505 research outputs found
Phase transitions in social sciences: two-populations mean field theory
A new mean field statistical mechanics model of two interacting groups of
spins is introduced and the phase transition studied in terms of their relative
size. A jump of the average magnetization is found for large values of the
mutual interaction when the relative percentage of the two populations crosses
a critical threshold. It is shown how the critical percentage depends on
internal interactions and on the initial magnetizations. The model is
interpreted as a prototype of resident-immigrant cultural interaction and
conclusions from the social sciences perspectives are drawn
Analysis of weighted networks
The connections in many networks are not merely binary entities, either
present or not, but have associated weights that record their strengths
relative to one another. Recent studies of networks have, by and large, steered
clear of such weighted networks, which are often perceived as being harder to
analyze than their unweighted counterparts. Here we point out that weighted
networks can in many cases be analyzed using a simple mapping from a weighted
network to an unweighted multigraph, allowing us to apply standard techniques
for unweighted graphs to weighted ones as well. We give a number of examples of
the method, including an algorithm for detecting community structure in
weighted networks and a new and simple proof of the max-flow/min-cut theorem.Comment: 9 pages, 3 figure
Generalized Master Equations for Non-Poisson Dynamics on Networks
The traditional way of studying temporal networks is to aggregate the
dynamics of the edges to create a static weighted network. This implicitly
assumes that the edges are governed by Poisson processes, which is not
typically the case in empirical temporal networks. Consequently, we examine the
effects of non-Poisson inter-event statistics on the dynamics of edges, and we
apply the concept of a generalized master equation to the study of
continuous-time random walks on networks. We show that the equation reduces to
the standard rate equations when the underlying process is Poisson and that the
stationary solution is determined by an effective transition matrix whose
leading eigenvector is easy to calculate. We discuss the implications of our
work for dynamical processes on temporal networks and for the construction of
network diagnostics that take into account their nontrivial stochastic nature
Universality in movie rating distributions
In this paper histograms of user ratings for movies (1,...,10) are analysed.
The evolving stabilised shapes of histograms follow the rule that all are
either double- or triple-peaked. Moreover, at most one peak can be on the
central bins 2,...,9 and the distribution in these bins looks smooth
`Gaussian-like' while changes at the extremes (1 and 10) often look abrupt. It
is shown that this is well approximated under the assumption that histograms
are confined and discretised probability density functions of L\'evy skew
alpha-stable distributions. These distributions are the only stable
distributions which could emerge due to a generalized central limit theorem
from averaging of various independent random avriables as which one can see the
initial opinions of users. Averaging is also an appropriate assumption about
the social process which underlies the process of continuous opinion formation.
Surprisingly, not the normal distribution achieves the best fit over histograms
obseved on the web, but distributions with fat tails which decay as power-laws
with exponent -(1+alpha) (alpha=4/3). The scale and skewness parameters of the
Levy skew alpha-stable distributions seem to depend on the deviation from an
average movie (with mean about 7.6). The histogram of such an average movie has
no skewness and is the most narrow one. If a movie deviates from average the
distribution gets broader and skew. The skewness pronounces the deviation. This
is used to construct a one parameter fit which gives some evidence of
universality in processes of continuous opinion dynamics about taste.Comment: 8 pages, 5 figures, accepted for publicatio
Cascades on clique-based graphs
peer-reviewedWe present an analytical approach to determining the expected cascade size in a broad range of dynamical models on the class of highly clustered random graphs introduced by Gleeson [J. P. Gleeson, Phys. Rev. E 80, 036107 (2009)]. A condition for the existence of global cascades is also derived. Applications of this approach include analyses of percolation, and Watts's model. We show how our techniques can be used to study the effects of in-group bias in cascades on social networks.PUBLISHEDpeer-reviewe
Collective Decision Dynamics in the Presence of External Drivers
We develop a sequence of models describing information transmission and
decision dynamics for a network of individual agents subject to multiple
sources of influence. Our general framework is set in the context of an
impending natural disaster, where individuals, represented by nodes on the
network, must decide whether or not to evacuate. Sources of influence include a
one-to-many externally driven global broadcast as well as pairwise
interactions, across links in the network, in which agents transmit either
continuous opinions or binary actions. We consider both uniform and variable
threshold rules on the individual opinion as baseline models for
decision-making. Our results indicate that 1) social networks lead to
clustering and cohesive action among individuals, 2) binary information
introduces high temporal variability and stagnation, and 3) information
transmission over the network can either facilitate or hinder action adoption,
