ISSN: 1439-2305

Number 184 – January 2014

PERSISTENCE IN CORPORATE

NETWORKS

Mishael Milakovic, Matthias Raddant, Laura Birg

Prsst♥ ♥ ♦r♣♦rt ♥t♦rs

s ♦

❯♥rst② ♦ ♠r

♠s♠♦♥♠r

tts ♥t

♥sttt ♦r t ❲♦r ♦♥♦♠② ♥ ❯♥rst② ♦

♠ttsr♥t

r r

❯♥rst② ♦ ött♥♥

rr♥♦tt♥♥

♥r②

strt

❲ ①♠♥ t ♣rtt r♣s ♦ r♠♥ ♦r♣♦rt ♦rs ♥ ♥ ♥ ♥t② ♦rs ♦ rt♦rs ♦ r ② ♥tr ♥ t ♥tr♥t♦r ♥ ♥s② ♦♥♥t ♠♦♥ t♠ss ♥♦ tr♦ ts ♣♣r s t ♦s ♦♥ t ②♥♠s ♦ ts ♥t♦rs r♠♥②s ♦r♣♦rt ♦r♥♥ s ①♣r♥ s♥♥t ♥s r♥ ts t♠ ♥tr s sst♥t tr♥♦r ♥ t ♥tt② ♦ ♦r ♠♠rs ②t ♦srt ♣rsst♥t ♣rs♥ ♦ ♥t♦r ♦r s ♥ r♦st t♦ ♥s ♥t t strt♦♥ ♦ ♠t♣ ♦r ♠♠rs♣s ♥♦t ♥ ssts tt ♦r ♣rsst♥ ♦r♥ts r♦♠ t ♦r ♣♣♦♥t♠♥t s♦♥s♦ r② ♣t③ ♦r♣♦rt♦♥s

♥tr♦t♦♥

❲ st② t t♠ ♦t♦♥ ♦ r♠♥ ♦r♣♦rt rt♦r ♥tr♦s t♥ ♥ ♥ tt ♣rsst♥t ♦r ♦ rt♦rs ♦ r ② ♥tr♥ t ♥t♦r ♥ ♥s② ♦♥♥t ♠♦♥ t♠ss sttst ♣r♦♣rts ♦ t ♥t♦r ♦r s♦ tt rt♦♥ ♦r t♠ ♥ s♣t ♦

s♥♥t ♥s ♥ ♦r♣♦rt ♦r♥♥ ♥ ♦♥sr tr♥♦r ♥ t♥tt② ♦ ♦r rt♦rs ♥ t♦ qst♦♥s ♦t t ♠♥s♠s ttr rs♣♦♥s ♦r t ♦r♥ ♦ ♣rsst♥t ♥t♦r ♦r

rt♦♥ rsr ♥ ♦r♥③t♦♥ ♥ ♠♥♠♥t s♥ s ♥stt t ♥♥ ♦ sr rt♦rs♣s ♦r ♦♥rs♣s ♦♥ r♠ ♣r♦r♠♥ ♣r♦tt② ♥ ♦r♣♦rt strt② ♥♥ qst♦♥ ♦r♦ ♦ ♥♥♥ t ♠♥t ♥ rt♦♥ ♦ ♣♦t ♥ rt♦♥trt♦♥s t ♦♣t♦♥ ♦ ♣♦s♦♥ ♣ ♣rts ♥ ♠♥② ♠♦r ♥ t♥rt♥ s ♥ ♥♥ ♦ rsts t♦ rr♥t sr r♥t sr②s ♦♥r♥t s♣ts ♦ t st ❬ ❪ ♥♦tr str♥♦ rsr ♥s♣r ② t ♥trs♣♥r② ♦r ♦ ❬❪ s ♠♣s③ tsttst ♣r♦♣rts ♦ ♦r♣♦rt ♥t♦rs ❬ ❪ ♥ ♦♥s ttrt♦r ♥tr♦s ①t t s♠ ♦r t r② t ♥tr♣rs♦♥st♥ t♥ ♥② t♦ rt♦rs s sr ♦rrs ♦ ♠♥t s♠rt♥ t ♥♠r ♦ rt♦rs ♥ t ♥t♦r ♥ t♦♥ ❬❪ r ttrt♦r ♥tr♦s r s♦ rtr③ ② r ♦ str♥ t②♣ ♦ t s♠ ♦r ♥t♦rs ♥tr♦ ② ❬❪ sq♥t② ♦r❬❪ ♥ ❬❪ s♦♥ r♦♠ r♥t ②t ♦♠♣♠♥tr② ♣♦♥ts ttt r ♦ str♥ s ♣rs♥t ② ♦♥strt♦♥ ♥ s♦ s s♥♦t ♥ ♥①♣t tr ♥ rt♦r ♥tr♦s ♥tt② t rs♦♥s tt rt♦rs ♦ t s♠ ♦♠♣♥② r ♥ ② ♥t♦♥ t♦ tr♦s t r ♠♦rt② ♦ rt♦rs srs ♦♥② ♦♥ s♥ ♦r♥ t ♥t♦r

♦♥♥t♦♥ s♦♠ s t tt t s♠ ♦r t t②♣② st♠sr♦♠ t ♣rs♥ ♦ ❵s ♥♦s t r ♥♠r ♦ ♥s t♦ ♦tr♥♦s ♥ t ♥t♦r ♥ t r strt♦♥ ♦ ♥♦s s ♥ s♦♥ t♦♦② ♣♦r ♥ ♠♥② ♦♠♣① ♥t♦rs ❬ ❪ ②t ♦r♣♦rt ♥tr♦s♦ ♥♦t ♥t♦ ts t♦r② rs♥ t qst♦♥ r t stss♠ ♦r ♣r♦♣rt② ♦ ♦r♣♦rt ♥t♦rs ♦♠s r♦♠ t♥

♥② t tt ♦r ♦ rt♦r ♥tr♦s ♥♥s t r♦ ♥trst r♦♣ ♦r♠t♦♥ s ♣r♦s② ♥ ♣t ♦rr ② ❬❪ ♥sr t♦rs sst ♣r♦rs t♦ ss② ♦r ♥t② ♦r ♦② ♣②rs ♥ ♦♠♣① ♥t♦rs ♦t ♥ t s♦ s♥s ❬ ❪ ♥♥ ♥trs♣♥r② ♣②ss ❬❪ t t ①st♥ ♦ ♥t♦r ♦r s♦s ♠♣t♦♥s ②♦♥ ♣rssr r♦♣ ♦r♠t♦♥ ♣rtr② ♦r ss♦ s♦♥ ♣r♦sss s♦♠t♠s rrr t♦ s ♣t♦♥ ♥ s ❬❪ ♥♠♣♦rt♥t strt♦♥ ♦ s ♣r♦ss s t s♦♥ ♦ stts ①♣tt♦♥s tsts ♦♣♥♦♥s tr♥ ♣♦st♦♥s t ♥ s②st♠ ♠ ♣ ♦ r ♥♠r ♦ ♥trt♥ tr♦♥♦s ♥ts ♥ ♥ s♦ ♣r♣s

❬❪ ♦r r ♦ s♠ ♦r ♥t♦rs ♥ t s♦ s♥s

s♦♠t ♥①♣t② tt t ①st♥ ♦ ♦r s ♦t♥ s♥t ♦rt s②st♠ ♣r♦♣t♦♥ ♦ s♦♥s ♥ s ♥ s s②st♠s ❬ ❪ ♣rs♥ ♦ rr ♦r♣r♣r② strtr ♥ ♦t♥t♠s t♦s②st♠ ♦♥♦r♠t② ♥♥ t ♣♦sst② tt t s♦ ♥trt♦♥s♦ ♦r ♥ts t♦ ♦♦r♥t ♥♠ s♣rts ♥ s②st♠ tt s sr♦rrs ♦ ♠♥t rr t♥ t s③ ♦ t ♦r ❲ tt t♣♦t♥t ♠♣t♦♥s ♦ ♦r ♠♣r rsts r st sss ♥ t ♦ts ttr ♣♦♥t

❲ ❬❪ s♦ t ①st♥ ♦ ♥t♦r ♦r ♥ ♠♦r r♥t ②rt② ♦srt♦♥s ♦♥ t t♠ ♦t♦♥ ♦ t ♦r ♥ rt♦r ♥t♦rs ♥ ♦ t ♠♥ ♥♥s ♦ t ♣rs♥t ♣♣r s tt ♥sttt♦♥ts ♠♦♥ t rst r♠♥ ♦♠♣♥s r ♠♥t♥ ♦r t♠ ♥ s♣t♦ ♦♥sr tr♥♦r ♥ t ♥tt② ♦ rt♦rs ♥ t ♦ ts tr♥♦rt ♦♠s ♠♣♦rt♥t t♦ ♥rst♥ t ♦r♥s ♦ ♣rsst♥t ♥t♦r ♦r♥ ♦r ♥②ss ssts tt ♦t t r♦♥strt♦♥ ♦ r♦♥ ts ♠♦♥r ♦r♣♦rt♦♥s s s tr ♣rr♥ ♦r rrt♥ ①♣r♥ rt♦rs t ♠t♣ ♦r ♠♠rs♣s r rs♣♦♥s ♦r t t♠ ♣rsst♥ ♦ ♥t♦r ♦r ♦ ♦r ♥♦ ts ♣♣r s t ♦♥② ♦♥ sst ♠ rr st② ② ❬❪ tt ♥②③s t ②♥♠s ♦ ♦r ♥t♦rs

r ♥♥s r ♦ ♣rtr ♥trst ♥ t ♦ r♥t ♠s tt t♦r♣♦rt ♥t♦r s♣② ♥ t r♠♥ s s ♥ stt ♦ ♥ t♦ ♥rs sr♦r ♦r♥tt♦♥ ♦ ♦♠♣♥s t strt r♦r♥tt♦♥♦ r ♥s ♥ t rs♥ ♥♥ ♦ t stt ♥ t ♥rstrtrst♦r ❬ ❪

♥ t r♠♥r ♦ ts ♣♣r s tt ts ♥ s ♣♣r♥t♥ t s sr♣t sttsts ♦ t ♦r♣♦rt ♥t♦r ②t t str♥ ♠♥s♠ ♦ ♦♠♣♥s tt tt r ♠♥s t♦ ♣rsr ♦r ♥t♦r ♦s ♥♥ s ♥②t♥ ♥rs♥ ♦r t♠

tr sr♣t♦♥ ♦ t tst ♣r♦ ② ♥t②♥ ♥ ♦♠♣r♥ ♦rs ♦ rt♦rs ♠♦♥ ♦r ss♠♣s rtr ♥②③ ♦t rr♥ ♣r♦ss ♠♦♥ ♦♠♣♥s ts ♣ tr♦♦t t ②rs❲ ♦♥ ② sss♥ ♠♦r ♥r ♠♣t♦♥s ♦ ♦r ♥♥s tt ♦②♦♥ t r♠ ♦ ♦r♣♦rt ♥t♦rs

tst

r ♦♠♣t♦♥ ♦ ♦r ♦♠♣♦st♦♥ t ♠ ♦r r♠♥②s ♦♥ ♥r rst ♣② tr ♦♠♣♥s ♥ ♥ trt②rst ♦♠♣♥s r st ♥ t r♠♥ st♦ ♥① ❳ tsr t♥♥① t ♥①t rst ♦♠♣♥s r st ♥ t ♣❳

