Who is Who in Phylogenetic Networks

Publication no #2190   Type :   Html | Bib | Both

Created: 2012-03-20 21:20:15     Modified: 2012-09-18 17:21:24

2190 An-Chiang Chu, Jesper Jansson, Richard Lemence, Alban Mancheron and Kun-Mao Chao. Asymptotic Limits of a New Type of Maximization Recurrence with an Application to Bioinformatics. In TAMC12, Vol. 7287:177-188 of LNCS, springer, 2012. Keywords: from triplets, galled network, level k phylogenetic network, phylogenetic network. Note: preliminary version.         Toggle abstract "We study the asymptotic behavior of a new type of maximization recurrence, defined as follows. Let k be a positive integer and p k(x) a polynomial of degree k satisfying p k(0) = 0. Define A 0 = 0 and for n ≥ 1, let A n = max 0≤i<n{A i+n kp k(i/n)}. We prove that lim n→∞A n/n n = sup{pk(x)/1-x k : 0≤x<1}. We also consider two closely related maximization recurrences S n and S′ n, defined as S 0 = S′ 0 = 0, and for n ≥ 1, S n = max 0≤i<n{S i + i(n-i)(n-i-1)/2} and S′ n = max 0≤i<n{S′ i + ( 3 n-i) + 2i( 2 n-i) + (n-i)( 2 i)}. We prove that lim n→∞ S′n/3( 3 n) = 2(√3-1)/3 ≈ 0.488033..., resolving an open problem from Bioinformatics about rooted triplets consistency in phylogenetic networks. © 2012 Springer-Verlag."