10,802 research outputs found
Transductive-Inductive Cluster Approximation Via Multivariate Chebyshev Inequality
Approximating adequate number of clusters in multidimensional data is an open
area of research, given a level of compromise made on the quality of acceptable
results. The manuscript addresses the issue by formulating a transductive
inductive learning algorithm which uses multivariate Chebyshev inequality.
Considering clustering problem in imaging, theoretical proofs for a particular
level of compromise are derived to show the convergence of the reconstruction
error to a finite value with increasing (a) number of unseen examples and (b)
the number of clusters, respectively. Upper bounds for these error rates are
also proved. Non-parametric estimates of these error from a random sample of
sequences empirically point to a stable number of clusters. Lastly, the
generalization of algorithm can be applied to multidimensional data sets from
different fields.Comment: 16 pages, 5 figure
Multifractal Analysis of Packed Swiss Cheese Cosmologies
The multifractal spectrum of various three-dimensional representations of
Packed Swiss Cheese cosmologies in open, closed, and flat spaces are measured,
and it is determined that the curvature of the space does not alter the
associated fractal structure. These results are compared to observational data
and simulated models of large scale galaxy clustering, to assess the viability
of the PSC as a candidate for such structure formation. It is found that the
PSC dimension spectra do not match those of observation, and possible solutions
to this discrepancy are offered, including accounting for potential luminosity
biasing effects. Various random and uniform sets are also analyzed to provide
insight into the meaning of the multifractal spectrum as it relates to the
observed scaling behaviors.Comment: 3 latex files, 18 ps figure
Gap Processing for Adaptive Maximal Poisson-Disk Sampling
In this paper, we study the generation of maximal Poisson-disk sets with
varying radii. First, we present a geometric analysis of gaps in such disk
sets. This analysis is the basis for maximal and adaptive sampling in Euclidean
space and on manifolds. Second, we propose efficient algorithms and data
structures to detect gaps and update gaps when disks are inserted, deleted,
moved, or have their radius changed. We build on the concepts of the regular
triangulation and the power diagram. Third, we will show how our analysis can
make a contribution to the state-of-the-art in surface remeshing.Comment: 16 pages. ACM Transactions on Graphics, 201
Construction and Application of an AMR Algorithm for Distributed Memory Computers
While the parallelization of blockstructured adaptive mesh refinement techniques is relatively straight-forward on shared memory architectures, appropriate distribution strategies for the emerging generation of distributed
memory machines are a topic of on-going research. In this paper, a locality-preserving domain decomposition is proposed that partitions the entire AMR hierarchy from the base level on. It is shown that the approach reduces the
communication costs and simplifies the implementation. Emphasis is put on the effective parallelization of the flux correction procedure at coarse-fine boundaries, which is indispensable for conservative finite volume schemes. An
easily reproducible standard benchmark and a highly resolved parallel AMR
simulation of a diffracting hydrogen-oxygen detonation demonstrate the proposed
strategy in practice
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