♦r ❳ ❳ s ♦♥ ♥ ♦♥t♥♥ t s♥t② rst♦♠♣♥s tt r ♥♦t ♥ ♥ t ❳ s♦ s ♥ t s♠♣ ♥ t ♥♠r ♦ ♦♠♣♥s ♥ t ❳ s rr♦♠ s♥t② t♦ t② s♦ s t sr♦rs ♠♦♥ t t♥t② ♦♠♣♥stt t t ❳ ♥ t s♠♣ ♦r r♣ t♦s tt ♥♦ ♦♥r①st t t ♥①t rst ♦♠♣♥s ♥

1993 1999 2005

r ♦♠♣♥② ♥t♦rs ♥t♦r ♦ r♠♥ rt♦r t♦♣ ♣♥ ♥ ♦♠♣♥② ♦tt♦♠ ♣♥♥tr♦s ♥ ♥ ♥② ♦♠♣♥s r s♦t r♦♠t r ♦♥♥t ♦♠♣♦♥♥ts ♥ s r♣ ♥s♣t♦♥ r②ssts tt ♥t♦r s ♦r♣r♣r② strtr

♦r t ♣r♣♦s ♦ ♦r st② ♦r♣♦rt ♦rs ♦♥sst ♦ ①t ♠♥♠♥t ❱♦rst♥ ♥ s♣rs♦r② ♦r stsrt ♦r♥ t♦ t♣rt♥♥t r♠♥ ♦ t② t♦ ♠t t st ♦r t♠s ♣r ②r§ ♦ t♥st③ ♦r t ①ts r ♣♣♦♥t ♦r ♠①♠♠♦ ②rs ♥ ♦t ♣♣♦♥t♠♥t s s ♣♦t♥t r♣♣♦♥t♠♥t ♥t♦ ♣♣r♦ ② t s♣rs♦r② ♦r § t ♥ t ♦ t ②r♠t ♦s q② s♣ ♥trs ♦ s① ②rs t♦ ♥rs t ♦♦♦ ♦sr♥ ♥s ♥ t ♦♠♣♦st♦♥ ♦ ♦r♣♦rt ♦rs ❲ ♦♠♣

♦ ♦♠♣♥s st♥t ♦ rt♦rs st♥t ♦ ♠♥ts r ♦r s③ r ♠♥ts ♣r rt♦r ♦♠♣♥② ♥s t♦t ♦♠♣♥② ♥s ♥t

♦r♣♦rt ♠♥t sttsts sr♣t sttsts ♦ ♦r s♠♣ strt st rs ♥ t♥♠r ♦ rt♦rs ♥ ♠♥ts ♦r t♠ ♥ ② ♥♦♥♥r rs♥ t ♥♠r ♦ ♥s t♥ ♦♠♣♥s tt r ♦r♠ ② ♠t♣ ♦r♠♠rs♣ ♥♦♥♥rt② s s ② t t tt rt♦r t b♠♥ts rts l(b) = b!/2(b− 2)! ♥s ♠♦♥ ♦♠♣♥s ♦r ♥st♥ rt♦r t b = 6 ♠♥ts rtrs ♥ s r♣ ② r♥t s♥♠♥t rt♦rs t♠ t♥ l(6) = 15 ♥s r r♠♦ r♦♠ t♥t♦r

t t ② ♦♥st♥ r♦s rs tt ♣ r♦rs ♦ t ♥♥ r♣♦rts ♦ ts ♦♠♣♥s ♥ ② rt♥ t♦ ♦♠♣♥s ♦r ♦♠ ♦♥♦t ♦t ♥♥ r♣♦rts r ♦♠♣♥s ♥ t s♠♣ ♥♦t r♣②t♦ ♦r ♥qr② tr ♦ t♠ t rt② ♠♥♦r ♠rt ♣t③t♦♥♥ s t ♦♠♣♥s ♥ tt ②r

sr♣t sttsts ♦ ♦r s♠♣ r♣♦rt ♥ s♦ rs♥ r ♦r s③ ♦r t♠ s ♠♥② t♦ tt②♠♦♥ r② r ♦r♣♦rt♦♥s ♥ s♦ t♦ t t tt t♦♥s ♦♥② ♦t t s♠♣s r ♦r s③ ♥ tt ②r

t n t ♥♠r ♦ rt♦rs ♥ ②r ♥ t c t ♥♠r ♦♦♠♣♥s ♥ tt ②r ♥ t ♥♥ ♠tr① M ♦ ♠♥s♦♥ n × ct mij = 1 rt♦r i s ♦♥ t ♦r ♦ ♦♠♣♥② j ♥ ③r♦ ♦trssrs t ♦r♣♦rt ♥t♦r ♥ ②r ♣r♦t♦♥ ♦♥t♦ rt♦rsD = MMT s t t ♥② ♠tr① ♦ rt♦r ♥tr♦s ts ♦♥ ♥trs q t t♦t ♥♠r ♦ ♦r ♠♠rs♣s ♦ rt♦r i ♥♦♥③r♦ ♥trs ♦ t ♦♥ ♦ D r♣rs♥t t t ♦ ♥s♦♥ ♦♥ ♦ ♠♥② ♦rs t♦ rt♦rs sr t♦tr ②♠♠tr②t ♣r♦t♦♥ ♦♥t♦ ♦rs B = MTM ②s t t ♥② ♠

rs♥r ♥ ♦r ♥st♥ s qr ② ♥③ ♥ t ♥♥ st♦r ❱ ♥ ❱ ♠r t♦ ♥ t tts ♥str②

tr① ♦ ♦♠♣♥② ♥tr♦s ts ♦♥ ♥trs ♦rrs♣♦♥ t♦ t ♦r s③♦ ♦♠♣♥② j ♥ ♦♦♥ ♥♦♥③r♦ ♠♥ts ♥t t ♥♠r ♦rt♦rs tt t♦ ♦♠♣♥s ♥ ♦♠♠♦♥ rst♥ ♥t♦rs rs♣② ♥ r ♥ r② r t ①st♥ ♦ ♦r ♥ ♣r♦t t r s♦ ssts tt t ♥♠r ♦ ♦r ♦♠♣♥s ♥ rt♦rsrss ♦r t♠ qst♦♥ s t♥ s ♦♥ ♠t ♣r♣s ♥tt②①♣t tr ♦r rt♦rs s♦ ♦♠ ss ♥♥t ss ♥tr ♦r ss♥s② ♦♥♥t ♠♦♥ t♠ss

♥②ss ♦ ♦rs ♦ rt♦rs

♥♦♠ ♥♠r ♥ ♥r ♦♣♠♥ts

♦ ♥rst♥ t ♦r♥s ♦ t s♠ ♦r t ♥ rt♦r ♥tr♦s ♥ t ♥strt t♦ ♦♦ t ♣♣r♦ ♦ ❬❪

❲ rst ♥ t♦ ♥t② ♦r ♦ rt♦rs ♦r ts ♣r♣♦s t s ♥strt t♦ ♦♥sr t rq♥② ♦ ♠t♣ ♦r ♠♠rs♣s s♦♥ ♥r

❲ strt r♦♠ t ♦srt♦♥ tt t st ♠♦rt② ♦ rt♦rs srs♦♥ st ♦♥ ♦r ♥ ♦♥t s♠♣ t♦t ①♣r♠♥t ♣♣♦s ttt rt♦rs ♥ s♠♣ r ♥st♥s t♥ ♥ tr♠♥t ♣r♦t② ♦ ♦sr♥ ♠t♣ ♦r ♠♠rs♣ s sq♥ ♦ k♥♣♥♥t r♥♦ trs rst♥ ♥ ♥♦♠ strt♦♥ ♦r ♦sr♥B = b t♦♥ ♦r ♠♠rs♣s

Pr[B = b] =

(k

b

)

pb (1− p)k−b,

r p s t ♣r♦t② ♦ sss ♦ ♦t♥♥ ♥ t♦♥ ♦r♠♠rs♣ ♦ strt t ♣r♦r ♦♥sr ♦r ①♠♣ t ②r tr r rt♦rs ♥ t♦t ♥ t ♥♠r ♦ ♠♥ts s ②♥k = 2143−1744 = 399 ♥ p = 1/1744 r strts t rst♥ ♥♦♠ strt♦♥s ♥ ♦♠♣rs t♠ t♦ t ♠♣r rt rq♥s♦ ♠t♣ ♦r ♠♠rs♣

♦r b > 3 t ♥♥ ♦ ♠t♣ ♦r ♠♠rs♣ s sr ♦rrs♦ ♠♥t r t♥ ♦ ①♣t ♥ sq♥ ♦ ♥♣♥♥tr♥♦ trs ssts tt rt♦rs t tr ♦r ♠♦r ♠♥tsr ♣r♦st② st♥t ♥ ts ♥ s♦♠ s♥s s♣ ♥ ♦①♣t t♦ ♦sr ♥t♦r ♦r ts rt♦rs r ♦♥♥t ♠♦♥t♠ss ts ♣♦t t ♥t♦r strtr ♠♦♥ rt♦rs t B ≥ b♦r ♠♠rs♣s ♥ r rs tt t rst♥ sr♣s

æ

æ

ææ

æ ææ æ æ

à

à

à

à

à

à

à

à

à

ì

ì

ìì

ìì

ì

ìì

ò

ò

ò

ò

ò

ò

ò

ò

ò

ô

ô

ô

ô ô

ôô

ç

ç

ç

ç

ç

ç

ç

1 2 3 4 5 6 7 8 9 10

10-12

10-10

10-8

10-6

10-4

0.01

1

1 2 3 4 5 6 7 8 9 10

No. of board memberships b

Fre

qu

encyHe

mp

iric

alv

s.b

ino

mia

lb

ench

mar

kL

ç 2005 binomial

ô 2005 empirical

ò 1999 binomial

ì 1999 empirical

à 1993 binomial

æ 1993 empirical

r ♦r ♠♠rs♣ ♥♠r t♦♣ rs s♦ t ♠♣r rt rq♥② ♦ ♠t♣ ♦r ♠♠rs♣ ♥ ♦ t tr ②rs t ♦tt♦♠ rs strt t ♥♦♠ ♣r♦t② ♦ ♦sr♥ ♠t♣ ♦r ♠♠rs♣ ♥ t rs♣tsq♥s ♦ ♥♣♥♥t r♥♦ trs sr ♥ t t①t s♠♦s rs t♦♥s ♦♥ ♥rs♥ ♦rrs ♦ ♠♥t ♦r b > 3

♦r b♦rs r ♥ t♦ r② r ①t♥t ♦♥♥t ❲ s♦ ♦srtt ♦t t ♥♠r ♦ rt♦rs ♥ t rt♦♥ ♦ ♦♠♣♥s tt r♦♥♥t ② t rs♣t ♦r rt♦rs rs ♦r t♠ ♥ ♦r s♠♣s♦♥ ♥ r

