305 research outputs found
An information theory based search for homogeneity on the largest accessible scale
We analyze the SDSS DR12 quasar catalogue to test the large-scale smoothness
in the quasar distribution. We quantify the degree of inhomogeneity in the
quasar distribution using information theory based measures and find that the
degree of inhomogeneity diminishes with increasing length scales which finally
reach a plateau at . The residual inhomogeneity
at the plateau is consistent with that expected for a Poisson point process.
Our results indicate that the quasar distribution is homogeneous beyond length
scales of .Comment: 5 pages, 2 figures, Corrected a few typos, Accepted for publication
in MNRAS Letter
Unravelling the Cosmic Web: An analysis of the SDSS DR14 with the Local Dimension
We analyze a volume limited galaxy sample from the SDSS to study the
environments of galaxies on different length scales in the local Universe. We
measure the local dimension of the SDSS galaxies on different length scales and
find that the sheets or sheetlike structures are the most prevalent pattern in
the cosmic web throughout the entire length scales. The abundance of sheets
peaks at and they can extend upto a length scales of
. Analyzing mock catalogues, we find that the sheets
are non-existent beyond in the Poisson
distributions. We find that the straight filaments in the SDSS galaxy
distribution can extend only upto a length scale of .
Our results indicate that the environment of a galaxy exhibits a gradual
transition towards higher local dimension with increasing length scales finally
approaching a nearly homogeneous network on large scales. We compare our
findings with a semi analytic galaxy catalogue from the Millennium Run
simulation which are in fairly good agreement with the observations. We also
test the effects of the number density of the sample and the cut-off in the
goodness of fit which shows that the results are nearly independent of these
factors. Finally we apply the method to a set of simulations of the segment Cox
process and find that it can characterize such distributions.Comment: 12 pages, 6 figures, 2 tables, Accepted for publication in MNRA
Testing homogeneity in the Sloan Digital Sky Survey Data Release Twelve with Shannon entropy
We analyze a set of volume limited samples from SDSS DR12 to quantify the
degree of inhomogeneity at different length scales using Shannon entropy. We
find that the galaxy distributions exhibit a higher degree of inhomogeneity as
compared to a Poisson point process at all length scales. Our analysis
indicates that signatures of inhomogeneities in the galaxy distributions
persist at least upto a length scale of . The galaxy
distributions appear to be homogeneous on a scale of and beyond. Analyzing a set of mock galaxy samples from a semi analytic
galaxy catalogue from the Millennium simulation we find a scale of transition
to homogeneity at .Comment: Added 2 new figures and expanded some discussion, Accepted for
publication in MNRA
Probing large scale homogeneity and periodicity in the LRG distribution using Shannon entropy
We quantify the degree of inhomogeneity in the Luminous Red Galaxy (LRG)
distribution from the SDSS DR7 as a function of length scales by measuring the
Shannon entropy in independent and regular cubic voxels of increasing grid
sizes. We also analyze the data by carrying out measurements in overlapping
spheres and find that it suppresses inhomogeneities by a factor of 5 to 10 on
different length scales. Despite the differences observed in the degree of
inhomogeneity both the methods show a decrease in inhomogeneity with increasing
length scales which eventually settle down to a plateau at . Considering the minuscule values of inhomogeneity at the plateaus
and their expected variations we conclude that the LRG distribution becomes
homogeneous at and beyond. We also use the
Kullback-Leibler divergence as an alternative measure of inhomogeneity which
reaffirms our findings. We show that the method presented here can effectively
capture the inhomogeneity in a truly inhomogeneous distribution at all length
scales. We analyze a set of Monte Carlo simulations with certain periodicity in
their spatial distributions and find periodic variations in their inhomogeneity
which helps us to identify the underlying regularities present in such
distributions and quantify the scale of their periodicity. We do not find any
underlying regularities in the LRG distribution within the length scales
probed.Comment: 11 pages, 6 figures, minor revision, Accepted for publication in
MNRA
Fuzzy Rough Relations
In this paper, the definition of fuzzy rough relation on a set will be
introduced and then it would be proved that the collection of such relations is
closed under different binary compositions such as, algebraic sum, algebraic
product etc. Also the definitions of reflexive, symmetric and transitive fuzzy
rough relations on a set are given and a few properties of them will be
investigated. Lastly, we define a operation, which is a composition of two
fuzzy rough relations, with the help of maxmin relation and thereafter it is
shown that the collection of such relations is closed under the operation.Comment: 8 page
Testing isotropy in the Universe using photometric and spectroscopic data from the SDSS
We analyze two volume limited galaxy samples from the SDSS photometric and
spectroscopic data to test the isotropy in the local Universe. We use
information entropy to quantify the global anisotropy in the galaxy
distribution at different length scales and find that the galaxy distribution
is highly anisotropic on small scales. The observed anisotropy diminishes with
increasing length scales and nearly plateaus out beyond a length scale of 200
Mpc/h in both the datasets. We compare these anisotropies with those predicted
by the mock catalogues from the N-body simulations of the Lambda CDM model and
find a fairly good agreement with the observations. We find a small residual
anisotropy on large scales which decays in a way that is consistent with the
linear perturbation theory. The slopes of the observed anisotropy converge to
the slopes predicted by the linear theory beyond a length scale of ~ 200 Mpc/h
indicating a transition to isotropy. We separately compare the anisotropies
observed across the different parts of the sky and find no evidence for a
preferred direction in the galaxy distribution.Comment: 14 pages, 10 figures, 1 table, Minor revisions, Accepted for
publication in MNRA
Nontrilocality: Exploiting nonlocality from three particle systems
In Phys. Rev. Lett. \textbf{104},170401 (2010), Branciard \textit{e.t al.}
first characterized the correlations arising in an entanglement swapping
network under the assumption that the sources generating the initially
uncorrelated quantum systems are independent. Precisely speaking, in Phys. Rev.
