An Introduction to Non-diffusive Transport Models

The process of diffusion is the most elementary stochastic transport process. Brownian motion, the representative model of diffusion, played a important role in the advancement of scientific fields such as physics, chemistry, biology and finance. However, in recent decades, non-diffusive transport processes with non-Brownian statistics were observed experimentally in a multitude of scientific fields. Examples include human travel, in-cell dynamics, the motion of bright points on the solar surface, the transport of charge carriers in amorphous semiconductors, the propagation of contaminants in groundwater, the search patterns of foraging animals and the transport of energetic particles in turbulent plasmas. These examples showed that the assumptions of the classical diffusion paradigm, assuming an underlying uncorrelated (Markovian), Gaussian stochastic process, need to be relaxed to describe transport processes exhibiting a non-local character and exhibiting long-range correlations. This article does not aim at presenting a complete review of non-diffusive transport, but rather an introduction for readers not familiar with the topic. For more in depth reviews, we recommend some references in the following. First, we recall the basics of the classical diffusion model and then we present two approaches of possible generalizations of this model: the Continuous-Time-Random-Walk (CTRW) and the fractional L\'evy motion (fLm)

Validation of Twitter opinion trends with national polling aggregates: Hillary Clinton vs Donald Trump

Measuring and forecasting opinion trends from real-time social media is a long-standing goal of big-data analytics. Despite its importance, there has been no conclusive scientific evidence so far that social media activity can capture the opinion of the general population. Here we develop a method to infer the opinion of Twitter users regarding the candidates of the 2016 US Presidential Election by using a combination of statistical physics of complex networks and machine learning based on hashtags co-occurrence to develop an in-domain training set approaching 1 million tweets. We investigate the social networks formed by the interactions among millions of Twitter users and infer the support of each user to the presidential candidates. The resulting Twitter trends follow the New York Times National Polling Average, which represents an aggregate of hundreds of independent traditional polls, with remarkable accuracy. Moreover, the Twitter opinion trend precedes the aggregated NYT polls by 10 days, showing that Twitter can be an early signal of global opinion trends. Our analytics unleash the power of Twitter to uncover social trends from elections, brands to political movements, and at a fraction of the cost of national polls

Organization and evolution of the UK far-right network on Telegram

The instant messaging platform Telegram has become popular among the far-right movements in the US and UK in recent years. These groups use public Telegram channels and group chats to disseminate hate speech, disinformation, and conspiracy theories. Recent works revealed that the far-right Telegram network structure is decentralized and formed of several communities divided mostly along ideological and national lines. Here, we investigated the UK far-right network on Telegram and are interested in understanding the different roles of different channels and their influence relations. We apply a community detection method, based on the clustering of a flow of random walkers, that allows us to uncover the organization of the Telegram network in communities with different roles. We find three types of communities: (1) upstream communities contain mostly group chats that comment on content from channels in the rest of the network; (2) core communities contain broadcast channels tightly connected to each other and can be seen as forming echo chambers; (3) downstream communities contain popular channels that are highly referenced by other channels. We find that the network is composed of two main sub-networks: one containing mainly channels related to the English-speaking far-right movements and one with channels in Russian. We analyze the dynamics of the different communities and the most shared external links in the different types of communities over a period going from 2015 to 2020. We find that different types of communities have different dynamics and share links to different types of websites. We finish by discussing several directions for further work

Centralities in complex networks

In network science complex systems are represented as a mathematical graphs consisting of a set of nodes representing the components and a set of edges representing their interactions. The framework of networks has led to significant advances in the understanding of the structure, formation and function of complex systems. Social and biological processes such as the dynamics of epidemics, the diffusion of information in social media, the interactions between species in ecosystems or the communication between neurons in our brains are all actively studied using dynamical models on complex networks. In all of these systems, the patterns of connections at the individual level play a fundamental role on the global dynamics and finding the most important nodes allows one to better understand and predict their behaviors. An important research effort in network science has therefore been dedicated to the development of methods allowing to find the most important nodes in networks. In this short entry, we describe network centrality measures based on the notions of network traversal they rely on. This entry aims at being an introduction to this extremely vast topic, with many contributions from several fields, and is by no means an exhaustive review of all the literature about network centralities.Comment: 10 pages, 3 figures. Entry for the volume "Statistical and Nonlinear Physics" of the Encyclopedia of Complexity and Systems Science, Chakraborty, Bulbul (Ed.), Springer, 2021 Updated versio

Influence of fake news in Twitter during the 2016 US presidential election

The dynamics and influence of fake news on Twitter during the 2016 US presidential election remains to be clarified. Here, we use a dataset of 171 million tweets in the five months preceding the election day to identify 30 million tweets, from 2.2 million users, which contain a link to news outlets. Based on a classification of news outlets curated by www.opensources.co, we find that 25% of these tweets spread either fake or extremely biased news. We characterize the networks of information flow to find the most influential spreaders of fake and traditional news and use causal modeling to uncover how fake news influenced the presidential election. We find that, while top influencers spreading traditional center and left leaning news largely influence the activity of Clinton supporters, this causality is reversed for the fake news: the activity of Trump supporters influences the dynamics of the top fake news spreaders.Comment: Updated to latest revised versio

