Complexity of the General Chromatic Art Gallery Problem

In the original Art Gallery Problem (AGP), one seeks the minimum number of guards required to cover a polygon $P$. We consider the Chromatic AGP (CAGP), where the guards are colored. As long as $P$ is completely covered, the number of guards does not matter, but guards with overlapping visibility regions must have different colors. This problem has applications in landmark-based mobile robot navigation: Guards are landmarks, which have to be distinguishable (hence the colors), and are used to encode motion primitives, \eg, "move towards the red landmark". Let $\chi_G(P)$, the chromatic number of $P$, denote the minimum number of colors required to color any guard cover of $P$. We show that determining, whether $\chi_G(P) \leq k$ is \NP-hard for all $k \geq 2$. Keeping the number of colors minimal is of great interest for robot navigation, because less types of landmarks lead to cheaper and more reliable recognition

Examination of phisical parameters of pectin gels extracted from fruit presscakes

In our study we aimed to investigate the rheologieal and colour characteristics of the pectin gels extracted from presscakes of berries. The pectins extracted from the presscakes of five different fruits such as black-currant, red-currant, raspberry, blackberry and elderberry, were used for the examinations. Tw o commercial materials were applied as controls: apple and citrus pectins. The rheologieal examinations showed that the pectins obtained from the red-currant presscake have the best gelificator properties. The analysis of the colour coordinates revealed that the gel of the citrus pectin used as control is very clear and translucent such as the pectin gel of the red-currant. The pectin gels of black-currant, blackberry, elderberry and raspberry contain a significant amount of colourants, in this way they are very dark

Correlation between prescribed daily dose, seizure freedom and defined daily dose in antiepileptic drug treatment

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