Transition due to preferential cluster growth of collective emotions in online communities

Abstract

We consider a preferential cluster growth in a one-dimensional stochastic model describing the dynamics of a binary chain with long-range memory. The model is driven by data corresponding to emotional patterns observed during online communities' discussions. The system undergoes a dynamical phase transition. For low values of the preference exponent, both states are observed during the string evolution in the majority of simulated discussion threads. When the exponent crosses a critical value, in the majority of threads an ordered phase emerges, i.e. from a certain time moment only one state is represented. The transition becomes discontinuous in the thermodynamical limit when the discussions are infinitely long and even an infinitely small preference exponent leads to the ordering behavior in every discussion thread. Numerical simulations are in a good agreement with approximated analytical formula.

Finite size induces crossover temperature in growing spin chains

“…The absence of the effect for the higher magnetic field is the result of a transition from a bistable to a monostable energy landscape of a pair of neighboring spins. We think that, although directly inspired by the clustering phenomena observed in the online emotional discussions [22,23] One can easily observe the convergence of s n to a constant value for a sufficiently large value of n. In fact, as p+q −1 < 1, we have lim n→∞ s n = (q − p)/(p + q − 2).…”

“…Such media often use a chronological structure of the incoming posts that can be easily regarded as a one-dimensional chain (i.e., the consecutive posts are represented by the nodes in the chain). The results of our previous analyses [22,23] indicate that one of the most dominant phenomena seen in such media is a strong dependence of the expressed emotion on the emotion of the last comment (i.e., the newest one).…”

“…10 and M v is number of data points fulfilling the condition Eq. (23). (23), which could suggest that the simplifications assumed in our model regarding the short-range memory of users could be inappropriate for this system.…”

“…In this paper we give clear reasons for choosing this very topology. In fact, our model is motivated by the recent research [22,23] on affective interactions among participants of Internet fora [24][25][26]. Such media often use a chronological structure of the incoming posts that can be easily regarded as a one-dimensional chain (i.e., the consecutive posts are represented by the nodes in the chain).…”

Growing spin model in deterministic and stochastic trees

“…However, there is no direct evidence that social processes that take place in hierarchical trees and scalefree networks can be described by this kind of dynamics. On the other hand the results of our previous analyses [10,11] indicate that one of the most dominant phenomena seen in online portals is a strong dependence of the expressed emotion on the emotion of the last comment (i.e., the newest one). In order to describe this process in setting of chronologically added comments (that form a chain) we have previously explicitly modified Ising model Hamiltonian by taking into account only node's left neighbor as well as equip our model with a growing component (a new node is quenched after a single update) [12].…”