1,225 research outputs found
Spreading gossip in social networks
We study a simple model of information propagation in social networks, where
two quantities are introduced: the spread factor, which measures the average
maximal fraction of neighbors of a given node that interchange information
among each other, and the spreading time needed for the information to reach
such fraction of nodes. When the information refers to a particular node at
which both quantities are measured, the model can be taken as a model for
gossip propagation. In this context, we apply the model to real empirical
networks of social acquaintances and compare the underlying spreading dynamics
with different types of scale-free and small-world networks. We find that the
number of friendship connections strongly influences the probability of being
gossiped. Finally, we discuss how the spread factor is able to be applied to
other situations.Comment: 10 pages, 16 figures, Revtex; Virt.J. of Biol. Phys., Oct.1 200
The dynamics of financial stability in complex networks
We address the problem of banking system resilience by applying
off-equilibrium statistical physics to a system of particles, representing the
economic agents, modelled according to the theoretical foundation of the
current banking regulation, the so called Merton-Vasicek model. Economic agents
are attracted to each other to exchange `economic energy', forming a network of
trades. When the capital level of one economic agent drops below a minimum, the
economic agent becomes insolvent. The insolvency of one single economic agent
affects the economic energy of all its neighbours which thus become susceptible
to insolvency, being able to trigger a chain of insolvencies (avalanche). We
show that the distribution of avalanche sizes follows a power-law whose
exponent depends on the minimum capital level. Furthermore, we present evidence
that under an increase in the minimum capital level, large crashes will be
avoided only if one assumes that agents will accept a drop in business levels,
while keeping their trading attitudes and policies unchanged. The alternative
assumption, that agents will try to restore their business levels, may lead to
the unexpected consequence that large crises occur with higher probability
Standard decomposition of expansive ergodically supported dynamics
In this work we introduce the notion of weak quasigroups, that are quasigroup
operations defined almost everywhere on some set. Then we prove that the
topological entropy and the ergodic period of an invertible expansive
ergodically supported dynamical system with the shadowing property
establishes a sufficient criterion for the existence of quasigroup operations
defined almost everywhere outside of universally null sets and for which is
an automorphism. Furthermore, we find a decomposition of the dynamics of in
terms of -invariant weak topological subquasigroups.Comment: 18 pages, the conditions on the entropy in Theorem 3.5 was improved.
Some small changes in the text, by adding more explanation
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