SISSY: An efficient and automatic algorithm for the analysis of EEG sources based on structured sparsity

Abstract

Over the past decades, a multitude of different brain source imaging algorithms have been developed to identify the neural generators underlying the surface electroencephalography measurements. While most of these techniques focus on determining the source positions, only a small number of recently developed algorithms provides an indication of the spatial extent of the distributed sources. In a recent comparison of brain source imaging approaches, the VB-SCCD algorithm has been shown to be one of the most promising algorithms among these methods. However, this technique suffers from several problems: it leads to amplitude-biased source estimates, it has difficulties in separating close sources, and it has a high computational complexity due to its implementation using second order cone programming. To overcome these problems, we propose to include an additional regularization term that imposes sparsity in the original source domain and to solve the resulting optimization problem using the alternating direction method of multipliers. Furthermore, we show that the algorithm yields more robust solutions by taking into account the temporal structure of the data. We also propose a new method to automatically threshold the estimated source distribution, which permits to delineate the active brain regions. The new algorithm, called Source Imaging based on Structured Sparsity (SISSY), is analyzed by means of realistic computer simulations and is validated on the clinical data of four patients.

Full text

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H9F=N9G H<9 G=A=@5F=HM 69HK99B H<9 CF=;=B5@ 5B8 H<9 9GH=A5H98 GCIF79 7CB
S;IF5H=CBG #: 5B8 89BCH9 H<9 CF=;=B5@ 5B8 9GH=A5H98 G9HG C: =B8=79G
C: 5@@ 8=DC@9G 69@CB;=B; HC 5B 57H=J9 D5H7< "5B8 5F9 H<9 BIA69FG C:
CF=;=B5@ 5B8 9GH=A5H98 57H=J9 8=DC@9G 5B8 rZ? 89BCH9G H<9 DCG=H=CB C: H<9
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7CFF9@5H=CB 7C9:S7=9BHG 69HK99B H<9 9GH=A5H98 D5H7< G=;B5@ 5B8 H<9 5J
9F5;98 G=;B5@ C: 5@@ 8=DC@9G 69@CB;=B; HC 5 D5H7< 19 H<9B 7CADIH9 H<9
A95B C: H<9 7CFF9@5H=CB 7C9:S7=9BHG :CF 5@@ D5H7<9G
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=B; H<9 ' A9H<C8 =AD@9A9BH98 =B )D9B'! !F5A:CFH 9H 5@ 
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D5FH=5@@M G9;A9BH98 6IH G=B79 H<9F9 K5G BC @9G=CB K9 IG98 H<9 H9A
D@5H9 <958 AC89@ H<5H K5G 9AD@CM98 :CF H<9 G=AI@5H=CBG CF 957< D5
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5B8 5J9F5;98 CF D5H=9BH  K9 5B5@MN98 H<9 5J9F5;9 C:  GD=?9G H<5H
5F9 A5L=A5@ CB 9@97HFC89 . :CF D5H=9BH  K9 7CBG=89F98 H<9 5J9F
5;9 C:  GD=?9G A5L=A5@ CB 9@97HFC89 . :CF D5H=9BH  K9 5B5@MN98
H<9 5J9F5;9 C:  GD=?9G A5L=A5@ CB 9@97HFC89 **)N 5B8 :CF D5H=9BH 
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H=9BH  <58 5@F958M IB89F;CB9 5 DF9J=CIG GIF;9FM K<9F9 D5FH C: H<9 @9:H
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B5@@M H<9 GCIF79 @C75@=N5H=CB F9GI@HG C: H<9 8=::9F9BH H9GH98 5@;CF=H<AG
K9F9 7CAD5F98 HC H<9 SB8=B;G C: H<9 -! 5B5@MG=G
3. Results
 $15/3-7);+0 :+-5)916:
#B CF89F HC 5B5@MN9 H<9 =BTI9B79 C: H<9 F9;I@5F=N5H=CB D5F5A9H9F
αCB H<9 D9F:CFA5B79 C: H<9 -#--3 5@;CF=H<A K9 7CBG=89F  D5H7<9G
5H 8=::9F9BH DCG=H=CBG 5B8 C: J5FM=B; G=N9G :FCA  ;F=8 8=DC@9G 56CIH
 7AZ HC  ;F=8 8=DC@9G 56CIH  7AZ .<9 D5H7<9G 5F9 @C75H98
CB H<9 =B:9F=CF D5F=9H5@ ;MFIG #B:*5 H<9 GID9F=CF :FCBH5@ ;MFIG -ID F
H<9 GID9F=CF C77=D=H5@ ;MFIG -ID)77 H<9 65G5@ H9ADCF5@ ;MFIG 5G.9
5B8 H<9 A=8H9ADCF5@ ;MFIG '=8.9 .<9 & J5@I9G C6H5=B98 :CF H<9G9
D5H7<9G 5F9 G<CKB =B =;  :CF G=L 8=::9F9BH J5@I9G C: H<9 D5F5A9H9F α
     5B8  5B8 :CF G=L 8=::9F9BH D5H7< G=N9G  
   5B8  D5H7< 8=DC@9G .C =ADFCJ9 H<9 F9GC@IH=CB C: H<9
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7CFF9GDCB8=B; HC & J5@I9G C:  AA 5B8 ACF9 75B 69 7CBG=89F98 HC
69 =B5779DH56@9 GI7< H<5H H<9 9L57H & J5@I9 =G C: BC DF57H=75@ =ADCF
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'CF9 D5FH=7I@5F@M :CF H<9 GID9FS7=5@ D5H7<9G #B:*5 -ID F 5B8 -ID)77
5 A=B=A5@ D5H7< G=N9 C:  8=DC@9G 7CFF9GDCB8=B; HC 56CIH  7AZ C:
7CFH9L =G F9EI=F98 HC M=9@8 577IF5H9 @C75@=N5H=CB F9GI@HG K<9F95G :CF H<9
@5H9F5@ D5H7< '=8.9 5B8 H<9 899D9F D5H7< 5G.9 H<9 D5H7<9G B998 HC 69
7CADCG98 C: 5H @95GH  8=DC@9G 7CFF9GDCB8=B; HC 56CIH  7AZ C: 7CF
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GCIF79 9GH=A5H9G 7<5B;9 CB@M G@=;<H@M K=H< GA5@@ J5F=5H=CBG C: H<9 D5F5
A9H9F α H<9 & J5@I9G ;9B9F5@@M =B7F95G9 K=H< =B7F95G=B; α GI7< H<5H
H<9 69GH F9GI@HG 5F9 57<=9J98 :CF R   CF R   .<9F9:CF9 K9 7CB
G=89F CB@M H<9 @5HH9F HKC J5@I9G =B H<9 :C@@CK=B;
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•-79B5F=C  H<F99 D5H7<9G K=H< A98=IA HC @5F;9 8=GH5B79G @C75H98 CB
H<9 GID9F=CF :FCBH5@ -ID F =B:9F=CF :FCBH5@ #B: F 5B8 GID9F=CF C7
7=D=H5@ -ID)77 ;MFIG
•-79B5F=C  H<F99 7@CG9 D5H7<9G @C75H98 CB H<9 A=8 H9ADCF5@ '=8.9
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•-79B5F=C  :CIF 7@CG9 D5H7<9G )77.9 '=8.9 -ID)77 #B:*5
•-79B5F=C  SJ9 7@CG9 D5H7<9G )77.9 '=8.9 #B:*5 -ID.9 GID9F=CF
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8IF9 :CF H<9 G97CB8 G79B5F=C D5H7<9G '=8.9 )77.9 5B8 #B:*5 #B H<9
SFGH GH9D H<9 K5H9FG<98 HF5BG:CFA D9FA=HG HC =89BH=:M 5 @5F;9 BIA69F
C: F9;=CBG  =B H<=G 9L5AD@9 GI7< H<5H H<9 5AD@=HI89G C: H<9 8=DC@9G
69@CB;=B; HC 957< F9;=CB 5F9 5DDFCL=A5H9@M =89BH=75@ #B H<9 G97CB8


