Generic Model Refactorings

Many modeling languages share some common concepts and principles. For example, Java, MOF, and UML share some aspects of the concepts\ud of classes, methods, attributes, and inheritance. However, model\ud transformations such as refactorings specified for a given language\ud cannot be readily reused for another language because their related\ud metamodels may be structurally different. Our aim is to enable a\ud flexible reuse of model transformations across various metamodels.\ud Thus, in this paper, we present an approach allowing the specification\ud of generic model transformations, in particular refactorings, so\ud that they can be applied to different metamodels. Our approach relies\ud on two mechanisms: (1) an adaptation based mainly on the weaving\ud of aspects; (2) the notion of model typing, an extension of object\ud typing in the model-oriented context. We validated our approach by\ud performing some experiments that consisted of specifying three well\ud known refactorings (Encapsulate Field, Move Method, and Pull Up Method)\ud and applying each of them onto three different metamodels (Java,\ud MOF, and UML)

Convex hulls of random walks, hyperplane arrangements, and Weyl chambers

We give an explicit formula for the probability that the convex hull of an n-step random walk in Rd does not contain the origin, under the assumption that the distribution of increments of the walk is centrally symmetric and puts no mass on affine hyperplanes. This extends the formula by Sparre Andersen (Skand Aktuarietidskr 32:27–36, 1949) for the probability that such random walk in dimension one stays positive. Our result is distribution-free, that is, the probability does not depend on the distribution of increments. This probabilistic problem is shown to be equivalent to either of the two geometric ones: (1) Find the number of Weyl chambers of type Bn intersected by a generic linear subspace of Rn of codimension d; (2) Find the conic intrinsic volumes of a Weyl chamber of type Bn. We solve the first geometric problem using the theory of hyperplane arrangements. A by-product of our method is a new simple proof of the general formula by Klivans and Swartz (Discrete Comput Geom 46(3):417–426, 2011) relating the coefficients of the characteristic polynomial of a linear hyperplane arrangement to the conic intrinsic volumes of the chambers constituting its complement. We obtain analogous distribution-free results for Weyl chambers of type An−1 (yielding the probability of absorption of the origin by the convex hull of a generic random walk bridge), type Dn, and direct products of Weyl chambers (yielding the absorption probability for the joint convex hull of several random walks or bridges). The simplest case of products of the form B1 ×···× B1 recovers the Wendel formula (Math Scand 11:109–111, 1962) for the probability that the convex hull of an i.i.d. multidimensional sample chosen from a centrally symmetric distribution does not contain the origin. We also give an asymptotic analysis of the obtained absorption probabilities as n → ∞, in both cases of fixed and increasing dimension d

On OCL as part of the metamodeling framework MOFLON

Abstract. The metamodeling framework MOFLON combines MOF 2.0, OCL 2.0 and graph transformations to generate sophisticated metamodel implementations. In this paper we describe the role of OCL in MOFLON. Furthermore, we present a set of constraints which corrects, completes and improves MOF 2.0 for the application as graph schema language.

MOFLON: A Standard-Compliant Metamodeling Framework with Graph Transformations

The crucial point in Model Driven Architecture (MDA 1) is that software and system development are based on abstract models that are successively transformed into more specific models, ideally resulting in the desired system. To this end, developers must be enabled to model different aspects like structure, behavior, consistency constraints of the system. This results in a variety of related models, which in turn need tool support on the metalevel. However, there is a lack of tools offering uniform support for metamodel definition, analysis, transformation, and integration. In this paper we present the metamodeling framework MOFLON that addresses these issues by bringing together the latest OMG standards with graph transformations and their formal semantics. MOFLON provides a combination of visual and textual notations and offers powerful modularization concepts. Using MOFLON, developers can generate code for specific tools needed to perform the desired modeling tasks