Interfaces (and Regional Congruence?) in Spin Glasses

We present a general theorem restricting properties of interfaces between thermodynamic states and apply it to the spin glass excitations observed numerically by Krzakala-Martin and Palassini-Young in spatial dimensions d=3 and 4. We show that such excitations, with interface dimension smaller than d, cannot yield regionally congruent thermodynamic states. More generally, zero density interfaces of translation-covariant excitations cannot be pinned (by the disorder) in any d but rather must deflect to infinity in the thermodynamic limit. Additional consequences concerning regional congruence in spin glasses and other systems are discussed.Comment: 4 pages (ReVTeX); 1 figure; submitted to Physical Review Letter

The Algebra of Strand Splitting. I. A Braided Version of Thompson's Group V

We construct a braided version of Thompson's group V.Comment: 27 page

The first-mover advantage in scientific publication

Mathematical models of the scientific citation process predict a strong "first-mover" effect under which the first papers in a field will, essentially regardless of content, receive citations at a rate enormously higher than papers published later. Moreover papers are expected to retain this advantage in perpetuity -- they should receive more citations indefinitely, no matter how many other papers are published after them. We test this conjecture against data from a selection of fields and in several cases find a first-mover effect of a magnitude similar to that predicted by the theory. Were we wearing our cynical hat today, we might say that the scientist who wants to become famous is better off -- by a wide margin -- writing a modest paper in next year's hottest field than an outstanding paper in this year's. On the other hand, there are some papers, albeit only a small fraction, that buck the trend and attract significantly more citations than theory predicts despite having relatively late publication dates. We suggest that papers of this kind, though they often receive comparatively few citations overall, are probably worthy of our attention.Comment: 7 pages, 3 figure

Realistic spin glasses below eight dimensions: a highly disordered view

By connecting realistic spin glass models at low temperature to the highly disordered model at zero temperature, we argue that ordinary Edwards-Anderson spin glasses below eight dimensions have at most a single pair of physically relevant pure states at nonzero low temperature. Less likely scenarios that evade this conclusion are also discussed.Comment: 18 pages (RevTeX; 1 figure; to appear in Physical Review E

Characterizing the structure of small-world networks

We give exact relations which are valid for small-world networks (SWN's) with a general `degree distribution', i.e the distribution of nearest-neighbor connections. For the original SWN model, we illustrate how these exact relations can be used to obtain approximations for the corresponding basic probability distribution. In the limit of large system sizes and small disorder, we use numerical studies to obtain a functional fit for this distribution. Finally, we obtain the scaling properties for the mean-square displacement of a random walker, which are determined by the scaling behavior of the underlying SWN

Clustering and preferential attachment in growing networks

We study empirically the time evolution of scientific collaboration networks in physics and biology. In these networks, two scientists are considered connected if they have coauthored one or more papers together. We show that the probability of scientists collaborating increases with the number of other collaborators they have in common, and that the probability of a particular scientist acquiring new collaborators increases with the number of his or her past collaborators. These results provide experimental evidence in favor of previously conjectured mechanisms for clustering and power-law degree distributions in networks.Comment: 13 pages, 2 figure

Mean-field solution of the small-world network model

The small-world network model is a simple model of the structure of social networks, which simultaneously possesses characteristics of both regular lattices and random graphs. The model consists of a one-dimensional lattice with a low density of shortcuts added between randomly selected pairs of points. These shortcuts greatly reduce the typical path length between any two points on the lattice. We present a mean-field solution for the average path length and for the distribution of path lengths in the model. This solution is exact in the limit of large system size and either large or small number of shortcuts.Comment: 14 pages, 2 postscript 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

A statistical network analysis of the HIV/AIDS epidemics in Cuba

The Cuban contact-tracing detection system set up in 1986 allowed the reconstruction and analysis of the sexual network underlying the epidemic (5,389 vertices and 4,073 edges, giant component of 2,386 nodes and 3,168 edges), shedding light onto the spread of HIV and the role of contact-tracing. Clustering based on modularity optimization provides a better visualization and understanding of the network, in combination with the study of covariates. The graph has a globally low but heterogeneous density, with clusters of high intraconnectivity but low interconnectivity. Though descriptive, our results pave the way for incorporating structure when studying stochastic SIR epidemics spreading on social networks

Matching Kasteleyn Cities for Spin Glass Ground States

As spin glass materials have extremely slow dynamics, devious numerical methods are needed to study low-temperature states. A simple and fast optimization version of the classical Kasteleyn treatment of the Ising model is described and applied to two-dimensional Ising spin glasses. The algorithm combines the Pfaffian and matching approaches to directly strip droplet excitations from an excited state. Extended ground states in Ising spin glasses on a torus, which are optimized over all boundary conditions, are used to compute precise values for ground state energy densities.Comment: 4 pages, 2 figures; minor clarification