"2pQ` /B2 KQ`T?QHQ;Bb+?2 JBiQb2/2i2FiBQM BM /2M a+?` ;HB+?i#BH/2`M BM #b+?MBii 9Xk mM/ BM /2M S?b2MFQMi`bi#BH/2`M BM #b+?MBii 9Xj pQ`;2bi2HHi rB`/- rB`/ xmM +?bi 2BM2 HH;2K2BM2 6Q`KmHB2`mM; /2` JBiQb2/2i2FiBQM Hb EHbbB}FiBQMbT`Q#H2K #2i`+?i2iX mb;M;bTmMFi Bbi 2BM Kƺ;HB+?2` JBiQb2FM/B/ix- /2` BM /2M a+?` ;HB+?i#BH/2`M /m`+?
2BM2M w2HHT7/ Q/2` BM /2M S?b2MFQMi`bi#BH/2`M /m`+? 2BM2M "BH/mbb+?MBii ;2;2#2M BbiX 6Ƀ` /B2b2M EM/B/i2M xrB`/ /B2 JBiQb2/2i2FiBQM Hb EHbbB}FiBQMbT`Q#H2K
K(x) =
! Mitose fallsp(x)>θ,
Nicht−Mitose sonst. U9XRV
7Q`KmHB2`i- #2B /2K /2` EHbbB}FiQ` K 7Ƀ` D2/2M JBiQb2FM/B/i2M x 2Mib+?2B/2i-Q# 2` 2BM2 w2HHi2BHmM; x2B;i Q/2` MB+?iX >B2` rB`/ #? M;B; pQM 2BM2K a+?r2HHr2`i θ 2Mib+?B2/2M- r2H+?2` EHbb2 2BM ;2;2#2M2` EM/B/i M;2?ƺ`iX m7#m2M/ m7 /B2b2`
6Q`KmHB2`mM; r2`/2M /B2 p2`r2M/2i2M 62?H2`KĽ2 /2}MB2`i mM/ p2`Mb+?mHB+?i- KBi /2` /B2 EHbbB}FiBQMb@ #xrX .2i2FiBQMb;2MmB;F2Bi MHvbB2`i rB`/X Mb+?HB2Ľ2M/ 7QH;i 2BM2 Fm`x2 ɂ#2`bB+?i /2` p2`r2M/2i2M J2i?Q/2M /2b Jb+?BM2HH2M G2`M2Mb- /B2 xmK h2BH ;2Mmixi r2`/2M- mK /B2 EHbbB}FiQ`2M xm i`BMB2`2MX
9XRXRX 62?H2`KĽ2 xm` "2m`i2BHmM; pQM EHbbB}FiQ`2M
.B2 :2MmB;F2Bi /2` JBiQb2/2i2FiBQM rB`/ KBi /2M 62?H2`KĽ2M MHvbB2`i- /B2 BM #@
b+?MBii jXkXk #xrX BM ##X jX3 7Ƀ` /B2 1pHmiBQM /2` w2HH/2i2FiBQM 2BM;27Ƀ?`i rm`/2MX .B2b2 r2`/2M MQ+? 2BMKH xmbKK2M;27bbi mM/ M /B2 pQ`;2bi2HHi2M EHbbB}FiBQMb@
T`Q#H2K2 M;2TbbiX
lK /B2 EHbbB}FiQ`2M xm 2pHmB2`2M- rB`/ /B2 Sensitivität = RP+FNRP R mM/ /b 62?@
H2`KĽ 1−Spezifität = 1− RN+FPRN = RN+FPFP #2i`+?i2i Up;HX h#X jXkVX >B2`#2B ;B#i 1−Spezifität /b 62?H2`KĽ M- rB2 pB2H2 /2` 2`FMMi2M JBiQb2M 7Hb+? Hb JBiQb2 2`FMMi rm`/2MX .B2 a2MbBiBpBi i /;2;2M ;B#i /2M Mi2BH pQM HH2M JBiQb2M M- /B2 FQ``2Fi ;27mM/2M rm`/2MX lK MmM /b o2`?Hi2M pQM 2BM2K EHbbB}FiQ` K(x) xm mMi2`bm+?2M- r2`/2M /B2b2 62?H2``i2M #? M;B; pQM 2BM2K a+?r2HHr2`i θ #2i`+?i2iX
"2B θ = 0 r2`/2M HH2 EM/B/i2M x Hb JBiQb2 2`FMMi UFN = 0V- #2` 2b r2`@
/2M HH2 LB+?i@JBiQb2M 7Hb+? FHbbB}xB2`i URN = 0V mM/ 2b 7QH;i 1−Spezifität = 1-Sensitivität = 1X "2B 2BM2K a+?r2HHr2`i θ = ∞ rB`/ F2BM2 JBiQb2 FQ``2Fi 2`FMMi URP = 0V- #2` HH2 LB+?i@JBiQb2M r2`/2M FQ``2Fi FHbbB}xB2`i UFP = 0V mM/ 2b ;BHi 1−Spezifität = 0,Sensitivität = 0X qB`/ /2` a+?r2HHr2`iθpQM y #Bb m7∞M;2?Q#2M mM/ /B2 q2`i2 7Ƀ`1−SpezifitätmM/ /2` a2MbBiBpBi i ;2;2M2BMM/2` m7;2i`;2M- bQ 2`@
;B#i bB+? 7Ƀ` D2/2M EHbbB}FiQ` 2BM2 +?`Fi2`BbiBb+?2 Em`p2- /B2 Hb _2+2Bp2` PT2`iBM;
*?`+i2`biB+U_P*V@Em`p2 #2x2B+?M2i rB`/ Up;HX ##X 9XkVX
.2` +?`Fi2`BbiBb+?2 S`K2i2` /B2b2` Em`p2 Bbi /B2 `2 lM/2` i?2 *m`p2 Ul*V- /2` /b AMi2;`H #xrX /B2 6H +?2 mMi2` /2` Em`p2 M;B#iX "2B 2BM2K QTiBK@
H2M EHbbB}FiQ` #2i` ;i /2` q2`i /2` l* Rc /2` b+?H2+?i2bi2 EHbbB}FiQ`- /2` KBi 2BM2` q?`b+?2BMHB+?F2Bi pQM 50% `B+?iB; ` i- 2``2B+?i 2BM2 l* pQM 12X M?M/ /2b
