585 research outputs found
Quantum phase diagram of the integrable p_x+ip_y fermionic superfluid
We determine the zero temperature quantum phase diagram of a p_x+ip_y pairing
model based on the exactly solvable hyperbolic Richardson-Gaudin model. We
present analytical and large-scale numerical results for this model. In the
continuum limit, the exact solution exhibits a third-order quantum phase
transition, separating a strong-pairing from a weak-pairing phase. The mean
field solution allows to connect these results to other models with p_x+ip_y
pairing order. We define an experimentally accessible characteristic length
scale, associated with the size of the Cooper pairs, that diverges at the
transition point, indicating that the phase transition is of a
confinement-deconfinement type without local order parameter. We show that this
phase transition is not limited to the p_x+ip_y pairing model, but can be found
in any representation of the hyperbolic Richardson-Gaudin model and is related
to a symmetry that is absent in the rational Richardson-Gaudin model.Comment: 12 figure
Photometric Solutions for Detached Eclipsing Binaries: selection of ideal distance indicators in the SMC
Detached eclipsing binary stars provide a robust one-step distance
determination to nearby galaxies. As a by-product of Galactic microlensing
searches, catalogs of thousands of variable stars including eclipsing binaries
have been produced by the OGLE, MACHO and EROS collaborations. We present
photometric solutions for detached eclipsing binaries in the Small Magellanic
Cloud (SMC) discovered by the OGLE collaboration. The solutions were obtained
with an automated version of the Wilson-Devinney program. By fitting mock
catalogs of eclipsing binaries we find that the normalized stellar radii
(particularly their sum) and the surface brightness ratio are accurately
described by the fitted parameters and estimated standard errors, despite
various systematic uncertainties. In many cases these parameters are well
constrained. In addition we find that systems exhibiting complete eclipses can
be reliably identified where the fractional standard errors in the radii are
small. We present two quantitatively selected sub-samples of eclipsing binaries
that will be excellent distance indicators. These can be used both for
computation of the distance to the SMC and to probe its structure. One
particularly interesting binary has a very well determined solution, exhibits
complete eclipses, and is comprised of well detached G-type, class giants.Comment: 29 pages, 12 figures. To be published in Ap
Inspiral, merger and ringdown of unequal mass black hole binaries: a multipolar analysis
We study the inspiral, merger and ringdown of unequal mass black hole
binaries by analyzing a catalogue of numerical simulations for seven different
values of the mass ratio (from q=M2/M1=1 to q=4). We compare numerical and
Post-Newtonian results by projecting the waveforms onto spin-weighted spherical
harmonics, characterized by angular indices (l,m). We find that the
Post-Newtonian equations predict remarkably well the relation between the wave
amplitude and the orbital frequency for each (l,m), and that the convergence of
the Post-Newtonian series to the numerical results is non-monotonic. To leading
order the total energy emitted in the merger phase scales like eta^2 and the
spin of the final black hole scales like eta, where eta=q/(1+q)^2 is the
symmetric mass ratio. We study the multipolar distribution of the radiation,
finding that odd-l multipoles are suppressed in the equal mass limit. Higher
multipoles carry a larger fraction of the total energy as q increases. We
introduce and compare three different definitions for the ringdown starting
time. Applying linear estimation methods (the so-called Prony methods) to the
ringdown phase, we find resolution-dependent time variations in the fitted
parameters of the final black hole. By cross-correlating information from
different multipoles we show that ringdown fits can be used to obtain precise
estimates of the mass and spin of the final black hole, which are in remarkable
agreement with energy and angular momentum balance calculations.Comment: 51 pages, 28 figures, 16 tables. Many improvements throughout the
text in response to the referee report. The calculation of multipolar
components in Appendix A now uses slightly different conventions. Matches
version in press in PR
Real-time event detection in field sport videos
This chapter describes a real-time system for event detection in sports broadcasts. The approach presented is applicable to a wide range of field sports. Using two independent event detection approaches that work simultaneously, the system is capable of accurately detecting scores, near misses, and other exciting parts of a game that do not result in a score. The results obtained across a diverse dataset of different field sports are promising, demonstrating over 90% accuracy for a feature-based event detector and 100% accuracy for a scoreboard-based detector detecting only score
The geometry of nonlinear least squares with applications to sloppy models and optimization
Parameter estimation by nonlinear least squares minimization is a common
problem with an elegant geometric interpretation: the possible parameter values
of a model induce a manifold in the space of data predictions. The minimization
problem is then to find the point on the manifold closest to the data. We show
that the model manifolds of a large class of models, known as sloppy models,
have many universal features; they are characterized by a geometric series of
widths, extrinsic curvatures, and parameter-effects curvatures. A number of
common difficulties in optimizing least squares problems are due to this common
structure. First, algorithms tend to run into the boundaries of the model
manifold, causing parameters to diverge or become unphysical. We introduce the
model graph as an extension of the model manifold to remedy this problem. We
argue that appropriate priors can remove the boundaries and improve convergence
rates. We show that typical fits will have many evaporated parameters. Second,
bare model parameters are usually ill-suited to describing model behavior; cost
contours in parameter space tend to form hierarchies of plateaus and canyons.
