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Roukny T.,IRIDIA | Roukny T.,Sbs Em Center rnheim | Bersini H.,IRIDIA | Pirotte H.,Sbs Em Center rnheim | And 2 more authors.
Scientific Reports | Year: 2013

The recent crisis has brought to the fore a crucial question that remains still open: what would be the optimal architecture of financial systems? We investigate the stability of several benchmark topologies in a simple default cascading dynamics in bank networks. We analyze the interplay of several crucial drivers, i.e., network topology, banks' capital ratios, market illiquidity, and random vs targeted shocks. We find that, in general, topology matters only-but substantially-when the market is illiquid. No single topology is always superior to others. In particular, scale-free networks can be both more robust and more fragile than homogeneous architectures. This finding has important policy implications. We also apply our methodology to a comprehensive dataset of an interbank market from 1999 to 2011.

Farr R.S.,Unilever | Farr R.S.,London Institute for Mathematical science | Griffiths E.,297 Sandy Bay Road
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics | Year: 2010

We adapt a recent theory for the random close packing of polydisperse spheres in three dimensions in order to predict the Hausdorff dimension dA of the Apollonian gasket in dimensions 2 and above. Our approximate results agree with published values in two and three dimensions to within 0.05% and 0.6%, respectively, and we provide predictions for dimensions 4-8. © 2010 The American Physical Society.

Farr R.S.,London Institute for Mathematical science | Farr R.S.,Colworth Science Park | Harer J.L.,Duke University | Fink T.M.A.,London Institute for Mathematical science | Fink T.M.A.,French National Center for Scientific Research
Physical Review Letters | Year: 2014

We introduce a simple class of distribution networks that withstand damage by being repairable instead of redundant. Instead of asking how hard it is to disconnect nodes through damage, we ask how easy it is to reconnect nodes after damage. We prove that optimal networks on regular lattices have an expected cost of reconnection proportional to the lattice length, and that such networks have exactly three levels of structural hierarchy. We extend our results to networks subject to repeated attacks, in which the repairs themselves must be repairable. We find that, in exchange for a modest increase in repair cost, such networks are able to withstand any number of attacks. © 2014 American Physical Society.

Rayneau-Kirkhope D.,University of Nottingham | Rayneau-Kirkhope D.,Aalto University | Mao Y.,University of Nottingham | Farr R.,Unilever | Farr R.,London Institute for Mathematical science
Physical Review Letters | Year: 2012

A fractal design is shown to be highly efficient both as a load bearing structure and as a general metamaterial. Through changing the hierarchical order of the structure, the scaling of material required for stability against loading can be manipulated. We show that the transition from solid to hollow beams changes the scaling in a manner analogous to increasing the hierarchical order by one. An example second order solid beam frame is constructed using rapid prototyping techniques. The optimal hierarchical order of the structure is found for different values of loading. Possible fabrication methods and applications are then discussed. © 2012 American Physical Society.

Coolen A.C.C.,Kings College London | Coolen A.C.C.,London Institute for Mathematical science | Takeda K.,Tokyo Institute of Technology
Philosophical Magazine | Year: 2012

We study the synchronous stochastic dynamics of the random field and random bond Ising chain. For this model the generating functional analysis method of De Dominicis leads to a formalism with transfer operators, similar to transfer matrices in equilibrium studies, but with dynamical paths of spins and (conjugate) fields as arguments, as opposed to replicated spins. In the thermodynamic limit the macroscopic dynamics is captured by the dominant eigenspace of the transfer operator, leading to a relatively simple and transparent set of equations that are easy to solve numerically. Our results are supported excellently by numerical simulations. © 2012 Copyright Taylor and Francis Group, LLC.

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