ t s♥ r ♥ ♦♥ ♥ ①trt t♠ s

♦t♦♥ ♦ rt♥s tt♥ ♥ t♦♥ ♠♣ ❬r ❪ s t rst ♦

♣rtt♦♥♥ ❬ ❪ s♥ ♣ s♣ ♦ sst ♦ ♣♦♥ts ❬Pr ❪

r ♥ ❬❩♦ ❪ ♦r ❱♦r♦♥♦ ♥ ❬♦tt♥st♥r ❪ ♥ t♦♥

t♦ t ♥ ♦♦t♣r♥ts t♦♥ trs r s♦♠t♠ ♥ r♥ t

♣r♦ss ❱r♠ t ❬❱r♠ ❪ ①trt s♠♥ts ♥ ♦♥ ♣♥s

t♦ ♥rt ♥② r♣s s r♣s r s t♦ tt ♦♠♠♦♥ ♥

s♣s s♣ ❯s♣ s♣ t♦ ♠♦ t ♦rrs♣♦♥♥ strtrs

r♠♥♥ ♣rts t ♣rts tt r ♥♦t ♠♦ ②t r s♠♣② r♣rs♥t

s rt♥r ♥s r t ❬r ❪ ♥rt ♠♣ ♦

t ♣r♦t ♦♥ ♣♥s s♦♠t♠ ♣ts ♥ t trtr

♥ ♦♠♣t rt♦♥s♣s t♥ ♣r♦t♦♥s r♦ ♥♦♠

♠♦♥ t ♦♥♥t♦♥s s s♦ t r♣ t ❬♦②♦ ❪ ♥ t♥

♣r♦t t♦ ♥ t♦ ♦♠♣t ♥ rt ♥ r♦♥strt♦♥

♥st ♦ rt② ♣r♦ss♥ t r ♠sr♠♥ts ❲ t ❬❲ ❪

s r② ♥s ♥ t t r ♦ ♥ s♠♣② t

♠s ♥ s ② tt r♥t trs r ♣rsr s♠♣t♦♥ s

s ♦♥ s♠♥t ♦♥str♥ts ♦♥ tt ♣r♠ts t ♥t ♥s

trtr r ♦♥ r♥ r♦♥strt♦♥

❬♥ ❪ ♥ s♠♣② ♦t♥ r♦♠ t r ♣♦♥t ♦

♦r ♥ ♥rt♦♥ ♠t♦s r sr ♥ ts ♥ t ♦r ♦

r♠ t ❬r♠ ❪

❲ ♠♥② rsrrs ♦s ♦♥ t ♥♥ ♣r♦♠ ♦ r♦♥strt♥

♥s ♦♥② r t ❬r ❪ ♦♠♣t t r♥ ♠♦♥ ②

s♦ ♦♥sr♥ ♠♦r ♦ts ♦ t r♥ ♥r♦♥♠♥t ♣r♦♣♦s ♠t♦

♦r ♦♠♣① r♥ s♥ r♦♥strt♦♥ s♦ ♦♥srs ♥ tt♦♥ ♥

r♦♥ r♦♥strt♦♥ rst ♥ ♣r♦♠ ♦ t r ♣♦♥t ♦ ♥

♦r sss ♥ r♦♥ tt♦♥ ♥ ♥♦♥ss s ♦♥ ② s♦♥

♦r♠t♦♥ ♥s r ♥rt r♦♠ r ①tr ♣r

♦♦♥ ♣♥r ♣ts ♥ s♠♣ t ♦♥str♥ ♠t♦♥ ♠t♦

r♦♥ s ♥rt ② ♠s♥ t r ♣♦♥ts s r♦♥ t

trs t ♠♦st ♦♠♥♥t ♠♥ts ♥ t tt♦♥ r r♦♥strt s♥

t♠♣t rt ♣s♦ s♣s t ♣r♠trs st♠t s♥

trs ♦rt♠ ♦♥♣t② ts ♦r s s♠r t♦ t ♠t♦ ♣rs♥t ♥

♣tr

♥ rr t♦ ♠♦♥ P ♥ ❱♦ss♠♥ ❬P ❪ ♣r♦♣♦s s♠♥

tt♦♥ ♦ t trrstr r t ♦r tt♥ ♣r♠tr ♠♦s ♦♥ s

♦tt♦♠♣ ♣r♦ss s s t♦ ①trt ♦♠tr ♥ s♠♥t trs ♥②

②♣♦ts③ ♠♦s ♦ ♦ ♣rts ♦ t ♥s r s t♦ ♥rt t

s ♥♦tr ♠t♦♦♦② s t♦ s r♠♠r rs tt ♣r♦♣r② sr

t rrr♥t strtrs ♦ s ♦r ①♠♣ r t ❬r ❪

①♣♦t r♠♠r rs ♦♥ trrstr r t ♦r r♦st r♦♥strt♦♥

♣r♦r ♠♦♥ ♦ ♥ strtrs s ♣r♦r♠ s ♦♥ ♦tt♦♠♣

♥ t♦♣♦♥ strt② rst ♦tt♦♠♣ r♦♥strt♦♥ srs s s♥ t♦

♥r r♠♠r rs s rs r t♥ ♥ ♥t♦ tr♥ t♦♣♦♥

r♦♥strt♦♥ s ♣♣r♦ ♦♣s t ♠ss♥ t ♥ ♥rts s②♥tt

s ♦r ts ♠t♦s r②♥ ♦♥② ♦♥ r t t s♠

♠tt♦♥ s♥ r t t♦♥ ♦t ♥♦r♠t♦♥ s s ♦♦rs t①trs

♣tr ♥tr♦t♦♥

t r t t♦ r♦r ♦♠♣r t♦ ♠t♦s s♥ ♠ t s ♠tt♦♥

s ♥tr♥s② ♥ t♦ t ♥tr ♦ t r t

♥trt ♥ t♦♠t ♠ts♦r ♠t♦s

♦ ♠♣r♦ t r♦♥strt♦♥ ♥ ♦r♦♠ t ♠tt♦♥s ♠♥t♦♥ ♦r

♦♥ ♠② s ♠ ♥♦r♠t♦♥ t t r t r t ❬r ❪ s

♦t ♠s ♥ r t t♦ ♣r♦ r② rt t①tr ♠♦ ♦

s r ♠♥ ♦r r ♦♠♥ t r t ♥rt r♦♠

♠♦♥t s♥♥rs t s rstr ♦♥t♦ ♦tr s♥ ♥♦r♠t♦♥

♦♥ t ♠♦t♦♥ ♥ ♦♥ t s♥♥r ♦r♥tt♦♥ ♥♦♥♦♥① ♦♣t♠③

t♦♥ ♠t♦ ♦♠♣ts t s♦t♦♥ ♦r t rstrt♦♥ ♥ s♠r s♦♥

t ❬ ❪ ♣r♦♣♦s ♥ ♥trt s♠ t♦ ♠r ♠s ♥ ♣♦♥t

♦s rst s ♥ ♥♥ t①tr ♠♦ ①trt♥ rt ②r ♦

♥s t ♠t♦ sss② tts r♣tt ♣ttr♥s ♦♥ s t♦ ssst

t r♦♥strt♦♥ ♦ ♥s t ♠ss♥ t ❩♥ t ❬❩♥ ❪ ♦♠

♥ r ♠ t t r t t♦ t♦♠t② ♥rt ♠t♣ ♦

ts ♦ t s♥ ♥ ♦rs♠♥t ♠♣ s ♥rt s ♦♥ t

♣r♥♣ rt♦♥s ♦ t ♥s ♥ ♥ ♦♣t♠③t♦♥ ♣♣r♦ s s t♦

♠r t s♠♥t s t♦tr ♥ ♥trst♥ s♣t ♦ tr ♦r s t ♣♦s

st② t♦ st r♥t ♠r♥ ♦♥ts r♥ t ♦♣t♠③t♦♥ ts ♦♥tr♦♥

t ♦ t r♦♥strt♦♥ r ♠s r ♥② ♣♣ t♦ t①tr t

♠ss ♦ t r♥ s♥s

♥trt♦♥ ♦ ♠t♣ s♦rs ♦ t s ♥♦t ②s ♣♦ss ♥ rstrt♦♥

t♥ t t r♠♥s ♥♦♥tr ts s t ♦r ♦ st♥ t ❬st♥ ❪

♦r ❲♥ t ❬❲♥ ❪ ♦r ①♠♣

t s ts ♠♣♦rt♥t t♦ ♥♦t tt ♥♣♥♥t② ♦ t t②♣s ♦ t s t

♣r♦♠ ♦ r♦♥strt♥ r② ♥s ♥ t r s♥s ♥r t s♠♥

ts s st ♥ ♦♣♥ ♣r♦♠ r♠♦r ♥ t ♠♦♥t ♦ t ♥

t♠② ♠♥♥r ♥rt♥ ♦♠♣t t trtt ♥ s♠♥tr

r♥ s♥s s st ♥♥ ts

t♦♥ ♦ r♥ r♦♥strt♦♥ ♠t♦s

t♦♥ ♦ r♥ r♦♥strt♦♥ ♠t♦s

♣rtr ♥ ♥ r♥ s♥ r♦♥strt♦♥ s t♦ t t r♦♥

strt♦♥ qt② ♥ tr♠ ♦ ♦♠♣t♥ss ♥ r② s♣t t ♥ ♦

♥r ♥♠r ♦r r♥ s♥ r♦♥strt♦♥ ♥♦ sts②♥ s♦t♦♥ s ②t

♥ ♣r♦♣♦s r② r♥t ♥♠r s sts ② t P ♦♠♠

♥t② ❬♦tt♥st♥r ❪ t t s ♥♦t ② s ②t t s t t♦ ♥ ♦♠♠♦♥

ss ♠♦♥ t ♠tt ♦ s♦t♦♥s ♣r♦♣♦s ♥ t trtr ❱r♦s s♣ts

①♣♥ ② ♥♦ ♦♠♠♦♥ ss s ♥ ♦♥ ②t

rst② ♦ ♠sr♠♥ts s s♦♥ ♠t♣ t s qt ♦r

rt② r♣rs♥t♥ r♥ s♥rs rst② ♥ t②♣s ♦ t r♦r♥

r t trrstr r t r♦r♥ ♠s ♥ ❱ ♠ss ♥ q

t② ♥st② ♦ r ♣♦♥t ♦ rs♦t♦♥ ♦ t ♠s ♠s t t

t♦ ♦♠♣r ♠t♦s s r♥t t

♦ r♦♥ trt ♥ r♥ r♦♥strt♦♥ t r♦♥ trt s rr②

♥ r♥ s♥r② ♦s r② q② ♦r t ②rs ♥ t s r②

t t♦ ss t♦ ♣t ♥ rt s②♥ts③ ♠♦s ♦ t

♥s ♦r t♦ tr rttr ♠♣s t ♣rs s

t② ♦ t t s ♦ t ♦st ♦ t qst♦♥s t

s ♦t♥ ♣r♦tt ② ♦♣②rt ♥ ts ♥♦t ♣② s ♠♥②

rsr ♣r♦ts ♥ t ♦♣rt ♦♥ tr ♦♥ t ♠ ♦♠♣rs♦♥

t♥ t♠ r② t s♥ t t s r♥t ♥ ♦t♥ ♥♦t

♦ ♦♠♠♦♥ t♦♥ t♥q ♥② tr r ♠♥② ②s ♦

t♥ t r♦♥strt ♠♦ ♥② ♠trs r s ♥ t trtr s

s t ♥ st♥ t s♦r st♥ t ♦r♦r t st♥

rr♦r s ♥♦t t ♦♥② ♠♣♦rt♥t rtr♦♥ t♦ ♦♥sr t rst♥ t♦♣♦♦②

♥ t ♦♠♣t♥ss r s♦ ♠♣♦rt♥t ♦r ♠♥② ♣♣rs s tr ♦♥

r♥t rtr♦♥ ♠s t t t♦ ♦♠♣r t ♠t♦s t

♦tr s♥ t ♠sr♠♥ts r♦♠ ①♣r♠♥ts r ♥♦t t♥ t s♠

rr♦r

♣tr ♥tr♦t♦♥

s r s♦♠ rs♦♥s tt ①♣♥ ② ♥♦ ♦♠♠♦♥ ♥♠r s ♥ ♦♣t

② t r♥ r♦♥strt♦♥ ♦♠♠♥t② ②t ♥♠r tt ♦s ♥♦t ♦r

♠t♦ ♦♠♣r t♦ ♦trs s t t♦ rt

r♥ t ①♣r♠♥ts ♥ ts tss ♥♦t ♥ ♥② ♣♣r♦♣rt ♥

♠r s ♦♠♣r ♦r ♣♣r♦s t ①st♥ ♠t♦s ♥ t

t♦ t st ♦ ♦r ♥♦ ♥ s♦♥ t♦ ♥rt ♦♦ r♦♥strt♦♥ ♦

r♥ s♥s ♣ r s t♥ t♦ ♦♠♣r ♦r ♣♣r♦s t ♠t♦s ♦ s♠

r t②♣ ♥ qt② ♦ t ♦r ①♠♣ ♦r ♥ ♦♣t♠③t♦♥ ♠t♦ ♣rs♥t

♥ ♣tr s ♦♠♣r t♦ ①st♥ ♠t♦s ♥ ♣rtr② t ♠t♦ ♦

s♦♠s t ❬s♦♠s ❪ r ♥ r♦♥strt♦♥ r♦♠ r♦r♥ r

t ♣rs♥t ♥ ♣tr s ♦♠♣r t t ♠t♦ ♦ ❩♦ t ❬❩♦ ❪

ss t s♠ t②♣ ♦ t ♦ s♠r qt② ♦♥r♥♥ ♦r ♥ r

♦♥strt♦♥ r♦♠ ❱ ♠ss s♦ ♣rs♥t ♥ ♣tr rst r♠♦

♦♠tr ts r♦♠ t ❱ ♠ss s♥ ♥ ♠♥♦ ♠ss ♦r

r ♦♠♣rs♦♥ t t ♠t♦ ♦ ♦♥t♥r t ❬♦♥t♥r ❪

♦s ♥ ♣r♦♣♦s ♠t♦s

Pr♦♠ stt♠♥t

s♣t sst♥t ♦rt s t♦♥ ♥ t♦♥ t♦ t t

t ♣r♦♠ ♦ t♦♠t② ♥ rt② r♦♥strt♥ r r♥

s♥s r♦♠ rs ♥♣t t ❱ ♠ss srs t t t r

♠♥s ♥ ♦♣♥ ♣r♦♠ rst s♠♣t♦♥ t♦ ♦r♦♠ ts ♥ s t♦

r♦♥strt t ♥s s st ♦ ♥ ♦①s t srs ♥ t

tr ♦♠♥♥t rt♦♥s ♥♦♥ ♥ t trtr s t ♥tt♥ ♦r

ss♠♣t♦♥ ❬♥s r ❱♥s ❪ s s♠♣t♦♥

♠s t ♣r♦♠ ♠♦r trt t t r♦♥strt♦♥ ♦s ♥♦t ②s t t

rt② ♠♦♥ ss♠♣t♦♥s ♦t♥ ♦rs♠♣② t s♥s r♦r

s♥ ♠t♦s tt r ♥♦t s ♦♥ ts ss♠♣t♦♥ ♦♥ s♦

tt sr ♥trt♦♥s ♣ t♦ ♣r♦♣r② r♦♥strt t ♥s ♥ ♥

♥r t r♦♥strt♦♥ t s♠♥ts t t s ♠t t♦ s♥ ♥

♦s ♥ ♣r♦♣♦s ♠t♦s

t t♠ s ♠tt♦♥ s ♥♦t ♣t ♦r ♠♦♥ t②s r♥

s♥ ♦♠♣♦s ♦ t♦s♥ ♦ ♥s s s♥ ② t♦♠t

♣♣r♦s r ①♣♥ ♥ t♦♥ tt t♦ r♥t t②♣s ♦ t

♥trst♥ ♣r♦♣rts ♦r s♦♥ t t ♣r♦♠ ♦ t♦♠t r♥

s♥ r♦♥strt♦♥ ❱ t ♣r♦s ♦r♥t r♣rs♥tt♦♥ ♦ t s♥ t

♠♣♦rt♥t ts t t ♦♥② ♠♦rt r② ♥ ♥♦ s♠♥ts r

t ♣r♦s ①tr♠② ♣rs ♥♦r♠t♦♥ ♦ t s♥ t♦t str♦♥ ♦r♥

♦r ♣♦t♦♠tr ♥♦r♠t♦♥ ♦♥ t ♦ts s♥♥ ♦t t t②♣s r tt♥

♠♦r ♥ ♠♦r ♦♠♠♦♥ ♥ ♣r t♦ qr r♥♥ t♦ t ♥ ♣r♦♠

t q♥tt② ♦ ♠sr♠♥t ♥ ts tr♦♥♦s qt② ♠s t ♥

♦r ♥♦ s ♥ r♦st r♥ r♦♥strt♦♥ ♠t♦s ♥ ♠♦r ♥t

♥② t ①st♥ ♠t♦s ♦r r♥ r♦♥strt♦♥ r② ♣r♦ s♠♥t ♥

♦r♠t♦♥ ♦♥ t s♥ ♠ts t ♣♦ss ♣♣t♦♥s ♦ s r♦♥strt♦♥s

r♦r t s ♦♦s tt ♣♣r♦s r s♠♥tr ① t♦

rs r♥t t②♣s ♦ t ② t♦♠t ①♣t r♦♠ t ♥tt♥ ♦r

ss♠♣t♦♥ ♥ ♣ ♦ ♥♥ r q♥tt② ♦ ♦♠♣t ♥ ♥♦♠♣t ♥

♦r♠t♦♥ r rqr t♥♥ t s♠♥ts ♦ t r♥ s♥ ♣ ♦r

t r♦♥strt♦♥ ♥ ♥ t r♥ ♦ ♣♦t♥t ♣♣t♦♥s ♦♥ ts

♣r♦♠s s t ♦ ♦ ts tss

♦♣ ♦ ♦r rsr

♦ rss ts ♣r♦♠s rstr♥ ♦r rsr t♦ ② t♦♠t ♠t♦s

♦r r s♥ r♦♥strt♦♥ ❲ ♦♥trt t♦ t stt♦trt ② ♣r♦♣♦s♥

♠t♦s ♦r r♥ s♥ ♥rst♥♥ ♥ r♦♥strt♦♥ ♣② t s♦♣

♦ ♦r rsr ♦rs t ♦♦♥ ♣r♦♣rts

t♦♠t ♣r♦ss♥ s♥ ♠st ♥rt t♦t sr ♥tr

t♦♥s s rtr♦♥ ♠s t s♦t♦♥s s ♥ r♦st

♥② rs r♥ r♦♥strt♦♥ s♦ t rs♦♥ t♠

♥ t♦ r♥ ♦♥ ♣rs♦♥ ♦♠♣tr s rtr♦♥ ♠s t s♦t♦♥

s t ♦♠♠♦♥ ♦♠♣tr

♣tr ♥tr♦t♦♥

♠♥t ♥ s♥ r♦♥strt♦♥ ♥r ② s♠♥t

♥ s s ♥ r♦♥ tt♦♥ t s ♥♦r♠t♦♥ s

♦r ♥♥ r♥t strts ♦ r♥ r♦♥strt♦♥ s s♠♥ts ♥

t r♥ ♦ ♣♦ss ♣♣t♦♥s ♦r ♦r ♠t♦s ♥ ♣ r♥ ♣♥♥

♣rt ♣♦♥ ♦♠♣♥② ♥ ♠tr② ❯♥♠♥♥ r ❱ t

♣♥♥ ♦♠♥s

r② r♦♥strt♦♥ s t♦ t t♦ r♥t ♣rs r

♥ r♦♥strt♦♥ t s ♠♣♦rt♥t t♦ ♣r♦ r♦♥strt♦♥ s rt s

♣♦ss t♦ ♥ t r♥ ♦ ♣♣t♦♥s s♠t♦♥ r♥ ♣♥♥

♣rs r♣rs♥tt♦♥ r♦♥strt♦♥ s t♦ ①tr♠② tt

t ♠s s ♠♥♠♠ ♥♠r ♦ ts st trtt ♥

rt ♣ r s t♥ t♦ r♣rs♥t ♠①♠♠ ♦ ts ♣r

sr♥ t t♦♣♦♦② ♦ t ♥s ♥ ♥rt♥ s♠♣ r♣rs♥tt♦♥

♦ t s♥

♦t tt t♦ ♦t t②♣s ♦ t r s ❱ t ♥ r t

♥♦♥ ♦ t♠ r s s♠t♥♦s② s sr ♥ t s♦♥ ♠t♦s ♥

t♦♥ ♦r♦r ♦♥rt♥ ♠ t t♦ ❱ ♠ss s t♥s t♦

t ♠t♦ ♦ ♣ t ❬♣ ❪ ♥♦ rtr ts ♦♥ ts ♣r♦ss r ♥

♥ ts tss

r

❲ ♣rs♥t ♥ ♣tr t r♥t ♠t♦s s ♥ t trtr ♦r r♥

s♥ ♠♦♥ ♥ r♦♥strt♦♥ ♦ t②♣s ♦ t r ♥ ❱ t

♦t♥ r♦♠ ♠ t ♥trst♥ ♣r♦♣rts ♥ rt ♥♦r♠t♦♥

♥ ♦r r♥ s♥ r♦♥strt♦♥ t♦♥② ♥♠r ♦ ♣r♦♠s r

♥t sr s♦rt② ♦♥srt♦♥s r r♦t t♦ t t♦ s♣②

t s♦♣ ♦ ts rsr ♥ t♦ r② t ♦r ♦♥ r♥ ts tss

♣tr srs t ♠♥ts r♣rs♥t♥ t r♥ s♥ r♦s

r♥ ♦ts ♥ t♦rs r sss rst♥ ♥ t ♥t♦♥ ♦ sss ♦

♠♥ts rtrsts ♦ ts sss r sss② sr s st

r

r P♣♥ strt♦♥ ♦ ♦r ♣♣r♦s ♥ rr♥ ♣trs t♥ ts

tss

ts t s ♦r t ♥t♦♥ ♦ r♥t sr♠♥t trs s r♥ t

s♠♥t ♥ t♦ ♥ ♠t♦s t r t ♥ ❱ ♠ss

r ♥② sr ①♠♣s ♦ s♠♥t ♥ r ♥ ♥ ♥tr

♦♠♥ Prts ♦ ♥ ♠t♦s ♣rs♥t ♥ ts ♣tr r ♣s ♥ ♦r

♣♣r ❬❱r ❪

♣tr ♣rs♥ts ♥ ♣♣r♦ ♦r tt♥ t♠♣t♣r♠ts ♥ r s♥s

♠t♦ tr♠♥s t ♥♠r ♦ ♦ts ♥ t s♥ s s tr rs♣

t ♣r♠trs s ♥ ♠t♦ ♥s r rsts ♥ ♥ ♣t ♦♠

♣tt♦♥ t♠ ❲ ♦♠♣r t t stt♦trt ♠t♦s ♥ t t

♥ts ♦ ts ♣♣r♦ ♠♦♥ ♦tr ①♣r♠♥ts ♥ ①♠♣ ♦r

tt♥ t♠♣ts trs t♥ r t t♦♣rt ♦r♥r Prts ♦

ts ♠t♦ r ♣s ♥ ♦r ♣♣rs ❬❱r ❱r ❪

♣tr ♣rs♥ts ♣♣r♦s ♦r r♥ ♠s s♠♣t♦♥ ♥ ♠♦♥ ♦

♣♣r♦s r ♣rs♥t ♦r r t ♥ ❱ ♠ss t ♠♣ss ♦♥ t

♥ ♠♦♥ ♣rt s t ♠♦st ♥♥ ♣r♦♠ ♦t ♣♣r♦s s

♣tr ♥tr♦t♦♥

t r♦♠ t ♠t♦s ♣rs♥t ♣tr Prts ♦ ts ♠t♦s r

♣s ♥ ♦r ♣♣r ❬❱r ❪

♣tr ♦♥s ts tss ♥ ♣rs♥ts s♦♠ ♥trst♥ tr rsr

rt♦♥s

♣tr

❯r♥ s♥ sr♣t♦♥ ♥

♥rst♥♥

♥tr♦t♦♥

❲ ♠♦st rsrrs ♦s ♦♥ ♥ r♦♥strt♦♥ s ♣r♦② t

♠♦st ♦♠♣① ♠♥t ♥ ♥ r♥ s♥ ♦ t♦ ♠♣s③ t ♠♣♦rt♥

♦ ♦tr s♥ ♠♥ts t♦♦ ♦t♥ ♥t t st tr st♥t sss ♦ ♠♥ts

♥ tt ♥ r♥ s♥s ♥ tt♦♥ ♥ r♦♥ s sss

r ♣rs♥t ♥ ♠♦st r♥ s♥s ♥r r♥t rtrsts ♣♥♥ ♦♥ t

qst♦♥ ♠t♦ r ♦r ❱ Pr♦ss♥ t ❱ ♠ss ♦♥ ♥ ss

t ♥ ss ♥t♦ t♦ ♠♦r ♠♥♥ ssss r♦♦ ♥

♥ ts st♦♥ rst ♥r sr♣t♦♥ ♦ ss s s ♦♥

② ♦♥sr♥ t♦ r♥t s♣ts ♦r ss ♥r sr♣t♦♥ ♥

stt♦♥ ♦ t ♠♣♦rt♥ ♦ ts ss ♥ r♥ s♥r② ♥ ss♠♣t♦♥s

r ♦♣t r♥ t ♠♦♥ ♦ t ss ♥ ts ♣tr t

sst♦♥ ♠t♦s s t♦ tt ss r sr sr♣t♦♥ ♦

r♥t ♦♠tr trs ♥ s♠rt② ♥t♦♥s s ♥ t♦♥ ♥

t♦♥ ♦♦ ② t ♥t♦♥ ♦ ♥r② ♥t♦♥s ❱r♦s ①♣r♠♥ts

r t♥ ♣r♦r♠ t♦ t t ♠t♦s t♦♥ ♥ t♦♥ ♦t

tt t ss♠♣t♦♥s sr r ♦r t ♠♦♥ r ♦♣ tr ♥

♣tr ♥ ♣tr

❲ ♥♦ ♦♥sr ss ♦ ♠♥ts ♥ ts ♣r♦♣rts

♣tr ❯r♥ s♥ sr♣t♦♥ ♥ ♥rst♥♥

r r ♣trs ♥ ♦rrs♣♦♥♥ t ♦ rs r♥ t r

② ♦♥t♦♥ ❯ ♠ ♥ Prs r♥ rt ♦r sss ♦ ♥trst

♥ tt♦♥ r♦♥ ♥ s♠ strtr r s② r♦♥③ ♦t t

♣♦♥ ♥ t r t ♦ rs t tt s s s ♦ ♥ t t t

② r♦♥ ♦ r② ♦♥t♦♥ ♥tr ♥ t ♥♦♠♠♦♥ ♥ strtrs

♦ Prs rt ♠s ♦rts② ♦ ♦♦ ❬♦♦ ❪

♥ ♥②ss s ss ♦ ♠♥ts s t ♦r ♦ t r♥ s♥ r♣

rs♥tt♦♥ ❲rs ♦tr sss ♥ ♥t ♥ ♠♥② ♠t♦s ♥

♠♥ts ②s ♥ ♥ ♥ t r♥ r♣rs♥tt♦♥ s r ♠♥t

♦ t s♥ s ♠♥t ♦♥sttts t ♠♦st ♥♥ ♣rt ♦ t r♦♥str

t♦♥ s♥ ts ♥s ♦ r♦s ♥ ♥q s♣s

♦♥strt♦♥ s ①♣♥ ♦r ②♣♦tss ♥t② ♦♣t ♥ t tr

tr s t♦ ♠♦ t ♥s s st ♦ ♦♥♥ ♦①s ♦ s♠r ♦r♥tt♦♥

s ♣♣r♦s ♥r② ♥♦♥ s ♥tt♥ ♦r s st t♦ ♠♥② ♣

♣rs ♦r ♠r♥ t② r♣rs♥tt♦♥ s ♣♣r♦ ♥♦rt♥t② ♦rs♠♣s

t ♦♠♣① ♥ t♦s ♣r♦♠ ♦ r♥ s♥ r♦♥strt♦♥ ♣rtr② ♦r ♦

r♦♣♥ ♥trs ♦r ①♠♣ ♦♥ rt ♦♥ ♥ s ♥q ♥ ♦♠♣①

♠t♥ ♥ strtrs t ♦♠ ♥ t ♥tr ♦ Prs ts ♦♠♣①

♥ ♥ ♥♦t ♣♦ss② ♣♣r♦①♠t t t ♥tt♥ ♦r r♣r

s♥tt♦♥

♥tr♦t♦♥

❱tt♦♥ ♥②ss ♠r♦s sts strt t s♦ ♥r♦♥

♠♥t ♥ ♦♥♦♠ ♠♣♦rt♥ ♦ r♥ r♥ s♣s ♦r ①♠♣ ❲♥

t ❬❲♥ ❪ s♦ ♦rrt♦♥ t♥ t rs♥ts ♥ ♥ t

♣r♦①♠t② ♦ r♥ s♣s t♥ ♠ rs ♠r② s t ❬s ❪

strss rs ♦ ♠♥ r♦♠ t ♣♦♣t♦♥ ♦r r♥ ♦♠♠♦♥ s♣s tt ♣r♦

s♥t s♦t♦♥ r♦♠ t ♥♦s② strss r♥ ♥r♦♥♠♥t ts tr♦r

♥ s♣♦r② strt r♥ s♣s s ② t♦ ♣r♦ qt rs ♦r t

♣♦♣t♦♥ ♦♥sq♥t② ♥ r♥ s♥ ② r♥ s♣s ♥ t

t♦♥ s♥ t ♥ ♦ t t③♥s ♣♥s ♦♥ t s strts t ♠♣♦rt♥t

r♦ ♣② ② t tt♦♥ ♥s ts s tt♥ ♥ r♦♥strt♥ ts

ss ♦ ♠♥ts ss trs t s ♦ r ♠♣♦rt♥ ♦r ♣r♦♣r r♣rs♥

tt♦♥ ♦ r♥ s♥ ♦t tt s♠♣ ♥ t r ♣trs ♦ ts s

♦r rs r♥ t r② ♦♥t♦♥ ❯ ♠ ♥ Prs

r♥ rt s ♥♦ t♦ ♥♦t t ♦r♠♥ ♣rs♥ ♦ r♥ s♣s ♥

tt♦♥ t♥ r♥ s♥rs rrss ♦ ts ♣rtr ♥ ♦ r♥③t♦♥

♦♥strt♦♥ s t tt♦♥ t♥ r♥ s♥s s ♦♥tr♦ ♥

♦♥str♥ ② r♥ ♠♥ts srr♦♥♥ t r♦s ♥s t t tt♦♥

♥ ts s ♠♦st② ♦♥sttt ♦ trs s r♥ t r♦♥strt♦♥ st♣ s

s♠ tt ♥ ♣♣r♦♣rt ♠♦♥ ♦ t tt♦♥ s ♦t♥ ② ♦♥② ♠♦♥

t trs s s♠♣ ♦♠tr s♣s ♣s♦ s♣ s♠♣s♦ s♣

♥ ♦♥ s♣

r♦♥ ♥②ss ♦♥trr② t♦ t st♥r s ♦ sr ♠r♥ ts

♠♥② ② r♥③ rs s s s♥♥ ♥ r♥s♦ rs ♥ ♠♥②

♦trs ② ♦♥ ② r♦♥ ♦r t s♦♣♥ ♥tr ♦ t ♥r②♥ trr♥ s

♦t♥ ♥t r♥ r♥ ♠♦♥ ♥ s ♦ ts t ♦♥ ♥♥ trr♥

t rs t ♦ t ♠♦♥ ♦ t r♦♥ rt♥② ♥♥ t

♦ r♥ r♣rs♥tt♦♥ ♦r ①♠♣ ♦♥ t strt♦♥ ♠ t

r♦♥ ♥♥♦t ♣r♦♣r② sr ② r t sr

♦♥strt♦♥ ♥ rt r♣rs♥tt♦♥ ♦ ♥ r♥ s♥ rqrs t♥

ts ss ♦ ♠♥ts ♥t♦ ♦♥t ♥ ♦rr t♦ ♣r♦♣r② r♣rs♥t t ♦ t♦♣♦♦②

♣tr ❯r♥ s♥ sr♣t♦♥ ♥ ♥rst♥♥

s ♥ rrr strtr ♠♥♦ sr ♥ ♥♦t ①♠♣ ♦ s

ss♠♣t♦♥s s t ♦r ♦ r t ❬r ❪ r r ♠s s rst

♥rt t t t♦ ♦② ♦r♥t r t♠tr② ♥

qr ♠s ♠t♦♥ s♠♣s t sr t♦ rt ♥ rt ♥ ♥ r♦♥

r♣rs♥tt♦♥

♠ strtr ♥②ss st ss ♦ r♥ ♠♥ts ♦♥sr r

s t ss ♦ s♠ strtrs ♥ ttrs s ss trs s♠ ts ♦ t

r♥ s♥ ♦ts ♦♥ t r♦♥ s s rs ♣str♥s tr ts ♥s

t ♥ ♦ts r♣rs♥t♥ s♠ rrrts ♦♥ t ♥s s s ♠♥②s

tts ♦r♠r♥♦s ♦♥s ♥ s♦ ♦♥ ♥tr♦t♦♥ ♦ ts ss ♦s

♠♦r ①t② r♥ r♦♥strt♦♥ ② ♦♥tr♦♥ t r ♦ ts ♦♥ ss

t♦ ♦t♥

♦♥strt♦♥ ❲ ♥♦t ♦r tt t r♥ r♦♥strt♦♥ s ♥♦t str♦♥②

♠♣r ② ♥t♥ ts ♦ts ♥ ♠② tr ♦r ♥♦t t♦ ♥

t♠ t♥ t r♦♥strt♦♥ ♣♥♥ ♦♥ t rqr r ♦ ts

s ts r s② ♥♦r ♥ t trtr t ♥ ①♣t♦♥ ♦ tr t

❬tr ❪ ♦ ♦s ♦♥ tt♥ ♥ r♦♥strt♥ ♦r♠rs r♦♠ r

r t

s ♠♦♥strt t s r② ♠♣♦rt♥t t♦ ♦♥sr t ♦r sss ♦ ♠♥ts

♥ tt♦♥ r♦♥ ♥ s♠ strtr ♦r ♥ rt r♦♥strt♦♥

♦ t r♥ s♥s ♦r t ♥s r♠♥ t ♠♦st ♥♥ ♣r♦♠

♥ ♦♥sr♥ ♦♠♣① ♥ rrr ♥ strtrs s Prs ♦♥

rt t tt♦♥ s ♦♠♥♣rs♥t ♥ r♥ s♥s s r ♣trs ♦♥

♥ t r♦♥ sr ♥ qt ♦♠♣① ♦r ② r♥ rs s r②

♦♥t♦♥ ♦♥ ♠ ♥② s♠ strtrs ♥ ♦♣t♦♥② ♥

r♥ t r♦♥strt♦♥ t♦ ♥rs t ♦ ts ♦ t r♥ ♠♦♥

♦t tt t♦ ♠♥② ts rrs ♥ tr ♠♥ts s ♥

♣♦♥s ♦♦s ♥♦t t♦ ♦♥sr t tr ♠♥ts ♥② r♥ t ♥ ♥

r♦♥strt♦♥ st♣s ♦ ♦r ♥♦ ♥♦ ♦♥ s ②t ♦r ♦♥ t tt♦♥ ♥

♣♣r♦ t r t

r♣rs♥tt♦♥ ♦ ts ♠♥t t♥ t ts rs♦♥ s tt rst t rr♥t

♣♣t♦♥s ♦r t♦♠t r♥ s♥s ♦ ♥♦t rqr ♥ rt tt♦♥ ♦

tr r s ts s♣t s ♥t ♥ ts ♠♥t s ♦t♥ ♠r t

t r♦♥ ♦♥ ♦t t②♣s ♦ t ❱ t ♥ r t ♦ ♥♦t rs♣♦♥

♣r♦♣r② t♦ t ♣rs♥ ♦ tr ♥ ts ♠♥t s tr♦r r♣rs♥t ♣♦♦r②

♦r ♥♦t t s r ♦♥ ♦r ♦♥ ♥ ♥♦t tt ♦s ♥s

t t ♠② ♥t ♥ r t tr s ♦ rtr rt♦♥ ♦r

♠♣r♦♥ t ♦♠♣t♥ss ♦ t r♥ ♥rst♥♥

♣♣r♦ t r t

♦♠tr trs

❲ ♦♥sr ♦r trs t♦ ♦ ♥trst ♦♥r♥♥ t sst♦♥ ♦ r

♣♦♥ts s ♥ tt♦♥ r♦♥ ♥ ♠ strtr ♦t tt t♦ ♦r

♠♦♥ ♣♣r♦ ♠ strtr ♠♥ts r r♦♠ r ♦♥ ♦♥sr s ♦♥

ss ♠♥ts ♥ rr s

r P♦♥t ♦ sst♦♥ ♥ r ♠ t ♥ t ss

♣♦♥t st rt ♦t tt t ♦r sss ♥ ♥ tt♦♥ ♥ r

r♦♥ ♥ r♥ ♥ ♥ t r ♦rrt② s♣rt ♠s ♦rts② ♦

♦♦ ❬♦♦ ❪

♣tr ❯r♥ s♥ sr♣t♦♥ ♥ ♥rst♥♥

t♦♥ t♦♥ ae s t t r♥ t♥ t t rr♥ ♦

♥ t ♣♦♥t t ♦♠♣♦♥♥t s ♦t♥ ② st♦r♠ ♥

②ss ♦♥ ♣♦♥t t♠tr② t♥ s ♦ s③ ♠①♠ s rtrr② s③ s

♦s♥ s♥ t r♥ts t♦ ♣♦♥ts ♦♥♥ t♦ t r♦♥ ♥ ♠♦st ♦ t

r♥ s♥r② ss ♠♣t② s r ♣ ② ①tr♣♦t♥ t s ♦ ts

♥♦r s tr s ♥ t ♦♦♥ ② rtr ② ♣♦♥t s

r♦♠ t r♦♥ t rr t ae tr ts

♦ ♦♥♣♥rt② ♦ ♦♥♣♥rt② ap s t qrt st♥ t♥

t ♣♦♥t ♥ t st sqr ♣♥ ♦♠♣t t ts s♣r ♥♦r♦♦

s♣r ♥♦r♦♦ ♦ ♠trs rs s ♦s♥ ♦rt♦♦♥ st♥

t♥ t ♣♦♥t ♥ t st tt♥ ♣♥ ♦ ts ♥♦r♦♦ s ♦ t

♦ ♣♥rt② r♦♥ t ♣♦♥t ♥ ♦tr ♦rs t ♠♦r ♣♥r t ♥♦r♦♦

s t ♦r t ap tr ts

ttr ttr as s t ♦ t s♣rs♦♥ ♦ t ♣♦♥t ❲♥ t ♥♠r

♦ ♦s ♦ t s♥ s ♥♦♥ as r♣rs♥ts ts ♥♠r as s t♥ ♦♥

♥ ♥♥t② ❲♥ t ♥♠r ♦ ♦ s ♥♥♦♥ as = 1 + |H| t |H| t

♠♥ rtr ♥s s♣r ♥♦r♦♦ s ♠♥s tt t ♠♦r rrr

t ♥♦r♦♦ s t r t as tr ts

♦ ♦♥♥rt② ♦ ♦♥♥rt② al s t qrt st♥ t♥

t ♣♦♥t ♥ t st sqr ♥ ♦♠♣t t ts s♣r ♥♦r♦♦

s ♠♥s tt t ♠♦r ♥r t ♥♦r♦♦ s t ♦r t al tr ts

s ttrts r t ② ♦r ♦♥ts αe αp αs ♥ αl ♥ t♥

♥♦r♠③ ♥ t ♥tr ❬❪ r♦ tr♥rr♦r ♣♣r♦ ♦t♥

t ♦♦♥ ♦r♠t♦♥

βe = min1,|ae|

αe

βp = min1,|ap|

αp

βs = aαss βl = min1,

|al|

αl

♣♣r♦ t r t

♦t tt αs s ♣♦st t ♦♥t s♠r ♦r q t♦ ♦♥ ♦t tt r♦♠

r ♦♥ ♥ t ♥t♦♥ . : [0, 1] −→ [0, 1] s s

x = 1− x, x ∈ [0, 1]

r P♦♥t ♦ sst♦♥ rst r♦ r♥ r t t ♥ t

ss ♣♦♥t st rt ♦t tt t ♦r sss ♥ ♥ tt♦♥

♥ r r♦♥ ♥ r♥ ♥ ♥ t r ♦rrt② s♣rt t♦

♦♦♥ r♦s strt t trs βe βp βs ♥ βp sr ♦ ♦t tt

♦r ttr s③t♦♥ s♣② βp ♥ βl

♥ ♦♥ ♥ s tt t trs ♣r♦♣r② βs s

♦r sttr ♣♦♥ts t tt♦♥ ♣♦♥ts r s βe s t

t ♣♦♥ts ♥ ♥ tt♦♥ ♣♦♥ts r s βp s ♦r

♣♦♥ts ♥ ♦② ♣♥r ♥♦r♦♦ r♦♥ ♥ ♥ r s ♥

βl s ♦r ♣♦♥ts ♥ ♦② ♥r ♥♦r♦♦ t rrs ♦ t

♥s r s

♥ t ♦♦♥ st♦♥s ♥ s♠rt② ♥t♦♥ Di : R3 −→ [0, 1]

