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8/3/2019 Hrlimann Kap7
1/37
3,;?0=
!,>?0=492 .:8;70C4?D B4?3
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0A> :BF H? MABL :G= MA> ?HEEHPBG@ K BL MH LAHP MA:M =>I>G=BG@ HG MA>BG?HKF:MBHG GM RHN K>BO> : KM:BG K>LNEM 0ABL BL =HG> BG MPH I:KML 0ABLK :==K>LL>L F:MKBL PA>K>:L MA> ?HEEHPBG@ K ?HL HG LBFNE:MBHGL0A> TKLM L> LM>K:L BGMKH=N= BG MA> IK>OBHNL K :G= =>:EL PBMA MA> K>E:MBHG ;>MP>>G :O:KB:;E> :G= MA> LRLM>F 0A> L>:EL PBMA MA> K>E:MBHG ;>MP>>G MPH
O:KB:;E>L @:BG LM:KMBG@ PBMA A:K=ER :GR BG?HKF:MBHG :G= ;>A:OBHK H? : LRLM>F BG MA> H? MBF> BMBL BFIHKM:GM MH M:D> MA> MBF> BGMH K:MBHG 0ABL BL =BL= E:M>K BG MABLK
&07,?4:9 -0?B009 ,9 070809? ,9/ ?30 >D>?08
=:>>48;,.?8,?=4C
%G L> MA> %) P:L BGMKH=N= MA> P:R 2>LM>K7 I \8 NL>L BM $> =>LL PBMA ABL %) : F>MAH= NL>= MH JN:EB?R MA>BGUN>G H? >: MHP:K=L : LRLM>F $> NL>L BM :L : IK>OBHNL LM>I ;>?HK> NL> MA> %) :L :G :G:ERLBL MHHE:?M>K MA> ( BL : :GR K>LMKBE>F>GML K>E:M>= MH F:KD :GBFI: %) HMA :EEHP MH O:EN> =BK> E:LM L>GM>G : ?HEEHPBG@ T@
NK> HG I 0A> >E>F>GM +IFBCJ9F BL : =BK>B@A;HK MH MA> >E>F>GM'F=79 PA>K>:L BJ9GHA9BH BL ?NKMA>K =HPG MA> ?HK> ?NKMA>K:P:R ?KHF MA> O:KB:;E> 'F=79 2>LM>K :L P>EE :L #HF>S :G= ,KH;LM :EEHP HG> MH
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! ! %!& $! !
Price Turnover Earnings Investment
S S S
"B@NK> :NL:E BFI: >E>F>GM 'F=79 MAKHN@A MH +IFBCJ9F :G=BJ9GHA9BH >O>G MAHN@A MA>K> BL GH =BK>E:MBHG ;>MP>>G 'F=79 :G= BJ9GHA9BH 0A>R F:R O:KR MA> LMK>G@MA H? MA> BFI: L>GL> MA:M MA> >\>K MA:G MA:M HG BJ9GHA9BH %G MABL L> L>GLBMBOBMR H?MABL BFI: KHE> H? :G >E>F>GM PBMABG : LRLM>F BL =BL=
'09>4?4A4?D :1 ?30 .=:>>48;,.?8,?=4C
L MA> ;:LB< >Q:FIE> ?HK MA> ?HEEHPBG@ =BL LRLM>F H? MA> IHINE:MBHG BL NL>= ;:L>= HG MA> FH=>E NL>= ;R /M>KF:G 7 I \8 :G= BL @BO>GBG T@NK> :L : (
1 Population
7 Population
relative tocarryingcapacity
B
R
B
R
4 Fractionalbirth rate 5 Fractional
death rateS
O
S
6 Carryingcapacity
O10 Maximum
degradationof carryingcapacity
S
B
Degradation
2 Birth
SS
S
3 Death
S S
O
9 Degradationof carryingcapacity
SS
O
8 Regeneration ofcarrying capacity
S
B
"B@NK> ,HINE:MBHG @KHPMA BG
8/3/2019 Hrlimann Kap7
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95H %G MABL FH=>E MA> M> ?HEEHPBG@ F>MAH=L :EE NL> MABL FH=>E
:L>= HG MABL %) MA:M HGER BGLMA> =BK>GM ?HK MABL K>LMKB MA> ( W:L :G :?M>K MAHN@AMW :G= MA>K>?HK> A:O> EBGD>=MA> O:KB:;E>L =BK>K> : =BK>= HG MA> ?: :GR ?NKMA>K BG?HKF:MBHG MA:G MA> EBGDL ;>MP>>G MA> O:KB:;E>L RHN >QBLM>G H? : EBGD ;R INMMBG@ MA> T@NK> BGMH MA> :=>JN:M> LJN:K>0A> K>LNEM H? MABL :G:ERLBL BL @BO>G BG M:;E>
0J0.? ?:
1=:8 '
,HINE:MBHG BKMA >:MA
"K: "K::MA K:M> :KKRBG@ @>G>K:MBHG H? < >@K:=:MBHG H? <
):Q =>@K H? <
$'
0:;E> :LB<
8/3/2019 Hrlimann Kap7
4/37
! ! %!& $! !
0 1 2 3 4
1
2
3
4
PS
AS
0
1
C
AB8
Variables atthe same spot:
= 2, 3, 9= 4, 5, 10= 6, 7
A
B
C
12
8
4
2
0.5
1
2
"B@NK> .HE>L : =B:@K:F PABL> O:KB:;E>L :K> G>NMK:E = MHMA> HMA>K O:KB:;E>L 0A> !E>F>GML LBMN:M>= :M IHBGM :K> MA> FHLM K>:O:KB:;E>L :L MA>R EB> HG MA> LMK:B@AM EBG> K>IK>L>GMBG@ MA> -O:EN> H? PBMAMA> EHP>LM O:EN> !E>F>GM BL MA> O:KB:;E> MA:M BL MA> FHLM ;N\>KBG@ :L BM BLLBMN:M>= HG MA> BLHJN:GM PBMA MA> O:EN> H? %G T@NK> HG I:@> BM BL :KMA:M MA> O:KB:;E> )9;9B9F5H=CB C: 75FFM=B; 75D57=HM FNLM ;> : I:LLBO> O:KB:;E>
BG MABL LRLM>F :L MA>K> :K> GH >E>F>GML MA:M BGUN>G BM0A> >\>K>GM L ?HK MA> :QBL BL @BO>G BG T@NK> >
MA> L H? MA> :QBL A:L ;>>G BG:L>= BM BL EH@BL FHO>MHP:K=L MA> IHBGM H? HKB@BG %? LHF>HG> KHE> H? >: BL:;LHENM> HG> PHNE= A:O> MH :K@N> MA:M :EE >E>F>GML :K> FHK> HK E>LL ;N\>KBG@ BGT@NK> = MH MA> KHE> MA>R A:= BG MA> IK>OBHNL T@NK>
0 2 4 8 10
2
4
6
10
PS
AS
0
C
AB8
Variables atthe same spot:
= 2, 3, 9= 4, 5, 10= 6, 7
A
B
C
75
50
25
12.5
0.5
1
2
6
8
1
"B@NK> .HE>L :G=>= :QBL
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! !$ ! ! &!
%M F:D>L MA>K>?HK> L>GL> MH BGM>KIK>M MA> KHE> H? MA> O:KB:;E>L :L K>E:MBO> KHE>LMH MA> HMA>KL PBMABG : LRLM>F
/HF> :NMAHKL =H GHM >QIEBLMKB =BK>= O:KB:;E>L:K> O:EN>= 0A> :K@NF>GM BL MA:M : O:KB:;E> GHM HGER >\>B@A;HKL
;NM :ELH O:KB:;E>L MA:M :K> ?NKMA>K =HPG MA> := MH: =BLMHKMBHG H? MA> KHE>L H? MA> >E>F>GML 0H BEENLMK:M> MABL >\> >E>F>GMLA:O> ;>>G :==BMBHG:EER O:EN>= BG M:;E>
0J0.? ?:
1=:8 '
,HINE:MBHG BKMA >:MA "K: "K::MA K:M> :KKRBG@ @>G>K:MBHG H? < >@K:=:MBHG H? <
):Q =>@K H?
