30,974 research outputs found

    Tackling the Minimal Superpermutation Problem

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    A superpermutation on nn symbols is a string that contains each of the n!n! permutations of the nn symbols as a contiguous substring. The shortest superpermutation on nn symbols was conjectured to have length i=1ni!\sum_{i=1}^n i!. The conjecture had been verified for n5n \leq 5. We disprove it by exhibiting an explicit counterexample for n=6n=6. This counterexample was found by encoding the problem as an instance of the (asymmetric) Traveling Salesman Problem, and searching for a solution using a powerful heuristic solver.Comment: 5 page

    Thomas Reid, Hume and theology

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    Joe Houston unfolds the subtlety of some of the fundamental aspects of Thomas Reid’s response to Hume’s scepticism and religious agnosticism. He discusses Hume’s awareness of the tension between scepticism and daily life; his foundationalist notions of rational belief; and the relation of modes of belief to the physical world, past events and causation. He then considers Reid’s counter-argument, that as humans we are constituted with belief-forming dispositions, and that there are no non-circular justifications available for each of the modes of belief-formation, only the principles of common sense.Publisher PD

    Effects of Violence on Youths\u27 Perceptions of Peer and Sibling Aggression

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    The present study examined the relationship between youth exposure to violence in the home and community and their perceptions of the acceptability of aggression in interactions involving peers and siblings. The importance of the context in which the violence occurs was investigated, as well the ability of parent-child attachment to buffer the effects of violence on aggressive attitudes. A diverse sample of 148 children, ages 9 to 14, completed measures of interparental, parent-child, and community aggression, as well as a measure of mother-child attachment. Youths also rated the acceptability of aggressive interactions between two peers and two siblings in written vignettes. Youths\u27 exposure to violence was related to perceptions of aggression as more acceptable, with parent-child aggression having the strongest association and community violence also having a unique contribution. Maternal attachment acted as a buffer between exposure to community violence and perceived acceptability of aggression, such that when exposed to high levels of community violence, youth with more secure maternal attachments perceived aggression as less acceptable than youths with less secure attachment. Finally, when examining peer and sibling interactions separately, parent-child conflict had the strongest relation with perceptions across contexts of peer and sibling aggression and community violence only predicted attitudes about peer aggression