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true positive proportion (tp/(tp + fn)
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0.5
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2 ROC = 0.85
3 ROC = 0.87
0.3
0.2
0.1
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false positive proportion (fp/(tn + fp))
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{ ˆzqFs”t | x}u¹n‰4xs”ˆ | ˆzwnq2ˆ:‡^2ys«x}p2v wfˆp2‡+vÓ^]‡^x}ufu]v+‡s9`•‰¼n£´¥p2xsºv { v^yzy¢q2v¢p2v+q ¹©jp4w]x}‰4v
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nw¹s”tGv&n‡s”ˆ§}v wfˆs”v+wPx | v+p ´F‰4v+wP‰:nN´™nyzw]x–t2nN§vn | nˆzu]y´ { v^yzy¢q2v¢p2v^q { ˆzqGsft:qGv^s”v^uf‰4ˆzp2v^q
.´¶s”t2v › x}u]sfˆzx}p¶x | sft2v › ufxsfv+ˆpœw]v+—(2v+pG‡+t
v Ô¾ˆ ƒv  sft2vžv+p ´E‰:v Ö { t2ˆ‡štn8‡^s”2nyzy´S‰:n Ðv^w
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s”tGvv+p ´F‰4v ֓ÇLxuX‰4xs”ˆ | w¡w]2‡štŠn8wXs”t2v^wfv•ˆsX‰¼n£´:¦v › x}w]wfˆ2yzv&sfx™q2v^Â2p2vs”t2v‰4v£n8p2ˆzp ¨x |
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| x}yyzx { ˆzp w]v+‡s”ˆzxp2w¡Gwfv+q › 22yˆzwftGv+q0§n8yz2v^w | x}u‰4xs”ˆ | { ˆzqGsft2w¡2nwfv^q†x}p4yªnºx}u”n$s”x}u³´Žq¢n8s”n
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s”tGv™q2v^§v+yzx › ‰:v^p.s•q¢n8sšn8wfv^sfw•nufv ½| x}uVsft2v™‰4x}w]s › nu]s  ‡+yx}wfvŽsfx†s”t2¯v Ð(p2x { p { ˆzqGsft2w  n8p2q
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s”tGufv+v › nwfw]v+w „t2v†nN§v+uf5n }¥v ÒW•p
¬ ÔLð }!} ֕x | s”tGv+wfv;‰4xsfˆ | w¨n8sŽˆq2v+p.s”ˆ | ´Eˆzp Šsft2™v Ð(p2x { p
‰4xs”ˆ | xF‡^‡+2u]ufv^p2‡+v^w4ˆwŽp2v+nufy´ › v+u | v+‡s  np2q¶s”tGv+ˆzu { ˆzqGsft2w™nu]v;‰:xw]s”y´ { ˆs”tGˆzp¶n | n8‡^s”xu
x | s { x:x | sft2v¨t(2‰:np q2v^sfv+u]‰:ˆp2v+q { ˆzqGsft2w 1Ç-ˆzp¢n8yzy´  sft2v¥n82ˆzyˆsj´:x |« Ê  Ê·sfx4Â2p2qŠs”tGv
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©jp¤nyyÉx | s”t2v¨Vv › v+ufˆ‰:v^p.s”wˆp˜s”tGˆzw&w]v+‡s”ˆzxp Ì Ê  Ê { nwu]2p¸2w]ˆzp ¼sft2vމ4x}w]s
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› nw]wfv^wžnp2q › u]v+q2ˆ‡^sfw¼s”t2v^ˆzu { ˆzqGsft2w†—(2ˆsfv { v+yy ¿„tGv¸yzx { v+w]s¼§n8yz2v˜x | ÒW•¬ | x}u†n8p(´
