24,769 research outputs found
Social Diffusion and Global Drift on Networks
We study a mathematical model of social diffusion on a symmetric weighted
network where individual nodes' states gradually assimilate to local social
norms made by their neighbors' average states. Unlike physical diffusion, this
process is not state conservational and thus the global state of the network
(i.e., sum of node states) will drift. The asymptotic average node state will
be the average of initial node states weighted by their strengths. Here we show
that, while the global state is not conserved in this process, the inner
product of strength and state vectors is conserved instead, and perfect
positive correlation between node states and local averages of their
self/neighbor strength ratios always results in upward (or at least neutral)
global drift. We also show that the strength assortativity negatively affects
the speed of homogenization. Based on these findings, we propose an adaptive
link weight adjustment method to achieve the highest upward global drift by
increasing the strength-state correlation. The effectiveness of the method was
confirmed through numerical simulations and implications for real-world social
applications are discussed.Comment: 7 pages, 3 figures; to appear in Phys. Rev.
Emergent user behavior on Twitter modelled by a stochastic differential equation
Data from the social-media site, Twitter, is used to study the fluctuations
in tweet rates of brand names. The tweet rates are the result of a strongly
correlated user behavior, which leads to bursty collective dynamics with a
characteristic 1/f noise. Here we use the aggregated "user interest" in a brand
name to model collective human dynamics by a stochastic differential equation
with multiplicative noise. The model is supported by a detailed analysis of the
tweet rate fluctuations and it reproduces both the exact bursty dynamics found
in the data and the 1/f noise
Mean-field analysis of the q-voter model on networks
We present a detailed investigation of the behavior of the nonlinear q-voter
model for opinion dynamics. At the mean-field level we derive analytically, for
any value of the number q of agents involved in the elementary update, the
phase diagram, the exit probability and the consensus time at the transition
point. The mean-field formalism is extended to the case that the interaction
pattern is given by generic heterogeneous networks. We finally discuss the case
of random regular networks and compare analytical results with simulations.Comment: 20 pages, 10 figure
Homophily, Cultural Drift and the Co-Evolution of Cultural Groups
In studies of cultural differentiation, the joint mechanisms of homophily and
influence have been able to explain how distinct cultural groups can form.
While these mechanisms normally lead to cultural convergence, increased levels
of heterogeneity can allow them to produce global diversity. However, this
emergent cultural diversity has proven to be unstable in the face of "cultural
drift"- small errors or innovations that allow cultures to change from within.
We develop a model of cultural differentiation that combines the traditional
mechanisms of homophily and influence with a third mechanism of 2network
homophily", in which network structure co-evolves with cultural interaction. We
show that if social ties are allowed to change with cultural influence, a
complex relationship between heterogeneity and cultural diversity is revealed,
in which increased heterogeneity can reduce cultural group formation while
simultaneously increasing social connectedness. Our results show that in
certain regions of the parameter space these co-evolutionary dynamics can lead
to patterns of cultural diversity that are stable in the presence of cultural
drift.Comment: (8 pages, 8 figures
Disseminating Research Information through Facebook and Twitter (DRIFT): presenting an evidence based framework
Background: The social media platform Facebook boasts over 1,284 million daily active users globally. It is also known that a large proportion of adults use the internet to seek health related information.Aim: to critically analyse the use of social media to engage parents of children with ADHD with clinical research findings.Methods: Observation and qualitative content analysis combined with Facebook insights was used to evaluate the levels of engagement and interaction with different types of research information.Results: Over 1100 people from 41 nations have engaged with the group. Sharing information through a range of Facebook functions was found to successfully achieve engagement and reach nationally and internationally for this demographic.Conclusion: Lay research users are eager to engage and understand clinical research and social media is an appropriate way to disseminate this. This article has proposed some methods and explanatory reasons for this phenomena.Implications for practice: It is known that social media can be used for effective communication. This article presents a much-needed evidence based framework that may be used by nursing and health researchers to successfully achieve this
First-passage distributions for the one-dimensional Fokker-Planck equation
We present an analytical framework to study the first-passage (FP) and
first-return (FR) distributions for the broad family of models described by the
one-dimensional Fokker-Planck equation in finite domains, identifying general
properties of these distributions for different classes of models. When in the
Fokker-Planck equation the diffusion coefficient is positive (nonzero) and the
drift term is bounded, as in the case of a Brownian walker, both distributions
may exhibit a power-law decay with exponent -3/2 for intermediate times. We
discuss how the influence of an absorbing state changes this exponent. The
absorbing state is characterized by a vanishing diffusion coefficient and/or a
diverging drift term. Remarkably, the exponent of the Brownian walker class of
models is still found, as long as the departure and arrival regions are far
enough from the absorbing state, but the range of times where the power law is
observed narrows. Close enough to the absorbing point, though, a new exponent
may appear. The particular value of the exponent depends on the behavior of the
diffusion and the drift terms of the Fokker-Planck equation. We focus on the
case of a diffusion term vanishing linearly at the absorbing point. In this
case, the FP and FR distributions are similar to those of the voter model,
characterized by a power law with exponent -2. As an illustration of the
general theory, we compare it with exact analytical solutions and extensive
numerical simulations of a two-parameter voter-like family models. We study the
behavior of the FP and FR distributions by tuning the importance of the
absorbing points throughout changes of the parameters. Finally, the possibility
of inferring relevant information about the steady-sate probability
distribution of a model from the FP and FR distributions is addressed.Comment: 17 pages, 8 figure
Relative entropy minimizing noisy non-linear neural network to approximate stochastic processes
A method is provided for designing and training noise-driven recurrent neural
networks as models of stochastic processes. The method unifies and generalizes
two known separate modeling approaches, Echo State Networks (ESN) and Linear
Inverse Modeling (LIM), under the common principle of relative entropy
minimization. The power of the new method is demonstrated on a stochastic
approximation of the El Nino phenomenon studied in climate research
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