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    Incompletely Specified Probabilistic Networks
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    Abstract:
    :Probabilistic networks, used as an adjunct or alternative to the logical models used in artificial intelligence (AI) and decision support systems (DSS), offer a way to compactly represent a distribution over a set of random variables. Nonetheless, the specification of a given network may require conditional probabilities that are simply unavailable. In this paper a means for analyzing incompletely specified networks is presented, and some general rules are derived from the application of the method to some simple networks. The use of the technique in MIS settings is illustrated.
    In this article, we present new results on simple points, minimal non-simple sets (MNS) and P-simple points. In particular, we propose new characterizations which hold in dimensions 2, 3 and 4, and which lead to efficient algorithms for detecting such points or sets. This work is settled in the framework of cubical complexes, and some of the main results are based on the properties of critical kernels.
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    We investigate simple endotrivial modules of finite quasi-simple groups and classify them in several important cases. This is motivated by a recent result of Robinson showing that simple endotrivial modules of most groups come from quasi-simple groups.
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    Abstract We investigate simple endotrivial modules of finite quasi-simple groups and classify them in several important cases. This is motivated by a recent result of Robinson [Bull. Lond. Math. Soc. 43 (2011), 712–716] showing that simple endotrivial modules of most groups come from quasi-simple groups.
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    We consider the fundamental relations β and γ in simple and 0-simple semihypergroups, especially in connection with certain minimal cardinality questions. In particular, we enumerate and exhibit all simple and 0-simple semihypergroups having order 3 where β is not transitive, apart of isomorphisms. Moreover, we show that the least order for which there exists a strongly simple semihypergroup where β is not transitive is 4. Finally, we prove that γ is transitive in all simple semihypergroups, and determine necessary and sufficient conditions for a 0-simple semihypergroup to have γ transitive. The latter results obviously hold also for simple and 0-simple semigroups.
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    In this paper, we investigate the properties of the [0-simple] simple subsemigroups of nonnegative matrices and show that the [0-simple] simple subsemigroups of Mn(S) are completely [0-simple] simple, where S is a strong ideal subset of R+ which has no ele- ments less than 1 except 0. Finally, we illustrate that the semigroup of nonnegative matriles is interesting.
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    We investigate simple endotrivial modules of finite quasi-simple groups and classify them in several important cases. This is motivated by a recent result of Robinson showing that simple endotrivial modules of most groups come from quasi-simple groups.
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