$'
0:;E> HPG MA> :==BMBHG:E =HPG MA> >FIA:LBS>= L RHN > MA>BFIHKM:G H? MA> >E>F>GM 95H>G LMK>LL>= :G= MA>K>?HK> BML BGUN>GBG:L>= %M :K@N>= MA:M : BG 95H\>@ MA> >E>F>GM 5FFM=B; 75D57=HM :L MA> ?>P>K EBOBG@ ;>BG@L MA>K> :K> MA> E>LLH? MA> LNEMBG@ K>E:MBO> KHE> H? >: H?MABL G>P %) BL LAHPG BG T@NK>
HFI:K>= MH MA> KHE>L H? >: BG MA> ;:LB< %) BG T@NK> HG I:@> MA> KHE> H? >E>F>GM 95H K>E:MBO>ER FBG MABL G>P %) "NKMA>K MA> O:KB:;E> 'CDI@5H=CB A:L EHLM BFIHKM:G :G= A:L
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! ! %!& $! !
0 2 4 51
2
3
4
6
PS
AS
0
A
B
8
Variables atthe same spot:
= 1, 6= 4, 5, 10
A
B
27
18
9
4.5 0.5
1
2
6
5
3
1 29
3
7
"B@NK> .HE>L NG=>K MA> BGUN>G H? =HPG MA> BGLI>QM LM>I LHF> ?NKMA>K BG?HKF:MBHG BL BG= BGMH MA> %) %? RHN A:O> FHK>BG?HKF:MBHG :;HNM MA> LRLM>F BG MA> L>GL> MA:M RHN P:GM MH :== BG?HKF:MBHG:;HNM MA> LMK>G@MA H? BFI:K> BL : K>G=>= P:R H? =HBG@ LH 0ABLF>MAH= A:L :EK>:=R ;>>G BGMKH=N= ;R 2>LM>K L>> I:@> \ ?:=P:R H? =HBG@ LH BL ;R NLBG@ MA> GNF;>KL MH PA>K> MA> T@NK>L LM:G= :L
>FIMR 9: [email protected] MA>K> BL GH =BK>MP>>G O:KB:;E> :G=
9: [email protected] B? O:KB:;E> =H>L GHM K>:KRIHHKER HK PBMA : AN@> MBF> E:@ HG L BG O:KB:;E>
B0,6 [email protected] B? O:KB:;E> K>::DER HG : LMKHG@ BG O:KB:;E> LN;IKHIHKMBHG:E
84//70 [email protected] B? O:KB:;E> K>: L:F>:L O:KB:;E> IKHIHKMBHG:E
>?=:92 [email protected] B? O:KB:;E> K>: =BLIKHIHKMBHG:M>ER AB@A
0ABL :IIKH:= :G= MA> K>LNEML :K> @BO>G BG M:;E> I
"HEEHPBG@ MA> K>LNEML H? MA> %) MA> KHE>L H? >: :K> K>IK>L>GM>= BGT@NK> HG I:@> HFI:K>= MH MA> ;:LB< %) MA> KHE> H? MA> O:KB:;E>'CDI@5H=CB A:L FHO>= MHP:K=L MA> F57H=CB5@6=FH< F5H9 A:L FHO>= :P:R ?KHF MA> LIHM 0ABL F>:GL MA:M BM BL : K>E:MBO>ER;>MM>K BG=B HMA>KL BG 0A> JN>LMBHG MA:M F:R KBL> BL=H>L BM F:D> L>GL> MA:M MA> F57H=CB5@ 6=FH< F5H9 LAHNE= ;> : ;>MM>K BG=BJN>LMBHG RHN A:O> MH :G:ERS> PAR >E>F>GM A:L : AB@A>K I:LLBO> LNF ,/ BG MA> O:KB:;E> F57H=CB5@ 6=FH< F5H9 K>BO>L : AB@A>K
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! !$ ! ! &!
0J0.? ?:
1=:8 '
,HINE:MBHG BKMA
>:MA "K: "K::MA K:M> :KKRBG@ @>G>K:MBHG H? < >@K:=:MBHG H? <
):Q =>@K H? <
$'
0:;E> %) BG BG?HKF:MBHG LMK>G@MAL
BFI:G :G= MA>G : M:D>G :L >@ BG ABG: PA>K> MA>RA:O> BGMKH=N= MA> HG> QIE:G:MBHG F:R ;> MA:M MA>?>KMBEBMR =>L ?:LM>K B? MA> >GOBKHGF>GM PHKL>GL = MH MA> K>=N >QI>GMBG@ MA> >QMK: BG?HKF:MBHG MA> KHE> H? >:E>F>GM
=B\>K>GMB:M>= >O>G ?NKMA>K
0 2 4 51
2
3
4
6
PS
AS
0
A
8
Variables atthe same spot:
= 2, 3, 9= 5, 10
A
B
27
18
9
4.5 0.5
1
2
6
5
3
1
6
4
1
B
7
"B@NK> .HE>L H? >: PA>G MA> BG?HKF:MBHG :;HNM LMK>G@MA BL BG=
!O>G MAHN@A MA>K> BL FHK> BG?HKF:MBHG INM BGMH MA> %) RHN FNLM D>>I BG
FBG= MA:M MA> E>O>E H? F>:LNK>F>GM BL LMBEE :G HK=BG:E L :L BGMKH=N= ;R/M>O>GL 7 I 8 /MKB:DBG@ MA> GNF;>KL HGER K>IK>L>GM MA> K:GDHK=>K H? MA> >GMBMB>L HFI:KBLHGL H? @K>:M>K :G= LF:EE>K F:=> $HP>O>K
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! ! %!& $! !
HI>K:MBHGL LN:GBG@E>LL0ABL F>:GL MA:M :G : LNF / HK ,/ H? ;R :==BG@ MAK>> BFI:L GHM A:O> MA> L:F> BFI:E>F>GM MA:M A:L HGER HG> H? :G= MA>K>?HK> :ELH :G / HK ,/ H? %M F>:GL
MA:M LNKIK>M:MBHGL :K> GHM ?:EL> %? HG> HI>K:M>L PBMA :G HK=BG:E L MH =>L :G= F>:LNK>MA> BFI:TG> MA> KHE> H? :G >E>F>GM BG : LRLM>F MA> K>LNEML FNLM ;>?:EL> 0ABL ?:>G :==K>LL>= LH ?:K
0A>K> BL : P:R MH P:M>K =HPG MABL :K@NF>GM +G> A:L MH :K@N> MA:M MA> E>O>EH? F>:LNK>F>GM NL>= BL :M E>:LM HG> E>O>E AB@A>K %? RHN NL> :G BGM>KO:E F>:LNK>F>GM MA> :IIEB>= HI>K:MBHGL PHNE= F:D> L>GL> 0H :O> LH MA> BGM>KIK>M:MBHGH? MA> T@NK>L A:L MH ;> FHK> H? MA> ?HEEHPBG@ DBG=
>FIMR 9: [email protected] MA>K> BL GH =BK>MP>>G O:KB:;E> :G=
9: [email protected] B? O:KB:;E> =H>L GHM K>:KRIHHKER HK PBMA : AN@> MBF> E:@ HG L BG O:KB:;E>
B0,6 [email protected] B? O:KB:;E> K>::DER HG : BG O:KB:;E>
84//70 [email protected] B? O:KB:;E> K>:
>?=:92 [email protected] B? O:KB:;E> K>:
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
6A,7@0
2>LM>K NL>L MA> DO:EN> MH LI> E>G@MA H? MA> :QBL BG MA> K>LNEMBG@ T@NK>LMH =>M>KFBG> MA> KHE> H? >:E>F>GM L>> I 0H K> DO:EN> BL=>TG>= :L
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! !$ ! ! &!
