Reduction and reconstruction of stochastic differential equations via symmetries

An algorithmic method to exploit a general class of infinitesimal symmetries for reducing stochastic differential equations is presented and a natural definition of reconstruction, inspired by the classical reconstruction by quadratures, is proposed. As a side result the well-known solution formula for linear one-dimensional stochastic differential equations is obtained within this symmetry approach. The complete procedure is applied to several examples with both theoretical and applied relevance

A compact ultrahigh-vacuum system for the in situ investigation of III/V semiconductor surfaces

A compact ultrahigh vacuum (UHV) system has been built to study growth and properties of III/V semiconductor surfaces and nanostructures. The system allows one to grow III/V semiconductor surfaces by molecular beam epitaxy (MBE) and analyze their surface by a variety of surface analysis techniques. The geometric structure is examined by scanning tunneling microscopy (STM), low-energy electron diffraction and reflection high-energy electron diffraction. The electronic properties of the surfaces are studied by angular resolved photoemission either in the laboratory using a helium discharge lamp or at the Berlin Synchrotron Radiation Facility BESSY. In order to meet the space restriction at BESSY the system dimensions are kept very small. A detailed description of the apparatus and the sample handling system is given. For the UHV-STM (Park Scientific Instruments, VP2) a new, versatile tip handling mechanism has been developed. It allows the transfer of tips out of the chamber and furthermore, the in situ tip cleaning by electron annealing. In addition, another more reliable in situ tip-preparation technique operating the STM in the field emission regime is described. The ability of the system is shown by an atomically resolved STM image of the c(4×4) reconstructed GaAs(001) surface

The VOISE Algorithm: a Versatile Tool for Automatic Segmentation of Astronomical Images

The auroras on Jupiter and Saturn can be studied with a high sensitivity and resolution by the Hubble Space Telescope (HST) ultraviolet (UV) and far-ultraviolet (FUV) Space Telescope spectrograph (STIS) and Advanced Camera for Surveys (ACS) instruments. We present results of automatic detection and segmentation of Jupiter's auroral emissions as observed by HST ACS instrument with VOronoi Image SEgmentation (VOISE). VOISE is a dynamic algorithm for partitioning the underlying pixel grid of an image into regions according to a prescribed homogeneity criterion. The algorithm consists of an iterative procedure that dynamically constructs a tessellation of the image plane based on a Voronoi Diagram, until the intensity of the underlying image within each region is classified as homogeneous. The computed tessellations allow the extraction of quantitative information about the auroral features such as mean intensity, latitudinal and longitudinal extents and length scales. These outputs thus represent a more automated and objective method of characterising auroral emissions than manual inspection.Comment: 9 pages, 7 figures; accepted for publication in MNRA

Unfolding the Hierarchy of Voids

We present a framework for the hierarchical identification and characterization of voids based on the Watershed Void Finder. The Hierarchical Void Finder is based on a generalization of the scale space of a density field invoked in order to trace the hierarchical nature and structure of cosmological voids. At each level of the hierarchy, the watershed transform is used to identify the voids at that particular scale. By identifying the overlapping regions between watershed basins in adjacent levels, the hierarchical void tree is constructed. Applications on a hierarchical Voronoi model and on a set of cosmological simulations illustrate its potential.Comment: 5 pages, 2 figure

Non-intersecting squared Bessel paths and multiple orthogonal polynomials for modified Bessel weights

We study a model of $n$ non-intersecting squared Bessel processes in the confluent case: all paths start at time $t = 0$ at the same positive value $x = a$, remain positive, and are conditioned to end at time $t = T$ at $x = 0$. In the limit $n \to \infty$, after appropriate rescaling, the paths fill out a region in the $tx$-plane that we describe explicitly. In particular, the paths initially stay away from the hard edge at $x = 0$, but at a certain critical time $t^*$ the smallest paths hit the hard edge and from then on are stuck to it. For $t \neq t^*$ we obtain the usual scaling limits from random matrix theory, namely the sine, Airy, and Bessel kernels. A key fact is that the positions of the paths at any time $t$ constitute a multiple orthogonal polynomial ensemble, corresponding to a system of two modified Bessel-type weights. As a consequence, there is a $3 \times 3$ matrix valued Riemann-Hilbert problem characterizing this model, that we analyze in the large $n$ limit using the Deift-Zhou steepest descent method. There are some novel ingredients in the Riemann-Hilbert analysis that are of independent interest.Comment: 59 pages, 11 figure

