On [summation of 1 raised to the power 1] equivalence relations over the natural numbers

"Vegeu el resum a l'inici del document del fitxer adjunt"

Statistical tests for scaling in the inter-event times of earthquakes in California

We explore in depth the validity of a recently proposed scaling law for earthquake inter-event time distributions in the case of the Southern California, using the waveform cross-correlation catalog of Shearer et al. Two statistical tests are used: on the one hand, the standard two-sample Kolmogorov-Smirnov test is in agreement with the scaling of the distributions. On the other hand, the one-sample Kolmogorov-Smirnov statistic complemented with Monte Carlo simulation of the inter-event times, as done by Clauset et al., supports the validity of the gamma distribution as a simple model of the scaling function appearing on the scaling law, for rescaled inter-event times above 0.01, except for the largest data set (magnitude greater than 2). A discussion of these results is provided.

Independent relations of left ventricular structure with the 24-hour urinary excretion of sodium and aldosterone.

Previous studies reported on the association of left ventricular mass index (LVMI) with urinary sodium or with circulating or urinary aldosterone. We investigated the independent associations of LVMI with the urinary excretion of both sodium and aldosterone. We randomly recruited 317 untreated subjects from a white population (45.1% women; mean age 48.2 years). Measurements included echocardiographic left ventricular (LV) properties, the 24-hour urinary excretion of sodium and aldosterone, plasma renin activity (PRA), and proximal (RNa(prox)) and distal (RNa(dist)) renal sodium reabsorption, assessed from the endogenous lithium clearance. In multivariable-adjusted models, we expressed changes in LVMI per 1-SD increase in the explanatory variables, while accounting for sex, age, systolic blood pressure, and the waist-to-hip ratio. LVMI increased independently with the urinary excretion of both sodium (+2.48 g/m(2); P=0.005) and aldosterone (+2.63 g/m(2); P=0.004). Higher sodium excretion was associated with increased mean wall thickness (MWT: +0.126 mm, P=0.054), but with no change in LV end-diastolic diameter (LVID: +0.12 mm, P=0.64). In contrast, higher aldosterone excretion was associated with higher LVID (+0.54 mm; P=0.017), but with no change in MWT (+0.070 mm; P=0.28). Higher RNa(dist) was associated with lower relative wall thickness (-0.81x10(-2), P=0.017), because of opposite trends in LVID (+0.33 mm; P=0.13) and MWT (-0.130 mm; P=0.040). LVMI was not associated with PRA or RNa(prox.) In conclusion, LVMI independently increased with both urinary sodium and aldosterone excretion. Increased MWT explained the association of LVMI with urinary sodium and increased LVID the association of LVMI with urinary aldosterone.