C3

Assortative mixing in networks is the tendency for nodes with the same attributes, or metadata, to link to each other. It is a property often found in social networks manifesting as a higher tendency of links occurring between people with the same age, race, or political belief. Quantifying the level of assortativity or disassortativity (the preference of linking to nodes with different attributes) can shed light on the factors involved in the formation of links and contagion processes in complex networks. It is common practice to measure the level of assortativity according to the assortativity coefficient, or modularity in the case of discrete-valued metadata. This global value is the average level of assortativity across the network and may not be a representative statistic when mixing patterns are heterogeneous. For example, a social network spanning the globe may exhibit local differences in mixing patterns as a consequence of differences in cultural norms. Here, we introduce an approach to localise this global measure so that we can describe the assortativity, across multiple scales, at the node level. Consequently we are able to capture and qualitatively evaluate the distribution of mixing patterns in the network. We find that for many real-world networks the distribution of assortativity is skewed, overdispersed and multimodal. Our method provides a clearer lens through which we can more closely examine mixing patterns in networks.

Link to arxiv paper:  https://arxiv.org/abs/1708.01236

Systemic risk arises as a multi-layer network phenomenon. Layers represent direct financial exposures of various types, including interbank liabilities, derivative or foreign exchange exposures. Another network layer of systemic risk emerges through common asset holdings of financial institutions. Strongly overlapping portfolios lead to similar exposures that are caused by price movements of the underlying financial assets. Based on the knowledge of portfolio holdings of financial agents we quantify systemic risk of overlapping portfolios. We present an optimization procedure, where we minimize the systemic risk in a given financial market by optimally rearranging overlapping portfolio networks, under the constraints that the expected returns and risks of the individual portfolios are unchanged. We explicitly demonstrate the power of the method on the overlapping portfolio network of sovereign exposure between major European banks by using data from the European Banking Authority stress test of 2016. We show that systemic-risk-efficient allocations are accessible by the optimization. In the case of sovereign exposure, systemic risk can be reduced by more than a factor of two, without any detrimental effects for the individual banks. These results are confirmed by a simple simulation of fire sales in the government bond market. In particular we show that the contagion probability is reduced dramatically in the optimized network.
 

The story of human progress is often described as a succession of ‘eras’ or ‘ages’ that are characterised by their most dominant technologies (e.g., the bronze age, the industrial revolution or the information age). In modern times, the fast pace of technological progress has accelerated the succession of eras. In addition, the increasing complexity of inventions has made the task of determining when eras begin and end more challenging, as eras are less about the dominance of a single technology and more about the way in which different technologies are combined. We present a data-driven method to determine and uncover technological eras based on networks and patent classification data. We construct temporal networks of technologies that co-appear in patents. By analyzing the evolution of the core-periphery structure and centrality time-series in these networks, we identify periods of time dominated by technological combinations which we identify as distinct ‘eras’. We test the performance of our method using a database of patents in Great Britain spanning a century, and identify five distinct eras.

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 to describe the behaviour of individuals and collectives over time and examine the structure of conversation over multiple timescales.
 

Protein interaction networks (PINs) allow the representation and analysis of biological processes in cells. Because cells are dynamic and adaptive, these processes change over time. Thus far, research has focused either on the static PIN analysis or the temporal nature of gene expression. By analysing temporal PINs using multilayer networks, we want to link these efforts. The analysis of temporal PINs gives insights into how proteins, individually and in their entirety, change their biological functions. We present a general procedure that integrates temporal gene expression information with a monolayer PIN to a temporal PIN and allows the detection of modular structure using multilayer modularity maximisation.

Through laboratory experiments, we examine the transport, settling and resuspension of sediments as well as the influence of floating particles upon damping wave motion.   Salt water is shown to enhance flocculation of clay and hence increase their settling rate.   In studies modelling sediment-bearing (hypopycnal) river plumes, experiments show that the particles that eventually settle through uniform-density fluid toward a sloping bottom form a turbidity current.  Meanwhile, even though the removal of particles should increase the buoyancy and hence speed of the surface current, in reality the surface current stops.  This reveals that the removal of fresh water carried by the viscous boundary layers surrounding the settling particles drains the current even when their concentration by volume is less than 5%. The microscopic effect of boundary layer transport by particles upon the large scale evolution is dramatically evident in the circumstance of a mesopycnal particle-bearing current that advances along the interface of a two-layer fluid.  As the fresh water rises and particles fall, the current itself stops and reverses direction.  As a final example, the periodic separation and consolidation of particles floating on a surface perturbed by surface waves is shown to damp faster than exponentially to attain a finite-time arrest as a result of efficiently damped flows through interstitial spaces between particles - a phenomenon that may be important for understanding the damping of surface waves by sea ice in the Arctic Ocean (and which is well-known to anyone drinking a pint with a proper head or a margarita with rocks or slush).