UNCORRECTED PROOF
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Fig. 1. -IAA5FM C: H<9 -! 5B5@MG9G C: H<9 :CIF D5H=9BHG (CH9 H<5H H<9 -! F9GI@HG 7CB79FB=B; H<9 =BH9F=7H5@ 9D=@9DH=7 57H=J=HM F9DCFH98 <9F9 5F9 H<CG9 H<5H 7CFF9GDCB8 69GH HC H<9
HCDC;F5D<M C: GD=?9G F97CF898 8IF=B; H<9 G75@D ! G9GG=CB .<9 SB8=B;G C: H<9 -! 5F9 =@@IGHF5H98 :CF 957< D5H=9BH CB H<9 D5H=9BHGD97=S7 A9G< =B7@I8=B; :CF D5H=9BH  K<9F9 H<9
7CFH=75@ GIF:579 7CI@8 69 G9;A9BH98 :FCA H<9 ',# 6IH BCH H<9 7CAD@9H9 <958 AC89@ K=H< 5 @5H9F5@ G9A=@5H9F5@ G<CK=B; H<9 =BGI@5 CF A9G=5@ J=9K 89D9B8=B; CB H<9 D5H=9BH .<9 F98
DC=BHG A5F? H<9 DF=A5FM =BH9F=7H5@ 57H=J=HM H<9 CF5B;9 DC=BHG =B8=75H9 DFCD5;5H98 =BH9F=7H5@ 57H=J=HM 5B8 H<9 6@I9 DC=BHG A5F? H<9 F9;=CBG H<5H <5J9 699B 5B5@MN98 6M -! 6IH 8C BCH
G<CK 5BM G=;B=:=75BH =BH9F=7H5@ 57H=J=HM  CF =BH9FDF9H5H=CB C: H<9 F9:9F9B79G HC 7C@CF =B H<=G S;IF9 @9;9B8 H<9 F9589F =G F9:9FF98 HC H<9 K96 J9FG=CB C: H<=G 5FH=7@9
GH9D H<9G9 F9;=CBG 5F9 A9F;98 IBH=@ CB@M F9;=CBG H<5H 5F9 @C75@ A5L
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H<9 5AD@=HIH9G C: H<9 F9A5=B=B; F9;=CBG 5F9 H<F9G<C@898 =B 5 H<=F8 GH9D
M=9@8=B; 5 GCIF79 7CBS;IF5H=CB K=H< CB@M H<F99 F9;=CBG H<5H 7CFF9GDCB8
HC H<9 D5H7<9G =B H<9 CF=;=B5@ GCIF79 8=GHF=6IH=CB
(9LH K9 7CAD5F9 H<9 D9F:CFA5B79 C: 8=::9F9BH -#--3 J5F=5BHG :CF H<9
:CIF 7CBG=89F98 G79B5F=CG HC H<9 D9F:CFA5B79 C: 7&),. -.10
5B8 L-C'/-# =;  G<CKG 6CLD@CHG C: H<9 & J5@I9G C6H5=B98
CJ9F  8=::9F9BH F95@=N5H=CBG :CF 957< G79B5F=C #H 75B 69 C6G9FJ98
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G79B5F=CG  5B8  CAD5F=B; H<9 F9GI@HG C: -#--3 :CF 8=::9F9BH J5@I9G
C: H<9 F9;I@5F=N5H=CB D5F5A9H9F α K9 BCH9 H<5H :CF R   =9 K=H<
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C: &-#--3 5B8 -#--3 =G F5H<9F GA5@@


UNCORRECTED PROOF
-+2-9-;)3 -<964)/- ???  ??????
Fig. 2. =DC@9 &C75@=N5H=CB FFCF & 7C898 =B 7C@CF H<9 GA5@@9F 6@I9 H<9 69HH9F :CF 8=::9F9BH D5H7< DCG=H=CBG 89D9B8=B; CB H<9 D5H7< G=N9 5B8 H<9 F9;I@5F=N5H=CB D5F5A9H9F α (CH9
H<5H H<9 IDD9F @=A=H C: H<9 & <5G 699B SL98 HC  AA A95B=B; H<5H & J5@I9G <=;<9F H<5B H<=G H<F9G<C@8 <5J9 699B F9D@5798 6M  AA  CF =BH9FDF9H5H=CB C: H<9 F9:9F9B79G HC 7C@CF
=B H<=G S;IF9 @9;9B8 H<9 F9589F =G F9:9FF98 HC H<9 K96 J9FG=CB C: H<=G 5FH=7@9
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K9 5@GC G<CK =B =;G – H<9 GCIF79 8=GHF=6IH=CBG H<5H 5F9 9GH=A5H98 6M
H<9 H9GH98 GCIF79 =A5;=B; 5@;CF=H<AG 5G K9@@ 5G H<9 H<F9G<C@898 GCIF79G
:CF H<9 8=::9F9BH -#--3 J5F=5BHG .<9G9 S;IF9G G<CK H<5H 5@@ A9H<C8G 9L
79DH 7&),. M=9@8 ;CC8 9GH=A5H9G C: H<9 H<F99 8=GH5BH D5H7<9G =B G79
B5F=C  9J9B H<CI;< L-C'/-# CJ9F9GH=A5H9G H<9 G=N9 C: H<9 D5H7<
-ID)77 "CK9J9F :CF H<9 H<F99 CH<9F G79B5F=CG H<5H =BJC@J9 G9J9F5@
7@CG9 D5H7<9G -.10 5B8 L-C'/-# 8C BCH KCF? K9@@ :5=@=B;
HC F97CJ9F 5@@ D5H7<9G @958=B; HC 658 9GH=A5H9G C: H<9 G<5D9G C: H<9
7CFF97H@M =89BH=S98 D5H7<9G 5B8 =B7@I8=B; GDIF=CIG GCIF79G :CF G79B5F
=CG  5B8  CF G79B5F=CG  5B8  H<9 GCIF79 8=GHF=6IH=CBG 9GH=A5H98
6M 7&),. G<CK <=;< 5AD@=HI89G 5H H<9 DCG=H=CBG C: H<9 D5H7<9G M9H
H<9M A5?9 =H 8=:S7I@H HC =B:9F H<9 D5H7< G=N9 5B8 G<5D9 5B8 5@GC =B
7@I89 <=;< 5AD@=HI89G 5H 5 DCG=H=CB H<5H 8C9G BCH 7CFF9GDCB8 HC 5 D5H7<
C: H<9 CF=;=B5@ GCIF79 7CBS;IF5H=CB CF G79B5F=C  5G :CF G79B5F=C 
7&),. :5=@G 7CAD@9H9@M HC F97CJ9F 5 7CFF97H GC@IH=CB CB79FB=B; H<9
D9F:CFA5B79 C: H<9 8=::9F9BH J5F=5BHG C: -#--3 K9 C6G9FJ9 H<5H :CF
R   H<9 5@;CF=H<A G<CKG GCA9 8=:S7I@H=9G =B F97CJ9F=B; 5@@ D5H7<9G
'CF9 D5FH=7I@5F@M H<9 D5H7<9G '=8.9 5B8 )77.9 K<=7< 5F9 @C75H98 =B
H<9 H9ADCF5@ @C69 5B8 H<IG <5J9 @CK9F 5AD@=HI89G 5H H<9 GIF:579 H<5B
H<9 D5H7<9G #B:*5 5B8 -ID)77 5F9 A=GG=B; =B H<9 9GH=A5H98 GCIF79 8=G
HF=6IH=CBG :CF G79B5F=CG  5B8  K<9F95G :CF G79B5F=C  H<9 5@;CF=H<A
8C9G BCH G9D5F5H9 H<9 SJ9 57H=J9 D5H7<9G LD@C=H=B; H<9 H9ADCF5@ GHFI7
HIF9 =B & -#--3 R   CB9 C6H5=BG GCA9K<5H =ADFCJ98 GCIF79 9G
H=A5H9G 6IH H<9 D9F:CFA5B79 =G 9B<5B798 ACF9 6M 7CBG=89F=B; H<9 588=
H=CB5@ F9;I@5F=N5H=CB H9FA R   .<9 69GH F9GI@HG 5F9 57<=9J98 :CF
&-#--3 K=H< R   #B H<=G 75G9 H<9 5@;CF=H<A 7CFF97H@M F97CJ9FG
5@@ D5H7<9G :CF 5@@ :CIF 7CBG=89F98 G79B5F=CG
IFH<9FACF9 =B =;  K9 5@GC G<CK H<9 9GH=A5H98 D5H7< G=;B5@G
:CF -#--3 =B 7CAD5F=GCB HC H<9 CF=;=B5@ G=AI@5H98 D5H7< 8MB5A=7G :CF
G79B5F=C  #H 75B 69 G99B H<5H -#--3 M=9@8G ;CC8 9GH=A5H9G C: H<9
GCIF79 8MB5A=7G #B D5FH=7I@5F :CF &-#--3 K=H< R   K<=7<
<5G G9D5F5H98 5@@ H<F99 D5H7<9G H<9 9GH=A5H98 D5H7< G=;B5@G G<CK H<5H
D5H7<9G )77.9 5B8 '=8.9 5F9 57H=J5H98 DF=CF HC H<9 D5H7< -ID)77 "CK
9J9F 8I9 HC H<9 GA5@@ 8=GH5B79 5B8 GA5@@ 89@5M 69HK99B H<9 G=;B5@G C:
D5H7<9G '=8.9 5B8 )77.9 H<9G9 D5H7<9G 5DD95F HC 69 G=AI@H5B9CIG@M