% /&. *
(
*
/
( GNF;>K H? O:KB:;E>L
# BG=BL
0A> B=>: BL MH :OHB= MA> =BL IK>OBHNL I:@>L %M @BO>L MA> PAHE>%) :G BFIK>LLBHG MA:M MA> KHE>L :K> :;LHENM> :G= GHM K>E:MBO> :L =BL=IKBHK 0ABL L> %M P:L L:B= MA:M MA>L BL G LH MA:M : O:KB:;E> PBMA :G / HK ,/ MA:M A:L MA> L:F> :FHNGM :LMA> GNF;>K H? O:KB:;E>L FNLM ;> BG MA> G>NMK:E :K>: 0A>K>?HK> MA> LI>G=L HG MA> GNF;>K H? >E>F>GML BG : LRLM>F 2>LM>K NL>L MA> GNF;>KL MH MH =>TG> MA> BFI: O:KB:;E> MH :GHMA>K 0ABL F>:GL MA:M : O:KB:;E>MA:M A:L : P>:D BGUN>G HG >O>KR HMA>K O:KB:;E> BG MA> LRLM>F :G= K>BO>L :P>:D BGUN>G ?KHF >O>KR HMA>K O:KB:;E> :M MA> L:F> MBF> BL : G>NMK:E O:KB:;E>:L BM PBEE ;> LBMN:M>= BG MA> GM>K H? MA> T@NK> HGL>JN>GMER : O:KB:;E> MA:M A:LLBFBE:K BGUN>G O:EN>= PHNE= ;> LBMN:M>= :MMA> O>KR MHI KB@AM K BG MA> K B? MA> DO:EN> BL : LRLM>F BL ;N\>KBG@ :G= TG:EER
B? MA> DO:EN> BL MA> LRLM>F BL *>NMK:E %)
%G M:;E> MA>K> :K> MPH >Q:FIE>L 0A> E>?M >Q:FIE> K>IK>L>GML : LRLM>FPA>K> >O>KR >E>F>GM A:L : P>:D BGUN>G HGMH :EE HMA>K O:KB:;E>L 0A> KB@AM>Q:FIE> L : LRLM>F PA>K> >:E>F>GM A:L : LMKHG@ BGUN>G HGMHHG> HMA>K O:KB:;E> HMA >Q:FIE>L A:O> BG L :K> G>NMK:E:G= MA>K>?HK> :K> LBMN:M>= BG MA> GM>K H? : KHE> =B:@K:F "NKMA>K MA> DO:EN>H? ;HMA LRLM>FL BL
% /&.
L MA> DO:EN> BL :;HO> MA> LRLM>F :L : PAHE> BL : HKR ;HMA LRLM>FL :K> NMK:E >E>F>GML
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! ! %!& $! !
PBMAHNM >QIMBHGL %M BL MH MA> K>:=>K MH => B? MABL F:D>L L>GL> 0ABL BL :LMKHG@ :K@NF>GM ?HK MA> IKHIHL:E MA:M MA> KHE> H? >:E>F>GM BL HGER MH ;> L>>GK>E:MBO>ER = MH MA> HMA>KL K:MA>K MA:G :;LHENM>ER :L MA> DO:EN> LN@@>LML1LBG@ MA> ?HKFNE: ?HK QBMR :L BGMKH=N= HG I:@> MA> :G:ERLBL ?HK ;HMA
FH=>EL BG M:;E> BL :L ?HEEHPL 0A> E>?M FH=>E E>F>GML :G= :GL MA:M MA> QBMR H? MA> E>?M >Q:FIE> BL "HK MA> KB@AM >Q:FIE>PA>K> MA>K> :K> :ELH >E>F>GML ;NM HGER K>E:MBHGL MA> G FNLL = MH MA> E>?M >Q:FIE>
9/4.,?:=> ,9/ .:9?=:77,-70 A,=4,-70>
%G MA> IK>OBHNL L> %)F>MAH= A:L ;>>G :G:ERS>= 0A>K>;R MA> LM:KMBG@ IHBGM P:L : FBGBF:E DGHPE>=@> :;HNM MA> LRLM>F %M A:L ;>>G LAHPG MA:MMA> %)F>MAH= BL O>KR L>GLBMBO> MHP:K=L AHP F:GR =BK>E:MBHGLABIL :K> O:EN>= "NKMA>K BG?HKF:MBHG A:L ;>>G :==>= BGMH MA> %) :G==BL= %M A:L ;>>G LAHPG MA:M MA> KHE>L H? MA> >E>F>GML :EP:RL A:O> MH ;>L>>G :L K>E:MBO> MH MA> HMA>KL
"HK =>KL I:LLBO> O:KB:;E>L :K> IK>=>LMBG:M>= MH ;> NL>= :L BG=BK>:L : O:KB:;E>L LAHNE= K>IK>L>GM LM>>K:;E> O:KB:;E>L MH BGUN>GMA> LRLM>F L MA>R A:O> : EHP ,/ MA>R :K> A:K=ER BGUN>G= ;R MA> LRLM>F?M>K BGUN>G LRLM>F ;R O:EN> H? LN MA> LRLM>F LAHNE= LM:;BEBS> BG : G>P R A:O> : AB@A ,/ %G MH=:RWLPHKE= F:G:@>KL PHNE= EBD> MH L>> MA> BGUN>G H? MA>BK =>=B:M>ER1G?HKMNG:M>ER MABL BL GHM :EP:RL IHLLB;E> :G= =>KL =H GHM A:O> MA>I:MB>G HK MBF> MH P:BM :G= L>> K>: LRLM>F K>E:MBHG ;>MP>>GMPH >E>F>GML GL> H? LMK>G@MA %M:ELH BGL : MBF> GM H>L : KM:BG K>: K>BO>K HER :?M>K : PABE> HK @K:=N:EER 0A> %) @BO>L :GLP>KL MH MA> JN>LMBHGAHP LMKHG@ BL : LI> BGM>K: LRLM>F NM BM =H>L GHML:R :GRMABG@ :;HNM BG PA:M MBF> ?K:F> MABL BGM>K:L IE: "HK MABLK>:LHG =>KL LAHNE= A:O> : @K>:M BGM>K>LM BG @>MMBG@ MH DGHP PA>G MA>
LRLM>F PBEE K>:K : O:KB:;E> HK K>LM BG=BG PBEE BG=B:G MA> LRLM>F BL JN:EBM:MBO> LHENMBHG BL IK>L>GM>= BG MA> ?HEEHPBG@ L>
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! !$ ! ! &!
(30 8,??0= :1 ?480
8;,.? :1 , A,=4,-70 49 ?30 .:@=>0 :1 ?480
%G MA> IK>OBHNL L> =BL BGM>K:MP>>G
: O:KB:;E> :G= MA> LRLM>F K>@:K=BG@ BML BFI: =BLL MA> BFI: O:KB:;E> MH MA> G>QM ;>A:O> HO>K MA> H? MBF> 0H BEENLMK:M> MA> IKH;E>F HG> BF:@BG>L MA:M MA> F:G:@>F>GM P:GML MHK:BL> IKH=N LM:\WL FHMBO:MBHG
motivation program productivityS
0H =H LH MA> >Q> IE:GL : FHMBO:MBHG IKH@K:F :G= MA>G BFIE>F>GML BM0ABL =HG> BGLM:GMER ;NM K:MA>K M:D>L MBF> 0A>K>?HK> MA> BFI: FHMBO:MBHG IKH@K:F O:KB>L HO>K MA> H? MBF> K:MA>K MA:G ;>BG@ : BFI: H? MBF> F:R EHHDLBFBE:K MH MA> HG> =K:PG BG T@ %G LM:@> MA> F:G:@>F>GM F:R :GGHNGMA> IKH@K:F HK A:O> : KH:= LAHP %G MABL LM:@> MA>R :K> @:BGBG@ BG=BOB=N:EL PAHEBD> MH CHBG MA> IKHC>:F HK ;> D>R IE:R>KL BG MA> FHMBO:MBHG IKH@K:FNKBG@ MABL LM:@> MA> BFI: IKH@K:F BL LM:KMBG@ MH BG:L> %M F:R>O>G EHHL> BFI: F>:GMBF> K>:LHG F:R ;> MA:M MA> PHKD?HK MABGDLBM BL CNLM :GHMA>K B=>: ;R MA> F:G:@>F>GM MH D>>I I>HIE> ;NLR *>O>KMA>E>LL
MA> FHMBO:MBHG IKH@K:F LM:KML IBG :G= A>G BFI:MK:GLBMBHG BGMH LM:@> BL UN>GM %G MABL LM:@> MA> IKH@K:F =BLIE:RL BML IHM>GMB:E:G= LH K>:L BML F:QBFNF BFI: MA> BGGMBO>L FHO> BGMH MA>MABK= LM:@> $>K> MA> FHMBO:MBHG IKH@K:F A:L ;>>G KNGGBG@ ?HK JNBM> : PABE> "HKMA> PHKD>KL MA> BGGMBO>L A:O> ;> ;:LB< :G= MA>K>?HK> :K> GHM FHMBO:MBG@:GRFHK> 0A> BFI:
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! ! %!& $! !
