Browsing by Subject "Computer Science, Software Engineering"

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    Behavior of different numerical schemes for random genetic drift
    (BIT Numerical Mathematics, 2019-09-01) Xu, S; Chen, M; Liu, C; Zhang, R; Yue, X
    In the problem of random genetic drift, the probability density of one gene is governed by a degenerated convection-dominated diffusion equation. Dirac singularities will always be developed at boundary points as time evolves, which is known as the fixation phenomenon in genetic evolution. Three finite volume methods: FVM1-3, one central difference method: FDM1 and three finite element methods: FEM1-3 are considered. These methods lead to different equilibrium states after a long time. It is shown that only schemes FVM3 and FEM3, which are the same, preserve probability, expectation and positiveness and predict the correct probability of fixation. FVM1-2 wrongly predict the probability of fixation due to their intrinsic viscosity, even though they are unconditionally stable. Contrarily, FDM1 and FEM1-2 introduce different anti-diffusion terms, which make them unstable and fail to preserve positiveness.
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    Computer aided restoration of handwritten character strokes
    (CAD Computer Aided Design, 2017-08-01) Sober, B; Levin, D
    © 2017 Elsevier Ltd This work suggests a new variational approach to the task of computer aided segmentation and restoration of incomplete characters, residing in a highly noisy document image. We model character strokes as the movement of a pen with a varying radius. Following this model, in order to fit the digital image, a cubic spline representation is being utilized to perform gradient descent steps, while maintaining interpolation at some initial (manually sampled) points. The proposed algorithm was used in the process of restoring approximately 1000 ancient Hebrew characters (dating to ca. 8th–7th century BCE), some of which are presented herein and show that the algorithm yields plausible results when applied on deteriorated documents.