♣tr ❯r♥ s♥ sr♣t♦♥ ♥ ♥rst♥♥

♦r ss ♥ tt♦♥ r♦♥ ♥ r♣rs♥ts t ♥rs

♦♥♥ tt t ♣♦♥t xi ♦♥s t♦ t s♣ ss ♦r ss cl

♦t♥ s♦r t♥ ③r♦ ♥ ♦♥ ③r♦ ♠♥s tr s str♦♥ ♦♥♥ t

♣♦♥t xi ♦♥s t♦ t ss cl ♦♥ ♠♥s ♦trs t♦ t s♠s ♦♥tr

♥tt t♦ ♥ ♥t♦♥s r♣rs♥t♥ t ♥rs ♦♥♥ t rt♦♥ s

s s ♥t♦♥s t♥ ♠♥♠st♦♥ ♣r♦♠ sr ♥ t♦♥

❱tt♦♥ s♠rt② ♥t♦♥

❱tt♦♥ s ♦t♥ ♣rs♥t ♥ r♥ s♥s ♥ r♣rs♥ts ② ♠♥t ♦s

tt♦♥ ♦♥sttts ♥♥ ♣r♦♠ ♥ tt♦♥ ♦ts s s

trs r ♦t♥ ♥ r② ♦s ♣r♦①♠t② t r♦♦s ♦ ♥s ♥ ♥ s♠♥

tt♦♥ ♦ ts t♦ sss s ♠♦s ♥ rr t♦ s♠ tt♦♥ ♠♥ts s

s ss t s ♥r tr t♦ ♦♥sr t♠ s r♦♥ ♦r tt♦♥ ♦r♦r

♠♥②s ♥ s♠ strs ♦♥ t r♦♦s r ♦② s♠r t♦ ss ②♥ ♦♥ t

r♦♥ s ♦♥trts t♦ ♣♦ss ♠ssst♦♥ ♦ tt♦♥ t ♥

♠♥ts

❲ ♦♥sr tr trs t♦ r♥t ♦♥r♥♥ t sst♦♥ ♦ t

♣♦♥ts s tt♦♥ ❱tt♦♥ ♣♦♥ts t♦♥ βe ≃ 1 ♥♦♥

♣♥rt② βp ≃ 1 ♥ sttr βs ≃ 1

s♠rt② ♥t♦♥ Di : R3 −→ [0, 1] s ♥ s

Di(xi) = 1− βe.βp.βs

♥ s♠rt② ♥t♦♥

❲ ♦♥sr tr trs t♦ r♥t ♦♥r♥♥ t sst♦♥ ♦ t

♣♦♥ts s ♥ ♥ ♣♦♥ts t♦♥ βe ≃ 1 ♦ ♥♦♥♣♥rt②

βp ≃ 0 ♥ ♦ sttr βs ≃ 0

s♠rt② ♥t♦♥ Di : R3 −→ [0, 1] s ♥ s

Di(xi) = 1− βe.βp.βs

♣♣r♦ t t❱ tr♦ t

r♦♥ s♠rt② ♥t♦♥

❲ ♦♥sr tr trs t♦ r♥t ♦♥r♥♥ t sst♦♥ ♦ t

♣♦♥ts s r♦♥ r♦♥ ♣♦♥ts ♦ t♦♥ βe ≃ 0 ♦ ♥♦♥♣♥rt②

βp ≃ 0 ♥ ♦ sttr βs ≃ 0

s♠rt② ♥t♦♥ Di : R3 −→ [0, 1] s ♥ s

Di(xi) = 1− βe.βp.βs

♠ strtr s♠rt② ♥t♦♥

❲ ♦♥sr tr trs t♦ r♥t ♦♥r♥♥ t sst♦♥ ♦ t

♣♦♥ts s ♣♦♥ts ♥♦♥♣♥rt② βp ≃ 1 ♥♦♥♥rt② βl ≃ 1

♥ sttr βs ≃ 1 ♦t tt t t♦♥ tr s ♥♦t ♥ t♥ ♥t♦

♦♥t s♥ ♠♥ts ♥ tr ♦♥ ♥s s s ♠♥②s ♦r ♦♥ t

r♦♥ s s s♠ ss

s♠rt② ♥t♦♥ Di : R3 −→ [0, 1] s ♥ s

Di(xi) = 1− βl.βp.βs

♣♣r♦ t t❱ tr♦ t

♦♠tr trs

♥ ts ♦r ❱ t s r♣rs♥t s ♠ss ❲ ♦♥sr ♦r trs

t♦ r♥t ♦♥r♥♥ t sst♦♥ ♦ t ts s♠♥t s s♠r t♦

t ♦♥ ♣rs♥t ♥ t♦♥ ♦r ♦r ♣♣r♦ s r♥t s♥ t t

s ♦tr rtrsts

♥② ♠t♦s ♥ ♣r♦♣♦s ♥ t trtr ♦r s♠♥t♥ s②♥tt

♠ss ❬♦rs ❪ t t♦ ♦r st ♥♦ ♥♦♥ s t t♦ r

♥ s♥ sst♦♥ r♦♠ ❱ ♠ss ❲ ♣r♦♣♦s s♦t♦♥ ♦r st♥s♥

s♣ sss ♦ r♥ ♦ts ♦r sss r ♦♥sr r♦♥ tt♦♥

♥ r♦♦ sst♦♥ rs ♦♥ s♠♣ t ♥t ♦♠tr ss♠♣

t♦♥s r♦♥ s rtr③ ② ♦② t srs ♦t ♦ t ♦tr

♣tr ❯r♥ s♥ sr♣t♦♥ ♥ ♥rst♥♥

r ❱ sst♦♥ ♥ r ♠ t ♥ t ss ❱ t

rt ♦t tt t ♦r sss ♥ tt♦♥ r♦♥ ♥ r

♦rrt② s♣rt ♠ ♦rts② ♦ ♦♦ ❬♦♦ ❪

sss tt♦♥ ♥ s♣② trs s rrr r srs

♠♥ts r rt strtrs ♦♥♥t♥ r♦♦ ♥ r♦♥ ♥ r♦♦

♠♥ts r ♠♥② ♦♠♣♦s ♦ ♣s♣♥r srs

rtrs str♥ s ❱ ♠ss r ①tr♠② ♥s ss②

♥ tr♥r t ♦ t♦ ♦t r♥♥♥ t♠ ♥ rr③t♦♥

♦♥str♥ts t rstrt ♠♣t ♥st r♦♣s ♦ ♦♥♥t ts tt

strs r ♦♥sr strs r ♦t♥ ② str♥ t ts t

s♠r ♠♥ rtrs ❬♦ts ❪ r♦♥ r♦♥ s s t♦ ♥t② r

r♦♣ ts t ♣r♦♣t♦♥ s rt② st s t t ♥② s ♥♦♥ s

str♥ ♣r♦r ♣rsrs t ♣♥r ♦♠♣♦♥♥ts s s♦♥ ♦♥

sr♠♥t ttrts r r♥t ♦♠tr ttrts r ♦♠♣t

r♦♠ t strs ♦ t ♠s ♦r st♥s♥ t r♥t sss ♦ ♥trst

t♦♥ ttrt ae ♦ t st♠ts t rt t ♦ ts ♥tr♦

t rs♣t t♦ t r♦♥ ② ♦♥sr♥ t fi ♦s ♥tr♦ s

♣♣r♦ t t❱ tr♦ t

r str♥ ♥ sr♠♥t ttrts str♥ ♣r♦r

r♦♣s ♦♥♥t ts ♥ s♠r ♠♥ rtrs t♦♣ t ♦♦r ♦r

rs♣♦♥♥ t♦ str ♦♠♥t♦♥ ♦ rtt② av t♦♥ ae ♥

♥♦♥♣♥rt② ap ttrts ♦s s t♦ st♥s sss ♦ ♥trst tr♦

♦♠tr ♥♦r♠t♦♥ ♦♥② ♦r ttr s③t♦♥ s♣② ae = 1− ae

❩ zi t t♦♥ ttrt s ♥ ②

ae(fi) =

√

zi − zmin

zmax − zmin

r zmin rs♣t② zmax r♣rs♥ts t ♠♥♠ rs♣t② ♠①♠ ❩

♦ t t ♥tr♦s ♦t ♥ ♥ ①t♥ s♣t ♥♦r♦♦ t

♦ ts s♣t ♥♦r♦♦ s t♦ r ♥♦ t♦ ♠t r♦♥ ♦♠♣♦♥♥ts

♥ s♠ ♥♦ t♦ r♦st t rs♣t t♦ ② r♦♥s ♥ ♣rt ts t

s ① t♦ 30 ♠trs s ttrt s ♥ t ♦♦♥ ② rtr

② t s r♦♠ t r♦♥ t r t ae ttrt ts

♥♦♥♣♥rt② ttrt ap ♠srs t r ♦ ♥♦♥♣♥rt② ♦ t ♦

♥♦r♦♦ ♦ t t s ①♣rss ②

ap(fi) =1

2H(fi) +

1

2

|λmin|

|λmax|

r H(fi) s t ♥♦r♠③ ss♥ rtr ♦ fi ♥ λmax rs♣t②

λmin s t st rs♣ ♦st ♥ ♦ t P ♦r t rts ♦

ts str ♥tt② ts ♠♥s tt t ♠♦r ♥♦♥♣♥r t ♥♦r♦♦ s

t r t ap ttrt ts

♣tr ❯r♥ s♥ sr♣t♦♥ ♥ ♥rst♥♥

rtt② ttrt av ♠srs t ♦r♥tt♦♥ ♦ t fi t rs♣t t♦ t

❩①s

av(fi) = 1− |ni · nz|

r ni s t t ♥♦r♠ ♥ nz s t ♥t t♦r ♦♥ t ❩①s s

ttrt s ♥ t ♦♦♥ ② ♠♦r rt t t s t r

t av ttrt ts

s tr ♦♠tr ttrts r ♦♠♣t ♦r t ♥ r ♥ ♥

t ♥tr ❬❪ ♥ ♦♥ ♥ s tt t trs ♣r♦♣r②

t strs r str t s♠r ♠♥ rtr ♣♥r r r t♥

t s♠ strs ae s ♦r ts ♥ t♠tr② ♥

♥ tt♦♥ ts r s av s ♦r rt strtrs s

♥ tr♥s r s ♥ ap s ♦r ♣♦♥ts ♥ rtr

tt♦♥ ♥ trs r s

♥ t ♦♦♥ st♦♥s ♥ s♠rt② ♥t♦♥ Di : F −→ [0, 1] ♦r

ss r♦♦ tt♦♥ r♦♥ ♥ r♣rs♥ts t ♥rs ♦♥♥ tt

t t fi ♦♥s t♦ t s♣ ss ♦r ss cl ♦t♥ s♦r

t♥ ③r♦ ♥ ♦♥ ③r♦ ♠♥s t t fi ♦♥s t♦ t ss cl ♦♥ ♠♥s

♦trs t♦ t s♠s ♦♥tr♥tt t♦ ♥ ♥t♦♥s r♣rs♥t♥ t

♥rs ♦♥♥ t rt♦♥ s s s ♥t♦♥s t♥ ♠♥♠st♦♥

♣r♦♠ sr ♥ t♦♥

❱tt♦♥ s♠rt② ♥t♦♥

❲ ♦♥sr t♦ trs t♦ r♥t ♦♥r♥♥ t sst♦♥ ♦ t

strs s tt♦♥ ❱tt♦♥ strs ♥♦♥♣♥rt② ap ≃ 1 ♥ ♦

rtt② av ≃ 0

s♠rt② ♥t♦♥ Di : F −→ [0, 1] ♦r t fi ♦ str s ♥ s

Di(fi) = 1− av.ap

♣♣r♦ t t❱ tr♦ t

♦♦ s♠rt② ♥t♦♥

❲ ♦♥sr tr trs t♦ r♥t ♦♥r♥♥ t sst♦♥ ♦ t

strs s r♦♦ ♦♦ strs ♦ ♥♦♥♣♥rt② ap ≃ 0 ♦ rtt②

av ≃ 0 ♥ t♦♥ ae ≃ 1

s♠rt② ♥t♦♥ Di : F −→ [0, 1] ♦r t fi ♦ str s ♥ s

Di(fi) = 1− ap · av · ae

s♠rt② ♥t♦♥

❲ ♦♥sr t♦ trs t♦ r♥t ♦♥r♥♥ t sst♦♥ ♦ t

strs s strs ♦ ♥♦♥♣♥rt② ap ≃ 0 ♥ rt

t② av ≃ 1

s♠rt② ♥t♦♥ Di : F −→ [0, 1] ♦r t fi ♦ str s ♥ s

Di(fi) = 1− ap · av

♣rtrt② ♦ ❱ ♠ss ♦♠♣r t♦ r r t s t ♣rs♥ ♦

rt strtrs tt ♥ ♣♦ss② r♣rs♥t ♥ s ♦r t s♠

rt② ♥t♦♥ Di(fi) tr② sr ♦s ♥♦t sr♠♥t rt t strtrs

♦ ♥s s ♥ rt t strtrs ♦ tt♦♥ tr♥s ♦

r trs r♦r s♠♣ ♣♦st ♣r♦ss♥ tst s ♣r♦r♠ t♦ r

strs s tt♦♥ ♥ rqr s st♣ s rtr sr ♥ t♦♥

r♦♥ s♠rt② ♥t♦♥

❲ ♦♥sr tr trs t♦ r♥t ♦♥r♥♥ t sst♦♥ ♦ t

strs s r♦♥ r♦♥ strs ♦ t♦♥ ae ≃ 0 ♦ ♥♦♥♣♥rt②

ap ≃ 0 ♥ ♦ rtt② av ≃ 0

s♠rt② ♥t♦♥ Di : F −→ [0, 1] ♦r t fi ♦ str s ♥ s

Di(fi) = 1− ap · av · ae

♣tr ❯r♥ s♥ sr♣t♦♥ ♥ ♥rst♥♥

①♣r♠♥ts

♥ s♠rt② ♥t♦♥ s ♥ ♦r ss ♦ ♠♥ts ♥♦♥s♣rs

♥r② ♠♥♠③t♦♥ ♣r♦♠ s ♦r♠t t♦ t t ♥ ts st♦♥

♣rs♥t ♥ ♥r② ♦r♠t♦♥ ♥ ♥ rsts ♦r r ♥ ❱ t

♠♥t③t♦♥ ♦ r t

♥♦♥s♣rs ♥r② ♠♥♠③t♦♥ ♣r♦♠ s ♥ t♦ ss② t ♣♦♥t

♦ r♣ts t α①♣♥s♦♥ ❬♦②♦ ❪ s s t♦ r s♦t♦♥ ♦s

t♦ t ♦ ♦♣t♠♠

♥r② s ♥ s

E(x) =∑

i

Di(xi) + γ∑

i=1..nj∈Nii<j

δ(xi, xj)

r δ(xi, xj) s t ♣rs ♥trt♦♥ t♥ t xi ♦ t ♣♦♥t i ♥ t

xj ♦ t ♣♦♥t j ♥ s t st♥r P♦tts ♠♦ t γ ♣r♠tr Ni

s t ♥♦r♥ ♣♦♥ts ♦ t ♣♦♥t i ♥ Di(xi) s t ♣rt t tr♠ ♥

s ♦♠♥t♦♥ ♦ t ♦r t ♦♠tr ttrts

Di(xi) =

βe.βp.βs if xi r♦♥

βe.βp.βs if xi tt♦♥

βp.βs.βl if xi

βe.βp.βs if xi ♥

♥t ♦♥rt♦♥ s ♦s♥ s argxmin∑

iDi(xi) ♥ ♥ s tt ♦r

♥r② ♥t♦♥ ts t rqr♠♥ts ♦r s♥ r♣ts ♦rt♠ t

♣r♠trs αe αp αs ♥ αl r st t♦ ♥ rs♣t② s

♣r♠trs r ♦t♥ tr♦ tr♥rr♦r ♣♣r♦ ♦ ♠

♣r♦ ② r♥♥ ♠t♦ t ♥♦t st ♦r ♦ ♦r s②st♠ ♦r

r♥ ♦ t ♥ ♦ ♥♦t t♥ t s ♥ssr② t♦ ♠ t s②st♠ r

rst♥ sst♦♥ s strt ♦♥ ♥

①♣r♠♥ts

r st ♦ r sst♦♥ rst ♦♠♥ t♦♣ ♥t ♣♦♥t ♦

r♦♥ ss ♦tt♦♠ ss ♦♥ ♦♠♥ t♦♣ t r♥t

sss ❱tt♦♥ ♥ r♦♥ ♦r t ss r t

❱tt♦♥ ss ♦tt♦♠ ♥ ss

♠♥t③t♦♥ ♦ ❱ t

♥ r♦ ♥♦♠ t ♣rs ♥trt♦♥s s s t♦

str ② ♦♥ ♦ t ♦r sss ♦ ♥trst ④r♦♥ tt♦♥

r♦♦ ⑥ qt② ♦ ♦♥rt♦♥ l s ♠sr ② t ♥r② U ♦ t

st♥r ♦r♠

U(l) =∑

i∈S

Di(li) + γ∑

i,j∈E

Vij(li, lj)

