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An LFT/SDP approach to the uncertainty analysis for state
A state estimator is an algorithm that computes the current state of a time-varying system from on-line measurements. Physical quantities such as measurements and parameters are characterised by uncertainty. Understanding how uncertainty affects the accuracy of state estimates is therefore a pre-requisite to the application of such techniques to real systems. In this paper we develop a method of uncertainty analysis based on linear fractional transformations (LFT) and obtain ellipsoid-of-confidence bounds by recasting the LFT problem into a semidefinite programming problem (SDP). The ideas are illustrated by applying them to a simple water distribution network
Binary black hole coalescence in the large-mass-ratio limit: the hyperboloidal layer method and waveforms at null infinity
We compute and analyze the gravitational waveform emitted to future null
infinity by a system of two black holes in the large mass ratio limit. We
consider the transition from the quasi-adiabatic inspiral to plunge, merger,
and ringdown. The relative dynamics is driven by a leading order in the mass
ratio, 5PN-resummed, effective-one-body (EOB), analytic radiation reaction. To
compute the waveforms we solve the Regge-Wheeler-Zerilli equations in the
time-domain on a spacelike foliation which coincides with the standard
Schwarzschild foliation in the region including the motion of the small black
hole, and is globally hyperboloidal, allowing us to include future null
infinity in the computational domain by compactification. This method is called
the hyperboloidal layer method, and is discussed here for the first time in a
study of the gravitational radiation emitted by black hole binaries. We
consider binaries characterized by five mass ratios, ,
that are primary targets of space-based or third-generation gravitational wave
detectors. We show significative phase differences between finite-radius and
null-infinity waveforms. We test, in our context, the reliability of the
extrapolation procedure routinely applied to numerical relativity waveforms. We
present an updated calculation of the gravitational recoil imparted to the
merger remnant by the gravitational wave emission. As a self consistency test
of the method, we show an excellent fractional agreement (even during the
plunge) between the 5PN EOB-resummed mechanical angular momentum loss and the
gravitational wave angular momentum flux computed at null infinity. New results
concerning the radiation emitted from unstable circular orbits are also
presented.Comment: 22 pages, 18 figures. Typos corrected. To appear in Phys. Rev.
Final spin of a coalescing black-hole binary: an Effective-One-Body approach
We update the analytical estimate of the final spin of a coalescing
black-hole binary derived within the Effective-One-Body (EOB) approach. We
consider unequal-mass non-spinning black-hole binaries. It is found that a more
complete account of relevant physical effects (higher post-Newtonian accuracy,
ringdown losses) allows the {\it analytical} EOB estimate to `converge towards'
the recently obtained {\it numerical} results within 2%. This agreement
illustrates the ability of the EOB approach to capture the essential physics of
coalescing black-hole binaries. Our analytical approach allows one to estimate
the final spin of the black hole formed by coalescing binaries in a mass range
() which is not presently covered by numerical
simulations.Comment: 8 pages, two figures. To appear in Phys. Rev.
Passive Sliders on Fluctuating Surfaces: Strong-Clustering States
We study the clustering properties of particles sliding downwards on a
fluctuating surface evolving through the Kardar-Parisi-Zhang equation, a
problem equivalent to passive scalars driven by a Burgers fluid. Monte Carlo
simulations on a discrete version of the problem in one dimension reveal that
particles cluster very strongly: the two point density correlation function
scales with the system size with a scaling function which diverges at small
argument. Analytic results are obtained for the Sinai problem of random walkers
in a quenched random landscape. This equilibrium system too has a singular
scaling function which agrees remarkably with that for advected particles.Comment: To be published in Physical Review Letter
Gravitational waves from oscillating accretion tori: Comparison between different approaches
Quasi-periodic oscillations of high density thick accretion disks orbiting a
Schwarzschild black hole have been recently addressed as interesting sources of
gravitational waves. The aim of this paper is to compare the gravitational
waveforms emitted from these sources when computed using (variations of) the
standard quadrupole formula and gauge-invariant metric perturbation theory. To
this goal we evolve representative disk models using an existing general
relativistic hydrodynamics code which has been previously employed in
investigations of such astrophysical systems. Two are the main results of this
work: First, for stable and marginally stable disks, no excitation of the black
hole quasi-normal modes is found. Secondly, we provide a simple, relativistic
modification of the Newtonian quadrupole formula which, in certain regimes,
yields excellent agreement with the perturbative approach. This holds true as
long as back-scattering of GWs is negligible. Otherwise, any functional form of
the quadrupole formula yields systematic errors of the order of 10%.Comment: 6 pages and 3 figures, RevTex, accepted for publication in Phys. Rev.
Dynamical vs. Auxiliary Fields in Gravitational Waves around a Black Hole
The auxiliary/dynamic decoupling method of hep-th/0609001 applies to
perturbations of any co-homogeneity 1 background (such as a spherically
symmetric space-time or a homogeneous cosmology). Here it is applied to compute
the perturbations around a Schwarzschild black hole in an arbitrary dimension.
The method provides a clear insight for the existence of master equations. The
computation is straightforward, coincides with previous results of
Regge-Wheeler, Zerilli and Kodama-Ishibashi but does not require any ingenuity
in either the definition of variables or in fixing the gauge. We note that the
method's emergent master fields are canonically conjugate to the standard ones.
In addition, our action approach yields the auxiliary sectors.Comment: 26 page
On Exact Statistical Properties of Multidimensional Indices Based on Principal Components, Factor Analysis, MIMIC and Structural Equation Models
Recent empirical literature has seen many multidimensional indices emerge as well-being or poverty measures, in particular indices derived from principal components and various latent variable models. Though such indices are being increasingly and widely employed, few studies motivate their use or report the standard errors or confidence intervals associated with these estimators. This paper reviews the different underlying models, reaffirms their appropriateness in this context, examines the statistical properties of resulting indices, gives analytical expressions of their variances and establishes certain exact relationships among the
Iso-array rewriting P systems with context-free iso-array rules
A new computing model called P system is a highly distributed and
parallel theoretical model, which is proposed in the area of membrane computing. Ceterchi et al. initially proposed array rewriting P systems by extending the notion of string rewriting P systems to arrays (2003). A theoretical model for picture generation using context-free iso-array grammar rules and puzzle iso-array grammar rules are introduced by Kalyani et al. (2004, 2006). Also iso-array rewriting P systems for iso-picture languages have been studied by Annadurai et al. (2008). In this paper we consider the context-free iso-array rules and context-free puzzle iso-array rules in iso-array rewriting P systems and examine the generative powers
of these P systems
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