PMC:1647278 / 31183-35107
Annnotations
{"target":"https://pubannotation.org/docs/sourcedb/PMC/sourceid/1647278","sourcedb":"PMC","sourceid":"1647278","source_url":"https://www.ncbi.nlm.nih.gov/pmc/1647278","text":"Under-represented pattern\nIn the case of an under-represented pattern we have\nS N = log 10 F − ( N ) with F − ( N ) ≜ ℙ μ N , π N ( N ≤ N obs ) . ( 25 ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaafaqaaeqadaaabaGaem4uam1aaSbaaSqaaGqabiab=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@6905@\nUsing a binomial approximation we get\nF − ( N ) ≃ ℙ ( ℬ ( ℓ h , P ( N ) ) ≤ N o b s ) = β − ( P ( N ) , N o b s + 1 , ℓ h − N o b s ) β ( N o b s + 1 , ℓ h − N o b s ) ( 26 ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBamrtHrhAL1wy0L2yHvtyaeHbnfgDOvwBHrxAJfwnaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaWaaeGaeaaakeaacqWGgbGrdaahaaWcbeqaaiabgkHiTaaakiabcIcaOGqabiab=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@8F8B@\nand, by the same method than in the over-represented case we finally have\nσ ≃ Q − t G × C × G ( 27 ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaaiiGacqWFdpWCcqWIdjYocqWGrbqudaahaaWcbeqaaiabgkHiTaaakmaakaaabaGaeeiiaaYaaWbaaSqabeaaieGacqGF0baDaaacbeGccqqFhbWrcqGHxdaTcqqFdbWqcqGHxdaTcqqFhbWraSqabaGccaWLjaGaaCzcamaabmaabaGaeGOmaiJaeG4naCdacaGLOaGaayzkaaaaaa@40AE@\nwhere\nQ − = p N obs + 1 ( 1 − p ) ℓ h − N obs − 1 ln ( 10 ) β − ( p , N obs + 1 , ℓ h − N obs ) ( 28 ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWGrbqudaahaaWcbeqaaiabgkHiTaaakiabg2da9maalaaabaGaemiCaa3aaWbaaSqabeaacqWGobGtdaWgaaadbaGaee4Ba8MaeeOyaiMaee4CamhabeaaliabgUcaRiabigdaXaaakiabcIcaOiabigdaXiabgkHiTiabdchaWjabcMcaPmaaCaaaleqabaGaeS4eHW2aaSbaaWqaaiabdIgaObqabaWccqGHsislcqWGobGtdaWgaaadbaGaee4Ba8MaeeOyaiMaee4CamhabeaaliabgkHiTiabigdaXaaaaOqaaiGbcYgaSjabc6gaUjabcIcaOiabigdaXiabicdaWiabcMcaPGGaciab=j7aInaaCaaaleqabaGaeyOeI0caaOGaeiikaGIaemiCaaNaeiilaWIaemOta40aaSbaaSqaaiabb+gaVjabbkgaIjabbohaZbqabaGccqGHRaWkcqaIXaqmcqGGSaalcqWItecBdaWgaaWcbaGaemiAaGgabeaakiabgkHiTiabd6eaonaaBaaaleaacqqGVbWBcqqGIbGycqqGZbWCaeqaaOGaeiykaKcaaiaaxMaacaWLjaWaaeWaaeaacqaIYaGmcqaI4aaoaiaawIcacaGLPaaaaaa@6C5B@","divisions":[{"label":"title","span":{"begin":0,"end":25}},{"label":"p","span":{"begin":26,"end":77}},{"label":"p","span":{"begin":78,"end":1010}},{"label":"p","span":{"begin":1011,"end":1048}},{"label":"p","span":{"begin":1049,"end":2317}},{"label":"p","span":{"begin":2318,"end":2391}},{"label":"p","span":{"begin":2392,"end":2891}},{"label":"p","span":{"begin":2892,"end":2897}}],"tracks":[]}