37,326 research outputs found
Manifold Constrained Low-Rank Decomposition
Low-rank decomposition (LRD) is a state-of-the-art method for visual data
reconstruction and modelling. However, it is a very challenging problem when
the image data contains significant occlusion, noise, illumination variation,
and misalignment from rotation or viewpoint changes. We leverage the specific
structure of data in order to improve the performance of LRD when the data are
not ideal. To this end, we propose a new framework that embeds manifold priors
into LRD. To implement the framework, we design an alternating direction method
of multipliers (ADMM) method which efficiently integrates the manifold
constraints during the optimization process. The proposed approach is
successfully used to calculate low-rank models from face images, hand-written
digits and planar surface images. The results show a consistent increase of
performance when compared to the state-of-the-art over a wide range of
realistic image misalignments and corruptions
Efficient computation of the gravitational wave spectrum emitted by eccentric massive black hole binaries in stellar environments
We present a fast and versatile method to calculate the characteristic
spectrum of the gravitational wave background (GWB) emitted by a
population of eccentric massive black hole binaries (MBHBs). We fit the
spectrum of a reference MBHB with a simple analytic function and show that the
spectrum of any other MBHB can be derived from this reference spectrum via
simple scalings of mass, redshift and frequency. We then apply our calculation
to a realistic population of MBHBs evolving via 3-body scattering of stars in
galactic nuclei. We demonstrate that our analytic prescription satisfactorily
describes the signal in the frequency band relevant to pulsar timing array
(PTA) observations. Finally we model the high frequency steepening of the GWB
to provide a complete description of the features characterizing the spectrum.
For typical stellar distributions observed in massive galaxies, our calculation
shows that 3-body scattering alone is unlikely to affect the GWB in the PTA
band and a low frequency turnover in the spectrum is caused primarily by high
eccentricities.Comment: 12 pages, 9 figures, published in MNRA
Quantum dynamics in a time-dependent cylindrical trap
Solutions to the Schr\"{o}dinger equation are examined for a particle inside
a cylindrical trap of a circular time-dependent cross-section. Analytical
expressions for energy and momentum expectation values are derived with respect
to the exact solutions; and the adiabatic and sudden change of the boundary are
discussed. The density profile as a function of time in a given observation
point, resembles the diffraction-in-time pattern observed in a suddenly
released particle but with an enhanced fringe visibility. Numerical
computations are presented for both contracting and expanding boxes.Comment: Accepted by Physics Letters
Boolean versus continuous dynamics on simple two-gene modules
We investigate the dynamical behavior of simple modules composed of two genes
with two or three regulating connections. Continuous dynamics for mRNA and
protein concentrations is compared to a Boolean model for gene activity. Using
a generalized method, we study within a single framework different continuous
models and different types of regulatory functions, and establish conditions
under which the system can display stable oscillations. These conditions
concern the time scales, the degree of cooperativity of the regulating
interactions, and the signs of the interactions. Not all models that show
oscillations under Boolean dynamics can have oscillations under continuous
dynamics, and vice versa.Comment: 8 pages, 10 figure
No tension between assembly models of supermassive black hole binaries and pulsar observations
Pulsar timing arrays (PTAs) are presently the only means to search for the
gravitational wave stochastic background from supermassive black hole binary
populations, considered to be within the grasp of current or near future
observations. However, the stringent upperlimit set by the Parkes PTA (Shannon
et al. 2013, 2015) has been interpreted as excluding at confidence the
current paradigm of binary assembly through galaxy mergers and hardening via
stellar interactions, suggesting evolution is accelerated (by stars and/or gas)
or stalled. Using Bayesian hierarchical modelling, we consider implications of
this upperlimit for a comprehensive range of astrophysical scenarios, without
invoking stalling nor more exotic physical processes. We find they are fully
consistent with the upperlimit, but (weak) bounds on population parameters can
be inferred. Bayes factors between models vary between --
and Kullback-Leibler divergences between characteristic amplitude prior and
