Hipsters on Networks: How a Small Group of Individuals Can Lead to an Anti-Establishment Majority

The spread of opinions, memes, diseases, and "alternative facts" in a population depends both on the details of the spreading process and on the structure of the social and communication networks on which they spread. In this paper, we explore how \textit{anti-establishment} nodes (e.g., \textit{hipsters}) influence the spreading dynamics of two competing products. We consider a model in which spreading follows a deterministic rule for updating node states (which describe which product has been adopted) in which an adjustable fraction $p_{\rm Hip}$ of the nodes in a network are hipsters, who choose to adopt the product that they believe is the less popular of the two. The remaining nodes are conformists, who choose which product to adopt by considering which products their immediate neighbors have adopted. We simulate our model on both synthetic and real networks, and we show that the hipsters have a major effect on the final fraction of people who adopt each product: even when only one of the two products exists at the beginning of the simulations, a very small fraction of hipsters in a network can still cause the other product to eventually become the more popular one. To account for this behavior, we construct an approximation for the steady-state adoption fraction on $k$-regular trees in the limit of few hipsters. Additionally, our simulations demonstrate that a time delay $\tau$ in the knowledge of the product distribution in a population, as compared to immediate knowledge of product adoption among nearest neighbors, can have a large effect on the final distribution of product adoptions. Our simple model and analysis may help shed light on the road to success for anti-establishment choices in elections, as such success can arise rather generically in our model from a small number of anti-establishment individuals and ordinary processes of social influence on normal individuals.Comment: Extensively revised, with much new analysis and numerics The abstract on arXiv is a shortened version of the full abstract because of space limit

The Achilles tendon total rupture score : a study of responsiveness, internal consistency and convergent validity on patients with acute Achilles tendon ruptures

Background The Achilles tendon Total Rupture Score was developed by a research group in 2007 in response to the need for a patient reported outcome measure for this patient population. Beyond this original development paper, no further validation studies have been published. Consequently the purpose of this study was to evaluate internal consistency, convergent validity and responsiveness of this newly developed patient reported outcome measure within patients who have sustained an isolated acute Achilles tendon rupture. Methods Sixty-four eligible patients with an acute rupture of their Achilles tendon completed the Achilles tendon Total Rupture Score alongside two further patient reported outcome measures (Disability Rating Index and EQ 5D). These were completed at baseline, six weeks, three months, six months and nine months post injury. The Achilles tendon Total Rupture Score was evaluated for internal consistency, using Cronbach's alpha, convergent validity, through correlation analysis and responsiveness, by analysing floor and ceiling effects and calculating its relative efficiency in comparison to the Disability Rating Index and EQ 5D scores. Results The Achilles tendon Total Rupture Score demonstrated high internal consistency (Cronbachs alpha > 0.8) and correlated significantly (p < 0.001) with the Disability Rating Index at five time points (pre-injury, six weeks, three, six and nine months) with correlation coefficients between -0.5 and -0.9. However, the confidence intervals were wide. Furthermore, the ability of the new score to detect clinically important changes over time (responsiveness) was shown to be greater than the Disability Rating Index and EQ 5D. Conclusions A universally accepted outcome measure is imperative to allow comparisons to be made across practice. This is the first study to evaluate aspects of validity of this newly developed outcome measure, outside of the developing centre. The ATRS demonstrated high internal consistency and responsiveness, with limited convergent validity. This research provides further support for the use of this outcome measure, however further research is required to advocate its universal use in patients with acute Achilles tendon ruptures. Such areas include inter-rater reliability and research to determine the minimally clinically important difference between scores

Collisional transport across the magnetic field in drift-fluid models

Drift ordered fluid models are widely applied in studies of low-frequency turbulence in the edge and scrape-off layer regions of magnetically confined plasmas. Here, we show how collisional transport across the magnetic field is self-consistently incorporated into drift-fluid models without altering the drift-fluid energy integral. We demonstrate that the inclusion of collisional transport in drift-fluid models gives rise to diffusion of particle density, momentum and pressures in drift-fluid turbulence models and thereby obviate the customary use of artificial diffusion in turbulence simulations. We further derive a computationally efficient, two-dimensional model which can be time integrated for several turbulence de-correlation times using only limited computational resources. The model describes interchange turbulence in a two-dimensional plane perpendicular to the magnetic field located at the outboard midplane of a tokamak. The model domain has two regions modeling open and closed field lines. The model employs a computational expedient model for collisional transport. Numerical simulations show good agreement between the full and the simplified model for collisional transport

Simulation of transition dynamics to high confinement in fusion plasmas

The transition dynamics from the low (L) to the high (H) confinement mode in magnetically confined plasmas is investigated using a first-principles four-field fluid model. Numerical results are in close agreement with measurements from the Experimental Advanced Superconducting Tokamak - EAST. Particularly, the slow transition with an intermediate dithering phase is well reproduced by the numerical solutions. Additionally, the model reproduces the experimentally determined L-H transition power threshold scaling that the ion power threshold increases with increasing particle density. The results hold promise for developing predictive models of the transition, essential for understanding and optimizing future fusion power reactors

Shear Flow Generation and Energetics in Electromagnetic Turbulence

Zonal flows are recognised to play a crucial role for magnetised plasma confinement. The genesis of these flows out of turbulent fluctuations is therefore of significant interest. We investigate the relative importance of zonal flow generation mechanisms via the Reynolds stress, Maxwell stress, and geodesic acoustic mode (GAM) transfer in drift-Alfv\'en turbulence. By means of numerical computations we quantify the energy transfer into zonal flows owing to each of these effects. The importance of the three driving ingredients in electrostatic and electromagnetic turbulence for conditions relevant to the edge of fusion devices is revealed for a broad range of parameters. The Reynolds stress is found to provide a flow drive, while the electromagnetic Maxwell stress is in the cases considered a sink for the flow energy. In the limit of high plasma beta, where electromagnetic effects and Alfv\'en dynamics are important, the Maxwell stress is found to cancel the Reynolds stress to a high degree. The geodesic oscillations, related to equilibrium pressure profile modifications due to poloidally asymmetric transport, can act as both sinks as drive terms, depending on the parameter regime. For high beta cases the GAMs are the main drive of the flow. This is also reflected in the frequency dependence of the flow, showing a distinct peak at the GAM frequency in that regime.Comment: 16 pages, 12 Figure

Self-trapping of impurities in Bose-Einstein condensates: Strong attractive and repulsive coupling

We study the interaction-induced localization -- the so-called self-trapping -- of a neutral impurity atom immersed in a homogeneous Bose-Einstein condensate (BEC). Based on a Hartree description of the BEC we show that -- unlike repulsive impurities -- attractive impurities have a singular ground state in 3d and shrink to a point-like state in 2d as the coupling approaches a critical value. Moreover, we find that the density of the BEC increases markedly in the vicinity of attractive impurities in 1d and 2d, which strongly enhances inelastic collisions between atoms in the BEC. These collisions result in a loss of BEC atoms and possibly of the localized impurity itself.Comment: 7 pages, 5 figure