Two examples of minimal Cheeger sets in the plane

We construct two minimal Cheeger sets in the Euclidean plane, i.e., unique minimizers of the ratio \u201cperimeter over area\u201d among their own measurable subsets. The first one gives a counterexample to the so- called weak regularity property of Cheeger sets, as its perimeter does not coincide with the 1-dimensional Hausdorff measure of its topological boundary. The second one is a kind of porous set, whose boundary is not locally a graph at many of its points, yet it is a weakly regular open set admitting a unique (up to vertical translations) nonparametric solution to the prescribed mean curvature equation, in the extremal case corresponding to the capillarity for perfectly wetting fluids in zero gravity

Acromegaly is associated with increased cancer risk: A survey in Italy

It is debated if acromegalic patients have an increased risk to develop malignancies. The aim of the present study was to assess the standardized incidence ratios (SIRs) of different types of cancer in acromegaly on a large series of acromegalic patients managed in the somatostatin analogs era. It was evaluated the incidence of cancer in an Italian nationwide multicenter cohort study of 1512 acromegalic patients, 624 men and 888 women, mean age at diagnosis 45 \uc2\ub1 13 years, followed up for a mean of 10 years (12573 person-years) in respect to the general Italian population. Cancer was diagnosed in 124 patients, 72 women and 52 men. The SIRs for all cancers was significantly increased compared to the general Italian population (expected: 88, SIR 1.41; 95% CI, 1.18-1.68, P < 0.001). In the whole series, we found a significantly increased incidence of colorectal cancer (SIR 1.67; 95% CI, 1.07-2.58, P = 0.022), kidney cancer (SIR 2.87; 95% CI, 1.55-5.34, P < 0.001) and thyroid cancer (SIR 3.99; 95% CI, 2.32-6.87, P < 0.001). The exclusion of 11 cancers occurring before diagnosis of acromegaly (all in women) did not change remarkably the study outcome. In multivariate analysis, the factors significantly associated with an increased risk of malignancy were age and family history of cancer, with a non-significant trend for the estimated duration of acromegaly before diagnosis. In conclusion, we found evidence that acromegaly in Italy is associated with a moderate increase in cancer risk

Measurement of the cosmic ray spectrum above 4×10184{\times}10^{18} eV using inclined events detected with the Pierre Auger Observatory

A measurement of the cosmic-ray spectrum for energies exceeding $4{\times}10^{18}$ eV is presented, which is based on the analysis of showers with zenith angles greater than $60^{\circ}$ detected with the Pierre Auger Observatory between 1 January 2004 and 31 December 2013. The measured spectrum confirms a flux suppression at the highest energies. Above $5.3{\times}10^{18}$ eV, the "ankle", the flux can be described by a power law $E^{-\gamma}$ with index $\gamma=2.70 \pm 0.02 \,\text{(stat)} \pm 0.1\,\text{(sys)}$ followed by a smooth suppression region. For the energy ($E_\text{s}$) at which the spectral flux has fallen to one-half of its extrapolated value in the absence of suppression, we find $E_\text{s}=(5.12\pm0.25\,\text{(stat)}^{+1.0}_{-1.2}\,\text{(sys)}){\times}10^{19}$ eV.Comment: Replaced with published version. Added journal reference and DO

Energy Estimation of Cosmic Rays with the Engineering Radio Array of the Pierre Auger Observatory

The Auger Engineering Radio Array (AERA) is part of the Pierre Auger Observatory and is used to detect the radio emission of cosmic-ray air showers. These observations are compared to the data of the surface detector stations of the Observatory, which provide well-calibrated information on the cosmic-ray energies and arrival directions. The response of the radio stations in the 30 to 80 MHz regime has been thoroughly calibrated to enable the reconstruction of the incoming electric field. For the latter, the energy deposit per area is determined from the radio pulses at each observer position and is interpolated using a two-dimensional function that takes into account signal asymmetries due to interference between the geomagnetic and charge-excess emission components. The spatial integral over the signal distribution gives a direct measurement of the energy transferred from the primary cosmic ray into radio emission in the AERA frequency range. We measure 15.8 MeV of radiation energy for a 1 EeV air shower arriving perpendicularly to the geomagnetic field. This radiation energy -- corrected for geometrical effects -- is used as a cosmic-ray energy estimator. Performing an absolute energy calibration against the surface-detector information, we observe that this radio-energy estimator scales quadratically with the cosmic-ray energy as expected for coherent emission. We find an energy resolution of the radio reconstruction of 22% for the data set and 17% for a high-quality subset containing only events with at least five radio stations with signal.Comment: Replaced with published version. Added journal reference and DO

Measurement of the Radiation Energy in the Radio Signal of Extensive Air Showers as a Universal Estimator of Cosmic-Ray Energy

We measure the energy emitted by extensive air showers in the form of radio emission in the frequency range from 30 to 80 MHz. Exploiting the accurate energy scale of the Pierre Auger Observatory, we obtain a radiation energy of 15.8 \pm 0.7 (stat) \pm 6.7 (sys) MeV for cosmic rays with an energy of 1 EeV arriving perpendicularly to a geomagnetic field of 0.24 G, scaling quadratically with the cosmic-ray energy. A comparison with predictions from state-of-the-art first-principle calculations shows agreement with our measurement. The radiation energy provides direct access to the calorimetric energy in the electromagnetic cascade of extensive air showers. Comparison with our result thus allows the direct calibration of any cosmic-ray radio detector against the well-established energy scale of the Pierre Auger Observatory.Comment: Replaced with published version. Added journal reference and DOI. Supplemental material in the ancillary file

Function of the GH/IGF-I axis in healthy middle aged male runners

In an attempt to examine the effect of prolonged physical activity on the function of the GH/IGF-1 axis during the aging process in man, we have evaluated basal and GHRH (GHRH-29: 1 microgram/kg i.v. as a bolus) stimulated GH secretion as well as basal plasma IGF-1 levels in a group of 25 healthy runners (50-60 years, mean age 55.5 +/- 0.6) and 24 age-matched relatively sedentary normal controls (mean age 55.8 +/- 0.7). The runners had a minimum distance in kilometers of 26 km/week for at least 15 years, and competed in distances ranging from 16 km to the marathon. In runners, GHRH induced an increase of GH which was significantly higher (p < 0.001) than that observed in the age-matched controls. Baseline IGF-1 levels were significantly higher (p < 0.001) in trained runners (171 +/- 8.4 micrograms/1) compared to the controls (91.1 +/- 5.5 micrograms/1). These data show that in middle-age prolonged physical activity increases the function of the GH/IGF-1 axis. To clarify the possible mechanisms underlying the GH/IGF-1 secretory pattern in the runners, the GH responses to both single and combined administration of GHRH and arginine (ARG: 30 g infused over 30 min), a GH secretagogue likely acting via inhibition of hypothalamic somatostatin release, were investigated in 6 runners (mean age 55 +/- 1.9 years) and 6 controls (mean age 55 +/- 0.9 years). ARG clearly increased the GH response to GHRH in the controls, whereas it was unable to further potentiate the GH-releasing effect of GHRH in runners, thus suggesting that the increased GH responsiveness to GHRH might be due to an exercise-related decrease in endogenous hypothalamic somatostatinergic activity

Analysis of HQ02 coil cross sections

United States. Department of Energy