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4 O( ) O( )

5 O( ) O( )

6 O( ) O( )

7 O( ) O( )

8 O( ) O( )

9 O( ) O( )

10 C A G C A C G A C A C U A G C A G U C A G U G U C A G A C U G C A I A C A G C A C G A C A C U A G C A G U C A G U G U C A G A C U G C A I A C A G C A C G A C A C U A G C A G U C A G U G U C A G A C U G C A I A GCACGACACUAGCAGUCAGUGUCAGACUGCAIACAGCACGACACUAGCAGUCAGUGUCAGACUGCAIACAGCACGACACUAGCAGUCAGUGUCA (((((...(((((...(((((...(((((...)))))...)))))...(((((...(((((...)))))...)))))...))))).

11 i+1 j 1 i i+1 j 1 j i j i i+1 j i i+1 j i j 1 j i j 1 j i k k+1 j i k k+1 j

12 γ(, + ) = = =. γ(, ) = max γ( +, ) + δ(, ); γ( +, ); γ(, ); max <<( ) [γ(, ) + γ( +, )]. {, : δ(, ) = { :, :, :, : } { :, : };,.

13 G G G A A C C U A G G G A A A U C C

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27 parms wc += gu; descr h5(minlen=6,maxlen=7) ss(len=2) h5(minlen=3,maxlen=4) ss(minlen=4,maxlen=11) h3 ss(len=1) h5(minlen=4,maxlen=5) ss(len=7) h3 ss(minlen=4,maxlen=21) h5(minlen=4,maxlen=5) ss(len=7) h3 h3 ss(len=4)

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38 O( )

39 O( )

40 O( ) O()

41 O( ) O()

42 O( ) O()

43

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47 unrestricted context sensitive context free regular

48 unrestricted context sensitive context free regular

49 α β

50 α β

51 α β

52 α β

53 ϵ ϵ L() { }

54 ϵ ϵ L() { }

55 ϵ ϵ L() { }

56 ϵ ϵ L() { }

57 S0 S1 S2 u S3 S4 S5 S6 a a S7 S8 S9 u S10 g S11 S12 s13 S14 c a S15 S16 g S17 S18 a g

58 S0 S1 S2 u S3 S4 S5 S6 a a S7 S8 S9 u S10 g S11 S12 s13 S14 c a S15 S16 g S17 S18 a g

59 S0 S1 S2 u S3 S4 S5 S6 a a S7 S8 S9 u S10 g S11 S12 s13 S14 c a S15 S16 g S17 S18 a g

60 S0 S1 S2 u S3 S4 S5 S6 a a S7 S8 S9 u S10 g S11 S12 s13 S14 c a S15 S16 g S17 S18 a g

61 ϵ ϵ

62 ϵ ϵ

63 ϵ ϵ

64

65

66

67

68 γ

69 γ

70 γ αβ αγβ

71 γ αβ αγβ

72 γ αβ αγβ α β

73 n-{p}-[st]-{p}

74 n-{p}-[st]-{p}

75 n-{p}-[st]-{p}......

76 n-{p}-[st]-{p}......

77 n-{p}-[st]-{p}......

