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**1 - 3**of**3**### Table 11. Avoidance of generalized patterns in permutations

"... In PAGE 19: ... Relations to several well studied combinatorial structures, such as set partitions (see [105]), Dyck paths (see [163]), Motzkin paths (see [66]) and involutions (see [200]), were shown there. The main results from that paper are given in Table11 , where Bn is the n-th Bell number, Cn is the n-th Catalan number, and Bstar n is the n-th Bessel number. For some other results on generalized permutation patterns see [63, 64, 113, 114, 115, 117, 118, 142, 146, 147].... In PAGE 19: ...Table 11. Avoidance of generalized patterns in permutations As in the paper by Simion and Schmidt [199], dealing with the classical patterns, Claes- son [62], Claesson and Mansour [63] considered a number of cases when permutations have to avoid two or more generalized patterns simultaneously (see Table11 ). In [113], Kitaev gave either an explicit formula or a recursive formula for almost all cases of simul- taneous avoidance of more than two generalized patterns of length three with no dashes, and listed what was known about double restrictions (the remaining cases were described... ..."

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### Table 1. Examples of symmetry classes

"... In PAGE 19: ... Relations to several well studied combinatorial structures, such as set partitions (see [105]), Dyck paths (see [163]), Motzkin paths (see [66]) and involutions (see [200]), were shown there. The main results from that paper are given in Table1 1, where Bn is the n-th Bell number, Cn is the n-th Catalan number, and Bstar n is the n-th Bessel number. For some other results on generalized permutation patterns see [63, 64, 113, 114, 115, 117, 118, 142, 146, 147].... In PAGE 19: ... patterns P |Sn(P )| description 1-23 Bn partitions of [n] 1-32 Bn partitions of [n] 2-13 Cn Dyck paths of length 2n 1-23, 12-3 Bstar n non-overlapping partitions of [n] 1-23, 1-32 In involutions in Sn 1-23, 13-2 Mn Motzkin paths of length n Table 11. Avoidance of generalized patterns in permutations As in the paper by Simion and Schmidt [199], dealing with the classical patterns, Claes- son [62], Claesson and Mansour [63] considered a number of cases when permutations have to avoid two or more generalized patterns simultaneously (see Table1 1). In [113], Kitaev gave either an explicit formula or a recursive formula for almost all cases of simul- taneous avoidance of more than two generalized patterns of length three with no dashes, and listed what was known about double restrictions (the remaining cases were described... ..."

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### Table 1. Output summary of the novoSNP, PolyPhred, and PolyBayes SNP analysis on the SCN1A mutation and MAPT SNP data sets analyzed under different quality cutoff values

"... In PAGE 4: ...Claes et al. 2003; Rademakers et al. 2004). All three programs provide a quality score for each detected variation. Depending on the quality score cutoff used, several SNPs are detected for each program ( Table1 ). At the lowest- quality cutoff score, novoSNP detected all 38 variations in the SCN1A data set that were previously observed by visual inspec- tion, including five INDELs, and missed only 10 out of 452 known SNPs (2.... In PAGE 4: ... At the lowest- quality cutoff score, novoSNP detected all 38 variations in the SCN1A data set that were previously observed by visual inspec- tion, including five INDELs, and missed only 10 out of 452 known SNPs (2.2%) and five out of 36 INDELs in the MAPT data set ( Table1 ). PolyPhred found all but three of the SNPs in the SCN1A data set at the lowest cutoff, but missed all five INDELs (Table 1A) while listing more false-positive INDELs (23) than novoSNP (nine).... In PAGE 4: ...2%) and five out of 36 INDELs in the MAPT data set (Table 1). PolyPhred found all but three of the SNPs in the SCN1A data set at the lowest cutoff, but missed all five INDELs ( Table1 A) while listing more false-positive INDELs (23) than novoSNP (nine). PolyPhred analysis of the MAPT data set showed that a large number of SNPs (172, or 38.... In PAGE 4: ... PolyPhred analysis of the MAPT data set showed that a large number of SNPs (172, or 38.1%) were not detected ( Table1 B) and also that only two of 36 INDELs were correctly identified, while the number of false-positive INDELs (101) was again higher compared to novoSNP (63). PolyBayes was included in this comparative analysis as it is often used for SNP discovery.... In PAGE 4: ... Because of these limitations, PolyBayes identified only a small percentage of the SNPs in the SCN1A data set (54.5%) and the MAPT data set (31%) ( Table1 ). An overall comparison of the true SNPs and false positives (FP) detected by the three programs is represented as a Venn diagram in Figure 2.... In PAGE 4: ... Somewhat surprisingly, most of the false positives were not shared between the different programs but were program-specific. The use of low-quality cutoff values resulted in a large num- ber of false positives for all three programs ( Table1 ). Using higher-quality cutoffs, at the expense of detecting less true varia- tions, diminished the number of false positives.... In PAGE 5: ...Table1 ). Even at a quality cutoff of 15, novoSNP detected con- siderably more SNPs compared to the lowest-quality cutoff for PolyPhred, with a lower false-positive rate than PolyPhred at the highest possible quality (Table 1).... In PAGE 5: ... Furthermore, novoSNP is not only able to efficiently detect INDELs but also provides the user with the cor- rect sequence of the INDEL. A high false-positive rate was observed for all three programs used in this study ( Table1 ; Fig. 2).... In PAGE 5: ... Another way is by relying on the quality scores assigned to the SNP. Indeed, the results presented here showed that the quality score given by novoSNP is a reliable measure of the cor- rectness of the SNP ( Table1 ). Using a relatively low cutoff score of 10, 97.... ..."

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