In this talk, I show how concepts from non-equilibrium statistical physics can be employed in the study of climate. The specific problem addressed is the geophysical-scale evolution of Arctic sea ice. Using an analogy with Brownian motion, the original evolution equation for the sea ice thickness distribution function by Thorndike et al. (J. Geophys. Res. 80(33), pp. 4501 — 4513, 1975) is transformed to a Fokker-Planck-like conservation law. The steady solution is $g(h) = {\cal N}(q) h^q \mathrm{e}^{-~ h/H}$, where $q$ and $H$ are expressible in terms of moments over the transition probabilities between thickness categories. The solution exhibits the functional form used in observational fits and shows that for $h \ll 1$, $g(h)$ is controlled by both thermodynamics and mechanics, whereas for $h \gg 1$ only mechanics controls $g(h)$. We also derive the underlying Langevin equation governing the dynamics of the ice thickness $h$, from which we predict the observed $g(h)$. Further, seasonality is introduced by using the Eisenman-Wettlaufer model (Proc. Natl. Acad. Sci. USA 106, pp. 28-32, 2009) for the thermal growth of sea ice. The time-dependent problem is studied by numerically integrating the Fokker-Planck equation. The results obtained from these numerical integrations and their comparison with satellite observations are discussed.

Numerical simulation provides an important contribution to the management of oil reservoirs, and the ‘reservoir simulator’ has been an essential tool for reservoir engineers since the 1970’s. I will describe the role of the ‘well model’ in reservoir simulation. Its main purpose is to determine the production and injection flows of the reservoir fluids at the surface under a variety of operating constraints, and to supply source and sink terms to the grid cells of the reservoir model.

Advances in well technology (horizontal, multilateral, and smart wells containing flow control devices) have imposed additional demands on the well model. It must allow the fluid mixture properties to vary with position in the well, and enable different fluid streams to comingle. Friction may make an important contribution to the local pressure gradient. To provide an improved representation of the physics of fluid flow, the well is discretised into a network of segments, where each segment has its own set of variables describing the multiphase flow conditions. Individual segments can be configured to represent flow control devices, accessing lookup tables or built-in correlations to determine the pressure drop across the device as a function of the flow conditions.

The ability to couple the wells to a production facility model such as a pipeline network is a crucial advantage for field development and optimization studies, particularly for offshore fields. I will conclude by comparing two techniques for combining a network model with the reservoir simulation. One method is to extend the simulator’s well model to include the network, providing a fully integrated reservoir/well/network simulation. The other method is to run the reservoir and facility models as separate simulations coupled by a ‘controller’, which periodically balances them by exchanging boundary conditions. The latter approach allows the engineer to use a choice of specialist facility simulators.

In contemporary ecology and mathematical biology undergraduate courses, textbooks focus on competition and predation models despite it being accepted that most species on Earth are involved in mutualist relationships. Mutualism is usually discussed more briefly in texts, often from an observational perspective, and obligate mutualism mostly not at all. Part of the reason for this is the lack of a simple math model to successfully explain the observations. Traditionally, particular nonlinearities  are used, which produce a variety of apparently disparate models.

The failure of the traditional linear model to describe coexisting mutualists has been documented from May (1973) through Murray (2001) to Bronstein (2015). Here we argue that this could be because of the use of carrying capacity, and propose the use of a nutrient pool instead, which implies the need for an autotroph (e.g. a plant) that converts nutrients into living resources for higher trophic levels. We show that such a linear model can successfully explain the major features of obligate mutualism when simple expressions for obligated growth are included.

Current technological progress has raised concerns about automation of tasks performed by workers resulting in job losses. Previous studies have used machine learning techniques to compute the automation probability of occupations and thus, studied the impact of automation on employment. However, such studies do not consider second-order effects, for example, an occupation with low automation probability can have a  surplus of labor supply due to similar occupations being automated. In this work, we study such second-order effects of automation using a network approach.  In our network – the Job Space – occupations are nodes and edges link occupations which share a significant amount of work activities. By mapping employment, automation probabilities into the network, and considering the movement of workers, we show that an occupation’s position in the network may be crucial to determining its employment future.