2,082 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
Classification of radiating compact stars
A classification of compact stars, depending on the electron distribution in velocity space and the density profiles characterizing their magnetospheric plasma, is proposed. Fast pulsars, such as NP 0532, X-ray sources such as Sco-X1, and slow pulsars are suggested as possible evolutionary stages of similar objects. The heating mechanism of Sco-X1 is discussed in some detail
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
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
On the Treves theorem for the AKNS equation
According to a theorem of Treves, the conserved functionals of the AKNS
equation vanish on all pairs of formal Laurent series of a specified form, both
of them with a pole of the first order. We propose a new and very simple proof
for this statement, based on the theory of B\"acklund transformations; using
the same method, we prove that the AKNS conserved functionals vanish on other
pairs of Laurent series. The spirit is the same of our previous paper on the
Treves theorem for the KdV, with some non trivial technical differences.Comment: LaTeX, 16 page
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