♠♦r ♦♥trt♥ t♦r t♦ ts ♦♣♠♥t s rt♥② t r♥tr♦r♠ ♦ r♠♥②s ♦r♣♦rt ♦r♥♥ ♦ r♦r♠ st ♥♠r ♦ ♥t♦♥ ♥ ♥tr♥t♦♥ rts♠s tt ♥ ♥st r♠♥②s trt♦♥ ♦r♣♦rt ♦r♥♥ ♠♦st② ♦♥r♥♥t ♥qt ♦s ♦♥ sr♦r ♥trsts ♥ t ♥qt ♥♣♥♥ ♦ s♣rs♦r② ♦rs rss ♦r ♥st♥ ♥ ♣rr♣s ♠t ♦r ♠♥♠♥t ♦r sr ♥♣♥♥ ♦ s♣rs♦r② ♦r ♠♠rs ♥ trr♥ ♦ t trt♦ st♦♠ tt♦r♠r ①ts sr s s♣rs♦r② ♦r r♠♥ ❲ t ♥♦ ♠s t st♥r③♥ st ♣rts ♥ ♦r♣♦rt ♦r♥♥ t ♦s♥♦t t stts ♦ ♦r♠② ♥♥ rtss t♦♥s r♦♠ rs t♦ ①♣t② st ♥ ♣③ ♦♥ ♥ ♥♥ ss§ t ♥ t ♦sr rs ♥ t r ♥♠r ♦ ♦r♠♠rs♣s s ♥♦t ♥ ♥①♣t tr r♦♠ ts ♣rs♣t t s ♥♦t♦rt② tt t ♦ t♦♦ t ♥ r② t ♣r♦♥♦♥ rs♥ r ♠♥ts ♥ ♦rs t♥ t ♥ s♠♣s

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

♥ t ♣♣♥① s♦s tt ♥ t rt♦rs t ①t ♣♦st♦♥s t♦♥② sr ♦♥ s♣rs♦r② ♦rs ♦ ♦tr ♦r♣♦rt♦♥s r♦♣ ♥ t rt♦ ♦ s♣rs♦r② ♦r ♠♠rs♣s ♣r ①t 228/569 = 0.4 ♥ 0.3 ♥ ♥ 0.17 ♥ strts tt ♦r♣♦rt ♦r♥♥ ♣rts ♥♥ ♦r t ♥stt t♠ ♣r♦ s r♥s s t♦ t qst♦♥ tr sr♥♥ ♦r s③s s♦ ♠♣s tt ♦r rt♦rs ♦♠ ss♥♥t ♦r t♠

♦t tt ♦r b♦rs r r♦♠ s♦ k♦rs r ♦♥strt s♥ ♥♦s ♠♥♠♠ r ❬❪

♥♦tr ♠t♦ ♦r ts ♥②ss ♦ t♦ s ♦r♣r♣r② ♠♦ ❬❪ ♥ ♦♥② ♥t t♦ s♦ tt st ♦ ♥♦s tt r② ♥t s ♦r s r♥t ♣♣r♦ r

tt♣♦r♣♦rt♦r♥♥♦♥①t♠rr♥t ♠♠rs ♦ t ♠♥♠♥t ♦r ♠st ♥♦t s♠t♥♦s② sr ♦♥ t

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

b = 2 b = 3 b = 4 b = 5 b = 6 b = 7 b = 8 b = 9 b = 10

1993

1999

2005

r t♦r strtr ♦ sss b♦rst♦r strtrs ♦r♠ ② ♦♥sr♥ rt♦rs t ♥ ♥rs♥ trs♦ ♦ ♦r ♠♠rs♣s B ≥ b♦t tt tr s ♦♥② ♦♥ ♥st♥ ♦ ♥ s♦t rt♦r t b ≥ 3 ♠♥ts ♥ ♥② ♦ t ②rs r Pr♥ t b− 7 ♦r s③ ♦ ♦rs ♥ t ♦r rt♦♥ ♦ ♦♠♣♥s ♥ t rs♣t ♦rs ♦t rs♦r t♠ s♦♥ ♥ ♠♦r t ♥ r

æ

æ

æ

æ

æ

æ

æ

æ

æ

à

à

à

à

à

à

à

à

à à

ì

ì

ì

ì

ì

ì

ì

1 2 3 4 5 6 7 8 9 10

0.001

0.005

0.010

0.050

0.100

0.500

1.000

1 2 3 4 5 6 7 8 9 10

b - core

Aver

age

sizeHn

orm

aliz

edL

ì 2005

à 1999

æ 1993

æ

æ

æ

æ

æ

æ

æ

æ

à

à

à

à

à

à

à

à à

ì

ì

ì

ì

ì

ì

2 3 4 5 6 7 8 9 10

0.0

0.2

0.4

0.6

0.8

1.0

2 3 4 5 6 7 8 9 10

b - core

Fra

ctio

nof

com

pan

ies

cover

edby

b-

core

ì 2005

à 1999

æ 1993

r rt♦rs ♥ ♦♠♣♥s ♦ b♦rs ♥♠r ♦ rt♦rs ♥ t rs♣t b♦rs t♦♣ ♣♥ rss ♦rt♠ s s t rt♦♥ ♦ ♦♠♣♥s tt r ♥ ② t rs♣tb♦r rt♦rs ♦tt♦♠ ♣♥

♥st② ♥ ♦r♣♦rt

♥tt② ♥t♦r ♦r ♦♥ssts ♦ rt♦rs tt r ② ♥tr ♥t ♥t♦r ♥ ♥s② ♦♥♥t ♠♦♥ t♠ss ♥st② ♦ t♥t r♣ D s ♥ ② t rt♦ ♦ t ①st♥ ♥♠r ♦ ♥s♥♦t |L|, t♦ t ♥♠r ♦ ♥s ♥ ♦♠♣t r♣ ♦ t s♠ s③♥♦t |N |

densityD =2|L|

|N |(|N | − 1),

s ② ♦♥strt♦♥ ♦♥♥ t♦ t ♥tr [0, 1] t ♣♥ ♦r strts tt t ♥st② ♦ b♦r sr♣s ♥rss tb ♥ tt t ♥st② ♦ t rs♣t ♦rs r♠♥s r② ♦♥st♥t♦r t♠ ♥ s♣t ♦ rs♥ ♦r s③ ♥ t♦♥ ♥ ssss t♦r♣♦rt r ♣r ♦r rt♦r ② t rt♦ ♦ st♥t ♦r ♦♠♣♥s t♦ t♥♠r ♦ ♦r rt♦rs t rt♦♥ ♥ tt ♦r ♦ ♥s② ♦♥♥trt♦rs ♣r♦② ②s t ♠♦r ♥sttt♦♥ ♣♦r t r ♥s♦♥sttt t ♦r ♥ t ♠♦r ♦♠♣♥s t② s♣♥ t s ♥♦t♦rt② ttts ♠sr ♦ ♦r ♣♦r s♦♥ ♥ t rt ♣♥ ♦ r t②♥rss ♦r t♠ s♦ t r♥t ♥ ♥ t ♥♠r ♦ ♦r ♠♠rs♣s♦s ♥♦t ♥ssr② ♠♥ tt ♦r rt♦rs ♥ r♠♥②s ♦r♣♦rt ♦r♥t♦r s♦ ♦♠ ss ♥♥t ♥②t♥ t sttsts s♦♥ ♥ t♦tt♦♠ ♣♥ ♦ r sst t ♦♣♣♦st

♥trt②

♦♠♣♠♥tr② ♣♣r♦ t♦ ♠sr♥ t ♠♣♦rt♥ ♦r ♥♥ ♦ rt♦rs s t♦ ♦♥sr tr ♥trt② ♥ t ♦r ♥t♦r ♦ rt♦r ♥tr♦s t C ♥♦t t rs♣t ♥② ♠trs ♦ t r ♦♥♥t♦♠♣♦♥♥ts ♦ D ♥ t rs♣t ②rs ♥ t V ♥♦t t st ♦ rt♦rs♦♥t♥ ♥ C s♦rtst ♣t t♥ t♦ rt♦rs u, v ∈ V s ♥♦♥s r♣ ♦s s ♥♦t ♥ssr② ♥q ♥ t ♥t ♦ t♦s dC(u, v) s ♥♦♥ s t r♣ st♥ t♥ t ♣r (u, v)

rst ♥trt② ♠sr ♦♥sr s ♦s♥ss ♥trt② ♠srs t st♥ ♦ ♥♦ t♦ ♦tr ♥♦s ♥ t ♥t♦r ♥ st②♣② ♥ s t r♣r♦ ♦ t s♠ ♦ ♦ss t♦ ♦tr ♥♦s♥ t ♥t♦r

closenessu = 1/∑

v∈V

dC(u, v) .

♥ ♦ t♦ ♦♠♣r t ♥trt② ♦ rt♦rs r♦ss ②rs ② t ♦s♥ss s♦r ♦ t rt♦r t ♠①♠ ♦s♥ss ♥trt②

æ

æ

æ

æ

æ

æ æ

æ

æ

à

à

à

à

à

àà

à à à

ì

ì

ì

ì

ì

ì

1 2 3 4 5 6 7 8 9 10

0

10

20

30

40

50

601 2 3 4 5 6 7 8 9 10

b - core

Core

den

sity

ì 2005

à 1999

æ 1993

æ

æ

æ

æ

æ

æ

æ

æ

æ

à

à

à

à

à

à

à

à

à à

ì

ì

ì

ì

ì

ì

ì

1 2 3 4 5 6 7 8 9 10

0

2

4

6

8

1 2 3 4 5 6 7 8 9 10

b - core

Core

pow

erHd

isti

nct

com

pan

ies

per

dir

ecto

rL

ì 2005

à 1999

æ 1993

r ♦r ♦♠♣♥s ♥ ♦r rt♦rs ♥st② ♦ b♦rs t♦♣ ♣♥ r♠♥s r② st ♦r t♠ s s t rt♦ ♦ st♥t ♦r ♦♠♣♥s t♦ ♦r rt♦rs ♦tt♦♠ ♣♥ ♥②t♥ ♦r ♥st② ♥ ♦r ♣♦r ♥rs s♣t t rs ♥ tr ♥♠r ♦ ♠♥ts ♦r t♠

♥ ②r ♥ ♦rr t♦ ♥♦r♠③ t s♦rs rt♦rs ♦ r ♠♦r ♥tr♥ ts s♥s s♦ ♥ ♣r♥♣ ttr t♦ r ♦t ♥t♦ t ♥tr♥t♦r ♦r str ♥ ♦♥ s♦

