On lattice profile of the elliptic curve linear congruential generators

Lattice tests are quality measures for assessing the intrinsic structure of pseudorandom number generators. Recently a new lattice test has been introduced by Niederreiter and Winterhof. In this paper, we present a general inequality that is satisfied by any periodic sequence. Then, we analyze the behavior of the linear congruential generators on elliptic curves (EC-LCG) under this new lattice test and prove that the EC-LCG passes it up to very high dimensions. We also use a result of Brandstätter and Winterhof on the linear complexity profile related to the correlation measure of order k to present lower bounds on the linear complexity profile of some binary sequences derived from the EC-LCG

Aethionema arabicum: a novel model plant to study the light control of seed germination

Timing of seed germination is crucial for seed plants and coordinated by internal and external cues, reflecting adaptations to different habitats. Physiological and molecular studies with lettuce and Arabidopsis thaliana have documented a strict requirement for light to initiate germination and identified many receptors, signalling cascades, and hormonal control elements. In contrast, seed germination of several other plants is inhibited by light, but the molecular basis of this converse response is unknown. We describe Aethionema arabicum (Brassicaceae) as a suitable model plant to investigate the mechanism of germination inhibition by light, as it comprises accessions with natural variation between light-sensitive and light-neutral responses. Inhibition occurs in red, blue or far-red light and increases with light intensity and duration. Gibberellins and abscisic acid are involved in the control of germination as in Arabidopsis, but transcriptome comparisons of light- and dark-exposed Aethionema arabicum seeds revealed that expression of genes for key regulators upon light exposure undergo converse changes, resulting in antipodal hormone regulation. This illustrates that similar modular components of a pathway in light-inhibited, light-neutral and light requiring germination among the Brassicaceae have been assembled by evolution to produce divergent pathways, likely as adaptive traits