RRP4 `B+?iB; TQbBiBp-FP4 7Hb+? TQbBiBp-FN4 7Hb+? M2;iBp-RN4 `B+?iB; M2;iBp
ee
9XRX MHvb2 pQM .2i2FiBQMb@ mM/ EHbbB}FiBQMbT`Q#H2K2M
l*@q2`i2b mM/ /2` _P*@Em`p2M r2`/2M /B2 JBiQb2/2i2FiBQM2M p2`;HB+?2MX .B2 M;2@
;2#2M2M q2`i2 rm`/2M KBi /2` JhG"@6mMFiBQMT2`7+mp2XK2`bi2HHiX Jb+?BM2HH2b G2`M2M pQM EHbbB}FiQ`2M
lK /B2 ;2bm+?i2M EHbbB}FiQ`2M xm 2`x2m;2M- rB`/ m7 p2`b+?B2/2M2 J2i?Q/2M /2b K@
b+?BM2HH2M G2`M2Mb xm`Ƀ+F;2;`Bz2M- KBi /2M2M 2BM2K *QKTmi2`T`Q;`KK #2B;2#`+?i r2`/2M FMM- rb 2BM2 JBiQb2 pQM 2BM2` LB+?i@JBiQb2 mMi2`b+?2B/2iX mb;M;bTmMFi /B2b2` J2i?Q/2M Bbi 2BM `2T` b2MiiBp2` h`BMBM;b/i2Mbix- /2` "2BbTB2H2 /2` JBiQb2M mM/ LB+?i@JBiQb2M 2Mi? HiX LmM rB`/ 2BM *QKTmi2`T`Q;`KK ;2Mmixi- mK /B2 lMi2`@
b+?B2/2 /2` #2B/2M ;2;2#2M2M EHbb2M xm mMi2`bm+?2M mM/ /B2 J2`FKH2 xm 2ti`?B2`2M-BM /2M2M bB+? /B2 EHbb2M K H2B+?i2bi2M mMi2`b+?2B/2M Hbb2MX .B2b2 J2`FKH2 r2`/2M
;2bT2B+?2`i mM/ FƺMM2M 7Q`iM ;2Mmixi r2`/2M- mK M2m2 .i2M xm FHbbB}xB2`2M- /X?X 7Ƀ`
2BM ;2;2#2M2b "BH/ rB`/ 2Mib+?B2/2M- Q# 2b 2BM2 JBiQb2 Q/2` 2BM2 LB+?i@JBiQb2 x2B;iX .B2@
b2b o2`7?`2M rB`/ Hb Ƀ#2`r+?i2b G2`Mp2`7?`2M #2x2B+?M2i- KBi /2K 2BM EHbbB}FiQ`
K 2`bi2HHi r2`/2M FMMX
.B2 :2MmB;F2Bi pQM 2BM2K i`BMB2`i2M EHbbB}FiQ`K rB`/ KBi >BH72 2BM2` x2?M7+?@
E`2mxpHB/B2`mM; mMi2`bm+?iX >B2`#2B r2`/2M /B2 ;2;2#2M2M h`BMBM;b/i2M T BM x2?M
;H2B+?;`QĽ2- /BbDmMFi2 J2M;2MT1, . . . . , T10mMi2`i2BHi Up;HX ##X 9XkU#VVX AM x2?M .m`+?@
H m72M rB`/ /2` EHbbB}FiQ` K KBi /2M .i2M T \Ti, i = 1, . . . ,10 i`BMB2`i- /X?X 2b rB`/ D2r2BHb 2BM2 :`mTT2 mb /2M h`BMBM;b/i2M 2Mi72`Mi mM/ KBi /2M Ƀ#`B;2M M2mM :`mTT2M rB`/ ;2H2`MiX .B2 mb;2Hbb2M2M .i2M Ti r2`/2M Hb h2bi/i2M ;2Mmixi- mK /B2 .2i2FiBQMb;2MmB;F2Bi xm #2biBKK2MX
UV _P*@Em`p2 mM/ l*X U#V a+?2K /2` E`2mxpHB/B2`mM;X
##BH/mM; 9XkX, .B2 *?`Fi2`BbiBF 2BM2b EHbbB}FiQ`b rB`/ Hb _P*@Em`p2 /`;2@
bi2HHi- BM /2` /B2 aT2xB}i i ;2;2M /B2 a2MbBiBpBi i m7;2i`;2M rB`/ UVX .B2 :2MmB;F2Bi /2` EHbbB}FiBQM rB`/ Hb l* M;2;2#2M- /B2 KBi 2BM2` x2?M7+?@E`2mxpHB/B2`mM;
#2biBKKi rB`/ U#VX AM /B2b2K "2BbTB2H #2x2B+?M2MT+, T− /B2 p2`b+?B2/2M2M EHbb2MX
ed
ETBi2H 9X JBiQb2/2i2FiBQM
##BH/mM; 9XjX, 6Ƀ` 2BM ;2;2#2M2b EHbbB}FiBQMbT`Q#H2K KBi xr2B EHbb2M T+, T−
#xrX+,−- #2`2+?M2i 2BM2 amTTQ`i o2+iQ` J+?BM2 UaoJV 2BM2 QTiBKH2 h`2MM2#2M2-/B2 /2M KBMBKH2M J`;BM U#biM/ /2` .i2MTmMFi2 xm /2` h`2MM2#2M2V KtBKB2`iX
9XRXkX EHbbB}FiBQM KBi 2BM2` amTTQ`i o2+iQ` J+?BM2 UaoJV
1BM2 amTTQ`i o2+iQ` J+?BM2 UaoJV Bbi 2BM Ƀ#2`r+?i2b G2`Mp2`7?`2M /2b Jb+?BM2H@
H2M G2`M2Mb- KBi /2K 2BM wr2B@EHbb2M@S`Q#H2K ;2Hƺbi rB`/ U*Q`i2b M/ oTMBF (kj)VX 6Ƀ` /B2 .i2MTmMFi2 /2` #2B/2M EHbb2M T+, T− rB`/ 2BM2 QTiBKH2 U>vT2`@V 1#2M2