♥♦tr ♠sr ♦ t ♥trt② ♦ ♥♦ u s r ♥trt② ♦♥strt ② s♠♠♥ t ♥♠r ♦ ♥s tt ♥♦ s degreeu =∑

v∈V Cuv ♥tt② rt♦rs ♦ ♠♥② ♥s ♦♠♣r t♦ tr♣rs r ♥ ♥ ♥t♦s ♣♦st♦♥ t② r t♦ ♥♥ ♠♥② ♦tr ♣rs ♦r t② ttr ss t♦ rs♦rs tr♦ tr ♠♥②♥s t r ♥trt② ♦♥② ts ♠♠t ts ♦ rt♦rs ♥t♦ ♦♥t ♥ s ♥♦r♠t♦♥ ♦t t st♥ t♦ rt♦rs tt r ♥♦t♠♠t ♥♦rs ♦r♦r rt♦rs t ♠♥② ♦r ♠♠rs♣s rt② r r ② ♦♥strt♦♥ s♥ t ♦r s③ strt♦♥ s rtrst s tt s ♣tr ② ts ♠♥

r♦r s♦ ♦♠♣t t ♥t♦r ♥trt② ❬❪ ♦r ♥♦s ♥V ♥t♦r ♥trt② ss♥s s♦rs ♦ rt ♠♣♦rt♥ t♦ rt♦rs ♥t ♥t♦r s ♦♥ t ♣r♥♣ tt ♦♥♥t♦♥s t♦ s♦r♥ rt♦rs♦♥trt ♠♦r t♦ rt♦rs s♦r t♥ q ♦♥♥t♦♥s t♦ ♦s♦r♥♣rs ♥ t ♥ ♥t♦r ♥trt② s tt t qt② ♦♥s s ♠♣♦rt♥t s rt♦rs ♦ r ♦♥♥t t♦ ♠♥② ♥♥t♣rs ♥ ①♣t t♦ ♠♣♦rt♥t t♠ss ♣♣♦s t ♥t♦r♥trt② s♦r ♦ ♥♦ u ♥♦t eu s ♣r♦♣♦rt♦♥ t♦ t ♥trt② s♦r♦ ts ♥♦rs

eu =1

λ

∑

v∈V

Cuv ev ,

r λ s ♦♥st♥t ♥ ♥ rt t t♦r ♦ ♥trt② s♦rs ♥♠tr① ♥♦tt♦♥ s λe = C · e s♦s tt e s ♥ ♥t♦r ♦ Ct ♦rrs♣♦♥♥ ♥ λ t s ♦♥♥♥t t♦ ♦♥sr t ♥t♦r♦rrs♣♦♥♥ t♦ t rst ♥ ♦ C s♥ ts ♠♥ts r ♥♦♥♥t ♦r♥ t♦ t Prr♦♥r♦♥s t♦r♠ ♥ s♦rs ② t ♠①♠♠ s♦r ♥ ②r t♦ ♥♦r♠③ t t r s♦s tt ♦r rt♦rs r ♥♦t ♦♥② ♥s② ♦♥♥t ♠♦♥ t♠sst tt t② r s♦ ♥rs♥② ♥tr ♥ t ♥tr ♥t♦r s ♥♦tr rtrst tt ♦♥ ♥tt② ①♣ts ♥ t ♥t♦♥ ♦ ♥t♦r♦r

♦r sss♦♥ ♦ t ♥♥ tt ♣♦r ♥ ♥trt② r ♥♦t q♥t s ❬❪

æ

æ

æ

æ

æ

ææ

æ

æ

à

à

à

à

à

à

à

àà à

ì

ì

ì

ì

ì

ìì

1 2 3 4 5 6 7 8 9 10

0.6

0.7

0.8

0.9

1.0

1 2 3 4 5 6 7 8 9 10

b - core

Av

erag

ecl

ose

nes

sce

ntr

alit

y

ì 2005

à 1999

æ 1993

æ

æ

æ

æ

æ

æ

æ

ææ

à

à

à

à

à

à

à

à

à à

ì

ì

ì

ì

ì

ì ì

1 2 3 4 5 6 7 8 9 10

1

2

3

4

5

6

7

8

9

10

1 2 3 4 5 6 7 8 9 10

1

2

3

4

5

6

7

8

9

10

b - core

No

rmal

ized

aver

age

deg

ree

cen

tral

ity

ì 2005

à 1999

æ 1993

æ

æ

æ

æ

æ

æ

æ

æ

æ

à

à

à

à

à

à

à

à

à à

ì

ì

ì

ì

ì

ì

ì

1 2 3 4 5 6 7 8 9 10

0.0

0.2

0.4

0.6

0.8

1 2 3 4 5 6 7 8 9 10

b - core

Av

erag

eei

gen

vec

tor

cen

tral

ity

ì 2005

à 1999

æ 1993

r ♥trt② ♦ rt♦rs♦r♠③ r ♥trt② ♠srs ♦ b♦r rt♦rs ♥ t rs♣t②rs ♦s♥ss t♦♣ r ♥tr ♥ ♥t♦r ♦tt♦♠ ♥trt②r♠♥ r② st ♦r t♠

♦r Prsst♥ ♥ ♥ r♥♦r

❲ r tt t strtr rtrsts ♦ rt♦r ♥tr♦s rst ♦r t♠ ♥ s♣t ♦ ♥s ♥ ♦r♣♦rt ♦r♥♥ ♥ rs♥ t r ♥♠r ♦ ♠♥ts ♦tt ② t ♣rsst♥ ♥ ♥t♦rstrtr ♥t t♦ ♥stt tr ♦r ♦ t ♦r strtr ♣♥s♦♥ t st♥s ♦ ♣rtr ♥ts

♦t♦♥ ♦ ♦♠♣♥② ♥s

♥ ♠♣♦rt♥t s♣t r ♦♥r♥s t ♥s ♥ t ♦♠♣♥② ♥t♦r rt♠ ♦t♦♥ ♦r ♦♥st ♣r♦s rs s♦♠ ♥♦t♦rt② ♣ttr♥s ♥ t ♦♠♣♥② ♥t♦r ♥t ♥s ♦ r t ♦♠♣♥s tt r♠♥ ♥ t s♠♣ ♥ t ♥①t ♣r♦♥ ♥♦t ♠r ♥ t ♠♥t♠ ♦ ts ♥s rst ♥ ♣ ♥ t ♦♦♥ ♣r♦ ♥ ss t st ♦♥ rt♦rs ♦♥st♥t② ♣rt ♦ ♦t ♦rs ♥ t♦♥ rt♦rs ♥rrt t♦ r♥♦r ①st♥ ♥s t♥ sr♥ ♦♥ r ♦♥ ♦rs t ♦ ts rt♦rs r r② sr♥ ♦♥ t st♦♥ ♦r ♥ t ♣r♦s ♣r♦ ♥ t② ♣♣♦♥t♠♥ts♦♥ r

♥ t r♠♥♥ ss r ♥ ①st♥ ♥ s ♠♥t♥tr♦ t rrt♠♥t ♦ ♥ rt♦rs t♦t ♦ rt♦rs s ♣♣♦♥t t♦ t ♣♦st♦♥s ♥ ts rt♦rs t♥ sr ♦♥ r♦♥ ♦rs t ♦ ts rt♦rs t st♦♥ ♠♥t ♥ t ♣r♦s ♣r♦ ♥ t② sr ♦♥ r ♦♥ ♦rs ♦ ♦sr tt ♦t ♦ t ♦♠♣♥② ♥s r ♥ ♠♥t♥ t♥ ♣r♦s s ♦♥sst♥t t rr ♥♥s ②❬❪ ♦♥ t r♦♥sttt♦♥ ♦ r♠♥ ♦r♣♦rt ♥tr♦s ♣♥ ♥ ♠♥tt sst♥t ♥♠r ♦ ♥s ♥ t ♥t ♦♠♣♥② ♥t♦r ♠t ♥♥t♥ ♥ ♥ tt t s♠♣ ♣r♦s ♥ ♦s♥ s♥t② r ♣rt t♦ rr♥t ♦r r♣♣♦♥t♠♥t s♦♥s t ♦sr

♣r♥t ♦ r♦♥strt ts ♠♦♥ r♠♥ ♦♠♣♥s s ♦r t♦ t♠sr t♥ ♣r♦s② ♦sr ♥ t ❯ ❬❪ r♦♠ ♥t♦r ♦r ♣rs♣t t♦ ♥trst♥ t♦ r② tr t ♣r♥t ♦ r♦♥sttt ts ♠♦♥ tr② rst ♦r ♦r♣♦rt♦♥s ♥ t ❯ s sst♥t② r t♥ ♥ t ♦r♥tr♥s ♥ ③r s♠♣

♠♥ rt♦r t tr ♠♥ts ♥ s♣♣♦s tt s s ♦♥ t ♦r ♦♦♠♣♥② ♠♥s t♦ ♣ r ♦♥ t ♦r ♦ ♦♠♣♥② ♦r strt rs♦♥s t♦ ♦rs s ♥trsts s s♦ srs ♦♥ t ♦r ♦ tr ♦♠♣♥② ♦♥sr t ♥ t♥ ♥ ♥t♥t♦♥ t ♥s ♥ r ♥♥t♥t♦♥②♣r♦ts

r♦♥sttt♦♥ ♦ ♥s ♦ rt♥② s♠ t♦ ♥t ♣♥♥ ♦r strt♦♥♥tt② ♠♦♥ r♠♥ ♦r♣♦rt♦♥s

♦♥② ts rs sst tt ♦♠♣♥s s♠ t♦ ♣rr t ♣♣♦♥t♠♥t ♦ rt♦rs ♦ r② sr ♦♥ sr ♦tr ♦rs s♣rtr② tr ♦r t ♠♥t♥♥ ♦ ♥sttt♦♥ ♥s ♦r t♠ ts rtr ♦t tt ts rt♦rs r ♣♣♦♥t ♦r ♣r② s♣rs♦r②♣r♣♦ss s♥ t ♦rt ♥♦ ♥ ♠♦♥t♦r♥ ♥ ♦ ❳ ♦♠♣♥ss sr② ♦♥sr ♥ ♥ ♦♦ ♦♠s ♥rs♥② ♣r♦t ♦♥ ♦ t ♣♣♦♥t♠♥ts s ♥ ①t ♣♦st♦♥ rq♥② strt♦♥♦ ①ts s♣rs♦r② ♦r ♠♠rs♣s ♥ ♥rtss s♦stt s♦♠ ①ts t♦♥② sr ♦♥ ♣ t♦ t♥ ♦tr ♦rs

rt♦r r

♥ ♠t♣ ♦r ♠♠rs♣s s♠ t♦ ss♥t ♦r ♦t t ①st♥ ♥ t ♣rsst♥ ♦ ♦r ♥t♦r s♦ ♥stt t sr♦ rt♦rs ♦r t♠ t ♦ t♦t ♦ rt♦rs ♥ t s♠♣ r st ♣rs♥t ♥ s sr rt ♦ ♦r t tr♥st♦♥ ts r s r♥ t rst s♦♥ tr♥st♦♥ ♣r♦ ♦ t sr♥ rt♦rs ♥ ♠♥ts ♦st t st ♦♥ ♠♥t t ts ♣r♥ts ♦♥tt rt♦rs t ♠t♣ ♠♠rs♣s ♠r② r sr♣r♦t② t♥ t st ♠♦rt② ♦ rt♦rs t s♥ ♠♥t tsr ♣r♦t② ♦♥t♦♥ ♦♥ t ♥♠r ♦ ①st♥ ♠♥ts s ♦r ♦r ♠♠rs t s♥ ♠♥t t ♥rss t♦ ♦r rt♦rs t t♦ ♠♥ts ♦r t♦s t tr ♠♥ts♥ ♦r t♦s t ♦r ♦r ♠♦r ♠♥ts t s♠s r t♦s② tt t ♣rsst♥t strtr ♦ r♠♥②s ♦r♣♦rt ♥t♦r s r♥② t rrt♠♥t s♦♥s ♦ r ♦♠♣♥s r rtr③ ② ♣r♦ss ♦ st r♣♠♥t tt ①♣rsss ts ♥ t rs ♦♥t ♠♥t♥♥ ♦ ♥s ♠♦♥ ♦♠♣♥s ♥ t ♦♥t♦♥ sr ♦rt♦rs ❲ t st ♠♦rt② ♦ rt♦rs ♥trs ♥ ①ts t ♦r♣♦rt ♥t♦r t♦t r ♥ ♣rtr② ♥tr ♥ t s♠ ♥♠r♦ ② ♦♥♥t ② rt♦rs rr♥ts ♣rsst♥t ♥t♦r ♦r ♦rt♠ ♦r♦r tt♦♥s ♥ t st♥s ♦ ② ♣②rs r ♠tt ②t r♦♥sttt♦♥ ♦ ts ♠♦♥ r ♦r♣♦rt♦♥s ♦ ♦r rt♦rs t♠t♣ ♠♠rs♣s ♦ ♦rr♦♦rt ts ♠ ♦♥sr t tr♥♦r♥ t ♥trt② ♦ ♦♠♣♥s ♥ rt♦rs t♥ ♣r♦s

s rs r s② t r♦♠ t tr♥st♦♥ ♠trs ♥ ♣♣♥①

♦♠♣♥s rt♦rs1993− 1999 1999− 2005 1993− 1999 1999− 2005

sr♦rs r♦♣♦ts

r

♥trt②

♦t ♦s♥ss ♥ (t)

