Nonspecific low back pain and sciatica are prevalent diseases among working adults and have become a worrying occupational health issue because they sometimes affect continuation or resumption of employment. Epidemiological studies that based questionnaires on workers' healthcare consumption have shown a higher prevalence of these disorders in certain industrial sectors. Thus, low back disorders are usually more prevalent among workers exposed to cumulative lumbar load such as manual handling, awkward postures of the trunk and whole-body vibrations. In addition, morphological and biomechanical studies have compared disc space narrowing and the intensity of lumbar workload. Although debated, the relationship between disc degeneration and biomechanical work exposures seems to be usually accepted by most authors. In response to a considerable need of prevention and compensation for workers, low back pain and/or disc disease can be recognized as an occupational diseases in several countries but the criteria of recognition remains heterogeneous from one country to another.
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Timed automata are among the most widely studied models for real-time systems. Silent transitions, i.e., e-transitions, have already been proposed in the original paper on timed automata by Alur and Dill. We show that class TLe of timed languages recognized by automata with e-transitions, is more robust and more expressive than the corresponding class TL without e-transitions. We then focus on e-transitions without reset, i.e. e-transitions which do not reset clocks. We propose an algorithm to construct, given a timed automaton, an equivalent one without such transitions. This algorithm is in two steps, it first suppresses the cycles of e-transitions without reset and then the remaining ones. Then, we prove that a timed automaton such that no e-transition which resets clocks lies on any directed cycle, can be effectively transformed into a timed automaton without e-transitions. Interestingly, this main result holds under the assumption of non-Zenoness and it is false otherwise. To complete the picture, we exhibit a simple timed automaton with an e-transition, which resets some clock, on a cycle and which is not equivalent to any e-free timed automaton. To show this, we develop a promising new technique based on the notion of precise action.
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