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.

Measuring and forecasting opinion trends from real-time social media is a long-standing goal of big-data analytics. Despite the large amount of work addressing this question, there has been no clear validation of online social media opinion trend with traditional surveys. Here we develop a method to infer the opinion of Twitter users by using a combination of statistical physics of complex networks and machine learning based on hashtags co-occurrence to build an in-domain training set of the order of a million tweets. We validate our method in the context of 2016 US Presidential Election by comparing the Twitter opinion trend with the New York Times National Polling Average, representing an aggregate of hundreds of independent traditional polls. The Twitter opinion trend follows the aggregated NYT polls with remarkable accuracy. We investigate the dynamics of the social network formed by the interactions among millions of Twitter supporters and infer the support of each user to the presidential candidates. 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 traditional surveys.

Understanding transport of thermal and suprathermal particles is a fundamental issue in laboratory, solar-terrestrial, and astrophysical plasmas. For laboratory fusion experiments, confinement of particles and energy is essential for sustaining the plasma long enough to reach burning conditions. For solar wind and magnetospheric plasmas, transport properties determine the spatial and temporal distribution of energetic particles, which can be harmful for spacecraft functioning, as well as the entry of solar wind plasma into the magnetosphere. For astrophysical plasmas, transport properties determine the efficiency of particle acceleration processes and affect observable radiative signatures. In all cases, transport depends on the interaction of thermal and suprathermal particles with the electric and magnetic fluctuations in the plasma. Understanding transport therefore requires us to understand these interactions, which encompass a wide range of scales, from magnetohydrodynamic to kinetic scales, with larger scale structures also having a role. The wealth of transport studies during recent decades has shown the existence of a variety of regimes that differ from the classical quasilinear regime. In this paper we give an overview of nonclassical plasma transport regimes, discussing theoretical approaches to superdiffusive and subdiffusive transport, wave-particle interactions at microscopic kinetic scales, the influence of coherent structures and of avalanching transport, and the results of numerical simulations and experimental data analyses. Applications to laboratory plasmas and space plasmas are discussed.

Inspired by suprathermal ion experiments in the basic plasma experiment TORPEX, the transport of suprathermal ions in ideal interchange mode turbulence is theoretically examined in the simple magnetized torus configuration. We follow ion tracer trajectories as specified by ideal interchange mode turbulence imported from a numerical simulation of drift-reduced Braginskii equations. Using the variance of displacements, σ2(t)∼tγ, we find that γ depends strongly on suprathermal ion injection energy and the relative magnitude of turbulent fluctuations. The value of γ also changes significantly as a function of time after injection, through three distinguishable phases: ballistic, interaction, and asymmetric. During the interaction phase, we find the remarkable presence of three regimes of dispersion: superdiffusive, diffusive, and subdiffusive, depending on the energy of the suprathermal ions and the amplitude of the turbulent fluctuations. We contrast these results with those from a “slab” magnetic geometry in which subdiffusion does not occur during the interaction phase. Initial results from TORPEX are consistent with data from a new synthetic diagnostic used to interpret our simulation results. The simplicity of the simple magnetized torus makes the present work of interest to analyses of more complicated contexts ranging from fusion devices to astrophysics and space plasma physics.

The understanding of the transport of suprathermal ions in the presence of turbulence is important for fusion plasmas in the burning regime that will characterize reactors, and for space plasmas to understand the physics of particle acceleration. Here, three-dimensional measurements of a suprathermal ion beam in the toroidal plasma device TORPEX are presented. These measurements demonstrate, in a turbulent plasma, the existence of subdiffusive and superdiffusive transport of suprathermal ions, depending on their energy. This result stems from the unprecedented combination of uniquely resolved measurements and first-principles numerical simulations that reveal the mechanisms responsible for the nondiffusive transport. The transport regime is determined by the interaction of the suprathermal ion orbits with the turbulent plasma dynamics, and is strongly affected by the ratio of the suprathermal ion energy to the background plasma temperature. Diffusion of tracers in a neutral fluid was observed by Brown and explained through collisional theory by Einstein and Smoluchowski [1,2]. Classical diffusive transport, originating from scale-fixed random walks with a typical step size, , and a typical waiting time between steps, τ , leads to a linear scaling of the mean-squared displacement with time and a diffusion coefficient given by 2 /τ . In many complex systems such as fusion and space plasmas [3], scale lengths or time scales are not well defined, thus transport cannot be modeled as a classical diffusive process. Generalizations of the classical diffusion model, such as Lévy walks [4][5][6] or fractional Lévy motion [7], allow introducing power-law distributions of the step sizes or waiting times and long-range temporal correlations, introducing a non-Gaussian and non-Markovian character. These generalizations result in nondiffusive transport characterized by a mean-squared displacement (variance of displacement) of an ensemble of individuals that does not necessarily scale linearly with time: (r(t) − r(0)) 2 ∝ t γ , with γ = 1 generally, where r(t) represents the positions of individuals and · indicates the ensemble average. When γ > 1 or γ < 1, the transport is called superdiffusive or subdiffusive, respectively. For the special case of classical diffusion γ = 1.Using time-resolved measurements we have recently shown that suprathermal ions are more sensitive to the intermittent turbulent structures in the basic plasma device TORPEX when their energy is smaller [8]. In this Rapid Communication, we present measurements of suprathermal ion transport in TORPEX carried out in three spatial dimensions and with varying input energies. We show that, as the ion energy is increased, the transport varies from subdiffusive to superdiffusive as predicted by numerical simulations.Although earlier experimental and numerical studies suggest that the transport of suprathermal ions in fusion devices and astrophysical plasmas is generally nondiffusive [9-12], * alexandre.bovet@epfl.ch direct measurements of suprathermal ion transport...