‰4xs”ˆ | ˆ´w ð } ]  np2q’‰¼np.´ž‰4xs”ˆ | wt¢n£§}²v ÒW•¬Àx |X~ ðð X„t2v–ufv^yªn8sfˆ§v { ˆqGs”tÔ qGˆzwf‡^xN§}v+u]v+q
‰4xs”ˆ | { ˆqGs”t’q2ˆ§Fˆq2v+q’.«´ ÐEpGx { p˜‰:x8s”ˆ | { ˆzqFs”t ֈzw ‡^yzx}w]v•sfx ~ ðð | x}u‰:np.´ž‰:x8s”ˆ | w „t2v
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bñ \`_
bñ db
bñYWfe
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WÆñ bb
bñ \QW
bñ db
bñYW]b
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ç¾âbç
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bñ \+Ø
ÆW ñ bb
bñ bb
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bñ áÓ
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bñ bb
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WÆñ bb×WÆñ bb bnñ \+c
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WÆñ bbׯW ñ bb bnñ eb
bñ __b ñ Ód W¾ñ e\
bñÝe`bèb ñÝce ªé bnñ c`_
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bnñÝØ`Ó bñ dd bñØØ
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„n2yzv ^w_¹3² nbnc E! :ê:ê ú  ¸_fô @ c$_ ú 4ú % ú &„t2vs”n2yzv
wftGx { w0s”tGv¥ÒW•¬  ufv^yªn8sfˆ§}v { ˆzqGsft  u]v+yzn8s”ˆ§}v†w]t2ˆ | s  n8p2q › nwfw { tGv+p | x2p2q·x | s”t2v;ºv+w³s
‰4xs”ˆ | q2ˆzw]‡+xN§}v^ufv+q¯.´ ¼ê¼êÀ| x}u™v£n‡štrÐ(p2x { pœ‰4xsfˆ | ‡+xp(s”nˆzpGv+q·ˆzpµsft2v;q2v^§v+yx › ‰4v+p.s
q¢n8s”nwfvs”w P„tGv•sj´ › v•x | ‰:xEq2v+y¦2wfv^q˜ˆwwft2x { p˜nºxQ§vs”t2v•q¢n$sšnw]v^s p¢n‰4v ¹„tGv–‡^x}yzG‰:p2w
ºv+p2v+n8s”t¸v+n‡št¸q¢n$sšnw]v^sVp¢n‰4v¨w]t2x { sft2v–ufv+w]2ysfw | x}u v+n‡št¸x | sft2v²Ð(p2x { p¸‰4xsfˆ | w ˆzpžs”t¢n$s
q¢n8s”nwfvs ë„t2vrwfˆ‰ › yv ™ˆufˆz‡štGyzv^s › ufˆx}u { nw;2w]v+q { ˆsftÊs”t2Év ™|šG›q¢n8s”nwfvs”w’np2qÄs”tGv
wð ‡+x}‰ › x}p2v+p.7
s ™ˆufˆz‡štGyzv^s¥‰:pˆ Es”2u]v › ufˆx}u { n8w:2w]v+q { ˆsft¯sft2v › ufxsfv+ˆp¯q2n8sšnw]v^sfw ¯„t2v
› nyˆzp2qGufx}‰4v•‡+x}p2w³s”ufnˆzp.s”w { v^ufv¥sfufˆv+q { ˆs”t’s”t2üv ™|šœ›Ÿq2n8sšnw]v^sfwnp2qŠwfv+yv+‡s”v+q¤n8Gs”x}‰:n8sfˆ
‡£n8yzy´:ˆ | s”tGv^´;ˆ‰ › u]xN§}v+qžs”tGv–x5 Ï]v+‡s”ˆ§v | 2p2‡^sfˆzx}«p Ó¡ÔPÕ»Ö
