The horizon problem for prevalent surfaces

We investigate the box dimensions of the horizon of a fractal surface defined by a function $f \in C[0,1]^2$. In particular we show that a prevalent surface satisfies the `horizon property', namely that the box dimension of the horizon is one less than that of the surface. Since a prevalent surface has box dimension 3, this does not give us any information about the horizon of surfaces of dimension strictly less than 3. To examine this situation we introduce spaces of functions with surfaces of upper box dimension at most \alpha, for \alpha $\in$ [2,3). In this setting the behaviour of the horizon is more subtle. We construct a prevalent subset of these spaces where the lower box dimension of the horizon lies between the dimension of the surface minus one and 2. We show that in the sense of prevalence these bounds are as tight as possible if the spaces are defined purely in terms of dimension. However, if we work in Lipschitz spaces, the horizon property does indeed hold for prevalent functions. Along the way, we obtain a range of properties of box dimensions of sums of functions

Measuring the atomic composition of planetary building blocks

Volatile molecules are critical to terrestrial planetary habitability, yet difficult to observe directly where planets form at the midplanes of protoplanetary disks. It is unclear whether the inner 1 AU of disks are volatile-poor or if this region is resupplied with ice-rich dust from colder disk regions. Dust traps at radial pressure maxima bounding disk gaps can cut off the inner disk from such volatile reservoirs. However, the trap retention efficiency and atomic composition of trapped dust have not been measured. We present a new technique to measure the absolute atomic abundances in gas accreting onto T Tauri stars and infer the bulk atomic composition and distribution of midplane solids retained in the disk around the young star TW Hya. We identify line emission from gas-phase material inside the dust sublimation rim of TW Hya. Gaussian decomposition of the strongest H Paschen lines isolates the inner disk hydrogen emission. We measure several key elemental abundances, relative to hydrogen, using a chemical photoionization model and infer dust retention in the disk. With a 1D transport model, we determine approximate radial locations and retention efficiencies of dust traps for different elements. Volatile and refractory elements are depleted from TW Hya's hot gas by factors of ~10^2 and up to 10^5, respectively. Dust traps beyond the CO and N2 snowline cumulatively sequester 96% of the total dust, while the trap at 2 AU retains 3% of the initial dust mass. The high depletions of Si, Mg, and Ca are explained by a third trap at 0.3 AU. TW Hya has a significant volatile reservoir rich in C- and N-ices in its outer ring structure. However, the lack of C resupply may leave the terrestrial planet-forming region dry and carbon-poor. Any planets that form within the silicate dust trap at 0.3 AU may resemble Earth in terms of the degree of their volatile depletion.Comment: Accepted for publication in A&A Letters. 6 pages, 3 figures, plus appendice

Distinct Signatures For Coulomb Blockade and Aharonov-Bohm Interference in Electronic Fabry-Perot Interferometers

Two distinct types of magnetoresistance oscillations are observed in two electronic Fabry-Perot interferometers of different sizes in the integer quantum Hall regime. Measuring these oscillations as a function of magnetic field and gate voltages, we observe three signatures that distinguish the two types. The oscillations observed in a 2.0 square micron device are understood to arise from the Coulomb blockade mechanism, and those observed in an 18 square micron device from the Aharonov-Bohm mechanism. This work clarifies, provides ways to distinguish, and demonstrates control over, these distinct physical origins of resistance oscillations seen in electronic Fabry-Perot interferometers.Comment: related papers at http://marcuslab.harvard.ed

High velocity clouds in the Galactic All Sky Survey I. Catalogue

We present a catalogue of high-velocity clouds (HVCs) from the Galactic All Sky Survey (GASS) of southern-sky neutral hydrogen, which has 57 mK sensitivity and 1 km/s velocity resolution and was obtained with the Parkes Telescope. Our catalogue has been derived from the stray-radiation corrected second release of GASS. We describe the data and our method of identifying HVCs and analyse the overall properties of the GASS population. We catalogue a total of 1693 HVCs at declinations < 0 deg, including 1111 positive velocity HVCs and 582 negative velocity HVCs. Our catalogue also includes 295 anomalous velocity clouds (AVCs). The cloud line-widths of our HVC population have a median FWHM of ~19 km/s, which is lower than found in previous surveys. The completeness of our catalogue is above 95% based on comparison with the HIPASS catalogue of HVCs, upon which we improve with an order of magnitude in spectral resolution. We find 758 new HVCs and AVCs with no HIPASS counterpart. The GASS catalogue will shed an unprecedented light on the distribution and kinematic structure of southern-sky HVCs, as well as delve further into the cloud populations that make up the anomalous velocity gas of the Milky Way.Comment: 21 pages, 14 figures, accepted for publication in ApJ

Assessing the Pharmacotherapy and Clinical Outcomes After Deep Brain Stimulation for Treatment-Refractory Obsessive–Compulsive Disorder: A Case–Cohort Study

Background: In the search for effective treatments for refractive obsessive–compulsive disorder (OCD), deep brain stimulation (DBS) serves as an alternative option for those with minimal response to pharmacotherapy. The rarity of reports regarding DBS use for OCD is attributed to the invasive nature of the procedure: placement of electrodes within targeted areas of the brain to provide neuromodulation. This treatment of last resort may decrease functional impairment and pharmacologic complications for a debilitating mental illness. This study compares the pharmacotherapy utilization and treatment outcomes of five treatment-refractory OCD patients after the placement of DBS with those of a matched cohort. Methods: This retrospective, single-center, case–cohort study reviewed the electronic medical records of five subjects treated with DBS for treatment-refractory OCD and compared them to a similar treatment-refractory cohort whose OCD was treated without the use of DBS. Control subjects were matched by age, sex, years since diagnosis, number of previous medication class trials, and additional clinical factors. Inclusion criteria were defined as those that are at least eighteen years of age, assigned a primary diagnosis of OCD per the ICD-10 classification, and received DBS treatment for refractory OCD. Exclusion criteria included comorbid psychotic disorders, unstable neurological or coagulation disorder(s), and/or an eating disorder diagnosis. The primary endpoint was the change in the number of psychotropic medications two years after implantation for the DBS cohort and two years after psychiatric decompensation for the comparator cohort. Secondary endpoints included: Y-BOCS (the Yale–Brown Obsessive–Compulsive Scale) changes over time, duration quantity of psychotropic medication classes prescribed, and additional symptomology scale changes. Results: Patients receiving DBS were more likely to be on fewer medications and trialed fewer medications after treatment. One out of the five patients was found to be a responder in Y-BOCS scoring after DBS treatment. A reduction in anxiety and depression symptoms was also seen in the HAM-A and HAM-D scales for those that received DBS. Conclusions: A reduction in psychiatric medications trialed during therapy was observed, as well as varying reductions in OCD, anxiety, and depression symptomology following DBS. Results from this study indicate that DBS implantation may contribute to a reduction in polypharmacy while displaying DBS’s potential impact on comorbid anxiety and depression symptoms. Given that the small sample size limits generalizability, additional prospective, randomized trials comparing the efficacy of DBS for OCD-specific symptomology and its overall impact on pharmacotherapy are needed in order to further establish the role of DBS as an accepted treatment option for OCD