In J. Shao et al., PRL 103, 108701 (2009) the authors claim that a model with majority rule coarsening exhibits in d=2 a percolation transition in the universality class of invasion percolation with trapping. In the present comment we give compelling
evidence, including high statistics simulations on much larger lattices, that this is not correct. and that the model is trivially in the ordinary percolation universality class.
Existing sequence alignment algorithms use heuristic scoring schemes which cannot be used as objective distance metrics. Therefore one relies on measures like the p- or log-det distances, or makes explicit, and often simplistic, assumptions about seq
uence evolution. Information theory provides an alternative, in the form of mutual information (MI) which is, in principle, an objective and model independent similarity measure. MI can be estimated by concatenating and zipping sequences, yielding thereby the normalized compression distance. So far this has produced promising results, but with uncontrolled errors. We describe a simple approach to get robust estimates of MI from global pairwise alignments. Using standard alignment algorithms, this gives for animal mitochondrial DNA estimates that are strikingly close to estimates obtained from the alignment free methods mentioned above. Our main result uses algorithmic (Kolmogorov) information theory, but we show that similar results can also be obtained from Shannon theory. Due to the fact that it is not additive, normalized compression distance is not an optimal metric for phylogenetics, but we propose a simple modification that overcomes the issue of additivity. We test sever
Background: Alignment of biological sequences such as DNA, RNA or proteins is one of the most widely used tools in computational bioscience. All existing alignment algorithms rely on heuristic scoring schemes based on biological expertise. Therefore,
these algorithms do not provide model independent and objective measures for how similar two (or more) sequences actually are. Although information theory provides such a similarity measure -- the mutual information (MI) -- previous attempts to connect sequence alignment and information theory have not produced realistic estimates for the MI from a given alignment. Results: Here we describe a simple and flexible approach to get robust estimates of MI from {it global} alignments. For mammalian mitochondrial DNA, our approach gives pairwise MI estimates for commonly used global alignment algorithms that are strikingly close to estimates obtained by an entirely unrelated approach -- concatenating and zipping the sequences. Conclusions: This remarkable consistency may help establish MI as a reliable tool for evaluating the quality of global alignments, judging the relative merits of different alignment algorithms, and estimating the significance of specific alignments. We expect that our approach can be extended to establish further connections between information theory and sequence alignment, including applications to local and multiple alignment procedures.
