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Stable border bases for ideals of points 总被引:1,自引:1,他引:0
John Abbott Claudia Fassino Maria-Laura Torrente 《Journal of Symbolic Computation》2008,43(12):883-894
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We consider orthogonal drawings of a plane graph G with specified face areas. For a natural number k, a k-gonal drawing of G is an orthogonal drawing such that the boundary of G is drawn as a rectangle and each inner face is drawn as a polygon with at most k corners whose area is equal to the specified value. In this paper, we show that every slicing graph G with a slicing tree T and a set of specified face areas admits a 10-gonal drawing D such that the boundary of each slicing subgraph that appears in T is also drawn as a polygon with at most 10 corners. Such a drawing D can be found in linear time. 相似文献
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Solomonoff’s central result on induction is that the prediction of a universal semimeasure M converges rapidly and with probability 1 to the true sequence generating predictor μ, if the latter is computable. Hence, M is eligible as a universal sequence predictor in the case of unknown μ. Despite some nearby results and proofs in the literature, the stronger result of convergence for all (Martin-Löf) random sequences remained open. Such a convergence result would be particularly interesting and natural, since randomness can be defined in terms of M itself. We show that there are universal semimeasures M which do not converge to μ on all μ-random sequences, i.e. we give a partial negative answer to the open problem. We also provide a positive answer for some non-universal semimeasures. We define the incomputable measure D as a mixture over all computable measures and the enumerable semimeasure W as a mixture over all enumerable nearly measures. We show that W converges to D and D to μ on all random sequences. The Hellinger distance measuring closeness of two distributions plays a central role. 相似文献
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A real x is called h-bounded computable , for some function h:N→N, if there is a computable sequence (xs) of rational numbers which converges to x such that, for any n∈N, at most h(n) non-overlapping pairs of its members are separated by a distance larger than 2-n. In this paper we discuss properties of h-bounded computable reals for various functions h. We will show a simple sufficient condition for a class of functions h such that the corresponding h-bounded computable reals form an algebraic field. A hierarchy theorem for h-bounded computable reals is also shown. Besides we compare semi-computability and weak computability with the h-bounded computability for special functions h. 相似文献
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