By Matthias Bernt, Kun-Mao Chao, Jyun-Wei Kao (auth.), Ben Raphael, Jijun Tang (eds.)
This e-book constitutes the refereed complaints of the twelfth foreign Workshop on Algorithms in Bioinformatics, WABI 2012, held in Ljubljana, Slovenia, in September 2012. WABI 2012 is considered one of six workshops which, besides the ecu Symposium on Algorithms (ESA), represent the ALGO annual assembly and makes a speciality of algorithmic advances in bioinformatics, computational biology, and structures biology with a selected emphasis on discrete algorithms and machine-learning equipment that deal with very important difficulties in molecular biology. The 35 complete papers provided have been rigorously reviewed and chosen from ninety two submissions. The papers comprise algorithms for various organic difficulties together with phylogeny, DNA and RNA sequencing and research, protein constitution, and others.
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Extra resources for Algorithms in Bioinformatics: 12th International Workshop, WABI 2012, Ljubljana, Slovenia, September 10-12, 2012. Proceedings
SingleEdgeCosts is called once for each edge e ∈ E, and the time spent for each call is proportional to the number of edges that are adjacent to the child node of e. Given that the preconditions and the postcondition in SingleEdgeCosts are maintained with each recursive call of this routine, the correctness of the algorithm follows. Theorem 2. Let T be a phylogenetic tree that consists of n nodes of which s are tips, and let r be a natural number with r ≤ s. The standard deviation of the MPD for a sample of exactly r tips of T is equal to: sdMPD (T , r) = c1 · T C 2 (T ) + (c2 − c1 ) where c1 = we · T C(e) − E2 (T , r), MPD T C 2 (u) + (c1 − 2c2 + c3 ) u∈S 4(r−2)(r−3) r(r−1)s(s−1)(s−2)(s−3) , c2 = e∈E 4(r−2) r(r−1)s(s−1)(s−2) , and c3 = 4 r(r−1)s(s−1) .
J. Comp. Biol. 9(2), 225–242 (2002) 4. : Fast recovery of evolutionary trees with thousands of nodes. J. Comp. Biol. 9(2), 277–297 (2002) 5. : Phylogenies without Branch Bounds: Contracting the Short, Pruning the Deep. In: Batzoglou, S. ) RECOMB 2009. LNCS, vol. 5541, pp. 451–465. Springer, Heidelberg (2009) 6. org/abs/math/0509575 Fast Phylogenetic Tree Reconstruction Using Locality-Sensitive Hashing 29 7. : Fast Neighbor Joining. , Yung, M. ) ICALP 2005. LNCS, vol. 3580, pp. 1263–1274. Springer, Heidelberg (2005) 8.
For every e ∈ desc(root(T )) 4. do SingleEdgeCosts(e, we (s − s(e)), we · s(e), tc). 5. return tc[·] È Algorithm. SingleEdgeCosts(e, SumAnc1 , SumAnc2 , tc) Input: A tree edge e, real numbers SumAnc1 and SumAnc2 , and (a reference to) the array tc that stores the computed T C(·) values of the tree edges Output: A real number which is equal to we · s(e) + l∈Oﬀ(e) wl · s(l). 1. Precondition 1: SumAnc1 = l∈Anc(e) wl (s − s(l)) 2. Precondition 2: SumAnc2 = l∈Anc(e) wl · s(l) ÈÈ È Eﬃcient Computation of Popular Phylogenetic Tree Measures 37 SumOﬀ ← 0 u ← child node of e for every l ∈ desc(u) do SumOﬀ ← SumOﬀ + SingleEdgeCost(l, SumAnc1 +wl (s−s(l)), SumAnc2 +wl ·s(l), tc) 7.
Algorithms in Bioinformatics: 12th International Workshop, WABI 2012, Ljubljana, Slovenia, September 10-12, 2012. Proceedings by Matthias Bernt, Kun-Mao Chao, Jyun-Wei Kao (auth.), Ben Raphael, Jijun Tang (eds.)