Phylogenetic Bootstrapping (BS) is a standard technique for inferring confidence values on phylogenetic trees that is based on reconstructing many trees from minor variations of the input data, trees called replicates. BS is used with all phylogenetic reconstruction approaches, but we focus here on the most popular, Maximum Likelihood (ML). Because ML inference is so computationally demanding, it has proved too expensive to date to assess the impact of the number of replicates used in BS on the quality of the support values. For the same reason, a rather small number (typically 100) of BS replicates are computed in real-world studies. Stamatakis et al. recently introduced a BS algorithm that is 1-2 orders of magnitude faster than previous techniques, while yielding qualitatively comparable support values, making an experimental study possible.In this paper, we propose stopping criteria, that is, thresholds computed at runtime to determine when enough replicates have been generated, and report on the first large-scale experimental study to assess the effect of the number of replicates on the quality of support values, including the performance of our proposed criteria. We run our tests on 17 diverse real-world DNA, single-gene as well as multi-gene, datasets, that include between 125 and 2,554 sequences. We find that our stopping criteria typically stop computations after 100-500 replicates (although the most conservative criterion may continue for several thousand replicates) while producing support values that correlate at better than 99.5% with the reference values on the best ML trees. Significantly, we also find that the stopping criteria can recommend very different numbers of replicates for different datasets of comparable sizes.Our results are thus two-fold: (i) they give the first experimental assessment of the effect of the number of BS replicates on the quality of support values returned through bootstrapping; and (ii) they validate

Phylogenetic bootstrapping (BS) is a standard technique for inferring confidence values on phylogenetic trees that is based on reconstructing many trees from minor variations of the input data, trees called replicates. BS is used with all phylogenetic reconstruction approaches, but we focus here on one of the most popular, maximum likelihood (ML). Because ML inference is so computationally demanding, it has proved too expensive to date to assess the impact of the number of replicates used in BS on the relative accuracy of the support values. For the same reason, a rather small number (typically 100) of BS replicates are computed in real-world studies. Stamatakis et al. recently introduced a BS algorithm that is 1 to 2 orders of magnitude faster than previous techniques, while yielding qualitatively comparable support values, making an experimental study possible. In this article, we propose stopping criteria--that is, thresholds computed at runtime to determine when enough replicates have been generated--and we report on the first large-scale experimental study to assess the effect of the number of replicates on the quality of support values, including the performance of our proposed criteria. We run our tests on 17 diverse real-world DNA--single-gene as well as multi-gene--datasets, which include 125-2,554 taxa. We find that our stopping criteria typically stop computations after 100-500 replicates (although the most conservative criterion may continue for several thousand replicates) while producing support values that correlate at better than 99.5% with the reference values on the best ML trees. Significantly, we also find that the stopping criteria can recommend very different numbers of replicates for different datasets of comparable sizes. Our results are thus twofold: (i) they give the first experimental assessment of the effect of the number of BS replicates on the quality of support values returned through BS, and (ii) they validate our proposals for stopping criteria. Practitioners will no longer have to enter a guess nor worry about the quality of support values; moreover, with most counts of replicates in the 100-500 range, robust BS under ML inference becomes computationally practical for most datasets. The complete test suite is available at http://lcbb.epfl.ch/BS.tar.bz2, and BS with our stopping criteria is included in the latest release of RAxML v7.2.5, available at http://wwwkramer.in.tum.de/exelixis/software.html.

Abstract-We introduce irregular product codes, a class of codes where each codeword is represented by a matrix and the entries in each row (column) of the matrix come from a component row (column) code. As opposed to standard product codes, we do not require that all component row codes nor all component column codes be the same. Relaxing this requirement can provide some additional attractive features such as allowing some regions of the codeword to be more error-resilient, providing a more refined spectrum of rates for finite lengths, and improved performance for some of these rates. We study these codes over erasure channels and prove that for any 0 < < 1, for many rate distributions on component row codes, there is a matching rate distribution on component column codes such that an irregular product code based on MDS codes with those rate distributions on the component codes has asymptotic rate 1 − and can decode on erasure channels having erasure probability < (and having alphabet size equal to the alphabet size of the component MDS codes).

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The aim of this work is to present a method in computer vision for model-based object recognition by integration of texture, color, and partial silhouette matching cues. As a test problem, a challenging task of distinguishing between cats and dogs are proposed. No condition is imposed on the images. In spite of high intraclass variability of two classes (especially dogs), accuracy rate of over 92% is achieved. A novel method for integration of color information to textures is also presented.