United States-Israel Binational Science Foundation

di Terra Santa.

Processing of gravity and magnetic maps shows that the basement of the Upper Rhine Graben area is characterized by a series of NE–SW trending discontinuities and elongated structures, identified in outcrops in the Vosges, Black Forest, and the Odenwald Mountains. They form a 40 km wide, N30–40° striking, sinistral wrench-zone that, in the Visean, shifted the Variscan and pre-Variscan structures by at least 43 km to the NE. Wrenching was associated with emplacement of several generations of plutonic bodies emplaced in the time range 340–325 Ma. The sub-vertical, NE–SW trending discontinuities in the basement acted as zones of weakness, susceptible to reactivation by subsequent tectonism. The first reactivation, marked by mineralizations and palaeomagnetic overprinting along NE–SW faults of the Vosges Mountains, results from the Liassic NW–SE extension contemporaneous with the break-up of Pangea. The major reactivation occurred during the Late Eocene N–S compression and the Early-Middle Oligocene E–W extension. The NE–SW striking basement discontinuities were successively reactivated as sinistral strike-slip faults, and as oblique normal faults. Elongated depocenters appear to form in association with reactivated Variscan wrench faults. Some of the recent earthquakes are located on NE–SW striking Variscan fault zones, and show sinistral strike-slip focal mechanisms with the same direction, suggesting also present reactivation.

We present three explicit constructions of hash functions, which exhibit a trade-off between the size of the family (and hence the number of random bits needed to generate a member of the family), and the quality (or error parameter) of the pseudo-random property it achieves. Unlike previous constructions, most notably universal hashing, the size of our families is essentially independent of the size of the domain on which the functions operate. The first construction is for the mixing property-mapping a proportional part of any subset of the domain to any other subset. The other two are for the extraction property-mapping any subset of the domain almost uniformly into a range smaller than it. The second and third constructions handle (respectively) the extreme situations when the range is very large or very small. We provide lower bounds showing our constructions are nearly optimal, and mention some applications of the new constructions.