16,222 research outputs found
Measuring the transition to homogeneity with photometric redshift surveys
We study the possibility of detecting the transition to homogeneity using
photometric redshift catalogs. Our method is based on measuring the fractality
of the projected galaxy distribution, using angular distances, and relies only
on observable quantites. It thus provides a way to test the Cosmological
Principle in a model-independent unbiased way. We have tested our method on
different synthetic inhomogeneous catalogs, and shown that it is capable of
discriminating some fractal models with relatively large fractal dimensions, in
spite of the loss of information due to the radial projection. We have also
studied the influence of the redshift bin width, photometric redshift errors,
bias, non-linear clustering, and surveyed area, on the angular homogeneity
index H2 ({\theta}) in a {\Lambda}CDM cosmology. The level to which an upcoming
galaxy survey will be able to constrain the transition to homogeneity will
depend mainly on the total surveyed area and the compactness of the surveyed
region. In particular, a Dark Energy Survey (DES)-like survey should be able to
easily discriminate certain fractal models with fractal dimensions as large as
D2 = 2.95. We believe that this method will have relevant applications for
upcoming large photometric redshift surveys, such as DES or the Large Synoptic
Survey Telescope (LSST).Comment: 14 pages, 14 figure
Dimensionality reduction and spectral properties of multilayer networks
Network representations are useful for describing the structure of a large
variety of complex systems. Although most studies of real-world networks
suppose that nodes are connected by only a single type of edge, most natural
and engineered systems include multiple subsystems and layers of connectivity.
This new paradigm has attracted a great deal of attention and one fundamental
challenge is to characterize multilayer networks both structurally and
dynamically. One way to address this question is to study the spectral
properties of such networks. Here, we apply the framework of graph quotients,
which occurs naturally in this context, and the associated eigenvalue
interlacing results, to the adjacency and Laplacian matrices of undirected
multilayer networks. Specifically, we describe relationships between the
eigenvalue spectra of multilayer networks and their two most natural quotients,
the network of layers and the aggregate network, and show the dynamical
implications of working with either of the two simplified representations. Our
work thus contributes in particular to the study of dynamical processes whose
critical properties are determined by the spectral properties of the underlying
network.Comment: minor changes; pre-published versio
Isocausal spacetimes may have different causal boundaries
We construct an example which shows that two isocausal spacetimes, in the
sense introduced by Garc\'ia-Parrado and Senovilla, may have c-boundaries which
are not equal (more precisely, not equivalent, as no bijection between the
completions can preserve all the binary relations induced by causality). This
example also suggests that isocausality can be useful for the understanding and
computation of the c-boundary.Comment: Minor modifications, including the title, which matches now with the
published version. 12 pages, 3 figure
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