The effect of bandwidth in scale-free network traffic

We model information traffic on scale-free networks by introducing the bandwidth as the delivering ability of links. We focus on the effects of bandwidth on the packet delivering ability of the traffic system to better understand traffic dynamic in real network systems. Such ability can be measured by a phase transition from free flow to congestion. Two cases of node capacity C are considered, i.e., C=constant and C is proportional to the node's degree. We figured out the decrease of the handling ability of the system together with the movement of the optimal local routing coefficient $\alpha_c$, induced by the restriction of bandwidth. Interestingly, for low bandwidth, the same optimal value of $\alpha_c$ emerges for both cases of node capacity. We investigate the number of packets of each node in the free flow state and provide analytical explanations for the optimal value of $\alpha_c$. Average packets traveling time is also studied. Our study may be useful for evaluating the overall efficiency of networked traffic systems, and for allevating traffic jam in such systems.Comment: 6 pages, 4 figure

Support and injective resolutions of complexes over commutative rings

Examples are given to show that the support of a complex of modules over a commutative noetherian ring may not be read off the minimal semi-injective resolution of the complex. The same examples also show that a localization of a semi-injective complex need not be semi-injective.Comment: 5 pages; major revisions; to appear in Homology, Homotopy and application

Matrix product state representation of non-Abelian quasiholes

We provide a detailed explanation of the formalism necessary to construct matrix product states for non-Abelian quasiholes in fractional quantum Hall model states. Our construction yields an efficient representation of the wave functions with conformal-block normalization and monodromy, and complements the matrix product state representation of fractional quantum Hall ground states.Comment: 14 pages, 2 figures; published versio

Notes on nonabelian (0,2) theories and dualities

In this paper we explore basic aspects of nonabelian (0,2) GLSM's in two dimensions for unitary gauge groups, an arena that until recently has largely been unexplored. We begin by discussing general aspects of (0,2) theories, including checks of dynamical supersymmetry breaking, spectators and weak coupling limits, and also build some toy models of (0,2) theories for bundles on Grassmannians, which gives us an opportunity to relate physical anomalies and trace conditions to mathematical properties. We apply these ideas to study (0,2) theories on Pfaffians, applying recent perturbative constructions of Pfaffians of Jockers et al. We discuss how existing dualities in (2,2) nonabelian gauge theories have a simple mathematical understanding, and make predictions for additional dualities in (2,2) and (0,2) gauge theories. Finally, we outline how duality works in open strings in unitary gauge theories, and also describe why, in general terms, we expect analogous dualities in (0,2) theories to be comparatively rare.Comment: 93 pages, LaTeX; v2: typos fixe

Novelty and Collective Attention

The subject of collective attention is central to an information age where millions of people are inundated with daily messages. It is thus of interest to understand how attention to novel items propagates and eventually fades among large populations. We have analyzed the dynamics of collective attention among one million users of an interactive website -- \texttt{digg.com} -- devoted to thousands of novel news stories. The observations can be described by a dynamical model characterized by a single novelty factor. Our measurements indicate that novelty within groups decays with a stretched-exponential law, suggesting the existence of a natural time scale over which attention fades

Gradient design of metal hollow sphere (MHS) foams with density gradients

This is the post-print version of the final paper published in Composites Part B: Engineering. The published article is available from the link below. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. Copyright @ 2011 Elsevier B.V.Metal hollow sphere (MHS) structures with a density gradient have attracted increasing attention in the effort to pursue improved energy absorption properties. In this paper, dynamic crushing of MHS structures of different gradients are discussed, with the gradients being received by stacks of hollow spheres of the same external diameter but different wall thicknesses in the crushing direction. Based on the dynamic performance of MHS structures with uniform density, a crude semi-empirical model is developed for the design of MHS structures in terms of gradient selections for energy absorption and protection against impact. Following this, dynamic responses of density graded MHS foams are comparatively analyzed using explicit finite element simulation and the proposed formula. Results show that the simple semi-empirical model can predict the response of density gradient MHS foams and is ready-to-use in the gradient design of MHS structures.The National Science Foundation of China and the State Key Laboratory of Explosion Science and Technology (Beijing Institute of Technology