33 research outputs found

    Real-space local polynomial basis for solid-state electronic-structure calculations: A finite-element approach

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    We present an approach to solid-state electronic-structure calculations based on the finite-element method. In this method, the basis functions are strictly local, piecewise polynomials. Because the basis is composed of polynomials, the method is completely general and its convergence can be controlled systematically. Because the basis functions are strictly local in real space, the method allows for variable resolution in real space; produces sparse, structured matrices, enabling the effective use of iterative solution methods; and is well suited to parallel implementation. The method thus combines the significant advantages of both real-space-grid and basis-oriented approaches and so promises to be particularly well suited for large, accurate ab initio calculations. We develop the theory of our approach in detail, discuss advantages and disadvantages, and report initial results, including the first fully three-dimensional electronic band structures calculated by the method.Comment: replacement: single spaced, included figures, added journal referenc

    Estimating evolutionary distances from spaced-word matches

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    International audienceAlignment-free methods are increasingly used to estimate distances between DNA and protein sequences and to reconstruct phylogenetic trees. Most distance functions used by these methods, however, are heuristic measures of dissimilarity, not based on any explicit model of evolution. Herein, we propose a simple estimator of the evolutionary distance between two DNA sequences calculated from the number of (spaced) word matches between them. We show that this distance function estimates the evolutionary distance between DNA sequences more accurately than other distance measures used by alignment-free methods. In addition, we calculate the variance of the number of (spaced) word matches depending on sequence length and mismatch probability
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