A:L : G>:KER B=>:E LBMN:MBHG .>?>KKBG@ MH MA> >Q:FIE> BG T@ HG I MA> : FHMBO:MBHG IKH@K:F HG IKH=NLHO>K MA> H? MBF> :G= >G=L HG : AB@A>K E>O>E 0ABL G>P >JNBEB;KBNF BLMA> F:G:@>F>GML BGM>GMBHG %G MA> L> :@BGGBG@ ;NM :L MA> BFI:@:MBO>MA> : M MA> >G= H? MA> MK:HO>K:EE BFI: ;>EHP MA> I>:D S>KH HK >O>G PHKL> G>@:MBO>
short-term middle-term long-termtime
acc.
influence
strong
middle
weak
"B@NK> M>KFBGHEH@R H? LMH BGUN>G =K:PG BG T@NK> BL MA>UHP :M : KM:BG IHBGM BG MBF> PA>K>:L MA> : LMHO>E 1LN:EER MH LAHP MABL QM HG> NL>L LBFNE:MBHG MHHEL
9?0=;=0?,?4:9 :1 48;,.? 49 ?30 .:@=>0 :1 ?480
?NKMA>K IKH;E>F :KBL>L MA:M MA> BFI:KBH= ;NMMA> BGUN>G BG:L>L MAKHN@A : 0ABL F:R ;> MKN> ?HKLHF> L $HP>O>K MA>K> :K> F:GR L PA>K> MABL =H>L GHM :IIER %? : TKF>@ LM:KML :G BGM>KG:E FHMBO:MBHG >FIEHR>>LMABGD BG MA> ;>@BGGBG@ MA:M MA> IKH@K:F BL GH @HH= :L MA>R A:O> :EK>:=R KNGMAKHN@A LHF> NGLNKG:E IKH@K:FL :G= MA>K>?HK> =H GHM ;>EB>O> BG MA>LNP IKH@K:F 3A>G MBF> I:LL>L MA> >FIEHR>>L LM:KM MH LNIIHKM
MABL FHMBO:MBHG IKH@K:F :G= LH MA> BFI: LA:KIERL PBMA F:GR FHMBO:MBHG BGGMBO>L MA>BK BGUN>G ?:=>L HO>K MBF>
/H :?M>K LHF> MBF> A:L I:LL>= MA> BFI:G=L MH S>KH 0A> IKH@K:FMA>K>?HK> IKH=NL GHP HGER MNKG /N GHMK>IK>L>GM>= BG MA> %) %M PHNE= MA>K>?HK> ;> IK:F>GM BG @:MA>KBG@ BG?HKF:MBHG :;HNM MA> ;>A:OBHK HO>K MA> H? MBF>
+G> P:R P:L IK>L>GM>= ;R MA> F>MAH= #)) BG K LM:KMBG@HG I:@> PA>K> MA> %FI:GM LM:@>L L> P:R BL MH %) 0ABL =HG>
;R %) ?HK LAHKMM>KF >\>M>KF >\>KF >\> IKH;E>F PBMA MABL :IIKH:KR=B[ NL>K MH => B? :G= AHP LMKHG@ :G >\> LHNK MH
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! !$ ! ! &!
MA> K>IMHK BG MA> MAK>> MBF> LI:GL BL K>= %M F:R ?NGEE B? :GBGUN>G BL EBG>:K BG MA> H? MBF> NM H?M>G MA> ?NMNK> =>O>EHIF>GM BL GHMEBG>:K 0A>K>?HK> MABL MHHE PHNE= IKH=N K:G=HF LHENMBHGL
IHLLB;E> LHENMBHG MH @:BG BG?HKF:MBHG :;HNM MA> ;>A:OBHK BG MA> H?
MBF> MA> ?4808,?=4C
!0,9492 :1 .=:>>?4808,?=4C
%G MA> TKLM L> ?H =BL :G= =>E:R :G= BML BGUN>G HG BFI:>G LAHPG MA:MMBF> BL :G BFIHKM:GM ?: K>= PA>G LHEOBG@ Q
IKH;E>FL $>G MA> B=>: H? : F:MKBQ 0) KHL> /H :L MA> %)@BO>L :GLP>KL MH MA> JN>LMBHG K>@:K=BG@ MA> KHE> H? : O:KB:;E> BG : LRLM>F MA>B=>: H? : 0) BL MH @BO> BG?HKF:MBHG :;HNM AHP ?:LM BFI::= MAKHN@A :LRLM>F 0A> :BF BL MH @BO> NL>KL : MHHE MH :LL>LL MA> KHE> H? :G >E>F>GM K>E:MBO>MH MA> HMA>KL BG : LRLM>F K>@:K=BG@ MBF> L BM BL MRI> H? BG?HKF:MBHG K>@:K=BG@ MA> GM MBF> 0A> G>QMI:K:@K:IA :==K>LL>L MA> L H? MA> >E>F>GML
:9>?=@.?4:9 ,9/ 49?0=;=0?,?4:9 :1 , .=:>>?4808,?=4C
0A> TKLM 0) BL :@:BG ;:L>= HG A:K=ER :GR BG?HKF:MBHG >QIM ?HK MA> DGHPGG MA> 0) L:F> O:EN>L :L MA> ;:LB< %) 0A>=B\>K>G EB>L BG MA> LNF H? MA> KHPL :G= L> :K> GHM G:F>= :L/ :G= ,/ ;NM K:MA>K :L 89@5M DFC8I7H=CB , :G= F979=J98 89@5M . 0A>, BL :G BG=B K>= >E>F>GMNM MA>K> BL : =B\>K>G BG \> LRLM>F MH MA>/ G >E>F>GM MA:M K>BO>L :G BFINEL> :G= A>G A:L :G BFINEL> MHP:K=L MA>LN=BG@ >E>F>GML MHM:E :FHNGM H? LMK>G@MA %M MA>K>?HK> F:D>LL>GL> MH :== MA>F NI :L PBMA MA> / %G =>E:R ;>A:O>L =B\>K>GMER
0A> =>E:R = ;R :G >E>F>GM HGER =>I>G=L HG MA> MBF> BG MA> L>GL> MA:M :=>E:R BL : LAHKM MBF> E:@ HK : EHG@ MBF> @:I %M =H>L GHM IKH=N :GR G>P UHPL$>G BM F:D>L L>GL> GHM MH :== MA> O:EN>L ;NM K:MA>K MH :O>K:@> H?MA> = =>E:RL :L BG MA> ?HEEHPBG@ ?HKFNE: PA>K> ( K>IK>L>GML MA> GNF;>KH? O:KB:;E>L BG MA> LRLM>F
-'# $
(
$>G MA> O:EN>L :K> :EP:RL ;>MP>>G MA> EHP>LM :G= MA> AB@A>LM K:M> NL>=PA>G >O:EN:MBG@ /BFBE:K MA> .O:EN> H? >:E>F>GM BL ?HEEHPBG@ ?HKFNE:
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! ! %!& $! !
-'# $
(
0A> ;:LB< 0) A:L MA> GNF;>KL BG MA> F:MKBQ :L A:L MA> ;:LB< %) BGM:;E> HG I:@> 0A> =B\>K>G HGER EB>L BG MA> E:LM KHP :G= K>MA> . K>LI , A:O> O:EN>L H? /NL GHM @>G>K:M> :GR:==BMBHG:E DGHPE>=@>
0A> G>QM LM>I BG :==BG@ BG?HKF:MBHG BL MH O:EN> MA> =>E:RL ;>MP>>G MA> >E>F>GML L @K:IABIK>L>GM:MBHGL :K> F:=> MH LAHP MA> =>E:R BG : LRLM>F MABLBG?HKF:MBHG LAHNE= :ELH ;> MK:GL?>KK>= BGMH : 0) IHLLB;E> P:R BL :FIMR 9: [email protected] MA>K> BL GH =BK>MP>>G O:KB:;E> :G=
4880/4,?07D B? O:KB:;E> K>:=B:M>ER HGL BG O:KB:;E>
>3:=??0=8 B? O:KB:;E> K>: =>E:RHG L BG O:KB:;E>
84//70?0=8 B? O:KB:;E> K>: MBF>=>E:R HG : BG O:KB:;E>
7:92?0=8 B? O:KB:;E> K>: =>E:RHG : BG O:KB:;E>
IIERBG@ MABL EBLM MH MA> >Q:FIE> K>LNEML BG MA> ?HEEHPBG@ 0) M:;E>
?480 ?:
1=:8 $
,HINE:MBHG BKMA >:MA ";K
"=K < ,KM< .H< H<
):QH<
&
0:;E> KHLLMBF>F:MKBQ
0ABL BG?HKF:MBHG MK:GL?>KK>= BGMH MA> T@NK> H? KHE> H? >:BG : LRLM>F G HG =>E:R "B@NK> LAHPL MA> IHLBMBHG H?>:E>F>GM :G= BML KHE> 0A>K> :K> ;:LBL :G >E>F>GM
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! !$ ! ! &!
