581 research outputs found
On the Critical Capacity of the Hopfield Model
We estimate the critical capacity of the zero-temperature Hopfield model by
using a novel and rigorous method. The probability of having a stable fixed
point is one when for a large number of neurons. This result
is an advance on all rigorous results in the literature and the relationship
between the capacity and retrieval errors obtained here for small
coincides with replica calculation results.Comment: Latex 36 page macros:
http://www.springer.de/author/tex/help-journals.htm
Central limit theorem for linear eigenvalue statistics of orthogonally invariant matrix models
We prove central limit theorem for linear eigenvalue statistics of
orthogonally invariant ensembles of random matrices with one interval limiting
spectrum. We consider ensembles with real analytic potentials and test
functions with two bounded derivatives.Comment: 19 page
Photon correlations for colloidal nanocrystals and their clusters
Images of semiconductor `dot in rods' and their small clusters are studied by
measuring the second-order correlation function with a spatially resolving ICCD
camera. This measurement allows one to distinguish between a single dot and a
cluster and, to a certain extent, to estimate the number of dots in a cluster.
A more advanced measurement is proposed, based on higher-order correlations,
enabling more accurate determination of the number of dots in a small cluster.
Nonclassical features of the light emitted by such a cluster are analyzed.Comment: 4 pages, 4 figure
- …