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

Preprints and Under Review

Multi-body Interactions and Non-Linear Consensus Dynamics on Networked Systems (2019)
L. Neuhäuser, A. Mellor, R. Lambiotte

[ArXiv] [Show abstract]

Multi-body interactions can reveal higher-order dynamical effects that are not captured by traditional two-body network models. In this work, we derive and analyse models for consensus dynamics on hypergraphs, where nodes interact in groups rather than in pairs. Our work reveals that multi-body dynamical effects that go beyond rescaled pairwise interactions can only appear if the interaction function is non-linear, regardless of the underlying multi-body structure. As a practical application, we introduce a specific non-linear function to model three-body consensus, which incorporates reinforcing group effects such as peer pressure. Unlike consensus processes on networks, we find that the resulting dynamics can cause shifts away from the average system state. The nature of these shifts depends on a complex interplay between the distribution of the initial states, the underlying structure and the form of the interaction function. By considering modular hypergraphs, we discover state-dependent, asymmetric dynamics between polarised clusters where multi-body interactions make one cluster dominate the other.

Annotated Hypergraphs: Models and Applications (2019)
P. Chowdrow, A.Mellor

[ArXiv] [Show abstract]

Hypergraphs offer a natural modeling language for studying polyadic interactions between sets of entities. Many polyadic interactions are asymmetric, with nodes playing distinctive roles. In an academic collaboration network, for example, the order of authors on a paper often reflects the nature of their contributions to the completed work. To model these networks, we introduce annotated hypergraphs as natural polyadic generalizations of directed graphs. Annotated hypergraphs form a highly general framework for incorporating metadata into polyadic graph models. To facilitate data analysis with annotated hypergraphs, we construct a role-aware configuration null model for these structures and prove an efficient Markov Chain Monte Carlo scheme for sampling from it. We proceed to formulate several metrics and algorithms for the analysis of annotated hypergraphs. Several of these, such as assortativity and modularity, naturally generalize dyadic counterparts. Other metrics, such as local role densities, are unique to the setting of annotated hypergraphs. We illustrate our techniques on six digital social networks, and present a detailed case-study of the Enron email data set.

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

Graph Comparison via the Non-backtracking Spectrum (2019)
A. Mellor, A. Grusovin

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

The comparison of graphs is a vitally important, yet difficult task which arises across a number of diverse research areas including biological and social networks. There have been a number of approaches to define graph distance however often these are not metrics (rendering standard data-mining techniques infeasible), or are computationally infeasible for large graphs. In this work we define a new metric based on the spectrum of the non-backtracking graph operator and show that it can not only be used to compare graphs generated through different mechanisms, but can reliably compare graphs of varying size. We observe that the family of Watts-Strogatz graphs lie on a manifold in the non-backtracking spectral embedding and show how this metric can be used in a standard classification problem of empirical graphs.

Event Graphs: Advances and Applications of Second-Order Time-Unfolded Temporal Network Models (2019)
A. Mellor

[Advances in Complex Systems] [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.

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

INET Complexity Seminar
University of Oxford, UK (Jun. 2019)
Invited Talk
[Link] [Show details]

Title: A Nonlinear Heterogeneous q-Voter Model with Zealotry

CCS 18 - Dynamics On and Of Complex Networks Satellite
Thessaloniki, Greece (Sep. 2018)
Invited Talk
[Link] [Show details]

Title: Collective Behaviour in Temporal Networks

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

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

Applied Nonlinear Dynamics Seminar
University of 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
University of 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
University of Oxford, UK (Nov. 2014)
Invited Poster
[Link] [Show details]

Title: Understanding Voting Preference and Influence in Social Media

Contributed Talks and Posters

Networks Semimar
University of Oxford, UK (Jun. 2019)
Contributed Talk
[Link] [Show details]

Title: Dynamics, Random Walks, and Graph Learning

NetSci 19
Burlington, VT, USA (May. 2019)
Contributed Talk
[Link] [Show details]

Title: Graph Comparison via the Non-backtracking Spectrum

SIAM Workshop on Network Science
Snowbird, UT, USA (May. 2019)
Contributed Poster
[Link] [Show details]

Title: Graph Comparison via the Non-backtracking Spectrum

SIAM Conference on Applications of Dynamical Systems
Snowbird, UT, USA (May. 2019)
Contributed Talk
[Link] [Show details]

Title: A Nonlinear Heterogeneous q-Voter Model with Zealotry

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

Title: Conversation and Collective Behaviour in Digital Communication

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

Title: Classifying Conversation in Digital Communication

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

Title: The Temporal Event Graph

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

Title: Classifying Conversation in Digital Communication

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

Title: The Temporal Event Graph

Theoretical Foundations for Statistical Network Analysis Workshop
Isaac Newton Institute, Cambridge, UK (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

Symposium on Machine Learning and Dynamical Systems
Imperial College London, UK (Feb. 2019)
Attendee
[Link]

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
ICMS Edinburgh, UK (Nov. 2013)
Attendee
[Link]


Supervision & Teaching

MSc in Mathematical Modelling and Scientific Computing (University of Oxford)
Student: Leonie Neuhauser (May 2018)
Title: Non-Linear Interactions and Temporal Dynamics on Higher-Order Networks (distinction)

Industrially Focused Mathematics (InFoMM) CDT DPhil (University of Oxford)
Student: Ambrose Yim (October 2018)
Title: Modelling Scientific growth using Topological Data Analysis (Elsevier)

Industrially Focused Mathematics (InFoMM) CDT Mini-project (University of Oxford)
Student: Ambrose Yim (July 2018)
Title: A Topological Analysis of Booking Networks (Emirates)

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

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

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

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

Part B Extended Essay (University of Oxford)
Student: Magdalena Georgieva (October 2017)
Title: Modelling the Spread and Optimising the Prevention of Biological Contagion Through Networks

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

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)
  • Physical Review Letters (PRL)
  • SIAM Journal on Matrix Analysis and Applications (SIAMX)