Influence of fake news in Twitter during the 2016 US presidential election

The dynamics and influence of fake news on Twitter during the 2016 US presidential election remains to be clarified. Here, we use a dataset of 171 million tweets in the five months preceding the election day to identify 30 million tweets, from 2.2 million users, which contain a link to news outlets. Based on a classification of news outlets curated by www.opensources.co, we find that 25% of these tweets spread either fake or extremely biased news. We characterize the networks of information flow to find the most influential spreaders of fake and traditional news and use causal modeling to uncover how fake news influenced the presidential election. We find that, while top influencers spreading traditional center and left leaning news largely influence the activity of Clinton supporters, this causality is reversed for the fake news: the activity of Trump supporters influences the dynamics of the top fake news spreaders

Anomalous Diffusion of Fast Ions in the Presence of Fishbone Instabilities in Tokamaks

Fast ions, whether produced by fusion reactions, or by ionisation of neutral beam, are expected to play a major role in the heating of burning plasmas. Therefore, the study of the fast ion’s behaviour in tokamaks is important for the future burning plasma experiments such as ITER. Understanding the effect of neutral beam injection on the current profile is also important for current profile control and for achieving steady state scenarios where non-inductive current drive is necessary. Several plasma discharges have been carried out in the MAST tokamak to investigate to which extent the q-profile may be modified by neutral beam current drive (NBCD). Transp simulations of the beam deposition during steady state experiments, with off-axis NBCD, have been carried out. It has been found that an anomalous diffusion (with a diffusion coef- ficient of roughly Db ∼ 0.5 m2 /s) of the fast ion is needed to explain the significantly lower neutron rate measured than predicted by the Transp code using an assumption of classical beam deposition and collisional ther- malisation. Transp simulations show that this diffusion broadens the fast ion deposition profile and may help to avoid harmful instabilities [1]. This anomalous diffusion is suspected to be caused by fishbone instabilities, as the time of the largest discrepancy between simulated and measured neutron rates correlates well with the highest magnitude of fishbone activity. The aim of this work is to investigate, with simulations of the Hagis code, if the interaction between fast ion resulting from off-axis NBCD and fishbone instabilities may be responsible for the fast ion anomalous diffusion needed to explain the observed neutron rate

Flow stability for dynamic community detection

Many systems exhibit complex temporal dynamics due to the presence of different processes taking place simultaneously. An important task in these systems is to extract a simplified view of their time-dependent network of interactions. Community detection in temporal networks usually relies on aggregation over time windows or consider sequences of different stationary epochs. For dynamics-based methods, attempts to generalize static-network methodologies also face the fundamental difficulty that a stationary state of the dynamics does not always exist. Here, we derive a method based on a dynamical process evolving on the temporal network. Our method allows dynamics that do not reach a steady state and uncovers two sets of communities for a given time interval that accounts for the ordering of edges in forward and backward time. We show that our method provides a natural way to disentangle the different dynamical scales present in a system with synthetic and real-world examples

Suprathermal ion transport in turbulent magnetized plasmas

Suprathermal ions, which have an energy greater than the quasi-Maxwellian background plasma temperature, are present in many laboratory and astrophysical plasmas. In fusion devices, they are generated by the fusion reactions and auxiliary heating. Controlling their transport is essential for the success of future fusion devices that could provide a clean, safe and abundant source of electric power to our society. In space, suprathermal ions include energetic solar particles and cosmic rays. The understanding of the acceleration and transport mechanisms of these particles is still incomplete. Basic plasma devices allow detailed measurements that are not accessible in astrophysical and fusion plasmas, due to the difficulty to access the former and the high temperatures of the latter. The basic toroidal device TORPEX offers an easy access for diagnostics, well characterized plasma scenarios and validated numerical simulations of its turbulence dynamics, making it the ideal platform for the investigation of suprathermal ion transport. This Thesis presents three-dimensional measurements of a suprathermal ion beam injected in turbulent TORPEX plasmas. The combination of uniquely resolved measurements and first-principle numerical simulations reveals the general non-diffusive nature of the suprathermal ion transport. A precise characterization of their transport regime shows that, depending on their energies, suprathermal ions can experience either a superdiffusive transport or a subdiffusive transport in the same background turbulence. The transport character is determined by the interaction of the suprathermal ion orbits with the turbulent plasma structures, which in turn depends on the ratio between the ion energy and the background plasma temperature. Time-resolved measurements reveal a clear difference in the intermittency of suprathermal ions time-traces depending on the transport regime they experience. Conditionally averaged measurements uncover the influence of field elongated turbulent structures, referred to as blobs, on the suprathermal ion beam. A theoretical model extending the Brownian motion to include non-Gaussian (Lévy) statistics and long-range temporal correlation is developed. This model successfully describes the evolution of the radial particle density from the numerical simulations and provides information on the microscopic processes underlying the non-diffusive transport of suprathermal ions