Predictability of extreme events in social media

It is part of our daily social-media experience that seemingly ordinary items (videos, news, publications, etc.) unexpectedly gain an enormous amount of attention. Here we investigate how unexpected these events are. We propose a method that, given some information on the items, quantifies the predictability of events, i.e., the potential of identifying in advance the most successful items defined as the upper bound for the quality of any prediction based on the same information. Applying this method to different data, ranging from views in YouTube videos to posts in Usenet discussion groups, we invariantly find that the predictability increases for the most extreme events. This indicates that, despite the inherently stochastic collective dynamics of users, efficient prediction is possible for the most extreme events.Comment: 13 pages, 3 figure

Analysis of the purchase and consumer behaviour towards direct purchase of food

The paper presented the methodic as well as selected results of own empiric research (face-to-face questionings in seven different questioning regions, n = 1488) to the analysis of the shopping behaviour and the attitudes towards direct purchase. To the analysis of the buying patterns a Kaufverhaltensindex (KVI) was introduced. In the regional comparison will be clear that the questioning regions of Baden-Württemberg and North Rhine-Westphalia show KVI by far highest, while the eastern questioning-regions (particularly Thuringia) are marked by the lowest KVI. Within the attitude measurement (factor analysis) six attitude-dimensions could be extracted. In particular are these: confidence in the emotional product quality, price- consciousness, socio-political motivation, confidence in the conventional food-offer, the orientation to convenience food and health consciousness. The analysis of the buying patterns-relevance (regression analysis) showed the distinct dominance of the attitude dimension to price consciousness. From the segmentation of the whole random check (cluster analysis) result four clusters (DV-sympathizers, price-conscious not-DV- buyers, direct buyers oriented to organic farming and a conventionally oriented DV-cluster). The analytic interpretation of buying patterns and soziodemographic variables as well as the regional affiliation allows a continuing characteristic and differentiation of the found clusters

Stochastic dynamics and the predictability of big hits in online videos

The competition for the attention of users is a central element of the Internet. Crucial issues are the origin and predictability of big hits, the few items that capture a big portion of the total attention. We address these issues analyzing 10 million time series of videos' views from YouTube. We find that the average gain of views is linearly proportional to the number of views a video already has, in agreement with usual rich-get-richer mechanisms and Gibrat's law, but this fails to explain the prevalence of big hits. The reason is that the fluctuations around the average views are themselves heavy tailed. Based on these empirical observations, we propose a stochastic differential equation with L\'evy noise as a model of the dynamics of videos. We show how this model is substantially better in estimating the probability of an ordinary item becoming a big hit, which is considerably underestimated in the traditional proportional-growth models.Comment: Manuscript (8 pages and 5 figures

Characterizing Weak Chaos using Time Series of Lyapunov Exponents

We investigate chaos in mixed-phase-space Hamiltonian systems using time series of the finite- time Lyapunov exponents. The methodology we propose uses the number of Lyapunov exponents close to zero to define regimes of ordered (stickiness), semi-ordered (or semi-chaotic), and strongly chaotic motion. The dynamics is then investigated looking at the consecutive time spent in each regime, the transition between different regimes, and the regions in the phase-space associated to them. Applying our methodology to a chain of coupled standard maps we obtain: (i) that it allows for an improved numerical characterization of stickiness in high-dimensional Hamiltonian systems, when compared to the previous analyses based on the distribution of recurrence times; (ii) that the transition probabilities between different regimes are determined by the phase-space volume associated to the corresponding regions; (iii) the dependence of the Lyapunov exponents with the coupling strength.Comment: 8 pages, 6 figure

Dynamics of a localized spin excitation close to the spin-helix regime

The time evolution of a local spin excitation in a (001)-confined two-dimensional electron gas subjected to Rashba and Dresselhaus spin-orbit interactions of similar strength is investigated theoretically and compared with experimental data. Specifically, the consequences of the finite spatial extension of the initial spin polarization is studied for non-balanced Rashba and Dresselhaus terms and for finite cubic Dresselhaus spin-orbit interaction. We show that the initial out-of-plane spin polarization evolves into a helical spin pattern with a wave number that gradually approaches the value $q_0$ of the persistent spin helix mode. In addition to an exponential decay of the spin polarization that is proportional to both the spin-orbit imbalance and the cubic Dresselhaus term, the finite width $w$ of the spin excitation reduces the spin polarization by a factor that approaches $\exp(-q_0^2 w^2/2)$ at longer times.Comment: 8 pages, 7 figure