0 21 2.50.5
1
1.5
2
3
RD
DP
0
A
4
8
Variables atthe same spot:
= 6, 9A
1.5
2.5
3
0.5
2 3
7
1
5
sluggish
accelerative
braking
lively
"B@NK> .HE> H? :G >E>F>GM BG MA> QM H? MBF>
4A07D G >E>F>GM MA:M BL LBMN:M>= BG MABL K IKH=NL :EFHLM GH MBF>=>E:R %M K>:=B:M>ER PA>G O:EN>L NI MA> K %M :ELH @BO>LL LMK:B@AM :P:R =HPG MA> L> O:KB:;E>L A:O> MA> :=O:GM:@>MA:M MA>BK ;>A:OBHK :=CNLML ?:LM MH L BG MA> >GOBKHGF>GM +G MA>HMA>K A:G= B? MA>R :K> BGOHEO>= BG : K>BG?HK>=;:R LI>>=NI MA> =>O>EHIF>GM 0A>R A:O> : LF:EE , :G= .
=,6492 !E>F>GML MA:M :K> LBMN:M>= MHP:K=L MABL K LEHP =HPG MA> =B??NLBHG 0A>R :GL MA:M MA>R:=CNLM K:MA>K ?:LM PA>G :G >E>F>GM NI MA> L ;NM MA> ?HEEHPBG@>E>F>GML :EB@G O>KR LEHP 0A>L> >E>F>GML PHKD :L : ;K:D> MA:M LEHPL =HPGMA> =B\NLBHG BG : LRLM>F
'7@224>3 0A>L> :K> MA> =NEE >E>F>GML 0A>R A:O> : AB@A , :G= . 0ABLF>:GL MA:M MA>L> >E>F>GML HI>K:M> O>KR LEHP %M M:D>L LHF> MBF> NGMBEMA>R K>LIHG= M MA> L:F> MBF> BM M:D>L BML MBF> NGMBE MA> L A:II>G=HPG MA> F :L I:KM H? MA>LRLM>F "NKMA>K :L MA>R LEHP =HPG MA> L BG MA> LRLM>F BM M:D>LI:MB>G NGMBE : LRLM>F TG=L BML G>P ;:E:G :?M>K :G BGM>KO>GMBHG 0A>R:K> MA> F:BG ?HK HO>KLM>>KBG@
..070=,?4A0 0A> E:LM @HKR BL F:=> NI H? >E>F>GML PBMA : AB@A . :G= :EHP , 0A>R ;>A:O> MA> HIIHLBM> P:R H? MA> ;K:DBG@ >E>F>GML %M M:D>LLHF> MBF> NGMBE BFINEL>L :KKBO> :M MA>L> >E>F>GML ;NM MA>R L>G= MA>F ?:LM?HKP:K=
0A> KHE>L H? MA> >E>F>GML A>EI MH F BG MA> L>GL> H? BL MA>LRLM>F :L : PAHE> K:MA>K U>QB;E> HK K:MA>K KB@B= :G : LRLM>F :=CNLM LPB?MERMH L BG MA> >GOBKHGF>GM HK BL BM K:MA>K LMB\ 0A> O:KB:;E>L MA:M :
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! ! %!& $! !
K>:=B:M>ER :K> MA> IK>?>K:;E> HG>L :L MA>R :K> >:LB>K MH A:G=E> +G MA>L>:K ;>LM >E>F>GML MH NL> :L BGM>KO>GMBHG IHBGML HK BG=BL H? BG?HKF:MBHG :K> G>>=>= BFI: 0A> G>QM L>%) :G= 0) MH@>MA>K
:8-49492 ?30 491:=8,?4:9 :1 ! ,9/ (!
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
3 12 0.52.5
2
3
5
DP
AS
0
A Variables atthe same spot:
= 2, 3= 4, 5= 6, 9= 8, 10
A
B
C
D
1.5 0
1
1
4
B
C
7
D
braking-active
lively-
active
lively-buffering
braking-buffering
"B@NK> %=>:E O:KB:;E> :K>: H? T@NK> LIEBM BGMH MA> ?HEEHPBG@ ?HNK LJN:K>L :G=MA>K>?HK> ;:LB< KHE>L
=,6492,.?4A0 A,=4,-70 0A>L> O:KB:;E>L A:O> : AB@A / :G= ,O:EN> :G=
:K> LBMN:M>= BG MA> MHI E>?M K 0A>L> O:KB:;E>L A:O> : AB@A BFI:K EHG@ I:MAL HK LEHP LIK>:=L PBMABG MA> LRLM>F 0A>R :K> ;>LM B? MA>LRLM>F LAHNE= NG=>K@H : LEHP ;NM K:MA>K LN;LM:GMB:E
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! !$ ! ! &!
4A07D,.?4A0 A,=4,-70 $:OBG@ : AB@A / :G= : EHP ,O:EN> F:D>L MA>F MA>B=>:E BGM>KO>GMBHG IHBGML PBMABG : LRLM>F :L L BFIE>F>GM>=K:MA>K ?:LM 0A>R :K> LBMN:M>= MHP:K=L MA> MHI KB@AM K %? MA>K>BL BFF>=B:M> G>>= ?HK :L> :K> MA> IHBGML H? BGM>KO>GMBHG %G :
PA>G MA>K> :K> EBJNB=BMR IKH;E>FL
4A07D-@J0=492 A,=4,-70 0A>L> >E>F>GML A:O> : EHP / :G= ,O:EN> :G=:K> IHLBMBHG>= G>:K MA> ;HMMHF KB@AM :K>: ,NMMBG@ MA> >G>K@R BGMH MA>L>O:KB:;E>L =H>L GHM FN LRLM>F :L MA>BK BFI: E:LM @HKR H? >E>F>GML :K> BG MA> =BK> ;HMMHF E>?M LIHM 0A>L> O:KB:;E>L A:O> K:MA>K EHP BFI: LAHKM :G= EHG@ M>KF :G= :K> MA>K>?HK> :ELH GHM O>KR BGM>K>LMBG@ :LBGM>KO>GMBHG IHBGML
0ABL :G:ERLBL BL : MHHE MH O:EN> MA> KHE> H? >E>F>GML BG ?HKF H? BFI: MHP:K=L : LRLM>F >E>F>GML :M LIHM =FH FHLM :IIKHIKB:M> BGM>KO>GMBHG IHBGML MH MA> LRLM>F
/BFBE:K MA> :G:ERL>L H? MA> KHE> H? O:KB:;E>L :L BG=B LRLM>F L %=>:E :MMKB;NM>L ?HKBG=B : AB@A ,/O:EN> :G= : EHP .O:EN> AB@A ,/O:EN> F>:GLMA:M :G >E>F>GM BL :\>= FHK> BGM>GL>ER B? L HF EHP .O:EN> F>:GL MA:M :G >E>F>GM K>:=B:M>ER B? L A:II>G
0A> O:EN>L :K> :@:BG M:D>G ?KHF M:;E> I K>LI M:;E> I 0A>K>LNEMBG@ KHE>L H? MA> >E>F>GML :K> @BO>G BG MA> LN;L>JN>GM T@NK> %G HK=>KMA:M MA> T@NK> K>:= :L MA> IK>OBHNL BG MA> L>GL> MA:M MA> FHLM BGM>K>LMBG@?: LBMN:M>= BG MA> MHI KB@AM K MA> :QBL H? . A:L ;>>G MNKG>=
3 12 0.52.5
2
3
5
RD
PS
0
A
Variables atthe same spot:
= 5, 10A
1.5 0
1
9
4 7
6 1
23
4
6
8
accelerative-reactive
lively-reactive
lively-buffering
accelerative-buffering
"B@NK> %=>:E BG=BL G:F>= :L ?HEEHPL
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! ! %!& $! !