♣tr ❯r♥ s♥ sr♣t♦♥ ♥ ♥rst♥♥

r Di ♥ Vij ♦♥sttt t ♥r② t tr♠ ♥ ♣r♦♣t♦♥ ♦♥str♥ts r

s♣t② ♥ ② t ♣r♠tr γ > 0 S ♥♦ts t st ♦ strs E

r♣rs♥ts t ♣rs ♦ ♥t strs t♦ strs ♥ ♥t t②

t st ♦♥ ♦♠♠♦♥ ♥ t ♥♣t tr♥r ♠s

r ♠♥t ♥ ♦r t②♣s ♦ r♥ ♦ts r ♥t r♦♠ ❱

♠ss r♦♦ r♦♥ ♥ tt♦♥ ♦t t rr③♥ tr♠ ♦ t

♥r② ♥ t ♦rrt♦♥ rs r♥ s♣t ♦♥sst♥② t♦ t ♥ ♦t ♥

♣rtr ♦ r♦♦s ♥ s r rt② s♣rt s s trs t♦

s s ♦s♣s

♥ t ssq♥t ♥ t ♦♠tr ttrt ♦ str s ①♣rss s

t rt s♠ ♦ t ttrts ♦ ts ts t tr♠ Di s ♦r♠t

s ♦♠♥t♦♥ ♦ t sr♠♥t ♦♠tr ttrts sr ♦ t

①♣r♠♥ts

② t r Afi ♦ t ♦ t str i t s ♥ ②

Di(li) =∑

fi

Afi ×

(1− ap · av · ae) li = r♦♥

(1− ap · av) li = tt♦♥

(1− ap · av) li =

(1− ap · av · ae) li = r♦♦

r a. = 1 − a. ♣rs ♥trt♦♥ Vij t♥ t♦ ♥t strs i

♥ j ♦rs ♦ s♠♦♦t♥ss t s ①♣rss ②

Vij(li, lj) = Cij · cosαij · 1li 6=lj

r 1. s t rtrst ♥t♦♥ Cij s t ♦♥♥t♦♥ ♥t t♥

strs i ♥ j ♦♠♣t s t s♠ ♦ t s ♦♠♠♦♥ t♦ t t♦ strs

♥ αi,j r♣rs♥ts t ♥ t♥ t st♠t ♥♦r♠s ♦ t strs i ♥

j ♦t tt s t ♥r② t tr♠ ♥ ♣rs ♣♦t♥t r t ② t

str rs ♥ ♦♥t♦r ♥ts ts ♥r② ♦r♠t♦♥ ♥ s♥ s t

s ♥r② t r♦♣♥ ♦♥str♥ts

♥ ♣♣r♦①♠t s♦t♦♥ ♦ ts ♥r② ♠♥♠③t♦♥ ♣r♦♠ s ♦♥ s♥

t αβ s♣ ♦rt♠ ❬♦②♦ ❪ ♥ ♦r ①♣r♠♥ts γ s ♥ st t♦ 0.5

♥ ♥ ♠♥ r♥♥ ts ♣r♠tr r♦♠ tr♥♥ tst t ♥♦t ♥

♣rt tt t s st ♦♥ r♥ ♦ ♥♣t ♠ss

♦ ♦rrt♦♥ s ♦ t ♦♠tr ♥ t♦♣♦♦ ts ♦♥t♥ ♥

t ♠ss tr t②♣s ♦ rr♦rs rq♥t② ♦r r♦♠ t ♥ ♥ ♥

t ♦♠♣① s♥s r♦♦ s♣rstrtrs s s ♠♥②s ♦r ♦r♠r♦s

♥ r♦♥② s tt♦♥ ts ♠♥ts ♥ t♦♦ s♠ ♥ t♦♦ rr

r t♦ ♦② ♣♥r ♣♦t♥t rt ♦♠♣♦♥♥ts ♦ r trs ♥

s ♥ ♦ tt♦♥ ♠♥ts ♥ s ♥

♦rr t♦ ♦rrt ts ♥ rr♦rs tr rs s ♦♥ s♠♣ r♥ ss♠♣t♦♥s

r ♦r♠t

strs s ♥ ♥t t♦ strs s

tt♦♥ ♥ r♦♥ ♠st tr♥ t♦ tt♦♥

♣tr ❯r♥ s♥ sr♣t♦♥ ♥ ♥rst♥♥

strs s tt♦♥ ♥ ♦♥② ♥t t♦ strs

s r♦♦ ♠st tr♥ t♦ r♦♦ s ss♠♣t♦♥ s rst ♦♥sr♥ r

trs ♥♥♦t ♦♥ ♦♥ t♦♣ ♦ r♦♦s

strs s ♥ ♦♥② srr♦♥ ② strs

s r♦♥ ♥♦ r♦♦ r♦♥ ♠st tr♥ t♦ tt♦♥

s strt ♦♥ ♥ ts tr s♠♣ rs ♦r♥t

♥ ♥ ♣rs♥ ♦ s♠ rrr r♦♦ s♣rstrtrs ♥ trs t ②♥r

s♣s ♥ ♣r♦r ♦s t s♥ t♦ ♦♠♣♦s ♥t♦ strs ♦

r♥ ♦ts s ♦♠♣♦st♦♥ ② rs t ♦♠♣①t② ♦ t ssq♥t

♦♣rt♦♥s s ♦ ♦ ♥s ♦r r♦♣ ♦ trs ♥ r♦♥strt ♥

♣♥♥t② ♥ t s♥ ♦t ♥② tt ♦♦♥ r② t ♥

♦♥ ♥ ♥♦t t♦ r♥ts ♦ r♥ ♦r t ♥ t r♥ ♥ r r♥

❲ ts t♦ ♦♦rs r ♦r t s♠ ss ♦ ♠♥ts tt♦♥ ts st♥t♦♥

s ♠ t♦ strt t t ♦ tr♥s ♠♥ts ♥ tt♦♥

♠♥ts ♠♥ts s tt♦♥ r♥ t ♦♣t♠③t♦♥ ♠t♦ r

s♦♥ ♥ t r♥ rs ts ② r s♦♥ ♥ r r♥

♦♠♣rs♦♥

t s t t♦ ♦♠♣r t ♥ rsts ♦ ts t♦ ♠t♦s q♥

ttt② s♥ t ♠t♦s ♣r♦ss t♦ r♥t t②♣s ♦ t t r♥t

rtrsts ♦r♦r tr s ♥♦ r♦♥ trt ♦r tr t

t②♣ s r t♥ ♥ ♦♠♣r♥ t rsts ♦ ♦t ♠t♦s

s② ♥ sss t ♥ts ♥ ♠tt♦♥s ♦ t ♠t♦s ② ♦♠♣rs♦♥

❱s② ♦t ♥ ♦r r t ♥ ❱ t r ♦♥♥♥ ♥

t ❱ ♥ s ♠♦r ♥♦r♠t s♥ ♥ r♦♦ ♠♥ts r

st♥s ♦♥② ♥ ♠♥ts r tt t r t s t

rst♥ ♥ ♦ ❱ t ♣r♦s ttr ♥rst♥♥ ♦ t s♥

♥ s♦t ♥ ♦r ♦ ♦ ♥s ♥ s② ①trt ② sr♥ ♦r t

♦♥♥t strs s roof ♥ facade

①♣r♠♥ts

r ♦ ♦rrt♦♥ t ♦ t rs ♦♥ t s♠♥t ♥ ♦♣ r♦

♥ t♦t rs ♣rs♥ts s♠ ♥♦♥sst♥s ♦tt♦♠ r♦ ♦rr

t♦♥ ♦ t ♥ ② ♣♣②♥ ♦♥ s♣ s♠♣ s♠♥t r ♦rrt♦♥s

r ♥t ② ♦r♥ rr♦s ♥ ts ①♠♣ ♦♥② ♦♥ r s t t t t♠ t♦

strt ts t ♦♥ t ♥ ♥ ♣rt ♦ rs r sss② ♣♣

♦♥r♥♥ tt♦♥ ss t tt♦♥ r② tr ♣♦st t r

t s ttr s♣② ♥ t ♥♠r ♦ rtr♥ ♣ss ♦ s ♥♦♥

♦r t ♥♠r ♦ ♠ssst♦♥s s ♣♦sts s r t r

t s s♥ ♠♥②s ♥ s♠ ttrs r s tt♦♥ t♦♦ ♥ t

s ♦ ❱ t ts ♠ssst♦♥ ♦ ♥ s tt♦♥ s ♦rrt r♥

t ♣♦st♣r♦ss♥ st♣

r♦♥ sst♦♥ ♣r♦s ♦♦ rsts ♥ ♦t ss ♦t ss r②

♦♥ ♦ st♦r♠ ♥②ss ♦ t t♠tr② ♠♣s tt ①♣t t♦

r♦♥ ♠♥t t♥ t ♥♦r♦♦ ♦♥sr r♥ t ①♣r♠♥ts

ts ss♠♣t♦♥ s ♠t ② ♦♥sr♥ ♥♦r♦♦ ♦ s③ t♥ 30 ♥

50m2 ♦r t♥ ①♣r♠♥ts ♦♥ ①tr♠② ② trr♥ r ②t t♦ ♦♥

t♦ ② t t ♣♣r♦ ❲♥ ♦♠♣r♥ t rst♥ r♦♥ ♠♥ts r♦♠

♣tr ❯r♥ s♥ sr♣t♦♥ ♥ ♥rst♥♥

r ♥ ❱ t ♥♦t tt t ♠t♦ ♦r ❱ t s st② ss

rt t t r♥ s ♥♦t s♥♥t ♥♦ t♦ t tr ts s t♦

t ♠t♦ ♦r t t②♣ ♦ t

♥② ♦t ♠t♦s r ♥♦t r♦st ♥ ♥♥♦♥ sss r ♣rs♥t ♥ t

s♥ ♦r ①♠♣ ♥ ♠t♦s t r ♦r ❱ t ♥♦rrt②

r ♥ t r♥ s♥ ♣rt② s ♥ ♠♥t ♣rt② s r♦♥

♠♥t s♦t♦♥ ♦ ♦♥sst ♥ ♥ t r ss t♦ t ♥ ♥

t♦ ♣r♦♣♦s sr♠♥t trs ♦r ts ss ♦t ♦r tt ts ss ♦

♠♥ts s s② ♥♦♠♠♦♥ ♥ ♥ r♥ s♥

♠♠r②

❲ sr t♦ ♠t♦s ♦r r♥ s♥ s♠♥ts ♥ ♥rst♥♥

r♦♠ r r t ♥ ❱ ♠ss

♣♣r♦ t r t

❲t ts ♣♣r♦ ♦t♥ ♥ ♦ ♣♦♥t ♦s s ♥ tt♦♥

r♦♥ ♥ s♠ ♠♥t s ♥ ♠♣r♦s t s♥ ♥rst♥♥ ♥

♣s t♦ r♦♥strt t s♥ ts s rtr ♦♣ ♥ ♣tr r♥ t

①♣r♠♥ts ♥♦t t rsts r ♠♦r rt ♥ t ♥♠r ♦ ♦s s

s♣ ♥ t r t tt♦♥ ♥ ♦♠s ♠♦r r♦st s♥ ♠♦st

♦ t ♠t♣♣s rtr♥s t♥ r t r tt♦♥ ♠♥ts ♦♥trr② t♦

t ♥ strt② ♦r ❱ t r t♦ st♣s r ♥ s st♦♥s

t ♥ ♦ t r t ♦s ♥♦t rqr ♣♦st♣r♦ss♥ st♣ s ♠②

♥t t ♥ ♠t♦ t r t s ♠♦r r♦st ♥ ♥r

♠tt♦♥s s ♣♣r♦ r♠♥s ♦② ss rt t♥ ts ❱ ♦♥

tr♣rt ♥ ♥♦t tt ♠♥②s ♥ ♦tr s♠ ♥ ♠♥ts r

s♦♠t♠s ♠s s tt♦♥ s s rt ② s♥ r ♦r t

♣s tr♠ ♦ t ♥r② ♥t♦♥ γ ♣r♠tr ♦r♠ s st

ts ♣♣r♦ ♦rs♠♦♦ts t ts rsts ♥ ♦rs♠♣ ♥ ♦ t

♠♠r②

r♥ s♥ ♥ t♦♥ ts ♠t♦ ♥♥♦t st♥s ♥ r♦♦ ♠♥ts

r♦♠ ♥ ♠♦st② t♦ ♥tr♥s ♠tt♦♥s ♦ t t qst♦♥ ♠t♦ s

t♦♥

♣♣r♦ t ❱ t

❲t t ♦♣ ♣♣r♦ ♦t♥ ♥ ♦ ❱ ♠ss s r♦♦

tt♦♥ ♥ r♦♥ ♦ t st ♦ ♦r ♥♦ r♥ ❱ ♠s

s♠♥ts s ♥r ♥ ♣r♦♣♦s ♦r ♥ ❱ t s ♠♦r ♦♠♣t ♥

s rt strtrs r♣rs♥t t ♥ ss s ♥ s♣t ♥t♦ t♦ s

t♦rs r♦♦ ♥ rst♥ r♥ s♥ ♥ s ♣r♦r♠ ♥

t♦ st♣s st♥r ♠t ♣♣r♦ ♦♦ ② s ♦ s♠♣

s♠♥t rs s s t♦ r ♥ s ❱ ♠s s♠♥t tt ②s

s♠♣t♦♥ ♣r♦ss sr ♥ ♣tr s s♠♥ts ♥ s♦ s ♦r

t①tr ♠♣♣♥ s♥ ♥rst♥♥ ♥ s♦ ♦♥

♠tt♦♥s r ♦rt♠ s rst ♠t t♦ ♦r sss ♦ r♥ ♦ts ♥

t s s♥t ♦r rt ♠♦♥ ♦ t ♥tr strts ♥ Prs s

♠♦r r♥ ♦♠♣♦♥♥ts ♦ t♥ ♥t♦ ♦♥t s s rs ❱♥s

♦r t r♦s ♦②♦ ♦♥ ts ♣♣r♦ s ss ♥r t♥ t ♦♥

♦r r t s♥ t tr s♠♥ts rs r ♣♣ r♥ ♣♦st♣r♦ss♥

st♣ ♥② ♥ t rr♥t stt ♣r♠trs ♥ ♦s♥ ♠♥②

♠♦r ♥r ♥ r♦st ♣♣r♦ ♦ ② t♦♠t② r♥♥

ts ♣r♠trs

♥ t ♣rs♥t ♥ ♠t♦s ♥ sst♦♥ ♦ t r♥ s♥

♠♥ts r ♥♦ t♦ ♦♣t ♣♣r♦♣rt r♦♥strt♦♥ strts ♦r ♦

t♠ s ♥ t ♦♦♥ t♦ ♣trs sr ♠t♦s ♦r r♦♥strt

♥ s♣ ♠♥ts ♦ ♥ r♥ s♥ rst ♥ ♣tr t♦♣♦♥ ♣♣r♦

s ♣rs♥t ♦r tt♥ ♥ ♠♦♥ ♠♥ts s s trs ♥ r r ♣♦♥t

♦s r ♦♥trt♦♥ s ♥ ♦♣t♠③t♦♥ ♠t♦ tt ♥ ♣♣ t♦ r

♦s ♣r♦♠s r♦♠ tt♥ ♦ts ♥ ♣♦♥t ♦s t♦ ♠♥ts ♥ ♠s

♣tr ❯r♥ s♥ sr♣t♦♥ ♥ ♥rst♥♥

♦♥ ♥ ♣tr ♦tt♦♠♣ ♣♣r♦s ♦r r♦♥strt♥ ♠♥ts r♦♠ r♥

s♥s r♣rs♥t ② r ♣♦♥t ♦s ♥ ❱ ♠ss r sr ❲t

r ♣♦♥t ♦s ♠t♦ ♦r t♦♠t ♥rt♦♥ ♦ ♦♠♣① ♥ ♠ss s

sr r②♥ ♦♥ t ♣♦♥t ♦ sst♦♥ t♥q ♣r♦♣♦s ♦ ❲t

❱ ♠ss ♥♣♥♥t ♣♣r♦s r sr t♦ t♦♠t② r♦♥strt

r♥ s♥ ♠♥ts ♥s tt♦♥ ♥ r♦♥

♣tr

t♦ ♦r ♦♠tr ♦t

tt♦♥ ♥ r s♥s

♥ ts ♣tr ♣rs♥t ♥r t♦♣♦♥ ♣♣r♦ ♦r ♦t t

t♦♥ ♥ r s♥s ♠♦♥ ♠t♣ ♣♣t♦♥s s s r ♥ ♦♥t♥

t♦♥ r♦ ♥ rr tt♦♥ t♦♥ ♠s ♥

t♦♥ ♦r ♣♣r♦ s♦ s t r r t t♦ tt ♣r♠tr

t♠♣ts ♦ trs t♥ r♥ ♠① ♥ ♠♦♥t♥♦s r t♦♥ ❲

s♦ tt ts ♣♣r♦ rs ♦♥ r♦ P♦♥t Pr♦sss PP s ♥

r ♥♦ t♦ ♣♣ ♦r r rt② ♦ ♣r♦♠s r♦♦t ts ♣tr

♥r r♦♥ ♥ rt ♦rs ♦♥ PPs ♣rs♥t ♦r♠r ♥

♥♦ ♦♣t♠③t♦♥ ♠t♦s ♦r t♠ ♥ r♦s ①♠♣s ♦ ♣r♦♠s tt

♥ s♦ t ts ♣♣r♦s

♦t tt tt♦♥ ♦ trs ♥s r t ♦♥sr s ♣rtr

s ♦r ♦r ♣♣r♦ ♥ ts s ♦♥ ♥ ♦♣t♦♥② s t ♥ t♥q

♣r♦♣♦s ♥ ♣tr s rss t ♣r♦♠ ♦♠♣①t② s♥ ♦♥② s♠

sst ♦ t ♣♦♥t ♦ ♥ t♦ ♣r♦ss ♠♥ t ♣♣r♦ r② ♥t

♥tr♦t♦♥

r♦ ♣♦♥t ♣r♦sss r ♣r♦st ♠♦s ♥tr♦ ② ❬② ❪

t♦ ①t♥ t trt♦♥ r♦ ♥♦♠ s ② s♥ ♥ ♦ts

♦r♠s♠ ♥ r♦ ♣♦♥t ♣r♦sss ♥ rss ♦t r♦♥t♦♥ ♣r♦♠s

② rt② ♠♥♣t♥ ♣r♠tr ♥tts ♥ ②♥♠ r♣s rs s r

rstrt t♦ ♥ ♣r♦♠s ♥ stt r♣s

♣tr t♦ ♦r ♦♠tr ♦t tt♦♥ ♥ r s♥s

s ♠t♠t t♦♦s ①♣♦t r♥♦♠ rs ♦s r③t♦♥s r ♦♥

rt♦♥s ♦ ♣r♠tr ♦ts ♦t ♥ ss♥ t♦ ♣♦♥t ♣♦st♦♥

♥ t s♥ ♥♠r ♦ ♦ts s ts r♥♦♠ r ♥ ts ♠st ♥♦t

st♠t ♦r s♣ ② sr ♥♦tr str♥t ♦ r♦ ♣♦♥t ♣r♦sss s

tr t② t♦ t ♥t♦ ♦♥t ♦♠♣① s♣t ♥trt♦♥s t♥ t ♦ts

♥ t♦ ♠♣♦s ♦ rr③t♦♥ ♦♥str♥ts ♥ s♥ ♣♦♥t ♣r♦ss s s②

s♣ ② tr ② ♠♥ts

♦♠ ♣r♠tr ♦ts ② ♥ ♥ ♥ srt ♥♦r ♦♥t♥

♦s ♦♠♥s ② s② ♦rrs♣♦♥ t♦ ♦♠tr ♥tts s♠♥ts

rt♥s rs ♦r ♣♥s t ♥ ♠♦r ♥r② ♥② t②♣ ♦ ♠t

♠♥s♦♥ ♥t♦♥ ♦♠♣①t② ♦ t ♦ts rt② ♠♣ts ♦♥ t

s③ ♦ t ♦♥rt♦♥ s♣

♥ ♥r② t s s t♦ ♠sr t qt② ♦ ♦♥rt♦♥ ♦ ♦ts

♥r② s t②♣② ♥ s ♦♠♥t♦♥ ♦ tr♠ ssss♥ t ♦♥sst♥②

♦ ♦ts t♦ t t ♥ tr♠ t♥ ♥t♦ ♦♥t s♣t ♥trt♦♥s

t♥ ♦ts ♥ r♦♥ ♦♥t①t

s♠♣r t ♦s t sr ♦r t ♦t ♦♥rt♦♥ ♠♥♠③♥ t

♥r② s t ♦♥rt♦♥ s♣ s ♦ r ♠♥s♦♥ ♥ t ♥r②

s s② ♥♦♥♦♥① ♦♥t r♦ s s♠♣rs ♣ ♦ ①♣♦r♥ t

♦ ♦♥rt♦♥ s♣ r rqr ♥ ♠♦st ss r♦ ♥ ♦♥t

r♦ ♦rt♠ ❬st♥s r♥ ❪

t ♦rs

r♦♥ ♥trst ♥ ts ♣r♦st ♠♦s s ♠♦tt ② t ♥ t♦

♠♥♣t ♣r♠tr ♦ts ♥trt♥ ♥ ♦♠♣① s♥s ♥② ♦rs r②♥

♦♥ ♣♦♥t ♣r♦sss ♥ r♥t② ♣r♦♣♦s t♦ rss t rt② ♦ ♠ ♥

s♦♥ ♣r♦♠s st ♦

P♦♣t♦♥ ♦♥t♥ ❬s♦♠s ❪ ♣r♦♣♦s ♣♦♥t ♣r♦ss ♦r ♦♥t♥

♣♦♣t♦♥s r♦♠ r ♠s ♥tt② ♥ ♣tr ② ♥ ♣s ❬ ❪

♣rs♥t ♣♦♥t ♣r♦ss ♦r s♠r ♣♣t♦♥ t t t♦ r♦ tt♦♥

♥tr♦t♦♥

r♦♠ r♦♥s ♣♦t♦s ♦r ♦ts r ♥ s st ♦ ♦② s♣

t♠♣ts r♥ r♦♠ tr♥♥ t t ♠s r s ② ❬❯ts ❪

t♦ tt ♣♦♣ ② ♣♦♥t ♣r♦ss ♥ r t ♦ts r s♣ ② ②♥rs

trtr ①trt♦♥ ❬♥ ❪ ♥ ❬♦st ❪ ♣r♦♣♦s ♣♦♥t ♣r♦

sss ♦r ①trt♥ ♥♥t♦rs r♦♠ ♠s ② t♥ ♥t♦ ♦♥t s♣t

♥trt♦♥s t♥ ♥s t♦ ♦r t ♦t ♦♥♥t♦♥ ♥ s♦ rt♥ t②♣s

♦ ♥ ♥t♦♥s ♠♦r ② t♦ ♣♣r ♥ r ♥t♦rs ❬t♦ ❪ ①t♥

ts ♥♥t♦r ♠♦s ♥ tr ♠♥s♦♥ ♦r r♦r♥ t ♦s♠ ♠♥t

♥t♦r r♦♠ ♣♦♥t ♦s r♣rs♥t♥ t ♠♣ ♦ t ❯♥rs ♥t♦♥

♣♦♥t ♣r♦sss ♦♣ ② ❬ ❪ ♦ t ①trt♦♥ ♦ ♥♥t♦rs

s♥ r♣s r♣rs♥tt♦♥ ♥t♦♥ ♣♦♥ts r ♥♦t ss♦t t♦ ♦

♠tr s♣s t r ♥st ♠r ② s♦♠ ♥s ♥t♥ t rt♦♥s

♦ t ♥t ♣♦♥ts s♦ tt ♥t♦♥♣♦♥t ♦♥rt♦♥ s q♥t t♦

♣♥r r♣ ❬rt♥r ❪ ♥ ❬ ❪ tt ♥s ② s♣♥ ♥

♦♥♥t♥ rt♥s r♦♠ r ♠s ttr s ♥ ①r② ♣♦♥t ♣r♦ss

♦ ♥s♠♥ts t♦ r♥♦r t rt♥ ①trt♦♥ rs t ♦r♠r ♠

t ♣♦♥t ♣r♦ss ♥t♦ ♠♦ t♦ ♣r♦ strtrr♥ s♠♥tt♦♥ ♦

♠s

①tr ♥②ss ❬②♥ ❪ ♦♣ ♠♦ ♦r t①tr r♦♥t♦♥

♥ t s♣t strt♦♥ ♦ s ②♣♦♥ts sr♠♥ts t t①trs

❬❩ ❪ sr ♥tr t①trs ② ②♦t ♦ t①t♦♥s ♥ s♥

s r③t♦♥ ♦ ♣♦♥t ♣r♦ss s♣ ② t①t♦♥ rr② ❬r ❪

♣rs♥t ♥r ♠♦ ♦r ①trt♥ r♥t t②♣s ♦ ♦♠tr trs

r♦♠ ♠s ♥♥ ♥ rt♥s ♥ ss ♠①tr ♦ ♦t ♥tr

t♦♥s r ♦♥sr s tt t ♣r♦ss ♥ r♦♥strt r rt② ♦ t①trs

t r♦♥t♦♥ ❬♥ s♦t ❪ ♦♣s ♣♦♥t ♣r♦ss ♦r tr

♥ rt♥r ♦♦r ♦ts r♦♠ ♦ ♠♦♥♦♠♥s♦♥ ♣♦♥t ♣r♦ss

s ♣r♦♣♦s ② ❬t ❪ ♦r ♠♦♥ s♥s ② ♠①trs ♦ ♣r♠tr

♣tr t♦ ♦r ♦♠tr ♦t tt♦♥ ♥ r s♥s

♥t♦♥s ♠♣♦s♥ ♣②s ♦♥str♥ts t♥ t s♥ ♠♦s

♦tt♦♥s

rsts ♦t♥ ② ts ♣♦♥t ♣r♦sss r ♦♥♥♥ ♥ ♦♠♣tt

t rs♣t t♦ ♦tr ♠s ♦ ♠t♦s t t ♣r♦r♠♥s r ♣rtr②

♠t ♥ tr♠s ♦ ♦♠♣tt♦♥ t♠ ♥ ♦♥r♥ stt② s♣② ♦♥

r s♥s s rs ①♣♥ ② ♥str② s ♥ rt♥t ♥t

♥♦ t♦ ♥trt ts ♠t♠t ♠♦s ♥ tr ♣r♦ts ♥ t ♦rs

♠♥t♦♥ ♥ t♦♥ ♠♣s③ ♦♠♣① ♠♦ ♦r♠t♦♥s ② ♣r♦♣♦s♥

♣r♠tr② s♦♣stt ♦ts ❬ r ❪ ♥ t♥qs

t♦ t ♦ts t♦ t t ❬❯ts ❪ ♥ ♥♦♥tr s♣t ♥trt♦♥s t♥

♦ts ❬t rt♥r ♥ ❪ ♦r ts ♦rs s② r②

♦♥ st♥r s♠♣♥ ♣r♦rs ♠♥② ♦♥ t rs ♠♣ r♦ ♥

♦♥t r♦ ♦rt♠ ❬r♥ ❪ ♦♠♣tt♦♥ t♠ ♥rt

② s s♠♣r s rs♦♥ ♦♥② r♦♠ t ♦ s♠ s③ ♦r ①♠♣ t

♥ ①trt♦♥ ♦rt♠ ♣r♦♣♦s ② ❬rt♥r ❪ rqrs r♦♥ s① ♦rs

r♦♠ ♥ ♠ ♣♦rt♦♥ ♦ s③ 1000 × 1000 ♣①s ♦♥② 0.25 ♠2 r

s♦t♦♥ s ♦♦s② ♥♦t rs♦♥ ♥ ♥ t ♥tr r ♥ stt

♠s

♥ t trtr ♦rs rss t ♦♣t♠③t♦♥ sss r♦♠ s

♦♠♣① ♠♦s ♣r♦♣♦s s♦t♦♥s r ♠♥② s ♦♥ s♦♠ ♠♣r♦♠♥ts

♦ t trt♦♥ s♠♣r

♠♣s♦♥ Pr♦♣♦s ② ❬r♥♥r ❪ ts ♦rt♠ s ♥

s♥ t♦ s♣♣ t s♠♣♥ ② ♦♠♥♥ s♦♥ ②♥♠s t

s♠♣r ♦t ♠♥s♠s ♣② r♥t r♦s t ♦r♠r ♣r♦r♠s

rrs ♠♣s t♥ t r♥t ss♣s rs t ttr ♦♥ts

st♦st s♦♥ t♥ ♦♥t♥♦s ss♣ t ♦ ♣r♦ss ♥

♦♥tr♦ ② ♦♠♠♦♥ r①t♦♥ ♣r♠tr ♦r ts ♦rt♠ s rstrt

t♦ s♣ ♥r② ♦r♠s ❬rst ♥ r ❪

♥tr♦t♦♥

tr♥ t ♦♥srt♦♥s ♥ s♦ s t♦ r t

s♠♣♥ t ♠♦r ♥② ❬ ❪ ♦♥ssts ♥ ♠♦♥ t

♣r♦♣♦st♦♥ r♥s ♦ t s♠♣r ♥ ♥t♦♥ ♦ sr♠♥t tsts r♦♠ t s♦

tt t rt♦ ♦ r♥t ♣rtrt♦♥s s str♦♥② ♥rs s strt② ♥

♥r♦s t ♣r♦♣♦st♦♥ r♥s r ♥♦t ♦rrt② st♠t r♦♠ t

Pr③t♦♥ ♠♥s♠s ♦♠ ♦rs s♦ ♣r♦♣♦s ♣r③t♦♥ ♣r♦

rs ② s♥ ♠t♣ ♥s s♠t♥♦s② ❬r♥ss ❪ ♦r ♦♠♣♦st♦♥

s♠s ♥ ♦♥rt♦♥ s♣s ♦ ① ♠♥s♦♥ ❬②r ♦♥③③ ❪

♦r t② r ♠t ② ♦rr ts ♥ r ♥♦t s♥ t♦ ♣r♦r♠

♦♥ r s♥s ♥ t♦♥ t ①st♥ ♦♠♣♦st♦♥ s♠s ♥♥♦t

s ♦r ♦♥rt♦♥ s♣s ♦ r ♠♥s♦♥ ♥ s ♦♥sq♥ t②

r ♥♦t ♣t t♦ s♠♣ ♣♦♥t ♣r♦sss Pr t♠♣r♥ ❬r ❪ r♥s

♠t♣ ♥s ♥ ♣r t r♥t t♠♣rtrs rq♥t② ①♥♥

♦♥rt♦♥s r♥ t s♠♣♥ s t♥q r♥s r♦st♥ss t♦ t ♦♦♥

s t r♠♥s s♦ ♥ ♣rt s ♥ ①♣♦rs t ♦♥rt♦♥

s♣

t♣ rts ♥ ts ♠♥s♠ s ♦♥ ♠t♣ rt♦♥ ♥

strt♦♥ ♦ ♦ts s s♦ ♥ ♦♣ t♦ rss ♣♦♣t♦♥ ♦♥t♥

♣r♦♠s ❬s♦♠s ❯ts ❪ rtss ts ♦rt♠ s s♠

tr♠♥st ♥ ♥ ♦♥② rss ♣r♦♠s ♥ ♦t ♥trt♦♥s r

s♠♣ ♥ t♦♥ ♦t rt♦♥s rqr t srt③t♦♥ ♦ t ♣♦♥t

♦♦r♥ts ♥s s♥♥t ♦ss ♦ r②

s tr♥t rs♦♥s ♦ t ♦♥♥t♦♥ s♠♣r ♦② ♦

t ♠♣r♦♠♥t ♦ ♦♣t♠③t♦♥ ♣r♦r♠♥s ♥ s♣ ♦♥t①ts t s

t ♥s ♥ tr♠s ♦ ♦♠♣tt♦♥ t♠ r♠♥ ♥ r s② r③ t

t ①♣♥s ♦ ♦♥r♥ stt② s♣② ♥ r s♥s ♥♥ st

♥t s♠♣r ♦r ♥r r♦ ♣♦♥t ♣r♦sss r② r♣rs♥ts ♥♥

♣r♦♠

♣tr t♦ ♦r ♦♠tr ♦t tt♦♥ ♥ r s♥s

P♦♥t Pr♦ss r♦♥

♥t♦♥s ♥ ♥♦tt♦♥s

♣♦♥t ♣r♦ss srs r♥♦♠ ♦♥rt♦♥s ♦ ♣♦♥ts ♥ ♦♥t♥♦s

♦♥ st K t♠t② s♣♥ ♣♦♥t ♣r♦ss Z s ♠sr ♠♣

♣♥ r♦♠ ♣r♦t② s♣ (Ω,A,P) t♦ t st ♦ ♦♥rt♦♥s ♦ ♣♦♥ts ♥ K

s tt

∀ω ∈ Ω, pi ∈ K,Z(ω) = p1, ..., pn(ω)

r n(ω) s t ♥♠r ♦ ♣♦♥ts ss♦t t t ♥t ω ❲ ♥♦t ② P

t s♣ ♦ ♦♥rt♦♥s ♦ ♣♦♥ts ♥ K s♦s r③t♦♥ ♦ ♣♦♥t

♣r♦ss ♦r K ⊂ R2

♠♦st ♥tr ♣♦♥t ♣r♦ss s t ♦♠♦♥♦s P♦ss♦♥ ♣r♦ss ♦r t

♥♠r ♦ ♣♦♥ts ♦♦s srt P♦ss♦♥ strt♦♥ rs t ♣♦st♦♥ ♦

t ♣♦♥ts s ♥♦r♠② ♥ ♥♣♥♥t② strt ♥ K P♦♥t ♣r♦sss ♥

s♦ ♣r♦ ♠♦r ♦♠♣① r③t♦♥s ♦ ♣♦♥ts ② ♥ s♣ ② ♥st②

h(.) ♥ ♥ P ♥ rr♥ ♠sr µ(.) ♥r t ♦♥t♦♥ tt t

♥♦r♠③t♦♥ ♦♥st♥t ♦ h(.) s ♥t

∫

p∈Ph(p)dµ(p) < ∞

♠sr µ(.) ♥ t ♥st② h(.) s s② ♥ t ♥t♥st② ♠sr

ν(.) ♦ ♥ ♦♠♦♥♦s P♦ss♦♥ ♣r♦ss s tt

∀B ∈ B(P), µ(B) =

∫

B

h(p)ν(dp)

♣②♥ ♥st② h(.) ♦s t ♥srt♦♥ ♦ t ♦♥sst♥② ♥ s♦ t r

t♦♥ ♦ s♣t ♥trt♦♥s t♥ t ♣♦♥ts ♦t s♦ tt h(.) ♥ ①♣rss

② s ♥r② U(.) s tt

h(.) ∝ exp−U(.)

♥tr♦t♦♥

r♦♥ ♣r♦♣rt②

♠r② t♦ r♥♦♠ s t r♦♥ ♣r♦♣rt② ♥ s ♥ ♣♦♥t ♣r♦ss

t♦ rt s♣t ♣♥♥② ♦ t ♣♦♥ts ♥ ♥♦r♦♦

♣♦♥t ♣r♦ss Z ♦ ♥st② h s r♦♥ ♥r t ♥♦r♦♦ rt♦♥s♣ ∼

♥ ♦♥② ∀p ∈ P s tt h(p) > 0

∀p ⊆ p h(p) > 0

∀u ∈ K h(p∪u)/h(p) ♦♥② ♣♥s ♦♥ u ♥ ts ♥♦rs p ∈ p : u ∼ p

①♣rss♦♥ h(p ∪ u)/h(p) ♥ ♥tr♣rt s ♦♥t♦♥ ♥t♥st②

r♦♥ ♣r♦♣rt② ♦r r♥♦♠ s ♥ ts ♥tr② ①t♥ ♥ s ♦

♣♦♥t ♣r♦sss ② ♥♥ s②♠♠tr rt♦♥s♣ t♥ t♦ ♣♦♥ts ♦ K s

s♦♥ tr t r♦♥ ♣r♦♣rt② s ss♥t t♦ tt t s♠♣♥ ♦ ♣♦♥t

♣r♦sss

r♦♠ ♣♦♥ts t♦ ♣r♠tr ♦ts

♣♦♥t pi ♥ ♠r ② t♦♥ ♣r♠trs mi s tt t ♣♦♥t

♦♠s ss♦t t ♥ ♦t xi = (pi,mi) s ♣r♦♣rt② s ♣rtr②

ttrt t♦ rss s♦♥ ♣r♦♠s rqr♥ t ♥ ♦ ♦♠♣① ♣r♠tr

♦ts ❲ ♥♦t ② C t ♦rrs♣♦♥♥ s♣ ♦ ♦t ♦♥rt♦♥s r

♦♥rt♦♥ s ♥ ② x = x1, ..., xn(x) ♦r ①♠♣ ♣♦♥t ♣r♦ss ♦♥

K×M t K ⊂ R2 ♥ t t♦♥ ♣r♠tr s♣ M =]− π

2 ,π2 ]× [lmin, lmax]

♥ s♥ s r♥♦♠ ♦♥rt♦♥s ♦ ♥s♠♥ts s♥ ♥ ♦r♥tt♦♥ ♥

♥t r t♦ ♣♦♥t s ♣♦♥t ♣r♦sss r s♦

♠r ♣♦♥t ♣r♦sss ♥ t trtr

♠♦st ♣♦♣r ♠② ♦ ♣♦♥t ♣r♦sss ♦rrs♣♦♥s t♦ t r♦ ♣♦♥t

♣r♦sss ♦ ♦ts s♣ ② s ♥rs ♦♥ C ♦ t ♦r♠

∀x ∈ C, U(x) =∑

xi∈x

D(xi) +∑

xi∼xj

V (xi, xj)

r ∼ ♥♦ts t s②♠♠tr ♥♦r♦♦ rt♦♥s♣ ♦ t r♦ ♣♦♥t

♣r♦ss D(xi) s ♥tr② t tr♠ ♠sr♥ t qt② ♦ ♦t xi t rs♣t

♣tr t♦ ♦r ♦♠tr ♦t tt♦♥ ♥ r s♥s

t♦ t ♥ V (xi, xj) ♣rs ♥trt♦♥ tr♠ t♥ t♦ ♥♦r♥ ♦ts

xi ♥ xj ∼rt♦♥s♣ s s② ♥ ♠t st♥ ε t♥ ♣♦♥ts

s tt

xi ∼ xj = (xi, xj) ∈ x2 : i > j, ||pi − pj ||2 < ε

♥ t sq ♦♥sr r♦ ♣♦♥t ♣r♦sss ♦ ts ♦r♠ ♦t tt ts ♥r②

♦r♠ s s♠rts t t st♥r ♠t ♥rs ♦r s ❬③s ❪

r ♣r♦♠ ♥ ♥ s♥ s ♥r③t♦♥ ♦ ts ♠♦s s

♣rtr s s t ♥ t♦♥

r r♦♠ t t♦ rt r③t♦♥s ♦ ♣♦♥t ♣r♦ss ♥ ♦ r♦

♣♦♥t ♣r♦ss ♥ ♦ r♦ ♣♦♥t ♣r♦ss ♦ ♥s♠♥ts r② s ♥s

r♣rs♥t t ♣rs ♦ ♣♦♥ts ♥trt♥ t rs♣t t♦ t ♥♦r♥ rt♦♥s♣

s s♣ r ② ♠t st♥ ε t♥ t♦ ♣♦♥ts q

♠t♦♥

P♦♥t ♣r♦sss r s② s♠t s♥ s♠♣r ❬r♥ ❪ t♦

sr ♦r t ♦♥rt♦♥ ♠♥♠③s t ♥r② U s s♠♣r ♦♥ssts ♦

s♠t♥ srt r♦ ♥ (Xt)t∈N ♦♥ t ♦♥rt♦♥ s♣ C ♦♥r♥

t♦rs trt ♥st② s♣ ② U t trt♦♥ t rr♥t ♦♥rt♦♥

x ♦ t ♥ s ♦② ♣rtr t♦ ♦♥rt♦♥ y ♦r♥ t♦ ♥st②

♥t♦♥ Q(x → .) ♣r♦♣♦st♦♥ r♥ ♣rtrt♦♥s r ♦

♥tr♦t♦♥

♠♥s tt x ♥ y r r② ♦s ♥ r ② ♥♦ ♠♦r t♥ ♦♥ ♦t ♥ ♣rt

♦♥rt♦♥ y s t♥ ♣t s t ♥ stt ♦ t ♥ t rt♥

♣r♦t② ♣♥♥ ♦♥ t ♥r② rt♦♥ t♥ x ♥ y ♥ r①t♦♥

♣r♠tr Tt r♥ Q ♥ ♦r♠t s ♠①tr ♦ sr♥s Qm

♦s♥ t ♣r♦t② qm s tt

Q(x → .) =∑

m

qmQm(x → .)

sr♥ s s② t t♦ s♣ t②♣s ♦ ♠♦s s t r

t♦♥r♠♦ ♦ ♥ ♦t rt ♥ t r♥ ♦r t ♠♦t♦♥ ♦ ♣

r♠trs ♦ ♥ ♦t tr♥st♦♥ tt♦♥ ♦r r♦tt♦♥ r♥s r♥

♠①tr ♠st ♦ ♥② ♦♥rt♦♥ ♥ C t♦ r r♦♠ ♥② ♦tr ♦♥

rt♦♥ ♥ ♥t ♥♠r ♦ ♣rtrt♦♥s rrt② ♦♥t♦♥ ♦ t r♦

♥ ♥ sr♥ s t♦ rrs t♦ ♣r♦♣♦s t ♥rs

♣rtrt♦♥ ts ♦♥ r♥ ♦♠♣tt♦♥ ♦r ♠ ♥ s♦♥ ♣r♦♠s ♥

♦♥ ♥ ❬s♦♠s ❪

♦rt♠ s♠♣r ❬r♥ ❪

♥t③ X0 = x0 ♥ T0 t t = 0

t trt♦♥ t t Xt = x

♦♦s sr♥ Qm ♦r♥ t♦ ♣r♦t② qm

Prtr x t♦ y ♦r♥ t♦ Qm(x → .)

♦♠♣t t r♥ rt♦

R =Qm(y → x)

Qm(x → y)exp

(

U(x)− U(y)

Tt

)

♦♦s Xt+1 = y t ♣r♦t② min(1, R) ♥ Xt+1 = x ♦trs

s♠♣r s ♦♥tr♦ ② t r①t♦♥ ♣r♠tr Tt t t♠

♣rtr ♣♥♥ ♦♥ t♠ t ♥ ♣♣r♦♥ ③r♦ s t t♥s t♦ ♥♥t② t♦

♦rt♠ rs ♦ Tt s ♥ssr② t♦ ♥sr t ♦♥r♥ t♦ t ♦

♠♥♠♠ r♦♠ ♥② ♥t ♦♥rt♦♥ ♦♥ ss str ♦♠tr rs

s ♥ ♣♣r♦①♠t s♦t♦♥ ♦s t♦ t ♦♣t♠♠ ❬② ♠♦♥ ❪

♣tr t♦ ♦r ♦♠tr ♦t tt♦♥ ♥ r s♥s

♣♣r♦

♠♣♥ ♥ ♣r

♦♥♥t♦♥ s♠♣r ♣r♦r♠s sss ♣rtrt♦♥s ♦♥ ♦

ts ♣r♦r s ♦♦s② ♦♥ ♥ st♦s s♣② ♦r r s

♣r♦♠s ♥tr t st ♥①♣♦r ♦r r♦ ♣♦♥t ♣r♦sss ♦♥ssts

♥ s♠♣♥ ♦ts ♥ ♣r ② ①♣♦t♥ tr ♦♥t♦♥ ♥♣♥♥ ♦t

s t s♣t ♥♦r♦♦ strt② ♠♣s ♣rtt♦♥♥ t s♣ K s♦

tt s♠t♥♦s ♣rtrt♦♥s r ♣r♦r♠ t ♦t♦♥s r ♥♦ ♣rt t♦ ♥♦t

♥trr ♥ r t ♦♥r♥ ♣r♦♣rts

r♦♠ sq♥t t♦ ♣r s♠♣♥

t (Xt)t∈N r♦ ♥ s♠t♥ r♦ ♣♦♥t ♣r♦ss t

②♥♠s ♥ cs ♣rtt♦♥ ♦ t s♣ K r ♦♠

♣♦♥♥t cs s ♦ s c1 ♥ c2 r s t♦ ♥♣♥♥t ♦♥

X t tr♥st♦♥ ♣r♦t② ♦r ♥② r♥♦♠ ♣rtrt♦♥ ♥ ♥ c1 t ♥②

t♠ t ♦s ♥♦t ♣♥ ♦♥ t ♦ts ♥ ♣rtrt♦♥s ♥ ♥ c2 ♥ rs

♥ ♥ ♠♦♥strt tt t tr♥st♦♥ ♣r♦t② ♦ t♦ sss ♣r

trt♦♥s ♥ ♥ ♥♣♥♥t s ♥r t t♠♣rtr Tt s q t♦

t ♣r♦t ♦ t tr♥st♦♥ ♣r♦ts ♦ ♣rtrt♦♥ ♥r t s♠

t♠♣rtr ♥ ♦tr ♦rs r③♥ t♦ sss ♣rtrt♦♥s ♦♥ ♥♣♥♥t

s t t s♠ t♠♣rtr s q♥t t♦ ♣r♦r♠♥ t♠ ♥ ♣r ♦ ♦

s♦ t s ♦♥sr t♦ s c1 ♥ c2 ♥♣♥♥t ♦♥ (Xt)t∈N ❲ ♥♦t ② x

r③t♦♥ ♦ t ♣♦♥t ♣r♦ss s tt x = (x1, x2, u) r x1 rs♣t②

x2 r♣rs♥ts t st ♦ ♣♦♥ts ♥ ♥ t c1 rs♣t② c2 ♥ u s

t r♠♥♥ st ♦ ♣♦♥ts ♥ ♥ K − c1, c2 t y ♥ ♦♥rt♦♥

♦ ♣♦♥ts ♦t♥ r♦♠ x ② t♦ ♣rtrt♦♥s ♦♥ t s c1 ♥ c2 s♦ tt

y = (y1, y2, u) s strt ♦♥

tr♥st♦♥ ♣r♦t② Pr[Xt+2 = y|Xt = x] ♦ ♠♦♥ r♦♠ t stt x t t♠

♣♣r♦

r strt♦♥ ♦ t q♥ t♥ t♦ sss ♣rtrt♦♥s ♦♥

♥♣♥♥t s c1 ♥ c2 ♥ t♦ s♠t♥♦s ♣rtrt♦♥s ♦♥

t t♦ t stt y t t♠ t+ 2 ♥ ①♣rss s

Pr[Xt+2 = y|Xt = x]

= Pr[Xt+2 = (y1, y2, u)|Xt+1 = (y1, x2, u)]

× Pr[Xt+1 = (y1, x2, u)|Xt = x]

+ Pr[Xt+2 = (y1, y2, u)|Xt+1 = (x1, y2, u)]

× Pr[Xt+1 = (x1, y2, u)|Xt = x]

♦r t t♠♣rtr ♣r♠tr s ♦♥st♥t t♥ t ♥ t+ 2 ♠♥s tt

Pr[Xt+2 = y|Xt+1 = (y1, x2, u)]

= Q((y1, x2, u) → y)

×min[

1, Q(y→(y1,x2,u))Q((y1,x2,u)→y) exp

(

U((y1,x2,u))−U(y)Tt+1

)]

= Q((y1, x2, u) → y)

×min[

1, Q(y→(y1,x2,u))Q((y1,x2,u)→y) exp

(

U((y1,x2,u))−U(y)Tt

)]

= Pr[Xt+1 = y|Xt = (y1, x2, u)]

s c1 ♥ c2 ♥ ♥♣♥♥t t tr♥st♦♥ ♣r♦t② ♦r t ♣rtrt♦♥

y2 ♥ ♥ c2 ♦s ♥♦t ♣♥ ② ♥t♦♥ ♦♥ x1 ♥ y1 s ♥

♣rtr

Pr[Xt+1 = (y1, y2, u)|Xt = (y1, x2, u)]

= Pr[Xt+1 = (x1, y2, u)|Xt = (x1, x2, u)]

s s t♦ t qt♦♥

Pr[Xt+2 = y|Xt+1 = (y1, x2, u)]

= Pr[Xt+1 = (x1, y2, u)|Xt = x]

♣tr t♦ ♦r ♦♠tr ♦t tt♦♥ ♥ r s♥s

♠r② ♦♥ ♥ ♠♦♥strt tt

Pr[Xt+2 = y|Xt+1 = (x1, y2, u)]

= Pr[Xt+1 = (y1, x2, u)|Xt = x]

♥② ② ♥srt♥ q ♥ ♥ q t ①♣t rst s ♦t♥

Pr[Xt+2 = y|Xt = x]

= 2! Pr[Xt+1 = (y1, x2, u)|Xt = x]

