Global properties of Stochastic Loewner evolution driven by Levy processes

Standard Schramm-Loewner evolution (SLE) is driven by a continuous Brownian motion which then produces a trace, a continuous fractal curve connecting the singular points of the motion. If jumps are added to the driving function, the trace branches. In a recent publication [1] we introduced a generalized SLE driven by a superposition of a Brownian motion and a fractal set of jumps (technically a stable L\'evy process). We then discussed the small-scale properties of the resulting L\'evy-SLE growth process. Here we discuss the same model, but focus on the global scaling behavior which ensues as time goes to infinity. This limiting behavior is independent of the Brownian forcing and depends upon only a single parameter, $\alpha$, which defines the shape of the stable L\'evy distribution. We learn about this behavior by studying a Fokker-Planck equation which gives the probability distribution for endpoints of the trace as a function of time. As in the short-time case previously studied, we observe that the properties of this growth process change qualitatively and singularly at $\alpha =1$. We show both analytically and numerically that the growth continues indefinitely in the vertical direction for $\alpha > 1$, goes as $\log t$ for $\alpha = 1$, and saturates for $\alpha< 1$. The probability density has two different scales corresponding to directions along and perpendicular to the boundary. In the former case, the characteristic scale is $X(t) \sim t^{1/\alpha}$. In the latter case the scale is $Y(t) \sim A + B t^{1-1/\alpha}$ for $\alpha \neq 1$, and $Y(t) \sim \ln t$ for $\alpha = 1$. Scaling functions for the probability density are given for various limiting cases.Comment: Published versio

PAS-positive lymphocyte vacuoles can be used as diagnostic screening test for Pompe disease

Screening of blood films for the presence of periodic acid-Schiff (PAS)-positive lymphocyte vacuoles is sometimes used to support the diagnosis of Pompe disease, but the actual diagnostic value is still unknown. We collected peripheral blood films from 65 untreated Pompe patients and 51 controls. Lymphocyte vacuolization was quantified using three methods: percentage vacuolated lymphocytes, percentage PAS-positive lymphocytes, and a PAS score depending on staining intensity. Diagnostic accuracy of the tests was assessed using receiver operating characteristic (ROC) curves. All three methods fully discerned classic infantile patients from controls. The mean values of patients with milder forms of Pompe disease were significantly higher than those of controls, but full separation was not obtained. The area under the ROC curve was 0.98 for the percentage vacuolated lymphocytes (optimal cutoff value 3; sensitivity 91%, specificity 96%) and 0.99 for the percentage PAS-positive lymphocytes and PAS score (optimal cutoff value 9; sensitivity 100%, specificity 98%). Our data indicate that PAS-stained blood films can be used as a reliable screening tool to support a diagnosis of Pompe disease. The percentage of PAS-positive lymphocytes is convenient for use in clinical practice but should always be interpreted in combination with other clinical and laboratory parameters

The Close AGN Reference Survey (CARS): Tracing the circumnuclear star formation in the super-Eddington NLS1 Mrk 1044

The host galaxy conditions for rapid supermassive black hole growth are poorly understood. Narrow-line Seyfert 1 (NLS1) galaxies often exhibit high accretion rates and are hypothesized to be prototypes of active galactic nuclei (AGN) at an early stage of their evolution. We present VLT MUSE NFM-AO observations of Mrk 1044, the nearest super-Eddington accreting NLS1. Together with archival MUSE WFM data we aim to understand the host galaxy processes that drive Mrk 1044's black hole accretion. We extract the faint stellar continuum emission from the AGN-deblended host and perform spatially resolved emission line diagnostics with an unprecedented resolution. Combining both MUSE WFM and NFM-AO observations, we use a kinematic model of a thin rotating disk to trace the stellar and ionized gas motion from 10$\,$kpc down to 30$\,$pc around the nucleus. Mrk 1044's stellar kinematics follow circular rotation, whereas the ionized gas shows tenuous spiral features in the center. We resolve a compact star forming circumnuclear ellipse (CNE) that has a semi-minor axis of 306$\,$pc. Within this CNE, the gas is metal rich and its line ratios are entirely consistent with excitation by star formation. With an integrated SFR of $0.19 \pm 0.05 \,{\rm M}_\odot\,{\rm yr}^{-1}$ the CNE contributes 27% of the galaxy-wide star formation. We conclude that Mrk 1044's nuclear activity has not yet affected the circumnuclear star formation. Thus, Mrk 1044 is consistent with the idea that NLS1s are young AGN. A simple mass budget consideration suggests that the circumnuclear star formation and AGN phase are connected and the patterns in the ionized gas velocity field are a signature of the ongoing AGN feeding.Comment: accepted for publication in A&A, 17 pages, 14 figures, 1 table, for Fig. 5 associated animation see https://youtube.com/watch?v=H_WSgWJSCf

A global view on star formation: The GLOSTAR Galactic plane survey. VII. Supernova remnants in the Galactic longitude range 28∘<l<36∘28^\circ<l<36^\circ

Context. While over 1000 supernova remnants (SNRs) are estimated to exist in the Milky Way, only less than 400 have been found to date. In the context of this apparent deficiency, more than 150 SNR candidates were recently identified in the D-configuration Very Large Array (VLA-D) continuum images of the 4--8 GHz global view on star formation (GLOSTAR) survey, in the Galactic longitude range $-2^\circ<l<60^\circ$. Aims. We attempt to find evidence of nonthermal synchrotron emission from 35 SNR candidates in the region of Galactic longitude range $28^\circ<l<36^\circ$, and also to study the radio continuum emission from the previously confirmed SNRs in this region. Methods. Using the short-spacing corrected GLOSTAR VLA-D+Effelsberg images, we measure ${\sim}6$ GHz total and linearly polarized flux densities of the SNR candidates and the SNRs that were previously confirmed. We also attempt to determine the spectral indices by measuring flux densities from complementary Galactic plane surveys and from the temperature-temperature plots of the GLOSTAR-Effelsberg images. Results. We provide evidence of nonthermal emission from four candidates that have spectral indices and polarization consistent with a SNR origin, and, considering their morphology, we are confident that three of these (G28.36+0.21, G28.78-0.44, and G29.38+0.10) are indeed SNRs. However, about $25\%$ of the candidates have spectral index measurements that indicate thermal emission, and the rest of them are too faint to have a good constraint on the spectral index yet. Conclusions. Additional observations at longer wavelengths and higher sensitivities will shed more light on the nature of these candidates. A simple Monte-Carlo simulation reiterates the view that future studies must persist with the current strategy of searching for SNRs with small angular size to solve the problem of the Milky Way's missing SNRs.Comment: To be published in A&A. 21 pages, 15 figure