Soundness of workflow nets: classification, decidability, and analysis

Workflow nets, a particular class of Petri nets, have become one of the standard ways to model and analyze workflows. Typically, they are used as an abstraction of the workflow that is used to check the so-called soundness property. This property guarantees the absence of livelocks, deadlocks, and other anomalies that can be detected without domain knowledge. Several authors have proposed alternative notions of soundness and have suggested to use more expressive languages, e.g., models with cancellations or priorities. This paper provides an overview of the different notions of soundness and investigates these in the presence of different extensions of workflow nets.We will show that the eight soundness notions described in the literature are decidable for workflow nets. However, most extensions will make all of these notions undecidable. These new results show the theoretical limits of workflow verification. Moreover, we discuss some of the analysis approaches described in the literature.

Effect of vitamin D supplementation on muscle strength: a systematic review and meta-analysis

Summary This systematic review demonstrates that vitamin D supplementation does not have a significant effect on muscle strength in vitamin D replete adults. However, a limited number of studies demonstrate an increase in proximal muscle strength in adults with vitamin D deficiency. Introduction The purpose of this study is to systematically review the evidence on the effect of vitamin D supplementation on muscle strength in adults. Methods A comprehensive systematic database search was performed. Inclusion criteria included randomised controlled trials (RCTs) involving adult human participants. All forms and doses of vitamin D supplementation with or without calcium supplementation were included compared with placebo or standard care. Outcome measures included evaluation of strength. Outcomes were compared by calculating standardised mean difference (SMD) and 95% confidence intervals. Results Of 52 identified studies, 17 RCTs involving 5,072 participants met the inclusion criteria. Meta-analysis showed no significant effect of vitamin D supplementation on grip strength (SMD −0.02, 95%CI −0.15,0.11) or proximal lower limb strength (SMD 0.1, 95%CI −0.01,0.22) in adults with 25(OH)D levels >25 nmol/L. Pooled data from two studies in vitamin D deficient participants (25(OH)D <25 nmol/L) demonstrated a large effect of vitamin D supplementation on hip muscle strength (SMD 3.52, 95%CI 2.18, 4.85). Conclusion Based on studies included in this systematic review, vitamin D supplementation does not have a significant effect on muscle strength in adults with baseline 25(OH)D >25 nmol/L. However, a limited number of studies demonstrate an increase in proximal muscle strength in adults with vitamin D deficiency. Keywords Muscle – Muscle fibre – Strength – Vitamin D