COXI C (Complexity OXford Imperial College) is a series of biannual workshops t o gather researchers from Oxford and Imperial College interested in Comple xity. The COXIC events are oriented towards t hemes in networks and complex systems and are a venue for younger scientis ts and also allow the presentation of early-stage work.

\n2pm Xiaoyue Xi (Imperial): Inferring the epidemiologic s
ources of infection from cross-sectionally sampled pathogen sequence data<
br /> 2.20pm Karel Devriendt (Oxford): Non-linear network dynamics with co
nsensus-dissensus bifurcation

2.40pm Rosalba Garcia-Millan (Imperial
): The Concealed Voter Model universality class

3pm Coffee brea k

\n 4pm Michael Schaub (Oxford): Graph Signal processing in the edg
e-space

4.20pm Bingsheng Chen (Imperial): The role of triplets in th
e evolution in time of networks

4.40pm Anatol E Wegner (UCL): Atomic
structures and the statistical mechanics of networks

5pm Pub

\n———————————————

\nAbstracts:

\n<
span style=\"font-family: Calibri\;\"><
span style=\"color: #000000\;\">**Xiaoyue Xi****
(Imperial): Inferring the epidemiologic sources of infection from cross-se
ctionally sampled pathogen sequence data**

Introduction:

UNAIDS are advocating targeted HI
V-1 prevention interventions. Targeting the population with the greatest t
ransmission potential acquires knowledge on transmission networks and Baye
sian techniques could be used to interpret transmission networks while con
sidering the heterogeneous sampling.

Methods:

Rakai Community
Cohort Study motivates our study. HIV-1 deep sequence data of 2\,652 indiv
iduals in Rakai District\, Uganda was evaluated with the phyloscanner meth
od to reconstruct HIV-1 transmission networks\, and the direction of trans
mission\, within a 70km2 area. Interpretation is complicated by considerab
le sampling differences between population strata. We developed a Bayesian
hierarchical model to adjust for participation and sequence sampling diff
erences while estimating the proportion of transmissions between populatio
n strata.

Results:

On simulations\, we were able to reduce the
worst case error in source attribution from 8.1% without sampling adjustm
ents to 3.4% with sampling adjustments in representative scenarios. On app
lication to real world analysis\, the maximum absolute differences between
estimates with and without adjustment were 7.0% when analyzing transmissi
on flows between geographical locations\, and 2.5% if transmissions betwee
n age groups are of interests.

Discussion:

Source attribution
algorithms should account for sampling differences to reduce estimation bi
as\, which is rarely considered in molecular epidemiology.

Our pro
posed method could be applied to analyse transmission flows under heteroge
neous sampling through transmission networks generated by phyloscanner or
other software with similar functionality.

**Karel Devriendt**** (Ox
ford)**: **Non-linear network dynamics with consensus-dissens
us bifurcation**

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

We device graph signal processing tools for the treatment of data d
efined on the edges of a graph. We first examine why conventional tools fr
om graph signal processing may not be suitable for the analysis of such si
gnals. More specifically\, we discuss how the underlying notion of a ‘sm
ooth signal’ inherited from (the typically considered variants of) the g
raph Laplacian are not suitable when dealing with edge signals that encode
a notion of flow. To overcome this limitation we introduce a class of fil
ters based on the Edge-Laplacian\, a special case of the Hodge-Laplacian f
or simplicial complexes of order one. We demonstrate how this Edge-Lapla
cian leads to low-pass filters that enforce (approximate) flow-conservatio
n in the processed signals. Moreover\, we show how these new filters can b
e combined with more classical Laplacian-based processing methods on the l
ine-graph and discuss applications of these ideas for signal smoothing\, s
emi-supervised and active learning for edge-signals on graphs.

**Bings
heng Chen (Imperial): The role of triplets in the evolution in time of net
works**

It has long been
recognized that the development of social networks may depend on interact
ions that go beyond the usual pair-wise relationships described by edges.
For instance\, the role of triadic closure in actor and lawyer networks. A
nother example is that local searches\, such as those modelled by random w
alks\, probe a network beyond the nearest neighbours and often lead to new
connections. In this project\, we developed a framework to illustrate tha
t the interactions between a pair of nodes are actually projections from h
igher order interactions between larger numbers of nodes in temporal netwo
rks which depends on previous snapshots of the network – temporal moti
fs. To simplify\, we selected triplets as the basic unit to describe the e
volution of edges and used this to describe the evolution or a network fro
m one time to the next. We have applied our methodology to several diffe
rent types of real-world data-sets\, including human contact networks\, em
ail networks\, a network of Wikipedia biographies\, a network of sharehold
ers and so on. We used several link prediction algorithms\, based on sever
al different edge evolution mechanisms\, as well as our triplet based meth
od 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 (UC
L): 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 ar bitrary topology. More specifically we consider canonical and microcanonic al ensembles corresponding to constraints placed on the counts and distrib utions of atomic subgraphs and derive general expressions for the entropy of such models. We also introduce a procedure that enables the distributio ns of multiple atomic subgraphs to be combined resulting in more coarse gr ained models. As a result we obtain a general class of models that can be parametrized in terms of basic building blocks and their distributions tha t includes many widely used models as special cases. These models include random graphs with arbitrary distributions of subgraphs (Karrer & Newman P RE 2010\, Bollobas et al. RSA 2011)\, random hypergraphs\, bipartite model s\, stochastic block models\, models of multilayer networks and their degr ee corrected and directed versions. We show that the entropy expressions f or all these models can be derived from a single expression that is charac terized by the symmetry groups of their atomic subgraphs.

\n\n

For enquiries\, please contact Florian Klimm.

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