UNCORRECTED PROOF
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Fig. 3. #@@IGHF5H=CB C: H<9 5IHCA5H=7 H<F9G<C@8=B; 5DDFC57< CF=;=B5@ GCIF79 8=GHF=6IH=CB HCD @9:H F9;=CBG =89BH=S98 6M H<9 K5H9FG<98 HF5BG:CFA =B GH9D  C: . HCD F=;<H F9A5=B=B;
F9;=CBG 5:H9F F9;=CB :IG=CB =B GH9D  C: . 6CHHCA @9:H 5B8 SB5@ F9GI@H 5:H9F H<F9G<C@8=B; C: F9;=CB 5AD@=HI89G =B GH9D  C: . 6CHHCA F=;<H
Fig. 4. CLD@CHG C: =DC@9 &C75@=N5H=CB FFCF & F9GI@HG H<9 @CK9F H<9 69HH9F C: H<9 H9GH98 GCIF79 =A5;=B; 5@;CF=H<AG :CF  8=::9F9BH AI@H=D5H7< G79B5F=CG 5B8  F95@=N5H=CBG K=H<
8=::9F9BH G=;B5@G 5B8 657?;FCIB8 57H=J=HM
57H=J5H98 =B H<9 =BJ9FG9 GC@IH=CB 5B8 H<9 GA5@@ H=A9 89@5M 75BBCH 69 F9
GC@J98 =B H<9 GCIF79 9GH=A5H=CB
+I5BH=H5H=J9@M H<9 D9F:CFA5B79 C: H<9 8=::9F9BH 5@;CF=H<AG =B 9GH=
A5H=B; H<9 GCIF79 H=A9 7CIFG9G =G 9J5@I5H98 IG=B; H<9 G=;B5@ 7CFF9@5H=CB
7C9:S7=9BHG K<=7< 5F9 ;=J9B =B .56@9  .<9 G=;B5@ 7CFF9@5H=CB 7C9:S
7=9BHG 57<=9J98 6M -#--3 5F9 7@95F@M <=;<9F H<5B H<CG9 :CF 5@@ CH<9F
A9H<C8G 'CF9CJ9F H<9 7CFF9@5H=CB 69HK99B H<9 CF=;=B5@ G=;B5@G 5B8
H<CG9 9LHF57H98 6M &-#--3 =G ;9B9F5@@M <=;<9F H<5B :CF H<9 G=;B5@G 9G
H=A5H98 6M -#--3 .<9 <=;<9GH 7CFF9@5H=CB 7C9:S7=9BHG 5F9 57<=9J98 6M
&-#--3 :CF R  


UNCORRECTED PROOF
-+2-9-;)3 -<964)/- ???  ??????
Fig. 5. *5H7<9G -ID F #B: F 5B8 -ID)77 G79B5F=C  =BJ9FG9 GC@IH=CBG C: 7&),. -.10 5B8 L-C'/-# 5B8 9GH=A5H98 GCIF79 8=GHF=6IH=CBG 5B8 H<F9G<C@898 GCIF79G :CF :CIF
J5F=5BHG C: -#--3
=B5@@M HC ;=J9 H<9 F9589F 5B =895 C: H<9 7CADIH5H=CB5@ 7CAD@9L
=HM C: H<9 8=::9F9BH 7CBG=89F98 GCIF79 =A5;=B; A9H<C8G K9 =B8=75H9 H<9
*/ H=A9G C: H<9 5@;CF=H<AG =B .56@9  CF 7CAD5F=GCB K9 5@GC DFC
J=89 H<9 */ H=A9 C: H<9 CF=;=B5@ 0- 5@;CF=H<A .<9 5@;CF=H<AG
5F9 =AD@9A9BH98 =B '5H@565 CB 5 7CADIH9F K=H< 5  !"N #B
H9@ CF9 = DFC79GGCF 5B8  ! C: ,' (CH9 <CK9J9F H<5H D5FHG C:
L-C'/-# 5F9 =AD@9A9BH98 =B  GI7< H<5H =HG */ H=A9 =G BCH 8=
F97H@M 7CAD5F56@9 HC H<5H C: H<9 CH<9F A9H<C8G CF 5@;CF=H<AG H<5H 75B
KCF? CB 5 G=B;@9 H=A9 G5AD@9 GI7< 5G 7&),. -#--3 5B8 0-
K9 =B8=75H9 H<9 */ H=A9 =: H<9 5@;CF=H<A =G 5DD@=98 HC CB9 H=A9 G5AD@9
K<9F95G :CF -.10 L-C'/-# 5B8 &-#--3 5@@  H=A9 G5A
D@9G 5F9 DFC79GG98 6M H<9 5@;CF=H<AG .<9 GA5@@9GH */ H=A9 =G F9EI=F98
6M 7&),. :C@@CK98 6M -#--3 K<=7< H5?9G 56CIH  G 5B8 K<=7< =G
AI7< :5GH9F H<5B 0- 6M 5 :57HCF C: 56CIH  .5?=B; =BHC 577CIBH
5@@ H=A9 G5AD@9G FIBB=B; &-#--3 H5?9G 56CIH  A=B K<9F95G 9L97IH
=B; -.10 H5?9G  G @CB;9F A5?=B; =H H<9 G@CK9GH C: 5@@ H9GH98 5@;C
F=H<AG
 !);+0 :-7)9);165
#B H<=G G97H=CB K9 5=A 5H 5B5@MN=B; ACF9 DF97=G9@M H<9 F9GC@IH=CB C:
H<9 7CBG=89F98 GCIF79 =A5;=B; 5@;CF=H<AG =9 H<9 75D56=@=HM HC G9D5
F5H9 HKC D5H7<9G 89D9B8=B; CB H<9=F 8=GH5B79 .C H<=G 9B8 K9 7CBG=89F 
D5H7<9G C: G=A=@5F :CFA 7: =;  5B8  8=::9F9BH 8=GH5B79G G H<9 G9D
5F5H=CB C: H<9 D5H7<9G 8C9G BCH CB@M 89D9B8 CB H<9=F 8=GH5B79 6IH 5@GC
CB H<9=F DCG=H=CB K9 GHI8M G9J9F5@ G79B5F=CG :CF 957< 8=GH5B79
•8=GH5B79  P 7A *  * *  * *  * *  * 5B8 * 
*
•8=GH5B79  P 7A *  * *  * *  * 5B8 *  *
•8=GH5B79  P 7A *  * *  * 5B8 *  *
•8=GH5B79  P 7A *  * 5B8 *  *


UNCORRECTED PROOF
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Fig. 6. *5H7<9G '=8.9 )77.9 5B8 #B:*5 G79B5F=C  =BJ9FG9 GC@IH=CBG C: 7&),. -.10 5B8 L-C'/-# 5B8 9GH=A5H98 GCIF79 8=GHF=6IH=CBG 5B8 H<F9G<C@898 GCIF79G :CF :CIF
J5F=5BHG C: -#--3
Fig. 7. *5H7<9G )77.9 '=8.9 -ID)77 5B8 #B:*5 G79B5F=C  =BJ9FG9 GC@IH=CBG C: 7&),. -.10 5B8 L-C'/-# 5B8 9GH=A5H98 GCIF79 8=GHF=6IH=CBG 5B8 H<F9G<C@898 GCIF79G
:CF :CIF J5F=5BHG C: -#--3
19 7CBG=89F HKC D5H7<9G HC 69 G9D5F5H98 =: H<9 9GH=A5H98 GCIF79
7CBS;IF5H=CB 7CBH5=BG HKC D5H7<9G GI7< H<5H CB9 9GH=A5H98 D5H7< CJ9F
@5DG K=H< H<9 SFGH CF=;=B5@ D5H7< 5B8 H<9 CH<9F 9GH=A5H98 D5H7< CJ9F
@5DG K=H< H<9 G97CB8 CF=;=B5@ D5H7< M 5B5@MN=B;  8=::9F9BH F95@=N5
H=CBG :CF 957< G79B5F=C K9 89H9FA=B9 H<9 DFC656=@=HM C: F9GC@IH=CB 5G
H<9 D9F79BH5;9 C: F95@=N5H=CBG :CF K<=7< H<9 D5H7<9G 5F9 G9D5F5H98 57
7CF8=B; HC H<9 56CJ9 7F=H9F=CB .<9 DFC656=@=HM C: F9GC@IH=CB =G H<9B 5J
9F5;98 CJ9F 5@@ G79B5F=CG 5GGC7=5H98 K=H< 5 ;=J9B D5H7< 8=GH5B79 .<9
F9GI@H=B; DFC656=@=H9G C: F9GC@IH=CB 5F9 @=GH98 =B .56@9  :CF 957< 8=G
H5B79 5B8 957< C: H<9 9L5A=B98 GCIF79 @C75@=N5H=CB 5@;CF=H<AG IF
H<9FACF9 .56@9  G<CKG H<9 7CFF9GDCB8=B; & J5@I9G G 75B 69 9L
D97H98 H<9 DFC656=@=HM C: F9GC@IH=CB ;9B9F5@@M =B7F95G9G K=H< =B7F95G
=B; D5H7< 8=GH5B79 K<=@9 H<9 & 897F95G9G CF 8=GH5B79  H<9 D5H7<9G
5F9 IGI5@@M BCH F9GC@J98 6IH 8I9 HC H<9=F DFCL=A=HM H<9 & J5@I9G 5F9
GA5@@9F H<5B :CF 8=GH5B79  CF  1=H< -#--3 5B8 5 D5F5A9H9F R  
 H<9 D5H7<9G 75B 69 G9D5F5H98 =B 5@ACGH 5@@ 75G9G :CF 8=GH5B79  CF
<=;<9F IFH<9FACF9 -#--3 :95HIF9G <=;<9F DFC656=@=H=9G C: F9GC@IH=CB
5B8 @CK9F & J5@I9G H<5B -.10 5B8 L-C'/-# =B D5FH=7I@5F
:CF R   J9B H<CI;< H<9 DFC656=@=HM C: F9GC@IH=CB =G GCA9H=A9G
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Fig. 8. *5H7<9G )77.9 '=8.9 #B:*5 -ID.9 5B8 -ID)77 G79B5F=C  =BJ9FG9 GC@IH=CBG C: 7&),. -.10 5B8 L-C'/-# 5B8 9GH=A5H98 GCIF79 8=GHF=6IH=CBG 5B8 H<F9G<C@898
GCIF79G :CF :CIF J5F=5BHG C: -#--3
Table 1
J9F5;9 G=;B5@ 7CFF9@5H=CB 7C9:S7=9BH 69HK99B CF=;=B5@ D5H7< G=;B5@G 5B8 9GH=A5H98 D5H7<
G=;B5@G
G=;B5@7CFF9@5H=CB

