Mathematically Rigorous Results In Sequence Matching.

我们启发式地推导了两个新的尺度参数方程。该方程可以高效、准确地进行估算。此外，我们还提出了基于路径反转恒等式和泊松聚类启发式的Gumbel前因子k的几个新公式。这个公式也提供了非常精确的结果。我们还探讨了统计数据的边缘效应。边缘效应是相关的，因为实序列有有限的长度，在序列匹配概率的渐近展开中产生一个校正项。这种边缘效应在有间隙匹配的统计数据中可能比在没有间隙匹配的统计数据中更重要，因为有间隙匹配往往更长，更容易耗尽匹配的序列。NCBI CoreTools现在的代码可以在不到1秒的时间内计算出所有修改后的Gumbel参数的实际精度。

We heuristically derived two new equations for the scale parameter . This equation can estimate nefficiently with high accuracy. In addition, we have proposed several new formulas for Gumbel pre-factor k based on a path reversal identity and the Poisson clumping heuristic. This formula also provides very accurate results. We also have explored edge effects on the statistics. Edge effects are relevant, because real sequences have limited lengths, generating a correction term in an asymptotic expansion of the probability of sequence matching. This edge effect is likely to be more important in the statistics of matching with gaps than it was in the statistics of matching without gaps, because gapped matches tend to be longer, exhausting the sequences being matched more easily. The NCBI CoreTools now has code that calculates all the modified Gumbel parameters to practical accuracies in less than 1 sec.