# 0xDE

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Professor of Computer Science at UC Irvine, researching graph algorithms and computational geometry. Wikipedian. Amateur photographer. Father of two.

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Professor of Computer Science at UC Irvine, researching graph algorithms and computational geometry. Wikipedian. Amateur photographer. Father of two.

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In my recent posting on four-dimensional polytopes containing linked or knotted cycles of edges, I showed pictures of linked cycles in three examples, the (3,3)-duopyramid, hypercube, and (in the comments) truncated 5-cell. All three of these have some much more special properties: the two linked cycles are induced cycles (there are no edges between two non-consecutive vertices in the same cycle), they include all the vertices in the graph, and their intersection with any two- or […]

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When I was asked earlier this year to write a short survey on k-best enumeration algorithms for the Springer Encyclopedia of Algorithms, I wrote a first draft before checking the formatting requirements. It ended up being approximately five pages of text and seven more pages of references, and I knew I would have to cut some of that. But then I did check the format, and saw that it needed to be much shorter, approximately two pages of text and a dozen references. I don't regret doing it this […]

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The number theory behind why you can't have both perfect fifths and perfect octaves on a piano keyboard (with bonus lattice quotient music theory link; G+)Sad news of Rudolf Halin's death (G+)Frankenstein vs The Glider Gun video (G+)Günter Ziegler on Dürer's solid (WP; MF; G+)Nature will make its articles back to 1869 free to share online, for certain values of "free" that you might or might not agree with (G+)Albert Carpenter's polyhedron models (G+)The only complete proof from
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The surface of a three-dimensional polyhedron is a two-dimensional space that's topologically equivalent to the sphere. By the Jordan curve theorem, every cycle of edges and vertices in this space cuts the surface into two topological disks. But the surface of a four-dimensional polytope is a three-dimensional space that's topologically equivalent to the hypersphere, or to three-dimensional Euclidean space completed by adding one point at infinity. So, just as in conventional Euclidean space,
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The exponential random graph model is a system for describing probability distributions on graphs, used to model social networks. One fixes a set of vertices, and determines a collection of "features" among the edges of this fixed set (such as whether or not a particular edge or combination of a small number of edges), each with an associated real-valued weights. Then to determine the probability of seeing a particular graph, one simply looks at which features it has; the probability is exp(sum […]

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