posterior lie between -- . Considering prior astrophysical
information on galaxy merger rates, recent upwards revisions of the black
hole-galaxy bulge mass relation (Kormendy & Ho 2013) are disfavoured at
against lighter models (e.g. Shankar et al. 2016). We also show, if
no detection is achieved once sensitivity improves by an order of magnitude,
the most optimistic scenario is disfavoured at .Comment: 20 pages, 7 figure
Self-fields in thin superconducting tapes: implications to the thickness effect in coated conductors
Most applications of superconductors, such as power transmission lines,
motors, generators, and transformers, require long cables through which large
currents circulate. Impressive progress has recently been achieved in the
current-carrying capability in conductors based on high-temperature
superconductors. Coated conductors are likely the best examples, consisting of
very good quality thin layers of YBCO superconductor grown on top of a metallic
tape with some intermediate layers. However, there is an important problem for
achieving large currents: a large decrease in transport critical-current
density Jc when increasing film thickness has been observed in coated
conductors made by all available techniques. Here, we theoretically explain the
nature and the ubiquitous presence of this so-called thickness effect by
analyzing the self-field created by the transport currents in the
superconductor, assuming a realistic field-dependent Jc. This knowledge can
help finding new ways to improve transport current in thick superconducting
films.Comment: 7 pages, 3 figure
Wavelet-based density estimation for noise reduction in plasma simulations using particles
For given computational resources, the accuracy of plasma simulations using
particles is mainly held back by the noise due to limited statistical sampling
in the reconstruction of the particle distribution function. A method based on
wavelet analysis is proposed and tested to reduce this noise. The method, known
as wavelet based density estimation (WBDE), was previously introduced in the
statistical literature to estimate probability densities given a finite number
of independent measurements. Its novel application to plasma simulations can be
viewed as a natural extension of the finite size particles (FSP) approach, with
the advantage of estimating more accurately distribution functions that have
localized sharp features. The proposed method preserves the moments of the
particle distribution function to a good level of accuracy, has no constraints
on the dimensionality of the system, does not require an a priori selection of
a global smoothing scale, and its able to adapt locally to the smoothness of
the density based on the given discrete particle data. Most importantly, the
computational cost of the denoising stage is of the same order as one time step
of a FSP simulation. The method is compared with a recently proposed proper
orthogonal decomposition based method, and it is tested with three particle
data sets that involve different levels of collisionality and interaction with
external and self-consistent fields
The Role of Center Vortices in QCD
Center vortices are unambiguously identified after Laplacian Center Gauge
fixing and their influence on confinement and chiral symmetry breaking is
investigated on a sample of SU(2) configurations at zero and finite
temperature.Comment: LaTeX, 4 pages, 3 figures, espcrc1.sty. Talk at PANIC '99, Uppsala,
Sweden, June 9
Singular limits for the bi-laplacian operator with exponential nonlinearity in
Let be a bounded smooth domain in such that for
some integer its -th singular cohomology group with coefficients in
some field is not zero, then problem
{\Delta^{2}u-\rho^{4}k(x)e^{u}=0 & \hbox{in}\Omega,
u=\Delta u=0 & \hbox{on}\partial\Omega,
has a solution blowing-up, as , at points of , for any
given number .Comment: 30 pages, to appear in Ann. IHP Non Linear Analysi
Complex viscosity behavior and cluster formation in attractive colloidal systems
The increase of the viscosity, which is observed in attractive colloidal
systems by varying the temperature or the volume fraction, can be related to
the formation of structures due to particle aggregation. In particular we have
studied the non trivial dependence of the viscosity from the temperature and
the volume fraction in the copolymer-micellar system L64. The comparison of the
experimental data with the results of numerical simulations in a simple model
for gelation phenomena suggests that this intriguing behavior can be explained
in terms of cluster formation and that this picture can be quite generally
extended to other attractive colloidal systems.Comment: 5 pages, 4 figure
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