♥ (t+ 1) ♦t

♥ ♥ (t) ♥ (t+ 1) ♦t

♥♦r♠③♥ (t)

r♥ (t+ 1)

♥

♥

♥trt②

|∆| ♦s♥ss ∆

♥♠r |∆|

♥ ∆ ♥♠r |∆|

♥♦r♠③ ∆

r♥♠r

r♥♦r tt② ♥ ♦♠♣♥② ♥ rt♦r ♥t♦rs ♥♦tt♦♥ ♦r r ♥trt② ♠srs rrs t♦ rs ♦r r♦♣♦ts ♦t ♥ t ♥trt② ♦ sr♦rs♥ t rr♥t ♥ (t) ♥ ♥①t ♥ (t+1) ♣r♦ ♥♠r s ♦r t ♥s ♥ ♥trt② ♥t ♦r♥ t♦ t ♣r♦r sr ♥ ts st♦♥

r♥♦r ♥ ♦♠♣♥② ♥ rt♦r ♥trt②

❲ strt ② t♥ t ♥ ♥ ♦ t tr ♥trt② ♠srs♦r sr♥ ♥♦s ♥ t ♦♥♥t ♦♠♣♦♥♥t strts tt♦t t♦ trs ♦ t ♦♠♣♥s t ♦♥② ♦♥ tr ♦ t rt♦rs sr♦♥st ♣r♦s s♣♥ ♦ rt♦rs s ♦♦② ♠t t s♠ s ♥♦t ♥ssr② tr ♦r ♦r♣♦rt♦♥s ts t t tt ♦t ♦ rt♦rs t ss t♥ ♦ ♦♠♣♥s r♦♣ ♦t t♥ ♣r♦ss ② ts ♥♦t ♥①♣t ♥ s♣t ♦ t ①♣t r♥ ♥ ttt ♠♥ s♦t ♥ ♥ ♥trt② s ♠sr ♦ rt② ♠♦♥sr♦rs s t s♠ ♦ ♠♥t ♦r ♦t ♦♠♣♥s ♥ rt♦rs♥ tt s♦t ♥s ♥ ♥trt② r rtr s♠ ♥ ♦t ss

♥ ♦rr t♦ ♣r♦♣r② ♦♠♣r t tr♥♦r tt② t♥ ♦♠♣♥s♥ rt♦rs ♥ t♦ s t s♦t ♥s ♥ ♥trt② t ♥♠r ♠sr ♦ ♣rsst♥ ♥ ♥trt② tt ♦♥ts ♦r t r♥t ss ♦ t ♦♠♣♥② ♥ rt♦r ♥t♦rs ♥ ♦r ♥♠r s ss♠ tt ♥♦s ♥trt② ♦ ♥ t♦ r② ♦sr ♥trt②♥ ♥①t ♣r♦s s♠♣ t q ♣r♦t② ♦rrs♣♦♥♥ t♦ ♥♦r♠②r♥♦♠ rr♥ ♦ ♥♦s s t r s♦t ♥ ♥ ♥trt②♦ ③r♦ ♥ t s ♦ ♣rt ♦♥srt♦♥ ♦ t rt ♣♦st♦♥ ♦♥♦s ♥ ♦ q t♦ t ♥♠r ♥ s ♦ ♦♠♣t②r♥♦♠ rr♥ ♦ sr♥ ♥♦s ♦r ♥trt② ♠srs ♦srtt t rt♦ ♦ t ♥♠r t♦ t ♦sr s rr ♦r ♦♠♣♥st♥ ♦r rt♦rs ♦t s s♦♥ tt sr♥ ♦♠♣♥s ①t s♥♥t② ss r♥♥ ♥ tr ♥trt② t♥ sr♥ rt♦rs♦♠♣r♥ r♦♣♦ts t sr♦rs ♦t ♦r ♦♠♣♥s ♥ rt♦rs ♥ tt sr♦rs r ②s sst♥t② ♠♦r ♥tr t♥ r♦♣♦ts s♦r♣♦rt ♥ ♥ tt t ♥♦r♠③ r s ♦t ♦♥ ♦rr ♦♠♥t r ♦r sr♦rs t♥ ♦r r♦♣♦ts ♦r♦r t r② ♦ r ♥t♦r ♥trt② ♦ r♦♣♦ts rtr ♠♣s tt t ♠♣♦rt♥♦ t r♦♣♦ts ♥♦rs s s♦ r② ♦ ♦♥ r ♥ s♠♠r②♦t ② ♥tr ♦♠♣♥s s s rt♦rs t♥ t♦ st② ♥tr r♦♣♦ts r ♦t ♥ ♠♦r ♣r♣r ♣♦st♦♥s ♦ t ♥t♦r ♦♠♣♥②♥t♦rs ①t ss tr♥♦r tt② t♥ rt♦r ♥t♦rs ♦t ♥ tsr ♦ sr♥ ♥♦s t s♦ ♥ t ♥trt② ♥s ♠♦♥ sr♦rs

tr ♠srs ♦ ♥trt② ①t st rs ♥ r ♥trt② t♥ t♦ ♥ ♥ ♥rs t♥ t♦ s r♣♦rt ♥ s s ♥ ♥t t s ♥s♣t♦♥ ♦ t ♥t♦r strtr ♥ r s♦s ♥ ♥rs♥♥♠r ♦ ♣r♣r ♥♦s ♥ ♥ ♥sr ♦rs ♥

♥t②♥ ♦♠♣♥② r♦♣s

r ♥♥s s♦ r str♦♥② sst tt s r s t ♣rsst♥ ♦ ♦r♣♦rt ♥t♦r ♦r s ♦♥r♥ ♦s②♥rt rt♦r rtrsts r rss ♠♣♦rt♥t t♥ t st rrt♠♥t ♣rts ♦ ♦♠♣♥s ♥ ♦ t♦ ♥t② qs ♠♦♥ t ♦♠♣♥s ♥ ♦r tst ♥s ♣rsst♥t strtrs s♦ ①st ♥ t ♥t♦r ♦ ♦♠♣♥② ♥tr♦s

♦ ♥t② ♥ s③ ♦♥♥t r♦♣s ss♥t② s ♣r♥♣♦♠♣♦♥♥t ♥②ss ♥ ♦♠♥ t t ♠t♥ ♦rt♠ ♣r♦r s sr ♥ t ♥ t s♣♣♠♥tr② ♥♦r♠t♦♥

r s♦rt ♥② ♠trs ♦r ♥ ♥♠r ♥ s③ ♦ ♥t qs s rs♥ ♥ t♦ s♣rsr♦r♣♦rt ♥t♦r ♦r t♠ ②t t ♥ ♥tt ♦r ♥t♦r ♦ ♦t ♦③♥ ♠♣ ♦r♣♦rt♦♥s

r s♦s t rs♦rt ♥② ♠trs ♦r ♥ ❲ ♣♦t ♦♠♣♥② qs t s♥♥ s③ r♦♠ t t♦ rt ♦♦ ②r♠s tt ♦ ♥♦t ①t s♣ ♦♥♥t♦♥ ♣ttr♥s ♥ r② ♦t ♥ r♦ i ♥ ♦♠♥ j r♣rs♥ts ♥ t♥ ♦♠♣♥② i ♥ j t s♣ ♥ ♣♦st♦♥ i, j ♦ ♥t tt t t♦ ♦♠♣♥s ♥♦rt♦rs ♥ ♦♠♠♦♥

♥ t s st ♣♦ss t♦ t ♦r ♦ ♦r ♥t♦r ♥t♦ ♦r♣♣♥sr♦♣s t ts strtr s♠s t♦ ♥ ② ♦r t♠ ♥♠r♦ r♠s tt ♦♥ t♦ q s ♦t ♥ ②t ts ♥♠r s s t s③ ♦ ♥t qs s sr♥♥ ♦r t♠ r r ♦rt♥ trt♦♥ r♠♥ ♦r♣♦rt ②ts tt ♣rsst♥t② s♦ ♣ ♥t rst qs ♥③ ②r ♦♠♠r③♥ ts ♥ ♦t♥ t♥s ♠♥s ②ss♥ r♣♣ ♥ ❱♦s♥ s ♣♣♥①♦r ts s s③t♦♥ ♦♥r♠s ♦r rr ♥♥s tt ♥ t♦r ♦ ♦♥♥t♥ss ♥ t ♦r♣♦rt ♥t♦r s rs♥ ②

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

sss♦♥

❲t ss♥t② ♦♠♣s r ❲ s♦ tt t ♦r♣♦rt♥t♦r ①ts ♦r tt ♦s ♥♦t ♦♠ ss ♥♥t ♦r t♠ ♥ s♣t♦ s♥♥t r♦r♠s ♥ ♦r♣♦rt ♦r♥♥ ♥ sst♥t r♥♥ ♥♥tr②♥①t ②♥♠s ♠♦♥ ♦r♣♦rt rt♦rs r r str♦♥ ♥t♦♥s tt st rrt♠♥t s♦♥s ♦ t r② rst ♦♠♣♥s rrs♣♦♥s ♦r ♦r ♣rsst♥ ♥ ts ♣r♦ss ♣♣rs r② ♥♣♥♥t ♦ ♦s②♥rt rt♦r rtrsts ♥ ♦s ♥♦t rqr ♠t②♦♥s♣rt♦r ♦ ♣s t str♥s ♥ t r♦♥