G79B5F=C

G79B5F=C

G79B5F=C

G79B5F=C

7&),.    
-.10    
L-C'/-#    
&-#--3 R    
&-#--3 R    
&-#--3
R
   
&-#--3
R
   
Table 2
'95B */ H=A9 5J9F5;98 CJ9F H<9  G79B5F=CG
5@;CF=H<A */H=A9=B
G97CB8G
5@;CF=H<AGKCF?=B;CB5H=A9G5AD@9
6MG5AD@965G=G
7&),. 
&-#--3
R

&-#--3
R
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0- 
5@;CF=H<AGH5?=B;=BHC577CIBH5@@H=A9
G5AD@9G
-.10 
L-C
'/-#

&-#--3
R

&-#--3
R

69HH9F :CF 7&),. H<9 & J5@I9G 5F9 7CBG=89F56@M <=;<9F H<5B :CF
-#--3 K<=7< A95BG H<5H H<9 CJ9F5@@ GCIF79 G9D5F5H=CB 5B8 @C75@=N5H=CB
:CF H<9 7CBG=89F98 G79B5F=CG =G 69GH K<9B IG=B; -#--3 K=H< R  
Fig. 9. -=L D5H7<9G 7CBG=89F98 :CF H<9 5B5@MG=G C: D5H7< G9D5F5H=CB
Table 3
J9F5;9 DFC656=@=HM C: F9GC@IH=CB :CF 957< GCIF79 @C75@=N5H=CB 5@;CF=H<A 5B8 :CF :CIF 8=:
:9F9BH D5H7< 8=GH5B79G
DFC656=@=HMC:
F9GC@IH=CB
8=GH5B79

