213,087 research outputs found
Approximating Nearest Neighbor Distances
Several researchers proposed using non-Euclidean metrics on point sets in
Euclidean space for clustering noisy data. Almost always, a distance function
is desired that recognizes the closeness of the points in the same cluster,
even if the Euclidean cluster diameter is large. Therefore, it is preferred to
assign smaller costs to the paths that stay close to the input points.
In this paper, we consider the most natural metric with this property, which
we call the nearest neighbor metric. Given a point set P and a path ,
our metric charges each point of with its distance to P. The total
charge along determines its nearest neighbor length, which is formally
defined as the integral of the distance to the input points along the curve. We
describe a -approximation algorithm and a
-approximation algorithm to compute the nearest neighbor
metric. Both approximation algorithms work in near-linear time. The former uses
shortest paths on a sparse graph using only the input points. The latter uses a
sparse sample of the ambient space, to find good approximate geodesic paths.Comment: corrected author nam
Collapse transition of a square-lattice polymer with next nearest-neighbor interaction
We study the collapse transition of a polymer on a square lattice with both
nearest-neighbor and next nearest-neighbor interactions, by calculating the
exact partition function zeros up to chain length 36. The transition behavior
is much more pronounced than that of the model with nearest-neighbor
interactions only. The crossover exponent and the transition temperature are
estimated from the scaling behavior of the first zeros with increasing chain
length. The results suggest that the model is of the same universality class as
the usual theta point described by the model with only nearest-neighbor
interaction.Comment: 14 pages, 5 figure
Magnetization Process of the Spin-1/2 Triangular-Lattice Heisenberg Antiferromagnet with Next-Nearest-Neighbor Interactions -- Plateau or Nonplateau
An triangular-lattice Heisenberg antiferromagnet with
next-nearest-neighbor interactions is investigated under a magnetic field by
the numerical-diagonalization method. It is known that, in both cases of weak
and strong next-nearest-neighbor interactions, this system reveals a
magnetization plateau at one-third of the saturated magnetization. We examine
the stability of this magnetization plateau when the amplitude of
next-nearest-neighbor interactions is varied. We find that a nonplateau region
appears between the plateau phases in the cases of weak and strong
next-nearest-neighbor interactions.Comment: 6pages, 7figures, to be published in J. Phys. Soc. Jp
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