..070=,?4A0=0,.?4A0 A,=4,-70 0A>L> >E>F>GML :K> EH= G>:K MA> MHI E>?MK :G= A:O> : AB@A ,/ :G= .O:EN> !O>G MAHN@A MA>R BG=B MA>FHH= H? MA> LRLM>F K:MA>K LMKHG@ER MA>R :K> LEHP BG K>:L> ?: IHLBMBHG>= MH MA> MHI KB@AM LIHML MA>R A:O> : AB@A ,/ :G= EHP .O:EN> MA>R A:O> MA> I>K?>:K BGM>GL>ER PBMA : LAHKM K>: HGL BG MA> LRLM>F
4A07D-@J0=492 & A,=4,-70 0A>L> O:KB:;E>L A:O> EHP ,/ :L P>EE :L EHP.O:EN>L :G= :K> LBMN:M>= BG MA> ;HMMHF KB@AM :K>: !O>G MAHN@A MA>RK>:R A:O> : FH=>K:M> >\> LRLM>F
..070=,?4A0-@J0=492 A,=4,-70 L MA>R A:O> : EHP ,/ :G= : AB@A .
O:EN> MA>R ;:K>ER K>:K:MBHG BG MA> LRLM>F :G= =H BM O>KR LEHPER0A>R :K> EH= MHP:K=L MA> ;HMMHF E>?M K :G= :K> GHM O>KR @HH= MH LRLM>F
0ABL L>LMB@:MBHG H? KHE> BL : MHHE MH >O:EN:M> MA> OB:;BEBMR H? :G>E>F>GM :L BG=B:LNK> MA> FHH= H? MA> LRLM>F >E>F>GM :M LIHM 'CDI@5H=CB F9@5H=J9 HC 7 BL MA> FHLM :IIKHIKB:M>BG=B:LNK>L L BG MA> LRLM>F %M K>BO>L LMKHG@ BFI:= MH ;:=ER
%G MABL L> ?H BGM>K:MP>>G :G >E>F>GM :G= MA>
LRLM>F BM BL I:KM H? 0A> K>LNEML H? :G >E>F>GM A:O> MH ;> BGM>KIK>M>= :EP:RL :LK>E:MBO> MH MA> HMA>K ?: LM:KMBG@ IHBGM P:L : LRLM>F PA>K> HGER MA>K> DGHPG NKBG@ MABL I:KM FHK> BG?HKF:MBHG P:L @:BG>= ;RP>B@AMBG@ MA> K>E:MBHGLABI ;>MP>>G MA> ?:>GBFI: >\>G=>= ;R @:BG>= BG?HKF:MBHG BGMH= KHE> T@NK>L %G MA> G>QM L> ?H K>E:MBHG ;>MP>>GMA> O:KB:;E>L
&07,?4:9 -0?B009 ?B: 070809?> 49 , >D>?08
0H :IIHBGM MA> KHE> H? >:E>F>GM BG : LRLM>F P:L MA> K>LNEM H? MA> IK>OBHNLL> H? :G:ERLBL BL GHM >GHN@A MA> G>QM LM>I BL MH :G:ERS> MA>K>E:MBHGL ;>MP>>G :EE >E>F>GML PBMABG : LRLM>F 0ABL L>L JN:EBM:MBO>:GLP>KL MH JN>LMBHGL H? MA> ?HKF AHP EHG@ =H>L BM M:D> NGMBE :G BFINEL> :M>E>F>GM :KKBO>L :M >E>F>GM HK AHP ;B@ BL MA> BFI:K> MA> K>E:MBHG P:L ;>MP>>G :G >E>F>GM:G= BML LRLM>F A>K> MA> ?H K>E:MBHG ;>MP>>G MA> >E>F>GML 0A>BGBMB:E IHLBMBHG MA:M : =>K P:GML MH : E>O>E H? : KM:BGO:KB:;E> 0A> JN>LMBHG BL GHP PA>K> LAHNE= MA> BGM>KO>GMBHG M:D> IE: :G= AHP
EHG@ PBEE BM @H NGMBE MA> PBLA>= E>O>E H? : KM:BG O:KB:;E> LM:KML HMA>K P:R KHNG= MA> LM:KMBG@ IHLBMBHG BL MA:M : F:G:@>K P:GML MH BGM>KO>G> :M :KM:BG IHBGM BG MA> LRLM>F 0A> JN>LMBHG GHP BL PA>K> LAHNE= MA>
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! !$ !$ ! &!
M:D> IE: BG MA> L>GL> H? PAB BL MA> B=>:E BG=BKO>GMBHG 0A> HNMEBG> H? MABL L> ?H MA>GHG BFI: >/07,D8,?=4C [email protected] :1 /07,D
:9>?=@.?4:9 :1 , -,>4. .=:>>/07,D8,?=4C
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GH FBQ PBMA MA> IKBHK BGMKH=N= 0) MA> F:MKBQ BL = E:RF:MKBQ) 0A> TKLM ) BL :@:BG ;:L>= HG A:K=ER :GR BG?HKF:MBHG >QIM ?HK MA>DGHPG L> F:KD>= ;R MA> T@NK> :L LAHPG BGM:;E>
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I:MA ;>MP>>G MPH GH=>L :K> @BO>G BG MA> ?HEEHPBG@ M:;E>
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LRLM>F K>:LI AHP LEHP L LIK>:= MAKHN@AHNM : LRLM>F
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%G MABL MA> ;HMMHF KHNM> BL ?:LM>K HK A:L E>LL =>E:R BG HMA>K PHK=L0H =H MABL MRI> H?
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0A> GHMBHG ?HK LN;IKHIHKMBHG:E :G= ?HK =BLIKHIHKMBHG:M>ER AB@A BL NL>=;> HG> BL MA> BGO>KLBHG H? MA> HMA>K LH MA:M B? MA>R :K> FNEMBIEB>= PBMA>:K IKHIHKMBHG:EBMR BL MA> K>LNEM 0ABL BL :GHMA>K LNIIHLBMBHG MA:M BL
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0A> TKLM I:KM H? L>:EL PBMA =>E:R PA>K>:L MA> L>LL>LMA> >\> MPH F>GMBHG>= I:KML :K> = %GUN>G BGMABL L>GL> F>:GL MA> \>E:R %M BL >BMA>K :;HNM AHP :G>E>F>GM BGUN>GL MA> HMA>KL HK AHP :G >E>F>GM BL BGUN>G= ;R HMA>KL
:B ,9 070809? 4> [email protected]/ -D ?30 :?30=>
0H H? BGUN>G MA> TKLM => F:=> BL HG PABE>F>GM MA> ?HL L MA> >Q:FIE> BL : FH=>E :;HNM IHINE:MBHG @KHPMAMA> ?HG MA> MRI> H? =>E:R A:L MH ;> =>TG>= :L !)=>I>G=L HG MA> I:MAL @BO>G ;R MA> =>E:RL "HK MA> >Q:FIE> MA> ) LAHPGBG M:;E> I ;:L>= HG MA> =>E:R F:MKBQ M:;E> I BL G;> BM BGL MA> FHLM BG?HKF:MBHG :;HNM =>E:R 0ABL ) BL ;:L>= HGP>B@AM>= >=@>L :G= LHEO>L MA> LAHKM>LM I:MA BG MA> L>GL> H? LAHKM>LM =>E:R :L>=
HG MA> ) MA> LIHG=BG@ !) LAHPG BG M:;E> I BL G>>=>= 0A>O:EN>L H? MA> TKLM : G>>=>= :G= MA>K>?HK> = BGMA> ?HEEHPBG@ M:;E>
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! ! %!& $! !
$:;@7,?4:9
*H=> *H
>E:R !\> ,HINE:MBHG BGG H? ) !)
