Comment on: Kinetic Roughening in Slow Combustion of Paper

We comment on a recent Letter by Maunuksela et al. [Phys. Rev. Lett. 79, 1515 (1997)].Comment: 1 page, 1 figure, http://polymer.bu.edu/~hmakse/Home.htm

Ising Model on Edge-Dual of Random Networks

We consider Ising model on edge-dual of uncorrelated random networks with arbitrary degree distribution. These networks have a finite clustering in the thermodynamic limit. High and low temperature expansions of Ising model on the edge-dual of random networks are derived. A detailed comparison of the critical behavior of Ising model on scale free random networks and their edge-dual is presented.Comment: 23 pages, 4 figures, 1 tabl

Detection of node group membership in networks with group overlap

Most networks found in social and biochemical systems have modular structures. An important question prompted by the modularity of these networks is whether nodes can be said to belong to a single group. If they cannot, we would need to consider the role of "overlapping communities." Despite some efforts in this direction, the problem of detecting overlapping groups remains unsolved because there is neither a formal definition of overlapping community, nor an ensemble of networks with which to test the performance of group detection algorithms when nodes can belong to more than one group. Here, we introduce an ensemble of networks with overlapping groups. We then apply three group identification methods--modularity maximization, k-clique percolation, and modularity-landscape surveying--to these networks. We find that the modularity-landscape surveying method is the only one able to detect heterogeneities in node memberships, and that those heterogeneities are only detectable when the overlap is small. Surprisingly, we find that the k-clique percolation method is unable to detect node membership for the overlapping case.Comment: 12 pages, 6 figures. To appear in Euro. Phys. J

Canonical Transformations in a Higher-Derivative Field Theory

It has been suggested that the chiral symmetry can be implemented only in classical Lagrangians containing higher covariant derivatives of odd order. Contrary to this belief, it is shown that one can construct an exactly soluble two-dimensional higher-derivative fermionic quantum field theory containing only derivatives of even order whose classical Lagrangian exhibits chiral-gauge invariance. The original field solution is expressed in terms of usual Dirac spinors through a canonical transformation, whose generating function allows the determination of the new Hamiltonian. It is emphasized that the original and transformed Hamiltonians are different because the mapping from the old to the new canonical variables depends explicitly on time. The violation of cluster decomposition is discussed and the general Wightman functions satisfying the positive-definiteness condition are obtained.Comment: 12 pages, LaTe