A phylogenetic tree, also called an ''evolutionary tree,'' is a leaf-labeled tree which represents the evolutionary history for a set of species, and the construction of such trees is a fundamental problem in biology. Here we address the issue of how many sequence sites are required in order to recover the tree with high probability when the sites evolve… (More)
Inferring evolutionary trees is an interesting and important problem in biology, but one that is computationally difficult as most associated optimization problems are NP-hard. Although many methods are provably statistically consistent (i.e. the probability of recovering the correct tree converges to 1 as the sequence length increases), the actual rate of… (More)
The construction of evolutionary trees is a fundamental problem in biology, and yet methods for reconstructing evolutionary trees are not reliable when it comes to inferring accurate topologies of large divergent evolutionary trees from realistic length sequences. We address this problem and present a new polynomial time algorithm for reconstructing… (More)
We describe how deletion-correcting codes may be enhanced to yield codes with double-strand DNA-sequence codewords. This enhancement involves abstractions of the pertinent aspects of DNA; it nevertheless ensures specificity of binding for all pairs of single strands derived from its codewords—the key desideratum of DNA codes– i.e. with binding feasible only… (More)
We study edge coloring games defining the so-called game chromatic index of a graph. It has been reported that the game chromatic index of trees with maximum degree ∆ = 3 is at most ∆ + 1. We show that the same holds true in case ∆ ≥ 6, which would leave only the cases ∆ = 4 and ∆ = 5 open.
We give a short and transparent bijective proof of the bichromatic binary tree theorem of Carter, Hendy, Penny, Sztkely and Wormald on the number of bichromatic evolutionary trees. The proof simplifies M.A. Steel's proof. Evolutionary trees are extensively studied structures in biostatistics. (These are leaf-coloured binary trees. For details see, e.g.,… (More)