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

BeppoSAX observations of the black hole candidates LMC X-1 and LMC X-3

We describe BeppoSAX observations of the black hole candidates LMC X--1 and LMC X--3 performed in Oct. 1997. Both sources can be modelled by a multicolor accretion disk spectrum, with temperature $\sim 1$ keV. However, there is some evidence that a thin emitting component coexists with the thick disk at these temperatures. In the direction of LMC X--1, we detected a significant emission above 10 keV, which we suspect originates from the nearby source PSR 0540-69. For LMC X--1, we estimate an absorbing column density of $\simeq 6\times 10^{21}$ cm$^{-2}$, which is almost ten times larger than that found for LMC X--3. In both sources, we find no indication of emission or absorption features whatsoever.Comment: 4 pages, 2 figures. Accepted for pubblication in the Proc. of 32nd Cospar scientific assembly, Nagoya, 13-15 July 199