32,349 research outputs found
Coherent frequentism
By representing the range of fair betting odds according to a pair of
confidence set estimators, dual probability measures on parameter space called
frequentist posteriors secure the coherence of subjective inference without any
prior distribution. The closure of the set of expected losses corresponding to
the dual frequentist posteriors constrains decisions without arbitrarily
forcing optimization under all circumstances. This decision theory reduces to
those that maximize expected utility when the pair of frequentist posteriors is
induced by an exact or approximate confidence set estimator or when an
automatic reduction rule is applied to the pair. In such cases, the resulting
frequentist posterior is coherent in the sense that, as a probability
distribution of the parameter of interest, it satisfies the axioms of the
decision-theoretic and logic-theoretic systems typically cited in support of
the Bayesian posterior. Unlike the p-value, the confidence level of an interval
hypothesis derived from such a measure is suitable as an estimator of the
indicator of hypothesis truth since it converges in sample-space probability to
1 if the hypothesis is true or to 0 otherwise under general conditions.Comment: The confidence-measure theory of inference and decision is explicitly
extended to vector parameters of interest. The derivation of upper and lower
confidence levels from valid and nonconservative set estimators is formalize
Decoherence due to contacts in ballistic nanostructures
The active region of a ballistic nanostructure is an open quantum-mechanical
system, whose nonunitary evolution (decoherence) towards a nonequilibrium
steady state is determined by carrier injection from the contacts. The purpose
of this paper is to provide a simple theoretical description of the
contact-induced decoherence in ballistic nanostructures, which is established
within the framework of the open systems theory. The active region's evolution
in the presence of contacts is generally non-Markovian. However, if the
contacts' energy relaxation due to electron-electron scattering is sufficiently
fast, then the contacts can be considered memoryless on timescales coarsened
over their energy relaxation time, and the evolution of the current-limiting
active region can be considered Markovian. Therefore, we first derive a general
Markovian map in the presence of a memoryless environment, by coarse-graining
the exact short-time non-Markovian dynamics of an abstract open system over the
environment memory-loss time, and we give the requirements for the validity of
this map. We then introduce a model contact-active region interaction that
describes carrier injection from the contacts for a generic two-terminal
ballistic nanostructure. Starting from this model interaction and using the
Markovian dynamics derived by coarse-graining over the effective memory-loss
time of the contacts, we derive the formulas for the nonequilibrium
steady-state distribution functions of the forward and backward propagating
states in the nanostructure's active region. On the example of a double-barrier
tunneling structure, the present approach yields an I-V curve with all the
prominent resonant features. The relationship to the Landauer-B\"{u}ttiker
formalism is also discussed, as well as the inclusion of scattering.Comment: Published versio
On the Coherence of WMAP and Planck Temperature Maps
The recent data release of ESA's Planck mission together with earlier WMAP
releases provide the first opportunity to compare high resolution full sky
Cosmic Microwave Background temperature anisotropy maps. To quantify the
coherence of these maps beyond the power spectrum we introduce Generalized
Phases, unit vectors in the (2l+1) dimensional representation spaces. For a
Gaussian distribution, Generalized Phases are random and if there is
non-Gaussianity, they represent most of the non-Gaussian information. The
alignment of these unit vectors from two maps can be characterized by their
angle, 0 deg expected for full coherence, and 90 deg for random vectors. We
analyze maps from both missions with the same mask and Nside=512 resolution,
and compare both power spectra and Generalized Phases. We find excellent
agreement of the Generalize Phases of Planck Smica map with that of the WMAP
Q,V,W maps, rejecting the null hypothesis of no correlations at 5 sigma for l's
l<700, l<900 and l<1100, respectively, except perhaps for l<10. Using
foreground reduced maps for WMAP increases the phase coherence. The observed
coherence angles can be explained with a simple assumption of Gaussianity and a
WMAP noise model neglecting Planck noise, except for low-intermediate l's there
is a slight, but significant off-set, depending on WMAP band. On the same
scales WMAP power spectrum is about 2.6% higher at a very high significance,
while at higher l's there appears to be no significant bias. Using our
theoretical tools, we predict the phase alignment of Planck with a hypothetical
perfect noiseless CMB experiment, finding decoherence at l > 2900; below this
value Planck can be used most efficiently to constrain non-Gaussianity.Comment: 8 pages, 8 figures, accepted for publication in MNRAS; minor
modifications and 2 new figures adde
Sparse Recovery from Combined Fusion Frame Measurements
Sparse representations have emerged as a powerful tool in signal and
information processing, culminated by the success of new acquisition and
processing techniques such as Compressed Sensing (CS). Fusion frames are very
rich new signal representation methods that use collections of subspaces
instead of vectors to represent signals. This work combines these exciting
fields to introduce a new sparsity model for fusion frames. Signals that are
sparse under the new model can be compressively sampled and uniquely
reconstructed in ways similar to sparse signals using standard CS. The
combination provides a promising new set of mathematical tools and signal
models useful in a variety of applications. With the new model, a sparse signal
has energy in very few of the subspaces of the fusion frame, although it does
not need to be sparse within each of the subspaces it occupies. This sparsity
model is captured using a mixed l1/l2 norm for fusion frames.
A signal sparse in a fusion frame can be sampled using very few random
projections and exactly reconstructed using a convex optimization that
minimizes this mixed l1/l2 norm. The provided sampling conditions generalize
coherence and RIP conditions used in standard CS theory. It is demonstrated
that they are sufficient to guarantee sparse recovery of any signal sparse in
our model. Moreover, a probabilistic analysis is provided using a stochastic
model on the sparse signal that shows that under very mild conditions the
probability of recovery failure decays exponentially with increasing dimension
of the subspaces
X-ray Variability Characteristics of the Seyfert 1 Galaxy NGC 3783
We have characterized the energy-dependent X-ray variability properties of
the Seyfert~1 galaxy NGC 3783 using archival XMM-Newton and Rossi X-ray Timing
Explorer data. The high-frequency fluctuation power spectral density function
(PSD) slope is consistent with flattening towards higher energies. Light curve
cross correlation functions yield no significant lags, but peak coefficients
generally decrease as energy separation of the bands increases on both short
and long timescales. We have measured the coherence between various X-ray bands
over the temporal frequency range of 6e-8 to 1e-4 Hz; this range includes the
temporal frequency of the low-frequency power spectral density function (PSD)
break tentatively detected by Markowitz et al. and includes the lowest temporal
frequency over which coherence has been measured in any AGN to date. Coherence
is generally near unity at these temporal frequencies, though it decreases
slightly as energy separation of the bands increases. Temporal
frequency-dependent phase lags are detected on short time scales; phase lags
are consistent with increasing as energy separation increases or as temporal
frequency decreases. All of these results are similar to those obtained
previously for several Seyfert galaxies and stellar-mass black hole systems.
Qualitatively, these results are consistent with the variability models of
Kotov et al. and Lyubarskii, wherein the X-ray variability is due to inwardly
propagating variations in the local mass accretion rate.Comment: Accepted for publication in The Astrophysical Journal, 2005, vol.
635, p. 180; version 2 has minor grammatical changes; 23 pages; uses
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