:L>= HG MA>L> O:EN>L T@NK> LAHPBG@ MA> BGUN>G MHP:K=L 'CDI@5H=CBBL :QBL BL =>E:R PA>K>:L MA> HMA>K BL MA> >\> BGUN>G H? ?: HG> BG=BLMA:M MA> BGUN>G BL =BLIKHIHKMBHG:M>ER AB@A 0A> I:KM ;>EHP S>KH BL MA> :K>:PA>K> >E>F>GML :K> LBMN:M>= MA:M BGUN>G 'CDI@5H=CB BG MA> HIIHLBM> =BK> L:F> BGM>KIK>M:MBHG :\>>G LM:M>= ?HK MA>MHI I:KM "BG:EER >E>F>GML HG MA> E>O>E H? S>KH =H GHM A:O> :GR HK HGER : O>KRP>:D BGUN>G HG 'CDI@5H=CB
0A> @K:IAB< LAHPL MA:M =FH\> BGUN>G= IHLBMBO>ER MA>G 95H
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! !$ !$ ! &!
K>=N= 0ABL F>:GL MA:M MA> :O>K:@> EB?> >QI>= ;RBFIKHOBG@ MA> F>=BKOB K>=NM BGBMB:E JN>LMBHG BG MABL @K:IAB< BL AHP :G= PA>G BL MA> >E>F>GM 'CDI@5H=CBBGUN>G= ;R : LI> HNM H? MA> LRLM>F "HK IHEBKL MA> @K:IA
LAHPL K>E:MBO>ER AHP LMKHG@ MA> BGBMB:E BFI: BGUN>G H? >O>KR O:KB:;E> BL MHP:K=L 'CDI@5H=CB %M A>EIL MH TG= MA>KB@AM BGM>KO>GMBHG IHBGM =>I>G=BG@ HG MA> @H:E
:B ,9 070809? [email protected]> ?30 :?30=>
>KL F:R ;> BG LBMN:MBHGL PA>K> MA>R :K> GHM L>:KBGM>KO>GMBHG IHBGM ;NM K:MA>K DGHP MA> BGM>KO>GMBHG IHBGM 0A>R :K> =PBMA MA> JN>LMBHG B? P> BGM>KO>G> PA:M PBEE A:II>G 0A>K>?HK> MA>R EBD> MHDGHP AHP : KM:BG O:KB:;E> BGUN>GL MA> HMA>KL BG PA:M =BK>E:R 0H LMBHG MA> E:R :G= >\> G>>=>= @:BG MA> !) =>I>G=L HG MA>G I:MA $>G MA> ) A:L MH ;> L>E>= TKLM +G FHK> MA> )PBMA MA> FHLM BG?HKF:MBHG BL IB= M:;E> I :G= A>G MA> K>E:M>=!) M:;E> I 0A> G>>=>= O:EN>L :K> BG >: TKLM KHP0A>R :K> GMK:EBS>= BG MA> ?HEEHPBG@ M:;E>
$:;@7,?4:9
*H=> *H
>E:R !\> ,HINE:MBHG HNM@HBG@ BGUN>G H? ) !)
:L>= HG MA>L> O:EN>L T@NK> BL BGUN>G MA:MMA> >E>F>GM 'CDI@5H=CB A:L MHP:K=L MA> K>: O:KB:;E>L BG MA> LRLM>F %M BL IK>=BG@ T@NK> HG I:@>
0A> P:R >\>LNEMBG@ O:EN>L :K> :EP:RL =B\>K>GM ?KHF
S>KH $>G MA> E>O>E H? S>KH NL>= MH BG=B MA:M : KM:BG >E>F>GM BLHNMLB=> H? MA> K>: NG=>KERBG@ >E>F>GM L MA> >E>F>GM )9;9B9F5H=CBC: 7 BL HGER :G BGINM O:KB:;E> H? MA> LRLM>F BM BL HNM H? MA> K>:E>F>GM :G= MA:M BGL 'CDI@5H=CB :L F>GMBHG>= :EK>:=R >:KEB>K HGL>JN>GMER BM BL IE:= HG MA> E>O>E H? S>KH "NKMA>K MA> >E>F>GM )9;9B9F5H=CB C: 7BL LBMN:M>= :M MA> ?:KMA>LM IHLLB;E> =>E:R H? MA> LRLM>F :L MA>K> BL GH BGUN>G:M :GR MBF>
,HEBKL := HNM H? T@NK> AHP 'CDI@5H=CB BGUN>GL MA>HMA>K >E>F>GML BG MA> LRLM>F 0A> BG?HKF:MBHG @:BG BL MA:M BM K>O>:EL GHM HGERMA> LMK>G@MA H? BFI:E:R L :G >Q:FIE> HG>
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! ! %!& $! !
0 842
-1
Delay
Effect 0
10
6
7 1
A 3
4
6
8
1
5
2
3-
1
3-1
1
3
2
3
1
3-
Variables atthe same spot:
= 2, 9A
"B@NK> $HP IHINE:MBHG BGUN>GL
IHLLB;E> IE: PHKD>KL BL ?KHF HO>KL>:L 0H:MMK:KL BGGMBO>L :K> BGMKH=N= >@ MA>R BK ?:FBEB>L PBMAMA>F %M M>G=L MA:M RHNG@ I>HIE> FHO> :;KH:= FHK> H?M>G MA:G >E=>KER $>G: CNO>G>LG H? LHMR ;>@BGL ?M>K RHNG@ I>HIE> A:O> L>MME>= MA>R P:GM MHLM:KM ?:FBEB>L $>G MA> ;BKMA K:M> LM:KML MH KBL> PBMA LHF> =>E:R %M M:D>L >O>GEHG@>K NGMBE MABL >QMK: IHINE:MBHG K>:L MA> :@> H? =>:MA 0A:M BL MA> K>:LHG
PAR BM M:D>L : ;B@@>K =>E:R NGMBE MA> GNF;>K H? =>:MAL PBEE KBL>
'@88,=D
0A> BGBMB:E IHLBMBHG P:L MA:M IHEBKL A:O> : LRLM>F MA:M MA>R P:GM MH:G:ERS> 0A> :G:ERLBL F:GB?HE= %M LAHNE= A>EI MH MA> BGM>KO>GMBHGIHBGM HK MA> BG=B: M> G:F>= \>L>GM>= 0ABL F>MAH= =>I>G=L HGMA> I:MA G ?KHF MA> LHNK MH MA> K>IMHK L : K>LNEM HG> DGHPL AHPLMKHG@ MA> >\>MP>>G MA> >E>F>GML :K> "NKMA>K BM LAHPL PAB HK H? TG:E LM>I BG?HKF:MBHG H? ) :G= !) BGMH : AHEBLMB E>F>GM PBMA :EE HMA>K >E>F>GML 0A>K>:K> MPH MRI>L H? IBL !BMA>K MA> ?H BL BGUN>G= ;R
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&' !
MA> HMA>KL HK AHP BM BGUN>GL MA> HMA>KL0ABL BG?HKF:MBHG MA> ?NG=:F>GM:E ?HK =>KL %M A>EIL MH
TG= MA> ;>LM BGM>KO>GMBHG IHBGM "NKMA>K BM A>EIL MH TG= MA> KB@AM BG=BKOBL> : LRLM>F BG @>G>K:E HK =NKBG@ IA:L>L H? L 0A>R :K> LBFIE>
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
9,7DE492 ,77 ;,?3>
0?B009 ?B: 9:/0>
0A> EH@BQM LM>I BL MH @>M FHK> BG?HKF:MBHG :;HNM MA> K>E:MBHGLABI ;>MP>>GMPH >E>F>GML BG : LRLM>F *HM HGER MH DGHP AHP MA> TKLM BGUN>G BL ?KHF :LHNK MH : K>IMHK ;NM MA> BGUN>G HO>K MA> H? MBF> 0H TG= :EE IHLLB;E>I:MAL ;>MP>>G MPH IK>=>TG>= GH=>L : I:MA TG=>K :E@HKBMAF P:L M:BEL :K> @BO>G BG :II>G=BQ LM:KMBG@ HG I:@> %GBMB:E IHLBMBHGL :K>:@:BG MA> MPH F:MKBL MA:M BG MA> FHLM BG?HKF:MBHG :;HNM MA> =BL=LRLM>F ,HINE:MBHG @KHPMA BG LIHG=BG@ >\> I @:BG RHN K>GM F:MKBQ PBMA E>LLBG?HKF:MBHG 0A> K>LNEMBG@ :O>F>GML A:O> MH ;> BGM>KIK>M>= : I:MA TG=BG@ :E@HKBMAF MA> ?HEEHPBG@ I:MA PBMA :II>G=:GMO:EN>L A:O> ;>>G IK>L>GM>= BG M:;E>
*H *H H? >=@>L >E:R !\> .>LNEML H? I:MA TG=BG@ ?KHF GH=> MH
0A>K> :K> MAK>> =B\>K>GM I:MAL LM:KMBG@ :M MA> >E>F>GM 'CDI@5H=CB :G= >G=BG@BG >E>F>GM =FH TKLM I:MA BL MA> LAHKM>LM I:MA :G= A:L ;>>G :G:ERS>=;R MA> >:KEB>K F>MAH=L 0A> L>O>K :K> :G= BM >:LB>K MH BGM>KIK>M MA> K>LNEM MA> ?HEEHPBG@
@K:IABIK>L>GM:MBHG H? :EE MAK>> I:MAL BL @BO>G BG T@NK> HG I L L>>G : BG 'CDI@5H=CB BL ?HEEHP>= ;R : BG =FH
L:F> =BK>K : F>=BNFM>KF NM MA> L:F> BG ,HINE:MBHG A:L :G
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! ! %!& $! !