× Pr[Xt+1 = (x1, y2, u)|Xt = x]

r 2! s t ♦♠♥t♦r ♦♥t ♦rrs♣♦♥♥ t♦ t ♥♠r ♦ ♣r♠t

t♦♥s ♦ ♣rtrt♦♥s ♥ t sq♥t ♥ s ♣r♦♦ ♥ s② ①t♥ ②

rrr♥ ♥ s ♦ n s ♠t② ♥♣♥♥t ♦♥ (Xt)t∈N t n > 2

♦ t♦ r♥t ♥♣♥♥

r ♥♣♥♥ ♦ s ♥ t t s t t ♦ t c2 s ♥♦t

r ♥♦ t♦ ♥sr t ♥♣♥♥ ♦ t s c1 ♥ c3 t t♦ r② ♣♦♥ts

♥ c1 ♥ c3 ♥♥♦t ♣rtr t t s♠ t♠ ♥ t rt s t s c1

♥ c3 r ♥♣♥♥t s q s sts

② ♥t♦♥ t♦ s r ♥♣♥♥t t tr♥st♦♥ ♣r♦t② ♦r ♥②

r♥♦♠ ♣rtrt♦♥ ♥ ♥ t rst ♦s ♥♦t ♣♥ ♦♥ t ♦ts ♥

♣rtrt♦♥s ♥ ♥ t s♦♥ ♥ rs t ♠♣s tt t t♦ s

♠st ♦t t ♠♥♠♠ st♥ r♦♠ ♦tr s strt ♥

ts st♥ ♠st t ♥t♦ ♦♥t t t ε ♦ t ♥♦r♥ rt♦♥s♣

♥ ② t r♦♥ ♣r♦♣rt② s♦ tt r② ♣♦ss ♦t ♥ ♥ t rst

♥♥♦t ♥♦r ♦ t ♦ts ♥ ♥ t s♦♥ s ♥ ♦t ♥

♣♣r♦

s♣ t♦ ♥♦tr r♥ ♣rtrt♦♥ t ♠♥♠♠ st♥ ♠st s♦

♦♥sr t ♥t ♦ t st ♠♦ ♦ s ♦t ♣rtrt♦♥ ♥♦t ②

δmax ♦♥sr♥ ts t♦ ♦♥str♥ts t ♥♣♥♥ t♥ t♦ s c1 ♥

c2 ♥ t♥ r♥t ♥

minp1∈c1, p2∈c2

||p1 − p2||2 ≥ ε+ 2δmax

♦ t♦ ♦♥strt ♣rtt♦♥

♥♦♥ ♦♥t♦♥ ♦r ♥sr♥ t ♥♣♥♥ q t ♦t

s ♥♦ t♦ ♥ ♣rtt♦♥♥ ♦ t s♣ K ♦♣t♠③♥ t ♣r♦r♠♥ ♦ t

s♠♣♥ ♥ ♣r

r r ♣rtt♦♥♥ s♠ ♦ K ♥ ♠♥s♦♥ t♦ t t s

r sqrs ♦ ♥t s③ rr♦♣ ♥t♦ 4 ♠sts ②♦ r ♥ r♥

s ♥t t♦ s ♦♥♥ t♦ r♥t ♠sts ♥ ♠♥s♦♥ tr

rt t s r s rr♦♣ ♥t♦ 8 ♠sts

♥tr ♦♥ssts ♦ ♣rtt♦♥♥ K ♥t♦ rr ♠♦s ♦ s t

s③ rtr t♥ ♦r q t♦ t ♠♥♠♠ st♥ t♥ ♥♣♥♥t s

t♦ ε + 2δmax s ♥ t♥ rr♦♣ ♥t♦ 2dimK sts s tt

s ♥t t♦ s ♦♥♥ t♦ r♥t sts strts t ♣rtt♦♥♥

s♠ ♦r dimK = 2 ♥ dimK = 3 s ♣rtt♦♥♥ s♠ r♥ts t

♠t ♥♣♥♥ t♥ t s ♦ s♠ st ♥ t sq s st

s ♠st st ♦ t② ♥♣♥♥t s ♦ ♠st ♥

ts ♣rtr s♠t♥♦s② s♥ ②♥♠s

♣tr t♦ ♦r ♦♠tr ♦t tt♦♥ ♥ r s♥s

♦r t ♥♠r ♦ s ♥ ♣rtr s♠t♥♦s② s ♠t

② t ♦♠♣tr rttr ♥ ♦r s ② t ♥♠r ♦ trts ♥

P❯ ❲♥ s♠♣♥ ♥ r s♥s ts ♥♠r s s② ♠ ♦r t♥ t

♥♠r ♦ s ♥ ♠st t ♦ ε + 2δmax s ♠♣♦s ♥ s♦t♦♥

♦ ♦♥sst ♥ ①♥ t t s♦ tt t ♥♠r ♦ ♥ ♠st ♥♥♦t

① t ♠①♠♠ ♥♠r ♦ s♠t♥♦s ♣rtrt♦♥s s ♦♣t♦♥ ♦s ♥♦t

t ♥t ♦ t r♦♥ ♣r♦♣rt② ♥ s t♦ r ♣r♦r♠♥s ♥

♣rt ♥ ♦rr t♦ ② ①♣♦t ♦t t ♣♦t♥t ♦ t ♦♠♣tr rttr

♥ t r♦♥ ♣r♦♣rt② ♥♦♥rr ♣rtt♦♥♥ ♦ K s rqr s

♣r♦♠ s rss ♥ t ♥①t st♦♥ r s♣t ♥♦r♠t♦♥ r♦♠ ♥♣t t

s ①♣♦t t♦ ② ♣rtt♦♥ K

tr♥ ♠♥s♠

rt♦♥ ♦ ♥♦♥rr ♣rtt♦♥♥ ♦K s s t♦ ♦♥sr ♣r♦♣♦st♦♥

r♥ strt t ♣♦♥ts ♥♦♥♥♦r♠② ♥ t s♣ K ♥ ♦tr ♦rs

♣rtrt♦♥s ♦ ♥♦t t s♠ ♦rr♥ ♦r♥ t♦ tr ♦t♦♥s ♥K ♦

s♥ s ♣r♦♣♦st♦♥ r♥ ♦♥ ♥s t♦ t ♥t♦ ♦♥t t rtrsts

♦ ♦sr s♥s ♦♥trr② t♦ t tr♥ s♦t♦♥ ♣r♦♣♦s ② ❬ ❪ ♦r

♠♥s♠ ♠st ♦♠♣t t t ♣r③t♦♥ ♦♥str♥ts ♠♥t♦♥ ♥

t♦♥

Pr♥♣

r ♦♥ssts ♥ rt♥ ♣r♦♣♦st♦♥ r♥ s ♥ ♠t♦♥ ♦ ♥♦r♠

sr♥s s♣t② rstrt ♦♥ t ♦♠♥ ♦ t s ♥ s ♠①tr

♦ sr♥s s t ♥trst♥ ♣r♦♣rt② ♦ st r♥t♥ t ♣r③t♦♥

♦ t s♠♣♥ ♥ t trtr ♠①trs ♦ sr♥s r rq♥t② s ♥

②♥♠s t♦ s♠t ♣♦♥t ♣r♦sss t t rstrt r♦ r

sr♥ s t t♦ ♣rtrt♦♥ t②♣ rt ♥ t tr♥st♦♥

r♦tt♦♥ t

♣♣r♦

r ♣♣rtt♦♥♥ tr ♥ ♠♥s♦♥ t♦ ss ♦ ♥trst

r s st♠t r♦♠ ♥ ♥♣t ♠ qtr s rt s♦ tt t

s r rrs② ♣rtt♦♥ ♦r♥ t♦ t ss ♦ ♥trst s

♦♠♣♦s ♦ ♦r ♠sts ②♦ r ♥ r♥ sts ♦ s t♦ r♥t

t s♠♣♥ ♣r③t♦♥ ♠t♦♥ ♦ t ♣r♦ts qc,t ♦r

t r♥t s ♦ t qtr ♥rts ♥st② ♠♣ ♦♥ t ♣♦♥ts t♦

♥♦♥♥♦r♠② strt ♥ t s♥ ♦t ♦ t ♥st② ♠♣ ♦ss ♦♥

t ss ♦ ♥trst ♣r♦rss② rs♥ ts ♥t♥st② ♥ ♠♦♥ ②

♠ ♦rts② ♦ ♦r ❱t ❬ ❱t ❪

sr♥ ♠t♦♥ ♠♥s♠ s r♥ ② s♣♣rtt♦♥♥ tr K

s ♥ s st ♦ L s♣rtt♦♥s ♦ K ♥♦t ② cs(1), .., cs

(L)

♥ ♦r♥③ s♦ tt ♦r i = 2..L cs(i) s s ♣rtt♦♥ ♦ cs

(i−1)

♦ t s♣♣rtt♦♥♥ tr ♦rrs♣♦♥s t♦ st ♦ s ♥ ♥

♥t s③ 1t♦2dimK rr ss♦♥ s♠ s ♦♥sr t♦

t s♣♣rtt♦♥♥ tr t②♣② qtr ♥ ♠♥s♦♥ t♦ ♥ ♥ ♦tr ♥

♠♥s♦♥ tr

♥ s♣♣rtt♦♥♥ tr ♥st② ♠♣ s♣②♥ ♦ t ♣♦♥ts

♠st s♣t② strt ♥ t s♣ K ♥ t♥ ♦♥strt rt♦♥

♦ ts ♥st② ♠♣ rs ♦♥ t ♠t♦♥ ♦ t ♥♦r♠ sr♥s s♣t②

rstrt t♦ t ss♣ s♣♣♦rt♥ r② ♦ t s♣♣rtt♦♥♥ tr K s

♥ ♥ q ♥ strt ♥

♣tr t♦ ♦r ♦♠tr ♦t tt♦♥ ♥ r s♥s

tr♥ s♣♣rtt♦♥♥ tr

♥ ♦rr t♦ rt r♥t s♣♣rtt♦♥♥ tr t t s s t♦

t ss♦♥ ❲ ss♠ tt ss ♦ ♥trst ♥ K ♥ t ♦ts

♣r♦t② t♦ ♦♥ t♦ ♥ r♦② st♥s r♦♠ t t

①trt♦♥ ♦ s ss s ♥♦t rss ♥ ts ♣tr ♥ s s♣♣♦s t♦

♦♥ ② s♠♥tt♦♥ ♦rt♠ ♦ t trtr ♣t t♦ t ♦♥sr

♣♣t♦♥ t ♥ ♦ t tr s ♥t♦ 2dimK s t t ♥①t

t ♦r♣s t t ♥ ss ♦ ♥trst rr ♦♠♣♦st♦♥

s st♦♣♣ ♦r tt t s③ ♦ t ♦♠s ♥r♦r t♦ ε+ 2δmax ♦r

tt t ♥♣♥♥ ♦♥t♦♥ q s ♥♦t ♦♥r

s♣♣rtt♦♥♥ tr ♦s t rt♦♥ ♦ ♣r♦♣♦st♦♥ r♥ ♥ ♥

♥t ② s ♣♦♥ts r ♥tr② ♥ ♥t② strt ♥ K ♥ t r ♦

♥trst t ♥t♥st② ♦ t ♥st② ♠♣ s ♠①♠ ❲♥ ♠♦♥ r r♦♠ t

ss ♦ ♥trst t ♥t♥st② ♣r♦rss② rss s s♦♥ ♥

♥ ♥sr t♦ ♥♦♥♥ ♥ t♦♥ t s♠♣♥ s ♥♦t sr② t

♥ t ss ♦ ♥trst s ♥rt② ①trt

Pr♦♣♦st♦♥ r♥ ♦r♠t♦♥

♥ s♣♣rtt♦♥♥ tr K ♦♠♣♦s ♦ L s ♥ 2dimK ♠sts ♦r

♥r ♣r♦♣♦st♦♥ r♥ Q ♥ t♥ ♦r♠t s ♠①tr ♦

♥♦r♠ sr♥s Qc,t sr♥ ♥ ♥ ♦♥ t c ♦ K ② t

♣rtrt♦♥ t②♣ t ∈ T s tt

∀x ∈ C, Q(x → .) =∑

c∈K

∑

t∈T

qc,tQc,t(x → .)

r qc,t > 0 s t ♣r♦t② ♦ ♦♦s♥ t sr♥ Qc,t(x → .)

♣r♦t② qc,t ♦s s t♦ s♣② t ♥t♥st② ♦ t ♥st② ♠♣ ♥ t

s♣♣rtt♦♥♥ tr ♥ ♣rt ts ♣r♦t② s ♦s♥ s

qc,t =Pr(t)

#s ♥ K

♣♣r♦

r Pr(t) ♥♦ts t ♣r♦t② ♦ ♦♦s♥ t ♣rtrt♦♥ t②♣ t ∈ T

①♣rss♦♥ ♦ qc,t q ♦s t ♥st s ♥ t s♣♣rtt♦♥♥ tr t♦

♦r s♦ tt t ♣rtrt♦♥s ♠♥② ♦s ♦♥ t ♦♠♥ s♣♣♦rt♥ t

ss ♦ ♥trst ♥ ts srr♦♥♥ s sss tr ♥ t♦♥ ♦tr

♣♦ss ①♣rss♦♥s ♠② ♦♠ ♠♦r ♥trst♥ ♥ t ss ♦ ♥trst ♥♥♦t

r② ①trt

♦r t②♣s ♦ ♣rtrt♦♥s r s② ♦♥sr ♥ ♣rt s♦ tt T = rt

♥ t tr♥st♦♥ r♦tt♦♥ s ❲♥ ♦ts sr ♣♦ss ♠♦s

t ♣rtrt♦♥s ♦♥sst♥ ♥ st♥ t ♠♦ ♦ ♥ ♦t ♥ s♦ s

♦t tt t ♣r♦♣♦st♦♥ r♥ Q s rrs s s♠ ♦ rrs sr♥s

♦t s♦ tt s ♣r♦♣♦st♦♥ r♥ ♦s s t♦ st t ♦ ♦♥rt♦♥

s♣ C s r♥t ② t sr♥s ♦ t ♦rsst ♦ K

s♠♣♥ ♣r♦r

r♥ ♥ ♥ q s ♠ ♥t♦ ②♥♠s s♦ tt t

♣r♦♣♦s s♠♣r ♦s ♥♠r ♦ s♠t♥♦s ♣rtrt♦♥s ♥rt ②

tr♥ ♣r♦♣♦st♦♥ r♥

♦rt♠

♣r♦♣♦s s♠♣r t ♥ ♦rt♠ ♥ s♥ s ♣r③

①t♥s♦♥ ♦ t trt♦♥ t tr♥ ♣r♦♣♦st♦♥ r♥ s

strt ♦♥ ♣rtrt♦♥ s ♦♠♣t② ♥♣♥♥t ♦ t ♦tr

♣rtrt♦♥s s♠t♥♦s② ♣r♦♣♦s ♥ t s ♦ t ♦♥sr ♠st

♦t tt t t♠♣rtr ♣r♠tr s ♣t tr srs ♦ s♠t♥♦s

♣rtrt♦♥s s tt t t♠♣rtr rs s q♥t t♦ ♦♦♥ s

② ♣t ♥ st♥r sq♥t s♠♣♥ ♦t s♦ tt t s♣

♣rtt♦♥♥ tr ♣r♦tts t s♠♣ r♦♠ ♠♦s ts ♥ ♣rt t s♠♣♥

s st♦♣♣ ♥ ♥♦ ♣rtrt♦♥ s ♥ ♣t r♥ rt♥ ♥♠r ♦

trt♦♥s

♣tr t♦ ♦r ♦♠tr ♦t tt♦♥ ♥ r s♥s

♦rt♠ r tr♥ ♣r s♠♣r

♥t③ X0 = x0 ♥ T0 t t = 0

♦♠♣t s♣♣rtt♦♥♥ tr K

t trt♦♥ t t Xt = x

♦♦s ♠st Smic ∈ K ♥ r♥ t②♣ t ∈ T ♦r♥ t♦ ♣r♦t②∑

c∈Smic

qc,t

♦r c ∈ Smic

Prtr x ♥ t c t♦ ♦♥rt♦♥ y ♦r♥ t♦ Qc,t(x → .)

t t r♥ rt♦

R =Qc,t(y → x)

Qc,t(x → y)exp

(

U(x)− U(y)

Tt

)

