Blowup of Jang's equation at outermost marginally trapped surfaces

The aim of this paper is to collect some facts about the blowup of Jang's equation. First, we discuss how to construct solutions that blow up at an outermost MOTS. Second, we exclude the possibility that there are extra blowup surfaces in data sets with non-positive mean curvature. Then we investigate the rate of convergence of the blowup to a cylinder near a strictly stable MOTS and show exponential convergence near a strictly stable MOTS.Comment: 15 pages. This revision corrects some typo

‘Paging Podiatry!’: an audit of acute inpatient podiatry referrals

For the analysis of small concentrations of organics in aqueous solutions, a novel add-on accessory for dual-beam / optical subtraction spectroscopy has been built for a commercial Fourier transform infrared spectrometer. A standard FT-IR instrument requires a sample measurement and a separate reference measurement, whereas the optical subtraction instrument directly measures the difference between sample and reference. This has a number of advantages. The time delay between the two measurements is eliminated, and the effective measurement time is improved by a factor of two. Moreover, the optical subtraction provides a large reduction in dynamic range of the measured signal, which prevents detector saturation, and enables effective use of dynamic range of the analog to digital converter in the FT-IR spectrometer. This results in an increased signal to noise ratio, compared to the standard FT-IR instrument. By changing detector and light source the instrument may be used for both near- and mid.-infrared spectroscopy. The increased sensitivity and stability of the optical subtraction instrument compared to the standard instrument is demonstrated by transmission measurements of aqueous urea solutions in the combination band region 4000 to 5000cm(-1) (2000 to 2500nm)

The area of horizons and the trapped region

This paper considers some fundamental questions concerning marginally trapped surfaces, or apparent horizons, in Cauchy data sets for the Einstein equation. An area estimate for outermost marginally trapped surfaces is proved. The proof makes use of an existence result for marginal surfaces, in the presence of barriers, curvature estimates, together with a novel surgery construction for marginal surfaces. These results are applied to characterize the boundary of the trapped region.Comment: 44 pages, v3: small changes in presentatio

Holocene regional gradients of dust provenance and flux between Talos Dome and Dome C, East Antarctica.

Aeolian sequences from Central East Antarctic ice cores provide climate and environmental information of hemispheric significance. Close to the margins of the ice sheet, high-elevation ice-free terrains protruding above the ice sheet surface can provide an additional input of fine dust particles to the atmosphere, making peripheral locations particularly interesting for the study of the regional climate evolution. In the Talos Dome area of East Antarctica, entrainment and transport of local mineral particles is merely influenced by local wind direction and strength, which in turn is tuned by regional climate changes. We investigate the spatial variability of modern and Holocene dust flux, grain size and isotopic (Sr-Nd) composition along a hypothetic transect from Talos Dome all through the interior of the ice sheet (Dome C/Vostok area), and compare the geochemical fingerprint of dust extracted from firn and ice cores to the equivalent size fraction of regolith and glacial deposits from high altitude Victoria Land sources. This study aims to better understand the environmental gradients of dust flux and provenance from the marginal Talos Dome site to the higher Dome C drainage area, with implications for the regional atmospheric circulation, while documenting the isotopic composition of local exposed sediments

Nonexistence of marginally trapped surfaces and geons in 2+1 gravity

We use existence results for Jang's equation and marginally outer trapped surfaces (MOTSs) in 2+1 gravity to obtain nonexistence of geons in 2+1 gravity. In particular, our results show that any 2+1 initial data set, which obeys the dominant energy condition with cosmological constant \Lambda \geq 0 and which satisfies a mild asymptotic condition, must have trivial topology. Moreover, any data set obeying these conditions cannot contain a MOTS. The asymptotic condition involves a cutoff at a finite boundary at which a null mean convexity condition is assumed to hold; this null mean convexity condition is satisfied by all the standard asymptotic boundary conditions. The results presented here strengthen various aspects of previous related results in the literature. These results not only have implications for classical 2+1 gravity but also apply to quantum 2+1 gravity when formulated using Witten's solution space quantization.Comment: v3: Elements from the original two proofs of the main result have been combined to give a single proof, thereby circumventing an issue with the second proof associated with potential blow-ups of solutions to Jang's equation. To appear in Commun. Math. Phy

