A stochastic model for the evolution of the Web

Recently several authors have proposed stochastic models of the growth of the Web graph that give rise to power-law distributions. These models are based on the notion of preferential attachment leading to the "rich get richer" phenomenon. However, these models fail to explain several distributions arising from empirical results, due to the fact that the predicted exponent is not consistent with the data. To address this problem, we extend the evolutionary model of the Web graph by including a non-preferential component, and we view the stochastic process in terms of an urn transfer model. By making this extension, we can now explain a wider variety of empirically discovered power-law distributions provided the exponent is greater than two. These include: the distribution of incoming links, the distribution of outgoing links, the distribution of pages in a Web site and the distribution of visitors to a Web site. A by-product of our results is a formal proof of the convergence of the standard stochastic model (first proposed by Simon)

Aspherical gravitational monopoles

We show how to construct non-spherically-symmetric extended bodies of uniform density behaving exactly as pointlike masses. These ``gravitational monopoles'' have the following equivalent properties: (i) they generate, outside them, a spherically-symmetric gravitational potential $M/|x - x_O|$; (ii) their interaction energy with an external gravitational potential $U(x)$ is $- M U(x_O)$; and (iii) all their multipole moments (of order $l \geq 1$) with respect to their center of mass $O$ vanish identically. The method applies for any number of space dimensions. The free parameters entering the construction are: (1) an arbitrary surface $\Sigma$ bounding a connected open subset $\Omega$ of $R^3$; (2) the arbitrary choice of the center of mass $O$ within $\Omega$; and (3) the total volume of the body. An extension of the method allows one to construct homogeneous bodies which are gravitationally equivalent (in the sense of having exactly the same multipole moments) to any given body.Comment: 55 pages, Latex , submitted to Nucl.Phys.

Nonlocality in kinetic roughening

We propose a phenomenological equation to describe kinetic roughening of a growing surface in presence of long range interactions. The roughness of the evolving surface depends on the long range feature, and several distinct scenarios of phase transitions are possible. Experimental implications are discussed.Comment: Replaced with the published version (Phys. Rev. Lett 79, 2502 (1997)). Eq. 1 written in a symmetrical form, references update

Flame front propagation I: The Geometry of Developing Flame Fronts: Analysis with Pole Decomposition

The roughening of expanding flame fronts by the accretion of cusp-like singularities is a fascinating example of the interplay between instability, noise and nonlinear dynamics that is reminiscent of self-fractalization in Laplacian growth patterns. The nonlinear integro-differential equation that describes the dynamics of expanding flame fronts is amenable to analytic investigations using pole decomposition. This powerful technique allows the development of a satisfactory understanding of the qualitative and some quantitative aspects of the complex geometry that develops in expanding flame fronts.Comment: 4 pages, 2 figure

Web dynamics

The global usage and continuing exponential growth of the World Wide Web poses a host of challenges to the research community. In particular, there is an urgent need to understand and manage the dynamics of the Web, in order to develop new techniques that will make the Web tractable. MARK LEVENE and ALEXANDRA POULOVASSILIS provide an overview of recent statistics relating to the size of the Web graph and its growth. They then briefly review some of the key areas relating to Web dynamics with reference to the recent literature. Finally, they summarise the talks given in a recent workshop devoted to Web dynamics, which was held in the beginning of January 2001 at the University of London

Web dynamics

The global usage and continuing exponential growth of the World Wide Web poses a host of challenges to the research community. In particular, there is an urgent need to understand and manage the dynamics of the Web, in order to develop new techniques that will make the Web tractable. MARK LEVENE and ALEXANDRA POULOVASSILIS provide an overview of recent statistics relating to the size of the Web graph and its growth. They then briefly review some of the key areas relating to Web dynamics with reference to the recent literature. Finally, they summarise the talks given in a recent workshop devoted to Web dynamics, which was held in the beginning of January 2001 at the University of London