8=GH5B79

8=GH5B79

8=GH5B79

7&),.    
-.10    
L-C'/-#    
&-#--3 R    
&-#--3 R    
&-#--3
R
   
&-#--3
R
   
Table 4
J9F5;9 & :CF 957< GCIF79 @C75@=N5H=CB 5@;CF=H<A 5B8 :CF :CIF 8=::9F9BH D5H7< 8=GH5B79G
&AA 8=GH5B79

8=GH5B79

8=GH5B79

8=GH5B79

7&),.    
-.10    
L-C'/-#    
&-#--3 R    
&-#--3 R    
&-#--3
R
   
&-#--3
R
   
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UNCORRECTED PROOF
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#B CF89F HC GHI8M H<9 DFCD5;5H=CB D<9BCA9B5 H<5H A5M DCH9BH=5@@M
C77IF 8IF=B; H<9 =BH9F=7H5@ GD=?9G C: H<9 7@=B=75@ 85H5 K9 <5J9 GMGH9A5H=
75@@M 5DD@=98 H<9 H9GH98 GCIF79 =A5;=B; 5@;CF=H<AG HC HKC H=A9 =BH9FJ5@G
7CFF9GDCB8=B; HC H<9 SFGH B9;5H=J9 K5J9 C: H<9 GD=?9 H=A9 =BH9FJ5@ 
5B8 HC H<9 GI6G9EI9BH DCG=H=J9 K5J9 H=A9 =BH9FJ5@  7: =;  CF
ACGH D5H=9BHG H<9 GCIF79 @C75@=N5H=CB F9GI@HG K9F9 GH56@9 CJ9F 6CH< H=A9
=BH9FJ5@G 5B8 K9 CB@M C6G9FJ98 5 DFCD5;5H=CB C: H<9 9D=@9DH=7 GD=?9 :CF
D5H=9BH  .<9F9:CF9 :CF D5H=9BH  K9 G<CK H<9 F9GI@HG :CF 6CH< H=A9
=BH9FJ5@G K<9F95G :CF H<9 CH<9F D5H=9BHG K9 CB@M 8=GD@5M H<9 F9GI@HG C6
H5=B98 :CF H=A9 =BH9FJ5@ 
CF D5H=9BH  GCIF79 @C75@=N5H=CB F9GI@HG C6H5=B98 K=H< H<9 8=:
:9F9BH 5@;CF=H<AG 5F9 8=GD@5M98 =B =;  7&),. -.10 5B8
L-C'/-# M=9@898 J9FM G=A=@5F F9GI@HG :CF 6CH< H=A9 =BH9FJ5@G K<=7<
=G K<M :CF H<9G9 A9H<C8G K9 CB@M G<CK H<9 GC@IH=CBG C6H5=B98 :CF H=A9
=BH9FJ5@  7&),. G<CKG <=;< 57H=J5H=CB C: H<9 F=;<H H9ADCF5@ @C69
5B8 F=;<H C77=D=H5@ 6F5=B F9;=CBG -.10 5B8 L-C'/-# =89BH=:M
5DDFCL=A5H9@M H<9 G5A9 GCIF79 F9;=CB =B H<9 F=;<H H9ADCF5@ @C69 CB
79FB=B; H<9 =89BH=S98 57H=J9 D5H7<9G H<9 :CIF H9GH98 J5F=5BHG C: -#--3
@958 HC 7CAD5F56@9 F9GI@HG GC K9 =@@IGHF5H9 CB@M H<9 F9GI@HG C: -#--3 :CF
R   5B8 :CF &-#--3 :CF R   CF H=A9 =BH9FJ5@  -#--3 =89B
H=S9G CB9 F9;=CB =B H<9 65G5@ 5GD97H C: H<9 F=;<H H9ADCF5@ DC@9 K<9F95G
:CF H=A9 =BH9FJ5@  H<9 9GH=A5H98 57H=J5H=CB =BJC@J9G H<9 DCGH9F=CF <5@:
C: H<9 F=;<H H9ADCF5@ @C69 5B8 H<9 F=;<H H9ADCFCC77=D=H5@ >IB7H=CB 7
7CF8=B; HC H<9 7@=B=75@ =BH9FDF9H5H=CB C: -! =BHF579F96F5@ 85H5 7:
=;  H<9 6F5=B F9;=CBG =BJC@J98 =B H<9 =BH9F=7H5@ 9D=@9DH=7 57H=J=HM =B
7@I89 H<9 F=;<H 65G5@ H9ADCF5@ DC@9 K=H< DCGH9F=CF 8=::IG=CB HC H<9 F=;<H
A=88@9 H9ADCF5@ @C69 .<9 GCIF79 =A5;=B; F9GI@HG C6H5=B98 6M -#--3
5B8 H<9 CH<9F H9GH98 GCIF79 =A5;=B; 5@;CF=H<AG 5F9 H<IG ACGH@M 7CB7CF
85BH K=H< H<9 SB8=B;G C: H<9 -! 5B5@MG=G "CK9J9F -.10 5B8
L-C'/-# 8C BCH G<CK H<9 57H=J5H=CB C: H<9 F=;<H H9ADCF5@ DC@9 5B8
7&),. @C75@=N9G 5@GC F=;<H C77=D=H5@ 6F5=B F9;=CBG K<=7< <5J9 BCH
699B C6G9FJ98 HC 69 =BJC@J98 =B 9D=@9DH=7 57H=J=HM =B H<9 -! F97CF8
=B;G CF 6CH< J5F=5BHG C: -#--3 K9 5@GC D@CH H<9 9GH=A5H98 H=A9 G=;
B5@G K=H<=B HKC G998 D5H7<9G 7CADF=G=B; 5DDFCL=A5H9@M  7AZ C: 7CFH9L
5B8 @C75H98 CB H<9 H9ADCF5@ DC@9 5B8 =B H<9 DCGH9F=CF H9ADCF5@ 7CFH9L
G99 =;  6CHHCA 79BH9F .<9G9 HKC D5H7<9G @=9 K=H<=B H<9 HKC 6F5=B
F9;=CBG =89BH=S98 6M -#--3 :CF H<9 HKC 7CBG=89F98 H=A9 =BH9FJ5@G =;
 6CHHCA G<CKG H<5H H<9 G=;B5@ C: H<9 H9ADCF5@ DC@9 =G 7<5F57H9F=N98
6M 5 <=;< B9;5H=J9 5AD@=HI89 =B H<9 SFGH H=A9 =BH9FJ5@ 7CFF9GDCB8=B; HC
H<9 A=B=AIA C: H<9 9D=@9DH=7 GD=?9 .<9 D5H7< =B H<9 DCGH9F=CF H9ADCF5@
@C69 5@GC <5G B9;5H=J9 5AD@=HI89 5H H<9 A=B=AIA C: H<9 GD=?9 6IH H<9
5AD@=HI89 =G AI7< GA5@@9F H<5B =B H<9 H9ADCF5@ DC@9 K<=7< 9LD@5=BG
K<M H<=G 57H=J5H=CB =G BCH J=G=6@9 =B H<9 H<F9G<C@898 -#--3 GC@IH=CB :CF
H=A9 =BH9FJ5@  CF H=A9 =BH9FJ5@  H<9 DCG=H=J9 K5J9 C: H<9 9D=@9DH=7
GD=?9 =G G@=;<H@M ACF9 DFCBCIB798 =B H<9 DCGH9F=CF H9ADCF5@ @C69 K=H<
5 GCA9K<5H <=;<9F 5AD@=HI89 5B8 @CB;9F 8IF5H=CB CAD5F=B; H<9 G=;
B5@G 9GH=A5H98 6M H<9 HKC J5F=5BHG C: -#--3 =H 75B 69 G99B H<5H :CF -#--3
K=H< R   H<9 G=;B5@G :95HIF9 GCA9 GA5@@ TI7HI5H=CBG 5B8 5F9 BCH 5@
K5MG H<9 G5A9 :CF H<9 8=DC@9G K=H<=B 957< D5H7< .<9 G=;B5@G 9LHF57H98
6M &-#--3 5F9 GACCH<9F 5B8 H<IG GCA9K<5H 95G=9F HC =BH9FDF9H 8I9 HC
H<9 9LD@C=H5H=CB C: H9ADCF5@ GHFI7HIF9 =B H<9 5@;CF=H<A
CF D5H=9BHG – K9 =@@IGHF5H9 =B =;  H<9 GCIF79 @C75@=N5H=CB F9
GI@HG C6H5=B98 K=H< -#--3 :CF R   5B8 &-#--3 :CF R   6CH<
5:H9F . =B 7CAD5F=GCB HC H<9 =BJ9FG9 GC@IH=CBG C: 7&),. -.10
5B8 L-C'/-# CF D5H=9BH  -#--3 5B8 7&),. @C75@=N9 H<9
Fig. 10. @=B=75@ 85H5 C: D5H=9BH  -CIF79 @C75@=N5H=CB C6H5=B98 :CF 9D=@9DH=7 GD=?9G A5L=A5@ CB 9@97HFC89 . .<9 HKC 7CBG=89F98 H=A9 =BH9FJ5@G 7CFF9GDCB8=B; HC H<9 SFGH 5B8 G97CB8
D5FH C: H<9 GD=?9 5F9 A5F?98 =B M9@@CK 5B8 CF5B;9 .<9 H=A9 DC=BHG CB9 K=H<=B 957< =BH9FJ5@ :CF K<=7< H<9 GCIF79 @C75@=N5H=CB F9GI@HG 5F9 8=GD@5M98 5F9 A5F?98 6M F98 8CHH98 @=B9G 5B8
7CFF9GDCB8 HC H<9 A=B=AIA 5B8 H<9 A5L=AIA C: H<9 9D=@9DH=7 GD=?9 CF 7&),. -.10 5B8 L-C'/-# K9 8=GD@5M CB@M H<9 F9GI@HG C6H5=B98 :CF H=A9 =BH9FJ5@  F9GI@HG :CF H=A9
=BH9FJ5@  5F9 7CAD5F56@9 CF -#--3 H<9 5AD@=HI89G C: H<9 6F5=B F9;=CBG =B57H=J9 577CF8=B; HC . <5J9 699B G9H HC  5B8 :CF 7&),. H<9 5AD@=HI89G C: H<9 6F5=B F9;=CBG BCH G9@97H98
6M H<9 !) <5J9 699B G9H HC  CF -#--3 K9 5@GC 8=GD@5M H<9 9GH=A5H98 GCIF79 8MB5A=7G K=H<=B HKC G998 D5H7<9G @C75H98 K=H<=B H<9 F9;=CBG @C75@=N98 8IF=B; H<9 SFGH 5B8 G97CB8 H=A9
=BH9FJ5@ *5@9 6@I9 5B8 D5@9 ;F99B G=;B5@G G<CK 8MB5A=7G C: =B8=J=8I5@ 8=DC@9G K=H<=B 957< D5H7< K<9F95G 85F? 6@I9 5B8 85F? ;F99B G=;B5@G 7CFF9GDCB8 HC H<9 5J9F5;9 G=;B5@G C: 957< D5H7<


