17,092 research outputs found
Approximating Loops in a Shortest Homology Basis from Point Data
Inference of topological and geometric attributes of a hidden manifold from
its point data is a fundamental problem arising in many scientific studies and
engineering applications. In this paper we present an algorithm to compute a
set of loops from a point data that presumably sample a smooth manifold
. These loops approximate a {\em shortest} basis of the
one dimensional homology group over coefficients in finite field
. Previous results addressed the issue of computing the rank of
the homology groups from point data, but there is no result on approximating
the shortest basis of a manifold from its point sample. In arriving our result,
we also present a polynomial time algorithm for computing a shortest basis of
for any finite {\em simplicial complex} whose edges have
non-negative weights
Evidence for A Two-dimensional Quantum Wigner Solid in Zero Magnetic Field
We report the first experimental observation of a characteristic nonlinear
threshold behavior from dc dynamical response as an evidence for a Wigner
crystallization in high-purity GaAs 2D hole systems in zero magnetic field. The
system under increasing current drive exhibits voltage oscillations with
negative differential resistance. They confirm the coexistence of a moving
crystal along with striped edge states as observed for electrons on helium
surfaces. However, the threshold is well below the typical classical levels due
to a different pinning and depinning mechanism that is possibly related to a
quantum process
Approximation of Random Slow Manifolds and Settling of Inertial Particles under Uncertainty
A method is provided for approximating random slow manifolds of a class of
slow-fast stochastic dynamical systems. Thus approximate, low dimensional,
reduced slow systems are obtained analytically in the case of sufficiently
large time scale separation. To illustrate this dimension reduction procedure,
the impact of random environmental fluctuations on the settling motion of
inertial particles in a cellular flow field is examined. It is found that noise
delays settling for some particles but enhances settling for others. A
deterministic stable manifold is an agent to facilitate this phenomenon.
Overall, noise appears to delay the settling in an averaged sense.Comment: 27 pages, 9 figure
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