Lett. \textbf{104},170401 (2010) and later in Phys. Rev. A \textbf{85},032119
(2012) the authors analyzed the importance of \textit{bilocal}(source
independence) assumption to lower down the restrictions over correlations for
revealing quantumness in the network where each of two sources generates a
bipartite entangled state. In this context one may find interest to
characterize correlations in a network involving independent sources which can
correlate more than two initially uncorrelated multipartite entangled quantum
systems. Our present topic of discussion basically analyzes such a network
scenario. Specifically we introduce \textit{trilocal network scenario} where
each of three sources independently generates a tripartite entangled quantum
system thereby exploring the role of source independence assumption to exploit
nonlocality in a network involving multipartite entanglement analogous to
bilocal assumption in a network where only bipartite entanglement was
considered. Interestingly, genuine entanglement content did not turn out to be
an essential requirement for exploiting nonlocality in such a scenario.
Moreover it is interesting to explore whether such a scenario can be
generalized so as to characterize correlations arising in a network involving
number of partite systems for any finite value of under source
independence assumption.Comment: 15 pages, 6 figures, revtex4, comments welcom
Simulating GHZ Correlations Relaxing Physical Constraints
Violation of Bell inequality (or, Bell-type inequalities) by nonlocal
correlations is justified by relaxation of at least one of the plausible
physical constraints used to model such inequality. Based on this fact, in this
letter we present a procedure to simulate three-qubit GHZ correlation relaxing
two constraints, determinism and no signaling simultaneously. We have also
derived the minimum amount of indeterminism and signaling to be introduced in a
system. The corresponding number of signaling and local bits of mutual
information needed to communicate are also provided and thus we are able to
focus on utility of relaxation of these two constraints as useful resources.Comment: 5 pages, 1 figure, revtex, submitted to PR
Efficient Test to Demonstrate Genuine Three Particle Nonlocality
According to the studies of genuine tripartite nonlocality in discrete
variable quantum systems conducted so far, Svetlichny inequality is considered
as the best Bell-type inequality to detect genuine (three way) nonlocality of
pure tripartite genuine entangled states. In the present work, we have
considered another Bell-type inequality (which has been reported as the -th
facet of local polytope in (J.-D. Bancal, et.al.,Phys. Rev.A
\textbf{88}, 014102 (2013)), to reveal genuine tripartite nonlocality of
generalized GHZ(Greenberger-Horne-Zeilinger) class and a subclass of extended
GHZ class states(\cite{ACN}) thereby proving the conjecture given by Bancal,
et.al.\cite{BAL} for the GGHZ class and the subclass of extended GHZ states. We
compare the violation of this inequality with Svetlichny inequality which
reveals the efficiency of the former inequality over the latter to demonstrate
genuine nonlocality using the above classes of quantum states. Even in some
cases discord monogamy score can be used as a better measure of quantum
correlation over Svetlichny inequality for those classes of pure states.
Besides, the -th facet inequality is found efficient not only for revealing
genuine nonlocal behavior of correlations emerging in systems using pure
entangled states but also in some cases of mixed entangled states over
Svetlichny inequality and some well known measures of entanglement .Comment: 16 pages, 11 figures, 2 tables, revtex, comments welcome, to appear
in J.Phys.
One Sided indeterminism alone is not a useful resource to simulate any nonlocal correlation
Determinism, no signaling and measurement independence are some of the
constraints required for framing Bell inequality. Any model simulating nonlocal
correlations must either individually or jointly give up these constraints.
Recently M. J. W. Hall (Phys Review A, \textbf{84}, 022102 (2011)) derived
different forms of Bell inequalities under the assumption of individual or
joint relaxation of those constraints on both(i.e., two) the sides of a
bipartite system. In this work we have investigated whether one sided
relaxation can also be a useful resource for simulating nonlocal correlations
or not. We have derived Bell-type inequalities under the assumption of joint
relaxation of these constraints only by one party of a bipartite system.
Interestingly we found that any amount of randomness in correlations of one
party in absence of signaling between two parties is incapable of showing any
sort of Bell-CHSH violation whereas signaling and measurement dependence
individually can simulate any nonlocal correlations. We have also completed the
proof of a recent conjecture due to Hall (Phys. Rev. A \textbf{82}, 062117
(2010); Phys. Rev. A \textbf{84}, 022102 (2011)) for one sided relaxation
scenario only.Comment: 7 pages, 4 figures, revtex, to appear in qi
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