UNCORRECTED PROOF
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Fig. 11. @=B=75@ 85H5 C: D5H=9BHG – -CIF79 @C75@=N5H=CB C6H5=B98 :CF 9D=@9DH=7 GD=?9G A5L=A5@ CB 9@97HFC89 . :CF D5H=9BH  CB 9@97HFC89 **)N :CF D5H=9BH  5B8 CB 9@97HFC89 . :CF
D5H=9BH  CF -#--3 H<9 5AD@=HI89G C: H<9 6F5=B F9;=CBG =B57H=J9 577CF8=B; HC . <5J9 699B G9H HC  5B8 :CF 7&),. H<9 5AD@=HI89G C: H<9 6F5=B F9;=CBG BCH G9@97H98 6M H<9 !) <5J9
699B G9H HC 
A5=B 57H=J5H=CB 5H H<9 A=B=AIA C: H<9 GD=?9 G=;B5@ CB H<9 @9:H H9ADCF5@
DC@9 &-#--3 :CF R   G<CKG 5 J9FM :C75@ 57H=J5H=CB 7&),.
M=9@8G 5 G=A=@5F GC@IH=CB 6IH H<9 =89BH=S98 6F5=B F9;=CBG 5F9 G@=;<H@M
ACF9 DCGH9F=CF -.10 @C75@=N9G 5 6F5=B F9;=CB =B H<9 @9:H =BGI@5 =
B5@@M L-C'/-# =89BH=S9G HKC D5H7<9G CB9 =B H<9 @9:H H9ADCF5@
DC@9 5B8 5BCH<9F CB9 =B H<9 @9:H =BGI@5 G F9DCFH98 =B =;  H<9 F9;=CBG
=BJC@J98 =B H<9 =BHF579F96F5@ =BH9F=7H5@ 57H=J=HM =B7@I89 H<9 @9:H H9ADCF5@
DC@9 H<9 =BGI@5 5B8 H<9 A9G=5@ 5GD97H C: H<9 @9:H H9ADCF5@ @C69 .<9 ACGH
7CB7CF85BH F9GI@H =G H<9F9:CF9 C6H5=B98 :FCA L-C'/-# 6IH -#--3
5B8 H<9 CH<9F H9GH98 5@;CF=H<AG 5F9 5@GC 56@9 HC F9HF=9J9 D5FH C: H<9 =B
H9F=7H5@ B9HKCF? =BJC@J98 8IF=B; -! F97CF8=B;G
CF D5H=9BH  H<9 HKC 7CBG=89F98 J5F=5BHG C: -#--3 @958 HC B95F@M
=89BH=75@ F9GI@HG G99 =;  A=88@9 @C75@=N=B; 5 D5H7< =B H<9 @9:H GI
D9F=CF DF97IB9IG .<9 A5L=A5@ 5AD@=HI89G 9GH=A5H98 6M 7&),. 5F9
5@GC 7CB79BHF5H98 =B H<=G 6F5=B F9;=CB 6IH =B 588=H=CB 7&),. 5@GC
G<CKG 5B 57H=J5H=CB C: H<9 F=;<H GID9F=CF DF97IB9IG 5B8 @C75@=N9G G9J
9F5@ CH<9F GA5@@ 6F5=B F9;=CBG =B C77=D=H5@ 5B8 H9ADCF5@ 5F95G C: H<9
@9:H <9A=GD<9F9 -.10 =89BH=S9G 5 @5F;9 D5H7< CB H<9 F=;<H GID9F=CF
DF97IB9IG =B5@@M L-C'/-# =89BH=S9G 5 BIA69F C: GA5@@ D5H7<9G
=B H<9 H=GGI9 F9A5=B=B; 5:H9F H<9 F9G97H=CB =B H<9 A9G=5@ 5B8 GID9F=CF
5GD97H C: H<9 C77=D=HCD5F=9H5@ F9;=CB .<9 -! F97CF8=B;G G<CK H<5H
H<9 9D=@9DH=7 GD=?9G CF=;=B5H9 :FCA H<9 6F5=B F9;=CBG 5FCIB8 H<9 F9
G97H98 5F95 5B8 :FCA H<9 DCGH9F=CF 7=B;I@5H9 ;MFIG #B D5FH=7I@5F H<9
@9:H A9G=5@ D5F=9HCC77=D=H5@ 6F5=B F9;=CBG 5B8 H<9 @9:H 65G5@ 5B8 GID9
F=CF DF97IB9IG 7: =;  5F9 DF=A5F=@M =BJC@J98 =B H<9 =BH9F=7H5@ 57H=J
=HM CF H<=G D5H=9BH H<9 GCIF79 @C75@=N5H=CB F9GI@HG C: L-C'/-# 5F9
H<IG H<9 ACGH 7CB7CF85BH K=H< H<9 -! 5B5@MG=G .<9 F9GI@HG C: -#--3
5F9 @9GG 7CB7CF85BH 6IH F9A5=B =B 69HH9F 5;F99A9BH K=H< =BHF579F96F5@
F97CF8=B;G H<5B H<CG9 C6H5=B98 6M 7&),. .<9 F9GI@HG C: -.10
8C BCH A5H7< H<9 C6G9FJ5H=CBG A589 =B H<9 -! 5B5@MG=G
#B 75G9 C: D5H=9BH  6CH< J5F=5BHG C: -#--3 @C75@=N9 5 6F5=B F9;=CB
CB H<9 F=;<H H9ADCF5@ DC@9 6IH H<=G F9;=CB =G G@=;<H@M GA5@@9F :CF &
-#--3 K=H< R   7&),. =89BH=S9G 5 @5F;9 BIA69F C: GA5@@ 6F5=B
F9;=CBG G75HH9F98 5@@ CJ9F H<9 F=;<H <9A=GD<9F9 6IH =BJC@J=B; =B D5F
H=7I@5F F=;<H A9G=5@ 5F95G -.10 5B8 L-C'/-# 6CH< G<CK 5B
57H=J5H=CB C: H<9 A9G=5@ D5FH C: H<9 F=;<H H9ADCF5@ DC@9 77CF8=B; HC
H<9 -! 5B5@MG=G H<9 6F5=B F9;=CB =BJC@J98 =B 9D=@9DH=7 GD=?9 57H=J
=HM 7CFF9GDCB8G HC H<9 5BH9F=CF D5FH C: H<9 F=;<H H9ADCF5@ @C69 A9G=5@@M
5B8 @5H9F5@@M .<=G =G 7CB7CF85BH K=H< H<9 SB8=B;G C: -#--3 -.10
5B8 L-C'/-# K<=7< F9HF=9J9 9=H<9F H<9 A9G=5@ CF H<9 @5H9F5@ 5GD97H
C: H<9 5BH9F=CF H9ADCF5@ F9;=CB K<=@9 H<9 GCIF79 @C75@=N5H=CB F9GI@H C:
7&),. 8C9G BCH A5H7< H<9 F9GI@HG :FCA H<9 =BHF579F96F5@ F97CF8=B;G
4. Discussion
1<=@9 H<9 SFGH 5@;CF=H<AG H<5H <5J9 699B DFCDCG98 :CF 6F5=B GCIF79
@C75@=N5H=CB CJ9F HKC 897589G 5;C 5F9 A5=B@M GI=H98 :CF H<9 =89BH=S75
H=CB C: :C75@ GCIF79G CJ9F H<9 D5GH :9K M95FG F9G95F7<9FG <5J9 D5=8
=B7F95G=B; 5HH9BH=CB HC H<9 =89BH=S75H=CB C: GD5H=5@@M 9LH9B898 GCIF79G
K<=7< <5G 699B H<9 HCD=7 C: G9J9F5@ DF9J=CIG GHI8=9G &=AD=H= 
F=GHCB 9H 5@  =B;  C@GH58  =FCH 9H 5@ 
<CK8<IFM 9H 5@  97?9F 9H 5@ 7 4<I 9H 5@  .<9
DFCDCG98 5@;CF=H<AG 5F9 65G98 CB 5 J5F=9HM C: 5DDFC57<9G =B7@I8=B;


