n e r e f n o C l a n o it a n r e t n I 7 1 0
2 ceonMathemaitcs ,ModelilngandSimulaitonTechnologiesandAppilcaitons(MMSTA2017) 8 7 9 : N B S
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3,*1CollegeofComputerandInformaitonScience,SouthwestUniverstiy,Chongqing,400715,China
2CollegeofComputerandInformaitonScience,SouthwestUniverstiy,Chongqing,400715,China
3BusinessCollegeSouthwestUniverstiy,Chongqing,402460,China
e r r o C
* spondingauthor
d r o w y e
K s :Communtiydeteciton ,Overlappingcommuntiystructure ,Infecitousdiseasemodel.
t c a r t s b
A .Therei sahugenumberofcomplexnetworksi nour ilfe,i ti sofgrea tsignificancet ostudy d e t a l e r d n a e r u t c u r t s l a c i g o l o p o t s t
i properties .CommunityStructurei soneoft hemos tcommonand y t r e p o r p t n a t r o p m
i , existi ng in mos tnetworks .Further research found overlapping community is l a e r o t e s o l c e r o
m -worldnetworks .Asaresult ,overlappingcommunitydetecitonispu tforwardfor . s k r o w t e n x e l p m o c f o s e i t r e p o r p d n a e r u t c u r t s c i s n i r t n i e h t g n i l a e v e
r Ahugenumberofalgorithms o t d e s o p o r p n e e b e v a
h discover community structures .Based on these principles and existing i p p a l r e v o g n it c e t e d r o f m h t i r o g l a t n e i c i f f e d n a t s a f a , s e h c r a e s e
r ngcommunitystructuresi sproposed i t l u M d e ll a c , r e p a p s i h t n
i -Pathogenic-Susceptible-Infected (MPSI) .I timproves the efficiency of s tl u s e r l a t n e m i r e p x E . n o i s i v i d p a l r e v o y r a s s e c e n n u s d i o v a d n a , p a l r e v o f o l e v e l e h t s l o r t n o c , n o i s i v i d l a e r r u o f n
o -world networks demonstrate tha tthe proposed method achieves high accuracy on . s k r o w t e n n i y t i n u m m o c g n i p p a l r e v o g n i t c e t e d
Introduciton
l a e r y n a
M -world systemstaketheformofnetworksinwhich thenodesrepresentingenittiesand o i t a l e r g n i t n e s e r p e r s k n i l e h
t nships between enttiies[1] ,such as the World Wide Web[2] ,emai l s k r o w t e n l a c i m e h c o i b d n a l a i c o s d n a , s k r o w t e
n [3,4] ,etc. There is a genera l property called s e r u t c u r t s y t i n u m m o
c [5,6] ,whose nodes are often clustered into tightly kni tgroups with a high n
e
d sityofwithin-groupconnecitonsandal owerdensityofbetween-groupconnections. , w o n o t p
U avas tnumberofcommunitydetectionalgorithmshavebeenproposed ,especially in r g n i d u l c n i , s e u q i n h c e t f o y t e i r a v e d i w a e s u s m h t i r o g l a e h T . s r a e y w e f t s a l e h
t emova lof high
-s e g d e s s e n n e e w t e
b [7,8] ,spectra lanalysis[9] ,detection of dense subgraphs[10] ,optimization of y t i r a l u d o
m [11,12] ,andmore[13,14,15,16,20] .
