We establish a close connection between the stable commutator length in free groups and the geometry of sails (roughly, the boundary of the convex hull of the set of integer lattice points) in integral polyhedral cones. This connection allows us to show that the scl norm is piecewise rational linear in free products of Abelian groups, and that it can be computed via integer programing. Furthermore, we show that the scl spectrum of non‐Abelian free groups contains elements congruent to every rational number modulo ℤ, and contains well‐ordered sequences of values with ordinal type ωω. Finally, we study families of elements w(p) in free groups obtained by surgery on a fixed element w in a free product of Abelian groups of higher rank, and show that scl(w(p)) → scl(w) as p → ∞.

We present a framework based on the Calculus of Inductive Constructions (CIC) and its associated tool the Coq proof assistant to allow certification of model transformations in the context of Model-Driven Engineering (MDE). The approached is based on a semi-automatic translation process from metamodels, models and transformations of the MDE technical space into types, propositions and functions of the CIC technical space. We describe this translation and illustrate its use in a standard case study.

Part 3: Examples and Case StudiesInternational audienceBusiness Process Management Systems (BPMS) provide support for modeling, developing, deploying, executing and evaluating business processes in an organization. Selecting a BPMS is not a trivial task, not only due to the many existing alternatives, both in the open source and proprietary realms, but also because it requires a thorough evaluation of its capabilities, contextualizing them in the organizational environment in which they will be used. In this paper we present a methodology to guide the systematic evaluation of BPMS that takes into account the specific needs of each organization. It provides a list of key characteristics of BPMS which are ranked by the organization and evaluated using test cases and quantitative criteria. We also present case studies of open source and proprietary BPMS evaluations following our proposal

Abstract-Business processes may accept variants based on specific business requirements of an organization, leading to the definition of a process family. There are many proposals for the modeling of the common and variable parts of a process family, as well as to support the customization of each process variant (i.e., process configuration or tailoring). In this article, we present the results of a detailed study about the modeling and customization of process families based on the Business Process Model and Notation (BPMN 2.0) standard, and we introduce BPMNext, a novel approach devised for this purpose. The language is an adaptation of BPMN 2.0 based on the ideas provided by vSPEM, a language for the modeling of software processes families. We also present a supporting tool and its application to a real case study about the assignment of positions in exchange programs.

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