9,897 research outputs found

    The space of ultrametric phylogenetic trees

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    The reliability of a phylogenetic inference method from genomic sequence data is ensured by its statistical consistency. Bayesian inference methods produce a sample of phylogenetic trees from the posterior distribution given sequence data. Hence the question of statistical consistency of such methods is equivalent to the consistency of the summary of the sample. More generally, statistical consistency is ensured by the tree space used to analyse the sample. In this paper, we consider two standard parameterisations of phylogenetic time-trees used in evolutionary models: inter-coalescent interval lengths and absolute times of divergence events. For each of these parameterisations we introduce a natural metric space on ultrametric phylogenetic trees. We compare the introduced spaces with existing models of tree space and formulate several formal requirements that a metric space on phylogenetic trees must possess in order to be a satisfactory space for statistical analysis, and justify them. We show that only a few known constructions of the space of phylogenetic trees satisfy these requirements. However, our results suggest that these basic requirements are not enough to distinguish between the two metric spaces we introduce and that the choice between metric spaces requires additional properties to be considered. Particularly, that the summary tree minimising the square distance to the trees from the sample might be different for different parameterisations. This suggests that further fundamental insight is needed into the problem of statistical consistency of phylogenetic inference methods.Comment: Minor changes. This version has been published in JTB. 27 pages, 9 figure

    A Kosloff/Basal method, 3D migration program implemented on the CYBER 205 supercomputer

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    Conventional finite difference migration has relied on approximations to the acoustic wave equation which allow energy to propagate only downwards. Although generally reliable, such approaches usually do not yield an accurate migration for geological structures with strong lateral velocity variations or with steeply dipping reflectors. An earlier study by D. Kosloff and E. Baysal (Migration with the Full Acoustic Wave Equation) examined an alternative approach based on the full acoustic wave equation. The 2D, Fourier type algorithm which was developed was tested by Kosloff and Baysal against synthetic data and against physical model data. The results indicated that such a scheme gives accurate migration for complicated structures. This paper describes the development and testing of a vectorized, 3D migration program for the CYBER 205 using the Kosloff/Baysal method. The program can accept as many as 65,536 zero offset (stacked) traces

    GOGMA: Globally-Optimal Gaussian Mixture Alignment

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    Gaussian mixture alignment is a family of approaches that are frequently used for robustly solving the point-set registration problem. However, since they use local optimisation, they are susceptible to local minima and can only guarantee local optimality. Consequently, their accuracy is strongly dependent on the quality of the initialisation. This paper presents the first globally-optimal solution to the 3D rigid Gaussian mixture alignment problem under the L2 distance between mixtures. The algorithm, named GOGMA, employs a branch-and-bound approach to search the space of 3D rigid motions SE(3), guaranteeing global optimality regardless of the initialisation. The geometry of SE(3) was used to find novel upper and lower bounds for the objective function and local optimisation was integrated into the scheme to accelerate convergence without voiding the optimality guarantee. The evaluation empirically supported the optimality proof and showed that the method performed much more robustly on two challenging datasets than an existing globally-optimal registration solution.Comment: Manuscript in press 2016 IEEE Conference on Computer Vision and Pattern Recognitio

    Clustering-Based Materialized View Selection in Data Warehouses

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    Materialized view selection is a non-trivial task. Hence, its complexity must be reduced. A judicious choice of views must be cost-driven and influenced by the workload experienced by the system. In this paper, we propose a framework for materialized view selection that exploits a data mining technique (clustering), in order to determine clusters of similar queries. We also propose a view merging algorithm that builds a set of candidate views, as well as a greedy process for selecting a set of views to materialize. This selection is based on cost models that evaluate the cost of accessing data using views and the cost of storing these views. To validate our strategy, we executed a workload of decision-support queries on a test data warehouse, with and without using our strategy. Our experimental results demonstrate its efficiency, even when storage space is limited
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