Event-Based Semantics of UML 2.X Concurrent Sequence Diagrams for Formal Verification

UML 2.X sequence diagrams(SD)are among privileged scenarios-based approaches dealing with the complexity of modeling the behaviors of some current systems.However,there are several issues related to the standard semantics of UML 2.X SD proposed by the Object Management Group(OMG).They mainly concern ambiguities of the interpretation of SDs,and the computation of causal relations between events which is not specifically laid out.Moreover,SD is a semi-formal language,and it does not support the verification of the modeled system.This justifies the considerable number of research studies intending to define formal semantics of UML SDs.We proposed in our previous work semantics covering the most popular combined fragments(CF)of control-flow ALT,OPT,LOOP and SEQ,allowing to model alternative,optional,iterative and sequential behaviors respectively.The proposed semantics is based on partial order theory relations that permit the computation of the precedence relations between the events of an SD with nested CFs.We also addressed the issue of the evaluation of the interaction constraint(guard)for guarded CFs,and the related synchronization issue.In this paper,we first extend our semantics,proposed in our previous work;indeed,we propose new rules for the computation of causal relations for SD with PAR and STRICT CFs(dedicated to modeling concurrent and strict behaviors respectively)as well as their nesting.Then,we propose a transformational semantics in Event-B.Our modeling approach emphasizes computation of causal relations,guard handling and transformational semantics into Event-B.The transformation of UML 2.X SD into the formal method Event-B allows us to perform several kinds of verification including simulation,trace acceptance,verification of properties,and verification of refinement relation between SDs.

The reliability of age measurements for Young Stellar Objects from Hertzsprung-Russell or color-magnitude diagrams

The possibility to estimate ages and masses of Young Stellar Objects （YSOs） from their location in the Hertzsprnng-Russell diagram （HRD） or a color- magnitude diagram provides a very important tool for the investigation of fundamen- tal questions related to the processes of star formation and early stellar evolution. Age estimates are essential for studies of the temporal evolution of circumstellar material around YSOs and the conditions for planet formation. The characterization of the age distribution of the YSOs in a star forming region allows researchers to reconstruct the star formation history and provides important information on the fundamental ques- tion of whether star formation is a slow or a fast process. However, the reliability of these age measurements and the ability to detect possible age spreads in the stellar population of star forming regions are fundamentally limited by several factors. The variability of YSOs, unresolved binary components, and uncertainties in the calibra- tions of the stellar parameters cause uncertainties in the derived luminosities that are usually much larger than the typical photometry errors. Furthermore, the pre-main se- quence evolution track of a YSO depends to some degree on the initial conditions and the details of its individual accretion history. I discuss how these observational and model uncertainties affect the derived isochronal ages, and demonstrate how neglect- ing or underestimating these uncertainties can easily lead to severe misinterpretations, gross overestimates of the age spread, and ill-based conclusions about the star for- marion history. These effects are illustrated by means of Monte-Carlo simulations of observed star clusters with realistic observational uncertainties. The most important points are as follows. First, the observed scatter in the HRD must not be confused with a genuine age spread, but is always just an upper limit to the true age spread. Second, histograms of isochronal ages naturally show a decreasing number of stars for ages above the median, a pattern that can be misinterpreted as an accelerating star formation rate. Third, it is emphasized that many star forming regions consist of sev- eral sub-groups, which often have different ages. If these distinct stellar populations cannot be disentangled （e.g., due to projection effects） and the HRD of all stars in the region is used for an age analysis, it is very difficult （often impossible） to discern between the scenario of an extended period of star formation （i.e. a large age spread） and the alternative concept of a temporal sequence of several discrete star formation episodes. Considering these factors, most observations of star forming regions suggest that age spreads are usually smaller than the corresponding crossing times, supporting the scenario of fast and dynamic star formation.