C3

A great deal of effort has gone into trying to model social influence --- including the spread of behavior, norms, and ideas --- on networks. Most models of social influence tend to assume that individuals react to changes in the states of their neighbors without any time delay, but this is often not true in social contexts, where (for various reasons) different agents can have different response times. To examine such situations, we introduce the idea of a timer into threshold models of social influence. The presence of timers on nodes delays the adoption --- i.e., change of state --- of each agent, which in turn delays the adoptions of its neighbors. With a homogeneous-distributed timer, in which all nodes exhibit the same amount of delay, adoption delays are also homogeneous, so the adoption order of nodes remains the same. However, heterogeneously-distributed timers can change the adoption order of nodes and hence the "adoption paths" through which state changes spread in a network. Using a threshold model of social contagions, we illustrate that heterogeneous timers can either accelerate or decelerate the spread of adoptions compared to an analogous situation with homogeneous timers, and we investigate the relationship of such acceleration or deceleration with respect to timer distribution and network structure. We derive an analytical approximation for the temporal evolution of the fraction of adopters by modifying a pair approximation of the Watts threshold model, and we find good agreement with numerical computations. We also examine our new timer model on networks constructed from empirical data.

Link to arxiv paper: https://arxiv.org/abs/1706.04252

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, behavioural representation of a temporal network, the temporal event graph (TEG).
The TEG describes the temporal network in terms of both inter-event time and two-event temporal motifs.
By considering the distributions of these quantities 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.

Identifying clusters or "communities" of densely connected nodes in networks is an active area of research, with relevance to many applications. Recent advances in the field have focused especially on temporal, multiplex, and other kinds of multilayer networks.

One method for detecting communities in multilayer networks is to maximise a generalised version of an objective function known as modularity. Writing down multilayer modularity requires the specification of two types of resolution parameters, and choosing appropriate values is crucial for uncovering meaningful community structure. In the simplest case, there are just two parameters, one controlling the sizes of detected communities, and the other influencing how much communities change from layer to layer. By establishing an equivalence between modularity optimisation and a multilayer maximum-likelihood approach to community detection, we are able to determine statistically optimal values for these two parameters. 

When applied to existing multilayer benchmarks, our optimized approach performs significantly better than using parameter choices guided by heuristics. We also apply the method to supermarket data, revealing changes in consumer behaviour over time.

The existence of planetary and stellar magnetic fields is attributed to the dynamo instability, the mechanism by which a background turbulent flow spontaneously generates a magnetic field by the constructive refolding of magnetic field lines. Many efforts have been made by several experimental groups to reproduce the dynamo instability in the laboratory using liquid metals. However, so far, unconstrained dynamos driven by turbulent flows have not been achieved in the intrinsically low magnetic Prandtl number $P_m$ (i.e. $Pm = Rm/Re << 1$) laboratory experiments. In this seminar I will demonstrate that the critical magnetic Reynolds number $Rm_c$ for turbulent non-helical dynamos in the low $P_m$ limit can be significantly reduced if the flow is submitted to global rotation. Even for moderate rotation rates the required energy injection rate can be reduced by a factor more than 1000. Our finding thus points into a new paradigm for the design of new liquid metal dynamo experiments.

The last 500 million years of Earth’s history have been punctuated by numerous episodes of abrupt climate change, some of them coincident with mass extinction events. Many of these climate events have been associated with massive volcanism, occurring during the emplacement of so-called Large Igneous Provinces (LIPs). Because of the significant impact of small modern eruptions on the Earth’s climate, a link between LIP volcanism and past climate change has been strongly advocated. Geochemical investigations of the sedimentary records which record major climate changes can give a profound insight into the proposed interactions between volcanic activity and climate. Mercury is a trace-gas emitted by modern volcanoes, which are the main source of this metal to the atmosphere. Ultimately atmospheric mercury is deposited in sediments, thus if enrichments in mercury are observed in sediments of the same age across the globe, a volcanic cause of these enrichments might be inferred. Osmium isotopes can also be used as a fingerprint of volcanic activity, as primitive basalts are enriched in unradiogenic 188Os. However, the continental crust is enriched in radiogenic 187Os. Therefore, the 187Os/188Os ratio can change with either more volcanic activity, or increased continental weathering during climate change. Changes in sedimentary mercury content and osmium isotopes can thus be used as markers of volcanism or weathering during climate events. However, a possible future step would be to quantify the amount of volcanism and/or weathering on the basis of these sedimentary excursions. The final part of this talk will introduce some simple quantitative models which may represent a first step towards such quantification, with the aim of further elaborating these models in the future.

I will describe our research on numerical methods for atmospheric dynamical cores based on compatible finite element methods. These methods extend the properties of the Arakawa C-grid to finite element methods by using compatible finite element spaces that respect the elementary identities of vector-calculus. These identities are crucial in demonstrating basic stability properties that are necessary to prevent the spurious numerical degradation of geophysical balances that would otherwise make numerical discretisations unusable for weather and climate prediction without the introduction of undesirable numerical dissipation. The extension to finite element methods allow these properties to be enjoyed on non-orthogonal grids, unstructured multiresolution grids, and with higher-order discretisations. In addition to these linear properties, for the shallow water equations, the compatible finite element structure can also be used to build numerical discretisations that respect conservation of energy, potential vorticity and enstrophy; I will survey these properties. We are currently developing a discretisation of the 3D compressible Euler equations based on this framework in the UK Dynamical Core project (nicknamed "Gung Ho"). The challenge is to design discretisation of the nonlinear operators that remain stable and accurate within the compatible finite element framework. I will survey our progress on this work to date and present some numerical results.

Following several decades of development by applied mathematicians, models of ocean wave interactions with sea ice floes are now in high demand due to the rapid recent changes in the world’s sea ice cover. From a mathematical perspective, the models are of interest due to the thinness of the floes, leading to elastic responses of the floes to waves, and the vast number of floes that waves encounter. Existing models are typically based on linear theories, but the thinness of the floes leads to the unique and highly nonlinear phenomenon of overwash, where waves run over the floes, in doing so dissipating wave energy and impacting the floes thermodynamically. I will give an overview of methods developed for the wave-floe problem, and present a new, bespoke overwash model, along with supporting laboratory experiments and numerical CFD simulations.

Let X be a smooth, complete geometrically connected curve defined over a one variable function field K over a finite field. Let G be a subgroup of the points of the Jacobian variety J of X defined over a separable closure of K with the property that G/p is finite, where p is the characteristic of K. Buium and Voloch, under the hypothesis that X is not defined over K^p, give an explicit bound for the number of points of X which lie in G (related to a conjecture of Lang, in the case of curves). In this joint work with Pazuki, we extend their result by requiring just that X is non isotrivial.

Let A be an abelian variety over the function field K of a curve over a finite field of characteristic p>0. We shall show that the group A(K^{p^{-\infty}}) is finitely generated, unless severe restrictions are put on the geometry of A. In particular, we shall show that if A is ordinary and has a point of bad reduction then A(K^{p^{-\infty}}) is finitely generated. This result can be used to give partial answers to questions of Scanlon, Ziegler, Esnault, Voloch and Poonen.

I will explain how to prove the exactness of the homotopy sequence of overconvergent p-adic fundamental groups for a smooth and projective morphism in characteristic p. We do so by first proving a corresponding result for rigid analytic varieties in characteristic 0, following dos Santos in the algebraic case. In characteristic p we proceed by a series of reductions to the case of a liftable family of curves, where we can apply the rigid analytic result. Joint work with Chris Lazda.