0 842
-1
Delay
Effect 0
6
A
B C
2
3-
1
3
2
3
1
3-Paths:
= 1-2= 1-7-4-2= 1-9-6-7-4-2
A
B
C
"B@NK> !\>E:R H? :EE I:MAL ?KHF IHINE:MBHG MH ;BKMA
:==BMBHG:E >\> =BK> EHG@M>KF 0ABL EHG@M>KF >\>O>G @K>:M>K MA:G MA> F>=BNFM>KF >\>= PBMA = MH
3AR BL MA> EHG@M>KF >\> =BK> ;>
MA> FH=>E BL ;:L>= HG MA> :LLNFIMBHG MA:M B? IHINE:MBHG KBL>L BM PBEE A:O> :G>@:MBO> >\> M:MBHG MA:M;> H? MA> KBL> BG IHINE:MBHG MA> >GOBKHGF>GML IHEENMBHG KBL>L MHH :G= MABL
>\>GOBKHGF>GM:E =:F:@> :G= A>G : => BG @:MBO> >\> ?>KMBEBMR :G= A>G K>=NLMA> GNF;>K H? ;BKMAL %? IHINE:MBHG =>L MA> >GOBKHGF>GM K :G=A:L : IHLBMBO> >\>KMBEBMR
3BMA MABL F>MAH= GHM HGER MA> >\>E:R H? MA> TKLM HK LAHKM>LM I:MABL LAHPG ;NM :ELH MA> ?NKMA>K >\>E:RL H? : HK F:GBINE:MBHG H?: O:KB:;E> MHP:K=L : L>E>= >E>F>GM
(:B,=/> :90 9:/0
0A> IK>OBHNL F>MAH= >QM>G=>= MH TG= GHM HGER MA> I:MAL BGBMB:MBG@ :M: LI> ;NM K:MA>K :EE I:MAL ?KHF >O>KR GH=> MHP:K=L : LI>M0A> F:MA>F:MBQM>GLBHGL :K> F>GMBHG>= BG :II>G=BQ I 0H LAHPAHP BM PHKDL MA> F>MAH= BL :@:BG :IIEB>= MH MA> LRLM>F H? IHINE:MBHG :L :EEF>MAH=L :K> BG MABL K 0A> GH=> H? BGM>K>LM BL :@:BG =FHE> MH LAHP MA> =B\>K>G MH MA> IK>OBHNL K>LNEM 0A> HNML :K> @BO>GBG M:;E> HG MA> ?HEEHPBG@ I
L HG> > MA>K> :K> I:MAL LM:KMBG@ :M : GH=> :G= >G=BG@ BG GH=> :EMAHN@A MAK>> I:MAL :K> ?>>=;: ?>>=;: ;:E:GK>:L GNF;>K BL : K>BG?HK>=;:G MH >: TKLM MA> ?HEEHPBG@T@NK> I BL :E>F>GM MA:M A:L >QI>KB>G= : >\> GH=> =FH FNLM
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&' !
*H *H H? >=@>L >E:R !\> .>LNEML H? I:MA TG=BG@ MHP:K=L GH=> *H
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! ! %!& $! !
D>>I BG FBG= MA:M MA> GNF;>KL @BO>G BG MA> T@NK> :K> GHM GH=>L GNF;>K ;NMI:MA GNF;>KL 0H L>> PAB BL MA> BGBMB:E GH=> HG> A:L MH 0A> MAK>> I:MAL MA:M P>K> =BLK>= BG MA> IK>OBHNL L>MP>>G MA>GH=> 'CDI@5H=CB :G= =FH I:MA GNF;>K K>LI BG T@NK>
0 14122
-1.5
Delay
Effect
0
10
1
2
3-
1
3
2
3
1
3-
1
1.5
-1
4 6 8
2 3
4
5 6
7
8 9
10
11
12 1314
15
16
17
18
20
21 23
22
19
"B@NK> ,:MAL ?KHF >O>KR GH=> MHP:K=L GH=> *H
0A> L:F> :IIKH:= MH TG= HNM AHP F:GR I:MAL E>:O> : KM:BGGH=> :G= K>: PBMA PAB\>E:R %M BL :;LM:BG>=
?KHF LAHPBG@ :G >Q:FIE>0ABL F>MAH= HGER F:D>L L>GL> B? MA>K> :K> GHM MHH F:GR IHLLB;E> I:MAL
+MA>KPBL> BM @>ML O>KR F MA:M :EE F>MAH=L LAHPG BGMABL K LMBEE A:O> K>F:BGL BG MA:M MA> :G:ERLBL BL :EP:RL : LG:ILAHM BG MA>L>GL> H? BM HGER LAHPL MA> TKLM BFI: =RG:FB< IB BL BG=B=
(=,9>4?4:9
0ABL K ;>@:G ;R LM:KMBG@ PBMA MA> DGHPG F>MAH= H? 2>LM>K 78 :G=
ABL MP>>G :G >E>F>GM :G= MA> LRLM>F BMBL I:KM H? 0A> >G= H? MA> L>L : LBFBE:K :G:ERLBL ;NM ?H :G= :L : K>LNEM MA> F:MKBQ P:L BGMKH=N= .>EB:GM HGBG?HKF:MBHG GM MA> :K >GMKHIR
=>>I>K :G:ERLBL H? MA> LRLM>F :EEHP>= MA> ?H MH K>E:MBHGL;>MP>>G BML >E>F>GML 0H =H LH MA> ?H BG MA> L>GL> H? =>E:RNGMBE BG?HKF:MBHG ?KHF HG> >E>F>GM K>E>:L>L L :M :GHMA>K >E>F>GM %G MA>IKHLL MA> =B\>K>GM MRI>L H? LAHKM>LM I:MAL P>K> :G:ERS>= 0A> K>LNEML P>K>D>IM BG E:RF:MKBL >I>G=:GM HG MA>L> LAHKM>LM I:MAL MA> >\>QIEHK>= :G= MA> K>LNEML P>K> = BG MA> \>
) :G= MA> !) MA> FB==E> I:KM P:L = 0A>L> MHHELA>EI IHEBKL MH F:D> LBFIE> :G:ERLBL :;HNM MA> E>F>GML BG :LRLM>F %M A>EIL MH TG= IHLLB;E> BGM>KO>GMBHG IHBGML :G= BG=B
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!!
LRLM>F 0BF> :G= >\HKM MH =H MABL MRI> H? :G:ERLBL :K> F:G:@>:;E> L : K>LNEMMA> >QI>G=BMNK>L :K> K:MA>K EHP
0A> =BL:=O:GM:@> H? MA>L> MHHEL BL MA:M MA>R :K> HGER : LG:ILAHM BG MA>L>GL> MA:M MA>R HGER F>GMBHG MA> TKLM >G >E>F>GML :G= =H GHM
L:R :GRMABG@ :;HNM MA> LB=> >\>F :G:ERLML A:O> :G BGM>K>LM MH @:MA>KDGHPE>=@> :;HNM LB=> >\>E>F>GML ;>A:O> BG MA> H? MBF>0H FHO> MHP:K=L LNKL MA> E:LM I:KM BGMKH=N= :G :G:ERLBL F>MAH= MH:G:ERS> GHM HGER MA> TKLM BFI: L>GL> H? MA> >:KEB>LM ;NM :EE TKLM BFI:MP>>G MPH >E>F>GML "NKMA>K MA> EBFBML H? LN ;>>G LAHPG BGMA> L>GL> MA:M BM @>ML