Dynamics of Rumor Spreading in Complex Networks

We derive the mean-field equations characterizing the dynamics of a rumor process that takes place on top of complex heterogeneous networks. These equations are solved numerically by means of a stochastic approach. First, we present analytical and Monte Carlo calculations for homogeneous networks and compare the results with those obtained by the numerical method. Then, we study the spreading process in detail for random scale-free networks. The time profiles for several quantities are numerically computed, which allow us to distinguish among different variants of rumor spreading algorithms. Our conclusions are directed to possible applications in replicated database maintenance, peer to peer communication networks and social spreading phenomena.Comment: Final version to appear in PR

Ice Age Epochs and the Sun's Path Through the Galaxy

We present a calculation of the Sun's motion through the Milky Way Galaxy over the last 500 million years. The integration is based upon estimates of the Sun's current position and speed from measurements with Hipparcos and upon a realistic model for the Galactic gravitational potential. We estimate the times of the Sun's past spiral arm crossings for a range in assumed values of the spiral pattern angular speed. We find that for a difference between the mean solar and pattern speed of Omega_Sun - Omega_p = 11.9 +/- 0.7 km/s/kpc the Sun has traversed four spiral arms at times that appear to correspond well with long duration cold periods on Earth. This supports the idea that extended exposure to the higher cosmic ray flux associated with spiral arms can lead to increased cloud cover and long ice age epochs on Earth.Comment: 14 pages, 3 figures, accepted for publication in Ap

Random Networks with Tunable Degree Distribution and Clustering

We present an algorithm for generating random networks with arbitrary degree distribution and Clustering (frequency of triadic closure). We use this algorithm to generate networks with exponential, power law, and poisson degree distributions with variable levels of clustering. Such networks may be used as models of social networks and as a testable null hypothesis about network structure. Finally, we explore the effects of clustering on the point of the phase transition where a giant component forms in a random network, and on the size of the giant component. Some analysis of these effects is presented.Comment: 9 pages, 13 figures corrected typos, added two references, reorganized reference

Matrix Assisted Formation of Ferrihydrite Nanoparticles in a Siloxane/Poly(Oxyethylene) Nanohybrid

Matrix-assisted formation of ferrihydrite, an iron oxide hydroxide analogue of the protein ferritin-core, in a sol-gel derived organic-inorganic hybrid is reported. The hybrid network (named di-ureasil) is composed of poly(oxyethylene) chains of different average polymer molecular weights grafted to siloxane domains by means of urea cross-linkages and accommodates ferrihydrite nanoparticles. Magnetic measurements, Fourier transform infrared and nuclear magnetic resonance spectroscopy reveal that the controlled modification of the polymer molecular weight allows the fine-tuning of the ability of the hybrid matrix to assist and promote iron coordination at the organic-inorganic interface and subsequent nucleation and growth of the ferrihydrite nanoparticles whose core size (2-4 nm) is tuned by the amount of iron incorporated. The polymer chain length, its arrangement and crystallinity, are key factors on the anchoring and formation of the ferrihydrite particles.Comment: 7 pages, 6 figures. To be published in J. Mater. Che

Vortex core size in interacting cylindrical nanodot arrays

The effect of dipolar interactions among cylindrical nanodots, with a vortex-core magnetic configuration, is analyzed by means of analytical calculations. The cylinders are placed in a N x N square array in two configurations - core oriented parallel to each other and with antiparallel alignment between nearest neighbors. Results comprise the variation in the core radius with the number of interacting dots, the distance between them and dot height. The dipolar interdot coupling leads to a decrease (increase) of the core radius for parallel (antiparallel) arrays

Cosmological perturbations in FRW model with scalar field within Hamilton-Jacobi formalism and symplectic projector method

The Hamilton-Jacobi analysis is applied to the dynamics of the scalar fluctuations about the Friedmann-Robertson-Walker (FRW). The gauge conditions are found from the consistency conditions. The physical degrees of freedom of the model are obtain by symplectic projector method. The role of the linearly dependent Hamiltonians and the gauge variables in Hamilton-Jacobi formalism is discussed.Comment: 11 page

Network Synchronization, Diffusion, and the Paradox of Heterogeneity

Many complex networks display strong heterogeneity in the degree (connectivity) distribution. Heterogeneity in the degree distribution often reduces the average distance between nodes but, paradoxically, may suppress synchronization in networks of oscillators coupled symmetrically with uniform coupling strength. Here we offer a solution to this apparent paradox. Our analysis is partially based on the identification of a diffusive process underlying the communication between oscillators and reveals a striking relation between this process and the condition for the linear stability of the synchronized states. We show that, for a given degree distribution, the maximum synchronizability is achieved when the network of couplings is weighted and directed, and the overall cost involved in the couplings is minimum. This enhanced synchronizability is solely determined by the mean degree and does not depend on the degree distribution and system size. Numerical verification of the main results is provided for representative classes of small-world and scale-free networks.Comment: Synchronization in Weighted Network

Analytical solution of a model for complex food webs

We investigate numerically and analytically a recently proposed model for food webs [Nature {\bf 404}, 180 (2000)] in the limit of large web sizes and sparse interaction matrices. We obtain analytical expressions for several quantities with ecological interest, in particular the probability distributions for the number of prey and the number of predators. We find that these distributions have fast-decaying exponential and Gaussian tails, respectively. We also find that our analytical expressions are robust to changes in the details of the model.Comment: 4 pages (RevTeX). Final versio