♥ t♦♥ t ①st♥ ♦ ♦r ♣r♦s ♥ tr♥t ①♣♥t♦♥♦r t s♠♦r t ♥ ♦r♣♦rt ♥tr♦s ♥ t s♥ ♦ srr strt♦♥s ♠♦♥ rt♦rs ♦r r♠s ♥ ♥ ♥♠r♦s s♦ ♦♥t①ts t ♥♠r ♦ ♥s ♥ ♥♦s ①ts rtrst s ♥ ♦s♥♦t s♣♥ ♥♦ ♦rrs ♦ ♠♥t t♦ ♣♦r ♦♥ ♦ s♣t tt ♦r strtrs r ♠♣♦rt♥t ♥ ♦tr s♦♦♦♥♦♠ ♦♥t①ts s ♥ rtr♥ t♦ ♥ ♠♣♦rt♥t strt♦♥ ♦ ts ♣♦♥t ♥ ♥♥♠rts ♦

r♠♥♥ ss ♦♥r♥s t t② ♦ ♦r ♥♥s ②♦♥ r♠♥②s♦♥ ♥r rst ♣② tr ♦♠♣♥s ♦ ♥ rs♦♥② ①♣t♦r rsts t♦ r♣rs♥tt ♦ t ♥tr r♠♥ ♦r♣♦rt ♥t♦r♥ r♦♠ t ♠♦r r♥t rsts ② ❬❪ ♦r s♥ ②r tr s rs♦♥ ♦r ♦♣t♠s♠ ♦♥sr♥ t rst r♠♥ ♦♠♣♥s ♥ ♦♥t♥ ♦r ♠♦r t♥ ♦ tt ②rs ♠rt ♣t③t♦♥ ♦ r♠♥②s st♦ ①♥ ts örs t② ♦sr r② s♠r ♠♥ts ♥ t ♠①♠♠ ♥♠r ♦ ♦r ♠♠rs♣s ♥ ♥ t ♥st②♥ r ♥trt② ♦ sss b♦rs ♦♥ ♥ ♠♦r ♠♣♦rt♥t②r♦♠ t ♣♦♥t ♦ t ♣rs♥t st② t② ♥ tt t ♣r♦♥♦♥ ♦rstrtr ♥ r♠♥②s ♦r♣♦rt ♥t♦r s r② ♦r♠ ② ♠♣♦♠♣♥s tr② st②♥ ♦r ♦s ♦♥ t ♦♥ ♥r rst ♦♠♣♥s r ♥ t② ①♠♥ t ♦r♣♦rt ♥t♦r ♥ s♥ ②r ♦rt② ♥♦r♠t♦♥ ♦♥ t t♠ ♦t♦♥ ♦ t ♥t♦r

s ♦r ②♥♠ ♥②ss rs ♦♥ t ♦tr ♥ t s ♥ trst trt② t♦ ♦rt② ♦r♣♦rt♦♥s tt r rs♣♦♥s ♥♦t ♦♥② ♦r t ①st♥ t s♦ t ♣rsst♥ ♦ ♦r ♦r t♠ ❲ t ♣rs♥ ♥♣rsst♥ ♦ ♦r ♦r♥t r♦♠ t ♣♣♦♥t♠♥t s♦♥s ♦ t rst♦r♣♦rt♦♥s ♦r ♥♥s tt r♦♦♠ ♦r t r♥ ♦ ♥

rt♦rs r♦♠ ♠r♦s♦♣ ♣♦♥t ♦ t r♥♥ ♥ ♥tr②♥①t ②♥♠s ♦ ♥ rt♦rs ♥ ♦r s♠♣ ♥st ♠♣s③ ts♠♥② ①s ♠♣♦rt♥ ♦ t ♥♠r ♦ ♠♣ ♠♥ts tt rt♦r s ♠t t ♥ ♣♦♥t ♥ t♠

sr♥♦r♥ ♠♥s♠ ♦ st r♣♠♥t ♦ ♦r ♠♠rss r♠♥ ♥ ♣ ♥ s♣t ♦ t ♣♣r♥t ♥ ♦ t ♦r♣♦rt ♥t♦r ♦ ♣r♣rs r ♥ r♣♦rts ♦ t ♦r♣♦rt ♥t♦rs tr rt② ①rt s♥ st rrt♠♥t ♠♥t♥s t s♠ ♦rrtrsts ♦ t ♦r♣♦rt ♥t♦r ♥ t s♥ ♦ ♣♦r r strt♦♥ ♠♦♥ rt♦rs ♦r ♦♠♣♥s s trt♦♥② ♥♥♦ t♦ ①♣♥ t s♠♦r ♣r♦♣rt② ♥ ♦tr ♠♣r② ♦sr♥t♦rs

♦ r t ♠♥ ♦♥trt♦♥ ♦ ts ♣♣r s rt♥② ♦ sr♣t ♥tr ❲ ♥♦t ♣r♦r♠ ♥② ♦♥r♠t♦r② sttst ①rss♥ t trt♦♥ s♥s s♦ tr s r② tt ♥②t♥ ♥ s② r♦t ♦ ♦r tr ♦r♣♦rt ♦r ♥♥s t st♥s ♦ ♥r♠s ♦r t♠ t ts r qst♦♥s tt ♦ sr② rss ♥tr rsr rtss ♦ t♦ tt t ①st♥♥ ♣rsst♥ ♦ ♦r s ♥trst♥ ♥ ts ♦♥ rt ♥ ♦s ②♦♥ ♦♥r♥s rr♥ ♣rssr r♦♣ ♥♥ s♣② ♥ t ♦♠st♦ sss ♦ s②st♠s rs♥ ♦r rt② t s ♥ s♦♥ tt ts②st♠ ♦♦r♥t♦♥ ♦ ♦♣♥♦♥s ①♣tt♦♥s ♦r ♥ ♥♠ s♣rtss ♥♦r♠♦s② tt ② t ①st♥ ♦ ♥t♦r ♦r ♥ ♦ r② ♠ s②st♠ ♠♦r r ①t② s ♦ tt ♥ ♦r ♥st♥♦ t rs ♦♦r♥t♦♥ ♦ tr♥ ♣♦st♦♥s ♥ ♥♥ ♠rts tt♣r r② ♥♥ rss r♦♠ ♦r ♣rs♣t t s rtr ♥♦t♦rt②tt ♥♥ ♠rts s♦ ①t ♦r ♥t♦r strtr t st ♥ t ♥st♥s ♦r t ♥ s♦ r ❬❪ ♥t♥ t tr♦r ♠♣♦rt♥ ♦ ♦r ♥t♦rs ♥ t s♦ s♥s

♥② ♣♦②♠rs r t♦ ♠ ♦r rt♦♥ ♦ ♣rssr r♦♣♥♥ ♦r rtrsts s♦ t t ♦rr♦♥t ♥ t s♥ ♦♣♦② ♥ ♦r♣♦rt ♦r♥♥ ♣rtr② ♥ t ♦ t t tt t rstrt♦♥s tt r r② ♥ ♣ t ♥♠r ♦ s♠t♥♦s♦r ♣♣♦♥t♠♥ts ♦r t ♠①♠♠ tr♠ ♦ sr ♦r ♣♦t♥t r♣♣♦♥t♠♥t r ♦♦s② ♥♦t s♥t t♦ rs t ♥♥ ♦ t ♦r♥t♦r ♠ ss ♣r♥t ts ①st♥

♥♦♠♥ts

s rsr s s♣♣♦rt ② t ❱♦s♥ ♦♥t♦♥ tr♦ tr r♥t♦♥ ♦♠♣① t♦rs s ♥trs♣♥r② P♥♦♠♥ ❲ r ♥tt♦ ♠♦♥ r♥♦ ♦r s sss♦♥s ♥ ♦♠♠♥ts

r♥s

❬❪ r♥♦ ♦ ♥ ♥t ♥♦t ♦♥ ♥sttt♦♥rr② ♥ ♦tt② ♥ ♥♥ ♠rts r♦♣♥ ♦r♥ ♦♥♥

❬❪ ♠♦♥ r♥♦ ♥ s ♦ t♦r strtr ♥ N ♣♥♥ ♥ ♥ts r♥ ♠♦s ♦r♥ ♦ ♦♥♦♠ ②♥♠s ♥ ♦♥tr♦

❬❪ rás ♥ rt ♠r♥ ♦ s♥ ♥ r♥♦♠ ♥t♦rs♥

❬❪ ttst♦♥ ♦♥ ♥ ❲s s♦♥ ♠♥ ②♥♠s♥ ♦r♣♦rt ♦rs P②s

❬❪ t♥♦ ttst♦♥ ♥ t♥③r♦ ttst ♣r♦♣rts ♦ ♦r♣♦rt ♦r ♥ rt♦r ♥t♦rs r♦♣♥ P②s ♦r♥

❬❪ ②r ♥ ö♣♥r s♥trt♦♥ ♦ ♦r♥③ ♣ts♠r♠♥ ♦r♣♦rt ♦r♥♥ ♥ t s ❲st r♦♣♥ P♦ts

❬❪ P ♦♥ P♦r ♥ ♥trt② ♠② ♦ ♠srs ♠r♥♦r♥ ♦ ♦♦♦②

❬❪ P♣ ♦♥ t♦r♥ ♥ t♥ ♣♣r♦s t♦ stts s♦rs♥ q ♥tt♦♥ ♦r♥ ♦ t♠t ♦♦♦②

❬❪ t♣♥ P ♦rtt ♥trt② ♥ ♥t♦r ♦ ♦ t♦rs

❬❪ t♣♥ P ♦rtt ♥t②♥ sts ♦ ② ♣②rs ♥ s♦ ♥t♦r♦♠♣tt♦♥ ♥ t♠t r♥③t♦♥ ♦r②

❬❪ t♣♥ P ♦rtt ♥ rt♥ rtt ♦s ♦ ♦r♣r♣r②strtrs ♦ t♦rs

❬❪ t♣♥ P ♦rtt ♥ P② ♦str ♥t♦r ♣r♠ ♥ ♦r♥③t♦♥ rsr r ♥ t②♣♦♦② ♦r♥ ♦ ♥♠♥t

❬❪ ♥ rss ♦s♣ s③ ♥r r ♥ ❲♥♣♥s ♥ st♦ ♦ ♥t♦rs ♥ ♦r♥③t♦♥s ♠t ♣rs♣t ♠② ♦ ♥♠♥t ♦r♥

❬❪ ♦ r ♥ t♥③r♦ ♦r♣♦rt ♦rs ♥t♦rs P②s

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

❬❪ s ♥ r ♠♦♥② ♥tr ♥♥♦t ♦ ♦♠♠r ♥s ♥ t ❯ s②st♠ ♦ ♦r♣♦rt ♦r♥♥ ♠♥strt♥ rtr②

❬❪ r s ♥ ❨♦♦ ♥ ❲②♥ r s♠ ♦r ♦ t♠r♥ ♦r♣♦rt t trt r♥③t♦♥

❬❪ ♦s♣ s③ s ♥t♦r t♦r② ♦ ♦r♥③t♦♥ ♦r ♣ t♦ ts ♣r♦♠ss ♥♠♥t ♥ r♥③t♦♥

❬❪ P ♥s ♥ ♠♥♥ ❲♥ ♦ ♥tr♦s ♠ttr tr♥ts♦rs ♦ ♥♦r♠t♦♥ ♥ ♥tr♦ ♥♥ ♠ ♣s

❬❪ ♠sr ♥ ♦ t ♦r♣♦rt ♦♠♠♥t② ♠str♠ ❯♥rst② Prss

❬❪ Pttr ♦♠ ♦r♣r♣r② ♦r♥③t♦♥ ♦ ♦♠♣① ♥t♦rs P②s

❬❪ ♦s♦♥ ♣♣ trt t ♥②ss ♣r♥r ❨♦r

❬❪ P r♦s ♥ ♦♥s ♥trt② ♥ ♦r♣♦rt ♥tr♦ ♥t♦rst② ♥ stt② ♠ rtr②

❬❪ s ♦ ♠♦♥ r♥♦ ♥ ♦♠s ① s♠ ♦r ♦t r♠♥ ♦r♣♦rt ♦r ♥t♦r ♦♠♣tt♦♥ ♥ t♠tr♥③t♦♥ ♦r②

❬❪ t ♥t③ ♥ rt③ ♥tr♦♥ rt♦rts ♥ ♥trstr♦♣ ♦r♠t♦♥ ♠r♥ ♦♦♦

❬❪ ③r ❲t ♦ ♥tr♦s ♦ ♥ ♥②ss rtq ♥ sss♠♥t ♦ rsr ♦♥ ♥tr♦♥ rt♦rts ♥♥ r ♦ s♦♦♦②♣s

❬❪ ♠♥ strtr ♥ ♥t♦♥ ♦ ♦♠♣① ♥t♦rs

❬❪ ♠♥ t♦rs ♥ ♥tr♦t♦♥ ①♦r ❯P ❨♦r

❬❪ r ♠♥ ♥ r♥ ♥♥ ♥ t♥ ♦♠♠♥t②strtr ♥ ♥t♦rs P②s

❬❪ r ♠♥ t♥ tr♦t③ ♥ ♥♥ ❲tts ♥♦♠ r♣s t rtrr② r strt♦♥s ♥ tr ♣♣t♦♥sP②s

❬❪ t Pr♦♥ ♠② s ♥ ♦r ②♦ ♥tr♦r♥③t♦♥ ♥t♦rs t t ♥t♦r r ♦ t ♠♣r trtr ♦♥ ♦♥t♦rs ♦r♥ ♦ ♥♠♥t

