Testing our statistical models

Comparing between the average of 50 random sequences, and the result of our formula (formula a - for computing the expectation: number of palindrome of length l, to be found in a genome sequence of length N).

We test the formula over 10 different models (each model has different parameters).

 Results summary rand1 rand2 rand3 rand4 rand5 rand6 rand7 rand8 rand9 rand10 n 5000 10000 10000 50000 50000 60000 70000 70000 70000 80000 l 11 12 10 11 8 9 12 15 10 16 G 4 5 10 5 40 15 2 50 50 30 x 2 2 1 1 0 1 0 1 1 3 Formula 3.14 2.25 3.24 2.43 31.26 102.50 0.01 0.15 105.48 9.38 Avg of sim' 3.14 2.46 3.62 3.2 32.96 106.34 0 0.3 106.5 8.96 std 1.86 1.47 2.03 2.16 2.96 12.58 0.00 0.46 6.48 2.57 There is a very good compatibility between the formula result and the average result of the 50 sequences. Here down a detail results on the 50 random sequences,                                      for each of the 10 models sim1 5 2 5 3 38 104 0 0 96 8 sim2 4 2 3 3 32 123 0 1 108 7 sim3 0 2 2 1 29 101 0 0 107 7 sim4 7 0 3 6 35 121 0 0 106 10 sim5 2 0 3 1 34 109 0 1 109 13 sim6 1 1 3 5 31 94 0 0 108 9 sim7 6 3 1 1 30 90 0 0 101 9 sim8 4 7 2 3 30 113 0 0 100 10 sim9 0 2 1 3 28 91 0 1 114 7 sim10 7 0 2 5 35 89 0 1 100 10 sim11 5 4 6 1 32 122 0 0 114 5 sim12 2 2 2 3 36 125 0 0 117 7 sim13 1 3 3 1 30 108 0 0 114 13 sim14 6 2 6 3 35 114 0 0 115 7 sim15 5 2 3 1 31 94 0 1 111 4 sim16 3 3 7 6 33 101 0 1 102 13 sim17 3 2 3 3 36 97 0 1 108 8 sim18 2 3 3 1 31 108 0 0 100 10 sim19 1 4 3 3 33 104 0 1 100 8 sim20 3 2 4 1 36 91 0 0 112 8 sim21 2 3 3 1 30 111 0 0 108 11 sim22 4 6 4 1 35 88 0 1 112 9 sim23 6 2 3 0 31 90 0 0 103 10 sim24 1 4 1 6 35 121 0 0 114 7 sim25 2 3 3 3 31 107 0 0 113 10 sim26 6 2 7 6 31 96 0 0 116 10 sim27 3 6 1 1 35 126 0 0 100 13 sim28 2 5 4 6 35 111 0 0 99 8 sim29 3 1 5 1 30 124 0 0 112 10 sim30 3 4 1 4 30 110 0 0 98 7 sim31 1 4 2 3 31 124 0 1 108 6 sim32 2 3 6 1 42 124 0 0 110 11 sim33 4 3 2 6 35 90 0 1 99 5 sim34 2 2 3 6 32 94 0 0 97 6 sim35 2 2 3 1 38 94 0 1 113 10 sim36 4 1 2 1 37 108 0 0 117 9 sim37 6 2 3 1 36 110 0 1 107 9 sim38 2 1 8 6 32 86 0 0 99 5 sim39 1 2 1 4 28 89 0 0 97 8 sim40 6 2 6 3 31 102 0 0 108 15 sim41 1 1 6 7 37 102 0 1 100 10 sim42 2 2 3 3 36 87 0 0 99 3 sim43 2 2 1 1 33 105 0 0 101 10 sim44 4 2 8 3 35 121 0 0 103 11 sim45 3 2 5 7 32 111 0 0 103 13 sim46 3 2 4 6 32 122 0 1 105 10 sim47 5 1 4 1 32 121 0 0 115 7 sim48 3 1 2 6 29 110 0 0 117 12 sim49 4 2 8 7 31 124 0 0 99 8 sim50 1 4 7 4 31 110 0 0 111 12