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Table 5 Fit parameters for the HMM

From: Accurate statistics for local sequence alignment with position-dependent scoring by rare-event sampling

  

HMM n = 0

HMM n = 1

L Q

L S

λ

10 4 λ 2

10 3 K

λ

10 4 λ 2

10 3 K

348

150

0.2890 ± 0.85%

 

49.4722 ± 7.27%

0.2310 ± 9.32%

 

21.4600 ± 66.56%

 

200

0.2894 ± 2.84%

 

50.0796 ± 24.47%

0.2274 ± 1.74%

 

20.1017 ± 13.25%

 

300

0.2895 ± 2.69%

 

53.3472 ± 24.00%

0.2240 ± 4.86%

 

17.8934 ± 37.22%

 

348

0.2988 ± 3.24%

 

72.2356 ± 30.15%

0.2234 ± 2.39%

 

16.8704 ± 18.79%

 

360

0.2895 ± 1.79%

 

51.9056 ± 16.04%

0.2220 ± 2.14%

 

16.3757 ±16.52%

 

400

0.2859 ± 3.49%

 

48.4496 ± 31.10%

0.2232 ± 2.40%

 

17.5141 ± 18.94%

 

500

0.2912 ± 6.63%

 

54.0687 ± 61.22%

0.2182 ± 2.39%

 

14.7371 ± 19.10%

 

600

0.2901 ± 3.38%

 

51.9412 ± 31.74%

0.2180 ± 2.59%

 

14.2439 ± 20.86%

  

HMM n = 2

HMM n = 3

L Q

L S

λ

104 λ2

K

λ

104 λ2

K

348

150

0.1968 ± 0.70%

2.9247 ± 1.37%

12.0400 ± 6.48%

0.1767 ± 0.44%

2.6797 ± 1.01%

7.4435 ± 3.72%

 

200

0.1947 ± 2.12%

 

9.8704 ± 14.29%

0.1795 ± 0.46%

2.3586 ± 0.92%

8.5733 ± 3.87%

 

300

0.1937 ± 3.60%

 

9.9597 ± 25.32%

0.1863 ± 0.41%

2.0008 ± 0.94%

11.7859 ± 5.63%

 

348

0.1888 ± 3.19%

 

8.1338 ± 22.42%

0.1876 ± 0.32%

1.9328 ± 0.89%

12.1223 ± 3.83%

 

360

0.1926 ± 3.17%

 

9.7957 ± 22.82%

0.1853 ± 0.27%

1.9530 ± 0.65%

10.8640 ± 2.65%

 

400

0.1934 ± 1.05%

 

9.9321 ± 8.22%

0.1757 ± 1.64%

 

7.1756 ± 11.58%

 

500

0.1919 ± 1.61%

 

9.3630 ± 12.32%

0.1783 ± 0.98%

 

7.7945 ± 7.18%

 

600

0.1912 ± 1.70%

 

9.3303 ± 13.25%

0.1768 ± 1.01%

 

7.4165 ± 8.19%

  

HMM n = 4

HMM n = 5

L Q

L S

λ

104 λ2

103K

λ

104 λ2

103K

348

150

0.1732 ± 0.47%

2.2119 ± 1.14%

7.4991 ± 6.08%

0.1710 ± 0.38%

2.0698 ± 0.92%

8.1950 ± 3.70%

 

200

0.1686 ± 0.28%

2.1187 ± 0.72%

6.4162 ± 3.14%

0.1657 ± 0.39%

1.8231 ± 1.14%

6.9148 ± 3.82%

 

300

0.1682 ± 0.36%

1.9635 ± 0.79%

6.5436 ± 4.22%

0.1599 ± 0.37%

1.7836 ± 0.79%

5.4451 ± 3.85%

 

348

0.1685 ± 0.35%

1.9408 ± 0.74%

7.3851 ± 3.34%

0.1580 ± 0.28%

1.7930 ± 0.68%

5.3049 ± 2.61%

 

360

0.1678 ± 0.42%

1.9421 ± 0.92%

6.5775 ± 4.07%

0.1605 ± 0.23%

1.7481 ± 0.50%

5.7512 ± 2.89%

 

400

0.1662 ± 0.18%

1.9782 ± 0.40%

6.4164 ± 2.32%

0.1587 ± 0.28%

1.7828 ± 0.73%

5.4513 ± 2.57%

 

500

0.1693 ± 0.24%

1.9047 ± 0.51%

7.0735 ± 2.11%

0.1587 ± 0.16%

1.7957 ± 0.40%

5.4770 ± 2.31%

 

600

0.1693 ± 0.17%

1.8994 ± 0.39%

7.1112 ± 2.06%

0.1575 ± 0.29%

1.8330 ± 0.58%

5.2125 ± 2.68%

  

HMM n = 6

HMM n = 7

L Q

L S

λ

104 λ2

103K

 

104 λ2

103K

348

150

0.1663 ± 0.49%

2.1403 ± 1.04%

7.9392 ± 5.83%

0.1646 ± 0.30%

2.1396 ± 0.65%

8.7088 ± 4.21%

 

200

0.1614 ± 0.25%

1.7767 ± 0.65%

6.7568 ± 2.30%

0.1574 ± 0.41%

1.7687 ± 1.17%

6.5219 ± 3.81%

 

