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

Fusion, collapse, and stationary bound states of incoherently coupled waves in bulk cubic media

We study the interaction between two localized waves that propagate in a bulk (two transverse dimensions) Kerr medium, while being incoherently coupled through cross-phase modulation. The different types of stationary solitary wave solutions are found and their stability is discussed. The results of numerical simulations suggest that the solitary waves are unstable. We derive sufficient conditions for when the wave function is bound to collapse or spread out, and we develop a theory to describe the regions of different dynamical behavior. For localized waves with the same center we confirm these sufficient conditions numerically and show that only when the equations and the initial conditions are symmetric are they also close to being necessary conditions. Using Gaussian initial conditions we predict and confirm numerically the power-dependent characteristic initial separations that divide the phase space into collapsing and diffracting solutions, and further divide each of these regions into subregions of coupled (fusion) and uncoupled dynamics. Finally we illustrate how, close to the threshold of collapse, the waves can cross several times before eventually collapsing or diffracting

Stata and the newcomer

During a long history with a lot of people involved, Stata has grown and flourished. It seems, however, that the needs of the newcomer don't get the attention they deserve. I switched from SPSS to Stata three years ago, and I am happy now, but I still remember my initial troubles. Also, when teaching Stata to new users, I see them repeatedly encounter the same problems and difficulties. During the presentation, I will demonstrate some shortcomings of Stata for new users. I will also give constructive suggestions for improvements. Some of the current problems, and some suggestions on how to overcome them, can be seen in my booklet "Introduction to Stata"; download it from www.biostat.au.dk/teaching/software.

Stretched exponential relaxation and ac universality in disordered dielectrics

This paper is concerned with the connection between the properties of dielectric relaxation and ac (alternating-current) conduction in disordered dielectrics. The discussion is divided between the classical linear-response theory and a self-consistent dynamical modeling. The key issues are, stretched exponential character of dielectric relaxation, power-law power spectral density, and anomalous dependence of ac conduction coefficient on frequency. We propose a self-consistent model of dielectric relaxation, in which the relaxations are described by a stretched exponential decay function. Mathematically, our study refers to the expanding area of fractional calculus and we propose a systematic derivation of the fractional relaxation and fractional diffusion equations from the property of ac universality.Comment: 8 pages, 2 figure