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The Temporal Event Graph

Andrew Mellor

Temporal networks are increasingly being used to model the interactions of complex systems. Most studies require the temporal aggregation of edges (or events) into discrete time steps to perform analysis. In this article we describe a static, lossless, and unique representation of a temporal network, the temporal event graph (TEG). The TEG describes the temporal network in terms of both the inter-event time and two-event temporal motif distributions. By considering these distributions in unison we provide a new method to characterise the behaviour of individuals and collectives in temporal networks as well as providing a natural decomposition of the network. We illustrate the utility of the TEG by providing examples on both synthetic and real temporal networks.

Arxiv

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Heterogeneous Out-of-Equilibrium Nonlinear q-Voter Model with Zealotry

Andrew Mellor, Mauro Mobilia, R.K.P. Zia

We study the dynamics of the out-of-equilibrium nonlinear q-voter model with two types of susceptible voters and zealots, introduced in [EPL 113, 48001 (2016)]. In this model, each individual supports one of two parties and is either a susceptible voter of type q1 or q2, or is an inflexible zealot. At each time step, a qi-susceptible voter (i=1,2) consults a group of qi neighbors and adopts their opinion if all group members agree, while zealots are inflexible and never change their opinion. This model violates detailed balance whenever q1≠q2 and is characterized by two distinct regimes of low and high density of zealotry. Here, by combining analytical and numerical methods, we investigate the non-equilibrium stationary state of the system in terms of its probability distribution, non-vanishing currents and unequal-time two-point correlation functions. We also study the switching times properties of the model by exploiting an approximate mapping onto the model of [Phys. Rev. E 92, 012803 (2015)] that satisfies the detailed balance, and also outline some properties of the model near criticality.

Physical Review E Arxiv

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Characterization of the Nonequilibrium Steady State of a Heterogeneous Nonlinear q-Voter Model with Zealotry Editor's Choice

Andrew Mellor, Mauro Mobilia, R.K.P. Zia

We introduce an heterogeneous nonlinear q-voter model with two types of susceptible voters and zealots, and study its non-equilibrium properties when the population is finite and well mixed. In this two-opinion model, each individual supports one of two parties and is either a susceptible voter of type q1 or q2, or is an inflexible zealot. At each time step, a qi-susceptible voter (i=1,2) consults a group of qi neighbors and adopts their opinion if all group members agree, while zealots are inflexible and never change their opinion. We show that this model violates the detailed balance whenever q1≠q2 and has surprisingly rich properties. Here, we focus on the characterization of the model’s non-equilibrium stationary state (NESS) in terms of its probability distribution and currents in the distinct regimes of low and high density of zealotry. We unveil the NESS properties in each of these phases by computing the opinion distribution and the circulation of probability currents, as well as the two-point correlation functions at unequal times (formally related to a “probability angular momentum”). Our analytical calculations obtained in the realm of a linear Gaussian approximation are compared with numerical results.

EPL (Europhysics Letters) Arxiv

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Influence of Luddism on Innovation Diffusion

Andrew Mellor, Mauro Mobilia, S. Redner, Alastair M. Rucklidge, Jonathan A. Ward

We generalize the classical Bass model of innovation diffusion to include a new class of agents --- Luddites --- that oppose the spread of innovation. Our model also incorporates ignorants, susceptibles, and adopters. When an ignorant and a susceptible meet, the former is converted to a susceptible at a given rate, while a susceptible spontaneously adopts the innovation at a constant rate. In response to the rate of adoption, an ignorant may become a Luddite and permanently reject the innovation. Instead of reaching complete adoption, the final state generally consists of a population of Luddites, ignorants, and adopters. The evolution of this system is investigated analytically and by stochastic simulations. We determine the stationary distribution of adopters, the time needed to reach the final state, and the influence of the network topology on the innovation spread. Our model exhibits an important dichotomy: when the rate of adoption is low, an innovation spreads slowly but widely; in contrast, when the adoption rate is high, the innovation spreads rapidly but the extent of the adoption is severely limited by Luddites.

