A survey of bacterial diversity in ticks, lice and fleas from Australia

We isolated bacteria from ticks, lice and fleas. Partial small subunit rRNA sequences were obtained for each isolate and the closest matches in the FastA database were determined. These bacteria were mostly Gram-positive (Firmicutes), although representatives from the Proteobacteria (alpha, beta, gamma subdivisions) and CFB group were also isolated. Most of the isolates we found were from genera that were present in most of the ectoparasites studied, but a few genera were restricted to one species of ectoparasite. The most commonly isolated genera were Stenotrophomonas, Staphylococcus, Pseudomonas, Acinetobacter and Bacillus. Species of Bacillus and Proteus, which have biopesticide potential, were found in some of these ectoparasites. Overall, the communities of bacteria were similar to those found in other studies of parasitic arthropods.

Pseudo-randomness of round-off errors in discretized linear maps on the plane

We analyze the sequences of round-off errors of the orbits of a discretized planar rotation, from a probabilistic angle. It was shown [Bosio & Vivaldi, 2000] that for a dense set of parameters, the discretized map can be embedded into an expanding p-adic dynamical system, which serves as a source of deterministic randomness. For each parameter value, these systems can generate infinitely many distinct pseudo-random sequences over a finite alphabet, whose average period is conjectured to grow exponentially with the bit-length of the initial condition (the seed). We study some properties of these symbolic sequences, deriving a central limit theorem for the deviations between round-off and exact orbits, and obtain bounds concerning repetitions of words. We also explore some asymptotic problems computationally, verifying, among other things, that the occurrence of words of a given length is consistent with that of an abstract Bernoulli sequence.