Suprathermal ions, created by fusion reactions or by additional heating, will play an important role in burning plasmas such as the ones in ITER or DEMO. Basic plasma experiments, with easy access for diagnostics and well-controlled plasma scenarios, are particularly suitable to investigate the transport of suprathermal ions in plasma waves and turbulence. Experimental measurements and numerical simulations have revealed that the transport of fast ions in the presence of electrostatic turbulence in the basic plasma toroidal experiment TORPEX is generally non-classical. Namely, the mean-squared radial displacement of the ions does not scale linearly with time, but r2(t)t , with = 1 generally, >1 corresponding to superdiffusion and <1 to subdiffusion. A generalization of the classical model of diffusion, the so-called fractional L ́evy motion, which encompasses power-law (L ́evy) statistics for the displacements and correlated temporal increments, leads to non-classical dynamics such as that observed in the experiments. On a macroscopic scale, this results in fractional differential operators, which are used to model non-Gaussian, non-local anomalous transport in a growing number of applied fields, including plasma physics. In this paper, we show that asymmetric fractional L ́evy motion can be described by a diffusion equation using spacefractional differential operator with skewness. Numerical simulations of tracers in TORPEX turbulence are performed. The time evolution of the radial particle position distribution is shown to be described by solutions of the fractional diffusion equation corresponding to asymmetric fractional L ́evy motion in sub-and superdiffusive cases.

Suprathermal ion turbulent transport in magnetized plasmas is generally nondiffusive, ranging from subdiffusive to superdiffusive depending on the interplay of the turbulent structures and the suprathermal ion orbits. Here, we present time-resolved measurements of the cross-field suprathermal ion transport in a toroidal magnetized turbulent plasma. Measurements in the superdiffusive regime are characterized by a higher intermittency than in the subdiffusive regime. Using conditional averaging, we show that, when the transport is superdiffusive, suprathermal ions are transported by intermittent field-elongated turbulent structures that are radially propagating. Understanding turbulent transport of suprathermal ions, i.e., ions with energies greater than the quasi-Maxwellian background plasma, is of paramount importance for a variety of laboratory and natural systems. In future fusion reactors such as ITER and DEMO, a good confinement of suprathermal ions, created by fusion reactions or additional heating, is necessary to reach and control burning plasma conditions [1,2]. In astrophysical plasmas, the understanding of solar energetic particles and of cosmic ray transport still has some gray areas [3,4]. For example, during impulsive solar energetic particle events, large fluctuations in intensity, called dropouts, were observed and are not fully understood [5].Experimental and numerical evidence suggests that suprathermal ion cross-field transport can be nondiffusive [6][7][8][9][10], characterized by a variance of particle displacements that does not scale linearly with time h½rðtÞ − rð0Þ 2 i ∝ t γ , with the transport exponent γ ≠ 1 generally. Here, rðtÞ indicates the particle positions. For 0 < γ < 1 the transport is subdiffusive, for 1 < γ < 2 superdiffusive. Classical diffusion corresponds to γ ¼ 1. In fusion experiments and astrophysical plasmas, measurements are limited to a few positions by high-temperature and diagnostics accessibility. In those cases, it is not possible to characterize the transport by the temporal evolution of the variance of displacements and information about the transport has to be inferred from the time trace statistics [11][12][13].In this Letter, we present first time-resolved measurements of the cross-field transport of suprathermal ions in a turbulent magnetized plasma. Previously, in the TORPEX device [14], by using three-dimensional time-averaged measurements of the width of a suprathermal ion beam in combination with numerical simulations (an example is shown in Fig. 1), we have shown that the transport of suprathermal ions varies from superdiffusive to subdiffusive as their energy is increased [8,10,[15][16][17][18][19]. We consider here two suprathermal ion energies, 30 and 70 eV, for which the radial transport was identified to be superdiffusive (γ ¼ 1.20) and subdiffusive (γ ¼ 0.51), respectively [10,18]. We show that the time traces of the suprathermal ion current show a clear difference in intermittency. Using the technique of conditional average sampling (CAS) [20,21],...

Basic aspects of fast ion transport in ideal interchange-mode unstable plasmas are investigated in the simple toroidal plasma device TORPEX. Fast ions are generated by a miniaturized lithium 6+ ion source with energies up to 1 keV, and are detected using a double-gridded energy analyzer mounted on a two-dimensional movable system in the poloidal cross-section. The signal-to-noise ratio is enhanced by applying a modulated biasing voltage to the fast ion source and using a synchronous detection scheme. An analog lock-in amplifier has been developed, which allows removing the capacitive noise associated with the voltage modulation. We characterize vertical and radial transport of the fast ions, which is associated with the plasma turbulence. Initial experimental results show a good agreement with numerical simulations of the fast ion transport in a global fluid simulation of the TORPEX plasma.