Efficient Resolution of Anisotropic Structures

We highlight some recent new delevelopments concerning the sparse representation of possibly high-dimensional functions exhibiting strong anisotropic features and low regularity in isotropic Sobolev or Besov scales. Specifically, we focus on the solution of transport equations which exhibit propagation of singularities where, additionally, high-dimensionality enters when the convection field, and hence the solutions, depend on parameters varying over some compact set. Important constituents of our approach are directionally adaptive discretization concepts motivated by compactly supported shearlet systems, and well-conditioned stable variational formulations that support trial spaces with anisotropic refinements with arbitrary directionalities. We prove that they provide tight error-residual relations which are used to contrive rigorously founded adaptive refinement schemes which converge in $L_2$. Moreover, in the context of parameter dependent problems we discuss two approaches serving different purposes and working under different regularity assumptions. For frequent query problems, making essential use of the novel well-conditioned variational formulations, a new Reduced Basis Method is outlined which exhibits a certain rate-optimal performance for indefinite, unsymmetric or singularly perturbed problems. For the radiative transfer problem with scattering a sparse tensor method is presented which mitigates or even overcomes the curse of dimensionality under suitable (so far still isotropic) regularity assumptions. Numerical examples for both methods illustrate the theoretical findings

Multiwavelength Transit Observations of the Candidate Disintegrating Planetesimals Orbiting WD 1145+017

We present multiwavelength, multi-telescope, ground-based follow-up photometry of the white dwarf WD 1145+017, that has recently been suggested to be orbited by up to six or more, short-period, low-mass, disintegrating planetesimals. We detect 9 significant dips in flux of between 10% and 30% of the stellar flux from our ground-based photometry. We observe transits deeper than 10% on average every ~3.6 hr in our photometry. This suggests that WD 1145+017 is indeed being orbited by multiple, short-period objects. Through fits to the multiple asymmetric transits that we observe, we confirm that the transit egress timescale is usually longer than the ingress timescale, and that the transit duration is longer than expected for a solid body at these short periods, all suggesting that these objects have cometary tails streaming behind them. The precise orbital periods of the planetesimals in this system are unclear from the transit-times, but at least one object, and likely more, have orbital periods of ~4.5 hours. We are otherwise unable to confirm the specific periods that have been reported, bringing into question the long-term stability of these periods. Our high precision photometry also displays low amplitude variations suggesting that dusty material is consistently passing in front of the white dwarf, either from discarded material from these disintegrating planetesimals or from the detected dusty debris disk. For the significant transits we observe, we compare the transit depths in the V- and R-bands of our multiwavelength photometry, and find no significant difference; therefore, for likely compositions the radius of single-size particles in the cometary tails streaming behind the planetesimals in this system must be ~0.15 microns or larger, or ~0.06 microns or smaller, with 2-sigma confidence.Comment: 16 pages, 12 figures, submitted to ApJ on October 8th, 201

The K2-ESPRINT Project. I. Discovery of the Disintegrating Rocky Planet K2-22b with a Cometary Head and Leading Tail

We present the discovery of a transiting exoplanet candidate in the K2 Field-1 with an orbital period of 9.1457 hr: K2-22b. The highly variable transit depths, ranging from $\sim$0\% to 1.3\%, are suggestive of a planet that is disintegrating via the emission of dusty effluents. We characterize the host star as an M-dwarf with $T_{\rm eff} \simeq 3800$ K. We have obtained ground-based transit measurements with several 1-m class telescopes and with the GTC. These observations (1) improve the transit ephemeris; (2) confirm the variable nature of the transit depths; (3) indicate variations in the transit shapes; and (4) demonstrate clearly that at least on one occasion the transit depths were significantly wavelength dependent. The latter three effects tend to indicate extinction of starlight by dust rather than by any combination of solid bodies. The K2 observations yield a folded light curve with lower time resolution but with substantially better statistical precision compared with the ground-based observations. We detect a significant "bump" just after the transit egress, and a less significant bump just prior to transit ingress. We interpret these bumps in the context of a planet that is not only likely streaming a dust tail behind it, but also has a more prominent leading dust trail that precedes it. This effect is modeled in terms of dust grains that can escape to beyond the planet's Hill sphere and effectively undergo `Roche lobe overflow,' even though the planet's surface is likely underfilling its Roche lobe by a factor of 2.Comment: 22 pages, 16 figures. Final version accepted to Ap

