387,370 research outputs found
Intrinsic Linking and Knotting in Virtual Spatial Graphs
We introduce a notion of intrinsic linking and knotting for virtual spatial
graphs. Our theory gives two filtrations of the set of all graphs, allowing us
to measure, in a sense, how intrinsically linked or knotted a graph is; we show
that these filtrations are descending and non-terminating. We also provide
several examples of intrinsically virtually linked and knotted graphs. As a
byproduct, we introduce the {\it virtual unknotting number} of a knot, and show
that any knot with non-trivial Jones polynomial has virtual unknotting number
at least 2.Comment: 13 pages, 13 figure
Dynamical linke cluster expansions: Algorithmic aspects and applications
Dynamical linked cluster expansions are linked cluster expansions with
hopping parameter terms endowed with their own dynamics. They amount to a
generalization of series expansions from 2-point to point-link-point
interactions. We outline an associated multiple-line graph theory involving
extended notions of connectivity and indicate an algorithmic implementation of
graphs. Fields of applications are SU(N) gauge Higgs systems within variational
estimates, spin glasses and partially annealed neural networks. We present
results for the critical line in an SU(2) gauge Higgs model for the electroweak
phase transition. The results agree well with corresponding high precision
Monte Carlo results.Comment: LATTICE98(algorithms
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