♦♦s Xt+1 = y t ♣r♦t② min(1, R) ♥ Xt+1 = x ♦trs

❯♣t Tt+1 = αTt

r ♥s♠ ♦ t s♠♣r t ♥ trt♦♥ ♠st s ♦s♥ ♥

t s♣♣rtt♦♥♥ tr r t st ♦ ②♦ s s s r♥ t②♣

r rts strt ② t ♥srt♦♥ ♦ ♦ts t r♥ t ♣r♦♣♦st♦♥

st♣ ♣rtrt♦♥ ♣r♦♣♦s s♠t♥♦s② ♥ ♦ t st ♠

st ♥♣♥♥t② r♦♠ ♦tr rt ♣rtrt♦♥ t♥ tr

♣t r♥ ♦t ♦r rt r ♦t r♥ t s♦♥ st♣ s♦♥s

r ♥♣♥♥t r②♥ ♦♥ t r♥ rt♦ ♦♠♣tt♦♥s ♥ ♥♠rs r♥♦♠②

♦s♥ ♥ t ♥tr [0, 1] s ♦r♠t ♥ q

①♣r♠♥ts

♠♣♠♥tt♦♥

♦rt♠ s ♥ ♠♣♠♥t ♦♥ P❯ s♥ ❯ tr s

t t♦ s♠t♥♦s ♣rtrt♦♥ s♦ tt ♦♣rt♦♥s r ♣r♦r♠ ♥ ♣r

♦r ♦ ♠st s♠♣r s ts t ♠♦r ♥t s t ♠st

♦♥t♥s ♠♥② s ♥ ♥r② s♣♥ s t s♥ s♣♣♦rt ② K s r

♦r♦r t ♦ s ♥ ♣r♦r♠♠ t♦ ♦ t♠♦♥s♠♥ ♦♣rt♦♥s ♥

♣rtr t trs ♦ ♥♦t ♦♠♠♥t t♥ ♦tr ♥ ♠♠♦r② ♦

s♥ ♣r♠ts st ♠♠♦r② ss ♠♠♦r② tr♥sr t♥ P❯ ♥ P❯

s s♦ ♥ ♠♥♠③ ② ♥①♥ t ♣r♠tr ♦ts ①♣r♠♥ts ♣r

s♥t ♥ ts st♦♥ ♥ ♣r♦r♠ ♦♥ 2.5 ③ ❳♦♥ ♦♠♣tr t

r♣s r r♦ rttrs

①♣r♠♥ts

①♣r♠♥ts t ♠s

P♦♣t♦♥ ♦♥t♥

♦rt♠ s ♥ t ♦♥ ♣♦♣t♦♥ ♦♥t♥ ♣r♦♠s r♦♠

rs ♠s s♥ ♣♦♥t ♣r♦ss ♥ t dimK = 2 ♣r♦♠

♣rs♥t ♥ ♦♥ssts ♥ tt♥ ♠rt♥ rs t♦ ①trt ♥♦r♠t♦♥

♦♥ tr ♥♠r tr s③ ♥ tr s♣t ♦r♥③t♦♥ ♣r♦♠ s ♥

rss ♣r♦s② ② ❬s♦♠s ❪ ♣♦♥t ♣r♦ss s ♠r ② ♣ss

r s♠♣ ♦♠tr ♦ts ♥ ② ♣♦♥t ♥tr ♦ ♠ss ♦ ♥ ♣s

♥ tr t♦♥ ♣r♠trs s ♦t s♣ s ♣t t♦ ♣tr

t r ♦♥t♦rs ♥r② s s♣ ② ♥tr② t tr♠ s ♦♥ t

ttr②② st♥ t♥ t r♦♠tr② ♥s ♥ ♦ts t ♦t ♥

♣rs ♥trt♦♥ ♣♥③♥ t str♦♥ ♦r♣♣♥ ♦ ♦ts ts ♦♥ t

♥r② r ♥ ♥ ♣♣♥① ♣r♦t② Pr(t) ♦ ♦♦s♥ t ♣rtrt♦♥

t②♣ t s st t♦ 0.2 t =rt ♥ t 0.4 t =tr♥st♦♥ 0.2 t =r♦tt♦♥

♥ 0.2 t =s ♥ ♦r ①♣r♠♥ts

♣tr t♦ ♦r ♦♠tr ♦t tt♦♥ ♥ r s♥s

r r ♦♥t♥ ② ♣♦♥t ♣r♦ss ♦ ♣ss rt ♦r t♥ t♥

t♦s♥ rs r ①trt ② ♦r ♦rt♠ ♥ ♠♥ts r♦♠ t r

s r ♠ ♠ qtr ♣rtt♦♥♥ t s♥ s s t♦ rt

♥st② ♠♣ s♦ tt t ♦ts r ♠♦r rq♥t② ♣r♦♣♦s ♥ t ♦t♦♥s

♦ ♥trst ♦t ♦♥ t r♦♣♣ ♣rts ♦ t rs r rt② ♣tr ②

♣ss ♥ s♣t ♦ t ♦ qt② ♦ t ♠ ♥ t ♣rt ♦r♣♣♥ ♦ rs

♠s ♦rts② ♦ ♦r ❱t ❬ ❱t ❪

tt② ♦ t r♦s s♠♣rs ♦♥ts ♦ rt♦♥ ♦ t

♥r② t♠ ♥ ♥♠r ♦ ♦ts r t t ♦♥r♥ r ♦♠♣t ♦r

50 s♠t♦♥s

♦♥t ♦ rt♦♥

♥r② t♠ ♦ts

❬r♥ ❪ 7.3% 4.2% 1.7%

Pr t♠♣r♥ ❬r ❪ 5.0% 20% 4.4%

❬ ❪ 8.1% 0.7% 1.8%

♠t♣ rt ♥ t ❬s♦♠s ❪ 5.0% 2.1% 1.3%

♦r s♠♣r t rr ♣rtt♦♥♥ 7.4% 6.2% 1.6%

♦r s♠♣r t s♣♣rtt♦♥♥ tr 4.4% 1.8% 1.1%

①♣r♠♥ts

r Pr♦r♠♥s ♦ t r♦s s♠♣rs t♦♣ r♣ srs t

♥r② rs ♦r t♠ r♦♠ t r ♠ ♣rs♥t ♥ t ♦♦r

♦ts ♦rrs♣♦♥ t♦ ♦rt♠ ♦♥r♥ ♦t tt t♠ s r♣rs♥t s♥

♦rt♠ s ♥ tt t s♦ ♦♥r♥ ♦ ❬r♥ ❪

❬ ❪ ♥ ♣r t♠♣r♥ ❬r ❪ ♦rt♠s s ♥♦t s♣② ♦♥

t r♣ ♦tt♦♠ r♣ s♦s t ♦t♦♥ ♦ t ♥♠r ♦ ♦ts r♥

t s♠♣♥ ♦♥trr② t♦ t ♦tr s♠♣rs t ♥♠r ♦ ♦ts ♦♥ ② ♦r

s♠♣r t ♥ t♦t s♣♣rtt♦♥♥ tr P s r② ♦s t♦ t r♦♥

trt ♥ ♦t tt st♠t♥ t ♦rrt ♥♠r ♦ ♦ts ♦s ♥♦t ♠♥

tt t ♦ts r ♦rrt② tt t♦ t t t t s ♥ ♠♣♦rt♥t rtr♦♥ ♦r

♣♦♣t♦♥ ♦♥t♥ ♣r♦♠s s ♥r♥ ② ❬♠♣ts② ❪

♣tr t♦ ♦r ♦♠tr ♦t tt♦♥ ♥ r s♥s

♦♠♣tt♦♥ t♠ qt② ♦ t r ♥r② ♥ stt② r t tr

♠♣♦rt♥t rtr s t♦ t ♥ ♦♠♣r t ♣r♦r♠♥ ♦ s♠♣rs

s s♦♥ ♦♥ ♦r ♦rt♠ ♦t♥s t st rsts ♦r

♦ t rtr ♦♠♣r t♦ t ①st♥ s♠♣rs ♥ ♣rtr r ttr

♥r② s ♦r ❬s♦♠s ❪ ♥ ♦r ❬r♥ ❪ s

♥♥t② r♥ ♦♠♣tt♦♥ t♠s s s s ♦r ❬s♦♠s ❪

♥ > 105 s ♦r ❬r♥ ❪ ❬ ❪ ♥ ❬r ❪ s♦ ♥r♥s

♥ ♠♣♦rt♥t ♠tt♦♥ ♦ t ♣♦♥t ♣r♦ss s♠♣r ♦ rr♥ ♦r ♣♦♣t♦♥

♦♥t♥ ❬s♦♠s ❪ ♦♠♣r t♦ ♦r ♦rt♠ ♥ t srt③t♦♥

♦ t ♦t ♣r♠trs rqr ♥ ❬s♦♠s ❪ ss ♣♣r♦①♠t tt♦♥

♥ ♦③t♦♥ ♦ ♦ts ①♣♥s t r qt② ♦ t r ♥r②

r ♦r ♦ t s♠♣r t ♥♦♥ r♥t s♣♣rtt♦♥♥ tr t♦♣

t ❲♥ t ss ♦ ♥trst ♥♥♦t ♦rrt② ①trt t s♣♣rtt♦♥♥

tr s ♦ ♦ qt② s s♦♥ ♦♥ t ♦s♣ ♥ r r ♦ ♥trst

s ♠ss ♦tt♦♠ t r♠ ♣r♦t② qc,t ♥ ♥ q ♦s ♥♦t

♣r♦r♠ ♦tt♦♠ ♥tr r♠s ♦r ♥trst♥ ♦s ♦r qc,t ♥ t♥

s s t ♥r ♦♥st♥t ♥ ②♣r♦ ♦r♠t♦♥s ♣r♦rss②

♦rs t st♦♥ ♦ t ♦rsst s ♥ t s♣♣rtt♦♥♥ tr r♣

r♣rs♥ts t ♣r♦t② ♦ st♥ t s♣♣rtt♦♥♥ tr s t

0 ♥ t ♦rsst ♦ t tr ♦tt♦♠ rt r♠ ♦t tt t s ♦

rr ♣rtt♦♥♥ ♥ ♦♠ s♣② ♥t ♥ s stt♦♥ t♦♣ rt

♥r② r♣s s♠♠r③♥ t ♣r♦r♠♥s ♦ ts r♥t ♦r♠t♦♥s

①♣r♠♥ts

stt② s ♥②③ ② t ♦♥t ♦ rt♦♥ ♥ s t st♥r

t♦♥ ♦r ♠♥ ♥ ♥♦♥ t♦ r♥t sttst ♠sr ♦r ♦♠♣r♥

♠t♦s ♥ r♥t ♠♥s r s♠♣r ♣r♦s ttr stt② t♥ t

①st♥ ♦rt♠s ♥♥ t ♠t♣ rt ♥ t s♠♣r s s♣

♣♦s t♦ ♣rtr② st t♥s t♦ ts s♠tr♠♥st ♠♥s♠ ♦t

tt t ♦rt♠ s ♣rtr② st ♥ tr♠s ♦ t♠ t s ♠♦r

② t♦ st ♥ ♦ ♠♥♠♠s s ♥r② rt♦♥ s ♠♣t ♦

t tr♥ ♠♥s♠ s s♦ ♠sr ② ♣r♦r♠♥ tsts t ♣r♦♣♦st♦♥

r♥ s ♦♥ rr ♣rtt♦♥♥ ♦ t s♣ K s

r ♠♣t ♦ t t s③ ♦♥ t ♦♠♣tt♦♥ t♠s t♦♣ ♣r♦r

♠♥s ♦ ♦r s♠♣r ♥ tst r♦♠ st ♦ s♠t ♠s ♦ ♣ss

♦rr♣t ② r ♥ ♥♦s ♦s s③ ♣r♦rss② ♥rss ♦tt♦♠ r

sts r s♣② ♦♥ t r♣ r♣rs♥t♥ t ♦t♦♥ ♦ t r t♠ ♦

tt♦♥ ♣r ♦t ♥ ♥t♦♥ ♦ t ♠ s③ ♠♥♠♠ r t♠ s

♠t r 15 ♠s ♥ t ♦♣t♠ ♦♣♥② ♦♥t♦♥s r r ♥ ts ①

♣r♠♥t t ♠ s③ s rt② ♣r♦♣♦rt♦♥ t♦ t ♥♠r ♦ s trs s

t s③ t t ♥st ♦ t trs s ♥t ♦r s♠t ♠s

♣tr t♦ ♦r ♦♠tr ♦t tt♦♥ ♥ r s♥s

r ♦♥t♥ r♦♠ t t ♠r♦s♦♣ ♠ ♠ r♦♥

rt s♦s t ♦t♦♥ ♦ tr♦ r♦ss rt r ♣♦♥t

♣r♦ss ♦ ♣ss ♣trs t s t r② rr♦rs s strt ♦♥ t

rt r♦♣ ♦♠ss♦♥s ♥ ♣♣r ♥ ♠♥② s r rr♦♣ ♥ t♥② r

♦t tt ♥ s s t s r② t t♦ s② tt t s ♥ ♦r ♥

①♣rt ♠s s♠t ② ❬♠ss♦ ❪

♣r♦r♠♥s rs t r♠♥ ttr t♥ t ①st♥ ♦rt♠s ♥

♣rtr t s♠♣r ♦ss stt② ♥ t ♦ts r tt ♥ ♦t ss

rt② t♥ ② s♥ r♥t s♣♣rtt♦♥♥ tr ♦r t s ♦

rr ♣rtt♦♥ ♦ K s ♥ ♥trst♥ s♦t♦♥ ♥ t ss ♦ ♥trst s ♥♦t

♦rrt② ①trt r♦♠ t t ♠♦r ♣rs② ♥ ♥tr ♣rts ♦ t ss

♦ ♥trst r ♦♠tt s s t♦ ♥rt s♣♣rtt♦♥♥ trs ♦ ♦ qt②

s♦s t ♦r ♦ t s♠♣r ♥ s stt♦♥ ♥ ♣rtr

♦♥ ♥ s tt t ♦r♠t♦♥ ♦ t ♣r♦t② qc,t ♣r♦♣♦s ♥t② ♥ q

s ♥♦t r♥t ♥②♠♦r ♥ ♥s t♦ ♠♦ ♥ ♦rr t♦ ♦r t st♦♥

♦ t ♦rsst s ♥ t s♣♣rtt♦♥♥ tr ♦♥st♥t ♦r ②♣r♦

♦r♠t♦♥s ♦r qc,t t♥ ♦♠ ♥trst♥ s♦t♦♥s s ♦ t ♦♥strt♦♥

♦ t ♥st② ♠♣ ♥♦t tt t s♠♣r s ♥♦t t ♥ t ♦♥t♦rs ♦ t

ss ♦ ♥trst r r♦

①♣r♠♥ts

♦♠♣rs♦♥s t t ♦♥t♥ ♣♣r♦ ♣r♦♣♦s ②

❬♠♣ts② ❪ r♦♠ t ♠r♦s♦♣ ♠s s♠t ② ❬♠ss♦ ❪

♥ s ♦rrs♣♦♥ t♦ t ♥♠r ♦ s tt ♥ st ♦ ♠s r

♦rt♠ ♣r♦s ttr st♠t♦♥ ♦ t ♥♠r ♦ s t♥ ♦t t L1 ♥

♦♥♦rr③t♦♥ rs♦♥s ♦ ❬♠♣ts② ❪ ♥ ♣rtr ♦r ♦rt♠

s ♠♦r rt r s r ② ♦♥♥trt

♦r ♠♣ts② ♠♣ts② r♦♥

♠t♦ L1r ♦♥♦r rt

s ♣ t t ♦trs ♦rt♠s ♥ tr♠s ♦ ♣r♦r♠♥s ♦♠s ♠♦r

♠r ♥ t ♥♣t s♥ s rr ♦♥trr② t♦ t ①st♥ s♠♣rs t

r t♠ ♦ tt♦♥ ♣r ♦t ♦ ♦r s♠♣r ♦s ♥♦t ①♣♦ ♥ ♥rs♥

t t s③ t t s ♥t r♥ t ♦♣t♠ ♦♣♥② ♦♥t♦♥s ♦ t

P❯ rttr s r♥ ts st tr s ♥ ♥♦ ①tr ♦st

♥ tr♠s ♦ ♦♠♣tt♦♥ t♠ ♦r s♥ t♦♥ trs ♦r ♥rs♥ t

♥♠r ♦ s♠t♥♦s ♣rtrt♦♥s r t♠ ♦ tt♦♥ ♣r ♦t

t♥ st② ♥rss ♦r ♦♠♥ st

♥ ♥ s♦ rsts ♦♥ ♦♥t♥ r♦♠ ♠r♦s♦♣

♠s s ♠s ♥ s♠t ② ❬♠ss♦ ❪ ♥ r ♣r♦

t r♦♥ trt t ①t ♥♠r ♥ ♦t♦♥ ♦ s r ♥♦♥ ♦r

♠ r ♦rt♠ s ♥ ♦♠♣r t♦ t s♣rs ♣♣r♦ ♣r♦♣♦s

♣tr t♦ ♦r ♦♠tr ♦t tt♦♥ ♥ r s♥s

② ❬♠♣ts② ❪ ♥ ♦t tt ♦♥trr② t♦ ♦r ♦rt♠ tr ♣

♣r♦ st rs ♥ st♠t ♥♠r ♦ s ♣r ♠s t♦t ♦t♥ ♥

♥t♥ t♠ s s♦♥ ♥ t r♦♦t ♠♥ sqr rr♦r

♥ tr♠s ♦ ♥♠r ♦ s r♦♠ ♦r s♠♣r s ♠♦r t♥ t ♦r t♥ r♦♠

❬♠♣ts② ❪

♦t ♥② tt t ♣r♦♣♦s ♠♦ s ♥r ♥ ♥ s ♦r ♠♥②

r♥t ♣♦♣t♦♥ ♦♥t♥ ♣r♦♠s s strt ♦♥ s ♠♦ ♦s

♥♦t st ♦♥t ♣♦♣t♦♥ t t s♦ ♣r♦s ♣ ♥♦r♠t♦♥ ♦♥ ts s♣t

♦r♥③t♦♥ ♥ ♦rr t♦ tr ♥ ♥②③ ts ♦r ♦t s♦ tt ♣ss ♥

ssttt ② ♥② t②♣ ♦ ♣r♠tr ♦ts ♥ t ♠♦ ♦r♠t♦♥

r Pr♦r♠♥s ♦ r♦s s♠♣rs ♦♥ ♦♥t♥ t♦♣ rt r♣

♣rs♥ts t ♣r♦r♠♥s ♦ t ①st♥ ♦rt♠s t♠ ♥ ♥r② r♦♠ ♠

r♦s♦♣ ♠ t ♦tt♦♠ ♦s♣s s♦ t qt② ♦ t r ♦♥rt♦♥s

r s♠♣r ♦s ♦t ♦ r♥♥♥ t♠ ♥ ♦♦ ♦♥rt♦♥ qt② ♠s

s♠t ② ❬♠ss♦ ❪

①♣r♠♥ts

r ❱r♦s ♣♦♣t♦♥ ♦♥t♥ ♣r♦♠s r ♦rt♠ ♣trs r

♥t ♦ts ♦ ♥trst ② ♣ss ♥ r s♥s s t♦♣ s r♦♠ ♣trs

♠ ♦♣♥ st♦♠t r♦♠ ♠r♦s♦♣ ♠s ♦ ♥ ♦tt♦♠ ②♦ s

r♦♠ r ♠s 1167 s rs♣t② 757 st♦♠t ♥ 87 t①s r tt

♥ 12 ♠♥ts rs♣t② 168 s♦♥s ♥ 165 s♦♥s ♦t tt t ♦♠♣t

t♦♥ t♠ s r ♦r tt♦♥ s t ♣rtt♦♥♥ s♠ ♦♥t♥s

s 75 s s♦♥ ♦♥ t ♦s♣s t ♦ts ♦ ♥trst r ♦②

tt ♥ s♣t ♦ t ♦♥♥trt♦♥ ♥ ♦r♣ ♦ ♦ts ♠s ♦rts②

♦ ♦r ❲ r ♥ ♦♦ ❬♦♦ ❪

♣tr t♦ ♦r ♦♠tr ♦t tt♦♥ ♥ r s♥s

trtr ①trt♦♥

r ♥♥t♦r ①trt♦♥ ② ♣♦♥t ♣r♦ss ♦ ♥s♠♥ts ♠

♥ t r♦ ♥st② ♠♣ rt t r♦ ♥t♦r s r♦r r s♠♥ts

② ♦r ♦rt♠ ♥ 16 s♦♥s r♦♠ t stt ♠ ♠r② t♦ ♠♦st

①st♥ ♠t♦s ♣rts ♦ t ♥t♦r ♥ ♦♠tt ♥ r♦s r ♥ ②

trs t s♦♠ ♦t♦♥s s s♦♥ ♦♥ t ♦s♣ ♠s ♦rts② ♦

♦rt♠ s s♦ ♥ tst ♦r r♦r♥ s♣ strtrs r♦♠ ♠s

♥ ts s ♥♥t♦rs ♣r♠tr ♦ts r s♣ ② ♥s♠♥ts

♥ s ♣♦♥t ♥tr ♦ ♠ss ♦ ♥s♠♥t ♥ t♦ t♦♥ ♣r♠

trs ♥t ♥ ♦r♥tt♦♥ ♦♥trr② t♦ t ♣♦♣t♦♥ ♦♥t♥ ♠♦ ♣r

♦s② s t ♣rs ♣♦t♥t ♥s ♦♥♥t♦♥ ♥trt♦♥ t♦ ♥ t

♥s♠♥ts s ♦♥str♥t ♦s t ♦t ♦♥rt♦♥s t♦ strtr

s ♥♥t♦rs ♦♥♥t♦♥ t♥ ♥s♠♥ts r♣rs♥t♥ ♥t♦♥ ♥

t ♥♥t♦r ts ♦♥ ts ♥r② ♦r♠t♦♥ ♥ ♦♥ ♥ ♣♣♥①

♣r♦t② Pr(t) ♦ ♦♦s♥ t ♣rtrt♦♥ t②♣ t s st t♦ 0.4 t =rt

♥ t 0.1 t =tr♥st♦♥ 0.4 t =r♦tt♦♥ ♥ 0.1 t =s ♥ ♦r

①♣r♠♥ts

r s♦s r♦ ♥t♦r ①trt♦♥ rst ♦t♥ r♦♠ stt

♠ r ♠t♦ s♥♥t② ♠♣r♦s t ♦♠♣tt♦♥ t♠s t rs♣t t♦

①st♥ ♠t♦s s t ♦♥ ❬♥♠r ❪ 16 s♦♥s r rqr ♥ ♦r

①♣r♠♥ts

♠ s P ♠♦

♦r s♠♣r 0.02 0.25 ♥

❬r ❪ 0.02 0.45 ♥

❬♦st ❪ 0.01 0.35 ♥

❬♦r② ❪ 0.01 0.50 ♣①

r ①trt♦♥ ♦ rr ♥t♦r r♦♠ stt ♠ ② r♥t ♠t

♦s r rst s s② ♦♠♣tt t rs♣t t♦ ①st♥ ♠t♦s

strtr ♦ t rr s ♦rrt② r♦r ② ♦♥♥t ♥s♠♥ts

r② ♦ ♦r ♦rt♠ ♥ tr♠s ♦ s P♦st s t rts s ♦♠♣tt

ttr t♥ ❬r ❪ ♥ ❬♦r② ❪ ♥ s♠r t♦ ❬♦st ❪ ♦t

tt ♦r ♦rt♠ s♥♥t② ♠♣r♦s t ♦♠♣tt♦♥ t♠s ♠s ♦rts②

♦

s ♦♠♣r t♦ 7 ♠♥ts ② ♠♣s♦♥ ♦rt♠ ❬r ❪ 155

♠♥ts ♦r s ♠t♦ ❬♦st ❪ ♥ 60 ♠♥ts ♦r ♥ t

♦♥t♦r ♣♣r♦ ❬♦r② ❪ ♥ ♥ s ♥ tt t s qt②

♦ ♦r ①trt ♥t♦rs s rt② ♥r♦r t♦ t♦s ♦ ❬♦st ❪ ♥

t q♥ttt rsts r s♠r t s tr ♠t♦ rs ♦♥ ②

♦r♠s♠ t t② ♥② ♠♦ rqr♥ ♠♥② ♣r♠trs r♦♥

t♥ ♦s t♥♥ ② tr ♥ rr♦r s t ts s sr ♣r♠trs

♥st ♦rs

♣tr t♦ ♦r ♦♠tr ♦t tt♦♥ ♥ r s♥s

①♣r♠♥ts t r t

r ♦rt♠ s ♥ tst t dimK = 3 ♦♥ ♥ ♦r♥ ♠♦ ♦r

①trt♥ ♣r♥ ♣r♠tr t♠♣ts r♦♠ ♥strtr ♣♦♥t ♦s

♦♥t♥♥ ♦t ♦ ♦trs ♥ ♥♦s s ♠♦ s ♥ s t♦ tt trs

r♦♠ sr s♥s ♦ r♥ ♥r♦♥♠♥ts ♦♠♣♦s ♦ ♠♥② ♦tr r♥t ♦ts

s s ♥s r♦♥ rs ♥s rs t s ♠♦ s♦ ♦s t

r♦♥t♦♥ ♦ t s♣s ♥ t②♣s ♦ trs ♦ts ss♦t t t

♣♦♥t ♣r♦ss ♦rrs♣♦♥ t♦ rr② ♦ r♥t t♠♣ts ♦ trs t ♥

♣♣♥① ♥ ♥tr② t tr♠ ♦ t ♥r② ♠srs

t st♥ r♦♠ ♣♦♥ts t♦ t sr ♦ t ♦t rs t ♣rs

♥trt♦♥ ts ♥t♦ ♦♥t ♦♥str♥ts ♦♥ ♦t ♦r♣♣♥ s s ♦♥ tr

t②♣ ♦♠♣tt♦♥ ♦♠♣r t♦ t ♦r♠r ♣♣t♦♥s t ♦♥rt♦♥ s♣

r r r♦♥t♦♥ r♦♠ ♣♦♥t ♦s ② ♣♦♥t ♣r♦ss s♣ ②

♣r♠tr ♠♦s ♦ trs r ♦rt♠ tts trs ♥ r♦♥③s tr

s♣s ♥ rs t ♥♣t s♥ ♣♦♥ts ♥tr ♥ t♦♣ rt ♥♣t

s♥ ♣♦♥ts r♥ ♥r♦♥♠♥ts ♥ s♣t ♦ ♦tr t②♣s ♦ r♥ ♥tts

♥s r ♥ ♥s ♦♥t♥ ♥ ♥♣t ♣♦♥t ♦s r ♦t s♥s ♥

r ♠ s ♦♥ t♦ ♦tt♦♠ rt t r♦♣♣ ♣rt t♦ ♣r♦ ♠♦r ♥tt

r♣rs♥tt♦♥ ♦ t s♥ ♥ t tr ♦t♦♥ ♦t ♦♥ t r♦♣♣ ♣rt ♦

t ♣r♠tr ♠♦s t t♦ t ♥♣t ♣♦♥ts ♦rrs♣♦♥♥ t♦ trs

①♣r♠♥ts

C s ♦ r ♠♥s♦♥ s♥ t ♦ts r ♣r♠tr② ♠♦r ♦♠♣① s

♦s ♦r ♦rt♠ t♦ ①♣♦t ♠♦r ♣② ts ♣♦t♥t r♦tt♦♥ r♥ s

♥♦t s r s♥ t ♦ts r ♥r♥t ② r♦tt♦♥ ♦r st♥

r♥ s s ♥ ♦rr t♦ ①♥ t t②♣ ♦ ♦ts ♦♥♦ ♣t ♥

s♠♣t ♣r♦t② Pr(t) ♦ ♦♦s♥ t ♣rtrt♦♥ t②♣ t s st t♦

0.4 t =rt ♥ t 0.2 t =tr♥st♦♥ 0.1 t =st♥ ♥ 0.3

t =s ♥ ♦r ①♣r♠♥ts

s♦s rsts ♦t♥ r♦♠ sr s♥s ♦ r r♥ ♥ ♥tr

♥r♦♥♠♥ts 30 rs♣t② 5.4 t♦s♥ trs r ①trt ♥ 96 rs♣ 53

♠♥ts ♦♥ t 3.7♠2 ♠♦♥t♥ r rs♣ 1♠2 r♥ r r♦♠ 13.8 rs♣

r ♦t♦♥ ♦ t ♦t ♦♥rt♦♥s r♥ t s♠♣♥ t

t♠♣rtr ♦ts ♦ ♦ qt② r rq♥t② ♣t ♥ t♦ ♥♦♥ r♥t

♦t ♦♥rt♦♥s t♦♣ t ♦s♣s ❲♥ t t♠♣rtr rss t

♣r♦ss ♦♠s ♣r♦rss② st t♦♣ rt ♦s♣s t ♦ t♠♣rtr

t rr♥t ♦t ♦♥rt♦♥ ♦s tr♦ s♦♠ ♦ st♠♥ts t ♣r♦ss

s st③♥ ♦s t♦ t ♦ ♠♥♠♠ ♦tt♦♠ rt ♦s♣s

♣tr t♦ ♦r ♦♠tr ♦t tt♦♥ ♥ r s♥s

2.3 ♠♦♥ ♥♣t ♣♦♥ts ♦♠♣tt♦♥ t♠s ♥ ♣♣r t ♥♥

♥♦♥tr ♦ts ♥ s r s♥s ② ♣♦♥t ♣r♦sss s ♥

t♦ ♦r ♥♦ s ♥♦t ♥ ♥t ♥♦ t♦ t ①tr♠ ♦♠♣①t②

♦ t stt s♣ ♦t s♦ tt t ♣r♦r♠♥s ♦ ♠♣r♦ ② r♥

t s♣ C t ♣♦♥t ♣r♦ss ♦♥ ♠♥♦s r t ③♦♦r♥t ♦

♣♦♥ts s tr♠♥ ② ♥ st♠t r♦♥ sr

t♥ t tt♦♥ qt② t r② ♦r ts ♣♣t♦♥ s t

ts s♥ ♥♦ r♦♥ trt ①sts s strt ♦♥ t r♦♣♣ ♣rt ♥

♠♥② ♥① t trs ♦♥ r♥t ③♦♥s r♦♠ r ♠s qr

t t sr s♥s ♦ts r ♦② ♦t ♥ tt t♦ t ♥♣t

♣♦♥ts t ♦♠ss♦♥s ♥ ♥ trs r srr♦♥ ② ♦tr t②♣s ♦ r♥

♥tts s s ♥s ♥♦♥♦r♣♣♥ ♦♥str♥t ♦ t ♥r② ♦s s

t♦ ♦t♥ stst♦r② rsts ♦r rs t tr ♦♥♥trt♦♥ rr♦rs ♠②

♦r ♥ st♥s♥ t tr t②♣ ♥ s♣t ♦ t tr ♦♠♣tt♦♥ tr♠ ♦ t

♥r② s♦s t ♦t♦♥ ♦ ♦t ♦♥rt♦♥s r♥ t s♠♣♥

♣r♦r

①♣r♠♥ts t r♦ ♥♦♠ s

s r♦ ♣♦♥t ♣r♦sss ♥ s♥ s ♥r③t♦♥ ♦ s

t t ♣♦t♥t ♦ ♦r s♠♣r ♦r ♦♣t♠③♥ ♥rs ♦r s ♥

♣r♦♠s ♥ trt♦♥ s r♣rs♥t s♠♣ ♣♦♥t ♣r♦sss ♥ t

t♦ ♦♦♥ rtrsts

t ♠♥s♦♥ ♦ t ♦♥rt♦♥ s♣ s ① r♣ strtr s ♥♦t

②♥♠ ♥②♠♦r t stt

t ♣r♠tr ♦ts ♦♠ s ♥t st ♦ ♥trs

❯♥r ts ♦♥t♦♥s t st♥r ♥r② ♦r♠ ♦ r♦ ♣♦♥t ♣r♦ss q

♥ r♦r♠t s

U(l) =∑

i∈V

Di(li) +∑

(i,j)∈E

V (li, lj)

①♣r♠♥ts

r V s t st ♦ rts ♣①s ♥ s ♦ ♠s E s t st ♦ s

♣rs ♦ ♥t rts ♥ l ∈ [1, N ]card(V) s ♦♥rt♦♥ ♦ s ♦r

V t N t ♥♠r ♦ s ♦ t ♣r♦♠ s ♦r♠t♦♥ s t② t

st♥r ♥r② ♦r ♥ ♣r♦♠s s sr ② ❬③s ❪ ♦t

tt tr s ♥♦ ♦♥str♥t ♠♣♦s ♦♥ t ♦r♠ ♦ t ♣rs ♥trt♦♥ tr♠ V

♥ s♥ ♦r s♠♣r s ♣♦♥t ♦♥sttts ♥ ♠♣♦rt♥t ♥t ♦♠♣r

t♦ r♣t s ♠t♦s

r ♠ s♠♥tt♦♥ t ♥♣t ♠s r♦♠ t♦♣ t♦ ♦tt♦♠ ♠

t ♣♥ts ♥ r s♦♥ ♦♠♥ sts ♦t♥ ② ♦r s♠♣r

② tr ♦♠♥ α①♣♥s♦♥ ♥ ② st ♦♠♥ ♦ r s ♥♦t t♦

t t s♠♥tt♦♥ ♠♦ s ♦♦s② ♥♦t ♦♣t♠ t t♦ ♦♠♣r

t rsts r♦♠ r♦s ♦♣t♠③t♦♥ t♥qs t r♥t ♥♣t ♠ s③s ♥

♥♦r♥ st♥s ε ♠s ♦rts② ♦ ♦♦ ❬♦♦ ❪

♥ ♦rr t♦ ♦♠♣r t ♣♦t♥t ♦ ♦r s♠♣r t t ♦tr ♦♣t♠③t♦♥

♦rt♠s ss♠ tt ♥♦ t ♥♦ ♥ ①trt r♦♠ t ♥♣t

♠s rr ♣rtt♦♥♥ s♠ s t♥ s ♥ t t

♣① r ♣rtr r♥♦♠② t ♦ s ♥ ② t ♥♣♥♥

♣tr t♦ ♦r ♦♠tr ♦t tt♦♥ ♥ r s♥s

♦♥t♦♥ q s δmax = 0 ♦ts r ① s♣t② t t ♦ s

♠st s♣r♦r ♦r q t♦ t ♠t st♥ ε ♦ t ♥♦r♦♦ rt♦♥s♣

♦r ♥st♥ ♥ s ♦ ♥ ♠ ♥ ♣r♦♠ t ♦r ♦♥♥①t②

♥♦r♦♦ t ♦♥t♦♥ s♠♣② ♠♣s tt ♥ ss♦t t♦ ♦♥

s♥ ♣①

♦r s♠♣r α①♣♥s♦♥ αβ s♣ P

♥r② t♠s ♥r② t♠s ♥r② t♠s ♥r② t♠s ♥r② t♠s

♠t

♣①s

s (×103) (×103) (×103) (×103) (×103)

ε = 1 ♣①

♣♥ts

♣①s

s (×103) (×103) (×103) (×103) (×103)

ε = 1 ♣①

r

♣①s

s (×106) (×106) (×103)

ε = 21 ♣①s

Pr♦r♠♥s ♦ r♦s ♦♣t♠③t♦♥ ♦rt♠s ♥ tr♠s ♦ r ♥

r② ♥ ♦♠♣tt♦♥ t♠ r♦♠ s♠ ♠ t ♥ ♦ ♣r♦r♠♥ ♦ ♦r

s♠♣r s rt② ♠♥♦r t r ♥r② s s♠r t♦ r♣s ♠t♦s

r♥♥♥ t♠s r st② ♠♣r♦ r♦♠ ♠ ♥ r ♥♦r

♦♦ st♥ r ♦r ♦rt♠ ♦♠s ♠♦r ♥trst♥ s t ♦♥♥

t♦♥ r♣s ♣♣r♦s ♥♦♥tr ♠♠♦r② ♣r♦♠s rs tr♠♥st

trt ♠t♦s r ①tr♠② s♦ ♦t tt t ♥r② r♦♠

t ♦rt♠ ♥ ♣♦♦r s ts ♦♣t♠③t♦♥ ♠t♦ ts st ♥ ♦

♠♥♠♠s

♣r♦r♠♥s ♦ ♦r s♠♣r ♥ tst r♦♠ s ♠♦ ♦r ♠

s♠♥tt♦♥ ♥tr② t tr♠ Di(li) ♠srs t qt② ♦ li t

①♣r♠♥ts

♣① i tr♦ ss♥ strt♦♥s ♦r ♣rs② t r♦♠tr② strt♦♥

♦ ss s ♠♦ ② ss♥ ♦s ♠♥ ♥ st♥r t♦♥ r

♠♦ ♣r♠trs t♦ st♠t ♦r ① ② sr ♣♦t♥t V ♦rrs♣♦♥s

t♦ t ♦♥♥t♦♥ P♦tts ♠♦ ❬ ❪ s♦ tt t ♥ s s♠♦♦t ♥

♦ ♥♦r♦♦ ♦ ♥t ε

♥ s♦ t ♣r♦r♠♥s ♦t♥ r♦♠ r♦s ♠s ♥

♣r♦s ♦♠♣rs♦♥s t t st♥r ♦♣t♠③t♦♥ t♥qs ♠①♣r♦t

Pr♦♣t♦♥ P ❬❲ss ❪ r♣t s ♦rt♠s ❬♦②♦ ❪

♥ trt ♦♥t♦♥ ♦s ❬s ❪ r s♠♣r ♦♠♣ts

t ts ♦rt♠s r♦♠ s♠ ♥♣t ♠ t r ♥r② s s②

st② r t♥ ② s♥ α①♣♥s♦♥ αβ s♣ ♦r P t t ♦♠♣tt♦♥

t♠ s ♦r ♥ ♦ t♠ ♦♠s s♣② ttrt ♥ t ♠ s③

♥ t ♥♦r♦♦ ♥t ♥rs ♥ ♣rtr t rsts ♦t♥ r♦♠

r s♦ tt ♦r s♠♣r ♣r♦♣♦ss ♥ ♥trst♥ tr♥t t♦ t st♥r

r♣s ♦♣t♠③t♦♥ t♥qs ♥♦♥tr ♠♠♦r② ♣r♦♠s r♦♠ s

r② ♠s r 8, 500× 8, 500 ♣①s t ♥♦r♦♦ rs ε = 21 ♣①s

r s♠♣r ♥ts r♦♠ tr ♥ts ♦♠♣r t♦ r♣t ♠t♦s

t ♥ ♣r♦r♠ r♦♠ r② ♠s t♦t ♠♠♦r② ♣r♦♠s t

♣♦t♥t tr♠ V ♥ ♥② ♦r♠ ♥ tr♥ ♣r♦♣♦st♦♥ r♥s ♥

♥tr♦ ♥ t s♠♣r ♦r ♥st♥ ♦♥ ♥ s ♥ tt♦r ♦♥ t

♥♣t ♠ t♦ s♣♣♦rt s♣♣rtt♦♥♥ tr ♥ t ♦st s ♦s

♦♥ s♦♥t♥ts rs t st s trt t ♦♠♦♥♦s ③♦♥s ♦ t

♠ ♦t s♦ tt t ♥♦r♦♦ st♥ ε ♥ ♦♥sr s r ♦♥

t ♠ ♦♠♥ ♥ ♣rtr ♦♥ ♥ s♣t② ♣t t ss♦♥ st♦♣♣♥

rtr♦♥ ♦ s ♥ ♥t♦♥ ♦ ♦ ♠①♠ ♥♦r♦♦ st♥s

rr② tt♣s♦♥s♦♦

♣tr t♦ ♦r ♦♠tr ♦t tt♦♥ ♥ r s♥s

♠♠r②

❲ ♣r♦♣♦s ♥ ♦rt♠ t♦ s♠♣ ♣♦♥t ♣r♦sss ♦s str♥ts r②

rst ♦♥ t r♦♥ ss♠♣t♦♥ tt ♥s t s♠♣♥ t♦ ♣r♦r♠ ♥

♣r ♥ s♦♥ ♦♥ t ♦♣t♦♥ ♦ tr♥ ♠♥s♠ ♦♥ ♥t

strt♦♥s ♦ t ♣♦♥ts ♥ t s♥ r ♦rt♠ ♠♣r♦s t ♣r♦r♠♥s ♦

t ①st♥ s♠♣rs ♥ tr♠s ♦ ♦♠♣tt♦♥ t♠s ♥ stt② s♣② ♦♥ r

s♥s r t ♥ s r② ♦♥sr t ♥ s t♦t ♣rtr rstr

t♦♥s ♦♥trr② t♦ ♠♦st s♠♣rs ♥ ♥ ♣♣rs s ♥ ♥trst♥ tr♥t t♦

t st♥r ♦♣t♠③t♦♥ t♥qs ♦r ♥ ♣r♦♠s

♦♥trt♦♥s ❲ ♣rs♥t ♥ ♦r♥ s♦t♦♥ t♦ rss t ♣r♦♠ ♦ ♥

♥ st ♥ ♥t s♠♣r ♦r PP rst② r ♦♠♣tt♦♥ t♠s

r♥t♥ ♦♥r♥ stt② ♥ qt② ♦ t r ♦♥rt♦♥s

r ♦rt♠ r♥s sr ♠♣♦rt♥t ♦♥trt♦♥s t♦ t

♠♣♥ ♥ ♣r ♦♥trr② t♦ t ♦♥♥t♦♥ s♠♣r ♠s

t s♦t♦♥ ♦ ② sss ♣rtrt♦♥s ♦r ♦rt♠ ♥ ♣r♦r♠

r ♥♠r ♦ ♣rtrt♦♥s s♠t♥♦s② s♥ ♥q ♥

r♦♥ ♣r♦♣rt② ♦ ♣♦♥t ♣r♦sss s ①♣♦t t♦ ♠ t ♦ s♠♣♥

♣r♦♠ s♣t② ♥♣♥♥t ♥ ♦ ♥♦r♦♦

tr♥ ♠♥s♠ P♦♥t ♣r♦sss ♠♥② s ♥♦r♠ ♣r♦♣♦st♦♥ r♥s

r ♦♠♣tt♦♥② s② t♦ s♠t t ♠ t s♠♣♥ ♣rt

r② s♦ ❲ ♣r♦♣♦s ♥ ♥t ♠♥s♠ ♦♥ t ♠♦t♦♥s

rt♦♥s ♦r r♠♦s ♦ ♦ts ② t♥ ♥t♦ ♦♥t s♣t ♥♦r♠t♦♥

①trt r♦♠ t ♦sr t ♦♥trr② t♦ t tr♥ s♦t♦♥s ♣r♦

♣♦s ② ❬ ❪ ♥ ❬ ❪ ♦r ♣r♦♣♦st♦♥ r♥ s ♥♦t t rt②

r♦♠ ♠ ♦♦ t s rt s♣♣rtt♦♥♥ tr ♥ ♦rr t♦

r♥t t s♠♣♥ ♣r③t♦♥

♥t P❯ ♠♣♠♥tt♦♥ ❲ ♣r♦♣♦s ♥ ♠♣♠♥tt♦♥ ♦♥ P❯

s♥♥t② rs ♦♠♣tt♦♥ t♠s t rs♣t t♦ ①st♥ ♦rt♠s

♥rs♥ stt② ♥ ♠♣r♦♥ t qt② ♦ t ♦t♥ s♦t♦♥

♠♠r②

♣♦t♥t ♦ P❯ s ♥t② ①♣♦t ♥ ♦t ♦♣t♠③♥ t ♥♠r

♦ ♦♣rt♦♥s ♥ ♣r ♥ ♠t♥ t ♠♠♦r② tr♥sr t♥ P❯ ♥

P❯

r♥ ♠♦s ♦r r♥ r♦♥strt♦♥ ♦ t t ♣r♦r♠♥ ♦ t s♠

♣r ♣r♦♣♦s ♦r♥ ♣♦♥t ♣r♦sss ♦r s♦♥ ♣r♦♠s ♥ ♣rtr

♠♦ ♦r tt♥ ♦♠♣① ♦ts ♥ rs ♣♦♥t ♦s s s♥

s ♠♦ s ♣♣ t♦ tr r♦♥t♦♥ r♦♠ sr s♥s ♦ r r♥ ♥

♥tr ♥r♦♥♠♥ts ♦ ♦r ♥♦ t s t rst ♣♦♥t ♣r♦ss s♠♣r

t♦ t t♦ ♣r♦r♠ ♥ s ② ♦♠♣① stt s♣s

♠tt♦♥s ❲ ♣r♦♣r② rss t ♥tr ♠tt♦♥ ♦ PPs tt

s t ♦♥r♥ t♠ r♥ ♦♣t♠③t♦♥ sss r♠♥ rst ♦r ♥♦

♦♣t♠③t♦♥ s♠ s ♥t ♦♥ ♦♥t♦♥ tt t t♠♣ts r s♠ ♦♠♣r

t♦ t s♥ s♦ tt ♥♠r♦s ♥♣♥♥t s♣r♦♠s ♥ s♦ s♠t♥

♦s② ♦♥ ♦♠♠♦♥ ♦♣t♠③t♦♥ ♠t♦s ♦r PPs ♥ st♦st r①t♦♥

♦ t ♥r② s rr s s♠t ♥♥♥ r t t♠♣rtr ♣

r♠tr ♣②s ♠♦r r♦ ♥ t ♦♥r♥ qt② strt♥ t♠♣rtr

s s t rs♥ s♣ t♦r t ♦♦♥ s ♥ st♠t

② ♦♥♥t♦♥ ♠t♦s ♥ ts ♦♥t①t ♦r ♠t♦ s ♥♦t r♥t t♥ ♣r

♦s ♦♣t♠③t♦♥ ♠t♦s ♥♦t ♣r♦♣♦s ♠♣r♦♠♥ts ♦r ♥s ♥ ts

s♣t

t♥ ss♠♣t♦♥ ♦ s♠ t♠♣ts s ♥♦t t ♦♥② ♠t♥ t♦r ♥

ts ♠t♦ s r② t♦♣♦♥ ♣♣r♦ PPs r ♥tr♥s② ♠t ② t

rr② ♦ ♦ts s ♦r ♠♦♥ ♥ t ♦♥t①t ♦ r♥ r♦♥strt♦♥ r♦♠

r t tr t②♣s ♦ t♠♣t trs ♣s♦s♣ tr ♦♥s♣

tr ♥ s♠♣s♦s♣ tr ♥ ♦♥② s♠♣ ♣r♠trs ♠♦s

♥ s PPs r ♥♦t ♣t ♦r ♠♦♥ ♥ strtrs t♦

♣♣rs tr ♦♣♥ ♥ ts rt♦♥ ❬rt♥r r ❪ r

tt t rst♥ r♥ ♠♦s r s♠♣st ♥ ♠t ② t rr② ♦ ♦ts

PPs r ♥♦t ① ♥♦ t♦ r♣rs♥t ♦♠♣① ♥ strtrs r♦r

ts t♦♣♦♥ ♣♣r♦ ts t ♠♦s tr tt♦♥ t s ♥♣♣r♦♣rt

♣tr t♦ ♦r ♦♠tr ♦t tt♦♥ ♥ r s♥s

♦r r♦♥strt♥ ♥s

Prs♣ts ♥ tr ♦r t ♦ ♥trst♥ t♦ ①t♥ t ♦rt♠ t♦

♣♦♥t ♣r♦sss ♥ ♦r rss♥ s♣t♦t♠♣♦r ♣r♦♠s ♥ ♦ts

♦ r♥ t♠ s♦ ♦♥ ♦ ♠♣r♦ t ♦rt♠ t♦ ♦♣t♠③ s

♥r② ♦r♠t♦♥s ♥ ♦♣ ♠♦r ♦♠♣tt s♦t♦♥ ② ♠♦♥ t

r♥ ♣r♦♣♦st♦♥ r♥ ♦s ♥st② ♠♣ s ♦ ♦r ♥t♥st② ♥ ♦♠♦♥♦s

r♦♥s

r ♣r♠trs r ♥ t♦ ♥ t ♥r②♥ ♠t♠t ♠♦

❲♥ ♦rrt② ♦s♥ ts ♣r♠trs r t sr s♣ r♥r♥ t

♣r♦♠ ♠♦r trt ♦r t rr♥t ♠♣♠♥tt♦♥ rs ♦♥ t♦s

♠♥ ♥t♥♥ ♦ ♣r♠trs r♥♥ ♣♣r♦ ♦r ts ♣r♠trs ②

s♣rs t♥qs ♥ t s ♦ rsts t♦ t♦♠t② st t ♦♦♥

s ♣r♠trs ❬❱r♥ ♥♠r ♥ ❪ ②t t♦

①♣♦r s ♦ rst② r♥r t ♦rrs♣♦♥♥ st♣ ss t♠♦♥s♠♥

♥ s♦♥② ♠♣r♦ t ♣r♦r♠♥s ② s♥ t ♣r♠tr stt♥s ♦♣t♠ ♥

rt♥ ② ♦t ♦♥r♥ t♠ ♥ qt② r ts ② t♦ ♥t r♦♠ ♥

t♦♠t r♥♥ st♣ ♦♠♣r t♦ t rr♥t ♠♥ tr♥rr♦r ts

t♦ t ♦ ♠♥t♦♥ ♠tt♦♥s ♦ t t♦♣♦♥ ♣♣r♦s ♦tt♦♠♣

s♦t♦♥s r ♦♥sr ♦r ♦♠♣① ♥ r♦♥strt♦♥ ♥ t ♥①t ♣tr

sr t♦ ♦tt♦♠♣ s♦t♦♥s ♦r r♦r♥ r ♥ ❱ t s

s ts s♦t♦♥s r② ♦♥ ss♠♣t♦♥s ♦♥ t r♥ s♥ strtrs ♥ r

♣♣r♦♣rt ♦r r♦♥strt♥ ♦♠♣① ♥s

♣tr

t♦s ♦r r♥ ♠s

r♦♥strt♦♥

♥ ts ♣tr ♣rs♥t t st t♦ ♦rt♠s ♦r r ♥ ❱ t

♦♥sst ♥ ♥rt♥ ♠♦s ♦ r♥ s♥s ❲ ♦r ♦t t t②♣s

t ♠ s t♦ t♦♠t② r♦♥strt r♥ ♠♥ts t s♥ ♠t♦s

♦r r t t♦♥ ♥ ❱ ♠ss t♦♥ r r♥t ♥

♠♥t r♥ ♥ t rqrs r♥t strts ♦r t ♥ t♦♥

♥ t♦♥ ♥ ♦r t r♦♥strt♦♥ ♦ t r♥ s♥ t♦♥ ♥

t♦♥ ♥ t ♥ st♣ s ♥ sr ♦r ♦s r ♦♥ t

r♦♥strt♦♥ ♣♣r♦s

r ♦r ♦ t r♦s t♥qs s ♦r r ♥ ❱ t ♦♥

t t ♠♦tt♦♥ r ♥ ♦ ♥ t♦♥ ♦♦ ② sr♣t♦♥ ♦ t

♠t♦♦♦② ♦r ♠♦♥ r♥ ♠♥ts t♦♥ ♥ t♦♥ ♥② ♥

ts ♣tr ♣r♦r♠ r♦s ①♣r♠♥ts t♦ t ♦t ♠t♦s

t♦♥

♥tr♦t♦♥

t♦♠t t② ♠♦♥ s ①♣r♥ ♥ ♥rs♥ ♥trst ♥ ♦♠♣tr

r♣s ♥ ♦♠♣tr ❱s♦♥ ♥ t st s rsr t♦♣ s ♣rtr②

♥♥ s t ♦♠♥s s♥ ♥rst♥♥ ♦t ♠♦♥ ♥ ♥ r

s ♣r♦ss♥ s ♠♥t♦♥ ♥ ❬❱♥s ss ❪ ♦ st♥t

♣r♦♠s r s② rss ♥ t trtr t② r♦♥strt♦♥ ♥ t② ♥r

t♦♥ ♦r♠r ♠s t♦ ♣r♦ rt ♦♠tr ♠♦s ♦ r♥ s♥s r♦♠

♣tr t♦s ♦r r♥ ♠s r♦♥strt♦♥

♣②s ♠sr♠♥ts s t ♥ ❬ss ❪ ♠♦st② ♥ ♥ t♦♠t ②

ttr ss ♣r♦r ♠♦♥ t♦ ♥rt rst ♠♦s ♦ ts ②

s♠♥t③ r♦♠ r♠♠t rs t ♣♦ss sr ♥trt♦♥ ❬❱♥s ❪

♥ ts ♦♦♥ ♦s ♦♥ t ♦r♠r t② r♦♥strt♦♥ ♣r♦♠

trtr ♦♥ r♥ s♥ r♦♥strt♦♥ r♦♠ r♦r♥ qst♦♥s s r

t② r t r♦s rt♦♥s ♥ ♥ ①♣♦r ❬ss ❪ ♥ ♥t

♣♣r♦ s s♥ ♣t ♠s r♦♠ str♦ s♦♥ s ♦♥sttts

♣♥♥t ♥♣ts ♦r ♠♦♥ ts r s② ② ♥♦s② ♦rs ♦

❬❩♥ ❪ ♥ ❬r ❪ ♣r♦♣♦s ♦♠♣t ♠♦s ♦ ♥s r♦♠

♣t ♠♣s t ♦r♠r s s♣ ♣rtt♦♥ r♥ ② ♦♠tr ♣r♠

ts rs t tr ss♠s ♦s ♦ r♥ strtrs s♥ ♦♥t r♦

s♠♣♥ ♠♦r ♠tt♦♥ ♦ ♣t ♠♣s ♦♠s r♦♠ t t② ♥ st♥

s♥ ♥s r♦♠ tt♦♥ tr t②♣s ♦ t r ♦♠♠♦♥② s

s t② ♦ ♥♦t sr t♦♦ ♠ r♦♠ ts ♠tt♦♥ s s r ♥ ❱

t s ♥trst♥ ♣r♦♣rts ♦r r♥ r♦♥strt♦♥ s t♦♥

♦tt♦♥s ♦r r t

r t ♠ r② ♣♦♣r ♥ t ♠ ♥ t♦ srs ♦ ♦rs

♠♥② ♦s ♦♥ ♣rs♥ ♥ ♦♠♣♦♥♥ts ♥ rt ①trt♦♥ ♦

♥ ♦♥t♦rs ❬P♦s ♦s r ❩♦ ♥ ❪

P♦♥ts ♥rt ② r qst♦♥ s②st♠s r s② r② rt t ♦♥

trr② t♦ ♣t ♠♣s t② r ♦♠tr② ♥strtr ♥ r r ♦ r♦♠tr

♥♦r♠t♦♥ P♥r ♣r♠ts r♣rs♥t t ♦rt ♦♠tr t♦♦s ♦r r♦r

♥ r♦♦s ♥ s ♦rts ♥ ♠ t♦rs ♣rs♥ t ♣♥s

❬♦s ❪ s♦r♥ ♦ rrts ❬❩♦ ❪ ♦r ♦♠♣♦s♥ t

r♥t strtrs ♦ ♥s ❬♥ ❪ s ♠t♦s ♠♥② ♦s ♦♥ ♥

r♦♥strt♦♥ r♦♠ ♦♠tr ♣♦♥t ♦

♦♠ ♠t♦s rss t r♥ r♦♥strt♦♥ ♣r♦♠ ② ♥rs ♣r♦r

♠♦♥ ♦♥ssts ♥ ♥♥ r♠♠t rs r♦♠ ♣②s ♠sr♠♥ts

s ♣♣r♦ ♣r♦♣♦ss ♦♥♥♥ ♥ ② s♠♥t③ ♠♦s ♦ s t

♣♣r♦ t r t

r♠♥s t② ①♣♦r ♦r r♦r♥ s t② r♦♥strt♦♥ s ♦♥strt♦♥ rs

r rr t♦ ♥②③ ♥ ♥

♦tt♦♥s ♦r ❱ t

❲t t r♥t ♥s ♥ t❱ tr♦ ❱ ❬t③ ❪ s♦♠

♥t t♥qs ♥ ♦♣ ♦r rt♥ ♥s ♠ss r♦♠ rs♦

t♦♥ ♠s ♦♥trr② t♦ ♣t ♠♣s ♥ r s♥s ts tr♥r ♠ss

tt ❱ ♠ss ♦♥sttt r r♣rs♥tt♦♥s ♥ t s♥s tt ♥

♦r♠t♦♥ s rtr ♦♥ t rt ♦♠♣♦♥♥ts ♦ t s♥ s t ♥

t♦♥ ♥ strt ♦♥ ❱ ♠ss r ♣rtr② rt

♥ ♣r♦ ♥ ♠♣rss ♠♦♥t ♦ ts sr♣ss♥ ♥ qt② t ♦tr

♠♦s ♦r s③t♦♥s ♣♣t♦♥s ② ♦♥sttts ♥ tr♥t t♦

st♥r ♣t ♠♣s ♥ r s♥s ♦r t♥ t♦♠t t② r♦♥strt♦♥

♣r♦♠s ♦rts ♥ ♠ t♦rs ♥srt♥ ♣r♠ts ♥ ♠s ♦r ♥

st♥ ❬r ❪ s r♦♥ r♦♥ ♥ trt ♥♦♥♥r ♠♥♠③t♦♥ ♦r

tt♥ s ♣r♠ts ❬♦♥t♥r ❪ s rt♦♥ ♣♣r♦ t♦ ♣♣r♦①

♠t t ♠s t st ♦ s♣ ♣r♦①s ♦r ❬ ❪ s ♦ ♠t rt♦♥s

t♥ ♣r♠ts tt r♦♠ t♦ ♥rt ♥ ③ s②♥tt ♠♦

♦ t ♠s

♣♣r♦ t r t

♥ strtr ①trt♦♥

♥ t ♣♦♥t ♦ s ss s♥ t ♦r♠s♠ ♣rs♥t ♥ t♦♥

t ♥①t st♣ ♦♥ssts ♥ ①trt♥ strtr ♥♦r♠t♦♥ r♦♠ t ♥

♠♥ts ♦ t s♥

♥ ♦♦t♣r♥ts ♥ ♦♦t♣r♥ts r ①trt ② ♣r♦t♥ t

♣♦♥ts s ♥ ♥ ♦♥ ❳❨r ♥ t♥ ② ♦② ♣r♦♣t♥

t ♥♦r♠t♦♥ ♦♥ t ♠♣t② s ♦ t r s t ♥ s r ♦t

♥ t♥ t ♣♦♥ts s r♦♥ ♥ t ♣♦♥ts s ♥ ♦r

♣tr t♦s ♦r r♥ ♠s r♦♥strt♦♥

r P♣♥ ♦ t ♣r♦♣♦s ♣♣r♦ ♦t tt t r t ss

t♦♥ s ♥ sr ♣r♦s② ♥ t♦♥

t ♥ ♦♥r② s t ② ♦♥ s③

♦♦ st♦♥s ♣♥r ♦♠♣♦♥♥ts ♦ t r♦♦s r tt ② r♦♥

r♦♥ ♥ ♦ t♦ s♦ ①trt ♥♦♥♣♥r ♠♥ts s♥ ♥ trt

♥♦♥♥r ♠♥♠③t♦♥ s s ♥rrqrt ♦♣t♠③t♦♥ t ts

s♦t♦♥ s ♥♦t rt♥ s ♦ ts ①♣♥s P❯ ♦st ♥ ♥♦♥♣♥r

r♦♦ ♥ ♣♣r♦①♠t ② s②s sq♥ ♦ s♠ ♣♥r strs t

stst♦r② rst ♥ ♠♦st ss ♣r♦♣t♦♥ ♦ t r♦♥ r♦♥ s s

♦♥ t rrt② ♦ t ♣♦♥t ♥♦r♠s ♥ ♦ ♥♦r♦♦

r♦♦ ♦♥t♦rs r ♦t tr♦ sq♥ ♦ ♦♥♥t s♠♥ts

♣♦♥ts r♣rs♥t♥ t ♥ s r tt s♥ t ♣s♣

♦rt♠ ❬ ❪ ♥ ts ♠t♦ s ♥r③t♦♥ ♦ t ♦♥①

♠t♦ ♥ ♦t♥s ttr rsts t♥ t ♦r♥ ♦♥① s t s♣

♦ r♦♦ s ♥♦t ♥ssr② ♦♥① ♦r t rqrs ♥ t♦♥ ♣r♠tr

α s s ♦ t rst♥ ♦♥t♦r s r ♦ rs α ♠♣t②

♣♣r♦ t r t

tr♥t♦♥ ♦ t ♣♦♥t ♦ ♦♥② ❳❨ ♦ ♣♦♥t s ♦♥sr s

♦♠♣t t♦ tr♠♥ st ♦ ♣♦ss αs♣s s t ♣♦♥t ♦ ♥st② ♥

♦r ①♣r♠♥ts s ♦t ♣♦♥ts ♣r sqr ♠tr t rst αs♣ t α > 3

s ♦♥sr ♦♥t♦r s t♥ s♠♣ s♥ ♥ ♣t ♦sPr

♦rt♠ ❬ ❪ ♣r♠tr ε s rqr t♦ st♦♣ t ♣r♦r

♦♥sttts r ♣♦♥t s t ♦♥tr♦s t s♠♣t♦♥ ♦ t ♦♥t♦rs

t s ♦♠♣t ② t♥ ♥t♦ ♦♥t t s③ ♦ t ♦♥t♦r

ε = εMin + (εMax − εMin).(1− e−nbRC )