❬❪ rt trtr ♥ ♦♠♣① t♦rs t ♦ts P②s ♣r♥r r♥

❬❪ rr② ♦♥s ♥ ♦♠ ①♥r ♠ ♦rs ♠♦♥ ♥tr♦♥rt♦rs t♦r strtr ♥ st♥ ♥ ♣rtt r♣s ♦♠♣tt♦♥ t♠t r♥③t♦♥ ♦r②

❬❪ ♥ttr strtr ♦r ♦ ②rs ♦ s♠♦r rsr♦ t♦rs

❬❪ ♦r r②ö ♥ P♣♥♠♦♦r♥ ♥t r stsrt ♠ ③s♥trr ♦♦♣rtt♦♥s③♥♥❩tsrt ür trsrtst

❬❪ t♣♥ ♠♥ t♦r strtr ♥ ♠♥♠♠ r ♦t♦rs

❬❪ ♦r♠ä r♥♦ ss ♥ ❲ ②r t♦♣♦♦② ♦ ♥tr♥ ♣②♠♥t ♦s P②s

❬❪ ♥ rstr tr♥s ♥ r ③r r♦♥t r♦♥sttt♦♥♥ t ♥t♦♥s ♦ ♥tr♦r♥③t♦♥ ♥tr♦s r①♠♥t♦♥♠♥strt ♥ rtr②

❬❪ r♥ ❯③③ s ♠r ♥ ① s♦s ♠♦r♥t♦rs ♥ ♠♥♠♥t s♥ rsr r r♦♣♥ ♥♠♥t

❬❪ ❯ ♦♥ ①r tt♦r ♦♥ s♣tr str♥ ttsts ♥ ♦♠♣t♥

❬❪ ❲tts ♥ tr♦t③ ♦t ②♥♠s ♦ ❵s♠♦r♥t♦rs tr

♣♣♠♥tr② ♥♦r♠t♦♥

str♥ Pr♦r

r r ss♥t② t♦ str♠s ♦ trtr t t tt♦♥♦ r♦♣s ♥ ♥t♦rs ❬❪ trt♦♥ ♣♣r♦ s r♣ ♣rtt♦♥♥ ♥ s♣ts t ♥t♦r ♥t♦ ① ♥♠r ♦ sr♣s ② s♣tr♦♠♣♦st♦♥ ♦ t s♦ r♣ ♣♥ ❬❪ r♣ ♣rtt♦♥♥♦rt♠s ♥ ♦♠ r② t♠ ♦♥s♠♥ t t ♠♦r sr♦s ♦♥r♥ s♦♥♣t s t ♥♠r ♦ s ♣rtt♦♥s s ♥r② ♥♦t ♥♦♥♦♠♠♥t② tt♦♥ tr♦r s ♦♣ ♦rt♠ ♣r♦rs tt♥♦♥③ t ♥♠r ♦ sr♣s ♥ t ♣rtt♦♥♥ ♣r♦ss ♦r ♥st♥② trt r♠♦ s ♦♥ t t♦♥ ♦ t♥♥ss s♦rs ❬❪❲ ♠♣♦② ♠①tr ♦ ts t♦ ♣♣r♦s r strt♥ r♦♠ ♣r♥♣ ♦♠♣♦♥♥t ♥②ss P ♥ ♦♠♥♥ t t s♦r♥ ♦rt♠tt rts r♦♣s s ♦♥ t rst ♦♠♣♦♥♥ts t♦t ♣r♥♥ t♥♠r ♦ sr♣s ♦♠♥t♦♥ ♦ P ♥ s♦♠ ♠t♥ ♦rt♠r♣rs♥ts rs♦♥ tr♥t t♦ ♦♠♠♥t② tt♦♥ ♦rt♠s ♥ ts♦ s♥s s t s③ ♦ tsts s ♥r② s♠r t♥ ♥ t♥tr s♥s

rst t t ♥② ♠tr① ♦ t r♠ ♥t♦r ♥ st♥r③ ts ♦♠♥s ② strt♥ t ♦♠♥ ♠♥ ♥ ♥ ② tst♥r t♦♥ ♦ ♦♠♥ ♥trs s ♥ ♥② ♠tr① s ♥♦tB ♦♠♥ ♥trs ♥ ♥♦ ♥tr♣rt s t rt ts ♦ t♦♠♣♥s ♥s t r♦ ♥trs rs♠ t rt tt♥t♦♥ r♠rs tr♦ ♥s r♦♠ ♦tr r♠s ❲ ♠sr t ♦rrt♦♥s ♦ ♥♣ttr♥s ② t♥ t ♠♣r ♦rrt♦♥ ♠tr① R = c−1

BTB ♦

♥ s t♦ ♥r r♠s s♠r rt ts ♥ tr ♥ ♣ttr♥ss ♦♥ ts ♦rrt♦♥ ♠tr① ♦♠♣t ♦r ♥ rs t ♣r♥♣♦♠♣♦♥♥ts F r ♥r ♦♠♥t♦♥s ♦ t ♦r♥ rs stt F = YB ♦♠♥ t♦rs ♥ Y rr② t ts ♦r ♥r ♥ t ♥ s♦♥ tt t s♦t♦♥ t♦ ts ♣r♦♠ ♠♦♥ts t♦s♦♥ ♦r F = VB r Y = V ♦♥t♥s t ♥t♦rs ♦ t ♦rrt♦♥ ♠tr① R ♦rr ② s♥♥ ♥s ❬❪ ♥t♦rst t st ♥s ♦♥t ♦r r ♠♦♥t ♦ t r♥ ♥t t ♦ ♥s st♥ ♦r ♥t♦rs ♥ ♦♠♣♦♥♥ts tt

♣♥ s s♣ ♦r♠ ♦ t ♥② ♠tr① ♦ t ♥t♦r r ttr ♦ t ♣♥ ♦rrs♣♦♥s t♦ t ♥♠r ♦ ♥s t♥ ♥♦s

♥t ♦ ts ♠t♦ s tt P s ♠♦r ♣rs♠♦♥♦s ♥ tr♥s♣r♥t t♥♦♠♠♥t② tt♦♥ ♦rt♠s ♥ ♣r♣s s♦ ttr ♥♦♥ ♠♦♥ s♦ s♥tstst♥ t ttr ♦♥t♦♥s ♦ ♦r ssq♥t ♥②ss ♥ ♦♥ ♥ ❬❪

♦♥trt r② tt t♦ t r♥ ♥ r ♦♥sq♥t② ♥t♦ strt t ♣r♥♣s tt s t♦ ♦r♠ r♦♣s ss♠ tt s

♦♥ s♦♠ ♦♠♣♦st♦♥ ♣♣r♦①♠t t ♥② ♠tr① B ② ♠♥s♦♥② r ♠tr① E r ♦t ♠trs ♦ ♦♥t♥ ♦♥s♦r ♥s ♥ ③r♦s ♦trs ♥ E ♥ ♦ ♦r r♥ t♥ B t♦ t♠♥s♦♥ rt♦♥ ♦ tr E s ♦♦ r♣rs♥tt♦♥ ♦ t♦r♥ ♥t♦r ss♥t② t♦ ♦♠♣r ♥ s♦r ② rr♥ t♦rrt ♠t♥ ♦ ♥s ♥ ♥♦♥♥s ♥ B ♥ E ♥ s②♠♠tr② ②♣♥s♥ t ♠t♥ ♦ ♥s t♦ ♥♦♥♥s ♥ tr rt♦♥ t♥s♠ ♣ ♦r t ♦♠♣rs♦♥ s t ♥② ♠trs ♦♦r ♦r♣♦rt ♥t♦rs r s♣rs tr♦r t ♥s r ♠♦r ♥♦r♠tt♥ ♥♦♥♥s s ♦♥srt♦♥s rst ♥ s♦r♥ ♦r rr♦r ♥t♦♥♦ t ♦r♠

s(E|B,Ω1...4) =c∑

i=1

c∑

j=1

Ω1,ijEijBij

︸ ︷︷ ︸

♥s t♦ ♥s

−c∑

i=1

c∑

j=1

Ω2,ij(1− Eij)Bij

︸ ︷︷ ︸

♥♦♥♥s t♦ ♥s

−

c∑

i=1

c∑

j=1

Ω3,ijEij(1−Bij)

︸ ︷︷ ︸

♥s t♦ ♥♦♥♥s

+c∑

i=1

c∑

j=1

Ω4,ij(1− Eij)(1−Bij)

︸ ︷︷ ︸

♥♦♥♥s t♦ ♥♦♥♥s

r Ω1...4 r♣rs♥t t♥ ♠trs t s ♦♠♠♦♥ t♦ ♦s ♦♥ t♠t♥ ♦ ♥s ♥ t rr♥ ♠tr①B ② q② t♥ t ♠s♠t♥♦ ♦r♥ ♥s Ω1,ij = Ω2,ij > Ω3,ij = Ω4,ij ❬❪

♦rt♠ ♣r♦r tt ♠♣♦② r t♦ s③ t r♦♣s♥ t ♥t♦r ♦♦s ①t② t ♣r♥♣s strt ♦ ♦♥②r♥ s tt ♥st ♦ ♦♠♣r♥ t♦ ♥r② ♥② ♠trs ♦♠♣r t ♥② ♠tr① t t ♣r♥♣ ♦♠♣♦♥♥ts r ♥♦t♥r② ♥ ♦♠♥s s♦♥ r♦♣s t♦ ♥t t♦ ♠tr♠s r ♥ ② t rst ♦♠♣♦♥♥ts rst♥ r♦♠ t P ♥ B

srs ♥s t ♦♠♣♦♥♥ts ♥ F sr t♦s ♥s ♥ ♦♠♣♥sr ♥♦r♠③ t ♦♠♥ t♦rs ♥ F ♥ ♦ ♦r s♥ ♥ ♥r② ♦♠♥ t ♥ ♠tr① ♦ ♥ ♣r♦s F t ♠♥s♦♥s c× 2cr ♥ ♦♠♥ ♦♥t♥s t ♥trs ♦ t ♣r♦s ♦r♥♥♦ ♦ ♦♠♥ t rrs s♥s s s♥ ♥ s ♥ssr② s♥t ♣r♥♣ ♦♠♣♦♥♥ts sr ♦♥② ♥ ①s t♥ t r s♣t ♦ ♥♦t ♥♦r♠ s ♦ t rt♦♥ s t ♦ ♦♥② st rst ♦♠♥s ♦ F ♥ t s♠rt② s♦r ♦r r♦♣r♣rs♥t ② ♦♠♥ ♥ F ♥ r♠ r♣rs♥t ② ♦♠♥

