2,111 research outputs found
Towards Building Deep Networks with Bayesian Factor Graphs
We propose a Multi-Layer Network based on the Bayesian framework of the
Factor Graphs in Reduced Normal Form (FGrn) applied to a two-dimensional
lattice. The Latent Variable Model (LVM) is the basic building block of a
quadtree hierarchy built on top of a bottom layer of random variables that
represent pixels of an image, a feature map, or more generally a collection of
spatially distributed discrete variables. The multi-layer architecture
implements a hierarchical data representation that, via belief propagation, can
be used for learning and inference. Typical uses are pattern completion,
correction and classification. The FGrn paradigm provides great flexibility and
modularity and appears as a promising candidate for building deep networks: the
system can be easily extended by introducing new and different (in cardinality
and in type) variables. Prior knowledge, or supervised information, can be
introduced at different scales. The FGrn paradigm provides a handy way for
building all kinds of architectures by interconnecting only three types of
units: Single Input Single Output (SISO) blocks, Sources and Replicators. The
network is designed like a circuit diagram and the belief messages flow
bidirectionally in the whole system. The learning algorithms operate only
locally within each block. The framework is demonstrated in this paper in a
three-layer structure applied to images extracted from a standard data set.Comment: Submitted for journal publicatio
Hamiltonian of a spinning test-particle in curved spacetime [Erratum: Phys. Rev. D 80, 104025 (2009)]
Using a Legendre transformation, we compute the unconstrained Hamiltonian of a spinning test-particle in a curved spacetime at linear order in the particle spin. The equations of motion of this unconstrained Hamiltonian coincide with the Mathisson-Papapetrou-Pirani equations. We then use the formalism of Dirac brackets to derive the constrained Hamiltonian and the corresponding phase-space algebra in the Newton-Wigner spin supplementary condition (SSC), suitably generalized to curved spacetime, and find that the phase-space algebra (q,p,S) is canonical at linear order in the particle spin. We provide explicit expressions for this Hamiltonian in a spherically symmetric spacetime, both in isotropic and spherical coordinates, and in the Kerr spacetime in Boyer-Lindquist coordinates. Furthermore, we find that our Hamiltonian, when expanded in Post-Newtonian (PN) orders, agrees with the Arnowitt-Deser-Misner (ADM) canonical Hamiltonian computed in PN theory in the test-particle limit. Notably, we recover the known spin-orbit couplings through 2.5PN order and the spin-spin couplings of type S_Kerr S (and S_Kerr^2) through 3PN order, S_Kerr being the spin of the Kerr spacetime. Our method allows one to compute the PN Hamiltonian at any order, in the test-particle limit and at linear order in the particle spin. As an application we compute it at 3.5PN order
Gravitational waves from inspiraling binary black holes
Binary black holes are the most promising candidate sources for the first
generation of earth-based interferometric gravitational-wave detectors. We
summarize and discuss the state-of-the-art analytic techniques developed during
the last years to better describe the late dynamical evolution of binary black
holes of comparable masses.Comment: References added and updated; few typos correcte
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.
Optical noise correlations and beating the standard quantum limit in advanced gravitational-wave detectors
The uncertainty principle, applied naively to the test masses of a
laser-interferometer gravitational-wave detector, produces a Standard Quantum
Limit (SQL) on the interferometer's sensitivity. It has long been thought that
beating this SQL would require a radical redesign of interferometers. However,
we show that LIGO-II interferometers, currently planned for 2006, can beat the
SQL by as much as a factor two over a bandwidth \Delta f \sim f, if their
thermal noise can be pushed low enough. This is due to dynamical correlations
between photon shot noise and radiation-pressure noise, produced by the LIGO-II
signal-recycling mirror.Comment: 12 pages, 2 figures; minor changes, some references adde
Symmetry breaking aspects of the effective Lagrangian for quantum black holes
The physical excitations entering the effective Lagrangian for quantum black
holes are related to a Goldstone boson which is present in the Rindler limit
and is due to the spontaneous breaking of the translation symmetry of the
underlying Minkowski space. This physical interpretation, which closely
parallels similar well-known results for the effective stringlike description
of flux tubes in QCD, gives a physical insight into the problem of describing
the quantum degrees of freedom of black holes. It also suggests that the
recently suggested concept of 'black hole complementarity' emerges at the
effective Lagrangian level rather than at the fundamental level.Comment: 11 pages, Latex,1 figur
Small mass plunging into a Kerr black hole: Anatomy of the inspiral-merger-ringdown waveforms
We numerically solve the Teukolsky equation in the time domain to obtain the
gravitational-wave emission of a small mass inspiraling and plunging into the
equatorial plane of a Kerr black hole. We account for the dissipation of
orbital energy using the Teukolsky frequency-domain gravitational-wave fluxes
for circular, equatorial orbits, down to the light-ring. We consider Kerr spins
, and compute the inspiral-merger-ringdown (2,2),
(2,1), (3,3), (3,2), (4,4), and (5,5) modes. We study the large-spin regime,
and find a great simplicity in the merger waveforms, thanks to the extremely
circular character of the plunging orbits. We also quantitatively examine the
mixing of quasinormal modes during the ringdown, which induces complicated
amplitude and frequency modulations in the waveforms. Finally, we explain how
the study of small mass-ratio black-hole binaries helps extending
effective-one-body models for comparable-mass, spinning black-hole binaries to
any mass ratio and spin magnitude.Comment: 20 pages, 15 figure
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