1,204 research outputs found
Spin connection formulations of real Lorentzian General Relativity
We derive the pure spin connection and constraint-free BF formulations of
real four-dimensional Lorentzian vacuum General Relativity. In contrast to the
existing complex formulations, an important advantage is that they do not
require the reality constraints that complicate quantization. We also consider
the corresponding modified gravity theories and point out that, contrary to
their self-dual analogues, they are not viable because they necessarily contain
ghosts. In particular, this constrains the set of potentially viable unified
theories one can build by extending the gauge group to the ones with the action
structure of General Relativity. We find, however, that the resulting theories
do not admit classical solutions. This issue can be solved by introducing extra
dynamical fields which, incidentally, could also provide a way to include a
matter sector.Comment: 20 page
Distributed Detection in Sensor Networks with Limited Range Sensors
We consider a multi-object detection problem over a sensor network (SNET)
with limited range sensors. This problem complements the widely considered
decentralized detection problem where all sensors observe the same object.
While the necessity for global collaboration is clear in the decentralized
detection problem, the benefits of collaboration with limited range sensors is
unclear and has not been widely explored. In this paper we develop a
distributed detection approach based on recent development of the false
discovery rate (FDR). We first extend the FDR procedure and develop a
transformation that exploits complete or partial knowledge of either the
observed distributions at each sensor or the ensemble (mixture) distribution
across all sensors. We then show that this transformation applies to
multi-dimensional observations, thus extending FDR to multi-dimensional
settings. We also extend FDR theory to cases where distributions under both
null and positive hypotheses are uncertain. We then propose a robust
distributed algorithm to perform detection. We further demonstrate scalability
to large SNETs by showing that the upper bound on the communication complexity
scales linearly with the number of sensors that are in the vicinity of objects
and is independent of the total number of sensors. Finally, we deal with
situations where the sensing model may be uncertain and establish robustness of
our techniques to such uncertainties.Comment: Submitted to IEEE Transactions on Signal Processin
General Relativistic Cosmological N-body Simulations I: time integration
This is the first in a series of papers devoted to fully general-relativistic
-body simulations applied to late-time cosmology. The purpose of this paper
is to present the combination of a numerical relativity scheme, discretization
method and time-integration algorithm that provides satisfyingly stable
evolution. More precisely, we show that it is able to pass a robustness test
and to follow scalar linear modes around an expanding homogeneous and isotropic
space-time. Most importantly, it is able to evolve typical cosmological initial
conditions on comoving scales down to tenths of megaparsecs with controlled
constraint and energy-momentum conservation violations all the way down to the
regime of strong inhomogeneity.Comment: 28 pages, 16 figure
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