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

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

Solvability of subprincipal type operators

In this paper we consider the solvability of pseudodifferential operators in the case when the principal symbol vanishes of order $k \ge 2$ at a nonradial involutive manifold $\Sigma_2$. We shall assume that the operator is of subprincipal type, which means that the $k$:th inhomogeneous blowup at $\Sigma_2$ of the refined principal symbol is of principal type with Hamilton vector field parallel to the base $\Sigma_2$, but transversal to the symplectic leaves of $\Sigma_2$ at the characteristics. When $k = \infty$ this blowup reduces to the subprincipal symbol. We also assume that the blowup is essentially constant on the leaves of $\Sigma_2$, and does not satisfying the Nirenberg-Treves condition (${\Psi}$). We also have conditions on the vanishing of the normal gradient and the Hessian of the blowup at the characteristics. Under these conditions, we show that $P$ is not solvable.Comment: Changed the formulation of Theorem 2.15, added an assuption. Corrected errors and clarified the arguments. Added reference

Multiwavelength Observations of the BL Lacertae Object PKS 2155-304 with XMM-Newton

The optical-UV and X-ray instruments on-board XMM-Ndewton provide an excellent opportunity to perform simultaneous observations of violently variable objects over a broad wavelength range. The UV and X-ray bright BL Lac object PKS 2155-304 has been repeatedly observed with XMM-Ndewton about twice per year. In this paper, we present a detailed analysis of the simultaneous multiwavelength variability of the source from optical to X-rays, based on the currently available XMM-Ndewton observations. These observations probed the intra-day multiwavelength variability at optical-UV and X-ray wavelengths of the source. The UV variability amplitude is substantially smaller than the X-ray one, and the hardness ratios of the UV to X-rays correlates with the X-ray fluxes: the brighter the source, the flatter the UV-X-ray spectra. On 2000 May 30-31 the UV and X-ray light curves were weakly correlated, while the UV variations followed the X-ray ones with no detectable lags on 2000 November 19-21. On 2001 November 30 the source exhibited a major X-ray flare that was not detected in the optical. The intra-day UV and X-ray variability presented here is not similar to the inter-day UV and X-ray variability obtained from the previous coordinated extensive multiwavelength campaigns on the source, indicating that different ``modes'' of variability might be operating in PKS 2155-304 on different timescales or from epoch to epoch.Comment: Accepted by Ap

Professional or amateur? The phonological output buffer as a working memory operator

The Phonological Output Buffer (POB) is thought to be the stage in language production where phonemes are held in working memory and assembled into words. The neural implementation of the POB remains unclear despite a wealth of phenomenological data. Individuals with POB impairment make phonological errors when they produce words and non-words, including phoneme omissions, insertions, transpositions, substitutions and perseverations. Errors can apply to different kinds and sizes of units, such as phonemes, number words, morphological affixes, and function words, and evidence from POB impairments suggests that units tend to substituted with units of the same kind-e.g., numbers with numbers and whole morphological affixes with other affixes. This suggests that different units are processed and stored in the POB in the same stage, but perhaps separately in different mini-stores. Further, similar impairments can affect the buffer used to produce Sign Language, which raises the question of whether it is instantiated in a distinct device with the same design. However, what appear as separate buffers may be distinct regions in the activity space of a single extended POB network, connected with a lexicon network. The self-consistency of this idea can be assessed by studying an autoassociative Potts network, as a model of memory storage distributed over several cortical areas, and testing whether the network can represent both units of word and signs, reflecting the types and patterns of errors made by individuals with POB impairment

Population synthesis of old neutron stars in the Galaxy

The paucity of old isolated accreting neutron stars in ROSAT observations is used to derive a lower limit on the mean velocity of neutron stars at birth. The secular evolution of the population is simulated following the paths of a statistical sample of stars for different values of the initial kick velocity, drawn from an isotropic Gaussian distribution with mean velocity $0\leq < V>\leq 550$ ${\rm km s^{-1}}$. The spin-down, induced by dipole losses and the interaction with the ambient medium, is tracked together with the dynamical evolution in the Galactic potential, allowing for the determination of the fraction of stars which are, at present, in each of the four possible stages: Ejector, Propeller, Accretor, and Georotator. Taking from the ROSAT All Sky Survey an upper limit of $\sim 10$ accreting neutron stars within $\sim 140$ pc from the Sun, we infer a lower bound for the mean kick velocity, \ga 200-300 ${\rm km s^{-1}}$. The same conclusion is reached for both a constant ($B\sim 10^{12}$ G) and a magnetic field decaying exponentially with a timescale $\sim 10^9$ yr. Present results, moreover, constrain the fraction of low velocity stars, which could have escaped pulsar statistics, to \la 1%.Comment: 8 pages, 4 PostScript figures, to appear in the proceedings of IAU Symposium 19