#2biBKKi- /B2 #2B/2 EHbb2M pQM2BMM/2` i`2MMi mM/ /2M KBMBKH2M J`;BM KtBKB2`i-/X?X /bb /B2 FɃ`x2bi2 .BbiMx /2` .i2MTmMFi2 xm /2` h`2MM2#2M2 KtBKB2`i rB`/ Up;HX
##X 9XjVX 1BM2 aoJ FMM mK 2BM2 E2`M2H7mMFiBQM 2`r2Bi2`i r2`/2M- KBi /2` /B2 .@
i2M BM 2BM2M ?ƺ?2` /BK2MbBQMH2M _mK T`QDBxB2`i r2`/2M Ua+?ƺHFQT7 M/ aKQH (Ryj)VX .B2b2 1`r2Bi2`mM; 2`Kƺ;HB+?i 2b- EHbbB}FiBQMbT`Q#H2K2 7Ƀ` MB+?i HBM2` b2T`B2`#`2 .i2M xm Hƺb2MX AK 6QH;2M/2M r2`/2M /`2B p2`b+?B2/2M2 E2`M2H ;2Mmixi, 2BM HBM2`2`
E2`M2H UG@aoJV- 2BM [m/`iBb+?2` E2`M2H UZ@aoJV mM/ 2BM :mbb@E2`M2H U:@aoJVX
9XkX JBiQb2/2i2FiBQM BM /2M a+?` ;HB+?i#BH/2`M
.B2 +?`Fi2`BbiBb+?2M J2`FKH2 2BM2` w2HHi2BHmM; bBM/ BM ##X 9XR ;2x2B;i, oQ` 2BM2`
JBiQb2 p2`HM;bKi bB+? /B2 "2r2;mM; 2BM2` w2HH2 mM/ bB2 rB`/ FH2BM2` mM/ `mM/2`- /X?X bB2 M/2`i B?`2 JQ`T?QHQ;B2X .B2 l`b+?2 /B2b2` o2` M/2`mM; HB2;i BM /2K #BQHQ;Bb+?2M S`Qx2bb- /2` r ?`2M/ 2BM2` w2HHi2BHmM; #H m7iX 1BM2 BMi`x2HHmH `2 ai`mFim`- /B2 Hb aTBM/2HTT`i #2x2B+?M2i rB`/- xB2?i /B2 w2HH2 xmbKK2M- mK /B2 `2THBxB2`i2 .L /2`
#2B/2M hQ+?i2`x2HH2M xm i`2MM2M U*KT#2HH 2i HX (Rd- ETX Rk)VX m7#m2M/ m7 /B2b2K Jmbi2` 2BM2` JBiQb2 r2`/2M p2`b+?B2/2M2 J2i?Q/2M pQ`;2bi2HHi- mK /B2 w2HHi2BHmM;2M xm /2i2FiB2`2M U##X 9XRVX >B2`xm rB`/ 2BM EHbbB}FiQ` BKTH2K2MiB2`i- /2` /B2 M/2`mM;
/2` w2HHKQ`T?QHQ;B2 /B`2Fi mb /2M w2HHT7/2M 2ti`?B2`i- /X?X /bb /B2 JBiQb2/2i2FiBQM /B`2Fi pQM /2M 1`;2#MBbb2M /2b w2HHi`+FBM; #? M;B; BbiX .B2 m7;#2 #2bi2?i /`BM-7Ƀ` D2/2M ;2;2#2M2M S7/ xm 2Mib+?2B/2M- Q# 2` BM 2BM2` JBiQb2 2M/2i Q/2` MB+?iX
JBi /2K 2BM;27Ƀ?`i2M EHbbB}FiQ` r2`/2M p2`b+?B2/2M2 KQ`T?QHQ;Bb+?2 S`K2i2`
;2Mmixi- mK 2BM2 JBiQb2 xm /2i2FiB2`2MX q2Bi2`?BM rB`/ MHvbB2`i- r2H+?2 mbrB`FmM;
/B2 M/2`mM; /2` w2HH/B+?i2 BM /2M p2`b+?B2/2M2M q+?bimKbT?b2M m7 /B2 JBiQb2/2@
i2FiBQM ?i Up;HX wmbKK2M7bbmM; m7 a2Bi2 dyVX wmM +?bi r2`/2M D2/Q+? /B2 _272`2Mx@
e3
9XkX JBiQb2/2i2FiBQM BM /2M a+?` ;HB+?i#BH/2`M
##BH/mM; 9X9X, .B2 JBiQb2/2i2FiBQM BM /2M a+?` ;HB+?i#BH/2`M #bB2`i m7 /2M M@
/2`mM;2M /2` w2HHKQ`T?QHQ;B2- /B2 mb /2M w2HHT7/2M 2ti`?B2`i r2`/2MX Hb h2bi/@
i2M r2`/2M /B2 w2HHT7/2 #xrX S7/2M/2M ;2Mmixi- /B2 KBi /2K w2HHi`+FBM; mb #@
b+?MBii kX9 2`bi2HHi rm`/2M mM/ KBi >BH72 /2` _272`2Mx/i2M *2h_2aX mM/ *2h_2aX"
Hb JBiQb2 Q/2` LB+?i@JBiQb2 2BM;2i2BHi rm`/2MX
/i2M *2h_2aX mM/ *2h_2aX" ;2Mmixi- mK 2BM2M aix pQM _272`2MxKBiQb2M 7Ƀ` /B2 1pHmiBQM /2` KQ`T?QHQ;Bb+?2M JBiQb2/2i2FiBQM xm 2`bi2HH2MX
9XkXRX h2bi/i2M /2` a+?` ;HB+?i#BH/2`
.B2 JBiQb2/2i2FiBQM rm`/2 KBi /2M w2HHi2BHmM;2M mb /2M _272`2Mx/i2M *2h_2a 2p@
HmB2`i Up;HX #b+?MBii jXkXR mM/ _TQTQ`if"2+F2` 2i HX (3)VX .B2b2 bi2HH2M xr2B ;2H#2Hi2
"BH/b2`B2M xm` o2`7Ƀ;mM;- /B2 BK a+?` ;HB+?iFQMi`bi m7;2MQKK2M rm`/2M U*2h_2aX Y *2h_2aX"VX .B2 "BH/b2`B2 *2h_2aX" 2Mi? Hi xmb ixHB+?
