Abstract: Model Based Design approaches for embedded systems aim at generating correct-by-construction control software, guaranteeing that the closed loop system (controller and plant) meets given system level formal specifications. This technical note addresses control synthesis for safety and reachability properties of possibly non-linear discrete time hybrid systems. By means of syntactical transformations that require non-linear terms to be Lipschitz continuous functions, we over-approximate non-linear dynamics with a linear system whose controllers are guaranteed to be controllers of the original system. We evaluate performance of our approach on meaningful control synthesis benchmarks, also comparing it to a state-of-the-art tool.

Abstract: Background: Interpretation of observational studies on associations between prefrontal cognitive functioning and hormone levels across the female menstrual cycle is complicated due to small sample sizes and poor replicability. Methods: This observational multisite study comprised data of n=88 menstruating women from Hannover, Germany, and Zurich, Switzerland, assessed during a first cycle and n=68 re-assessed during a second cycle to rule out practice effects and false-positive chance findings. We assessed visuospatial working memory, attention, cognitive bias and hormone levels at four consecutive time-points across both cycles. In addition to inter-individual differences we examined intra-individual change over time (i.e., within-subject effects). Results: Oestrogen, progesterone and testosterone did not relate to inter-individual differences in cognitive functioning. There was a significant negative association between intra-individual change in progesterone and change in working memory from pre-ovulatory to mid-luteal phase during the first cycle, but that association did not replicate in the second cycle. Intra-individual change in testosterone related negatively to change in cognitive bias from menstrual to pre-ovulatory as well as from pre-ovulatory to mid-luteal phase in the first cycle, but these associations did not replicate in the second cycle. Conclusions: There is no consistent association between women's hormone levels, in particular oestrogen and progesterone, and attention, working memory and cognitive bias. That is, anecdotal findings observed during the first cycle did not replicate in the second cycle, suggesting that these are false-positives attributable to random variation and systematic biases such as practice effects. Due to methodological limitations, positive findings in the published literature must be interpreted with reservation.