m h t i r o g l a n o i t a g a p o r p l e b a l e h t s i s e i t i n u m m o c g n i t c e t e d r o f s m h t i r o g l a t s e t s a f e h t f o e n
O called
theRAKalgorithm[17]. However ,onlydisjoin tcommunitiescanbedetected .Based on this ,Steve d e m a n , s k r o w t e n e g r a l y r e v n i e r u t c u r t s y t i n u m m o c g n i p p a l r e v o g n i d n i f r o f m h t i r o g l a n a d e s o p o r p A R P O
C [18](CommunityOverlapPropagationAlgorithm).Avertexi sablet ocarrymulitplel abels , o t g n o l e b n a c x e t r e v a n e h
t vcommuniites ,where visaparameteri nt hisalgorithm.Inaddition,t his . s k r o w t e n e t it r a p i b d n a d e t h g i e w e l d n a h o t e l b a o s l a s i m h t i r o g l
a Ahn[19] proposed a nove l
s t s i s n o c y t i n u m m o c a : t n i o p w e i
v ofase tofl inksandanetworki sorganizedbyahierarchyofl inks . h p a r g w e n a , s i t a h
T utiilzeorigina lnodestobeedges ,andlinkstobenodes .Thendivides thenew h
p a r
g using anon-overlapping community discovery method .Sinceanodecan belong tomultiple k n i l f o y ti l i b a e h t d e v o r p h c i h w , y l i s a e d n u o f e b n a c y t i n u m m o c g n i p p a l r e v o e h t , s e g d
e -centric
.t n i o p w e i
v Probably the best-known algorithm for finding community structure is Girvan and N G d e m a n m h t i r o g l a s ’ n a m w e
N [8] .Thealgorithmbasedont hebetweenness ,whichbetweennessof e
g d
e edefinedasthenumberofshortes tpaths ,betweenal lpairsofverticestha tpassalonge .Steve A G N O C d e m a n h c i h w , s e c i t r e v g n i tt i l p s f o d o h t e m c i f i c e p s a h t i w m h t i r o g l a N G s d n e t x
e [21]
r e t s u l C
, d e s o p o r p n e e b e v a h s m h t i r o g l a g n i t c e t e d y t i n u m m o c g n i p p a l r e v o f o r e b m u n p u o r g a h g u o h t l A
y n a m l l i t s e r a e r e h
t disadvantagescomparedwtihnon-overlappingcommunitydetecting ,suchashigh . y t il i b a t s n i e h t d n a , d e l l o r t n o c n u g n i p p a l r e v o , y c a r u c c a l a r u t c u r t s w o l , y t i x e l p m o c n o i t a t u p m o c
s e h c r a e s e r e v o b a y b d e r i p s n
I [22,25] ,an efficien talgorithm for detecting overlapping community l
a n o i ti d a r t n o d e s a b s e r u t c u r t
s SI(Susceptible-Infected)mode lin complex networksisproposed in s e d o n e g n i r f e h t f o p i h s r e n w o e h t e n i m r e t e d o t s i m h t i r o g l a e h t f o y g e t a r t s y e k e h T . e l c i t r a s i h t
s i n o i s i v i d y t i n u m m o c g n i p p a l r e v O . y l d e t a e p e
r no taffected by the order of joining the vertices , . g n i t c e t e d r e t f a l e v e l n i a t r e c a s a h d n a y t i n u m m o c f o n o i s i v i d y r a s s e c e n n u e h t g n i d i o v
a The
e c n a m r o f r e
p of this algorithm is assessed using four real-word networks .Experimenta lresults h
t t a h t e t a r t s n o m e
d e algorithm is able to detec toverlapping community structures efficiently . .
y h c r a r e i h t n a c i f i n g i s s a h y t i n u m m o c g n i p p a l r e v o f o n o i t c e t e d e h t , e r o m r e h t r u F
RelatedW ko r e l b it p e c s u
S -InfectedMo del
: e r a s n o it p m u s s a y e k e h T
) 1
( Eachnodeisassignedwithoneoft wostatus :SforsusceptibleandIfori nfected. )
2
( Thei nfectioncanbespreadfromi nfectednodet onearbysuscepitblenodes. )
3
( Nodecannott ransfert osusceptiblestatusafteri nfecitng. )
4
( β representst heprobabilityoft hei nfectiont ospreadalongt het iepersimulationstep.
y ti r a l u d o M
d e n i a t b o n e e w t e b s e i t i l a u
Q parttiions are compared by modularity[23,24] .The modularity of a r
a l a c s a s i n o i t i t r a
p tha tvalues from - 21 o/ t 1andi tcanbeusedt omeasurest hedensityof ilnksi nside u
m m o
c niitesaswel laslinksbetweencommuniites.