S?b2MFQMi`bim7M?K2M-/ ?B2` 2BM2 S?b2MFQMi`bim7M?K2M-/QTT2Hi2 EQMi`bi2BMbi2HHmM; p2`r2MS?b2MFQMi`bim7M?K2M-/2i rm`S?b2MFQMi`bim7M?K2M-/2 Up;HX #b+?MBii kXkXkVX a+?` ;HB+?i#BH/2` U*2h_2aX Y *2h_2aX"V
lK /B2 KQ`T?QHQ;Bb+?2M M/2`mM;2M 2BM2` w2HH2 xm 2ti`?B2`2M- r2`/2M /B2 EQMim`2M pQM m72BMM/2`7QH;2M/2M w2HH2M ;2Mmixi- /B2 BM /2M w2HHT7/2M ;2bT2B+?2`i bBM/X aQ@
KBi Bbi /B2b2 JBiQb2/2i2FiBQM /B`2Fi pQM /2K xm;`mM/2HB2;2M/2M w2HHi`+FBM; #? M;B;X .B2 2`bi2HHi2M w2HHT7/2 FƺMM2M /?2` Hb mb;M;bTmMFi 7Ƀ` /B2 p2`r2M/2i2M h2bi/@
i2M ;2Mmixi r2`/2M, 6Ƀ` D2/2M S7/ rB`/ 2Mib+?B2/2M- Q# 2` BM 2BM2` w2HHi2BHmM; 2M/2i Q/2` MB+?iX lK _272`2Mx/i2M 7Ƀ` /B2 KQ`T?QHQ;Bb+?2 JBiQb2/2i2FiBQM xm ;2M2`B2`2M-rm`/2 /2` w2HHi`+FBM;@H;Q`Bi?Kmb mb #b+?MBii kX9 ;2Mmixi- mK BM /2M "BH/b2`B2M pQM *2h_2aX mM/ *2h_2aX" BMBiBH2 w2HHT7/2 xm 2`bi2HH2MX JBi >BH72 /2` ;2H#2Hi2M JBiQb2M rm`/2M /B2b2 w2HHT7/2 Mb+?HB2Ľ2M/ Hb JBiQb2 Q/2` LB+?i@JBiQb2 FHbbB}xB2`i Up;HX ##X 9X9VX wm /2M kyRN JBiQb2M- /B2 BM *2h_2aX 2Mi?Hi2M bBM/- rm`/2M RNyj FQ``2bTQM/B2`2M/2 w2HHT7/2 ;27mM/2MX .B2 72?H2M/2M RRe w2HHi2BHmM;2M bBM/ MB+?i BM /2M h2bi/i2M 2Mi?Hi2M- r2BH /B2 xm;2?ƺ`B;2M KBiQiBb+?2M w2HH2M MB+?i FQ``2Fi 2`FMMi r2`@
/2M FQMMi2M- rb /2iBHHB2`i BM /2` wmbKK2M7bbmM; m7 a2Bi2 dd #2b+?`B2#2M rB`/X .B2 Mx?H /2` MB+?i@KBiQiBb+?2M S7/2 HB2;i #2B7277X 6Ƀ` _272`2Mx/i2Mbix *2h_2aX" 2`@
;#2M bB+? MHQ; 8jd KBiQiBb+?2 mM/ kdRy MB+?i@KBiQiBb+?2 w2HHT7/2X AM /B2b2M .i2M rm`/2M je JBiQb2M MB+?i 2`FMMi- rb 2BM2K 62?H2` pQM 6.3%2MibT`B+?iX
eN
ETBi2H 9X JBiQb2/2i2FiBQM
w2BiHB+?2 M/2`mM; /2` w2HHKQ`T?QHQ;B2
1BM2 +?`Fi2`BbiBb+?2 1B;2Mb+?7i /2` #2Q#+?i2i2M w2HHTQTmHiBQM2M Bbi /B2
M/2`mM; B?`2` w2HHKQ`T?QHQ;B2 Ƀ#2` /B2 w2Bi, .B2 :`ƺĽ2 #xrX 6Q`K /2` w2HH2M FQ``2HB2`i bi`F KBi /2` w2HH/B+?i2 mM/ M/2`i bB+? BK Gm72 2BM2b GM;x2Bi2tT2@
`BK2Mi2bX .B2b2 M/2`mM; #22BM~mbbi /b ivTBb+?2 KQ`T?QHQ;Bb+?2 Jmbi2` 2BM2`
w2HHi2BHmM;- / bB+? xX"X /B2 H M;HB+?2M w2HH2M xm "2;BMM 2BM2` w2Bib2`B2 bi `F2`
xmbKK2MxB2?2M Hb /B2 w2HH2M xmK 1M/2 /2` w2Bib2`B2 Up;HX ##X 9X8VX
##BH/mM; 9X8X, M/2`mM; /2` w2HHKQ`T?QHQ;B2 Ƀ#2` /B2 w2BiX .B2 "BH/2` x2B@
;2M 2BM2M mbb+?MBii /2` "BH/b2`B2 mb /2K .i2Mbix *2h_2aX- Zm2HH2, "2@
+F2` M/ J/Mv JKHQmF (k- 6B;X R)X
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M/2`mM;2M xm mMi2`bm+?2M- / /B2 #2Q#+?i2i2 w2HHTQTmHiBQM HH2 ai/B2M 2BM2` q+?bimKbFm`p2 /m`+?H m7iX aQ Bbi 2b Kƺ;HB+?- /b o2`?Hi2M /2`b2H#2M w2HHTQTmHiBQM #2B mMi2`b+?B2/HB+?2M w2HH/B+?i2M xm MHvbB2`2MX .B2 w2HH/B+?i2-/B2 Mx?H /2` w2HH2M mM/ w2HH/B+?i2-/B2 6H +?2 /2` w2HH2M Bbi BM ##X 9Xe ;2;2#2MX AK 6QH;2M/2M rB`/ /B2 w2Bib2`B2 BM /`2B q+?bimKbT?b2M 0−10h,10−40h mM/
