2,187 research outputs found
Uncovering Low-Dimensional Topological Structure in the QCD Vacuum
Recently, we have pointed out that sign-coherent 4-dimensional structures can
not dominate topological charge fluctuations in QCD vacuum at all scales. Here
we show that an enhanced lower-dimensional coherence is possible. In pure SU(3)
lattice gauge theory we find that in a typical equilibrium configuration about
80% of space-time points are covered by two oppositely-charged connected
structures built of elementary 3-dimensional coherent hypercubes. The
hypercubes within the structure are connected through 2-dimensional common
faces. We suggest that this coherence is a manifestation of a low-dimensional
order present in the QCD vacuum. The use of a topological charge density
associated with Ginsparg-Wilson fermions ("chiral smoothing") is crucial for
observing this structure.Comment: 3 pages, 1 figure; Proceedings of the "Confinement V" Conference,
Gargnano, Italy, Sep 10-14, 200
A new and flexible method for constructing designs for computer experiments
We develop a new method for constructing "good" designs for computer
experiments. The method derives its power from its basic structure that builds
large designs using small designs. We specialize the method for the
construction of orthogonal Latin hypercubes and obtain many results along the
way. In terms of run sizes, the existence problem of orthogonal Latin
hypercubes is completely solved. We also present an explicit result showing how
large orthogonal Latin hypercubes can be constructed using small orthogonal
Latin hypercubes. Another appealing feature of our method is that it can easily
be adapted to construct other designs; we examine how to make use of the method
to construct nearly orthogonal and cascading Latin hypercubes.Comment: Published in at http://dx.doi.org/10.1214/09-AOS757 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Tight upper bound on the maximum anti-forcing numbers of graphs
Let be a simple graph with a perfect matching. Deng and Zhang showed that
the maximum anti-forcing number of is no more than the cyclomatic number.
In this paper, we get a novel upper bound on the maximum anti-forcing number of
and investigate the extremal graphs. If has a perfect matching
whose anti-forcing number attains this upper bound, then we say is an
extremal graph and is a nice perfect matching. We obtain an equivalent
condition for the nice perfect matchings of and establish a one-to-one
correspondence between the nice perfect matchings and the edge-involutions of
, which are the automorphisms of order two such that and
are adjacent for every vertex . We demonstrate that all extremal
graphs can be constructed from by implementing two expansion operations,
and is extremal if and only if one factor in a Cartesian decomposition of
is extremal. As examples, we have that all perfect matchings of the
complete graph and the complete bipartite graph are nice.
Also we show that the hypercube , the folded hypercube ()
and the enhanced hypercube () have exactly ,
and nice perfect matchings respectively.Comment: 15 pages, 7 figure
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