London Institute of Mathematical science

London, United Kingdom

London Institute of Mathematical science

London, United Kingdom
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Caravelli F.,London Institute of Mathematical science
International Journal of Parallel, Emergent and Distributed Systems | Year: 2017

We discuss the properties of the dynamics of purely memristive circuits using a recently derived consistent equation for the internal memory of the circuit. In particular, we show that the amount of memory in a memristive circuit is constrained by the conservation laws, and that the dynamics preserves these symmetry by means of a projection on this subspace. We obtain these results both for current and voltage controlled linear memristors. Moreover, we discuss other symmetries of the dynamics under various transformations, and study the weak and strong non-linear regimes. In the strong regime, we derive a constrained conservation law for the internal memory. In particular, we are able to show that for the case of purely passive or active systems, the eigenvalues of the Jacobian are always real, implying that oscillations can emerge only for mixtures. Our last result concerns the weak non-linear regime, showing that the internal memory dynamics can be interpreted as a constrained gradient descent, and provide the functional being minimized. These results provide another direct connection between memristors and learning. © 2017 Informa UK Limited, trading as Taylor & Francis Group

Lopez-Corredoira M.,Institute of Astrophysics of Canarias | Lopez-Corredoira M.,University of La Laguna | Gabrielli A.,CNR Institute for Complex Systems | Gabrielli A.,IMT Institute of Advanced Studies | Gabrielli A.,London Institute of Mathematical Science
Physica A: Statistical Mechanics and its Applications | Year: 2013

The purpose of our study is to understand the mathematical origin in real space of modulated and damped sinusoidal peaks observed in cosmic microwave background radiation anisotropies. We use the theory of the Fourier transform to connect localized features of the two-point correlation function in real space to oscillations in the power spectrum. We also illustrate analytically and by means of Monte Carlo simulations the angular correlation function for distributions of filled disks with fixed or variable radii capable of generating oscillations in the power spectrum. While the power spectrum shows repeated information in the form of multiple peaks and oscillations, the angular correlation function offers a more compact presentation that condenses all the information of the multiple peaks into a localized real space feature. We have seen that oscillations in the power spectrum arise when there is a discontinuity in a given derivative of the angular correlation function at a given angular distance. These kinds of discontinuities do not need to be abrupt in an infinitesimal range of angular distances but may also be smooth, and can be generated by simply distributing excesses of antenna temperature in filled disks of fixed or variable radii on the sky, provided that there is a non-null minimum radius and/or the maximum radius is constrained. © 2012 Elsevier B.V. All rights reserved.

Quattrociocchi W.,Northeastern University | Quattrociocchi W.,London Institute of Mathematical science | Caldarelli G.,London Institute of Mathematical science | Caldarelli G.,CNR Institute for Complex Systems | And 2 more authors.
Scientific Reports | Year: 2014

The inner dynamics of the multiple actors of the informations systems - i.e, T.V., newspapers, blogs, social network platforms, - play a fundamental role on the evolution of the public opinion. Coherently with the recent history of the information system (from few main stream media to the massive diffusion of socio-technical system), in this work we investigate how main stream media signed interaction might shape the opinion space. In particular we focus on how different size (in the number of media) and interaction patterns of the information system may affect collective debates and thus the opinions' distribution. We introduce a sophisticated computational model of opinion dynamics which accounts for the coexistence of media and gossip as separated mechanisms and for their feedback loops. The model accounts also for the effect of the media communication patterns by considering both the simple case where each medium mimics the behavior of the most successful one (to maximize the audience) and the case where there is polarization and thus competition among media memes. We show that plurality and competition within information sources lead to stable configurations where several and distant cultures coexist.

Scala A.,CNR Institute for Complex Systems | Scala A.,London Institute of Mathematical science
European Physical Journal: Special Topics | Year: 2013

Standard algorithms used for the numerical integration of the Langevin equation require that interactions should slowly vary during the integration time-step. This in not the case for hard-body systems, where there is no clear-cut between the correlation time of the noise and the time-scale of the interactions. Starting with a short time approximation of the Smoluchowski equation, we introduce an algorithm for the simulation of the over-damped Brownian dynamics of polydisperse hard-spheres in absence of hydrodynamic interactions and briefly discuss the extension to the case of external drifts. © 2013 EDP Sciences and Springer.

Banchi L.,University College London | Caravelli F.,Invenia Labs | Caravelli F.,London Institute of Mathematical science
Classical and Quantum Gravity | Year: 2016

In the present paper we study the evolution of the modes of a scalar field in a cyclic cosmology. In order to keep the discussion clear, we study the features of a scalar field in a toy model, a Friedman-Robertson-Walker Universe with a periodic scale factor, in which the Universe expands, contracts and bounces infinite times, in the approximation in which the dynamic features of this Universe are driven by some external factor, without the backreaction of the scalar field under study. In particular, we show that particle production exhibits features of the cyclic cosmology. Also, by studying the Berry phase of the scalar field, we show that contrary to what is commonly believed, the scalar field carries information from one bounce to another in the form of a global phase which occurs as generically non-zero. The Berry phase is then evaluated numerically in the case of the effective loop quantum cosmology closed Universe. We observe that Berry's phase is non-zero, but that in the quantum regime the particle content is non-negligible. © 2016 IOP Publishing Ltd.