78 G A A G A G G A N-N N-N N-N N-N N-N N-N

79 G A A G A G G A N-N N-N N-N N-N N-N N-N

80 G A A G A G G A N-N N-N N-N N-N N-N N-N

81

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92 G A A G G-C A-U U-A

93 G A A G G-C A-U U-A

94 G A A G G-C A-U U-A

95 G A A G G-C A-U U-A

96 G A A G G-C A-U U-A

97 G A A G G-C A-U U-A

98 G A A G G-C A-U U-A

99 G A A G G-C A-U U-A

100 S0 S1 S2 u S3 S4 S5 S6 a a S7 S8 S9 S10 u g S11 S12 c

101 S0 S1 S2 u S3 S4 S5 S6 a a S7 S8 S9 S10 u g S11 S12 s13 S14 c a S15 S16 g S17 S18 a g

102 α α

103 α α

104 α α

105 α α (, ) = { [, + ]}

106 α α (, ) = { [, + ]} =

107 α α (, ) = { [, + ]} =

108 α α (, ) = { [, + ]} = (, ) =

109 α α (, ) = { [, + ]} = (, ) = { [, ] }

110 α α (, ) = { [, + ]} = > (, ) = { [, ] }

111 α α (, ) = { [, + ]} = > (, ) = { [, ] }

112 α α (, ) = { [, + ]} = > (, ) = { [, ] } (, ) = {, [, + ], [ +, + ], < }

113 (, ) = { [, + ]} =,,, =,,, = =,, =,,

114 (, ) = { [, + ]} =,,, =,,, = =,, =,,

115 (, ) = { [, + ]} =,,, =,,, = =,, =,,

116 (, ) = { [, + ]} =,,, =,,, = =,, =,,

117 (, ) = { [, + ]} =,,, =,,, = =,, =,,

118 (, ) = { [, + ]} =,,, =,,, = =,, =,,

119 (, ) = { [, + ]} =,,, =,,, = =,, =,,

120 (, ) = { [, + ]} =,,, =,,, = =,, =,,

121 (, ) = { [, + ]} =,,, =,,, = =,, =,,

122 (, ) = { [, + ]} =,,, =,,, = =,, =,,

123 (, ) = { [, + ]} =,,, =,,, = =,, =,,

124 (, ) = { [, + ]} =,,, =,,, = =,, =,,

125 (, ) = { [, + ]} =,,, =,,, = =,, =,,

126 (, ) = { [, + ]} =,,, =,,, = =,, =,,

127 (, ) = { [, + ]} =,,, =,,, = =,, =,,

128 (, ) = { [, + ]} =,,, =,,, = =,, =,,

129 (, ) = { [, + ]} =,,, =,,, = =,, =,,

130 (, ) = { [, + ]} =,,, =,,, = =,, =,,

131 (, ) = { [, + ]} =,,, =,,, = =,, =,,

132 (, ) = { [, + ]} =,,, =,,, = =,, =,,

133 b a a b a A B S

134 b a a b a A B S

135 b a a b a A B S

136 b a a b a A B S

137 b a a b a A B S

138 b a a b a A B S B A C C

139 b a a b a A B S B A C C

140 b a a b a A B A A C B C B S

141 { Initialization } for i = 1 to n do V(i,1) = { is a production and s[i] = } { Iteration } for l = 2 to n do for i = 1 to n - l + 1 do V(i,l) = for k = 1 to l - 1 do V(i,l) = V(i,l) {, B V(i,k) and C V(i+k,l-k)} O( ) O( )

142 { Initialization } for i = 1 to n do V(i,1) = { is a production and s[i] = } { Iteration } for l = 2 to n do for i = 1 to n - l + 1 do V(i,l) = for k = 1 to l - 1 do V(i,l) = V(i,l) {, B V(i,k) and C V(i+k,l-k)} O( ) O( )

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148 (.. )

149 (.. )

150 (.. )

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154 (.) : (.) : (.) : (.) : (.) : (.) :

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158 =,..,,, (, ) (),,

159 =,..,,, (, ) (),,

160 =,..,,, (, ) (),,

161 =,..,,, (, ) (),,

162 =,..,,, (, ) (),,

163 { Initialization } for = to, = to γ(,, ) = ( ) { Iteration } for = to, = to +, = to γ(,, ) = max, max =,..., {γ(,, )γ( +,, ) (, )} { Termination } log (, ˆπ θ) = γ(,, ).

164 { Initialization } for i = 1 to n do V(i,1) = { is a production and s[i] = } { Iteration } for l = 2 to n do for i = 1 to n - l + 1 do V(i,l) = for k = 1 to l - 1 do V(i,l) = V(i,l) {, B V(i,k) and C V(i+k,

165 b a a b a A B S B A C C

166 { Initialization } for = to, = to γ(,, ) = ( ) { Iteration } for = to, = to +, = to γ(,, ) = max, max =,..., {γ(,, )+γ(+,, )+log (, )} { Termination } log (, ˆπ θ) = γ(,, ).