40−52h 2BM;2i2BHi- mK /2M 1BM~mbb /2` KQ`T?QHQ;Bb+?2M M/2`mM; m7 /B2 JBiQb2/2i2FiBQM xm mMi2`bm+?2MX
##BH/mM; 9XeX, M/2`mM; /2` w2HHT`K2i2` pQM .i2Mbix *2h_2aX Ƀ#2`
/B2 w2Bi- Zm2HH2, "2+F2` M/ J/Mv JKHQmF (k- 6B;X k)X .B2 x2BiHB+?2M :`2Mx2M /2` q+?bimKbT?b2M bBM/ Hb ;2bi`B+?2Hi2 GBMB2M 2BM;2x2B+?M2iX
dy
9XkX JBiQb2/2i2FiBQM BM /2M a+?` ;HB+?i#BH/2`M 9XkXkX JQ`T?QHQ;Bb+?2 JBiQb2/2i2FiBQM
AM /2K 7QH;2M/2M #b+?MBii r2`/2M p2`b+?B2/2M2 EHbbB}FiQ`2M pQ`;2bi2HHi- /B2 2B@
M2 w2HHi2BHmM; M?M/ /2` KQ`T?QHQ;Bb+?2M M/2`mM; /2` w2HHFQMim`2M }M/2M FƺM@
M2MX .B2 o2`7Q`KmM; /2` w2HHFQMim` rB`/ KBi >BH72 /2` KQ`T?QHQ;Bb+?2M 1B;2Mb+?7@
i2M 2BM2` w2HH2 #2`2+?M2i- /B2 BM #b+?MBii kX9 /2}MB2`i rm`/2MX AM /2K o2FiQ` ft = [fx, fy, fA, fH, fK, fL, fO]r2`/2M SQbBiBQM- 6H +?2- >2HHB;F2Bi- EQKTFi?2Bi- G M;2 mM/
P`B2MiB2`mM; 2BM2` w2HH2 xmK w2BiTmMFi t ;2bT2B+?2`iX JBi >BH72 /B2b2b o2FiQ`b rB`/
/B2 KQ`T?QHQ;Bb+?2 *?`Fi2`BbB2`mM; 2BM2b ;2bKi2M w2HHT7/2b pi /2` G M;2 N Hb fi = {ft1, . . . , ftN} ;2bT2B+?2`i- rQ#2B ft1, . . . , ftN /B2 1BM;2b+?7i2M /2` w2HH2M mb S7/pi M;2#2MX . /B2 SQbBiBQM mM/ /B2 P`B2MiB2`mM; 2BM2` w2HH2 7Ƀ` /B2 JBiQb2/2i2F@
iBQM mM2`?2#HB+? bBM/- rB`/ /2` `2/mxB2`i2 o2FiQ`f˜t= [fA, fH, fK, fL];2Mmixi- mK /2M .Bz2`2Mx2Mp2FiQ`
di = {∆f˜t1, . . . ,∆f˜tN}mit∆f˜tj = ˜ftj+1−f˜tj = [∆fA,∆fH,∆fK,∆fL], j= 1, . . . , N−1 xm #2`2+?M2MX >B2` ;B#i∆f˜tj /B2 M/2`mM; BM 2BM2K w2Bib+?`Bii M mM/N /B2 G M;2 /2b w2HHT7/2bX 6Ƀ` D2/2M ;2;2#2M2M w2HHT7/ pi rB`/ 2BM .Bz2`2Mx2Mp2FiQ`di #2`2+?M2iX
.B2 :`mM/H;2 /2` MmM 7QH;2M/2M JBiQb2/2i2FiBQM Bbi /B2 M/2`mM; /2` J2`FKH2 BM f˜tX lK /B2b2 K2bb#` xm K+?2M- rB`/ /B2 o2`i2BHmM; /2` M/2`mM;2M /2` :`ƺĽ2
∆fA- /2` AMi2MbBi i ∆fH- /2` EQKTFi?2Bi ∆fK mM/ /2` G M;2 ∆fL Hb K2?`/BK2M@
bBQMH2 LQ`KHp2`i2BHmM; KBi /2` EQp`BMx Σ ∈ R4×4 mM/ /2K JBii2Hr2`i µ ∈ R4
;2b+? ixiX .B2b2 o2`i2BHmM; rB`/ M?M/ HH2` 72?H2`7`2B2M S7/2 2`KBii2Hi- /B2 miQ@
KiBbB2`i mb /2M w2HHi`+FBM;@1`;2#MBbb2M 2ti`?B2`i r2`/2MX aQKBi Bbi F2BM b2T`i2`
h`BMBM;bb+?`Bii MQir2M/B;X JBi /B2b2M S`K2i2`M rB`/ /B2 q?`b+?2BMHB+?F2Bi
pm(di) = 1
M;2;2#2M- /B2 Hb :`mM/H;2 7Ƀ` /B2 7QH;2M/2M EHbbB}FiQ`2M /B2MiX .B2 7QH;2M/2 GBbi2 HB272`i 2BM2M ɂ#2`#HB+F Ƀ#2` /B2 BKTH2K2MiB2`i2M- KQ`T?QHQ;Bb+?2M JBiQb2/2i2FiBQM2MX
Ç LBp2 .2i2FiBQM KYX .2` MBp2 EHbbB}FiQ` KY /2i2FiB2`i D2/2M w2HHT7/
pi Hb JBiQb2- /2` xr2B L+?7QH;2` ?iX "2B 2BM2` 72?H2`HQb2M w2HH/2i2FiBQM mM/
