62,383 research outputs found
The scaling limits of the Minimal Spanning Tree and Invasion Percolation in the plane
We prove that the Minimal Spanning Tree and the Invasion Percolation Tree on
a version of the triangular lattice in the complex plane have unique scaling
limits, which are invariant under rotations, scalings, and, in the case of the
MST, also under translations. However, they are not expected to be conformally
invariant. We also prove some geometric properties of the limiting MST. The
topology of convergence is the space of spanning trees introduced by Aizenman,
Burchard, Newman & Wilson (1999), and the proof relies on the existence and
conformal covariance of the scaling limit of the near-critical percolation
ensemble, established in our earlier works.Comment: 56 pages, 21 figures. A thoroughly revised versio
Social learning strategies modify the effect of network structure on group performance
The structure of communication networks is an important determinant of the
capacity of teams, organizations and societies to solve policy, business and
science problems. Yet, previous studies reached contradictory results about the
relationship between network structure and performance, finding support for the
superiority of both well-connected efficient and poorly connected inefficient
network structures. Here we argue that understanding how communication networks
affect group performance requires taking into consideration the social learning
strategies of individual team members. We show that efficient networks
outperform inefficient networks when individuals rely on conformity by copying
the most frequent solution among their contacts. However, inefficient networks
are superior when individuals follow the best member by copying the group
member with the highest payoff. In addition, groups relying on conformity based
on a small sample of others excel at complex tasks, while groups following the
best member achieve greatest performance for simple tasks. Our findings
reconcile contradictory results in the literature and have broad implications
for the study of social learning across disciplines
Universality for critical heavy-tailed network models: Metric structure of maximal components
We study limits of the largest connected components (viewed as metric spaces)
obtained by critical percolation on uniformly chosen graphs and configuration
models with heavy-tailed degrees. For rank-one inhomogeneous random graphs,
such results were derived by Bhamidi, van der Hofstad, Sen [Probab. Theory
Relat. Fields 2018]. We develop general principles under which the identical
scaling limits as the rank-one case can be obtained. Of independent interest,
we derive refined asymptotics for various susceptibility functions and the
maximal diameter in the barely subcritical regime.Comment: Final published version. 47 pages, 6 figure
Community tracking in a cMOOC and nomadic learner behavior identification on a connectivist rhizomatic learning network
This article contributes to the literature on connectivism, connectivist MOOCs (cMOOCs) and rhizomatic learning by examining participant interactions, community formation and nomadic learner behavior in a particular cMOOC, #rhizo15, facilitated for 6 weeks by Dave Cormier. It further focuses on what we can learn by observing Twitter interactions particularly. As an explanatory mixed research design, Social Network Analysis and content analysis were employed for the purposes of the research. SNA is used at the macro, meso and micro levels, and content analysis of one week of the MOOC was conducted using the Community of Inquiry framework. The macro level analysis demonstrates that communities in a rhizomatic connectivist networks have chaotic relationships with other communities in different dimensions (clarified by use of hashtags of concurrent, past and future events). A key finding at the meso level was that as #rhizo15 progressed and number of active participants decreased, interaction increased in overall network. The micro level analysis further reveals that, though completely online, the nature of open online ecosystems are very convenient to facilitate the formation of community. The content analysis of week 3 tweets demonstrated that cognitive presence was the most frequently observed, while teaching presence (teaching behaviors of both facilitator and participants) was the lowest. This research recognizes the limitations of looking only at Twitter when #rhizo15 conversations occurred over multiple platforms frequented by overlapping but not identical groups of people. However, it provides a valuable partial perspective at the macro meso and micro levels that contribute to our understanding of community-building in cMOOCs
Analyzing the Facebook Friendship Graph
Online Social Networks (OSN) during last years acquired a\ud
huge and increasing popularity as one of the most important emerging Web phenomena, deeply modifying the behavior of users and contributing to build a solid substrate of connections and relationships among people using the Web. In this preliminary work paper, our purpose is to analyze Facebook, considering a signi�cant sample of data re\ud
ecting relationships among subscribed users. Our goal is to extract, from this platform, relevant information about the distribution of these relations and exploit tools and algorithms provided by the Social Network Analysis (SNA) to discover and, possibly, understand underlying similarities\ud
between the developing of OSN and real-life social networks
The role of network topology on extremism propagation with the Relative Agreement opinion dynamics
In (Deffuant et al., 2002), we proposed a simple model of opinion dynamics,
which we used to simulate the influence of extremists in a population.
Simulations were run without any specific interaction structure and varying the
simulation parameters, we observed different attractors such as predominance of
centrism or of extremism. We even observed in certain conditions, that the
whole population drifts to one extreme of the opinion, even if initially there
are an equal number of extremists at each extreme of the opinion axis. In the
present paper, we study the influence of the social networks on the presence of
such a dynamical behavior. In particular, we use small-world networks with
variable connectivity and randomness of the connections. We find that the drift
to a single extreme appears only beyond a critical level of connectivity, which
decreases when the randomness increases.Comment: 15 pages, 9 figure
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