Recurrence interval statistics of cellular automaton seismicity models

The recurrence interval statistics for regional seismicity follows a universal distribution function, independent of the tectonic setting or average rate of activity (Corral, 2004). The universal function is a modified gamma distribution with power-law scaling of recurrence intervals shorter than the average rate of activity and exponential decay for larger intervals. We employ the method of Corral (2004) to examine the recurrence statistics of a range of cellular automaton earthquake models. The majority of models has an exponential distribution of recurrence intervals, the same as that of a Poisson process. One model, the Olami-Feder-Christensen automaton, has recurrence statistics consistent with regional seismicity for a certain range of the conservation parameter of that model. For conservation parameters in this range, the event size statistics are also consistent with regional seismicity. Models whose dynamics are dominated by characteristic earthquakes do not appear to display universality of recurrence statistics.

Further evidence of linkage at 7p22 with familial hyperaldosteronism type II and exclusion of genetic defects in the RBAK coding regions

Once thought rare, primary aldosteronism (PAL) is now reported to be responsible for 5–10% of hypertension. Unlike familial hyperaldosteronism type I (FH-I), FH-II is not glucocorticoidremediable and not associated with the hybrid CYP11B1/CYP11B2 gene mutation. At least five times more common than FH-I, FH-II is clinically indistinguishable from apparently sporadic PAL, suggesting an even higher incidence. Studies performed in collaboration with C Stratakis (NIH, Bethesda) on our largest Australian family (eight affected members) demonstrated linkage at chromosome 7p22. Linkage at this region was also found in a South American family (DNA provided by MI New, Mount Sinai School of Medicine, New York) and in a second Australian family. The combined multipoint LOD score for these 3 families is 4.61 (q = 0) with markers D7S462 and D7S517, providing strong support for this locus harbouring mutations responsible for FH-II. A newly identified recombination event in our largest Australian family has narrowed the region of linkage by 1.8 Mb, permitting exclusion of approximately half the genes residing in the originally reported 5 Mb linked locus. Candidate genes that are involved in cell cycle control are of interest as adrenal hyperplasia and adrenal adenomas are common in FH-II patients. A novel candidate gene in this linked region produces the retinoblastoma-associated Kruppel-associated box protein (RBaK) which interacts with the retinoblastoma gene product to repress the expression of genes activated by members of the E2F family of transcription factors.

Axiomatisation of an Interval Calculus for Theorem Proving

We provide an axiomatisation of the Timed Interval Calculus, a set-theoretic notation for expressing properties of time intervals. We implement the axiomatisation in the Ergo theorem prover in order to allow the machine-checked proof of laws for reasoning about predicates expressed using interval operators. These laws can be then used in the machine-assisted verification of real-time applications.