UNCORRECTED PROOF
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9LH9B898 GCIF79 G75BB=B; 5M9G=5B H9BGCF65G98 5B8 GD5FG9 A9H<C8G
1<9B 7CB:FCBH98 K=H< 85H5 C: G9J9F5@ G=AI@H5B9CIG@M 57H=J9 9LH9B898
GCIF79G H<9 0- 5@;CF=H<A <5G DFCJ98 HC 69 CB9 C: H<9 ACGH
DFCA=G=B; A9H<C8G 97?9F 9H 5@ 6  =B D5FH=7I@5F =B H<9 75G9
C: 7CFF9@5H98 57H=J=H=9G 5B8 <5G 699B GI779GG:I@@M 9AD@CM98 :CF H<9 @C
75@=N5H=CB C: 6F5=B F9;=CBG =BJC@J98 =B =BH9F=7H5@ 9D=@9DH=7 GD=?9 G=;B5@G
4<I 9H 5@ 
#B H<=G D5D9F K9 <5J9 GHF=J98 HC :IFH<9F =ADFCJ9 H<9 @C75@=N5H=CB
C: 9LH9B898 GCIF79G 6M DF9G9BH=B; 5 B9K F9;I@5F=N98 @95GH GEI5F9G 5@
;CF=H<A 75@@98 -#--3 K<=7< 6I=@8G CB H<9 0- A9H<C8 G H<9
0- 5@;CF=H<A F9;I@5F=N5H=CB CB@M 5DD@=9G HC H<9 ;F58=9BH C: H<9
GCIF79 8=GHF=6IH=CB =9 H<9 J5F=5H=CB5@ A5D K<=7< =G =BJ5F=5BH K=H< F9
GD97H HC 5B 58898 7CBGH5BH =B H<9 CF=;=B5@ GCIF79 8CA5=B =H @95J9G 5B
CD9B=B; :CF GCIF79 9GH=A5H9G H<5H 5F9 5AD@=HI896=5G98 .<=G DFC6@9A =G
GI779GG:I@@M H57?@98 6M H<9 588=H=CB5@ ZBCFA F9;I@5F=N5H=CB H9FA 9A
D@CM98 6M -#--3 "CK9J9F 5G H<9 G=B;@9D5H7< G=AI@5H=CB F9GI@HG G<CK
H<9 K9=;<H C: H<=G 588=H=CB5@ F9;I@5F=N5H=CB H9FA G<CI@8 69 @9:H GA5@@
7CAD5F98 HC H<9 K9=;<H C: H<9 J5F=5H=CB5@ A5D F9;I@5F=N5H=CB H9FA 69
75IG9 H<9 EI5@=HM C: H<9 GCIF79 9GH=A5H9G 897@=B9G K=H< =B7F95G=B; =B
TI9B79 C: H<=G H9FA .<=G =G GCA9K<5H GIFDF=G=B; 5G CB9 7CI@8 <5J9
9LD97H98 H<=G GD5FG=HM=B8I7=B; H9FA HC <9@D =89BH=:M D5H7<9G C: GA5@@
G=N9 39H H<9 G=AI@5H=CBG <5J9 G<CKB H<5H 69G=89G 5JC=8=B; H<9 5AD@=
HI896=5G H<9 B9K F9;I@5F=N5H=CB H9FA =G CB@M IG9:I@ =B H<9 7CBH9LH C:
AI@H=D@9 D5H7<9G K<9F9 =H <9@DG HC G9D5F5H9 7@CG9 D5H7<9G 5G 89ACB
GHF5H98 6M H<9 GA5@@9F & J5@I9G :CF G79B5F=CG – 5B8 H<9 <=;<9F DFC6
56=@=H=9G C: D5H7< G9D5F5H=CB 6IH BCH :CF F97CJ9F=B; G=B;@9 D5H7<9G C:
GA5@@ G=N9 )B H<9 CH<9F <5B8 CIF C6G9FJ5H=CB H<5H D5H7<9G 7CADF=G=B;
@9GG H<5B  7AZ C: H<9 7CFH=75@ GIF:579 75BBCH 69 577IF5H9@M =89BH=S98
=B89D9B89BH@M C: H<9 9AD@CM98 F9;I@5F=N5H=CB GHF5H9;M =G 7CFFC6CF5H98
6M DF9J=CIG ! 5B8 '! GHI8=9G K<=7< <5J9 G<CKB H<5H 5 79FH5=B
5F95 C: 7CFH9L ;9B9F5@@M H<9 A=B=AIA 5F95 =G G5=8 HC 69  7AZ B998G
HC 69 57H=J9 HC C6H5=B 5 G=;B5@ C: GI:S7=9BH 5AD@=HI89 HC 69 A95GIF56@9
5H H<9 GIF:579 '=?IB= 9H 5@  )=G<= 9H 5@  -<=;9HC 9H 5@
 !5J5F9H 9H 5@  .5C 9H 5@  '9F@9H 5B8 !CHA5B 
69FGC@9 
C@@CK=B; )I 9H 5@  !F5A:CFH 9H 5@  K9 <5J9 5@GC 7CB
G=89F98 9LD@C=H=B; H<9 H9ADCF5@ GHFI7HIF9 C: H<9 85H5 6M F9D@57=B; H<9
ZBCFA =B H<9 F9;I@5F=N5H=CB H9FAG 6M H<9 &BCFA G H<9 G=AI@5
H=CBG G<CK H<=G 7CBG=89F56@M =ADFCJ9G H<9 9GH=A5H98 H=A9 7CIFG9G C: H<9
GCIF79G 5B8 @958G HC ACF9 FC6IGH GCIF79 9GH=A5H9G =B D5FH=7I@5F =B H<9
75G9 C: G9J9F5@ 7@CG9 D5H7<9G K<9F9 =H :57=@=H5H9G H<9 D5H7< G9D5F5H=CB
CBHF5FM HC H<9 A9H<C8 DFCDCG98 =B &=AD=H=  L-C'/-#
5B8 -.10 -#--3 =G BCH 65G98 CB 5 D5F5A9H9F=N5H=CB C: H<9 8=GHF=6
IH98 GCIF79 .<=G A5?9G =H ACF9 T9L=6@9 K=H< F9GD97H HC H<9 :CFA C:
H<9 D5H7<9G 5G =H 75B H<9CF9H=75@@M F97CJ9F 5 D5H7< C: 5BM :CFA K=H<
CIH DF9:9F9B79 :CF 7=F7I@5FG<5D98 GCIF79 F9;=CBG @=?9 L-C'/-# CF
-.10 -H=@@ K9 <5J9 C6G9FJ98 H<5H -#--3 5@GC G99AG HC <5J9 79FH5=B
DF9:9F9B79G :CF D5H7< ;9CA9HF=9G K<=7< 75BBCH 69 7<5F57H9F=N98 =B ;9B
9F5@ 5G H<9M 89D9B8 CB H<9 @C75@ 7<5F57H9F=GH=7G C: H<9 7CFH=75@ GIF:579
A9G<
 ;9B9F5@ DFC6@9A K=H< 5@;CF=H<AG 69@CB;=B; HC H<9 :5A=@M C: F9;I
@5F=N98 @95GH GEI5F9G 5DDFC57<9G =G H<9 7<C=79 C: H<9 F9;I@5F=N5H=CB D5
F5A9H9F ):H9B H<=G D5F5A9H9F =G 58>IGH98 577CF8=B; HC H<9 BC=G9 @9J9@
K<=7< B998G HC 69 9GH=A5H98 :FCA H<9 A95GIF9A9BHG 6M 5B5@MN=B; 5
GI=H56@9 85H5 =BH9FJ5@ #B H<=G D5D9F K9 <5J9 7CBG=89F98 5B 5@H9FB5
H=J9 5DDFC57< K<9F9 H<9 F9;I@5F=N5H=CB D5F5A9H9F =G CDH=A=N98 K=H< F9
GD97H HC H<9 ZBCFA 7CBGHF5=BH K<=7< A5L=A=N9G H<9 GD5FG=HM C: H<9 GC
@IH=CB .<=G GHF5H9;M KCF?G J9FM K9@@ :CF G=B;@9D5H7< G79B5F=CG "CK
9J9F =B H<9 75G9 C: AI@H=D@9 D5H7<9G H<=G 5DDFC57< H9B8G HC 9@=A=B5H9
D5H7<9G K=H< K95? 5AD@=HI89G .<9 F9;I@5F=N5H=CB D5F5A9H9F H<5H =G 5I
HCA5H=75@@M G9@97H98 IG=B; H<=G A9H<C8 G<CI@8 H<IG 69 J=9K98 5G 5 A5L
=AIA J5@I9 H<5H ;=J9G 5 ;CC8 =B8=75H=CB C: 5B 589EI5H9 D5F5A9H9F #B
DF57H=79 HC 5JC=8 CJ9F@CC?=B; K95?9F GCIF79G =H =G <CK9J9F 58J=G56@9
HC 7<97? H<9 GCIF79 8=GHF=6IH=CBG C6H5=B98 :CF GCA9K<5H GA5@@9F F9;I
@5F=N5H=CB D5F5A9H9FG (9J9FH<9@9GG GC :5F CIF 9LD9F=9B79 K=H< H<9 B9K
F9;I@5F=N5H=CB GHF5H9;M CB F95@ ! F97CF8=B;G =G DCG=H=J9
.C 89@=B95H9 H<9 GCIF79 F9;=CBG 65G98 CB H<9 GCIF79 =A5;=B; GC@I
H=CBG H<9 @5HH9F <5J9 HC 69 H<F9G<C@898 .C H<=G 9B8 K9 <5J9 DFCDCG98
HC 9AD@CM 5B . A9H<C8 65G98 CB HCC@G :FCA =A5;9 DFC79GG=B; .C CIF
?BCK@98;9 H<=G =G H<9 SFGH H=A9 H<5H 5B . A9H<C8 H<5H =G BCH 65G98 CB
5 G=AD@9 5AD@=HI89 H<F9G<C@8 =G DF9G9BH98 =B H<9 7CBH9LH C: 6F5=B GCIF79
=A5;=B; .<9 58J5BH5;9 C: H<9 DFCDCG98 5DDFC57< =G H<5H =H =G ACF9 C6
>97H=J9 H<5B G9@97H=B; 5 SL98 H<F9G<C@8 :CF H<9 8=DC@9 5AD@=HI89G G
H<9 . 5DDFC57< G9;A9BHG H<9 GCIF79 8=GHF=6IH=CB 65G98 CB H<9 ;F58=
9BH =H 5@GC D9FA=HG HC 89@=B95H9 GCIF79 F9;=CBG K<CG9 5AD@=HI89 =G CB@M
G@=;<H@M @5F;9F H<5B H<5H C: GIFFCIB8=B; ;F=8 8=DC@9G 5B8 K<=7< KCI@8
<5J9 699B J9FM 8=:S7I@H HC F97C;B=N9 IG=B; 5 SL98 5AD@=HI89 H<F9G<C@8
M 7CBHF5GH H<=G 5DDFC57< <5G GCA9 8=:S7I@H=9G =B 589EI5H9@M H<F9G<C@8
=B; GCIF79 8=GHF=6IH=CBG K=H< J9FM ;F58I5@ 5AD@=HI89 7<5B;9G 6975IG9 =B
H<=G 75G9 H<9F9 =G BC G=;B=:=75BH 7<5B;9 =B ;F58=9BH H<5H 75B 69 9LD@C=H98
:CF H<9 89@=B95H=CB C: H<9 GCIF79G "CK9J9F K=H< 5B 5DDFCDF=5H9 7<C=79
C: H<9 F9;I@5F=N5H=CB D5F5A9H9F H<=G ?=B8 C: GCIF79 8=GHF=6IH=CB G<CI@8
BCH C77IF IG=B; -#--3
CF H<9 G=AI@5H=CBG 7CB8I7H98 =B H<=G D5D9F K9 IG9 H<9 G5A9 JC@
IA9 7CB8I7HCF 5B8 GCIF79 GD579 :CF H<9 :CFK5F8 5B8 H<9 =BJ9FG9 DFC6
@9A H<9F96M B9;@97H=B; H<9 =AD57H C: AC89@=B; 9FFCFG CB H<9 GCIF79 @C
75@=N5H=CB F9GI@HG "CK9J9F H<9 AC89@=B; 9FFCFG KCI@8 =BTI9B79 H<9 F9
GI@HG C: 5@@ GCIF79 @C75@=N5H=CB 5@;CF=H<AG GI7< H<5H H<9=F B9;@=;9B79 8C9G
BCH ;=J9 5BM 58J5BH5;9 HC H<9 DFCDCG98 A9H<C8 =B D5FH=7I@5F (9J9FH<9
@9GG H<9 FC6IGHB9GG HC AC89@=B; 9FFCFG C: 8=::9F9BH GCIF79 @C75@=N5H=CB
5@;CF=H<AG =G 5B =BH9F9GH=B; GI6>97H H<5H G<CI@8 69 =BJ9GH=;5H98 =B :IHIF9
GHI8=9G
.C J5@=85H9 H<9 DFCDCG98 5@;CF=H<A CB 7@=B=75@ 85H5 K9 <5J9 7CB
G=89F98 ! F97CF8=B;G C: :CIF 9D=@9DH=7 D5H=9BHG #B 5@@ 75G9G H<9 6F5=B
F9;=CBG =89BH=S98 6M -#--3 5F9 7CB7CF85BH K=H< H<9 SB8=B;G C: 5B -!
5B5@MG=G K<=7< K5G D9F:CFA98 5G D5FH C: H<9 DF9GIF;=75@ 9J5@I5H=CB C:
H<9G9 D5H=9BHG CAD5F98 HC H<9 CH<9F H9GH98 A9H<C8G -#--3 =G ACF9
FC6IGH H<5B -.10 5B8 7&),. K<=7< GCA9H=A9G @958 HC F9GI@HG
H<5H 5F9 @9GG 7CB7CF85BH K=H< H<9 -! 5B5@MG=G IFH<9FACF9 -#--3 =G
ACF9 DF97=G9 =B 89@=B95H=B; H<9 57H=J9 6F5=B F9;=CBG H<5B 7&),. =
B5@@M :CF CB9 D5H=9BH H<9 GCIF79 @C75@=N5H=CB F9GI@HG C6H5=B98 6M -#--3
5F9 ACF9 7CB7CF85BH K=H< H<9 SB8=B;G C: H<9 -! 5B5@MG=G H<5B H<CG9
C: L-C'/-# 6975IG9 -#--3 577IF5H9@M 7<5F57H9F=N9G H<9 DFCD5;5
H=CB C: H<9 9D=@9DH=7 57H=J=HM K<=7< =G BCH H<9 75G9 :CF L-C'/-# )B
H<9 CH<9F <5B8 L-C'/-# @958G HC G@=;<H@M ACF9 7CB7CF85BH F9GI@HG
K=H< H<9 -! :CF HKC CH<9F D5H=9BHG CF H<9 @5GH D5H=9BH -#--3 5B8
L-C'/-# D9F:CFA 9EI5@@M K9@@ CF 5@@ D5H=9BHG K9 8C BCH C6G9FJ9
6=; 8=::9F9B79G =B H<9 @C75@=N98 6F5=B F9;=CBG K<9B 7CBG=89F=B; H<9 8=:
:9F9BH J5F=5BHG C: -#--3 "CK9J9F CB G=AI@5H98 85H5 H<9 D9F:CFA5B79
=ADFCJ9A9BH C: &-#--3 K=H< R   CJ9F -#--3 K=H< R   K5G
CB@M C6G9FJ98 =B H<9 75G9 C: 8=:S7I@H G79B5F=CG K=H< AI@H=D@9 D5H7<9G
GC H<9 G=A=@5F=HM C: H<9 F9GI@HG C: H<9G9 A9H<C8G CB H<9 7CBG=89F98 7@=B
=75@ 85H5 7CI@8 69 9LD@5=B98 6M H<9 :57H H<5H H<9 IB89F@M=B; GCIF79 7CB
S;IF5H=CBG 5F9 @9GG 7CAD@9L =B5@@M H<9 9LD@C=H5H=CB C: H9ADCF5@ GHFI7
HIF9 65G98 CB H<9 &BCFA <5G 5@GC 699B G<CKB HC =ADFCJ9 H<9 =BH9F
DF9H56=@=HM C: H<9 9GH=A5H98 H=A9 G=;B5@G =B H<9 75G9 C: 7@=B=75@ ! 85H5
5. Conclusion
#B 7CB7@IG=CB H<9 7CADIH9F G=AI@5H=CBG <5J9 G<CKB H<5H H<9 -#--3
5@;CF=H<A DFCDCG98 =B H<=G D5D9F =G 69HH9F =B G9D5F5H=B; AI@H=D@9 57H=J9
D5H7<9G H<5B H<9 CH<9F H9GH98 GCIF79 =A5;=B; A9H<C8G DFCJ=89G 5B =A
DFCJ98 9GH=A5H=CB C: H<9 GCIF79 H=A9 G=;B5@G 6M F9GCFH=B; HC H<9 &
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9L5AD@9G <5J9 7CBSFA98 H<5H -#--3 M=9@8G F9GI@HG H<5H 5F9 7CB7CF85BH
K=H< H<9 9LD97H5H=CBG CB H<9 9D=@9DH=7 6F5=B F9;=CBG 65G98 CB 5B -!
5B5@MG=G .<9F9:CF9 -#--3 DFCJ9G HC 69 5 DFCA=G=B; A9H<C8 :CF H<9 F9


