For a full list of publications please see my Google Scholar Page.

Preprints and Under Review

Event Graphs: Advances and Applications of Second-Order Time-Unfolded Temporal Network Models (2018)
A. Mellor

[ArXiv] [Show abstract]

Recent advances in data collection and storage have allowed both researchers and industry alike to collect data in real time. Much of this data comes in the form of 'events', or timestamped interactions, such as email and social media posts, website clickstreams, or protein-protein interactions. This of type data poses new challenges for modelling, especially if we wish to preserve all temporal features and structure. We propose a generalised framework to explore temporal networks using second-order time-unfolded models, called event graphs. Through examples we demonstrate how event graphs can be used to understand the higher-order topological-temporal structure of temporal networks and capture properties of the network that are unobserved when considering either a static (or time-aggregated) model. Furthermore, we show that by modelling a temporal network as an event graph our analysis extends easily to consider non-dyadic interactions, known as hyper-events.

Analysing Collective Behaviour in Temporal Networks Using Event Graphs and Temporal Motifs (2018)
A. Mellor

[ArXiv] [Show abstract]

Many studies of digital communication, in particular of Twitter, use natural language processing (NLP) to find topics, assess sentiment, and describe user behaviour. In finding topics often the relationships between users who participate in the topic are neglected. We propose a novel method of describing and classifying online conversations using only the structure of the underlying temporal network and not the content of individual messages. This method utilises all available information in the temporal network (no aggregation), combining both topological and temporal structure using temporal motifs and inter-event times. This allows us create an embedding of the temporal network in order to describe the behaviour of individuals and collectives over time and examine the structure of conversation over multiple timescales.

Journal Articles

The Temporal Event Graph (2017)
A. Mellor

[Journal of Complex Networks] [ArXiv] [Show abstract]

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.

Heterogeneous Out-of-Equilibrium Nonlinear q-Voter Model with Zealotry (2017)
A. Mellor, M. Mobilia, R.K.P. Zia

[Physical Review E] [ArXiv] [Show abstract]

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.

Characterization of the Nonequilibrium Steady State of a Heterogeneous Nonlinear q-Voter Model with Zealotry (2016)
A. Mellor, M. Mobilia, R.K.P. Zia

[EPL (Europhysics Letters)] [ArXiv] [Show abstract]

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.

Influence of Luddism on Innovation Diffusion (2015)
A. Mellor, M. Mobilia, S. Redner, A. M. Rucklidge, J. A. Ward

[Physical Review E] [ArXiv] [Show abstract]

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.


Invited Talks and Posters

CCS Satellite - Dynamics On and Of Complex Networks
Thessaloniki, Greece (Sep. 2018)
Invited Talk
[Show details]

Title: Collective Behaviour in Temporal Networks

Higher Order Networks Satellite - NetSci 18
Paris, France (Jun. 2018)
Invited Talk
[Show details]

Title: Eventgraphs: Time-unfolded Second-order Temporal Network Models

Applied Nonlinear Dynamics Seminar
Bristol, UK (Apr. 2017)
Invited Talk
[Link] [Show details]

Title: A Heterogeneous Out-of-Equilibrium Nonlinear q-Voter Model with Zealotry

KTN Alan Tayler Day
Oxford, UK (Nov. 2016)
Invited Talk
[Link] [Show details]

Title: Monitoring and Modelling Social Networks

Nonlinear Dynamics Seminar (LAND)
University of Leeds, UK (Feb. 2016)
Invited Talk
[Link] [Show details]

Title: Characterization of the Nonequilibrium Steady State of a Heterogeneous Nonlinear q-Voter Model with Zealotry

Dynamical Networks and Network Dynamics Workshop
ICMS Edinburgh, UK (Jan. 2016)
Invited Talk
[Link] [Show details]

Title: Simple Motifs and Centrality in Temporal Networks

CabDyn Journal Club
University of Oxford, UK (Aug. 2015)
Invited Talk
[Link] [Show details]

Title: Influence of Luddism on Innovation Diffusion

KTN Alan Tayler Day
Oxford, UK (Nov. 2014)
Invited Poster
[Link] [Show details]