2BM2K 72?H2`HQb2M w2HHi`+FBM; Bbi /B2b2` EHbbB}FiQ` BM /2` G;2- HH2 JBiQb2M xm 2ti`?B2`2M- /X?X r2MM /B2 MM?K2M /2b MBp2M h`+FBM; 2`7ɃHHi r `2M- rɃ`/2 /B2 MBp2 JBiQb2/2i2FiBQM 2BM2 pQHHbi M/B;2 :2M2HQ;B2 2ti`?B2`2MX
Ç aBM;H2 62im`2 JtBKmK GBF2HB?QQ/ UKsf mlVX 6Ƀ` D2/2M ;2;2#2M2M S7/
pi FMM KBi >BH72 /2` .Bz2`2Mx2Mp2FiQ`2M di 2BM EHbbB}FiQ` Ksf ml M;2;2#2M r2`/2M- /2` KBi
dR
ETBi2H 9X JBiQb2/2i2FiBQM
2Mib+?2B/2i- Q# /2` S7/ pi BM 2BM2` w2HHi2BHmM; 2M/2i- /X?X 2b rB`/ 2BM2 2BMx2HM2-KQ`T?QHQ;Bb+?2 1B;2Mb+?7i ;2Mmixi- mK /B2 q?`b+?2BMHB+?F2Bi 7Ƀ` 2BM2 JBiQb2 BM D2/2K /2` H2ixi2M 7ɃM7 w2Bib+?`Bii2 xm #2`2+?M2MX .B2b2 7ɃM7 w2Bib+?`Bii2 bBM/
MQir2M/B;- / /b KBiQiBb+?2 Jmbi2` bB+?i#` rB`/- #2pQ` bB+? 2BM2 w2HH2 BM xr2B b2T`i2 hQ+?i2`x2HH2M i2BHi mM/ /2` w2HHT7/ 2M/2iX
Ç Uj@S?b2V JmHiB 62im`2 JtBKmK GBF2HB?QQ/ UKmf ml mM/ K3p−mf mlVX .2` EHbbB}FiQ` Kmf ml(pi,ω) Mmixi /B2b2H#2 EHbbB}FiBQM mb :HX U9XjV- /B2 KBi /2K EHbbB}FiQ` Ksf ml 2BM;27Ƀ?`i rm`/2X .2` lMi2`b+?B2/ xrBb+?2M /2M
#2B/2M o2`bBQM2M Bbi /B2 Mx?H /2` p2`r2M/2i2M 1B;2Mb+?7i2M, q ?`2M/ /2`
Ksf ml Mm` 2BM 2BMx2HM2b 62im`2 Mmixi- FMM /2`Kmf ml KBiω ∈ [0,1]4 2BM2 pQM BMb;2bKi R8 biiBb+?2M EQK#BMiBQM2M mbr ?H2M- /B2 BM h#X 9XR m7;2HBbi2i bBM/X AM 2BM2` xr2Bi2M o2`bBQM rB`/ 2BM2 /TiBp2 o2`bBQM p2`r2M/2i- /B2 BM D2/2`
/2` /`2B q+?bimKbT?b2M 2BM2 M/2`2 EQK#BMiBQM mbr ?HiX .B2b2` /TiBp2 EHbbB}FiQ` rB`/ Hb j@S?b2M /TiB2`i2`Kmf ml #xrX HbK3p−mf ml#2x2B+?M2iX Ç GBM2`@ f Zm/`iB+@ f :mbbBM amTTQ`i o2+iQ` J+?BM2 UKmorph−svmVX AM 2BM2K r2Bi2`2M Mbix rm`/2M /B2 ;2H#2Hi2M w2HHT7/2 ;2Mmixi- mK KBi 2BM2`
aoJ /b Jmbi2` 2BM2` JBiQb2 #xrX /2M lMi2`b+?B2/ xrBb+?2M 2BM2` JBiQb2 mM/
2BM2` LB+?i@JBiQb2 xm H2`M2MX >B2`xm rm`/2 pQM HH2M RNyj h2biKBiQb2M /B2 .Bz2@
`2Mx∆f˜tj ∈R4#2`2+?M2iX aQKBi 2Mi? Hi /B2 JBiQb2@EHbb2TmitoseRNyj o2FiQ`2MX .B2 EHbb2 /2` LB+?i@JBiQb2M rB`/ HbTzelle #2x2B+?M2i mM/ rm`/2 KBi /2M dkdd w2HHT7/2M 2`bi2HHi- /B2 MB+?i KBi 2BM2` JBiQb2 2M/2MX 6Ƀ` D2/2M /B2b2` S7/2 rm`@
/2M /B2 H2ixi2M 7ɃM7 .Bz2`2Mx2M ∆f˜zelle ∈R4 #2`2+?M2iX Mb+?HB2Ľ2M/ rm`/2 7Ƀ`
D2/2M S7/ /B2 .Bz2`2Mx KBi /2` FH2BMbi2M q?`b+?2BMHB+?F2Bi mb;2r ?Hi- /X?X 2b rm`/2M /B2 .Bz2`2Mx2M ;2r ?Hi- /B2 /B2 ;`ƺĽi2 ?MHB+?F2Bi xm 2BM2` JBiQb2 x2B;2MX .B2 #2B/2M EHbb2M Tzelle, Tmitose rm`/2M ;2Mmixi- mK 2BM2 aoJ KBi 2BM2K HBM2@
`2M UKmorph−lsvmV- 2BM2K [m/`iBb+?2M UKmorph−qsvmV mM/ 2BM2K :mbb@E2`M2H UKmorph−gsvmV xm i`BMB2`2MX Mb+?HB2Ľ2M/ rB`/ KBiKmorph−svm( ˜fkand)>0 2Mi@
b+?B2/2M- Q#f˜kand2BM2 JBiQb2 x2B;i Q/2` MB+?iX 1b rm`/2 7Ƀ` D2/2 q+?bimKbT?b2 U0h−10h,10h−40h,40h−EndeV 2BM b2T`i2` EHbbB}FiQ` #2`2+?M2iX AM /2K G2`Mb+?`Bii rm`/2 2BM aQ7i@J`;BM ;2Mmixi- /X?X 2b rm`/2M KBMBKH2 62?HFHbbB@
