Analysis of Basis Pursuit Via Capacity Sets

Finding the sparsest solution $\alpha$ for an under-determined linear system of equations $D\alpha=s$ is of interest in many applications. This problem is known to be NP-hard. Recent work studied conditions on the support size of $\alpha$ that allow its recovery using L1-minimization, via the Basis Pursuit algorithm. These conditions are often relying on a scalar property of $D$ called the mutual-coherence. In this work we introduce an alternative set of features of an arbitrarily given $D$, called the "capacity sets". We show how those could be used to analyze the performance of the basis pursuit, leading to improved bounds and predictions of performance. Both theoretical and numerical methods are presented, all using the capacity values, and shown to lead to improved assessments of the basis pursuit success in finding the sparest solution of $D\alpha=s$

SDSS J105754.25+275947.5: a period-bounce eclipsing cataclysmic variable with the lowest-mass donor yet measured

We present high-speed, multicolour photometry of the faint, eclipsing cataclysmic variable (CV) SDSS J105754.25+275947.5. The light from this system is dominated by the white dwarf. Nonetheless, averaging many eclipses reveals additional features from the eclipse of the bright spot. This enables the fitting of a parameterised eclipse model to these average light curves, allowing the precise measurement of system parameters. We find a mass ratio of q = 0.0546 $\pm$ 0.0020 and inclination i = 85.74 $\pm$ 0.21$^{\circ}$. The white dwarf and donor masses were found to be M$_{\mathrm{w}}$ = 0.800 $\pm$ 0.015 M$_{\odot}$ and M$_{\mathrm{d}}$ = 0.0436 $\pm$ 0.0020 M$_{\odot}$, respectively. A temperature T$_{\mathrm{w}}$ = 13300 $\pm$ 1100 K and distance d = 367 $\pm$ 26 pc of the white dwarf were estimated through fitting model atmosphere predictions to multicolour fluxes. The mass of the white dwarf in SDSS 105754.25+275947.5 is close to the average for CV white dwarfs, while the donor has the lowest mass yet measured in an eclipsing CV. A low-mass donor and an orbital period (90.44 min) significantly longer than the period minimum strongly suggest that this is a bona fide period-bounce system, although formation from a white dwarf/brown dwarf binary cannot be ruled out. Very few period-minimum/period-bounce systems with precise system parameters are currently known, and as a consequence the evolution of CVs in this regime is not yet fully understood

Specific heat and magnetic measurements in Nd0.5Sr0.5MnO3, Nd0.5Ca0.5MnO3 and Ho0.5Ca0.5MnO3 samples

We studied the magnetization as a function of temperature and magnetic field in the compounds Nd0.5Sr0.5MnO3, Nd0.5Ca0.5MnO3 and Ho0.5Ca0.5MnO3. It allowed us to identify the ferromagnetic, antiferromagnetic and charge ordering phases in each case. The intrinsic magnetic moments of Nd3+ and Ho3+ ions experienced a short range order at low temperatures. We also did specific heat measurements with applied magnetic fields between 0 and 9 T and temperatures between 2 and 300 K in all three samples. Close to the charge ordering and ferromagnetic transition temperatures the specific heat curves showed peaks superposed to the characteristic response of the lattice oscillations. Below 10 K the specific heat measurements evidenced a Schottky-like anomaly for all samples. However, we could not successfully fit the curves to either a two level nor a distribution of two-level Schottky anomaly. Our results indicated that the peak temperature of the Schottky anomaly was higher in the compounds with narrower conduction band.Comment: submitted to PR

Narrow genetic base in forest restoration with holm oak (Quercus ilex L.) in Sicily

In order to empirically assess the effect of actual seed sampling strategy on genetic diversity of holm oak (Quercus ilex) forestations in Sicily, we have analysed the genetic composition of two seedling lots (nursery stock and plantation) and their known natural seed origin stand by means of six nuclear microsatellite loci. Significant reduction in genetic diversity and significant difference in genetic composition of the seedling lots compared to the seed origin stand were detected. The female and the total effective number of parents were quantified by means of maternity assignment of seedlings and temporal changes in allele frequencies. Extremely low effective maternity numbers were estimated (Nfe $\approx$ 2-4) and estimates accounting for both seed and pollen donors gave also low values (Ne $\approx$ 35-50). These values can be explained by an inappropriate forestry seed harvest strategy limited to a small number of spatially close trees