r nb s t ♥♠r ♦ ♣♦♥ts ♦ t ♦♥t♦r εMin ♥ εMax r rs♣t②

t ♦r ♥ ♣♣r ♦♥s ① t♦ 0.03 ♥ 0.3 ♥ RC s t ♠♥ ♥♠r ♦

♣♦♥ts ① t♦ 50 ♥ ♥ ♥rst♥ tt s♠ ♦♥t♦r rqrs ♠♦r ts

♦ ε rs r ♦♥t♦r ♦s ♥♦t ε

♥② s♦♠ strtr st♠♥ts r ♠ ♦♥ t r♦♦ st♦♥s ♥ ♦rr t♦ ♦♥

♥t t♠ ♥ t② r ♦s ♥♦ ♥♦r♦♦ rt♦♥s♣ t♥ r♦♦

st♦♥s s ♥ t♦ r♦♦ ♦♠♣♦♥♥ts r ♥♦rs tr ♥ st♥

s ♥r♦r t♦ ♦♥ ♠tr ♦r ♣r ♦ ♥♦r♥ r♦♦ st♦♥s t r♦♦ ♦♥t♦r

♣♦♥ts ♦ ♥trst r t♥ ♣r♦t ♦♥ t ♥ ♥trst♥ t t♦ ♣♥s ❲

ts st♣ ♠② s♥t ♦r s♠♣ ♥ ♥ #1 ♦♥ t

♦s ♥♦t r♥t② trtt r♦♥strt♦♥

♦♠♣t ♠s ♥rt♦♥

st st ♦s s t♦ ♥rt trtt ♥ ♦♠♣t ♠s r♦♠ t

strtr ♥♦r♠t♦♥ ①trt ♣r♦s②

s ♥t③t♦♥ ♥ ♥t ♠s s ♥rt r♦♠ t rr ❳❨r

s ♦r ♦♠♣t♥ t ♥ ♦♦t♣r♥ts s ♦ t r r s

♥tr♦r t ♦r ♦♥r② ♣♥♥ ♦♥ tr t ♦♥s t♦ t ♥s

t t ♦r t ♦♥r② st♦rs ♦ t ♥ ♦♦t♣r♥ts s ♦r

♥tr♦r ♦r t tst tr t ♥tr s ♦t ♥s t

♣♥♠tr ♣r♦t♦♥ ♦ t r♦♦ st♦♥s ①trt ♥ t♦♥ ♦ ss

♣tr t♦s ♦r r♥ ♠s r♦♥strt♦♥

t♦ st♥s

♥tr ♦♥s t♦ ♦♥ ♦r ♠♦r r♦♦ st♦♥s ♦r ♦♥r♥ r♦♦

st♦♥ t ♥tr s rt② ♣r♦t ♦♥ t ♣♥ t♦ rt

♣♦t♥t rt① rt① ♥ t st Z s ♣t t♦ ♥rt

t ♠s

♥tr ♦s ♥♦t ♦♥ t♦ r♦♦ st♦♥ rt① s ♦♠♣t s t

rt ♣r♦t♦♥ ♦ t ♥tr t♦ t ♦sst r♦♦ st♦♥ ♦r ♦♥②

♥tr♦r s r ♦♥sr r ♥ ♦rr t♦ ♦♥t♥ t ♣r♦♣t♦♥ s

s ♦s t♦ t ♦s ♥s t ♠s t♦t ♥♥ ts t♦♣♦♦②

r s ♥t③t♦♥ ♥ ♦♦t♣r♥t t ♥ ♥t ♠s rt

tr sss ♥tr♦r t ♥ ♦♥r② r rs♣t② r♣rs♥t ♥

♣♥ ♥

s s♠♣t♦♥ t t♦♣♦♦② ♣rsrt♦♥ qr s ♦♣s

♠t♦♥ s ♦rt♠ ❬r♥ ❪ s♥ t♦♣♦♦ ♣rsrt♦♥ ♦♥str♥ts

s trt② s t♦ ♥t② r t s③ ♦ t ♠s s ♣r♦ss ♣rsrs

t ♠s t♦♣♦♦② ② s♥ qrt rr♦r ♠sr ♦r t ♦st ♥t♦♥ ♥

② ♠♥♠③♥ t ♥ ♦t♦♥ rr♦r ♦r t ♣♠♥t ♥t♦♥ s ♣♥r

s strtrs ♦ t ♥ r ♣rsr r♥ t ♠s s♠♣t♦♥

♠t♦♥ ♣r♦ss s st♦♣♣ ♥ t ♥♠r ♦ ♥♦t♥tr♦r rts s ♦♥

♥r ♦ ts ♥t ♥♠r s ♣♦st♣r♦ss st♣ t r♠♥♥ ts r♦♠

t ♦♥r② r t rst s strt ♦♥

♣♣r♦ t t❱ tr♦ t

♣♣r♦ t t❱ tr♦ t

r ♣♣r♦①♠t♦♥

tr t ♥tt♦♥ ♥ t ①trt♦♥ ♦ t r♥ ♠♥ts r♦♠ t s♥

s t♦♥ t ♥①t st♣ ♦♥ssts ♥ ♥t②♥ t ♦♠tr s♣ ♦

t ♦ts ♥ ♦rr t♦ s♠♣② t t♦ ♦♠♣t ♥ strtr ♠♦s ♥s

trs ♥ r♦♥ r ♣r♦ss s♣rt② ♣r♦♠ t sr ♣♣r♦①♠t♦♥

♦♠s r♦♠ t t tt t ♦♠tr② ♦ ♥s s ② strtr ② ♥t♦♥

♦♠tr ♥ ♥ s♣ ♣rtt♦♥ ② ♣♥s s ♦♣t t♦ r♥t

♦♠♣t♥ss ♠t s ♦ strtrs ♥ ♣rsrt♦♥ ♦ s♠♥t ♥♦r♠t♦♥

P♥ ②♣♦tss P♥r ♣r♠ts r ①trt r♦♠ t ♥♣t ♠s ♦♠

♣♦♥♥ts s r♦♦ ♥ ♥st ♦ tt♥ ♣♥s ② st♥r t

♥qs s ♦♥ ♥s ♦r r♦♥ r♦♥ ♦rt♠s r② ♦♥ t r② ①st♥

rtrs str♥ ♣r♦r♠ ♥ t♦♥ strs t ♦ ♣♥rt②

ttrt ap ♥ t r A r t♦ ♥rt ♣♥s ♥ ♦r ①♣r

♠♥ts str s st ap < 0.3 ♥ A > 10m2 ♦r st str

t ♣♥ ♠♥♠③♥ t st sqr rr♦r t♦ ts rts s t♥ ①trt

♦ rr③t♦♥ ♦ ♣♥s ♠♣♦s♥ ♦ rrts ♦♥ ♣♥ ②♣♦t

ss ♦s t ♠♦s ♦ ♥s t♦ s② ♠♦r ♦♥sst♥t ② rst♥

♣♥ ♣♦st♦♥s ♥ ♦r♥tt♦♥s s♦r♥ ♦ rrts s s♦ ♦ ♥trst

♦r r♥ t ♦♠♣①t② ♦ t ssq♥t s♣ ♣rtt♦♥♥ ② t ♣♥s

r ♠t♦s ♥ ♣r♦♣♦s ♥ t trtr ♦r ♥trt ♦♠t

r ♠♦♥ ❬ ❪ rs ♥ r♦♥strt♦♥ ❬❩♦ ❪ ♦r

♠♦r ♥r② ♦♠tr s♣ tt♥ ♥r rr③t♦♥ ♦♥str♥ts ❬ ❪

s ♠t♦s r r② ♥t t ♥ ♦ts ♦♥t♥♥ ♣r♠ts

t r ♥♦t ♣t t♦ t s ♦ t② ♥ t♦s♥s ♦ ♣♥s r s②

tt ♣r km2 ♥ t♦ r② r♥♥♥ t♠s

♦ rss ts ♣r♦♠ ♣r♦♣♦s ♣r♦r s ♦♥ r②♥tr ♦♣

rt♦♥s ♦r t②♣s ♦ ♣rs ♥trt♦♥s t♥ ♣♥s r ♦♥sr ②

♣tr t♦s ♦r r♥ ♠s r♦♥strt♦♥

♥♦t♥ P1 ♥ P2 t♦ ♣♥s ♥ rs♣t ♥t ♥♦r♠s n1 ♥ n2 ♥

♥tr♦s c1 ♥ c2 ♦♥ ♥ ♦r♠t ts rt♦♥s♣s ♥r ♥ ♦r♥tt♦♥

t♦r♥ ε ♥ ♥ ♥ st♥ t♦r♥ d

Prs♠ P1 ♥ P2 r ε♣r |n1 · n2| ≥ 1− ε

rt♦♦♥t② P1 ♥ P2 r ε♦rt♦♦♥ |n1 · n2| ≤ ε

❩s②♠♠tr② P1 ♥ P2 r ε❩s②♠♠tr ||n1 · nz| − |n2 · nz|| ≤ ε r

nz s t ♥t t♦r ♦♥ t rt ①s

♦♣♥rt② P1 ♥ P2 r dε♦♣♥r t② r ε♣r ♥

|d⊥(c1, P2) + d⊥(c2, P1)| < 2d r d⊥(c, P ) r♣rs♥ts t ♦rt♦♦♥

st♥ t♥ ♣♦♥t c ♥ ♣♥ P

r rt♦♥s♣s ♣rs♠ ♦rt♦♦♥t② ♥ ❩s②♠♠tr② r

t t♦ ♣♥ ♦r♥tt♦♥ ♦♣♥rt② s ♣rtr s ♦ ♣rs♠ ♥♥

rt ♣♦st♦♥♥ ♦♥str♥t ♦♥ ♣♥s s ♦r rt♦♥s♣s ♦♥sttt t

♠♦st s rrts tt ♥ t♥ ♥t♦ ♦♥t ♦r ♠♦♥ ♥s t

♣♥r ♠♥ts

♣r♦r ♦♣t ♦r rr③♥ ♣♥s rs ♦♥ ♦r st♣s

P♥s r rst rr♦♣ ♦r♥ t♦ ♣rs♠ ❲ ♣r r♦♣

st ♦ ♣♥s r ♠t② ε♣r

t♦♥s♣s ♦ ♦rt♦♦♥t② ♥ ❩s②♠♠tr② r t♥ tt t♥

t ♣r r♦♣s ♦ ♣r r♦♣s r ε♦rt♦♦♥ rs♣t②

ε❩s②♠♠tr tr rs♣t rt r②♥tr ♣♥s r ε

♦rt♦♦♥ rs♣ ε❩s②♠♠tr

rt r②♥tr ♣♥ ♦ ♣r r♦♣ s r♦r♥t

♦r♥ t♦ ♦rt♦♦♥t② ♥ ❩s②♠♠tr② ❲ ♣r♦♣t t ♥♦r♠t♦♥ ♦

♦rt♦♦♥t② ♥ ❩s②♠♠tr② ♥ t ♦rt♦♦♥ r♣ r♦♠ t ♣r r♦♣

t t st ♠t r t♦ t ♣r r♦♣ t t ♦st ♠

t r ♦r♥tt♦♥ ♦ st ♣♥ s st ② ♦♥str♥♥

ts ♥♦r♠ t♦ ♦rt♦♦♥ ♥ ♥t② ❩s②♠♠tr t♦ t ♥♦r♠ ♦ t

r ♦ ♣♥ ♦rrs♣♦♥s t♦ t r ♦ ts str

♣♣r♦ t t❱ tr♦ t

♣r r♦♣ s♥ t ♥♦r♠t♦♥ rst ♥♦r♠ s ss♥

t♦ r② ♣♥ ♦ t ♦♥sr ♣r r♦♣ s s♠ ♦s s t♦ ♦

t ♣♦t♥t ♦♥ts ♦ rt♦♥s♣s s t ♣r♦♣t♦♥ ♦s ♥♦t ♦♦♣ ♥ t

♦rt♦♦♥t② r♣ ♣r♦rt② ♥ ♥ t♦ t ♣r r♦♣s ♦ r

r P♥ rr③t♦♥ Prtt♦♥♥ t s♣ r♦♠ t ♥t ♣♥r

②♣♦tss t♦♣ t s t♦ ♥s ♥ rrr st ♦ s t♦♣ rt r ♣♥

rr③t♦♥ ♣r♦r ♦t ♣r♦s strtr ♦r♥ t♥ ♣♥ ②♣♦tss

♥ str♦♥② rs t ♥♠r ♦ s ♥ t s♣ ♣rtt♦♥ ♦♦r ♥ t

♦r♥tt♦♥ st♣ rs♣t② ♥ t ♣♦st♦♥ st♣ r♣rs♥ts ♣r r♦♣ rs♣

st ♦ ♦♣♥r ♣♥s P♥ ♥♦r♠s r rst r♥ t ♦r♥tt♦♥ st♣

② ♣r♦♣t♥ ♦rt♦♦♥t② ♥ ❩s②♠♠tr② ♦♥str♥ts r♦♠ t st ♣r

r♦♣ t♦ t s♠st ♦♥ s ♥♠rs ♦♥ t ♦rt♦♦♥t② r♣

♣tr t♦s ♦r r♥ ♠s r♦♥strt♦♥

♠t r ♦♠ rt♦♥s♣s t♥ ♣r r♦♣s ♥ r♦♥ t

ts s t ♣r t♦ ♣② ♦r ♥r ♦♠♣①t② ♥ st r♥♥♥ t♠

ts ♦ ♦♣♥r ♣♥s r ①trt r♦♠ ♣r r♦♣ t d

ε♦♣♥r ♣♥s r rr♦♣ ♥ tr ♣♦st♦♥ s rst ♦♥t♦ t

rt r②♥tr ♥tr♦ ♦ t ♣♥s

s strt ♦♥ ts ♣r♦r ♦♥sttts st s♦t♦♥ t♦ ♦t

r t ♣♥ ②♣♦tss ♥ r♥♦r rrts t♦t trt② rtt♥

♣r♠ts s ♥ ❬❩♦ ❪ ♦r ❬ ❪ s♦♥s r rqr ♦r rr③♥

sr t♦s♥s ♦ ♣♥s ♥ ♦r ①♣r♠♥ts t ♦r♥tt♦♥ t♦r♥ ε ♥ t

st♥ t♦r♥ d r ① t♦ ♣♣r♦①♠t② r ♥ ♥ ♦♥

♠tr rs♣t②

r ①trt♦♥ t srt ♦r♠t♦♥

❲rs t ♣♥ rr③t♦♥ s ♣r♦r♠ ♦♥ t ♥tr s♥ t sr

①trt♦♥ r♦♠ t s♣ ♣rtt♦♥ ♥ ② t ♣♥s ♥ r③ t ♠♦r

♦ s s ♥ ♦s ♦r s♦t ♦ss r s♣t② s♦♥♥t ❲

tr♦r s♣rt t ♦♥♥t ♦♠♣♦♥♥ts s ♦r r♦♦ ♥t♦ st ♦

s♠ss s♦ tt t② ♥ trt ♥♣♥♥t②

♦♠♣t♥ t ①t ♦♠tr② ♦ s♣ ♣rtt♦♥ ② ♣♥s s rt

♦♣rt♦♥ ♦s ♦rt♠ ♦♠♣①t② s r② ①st♥ ♦rs r②♥ ♦♥

♣♥ rr♥♠♥ts tr② t♦ r t ♦rt♠ ♦♠♣①t② ♥ ❬r ❪

♣♥ ②♣♦tss r rstrt t♦ t ♥tt♥♦r ss♠♣t♦♥ s s♦t♦♥

♥ t t♦rs t♦ ♦♥sr r s ♣rtt♦♥ s qt ♠t ♥ ♣rt

♠t♦ ♣r♦♣♦s ② ❬ ❪ ♦♥ssts ♥ ♣rtt♦♥♥ t s♣ t

♣♦②r ♦♠♣① ♦♥ ♥t ♥ t♦ ♦♥② t s ♦s t♦ t ♣♥r

♣r♠t ♥♥♥ t♠ ♥ ♦r s② ① ♥ ♦r ♥ ♥ t

♦♥② ♥r ♣♥s ♥st ♣r♦♣♦s ♥ ♦r♥ srt ♦r♠t♦♥ ♦

t ♣r♦♠ ② ♦♠♥♥ ♥r② ♣ Prtt♦♥♥ P trs t ♦♠tr

♦♣♥② r ② s t♦ ♦ t t♠♦♥s♠♥ ♦♠♣tt♦♥ ♦ t

①t ♦♠tr② ♦ t s r♥ t ♣rtt♦♥♥ ♦ t s♣

♣♣r♦ t t❱ tr♦ t

r srt s♣ ♣rtt♦♥♥ ♥♦rs r s ♥tr♦r ♦r ①tr♦r

t♦ t ♥♣t ♠s ② r② st♥ t t ♣♥ ♥srt♦♥ ♦t t ♥♦rs ♦

t srt s♣ t♦♣ ♥ t P tr ♦tt♦♠ r ♣t tr t st ♣♥

♥srt♦♥ t ♥♦r st s ♦♠♣♦s ♥t♦ srt s rt ♦♦r ♣♦♥ts r♦♠

♦♥ ♥ ♦♠♣t srt ♦♠ ♦r t rt♦ ♦ ♥tr♦r①tr♦r ♥♦rs

s s ♥t② t ♥t s ♥ t ♦♣t♠ t ♦ ♦r srt ♣r♦♠

s ♦♥ t sr ♥ ①trt ② ♦♠♣t♥ t ①t ♦♠tr② ♦ ts

r♦♠ t P tr s r♦ss ② t r t

❲ rst rt ♥ ♦r♥t ♦♥ ♦① ♦ t s♠s ♥ ♣♦♥ts r

rr② s♠♣ ♦r♥ t♦ t tr rt♦♥s ♦ t ♦♥♥ ♦①

♣♦♥t ♥ ♥♦r s ss♦t t♦ ♥① ♥ t♦ ♥r② ♥♠r

s♣②♥ tr t ♣♦♥t s ♥tr♦r ♦r ①tr♦r t♦ t ♥♣t ♠s sr s

t ♠s s ♥♦t trtt r② st♥ s s t♦ st♥s ♥tr♦r r♦♠ ①tr♦r

♥♦rs r t s♣②♥ t st♥ t♥ t♦ ♥♦r♥ ♥♦rs

s ♣r♠tr ♦ t ♦rt♠ ♦r t t ♠♦r rt t rst

♥ ♦r ①♣r♠♥ts ts s ① t♦ ♠tr s strt ♥

♣♥ ②♣♦tss r sss② ♠ ♥ t ♦♥♥ ♦① ♥ t♦ t

♦♥strt♦♥ ♦ P tr ♥st ♦ ♦♠♣t♥ t ①t ♦♠tr② ♦ t s

♦r r② ♠ ♣♥ ♦♥② ♣t t ♥① ss♦t t♦ ♥♦r

s srt s♠ ♦s s t♦ q② st♠t ♥♦r♠t♦♥ s s ♦♠

♥② t rs ♥ ♣♦st♦♥ t rs♣t t♦ t ♥♣t ♠s

♠♥t ♦r♠t♦♥ s s t♦ ♥ t ♥s♦ts ♥ ♦ t s

t sr ♥ t t ♥tr t♥ ♥s ♥ ♦ts t s ♦♥sr

r♣ (C, E) C = c1, ..., cn s t st ♦ ♥♦s ♦rrs♣♦♥♥ t♦ t s ♥

♣tr t♦s ♦r r♥ ♠s r♦♥strt♦♥

② t s♣ ♣rtt♦♥ E = e1, ..., em s t st ♦ s r♣rs♥t♥ t ts

s♣rt♥ t♦ ♥t s t ♥ t r♣ (C, E) ♦♥ssts ♥ s♣rt♥ t

st ♦ s C ♥ t♦ s♦♥t sts Cin ♥ Cout st ♦ s t♥ Cin ♥ Cout

♦rrs♣♦♥s t♦ st ♦ tr♥r ts ♦r♠♥ sr S ⊂ E

♥ ♦rr t♦ ♠sr t qt② ♦ t sr S ♥ ② t t (Cin, Cout)