167 ( ) ( )

168 { Initialization } for = to, = to α(,, ) = ( ) { Iteration } for = to, = to +, = to α(,, ) = {α(,, )α(+,, )(, )} = = =,..., { Termination } log ( θ) = α(,, ).

169 b a a b a A B S b a a b a A B S B A C C b a a b a A B S B A C C

170

171

172 S1 S2 S3 S4 ( ( ( (.. ) ) ) ) G G A G A U C U C C G G G G A - C C C C U G G G A A C C C A G G G G A U C C C U G G G G A A C C C C ϵ

173 S1 S2 S3 S4 ( ( ( (.. ) ) ) ) G G A G A U C U C C G G G G A - C C C C U G G G A A C C C A G G G G A U C C C U G G G G A A C C C C ϵ

174 # STOCKHOLM 1.0 #=GF AU Koala DA0260 GGGCGAAUAGUGUCAGC.GGGAGCACACCAGACUUGCAUCUGGUAG.GGAGGGUUCGAGUCCCUCUUUGUCCACC #=GR DA0260 SS (((((((..((((...)))).(((((...)))))...(((((...))))))))))))... DA0261 GGGCGAAUAGUGUCAGC.GGGAGCACACCAGACUUGCAUCUGGUAG.GGAGGGUUCGAGUCCCUCUUUGUCCACC #=GR DA0261 SS (((((((..((((...)))).(((((...)))))...(((((...))))))))))))... DA0340 GGGCUCGUAGCUCAGC..GGGAGAGCGCCGCCUUUGCAGGCGGAGGCCGCGGGUUCAAAUCCCGCCGAGUCCA.. #=GR DA0340 SS (((((((..((((...)))).(((((...)))))...(((((...))))))))))))... DA0380 GGGCCCAUAGCUCAGU..GGUAGAGUGCCUCCUUUGCAGGAGGAUGCCCUGGGUUCGAAUCCCAGUGGGUCCA.. #=GR DA0380 SS (((((((..((((...)))).(((((...)))))...(((((...))))))))))))... DA0420 GGGCCCAUAGCUCAGU..GGUAGAGUGCCUCCUUUGCAGGAGGAUGCCCUGGGUUGGAAUCCCAGUGGGUCCA.. #=GR DA0420 SS (((((((..((((...)))).(((((...)))))...(((((...))))))))))))... DA0580 GGGCCCGUAGCUCAGACUGGGAGAGCGCCGCCCUUGCAGGCGGAGGCCCCGGGUUCAAAUCCCGGUGGGUCCA.. #=GR DA0580 SS (((((((..((((...)))).(((((...)))))...(((((...))))))))))))... DA0620 GGGCCCGUAGCUCAGACUGGGAGAGCGCCGCCCUUGCAGGCGGAGGCCCCGGGUUCAAAUCCCGGUGGGUCCA.. #=GR DA0620 SS (((((((..((((...)))).(((((...)))))...(((((...))))))))))))...

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179 # STOCKHOLM 1.0 #=GS Holley DE trna-ala that Holley sequenced from Yeast genome Holley GGGCGTGTGGCGTAGTCGGTAGCGCGCTCCCTTAGCATGGGAGAGGtCTCCGGTTCGATTCCGGACTCGTCCA #=GR Holley SS (((((.(..((((...)))).(((((...)))))...(((((...)))))).))))). //

180 O( )

181 O( )

182 O( )

183 O( )

184

185 S0 S1 S2 u S3 S4 S5 S6 a a... S8 u

186 S0 # STOCKHOLM 1.0 S1 S2 #=GC SS_cons <<<<..>>>> seq1 GGAGAUCUCC seq2 GGGGAUCCCC seq3 UGGGAACCCA seq4 GGGGAUCCCU seq5 GGGGAACCCC // u S3 S4 S5 S6 a... a S8 u

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SnoPatrol: How many snorna genes are there? Supplementary

SnoPatrol: How many snorna genes are there? Supplementary SnoPatrol: How many snorna genes are there? Supplementary materials. Paul P. Gardner 1, Alex G. Bateman 1 and Anthony M. Poole 2,3 1 Wellcome Trust Sanger Institute, Wellcome Trust Genome Campus, Hinxton,

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