UNCORRECTED PROOF
-+2-9-;)3 -<964)/- ???  ??????
7CBGHFI7H=CB C: 9LH9B898 6F5=B GCIF79G =B D5FH=7I@5F :CF 5DD@=75H=CB =B
9D=@9DGM
IHIF9 KCF? K=@@ 7CBG=GH =B 9LH9B8=B; H<9 . 5DDFC57< HC CH<9F
GCIF79 =A5;=B; 5@;CF=H<AG 6M A5?=B; =H ACF9 FC6IGH HC 8=::9F9BH 7<5F
57H9F=GH=7G C: 9GH=A5H98 GCIF79 8=GHF=6IH=CBG IFH<9FACF9 K9 K=@@ 5D
D@M H<9 -#--3 5@;CF=H<A HC ACF9 9L5AD@9G C: 7@=B=75@ 85H5 =B CF89F HC
7CBSFA H<9 DF9@=A=B5FM F9GI@HG C: H<=G D5D9F BCH<9F F9G95F7< 8=F97H=CB
K=@@ 69 H<9 5DD@=75H=CB C: H<9 -#--3 5@;CF=H<A :CF GC@J=B; H<9 9@97HFC75F
8=C;F5D<M =BJ9FG9 DFC6@9A
Acknowledgements
" 97?9F K5G D5FH@M GIDDCFH98 6M CBG9=@ ,é;=CB5@ * 5B8
6M (,- F5B79 .<9 KCF? C: * CACB K5G D5FH@M :IB898 6M H<9
IFCD95B ,9G95F7< CIB7=@ IB89F H<9  H< :F5A9KCF? DFC;F5AA9
* !F5BH ;F99A9BH BC 
References
@=N589<  !C@8:5F6   -97CB8)F89F CB9 *FC;F5AA=B; ,IH;9FG /B=J9F
G=HM Q .97< ,9D
5=@@9H - 'CG<9F $ &95<M ,'  @97HFCA5;B9H=7 6F5=B A5DD=B; # -=;B5@
*FC79GG '5;  (CJ9A69F  Q
5@85GG5FF9 & 'CIF5C'=F5B85 $ *CBH=@ '  -HFI7HIF98 GD5FG=HM AC89@G :CF 6F5=B
897C8=B; :FCA :AF= 85H5 #B *FC7998=B;G C: *,(# CB:9F9B79 DD –
97?9F " @69F5 & CACB * !F=6CBJ5@ , '9F@9H # 5 5GH J5F=5H=CB65G98
A9H<C8G :CF H<9 5B5@MG=G C: 9LH9B898 6F5=B GCIF79G #B *FC7998=B;G C: /-#*) &=G
6CB *CFHI;5@
97?9F " @69F5 & CACB * !F=6CBJ5@ , 19B8@=B;  '9F@9H # 6  D9F:CF
A5B79 GHI8M C: J5F=CIG 6F5=B GCIF79 =A5;=B; 5DDFC57<9G #B *FC7998=B;G C: #--*
@CF9B79 #H5@M DD –
97?9F " @69F5 & CACB * !F=6CBJ5@ , 19B8@=B;  '9F@9H #  F5=B
GCIF79 =A5;=B; :FCA GD5FG9 HC H9BGCF AC89@G # -=;B5@ *FC79GG '5;  (CJ9A
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97?9F " @69F5 & CACB * "55F8H ' =FCH ! 19B8@=B;  !5J5F9H ' éB5F
! '9F@9H #  ! 9LH9B898 GCIF79 @C75@=N5H=CB H9BGCF65G98 JG 7CBJ9BH=CB5@
A9H<C8G (9IFC#A5;9  I;IGH Q
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C@GH58  05B 099B  (CK5? ,  -D579H=A9 9J9BH GD5FG9 D9B5@=N5H=CB :CF A5;
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CM8 - *5F=?< ( <I  *9@95HC  7?GH9=B $  =GHF=6IH98 CDH=A=N5H=CB
5B8 GH5H=GH=75@ @95FB=B; J=5 5@H9FB5H=B; 8=F97H=CB A9H<C8 C: AI@H=D@=9FG CIB8 .F9B8G
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9@=B; 6M 7CADF9GG=J9 B9IFCA5;B9H=7 HCAC;F5D<M (9IFC#A5;9 '5M 
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GD5H=5@@M 9LH9B898 ;9B9F5HCFG :CF 9D=@9DH=7 57H=J=HM 7CAD5F=B; 9BHFCD=7 5B8 <=9F5F7<=
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