The Kepler Catalog of Stellar Flares

A homogeneous search for stellar flares has been performed using every available Kepler light curve. An iterative light curve de-trending approach was used to filter out both astrophysical and systematic variability to detect flares. The flare recovery completeness has also been computed throughout each light curve using artificial flare injection tests, and the tools for this work have been made publicly available. The final sample contains 851,168 candidate flare events recovered above the 68% completeness threshold, which were detected from 4041 stars, or 1.9% of the stars in the Kepler database. The average flare energy detected is ~$10^{35}$ erg. The net fraction of flare stars increases with $g-i$ color, or decreasing stellar mass. For stars in this sample with previously measured rotation periods, the total relative flare luminosity is compared to the Rossby number. A tentative detection of flare activity saturation for low-mass stars with rapid rotation below a Rossby number of ~0.03 is found. A power law decay in flare activity with Rossby number is found with a slope of -1, shallower than typical measurements for X-ray activity decay with Rossby number.Comment: 15 pages, 8 figures, ApJ accepted. Code is available online: http://github.com/jradavenport/appaloos

How well can we estimate a sparse vector?

The estimation of a sparse vector in the linear model is a fundamental problem in signal processing, statistics, and compressive sensing. This paper establishes a lower bound on the mean-squared error, which holds regardless of the sensing/design matrix being used and regardless of the estimation procedure. This lower bound very nearly matches the known upper bound one gets by taking a random projection of the sparse vector followed by an $\ell_1$ estimation procedure such as the Dantzig selector. In this sense, compressive sensing techniques cannot essentially be improved

Compressive Sensing of Analog Signals Using Discrete Prolate Spheroidal Sequences

Compressive sensing (CS) has recently emerged as a framework for efficiently capturing signals that are sparse or compressible in an appropriate basis. While often motivated as an alternative to Nyquist-rate sampling, there remains a gap between the discrete, finite-dimensional CS framework and the problem of acquiring a continuous-time signal. In this paper, we attempt to bridge this gap by exploiting the Discrete Prolate Spheroidal Sequences (DPSS's), a collection of functions that trace back to the seminal work by Slepian, Landau, and Pollack on the effects of time-limiting and bandlimiting operations. DPSS's form a highly efficient basis for sampled bandlimited functions; by modulating and merging DPSS bases, we obtain a dictionary that offers high-quality sparse approximations for most sampled multiband signals. This multiband modulated DPSS dictionary can be readily incorporated into the CS framework. We provide theoretical guarantees and practical insight into the use of this dictionary for recovery of sampled multiband signals from compressive measurements

Signal Space CoSaMP for Sparse Recovery with Redundant Dictionaries

Compressive sensing (CS) has recently emerged as a powerful framework for acquiring sparse signals. The bulk of the CS literature has focused on the case where the acquired signal has a sparse or compressible representation in an orthonormal basis. In practice, however, there are many signals that cannot be sparsely represented or approximated using an orthonormal basis, but that do have sparse representations in a redundant dictionary. Standard results in CS can sometimes be extended to handle this case provided that the dictionary is sufficiently incoherent or well-conditioned, but these approaches fail to address the case of a truly redundant or overcomplete dictionary. In this paper we describe a variant of the iterative recovery algorithm CoSaMP for this more challenging setting. We utilize the D-RIP, a condition on the sensing matrix analogous to the well-known restricted isometry property. In contrast to prior work, the method and analysis are "signal-focused"; that is, they are oriented around recovering the signal rather than its dictionary coefficients. Under the assumption that we have a near-optimal scheme for projecting vectors in signal space onto the model family of candidate sparse signals, we provide provable recovery guarantees. Developing a practical algorithm that can provably compute the required near-optimal projections remains a significant open problem, but we include simulation results using various heuristics that empirically exhibit superior performance to traditional recovery algorithms

Static force tests of a sharp leading edge delta-wing model at ambient and cryogenic temperatures with a description of the apparatus employed

A sharp leading edge delta-wing model was tested through an angle-of-attack range at Mach numbers of 0.75, 0.80, and 0.85 at both ambient and cryogenic temperatures in the Langley 1/3-meter transonic cryogenic tunnel. Total pressure was varied with total temperature in order to hold test Reynolds number constant at a given Mach number. Agreement between the aerodynamic data obtained at ambient and cryogenic temperatures indicates that flows with leading-edge vortex effects are duplicated properly at cryogenic temperatures. The test results demonstrate that accurate aerodynamic data can be obtained by using conventional force-testing techniques if suitable measures are taken to minimize temperature gradients across the balance and to keep the balance at ambient (warm) temperatures during cryogenic operation of the tunnel