7,861 research outputs found
Effects of Hippocampal Inactivation on the Performance of a Three-Dimensional Object Discrimination Task by Environmentally Enriched Rats
This study was an attempt to show that enriched rats can learn a three dimensional object visual discrimination DMTS and DNMTS task. The task utilized toys from the EC for sample objects on an alternating arm Y-maze. Any subjects which were successful in learning the task were to then be tested as to the effects of reversible inactivation of the hippocampus on the performance of these tasks
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
A Morse index theorem for elliptic operators on bounded domains
Given a selfadjoint, elliptic operator , one would like to know how the
spectrum changes as the spatial domain is
deformed. For a family of domains we prove that the
Morse index of on differs from the Morse index of on
by the Maslov index of a path of Lagrangian subspaces on the
boundary of . This is particularly useful when is a domain
for which the Morse index is known, e.g. a region with very small volume. Then
the Maslov index computes the difference of Morse indices for the "original"
problem (on ) and the "simplified" problem (on ). This
generalizes previous multi-dimensional Morse index theorems that were only
available on star-shaped domains or for Dirichlet boundary conditions. We also
discuss how one can compute the Maslov index using crossing forms, and present
some applications to the spectral theory of Dirichlet and Neumann boundary
value problems.Comment: 21 pages; weaker regularity assumptions than in the first versio
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