Feedback controllability for blowup points of semilinear heat equations
Ping Lin
Discrete & Continuous Dynamical Systems - B 2017, 22(4): 1425-1434 doi: 10.3934/dcdsb.2017068

This paper studies a controllability problem for blowup points of two classes of semilinear heat equations.Our goal to act controls on the systems we studied is to make the corresponding solutions blow upat given points. This differs with the controllability problem of equations with the property of blowup in the references, where the purpose of using controls is to prevent blowupby controls. We obtain the feedback controls for our controllability problem of blowup points.

keywords: Blowup point semilinear heat equation feedback controllability for blowup point
Retinal vessel segmentation using a finite element based binary level set method
Zhenlin Guo Ping Lin Guangrong Ji Yangfan Wang
Inverse Problems & Imaging 2014, 8(2): 459-473 doi: 10.3934/ipi.2014.8.459
In this paper we combine a few techniques to label blood vessels in the matched filter (MF) response image by using a finite element based binary level set method. An operator-splitting method is applied to numerically solve the Euler-Lagrange equation from minimizing an energy functional. Unlike the traditional MF methods, where a threshold is difficult to be selected, our method can automatically get more precise blood vessel segmentation using an enhanced edge information. In order to demonstrate the good performance, we compare our method with a few other methods when they are applied to a publicly available standard database of coloured images (with manual segmentations available too).
keywords: operator-splitting. Retinal vessel segmentation binary level set method
Portfolio optimization and risk measurement based on non-dominated sorting genetic algorithm
Ping-Chen Lin
Journal of Industrial & Management Optimization 2012, 8(3): 549-564 doi: 10.3934/jimo.2012.8.549
This paper introduces a multi-objective genetic algorithm (MOGA) in regard to the portfolio optimization issue in different risk measures, such as mean-variance, semi-variance, mean-variance-skewness, mean-absolute-deviation and lower-partial-moment to optimize risk of portfolio. This study introduces a PONSGA model by appling the non-dominated sorting genetic algorithm (NSGA-II) to maximize both the expected return and the skewness of portfolio as well as to simultaneously minimize different portfolio risks. The experimental results demonstrated that the PONSGA approach is significantly superior to the GA in all performances, examined such as the coefficient of variation, Sharpe index, Sortino index and portfolio performance index. The statistical significance tests also showed that the NSGA-II models outperformed the GA models in different risk measures.
keywords: 49 and 90.

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