q2ˆwf‡+xN§v+ufv^q { ˆzqGsft2wsfv+p2q¥sfxºv¡s”xEx&w]‰¼n8yzy { t2v^pŽs”t2vq2n8sšnw]v^s-ˆzw§}v+u³´Žw]‰¼nyŒy Ô ˆ ®v  q¢n8sšn8wfv^sfw
yzˆ › npGq | nufp { t2ˆ‡štr‡+x}p.s”nˆzprx}pGy´žÂ2§}v™w]v+—(2v^p2‡+v^w¨v+n‡št Ö¤„t2v™u]v+yzn8s”ˆ§}v¥w]t2ˆ | sfFw Ô w]t2ˆ | s&x |
q2ˆwf‡+xN§v+ufv^q·‰:xsfˆ | q2ˆ§Eˆq2v+qµ.*´ Ð(p2x { p·‰:xsfˆ | { ˆzqGsft Ö¨n8ufv¼‰4x}w³s”y´¸‡+yzxwfv:sf‡x +v^ufx ŽÍ˜x}w³s
wftGˆ | s”w n8ufv•q22v•wfˆ‰ › y´4s”x™s”t2v•q2ˆwf‡^xQ§v+u]v+qЉ4xsfˆ | ºv+ˆzp 4w]t2x}u³s”v+usft¢np;s”t2Ãv Ð(p2x { pЉ4xsfˆ |
„t2v&sft2ufv^³v Ð(p2x { Žp ™|šœ› › nyˆzp2q2u]x}‰4v‰:xsfˆ | wPnu]vnyyºqGv^s”v^‡^sfv+q;.´ :ê:ê n8p2q†ufv › xu]s”v^q
nw wfG‡št š°x0v+ufu]x}p2v^x}2w › nyzˆp2q2u]x}‰:ˆ‡V‰4xsfˆ | wnu]v•ufv › x}u³s”v+q’.´ ¼ê¼ê
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k #E ú ¸eÏ FF' ‹c[ ú ½ ú ŠW3 n Jú a 6ú % ú ›&w¨‡£np¦v4wfv^v+p¶ˆpÁsft2v¼t2ˆw]sfx_}u”n8‰ˆzp$Ç-ˆ#2ufv™ ^] ¼ê¼ê 2wfˆp¸n.6-G-1092
‰4xFq2v^y2q2ˆwf‡+xN§v+ufw ~}~ } x | sft2v ~ w Ø ‰:x8s”ˆ | w³ì‡+x}p.s”nˆzp2v^q:ˆpŽs”t2v q¢n$sšnw]v^s”w { ˆs”t2ˆpŽÂ2§}v › nw]wfv+w
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40
number of motifs (total 135)
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46
30
30
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20
27
16
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10
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8
8
ð ñ ò ó ô õ
1
2
3
4
5
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pass where motif found
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b ñ \\ Zbñ bÓ+a bñ d^c Zbñ Ó`_+a bñØØ Zbnñ Ó$Wfa W¾ñ c^c ZbñØ£W”a élbñ bd Zbñ _^á+a
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wftGx { p:ˆzp0s”t2v t2ˆw]sf_x }u”n8‰ #›TÐEpGx { p:‰:x8s”ˆ | ˆ | Ï]2q}v+q4s”x•t¢n£§}vV¦v^v+p | x}2p2q4ˆ | s”t2v ¼ê¼ê
‰4xs”ˆ | t¢n8²w ÒW•¬ëxN§v+¯u ð â }!} ¼„t2v:yªnw³s¨‡^x}yzG‰:pÁ‰¼n8u7Ðv^qœüþý_ˆ†ufv › ufv^wfv+p.sfw¯Ð(p2x { p¶‰:xsfˆ | w
{ t2ˆ‡št { v+u]v¥p2xs | x2p2q’(´ :ê:ê { ˆsft2ˆzp;Â2§v › n8wfwfv^w ›V§}v^u”n5v™Ô¾w]sšn8p2q¢nu]q˜q2v§Eˆªn8sfˆzx}p Ö
