April 20, 2017

Download Algorithms in Bioinformatics: First International Workshop, by István Miklós, Zoltán Toroczkai (auth.), Olivier Gascuel, PDF

By István Miklós, Zoltán Toroczkai (auth.), Olivier Gascuel, Bernard M. E. Moret (eds.)

This booklet constitutes the refereed lawsuits of the 1st overseas Workshop on Algorithms in Bioinformatics, WABI 2001, held in Aarhus, Denmark, in August 2001.
The 23 revised complete papers provided have been rigorously reviewed and chosen from greater than 50 submissions. one of the matters addressed are detailed and approximate algorithms for genomics, series research, gene and sign popularity, alignment, molecular evolution, constitution selection or prediction, gene expression and gene networks, proteomics, practical genomics, and drug layout; methodological issues from algorithmics; high-performance ways to challenging computational difficulties in bioinformatics.

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Extra info for Algorithms in Bioinformatics: First International Workshop, WABI 2001 Århus Denmark, August 28–31, 2001 Proceedings

Example text

QED 3 Model of Random Maps Our model of random maps is that cut sites are randomly and uniformly distributed, so that the distance between cut sites is a random variable X with an exponential distribution and probability density f (x) = L1 e−x/L , where L is the average distance between cut sites. Here we assume that all cut sites are indistinguishable from each other. First we consider the case with no misaligned cuts, so that the only errors in the proposed overlap region are sizing errors. Thus our alignment data consists of two maps with fragment sizes x1 , .

3. Repeat this step for i = 1, . , n: Starting from the previous aligned cut site scan to the right on both maps until s i sites have been seen and mark the last one, which could be on either map. Then scan to the right from that cut site on the opposite map only until r i cut sites have been seen and align the last (r i th) one with the previously marked cut site. This defines the ith set of aligned fragments. Realign the maps so that this pair of cut sites coincide. 4. After aligning the last ((n + 1)th) cut site, scan right on both maps until a total of m + 2 cut sites have been seen (including all cut sites seen in previous steps).

To complete our computation of the False Positive Likelihood F P for a particular pair of maps D 1 and D2 , we need to consider the multiple possible choices of overlaps of n or more fragments. Let the two molecules contain N 1 and N2 fragments with N1 ≤ N2 . If n < N1 there will be exactly 4 possible ways of forming an overlap of n fragments. Otherwise, if n = N 1 there will be 2(N2 − N1 + 1) ways of forming an n fragment overlap. Each such overlap has the same independent probability P n . Thus with 4 possible overlaps, the probability F P n of finding at least 1 overlap of n fragments between two random maps as good as the actual alignment is bounded by the probability F Pn ≤ 1 − (1 − Pn )4 ≤ 4Pn .

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