Weak capture of protons by protons

The cross section for the proton weak capture reaction $^1H(p,e^+\nu_e)^2H$ is calculated with wave functions obtained from a number of modern, realistic high-precision interactions. To minimize the uncertainty in the axial two-body current operator, its matrix element has been adjusted to reproduce the measured Gamow-Teller matrix element of tritium $\beta$ decay in model calculations using trinucleon wave functions from these interactions. A thorough analysis of the ambiguities that this procedure introduces in evaluating the two-body current contribution to the pp capture is given. Its inherent model dependence is in fact found to be very weak. The overlap integral $\Lambda^2(E=0)$ for the pp capture is predicted to be in the range 7.05--7.06, including the axial two-body current contribution, for all interactions considered.Comment: 17 pages RevTeX (twocolumn), 5 postscript figure

Sum rules and energy scales in the high-temperature superconductor YBa2Cu3O6+x

The Ferrell-Glover-Tinkham (FGT) sum rule has been applied to the temperature dependence of the in-plane optical conductivity of optimally-doped YBa_2Cu_3O_{6.95} and underdoped YBa_2Cu_3O_{6.60}. Within the accuracy of the experiment, the sum rule is obeyed in both materials. However, the energy scale \omega_c required to recover the full strength of the superfluid \rho_s in the two materials is dramatically different; \omega_c \simeq 800 cm^{-1} in the optimally doped system (close to twice the maximum of the superconducting gap, 2\Delta_0), but \omega_c \gtrsim 5000 cm^{-1} in the underdoped system. In both materials, the normal-state scattering rate close to the critical temperature is small, \Gamma < 2\Delta_0, so that the materials are not in the dirty limit and the relevant energy scale for \rho_s in a BCS material should be twice the energy gap. The FGT sum rule in the optimally-doped material suggests that the majority of the spectral weight of the condensate comes from energies below 2\Delta_0, which is consistent with a BCS material in which the condensate originates from a Fermi liquid normal state. In the underdoped material the larger energy scale may be a result of the non-Fermi liquid nature of the normal state. The dramatically different energy scales suggest that the nature of the normal state creates specific conditions for observing the different aspects of what is presumably a central mechanism for superconductivity in these materials.Comment: RevTeX 4 file, 9 pages with 7 embedded eps figure

Parkinson's disease age at onset genome-wide association study : Defining heritability, genetic loci, and α-synuclein mechanisms

Background Increasing evidence supports an extensive and complex genetic contribution to PD. Previous genome-wide association studies (GWAS) have shed light on the genetic basis of risk for this disease. However, the genetic determinants of PD age at onset are largely unknown. Objectives To identify the genetic determinants of PD age at onset. Methods Using genetic data of 28,568 PD cases, we performed a genome-wide association study based on PD age at onset. Results We estimated that the heritability of PD age at onset attributed to common genetic variation was similar to 0.11, lower than the overall heritability of risk for PD (similar to 0.27), likely, in part, because of the subjective nature of this measure. We found two genome-wide significant association signals, one at SNCA and the other a protein-coding variant in TMEM175, both of which are known PD risk loci and a Bonferroni-corrected significant effect at other known PD risk loci, GBA, INPP5F/BAG3, FAM47E/SCARB2, and MCCC1. Notably, SNCA, TMEM175, SCARB2, BAG3, and GBA have all been shown to be implicated in alpha-synuclein aggregation pathways. Remarkably, other well-established PD risk loci, such as GCH1 and MAPT, did not show a significant effect on age at onset of PD. Conclusions Overall, we have performed the largest age at onset of PD genome-wide association studies to date, and our results show that not all PD risk loci influence age at onset with significant differences between risk alleles for age at onset. This provides a compelling picture, both within the context of functional characterization of disease-linked genetic variability and in defining differences between risk alleles for age at onset, or frank risk for disease. (c) 2019 International Parkinson and Movement Disorder SocietyPeer reviewe

Five new post-main-sequence debris disks with gaseous emission

Observations of debris disks, the products of the collisional evolution of rocky planetesimals, can be used to trace planetary activity across a wide range of stellar types. The most common end points of stellar evolution are no exception, as debris disks have been observed around several dozen white dwarf stars. But instead of planetary formation, post-main-sequence debris disks are a signpost of planetary destruction, resulting in compact debris disks from the tidal disruption of remnant planetesimals. In this work, we present the discovery of five new debris disks around white dwarf stars with gaseous debris in emission. All five systems exhibit excess infrared radiation from dusty debris, emission lines from gaseous debris, and atmospheric absorption features indicating ongoing accretion of metal-rich debris. In four of the systems, we detect multiple metal species in emission, some of which occur at strengths and transitions previously unseen in debris disks around white dwarf stars. Our first year of spectroscopic follow-up hints at strong variability in the emission lines that can be studied in the future, expanding the range of phenomena these post-main-sequence debris disks exhibit.Published versio