› v+u | xuf‰:np2‡+vx | ¦v^w]s‰:x8s”ˆ | w | x2p2q¥.´ :ê:ê ˆp–sft2v 'Ø Å¹u]x}wfˆs”vq¢n8s”nwfvs”w§v+u]wf2w-nyzy ~ w Ø
Ð(p2x { p;‰:x8s”ˆ | w › u]v+w]v+p.s ˆzp4s”t2vVq¢n8sšn8wfv^sfwˆzwPwftGx { p;ˆp:sft2v&sšn82yzv°¦v^p2v£n$s”t¼sft2vt2ˆw]s”5
x }u”n‰
„t2²v 6-/-1092¨wfv^—EGv+p2‡^v‰:xEq2v+y¢sj´ › v { nwX2w]v+qžnyx}p { ˆsft:s”tG²v wð ‡+x}‰ › x}p2v+p.s ™ˆzu]ˆz‡št2yv^s
‰41ˆ Es”2u]v › ufˆx}u
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„t2v–t2ˆ#tŠn£§}v^u”n5v²ÒW•¬Àx | s”tGv :ê:ê ‰:xsfˆ | w‡+np˜ºv–wfv+v^p¸ˆzp;sft2v–s”n2yv–ºv+pGv£n8sft˜s”tGv
t2ˆw]s”5x }u”n‰ÿˆ[
p Ç#ˆ }2u]v4 à] ’„tGv;n£§}v+ufn5}v:ufv+‡+nyzyPnpGq › ufv^‡+ˆwfˆzxpSx | sft2v+w]v¼‰4xs”ˆ | w•2wfˆp
s”tGv :ê:ê }v+pGv+u”n$s”v+qžs”tGufv+w]t2x}yq2w°nufv•ºxs”t’n ›2› ufšx Fˆz‰:n8s”v^y´ g ð.<
„t2v‰4xsfˆ | w | x}2pGq†.´ :ê:ê sfv+p2q:s”x¥ºv { ˆzq2v^uXx}p¼nN§v+uf5n }vVsft¢np¼sft2v { ˆqGs”tGw
x | s”tGv0Åu]x}wfˆs”v™w]#ˆ }p¢n$s”2u]v+w ¨„t2v™wf
ˆ }p¢n8sf2ufv^w { v^ufv0w › v+‡^ˆÂ¢‡+nyzy´Š‡^ufv+n8s”v^qÁsfx;¦v0nww]t2x}u³s
nw › x}w]wfˆzGyzvnpGq;w]s”ˆyzyºq2ˆzw]‡+u]ˆz‰4ˆzp¢n8sfv ¦vs { v^v+p’‰:v^‰Ž¦v^ufwn8p2qžp2x}p ‰:v^‰Ž¦v^ufw¡x | n › ufxsfv+ˆp
| n‰4ˆzy´ ›&wއ+np¶¦v¼wfv+v^p | ufx}‰ÿs”tGv;n£§}v+uf5n }vžnpGq¶w]sšn8p2q¢nu]q¶q2v^§Eˆªn$s”ˆzxpSx | s”tGv†ufv^yªn8sfˆ§}v
{ ˆzqFs”t2w°x | sft2v ¼ê¼ê ‰:xsfˆ | w  ‰:xw]s ¼ê¼ê ‰4xs”ˆ | { ˆqGs”t2wVnu]v { ˆs”t2ˆp˜n | n‡^sfx}u x | s { x
x | s”t2v•t(2‰:np ‡št2x}wfv^p˜w]#ˆ }p2n8s”2u]v { ˆzqGsft2w „t2v :ê:ê ‰:xsfˆ | wn8ufv‡+v^p.s”v+u]v+qrn$s x}up2v£n8u
s”tG·v Ð(p2x { p’‰:x8s”ˆ | wXnw ˆzp2qGˆz‡^sfv+q;.´†sft2v§n8yz2vx | u]v+yªn$s”ˆ§vwft2ˆ | Ws }ˆ§}v+pžˆpžsft2vsšn82yzv ¹„t2v
‰:n Ï]x}ufˆsj´Žx |½¼ê¼ê ‰:x8s”ˆ | wn8ufv°wft2ˆ | s”v+q4p2x¨‰:x}u]vs”t¢np Ø ð.<ëx | s”t2v { ˆzqFs”t4x | sft2³v Ð(p2x { p
‰4xs”ˆ |
%Ët2vs”t2v^us”ufnˆzpGv+q–x}p¨t2ny | s”t2vP‰:v^‰Žºv+ufwx | nVŹu]x}wfˆs”v | n‰:ˆy´Vx}ux}pŽn8yzy}x | s”t2v^‰ 
¼ê¼ê 2wf¢n8yzy´4¢p2qGwVn™‰4xs”ˆ | { t2ˆz‡štž‰:n8s”‡štGv+ws”t2¨v Ð(p2x { p˜‰:xsfˆ | Ô¾ˆ ƒv  { ˆsf«t ÒW•¬ËxN§}v^u
