The Maxwell-Chern-Simons theory is canonically quantized in the Coulomb gauge by using the Dirac bracket quantization procedure. The determination of the Coulomb gauge polarization vector turns out to be intrincate. A set of quantum Poincaré densities obeying the Dirac-Schwinger algebra, and, there-

Model transformation programs are iteratively refined, restructured, and evolved due to many reasons such as fixing bugs and adapting existing transformation rules to new metamodels version. Thus, modular design is a desirable property for model transformations as it can significantly improve their evolution, comprehensibility, maintainability, reusability, and thus, their overall quality. Although language support for modularization of model transformations is emerging, model transformations are created as monolithic artifacts containing a huge number of rules. To the best of our knowledge, the problem of automatically modularizing model transformation programs was not addressed before in the current literature. These programs written in transformation languages, such as ATL, are implemented as one main module including a huge number of rules. To tackle this problem and improve the quality and maintainability of model transformation programs, we propose an automated search-based approach to modularize model transformations based on higher-order transformations. Their application and execution is guided by our search framework which combines an in-place transformation engine and a search-based algorithm framework. We demonstrate the feasibility of our approach by using ATL as concrete transformation language and NSGA-III as search algorithm to find a trade-off between different well-known conflicting design metrics for the fitness functions to evaluate the generated modularized solutions. To validate our approach, we apply it to a comprehensive dataset of model transformations. As the study shows, ATL transformations can be modularized automatically, efficiently, and effectively by our approach. We found that, on average, the majority of recommended modules, for all the ATL programs, by NSGA-III are considered correct with more than 84% of precision and 86% of recall when compared to manual solutions provided by active developers. The statistical analysis of our experiments over several runs shows that NSGA-III performed significantly better than multi-objective algorithms and random search. We were not able to compare with existing model transformations modularization approaches since our study is the first to address this problem. The software developers considered in our experiments confirm the relevance of the recommended modularization solutions for several maintenance activities based on different scenarios and interviews.

Model transformations are an important cornerstone of model‐driven engineering, a discipline which facilitates the abstraction of relevant information of a system as models. The success of the final system mainly depends on the optimization of these models through model transformations. Currently, the application of transformations is realized either by following the apply‐as‐long‐as‐possible strategy or by the provision of explicit rule orchestrations. This implies two main limitations. First, the optimization objectives are implicitly hidden in the transformation rules and their orchestration. Second, manually finding the best orchestration for a particular scenario is a major challenge due to the high number of possible combinations. To overcome these limitations, we present a novel framework that builds on the non‐intrusive integration of optimization and model transformation technologies. In particular, we formulate the transformation orchestration task as an optimization problem, which allows for the efficient exploration of the transformation space and explication of the transformation objectives. Our generic framework provides several search algorithms and guides the user in providing a proper search configuration. We present different instantiations of our framework to demonstrate its feasibility, applicability, and benefits using several case studies. Copyright © 2016 John Wiley & Sons, Ltd.

We study the quantization and the one-loop renormalization of the model resulting from the coupling of charged fermions with a Chern–Simons field, in the Coulomb gauge. A proof of the Lorentz covariance of the physical quantities follows after establishing the Dirac–Schwinger algebra for the Poincaré densities and the transformation properties of the fields under the Poincaré group. The Coulomb gauge one-loop renormalization program is, afterwards, implemented. The noncovariant form of the one-loop fermion propagator, Chern–Simons field propagator and the vertex are explicitly obtained. Finally, the electron anomalous magnetic moment is calculated stressing that, due to the peculiarities of the Coulomb gauge, the contributions from the self-energy diagrams turn out to be essential.

Many model transformation scenarios require flexible execution strategies as they should produce models with the highest possible quality. At the same time, transformation problems often span a very large search space with respect to possible transformation results. Recently, different proposals for finding good transformation results without enumerating the complete search space have been proposed by using meta-heuristic search algorithms. However, determining the impact of the different kinds of search algorithms, such as local search or global search, on the transformation results is still an open research topic. In this paper, we present an extension to MOMoT, which is a search-based model transformation tool, for supporting not only global searchers for model transformation orchestrations, but also local ones. This leads to a model transformation framework that allows as the first of its kind multi-objective local and global search. By this, the advantages and disadvantages of global and local search for model transformation orchestration can be evaluated. This is done in a case-study-based evaluation, which compares different performance aspects of the local-and global-search algorithms available in MOMoT. Several interesting conclusions have been drawn from the evaluation: (1) local-search algorithms perform reasonable well with respect to both the search exploration and the execution time for small input models, (2) for bigger input models, their execution time can be similar to those of global-search algorithms, but global-search algorithms tend to outperform local-search algorithms in terms of search exploration, (3) evolutionary algorithms show limitations in situations where single changes of the solution can have a significant impact on the solution's fitness.