Discovery of the Transiting Planet Kepler-5B

We present 44 days of high duty cycle, ultra precise photometry of the 13th magnitude star Kepler-5 (KIC 8191672, T(eff) = 6300 K, log g = 4.1), which exhibits periodic transits with a depth of 0.7%. Detailed modeling of the transit is consistent with a planetary companion with an orbital period of 3.548460 +/- 0.000032 days and a radius of 1.431(-0.052)(+0.041) R(J). Follow-up radial velocity measurements with the Keck HIRES spectrograph on nine separate nights demonstrate that the planet is more than twice as massive as Jupiter with a mass of 2.114(-0.059)(+0.056) M(J) and a mean density of 0.894 +/- 0.079 g cm(-3).NASA's Science Mission DirectorateAstronom

Relativistic separable dual-space Gaussian Pseudopotentials from H to Rn

We generalize the concept of separable dual-space Gaussian pseudopotentials to the relativistic case. This allows us to construct this type of pseudopotential for the whole periodic table and we present a complete table of pseudopotential parameters for all the elements from H to Rn. The relativistic version of this pseudopotential retains all the advantages of its nonrelativistic version. It is separable by construction, it is optimal for integration on a real space grid, it is highly accurate and due to its analytic form it can be specified by a very small number of parameters. The accuracy of the pseudopotential is illustrated by an extensive series of molecular calculations

Approximation of integral operators using product-convolution expansions

International audienceWe consider a class of linear integral operators with impulse responses varying regularly in time or space. These operators appear in a large number of applications ranging from signal/image processing to biology. Evaluating their action on functions is a computationally intensive problem necessary for many practical problems. We analyze a technique called product-convolution expansion: the operator is locally approximated by a convolution, allowing to design fast numerical algorithms based on the fast Fourier transform. We design various types of expansions, provide their explicit rates of approximation and their complexity depending on the time varying impulse response smoothness. This analysis suggests novel wavelet based implementations of the method with numerous assets such as optimal approximation rates, low complexity and storage requirements as well as adaptivity to the kernels regularity. The proposed methods are an alternative to more standard procedures such as panel clustering, cross approximations, wavelet expansions or hierarchical matrices

Association of Heart Failure With Outcomes Among Patients With Peripheral Artery Disease: Insights From EUCLID.

Background Peripheral artery disease (PAD) and heart failure (HF) are each independently associated with poor outcomes. Risk factors associated with new-onset HF in patients with primary PAD are unknown. Furthermore, how the presence of HF is associated with outcomes in patients with PAD is unknown. Methods and Results This analysis examined risk relationships of HF on outcomes in patients with symptomatic PAD randomized to ticagrelor or clopidogrel as part of the EUCLID (Examining Use of Ticagrelor in Peripheral Arterial Disease) trial. Patients were stratified based on presence of HF at enrollment. Cox models were used to determine the association of HF with outcomes. A separate Cox model was used to identify risk factors associated with development of HF during follow-up. Patients with PAD and HF had over twice the rate of concomitant coronary artery disease as those without HF. Patients with PAD and HF had significantly increased risk of major adverse cardiovascular events (hazard ratio [HR], 1.31; 95% CI, 1.13-1.51) and all-cause mortality (HR, 1.39; 95% CI, 1.19-1.63). In patients with PAD, the presence of HF was associated with significantly less bleeding (HR, 0.65; 95% CI, 0.45-0.96). Characteristics associated with HF development included age ≥66 (HR, 1.29; 95% CI, 1.18-1.40 per 5 years), diabetes mellitus (HR, 1.85; 95% CI, 1.41-2.43), and weight (bidirectionally associated, ≥76 kg, HR, 0.77; 95% CI, 0.64-0.93; <76 kg, HR, 1.12; 95% CI, 1.07-1.16). Conclusions Patients with PAD and HF have a high rate of coronary artery disease with a high risk for major adverse cardiovascular events and death. These data support the possible need for aggressive treatment of (recurrent) atherosclerotic disease in PAD, especially patients with HF