title: Generalised Sandpile Dynamics on Artificial and Real-World Directed Networks.
abstract: The main finding of this paper is a novel avalanche-size exponent τ ≈ 1.87 when the generalised sandpile dynamics evolves on the real-world Japanese inter-firm network. The topology of this network is non-layered and directed, displaying the typical bow tie structure found in real-world directed networks, with cycles and triangles. We show that one can move from a strictly layered regular lattice to a more fluid structure of the inter-firm network in a few simple steps. Relaxing the regular lattice structure by introducing an interlayer distribution for the interactions, forces the scaling exponent of the avalanche-size probability density function τ out of the two-dimensional directed sandpile universality class τ = 4/3, into the mean field universality class τ = 3/2. Numerical investigation shows that these two classes are the only that exist on the directed sandpile, regardless of the underlying topology, as long as it is strictly layered. Randomly adding a small proportion of links connecting non adjacent layers in an otherwise layered network takes the system out of the mean field regime to produce non-trivial avalanche-size probability density function. Although these do not display proper scaling, they closely reproduce the behaviour observed on the Japanese inter-firm network.
authors.affiliation: Department of Physics, Blackett Laboratory, Imperial College London, Prince Consort Road, South Kensington Campus, London SW7 2AZ, United Kingdom.|Centre for Complexity Science, Electrical & Electronic Engineering Building, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom.
authors.forename: Nicky
authors.initials: N
authors.lastname: Zachariou
authors.affiliation: Department of Physics, Blackett Laboratory, Imperial College London, Prince Consort Road, South Kensington Campus, London SW7 2AZ, United Kingdom.|Centre for Complexity Science, Electrical & Electronic Engineering Building, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom.|Centre for Neuroimaging Sciences, Institute of Psychiatry, Psychology and Neuroscience, De Crespigny Park, King's College London, London SE5 8AF, United Kingdom.
authors.forename: Paul
authors.initials: P
authors.lastname: Expert
authors.affiliation: Department of Computational Intelligence and Systems Science, Interdisciplinary Graduate School of Science and Engineering, Tokyo Institute of Technology, 4259 Nagatsuta-cho, Midori-ku, Yokohama 226-8502, Japan.
authors.forename: Misako
authors.initials: M
authors.lastname: Takayasu
authors.affiliation: Department of Physics, Blackett Laboratory, Imperial College London, Prince Consort Road, South Kensington Campus, London SW7 2AZ, United Kingdom.|Centre for Complexity Science, Electrical & Electronic Engineering Building, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom.
authors.forename: Kim
authors.initials: K
authors.lastname: Christensen
mesh_terms: D003132:Commerce / Q000706:statistics & numerical data*; D003198:Computer Simulation; D060909:Economics, Behavioral / Q000706:statistics & numerical data*; D006801:Humans; D007564:Japan; D018803:Models, Economic; D011336:Probability