d e t h g i e w f o e s a c e h t n i , s k n i l r i e h t n o s t h g i e w e v a h t a h t s k r o w t e n e r a s k r o w t e n d e t h g i e w e h T
s a d e n i f e d s i t i , s k r o w t e
n [24]
𝑄 � 21𝑚∑ �𝑖,𝑗 𝐴𝑖𝑗� 𝑘2𝑖𝑚𝑘𝑗�𝛿�𝑐𝑖,𝑐𝑗�. ( 1)
e r e h
w 𝐴𝑖𝑗 representst heweigh toft heedgebetweeniandj ,𝑘𝑖 � ∑𝑗𝐴𝑖𝑗 ist hesumoft heweights x
e t r e v o t d e h c a t t a s e g d e e h t f
o i ,𝑐𝑖 isthe community to which vertex i isassigned ,thefunction
δ(𝑢,𝑣) is1i f 𝑢� 𝑣 and0otherwiseand 𝑚� 1
2∑𝑖𝑗𝐴𝑖𝑗. g
n it c e t e
D Communi ite sbyLouvainAlgortihm
f o s k r o w t e n d e t h g i e w a h ti w s t r a t s m h t i r o g l a e h t t a h t e m u s s
A Nnodes .Assignadifferen tcommunity e
d o n h c a e o
t insidethenetwork .Asaresutl ,thenumberofcommunitiesist hesamewithnodes .Thi s m
h t i r o g l
a operatesast hefollowingtwophases[25] . e
s a h p t s r i F ) 1 (
①．Fornodei ,evaluatethegainofmodularitywithallt heneighbors(removingnode ifrom tis f
o y t i n u m m o c e h t n i t i g n i c a l p y b d n a y t i n u m m o
c i ts neighbor node j) .The increasemen tin y
t i r a l u d o
m Δ𝑄 tha tobtainedbymovingani solatednodeIi ntoacommunityCcanbecalculatedb y:
∆Q� �∑𝑖𝑛+2𝑘𝑖,𝑖𝑛
2𝑚 � �
∑𝑡𝑜𝑡+𝑘𝑖
2𝑚 �
2
�� �∑𝑖𝑛
2𝑚 � �
∑𝑡𝑜𝑡
2𝑚 � 2
� �𝑘𝑖
2𝑚� 2
� . ( 2)
e r e h
w ∑𝑖𝑛 ist hesumoft heweightsoft hel inksi nsideC ,∑𝑡𝑜𝑡 ist hesumoft heweightsoft hel inks n
i e d o n o t t n e d i c n
i C ,𝑘𝑖 isthesumoftheweightsofthelinksinciden ttonodei ,𝑘𝑖,𝑖𝑛 isthesum
i C m
e s a h p d n o c e S ) 2 ( ①
�Building a new network whose nodesare transferred from communtiiesfound in thefirs t . e s a h p
②．Forthenewnetworkbuil tfromstep① ,repeait ngthefirs tphase.
③．Repea tstep① ,unitlt herearenomorechangesandamaximumofmodularityi sobtained. e s e h t f o y t i x e l p m o c e h t t a h t w o h s r e t u p m o c y b d e t a r e p o s k r o w t e n r a l u d o m e g r a l f o s n o i t a l u m i S . a t a d e s r a p s d n a l a c i p y t n o r a e n i l e r a s k r o w t e n A I S P
M lgortihmo fOverlappingCommuntiy o t g n i d n e t x
E OverlappingCommun tiy
. ) I ( d e t c e f n i d n a ) S ( e l b i t p e c s u s o t n i d e d i v i d s a w n o i t a l u p o p l a t o t e h t , l e d o m I S l a n i g i r o e h t n I d e t c e f n i n a m r o f y l l a u t n e v e n a c n o it c e f n i l a n o i t a r s i h t , k r o w t e n x e l p m o c a o t t p e c n o c e h t g n i y l p p A w , e s a e s i d e m a s e h t h t i w d e t c e f n i s l a u d i v i d n i e r e h w , e l c r i
c hichwecal lacommunitystructure .Here , , k r o w t e n l a i t i n i e h t n i t s i x e n o i t c e f n i f o s e c r u o s t n e r e f f i d e l p it l u m w o l l a o t l e d o m I S e h t d n e t x e e w s e s a e s i d s u o i t c e f n i t n e r e f f i d h t i w d e t c e f n i s l a u d i v i d n i e s o h t s n a e m h c i h
w inthebeginning .Thent hey c a e t c e f n
i hotherwithouti nfluence .Aftert hewholeprocess ,eachi nfectiousdiseaseformsacolony , s e s a e s i d t n e r e f f i d f o r e b m u n a h t i w d e t c e f n i e b y a m l a u d i v i d n i n a d n
a tha tcanbedividedi ntomulitple . e m i t e m a s e h t t a s p u o r g l t c e r i d s e x e t r e v e h t e k a t e w , e r e
