4,381 research outputs found
Log-Concave Duality in Estimation and Control
In this paper we generalize the estimation-control duality that exists in the
linear-quadratic-Gaussian setting. We extend this duality to maximum a
posteriori estimation of the system's state, where the measurement and
dynamical system noise are independent log-concave random variables. More
generally, we show that a problem which induces a convex penalty on noise terms
will have a dual control problem. We provide conditions for strong duality to
hold, and then prove relaxed conditions for the piecewise linear-quadratic
case. The results have applications in estimation problems with nonsmooth
densities, such as log-concave maximum likelihood densities. We conclude with
an example reconstructing optimal estimates from solutions to the dual control
problem, which has implications for sharing solution methods between the two
types of problems
A late-time transition in the equation of state versus Lambda-CDM
We study a model of the dark energy which exhibits a rapid change in its
equation of state w(z), such as occurs in vacuum metamorphosis. We compare the
model predictions with CMB, large scale structure and supernova data and show
that a late-time transition is marginally preferred over standard Lambda-CDM.Comment: 4 pages, 1 figure, to appear in the proceedings of XXXVIIth
Rencontres de Moriond, "The Cosmological Model", March 200
Machine Learning Classification of SDSS Transient Survey Images
We show that multiple machine learning algorithms can match human performance
in classifying transient imaging data from the Sloan Digital Sky Survey (SDSS)
supernova survey into real objects and artefacts. This is a first step in any
transient science pipeline and is currently still done by humans, but future
surveys such as the Large Synoptic Survey Telescope (LSST) will necessitate
fully machine-enabled solutions. Using features trained from eigenimage
analysis (principal component analysis, PCA) of single-epoch g, r and
i-difference images, we can reach a completeness (recall) of 96 per cent, while
only incorrectly classifying at most 18 per cent of artefacts as real objects,
corresponding to a precision (purity) of 84 per cent. In general, random
forests performed best, followed by the k-nearest neighbour and the SkyNet
artificial neural net algorithms, compared to other methods such as na\"ive
Bayes and kernel support vector machine. Our results show that PCA-based
machine learning can match human success levels and can naturally be extended
by including multiple epochs of data, transient colours and host galaxy
information which should allow for significant further improvements, especially
at low signal-to-noise.Comment: 14 pages, 8 figures. In this version extremely minor adjustments to
the paper were made - e.g. Figure 5 is now easier to view in greyscal
Adiabatic Gravitational Perturbation During Reheating
We study the possibilities of parametric amplification of the gravitational
perturbation during reheating in single-field inflation models. Our result
shows that there is no additional growth of the super-horizon modes beyond the
usual predictions.Comment: Refs added; New version to appear in PR
Electrical Tuning of Single Nitrogen-Vacancy Center Optical Transitions Enhanced by Photoinduced Fields
We demonstrate precise control over the zero-phonon optical transition
energies of individual nitrogen-vacancy (NV) centers in diamond by applying
multiaxis electric fields, via the dc Stark effect. The Stark shifts display
surprising asymmetries that we attribute to an enhancement and rectification of
the local electric field by photoionized charge traps in the diamond. Using
this effect, we tune the excited-state orbitals of strained NV centers to
degeneracy and vary the resulting degenerate optical transition frequency by
>10 GHz, a scale comparable to the inhomogeneous frequency distribution. This
technique will facilitate the integration of NV-center spins within photonic
networks.Comment: 10 pages, 6 figure
A mechanistic model of connector hubs, modularity, and cognition
The human brain network is modular--comprised of communities of tightly
interconnected nodes. This network contains local hubs, which have many
connections within their own communities, and connector hubs, which have
connections diversely distributed across communities. A mechanistic
understanding of these hubs and how they support cognition has not been
demonstrated. Here, we leveraged individual differences in hub connectivity and
cognition. We show that a model of hub connectivity accurately predicts the
cognitive performance of 476 individuals in four distinct tasks. Moreover,
there is a general optimal network structure for cognitive
performance--individuals with diversely connected hubs and consequent modular
brain networks exhibit increased cognitive performance, regardless of the task.
Critically, we find evidence consistent with a mechanistic model in which
connector hubs tune the connectivity of their neighbors to be more modular
while allowing for task appropriate information integration across communities,
which increases global modularity and cognitive performance
Gravitational waves in preheating
We study the evolution of gravitational waves through the preheating era that
follows inflation. The oscillating inflaton drives parametric resonant growth
of scalar field fluctuations, and although super-Hubble tensor modes are not
strongly amplified, they do carry an imprint of preheating. This is clearly
seen in the Weyl tensor, which provides a covariant description of
gravitational waves.Comment: 8 pages, 8 figures, Revte
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