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

Inverse Cubic Law for the Probability Distribution of Stock Price Variations

The probability distribution of stock price changes is studied by analyzing a database (the Trades and Quotes Database) documenting every trade for all stocks in three major US stock markets, for the two year period Jan 1994 -- Dec 1995. A sample of 40 million data points is extracted, which is substantially larger than studied hitherto. We find an asymptotic power-law behavior for the cumulative distribution with an exponent alpha approximately 3, well outside the Levy regime 0< alpha <2.Comment: 5 pages, 4 figures, RevTex 2 figures adde

Topological Properties of Citation and Metabolic Networks

Topological properties of "scale-free" networks are investigated by determining their spectral dimensions $d_S$, which reflect a diffusion process in the corresponding graphs. Data bases for citation networks and metabolic networks together with simulation results from the growing network model \cite{barab} are probed. For completeness and comparisons lattice, random, small-world models are also investigated. We find that $d_S$ is around 3 for citation and metabolic networks, which is significantly different from the growing network model, for which $d_S$ is approximately 7.5. This signals a substantial difference in network topology despite the observed similarities in vertex order distributions. In addition, the diffusion analysis indicates that whereas the citation networks are tree-like in structure, the metabolic networks contain many loops.Comment: 11 pages, 3 figure

Scaling Behavior of Driven Interfaces Above the Depinning Transition

We study the depinning transition for models representative of each of the two universality classes of interface roughening with quenched disorder. For one of the universality classes, the roughness exponent changes value at the transition, while the dynamical exponent remains unchanged. We also find that the prefactor of the width scales with the driving force. We propose several scaling relations connecting the values of the exponents on both sides of the transition, and discuss some experimental results in light of these findings.Comment: Revtex 3.0, 4 pages in PRL format + 5 figures (available at ftp://jhilad.bu.edu/pub/abbhhss/ma-figures.tar.Z ) submitted to Phys Rev Let

Dynamics of Surface Roughening with Quenched Disorder

We study the dynamical exponent $z$ for the directed percolation depinning (DPD) class of models for surface roughening in the presence of quenched disorder. We argue that $z$ for $(d+1)$ dimensions is equal to the exponent $d_{\rm min}$ characterizing the shortest path between two sites in an isotropic percolation cluster in $d$ dimensions. To test the argument, we perform simulations and calculate $z$ for DPD, and $d_{\rm min}$ for percolation, from $d = 1$ to $d = 6$.Comment: RevTex manuscript 3 pages + 6 figures (obtained upon request via email [email protected]