♥tr♦ ♦st ♥t♦♥ C ♦ t ♦r♠

C(S) =∑

ck∈Cout

Vck g(ck) +∑

ck∈Cin

Vck (1− g(ck)) + β∑

ei∈S

Aei

r Vck s t srt ♦♠ ♦ ck ♥ ② t ♥♠r ♦ ♥♦rs ♥ ck

g(ck) s ♥t♦♥ ♠sr♥ t ♦r♥ ♦ t t rs♣t t♦ t

rt♦ ♦ ♥tr♦r①tr♦r ♥♦rs ♥ Aei s t srt r ♦ t ei ♦♠♣t

s t ♥♠r ♦ ♣rs ♦ ♥♦rs ♦♥♥ t♦ ♦♥ ♦ t t♦ s ♥

♥t ♥ st♥r ♦♥♥①t② ♥♦r♦♦ t♦ rst s♠s ♦ t

♦st ♥t♦♥ C ♥ s♥ s t tr♠ ♥ t ♦♥♥t♦♥ ♥r② ♦r♠t♦♥

rs t rt s♠ t ② t ♣r♠tr β ≥ 0 ts s rr③t♦♥

tr♠ ♦r♥ s♠ r srs ♦♣t♠ t ♠♥♠③♥ t ♦st C(S) s

♦t♥ s♥ t ♠①♦ ♦rt♠ ❬♦②♦ ❪

♥t♦♥ g(ck) s ♥ ♥ t ♥tr ❬❪ t s tr ss♥♥ t

♥s t♦ ck s ♦r♥t t t rt♦ rin ♦ ♥tr♦r ♥♦rs ♦♥t♥ ♥

ck t s ♥ ②

g(ck) =(2rin − 1)× |2rin − 1|α + 1

2

r α s r t♥♥ t t s♥stt② ♦ ♥t♦♥ g s strt

♦♥ ♥ s♦♠ ss ♥ r ♦ ♥♦rs s stt♦♥ rss

♥ t s t♥ ♦♠♣r t♦ t t ♦ t ♦♣♥② r s

♥♦t t♥ ♥t♦ ♦♥t ♥ t ♦st ♥t♦♥ C s ts srt ♦♠ s ♥ s

♣♣r♦①♠t♦♥ s s t♦ ♣♦t♥t② ♦♠t s r s♠ t t s ♦ t

r t ♦t ♦r tt s stt♦♥s r rr ♥ ♣rt t♥ t♦ ♣♥

rr③t♦♥ ♠ts t ♥♠r ♦ t♥ s

♦♣t♠ t ♦rrs♣♦♥s t♦ sst ♦ ts ♦♠♣♦s♥ t sr s

strt ♦♥ ①t ♦♠tr② ♦ ts ts s t♥ ♦♠♣t r♦♠

♣♣r♦ t t❱ tr♦ t

r ♦r ♦ t ♥t♦♥ g t rs♣t t♦ rin ♦♦s♥ α = 0 s

♥r ♣♥③t♦♥ ♥ ♥t♦♥ ♦ t rt♦ rin ♥rs♥ α s ♠♦r ♥♦r♠

♣♥③t♦♥ ♥ t rt♦ rin s ♦s t♦ ♠♣t ♦ t t tr♠ ♥ t

♦st ♥t♦♥ s r ♦r♥ srs ♦ ♦ r t♦♣ ♠♦ α < 0 g

str♦♥② ♣♥③s s t ♥♦♥ ♦♥sst♥t rt♦

t P tr t♦t ♦♣rt♥ t ♦tr ts ♦♥t♥♦s ♦r♠t♦♥ ♦

ts s♣ ♣rtt♦♥ ♣r♦♠ s ♥ ♠♣♠♥t s♥ t ♣♦②r♦♥ t

strtr ♦ ❬ ❪ ♥ ♦ t♠ ♦t♥ ② ♦r srt ♦r♠t♦♥ s

r② r♥♥♥ t♠ ♥ r ② t♦r ♦s t♦ r♦♠ t ①♠♣ ♦

♦♥ ♥s t r♦s s ts

♣♥♥ ♦♥ t ♣♣t♦♥ ♦♠♥ t r♣rs♥tt♦♥ ♦ ♥s ♠st ♦♥

t♥ r♥t ♠♦♥t ♦ ♦♠tr ts s strt ♦♥ t srs

t ♣♦sst② t♦ st t♥ tr r♥t

t ♣r♦s s♠♣ sr♣t♦♥ ♦ ♥s ② r♣rs♥t♥ s

② ♣s♣♥r ♦♠♣♦♥♥ts ♥ r♦♦s ② ♦r③♦♥t t srs

sr♣t♦♥ s s ♦r ①♠♣ t♦ s♠t t ♣r♦♣t♦♥ ♦ tr♦♠♥t

s t♦ ♦♣t♠③ t ♦t♦♥ ♦ rss ♥t♥♥ ❲ ①trt srs

② ♦♥sr♥ ♦♥② rt ♣♥s s r♥ t s♣ ♣rt

♣tr t♦s ♦r r♥ ♠s r♦♥strt♦♥

r s ts r ♦rt♠ ♣r♦s ♠♦s ♦ ♥s

t tr r♥t s ts ♠♦s ♣r♦ s♠♣st

sr♣t♦♥ ♦ r♦♦s st t♦ r♥t t②♣s ♦ r♥ rs s s t②♣ ♥♥

strts ♦r ♥str ♦♠♣①s ♥ ♠♦s ♠♦r t

sr♣t♦♥ ♦ r♦♦s s♥ ♣s♣♥r strtrs ♥ ♠♦s r

♣t t♦ rs♥t rs ♥ ♥s ♦♥t♦♥s

t♦♥♥ t t ♦ t ♦r③♦♥t r♦♦s ♥ ♥ ② t ♠♥ ③

♥ t ♦♥sr ♣♦rt♦♥ ♦ t ♥♣t ♠s

♠♦s ♠♦r r♥ sr♣t♦♥ ♦ t r♦♦s ② ♣s

♣♥r ♦♠♣♦♥♥ts r♥ t ②♣♦tss ♦ ♦r③♦♥t t r♦♦s

② r s② ♦♥sr ♦r r♥ ♣♥♥♥ ♣♣t♦♥s t ♣♥

②♣♦tss r t♥ ♥t♦ ♦♥t r♥ t s♣ ♣rtt♦♥♥ ♦r ♦t♥♥

srs

♣♣r♦ t t❱ tr♦ t

s r♣rs♥tt♦♥ s s♠r t♦ ♥ tr♠s ♦ ♦♠♣♦

♥♥ts ♥ r♦♦ st♦♥s t s♦ ♠♦s t r♦♦ s♣rstrtrs s ♠♥②s

♦r ♦r♠r♥♦s ♠♦s r ♦t♥ ② tt♥ s♠ ttr

♦♠♣♦♥♥ts ♥ t ♥♣t ♠s ♦r ♣rs② strs s r♦♦ t

♥♦t t ♥♦ t♦ ♥rt ♣♥ ②♣♦tss r st ♥ rr♦♣ ②

♦♥♥t ♦♠♣♦♥♥ts rt♥r ♦ s t♥ tt ♦♥ str

r♦♣ ♥ ♥trt t♦ t ♠♦

♦♥ trs ♥ r♦♥

s ♣♣r♥ ♦ trs r♦♠ ❱ ♠ss s ♥♦t ♣♣♥ s strt

♦♥ tr s♣s s② ♦rrs♣♦♥ t♦ s♠ ♦♠s t ② sr

st♥r ♣s♦ tr ♠♦ ♦s ♦♠♣t♦♥ ♥ r♥r♥ s ♣t

r tt♦♥ ♥ ♠♦♥ ♦ trs rs ♥ ❱ ♠ss t♦♣ t r♥

♦♠♣♦♥♥ts r tt r♦♠ ♥ t♦♥ ♠♣ ② ①trt♥ t ♦ ♠①♠

t♦♣ rt r ♦ts r♣rs♥t♥ t ♥tr ♦ ♠ss ♦ t tt trs ♥ t

♥tr ♦ ♠ss s ♦t tr t♦♥ ♣r♠trs ♦tt♦♠ t r t♥ ♦♥

② tt♥ s♠♣s♦s t♦ ♠s rts ♦tt♦♠ rt

♣tr t♦s ♦r r♥ ♠s r♦♥strt♦♥

t♦ r r♥ s♥s s ♦♥sr t♦ ③ ts ♠♥ts r♦♠ t ♥♣t ♠s

s rt② ♠t♥ t tr ♠♦s t♦ ♠s s ♦♠♣tt♦♥② ①♣♥s t

♥tr ♦ ♠ss ♦ tr s rst ♦t ② tt♥ t ♦ ♠①♠ r♦♠ ♥

t♦♥ ♠♣ rt r♦♠ t ♣rts ♦ t ♥♣t ♠s s tr ♦tr

♣r♠trs ♦ t t♠♣t s s t t ♥ t ♥♦♣② rs r t♥ ♦♥

② ♠♥♠③♥ t ♥ st♥ r♦♠ rts t♦ s♠♣s

r♦♥ ♦♥t♥s ♠♥② r♥ ts s s rs ♦r tr s♥s ♦

♥♦t ♥ t♦ ♣rsr t ♠s ♦ t r♦♥ s ♣r♦ ② tr♥t♥

st ♦ ♣♦♥ts rr② ♣♦st♦♥ ♦♥ ❳❨r t ❩ ♦ ts ♣♦♥ts ♥

♥ ② t r♦♥ ♠♣ s ♥ t♦♥ t♦ ♦♠♣t t t♦♥ ttrt ae

①♣r♠♥ts

①♣r♠♥ts t r t

r ♦♥strt♦♥ ♦ r♦s ♥s ♥ r♥ rs r ♣♦♥t ♦

t ♥ ♦r ♠ss ♠♦ rt

r ♠t♦ s ♥ tst ♦♥ r♥t ♣♦♥t ♦ ♥sts ♣rs♥ts

①♣r♠♥ts

r ♦♠♣t♥ss ♥ r② t♦♥ ♦r ♠s t ♠s ② ❩♦

t ❬❩♦ ❪ ♠ ♥ t s♦r st♥ ♦ ♦r ♠s t rs♣t t♦

t r♦♥strt♦♥ ② ❬❩♦ ❪ rt ♦♦r s r ♥♦ rr♦r t♦ rr♦r

s♣r♦r t♦ 1 ♠tr

rsts ♦t♥ r♦♠ r♦s t②♣s ♦ ♥s ♥ ♥s r♥ rs

❱s ♦♥srt♦♥s ♠t♦ ♣r♦♣♦ss ♦♥♥♥ ♠♦s ♥ t

♥ strtr s ♦rrt② rtr s strt ♦♥ t rst #1 t

♥ ♦♠♣♦♥♥ts r ♦♣t♠② r♣rs♥t ② t ♠s ♥ tr♠s ♦ rts ♥

ts rt♥r ♦ t ♥ s sr ② t♦ ♦♠♣♠♥tr②

tr♥r ts s s r♦♦ st♦♥ s ♠♦ ② ♦♥ ♦r t♦ ts

♥♦♥♣♥r r♦♦ st♦♥s r ♣♣r♦①♠t ② ♣s ♣♥r s♣s t s

r♥r♥ s ♥♦t ②s stst♦r② s s♦♥ ♦♥ t rst #6 t t s♣r

r♦♦

♦♠♣t♥ss ♥ r② ssss♠♥ts r r♦♥strt♦♥ s ♦♠♣r

t t rst ♦t♥ ② ❬❩♦ ❪ ♥ r ♠s s ttr

♦♠♣t♥ss 43 rts 69 ts ❱ 133 rts 228 ts ♥

s♠r r② ♥ t r s♦r st♥ ♦ ♦r ♠s t rs♣t

t♦ t r♦♥strt♦♥ ② ❬❩♦ ❪ s 0.16 ♠tr ♦r ♦♥ ♥ ♥♦t

tt s♠ ♠♥② s ♥ ♦♠tt ♥ ♦r r♦♥strt♦♥ s♦r

st♥ s ♠①♠ t ts ♦t♦♥ 1.12 ♠tr r ♠t♦ ♦ss ♦♥

t r♦♦ st♦♥ r♦♥strt♦♥ ♥ s ♥♦t s♥ ♦r tt♥ t s♠ ♣♥r

♣tr t♦s ♦r r♥ ♠s r♦♥strt♦♥

♦♠♣♦♥♥ts s s ♦r♠r♥♦s ♥ ♠♥②s s♣t t♦s s♠ ♦♠tt

strtrs t r rr♦r s r② stst♦r② ♣rtr② ♦♥sr♥ t

♥ ♥ tr♠s ♦ ♦♠♣t♥ss ♦r♦r t♦ ♠ r ♦♠♣rs♦♥ t t

rst ♦t♥ ② ❬❩♦ ❪ ♦s♥ t♦ s tr ♠t♦ t♦ ♥rt

♥ ♠s t s♠r r s♦r rr♦r ♦ ♠tr ♠s ♦

t♥ st s ♦r ♦♠♣t♥ss 76 rts 124 ts ♦♠♣r t♦ ♦r rst

Pr♦r♠♥s ♦♠♣t♥ t♠s r rs♦♥ t♥ t♦ t ♦♠♣t

t♦♥ ♦♠tr② ♦rt♠s rr② ❬ ❪ s t♦ ♣r♦r♠ ♦r

♦♠tr② ♦♣rt♦♥s rst #8 ♦♥ r♣rs♥t♥ ♥s r♥ r

r ♥♣t 139983 ♣♦♥ts s ♥ ♦t♥ ♥ 9 ♠♥ts rst♥ ♠s

s 3450 rts ♥ 578 ts

①♣r♠♥ts t ❱ t

r ♦rt♠ s ♥ tst r♦♠ r♥t tsts ♥rt ② ❬♣ ❪

r♦♠ t❱ tr♦ r ♠s ♦rt♠ s ♥ ♠♣♠♥t ♥

s♥ t ♦♠♣tt♦♥ ♦♠tr② ♦rt♠s rr② ❬ ❪

♣r♦s t s ♦♠tr t♦♦s ♦r ♠s ♥②ss ♥ ♥rt♦♥ r s♣ts

t♦ ♦♥sr t♦ t ♦r ♦rt♠ ♥ ♣rtr t s♠♥t ♥

♦rrt♥ss t s qt② t ♦♠tr r② ♥ r♥♥♥ t♠s ♦t tt

s ♠♥t♦♥ ♥ ❬ss ❪ t t♦♥ ♦ r♥ s♥ ♠♦s s s②

t ts s ♥♦ ♥♠r ♥♦r r♦♥ rt ①st ♥ t ♦r♦r

♠♦st ♦ ①st♥ t♦♠t t② ♠♦♥ ♠t♦s s r ♥♣ts ♥ ♥♥♦t

♣t t♦ t ❱ ♠s ♦♥t①t ❲ ♥st ♦♠♣r t r♥t st♥r

sr ♣♣r♦①♠t♦♥ ♦rt♠s

♦st♥ss s ♠♥t♦♥ ♥ t♦♥ ♥♣t ♠ss r ♥s ♥ t

♥ sts ♦t♥ r♥ t ♦t ♥tt♦♥ st♣ r ♦ ♦♦ qt②

♦t rr③♥ tr♠ ♦ t ♥r② ♥ t ♦rrt♦♥ rs r♥ s♣t ♦♥ss

t♥② ♥ ♠t ♥tt♦♥ rr♦rs ♥ ♥ t ♣rs♥ ♦ ♠r ♦ts s s

①♣r♠♥ts

r r s r♥ s♥ ③t♦♥ 7th strt ♦ Prs ♣

♣r♦①♠t② ♠2 s ③ t tr s ♦ t ♦tt♦♠ r♦♠ ♥s

❱ ♠s ts s♠♥t ♥ t♦♣ rt ♣r♦s ♥ rt

♥tt♦♥ ♦ t ♦ts ♦ ♥trst s s ♦♠♣rs♦♥ t t t♦♣ t r

♠ tr ♠♦s r ♦♠♣t ♦♠tr②strtr ♥ s♠♥

t③ ♠ ♦rts② ♦ ♦♦ ❬♦♦ ❪

tr ♦♥r♥♥ sr ♣♣r♦①♠t♦♥ t s ♦ s♣ ♣rtt♦♥s r♥ ②

♣♥r ②♣♦tss ♦ s t♦ ♦t♥ ♦♠♣t ♥ ♦♠tr② strtr ♠♦s

♦ ♥s t ttr r② t♥ t st♥r sr ♣♣r♦①♠t♦♥ t

♥qs ❬r♥ ♦♥t♥r ❪ s s♦♥ ♥ ♥ ♣rtr ♦r

♠♦s r ♥♦t t ② ♦s ♥ t♦♣♦♦ rr♦rs ♦♥t♥ ♥ t ♥♣t ♠s

s s♦♥ t t r♦♥t ♦ t r ①♠♣ sr♣t♦♥ s

s♦ ♥ ♥trst♥ ♥t t rs♣t t♦ t st♥r sr ♣♣r♦①♠t♦♥

t♥qs s t s ♦♠♣t ♠♦s ♣rsr♥ r♦♦ ts s s ♠♥②s

♥ ♦r♠r♥♦s

Pr♦r♠♥s Pr♦r♠♥ s♣ts rt t♦ r♥♥♥ t♠ ♥ st② r

♠♣♦rt♥t t♦♥ rtr s t♥ ♦rts ♥ ♠ t♦ s♥ st

♦rt♠ t♦ ③ r r♥ s♥s strts t ♣r♦r♠♥

♦ ♦r ♦rt♠ r♦♠ r♥ s♥s ♦ r♥t s③s ♠♦st t♠♦♥s♠♥

♣tr t♦s ♦r r♥ ♠s r♦♥strt♦♥

♦♣rt♦♥ s t sr ①trt♦♥ ♥ ♠♦r ♣rs② t ♦♠♣tt♦♥ ♦ t ①t

♦♠tr② ♦ t ts st ② t r♣t ♦ ♦ ♥s r ② ♣r♦

ss ♥ ♣♣r♦①♠t② s♦♥s ♦r t ♠♦ ♥ ♠♥ts ♦r t

♠♦ ss t♥ ♠♥ts rs♣t② ♦rs r ♥ssr② t♦ ③ 1km2

♥s r♥ r t rs♣ ♠♦ ♦♠♣①t② s ♣rtr②

♣♣♥ s ss t♥ ts r rqr t♦ ♠♦ ♥s t

♦♠♣rs♦♥

t s t t♦ ♦♠♣r t r♦♥strt♦♥ rsts ♦ t t♦ ♠t♦s s t②

♣r♦ss r♥t t②♣s ♦ t s ♦♠♣r t rsts ♦ ♠t♦

t stt♦trt ♠t♦s ♦♣ ♦r t s♠ t t②♣ ♦r♦r

♦ ♥♦t t ♦r t rst♥ ♠♦ t♦♥ ♦ t r② s

♦t♥ ② t♥ t s♦r st♥ ♦ t r♦♥strt♦♥ t t ♦r♥

t s t♦♥ s ♦♥ tr s♦t♥ s♥ ♥ r♦♠ t s♥

♦t ♣♣r♦s ♦rrt② r♦♥strt ♥s ♠♥② ♦♠♣♦s ♦ ♣s

♠♥t♥

P♥rr③t♦♥

rs♥r♦♥

♦♠♣①t②

r s s s s s

ts ts

♥ ♦s s s s s s

ts ts

Prs 7th strt s s s

ts ♠♥ ♠♥ ts

♥♥♥ t♠ ♥ ♠♦ ♦♠♣①t② r♦♠ r♥ s♥s ♦ r♥t s③s

tsts ♥ ♣r♦r♠ ♦♥ ♥ ♥t ♦r ♦ t ③ ♦t tt t♠

rqr ♦r ①trt♥ ♥ ♠♦s ♥ ♦♥sr s s♠r s

s♣rstrtr r♦♥strt♦♥ t♠ s ♥ ♦♠♣①t② rrs t ♥♠r

♦ ts ♦ t ♥ ♠♦s t

①♣r♠♥ts

r ♦♠tr r② ♦s ♣r♦ ② ♦r s②st♠ t r♥t s

r ♦♠♣r t♦ st♥r sr ♣♣r♦①♠t♦♥ ♦rt♠s ❬r♥ ❪

♥ ❱ ❬♦♥t♥r ❪ ② ♠sr♥ t s♦r st♥ s r♦♠

t t♦ r t♦ t ♥t ♠s ♦♠♣①t② ♦ t ♥ ❱

♠♦s r ♥t ♣♣r♦① ts rs ♠♦ s ♦r ts

♦♦t ♥ qr rr♦r ♦ t ♠♦ s r t♥ ♦r

♥ ❱ ♠♦s t r♦♦ ♥ ♣♦♦r② sr ♠♦ t♦t ♣♥

rr③t♦♥ s ♦r t♥ t ♠♦ t ♣♥r rr③t♦♥

t s s② ss ♣♣♥ ♥ ♠♦r t♠♦♥s♠♥

♣♥r srs ❲ s t ♠ts ♦ ♦r ♣♣r♦s ♥ ♥s ss ♦ ♥s

t ♥♦♥♣♥r srs s s rs ♦r ♦♠s ♥ ts ss s♠ rtts

r s ♦♥ t rst♥ ♠ss t t ♦r r♦♥strt♦♥ ♦ t r♥ s♥

r♠♥s ♦♥♥♥

t♦♦♦② ♦♥r♥♥ t ♠t♦♦♦s ♦ ♦t ♠s ♥rt♦♥ ♠t♦s

♥♦t tt t ♠t♦ ♦r r t s ♠♦r s♥st t♦ ♠ss♥ t t♥

ts ❱ ♦♥tr♣rt ♥ t ❱ t ♦♠tr s♣ ♣rtt♦♥♥ s

♣r♦r♠ ♥ s r r♦♥strt ♥ tr s ♥♦ t t♦ s♣♣♦rt ts

s♦♥ s ♦r s ♦♥tr♦ ② t s♠♦♦t♥ss tr♠ ♥ t ♥r② ♦r♠

♣tr t♦s ♦r r♥ ♠s r♦♥strt♦♥

t♦♥ β ♣r♠tr q ♣♣r♦ t ❱ s ts ♠♦r rs♥t t♦

♠ss♥ t ♥ ♥♦s t♥ t ♣♣r♦ ♦r r t

t② ♦t ♣♣r♦s r ② t♦♠t ♥ ♥ ♥ r s♥s

♦r t ♣♣r♦ ♦r ❱ ts ♦♥r t♦ r♦♥strt ♥ r♥ s♥ ♦ s♠

s③ ♦♠♣r t♦ t ♣♣r♦ ♦r r t ♥ t ♣♣r♦ ♦r ❱ t

ss ♦♠tr s♣ ♣rtt♦♥♥ tt s ♦st② ♥ rqrs ♠♦r ♦♠♣tt♦♥

rs♦r t♥ t ♦tr ♠t♦ ♦t tt r♥ t ①♣r♠♥ts ♦t ♣♣r♦s

r ♥♦t ♠t ② t ♠♠♦r② s ♥ ♦ sss② ♣r♦ss r♥ r ♦

r s③ ♣♣r♦①♠t② 1♠2

♦♥strt♦♥ qt② ❲t rs♣t t♦ t r♦♥strt♦♥ qt② t ♣

♣r♦ ♦r r t ♥rts ♥s t r♦♥strt♦♥ rr♦r r♦♥

♠tr r s♠r t♦ t♦s r♣♦rt ♥ t ♦r ♦ ❩♦ t ❬❩♦ ❪ t

t ttr ♦♠♣t♥ss ♣♣r♦ ♦r ❱ t s r r♦♥strt♦♥

rr♦r r♦♥ ♠tr r t ♥ ♥ ttr ♦♠♣t♥ss t str♦♥r

rr③t♦♥ ♦ t ♥s ♦♠♣r t♦ st♥r sr ♣♣r♦①♠t♦♥ ♠t

♦s ❬♦♥t♥r ❪ ♥ ❬r♥ ❪ ♦r ♣♣r♦ ♦r ❱ ♥rts

♠♦r rt ♠ss ♦t ♦r ♣♣r♦s t r ♥ ❱ t ♥rt

rt ♥ ♦♥♥♥ r♦♥strt♦♥ ♦♠♣r t♦ ♦tr stt♦trt ♠t♦s

tt ♠♣♦② s♠r t

①t② ♥② t ♣♣r♦ ♦r ❱ t s ① ♥♦ t♦ rr t

sr s r♦♠ r s♠♣ ♦① ♥ r♣rs♥tt♦♥s t♦

r t r♣rs♥tt♦♥s t ♠♥②s s ts ♣♣r♦ s

♠♦r rst t♥ t ♣♣r♦ ♦r r t ♦s ♥♦t st♥s t

♠♥ts ♦ t ♥s ♥ t♦ s♥t② t ♥t ♦ t s♠♥ts

♦t♥ tr ♥ t t

♦♠♣r t♦ ♦tr t ♣♣r♦ t ❱ t s♠s t♦ st② ttr

♥ tr♠s ♦ s r♥r♥ rstt② ♥ r♦st♥ss

♠♠r②

♠♠r②

♣♣r♦ t r t

❲ ♣r♦♣♦s ♥ ♦r♥ ♠t♦ ♦r r♦♥strt♥ ♥s r♦♠ r r

r ♠t♦ ♦rs ♥ rt r♣rs♥tt♦♥ ♥ ♣r♦r♠s st ♦♥ r♥ ♦

t rst♥ ♠s s ts rts s ♥tr♦r ♦♥r② ♦r t

♥ s ss♦t t t r♦♦ strtrs s t♦ ♥rt t♠ s s♠♥t

♣r♦s t♦♥ ♥♦r♠t♦♥ tt ♦ s ♦r t①tr♥ r♥ ♣♥♥

t ♥② ♦r ♠ss ♠♦ s ①tr♠② ♦♠♣t ♥ rt

♦♥trt♦♥s r ♦r ♣rs♥ts ♥♥♦t s♦t♦♥s ♥ t ② rst t

♥ ♥t ♦ t ♠ss r♣rs♥tt♦♥s s s t ♣r♠ts ♣

♣r♦ ♥ s♦♥ ♣r♦♥ ♦t s♠♥t ♥♦r♠t♦♥ ♥ t r♣rs♥tt♦♥

♥ rst r♦♥strt♦♥ ❲ ♦s ♦♥ r♦♥strt♥ t ♥s ♥

♥♦t ♦♥sr t ♦tr r♥ ♠♥ts r ① ② t ♣♦♥t ♦ s

st♦♥ ♣r♦ss ❲ ♠♦♥strt tt ♦r rsts s st rts

r♠♥♥ rt ♦r ♥rt♥ t ♥ ♠s ♦♣t t♦st♣ strt②

strt ♦♥ rst r♦♠ t ♣♦♥t ♦ s ♣tr

①trt ♠♥♥ ♥ strtrs r♦♠ t ♣♦♥ts s ♥

t ♥ t♦♥ ♦♥ t ♥rt♦♥ ♦ ♦♠♣t ♠s ♣rsr♥ t

♥ strtr s ♣rs♥t ♥ t♦♥ ①♣r♠♥t rsts r s♦♥ ♥

sss ♥ t♦♥

♠tt♦♥s r ♠t♦ s sr ♠tt♦♥s rst s ♦r t

qr ♠t♦♥ st♦♣ rtr ♣r♦s ♦♦ rsts ♥ ♠♦st ss t t ♠②

s♦ r♠♦ t♦♦ ♠♥② s rtr♠♦r s ♥ s ♦♥ sq♥

♦ s♠ ♣♥r r♦♦s s ♥♦t ②s st ♦r s♦♠ ♥♦♥♣♥r r♦♦s t

r t♦r ♦♥ rst #2 ♥ t s♣r ♥ ♦♥ rst #6

Prs♣ts ♥ tr ♦r t ♦ ♥trst♥ t♦ s ♠s ♠t♦♥

s♠ tt ♣t t st♦♣ rtr t♦ t t②♣ ♦ ♥ ♠♦r rt② ♦r

♦r ♥s t ♥♦♥♣♥r strtrs ♠② ♥♦t r♣rs♥t t ♦r

♣tr t♦s ♦r r♥ ♠s r♦♥strt♦♥

rr♥t ♠t♦ ♥ ♦r♥ ♦♥ ♥♦♥♣♥r strtr ①trt♦♥ ♦ ♠♣r♦ t

rsts ♥♦tr ♥trst♥ ♦ t♦ ssttt t rr ❳❨r ♦ ♦r

♠t♦ ② qtr ♥ ♦rr t♦ r t ♦♠♣tt♦♥ ♦♠♣①t②

♣♣r♦ t ❱ t

❲ ♣rs♥t ♥ ♦rt♠ ♦r ③♥ r♥ s♥s r♦♠ ♥s s♠♥t③

♠ss ♥rt ② t❱ tr♦ s②st♠ r ♣♣r♦ s t

s r♦♥ tt♦♥ r♦♦ ♥ s ♣tr ♦r ♣♣r♦①♠t♥

tr s♣s ② ♦♠♣t ♥ ♦♠tr② strtr ♠♦s t r♥t s ♦

t ♥ t♦♥ t♦ ♥ ♥t t ♠♥ ♥t ♦ ♦r ♣♣r♦ s ts

r♦st♥ss t♦ ♦♠tr ♥ t♦♣♦♦ ts ♦♥t♥ ♥ t ♥♣t ♠ss r

♣♥ rr③t♦♥ ♣r♦r ♥ srt ♦r♠t♦♥ ♦ t sr ①trt♦♥

♣r♦♠ ♦♥sttt t♦ t♥ ♦♥trt♦♥s ♣♣♥ ♣r♦r♠♥ ♥ tr♠s ♦

♦♠♣tt♦♥ t♠ ♥ st② r ♠♦♥strt

♦♥trt♦♥s ♦ t st ♦ ♦r ♥♦ t ♦ ♥srt♥ ♦t s♠♥t

♥ strtr ♥♦r♠t♦♥ ♥ ♣r②♦♠tr ♥s ♠s s st ♥①♣♦r

♦r r♥ ♦♥t①t ② ♦♥sr♥ ♠s s t ♠ ♠s ③t♦♥

♦ ♦rrs♣♦♥ t♦ s♠♥t ♠ s♠♥tt♦♥ t s♣ ♣r♦rs ♦♥trr②

t♦ t ①st♥ t② ♠♦♥ ♠t♦s ♦r ♦rt♠ ♣r♦s r♣rs♥tt♦♥ ♦

♥s t r♦s s s♦ tt t ♠♦s ♥ s ♥ r♥t ♣♣t♦♥

♦♥t①ts

r♦♠ t♥ ♣♦♥t ♦ ♣r♦♣♦s sr ♦♥trt♦♥s t♦ t

♣r♠ts sr r♦♥strt♦♥ ♣r♦♠ r ♠ s t♦ rr t

♥② ♥ ♣r♦ss♥ ♠ss t ①st♥ ♦rt♠s ♦r tt♥ ♥ r

r③♥ ♦♠tr ♣r♠ts s s ♠t♦s ♦r ①trt♥ srs r♦♠ ♣♥r

s ♣rtt♦♥s ♦ t s♣ ♣r♦ ♦♦ rsts ♥ ♣rt t t② r ♥♦t

s♥ t♦ t ♠ss tsts ♥r rs♦♥ ♦♠♣tt♦♥ t♠ ♦r ♥st♥

t ♥♠r ♦ ♣♥s tt r♦♠ 1km2 s③ ❱ ♠s ♥ s② ① t♥

t♦s♥s ♥ ♦r ①♣r♠♥ts ①st♥ ♠t♦s s② rqr s ♠ s t♥

♠♥ts t♦ ♦♥ ♦r t♦ t st ♦♥ ♥r ♣♥s

♠♠r②

♠tt♦♥s r ♦rt♠ s ♠t t♦ ♠♦♥ t ♥s t ♣s

♣♥r ♦♠♣♦♥♥ts ♦♠s rstrt ♥ ♥ t t②♣ ♥s

t rrr s♣s s s t ♦♠ ♦ t ♦ ♠tr Prs ♥

s♦♥ ♥♦t ♠tt♦♥ ♦♥r♥s t rs ❱ ♠ss r

♥t♦ sr ts ♦r st♦r rs♦♥s ♦r ♦rt♠ ♣r♦sss t ts ♥♣♥♥t②

t♦t ♥♦r♥ ♦♥sst♥② t♥ t ♥♦r♥ ts ♥s ♦t ♥

t♥ t♦ ts ♥ ts ♦♥t♥ ♦♠tr rtts

Prs♣ts ♥ t ♣rs♣t ♣♥ t♦ ♠♣r♦ t r② ♦ ♦r ♠♦s

② ♦♥sr♥ ♦♠tr ♣r♠ts tt r ♥♦t ♥ssr② ♣♥r ❲ s♦ ♥s

①t♥♥ ts ♣♣r♦ ♥ ♦rr t♦ t ♠♦r s ♦r t ♠♦♥ ♦

♥s ♥ ♣rtr ♥ tt♥ ♦♠♣♦♥♥ts s ♦♦rs ♦r ♥♦s s

♦♥sttts ♥♥ ts s tt ♦♠tr ♥♦r♠t♦♥ s ♦♥t♥ ♦♥ s

r♦♠ t♥ ♣♦♥t ♦ t ♠t♦ ♣r♦ss♥ ❱ ♠ss ss ♥♦

s♣ ♣rtt♦♥♥ s s♣ ♣rtt♦♥ r♣♦rts ♠♣r♦ rsts ② rstr♥♥ t

♥♠r ♦ s ♥ t♦ r♦♥strt t♦ t strt ♠♥♠♠ ♦r t

r♦♥strt♦♥ ♦ t st s r♠♥s ♦st② s♥ t ♦♠♣tt♦♥ ♦ ♠t♣

♣♥♥trst♦♥s r st ♥ ♥ r♦♥strt♦♥ rs ♦♥

♥♠r ♦ ①t rt♠t ♦♣rt♦♥s r t♠ ♦♥s♠♥ ❯s♥ t ♠t♦

♦ ♠♣♥ t ❬♠♣♥ ❪ ♥①t rt♠t t♦ t s②st♠ r♥

t ♦♠ ♣rtt♦♥♥ s t♦♥ ♦♠♣♦♥♥t s♦ ♠♣r♦ ♦r ♣♣r♦

♥ tr♠s ♦ ♣r♦r♠♥s

♣tr

♦♥s♦♥ ♥ tr ♦r

♦♥s♦♥

s P tss ♣rs♥t ①♣♦r ♥♦ t♥qs ♥ t r♥ r♦♥str

t♦♥ s♥ r ♥ ❱ ♠ss ♦r ♥ t♦♠t ♥ rt ♠♦♥ ♦

ts ♦r ♦t t②♣s ♦ t t♦st♣ ♣♣♥ s s♥ s

t ♥♣t t ♥t♦ r♥rt sss s s ♥ tt♦♥ r♦♥ ♦r

s♠ ♠♥t ♥ t♥ t♦♠t② ♥rts ♦♠♣t ♠ss ♦ t r♥

s♥ ♦♣♦♥ ♥ ♦tt♦♠♣ ♣♣r♦s r t t♦ r♦♥strt r♥

♠♥ts s♥ ♦ ♦t ♣♣♥s s ♦♥str♥ ② ♠♣♦rt♥t ♦♥srt♦♥s

r t♦♠t ♣r♦ss♥ ♥② s♠♥t ♥

r② ♥ s♣rs r♣rs♥tt♦♥ s ♦♥srt♦♥s r ♥ ♥ ts ♥

t♦♥

s♠♥t ♥ s ♣rt ♦ t rst st♣ ♦ ♣♣♥ s ♠♣♦rt♥t

♣r♦ss s ♣rs♥t ♥ ♣tr r sr ♥ ♠t♦s s ♦♥

♥ ♥r② ♠♥♠③t♦♥ ♦r♠s♠ ♦r r ♥ ❱ t s ♥ s♦ t♦

♠♥♥ ♥ t♦ ♦♥trt t♦ t s♥ ♥rst♥♥ ♥ r♦♥strt♦♥ ❲

s♦ t ♥ts ♦ s♥ ❱ ♠ss ♦r r r t ♦r s♥ ♥

s♥ t ♦r♠r s♦ srs t rt strtrs ♦ t s♥ s t ♥

♦ ❱ t s ♠♦r ♦♠♣t ♥ ♥♦r♠t t♦ t ♥ ♠t♦ ♦r

r t r♠♥s s♠♣ t ①♣r♠♥ts s♦♥ ♦t♥ rt rsts

❲ ♥ ♦r s♠♣ ♦♠tr trs ♦♠♣t ♦r ♣♦♥t r ♣rt ♦

♥♦ ♥r② ♦r♠t♦♥ s♦t♦♥ s t ♥ tt s t ♦st

♥r② s qt st ♥ rs ♦♥ ss♠♣t♦♥s ♦♥ t s♥ ♦r♦r ♥

t ♥t ♦ t ①tr ♥♦r♠t♦♥ r♦t ② t r t♥♦♦② s s

♣tr ♦♥s♦♥ ♥ tr ♦r

t ♥♠r ♦ ♦s rtr♥ t ♠♣t ♦ t r t t t♦ s♥ ♥

♥r② tt s rs♥t t♦ ♥ rr♦rs ♦♥r♥♥ t ❱ ♠s ♥

♦t♥ ♥ ♥ ♠♦r ♣rs s♠♥t ♥ t♥ t r r t

①♣r♠♥ts ♣r♦ t ❱ ♥ t♦ rt ♥ ♦♥sst♥t s♥ ss

t♥♥ ♣r♠trs t♥ ♥ ♦r ♥ r t ♦r t ♣♣r♦ s

♦♠♣♦s ♦ ♣♦st♣r♦ss♥ st♣ ♦♥sst♥ ♥ s s♠♥t rs ♠♣r♦s

t qt② ♦ t rsts t ♠s t ss ♥r ♥ ① t♦tr ♦t

♥ ♠t♦s r ♥s♣rs ♥ ② t♦♠t ② ♦♥trt s

♥♦ ♥ s♠♣ t t ♥ ♣♣r♦s ♦r r♥ s♥ ♥rst♥♥

♦ ♦r st ♥♦ r t rst t♦ sr ♥ ♥ ♥ t

s t♦ ♥srt ♦t s♠♥t ♥♦r♠t♦♥ ♥ ♦♠tr strtrs ♥t♦ ❱ ♠ss

♦ r♥ s♥s

s♦♥ st♣ ♦ t ♣♣♥ s ♣rs♥t ♥ t ssq♥t t♦ ♣trs

♣tr ♥ ♣tr r t r♦♥strt♦♥ ♦ t r♥ ♠♥ts ♥t♦

♠ss s t ♦t sr ♠t♦s ♦♥ ♦r t②♣ ♦ t s

t ♥ ♣♣ r♥t strts ♦r t②♣ ♦ r♥ ♠♥ts

r♦♠ r r t t♦♥ ♣r♦♣♦s t♦ ♠t♦s t♦ ♠s r

♥t t②♣ ♦ r♥ ♠♥ts ♥ ♠t♦ rs ♦♥ rr② ♦ s♠♣ t♠♣ts

♥ s ♣ ♠♦♥ ♦tr t♥s ♦ tt♥ trs ♥ t r ♣♦♥t ♦ ♥

♥rt♥ ♣r♠tr s♣s ♠ss ♦ trs ♣tr t♥q rs

♦♥ ♠t♠t ♠♦ s t ♥t ♦ ♥ ♥r ♥ r♦st t s

♥♦♥ t♦ r ♦♥♥♥ rsts s ♦♥ s ♣r♦♣r ♠♦♥ ♦ t ♣r♦♠ ♥t♦

♥ ♥r② ♠♥♠③t♦♥ ♦r♠s♠ s ♥ ❲ ts ♠t♠t ♠♦ r②

①st ♠♦r ♦♥trt♦♥ ♥ ts tss s t ♥♦ ♦♣t♠③t♦♥ s♠ ①♣♦t

♥ ♣r t♥qs t♦ ♦♥r str ❲ s♦ ♠♣r♦♠♥ts ♦♠♣r t♦

♣r♦s ♦♣t♠③t♦♥ ♠t♦s tr♦ r♦s t②♣ ♦ ①♣r♠♥ts ♥ strt

t ♣♦t♥t ♦ ♦r ♠t♦ ♦♥ ♣r♦♠s t ♦♠♣①t② ♥r tt♥ ♦r

s♦♥ ♠t♦ r ♦ ♥② ♣r♦r ♦♥ s♣s r♦♥strt ♠♦r ♦♠♣①

♥ ♥q strtrs r ♦♠♠♦♥ t ♥s s s r③ ② tt

♥ ♣♥r ♣ts ♥s t ♣♦♥t ♦s t ♦♦ ♦rs ♠s r♦♥strt♦♥

s t♥ ♦♠♣t ② ♥ ♦♣s ♠t♦♥ ♣tr ❲ ts

t♦♦

♣♣r♦ st②s s♠♣ ♥ strt♦rr t s ♦♦ rsts ♥ tr♠ ♦ r②

♥ tt r♦♥strt♦♥ s sss r♥ t ①♣r♠♥ts

♥ ♦♠♣rs♦♥s t t ♦r ♦ ❩♦ t ❬❩♦ ❪

r♦♠ ❱ ♠ss t♦♥ ♠t♦ ♦r r♦♥strt♥ t ♠♥ts

♦ t s♥ s sr ♦♦s r♥t ♠♦♥ strts ♦r t②♣

♦ ♠♥ts ♥s tt♦♥ ♥ r♦♥ ♣tr ♠♦♥ ♦

t ♥s s ① ♥♦ t♦ ♥rt ♠t♣ ♦ ts ♦

♥ ♣rs ♦♥tr♦ ♦♥ t ③t♦♥ ♦ t r♥ s♥ s s

② s♥ ♥ ♥♦ srt ♦r♠t♦♥ ♦ t s♣ ♣rtt♦♥♥ ♣r♦♠ ♦♠♥

t ♦ rr③t♦♥ s♠ ♦r r♥ strtrs ♦t srt ♦r♠

t♦♥ ♥ ♦ rr③t♦♥ ♦♥trt ♥ t ② ♥ t♦rs ♠♦r

♣rs r♥ s♥ ③t♦♥ ①♣r♠♥ts ♦♥ ♦♠♣① r♥ strtrs s

trt t r♦st♥ss ♥ st② ♦ ♦r s②st♠ r♦♥strt♦♥ ♠t♦ s

s♦ ♥ tst ♦r r② ♥ tt r♦♥strt♦♥ ② ①♣r♥

♥ s♥ ♥ r♦♥strt♦♥ ♥ ♦♠♣r♥ t rsts ♦t♥ t ♦tr

♥♦♥ r♦♥strt♦♥ t♥qs ♥ ♣rtr② t ❱rt♦♥ ♣ ♣♣r♦①

♠t♦♥ ❬♦♥t♥r ❪

♦t tt s♣ r s ♥ t♥ t♦ s♥ ♦t ♣♣♥s t♦ ② t♦

♠t ♥ ♥t ♦t ♣♣♥s r t ② ①♣r♠♥ts ♦♥ r

♥ ♦♠♣① r♥ s♥s

t♦♦

♥ s♣t ♦ ♠♥② ♦♥trt♦♥s t♦ t♦♠t r♥ s♥ r♦♥strt♦♥ st

♥♠r♦s ♠♣♦rt♥t ♣r♦♠s r♠♥ ♥s♦

ssss♥ t stt♦trt ♦♥ ♥ ♥♦t tt ♠♥② s♦t♦♥s r② ♦♥ s

s♠♣t♦♥s ♦♥ t s♥ ♦r ♦♥ t t ♠ts tr ①t② ♥② ♦rs r

♥ t r② ♥rr♦s♦♣ ♣r♦♠s ♦s ♣r♦♣♦s s♦t♦♥s ♥ r②

tr♥srr t♦ ♦tr ♣r♦♠s ♦r t②♣ ♦ t ♥ t♦♥ ♠♦st ♦ t♠ s ♦♥②

s♥ t②♣ ♦ t t t t♠ s♦♥ ♥ ts tss t②♣ ♦

♣tr ♦♥s♦♥ ♥ tr ♦r

t s ♥q ♥ts r r② s ♦r r♥ s♥ r♦♥strt♦♥

❲ tr s ♣♦t♥t ♥ ♦♣♥ ♠♦r ♥r ♥ ① s♦t♦♥s

♦ s r♥t t②♣s ♦ t s♠t♥♦s②

♥ ♦♠♣tr s♦♥ ♥ ♠♥ r♥♥ ♠ ♦rt ♥ ♠ t♦rs

t♦♠t r♥♥ t♥qs ♥ ♣♣ ♦r r♥ s♠♥t③t♦♥ ♥ r

♦♥strt♦♥ ♦ rt♦♥s s♠ ♣r♦♠s♥ rst tt ②r s②st♠

♠①♥ r♦st s♣rs ♣r♦r ♣♣r♦s t ① ♥r ♠s r♦♥

strt♦♥ s rt♦♥ ♦r tr rsrs ♦♥ ♠♣rss ♦r ♦♥ t♦♠t

♣r♦ss♥ ♦ r ♦t♦♥s ♦ ♣trs r♦♠ ♦♥♥ srs r♥t② ♠

♣t t s t♦ rt♦♥s r sr② st t ♣rrs♦rs ♦r ♥ rsr

♣r♦ts ♣r♦② t♦ ♠♣♦rt♥t ♦♥trt♦♥s

♥ ♦♠tr② ♣r♦ss♥ r tr♥ ♦r strtrr ♠t♦s s ♥ ♦

sr ❬tr ❪ rsr ♦rt ♠ t ♥r♥ ♠♦s t s♣

s♠♥t ♥ t♦♣♦♦ rt♦♥s♣s r s ♥ r♥ ♠♦♥

r③t♦♥ s②♠♠tr② tt♦♥ ♥t♦♥ ♥②ss r t ♦ ♠♥② s♣ts

♦ ♦♥trt t♦ ttr ③t♦♥ ♦ r♥ s♥s s s♠s t♦

♣r♦♠s♥ rt♦♥ ♦r r♥ s♥ r♦♥strt♦♥

♥ t r♠♦t s♥s♥ ♦♠♠♥t② ♠♦r ♥ ♠♦r t♥qs s t s♦♥

♣♣r♦s t♦ ♥t r♦♠ t r♥ rtrsts ♦ t t ♦r ①♠♣

rsrrs ♥ stt ♠r② ♦t♥ ①♥t rsts ② s♥ ♠ts♣tr

♥②ss ♠①s r♦s s♦rs ♦ t s♠t♥♦s② ♠r② t r♦

♦ sr② ♦♠♠♥t② r② ♥♦ t ♥ts ♦ s♥ s♠t♥♦s②

sr s♥♥rs r♥ ♠♥ ♥ s♦♥r s♥s♦rs ❲ ♦♥② t ts r② st ♦

rsr s♥ r♦s t②♣s ♦ t ♥ s♥ t♠ s♠t♥♦s② s♠s r②

♣r♦♠s♥ t♥q ♥ ①♣t t t♦ ♦♠ ♥ ♠♦r ♠♣♦rt♥t ♥ t ♥r

tr

t♦tr ♠♥② ♦rs r♦♠ r♦s ♦♠♠♥ts ♥ ♦♥trt t♦ t s♠

♦ ♦ ③♥ ♥ r♦♥strt♥ r r♥ s♥s ② s② ♣r♦♥

♠♦s ♦ ts t ttr s♠♥t t ♦ rsr ♦ ♦ t♦ t ♥①t

♥trst♥ ♣r♦♠ ♦ ♦♠♣t ♥t♦♥ ♥②ss ♦ r r♥ s♥s

t♦♦

ttrt ♥ ♥ ♠t♣ ♦♠♥s ♥ s sst♥t

♣♦t♥t ♥ t r ♦ ♠ rsr ♥ ♥str②

♣♣♥①

♣♣♥①

P♦♣t♦♥ ♦♥t♥ ♠♦

t x ♥♦t ♦♥rt♦♥ ♦ ♣ss ♦r t ♥tr ♦ ♠ss ♦ ♥ ♣s

s ♦♥t♥ ♥ t ♦♠♣t st K s♣♣♦rt♥ t ♥♣t ♠ s

♥r② ♦♦s t ♦r♠ s♣ ② q ♥tr② t tr♠ D(xi) ♥ t

♣♦t♥t V (xi, xj) r ♥ ②

D(xi) =

1− d(xi)d0

d(xi) < d0

exp(d0−d(xi)d0

)− 1 ♦trs

V (xi, xj) = βA(xi ∩ xj)

min(A(xi), A(xj))

r

• d(xi) r♣rs♥ts t ttr②② st♥ t♥ t r♦♠tr② ♥s

♥ ♦ts t ♦t xi

d(xi) =(min −mout)

2

4(σ2in + σ2

out)−

1

2ln(

2σinσoutσ2in + σ2

out

)

r min ♥ σin rs♣t② mout ♥ σout r t ♥t♥st② ♠♥ ♥

st♥r t♦♥ ♥ Sin rs♣t② ♥ Sout

• d0 s ♦♥t ①♥ t s♥stt② ♦ t ♦t tt♥ r t

♦ d0 t ♠♦r st t ♦t tt♥ ♥ ♣rtr d0 s t♦

♥ t ♥♣t ♠s r ♦rr♣t ② s♥♥t ♠♦♥t ♦ ♥♦s

• A(xi) s t r ♦ ♦t xi

• β s ♦♥t t♥ t ♥♦♥♦r♣♣♥ ♦♥str♥t t rs♣t t♦ t

t tr♠

♦t tt s ♠t♠t tt♦♥ s s ♥ ♣rt t♦ r♦② ①trt t

ss ♦ ♥trst r♦♠ t ♠ ♦ rs ♦r rt♥ s♣♣rtt♦♥♥ tr

♣♣♥① ♣♣♥①

r ts ♥ tr ♣r♠trs ♦r t r♦s ♣rs♥t ♠♦s t

♣ss ♥ ♠ ♥s♠♥ts r ♥ ② ♣♦♥t p ∈ K ♥tr ♦ ♠ss

♦ t ♦t ♥ s♦♠ ♠rs s t♦♥ ♣r♠trs r t s♠♠♦r

①s b t s♠♠♥♦r ①s a ♥ t ♥ θ ♦r ♥ ♣s ♥ t s♠♥t b

t s♠t a t ♦r♥tt♦♥ θ ♥ t ♥♦r ♥t c ♦r ♥s♠♥t

♥s rs♣t② ♦rr♥ ♦♠ ♦ t ♦t s ♥♦t ② Sin rs♣t②

Sout ♥♦rs r ♥♦t ② A1 ♥ A2 rt trs r ♥ ②

♣♦♥t p ∈ K ♥tr ♦ ♠ss ♦ t ♦t t②♣ t ∈ ♦♥♦ ♣s♦

s♠♣s♦ strt ♦♥ ♥ 3 t♦♥ ♣r♠trs r t

♥♦♣② t a t tr♥ t b ♥ t ♥♦♣② ♠tr c ②♥r

♦♠ Cxi r♣rs♥ts t ttrt♦♥ s♣ ♦ ♦t xi ♥ t ♥♣t ♣♦♥ts

r s t♦ ♠sr t qt② ♦ ts ♦t

♥♥t♦r ①trt♦♥ ♠♦

♥s♠♥t s ♥ ② ♣r♠trs ♥♥ t ♣♦♥t ♦rrs♣♦♥

♥ t♦ t ♥tr ♦ ♠ss ♦ t ♦t ♠r② t♦ t ♣♦♣t♦♥

♦♥t♥ ♠♦ t ♥ ♣♣♥① t tt♥ qt② t rs♣t t♦ t t

s s ♦♥ t ttr②② st♥ t ♥tr② t tr♠ D(xi) ♦ t ♥r②

s ♥ ② q ♣♦t♥t V (xi, xj) ♣♥③s str♦♥ ♦t ♦r♣s s

q t s♦ ts ♥t♦ ♦♥t ♦♥♥t♦♥ ♥trt♦♥ ♥ ♦rr t♦ ♦r t

♥♥ ♦ t ♥s♠♥ts ♣♦t♥t tr♠ s ts ♥ ②

V (xi, xj) = β1A(xi ∩ xj)

min(A(xi), A(xj))+ xi∼ncxj

× β2f(xi, xj)

r

• β1 ♥ β2 r t♦ ♦♥ts ♥ rs♣t② t ♥♦♥♦r♣♣♥ ♥

♦♥♥t♦♥ ♦♥str♥ts t rs♣t t♦ t t tr♠

• ∼nc s t ♥♦♥♦♥♥t♦♥ rt♦♥s♣ t♥ t♦ ♦ts xi ∼nc xj t

♥♦r rs ♦ xi ♥ xj s ♦ ♥♦t ♦r♣

• condition s t ♥t ♥t♦♥ rtr♥♥ ♦♥ ♥ ♦♥t♦♥ s ♥

③r♦ ♦trs

• f(xi, xj) s s②♠♠tr ♥t♦♥ t♥ t ♣♥③t♦♥ ♦ t♦ ♥♦♥

♦♥♥t ♦ts xi ♥ xj t rs♣t t♦ tr r tt♥ qt②

♥t♦♥ f s ♥tr♦ t♦ st② r① t ♦♥♥t♦♥ ♦♥str♥t ♥ t

t♦ ♦ts r ♦ r② ♦♦ qt②

s ♦r t r ♦♥t♥ ♣r♦♠ s ♠t♠t tt♦♥ s ♥ s

t♦ r♦② ①trt t ss ♦ ♥trst r♦♠ t r ♠ s♦♥ ♦♥

♥ t ♣①s ♦rrs♣♦♥♥ t♦ t ss r♦ ♥ ts ♠ r rt② rt

♦♠♣r t♦ t r♦♥ s♠♥t rst s ♦♦s② ♥♦t ♦♣t♠ t

s♥t t♦ rt ♥ ♥t s♣♣rtt♦♥♥ tr

r r♦♥t♦♥ ♠♦ ♦r♠t♦♥

t x r♣rs♥t ♦♥rt♦♥ ♦ ♠♦s ♦ trs r♦♠ t♠♣t rr②

sr ♥ ♥tr ♦ ♠ss p ♦ tr s ♦♥t♥ ♥ t ♦♠♣t

st K s♣♣♦rt♥ t ♦♥♥ ♦① ♦ t ♥♣t ♣♦♥t ♦ ❲

♥♦t ② ∂xi t sr ♦ t ♦t xi ♥ ② Cxi t ②♥r ♦♠ ♥

rt ①s ♣ss♥ tr♦ t ♥tr ♦ ♠ss ♦ xi ♥ t ♥♣t ♣♦♥ts

r ♦♥sr t♦ ♠sr t qt② ♦ xi ♥tr② t tr♠ D(xi) ♥ t

♣♣♥① ♣♣♥①

r rr② ♦ tr ♠♦s t ♦ts r s♣ ② ♣♦♥t ♥tr

♦ ♠ss strt ② r ♦t ♥ t♦♥ ♣r♠trs rr♦s ♥♥

t ♥♦♣② t②♣ ♦s s♣ ♥ ♦♥♦ ♣♥ ♦r r ♣s♦

♣♦♣r ♦r t ♦r s♠♣s♦ ♦ ♦r ♠♣

♣rs ♣♦t♥t V (xi, xj) r ♥ ②

D(xi) =1

|Cxi|

∏

pc∈Cxi

γ(d(pc, ∂xi))

