11,623 research outputs found
Detecting Unspecified Structure in Low-Count Images
Unexpected structure in images of astronomical sources often presents itself
upon visual inspection of the image, but such apparent structure may either
correspond to true features in the source or be due to noise in the data. This
paper presents a method for testing whether inferred structure in an image with
Poisson noise represents a significant departure from a baseline (null) model
of the image. To infer image structure, we conduct a Bayesian analysis of a
full model that uses a multiscale component to allow flexible departures from
the posited null model. As a test statistic, we use a tail probability of the
posterior distribution under the full model. This choice of test statistic
allows us to estimate a computationally efficient upper bound on a p-value that
enables us to draw strong conclusions even when there are limited computational
resources that can be devoted to simulations under the null model. We
demonstrate the statistical performance of our method on simulated images.
Applying our method to an X-ray image of the quasar 0730+257, we find
significant evidence against the null model of a single point source and
uniform background, lending support to the claim of an X-ray jet
Multi-scale Modularity in Complex Networks
We focus on the detection of communities in multi-scale networks, namely
networks made of different levels of organization and in which modules exist at
different scales. It is first shown that methods based on modularity are not
appropriate to uncover modules in empirical networks, mainly because modularity
optimization has an intrinsic bias towards partitions having a characteristic
number of modules which might not be compatible with the modular organization
of the system. We argue for the use of more flexible quality functions
incorporating a resolution parameter that allows us to reveal the natural
scales of the system. Different types of multi-resolution quality functions are
described and unified by looking at the partitioning problem from a dynamical
viewpoint. Finally, significant values of the resolution parameter are selected
by using complementary measures of robustness of the uncovered partitions. The
methods are illustrated on a benchmark and an empirical network.Comment: 8 pages, 3 figure
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