H y connected totheinfected assusceptible ,after apropagation d e t c e f n i w e n o n s i e r e h t li t n u , s e x e t r e v d e t c e f n i w e n h t i w n o i t a g a p o r p f o e m it d n o c e s e h t e k a t , s s e c o r p e m a s e h t t o n s i s s e c o r p n o i t c e f n i w e n h c a e f o e t a r e h t t a h t g n i t o n h t r o w s i t I . s e x e t r e
v ,andeach itme
e h t , ll a m s y r e v s i s s e c o r p n o i t c e f n i f o e t a r e h t n e h w t a h t d n u o f t n e m i r e p x e e h T . s e s a e r c e d t i t e s e w , o S . n o i s i v i d y t i n u m m o c e l o h w e h t n o e c n e u l f n i t n a c i f i n g i s l a u t c a o n s a h s s e c o r p n o i t a g a p o r p h w s s e c o r p n o i t a g a p o r p e h t p o t s , d l o h s e r h t e h
t enratelessthan acertainvalue .Weassumetha tthe s i s e m it n o it c e f n i f o r e b m u
n 𝛿 ,then theprobabliity ofeach processis 𝛽𝛿 ,when the 𝛽𝛿 isunder
β/10,t heprocessi send .Thati s,t hemaximumof 𝛿 is3-5i ngenera.l
I S P M e h
T Algortihm
I S P M e h
T algorithmproposedbyt hisessayi sprincipallybasedont woi deas .Firs,tt heoverlapping . y l h g u o r e d i c n i o c t u b , r e h t o n a e n o f o t n e d n e p e d n i t o n s i e r u t c u r t s y t i n u m m o c t n i o j s i d d n a y t i n u m m o c a t o n d n a , y l t n e d n e p e d n i s d a e r p s e s a e s i d s u o i t c e f n i e n o , y l d n o c e
S ffec teachotheri nepidemicmodel . h g u o r h t , s e s a e s i d s u o it c e f n i f o r e b m u n t n e r e f f i d h t i w d e t c e f n i x e t r e v e m a s e h t g n i k a m y l l a u t n e v E g n i p p a l r e v o e h t d n i f y l l a n i f n a c e w , y t i n u m m o c e n o o t n i n o i t c e f n i s u r i v e m a s h t i w x e t r e v e h t g n i d i v i d . y t i n u m m o c r o g l a e h
T ithm is appiled to the unweighted networks ,and thedivision resultsareonly used to e c u d e r o t y t i r a l u d o m n i a g e v it a l e r e s u e w o s , s t l u s e r e t a r u c c a l a n i f e h t t o n , s n o i t a i c o s s a y z z u f e z i l a i t i n i : s i e r e h t y t i r a l u d o m f o n i a g e h t o s , y t i x e l p m o c
∆𝑄‘� 𝑘
𝑖,𝑖𝑛� ∑𝑡𝑜𝑚𝑡�𝑘𝑖 . ( 3)
e r e h
w ∑𝑡𝑜𝑡 isthe sum of theedgesinciden tto nodein C ,𝑘𝑖 isthesum of theedgesinciden tto
x e t r e
v i ,𝑘𝑖,𝑖𝑛 ist hesumoft heedgesfromitonodesi nCandmist hesumoft heedges. e
h
T wholeMPSIalgorithmi spresentedinfigure1and2 .Theparameter 𝑛𝑒𝑖𝑔�𝑏𝑜𝑟𝑠(𝑥) ist hese t x e t r e v f o s r o b h g i e n f
o x .And parameter 𝑒𝑑𝑔𝑒(𝑥,𝑦) meansthatthereisan edgebetween vertexx
d n
m h t i r o g l a I S P M e h T . 1 e r u g i
F .
) t n o c ( m h t i r o g l a I S P M e h T . 2 e r u g i
F .
d e t h g i e
W Networks
y t i r a l u d o m f o n i a g e h t e c a l p e r y l p m i s e w , s k r o w t e n d e t h g i e w o t I S P M d n e t x e o
T Δ𝑄′ ←∆𝑄 .In
y b , n o i t a r e p o e t a g a p o r
p β← β𝑤𝑥𝑦/𝑤𝑎𝑣𝑒𝑟𝑎𝑔𝑒 ,where 𝑤𝑥𝑦 ist heweigh toft heedge{x ,y} ,𝑤𝑎𝑣𝑒𝑟𝑎𝑔𝑒 e
t c e f n i n e e w t e b s e g d e l l a f o e u l a v e g a r e v a e h t s
i dvertexesandvertexesi nt hiscommunity .