V (xi, xj) = β1Voverlap(xi, xj) + β2Vcompetition(xi, xj)

r

• |Cxi| s ♦♥t ♥♦r♠③♥ t ♥tr② t tr♠ t rs♣t t♦ t

♥♠r ♦ ♥♣t ♣♦♥ts ♦♥t♥ ♥ Cxi

• d(pc, ∂xi) s st♥ ♠sr♥ t ♦r♥ ♦ t ♣♦♥t pc t rs♣t t♦

t ♦t sr ∂xi d s ♥♦t t trt♦♥ ♦rt♦♦♥ st♥ r♦♠ ♣♦♥t

t♦ sr s s r trs ♦ ♥♦t sr ♣s♦♦♥♦ s♣s

♥♣t ♣♦♥ts r ♥♦t ♦♠♦♥♦s② strt ♦♥ t ♦t sr r

d s ♥ s t ♦♠♥t♦♥ ♦ t ♣♥♠tr st♥ t ♣r♦t♦♥

♥ t ♣♥ ♦ qt♦♥ z = 0 ♦ t ♥ st♥ ♥ t t♠tr

rt♦♥ s tt ♣♦♥ts ♦ts t ♦t r ♠♦r ♣♥③ t♥ ♥s

♣♦♥ts ♦t tt d s ♥r♥t ② r♦tt♦♥ r♦♥ t ❩①s

• γ(.) ∈ [−1, 1] s qt② ♥t♦♥ s strt② ♥rs♥

• Voverlap s t ♣rs ♣♦t♥t ♣♥③♥ str♦♥ ♦r♣♣♥ t♥ t♦

♦ts ♥ ♥ ②

Voverlap(xi, xj) =A(xi ∩ xj)

min(A(xi), A(xj))

r A(xi) s t r ♦ t ♦t xi ♣r♦t ♦♥t♦ t ♣♥ ♦ qt♦♥

z = 0

• Vcompetition s t ♣rs ♣♦t♥t ♦r♥ s♠r tr t②♣ t ♥ ♦

♥♦r♦♦

Vcompetition(xi, xj) = ti 6=tj

r . s t ♥t ♥t♦♥

• β1 ♥ β2 r t♦ ♦♥ts t♥ rs♣t② t ♥♦♥♦r♣♣♥ ♦♥

str♥t ♥ t ♦♠♣tt♦♥ tr♠ t rs♣t t♦ t t tr♠

♥ ♦rr t♦ r♦② ①trt t ss ♦ ♥trst r♦♠ t ♣♦♥t ♦s t sttr

sr♣t♦r ♣r♦♣♦s ② ❬r ❪ s s t♦ ♥t② t ♣♦♥ts ♣♦t♥t②

♦rrs♣♦♥ t♦ trs

♦r♣②

❬r ❪ r ♥② ♠♦♥ rss t③ ♥

③s ♥ ♦♠ ♥ ② ♥ ❱ t ♦♥ ♣s

♥

❬r♠ ❪ r♠ ♦t♦♣♦♦s ♥ ♥♥ ♥ t

r② ♦ r t r ♦s ♥ t♦s P rts

t♦r rt② ♦ ♥ rt srt♦♥ ♦♠ ♦ ♥tr♥t♦♥

ss♦t♦♥ ♦ ♦s② ②♠♣♦s ♣r♥r t ♦♥ ♣

❬② ❪ ② ♥ ❱ s♦t t♦st ♦♠tr② ♠♦s ♥

s♦♥ ♦r♥ ♦ ♣♣ ttsts ♦ ♥♦ t

♦♥ ♣s ♥

❬r ❪ r ♥rt♦♥ ♥ ♣♣t♦♥ ♦ rs ♦r qt② ♣♥♥t

r♦♥strt♦♥ ♦r♥ ♦ P♦t♦r♠♠tr② ♥ ♠♦t ♥s♥

♦ ♥♦ t ♦♥ ♣

❬♥♠r ❪ ❲ ♥♠r ♦♠♣t♥ t ♥t ♠♣rtr ♦ ♠t

♥♥♥ ♦♠♣tt♦♥ ♣t♠③t♦♥ ♥ ♣♣t♦♥s ♦ ♥♦

t ♦♥ ♣

❬♥ ❪ ♥ t♥ ❳ s♦♠s ♥ ❩r Pr♠

tr st♠t♦♥ ♦r ♠r ♣♦♥t ♣r♦ss t♥ r♠♦r ♦ ♠t♠♥

s♦♥ s♣ ①trt♦♥ r♦♠ r♠♦t s♥s♥ ♠s ♥ P ♦♠♠ss♦♥

❲ t ♦♥ ♣

❬♥♠r ❪ ♥♠r tsts rsts ♥ t♦♥ t♦♦s t

tt♣s♦♣♥rr♠♠rs♦r♥tr♥♠r

t♦♥t♠ t ♦♥ ♣

❬s ❪ s ♥ t ttst ♥②ss ♦ rt② Ptrs ♦r♥ ♦

t ♦② ttst ♦t② ♦ ♥♦ t ♦♥ ♣

❬♦ts ❪ ♦ts ♦t P② P ③ ♥ ② Ptrs

t ♦♥ ♣

♦r♣②

❬♦②♦ ❪ ❨ ♦②♦ ❱sr ♥ ❩ st ♣♣r♦①♠t ♥r② ♥

♠③t♦♥ r♣ ts r♥s P ♦ ♥♦ t

♦♥ ♣s ♥

❬♦②♦ ❪ ❨ ♦②♦ ♥ ❱ ♦♠♦♦r♦ ♥ ①♣r♠♥t ♦♠♣rs♦♥ ♦

♥t①♦ ♦rt♠s ♦r ♥r② ♥♠③t♦♥ ♥ ❱s♦♥

r♥s P ♦ ♥♦ t ♦♥ ♣

❬②r ❪ ②r rs ♥ r♦ ♥ t ♣rst♦♥ ♦

s ♠ ♣r♦ss♥ ♥ ♥tr♥t♦♥ ②♠♣♦s♠ ♦♥ Pr ♥

strt Pr♦ss♥ t ♦♥ ♣

❬♠♣♥ ❪ ♠♣♥ ♥ ♦t ①t ♥ ♦st ♥trst♦♥s

♦r P♦②♦♥ ss ♦♠♣tr r♣s ♦r♠ ♦ ♥♦ t

♦♥ ♣

❬ ❪ ♦♠♣tt♦♥ ♦♠tr② ♦rt♠s rr②

♦r t ♦♥ ♣s ♥

❬ ❪ ❲ ♦rst♥r ♥ ❨ ❨♥ ♦♠♥ r♦ ♥♦♠ s

♥ r P♦♥t Pr♦sss t♦ ①trt ♥ r♦♠ ♠♦t② ♥s ♠

s ♥ P ♦♠♠ss♦♥ ❲ ❱ t ♦♥ ♣

❬ ❪ ❲ ♦rst♥r ♥ r ♦r♥ ♥♥t♦rs ♥ ♠

s ② ♥t♦♥♣♦♥t ♣r♦sss ♥ ❱P t ♦♥ ♣

❬ ❪ P tt ♥ P P♦♥s ♦st PsP♥r

♦♥strt♦♥ ♥ ♦♠♣t♦♥ r♦♠ r ❯♥strtr P♦♥t

t ♥ ❱P t ♦♥ ♣

❬♣♦ ❪ ♣♦ ♥ ♦rts♦♥ ♠♦s ♦ rttr s♥s r♦♠

♥rt ♠s ♥ ♥s♥ ♣♦♥ts ♥ ♠ ♥②ss ♥ Pr♦ss♥

t ♦♥ ♣s ♥

❬♦♥t♥r ❪ ♦♥t♥r P ③ ♥ sr♥ ❱rt♦♥ s♣

♣♣r♦①♠t♦♥ ♥ P t ♦♥ ♣s

♥

❬♦♥s ❪ ♦♥s ♣♣ ♣♣r♦ t♦ r t♠ t

♥ ♥ ❱P t ♦♥ ♣

♦r♣②

❬♦r♥s ❪ ♦r♥s ♦r♥s ♥ ❱♥ ♦♦ ❯r♥ ♥

♦♥ ♥trt♥ ♦♥t♦♥ ♥ ♦♥strt♦♥ ❱ ♦ ♥♦

t ♦♥ ♣

❬ ❪ P ②♦r ♥ ♦♥ ♥ r♥r♥

rttr r♦♠ ♣♦t♦r♣s ②r ♦♠tr② ♥ ♠s ♣♣r♦

♥ P t ♦♥ ♣

❬♥s ❪ P ♥s r ♥ str ♥t s t♦s

♦r st♠t♥ ♥tt♥ r♠s ♥ ❯r♥ ♠r② ♥ ❱ t

♦♥ ♣

❬s♦♠s ❪ ❳ s♦♠s ♥♦s ♥ ❩③♥ t ①trt♦♥

❯s♥ t♦st rt♥t ②♥♠s ♥ ♦♥t♥♠ ♦r♥ ♦

t♠t ♠♥ ♥ ❱s♦♥ ♦ ♥♦ t ♦♥ ♣s

♥

❬s♦♠s ❪ ❳ s♦♠s t♦st ♦♠tr② ♦r ♠ ♥②ss ❲②

t ♦♥ ♣

❬ ❪ P ♦rr ♥ ♣♦ ♦♥ ♥ ♥tr♣rtt♦♥

♦ rttr r♦♠ r ♠s ❱ ♦ ♥♦ t ♦♥

♣s ♥

❬ ❱t ❪ ♦r ❱t tt♣t♦rt♦r t ♦♥

♣s ♥

❬ ❪ P ♥r② ❳ ♥ ♥ ♦♠♥ t③ ♥

♦① ♥trt ♠♦♥ ♦ ♥♦♦r ♥r♦♥♠♥ts t ♦♥s♠r

♣t ♠r ♥ ❯♦♠♣ t ♦♥ ♣

❬r ❪ r ♥ ♠ Pr t♠♣r♥ ♦r② ♣♣t♦♥s ♥

♥ ♣rs♣ts P②s ♠str② ♠ P②ss ♦ ♥♦

t ♦♥ ♣s ♥

❬r ❪ r ♥ ❩♦r ♥ t♦♠t t♦ ♦r r r♦♥

s t② ♦ qst♦♥ ❱ ♦ ♥♦ t ♦♥ ♣s

♥

♦r♣②

❬r ❪ ❨ r rss t③ ♥ ③s ♥tt♥

♦r str♦ ♥ ❱P t ♦♥ ♣s ♥

❬r ❪ ❨ r rss t③ ♥ ③s ♦rs

♥tr♥ts ♠t str♦ ♥ ❱P t ♦♥ ♣s ♥

❬r♥ ❪ r♥ ♥ P rt r ♠♣t♦♥ ❯s♥ r

rr♦r trs ♥ P t ♦♥ ♣s ♥

❬ ❪ ❲ ♥ ♦♥s r ♣♦♥t ♣r♦sss ♦r r♦ ♦♥t♥ ♥

❱P t ♦♥ ♣s ♥

❬♦♥♦r♠ts ❪ ♦♥♦r♠ts ♦♥♦r♠ts ♣s tt♣

♦♥♦r♠ts♦♠♦♦♥♥rts♦♦s♠♦s ❬♥♥

ss ②❪ t ♦♥ ♣

❬♦s ❪ ♦s rss ♥ t③ t❱ tr♦ st

♥ ❱P t ♦♥ ♣

❬♦s ❪ ♦s ♥② rss ♦♣♣ ♥ t③ t

❱ tr♦ ♦r ♦♠♠♥t② P♦t♦ ♦t♦♥s ♥ ❱ t ♦♥

♣s ♥

❬♦♥③③ ❪ ♦♥③③ ❨ ♦ rtt♦♥ ♥ str♥ Pr s

♠♣♥ r♦♠ ♦♦r s t♦ ♥ ♥t♦♥ rs ♦r♥ ♦ ♥

r♥♥ sr ♦ t ♦♥ ♣

❬♦♦ ❪ rt ♦♦ tt♣rt♦♦♦♠ t ♦♥ ♣s

♥

❬r♥ ❪ P r♥ rs ♠♣ r♦ ♥s ♦♥t r♦ ♦♠♣tt♦♥

♥ ②s♥ ♠♦ tr♠♥t♦♥ ♦♠tr ♦ ♥♦ t

♦♥ ♣s ♥

❬r♥♥r ❪ ❯ r♥♥r ♥ r ♣rs♥tt♦♥s ♦ ♥♦ ♥

♦♠♣① ②st♠s ♦r♥ ♦ t ♦② ttst ♦t② ♦ ♥♦

t ♦♥ ♣

❬ ❪ Ptr r♠r ♥ ♥tr ♦ ♠♣♣♥

♦r ♣♦♥t ♦ ♦t♦♥ ♥ r♥ rs Pr♦r♠♥ st

♦r♣②

♥tr♥t♦♥ rs ♦ t P♦t♦r♠♠tr② ♠♦t ♥s♥ ♥ ♣t

♥♦r♠t♦♥ ♥s ♦ ♣s t ♦♥ ♣s

♥

❬ ❪ ♥ ♦t ♥r ♥②ss ♦ ♦♥♥r ♦♥

str♥ts ♦r ♥trt ♦♠tr ♠♦♥ ♥ r♦r♣s t

♦♥ ♣

❬♥ ❪ ♥ ❩❲ ♥ ❩ ♥ ♠ ♠♥tt♦♥ ② ♥

t ♠♣s♦♥ t♦ r♥s P ♦ ♥♦ t

♦♥ ♣

❬r♥ss ❪ r♥ss ♥ P r♥ Pr ♥s ② rt♦♥ ♥

rrs ♠♣ ♦r ♦t r♦♥t♦♥ ♥ ❱ t ♦♥

♣

❬st♥s ❪ ❲ st♥s ♦♥t r♦ s♠♣♥ s♥ r♦ ♥s ♥

tr ♣♣t♦♥s ♦♠tr ♦ ♥♦ t ♦♥ ♣

❬♥ ❪ ❱ ♥ ♦r♠♥ ❲r ♥ P ♦rr

♥ ♠♦s ♦ rr s♥s r♦♠ strtr ♥ ♠♦t♦♥ ♥ ❱

t ♦♥ ♣

❬♣ ❪ ❱ ♣ r♥ P tt ♥ P P♦♥s ♦rs

rs♦t♦♥ rs ♠t str♦ ♥ ❱P t ♦♥ ♣s

♥

❬♦r♥♥ ❪ ♦r♥♥ ♥ ♦t rr ❱♦♠tr t

tr♦ ♦♥strt♦♥ ♦ ♥♦ rs s ♦♥ r♣ ♠♥

♥ ❱P t ♦♥ ♣

❬③ ❪ ③ ♠ s ♦②♥① ♦♠ P ♦

♦tt♦♥ ♦s r♠♥ s♦♥ ♥ t③♦♥ ♥t

s♦♥ rt♠ r♦♥strt♦♥ ♥ ♥trt♦♥ s♥ ♠♦♥ ♣t

♠r ♥ ❯sr ♥tr s♦tr ♥ t♥♦♦② t ♦♥ ♣

❬♥♦s ❪ ♥♦s ♥ P t r♦♥strt♦♥ ♣rsr♥

②s♣♣♦rt srs ♥ ❱P t ♦♥ ♣s ♥

♦r♣②

❬♥ ❪ ♥ P ♥ ♥ ♦♥ ②♠♠tr rttr ♠♦♥ t

s♥ ♠ ♦ ♥♦ t ♦♥ ♣

❬ ❪ ♥ ♥② ♥ r♦♥strt♦♥ r♦♠ r

s ♦♥ ♦♠♣♦st♦♥ ♣♣r♦ ♥tr♥t♦♥ rs ♦ t

P♦t♦r♠♠tr② ♠♦t ♥s♥ ♥ ♣t ♥♦r♠t♦♥ ♥ ♦

♥♦ ❲ t ♦♥ ♣

❬♦rs ❪ ♦rs rt③♠♥♥ ♥ ♥ r♥♥ s

♠♥tt♦♥ ♥ ♥ ♥ P t ♦♥ ♣

❬♥ ❪ ♥ ③s ♥ ♥♥ ♦s♦♥s ♥ ♥s ♠t

str♦ ♥ ❱P t ♦♥ ♣

❬③♥ ❪ ③♥ ♦t♦ ♥ ♦♣♣ P♦ss♦♥ sr r♦♥

strt♦♥ ♥ P t ♦♥ ♣

❬♠ ❪ ♠ ♥ ♦♥ ❯r♥ s♥ ♥rst♥♥ r♦♠ r ♥

r♦♥ t ♥ ❱s♦♥ ♥ ♣♣t♦♥s ♦ ♥♦

t ♦♥ ♣

❬♦st ❪ ♦st ❳ s♦♠s ♥ ❩r P♦♥t Pr♦sss ♦r ❯♥

s♣rs ♥ t♦r ①trt♦♥ ♥ ♠♦t ♥s♥ r♥s P

♦ ♥♦ t ♦♥ ♣s ♥

❬r ❪ r ❳ s♦♠s ❩r ♥ Prr♦ts♥②

trtr ♣♣r♦ ♦r ♥ r♦♥strt♦♥ r♦♠ s♥

r♥s P ♦ ♥♦ t ♦♥ ♣s ♥

❬r ❪ r ♠r ♥ ❳ s♦♠s ♦♠tr tr

①trt♦♥ ② tr P♦♥t Pr♦ss r♥s P ♦

♥♦ t ♦♥ ♣s ♥

❬r ❪ r r♥ ♥ r ♥srt♦♥ ♦ Pr♠ts

♥ ss ♣rs♥tt♦♥s ♦rs ♦♠♣t ♦s Prsr♥ t

ts r♥s ♦♥ P ♦ ♥♦ t ♦♥ ♣

❬r ❪ r ♥ t rt♥ rs t② ♠♦s r♦♠

♣♦♥t ♦s r♦st ♣♣r♦ t ②r r♣rs♥tt♦♥ ❱ ♦

♥♦ t ♦♥ ♣s ♥

♦r♣②

❬t♦ ❪ t♦ rs ♥ t♥s♦♥ s ♦rrt♦♥ ♦r

❱♠t r ♥♥♥ ♦ ♦ tr♦♣s ♦r trtr rtr③

t♦♥ ♦ ♥s ♥ ♦ ♥♥r♥ ♦ ♥♦ t ♦♥

♣

❬♠ss♦ ❪ ♠ss♦ P s♦r ♥♠♠ tt♥♥ ♥

❨r ♦♠♣tt♦♥ r♠♦r ♦r s♠t♥ ♦rs♥ ♠r♦

s♦♣ ♠s t ♣♦♣t♦♥s r♥s ♦♥ ♦ ♥♦

t ♦♥ ♣s ♥

❬♠♣ts② ❪ ❱ ♠♣ts② ♥ ❩ssr♠♥ r♥♥ ♦ ♦♥t ts ♥

♠s ♥ P t ♦♥ ♣s ♥

❬ ❪ ❩ r♦ r♥♦♠ ♠♦♥ ♥ ♠ ♥②ss ♣r♥r

t ♦♥ ♣

❬ ❪ ❨ ❳ ❲ ❨ r②st♦ r ♦♥r ♥ tr

♦t ♦♥sst♥t② tt♥ Pr♠ts ② s♦r♥ ♦ t♦♥s ♥

P t ♦♥ ♣s ♥

❬♥ ❪ ♥ ♦ ❨ ❩♦ ❨ ❩♥ ♥ ❨♥

♠♥t ♦♠♣♦st♦♥ ♥ ♦♥strt♦♥ ♦ s♥t ♥s r♦♠

t ♥ P t ♦♥ ♣

❬ ❪ ♦♥t r♦ strts ♥ s♥t ♦♠♣t♥ ♣r♥r

t ♦♥ ♣

❬ ❪ rr ♥ ♥ ♥ ❩♦r ♥♦♦r

♦③t♦♥ ♥ s③t♦♥ s♥ ♠♥♦♣rt ♣ s②st♠ ♥

♥♦♦r P♦st♦♥♥ ♥ ♥♦♦r t♦♥ t ♦♥ ♣s ♥

❬s ❪ s ❱r PP r♦♥♥ ❱rs ♥ P ♣r♥

r r♥ s♣ r♥t② ♥ t ♦ str♦♥ s t rt♦♥ ♦r♥

♦ ♣♠♦♦② ♥ ♦♠♠♥t② t ♦ ♥♦ t ♦♥

♣

❬t ❪ t r ♦① ❯ ♦r rtr ♥ ♣

r P♦♥t Pr♦ss ♦r ♦♥ r ❲♦r♠s r♥s ♦♥ P

♦ ♥♦ t ♦♥ ♣s ♥

♦r♣②

❬st♥ ❪ st♥ ♣♥r ♥ sr t♦♠t rstrt♦♥ ♦

♥ ♦♣t ♠s ♦ r♥ s♥s ♥ ❱P t ♦♥ ♣

❬r♦s♦t ❪ ❱rt rt r♦s♦t tt♣♠r♦s♦t♦♠♠♣s

t ♦♥ ♣

❬tr ❪ tr ❲♥ ❩♥ ♦♥r ♥ ♦♦

trtrr ♣ Pr♦ss♥ ♥ r♦r♣s t ♦♥

♣

❬ss ❪ P ss P ❲♦♥ ❲♠♠r ♥ ♦♦

♥ ❲ Prt♦r r② ♦ ❯r♥ ♦♥strt♦♥ ♦♠♣tr r♣s

♦r♠ t ♦♥ ♣s ♥

❬♥ ❪ ♥ r ❩♥ ♦♥r ♥ ♥ ♠rt♦①s ♦r

♥trt ❯r♥ ♦♥strt♦♥ ♥ P t ♦♥ ♣

❬ ❪ t♦♥ ♥tr ♦r r♦r♥ sr ♣♣♥ tt♣

♥♠ ❬♥♥ ss ②❪ t

♦♥ ♣

❬②♥ ❪ ②♥ t ♥ ♦t ♣t sttsts ♦

s ②♣♦♥ts ♦r t①tr r♦♥t♦♥ ♥ ❱ t ♦♥ ♣

❬ ❪ ♣ tt♣s♥♦♦t♦st

trstr② ❬♥♥ ss ②❪ t ♦♥ ♣

❬s ❪ s r ♥ P ③ ♥♦♦r ♥ ♦♥strt♦♥ s♥

Pr♠tr♥ ♣ Prtt♦♥♥ ♥ r♣t ♥ r♦r♣s ❲♦r

s♦♣ ♦♥ ❯r♥ t ♦♥ ♥ ❱sst♦♥ t ♦♥ ♣

❬♥ss ❪ ♥ss rtq ♦ trtrr♦♠♦t♦♥ ♦rt♠s ♦♠

♣tr ❱s♦♥ ♥ ♠ ❯♥rst♥♥ ♦ ♥♦ t ♦♥

♣

❬♣♥t♦♣♦r♣② ❪ ♣♥t♦♣♦r♣② ♣♥t♦♣♦r♣② ♣ tt♣

♦♣♥t♦♣♦r♣②♦r ❬♥♥ ss ②❪ t ♦♥

♣s ♥

♦r♣②

❬rt♥r ❪ rt♥r ❳ s♦♠s ♥ ❩r r P♦♥t Pr♦ss ♦

t♥s ♥ ♠♥ts ♦r t♦♠t ♥②ss ♦ t t♦♥ ♦s

r♥s P ♦ ♥♦ t ♦♥ ♣s ♥

❬Pr ❪ Pr ❨ ♦ ♥ ❨ t♦♠t ①trt♦♥ ♦ r ♦♠

♣① ♥s s♥ r t ♥ t ♠♣s ♥tr♥t♦♥ rs

♦ t P♦t♦r♠♠tr② ♠♦t ♥s♥ ♥ ♣t ♥♦r♠t♦♥ ♥

t ♦♥ ♣

❬P♦s ❪ P♦s ♥ ❨♦ t♦♠t r♦♥strt♦♥ ♦ ts r♦♠ r♠♦t

s♥s♦r t ♥ ❱P t ♦♥ ♣s ♥

❬P ❪ P ♥ ❱♦ss♠♥ ♥♦ s r♦♥strt♦♥ ♦ ♥

♠♦s r♦♠ trrstr sr s♥♥♥ t ♦r♥ ♦ P♦t♦r♠♠tr② ♥

♠♦t ♥s♥ ♦ ♥♦ t ♦♥ ♣

❬♦r② ❪ ♦r② r♠②♥ ♥ ❩r r rr t ♦♥

t♦rs ❱ ♦ ♥♦ t ♦♥ ♣

❬♦tt♥st♥r ❪ ♦tt♥st♥r r♥r ♦ ♥

t♦♠t ♥t♦♥ ♦ r♦♦ ♣♥s r♦♠ r t ♥tr♥t♦♥ rs

♦ t P♦t♦r♠♠tr② ♠♦t ♥s♥ ♥ ♣t ♥♦r♠t♦♥ ♥s

♦ ♥♦ ❲ t ♦♥ ♣

❬♦tt♥st♥r ❪ ♦tt♥st♥r ♦♥ ♥ r r

♥t③ ♥ ❯ rt♦♣ P ♥♠r ♥ ❯r♥ t s

st♦♥ ♥ ♥ ♦♥strt♦♥ ♦r♥ ♦ P♦t♦r♠♠tr② ♥

♠♦t ♥s♥ ♦ ♥♦ t ♦♥ ♣

❬ ❪ ♥ ❯rrt ♥♦♦ ♦ ♦♠♣tt♦♥ ♦♠tr② s

r t ♦♥ ♣s ♥

❬♠♦♥ ❪ P ♠♦♥ P ♥ ♥ r♦st ts ♦♥trs ♥ ♠

♣r♦♠♥ts ♦r s♠t ♥♥♥ ♦♥♦r♣s ♦♥ t♠t

♦♥ ♥ ♦♠♣tt♦♥ t ♦♥ ♣

❬tr ❪ tr ♦♥t♦♥ ♦ ♦r♠rs r♦♠ r t s♥ s♣♣♦rt t♦r

♠♥ ♥ t ♦♥ ♣

♦r♣②

❬♥ ❪ ♥ ❲ ♥ ♥ ♥t ♦r P♦♥t

♦ ♣ tt♦♥ ♦♠♣tr r♣s ♦r♠ ♦ ♥♦

t ♦♥ ♣

❬t③ ❪ t③ rss rst♥ ♥ ③s

♦♠♣rs♦♥ ♥ t♦♥ ♦ t❱ tr♦ ♦♥strt♦♥ ♦rt♠s

♥ ❱P t ♦♥ ♣s ♥

❬♥ ❪ ♥ t② ③s r ♥ P♦②s ♥

trt rttr ♦♥ r♦♠ ❯♥♦rr P♦t♦ ♦t♦♥s

P s t ♦♥ ♣s ♥

❬rst ❪ rst ❯ r♥♥r ♥s♥ ♥ r ♠♣

s♦♥ r♦ ♣r♦sss ♦♥ ♦rt♦♦♥ r♦♣s ♦r ♦t ♣♦s st♠t♦♥

♦r♥ ♦ ttst P♥♥♥ ♥ ♥r♥ ♦ ♥♦ t

♦♥ ♣

❬t♦ ❪ t♦ ❱ rt♥③ ♥ r tr ♠♥s♦♥ ♦t ♣♦♥t

♣r♦ss ♦r tt♦♥ ♦ ♦s♠ ♠♥ts ♦r♥ ♦ t ♦② ttst

♦t② ♦ ♥♦ t ♦♥ ♣

❬trst ❪ trst s♦♥ ♦♥t ♥ ♦♥♦ ♦

♥♦ ♦♣t♠st♦♥ ♦r ♦♥st♥t t♠ s ♥ ❱ t

♦♥ ♣

❬♥ ❪ ♥ ♥ ♥ ❩♥ r ♣♦♥t ♣r♦ss ♦r srtr

①trt♦♥ ♦♥ ♥♦r♠ ♥ ❱P t ♦♥ ♣s ♥

❬③s ❪ ③s ❩ rst♥ ❱sr ❱ ♦♠♦♦r♦

r ♣♣♥ ♥ ♦tr ♦♠♣rt t② ♦ ♥r② ♥

♠③t♦♥ t♦s ♦r r♦ ♥♦♠ s t ♠♦♦t♥sss Pr♦rs

r♥s P ♦ ♥♦ t ♦♥ ♣s ♥

❬♦s ❪ ♦s P ♦r♦ ♥ sr tt♥ ♥ ♣rs♥ r

ttr t t② s r♦♠ r♥ t ♥ ❱P t ♦♥ ♣

❬ ❪ ❩ ♥ ❩ ♠ ♠♥tt♦♥ ② tr♥ r♦ ♥

♦♥t r♦ r♥s P ♦ ♥♦ t ♦♥ ♣s

♥

♦r♣②

❬❯ ❪ ❯ ❲♦r ❯r♥③t♦♥ Pr♦s♣ts s♦♥ ts

❨♦r ❯♥t t♦♥s ♣rt♠♥t ♦ ♦♥♦♠ ♥ ♦ rsP♦♣t♦♥

s♦♥ tt♣s♥♦r♥♣♣❲❯P❴ts♣

❬♥♥ ss ②❪ t ♦♥ ♣

❬❯❱ ❪ ❯❱ ❯❱ ♥str♠♥t tt♣t②

♥♦♦r♣r♦t❴s♣♣♦rttstst♠ ❬♥♥ ss

②❪ t ♦♥ ♣

❬❯ ❪ ❯ ❯ ♣ tt♣s♠ssss♦ ❬♥♥

ss ②❪ t ♦♥ ♣

❬❯ts ❪ ❯ts ♥ ♥ r P♦♥t Pr♦ss ♦ ♦r t

❱ P♦♣ tt♦♥ ♥ ❱P t ♦♥ ♣s ♥

❬♥ s♦t ❪ ♥ s♦t ♣t ♣ t♦♥ ♦r ❱r

♠r ♦ ♦♥ ts ❯s♥ r♦ q♥t t Pr♦sss

r♥s P ♦ ♥♦ t ♦♥ ♣

❬❱♥s ❪ ❱♥s ♥ ♥s ♥ ♦♥strt♦♥ s♥

♥tt♥❲♦r r♠♠rs ♥ ❱P t ♦♥ ♣

❬❱♥s ❪ ❱♥s P ❲♦♥ P r P ❲ ♥

❲ts♦♥ ♦♥ t ♣♣r♥ ♥ ♦r ♦ ❯r♥ ♣s ♥

r♦r♣s t ♦♥ ♣s ♥

❬❱r♥ ❪ ❱r♥ ♥ P ♦♦♦♥ st ♠t♦ ♦r ♥r③

strt♥ t♠♣rtr tr♠♥t♦♥ ♥ ♦♠♦♥♦s t♦st s♠t ♥

♥♥ s②st♠s ♦♠♣trs ♣rt♦♥s sr ♦ ♥♦

t ♦♥ ♣

❬❱r ❪ ❨ ❱r r ♥ ❩r ♥rt♥ ♦♠♣t ♠ss

♥r ♣♥r ♦♥str♥ts ♥ t♦♠t ♣♣r♦ ♦r ♠♦♥ ♥s r♦♠

r ♥ P t ♦♥ ♣s ♥

❬❱r ❪ ❨ ❱r ♥ r ♥t ♦♥t r♦ s♠♣r ♦r tt♥

♣r♠tr ♦ts ♥ r s♥s ♥ ❱ t ♦♥ ♣

❬❱r ❪ ❨ ❱r ♥ r tt♥ ♣r♠tr ♦ts ♥ r s♥s

② ♦♥t r♦ s♠♣♥ ❱ t ♦♥ ♣

♦r♣②

❬❱r♠ ❪ ❱ ❱r♠ ♠r ♥ s ♥ tt♦♥ ♥ ♦♥

r♦♠ r t ♥ ❱P t ♦♥ ♣

❬❲ ❪ ❲ ♥ ♥ ♥ r♦♠ t t sr ♠♦

s t♦ t② ♠♦s s♥ ♦♥str♥ s♠♣t♦♥ P♦t♦r♠♠tr r♥

r♥♥ ♦♥♦r♠t♦♥ t ♦♥ ♣

❬❲♥ ❪ ❲♥ ♦rs r♥ ♠♦♥ s♥ ♠♦ ♥ ♠

s ❯♥rst② rrs t ♦♥ ♣s ♥

❬❲ss ❪ ❨ ❲ss ♥ ❲ r♠♥ ♥ t ♦♣t♠t② ♦ s♦t♦♥s ♦ t

♠①♣r♦t ♣r♦♣t♦♥ ♦rt♠ ♥ rtrr② r♣s r♥s

♦♥ ♥♦r♠t♦♥ ♦r② ♦ ♥♦ t ♦♥ ♣

❬❲♥ ❪ ❲ ❲♥ ♥ ①♠♥t♦♥ ♦ t ♠♣ts ♦ ❯r♥③t♦♥

♦♥ r♥ ♣ ss ♥ ❲tr s♦rs ♦♣ ♥ ♦♣

♥ ❲♦r Prs♣t P tss ❯ ❯♥rst② ♦t ♦r♥

t ♦♥ ♣

❬❩rs ❪ ❩rs ♦②r ♥ ♦r r♥s♦rs t♦♣♦♦②

♣t ♠ss ♣♣r♦ t♦ sr ♦t♦♥ ♥ ❱ t

♦♥ ♣

❬❩♥ ❪ ❩♥ r r♥r ♥ s♦ s♦♥ ♦ tr

♥ rs ♥♦r♠t♦♥ ♦r ❯r♥ ♥s ♦♥ r♦♠ r ♠

r② ♥ ❱ t ♦♥ ♣s ♥

❬❩♦ ❪ ❨ ❩♦ ♥ ❯ ♠♥♥ st ♥ ①t♥s ♥ ♠♦♥

r♦♠ r♦r♥ t ♥ ♥s ♥ ♦r♣ ♥♦r♠t♦♥ s②st♠s

t ♦♥ ♣

❬❩♦ ❪ ❨ ❩♦ ♥ ❯ ♠♥♥ ♦♥t♦r♥ ♦st ♣

♣r♦ t♦ rt♥ ♥ ♦s r♦♠ r P♦♥t ♦s ♥

❱ t ♦♥ ♣s ♥

❬❩♦ ❪ ❨ ❩♦ ♥ ❯ ♠♥♥ ♥ ♦♥ ② s♦r♥

♦ rts ♥ ❱P t ♦♥ ♣s ♥

❬❩♦ ❪ ❨ ❩♦ ♥ ❱ ♦t♥ ♥s ♥ ♦♥strt♦♥ t P♦♥ts ♦

♥trst ♥ P t ♦♥ ♣

♦r♣②

❬❩ ❪ ❩ ♦ ❨❩ ❲♥ ♥ ❩ ❳ ❲t r ①t♦♥s ❱

t ♦♥ ♣