Exact Solution of Random Graphs for Cluster Fragmentation

Exact Solution and Multifractal Analysis of a Multivariable Fragmentation Model

Most theoretical kinetic approaches proposed so far to describe fragmentation processes rely on the assumption that the fragments can be characterized by a unique relevant variable, for example their size or mass h. We investigate the consequences of introducing additional variables by considering a fragmentation model in which the fragments are described by two internal variables, h, w, and a ...

Exact solution for single-scale Gaussian random transport.

A quadrature expression is derived for the probability density function of passive tracers advected from a point by a one-dimensional, single-scale, Gaussian velocity field. The effect of trapping on the tracer moments and the Lagrangian velocity variance is explicitly demonstrated.

Vertex-cover in random graphs with small connectivity: an exact solution

We consider the vertex-cover problem on a finite-connectivity random graph with N vertices and connectivity c. For c smaller than 1/e, we prove that the cardinality of the minimal vertex cover is given by [1 W(c)(2 + W(c))/ 2 c] N + o(N), where W is the Lambert W function, as obtained by Hartmann and Weigt, [1], using the replica approach. The result is obtained in a very simple way and it is b...

Large Deviations and Exact Asymptotics for Constrained Exponential Random Graphs

Horizontal visibility graphs: exact results for random time series.

The visibility algorithm has been recently introduced as a mapping between time series and complex networks. This procedure allows us to apply methods of complex network theory for characterizing time series. In this work we present the horizontal visibility algorithm, a geometrically simpler and analytically solvable version of our former algorithm, focusing on the mapping of random series (se...