Interface Motion and Pinning in Small World Networks

We show that the nonequilibrium dynamics of systems with many interacting elements located on a small-world network can be much slower than on regular networks. As an example, we study the phase ordering dynamics of the Ising model on a Watts-Strogatz network, after a quench in the ferromagnetic phase at zero temperature. In one and two dimensions, small-world features produce dynamically frozen configurations, disordered at large length scales, analogous of random field models. This picture differs from the common knowledge (supported by equilibrium results) that ferromagnetic short-cuts connections favor order and uniformity. We briefly discuss some implications of these results regarding the dynamics of social changes.Comment: 4 pages, 5 figures with minor corrections. To appear in Phys. Rev.

Classical and Quantum Solitons in the Symmetric Space Sine-Gordon Theories

We construct the soliton solutions in the symmetric space sine-Gordon theories. The latter are a series of integrable field theories in 1+1-dimensions which are associated to a symmetric space F/G, and are related via the Pohlmeyer reduction to theories of strings moving on symmetric spaces. We show that the solitons are kinks that carry an internal moduli space that can be identified with a particular co-adjoint orbit of the unbroken subgroup H of G. Classically the solitons come in a continuous spectrum which encompasses the perturbative fluctuations of the theory as the kink charge becomes small. We show that the solitons can be quantized by allowing the collective coordinates to be time-dependent to yield a form of quantum mechanics on the co-adjoint orbit. The quantum states correspond to symmetric tensor representations of the symmetry group H and have the interpretation of a fuzzy geometric version of the co-adjoint orbit. The quantized finite tower of soliton states includes the perturbative modes at the base.Comment: 53 pages, additional comments and small errors corrected, final journal versio

Distribution of hammerhead and hammerhead-like RNA motifs through the GenBank

Hammerhead ribozymes previously were found in satellite RNAs from plant viroids and in repetitive DNA from certain species of newts and schistosomes. To determine if this catalytic RNA motif has a wider distribution, we decided to scrutinize the GenBank database for RNAs that contain hammerhead or hammerhead-like motifs. The search shows a widespread distribution of this kind of RNA motif in different sequences suggesting that they might have a more general role in RNA biology. The frequency of the hammerhead motif is half of that expected from a random distribution, but this fact comes From the low CpG representation in vertebrate sequences and the bias of the GenBank for those sequences. Intriguing motifs include those found in several families of repetitive sequences, in the satellite RNA from the carrot red leaf luteovirus, in plant viruses like the spinach latent virus and the elm mottle virus, in animal viruses like the hepatitis E virus and the caprine encephalitis virus, and in mRNAs such as those coding for cytochrome P450 oxidoreductase in the rat and the hamster

Phase transition in a stochastic prime number generator

We introduce a stochastic algorithm that acts as a prime number generator. The dynamics of such algorithm gives rise to a continuous phase transition which separates a phase where the algorithm is able to reduce a whole set of integers into primes and a phase where the system reaches a frozen state with low prime density. We present both numerical simulations and an analytical approach in terms of an annealed approximation, by means of which the data are collapsed. A critical slowing down phenomenon is also outlined.Comment: accepted in PRE (Rapid Comm.

Number theoretic example of scale-free topology inducing self-organized criticality

In this work we present a general mechanism by which simple dynamics running on networks become self-organized critical for scale free topologies. We illustrate this mechanism with a simple arithmetic model of division between integers, the division model. This is the simplest self-organized critical model advanced so far, and in this sense it may help to elucidate the mechanism of self-organization to criticality. Its simplicity allows analytical tractability, characterizing several scaling relations. Furthermore, its mathematical nature brings about interesting connections between statistical physics and number theoretical concepts. We show how this model can be understood as a self-organized stochastic process embedded on a network, where the onset of criticality is induced by the topology.Comment: 4 pages, 3 figures. Physical Review Letters, in pres

Fitting Ranked English and Spanish Letter Frequency Distribution in U.S. and Mexican Presidential Speeches

The limited range in its abscissa of ranked letter frequency distributions causes multiple functions to fit the observed distribution reasonably well. In order to critically compare various functions, we apply the statistical model selections on ten functions, using the texts of U.S. and Mexican presidential speeches in the last 1-2 centuries. Dispite minor switching of ranking order of certain letters during the temporal evolution for both datasets, the letter usage is generally stable. The best fitting function, judged by either least-square-error or by AIC/BIC model selection, is the Cocho/Beta function. We also use a novel method to discover clusters of letters by their observed-over-expected frequency ratios.Comment: 7 figure