Xiaoyang Gu
Iowa State University
24 Papers
144 Citations
Xiaoyang Gu is an academic researcher from Iowa State University. The author has contributed to research in topics: Hausdorff dimension & Effective dimension. The author has an hindex of 9, co-authored 24 publications. Previous affiliations of Xiaoyang Gu include LinkedIn.
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Papers
•Posted Content
Zeta-Dimension
David Doty,Xiaoyang Gu,Jack H. Lutz,Elvira Mayordomo,Philippe Moser +4 more
- 22 Mar 2005
TL;DR: The zeta dimension of a set A of positive integers is the infimum s such that the sum of the reciprocals of the s-th powers of the elements of A is finite Zeta-dimension serves as a fractal dimension on the positive integers that extends naturally usefully to discrete lattices as discussed by the authors.
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Points on Computable Curves
Xiaoyang Gu,Jack H. Lutz,Elvira Mayordomo +2 more
- 21 Oct 2006
TL;DR: In this paper, a computable extension of the analyst's traveling salesman theorem is presented, where a point in Euclidean space lies on some computable curve of finite length if and only if it is "permitted" by a Jones constriction, which is an explicit assignment of a rational cylinder to each tile in such a way that, when the radius of the cylinder corresponding to a tile is used in place of the "width of K" in each tile, the square beta sum is finite.
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•Journal Article
Points on Computable Curves
TL;DR: The main part of the proof is the construction of a computable curve of finite length traversing all the points permitted by a given Jones constriction, which uses the main ideas of Jones's "farthest insertion" construction, but takes a very different form.
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•Posted Content
Points on Computable Curves
TL;DR: In this paper, a computable extension of the analyst's traveling salesman theorem for higher-dimensional Euclidean spaces has been presented, where the main part is the construction of a curve of finite length traversing all the points permitted by a given Jones constriction.
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•Posted Content
Curves That Must Be Retraced
TL;DR: A polynomial time computable plane curve that has finite length, does not intersect itself, and is smooth except at one endpoint, but has the following property: for every computable parametrization f of @C and every positive integer m, there is some positive-length subcurve of @ C that f retraces at least m times.
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