Only the Lonely: H I Imaging of Void Galaxies

Void galaxies, residing within the deepest underdensities of the Cosmic Web, present an ideal population for the study of galaxy formation and evolution in an environment undisturbed by the complex processes modifying galaxies in clusters and groups, as well as provide an observational test for theories of cosmological structure formation. We have completed a pilot survey for the HI imaging aspects of a new Void Galaxy Survey (VGS), imaging 15 void galaxies in HI in local (d < 100 Mpc) voids. HI masses range from 3.5 x 10^8 to 3.8 x 10^9 M_sun, with one nondetection with an upper limit of 2.1 x 10^8 M_sun. Our galaxies were selected using a structural and geometric technique to produce a sample that is purely environmentally selected and uniformly represents the void galaxy population. In addition, we use a powerful new backend of the Westerbork Synthesis Radio Telescope that allows us to probe a large volume around each targeted galaxy, simultaneously providing an environmentally constrained sample of fore- and background control sample of galaxies while still resolving individual galaxy kinematics and detecting faint companions in HI. This small sample makes up a surprisingly interesting collection of perturbed and interacting galaxies, all with small stellar disks. Four galaxies have significantly perturbed HI disks, five have previously unidentified companions at distances ranging from 50 to 200 kpc, two are in interacting systems, and one was found to have a polar HI disk. Our initial findings suggest void galaxies are a gas-rich, dynamic population which present evidence of ongoing gas accretion, major and minor interactions, and filamentary alignment despite the surrounding underdense environment.Comment: 53 pages, 18 figures, accepted for publication in AJ. High resolution available at http://www.astro.columbia.edu/~keejo/kreckel2010.pd

Recruiting Hard-to-Reach Subjects for Exercise Interventions: A Multi-Centre and Multi-Stage Approach Targeting General Practitioners and Their Community-Dwelling and Mobility-Limited Patients

The general practitioner (GP)’s practice appears to be an ideal venue for recruiting community-dwelling older adults with limited mobility. This study (Current Controlled Trials ISRCTN17727272) aimed at evaluating the recruiting process used for a multi-centre exercise intervention (HOMEfit). Each of six steps resulted in an absolute number of patients (N1–N6). Sex and age (for N4–N6) and reasons for dropping out were assessed. Patient database screening (N1–N3) at 15 GP practices yielded N1 = 5,990 patients aged 70 and above who had visited their GP within the past 6 months, N2 = 5,467 after exclusion of institutionalised patients, N3 = 1,545 patients eligible. Using a pre-defined limitation algorithm in order to conserve the practices’ resources resulted in N4 = 1,214 patients (80.3 ± 5.6 years, 68% female), who were then officially invited to the final assessment of eligibility at the GP’s practice. N5 = 434 patients (79.5 ± 5.4 years, 69% female) attended the practice screening (n = 13 of whom had not received an official invitation). Finally, N6 = 209 (79.8 ± 5.2 years, 74% female) were randomised after they were judged eligible and had given their written informed consent to participate in the randomised controlled trial (overall recruitment rate: 4.4%). The general strategy of utilising a GP’s practice to recruit the target group proved beneficial. The data and experiences presented here can help planners of future exercise-intervention studies

Cavity evolution in relativistic self-gravitating fluids

We consider the evolution of cavities within spherically symmetric relativistic fluids, under the assumption that proper radial distance between neighboring fluid elements remains constant during their evolution (purely areal evolution condition). The general formalism is deployed and solutions are presented. Some of them satisfy Darmois conditions whereas others present shells and must satisfy Israel conditions, on either one or both boundary surfaces. Prospective applications of these results to some astrophysical scenarios is suggested.Comment: 10 pages Revtex. To appear in Class. Quantum Grav

Arbitrage and deflators in illiquid markets

This paper presents a stochastic model for discrete-time trading in financial markets where trading costs are given by convex cost functions and portfolios are constrained by convex sets. The model does not assume the existence of a cash account/numeraire. In addition to classical frictionless markets and markets with transaction costs or bid-ask spreads, our framework covers markets with nonlinear illiquidity effects for large instantaneous trades. In the presence of nonlinearities, the classical notion of arbitrage turns out to have two equally meaningful generalizations, a marginal and a scalable one. We study their relations to state price deflators by analyzing two auxiliary market models describing the local and global behavior of the cost functions and constraints

Anaerobic degradation of 2-propanol: Laboratory and pilot-scale studies

The anaerobic degradation of 2-propanol, an important industrial solvent, was scaled-up from batch assays to a pilot expanded granular sludge bed (EGSB) reactor at 25 °C. Batch studies indicated that 2-propanol followed Haldane kinetics, with a maximum rate at 10 g COD L−1. Concentrations as high as 25 g COD L−1 did not inhibit the degradation of ethanol, a common co-solvent. Similar specific methanogenic activities (SMA) were obtained for water-solvent and water-brewery sludges (88 and 77 ml CH4 g-VS−1 d−1 at 5 g COD L−1). Continuous degradation showed a lag-phase of three weeks with water-brewery sludge. Increases in 2-propanol load from 0.05 to 0.18 kg COD kg-VS−1 d−1 caused a shift from the consumption of soluble matter to methane production, indicating polyhydroxybutyrates (PHB) accumulation. Conversely, smooth increases of up to 0.29 kg COD kg-VS−1 d−1 allowed 2-propanol degradation without PHB accumulation. The slowdown rate of 2-propanol-oxidizer and acetate-utilizing methanogen bacteria below 20 °C adversely impacted both removal and CH4 yield