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In cloud computing systems, elastic events and stragglers increase the uncertainty of the system, leading to computation delays. Coded elastic computing (CEC) introduced by Yang et al. in 2018 is a framework which mitigates the impact of elastic events using Maximum Distance Separable (MDS) coded storage. It proposed a CEC scheme for both matrix-vector multiplication and general matrix-matrix multiplication applications. However, in these applications, the proposed CEC scheme cannot tolerate stragglers due to the limitations imposed by MDS codes. In this paper we propose a new elastic computing scheme using uncoded storage and Lagrange coded computing approaches. The proposed scheme can effectively mitigate the effects of both elasticity and stragglers. Moreover, it produces a lower complexity and smaller recovery threshold compared to existing coded storage based schemes. 

Abstract The ionization fraction is a key figure of merit for optimizing the performance of plasma device. This work presents an optical emission spectroscopy (OES) method to determine the ionization fraction in low-temperature xenon plasma. The emission line-ratio of xenon ionic and atomic 6p–6stransitions is used in this method. A comprehensive collisional-radiative model developed in our previous work is employed to describe the relationship between the line-ratios and the plasma parameters. It is found that some special line-ratios have a sensitive relationship to the ionization fraction, e.g. the ratio of the 460.30 nm line and 828.01 nm lines. These line-ratios are selected for the diagnostic method. The method is demonstrated in a magnetized discharge chamber. The axially-resolved emission spectra of the ionization chamber are measured, and from those the ionization fraction along the chamber axis is determined via the OES method. The axially-resolved ionization fraction is found to be dependent on the magnetic field and agrees well with those obtained from a Langmuir probe. In the experiment, the probe is overheated under some conditions, possibly due to the bombardment by energetic particles. In this case, no results can be obtained from the probe, while the OES method can still obtain reasonable results. Combined with optical tomography and spectral imaging technology, the OES method can also provide the spatial distribution of the ionization fraction, which is needed for revealing the discharge mechanisms of plasma devices.