On the low dimensional dynamics of structured random networks

Using a generalized random recurrent neural network model, and by extending our recently developed mean-field approach [J. Aljadeff, M. Stern, T. Sharpee, Phys. Rev. Lett. 114, 088101 (2015)], we study the relationship between the network connectivity structure and its low dimensional dynamics. Each connection in the network is a random number with mean 0 and variance that depends on pre- and post-synaptic neurons through a sufficiently smooth function $g$ of their identities. We find that these networks undergo a phase transition from a silent to a chaotic state at a critical point we derive as a function of $g$. Above the critical point, although unit activation levels are chaotic, their autocorrelation functions are restricted to a low dimensional subspace. This provides a direct link between the network's structure and some of its functional characteristics. We discuss example applications of the general results to neuroscience where we derive the support of the spectrum of connectivity matrices with heterogeneous and possibly correlated degree distributions, and to ecology where we study the stability of the cascade model for food web structure.Comment: 16 pages, 4 figure

A self-consistent stellar and 3D nebular model for Planetary Nebula IC418

We present a coherent stellar and nebular model reproducing the observations of the Planetary Nebula IC418. We want to test whether a stellar model obtained by fitting the stellar observations is able to satisfactory ionize the nebula and reproduce the nebular observations, which is by no mean evident. This allows us to determine all the physical parameters of both the star and the nebula, including the abundances and the distance. We used all the observational material available (FUSE, IUE, STIS and optical spectra) to constrain the stellar atmosphere model performed using the CMFGEN code. The photoionization model is done with Cloudy_3D, and is based on CTIO, Lick, SPM, IUE and ISO spectra as well as HST images. More than 140 nebular emission lines are compared to the observed intensities. We reproduce all the observations for the star and the nebula. The 3D morphology of the gas distribution is determined. The effective temperature of the star is 36.7kK. Its luminosity is 7700 solar luminosity. We describe an original method to determine the distance of the nebula using evolutionary tracks. No clumping factor is need to reproduce the age-luminosity relation. The distance of 1.25 kpc is found in very good agreement with recent determination using parallax method. The chemical composition of both the star and the nebula are determined. Both are Carbon-rich. The nebula presents evidence of depletion of elements Mg, Si, S, Cl (0.5 dex lower than solar) and Fe (2.9 dex lower than solar). This is the first self-consistent stellar and nebular model for a Planetary Nebula that reproduces all the available observations ranging from IR to UV, showing that the combined approach for the modeling process leads to more restrictive constraints and, in principle, more trustworthy results.Comment: Accepted for publication in Astronomy and Astrophysics. V2: after corrections language edito

Neural Decision Boundaries for Maximal Information Transmission

We consider here how to separate multidimensional signals into two categories, such that the binary decision transmits the maximum possible information transmitted about those signals. Our motivation comes from the nervous system, where neurons process multidimensional signals into a binary sequence of responses (spikes). In a small noise limit, we derive a general equation for the decision boundary that locally relates its curvature to the probability distribution of inputs. We show that for Gaussian inputs the optimal boundaries are planar, but for non-Gaussian inputs the curvature is nonzero. As an example, we consider exponentially distributed inputs, which are known to approximate a variety of signals from natural environment.Comment: 5 pages, 3 figure

Detection of Fluorine in the Halo Planetary Nebula BoBn 1: Evidence For a Binary Progenitor Star

We have found the fluorine lines [F IV] 3996.92A,4059.90A in the extremely metal-poor ([Ar/H] = -2.10+/-0.21) halo planetary nebula (PN) BoBn 1 in high-dispersion spectra from the 8.2-m VLT/UVES archive. Chemical abundance analysis shows that the fluorine abundance is [F/H] = +1.06+/-0.08, making BoBn 1 the most fluorine-enhanced and metal-poor PN among fluorine-detected PNe and providing new evidence that fluorine is enhanced by nucleosynthesis in low mass metal-poor stars. A comparison with the abundances of carbon-enhanced metal-poor (CEMP) stars suggests that BoBn 1 shares their origin and evolution with CEMP-s stars such as HE1305+0132. BoBn 1 might have evolved from a binary consisting of ~2 Msun primary and ~0.8 Msun secondary stars.Comment: 13 pages, 3 figures, accepted by ApJ Letter

Enhancement of tunneling from a correlated 2D electron system by a many-electron Mossbauer-type recoil in a magnetic field

We consider the effect of electron correlations on tunneling from a 2D electron layer in a magnetic field parallel to the layer. A tunneling electron can exchange its momentum with other electrons, which leads to an exponential increase of the tunneling rate compared to the single-electron approximation. Explicit results are obtained for a Wigner crystal. They provide a qualitative and quantitative explanation of the data on electrons on helium. We also discuss tunneling in semiconductor heterostructures.Comment: published version, 4 pages, 2 figures, RevTeX 3.