How self-organized networks develop, mature and degenerate is a key question for sociotechnical, cyberphysical and biological systems with potential applications from tackling violent extremism through to neurological diseases. So far, it has proved impossible to measure the continuous-time...

We are able to unify various disparate claims and results in the literature, that stand in the way of a unified description and understanding of human conflict. First, we provide a reconciliation of the numerically different power-law exponent values for fatality distributions across entire wars...

The problem of finding the most efficient way to pack spheres has an illustrious history, dating back to the crystalline arrays conjectured by Kepler and the random geometries explored by Bernal in the 1960s. This problem finds applications spanning from the mathematician’s pencil, the...

We study the joint probability distribution of normal and tangential frictional forces in jammed granular media, Pμ(ft,fn), for various values of the friction coefficient μ, especially when μ=∞. A universal scaling law is found to collapse the data for μ=0 to ∞, demonstrating a link...

We review recent findings of self-similarity in complex networks. Using the box-covering technique, it was shown that many networks present a fractal behavior, which is seemingly in contrast to their small-world property. Moreover, even non-fractal networks have been shown to present a...

The nature of randomness in disordered packings of frictional and frictionless spheres is investigated using theory and simulations of identical spherical grains. The entropy of the packings is defined through the force and volume ensemble of jammed matter and this is shown to be difficult to...

We introduce a “Hamiltonian”-like function, called the volume function, indispensable to describe the ensemble of jammed matter such as granular materials and emulsions from a geometrical point of view. The volume function represents the available volume of each particle in the jammed...

We investigate the existence of random close and random loose packing limits in two-dimensional packings of monodisperse hard disks. A statistical mechanics approach–based on several approximations to predict the probability distribution of volumes–suggests the existence of the limiting...