Sleep disordered breathing and vascular function in patients with chronic mountain sickness and healthy high-altitude dwellers.

Background Chronic mountain sickness (CMS) is often associated with vascular dysfunction, but the underlying mechanism is unknown. Sleep disordered breathing (SDB) frequently occurs at high altitude. At low altitude SDB causes vascular dysfunction. Moreover, in SDB, transient elevations of right-sided cardiac pressure may cause right-to-left shunting in the presence of a patent foramen ovale (PFO) and, in turn, further aggravate hypoxemia and pulmonary hypertension. We speculated that compared to healthy high-altitude dwellers, in patients with CMS, SDB and nocturnal hypoxemia are more pronounced and related to vascular dysfunction. Methods We performed overnight sleep recordings, and measured systemic and pulmonary-artery pressure in 23 patients with CMS (mean±SD age 52.8±9.8 y) and 12 healthy controls (47.8±7.8 y) at 3600 m. In a subgroup of 15 subjects with SDB, we searched for PFO with transesophagal echocardiography. Results The major new findings were that in CMS patients, a) SDB and nocturnal hypoxemia was more severe (P<0.01) than in controls (apnea/hypopnea index, AHI, 38.9±25.5 vs. 14.3±7.8[nb/h]; SaO2, 80.2±3.6 vs. 86.8±1.7[%], CMS vs. controls), and b) AHI was directly correlated with systemic blood pressure (r=0.5216, P=0.001) and pulmonary-artery pressure (r=0.4497, P=0.024). PFO was associated with more severe SDB (AHI 48.8±24.7 vs. 14.8±7.3[nb/h], P=0.013, PFO vs. no PFO) and hypoxemia. Conclusion SDB and nocturnal hypoxemia are more severe in CMS patients than in controls and are associated with systemic and pulmonary vascular dysfunction. The presence of a PFO appeared to further aggravate SDB. Closure of PFO may improve SDB, hypoxemia and vascular dysfunction in CMS patients. Clinical Trials Gov Registration NCT01182792.

Reconstruction of Holocene vegetation dynamics at Lac de Bretaye, a high-mountain lake in the Swiss Alps

A deeper understanding of past vegetation dynamics is required to better assess future vegetation responses to global warming in the Alps. Lake sediments from Lac de Bretaye, a small subalpine lake in the Northern Swiss Alps (1780 m a.s.l.), were analysed to reconstruct past vegetation dynamics for the entire Holocene, using pollen, macrofossil and charcoal analyses as main proxies. The results show that timberline reached the lake’s catchment area at around 10,300 cal. BP, supporting the hypothesis of a delayed postglacial afforestation in the Northern Alps. At the same time, thermophilous trees such as Ulmus, Tilia and Acer established in the lowlands and expanded to the altitude of the lake, forming distinctive boreo-nemoral forests with Betula, Pinus cembra and Larix decidua. From about 5000 to 3500 cal. BP, thermophilous trees declined because of increasing human land use, mainly driven by the mass expansion of Picea abies and severe anthropogenic fire activity. From the Bronze Age onwards (c. 4200–2800 cal. BP), grazing indicators and high values for charcoal concentration and influx attest an intensifying human impact, fostering the expansion of Alnus viridis and Picea abies. Hence, biodiversity in alpine meadows increased, whereas forest diversity declined, as can be seen in other regional records. We argue that the anticipated climate change and decreasing human impact in the Alps today will not only lead to an upward movement of timberline with consequent loss of area for grasslands, but also to a disruption of Picea abies forests, which may allow the re-expansion of thermophilous tree species.

Functional equations and the Cauchy mean value theorem

The aim of this note is to characterize all pairs of sufficiently smooth functions for which the mean value in the Cauchy mean value theorem is taken at a point which has a well-determined position in the interval. As an application of this result, a partial answer is given to a question posed by Sahoo and Riedel.

The Hasse-Minkowski Theorem

The Hasse-Minkowski theorem concerns the classification of quadratic forms over global fields (i.e., finite extensions of Q and rational function fields with a finite constant field). Hasse proved the theorem over the rational numbers in his Ph.D. thesis in 1921. He extended the research of his thesis to quadratic forms over all number fields in 1924. Historically, the Hasse-Minkowski theorem was the first notable application of p-adic fields that caught the attention of a wide mathematical audience. The goal of this thesis is to discuss the Hasse-Minkowski theorem over the rational numbers and over the rational function fields with a finite constant field of odd characteristic. Our treatments of quadratic forms and local fields, though, are more general than what is strictly necessary for our proofs of the Hasse-Minkowski theorem over Q and its analogue over rational function fields (of odd characteristic). Our discussion concludes with some applications of the Hasse-Minkowski theorem.

A Median Voter Theorem for Postelection Politics

We analyze a model of 'postelection politics', in which (unlike in the more common Downsian models of 'preelection politics') politicians cannot make binding commitments prior to elections. The game begins with an incumbent politician in office, and voters adopt reelection strategies that are contingent on the policies implemented by the incumbent. We generalize previous models of this type by introducing heterogeneity in voters' ideological preferences, and analyze how voters' reelection strategies constrain the policies chosen by a rent-maximizing incumbent. We first show that virtually any policy (and any feasible level of rent for the incumbent) can be sustained in a Nash equilibrium. Then, we derive a 'median voter theorem': the ideal point of the median voter, and the minimum feasible level of rent, are the unique outcomes in any strong Nash equilibrium. We then introduce alternative refinements that are less restrictive. In particular, Ideologically Loyal Coalition-proof equilibrium also leads uniquely to the median outcome.