170 research outputs found
Inference of entropies of discrete random variables with unknown cardinalities
We examine the recently introduced NSB estimator of entropies of severely
undersampled discrete variables and devise a procedure for calculating the
involved integrals. We discover that the output of the estimator has a well
defined limit for large cardinalities of the variables being studied. Thus one
can estimate entropies with no a priori assumptions about these cardinalities,
and a closed form solution for such estimates is given.Comment: 8 page
Potential and field singularity at a surface point charge
The behavior of the magnetic potential near a point charge (fluxon) located
at a curved regular boundary surface is shown to be essentially different from
that of a volume point charge. In addition to the usual inverse distance
singularity, two singular terms are generally present. The first of them, a
logarithmic one, is axially symmetric with respect to the boundary normal at
the charge location, and proportional to the sum of the two principal
curvatures of the boundary surface at this point, that is, to the local mean
curvature. The second term is asymmetric and proportional to the difference of
the two principal curvatures in question; it is also bounded at the charge
location. Both terms vanish, apparently, if the charge is at a planar point of
the boundary, and only in this case. The field in the charge vicinity behaves
accordingly, featuring generally two singular terms proportional to the inverse
distance, in addition to the main inverse distance squared singularity. This
result is significant, in particular, for studying the interaction of magnetic
vortices in type II superconductors.Comment: 5 pages, 1 figure, RevTeX
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