1,840 research outputs found
Exploring the randomness of Directed Acyclic Networks
The feed-forward relationship naturally observed in time-dependent processes
and in a diverse number of real systems -such as some food-webs and electronic
and neural wiring- can be described in terms of so-called directed acyclic
graphs (DAGs). An important ingredient of the analysis of such networks is a
proper comparison of their observed architecture against an ensemble of
randomized graphs, thereby quantifying the {\em randomness} of the real systems
with respect to suitable null models. This approximation is particularly
relevant when the finite size and/or large connectivity of real systems make
inadequate a comparison with the predictions obtained from the so-called {\em
configuration model}. In this paper we analyze four methods of DAG
randomization as defined by the desired combination of topological invariants
(directed and undirected degree sequence and component distributions) aimed to
be preserved. A highly ordered DAG, called \textit{snake}-graph and a
Erd\:os-R\'enyi DAG were used to validate the performance of the algorithms.
Finally, three real case studies, namely, the \textit{C. elegans} cell lineage
network, a PhD student-advisor network and the Milgram's citation network were
analyzed using each randomization method. Results show how the interpretation
of degree-degree relations in DAGs respect to their randomized ensembles depend
on the topological invariants imposed. In general, real DAGs provide disordered
values, lower than the expected by chance when the directedness of the links is
not preserved in the randomization process. Conversely, if the direction of the
links is conserved throughout the randomization process, disorder indicators
are close to the obtained from the null-model ensemble, although some
deviations are observed.Comment: 13 pages, 5 figures and 5 table
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
Experimental bilocality violation without shared reference frames
Non-classical correlations arising in complex quantum networks are attracting
growing interest, both from a fundamental perspective and for potential
applications in information processing. In particular, in an entanglement
swapping scenario a new kind of correlations arise, the so-called nonbilocal
correlations that are incompatible with local realism augmented with the
assumption that the sources of states used in the experiment are independent.
In practice, however, bilocality tests impose strict constraints on the
experimental setup and in particular to presence of shared reference frames
between the parties. Here, we experimentally address this point showing that
false positive nonbilocal quantum correlations can be observed even though the
sources of states are independent. To overcome this problem, we propose and
demonstrate a new scheme for the violation of bilocality that does not require
shared reference frames and thus constitute an important building block for
future investigations of quantum correlations in complex networks.Comment: 10 page
Type Ia Supernova Light Curve Inference: Hierarchical Bayesian Analysis in the Near Infrared
We present a comprehensive statistical analysis of the properties of Type Ia
SN light curves in the near infrared using recent data from PAIRITEL and the
literature. We construct a hierarchical Bayesian framework, incorporating
several uncertainties including photometric error, peculiar velocities, dust
extinction and intrinsic variations, for coherent statistical inference. SN Ia
light curve inferences are drawn from the global posterior probability of
parameters describing both individual supernovae and the population conditioned
on the entire SN Ia NIR dataset. The logical structure of the hierarchical
model is represented by a directed acyclic graph. Fully Bayesian analysis of
the model and data is enabled by an efficient MCMC algorithm exploiting the
conditional structure using Gibbs sampling. We apply this framework to the
JHK_s SN Ia light curve data. A new light curve model captures the observed
J-band light curve shape variations. The intrinsic variances in peak absolute
magnitudes are: sigma(M_J) = 0.17 +/- 0.03, sigma(M_H) = 0.11 +/- 0.03, and
sigma(M_Ks) = 0.19 +/- 0.04. We describe the first quantitative evidence for
correlations between the NIR absolute magnitudes and J-band light curve shapes,
and demonstrate their utility for distance estimation. The average residual in
the Hubble diagram for the training set SN at cz > 2000 km/s is 0.10 mag. The
new application of bootstrap cross-validation to SN Ia light curve inference
tests the sensitivity of the model fit to the finite sample and estimates the
prediction error at 0.15 mag. These results demonstrate that SN Ia NIR light
curves are as effective as optical light curves, and, because they are less
vulnerable to dust absorption, they have great potential as precise and
accurate cosmological distance indicators.Comment: 24 pages, 15 figures, 4 tables. Accepted for publication in ApJ.
Corrected typo, added references, minor edit
- …