2,763 research outputs found

    Synthesizing species trees from gene trees using the parameterized and graph-theoretic approaches

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    Gene trees describe how parts of the species have evolved over time, and it is assumed that gene trees have evolved along the branches of the species tree. However, some of gene trees are often discordant with the corresponding species tree due to the complicated evolution history of genes. To overcome this obstacle, median problems have emerged as a major tool for synthesizing species trees by reconciling discordance in a given collection of gene trees. Given a collection of gene trees and a cost function, the median problem seeks a tree, called median tree, that minimizes the overall cost to the gene trees. Median tree problems are typically NP-hard, and there is an increased interest in making such median tree problems available for large-scale species tree construction. In this thesis work, we first show that the gene duplication median tree problem satisfied the weaker version of the Pareto property and propose a parameterized algorithm to solve the gene duplication median tree problem. Second, we design two efficient methods to handle the issues of applying the parameterized algorithm to unrooted gene trees which are sampled from the different species. Third, we introduce the graph-theoretic formulation of the Robinson-Foulds median tree problem and a new tree edit operation. Fourth, we propose a new metric between two phylogenetic trees and examine the statistical properties of the metric. Finally, we propose a new clustering criteria in a bipartite network and propose a new NP-hard problem and its ILP formulation

    Surrogate regression modelling for fast seismogram generation and detection of microseismic events in heterogeneous velocity models

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    This is the author accepted manuscript. The final version is available from Oxford University Press (OUP) via the DOI in this record.Given a 3D heterogeneous velocity model with a few million voxels, fast generation of accurate seismic responses at specified receiver positions from known microseismic event locations is a well-known challenge in geophysics, since it typically involves numerical solution of the computationally expensive elastic wave equation. Thousands of such forward simulations are often a routine requirement for parameter estimation of microseimsic events via a suitable source inversion process. Parameter estimation based on forward modelling is often advantageous over a direct regression-based inversion approach when there are unknown number of parameters to be estimated and the seismic data has complicated noise characteristics which may not always allow a stable and unique solution in a direct inversion process. In this paper, starting from Graphics Processing Unit (GPU) based synthetic simulations of a few thousand forward seismic shots due to microseismic events via pseudo-spectral solution of elastic wave equation, we develop a step-by-step process to generate a surrogate regression modelling framework, using machine learning techniques that can produce accurate seismograms at specified receiver locations. The trained surrogate models can then be used as a high-speed meta-model/emulator or proxy for the original full elastic wave propagator to generate seismic responses for other microseismic event locations also. The accuracies of the surrogate models have been evaluated using two independent sets of training and testing Latin hypercube (LH) quasi-random samples, drawn from a heterogeneous marine velocity model. The predicted seismograms have been used thereafter to calculate batch likelihood functions, with specified noise characteristics. Finally, the trained models on 23 receivers placed at the sea-bed in a marine velocity model are used to determine the maximum likelihood estimate (MLE) of the event locations which can in future be used in a Bayesian analysis for microseismic event detection.This work has been supported by the Shell Projects and Technology. The Wilkes high performance GPU computing service at the University of Cambridge has been used in this work

    A SOLUTION ALGORITHM FOR p-MEDIAN LOCATION PROBLEM ON UNCERTAIN RANDOM NETWORKS

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    This paper investigatesthe classical pp-median location problem in a network in which some of the vertex weights and the distances between vertices are uncertain and while others are random. For solving the pp-median problem in an uncertain random network, an optimization model based on the chance theory is proposed first and then an algorithm is presented to find the pp-median. Finally, a numerical example is given to illustrate the efficiency of the proposed metho
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