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

Gel Electrophoresis of DNA Knots in Weak and Strong Electric Fields

Gel electrophoresis allows to separate knotted DNA (nicked circular) of equal length according to the knot type. At low electric fields, complex knots being more compact, drift faster than simpler knots. Recent experiments have shown that the drift velocity dependence on the knot type is inverted when changing from low to high electric fields. We present a computer simulation on a lattice of a closed, knotted, charged DNA chain drifting in an external electric field in a topologically restricted medium. Using a simple Monte Carlo algorithm, the dependence of the electrophoretic migration of the DNA molecules on the type of knot and on the electric field intensity was investigated. The results are in qualitative agreement with electrophoretic experiments done under conditions of low and high electric fields: especially the inversion of the behavior from low to high electric field could be reproduced. The knot topology imposes on the problem the constrain of self-avoidance, which is the final cause of the observed behavior in strong electric field.Comment: 17 pages, 5 figure

Interfaces and the edge percolation map of random directed networks

The traditional node percolation map of directed networks is reanalyzed in terms of edges. In the percolated phase, edges can mainly organize into five distinct giant connected components, interfaces bridging the communication of nodes in the strongly connected component and those in the in- and out-components. Formal equations for the relative sizes in number of edges of these giant structures are derived for arbitrary joint degree distributions in the presence of local and two-point correlations. The uncorrelated null model is fully solved analytically and compared against simulations, finding an excellent agreement between the theoretical predictions and the edge percolation map of synthetically generated networks with exponential or scale-free in-degree distribution and exponential out-degree distribution. Interfaces, and their internal organization giving place from "hairy ball" percolation landscapes to bottleneck straits, could bring new light to the discussion of how structure is interwoven with functionality, in particular in flow networks.Comment: 20 pages, 4 figure

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

MIXED INCOME HOUSING, A REVITALIZATION PROJECT IN MEDELLIN,COLOMBIA

Settled in the Central branch of the Andes mountain chain, the city of Medellin (3 million inhabitants) has occupied most of the land available for urbanization. This pattern has led to the appropriation, use and development of topographically unstable slopes that often represent geological risks and little by little destroys one of the city's most valuable attributes: the beauty of its geographic location. In spite of the deterioration and the correspondent decline in the architectural landscape, downtown Medellin continues to be a vibrant market for both formal and informal commerce and services activities out of which numerous low-income families survive, not to mention its value as a historical urban setting where Medellin was founded and where the first commercial and governmental institutions shaped the city life. All this calls for an urban policy that creatively re-evaluates the growing possibilities of Medellin. Based on the frame summarized above, and following the basic guidelines of an existing partial plan for a deteriorated but historically valuable downtown area (area of intervention for this purpose), formulated by the Government of Medellin, I propose: First, to develop a schematic housing system that complies with the normative plan, critique it and decide whether it should be pursued or improved. Second, to design a mixed-income housing system that: Responds to the socio-economic characteristics of traditional inhabitants to the area while responding to the need for a functional mixture of housing, services and commercial activities. Help solve the existing housing deficit Connect the neighborhood to the urban fabri

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

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

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

Endocytic recycling via the TGN underlies the polarized hyphal mode of growth

Intracellular traffic in Aspergillus nidulans hyphae must cope with the challenges that the high rates of apical extension (1μm/min) and the long intracellular distances (>100 μm) impose. Understanding the ways in which the hyphal tip cell coordinates traffic to meet these challenges is of basic importance, but is also of considerable applied interest, as fungal invasiveness of animals and plants depends critically upon maintaining these high rates of growth. Rapid apical extension requires localization of cell-wall-modifying enzymes to hyphal tips. By combining genetic blocks in different trafficking steps with multidimensional epifluorescence microscopy and quantitative image analyses we demonstrate that polarization of the essential chitin-synthase ChsB occurs by indirect endocytic recycling, involving delivery/exocytosis to apices followed by internalization by the sub-apical endocytic collar of actin patches and subsequent trafficking to TGN cisternae, where it accumulates for ~1 min before being re-delivered to the apex by a RAB11/TRAPPII-dependent pathway. Accordingly, ChsB is stranded at the TGN by Sec7 inactivation but re-polarizes to the apical dome if the block is bypassed by a mutation in geaAgea1 that restores growth in the absence of Sec7. That polarization is independent of RAB5, that ChsB predominates at apex-proximal cisternae, and that upon dynein impairment ChsB is stalled at the tips in an aggregated endosome indicate that endocytosed ChsB traffics to the TGN via sorting endosomes functionally located upstream of the RAB5 domain and that this step requires dynein-mediated basipetal transport. It also requires RAB6 and its effector GARP (Vps51/Vps52/Vps53/Vps54), whose composition we determined by MS/MS following affinity chromatography purification. Ablation of any GARP component diverts ChsB to vacuoles and impairs growth and morphology markedly, emphasizing the important physiological role played by this pathway that, we propose, is central to the hyphal mode of growth