300

0.1551 ± 0.28%

1.5986 ± 0.80%

5.2551 ± 3.18%

0.1514 ± 0.26%

1.4638 ± 0.62%

5.0238 ± 4.34%

 

348

0.1531 ± 0.20%

1.5993 ± 0.55%

4.9132 ± 2.71%

0.1482 ± 0.33%

1.4755 ± 0.77%

4.4535 ± 4.13%

 

360

0.1536 ± 0.34%

1.6036 ± 1.02%

4.9160 ± 3.41%

0.1490 ± 0.39%

1.4479 ± 0.93%

4.6858 ± 3.28%

 

400

0.1537 ± 0.27%

1.5713 ± 0.62%

4.9524 ± 3.05%

0.1494 ± 0.24%

1.4328 ± 0.70%

4.6867 ± 2.08%

 

500

0.1519 ± 0.23%

1.6229 ± 0.67%

4.6812 ± 2.14%

0.1472 ± 0.29%

1.4706 ± 0.63%

4.2881 ± 2.50%

 

600

0.1489 ± 0.15%

1.7148 ± 0.33%

4.2283 ± 2.16%

0.1460 ± 0.18%

1.5193 ± 0.49%

4.2679 ± 1.74%

  

HMM n = 8

HMM n = 9

L Q

L S

λ

104 λ2

103K

λ

104 λ2

103K

348

150

0.1595 ± 0.47%

2.2162 ± 1.01%

7.5355 ± 4.01%

0.1603 ± 0.23%

2.1517 ± 0.48%

8.0273 ± 2.17%

 

200

0.1534 ± 0.55%

1.8019 ± 1.46%

5.9224 ± 5.25%

0.1508 ± 0.14%

1.7854 ± 0.28%

6.3535 ± 1.89%

 

300

0.1473 ± 0.47%

1.3916 ± 1.24%

4.8483 ± 4.01%

0.1413 ± 0.12%

1.4118 ± 0.35%

4.2141 ± 1.43%

 

348

0.1458 ± 0.32%

1.3409 ± 0.85%

4.6141 ± 3.69%

0.1398 ± 0.10%

1.3281 ± 0.33%

3.9661 ± 1.44%

 

360

0.1469 ± 0.34%

1.2868 ± 0.90%

4.9271 ± 2.73%

0.1400 ± 0.16%

1.2888 ± 0.43%

4.0126 ± 1.79%

 

400

0.1440 ± 0.34%

1.3591 ± 1.05%

4.0064 ± 3.48%

0.1382 ± 0.25%

1.2954 ± 0.67%

3.7257 ± 2.14%

 

500

0.1433 ± 0.29%

1.3382 ± 0.85%

3.9952 ± 2.70%

0.1352 ± 0.14%

1.3472 ± 0.42%

3.1780 ± 1.68%

 

600

0.1416 ± 0.33%

1.3760 ± 0.94%

3.7782 ± 3.14%

0.1359 ± 0.13%

1.3399 ± 0.38%

3.3536 ± 1.49%

  

HMM n = 10

HMM n = 11

L Q

L S

λ

104 λ2

103K

λ

104 λ2

103K

348

150

0.1552 ± 0.14%

2.2225 ± 0.30%

6.7936 ± 2.08%

0.1455 ± 0.14%

2.3813 ± 0.15%

4.9660 ± 3.82%

 

200

0.1459 ± 0.22%

1.8336 ± 0.37%

5.7585 ± 3.30%

0.1417 ± 0.17%

1.8428 ± 0.35%

5.1264 ± 2.07%

 

300

0.1370 ± 0.22%

1.4024 ± 0.56%

3.8087 ± 1.79%

0.1324 ± 0.27%

1.3842 ± 0.68%

3.2129 ± 2.79%

 

348

0.1353 ± 0.15%

1.2962 ± 0.38%

3.5507 ± 1.68%

0.1316 ± 0.22%

1.2518 ± 0.69%

3.1546 ± 1.94%

 

360

0.1343 ± 0.13%

1.2830 ± 0.36%

3.4674 ± 1.39%

0.1297 ± 0.25%

1.2737 ± 0.52%

2.9445 ± 2.81%

 

400

0.1334 ± 0.16%

1.2602 ± 0.38%

3.2164 ± 1.71%

0.1302 ± 0.20%

1.2160 ± 0.56%

2.9704 ± 1.59%

 

500

0.1307 ± 0.16%

1.3013 ± 0.46%

2.8331 ± 1.22%

0.1280 ± 0.30%

1.2426 ± 0.86%

2.7433 ± 2.73%

 

600

0.1305 ± 0.23%

1.3097 ± 0.56%

2.8239 ± 1.82%

0.1257 ± 0.22%

1.2908 ± 0.55%

2.4921 ± 1.79%

  1. The table shows the fit parameters of the score distribution Prob(S = s| # of helices = n) for 1 ≤ n ≤ 11 for L Q = 348 and different subject lengths. For entries, where λ2 is left out, a suitable fit (with a small reduced χ2 value) to the modified Gumbel distribution Eq. (15) was not possible and only the Gumbel parameters of the high probability region are shown.