Local sequence alignments statistics: deviations from Gumbel statistics in the rare-event tail

<p>Abstract</p> <p>Background</p> <p>The optimal score for ungapped local alignments of infinitely long random sequences is known to follow a Gumbel extreme value distribution. Less is known about the important case, where gaps are allowed. For this case, the distribution is only known empirically in the high-probability region, which is biologically less relevant.</p> <p>Results</p> <p>We provide a method to obtain numerically the biologically relevant rare-event tail of the distribution. The method, which has been outlined in an earlier work, is based on generating the sequences with a parametrized probability distribution, which is biased with respect to the original biological one, in the framework of Metropolis Coupled Markov Chain Monte Carlo. Here, we first present the approach in detail and evaluate the convergence of the algorithm by considering a simple test case. In the earlier work, the method was just applied to one single example case. Therefore, we consider here a large set of parameters:</p> <p>We study the distributions for protein alignment with different substitution matrices (BLOSUM62 and PAM250) and affine gap costs with different parameter values. In the logarithmic phase (large gap costs) it was previously assumed that the Gumbel form still holds, hence the Gumbel distribution is usually used when evaluating p-values in databases. Here we show that for all cases, provided that the sequences are not too long (<it>L </it>> 400), a "modified" Gumbel distribution, i.e. a Gumbel distribution with an additional Gaussian factor is suitable to describe the data. We also provide a "scaling analysis" of the parameters used in the modified Gumbel distribution. Furthermore, via a comparison with BLAST parameters, we show that significance estimations change considerably when using the true distributions as presented here. Finally, we study also the distribution of the sum statistics of the <it>k </it>best alignments.</p> <p>Conclusion</p> <p>Our results show that the statistics of gapped and ungapped local alignments deviates significantly from Gumbel in the rare-event tail. We provide a Gaussian correction to the distribution and an analysis of its scaling behavior for several different scoring parameter sets, which are commonly used to search protein data bases. The case of sum statistics of <it>k </it>best alignments is included.</p

Atmospheric effects on extensive air showers observed with the surface detector of the Pierre Auger observatory

International audienceAtmospheric parameters, such as pressure , temperature and density ∝, affect the development of extensive air showers initiated by energetic cosmic rays. We have studied the impact of atmospheric variations on extensive air showers by means of the surface detector of the Pierre Auger Observatory. The rate of events shows a ∼10% seasonal modulation and ∼2% diurnal one. We find that the observed behaviour is explained by a model including the effects associated with the variations of and . The former affects the longitudinal development of air showers while the latter influences the Molière radius and hence the lateral distribution of the shower particles. The model is validated with full simulations of extensive air showers using atmospheric profiles measured at the site of the Pierre Auger Observatory

Atmospheric effects on extensive air showers observed with the surface detector of the Pierre Auger observatory

International audienceAtmospheric parameters, such as pressure , temperature and density ∝, affect the development of extensive air showers initiated by energetic cosmic rays. We have studied the impact of atmospheric variations on extensive air showers by means of the surface detector of the Pierre Auger Observatory. The rate of events shows a ∼10% seasonal modulation and ∼2% diurnal one. We find that the observed behaviour is explained by a model including the effects associated with the variations of and . The former affects the longitudinal development of air showers while the latter influences the Molière radius and hence the lateral distribution of the shower particles. The model is validated with full simulations of extensive air showers using atmospheric profiles measured at the site of the Pierre Auger Observatory

Atmospheric effects on extensive air showers observed with the surface detector of the Pierre Auger observatory

International audienceAtmospheric parameters, such as pressure , temperature and density ∝, affect the development of extensive air showers initiated by energetic cosmic rays. We have studied the impact of atmospheric variations on extensive air showers by means of the surface detector of the Pierre Auger Observatory. The rate of events shows a ∼10% seasonal modulation and ∼2% diurnal one. We find that the observed behaviour is explained by a model including the effects associated with the variations of and . The former affects the longitudinal development of air showers while the latter influences the Molière radius and hence the lateral distribution of the shower particles. The model is validated with full simulations of extensive air showers using atmospheric profiles measured at the site of the Pierre Auger Observatory