946 research outputs found
Representational capacity of a set of independent neurons
The capacity with which a system of independent neuron-like units represents
a given set of stimuli is studied by calculating the mutual information between
the stimuli and the neural responses. Both discrete noiseless and continuous
noisy neurons are analyzed. In both cases, the information grows monotonically
with the number of neurons considered. Under the assumption that neurons are
independent, the mutual information rises linearly from zero, and approaches
exponentially its maximum value. We find the dependence of the initial slope on
the number of stimuli and on the sparseness of the representation.Comment: 19 pages, 6 figures, Phys. Rev. E, vol 63, 11910 - 11924 (2000
An associative network with spatially organized connectivity
We investigate the properties of an autoassociative network of
threshold-linear units whose synaptic connectivity is spatially structured and
asymmetric. Since the methods of equilibrium statistical mechanics cannot be
applied to such a network due to the lack of a Hamiltonian, we approach the
problem through a signal-to-noise analysis, that we adapt to spatially
organized networks. The conditions are analyzed for the appearance of stable,
spatially non-uniform profiles of activity with large overlaps with one of the
stored patterns. It is also shown, with simulations and analytic results, that
the storage capacity does not decrease much when the connectivity of the
network becomes short range. In addition, the method used here enables us to
calculate exactly the storage capacity of a randomly connected network with
arbitrary degree of dilution.Comment: 27 pages, 6 figures; Accepted for publication in JSTA
A model problem for the initial-boundary value formulation of Einstein's field equations
In many numerical implementations of the Cauchy formulation of Einstein's
field equations one encounters artificial boundaries which raises the issue of
specifying boundary conditions. Such conditions have to be chosen carefully. In
particular, they should be compatible with the constraints, yield a well posed
initial-boundary value formulation and incorporate some physically desirable
properties like, for instance, minimizing reflections of gravitational
radiation.
Motivated by the problem in General Relativity, we analyze a model problem,
consisting of a formulation of Maxwell's equations on a spatially compact
region of spacetime with timelike boundaries. The form in which the equations
are written is such that their structure is very similar to the
Einstein-Christoffel symmetric hyperbolic formulations of Einstein's field
equations. For this model problem, we specify a family of Sommerfeld-type
constraint-preserving boundary conditions and show that the resulting
initial-boundary value formulations are well posed. We expect that these
results can be generalized to the Einstein-Christoffel formulations of General
Relativity, at least in the case of linearizations about a stationary
background.Comment: 25 page
The Neutron Stars Census
The paucity of old isolated accreting neutron stars in ROSAT observations is
used to derive a lower limit on the mean velocity of neutron stars at birth.
The secular evolution of the population is simulated following the paths of a
statistical sample of stars for different values of the initial kick velocity,
drawn from an isotropic Gaussian distribution with mean velocity . The spin--down, induced by dipole losses and the
interaction with the ambient medium, is tracked together with the dynamical
evolution in the Galactic potential, allowing for the determination of the
fraction of stars which are, at present, in each of the four possible stages:
Ejector, Propeller, Accretor, and Georotator. Taking from the ROSAT All Sky
Survey an upper limit of accreting neutron stars within pc
from the Sun, we infer a lower bound for the mean kick velocity, corresponding to a velocity dispersion
km s. The same conclusion is reached for both
a constant magnetic field ( G) and a magnetic field decaying
exponentially with a timescale yr. Such high velocities are
consistent with those derived from radio pulsar observations. Present results,
moreover, constrain the fraction of low velocity stars, which could have
escaped pulsar statistics, to less than 1%.Comment: 13 pages, 6 PostScript figures, accepted to Ap
Population synthesis of old neutron stars in the Galaxy
The paucity of old isolated accreting neutron stars in ROSAT observations is
used to derive a lower limit on the mean velocity of neutron stars at birth.
The secular evolution of the population is simulated following the paths of a
statistical sample of stars for different values of the initial kick velocity,
drawn from an isotropic Gaussian distribution with mean velocity . The spin-down, induced by dipole losses and the
interaction with the ambient medium, is tracked together with the dynamical
evolution in the Galactic potential, allowing for the determination of the
fraction of stars which are, at present, in each of the four possible stages:
Ejector, Propeller, Accretor, and Georotator. Taking from the ROSAT All Sky
Survey an upper limit of accreting neutron stars within pc
from the Sun, we infer a lower bound for the mean kick velocity, \ga
200-300 . The same conclusion is reached for both a constant
( G) and a magnetic field decaying exponentially with a
timescale yr. Present results, moreover, constrain the fraction of
low velocity stars, which could have escaped pulsar statistics, to \la 1%.Comment: 8 pages, 4 PostScript figures, to appear in the proceedings of IAU
Symposium 19
Young close-by neutron stars: the Gould Belt vs. the Galactic disc
We present new population synthesis calculations of close young neutron
stars. In comparison with our previous investigation we use a different neutron
star mass spectrum and different initial spatial and velocity distributions.
The results confirm that most of ROSAT dim radioquiet isolated neutron stars
had their origin in the Gould Belt. Several tens of young neutron stars can be
identified in future in ROSAT data at low galactic latitudes and some of them
also can be EGRET unidentified sources.Comment: 14 pages, 8 figures, submitted to Ap&SS, corrected some typo
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