ð â }!} Ö-x}p4x}p2v x | s”t2v¢u]w]s | v { › nwfw]v+w P„tGˆzwˆzwv^§Eˆq2v+p.s | ufx}‰ës”t2v°ufv^wf2ys”wx | s”t2v ¢ufw³ss”v+w³s
wftGx { p¤ˆp Ç-
ˆ }2ufv– xw‡™npGqŠs”t2v¥t2ˆzw³s”_x }ufn‰ ˆz.p Ç-#ˆ }Gufv¨ ^wˆÔ,n Ö y%Ët2v+p¸sfu”nˆp2v+qŠx}p¸t¢ny |
s”tGv ÐEpGx { pÁwfv^—(2v+p2‡^v+w¨ˆzp¤n | n‰4ˆzy´žGwfˆzp žn$
p -G-1092žw]v+—(2v^p2‡+v4‰:xEq2v^y Ì:ê:ê| nˆyzwVsfx
¢p2q¸sft2²v Ð(p2x { p¤‰4xs”ˆ | x}p2y´;s”t2u]v+v¥sfˆz‰4v+w°x}Gs&x | 'Ø ¼Ç-#ˆ }Gufv• xw˜Ô  Ö wft2x { wsft¢n8s { tGv+p
nyyLsft2v&‰4v+‰¥¦v^ufwPx | s”tGv | n‰4ˆzy´™nu]v › u]v+wfv^p.s  sft2³v Ð(p2x { p;‰4xs”ˆ | ˆp†nyyºGGs | x}GuPsfu”nˆp2ˆzp wfvs”w¨ˆzw•q2ˆzw]‡+xN§}v^ufv^q –› ‡+x}‰ › nu]ˆzwfxpx | s”t2v0s { xŠt2ˆw]s”5x }u”n‰4wufv§}v+nyzw•s”t¢n$s¨sft2v:p(2‰¥¦v^u
x | sfˆz‰4v+wVsft¢n8sVs”t2¯v Ð(p2x { p¤‰4xs”ˆ | ˆzw | x}2p2qrx}p˜s”t2v¥Â2ufw]s › nwfwˆw&ˆwV§Eˆzu³s”¢nyy´ž2p2Pn Ìv^‡^sfv+q
.´žufv^‰:xN§Eˆzp 0t¢n8y | x | sft2v•wfv^—EGv+p2‡^v+w | u]x}‰Ín4Źufx}w]ˆs”v | n‰4ˆzy´ „t2v¨‡^x}ufu]v+yzn8s”ˆx}p;¦vs { v^v+p
s”tGv–p(2‰¥¦v^ux | w]v+—(2v^p2‡+v^w&ˆzp†sft2v•q¢n8s”nwfvs°np2q ÒW•¬Ëˆwq2ˆzw]‡+2w]wfv+q ­ v+‡s”ˆx}p; \M 6 ¹„t2v
‰4xs”ˆ | { ˆqGs”t2w–‡št2x}w]v+p¶.´ ¼ê¼ê { ˆsftsft2v¼w]‰¼nyyzv^us”u”n8ˆzp2ˆp žwfv^sfw¥q2x˜p2xs¨‡+x}u]ufv^w › x}p2q
nw‡^yzx}w]v+y´˜s”x;s”tGv { ˆqGs”tGwx | sft2v4Źufx}w]ˆs”v™w]#ˆ }p2n8s”2u]v+w•nw•w]v+v+pÁ.´¸s”tGv4tG#ˆ }t2v^uw]s”np2q¢nu]q
q2v§Fˆzn8s”ˆx}p;x | ufv+yzn8s”ˆ§}v { ˆqGs”t’ˆzpžyˆzp2v ~ nw ‡^x}‰ › nufv^q { ˆs”tžyzˆp2Wv ]Žx | „-nGyzv xw‡
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Qî
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5
1
2
3
30
15
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3
4
5
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6
ð ñ ò ó ô õ
0
ö
3
16
13
10
15
10
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6
ò ÷
20
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÷
16
5
18
5
4
ð ñ ò ó ô õ
0
20
ù
31
25
number of motifs (total 75)
30
29
25
number of motifs (total 75)
35
35
?
1
pass where motif found
2
3
4
5
?
pass where motif found
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