Blending Timed Formal Models with Clock Transition Systems
FUNDAMENTA INFORMATICAE
Authors: Jard, Claude; Lime, Didier; Roux, Olivier H.
Abstract
Networks of Timed Automata (NTA) and Time Petri Nets (TPNs) are well-established formalisms used to model, analyze and control industrial real-time systems. The underlying theories are usually developed in different scientific communities and both formalisms have distinct strong points: for instance, conciseness for TPNs and a more flexible notion of urgency for NTA. The objective of the paper is to introduce a new model allowing the joint use of both TPNs and NTA for the modeling of timed systems. We call it Clock Transition System (CTS). This new model incorporates the advantages of the structure of Petri nets, while introducing explicitly the concept of clocks. Transitions in the network can be guarded by an expression on the clocks and reset a subset of them as in timed automata. The urgency is introduced by a separate description of invariants. We show that CTS allow to express TPNs (even when unbounded) and NTA. For those two classical models, we identify subclasses of CTSs equivalent by isomorphism of their operational semantics and provide (syntactic) translations. The classical state-space computation developed for NTA and then adapted to TPNs can easily be defined for general CTSs. Armed with these merits, the CTS model seems a good candidate to serve as an intermediate theoretical and practical model to factor out the upcoming developments in the TPNs and the NTA scientific communities.
Low-dose CT detects more progression of bone formation in comparison to conventional radiography in patients with ankylosing spondylitis: results from the SIAS cohort
ANNALS OF THE RHEUMATIC DISEASES
Authors: de Koning, Anoek; de Bruin, Freek; van den Berg, Rosaline; Ramiro, Sofia; Baraliakos, Xenofon; Braun, Juergen; van Gaalen, Floris A.; Reijnierse, Monique; van der Heijde, Desiree
Abstract
Objectives To compare the CT Syndesmophyte Score (CTSS) for low-dose CT (ldCT) with the modified Stoke Ankylosing Spondylitis Spine Score (mSASSS) for conventional radiographs (CR) in patients with ankylosing spondylitis (AS). Methods Patients with AS in the Sensitive Imaging in Ankylosing Spondylitis cohort had lateral cervical and lumbar spine CR and whole spine ldCT at baseline and 2years. CR and ldCT images were scored by two readers, paired by patient, blinded to time order, per imaging modality. For the total score analysis, we used average scores of readers per corner on CR or quadrant on ldCT. For the syndesmophyte analysis we used individual reader and consensus scores, regarding new or growing syndesmophyte at the same corner/quadrant. Results 50 patients were included in the syndesmophyte analysis and 37 in the total score analysis. Mean (SD) status scores for mSASSS (range 0-72) and CTSS (range 0-552) at baseline were 17.9 (13.8) and 161.6 (126.6), and mean progression was 2.4 (3.8) and 17.9 (22.1). Three times as many patients showed new or growing syndesmophytes at 3quadrants on ldCT compared with 3corners on CR for individual readers; for consensus this increased to five times. In 50 patients, 36 new or growing syndesmophytes are seen on CR compared with 151 on ldCT, most being found in the thoracic spine. Conclusions ldCT, covering the whole spine, detects more progression in the form of new and growing syndesmophytes in patients with AS compared with CR, which is limited to the cervical and lumbar spine. Most progression occurred in the thoracic spine.