Reasoning about transfinite sequences

We introduce a family of temporal logics to specify the behavior of systems with Zeno behaviors. We extend linear-time temporal logic LTL to authorize models admitting Zeno sequences of actions and quantitative temporal operators indexed by ordinals replace the standard next-time and until future-time operators. Our aim is to control such systems by designing controllers that safely work on $\omega$-sequences but interact synchronously with the system in order to restrict their behaviors. We show that the satisfiability problem for the logics working on $\omega^k$-sequences is EXPSPACE-complete when the integers are represented in binary, and PSPACE-complete with a unary representation. To do so, we substantially extend standard results about LTL by introducing a new class of succinct ordinal automata that can encode the interaction between the different quantitative temporal operators.Comment: 38 page

Mathematische Theorie des Verhaltens endlicher Automaten

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/93682/1/19620420106_ftp.pd

Clinical efficacy of amoxycillin/clavulanate in laparoscopically confirmed salpingitis

To test the efficacy and safety of amoxycillin/clavulanate (Augmenting 102 hospital patients with laparoscopically confirmed acute salpingitis were treated with paren-teral amoxycillin/clavulanate (l.2g qid for three days) followed by oral amoxycillin/ clavulanate (two tablets of 625 mg tid for a further six days). Bacteriological samples were obtained from the cervix uteri and the pouch of Douglas. One hundred patients were assessable for clinical outcome using several variables including pain scores. Amoxycillin/clavulanate alone was effective in 95 patients (95%). Three patients (3%) responded to amoxycillin/clavulanate with marked improvement but another antibiotic was subsequently added to their treatment regimen. Treatment failed in two patients. At follow-up two weeks after hospital discharge, three patients (3.8%) had relapsed or were re-infected. Adverse drug events included one case of drug fever, one case of rash and one case of severe diarrhoea. Treatment was stopped in all three cases. Gastrointestinal reactions, mainly mild diarrhoea, were seen in 31 patients. No clinically relevant changes in haematological or clinical chemical indices were attributable to the amoxycillin/clavulanate treatment. We conclude that amoxycillin/clavulanate is a clinically effective and safe treatment for acute salpingiti

The minimal important difference of the hospital anxiety and depression scale in patients with chronic obstructive pulmonary disease

BACKGROUND: Interpretation of the Hospital Anxiety and Depression Scale (HADS), commonly used to assess anxiety and depression in COPD patients, is unclear. Since its minimal important difference has never been established, our aim was to determine it using several approaches. METHODS: 88 COPD patients with FEV1 /= 0.5 we performed linear regression analyses to predict the minimal important difference from the anchors. As distribution-based approach we used the Effect Size approach. RESULTS: Based on CRQ emotional function and mastery domain as well as on total scores, the minimal important difference was 1.41 (95% CI 1.18-1.63) and 1.57 (1.37-1.76) for the HADS anxiety score and 1.68 (1.48-1.87) and 1.60 (1.38-1.82) for the HADS total score. Correlations of the HADS depression score and CRQ domain and Feeling Thermometer scores were < 0.5. Based on the Effect Size approach the MID of the HADS anxiety and depression score was 1.32 and 1.40, respectively. CONCLUSION: The minimal important difference of the HADS is around 1.5 in COPD patients corresponding to a change from baseline of around 20%. It can be used for the planning and interpretation of trials

Partially Ordered Two-way B\"uchi Automata

We introduce partially ordered two-way B\"uchi automata and characterize their expressive power in terms of fragments of first-order logic FO[<]. Partially ordered two-way B\"uchi automata are B\"uchi automata which can change the direction in which the input is processed with the constraint that whenever a state is left, it is never re-entered again. Nondeterministic partially ordered two-way B\"uchi automata coincide with the first-order fragment Sigma2. Our main contribution is that deterministic partially ordered two-way B\"uchi automata are expressively complete for the first-order fragment Delta2. As an intermediate step, we show that deterministic partially ordered two-way B\"uchi automata are effectively closed under Boolean operations. A small model property yields coNP-completeness of the emptiness problem and the inclusion problem for deterministic partially ordered two-way B\"uchi automata.Comment: The results of this paper were presented at CIAA 2010; University of Stuttgart, Computer Scienc

Complementation of Rational Sets on Scattered Linear Orderings of Finite Rank

International audienceIn a preceding paper, automata have been introduced for words indexed by linear orderings. These automata are a generalization of automata for finite, infinite, bi-finite and even transfinite words studied by Buchi Kleene's theorem has been generalized to these words. We show that deterministic automata do not have the same expressive power. Despite this negative result, we prove that rational sets of words of finite ranks are closed under complementation

On the Sets of Real Numbers Recognized by Finite Automata in Multiple Bases

This article studies the expressive power of finite automata recognizing sets of real numbers encoded in positional notation. We consider Muller automata as well as the restricted class of weak deterministic automata, used as symbolic set representations in actual applications. In previous work, it has been established that the sets of numbers that are recognizable by weak deterministic automata in two bases that do not share the same set of prime factors are exactly those that are definable in the first order additive theory of real and integer numbers. This result extends Cobham's theorem, which characterizes the sets of integer numbers that are recognizable by finite automata in multiple bases. In this article, we first generalize this result to multiplicatively independent bases, which brings it closer to the original statement of Cobham's theorem. Then, we study the sets of reals recognizable by Muller automata in two bases. We show with a counterexample that, in this setting, Cobham's theorem does not generalize to multiplicatively independent bases. Finally, we prove that the sets of reals that are recognizable by Muller automata in two bases that do not share the same set of prime factors are exactly those definable in the first order additive theory of real and integer numbers. These sets are thus also recognizable by weak deterministic automata. This result leads to a precise characterization of the sets of real numbers that are recognizable in multiple bases, and provides a theoretical justification to the use of weak automata as symbolic representations of sets.Comment: 17 page

Ecological strategies in stable and disturbed environments depend on species specialisation

Ecological strategies are integral to understanding species survival in different environments. However, how habitat specialisation is involved in such strategies is not fully understood, particularly in heterogeneous and disturbed environments. Here, we studied the trait associations between specialisation, dispersal ability, competitiveness, reproductive investment and survival rate in a spatially explicit metacommunity model under various disturbance rates. Though no unique trait values were associated with specialisation, relationships were uncovered depending on environmental factors. We found strong trait associations mainly for generalist species, while specialist species exhibited a larger range of trait combinations. Trait associations were driven first by the disturbance rate and second by species’ dispersal ability and generation overlap. With disturbance, low dispersal ability was strongly selected against, for specialists as well as for generalists. Our results demonstrate that habitat specialisation is critical for the emergence of trait strategies in metacommunities and that disturbance in interaction with dispersal ability limits not only the range of trait values but also the type of possible trait associations