The topology of large Open Connectome networks for the human brain

The structural human connectome (i.e.\ the network of fiber connections in the brain) can be analyzed at ever finer spatial resolution thanks to advances in neuroimaging. Here we analyze several large data sets for the human brain network made available by the Open Connectome Project. We apply statistical model selection to characterize the degree distributions of graphs containing up to $\simeq 10^6$ nodes and $\simeq 10^8$ edges. A three-parameter generalized Weibull (also known as a stretched exponential) distribution is a good fit to most of the observed degree distributions. For almost all networks, simple power laws cannot fit the data, but in some cases there is statistical support for power laws with an exponential cutoff. We also calculate the topological (graph) dimension $D$ and the small-world coefficient $\sigma$ of these networks. While $\sigma$ suggests a small-world topology, we found that $D < 4$ showing that long-distance connections provide only a small correction to the topology of the embedding three-dimensional space.Comment: 14 pages, 6 figures, accepted version in Scientific Report

Rare regions of the susceptible-infected-susceptible model on Barabási-Albert networks

I extend a previous work to susceptible-infected-susceptible (SIS) models on weighted Barabási-Albert scale-free networks. Numerical evidence is provided that phases with slow, power-law dynamics emerge as the consequence of quenched disorder and tree topologies studied previously with the contact process. I compare simulation results with spectral analysis of the networks and show that the quenched mean-field (QMF) approximation provides a reliable, relatively fast method to explore activity clustering. This suggests that QMF can be used for describing rare-region effects due to network inhomogeneities. Finite-size study of the QMF shows the expected disappearance of the epidemic threshold λc in the thermodynamic limit and an inverse participation ratio ∼0.25, meaning localization in case of disassortative weight scheme. Contrarily, for the multiplicative weights and the unweighted trees, this value vanishes in the thermodynamic limit, suggesting only weak rare-region effects in agreement with the dynamical simulations. Strong corrections to the mean-field behavior in case of disassortative weights explains the concave shape of the order parameter ρ(λ) at the transition point. Application of this method to other models may reveal interesting rare-region effects, Griffiths phases as the consequence of quenched topological heterogeneities

Slow dynamics and rare-region effects in the contact process on weighted tree networks

We show that generic, slow dynamics can occur in the contact process on complex networks with a tree-like structure and a superimposed weight pattern, in the absence of additional (non-topological) sources of quenched disorder. The slow dynamics is induced by rare-region effects occurring on correlated subspaces of vertices connected by large weight edges, and manifests in the form of a smeared phase transition. We conjecture that more sophisticated network motifs could be able to induce Griffiths phases, as a consequence of purely topological disorder.Comment: 12 pages, 10 figures, final version appeared in PR

HAT-P-32b and HAT-P-33b: Two Highly Inflated Hot Jupiters Transiting High-jitter Stars

We report the discovery of two exoplanets transiting high-jitter stars. HAT-P-32b orbits the bright V = 11.289 late-F-early-G dwarf star GSC 3281-00800, with a period P = 2.150008 ± 0.000001 d. The stellar and planetary masses and radii depend on the eccentricity of the system, which is poorly constrained due to the high-velocity jitter (~80 m s^(–1)). Assuming a circular orbit, the star has a mass of 1.16 ± 0.04 M_☉ and radius of 1.22 ± 0.02 R_☉, while the planet has a mass of 0.860 ± 0.164 M_J and a radius of 1.789 ± 0.025 R_J. The second planet, HAT-P-33b, orbits the bright V = 11.188 late-F dwarf star GSC 2461-00988, with a period P = 3.474474 ± 0.000001 d. As for HAT-P-32, the stellar and planetary masses and radii of HAT-P-33 depend on the eccentricity, which is poorly constrained due to the high jitter (~50 m s^(–1)). In this case, spectral line bisector spans (BSs) are significantly anti-correlated with the radial velocity residuals, and we are able to use this correlation to reduce the residual rms to ~35 m s^(–1). We find that the star has a mass of 1.38 ± 0.04 M_☉ and a radius of 1.64 ± 0.03 R_☉ while the planet has a mass of 0.762 ± 0.101 M_J and a radius of 1.686 ± 0.045 R_J for an assumed circular orbit. Due to the large BS variations exhibited by both stars we rely on detailed modeling of the photometric light curves to rule out blend scenarios. Both planets are among the largest radii transiting planets discovered to date

Dissipative spin chains: Implementation with cold atoms and steady-state properties

We propose a quantum optical implementation of a class of dissipative spin systems, including the XXZ and Ising model, with ultra-cold atoms in optical lattices. Employing the motional degree of freedom of the atoms and detuned Raman transitions we show how to obtain engineerable dissipation and a tunable transversal magnetic field, enabling the study of the dynamics and steady-states of dissipative spin models. As an example of effects made accessible this way, we consider small spin chains and weak dissipation and show by numerical simulation that steady-state expectation values display pronounced peaks at certain critical system parameters. We show that this effect is related to degeneracies in the Hamiltonian and derive a sufficient condition for its occurrence.Comment: 14 pages, 10 figures, published version, includes new figure and several small change