Diffusion-Reorganized Aggregates: Attractors in Diffusion Processes?

A process based on particle evaporation, diffusion and redeposition is applied iteratively to a two-dimensional object of arbitrary shape. The evolution spontaneously transforms the object morphology, converging to branched structures. Independently of initial geometry, the structures found after long time present fractal geometry with a fractal dimension around 1.75. The final morphology, which constantly evolves in time, can be considered as the dynamic attractor of this evaporation-diffusion-redeposition operator. The ensemble of these fractal shapes can be considered to be the {\em dynamical equilibrium} geometry of a diffusion controlled self-transformation process.Comment: 4 pages, 5 figure

Computing the output distribution and selection probabilities of a stack filter from the DNF of its positive Boolean function

Many nonlinear filters used in practise are stack filters. An algorithm is presented which calculates the output distribution of an arbitrary stack filter S from the disjunctive normal form (DNF) of its underlying positive Boolean function. The so called selection probabilities can be computed along the way.Comment: This is the version published in Journal of Mathematical Imaging and Vision, online first, 1 august 201

Lossy Compression of Electron Diffraction Patterns for Ptychography via Change of Basis

Ptychography is a computational imaging technique that has risen in popularity in the x-ray and electron microscopy communities in the past half decade. One of the reasons for this success is the development of new high performance electron detectors with increased dynamic range and readout speed, both of which are necessary for a successful application of this technique. Despite the advances made in computing power, processing the recorded data remains a challenging task, and the growth in data rate has made the size of the resulting datasets a bottleneck for the whole process. Here we present an investigation into lossy compression methods for electron diffraction patterns that retain the necessary information for ptychographic reconstructions, yet lead to a decrease in data set size by three or four orders of magnitude. We apply several compression methods to both simulated and experimental data - all with promising results

The Opportunity Process for Optimal Consumption and Investment with Power Utility

We study the utility maximization problem for power utility random fields in a semimartingale financial market, with and without intermediate consumption. The notion of an opportunity process is introduced as a reduced form of the value process of the resulting stochastic control problem. We show how the opportunity process describes the key objects: optimal strategy, value function, and dual problem. The results are applied to obtain monotonicity properties of the optimal consumption.Comment: 24 pages, forthcoming in 'Mathematics and Financial Economics

The Factory and the Beehive. II. Activity and Rotation is Praesepe and the Hyades

Open clusters are collections of stars with a single, well-determined age, and can be used to investigate the connections between angular-momentum evolution and magnetic activity over a star\u27s lifetime. We present the results of a comparative study of the relationship between stellar rotation and activity in two benchmark open clusters: Praesepe and the Hyades. As they have the same age and roughly solar metallicity, these clusters serve as an ideal laboratory for testing the agreement between theoretical and empirical rotation-activity relations at 600 Myr. We have compiled a sample of 720 spectra—more than half of which are new observations—for 516 high-confidence members of Praesepe; we have also obtained 139 new spectra for 130 high-confidence Hyads. We have also collected rotation periods (P rot) for 135 Praesepe members and 87 Hyads. To compare Hα emission, an indicator of chromospheric activity, as a function of color, mass, and Rossby number Ro , we first calculate an expanded set of χ values, with which we can obtain the Hα to bolometric luminosity ratio, L Hα/L bol, even when spectra are not flux-calibrated and/or stars lack reliable distances. Our χ values cover a broader range of stellar masses and colors (roughly equivalent to spectral types from K0 to M9), and exhibit better agreement between independent calculations, than existing values. Unlike previous authors, we find no difference between the two clusters in their Hα equivalent width or L Hα/L bol distributions, and therefore take the merged Hα and P rot data to be representative of 600 Myr old stars. Our analysis shows that Hα activity in these stars is saturated for . Above that value activity declines as a power-law with slope , before dropping off rapidly at Ro 0.4. These data provide a useful anchor for calibrating the age-activity-rotation relation beyond 600 Myr

Facet ridge end points in crystal shapes

Equilibrium crystal shapes (ECS) near facet ridge end points (FRE) are generically complex. We study the body-centered solid-on-solid model on a square lattice with an enhanced uniaxial interaction range to test the stability of the so-called stochastic FRE point where the model maps exactly onto one dimensional Kardar-Parisi-Zhang type growth and the local ECS is simple. The latter is unstable. The generic ECS contains first-order ridges extending into the rounded part of the ECS, where two rough orientations coexist and first-order faceted to rough boundaries terminating in Pokrovsky-Talapov type end points.Comment: Contains 4 pages, 5 eps figures. Uses RevTe

The Factory and the Beehive III: PTFEB132.707+19.810, a Low-Mass Eclipsing Binary in Praesepe Observed by PTF and K2

Theoretical models of stars constitute a fundamental bedrock upon which much of astrophysics is built, but large swaths of model parameter space remain uncalibrated by observations. The best calibrators are eclipsing binaries in clusters, allowing measurement of masses, radii, luminosities, and temperatures, for stars of known metallicity and age. We present the discovery and detailed characterization of PTFEB132.707+19.810, a P=6.0 day eclipsing binary in the Praesepe cluster ($\tau$~600--800 Myr; [Fe/H]=0.14$\pm$0.04). The system contains two late-type stars (SpT$_P$=M3.5$\pm$0.2; SpT$_S$=M4.3$\pm$0.7) with precise masses ($M_p=0.3953\pm0.0020$~$M_{\odot}$; $M_s=0.2098\pm0.0014$~$M_{\odot}$) and radii ($R_p=0.363\pm0.008$~$R_{\odot}$; $R_s=0.272\pm0.012$~$R_{\odot}$). Neither star meets the predictions of stellar evolutionary models. The primary has the expected radius, but is cooler and less luminous, while the secondary has the expected luminosity, but is cooler and substantially larger (by 20%). The system is not tidally locked or circularized. Exploiting a fortuitous 4:5 commensurability between $P_{orb}$ and $P_{rot,prim}$, we demonstrate that fitting errors from the unknown spot configuration only change the inferred radii by <1--2%. We also analyze subsets of data to test the robustness of radius measurements; the radius sum is more robust to systematic errors and preferable for model comparisons. We also test plausible changes in limb darkening, and find corresponding uncertainties of ~1%. Finally, we validate our pipeline using extant data for GU Boo, finding that our independent results match previous radii to within the mutual uncertainties (2--3%). We therefore suggest that the substantial discrepancies are astrophysical; since they are larger than for old field stars, they may be tied to the intermediate age of PTFEB132.707+19.810.Comment: Accepted to ApJ; 36 pages, 19 figures, 8 tables in two-column AASTEX6 forma

Main problems experienced by children with epidermolysis bullosa:A qualitative study with semi-structured interviews

The objective of this study was to identify and specify the problems of children with epidermolysis bullosa. The questions explored were: (i) What do children with epidermolysis bullosa experience as the most difficult problems; (it) What is the impact of these problems on their daily life; and (iii) Do these experiences differ between mildly and severely affected children? Qualitative research methodology was used, comprising a series of semi-structured interviews with children with different (sub)types of epidermolysis bullosa. The interviews were analysed systematically with help of the qualitative software package Atlas-ti. Five main themes were found: (i) having an itchy skin, (ii) being in pain, (iii) having difficulties with participation, (iv) lack of understanding of others, and (v) the feeling of being different. Severely affected children suffered most from itch and treatment-related pain. Mildly affected children had more problems with activity-related pain. Mildly affected children also had more concerns about their appearance and the teasing and staring of others than did severely affected children. Both groups had difficulties with participation, the visibility of their disease and the feeling of being different