Title: Understanding Voting Preferene and Influence in Social Media

Contributed Talks and Posters

Conference of Complex Systems
Thessaloniki, Greece (Sep. 2018)
Contributed Talk
[Show details]

Title: Conversation and Collective Behaviour in Digital Communication

COXIC
Imperial College, London (Apr. 2018)
Contributed Talk
[Show details]

Title: Classifying Conversation in Digital Communication

CompleNet 2018
Northeastern University, USA (Mar. 2018)
Contributed Talk
[Link] [Show details]

Title: The Temporal Event Graph

Networks Journal Club Semimar
University of Oxford, UK (Jan. 2018)
Contributed Talk
[Show details]

Title: Classifying Conversation in Digital Communication

Networks Journal Club Semimar
University of Oxford, UK (Nov. 2017)
Contributed Talk
[Show details]

Title: The Temporal Event Graph

Theoretical Foundations for Statistical Network Analysis Workshop
Isaac Newton Institute, Cambridge (Nov. 2016)
Contributed Poster
[Link] [Show details]

Title: Analysing Patterns in Digital Communication

Young Researchers In Mathematics Conference
University of Oxford, UK (Aug. 2015)
Contributed Talk
[Link] [Show details]

Title: Influence of Luddism on Innovation Diffusion

Collective Dynamics \& Evolving Networks Workshop
University of Bath, UK (Jul. 2015)
Contributed Talk
[Link] [Show details]

Title: Influence of Luddism on Innovation Diffusion

European Conference of Complex Systems
Lucca, Italy (Sep. 2014)
Contributed Poster
[Link] [Show details]

Title: Using Communicability for Infectional Analysis on Temporal Networks

Schools

Santa Fe Institute Complex Systems Summer School
Santa Fe, NM, USA (Jun. 2016)
Attendee
[Link]

Complexity Science Summer School
University of Warwick, UK (Jun. 2015)
Attendee
[Link]

Complex Networks Thematic School
Les Houches, France (Apr. 2014)
Attendee
[Link]

Attended

Networks Workshop: from Matrix Functions to Quantum Physics
University of Oxford, UK (Aug. 2017)
Attendee
[Link]

Fluctuation driven phenomena in non-equilibrium statistical mechanics symposium
University of Warwick, UK (Sep. 2015)
Attendee
[Link]

Big Data and Social Media Workshop
Edinburgh, UK (Nov. 2013)
Attendee
[Link]


Teaching

Industrially Focused Mathematics (InFoMM) CDT Mini-project (University of Oxford)
Student: Victor (Sheng) Wang (2018)
Title: Predicting User Cancellation (WhizzMaths)

Industrially Focused Mathematics (InFoMM) CDT Mini-project (University of Oxford)
Student: Ambrose Yim (2018)
Title: Objective-Oriented Organisation Management (BT)

Industrially Focused Mathematics (InFoMM) CDT Mini-project (University of Oxford)
Student: Lingyi Yang (2018)
Title: Customer Lifetime Value Models (Emirates)

MSc in Mathematical Modelling and Scientific Computing (University of Oxford)
Student: Zetian Gao (2017)
Title: Spatiotemporal Analysis of Air-Travel Networks

MSc in Mathematical Modelling and Scientific Computing (University of Oxford)
Student: Mengfan Zhang (2018)
Title: The Rise of Digital-born Media Outlets for Twitter News Dissemination

MSc in Mathematical Modelling and Scientific Computing (University of Oxford)
Student: Angelica Grusovin (2018)
Title: Temporal Booking Patterns of the Social Costumer

Part B Extended Essay (University of Oxford)
Student: Magdalena Georgieva (2018)
Title: Modelling the Spread and Optimising the Prevention of Biological Contagion Through Networks

Reviews

  • European Physics Letters (EPL)
  • Journal of Statistical Mechanics (JSTAT)
  • New Journal of Physics (NJP)
  • European Physical Journal B (EPJ B)
  • Physical Review E (PRE)
  • Dynamics On and Of Complex Networks (DOOCN)
  • NetSciX (NetSciX)