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Coolen A.C.C.,King's 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.

Roberts E.S.,King's College London | Coolen A.C.C.,King's College London | Coolen A.C.C.,London Institute for Mathematical science
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics | Year: 2012

Randomizing networks using a naive "accept-all" edge-swap algorithm is generally biased. Building on recent results for nondirected graphs, we construct an ergodic detailed balance Markov chain with nontrivial acceptance probabilities for directed graphs, which converges to a strictly uniform measure and is based on edge swaps that conserve all in and out degrees. The acceptance probabilities can also be generalized to define Markov chains that target any alternative desired measure on the space of directed graphs in order to generate graphs with more sophisticated topological features. This is demonstrated by defining a process tailored to the production of directed graphs with specified degree-degree correlation functions. The theory is implemented numerically and tested on synthetic and biological network examples. © 2012 American Physical Society.

Mozeika A.,King's College London | Coolen A.C.C.,King's College London | Coolen A.C.C.,London Institute for Mathematical science
Journal of Physics A: Mathematical and Theoretical | Year: 2015

We study spin systems on Bethe lattices constructed from d-dimensional hypercubes. Although these lattices are not tree-like, and therefore closer to real cubic lattices than Bethe lattices or regular random graphs, one can still use the Bethe-Peierls method to derive exact equations for the magnetization and other thermodynamic quantities. We compute phase diagrams for ferromagnetic Ising models on hypercubic Bethe lattices with dimension d = 2, 3, and 4. Our results are in good agreement with the results of the same models on d-dimensional cubic lattices, for low and high temperatures, and offer an improvement over the conventional Bethe lattice with connectivity . © 2015 IOP Publishing Ltd.

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.

Bordino I.,Yahoo! | Battiston S.,ETH Zurich | Caldarelli G.,CNR Institute for Complex Systems | Caldarelli G.,London Institute for Mathematical science | And 4 more authors.
PLoS ONE | Year: 2012

We live in a computerized and networked society where many of our actions leave a digital trace and affect other people's actions. This has lead to the emergence of a new data-driven research field: mathematical methods of computer science, statistical physics and sociometry provide insights on a wide range of disciplines ranging from social science to human mobility. A recent important discovery is that search engine traffic (i.e., the number of requests submitted by users to search engines on the www) can be used to track and, in some cases, to anticipate the dynamics of social phenomena. Successful examples include unemployment levels, car and home sales, and epidemics spreading. Few recent works applied this approach to stock prices and market sentiment. However, it remains unclear if trends in financial markets can be anticipated by the collective wisdom of on-line users on the web. Here we show that daily trading volumes of stocks traded in NASDAQ-100 are correlated with daily volumes of queries related to the same stocks. In particular, query volumes anticipate in many cases peaks of trading by one day or more. Our analysis is carried out on a unique dataset of queries, submitted to an important web search engine, which enable us to investigate also the user behavior. We show that the query volume dynamics emerges from the collective but seemingly uncoordinated activity of many users. These findings contribute to the debate on the identification of early warnings of financial systemic risk, based on the activity of users of the www. © 2012 Bordino et al.

Farmer J.D.,University of Oxford | Farmer J.D.,Santa Fe Institute | Lafond F.,University of Oxford | Lafond F.,London Institute for Mathematical science | Lafond F.,Maastricht University
Research Policy | Year: 2016

Recently it has become clear that many technologies follow a generalized version of Moore's law, i.e. costs tend to drop exponentially, at different rates that depend on the technology. Here we formulate Moore's law as a correlated geometric random walk with drift, and apply it to historical data on 53 technologies. We derive a closed form expression approximating the distribution of forecast errors as a function of time. Based on hind-casting experiments we show that this works well, making it possible to collapse the forecast errors for many different technologies at different time horizons onto the same universal distribution. This is valuable because it allows us to make forecasts for any given technology with a clear understanding of the quality of the forecasts. As a practical demonstration we make distributional forecasts at different time horizons for solar photovoltaic modules, and show how our method can be used to estimate the probability that a given technology will outperform another technology at a given point in the future. © 2016 The Authors

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.

Zlatic V.,CNR Institute of Neuroscience | Zlatic V.,Ruder Boskovic Institute | Gabrielli A.,CNR Institute of Neuroscience | Gabrielli A.,CNR Institute for Complex Systems | And 2 more authors.
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics | Year: 2010

We present an approach of topology biased random walks for undirected networks. We focus on a one-parameter family of biases, and by using a formal analogy with perturbation theory in quantum mechanics we investigate the features of biased random walks. This analogy is extended through the use of parametric equations of motion to study the features of random walks vs parameter values. Furthermore, we show an analysis of the spectral gap maximum associated with the value of the second eigenvalue of the transition matrix related to the relaxation rate to the stationary state. Applications of these studies allow ad hoc algorithms for the exploration of complex networks and their communities. © 2010 The American Physical Society.

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.

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.

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