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 ($Q_a=M$), the lower limit on the black hole mass for avoiding the polarization of the surrounding medium is $M\gg (10^{-15}\div 10^{-11})m_p$ ($m_p$ is the proton mass), according to the assumed value of the axion mass ($m_a\simeq (10^{-3}\div 10^{-6})~eV$). 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 ($Q_a<M$), 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 $A$, the space \hilb_A(A^*) of the Hilbert spaces that are continuously embedded in $A^*$ and are $^*$-invariant under the dual left regular action of $A$ 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 $\sim 100$. 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 ($V<100 km s^{-1}$) and that magnetic field decay guides the evolution. In the second, NSs move with high speed ($V>100$ km s$^{-1}$) 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