The role of clustering and gridlike ordering in epidemic spreading

The spreading of an epidemic is determined by the connectiviy patterns which underlie the population. While it has been noted that a virus spreads more easily on a network in which global distances are small, it remains a great challenge to find approaches that unravel the precise role of local interconnectedness. Such topological properties enter very naturally in the framework of our two-timestep description, also providing a novel approach to tract a probabilistic system. The method is elaborated for SIS-type epidemic processes, leading to a quantitative interpretation of the role of loops up to length 4 in the onset of an epidemic.Comment: Submitted to Phys. Rev. E; 15 pages, 11 figures, 5 table

The role of the Berry Phase in Dynamical Jahn-Teller Systems

The presence/absence of a Berry phase depends on the topology of the manifold of dynamical Jahn-Teller potential minima. We describe in detail the relation between these topological properties and the way the lowest two adiabatic potential surfaces get locally degenerate. We illustrate our arguments through spherical generalizations of the linear T x h and H x h cases, relevant for the physics of fullerene ions. Our analysis allows us to classify all the spherical Jahn-Teller systems with respect to the Berry phase. Its absence can, but does not necessarily, lead to a nondegenerate ground state.Comment: revtex 7 pages, 2 eps figures include

On the High-dimensional Bak-Sneppen model

We report on extensive numerical simulations on the Bak-Sneppen model in high dimensions. We uncover a very rich behavior as a function of dimensionality. For d>2 the avalanche cluster becomes fractal and for d \ge 4 the process becomes transient. Finally the exponents reach their mean field values for d=d_c=8, which is then the upper critical dimension of the Bak Sneppen model.Comment: 4 pages, 3 eps figure

Universality and Crossover of Directed Polymers and Growing Surfaces

We study KPZ surfaces on Euclidean lattices and directed polymers on hierarchical lattices subject to different distributions of disorder, showing that universality holds, at odds with recent results on Euclidean lattices. Moreover, we find the presence of a slow (power-law) crossover toward the universal values of the exponents and verify that the exponent governing such crossover is universal too. In the limit of a 1+epsilon dimensional system we obtain both numerically and analytically that the crossover exponent is 1/2.Comment: LateX file + 5 .eps figures; to appear on Phys. Rev. Let

Critical exponents of the anisotropic Bak-Sneppen model

We analyze the behavior of spatially anisotropic Bak-Sneppen model. We demonstrate that a nontrivial relation between critical exponents tau and mu=d/D, recently derived for the isotropic Bak-Sneppen model, holds for its anisotropic version as well. For one-dimensional anisotropic Bak-Sneppen model we derive a novel exact equation for the distribution of avalanche spatial sizes, and extract the value gamma=2 for one of the critical exponents of the model. Other critical exponents are then determined from previously known exponent relations. Our results are in excellent agreement with Monte Carlo simulations of the model as well as with direct numerical integration of the new equation.Comment: 8 pages, three figures included with psfig, some rewriting, + extra figure and table of exponent

Expansion Around the Mean-Field Solution of the Bak-Sneppen Model

We study a recently proposed equation for the avalanche distribution in the Bak-Sneppen model. We demonstrate that this equation indirectly relates $\tau$,the exponent for the power law distribution of avalanche sizes, to $D$, the fractal dimension of an avalanche cluster.We compute this relation numerically and approximate it analytically up to the second order of expansion around the mean field exponents. Our results are consistent with Monte Carlo simulations of Bak-Sneppen model in one and two dimensions.Comment: 5 pages, 2 ps-figures iclude

Constraints on primordial non-Gaussianity from WMAP7 and Luminous Red Galaxies power spectrum and forecast for future surveys

We place new constraints on the primordial local non-Gaussianity parameter f_NL using recent Cosmic Microwave Background anisotropy and galaxy clustering data. We model the galaxy power spectrum according to the halo model, accounting for a scale dependent bias correction proportional to f_NL/k^2. We first constrain f_NL in a full 13 parameters analysis that includes 5 parameters of the halo model and 7 cosmological parameters. Using the WMAP7 CMB data and the SDSS DR4 galaxy power spectrum, we find f_NL=171\pm+140 at 68% C.L. and -69<f_NL<+492 at 95% C.L.. We discuss the degeneracies between f_NL and other cosmological parameters. Including SN-Ia data and priors on H_0 from Hubble Space Telescope observations we find a stronger bound: -35<f_NL<+479 at 95% C.L.. We also fit the more recent SDSS DR7 halo power spectrum data finding, for a \Lambda-CDM+f_NL model, f_NL=-93\pm128 at 68% C.L. and -327<f_{NL}<+177 at 95% C.L.. We finally forecast the constraints on f_NL from future surveys as EUCLID and from CMB missions as Planck showing that their combined analysis could detect f_NL\sim 5.Comment: 10 pages, 5 figures, 3 table

Clarification of the Bootstrap Percolation Paradox

We study the onset of the bootstrap percolation transition as a model of generalized dynamical arrest. We develop a new importance-sampling procedure in simulation, based on rare events around "holes", that enables us to access bootstrap lengths beyond those previously studied. By framing a new theory in terms of paths or processes that lead to emptying of the lattice we are able to develop systematic corrections to the existing theory, and compare them to simulations. Thereby, for the first time in the literature, it is possible to obtain credible comparisons between theory and simulation in the accessible density range.Comment: 4 pages with 3 figure

Variational collocation for systems of coupled anharmonic oscillators

We have applied a collocation approach to obtain the numerical solution to the stationary Schr\"odinger equation for systems of coupled oscillators. The dependence of the discretized Hamiltonian on scale and angle parameters is exploited to obtain optimal convergence to the exact results. A careful comparison with results taken from the literature is performed, showing the advantages of the present approach.Comment: 14 pages, 10 table