}FiBQM2M BM /2M h`BMBM;b/i2M xm;2Hbb2MX oQ` /2K h`BMBM;bb+?`Bii rm`/2M /B2 .i2M MQ`KHBbB2`i- BM/2K bB2 pQK JBii2Hr2`i #27`2Bi mM/ m7 1BM?2Bibp`BMx bFHB2`i rm`/2MX
9XkXjX 1pHmiBQM /2` KQ`T?QHQ;Bb+?2M JBiQb2/2i2FiBQM2M
6Ƀ` /B2 mbr2`imM; mM/ MHvb2 /2` KQ`T?QHQ;Bb+?2M JBiQb2/2i2FiBQM rm`/2 /2` _2@
72`2Mx/i2Mbix *2h_2aX ;2MmixiX .B2 pQHHbi M/B; m7;2x2B+?M2i2 q+?bimKbFm`p2
dk
9XkX JBiQb2/2i2FiBQM BM /2M a+?` ;HB+?i#BH/2`M
2`Kƺ;HB+?i 2b- /2M 1BM~mbb /2` p2`b+?B2/2M2M S`K2i2` m7 /B2 JBiQb2/2i2FiBQM /2@
iBHHB2`i xm mMi2`bm+?2M Up;HX ##X 9X8 mM/ ##X 9XeVX 6Ƀ` /B2 1pHmiBQM rm`/2M /B2 2`bi2HHi2M _272`2MxKBiQb2M p2`r2M/2i- /B2 mb RNyj JBiQb2M mM/ dkdd LB+?i@JBiQb2M
#2bi2?2M Up;HX ##X 9X9VX
mbr2`imM; 7Ƀ` /2M Ksf ml mM/ Kmf ml EHbbB}FiQ`
.B2 .2i2FiBQMb;2MmB;F2Bi /2bKsf ml EHbbB}FiQ`b Bbi 7Ƀ` /B2 p2`b+?B2/2M2M S`K2i2`
BM ##X 9Xd Hb _P*@Em`p2 ;2x2B;iX >B2` Bbi /2miHB+? xm 2`F2MM2M- /bb /B2 #2bi2M 1`@
;2#MBbb2 KBi /2` M/2`mM; /2` w2HHH M;2 2`xB2Hi r2`/2MX .b b+?H2+?i2bi2 .2i2FiBQMb2`@
;2#MBb rm`/2 KBi /2` M/2`mM; /2` >2HHB;F2Bi /2` w2HH2M 2``2B+?iX JBi /2M S`K2i2`M G M;2- :`ƺĽ2 mM/ EQKTFi?2Bi r2`/2M /B2 JBiQb2M KBi mMi2`b+?B2/HB+?2M :2MmB;@
F2Bi2M ;27mM/2M- Q#rQ?H /B2b2 S`K2i2` b2?` ?MHB+?2 1B;2Mb+?7i2M /2` w2HHFQMim`
#2b+?`2B#2M, .B2 EQKTFi?2Bi rB`/ xX"X mb /2` 6H +?2 #2`2+?M2iX 1BM2 ɂ#2`bB+?i /2`
.2i2FiBQMb;2MmB;F2Bi HH2` S`K2i2`FQK#BMiBQM2M /2`Ksf ml mM/Kmf ml EHbbB}F@
iQ`2M Bbi BM h#X 9XR m7;2HBbi2iX AMb;2bKi x2B;i bB+?- /bb /B2 G M;2 /2` p2`H bbHB+?bi2 S`K2i2` Bbi- mK 2BM2 JBiQb2 xm /2i2FiB2`2MX
AM ##X 9Xd rB`/ /B2 .2i2FiBQMb;2MmB;F2Bi /2` 2BMx2HM2M S`K2i2` /2bKsf ml EHbbB@
}FiQ`b Ƀ#2` /B2 w2Bi p2`;HB+?2MX >B2`xm rm`/2M /B2 l*@q2`i2 7Ƀ` HH2 w2Bi72Mbi2` pQM 8 aimM/2M #2`2+?M2iX qB2/2` Bbi xm 2`F2MM2M- /bb /2`Ksf ml EHbbB}FiQ` M?M/ /2`
G M;2 /B2 #2bi2M 1`;2#MBbb2 HB272`iX q ?`2M/ /B2 S`K2i2` G M;2 mM/ >2HHB;F2Bi /m`+?@
;2?2M/ K #2bi2M #xrX b+?H2+?i2bi2M ;22B;M2i bBM/- mK w2HHi2BHmM;2M xm }M/2M- M/2`i bB+? /B2 .2i2FiBQMb;2MmB;F2Bi 7Ƀ` /B2 S`K2i2` EQKTFi?2Bi mM/ 6H +?2, q ?`2M/
/B2 6H +?2 2BM2` w2HHFQMim` BM /2` 2`bi2M > H7i2 b2?` ;mi2 _2bmHii2 HB272`i UAU C >0.8V mM/ K 1M/2 #7 HHi UAU C <0.75V- bi2B;i /B2 .2i2FiBQMb`i2 /2bKsf ml- /2` /B2 EQK@
TFi?2Bi Mmixi pQM 2BM2` AU C ≈ 0.65 xm AU C > 0.8X .B2b2 M/2`mM; Bbi KBi /2`
w2HHKQ`T?QHQ;B2 xm 2`FH `2M- /B2 bB+? #? M;B; pQM /2` w2HH/B+?i2 bi`F M/2`i Up;HX
##X 9X8 mM/ ##X 9XeVX
h#2HH2 9XRX, o2`;H2B+? HH2` EQK#BMiBQM2M pQM biiBb+?2M- KQ`T?QHQ;Bb+?2M 1B;2M@
b+?7i2M Hb l*@q2`iX .B2 1BMi2BHmM; x2B;i /B2 _2bmHii2 /2b Ksf ml mM/ /2b Kmf ml