D'Agostino G.,ENEA | Scala A.,University of Rome La Sapienza | Scala A.,London Institute of Mathematical science | Zlatic V.,Ruder Boskovic Institute | And 2 more authors.
EPL | Year: 2012

By analysing the diffusive dynamics of epidemics and of distress in complex networks, we study the effect of the assortativity on the robustness of the networks. We first determine by spectral analysis the thresholds above which epidemics/failures can spread; we then calculate the slowest diffusional times. Our results shows that disassortative networks exhibit a higher epidemiological threshold and are therefore easier to immunize, while in assortative networks there is a longer time for intervention before epidemic/failure spreads. Moreover, we study by computer simulations the sandpile cascade model, a diffusive model of distress propagation (financial contagion). We show that, while assortative networks are more prone to the propagation of epidemic/failures, degree-targeted immunization policies increases their resilience to systemic risk. © 2012 Europhysics Letters Association.

Zhou D.,Boston University | Stanley H.E.,Boston University | D'Agostino G.,ENEA | Scala A.,University of Rome La Sapienza | Scala A.,London Institute of Mathematical science
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics | Year: 2012

It was recently recognized that interdependencies among different networks can play a crucial role in triggering cascading failures and, hence, systemwide disasters. A recent model shows how pairs of interdependent networks can exhibit an abrupt percolation transition as failures accumulate. We report on the effects of topology on failure propagation for a model system consisting of two interdependent networks. We find that the internal node correlations in each of the two interdependent networks significantly changes the critical density of failures that triggers the total disruption of the two-network system. Specifically, we find that the assortativity (i.e., the likelihood of nodes with similar degree to be connected) within a single network decreases the robustness of the entire system. The results of this study on the influence of assortativity may provide insights into ways of improving the robustness of network architecture and, thus, enhance the level of protection of critical infrastructures. © 2012 American Physical Society.

Sebastio S.,London Institute of Mathematical science | Scala A.,London Institute of Mathematical science
Proceedings - 2015 IEEE Conference on Collaboration and Internet Computing, CIC 2015 | Year: 2015

The growing demand of computational resources has shifted users towards the adoption of cloud computing technologies. Cloud allows users to transparently access to remote computing capabilities as an utility. The volunteer computing paradigm, another ICT trend of the last years, can be considered a companion force to enhance the cloud in fulfilling specific domain requirements, such as computational intensive requests. Combining the spared resources provided by volunteer nodes with few data centers is possible to obtain a robust and scalable cloud platform. The price for such benefits relies in increased challenges to design and manage a dynamic complex system composed by heterogeneous nodes. Task execution requests submitted in the volunteer cloud are usually associated with Quality of Service requirements e.g., Specified through an execution deadline. In this paper, we present a preliminary evaluation of a cloud partitioning approach to distribute task execution requests in volunteer cloud, that has been validated through a simulation-based statistical analysis using the Google workload data trace. © 2015 IEEE.

Scala A.,University of Rome La Sapienza | Scala A.,London Institute of Mathematical science
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics | Year: 2012

The blossoming of interest in colloids and nanoparticles has given renewed impulse to the study of hard-body systems. In particular, hard spheres have become a real test system for theories and experiments. It is therefore necessary to study the complex dynamics of such systems in presence of a solvent; disregarding hydrodynamic interactions, the simplest model is the Langevin equation. Unfortunately, standard algorithms for the numerical integration of the Langevin equation require that interactions are slowly varying during an integration time step. This is not the case for hard-body systems, where there is no clear-cut distinction between the correlation time of the noise and the time scale of the interactions. Starting first from a splitting of the Fokker-Plank operator associated with the Langevin dynamics, and then from an approximation of the two-body Green's function, we introduce and test two algorithms for the simulation of the Langevin dynamics of hard spheres. © 2012 American Physical Society.

Ahnert S.E.,University of Cambridge | Fink T.M.A.,London Institute of Mathematical science
Journal of the Royal Society Interface | Year: 2016

Network motifs have been studied extensively over the past decade, and certain motifs, such as the feed-forward loop, play an important role in regulatory networks. Recent studies have used Boolean network motifs to explore the link between form and function in gene regulatory networks and have found that the structure of a motif does not strongly determine its function, if this is defined in terms of the gene expression patterns the motif can produce. Here, we offer a different, higher-level definition of the 'function' of a motif, in terms of two fundamental properties of its dynamical state space as a Boolean network. One is the basin entropy, which is a complexity measure of the dynamics of Boolean networks. The other is the diversity of cyclic attractor lengths that a given motif can produce. Using these two measures, we examine all 104 topologically distinct three-node motifs and show that the structural properties of a motif, such as the presence of feedback loops and feed-forward loops, predict fundamental characteristics of its dynamical state space, which in turn determine aspects of its functional versatility. We also show that these higher-level properties have a direct bearing on real regulatory networks, as both basin entropy and cycle length diversity show a close correspondence with the prevalence, in neural and genetic regulatory networks, of the 13 connected motifs without self-interactions that have been studied extensively in the literature. © 2016 The Authors.

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