2,186 research outputs found
A theoretical model of neuronal population coding of stimuli with both continuous and discrete dimensions
In a recent study the initial rise of the mutual information between the
firing rates of N neurons and a set of p discrete stimuli has been analytically
evaluated, under the assumption that neurons fire independently of one another
to each stimulus and that each conditional distribution of firing rates is
gaussian. Yet real stimuli or behavioural correlates are high-dimensional, with
both discrete and continuously varying features.Moreover, the gaussian
approximation implies negative firing rates, which is biologically implausible.
Here, we generalize the analysis to the case where the stimulus or behavioural
correlate has both a discrete and a continuous dimension. In the case of large
noise we evaluate the mutual information up to the quadratic approximation as a
function of population size. Then we consider a more realistic distribution of
firing rates, truncated at zero, and we prove that the resulting correction,
with respect to the gaussian firing rates, can be expressed simply as a
renormalization of the noise parameter. Finally, we demonstrate the effect of
averaging the distribution across the discrete dimension, evaluating the mutual
information only with respect to the continuously varying correlate.Comment: 20 pages, 10 figure
Replica symmetric evaluation of the information transfer in a two-layer network in presence of continuous+discrete stimuli
In a previous report we have evaluated analytically the mutual information
between the firing rates of N independent units and a set of multi-dimensional
continuous+discrete stimuli, for a finite population size and in the limit of
large noise. Here, we extend the analysis to the case of two interconnected
populations, where input units activate output ones via gaussian weights and a
threshold linear transfer function. We evaluate the information carried by a
population of M output units, again about continuous+discrete correlates. The
mutual information is evaluated solving saddle point equations under the
assumption of replica symmetry, a method which, by taking into account only the
term linear in N of the input information, is equivalent to assuming the noise
to be large. Within this limitation, we analyze the dependence of the
information on the ratio M/N, on the selectivity of the input units and on the
level of the output noise. We show analytically, and confirm numerically, that
in the limit of a linear transfer function and of a small ratio between output
and input noise, the output information approaches asymptotically the
information carried in input. Finally, we show that the information loss in
output does not depend much on the structure of the stimulus, whether purely
continuous, purely discrete or mixed, but only on the position of the threshold
nonlinearity, and on the ratio between input and output noise.Comment: 19 pages, 4 figure
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
Neutron stars accreting the ISM: Are they fast or slow objects ?
Old neutron stars (ONSs) which have radiated away their internal and
rotational energy may still shine if accreting the interstellar medium. Rather
stringent limits from the analysis of ROSAT surveys indicate that most
optimistic predictions on ONSs observability are in excess of a factor as large
as . Here we explore two possible evolutionary scenarios that may
account for the paucity of ONSs. In the first it is assumed that the ONS
population is not too fast () and that magnetic field decay
guides the evolution. In the second, NSs move with high speed ( km
s) and preserve their magnetic field at birth. We find that according to
the former scenario most ONSs are now in the propeller phase, while in the
latter nearly all ONSs are silent, dead pulsars.Comment: 5 pages including 2 postscript figures, to appear in the proceedings
of Rome BeppoSax-RossiXTE meetin
Stability of the replica symmetric solution for the information conveyed by by a neural network
The information that a pattern of firing in the output layer of a feedforward
network of threshold-linear neurons conveys about the network's inputs is
considered. A replica-symmetric solution is found to be stable for all but
small amounts of noise. The region of instability depends on the contribution
of the threshold and the sparseness: for distributed pattern distributions, the
unstable region extends to higher noise variances than for very sparse
distributions, for which it is almost nonexistant.Comment: 19 pages, LaTeX, 5 figures. Also available at
http://www.mrc-bbc.ox.ac.uk/~schultz/papers.html . Submitted to Phys. Rev. E
Minor change
Persistent and Transient Blank Field Sources
Blank field sources (BFS) are good candidates for hosting dim isolated
neutron stars (DINS). The results of a search of BFS in the ROSAT HRI images
are revised. We then focus on transient BFS, arguing that they belong to a
rather large population. The perspectives of future research on DINS are then
discussed.Comment: 3 pages, 0 figures. Paper presented at the Conference "Isolated
Neutron Stars: from the interior to the surface", London, April 2006.
Astrophysics and Space Science, in pres
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