2,648 research outputs found
Randomized Algorithms for the Loop Cutset Problem
We show how to find a minimum weight loop cutset in a Bayesian network with
high probability. Finding such a loop cutset is the first step in the method of
conditioning for inference. Our randomized algorithm for finding a loop cutset
outputs a minimum loop cutset after O(c 6^k kn) steps with probability at least
1 - (1 - 1/(6^k))^c6^k, where c > 1 is a constant specified by the user, k is
the minimal size of a minimum weight loop cutset, and n is the number of
vertices. We also show empirically that a variant of this algorithm often finds
a loop cutset that is closer to the minimum weight loop cutset than the ones
found by the best deterministic algorithms known
Cosmic Bulk Flow and the Local Motion from Cosmicflows-2
Full sky surveys of peculiar velocity are arguably the best way to map the
large scale structure out to distances of a few times 100 Mpc/h. Using the
largest and most accurate ever catalog of galaxy peculiar velocities
"Cosmicflows-2", the large scale structure has been reconstructed by means of
the Wiener filter and constrained realizations assuming as a Bayesian prior
model the LCDM model with the WMAP inferred cosmological parameters. The
present paper focuses on studying the bulk flow of the local flow field,
defined as the mean velocity of top-hat spheres with radii ranging out to R=500
Mpc/h. The estimated large scale structures, in general, and the bulk flow, in
particular, are determined by the tension between the observational data and
the assumed prior model. A prerequisite for such an analysis is the requirement
that the estimated bulk flow is consistent with the prior model. Such a
consistency is found here. At R=50(150) Mpc/h the estimated bulk velocity is
250+/-21 (239+/-38) km/s. The corresponding cosmic variance at these radii is
126(60)km/s, which implies that these estimated bulk flows are dominated by the
data and not by the assumed prior model. The estimated bulk velocity is
dominated by the data out to R~200 Mpc/h, where the cosmic variance on the
individual Supergalactic Cartesian components (of the r.m.s. values) exceeds
the variance of the Constrained Realizations by at least a factor of 2. The
supergalactic SGX and SGY components of the CMB dipole velocity are recovered
by the Wiener filter velocity field down to a very few km/s. The SGZ component
of the estimated velocity, the one that is most affected by the Zone of
Avoidance, is off by 126 km/s (an almost 2 sigma discrepancy).Comment: 10 pages, accepted for MNRA
Fast Structuring of Radio Networks for Multi-Message Communications
We introduce collision free layerings as a powerful way to structure radio
networks. These layerings can replace hard-to-compute BFS-trees in many
contexts while having an efficient randomized distributed construction. We
demonstrate their versatility by using them to provide near optimal distributed
algorithms for several multi-message communication primitives.
Designing efficient communication primitives for radio networks has a rich
history that began 25 years ago when Bar-Yehuda et al. introduced fast
randomized algorithms for broadcasting and for constructing BFS-trees. Their
BFS-tree construction time was rounds, where is the network
diameter and is the number of nodes. Since then, the complexity of a
broadcast has been resolved to be rounds. On the other hand, BFS-trees have been used as a crucial building
block for many communication primitives and their construction time remained a
bottleneck for these primitives.
We introduce collision free layerings that can be used in place of BFS-trees
and we give a randomized construction of these layerings that runs in nearly
broadcast time, that is, w.h.p. in rounds for any constant . We then use these
layerings to obtain: (1) A randomized algorithm for gathering messages
running w.h.p. in rounds. (2) A randomized -message
broadcast algorithm running w.h.p. in rounds. These
algorithms are optimal up to the small difference in the additive
poly-logarithmic term between and . Moreover, they imply the
first optimal round randomized gossip algorithm
Goodness-of-fit analysis of the Cosmicflows-2 database of velocities
The goodness-of-fit (GoF) of the Cosmicflows-2 (CF2) database of peculiar
velocities with the LCDM standard model of cosmology is presented. Standard
application of the Chi^2 statistics of the full database, of its 4,838 data
points, is hampered by the small scale nonlinear dynamics which is not
accounted for by the (linear regime) velocity power spectrum. The bulk velocity
constitutes a highly compressed representation of the data which filters out
the small scales non-linear modes. Hence the statistics of the bulk flow
provides an efficient tool for assessing the GoF of the data given a model. The
particular approach introduced here is to use the (spherical top-hat window)
bulk velocity extracted from the Wiener filter reconstruction of the 3D
velocity field as a linear low pass filtered highly compressed representation
of the CF2 data. An ensemble 2250 random linear realizations of the WMAP/LCDM
model has been used to calculate the bulk velocity auto-covariance matrix. We
find that the CF2 data is consistent with the WMAP/LCDM model to better than
the 2 sigma confidence limits. This provides a further validation that the CF2
database is consistent with the standard model of cosmology.Comment: submitted to MNRAS, V2 : solved page sizing proble
The Arrowhead Mini-Supercluster of Galaxies
Superclusters of galaxies can be defined kinematically from local evaluations
of the velocity shear tensor. The location where the smallest eigenvalue of the
shear is positive and maximal defines the center of a basin of attraction.
Velocity and density fields are reconstructed with Wiener Filter techniques.
Local velocities due to the density field in a restricted region can be
separated from external tidal flows, permitting the identification of
boundaries separating inward flows toward a basin of attraction and outward
flows. This methodology was used to define the Laniakea Supercluster that
includes the Milky Way. Large adjacent structures include Perseus-Pisces, Coma,
Hercules, and Shapley but current kinematic data are insufficient to capture
their full domains. However there is a small region trapped between Laniakea,
Perseus-Pisces, and Coma that is close enough to be reliably characterized and
that satisfies the kinematic definition of a supercluster. Because of its
shape, it is given the name the Arrowhead Supercluster. This entity does not
contain any major clusters. A characteristic dimension is ~25 Mpc and the
contained mass is only ~10^15 Msun.Comment: Accepted for publication in The Astrophysical Journal. Video can be
viewed at http://irfu.cea.fr/arrowhea
Filaments from the galaxy distribution and from the velocity field in the local universe
The cosmic web that characterizes the large-scale structure of the Universe
can be quantified by a variety of methods. For example, large redshift surveys
can be used in combination with point process algorithms to extract long
curvilinear filaments in the galaxy distribution. Alternatively, given a full
3D reconstruction of the velocity field, kinematic techniques can be used to
decompose the web into voids, sheets, filaments and knots. In this paper we
look at how two such algorithms - the Bisous model and the velocity shear web -
compare with each other in the local Universe (within 100 Mpc), finding good
agreement. This is both remarkable and comforting, given that the two methods
are radically different in ideology and applied to completely independent and
different data sets. Unsurprisingly, the methods are in better agreement when
applied to unbiased and complete data sets, like cosmological simulations, than
when applied to observational samples. We conclude that more observational data
is needed to improve on these methods, but that both methods are most likely
properly tracing the underlying distribution of matter in the Universe.Comment: 6 Pages, 2 figures, Submitted to MNRAS Letter
Hitting Diamonds and Growing Cacti
We consider the following NP-hard problem: in a weighted graph, find a
minimum cost set of vertices whose removal leaves a graph in which no two
cycles share an edge. We obtain a constant-factor approximation algorithm,
based on the primal-dual method. Moreover, we show that the integrality gap of
the natural LP relaxation of the problem is \Theta(\log n), where n denotes the
number of vertices in the graph.Comment: v2: several minor changes
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