2,345 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
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
The vacuum polarization around an axionic stringy black hole
We consider the effect of vacuum polarization around the horizon of a 4
dimensional axionic stringy black hole. In the extreme degenerate limit
(), the lower limit on the black hole mass for avoiding the polarization
of the surrounding medium is ( is the
proton mass), according to the assumed value of the axion mass (). In this case, there are no upper bounds on the mass
due to the absence of the thermal radiation by the black hole. In the
nondegenerate (classically unstable) limit (), the black hole always
polarizes the surrounding vacuum, unless the effective cosmological constant of
the effective stringy action diverges.Comment: 7 pages, phyzzx.tex, ROM2F-92-3
Some remarks on the GNS representations of topological -algebras
After an appropriate restatement of the GNS construction for topological
-algebras we prove that there exists an isomorphism among the set
\cycl(A) of weakly continuous strongly cyclic -representations of a
barreled dual-separable -algebra with unit , the space \hilb_A(A^*) of
the Hilbert spaces that are continuously embedded in and are
-invariant under the dual left regular action of and the set of the
corresponding reproducing kernels. We show that these isomorphisms are cone
morphisms and we prove many interesting results that follow from this fact. We
discuss how these results can be used to describe cyclic representations on
more general inner product spaces.Comment: 34 pages. Minor changes. To appear in J. Math. Phys. 49 (4) Apr-0
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
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
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