2,765 research outputs found
Curvature blow up in Bianchi VIII and IX vacuum spacetimes
The maximal globally hyperbolic development of non-Taub-NUT Bianchi IX vacuum
initial data and of non-NUT Bianchi VIII vacuum initial data is C2
inextendible. Furthermore, a curvature invariant is unbounded in the incomplete
directions of inextendible causal geodesics.Comment: 20 pages, no figures. Submitted to Classical and Quantum Gravit
Asymptotic silence-breaking singularities
We discuss three complementary aspects of scalar curvature singularities:
asymptotic causal properties, asymptotic Ricci and Weyl curvature, and
asymptotic spatial properties. We divide scalar curvature singularities into
two classes: so-called asymptotically silent singularities and non-generic
singularities that break asymptotic silence. The emphasis in this paper is on
the latter class which have not been previously discussed. We illustrate the
above aspects and concepts by describing the singularities of a number of
representative explicit perfect fluid solutions.Comment: 25 pages, 6 figure
High-dimensional Ising model selection using -regularized logistic regression
We consider the problem of estimating the graph associated with a binary
Ising Markov random field. We describe a method based on -regularized
logistic regression, in which the neighborhood of any given node is estimated
by performing logistic regression subject to an -constraint. The method
is analyzed under high-dimensional scaling in which both the number of nodes
and maximum neighborhood size are allowed to grow as a function of the
number of observations . Our main results provide sufficient conditions on
the triple and the model parameters for the method to succeed in
consistently estimating the neighborhood of every node in the graph
simultaneously. With coherence conditions imposed on the population Fisher
information matrix, we prove that consistent neighborhood selection can be
obtained for sample sizes with exponentially decaying
error. When these same conditions are imposed directly on the sample matrices,
we show that a reduced sample size of suffices for the
method to estimate neighborhoods consistently. Although this paper focuses on
the binary graphical models, we indicate how a generalization of the method of
the paper would apply to general discrete Markov random fields.Comment: Published in at http://dx.doi.org/10.1214/09-AOS691 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
New Non-Diagonal Singularity-Free Cosmological Perfect-Fluid Solution
We present a new non-diagonal G2 inhomogeneous perfect-fluid solution with
barotropic equation of state p=rho and positive density everywhere. It
satisfies the global hyperbolicity condition and has no curvature singularity
anywhere. This solution is very simple in form and has two arbitrary constants.Comment: Latex, no figure
Geographic Gossip: Efficient Averaging for Sensor Networks
Gossip algorithms for distributed computation are attractive due to their
simplicity, distributed nature, and robustness in noisy and uncertain
environments. However, using standard gossip algorithms can lead to a
significant waste in energy by repeatedly recirculating redundant information.
For realistic sensor network model topologies like grids and random geometric
graphs, the inefficiency of gossip schemes is related to the slow mixing times
of random walks on the communication graph. We propose and analyze an
alternative gossiping scheme that exploits geographic information. By utilizing
geographic routing combined with a simple resampling method, we demonstrate
substantial gains over previously proposed gossip protocols. For regular graphs
such as the ring or grid, our algorithm improves standard gossip by factors of
and respectively. For the more challenging case of random
geometric graphs, our algorithm computes the true average to accuracy
using radio
transmissions, which yields a factor improvement over
standard gossip algorithms. We illustrate these theoretical results with
experimental comparisons between our algorithm and standard methods as applied
to various classes of random fields.Comment: To appear, IEEE Transactions on Signal Processin
Bianchi VIII Empty Futures
Using a qualitative analysis based on the Hamiltonian formalism and the
orthonormal frame representation we investigate whether the chaotic behaviour
which occurs close to the initial singularity is still present in the far
future of Bianchi VIII models. We describe some features of the vacuum Bianchi
VIII models at late times which might be relevant for studying the nature of
the future asymptote of the general vacuum inhomogeneous solution to the
Einstein field equations.Comment: 22 pages, no figures, Latex fil
An Ecological Risk Model for Early Childhood Anxiety: The Importance of Early Child Symptoms and Temperament
Childhood anxiety is impairing and associated with later emotional disorders. Studying risk factors for child anxiety may allow earlier identification of at-risk children for prevention efforts. This study applied an ecological risk model to address how early childhood anxiety symptoms, child temperament, maternal anxiety and depression symptoms, violence exposure, and sociodemographic risk factors predict school-aged anxiety symptoms. This longitudinal, prospective study was conducted in a representative birth cohort (n=1109). Structural equation modeling was used to examine hypothesized associations between risk factors measured in toddlerhood/preschool (age=3.0 years) and anxiety symptoms measured in kindergarten (age=6.0 years) and second grade (age= 8.0 years). Early child risk factors (anxiety symptoms and temperament) emerged as the most robust predictor for both parent-and child-reported anxiety outcomes and mediated the effects of maternal and family risk factors. Implications for early intervention and prevention studies are discussed
Global dynamics of the mixmaster model
The asymptotic behaviour of vacuum Bianchi models of class A near the initial
singularity is studied, in an effort to confirm the standard picture arising
from heuristic and numerical approaches by mathematical proofs. It is shown
that for solutions of types other than VIII and IX the singularity is velocity
dominated and that the Kretschmann scalar is unbounded there, except in the
explicitly known cases where the spacetime can be smoothly extended through a
Cauchy horizon. For types VIII and IX it is shown that there are at most two
possibilities for the evolution. When the first possibility is realized, and if
the spacetime is not one of the explicitly known solutions which can be
smoothly extended through a Cauchy horizon, then there are infinitely many
oscillations near the singularity and the Kretschmann scalar is unbounded
there. The second possibility remains mysterious and it is left open whether it
ever occurs. It is also shown that any finite sequence of distinct points
generated by iterating the Belinskii-Khalatnikov-Lifschitz mapping can be
realized approximately by a solution of the vacuum Einstein equations of
Bianchi type IX.Comment: 16 page
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