Every K-trivial set is computable from an incomplete Martin-Löf random set, i.e., a Martin-Löf random set that does not compute the halting problem. A major objective in algorithmic randomness is to understand how random sets and computably enumerable (c.e.) sets interact within the Turing degrees. At some level of randomness all interesting interactions cease. The lower and upper cones of nonc...

Aeruginosins are bioactive oligopeptides that are produced in high structural diversity by strains of the bloom-forming cyanobacterial genera Microcystis and Planktothrix. A hallmark of aeruginosins is the unusual Choi moiety central to the tetrapeptides, while other positions are occupied by variable moieties in individual congeners. Here we report on three aeruginosin synthetase gene clusters...

We consider weak lumpability of general nite homogeneous Markov chains evolving in discrete time, that is when a lumped Markov chain with respect to a partition of the initial state space is also a homogeneous Markov chain. We show that weak lumpabilityis equivalent to the existence of a decomposable polyhedral cone which is positively invariant by the transition probability matrix of the origi...

The phytohormone auxin regulates many aspects of growth and development in land plants, but the origin and evolution of auxin signaling and response mechanisms remain largely unknown. Indeed, it remains to be investigated whether auxin-related pathways diverged before the emergence of land plants. To address this knowledge deficit, we analyzed auxin responses in the charophyte alga Klebsormidiu...

Arsenic speciation analysis was performed in two human urine certified reference materials (NIES No. 18 and NIST SRM2670a) and three human urine control materials (Seronorm, Medisafe and Lyphocheck). The samples were diluted 1 1 3 prior to analysis by gradient elution anion or cation exchange high-performance liquid chromatography (HPLC) coupled with inductively coupled plasma mass spectrometry...

Roles of nutrients and other environmental variables in development of cyanobacterial bloom and its toxicity are complex and not well understood. We have monitored the photoautotrophic growth, total microcystin concentration, and microcystins synthetase gene (mcyA) expression in lab-grown strains of Microcystis NIES 843 (reference strain), KW (Wangsong Reservoir, South Korea), and Durgakund (Va...

This is the second update on the status of open problems in Computability and Randomness [17]. The first appeared in March 2011.