We define ruling invariants for even-valence Legendrian graphs in standard contact three-space. prove that rulings exist if and only the DGA of graph, introduced by first two authors, has an augmentation. set up usual polynomials various notions gradedness graph is four-valent, then ungraded polynomial appears Kauffman-Vogel's version Kauffman polynomial. Our are compatible with certain vertex-...

This paper presents an improved zone content class$cation method and its performance evaluation. We added two new features to the feature vector from one previously published method [l]. We assumed different independence relationship in two zone sets. We used an optimized binary decision tree to estimate the maximum Zone content class probability in one set while used Viterbi algorithm to find ...

We study the formation of a ruling coalition in non-democratic societies where institutions do not enable political commitments. Each individual is endowed with a level of political power. The ruling coalition consists of a subset of the individuals in the society and decides the distribution of resources. A ruling coalition needs to contain enough powerful members to win against any alternativ...