44,858 research outputs found
Dynamic hierarchies in temporal directed networks
The outcome of interactions in many real-world systems can be often explained
by a hierarchy between the participants. Discovering hierarchy from a given
directed network can be formulated as follows: partition vertices into levels
such that, ideally, there are only forward edges, that is, edges from upper
levels to lower levels. In practice, the ideal case is impossible, so instead
we minimize some penalty function on the backward edges. One practical option
for such a penalty is agony, where the penalty depends on the severity of the
violation. In this paper we extend the definition of agony to temporal
networks. In this setup we are given a directed network with time stamped
edges, and we allow the rank assignment to vary over time. We propose 2
strategies for controlling the variation of individual ranks. In our first
variant, we penalize the fluctuation of the rankings over time by adding a
penalty directly to the optimization function. In our second variant we allow
the rank change at most once. We show that the first variant can be solved
exactly in polynomial time while the second variant is NP-hard, and in fact
inapproximable. However, we develop an iterative method, where we first fix the
change point and optimize the ranks, and then fix the ranks and optimize the
change points, and reiterate until convergence. We show empirically that the
algorithms are reasonably fast in practice, and that the obtained rankings are
sensible
Dwelling Quietly in the Rich Club: Brain Network Determinants of Slow Cortical Fluctuations
For more than a century, cerebral cartography has been driven by
investigations of structural and morphological properties of the brain across
spatial scales and the temporal/functional phenomena that emerge from these
underlying features. The next era of brain mapping will be driven by studies
that consider both of these components of brain organization simultaneously --
elucidating their interactions and dependencies. Using this guiding principle,
we explored the origin of slowly fluctuating patterns of synchronization within
the topological core of brain regions known as the rich club, implicated in the
regulation of mood and introspection. We find that a constellation of densely
interconnected regions that constitute the rich club (including the anterior
insula, amygdala, and precuneus) play a central role in promoting a stable,
dynamical core of spontaneous activity in the primate cortex. The slow time
scales are well matched to the regulation of internal visceral states,
corresponding to the somatic correlates of mood and anxiety. In contrast, the
topology of the surrounding "feeder" cortical regions show unstable, rapidly
fluctuating dynamics likely crucial for fast perceptual processes. We discuss
these findings in relation to psychiatric disorders and the future of
connectomics.Comment: 35 pages, 6 figure
Global network structure of dominance hierarchy of ant workers
Dominance hierarchy among animals is widespread in various species and
believed to serve to regulate resource allocation within an animal group.
Unlike small groups, however, detection and quantification of linear hierarchy
in large groups of animals are a difficult task. Here, we analyse
aggression-based dominance hierarchies formed by worker ants in Diacamma sp. as
large directed networks. We show that the observed dominance networks are
perfect or approximate directed acyclic graphs, which are consistent with
perfect linear hierarchy. The observed networks are also sparse and random but
significantly different from networks generated through thinning of the perfect
linear tournament (i.e., all individuals are linearly ranked and dominance
relationship exists between every pair of individuals). These results pertain
to global structure of the networks, which contrasts with the previous studies
inspecting frequencies of different types of triads. In addition, the
distribution of the out-degree (i.e., number of workers that the focal worker
attacks), not in-degree (i.e., number of workers that attack the focal worker),
of each observed network is right-skewed. Those having excessively large
out-degrees are located near the top, but not the top, of the hierarchy. We
also discuss evolutionary implications of the discovered properties of
dominance networks.Comment: 5 figures, 2 tables, 4 supplementary figures, 2 supplementary table
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