Abstract: Model based design is particularly appealing in
software based control systems (e.g., embedded
software) design, since in such a case system
level specifications are much easier to define
than the control software behavior itself. In
turn, model based design of embedded systems
requires modeling both continuous subsystems
(typically, the plant) as well as discrete
subsystems (the controller). This is typically
done using hybrid systems. Mixed Integer Linear
Programming (MILP) based abstraction techniques
have been successfully applied to automatically
synthesize correct-by-construction control
software for discrete time linear hybrid systems,
where plant dynamics is modeled as a linear
predicate over state, input, and next state
variables. Unfortunately, MILP solvers require
such linear predicates to be conjunctions of
linear constraints, which is not a natural way of
modeling hybrid systems. In this paper we show
that, under the hypothesis that each variable
ranges over a bounded interval, any linear
predicate built upon conjunction and disjunction
of linear constraints can be automatically
translated into an equivalent conjunctive
predicate. Since variable bounds play a key role
in this translation, our algorithm includes a
procedure to compute all implicit variable bounds
of the given linear predicate. Furthermore, we
show that a particular form of linear predicates,
namely guarded predicates, are a natural and
powerful language to succinctly model discrete
time linear hybrid systems dynamics. Finally, we
experimentally show the feasibility of our
approach on an important and challenging case
study taken from the literature, namely the
multi-input Buck DC-DC Converter. As an example,
the guarded predicate that models (with 57
constraints) a 6-inputs Buck DC-DC Converter is
translated in a conjunctive predicate (with 102
linear constraints) in about 40 minutes.

Abstract: Basic properties of rewriting systems can be stated in the framework of abstract reduction systems (ARS). Properties like confluence (or Church-Rosser, CR) and weak confluence (or weak Church-Rosser, WCR) and their relationships can be studied in this setting: as a matter of fact, well-known counterexamples to the implication WCR CR have been formulated as ARS. In this paper, starting from the observation that such counterexamples are structurally similar, we set out a graph-theoretic characterization of WCR ARS that is not CR in terms of a suitable class of reduction graphs, such that in every WCR not CR ARS, we can embed at least one element of this class. Moreover, we give a tighter characterization for a restricted class of ARS enjoying a suitable regularity condition. Finally, as a consequence of our approach, we prove some interesting results about ARS using the mathematical tools developed. In particular, we prove an extension of the Newman’s lemma and we find out conditions that, once assumed together with WCR property, ensure the unique normal form property. The Appendix treats two interesting examples, both generated by graph-rewriting rules, with specific combinatorial properties.

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.