Noise-induced memory in extended excitable systems

We describe a form of memory exhibited by extended excitable systems driven by stochastic fluctuations. Under such conditions, the system self-organizes into a state characterized by power-law correlations thus retaining long-term memory of previous states. The exponents are robust and model-independent. We discuss novel implications of these results for the functioning of cortical neurons as well as for networks of neurons.Comment: 4 pages, latex + 5 eps figure

Star clusters and the structure of the ISM. Tunnels and wakes in giant extragalactic HII regions

Several structures have been discovered embedded in regions of recent or ongoing star formation, which point to the importance of the interaction between fast moving wind-blowing stars and their environment. Using hydrodynamic simulations, we investigate the passage through the interstellar medium of a supersonic stellar wind source, and show how it can naturally lead to the formation of tubes, channels and swamps of globules as interfaces are crossed. The results are in excellent agreement with observation of 30 Doradus.Comment: 12 pages + 5 figures (GIF format) - Accepted for pub. in Astrophys. J. Letter

The Unusual Variability of the Large Magellanic Cloud Planetary Nebula RPJ 053059-683542

We present images and light curves of the bipolar Planetary Nebula RPJ 053059-683542 that was discovered in the Reid-Parker AAO/UKST H-alpha survey of the Large Magellanic Cloud (LMC). The emission from this object appears entirely nebular, with the central star apparently obscured by a central band of absorption that bisects the nebula. The light curves, which were derived from images from the SuperMACHO project at CTIO, showed significant, spatially resolved variability over the period 2002 January through 2005 December. Remarkably, the emission from the two bright lobes of the nebula vary either independently, or similarly but with a phase lag of at least one year. The optical spectra show a low level of nebular excitation, and only modest N enrichment. Infrared photometry from the 2MASS and SAGE surveys indicates the presence of a significant quantity of dust. The available data imply that the central star has a close binary companion, and that the system has undergone some kind of outburst event that caused the nebular emission to first brighten and then fade. Further monitoring, high-resolution imaging, and detailed IR polarimetry and spectroscopy would uncover the nature of this nebula and the unseen ionizing source.Comment: Accepted for ApJ Letters; 6 page

High-order gauge-invariant perturbations of a spherical spacetime

We complete the formulation of a general framework for the analysis of high-order nonspherical perturbations of a four-dimensional spherical spacetime by including a gauge-invariant description of the perturbations. We present a general algorithm to construct these invariants and provide explicit formulas for the case of second-order metric perturbations. We show that the well-known problem of lack of invariance for the first-order perturbations with l=0,1 propagates to increasing values of l for perturbations of higher order, owing to mode coupling. We also discuss in which circumstances it is possible to construct the invariants

Second and higher-order perturbations of a spherical spacetime

The Gerlach and Sengupta (GS) formalism of coordinate-invariant, first-order, spherical and nonspherical perturbations around an arbitrary spherical spacetime is generalized to higher orders, focusing on second-order perturbation theory. The GS harmonics are generalized to an arbitrary number of indices on the unit sphere and a formula is given for their products. The formalism is optimized for its implementation in a computer algebra system, something that becomes essential in practice given the size and complexity of the equations. All evolution equations for the second-order perturbations, as well as the conservation equations for the energy-momentum tensor at this perturbation order, are given in covariant form, in Regge-Wheeler gauge.Comment: Accepted for publication in Physical Review

Topological Effects of Synaptic Time Dependent Plasticity

We show that the local Spike Timing-Dependent Plasticity (STDP) rule has the effect of regulating the trans-synaptic weights of loops of any length within a simulated network of neurons. We show that depending on STDP's polarity, functional loops are formed or eliminated in networks driven to normal spiking conditions by random, partially correlated inputs, where functional loops comprise weights that exceed a non-zero threshold. We further prove that STDP is a form of loop-regulating plasticity for the case of a linear network comprising random weights drawn from certain distributions. Thus a notable local synaptic learning rule makes a specific prediction about synapses in the brain in which standard STDP is present: that under normal spiking conditions, they should participate in predominantly feed-forward connections at all scales. Our model implies that any deviations from this prediction would require a substantial modification to the hypothesized role for standard STDP. Given its widespread occurrence in the brain, we predict that STDP could also regulate long range synaptic loops among individual neurons across all brain scales, up to, and including, the scale of global brain network topology.Comment: 26 pages, 5 figure

Quantum time uncertainty in Schwarzschild-anti-de Sitter black holes

The combined action of gravity and quantum mechanics gives rise to a minimum time uncertainty in the lowest order approximation of a perturbative scheme, in which quantum effects are regarded as corrections to the classical spacetime geometry. From the nonperturbative point of view, both gravity and quantum mechanics are treated on equal footing in a description that already contains all possible backreaction effects as those above in a nonlinear manner. In this paper, the existence or not of such minimum time uncertainty is analyzed in the context of Schwarzschild-anti-de Sitter black holes using the isolated horizon formalism. We show that from a perturbative point of view, a nonzero time uncertainty is generically present owing to the energy scale introduced by the cosmological constant, while in a quantization scheme that includes nonperturbatively the effects of that scale, an arbitrarily high time resolution can be reached.Comment: 10 pages, version published in Physical Review