Experiments l a e R n o I S P
M Networks
s e g d e f o y t i s n e d e v i t a l e r e h t y b d e s s e s s a y l l a u s u s i m h t i r o g l a f o y ti l a u q e h t , s k r o w t e n x e l p m o c r o F
. s e it i n u m m o c n e e w t e b d n a s e i t i n u m m o c n i h t i
w Modularity isthemos tcommon measurement .The t
n a i r a v w e n a t u b , s e it i n u m m o c t n i o j s i d r o f y l n o d e n i f e d s i e r u s a e m y t i r a l u d o m d l
o [26]tha tisalso
. s e i ti n u m m o c g n i p p a l r e v o r o
f Overlapmodulartiy 𝑄𝑜𝑣 isusedasameasurementforexperimentsi n .
r e p a p s i h
t It’svaluedependsont woaspects:thenumberofcommunitiest ha teachvertexbelongst o ,
1 e s a h P
: s e g n a h c e r a e r e h t e l i h W
x e t r e v y n a r o F ) 1
( x:
y=Calculate(x ,neighbors(x) ).
(2)Ify> 0
t n i o
J (x ,y) .
f I ) 3
( 𝑖𝑚𝑝𝑟𝑜𝑣𝑒𝑚𝑒𝑛𝑡� 0: . ) 1 ( p e t s m o r f t a e p e R
: k r o w t e n w e n a g n i d l i u B ) 4 (
Nodesaret hecommuniitesfoundbefore. 2
e s a h P
y t i n u m m o c h c a e r o
F A:
x e t r e v r o F ) 1
( x(𝑥∈𝐴)&& 𝑦∉𝐴: f
I 𝑒𝑑𝑔𝑒(𝑥,𝑦) exist:
𝑒 𝑡 𝑎 𝑔 𝑎 𝑝 𝑜 𝑟
𝑃 (𝐴,𝑦). f
I ) 2
( yInfect: x =y.
. ) 1 ( p e t s m o r f t a e p e R e t a l u c l a
C (x ,neighbors(x) ): n
i a
g = 0.
h c a e r o
F y inneighbors(x) : f
I Evaluate (x, y)>gain: y =neighbors(x) .
n r u t e
R y.
e t a u l a v
E (x ,y) : e v o m e r f
I Communtiy(x)&& 𝐶𝑜𝑚𝑚𝑢𝑛𝑖𝑡𝑦�𝑦�←𝐶𝑜𝑚𝑚𝑢𝑛𝑖𝑡𝑦(𝑦)∪ 𝑥 ,Δ𝑄′� 0:
n r u t e
R Δ𝑄′
t n i o
J (x, y) :
𝑦 𝑡 𝑖 𝑛 𝑢 𝑚 𝑚 𝑜
𝐶 �𝑦�←𝐶𝑜𝑚𝑚𝑢𝑛𝑖𝑡𝑦(𝑦)∪ 𝑥. e
t a g a p o r
P (a ,x) :
I S P M f o s t l u s e r d n a d e s u s k r o w t e n l a e R . 1 e l b a
T .
e m a
N Vertices Edges k 𝑸𝒐𝒗 Overlap Executiont ime[s] z
z a
J 1 98 2742 0.62 0.803 1.005 0.05 n
i e t o r
P 2445 6265 0.74 0.412 1.132 0.21 g
o l
B 3982 6803 0.47 0.610 1.143 0.82 li
a m
E 5451 5451 0.51 0.439 1.021 2.34
e h t f o s e it r e p o r
P Algortihm
) 1
( Thevalueof 𝑄𝑜𝑣 l e v e l p a l r e v o e h
T k isrelated to theparittioning of theenitre network .Figure 3 presents value f
o s e g n a h
c 𝑄𝑜𝑣 indifferen tnetworkswithk’svariations .Aswecansee,t hemaximum k’sl ocation e h T . e m a s t o n s i k r o w t e n t n e r e f f i d n i d e t a g a p o r p s r e y a l f o r e b m u n e h t e s u a c e b , y r a v k r o w t e n h c a e f o
.t s e t a l e h t t a s r a e p p a n i e t o r P e h t f o e u l a v m u m i x a m
f o s e g n a h c e u l a V . 3 e r u g i
F 𝑄𝑜𝑣 amongdifferen tnetworks.
