Statistical Analysis of Genealogical Trees for Polygamic Species

Repetitions within a given genealogical tree provides some information about the degree of consanguineity of a population. They can be analyzed with techniques usually employed in statistical physics when dealing with fixed point transformations. In particular we show that the tree features strongly depend on the fractions of males and females in the population, and also on the offspring probability distribution. We check different possibilities, some of them relevant to human groups, and compare them with simulations.Comment: 2 eps figs, Fig.2 changed to meet cond-mat size criteri

Levy-Nearest-Neighbors Bak-Sneppen Model

We study a random neighbor version of the Bak-Sneppen model, where "nearest neighbors" are chosen according to a probability distribution decaying as a power-law of the distance from the active site, P(x) \sim |x-x_{ac }|^{-\omega}. All the exponents characterizing the self-organized critical state of this model depend on the exponent \omega. As \omega tends to 1 we recover the usual random nearest neighbor version of the model. The pattern of results obtained for a range of values of \omega is also compatible with the results of simulations of the original BS model in high dimensions. Moreover, our results suggest a critical dimension d_c=6 for the Bak-Sneppen model, in contrast with previous claims.Comment: To appear on Phys. Rev. E, Rapid Communication

Extended navigability of small world networks: exact results and new insights

Navigability of networks, that is the ability to find any given destination vertex starting from any other vertex, is crucial to their usefulness. In 2000 Kleinberg showed that optimal navigability could be achieved in small-world networks provided that a special recipe was used to establish long range connections, and that a greedy algorithm, that ensures that the destination will be reached, is used. Here we provide an exact solution for the asymptotic behavior of such a greedy algorithm as a function of the system's parameters. Our solution enables us to show that the original claim that only a very special construction is optimal can be relaxed depending on further criteria, such as, for example, cost minimization, that must be satisfied.Comment: Presented at the BCNet Workshop in Barcelona on December 12 2008; submitted to PR

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

Reconstructing Orbits of Galaxies in Extreme Regions (ROGER) III: galaxy evolution patterns in projected phase space around massive X-ray clusters

We use the ROGER code by de los Rios et al. to classify galaxies around a sample of X-ray clusters into five classes according to their positions in the projected phase space diagram: cluster galaxies, backsplash galaxies, recent infallers, infalling galaxies, and interlopers. To understand the effects of the cluster environment to the evolution of galaxies, we compare across the five classes: stellar mass, specific star formation rate, size, and morphology. Following the guidelines of Coenda et al., a separate analysis is carried out for red and blue galaxies. For red galaxies, cluster galaxies differ from the other classes, having a suppressed specific star formation rate, smaller sizes, and are more likely to be classified as ellipticals. Differences are smaller between the other classes, however backsplash galaxies have significantly lower specific star formation rates than early or recent infalling galaxies. For blue galaxies, we find evidence that recent infallers are smaller than infalling galaxies and interlopers, while the latter two are comparable in size. Our results provide evidence that, after a single passage, the cluster environment can diminish a galaxy's star formation, modify its morphology, and can also reduce in size blue galaxies. We find evidence that quenching occurs faster than morphological transformation from spirals to ellipticals for all classes. While quenching is evidently enhanced as soon as galaxies get into clusters, significant morphological transformations require galaxies to experience the action of the physical mechanisms of the cluster for longer timescales.Comment: Accepted in MNRAS, 11 pages, 7 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

The Anisotropic Bak-Sneppen model

The Bak-Sneppen model is shown to fall into a different universality class with the introduction of a preferred direction, mirroring the situation in spin systems. This is first demonstrated by numerical simulations and subsequently confirmed by analysis of the multitrait version of the model, which admits exact solutions in the extremes of zero and maximal anisotropy. For intermediate anisotropies, we show that the spatiotemporal evolution of the avalanche has a power law `tail' which passes through the system for any non-zero anisotropy but remains fixed for the isotropic case, thus explaining the crossover in behaviour. Finally, we identify the maximally anisotropic model which is more tractable and yet more generally applicable than the isotropic system

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

Bethe approximation for self-interacting lattice trees

In this paper we develop a Bethe approximation, based on the cluster variation method, which is apt to study lattice models of branched polymers. We show that the method is extremely accurate in cases where exact results are known as, for instance, in the enumeration of spanning trees. Moreover, the expressions we obtain for the asymptotic number of spanning trees and lattice trees on a graph coincide with analogous expressions derived through different approaches. We study the phase diagram of lattice trees with nearest-neighbour attraction and branching energies. We find a collapse transition at a tricritical theta point, which separates an expanded phase from a compact phase. We compare our results for the theta transition in two and three dimensions with available numerical estimates.Comment: 10 pages, 3 figures, to be published in Europhysics Letter