EHbbB}FiQ`bX
dj
ETBi2H 9X JBiQb2/2i2FiBQM
0 0.2 0.4 0.6 0.8 1
0 0.2 0.4 0.6 0.8 1
R@aT2xB}i i
a2MbBiBpBi i ∆fA- 6H +?2
∆fH- >2HHB;F2Bi
∆fL- G M;2
∆fK- EQKTFi?2Bi K3p−mf ml- /TiBp
UV _P*@Em`p2X
0 10 20 30 40 50
0.5 0.6 0.7 0.8 0.9 1
w2Bi BM aimM/2M
l*
S?b2 A S?b2 AA S?b2 AAA
U#V w2Bi#? M;B;2 l*@q2`i2X
##BH/mM; 9XdX, .B2 :2MmB;F2Bi /2` 2BMx2HM2M- KQ`T?QHQ;Bb+?2M S`K2i2`
∆fA,∆fH,∆fL,∆fK /2b Ksf ml mM/ /2b /TiB2`i2M K3p−mf ml EHbbB}FiQ`b bBM/ Hb _P*@Em`p2 UV mM/ x2Bi#? M;B;2 l*@q2`i2 M;2;2#2M- /B2 BM 2BM2K w2Bi72Mbi2` pQM 7ɃM7 aimM/2M #2`2+?M2i rm`/2M U#VX .B2 w2HHKQ`T?QHQ;B2 M/2`i bB+? KBi xmM2?K2M/2`
EQM~m2Mx mM/ #2rB`Fi 2BM2 #M2?K2M/2 U6H +?2∆fAV Q/2` xmM2?K2M/2 :2MmB;F2Bi UEQKTFi?2Bi∆fKV /2` JBiQb2/2i2FiBQMX
d9
9XkX JBiQb2/2i2FiBQM BM /2M a+?` ;HB+?i#BH/2`M
/TiBQM M /B2 q+?bimKbT?b2M UK3p−mf mlV
.B2 mbr2`imM; BM ##X 9Xd x2B;i- /bb /B2 M/2`mM; /2` w2HH/B+?i2 mM/ /2`
/KBi FQ``2HB2`2M/2M M/2`mM; /2` JQ`T?QHQ;B2 xm 2BM2` b+?rMF2M/2M :2Mm@
B;F2Bi /2` JBiQb2/2i2FiBQM2M 7Ƀ?`iX lK /B2 .2i2FiBQMbT2`7Q`KM+2 Ƀ#2` /B2 w2Bi mbxm;H2B+?2M- FƺMM2M /B2 p2`r2M/2i2M S`K2i2` M /B2 D2r2BHB;2 q+?bimKb@
T?b2 M;2Tbbi r2`/2MX .B2b2 /TiBQM rm`/2 BM /2K K3p−mf ml EHbbB}xB2`2`
`2HBbB2`i- /2` x2Bi#? M;B; /B2 #2bi2 S`K2i2`FQK#BMiBQM /2` D2r2BHB;2M q+?b@
imKbT?b2 mbr ?HiX 1b Bbi H2B+?i Kƺ;HB+?- /B2 x2BiHB+?2 /TiBQM xm 2`r2Bi2`M mM/
/B2 S`K2i2`r?H M /B2 EQM~m2Mx- w2HH/B+?i2 Q/2` w2HH;`ƺĽ2 xm FQTT2HMX .B2 #2bi2 S`K2i2`FQK#BMiBQM2M /2` D2r2BHB;2M q+?bimKbT?b2 rm`/2 KBi
>BH72 /2` _272`2Mx/i2M *2h_2aX 2`KBii2HiX >B2`7Ƀ` rm`/2M /B2 _272`2MxKBiQb2M BM /`2B :`mTT2M 2BM;2i2BHi U0h−10h,10h−40h,40h−EndeV- /B2 /2M q+?bimKb@
T?b2M 2MibT`2+?2MX Mb+?HB2Ľ2M/ rm`/2M HH2 7ɃM7x2?M S`K2i2`FQK#BMiBQM2M BM D2/2` /2` /`2B S?b2M ;2i2bi2i mM/ /B2 EQK#BMiBQM KBi /2M ?ƺ+?bi2M l*@
q2`i2M #2biBKKiX .B2 ;2r ?Hi2M S`K2i2`- /B2 7Ƀ` /B2 /TiBQM /2bK3p−mf ml p2`r2M/2i rm`/2M- bBM/ BM /2` ##X 9X3 M;2;2#2MX
qB2 2`r`i2i HB272`i2 /2` /TiB2`i2 EHbbB}FiQ` K3p−mf ml #2bb2`2 1`;2#MBbb2 Hb /2` Ksf ml Q/2` /2` Kmf mlUp;HX ##X 9XdVX 1BM2 pQHHbi M/B;2 GBbi2 HH2` S`@
K2i2`FQK#BMiBQM2M BM D2/2` /2` /`2B S?b2M Bbi BK M?M; BM h#X XR ;2;2#2MX q+?bimKbT?b2 w2BiBMi2`pHH S`K2i2`
AX UG; S?b2V 0h−10h ∆fA
AAX U1tTX q+?bimKbV 10h−40h ∆fL,∆fK,∆fH
AAAX UaiiBQM `2 S?b2V 40h−Ende ∆fK,∆fL
##BH/mM; 9X3X, S`K2i2`FQK#BMiBQM 7Ƀ` /2M EHbbB}FiQ` K3p−mf mlX
9XkX9X :`2Mx2M /2` KQ`T?QHQ;Bb+?2M EHbbB}FiQ`2M
.B2 mMi2`bm+?i2M EHbbB}FiQ`2M Ksf ml mM/ Kmf ml x2B;2M- /bb 2BM2 JBiQb2 Ƀ#2` /B2
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