10,315 research outputs found
Twisting type-N vacuum fields with a group
We derive the equations corresponding to twisting type-N vacuum gravitational
fields with one Killing vector and one homothetic Killing vector by using the
same approach as that developed by one of us in order to treat the case with
two non-commuting Killing vectors. We study the case when the homothetic
parameter takes the value -1, which is shown to admit a reduction to a
third-order real ordinary differential equation for this problem, similar to
that previously obtained by one of us when two Killing vectors are present.Comment: LaTeX, 11 pages. To be published in Classical and Quantum Gravit
Full photon statistics of a light beam transmitted through an optomechanical system
In this paper, we study the full statistics of photons transmitted through an
optical cavity coupled to nanomechanical motion. We analyze the entire temporal
evolution of the photon correlations, the Fano factor, and the effects of
strong laser driving, all of which show pronounced features connected to the
mechanical backaction. In the regime of single-photon strong coupling, this
allows us to predict a transition from sub-Poissonian to super-Poissonian
statistics for larger observation time intervals. Furthermore, we predict
cascades of transmitted photons triggered by multi-photon transitions. In this
regime, we observe Fano factors that are drastically enhanced due to the
mechanical motion.Comment: 8 pages, 7 figure
New first integral for twisting type-N vacuum gravitational fields with two non-commuting Killing vectors
A new first integral for the equations corresponding to twisting type-N
vacuum gravitational fields with two non-commuting Killing vectors is
introduced. A new reduction of the problem to a complex second-order ordinary
differential equation is given. Alternatively, the mentioned first integral can
be used in order to provide a first integral of the second-order complex
equation introduced in a previous treatment of the problem.Comment: 7 pages, LaTeX, uses ioplppt.sty and iopl12.sty; to be published in
Class. Quantum Gra
Quantum measurement problem and cluster separability
A modified Beltrametti-Cassinelli-Lahti model of measurement apparatus that
satisfies both the probability reproducibility condition and the
objectification requirement is constructed. Only measurements on microsystems
are considered. The cluster separability forms a basis for the first working
hypothesis: the current version of quantum mechanics leaves open what happens
to systems when they change their separation status. New rules that close this
gap can therefore be added without disturbing the logic of quantum mechanics.
The second working hypothesis is that registration apparatuses for microsystems
must contain detectors and that their readings are signals from detectors. This
implies that separation status of a microsystem changes during both preparation
and registration. A new rule that specifies what happens at these changes and
that guarantees the objectification is formulated and discussed. A part of our
result has certain similarity with 'collapse of the wave function'.Comment: 31 pages, no figure. Published versio
Spike-and-Slab Priors for Function Selection in Structured Additive Regression Models
Structured additive regression provides a general framework for complex
Gaussian and non-Gaussian regression models, with predictors comprising
arbitrary combinations of nonlinear functions and surfaces, spatial effects,
varying coefficients, random effects and further regression terms. The large
flexibility of structured additive regression makes function selection a
challenging and important task, aiming at (1) selecting the relevant
covariates, (2) choosing an appropriate and parsimonious representation of the
impact of covariates on the predictor and (3) determining the required
interactions. We propose a spike-and-slab prior structure for function
selection that allows to include or exclude single coefficients as well as
blocks of coefficients representing specific model terms. A novel
multiplicative parameter expansion is required to obtain good mixing and
convergence properties in a Markov chain Monte Carlo simulation approach and is
shown to induce desirable shrinkage properties. In simulation studies and with
(real) benchmark classification data, we investigate sensitivity to
hyperparameter settings and compare performance to competitors. The flexibility
and applicability of our approach are demonstrated in an additive piecewise
exponential model with time-varying effects for right-censored survival times
of intensive care patients with sepsis. Geoadditive and additive mixed logit
model applications are discussed in an extensive appendix
Vacuum spacetimes with a spacelike, hypersurface-orthogonal Killing vector: reduced equations in a canonical frame
The Newman-Penrose equations for spacetimes having one spacelike Killing
vector are reduced -- in a geometrically defined "canonical frame'' -- to a
minimal set, and its differential structure is studied. Expressions for the
frame vectors in an arbitrary coordinate basis are given, and
coordinate-independent choices of the metric functions are suggested which make
the components of the Ricci tensor in the direction of the Killing vector
vanish.Comment: 13 pages, no figures, LaTeX, to be published in Class. Quantum
Gravity; v2: added/rephrased content, corrected typos, changed 1 referenc
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