From metastable to coherent sets- Time-discretization schemes.

Given a time-dependent stochastic process with trajectories x(t) in a space Ω, there may be sets such that the corresponding trajectories only very rarely cross the boundaries of these sets. We can analyze such a process in terms of metastability or coherence. Metastable setsM are defined in space M⊂Ω, and coherent setsM(t)âŠ‚Ω are defined in space and time. Hence, if we extend the space Ω by the time-variable t, coherent sets are metastable sets in Ω×[0,∞) of an appropriate space-time process. This relation can be exploited, because there already exist spectral algorithms for the identification of metastable sets. In this article, we show that these well-established spectral algorithms (like PCCA+, Perron Cluster Cluster Analysis) also identify coherent sets of non-autonomous dynamical systems. For the identification of coherent sets, one has to compute a discretization (a matrix T) of the transfer operator of the process using a space-time-discretization scheme. The article gives an overview about different time-discretization schemes and shows their applicability in two different fields of application.

Influence of meteorological parameters during the preceding fall and winter on the questing activity of nymphal Ixodes ricinus ticks.

Wood ticks, Ixodes ricinus L., serve as vectors for various pathogens and are ubiquitous throughout Central Europe. Survival and development of I. ricinus depend on biotic and abiotic factors. We examined whether relative humidity (RH), air (T a ) and soil temperatures (T s ), or snow depth during November through February affect the questing activity of ticks during their subsequent season of activity. We related the number of host-seeking nymphs to meteorological parameters measured in close proximity at minutely intervals over the period of 6 years (2010-2015) in an urban park in Berlin. We defined thresholds at which associations appeared strongest. Although the annual variations in RH, T a , and snow depth were typical of the mid-latitudes, the questing activity of nymphs during their first peak of activity (March through July) varied among the 6 years more than threefold. The accumulated hours of RH below 77% in 2 m height during November through February affected the questing activity of nymphs during the following activity peak. In contrast to T a , accumulated hours of T s below -1 °C in 0.02 m depth or below -4 °C in 0.05 m depth during the preceding period significantly influenced the average number of nymphs questing during spring. Our observations suggest that RH, T s , and snow cover during the preceding months affect the questing activity of nymphal I. ricinus during their first peak of activity. Snow cover serves as an insulator between the atmosphere and soil, which not only stabilizes T s but also appears to protect ticks from exposure to frost and frequent temperature shifts.