COXIC (Complexity OXford Imperial College) is a series of biannual workshops to gather researchers from Oxford and Imperial College interested in Complexity. The COXIC events are oriented towards themes in networks and complex systems and are a venue for younger scientists and also allow the presentation of early-stage work.

Programme: The workshops consists of short talks given by young researchers (PhD students and post-docs) and of informal discussions. 

2pm Xiaoyue Xi (Imperial): Inferring the epidemiologic sources of infection from cross-sectionally sampled pathogen sequence data
2.20pm Karel Devriendt (Oxford): Non-linear network dynamics with consensus-dissensus bifurcation
2.40pm Rosalba Garcia-Millan (Imperial): The Concealed Voter Model universality class

3pm  Coffee break

4pm Michael Schaub (Oxford): Graph Signal processing in the edge-space
4.20pm Bingsheng Chen (Imperial): The role of triplets in the evolution in time of networks
4.40pm Anatol E Wegner (UCL): Atomic structures and the statistical mechanics of networks

5pm Pub



Xiaoyue Xi (Imperial): Inferring the epidemiologic sources of infection from cross-sectionally sampled pathogen sequence data

UNAIDS are advocating targeted HIV-1 prevention interventions. Targeting the population with the greatest transmission potential acquires knowledge on transmission networks and Bayesian techniques could be used to interpret transmission networks while considering the heterogeneous sampling.
Rakai Community Cohort Study motivates our study. HIV-1 deep sequence data of 2,652 individuals in Rakai District, Uganda was evaluated with the phyloscanner method to reconstruct HIV-1 transmission networks, and the direction of transmission, within a 70km2 area. Interpretation is complicated by considerable sampling differences between population strata. We developed a Bayesian hierarchical model to adjust for participation and sequence sampling differences while estimating the proportion of transmissions between population strata.
On simulations, we were able to reduce the worst case error in source attribution from 8.1% without sampling adjustments to 3.4% with sampling adjustments in representative scenarios. On application to real world analysis, the maximum absolute differences between estimates with and without adjustment were 7.0% when analyzing transmission flows between geographical locations, and 2.5% if transmissions between age groups are of interests.
Source attribution algorithms should account for sampling differences to reduce estimation bias, which is rarely considered in molecular epidemiology. 
Our proposed method could be applied to analyse transmission flows under heterogeneous sampling through transmission networks generated by phyloscanner or other software with similar functionality.

Karel Devriendt (Oxford): Non-linear network dynamics with consensus-dissensus bifurcation

In network dynamics, one models real-world systems by considering interacting agents (nodes) whose state changes over time due to some local interactions (links) with other agents. One of the many questions considered for such systems is how they are able to achieve global synchronization, coordination or consensus despite their local nature. At the same time, it is realized that apart from supporting consensus the same systems can also exhibit other, possibly opposite phenomena such as polarization or clustering. To unite these different dynamic behaviours, we introduce a non-linear network dynamical system which, depending on the parameter regime, exhibits either a global consensus state or states dominated by dissensus between neighbouring nodes. Our system appears naturally as an approximation to more general dynamics yet allows for a thorough theoretical study. We describe some interesting features of the system, with a focus on the stationary solutions.

Rosalba Garcia-Millan (Imperial): The Concealed Voter Model universality class

The Concealed Voter Model (CVM) is an extension of the original Voter Model, a model of opinion formation where two opposed opinions compete until consensus is reached. In the CVM, agents express either opinion not only publicly, they also hold a private opinion, which they may disclose or change. In this talk I will explain how the new interactions tend to delay the consensus time, although the asymptotic behaviour is unchanged. I will show that the critical exponents, calculated via renormalised field theory, are the same for both models, implying that both belong to the compact directed percolation universality class.

Michael Schaub (Oxford): Graph Signal processing in the edge-space

We device graph signal processing tools for the treatment of data defined on the edges of a graph. We first examine why conventional tools from graph signal processing may not be suitable for the analysis of such signals. More specifically, we discuss how the underlying notion of a ‘smooth signal’ inherited from (the typically considered variants of) the graph Laplacian are not suitable when dealing with edge signals that encode a notion of flow. To overcome this limitation we introduce a class of filters based on the Edge-Laplacian, a special case of the Hodge-Laplacian for simplicial complexes of order one.  We demonstrate how this Edge-Laplacian leads to low-pass filters that enforce (approximate) flow-conservation in the processed signals. Moreover, we show how these new filters can be combined with more classical Laplacian-based processing methods on the line-graph and discuss applications of these ideas for signal smoothing, semi-supervised and active learning for edge-signals on graphs. 

Bingsheng Chen (Imperial): The role of triplets in the evolution in time of networks

It has long been recognized that the development of social networks may depend on interactions that go beyond the usual pair-wise relationships described by edges. For instance, the role of triadic closure in actor and lawyer networks. Another example is that local searches, such as those modelled by random walks, probe a network beyond the nearest neighbours and often lead to new connections. In this project, we developed a framework to illustrate that the interactions between a pair of nodes are actually projections from higher order interactions between larger numbers of nodes in temporal networks  which depends on previous snapshots of the network – temporal motifs. To simplify, we selected triplets as the basic unit to describe the evolution of edges and used this to describe the evolution or a network from one time to the next.  We have applied our methodology to several different types of real-world data-sets, including human contact networks, email networks, a network of Wikipedia biographies, a network of shareholders and so on. We used several link prediction algorithms, based on several different edge evolution mechanisms, as well as our triplet based method and we showed that in many real networks that our predictions based on triplet dynamics perform better than other mechanisms such as those based on preferential attachment or an assortative model.

Anatol E Wegner (UCL): Atomic structures and the statistical mechanics of networks

We consider random graph models where graphs are generated by connecting not only pairs of nodes by edges but also larger subsets of nodes by copies of small atomic subgraphs of arbitrary topology. More specifically we consider canonical and microcanonical ensembles corresponding to constraints placed on the counts and distributions of atomic subgraphs and derive general expressions for the entropy of such models. We also introduce a procedure that enables the distributions of multiple atomic subgraphs to be combined resulting in more coarse grained models. As a result we obtain a general class of models that can be parametrized in terms of basic building blocks and their distributions that includes many widely used models as special cases. These models include random graphs with arbitrary distributions of subgraphs (Karrer & Newman PRE 2010, Bollobas et al. RSA 2011), random hypergraphs, bipartite models, stochastic block models, models of multilayer networks and their degree corrected and directed versions. We show that the entropy expressions for all these models can be derived from a single expression that is characterized by the symmetry groups of their atomic subgraphs.


For enquiries, please contact Florian Klimm.