Nucleon spin decomposition and differential geometry

In the last few years, the so-called Chen et al. approach of the nucleon spin decomposition has been widely discussed and elaborated on. In this letter we propose a genuine differential geometric understanding of this approach. We mainly highligth its relation to the "dressing field method" we advocated in [C. Fournel, J. Fran\c{c}ois, S. Lazzarini, T. Masson, Int. J. Geom. Methods Mod. Phys. 11, 1450016 (2014)]. We are led to the conclusion that the claimed gauge-invariance of the Chen et al. decomposition is actually unreal.Comment: 9 pages. v3: minor corrections in the text, addition of a new referenc

Local description of generalized forms on transitive Lie algebroids and applications

In this paper we study the local description of spaces of forms on transitive Lie algebroids. We use this local description to introduce global structures like metrics, $\ast$-Hodge operation and integration along the algebraic part of the transitive Lie algebroid (its kernel). We construct a \v{C}ech-de Rham bicomplex with a Leray-Serre spectral sequence. We apply the general theory to Atiyah Lie algebroids and to derivations on a vector bundle

Gauge field theories: various mathematical approaches

This paper presents relevant modern mathematical formulations for (classical) gauge field theories, namely, ordinary differential geometry, noncommutative geometry, and transitive Lie algebroids. They provide rigorous frameworks to describe Yang-Mills-Higgs theories or gravitation theories, and each of them improves the paradigm of gauge field theories. A brief comparison between them is carried out, essentially due to the various notions of connection. However they reveal a compelling common mathematical pattern on which the paper concludes.Comment: 33 pages. To be published in the book: Mathematical Structures of the Universe (Copernicus Center Press, Krak\'ow, Poland, 2014

Formulation of gauge theories on transitive Lie algebroids

In this paper we introduce and study some mathematical structures on top of transitive Lie algebroids in order to formulate gauge theories in terms of generalized connections and their curvature: metrics, Hodge star operator and integration along the algebraic part of the transitive Lie algebroid (its kernel). Explicit action functionals are given in terms of global objects and in terms of their local description as well. We investigate applications of these constructions to Atiyah Lie algebroids and to derivations on a vector bundle. The obtained gauge theories are discussed with respect to ordinary and to similar non-commutative gauge theories.Comment: 30 pages. Final version. arXiv admin note: substantial text overlap with arXiv:1109.428

Cartan Connections and Atiyah Lie Algebroids

This work extends previous developments carried out by some of the authors on Ehresmann connections on Atiyah Lie algebroids. In this paper, we study Cartan connections in a framework relying on two Atiyah Lie algebroids based on a $H$-principal fiber bundle $\mathcal{P}$ and its associated $G$-principal fiber bundle $\mathcal{Q} := \mathcal{P} \times_H G$, where $H \subset G$ defines the model for a Cartan geometry. The first main result of this study is a commutative and exact diagram relating these two Atiyah Lie algebroids, which allows to completely characterize Cartan connections on $\mathcal{P}$. Furthermore, in the context of gravity and mixed anomalies, our construction answers a long standing mathematical question about the correct geometrico-algebraic setting in which to combine inner gauge transformations and infinitesimal diffeomorphisms.Comment: 27 pages. Published versio

The jointly scheduling of hard periodic tasks with soft aperiodic events within the Real-Time Specification for Java (RTSJ)

The studied problem is the jointly scheduling of hard periodic tasks with soft aperiodic events, where the response times of soft tasks have to be as low as possible while the warranty to meet their deadlines has to be given to hard tasks. A lot of theoretical solutions have been proposed these past two decades but we are interested on the implementability of these solutions under the real-time specification for Java (RTSJ), without changing the scheduler. This led us to adapt the existing algorithms to operate at a user land level in the system, to propose some optimizations and counter measures in order to balance the lost of performances and finally to set up an approximate slack stealer algorithm specifically designed to take into account RTSJ restrictions. We propose new classes to extend the RTSJ API's to implement these mechanisms and some minor modification suggestions to existing ones as a feed back from our RTSJ experiences. We demonstrates the efficiency of the modified algorithms through extensive simulations and the implementability on available RTSJ compliant virtual machine by an overhead measure in real situation with the RTSJ JamaïcaVM from Aïcas. We also measure the overhead on LejosRT, an RTSJ compliant firmware for Lego Mindstorms NXT in development

The Design and Implementation of Real-time Event-based Applications with RTSJ

International audienceThis paper presents a framework to design real-time event-based applications using Java. The Real-Time Specification for Java (RTSJ) is well designed for hard periodic real-time systems. Though it also proposes classes to model asynchronous events and deal with sporadic or aperiodic tasks, it remains insufficient. The literature proposes the use of periodic servers called task servers to handle nonperiodic traffics in real-time systems. Unfortunately, there is no support for task servers in RTSJ. In order to fix this lack, we propose an RTSJ extension model. To validate our design, we adapt and implement two policies: the polling server and the deferrable server policies. To show how effi- cient these policies are, we compare implementation results and results obtained with a discrete-event-based simulato

RTSJ Extensions: Event Manager and Feasibility Analyzer

International audienceWe present in this paper our experience on the implementation with RTSJ of advanced algorithms to handle aperiodic traffic. We have adapted existing algorithms in order to take into account some constraints brought about by the use of Java language, and our aim which is to propose a portable mechanism. To circumscribe some difficulties, we had to use some programming ruses which could be better integrated into the specification. From these experiences resulted a set of modifications to the specification which we propose to submit to the community in this paper, in addition to a unified event manager framework

Slack-Time Computation for Temporal Robustness in Embedded Systems

International audienceWe propose to handle execution duration overruns (temporal faults) in real-time embedded systems. When a temporal fault occurs, the slack time can be dynamically determined and assigned to the faulty task in order to complete its treatment. This mechanism improves the temporal robustness of real-time systems. We demonstrate that an approximate slack stealer algorithm like the MASS algorithm is a good solution for real-time embedded systems. We validate the feasibility of this approach by an implementation on the Lego Mindstorm NXT platform

YARTISS: A Tool to Visualize, Test, Compare and Evaluate Real-Time Scheduling Algorithms

International audienceIn this paper, we present a free software written in Java, YARTISS, which is a real-time multiprocessor scheduling simulator. It is aimed at comparing user-customized algorithms with ones from the literature on real-time scheduling. This simulator is designed as an easy-to-use modular tool in which new modules can be added without the need to decompress, edit nor recompile existing parts. It can simulate the execution of a large number of concurrent periodic independent task sets on multiprocessor systems and generate clear visual results of the scheduling process (both schedules and tunable metrics presentations). Other task models are already implemented in the simulator, like graph tasks with precedence constraints and it is easily extensible to other task models. Moreover, YARTISS can simulate task sets in which energy consumption is a scheduling parameter in the same manner as Worst Case Execution Time (WCET)