♥ B s rsts ♥ ♠tr① S ♦ s♦rs ♦r r♠s ♥ r♦♣s t♠♥s♦♥ c × 2k r k s t ♥♠r ♦ ♥ ♣r♥♣ ♦♠♣♦♥♥ts♠♦r ♦♥ k ♦ ♥ t s♥ ♥ t ♥♠r ♦ r♦♣s G ≤ 2k ts ♦ ♥s ♥ ♥♦♥♥s ♥ ♣♣r♦①♠t ② t♥♠r ♦ ♥s rss ♥♦♥♥s ♥ t ♦r♥ ♥t♦r ♥ t r♣♥st② s ♦♥② ♦t st Ω3 = Ω4 = 0 rtr♠♦r ♦ ♥♦t♥ t♦ r♥tt t t ♦ s♥ ♥ s t s r② ♦♥t♥♥ t rs♣t s ♦ t ♥ ♣r♦ F ♥ Ω1 = Ω2 = 1 ♦t♦r tt ♥ ♦♥trst t♦ E t ♥ ♣r♦ F s ♥♦t ♥r② ♠tr① t♦♥t♥s t rt ts ♦ ♥s tr♦r st② ♥tr♦ ♠tr①Θ tt tr♥sts F ♥t♦ ♥r② ♦r♠ s tt Θjg = 1 Fjg > 0 ♥ ③r♦♦trs

Sig =c∑

j=1

Θjg(FjgBji)2 −

c∑

j=1

(Θjg − 1)(FjgBji)2

♦r i = 1, . . . , c ♥ g = 1, . . . , G s Θ ♥srs tt s♠ ♦r ♣♦st ♥trs ♥ F ♥ t rst s♠ ♥ ♦r ♥t ♥trs ♥ ts♦♥ s♠ ♦r r② ♦rrt ♠t tt ♠♥s r♠ i s ♥ t♦♦♠♣♥② j r t ♥ ♣r♦ ♦ sst ♦♥ ♥rs t s♦rtt r♠ i ♦t♥s ♦r r♦♣ g ② t sqr ♥tr② ♥ t ♥ ♣r♦②♠♠tr② t r♠ s ♥ r ♦ ♥♦t ①♣t ♦♥ tts s♦r r♠ s ♥♦ ss♥ t♦ t r♦♣ ♦r t s tst s♦r ② ♥t②♥ t ♠①♠ ♥ r♦ ♦ S r r ♦♦rs qt r♠s tt s♦r rtr ♣♦♦r② ♥ ♦ t r♦♣s s♠♣②s t② ♦ ♥♦t ♦♥ t♦ ♥② s r♠s tr r② ♥st♦ ♥ t ♦r ♥q ♥ ♣ttr♥ ♦ tr ♦t s r♠s st trs♦ ♥ ♦r s♦r♥ ♣r♦r ②t t tr♥s ♦t tt t r♦♣♥ sqt r♦st t rs♣t t♦ t ①t ♦ ts trs♦

rt ♣♦♥t ♥ ♥② P ♥②ss ♦♥r♥s t qst♦♥ ♦ ♠♥②♦♠♣♦♥♥ts k t♦ ♥ ♥ t rst ♣ ♥ ♦r ♦♥t①t ♥ t ♥strt t♦ ♦ ♠♥② ♦♠♣♦♥♥ts rt r♦♣s ♦♥t♥♥ t sttr r♠s r♣rs♥t♥ rtr ♦♥srt rtr♦♥ ♦r ♥♥ r♦♣

t st s♦r ♦ r♠ s ♥♦t rtr t♥ t ♠♥ ♣s st♥r t♦♥♦ s♦rs t♥ r♦♣ ♦ ♥♦t ♠t t r♠ t♦ t r♦♣ ①t t♥♥ ♦ tstrs♦ s ♦ ♦rs rtrr② ♦♦s♥ ♠ rr trs♦ s t♦ s♠rt ♠♦r ♦♠♦♥♦s r♦♣s s♦♠ r♠s ♠t ♥♦t ♠t t s ♦ s♥r♥ ♥ ♠ ♦r trs♦ ♥t r♦♣s ② ♠t♥ ♣r♣rr♠s tt ♦♥② s♦ ♠r♥ s♠rt② ♥ t ♥ ♣ttr♥ ♥ ♥tr r♦♣ tr♥s ♦tt♦ r ♦♠♣r t♦ t ♥tr st ♦ r♠s ♦r q♥t♣♣r♦ s qt r♦st ♥t ①t ♦ t trs♦ s ♥♦t r ♦r t ♦r rsts ♥ rr tststs ♣r♠tr ♦ rt♥② ♥♦♥③

r ♦rt♠ trt② ♥rss t ♥♠r ♦ ♣r♥♣ ♦♠♣♦♥♥ts ♥st♦♣s ♥ t st ♥ ♦♠♣♦♥♥t ♥♦ ♦♥r ♣r♦s ♥ t♦♥r♦♣ t tr♥s ♦t tt ♦♥② rt♦♥ ♦ t r♠s ♥ ♠♣♣ t♦r♦♣s t t rtst ♥s ♦♥t♥ ♦r r♦② ♣r♥t ♦t♦t r♥ ♥ t s♠st r♥t ♥s ♦♥t♥ ♦r r♦② ♣r♥t ♦ t♦t r♥ ❲ ♥r ♥ ♠♦r t♥ t rst ♥s t♦ rt s♥♥t r♦♣s tt s t♦ s② tt t ♥s♦♥ ♦ ♠♦rt♥ t rst ♥s s t♦ r♦♣s ♦ s③ s♠r t♥ tr

♥② trs ♦rt ② qs

0 10 20 30 40 50 60 70 80 90

ALLIANZBAYER

DEGUSSADRESDNER B.

LINDELUFTHANSA

METALLGES.RWE

SIEMENSVEBA

COMMERZB.HOCHTIEF

KARSTADTMAN

THYSSENBAY. VEREINSB.

DEUTZDIDIER

G. GLASKLoeCKNER

PWASCHM.−LUBECA

SPARVIAG

BASFCONTINENTAL

DTSCHE B.HEIDELB. C.

KSBRHEINEL.

SueDZUCKERVOLKSW.

BABCOCKBHF

BREM. VULKANDOUGLAS

FELTEN+G.PREUSSAG

WAYSS+FR.RHEINMET.

STRABAGVEW

ALTANAAMB

BRAU+BRUNNENIKB

AEGBANKGES. BERLIN

DAIML.−BENZKAUFHOF

AGIVASKO

AVABARMAG

BAY. HYPO+W.BANKBEIERSD.

BEWAGBILF.+BERGER

BMWBUDERUS

COLONIACOMP. 2000DBV WINT.

DEPFADLW

DueRRESCADA

FAG KUGELF.FRESENIUS

GEAGEHE

GROHEHENKELHERLITZ

HOECHSTHORNBACH

HORTENIVG

IWKAJUNGHEINRICH

KAMPAKOLBENSCHM.

KRONESKRUPP

LEIFHEITMANNESM.

MOKSELP. HOLZM.PORSCHE

SALAMANDERSAP

SCHERINGVARTA

VILL.+BOCHVOLKSF.

WELLAWERU

r s♦rt ♥② ♠tr①

0 10 20 30 40 50 60 70 80 90 100

ALLIANZBAYER

DRESDNER B.DTSCHE B.HOCHTIEF

LINDEMANNESM.

MGMueNCH. RueCK

SIEMENSTHYSSEN KRUPP

VEBAVOLKSW.

BILF.+BERGERBMW

DAIMLER−C.DEGUSSA

HEIDELB. C.HENKEL

LUFTHANSASCHWARZ PH.

TELEKOMG. GLAS

K+SKLoeCKNER

PHOENIXSCHERING

SCHM.−LUBECAVIAGAMB

COMMERZB.HUGO BOSS

MANFAG KUGELF.

HVBSKW

BANKGES. BERLINCONTINENTAL

IVGSueDZUCKER

ADIDASAGIV

ALTANAAVA

AXA COLONIABABCOCK B.

BASFBEATE UHSE

BEIERSD.BEWAG

BHWBRAU+BRUNNEN

BUDERUSDBV WINT.

DEPFADEUTZ

DOUGLASDYCKERHOFF

DueRRESCADA

FIELMANNFRESENIUS

FRESENIUS MCGEHE

GOLD−ZACKHANN. RueCK

HEIDELB. DRUCKIKB

IWKAJENOPTIK

JUNGHEINRICHKAMPS

KARSTADT−Q.KIEKERT

KOLBENSCHM.KRONES

KSBMERCKMETRO

MLPP. HOLZM.PORSCHE

PREUSSAGPRO7PUMA

RHEINMET.RHoeN−KL.

RWESAP

SGL CARBONSIXT

SOFTWARESPAR

STINNESTARKETT S.

VARTAVICTORIAVOSSLOH

WCMWELLA

r s♦rt ♥② ♠tr①

0 10 20 30 40 50 60 70 80 90 100

ALLIANZBAYER

COMMERZB.DTSCHE B.HOCHTIEF

LINDELUFTHANSA

MueNCH. RueCKRWE

SIEMENSTHYSSEN KRUPP

TUIVOLKSW.

HANN. RueCK

HEIDELB. DRUCKPFLEIDERER

AAREAL B.DEPFA

DTSCHE POSTDTSCHE TEL.

IKB

KARSTADT−Q.POSTBANK

DTSCHE BoeRSESAP

SCHERINGDAIMLER−C.

DOUGLAS

LOEWEBASFBMW

HEIDELB. C.INFINEON

MANADIDAS

ALTANA

AMB GEN.AWD

BEIERSD.BERU

BILF.+BERGERCELANESE

CELESIO

COMDIRECTCONTINENTAL

DTSCHE EUROSH.DYCKERHOFF

EADSEON

ESCADA

FIELMANNFRAPORT

FRESENIUSFRESENIUS MC

GEAGFK

GILDEMEISTER

HENKELHORNBACH

HUGO BOSSHVB

HYPO REAL E.INDUS

IVG

IWKAJENOPTIK

JUNGHEINRICHK+S

KLoeCKNERKRONES

KoeNIG+B.LANXESS

LEONIMEDIONMERCKMETRO

MLPMPCMTU

NORDDTSCHE A.PREMIERE

PRO7PUMA

RHEINMET.RHoeN−KL.

SALZG.

SCHWARZ PH.SGL CARBON

SIXTSOFTWARE

STADASueDZUCKER

TECHEM

TELEPLANTHIEL−L.

VIVACONVOSSLOH

WCMWINCOR−NIXD.

ZAPF

r s♦rt ♥② ♠tr①

♣♣♠♥tr② ♥♦r♠t♦♥ s

r rq♥② strt♦♥ ♦ ♠♥ts

②r ①ts ♦ t♦♥ ♠♥ts

rq♥② ♦ ①ts s♣rs♦r② ♦r ♠♠rs♣s

♦ ♠♥ts ♥

♦

♠♥

ts

♥

r♥st♦♥ ♠tr① ♦r ♦r ♠♠rs♣ r♥

♦ ♠♥ts ♥

♦♠♥

ts

♥

r♥st♦♥ ♠tr① ♦r ♦r ♠♠rs♣ r♥

♦ ♠♥ts ♥

♦

♠♥

ts

♥

r♥st♦♥ ♠tr① ♦r ♦r ♠♠rs♣ r♥