C3

The structure of the state of art of scientific research is an important object of study motivated by the understanding of how research evolves and how new fields of study stem from existing research. In the last years complex networks tools contributed to provide insights on the structure of research, through the study of collaboration, citation and co-occurrence networks, in particular keyword co-occurrence networks proved useful to provide maps of knowledge inside a scientific domain. The network approach focuses on pairwise relationships, often compressing multidimensional data structures and inevitably losing information. In this paper we propose to adopt a simplicial complex approach to co-occurrence relations, providing a natural framework for the study of higher-order relations in the space of scientific knowledge. Using topological methods we explore the shape of concepts in mathematical research, focusing on homological cycles, regions with low connectivity in the simplicial structure, and we discuss their role in the understanding of the evolution of scientific research. In addition, we map authors’ contribution to the conceptual space, and explore their role in the formation of homological cycles.

Authors: Daniele Cassese, Vsevolod Salnikov, Renaud Lambiotte
 

We study how the synchronizability of a diffusive network increases (or decreases) when we add some links in its underlying graph. This is of interest in the context of power grids where people want to prevent from having blackouts, or for neural networks where synchronization is responsible of many diseases such as Parkinson. Based on spectral properties for Laplacian matrices, we show some classification results obtained (with Tiago Pereira and Philipp Pade) with respect to the effects of these links.
 

Online discussions are the essence of many social platforms on the Internet. Discussion platforms are receiving increasing interest because of their potential to become deliberative spaces. Although previous studies have proposed approaches to measure online deliberation using the complexity of discussion networks as a proxy, little research has focused on how these networks are affected by changes of platform features.

In this talk, we will focus on how interfaces might influence the network structures of discussions using techniques like interrupted time series analysis and regression discontinuity design. Futhermore, we will review and extend state-of-the-art generative models of discussion threads to explain better the structure and growth of online discussions.
 

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.