9,607 research outputs found
The Degrees of Freedom of the Group Lasso
This paper studies the sensitivity to the observations of the block/group
Lasso solution to an overdetermined linear regression model. Such a
regularization is known to promote sparsity patterns structured as
nonoverlapping groups of coefficients. Our main contribution provides a local
parameterization of the solution with respect to the observations. As a
byproduct, we give an unbiased estimate of the degrees of freedom of the group
Lasso. Among other applications of such results, one can choose in a principled
and objective way the regularization parameter of the Lasso through model
selection criteria
Clustering properties of rectangular Macdonald polynomials
The clustering properties of Jack polynomials are relevant in the theoretical
study of the fractional Hall states. In this context, some factorization
properties have been conjectured for the -deformed problem involving
Macdonald polynomials. The present paper is devoted to the proof of this
formula. To this aim we use four families of Jack/Macdonald polynomials:
symmetric homogeneous, nonsymmetric homogeneous, shifted symmetric and shifted
nonsymmetric.Comment: 43 pages, 2 figure
Breaking anchored droplets in a microfluidic Hele-Shaw cell
We study microfluidic self digitization in Hele-Shaw cells using pancake
droplets anchored to surface tension traps. We show that above a critical flow
rate, large anchored droplets break up to form two daughter droplets, one of
which remains in the anchor. Below the critical flow velocity for breakup the
shape of the anchored drop is given by an elastica equation that depends on the
capillary number of the outer fluid. As the velocity crosses the critical
value, the equation stops admitting a solution that satisfies the boundary
conditions; the drop breaks up in spite of the neck still having finite width.
A similar breaking event also takes place between the holes of an array of
anchors, which we use to produce a 2D array of stationary drops in situ.Comment: 5 pages, 4 figures, to appear in Phys. Rev. Applie
Recommended from our members
Computational Methods for Parameter Estimation in Climate Models
Intensive computational methods have been used by Earth scientists in a wide range of problems in data inversion and uncertainty quantification such as earthquake epicenter location and climate projections. To quantify the uncertainties resulting from a range of plausible model configurations it is necessary to estimate a multidimensional probability distribution. The computational cost of estimating these distributions for geoscience applications is impractical using traditional methods such as Metropolis/Gibbs algorithms as simulation costs limit the number of experiments that can be obtained reasonably. Several alternate sampling strategies have been proposed that could improve on the sampling efficiency including Multiple Very Fast Simulated Annealing (MVFSA) and Adaptive Metropolis algorithms. The performance of these proposed sampling strategies are evaluated with a surrogate climate model that is able to approximate the noise and response behavior of a realistic atmospheric general circulation model (AGCM). The surrogate model is fast enough that its evaluation can be embedded in these Monte Carlo algorithms. We show that adaptive methods can be superior to MVFSA to approximate the known posterior distribution with fewer forward evaluations. However the adaptive methods can also be limited by inadequate sample mixing. The Single Component and Delayed Rejection Adaptive Metropolis algorithms were found to resolve these limitations, although challenges remain to approximating multi-modal distributions. The results show that these advanced methods of statistical inference can provide practical solutions to the climate model calibration problem and challenges in quantifying climate projection uncertainties. The computational methods would also be useful to problems outside climate prediction, particularly those where sampling is limited by availability of computational resources.National Science Foundation OCE-0415251CONACyT-Mexico 159764Institute for Geophysic
- …