Physical Review E Arxiv


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Bristol Applied Nonlinear Dynamics Seminar

Bristol, UK (28th April 2017)
Invited Speaker: A Heterogeneous Out-of-Equilibrium Nonlinear q-Voter Model with Zealotry

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KTN Alan Tayler Day

Oxford, UK (28th November 2016)
Invited Speaker

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Santa Fe Institute Complex Systems Summer School

Santa Fe, NM, USA (12th June 2016)
Attendee

The program consists of an intensive series of lectures, laboratories, and discussion sessions focusing on foundational ideas, tools, and current topics in complex systems research. These include nonlinear dynamics and pattern formation, scaling theory, information theory and computation theory, adaptation and evolution, network structure and dynamics, adaptive computation techniques, computer modeling tools and specific applications of these core topics to various disciplines.

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LAND Seminar Leeds

University of Leeds, UK (16th February 2016)
Invited Speaker: Characterization of the Nonequilibrium Steady State of a Heterogeneous Nonlinear q-Voter Model with Zealotry

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Dynamical Networks and Network Dynamics Workshop

ICMS Edinburgh, UK (18th - 22nd January 2016)
Invited Speaker: Simple Motifs and Centrality in Temporal Networks

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Fluctuation driven phenomena in non-equilibrium statistical mechanics symposium

University of Warwick, UK (21st - 25th September 2015)
Attendee

This workshop explored topics such as recent advances in the extension of the formalism of large deviation theory to describe non-equilibrium fluctuations, anomalous scaling in reaction diffusion systems and stochastic aggregation and nonequilibrium phase transitions such as gelation and out-of-equilibrium condensation. It also included work on systems where rigorous mathematical progress is being made such as in understanding condensation in interacting particle systems for which exact stationary stationary measures are known and the use of fluctuation theorems to characterise non-equilibrium fluctuations.

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CabDyn Journal Club

University of Oxford, UK (20th August 2015)
Invited Speaker: The Role of Luddism on Innovation Diffusion

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Young Researchers In Mathematics Conference

University of Oxford, UK (17th - 20th August 2015)
Presentation: The Role of Luddism on Innovation Diffusion

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Collective Dynamics & Evolving Networks Workshop

University of Bath, UK (6th - 8th July 2015)
Presentation: The Role of Luddism on Innovation Diffusion

A three-day workshop at the University of Bath on the analysis of models of collective dynamics and evolutionary networks, and their use across physical, social, financial and biological applications.

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Complexity Science Summer School

University of Warwick, UK (9th - 12th June 2015)
Presentation: The Role of Luddism on Innovation Diffusion

This year's Warwick Graduate Summer School in Complexity Science will provide graduate students and researchers in the mathematical sciences with an introduction to modern theoretical and computational tools for tackling the challenges posed by such modeling and optimsation problems.

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KTN Alan Tayler Day

Oxford, UK (19th November 2014)
Poster Presentation: Understanding Voting Preference and Influence in Social Media

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European Conference of Complex Systems

Lucca, Italy (22nd - 26th September 2014)
Poster Presentation: Using Communicability for Infection Analysis on Temporal Networks

Major international conference and event in the area of complex systems and interdisciplinary science in general.

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Complex Networks Thematic School

Les Houches, France (7th - 18th April 2014)
Attendee

The school aims at giving a solid fundamental background to Master and PhD students and young researchers working with or on complex networks, by introducing the main concepts and tools that are useful in this field. The school will introduce the concepts and tools of graph theory, statistical physics, statistical analysis, modeling, and visualization used in the field of complex networks.

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Big Data and Social Media Workshop

Edinburgh, UK (28th November 2013)
Attendee

The event brings together people in commerce, government and academia, covering technical issues (data, collection, algorithms, high performance computing) and implications for marketing, healthcare, social sciences and the study of human interaction (questions of interest, limitations, pitfalls).

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