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

The Oxygen Abundance in the Solar Neighborhood

We present a homogeneous analysis of the oxygen abundance in five H II regions and eight planetary nebulae (PNe) located at distances lower than 2 kpc and with available spectra of high quality. We find that both the collisionally excited lines and recombination lines imply that the PNe are overabundant in oxygen by about 0.2 dex. An explanation that reconciles the oxygen abundances derived with collisionally excited lines for H II regions and PNe with the values found for B-stars, the Sun, and the diffuse ISM requires the presence in H II regions of an organic refractory dust component that is not present in PNe. This dust component has already been invoked to explain the depletion of oxygen in molecular clouds and in the diffuse interstellar medium.Comment: 5 pages, 1 figure, accepted for publication in ApJ Letter

Abundances of s-process elements in planetary nebulae: Br, Kr & Xe

We identify emission lines of post-iron peak elements in very high signal-to-noise spectra of a sample of planetary nebulae. Analysis of lines from ions of Kr and Xe reveals enhancements in most of the PNe, in agreement with the theories of s-process in AGB star. Surprisingly, we did not detect lines from Br even though s-process calculations indicate that it should be produced with Kr at detectable levels.Comment: 2 pages, 1 figure, to be published in the Proceedings of the IAU Symposium 234: Planetary Nebulae in Our Galaxy and Beyond, eds. M.J. Barlow, R.H. Mende

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