Exploring Task Mappings on Heterogeneous MPSoCs using a Bias-Elitist Genetic Algorithm

Exploration of task mappings plays a crucial role in achieving high performance in heterogeneous multi-processor system-on-chip (MPSoC) platforms. The problem of optimally mapping a set of tasks onto a set of given heterogeneous processors for maximal throughput has been known, in general, to be NP-complete. The problem is further exacerbated when multiple applications (i.e., bigger task sets) and the communication between tasks are also considered. Previous research has shown that Genetic Algorithms (GA) typically are a good choice to solve this problem when the solution space is relatively small. However, when the size of the problem space increases, classic genetic algorithms still suffer from the problem of long evolution times. To address this problem, this paper proposes a novel bias-elitist genetic algorithm that is guided by domain-specific heuristics to speed up the evolution process. Experimental results reveal that our proposed algorithm is able to handle large scale task mapping problems and produces high-quality mapping solutions in only a short time period.Comment: 9 pages, 11 figures, uses algorithm2e.st

The Epstein-Glaser causal approach to the Light-Front QED4_{4}. I: Free theory

In this work we present the study of light-front field theories in the realm of axiomatic theory. It is known that when one uses the light-cone gauge pathological poles $(k^{+}) ^{-n}$ arises, demanding a prescription to be employed in order to tame these ill-defined poles and to have correct Feynman integrals due to the lack of Wick rotation in such theories. In order to shed a new light on this long standing problem we present here a discussion based on the use rigorous mathematical machinery of distributions combined with physical concepts, such as causality, to show how to deal with these singular propagators in a general fashion without making use of any prescription. The first step of our development will consist in showing how analytic representation for propagators arises by requiring general physical properties in the framework of Wightman's formalism. From that we shall determine the equal-time (anti)commutation relations in the light-front form for the scalar, fermionic fields and for the dynamical components of the electromagnetic field. In conclusion, we introduce the Epstein-Glaser causal method in order to have a mathematical rigorous treatment of the free propagators of the theory, allowing us to discuss the general treatment for propagators of the type $(k^{+}) ^{-n}$. Moreover, we show that at given conditions our results reproduce known prescriptions in the literature.Comment: 34 pages, v2 matching the published versio

Cosmological perturbations in FRW model with scalar field within Hamilton-Jacobi formalism and symplectic projector method

The Hamilton-Jacobi analysis is applied to the dynamics of the scalar fluctuations about the Friedmann-Robertson-Walker (FRW). The gauge conditions are found from the consistency conditions. The physical degrees of freedom of the model are obtain by symplectic projector method. The role of the linearly dependent Hamiltonians and the gauge variables in Hamilton-Jacobi formalism is discussed.Comment: 11 page

Causal approach for the electron-positron scattering in Generalized Quantum Electrodynamics

In this paper we study the generalized electrodynamics contribution for the electron-positron scattering process, $e^{-}e^{+}\rightarrow e^{-}e^{+}$, the Bhabha scattering. Within the framework of the standard model, for energies larger when compared to the electron mass, we calculate the cross section expression for the scattering process. This quantity is usually calculated in the framework of the Maxwell electrodynamics and, by phenomenological reasons, corrected by a cut-off parameter. On the other hand, by considering the generalized electrodynamics instead of Maxwell's, we can show that the effects played by the Podolsky mass is actually a natural cut-off parameter for this scattering process. Furthermore, by means of experimental data of Bhabha scattering we will estimate its lower bound value. Nevertheless, in order to have a mathematically well defined description of our study we shall present our discussion in the framework of the Epstein-Glaser causal theory.Comment: 24 pages, V2 to match published versio

A Characterization of Deterministic Sampling Patterns for Low-Rank Matrix Completion

Low-rank matrix completion (LRMC) problems arise in a wide variety of applications. Previous theory mainly provides conditions for completion under missing-at-random samplings. This paper studies deterministic conditions for completion. An incomplete $d \times N$ matrix is finitely rank-$r$ completable if there are at most finitely many rank-$r$ matrices that agree with all its observed entries. Finite completability is the tipping point in LRMC, as a few additional samples of a finitely completable matrix guarantee its unique completability. The main contribution of this paper is a deterministic sampling condition for finite completability. We use this to also derive deterministic sampling conditions for unique completability that can be efficiently verified. We also show that under uniform random sampling schemes, these conditions are satisfied with high probability if $O(\max\{r,\log d\})$ entries per column are observed. These findings have several implications on LRMC regarding lower bounds, sample and computational complexity, the role of coherence, adaptive settings and the validation of any completion algorithm. We complement our theoretical results with experiments that support our findings and motivate future analysis of uncharted sampling regimes.Comment: This update corrects an error in version 2 of this paper, where we erroneously assumed that columns with more than r+1 observed entries would yield multiple independent constraint