1,498 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
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
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
Is the Bursting Radio-source GCRT J1745-3009 a Double Neutron Star Binary ?
GCRT J1745-3009 is a peculiar transient radio-source in the direction of the
Galactic Center. It was observed to emit a series of ~ 1 Jy bursts at 0.33 GHz,
with typical duration ~ 10 min and at apparently regular intervals of ~ 77 min.
If the source is indeed at the distance of the Galactic Center as it seems
likely, we show that its observational properties are compatible with those
expected from a double neutron star binary, similar to the double pulsar system
J0737-3039. In the picture we propose the (coherent) radio emission comes from
the shock originating in the interaction of the wind of the more energetic
pulsar with the magnetosphere of the companion. The observed modulation of the
radio signal is the consequence of an eccentric orbit, along which the
separation between the two stars varies. This cyclically drives the shock
inside the light cylinder radius of the less energetic pulsar.Comment: 5 pages, 3 figures, accepted for publication in The Astrophysical
Journal Letters, comment on geodetic precession adde
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
On Decoding the Responses of a Population of Neurons from Short Time Windows
The effectiveness of various stimulus identification (decoding) procedures for extracting the information carried by the responses of a population of neurons to a set of repeatedly presented stimuli is studied analytically, in the limit of short time windows. It is shown that in this limit, the entire information content of the responses can sometimes be decoded, and when this is not the case, the lost information is quantified. In particular, the mutual information extracted by taking into account only the most likely stimulus in each trial turns out to be, if not equal, much closer to the true value than that calculated from all the probabilities that each of the possible stimuli in the set was the actual one. The relation between the mutual information extracted by decoding and the percentage of correct stimulus decodings is also derived analytically in the same limit, showing that the metric content index can be estimated reliably from a few cells recorded from brief periods. Computer simulations as well as the activity of real neurons recorded in the primate hippocampus serve to confirm these results and illustrate the utility and limitations of the approach
Estimating probabilities from experimental frequencies
Estimating the probability distribution 'q' governing the behaviour of a
certain variable by sampling its value a finite number of times most typically
involves an error. Successive measurements allow the construction of a
histogram, or frequency count 'f', of each of the possible outcomes. In this
work, the probability that the true distribution be 'q', given that the
frequency count 'f' was sampled, is studied. Such a probability may be written
as a Gibbs distribution. A thermodynamic potential, which allows an easy
evaluation of the mean Kullback-Leibler divergence between the true and
measured distribution, is defined. For a large number of samples, the
expectation value of any function of 'q' is expanded in powers of the inverse
number of samples. As an example, the moments, the entropy and the mutual
information are analyzed.Comment: 10 pages, 3 figures, to be published in Physical Review
Hardy-Carleman Type Inequalities for Dirac Operators
General Hardy-Carleman type inequalities for Dirac operators are proved. New
inequalities are derived involving particular traditionally used weight
functions. In particular, a version of the Agmon inequality and Treve type
inequalities are established. The case of a Dirac particle in a (potential)
magnetic field is also considered. The methods used are direct and based on
quadratic form techniques
Broad-band X-ray spectra of the persistent black hole candidates LMC X-1 and LMC X-3
We report on observations of the two persistent black hole candidates LMC X-3
and LMCX-1 performed with \BS in October 1997. The flux of LMC X-1 was possibly
measured up to 60 keV, but there is a possible confusion with PSR 0540-69. Fits
with an absorbed multicolor disk black body are not satisfactory, while the
superposition of this model with a power law is acceptable. The sources showed
little variations during the observations. However in LMC X-1 some X-ray color
dependence on intensity is apparent, indicating a hardening of the spectrum in
the second half of the observation. The inner disk radius and temperature
change, featuring the same (anti)correlation found in {\it RXTE} data (Wilms et
al. 2000). QPOs were searched for. In LMC X-3 none was detected; in LMCX-1 a 3
sigma upper (9% rms) limit is given at 0.07 Hz, the frequency of the QPO
discovered with Ginga.Comment: 10 pages, 5 figures. To be published in the ApJ Supplement
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