Geometrically, we understand this inconvenient parametrization as an extremely
skewed coordinate basis and show that it induces a large parameter-effects
curvature on the manifold. Using coordinates based on geodesic motion, these
narrow canyons are transformed in many cases into a single quadratic, isotropic
basin. We interpret the modified Gauss-Newton and Levenberg-Marquardt fitting
algorithms as an Euler approximation to geodesic motion in these natural
coordinates on the model manifold and the model graph respectively. By adding a
geodesic acceleration adjustment to these algorithms, we alleviate the
difficulties from parameter-effects curvature, improving both efficiency and
success rates at finding good fits.Comment: 40 pages, 29 Figure
Thermal Emission of WASP-14b Revealed with Three Spitzer Eclipses
Exoplanet WASP-14b is a highly irradiated, transiting hot Jupiter. Joshi et
al. calculate an equilibrium temperature Teq of 1866 K for zero albedo and
reemission from the entire planet, a mass of 7.3 +/- 0.5 Jupiter masses and a
radius of 1.28 +/- 0.08 Jupiter radii. Its mean density of 4.6 g/cm3 is one of
the highest known for planets with periods less than 3 days. We obtained three
secondary eclipse light curves with the Spitzer Space Telescope. The eclipse
depths from the best jointly fit model are +/- at 4.5
{\mu}m and +/- at 8.0 {\mu}m. The corresponding brightness
temperatures are 2212 +/- 94 K and 1590 +/- 116 K. A slight ambiguity between
systematic models suggests a conservative 3.6 {\mu}m eclipse depth of
+/- and brightness temperature of 2242 +/- 55 K. Although extremely
irradiated, WASP-14b does not show any distinct evidence of a thermal
inversion. In addition, the present data nominally favor models with day night
energy redistribution less than . The current data are generally
consistent with oxygen-rich as well as carbon-rich compositions, although an
oxygen-rich composition provides a marginally better fit. We confirm a
significant eccentricity of e = 0.087 +/- 0.002 and refine other orbital
parameters.Comment: 16 pages, 16 figure
Foreground removal from CMB temperature maps using an MLP neural network
One of the main obstacles in extracting the Cosmic Microwave Background (CMB)
signal from observations in the mm-submm range is the foreground contamination
by emission from galactic components: mainly synchrotron, free-free and thermal
dust emission. Due to the statistical nature of the intrinsic CMB signal it is
essential to minimize the systematic errors in the CMB temperature
determinations. Following the available knowledge of the spectral behavior of
the galactic foregrounds simple, power law-like spectra have been assumed. The
feasibility of using a simple neural network for extracting the CMB temperature
signal from the combined CMB and foreground signals has been investigated. As a
specific example, we have analysed simulated data, like that expected from the
ESA Planck Surveyor mission. A simple multilayer perceptron neural network with
2 hidden layers can provide temperature estimates, over more than 80 percent of
the sky, that are to a high degree uncorrelated with the foreground signals. A
single network will be able to cover the dynamic range of the Planck noise
level over the entire sky.Comment: Accepted for publication in Astrophysics and Space Scienc
When the optimal is not the best: parameter estimation in complex biological models
Background: The vast computational resources that became available during the
past decade enabled the development and simulation of increasingly complex
mathematical models of cancer growth. These models typically involve many free
parameters whose determination is a substantial obstacle to model development.
Direct measurement of biochemical parameters in vivo is often difficult and
sometimes impracticable, while fitting them under data-poor conditions may
result in biologically implausible values.
Results: We discuss different methodological approaches to estimate
parameters in complex biological models. We make use of the high computational
power of the Blue Gene technology to perform an extensive study of the
parameter space in a model of avascular tumor growth. We explicitly show that
the landscape of the cost function used to optimize the model to the data has a
very rugged surface in parameter space. This cost function has many local
minima with unrealistic solutions, including the global minimum corresponding
to the best fit.
Conclusions: The case studied in this paper shows one example in which model
parameters that optimally fit the data are not necessarily the best ones from a
biological point of view. To avoid force-fitting a model to a dataset, we
propose that the best model parameters should be found by choosing, among
suboptimal parameters, those that match criteria other than the ones used to
fit the model. We also conclude that the model, data and optimization approach
form a new complex system, and point to the need of a theory that addresses
this problem more generally
Radio Interferometric Calibration Using The SAGE Algorithm
The aim of the new generation of radio synthesis arrays such as LOFAR and SKA
is to achieve much higher sensitivity, resolution and frequency coverage than
what is available now, especially at low frequencies. To accomplish this goal,
the accuracy of the calibration techniques used is of considerable importance.
Moreover, since these telescopes produce huge amounts of data, speed of
convergence of calibration is a major bottleneck. The errors in calibration are
due to system noise (sky and instrumental) as well as the estimation errors
introduced by the calibration technique itself, which we call solver noise. We
define solver noise as the distance between the optimal solution (the true
value of the unknowns, uncorrupted by the system noise) and the solution
obtained by calibration. We present the Space Alternating Generalized
Expectation Maximization (SAGE) calibration technique, which is a modification
of the Expectation Maximization algorithm, and compare its performance with the
traditional Least Squares calibration based on the level of solver noise
introduced by each technique. For this purpose, we develop statistical methods
that use the calibrated solutions to estimate the level of solver noise. The
SAGE calibration algorithm yields very promising results both in terms of
accuracy and speed of convergence. The comparison approaches we adopt introduce
a new framework for assessing the performance of different calibration schemes.Comment: 12 pages, 10 figures, Accepted for publication in MNRA
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