The Jang equation reduction of the spacetime positive energy theorem in dimensions less than eight

We extend the Jang equation proof of the positive energy theorem due to R. Schoen and S.-T. Yau from dimension $n=3$ to dimensions $3 \leq n <8$. This requires us to address several technical difficulties that are not present when $n=3$. The regularity and decay assumptions for the initial data sets to which our argument applies are weaker than those of R. Schoen and S.-T. Yau. In recent joint work with L.-H. Huang, D. Lee, and R. Schoen we have given a different proof of the full positive mass theorem in dimensions $3 \leq n < 8$. We pointed out that this theorem can alternatively be derived from our density argument and the positive energy theorem of the present paper.Comment: All comments welcome! Final version to appear in Comm. Math. Phy

Operational sex ratio, sexual conflict and the intensity of sexual selection.

Modern sexual selection theory indicates that reproductive costs rather than the operational sex ratio predict the intensity of sexual selection. We investigated sexual selection in the polygynandrous common lizard Lacerta vivipara. This species shows male aggression, causing high mating costs for females when adult sex ratios (ASR) are male-biased. We manipulated ASR in 12 experimental populations and quantified the intensity of sexual selection based on the relationship between reproductive success and body size. In sharp contrast to classical sexual selection theory predictions, positive directional sexual selection on male size was stronger and positive directional selection on female size weaker in female-biased populations than in male-biased populations. Thus, consistent with modern theory, directional sexual selection on male size was weaker in populations with higher female mating costs. This suggests that the costs of breeding, but not the operational sex ratio, correctly predicted the strength of sexual selection

Automatic diagnosis of the 12-lead ECG using a deep neural network

The role of automatic electrocardiogram (ECG) analysis in clinical practice is limited by the accuracy of existing models. Deep Neural Networks (DNNs) are models composed of stacked transformations that learn tasks by examples. This technology has recently achieved striking success in a variety of task and there are great expectations on how it might improve clinical practice. Here we present a DNN model trained in a dataset with more than 2 million labeled exams analyzed by the Telehealth Network of Minas Gerais and collected under the scope of the CODE (Clinical Outcomes in Digital Electrocardiology) study. The DNN outperform cardiology resident medical doctors in recognizing 6 types of abnormalities in 12-lead ECG recordings, with F1 scores above 80% and specificity over 99%. These results indicate ECG analysis based on DNNs, previously studied in a single-lead setup, generalizes well to 12-lead exams, taking the technology closer to the standard clinical practice

The Influence of the effect of solute on the thermodynamic driving force on grain refinement of Al alloys

Grain refinement is known to be strongly affected by the solute in cast alloys. Addition of some solute can reduce grain size considerably while others have a limited effect. This is usually attributed to the constitutional supercooling which is quantified by the growth restriction factor, Q. However, one factor that has not been considered is whether different solutes have differing effects on the thermodynamic driving force for solidification. This paper reveals that addition of solute reduces the driving force for solidification for a given undercooling, and that for a particular Q value, it is reduced more substantially when adding eutectic-forming solutes than peritectic-forming elements. Therefore, compared with the eutectic-forming solutes, addition of peritectic-forming solutes into Al alloys not only possesses a higher initial nucleation rate resulted from the larger thermodynamic driving force for solidification, but also promotes nucleation within the constitutionally supercooled zone during growth. As subsequent nucleation can occur at smaller constitutional supercoolings for peritectic-forming elements, a smaller grain size is thus produced. The very small constitutional supercooling required to trigger subsequent nucleation in alloys containing Ti is considered as a major contributor to its extraordinary grain refining efficiency in cast Al alloys even without the deliberate addition of inoculants.The Australian Research Council (ARC DP10955737)