depending on the influence of the global broadcast relative to the social
network. Our framework highlights the essential role of local interactions
between agents in predicting collective behavior of the population as a whole.Comment: 14 pages, 7 figure
Attention on Weak Ties in Social and Communication Networks
Granovetter's weak tie theory of social networks is built around two central
hypotheses. The first states that strong social ties carry the large majority
of interaction events; the second maintains that weak social ties, although
less active, are often relevant for the exchange of especially important
information (e.g., about potential new jobs in Granovetter's work). While
several empirical studies have provided support for the first hypothesis, the
second has been the object of far less scrutiny. A possible reason is that it
involves notions relative to the nature and importance of the information that
are hard to quantify and measure, especially in large scale studies. Here, we
search for empirical validation of both Granovetter's hypotheses. We find clear
empirical support for the first. We also provide empirical evidence and a
quantitative interpretation for the second. We show that attention, measured as
the fraction of interactions devoted to a particular social connection, is high
on weak ties --- possibly reflecting the postulated informational purposes of
such ties --- but also on very strong ties. Data from online social media and
mobile communication reveal network-dependent mixtures of these two effects on
the basis of a platform's typical usage. Our results establish a clear
relationships between attention, importance, and strength of social links, and
could lead to improved algorithms to prioritize social media content
Academic team formation as evolving hypergraphs
This paper quantitatively explores the social and socio-semantic patterns of
constitution of academic collaboration teams. To this end, we broadly underline
two critical features of social networks of knowledge-based collaboration:
first, they essentially consist of group-level interactions which call for
team-centered approaches. Formally, this induces the use of hypergraphs and
n-adic interactions, rather than traditional dyadic frameworks of interaction
such as graphs, binding only pairs of agents. Second, we advocate the joint
consideration of structural and semantic features, as collaborations are
allegedly constrained by both of them. Considering these provisions, we propose
a framework which principally enables us to empirically test a series of
hypotheses related to academic team formation patterns. In particular, we
exhibit and characterize the influence of an implicit group structure driving
recurrent team formation processes. On the whole, innovative production does
not appear to be correlated with more original teams, while a polarization
appears between groups composed of experts only or non-experts only, altogether
corresponding to collectives with a high rate of repeated interactions
Correlation between centrality metrics and their application to the opinion model
In recent decades, a number of centrality metrics describing network
properties of nodes have been proposed to rank the importance of nodes. In
order to understand the correlations between centrality metrics and to
approximate a high-complexity centrality metric by a strongly correlated
low-complexity metric, we first study the correlation between centrality
metrics in terms of their Pearson correlation coefficient and their similarity
in ranking of nodes. In addition to considering the widely used centrality
metrics, we introduce a new centrality measure, the degree mass. The m order
degree mass of a node is the sum of the weighted degree of the node and its
neighbors no further than m hops away. We find that the B_{n}, the closeness,
and the components of x_{1} are strongly correlated with the degree, the
1st-order degree mass and the 2nd-order degree mass, respectively, in both
network models and real-world networks. We then theoretically prove that the
Pearson correlation coefficient between x_{1} and the 2nd-order degree mass is
larger than that between x_{1} and a lower order degree mass. Finally, we
investigate the effect of the inflexible antagonists selected based on
different centrality metrics in helping one opinion to compete with another in
the inflexible antagonists opinion model. Interestingly, we find that selecting
the inflexible antagonists based on the leverage, the B_{n}, or the degree is
more effective in opinion-competition than using other centrality metrics in
all types of networks. This observation is supported by our previous
observations, i.e., that there is a strong linear correlation between the
degree and the B_{n}, as well as a high centrality similarity between the
leverage and the degree.Comment: 20 page
Cooperation for public goods under uncertainty
Everyone wants clean air, peace and other public goods but is tempted to
freeride on others' efforts. The usual way out of this dilemma is to impose
norms, maintain reputations and incentivize individuals to contribute. In
situations of high uncertainty, however, such as confrontations of protesters
with a dictatorial regime, the usual measures are not feasible, but cooperation
can be achieved nevertheless. We use an Ising model with asymmetric spins that
represent cooperation and defection to show numerically how public goods can be
realized. Under uncertainty, people use the heuristic of conformity. The
turmoil of a confrontation causes some individuals to cooperate accidentally,
and at a critical level of turmoil, they entail a cascade of cooperation. This
critical level is much lower in small networks
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