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Regularising Ill-posed Discrete Optimisation: Quests with P Systems

Nicolescu R., Gimel’farb G., Morris J., Delmas P., Gong R.

Fundamenta Informaticae

2014

Vol. 131, nr 3-4

465--483

We propose a novel approach to justify and guide regularisation of an ill-posed one-dimensional global optimisation with multiple solutions using a massively parallel (P system) model of the solution space. Classical optimisation assumes a well-posed problem with a stable unique solution. Most of important practical problems are ill posed due to an unstable or non-unique global optimum and are regularised to get a unique best-suited solution. Whilst regularisation theory exists largely for unstable unique solutions, its recommendations are often routinely applied to inverse optical problems with essentially non-unique solutions, e.g. computer stereo vision or image segmentation, typically formulated in terms of global energy minimisation. In these cases the recommended regularisation becomes purely heuristic and does not guarantee a unique solution. As a result, classical optimisation algorithms: dynamic programming (DP) and belief propagation (BP) – meet with difficulties. Our recent concurrent propagation (CP), leaning upon the P systems paradigm, extends DP and BP to always detect whether the problem is ill posed or not and store in the ill-posed case an entire space of solutions that yield the same global optimum. This suggests a radically new path to proper regularisation: select the best-suited unique solution by exploring statistical and structural features of this space. We propose a P systems based implementation of CP and set out as a case study an application of CP to the image matching problem in stereo vision.

Study on absorption and mechanical properties of rubber sheet absorbers

Gong R., He Y., Li X., Liu C., Wang X.

Materials Science Poland

2007

Vol. 25, No. 4

1001--1010

Based on the impedance matching principle and electromagnetic wave propagating law, double-layer absorbers with impedance-matching structure were designed both theoretically and experimentally. Microwave absorbers were prepared by mixing a commercially available rubber with magnetic micropowder (MMP) and/or dielectric materials. The first layer, made up of MMP has large permeability and magnetic loss, while the second layer (matching layer), comprised of MMP and/or dielectric material, has frequency dispersion with the parameters of permittivity and permeability to match the incidence free space over a wide frequency range. Experiments showed that the matching layer plays a key role in the absorption. Electromagnetic parameters and thickness need to be controlled precisely to achieve high absorption. It was reasoned out that with increasing electromagnetic performance of matching layer, matching thickness will decrease. Tests showed that the reflectivity was below -10 dB for samples 1 and 2, and below - 8 dB for samples 3-6 in the frequency range of 8-18 GHz. Finally, mechanical characteristics were also investigated with tensile strength above 10 MPa, indicating that the materials may find practical use in the engineering of microwave absorbers.