) 2
( MPSIondolphinnetwork o
h t e m I S P M e h
T disapplied to dolphinnetwork to demonstratethehierarchy .Afterphase1 ,the t n e s e r p e r s e p a h s e h t , 4 e r u g i f n o d e w o h s s ’ ti s A . s e it i n u m m o c t n i o j s i d e e r h t o t n i d e d i v i d s i k r o w t e n
e it i n u m m o c p a l r e v o o t s e i t i n u m m o c e h t d n e t x e e w , n e h T . y t i n u m m o c t n e r e f f i
d st hroughphase2 .The
l a c i h c r a r e i h e h t n i a t b o n a c e w o s , 3 e r u g i f s a h p a r g l a c i h c r a r e i h s a t n e s e r p e r n a c s s e c o r p n o i t a g a p o r p
d e d d a y l w e n e h t t n e s e r p e r s t o d d n a , s e it i n u m m o c e e r h t e h t t n e s e r p e r s d u o l c e h T . y l i s a e p i h s n o it a l e r
d e t u c e x e s s e c o r p e h T . s e x e t r e
v threet imes ,wej ustt aket wot imespropagationprocessi nt here ,and .
5 e r u g i f n o s t l u s e r t e
g Dashed lines stand for the propagation process ,and the black lines are .
s e i t i n u m m o c n e e w t e b s p i h s n o it a l e r
l a c i h c r a r e i h s ’ e r u t c u r t s y t i n u m m o c e h T . 4 e r u g i
F graphofdolphinnetwork. 2
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3 . 0
4 . 0
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6 . 0
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8 . 0
9 . 0
1
0 0.2 0.4 0.6 0.8 1 1.2
𝑄
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p a lr e v
o levelk
z z a
k r o w t e n n i h p l o d f o s s e c o r p n o i t a g a p o r p e h T . 5 e r u g i
F .
h ti w n o si r a p m o
C OtherAlgortihm
o s l a e
W compareothert woalgorithmsont hoserea lnetworks .Execution itmeandmodularityamong .
2 e l b a T y b d e t n e s e r p e r a s m h t i r o g l a e s e h
t MPSIgives thebes taveragemodularity and execution e
h T . d e t s e t k r o w t e n y r e v e r o f e m i
t 𝑄𝑜𝑣 ofMPSIhereisthemaximumvaluewithdifferen toverlap .l
e v e l
s k r o w t e n l a e r n o s m h t i r o g l a r e h t o h t i w I S P M f o n o s i r a p m o C . 2 e l b a
T .
e
ma
N
I
S
P
M 𝑄𝑣𝑜
G
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]3
=h
[ 𝑄𝑜𝑣
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]s[
e
mi
T
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]3
=h
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]s[
e
mi
T
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]s[
e
mi
T
z z a
J 0.803 0.518 0.641 0.05 52.8 4 .5 n
i e t o r
P 0.412 0.380 0.169 0.21 96.5 9 8 g
o l
B 0.610 0.527 0.506 0.82 33.5 1 17 l
i a m
E 0.439 0.265 0.098 2.34 6 17 41.3
y r a m m u S
n i d e s o p o r p m h t i r o g l a I S P M e h
T this essay is able to discovering overlapping communtiies s
k r o w t e n x e l p m o c f o a e r a e h t n i y l e v it c e f f
e .Community structure results between overlap and m i s s i e r u t c u r t s s t i f o t s o m t a h t d i a s e b n a c t i , s k r o w t e n l a e r e h t n i t n e r e f f i d y l e r i t n e t o n s i t n i o j s i
d ilar .
e k a t e w , e r o f e r e h t , t s a f y t i n u m m o c d e d i v i d m h t i r o g l a t c e t e d y t i n u m m o c t n i o j s i d , w o n k l l a e w s A
, y l k c i u q s e i ti n u m m o c ’ s e d o n e h t f o t s o m d n i f , m h t i r o g l a t c e t e d y t i n u m m o c t n i o j s i d e h t f o e g a t n a v d a
m it d n o c e s e h t n i g n i g n o l e b e d o n e g n i r f w e f a e g d u j n e h
t e .Through this method ,avoid the e h t f o y t i l i b a t s e h t e r u s n e d n a , p a l r e v o f o l e v e l e h t f o l o r t n o c e h t e z il a e r , s n o i s i v i d y r a s s e c e n n u
. e m i t e m a s e h t t a n o i t c e t e d
Acknowledgement
o i t a d n u o F e c n e i c S l a r u t a N l a n o i t a N e h t y b d e t r o p p u s y l l a i c n a n i f s a w k r o w s i h
T n of China
. ) 2 9 2 1 7 2 1 4 (
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