Browsing by Author "Herbst, B. M."

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    Discretizations, integrable systems and computation
    (2001) Ablowitz, M. J.; Herbst, B. M.; Schober, C. M.
    Discretizations and associated numerical computation of solutions of certain integrable systems, such as the nonlinear Schrödinger equation (NLS) and the sine-Gordon (sG) equations with periodic boundary values can lead to instabilities, chaotic and spurious results. The chaos can be due to truncation errors or even roundoff errors and can be traced to the fact that these integrable systems are strongly unstable when the initial values are in the neighbourhood of homoclinic manifolds. By using the associated nonlinear spectral transform of the NLS equation and tracking the evolution of relevant eigenvalues one can observe and relate crossing of homoclinic manifolds to the temporal chaos in the waveforms when the initial data is even. For general initial values, even though there is no crossing of the unperturbed homoclinic manifolds, the waveforms still exhibit chaotic phenomena which can be related to the evolution of the spectrum. This paper reviews the current understanding of this intriguing phenomena and also compares the implementation of certain symplectic integrators and Runge-Kutta algorithms for the NLS and sG equations in regions of phase space proximate to the homoclinic manifolds.
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    Offline signature verification using the discrete Radon transform and a hidden Markov model
    (Hindawi, 2004) Coetzer, J.; Herbst, B. M.; Du Preez, J. A.
    We developed a system that automatically authenticates offline handwritten signatures using the discrete Radon transform (DRT) and a hidden Markov model (HMM). Given the robustness of our algorithm and the fact that only global features are considered, satisfactory results are obtained. Using a database of 924 signatures from 22 writers, our system achieves an equal error rate (EER) of 18% when only high-quality forgeries (skilled forgeries) are considered and an EER of 4.5% in the case of only casual forgeries. These signatures were originally captured offline. Using another database of 4800 signatures from 51 writers, our system achieves an EER of 12.2% when only skilled forgeries are considered. These signatures were originally captured online and then digitally converted into static signature images. These results compare well with the results of other algorithms that consider only global features.