Extending a result by Alon, Linial, and Meshulam to abelian groups, we prove that if G is a finite abelian group of exponent m and S is a sequence of elements of G such that any subsequence of S consisting of at least $$|S| - m\ln |G|$$ elements generates G, then S is an additive basis of G . We also prove that the additive span of any l generating sets of G contains a coset of a subgroup of size at least $$|G{|^{1 - c{ \in ^l}}}$$ for certain c=c(m) and $$ \in=\in (m) < 1$$; we use the probabilistic method to give sharper values of c(m) and $$ \in (m)$$ in the case when G is a vector space; and we give new proofs of related known results.

In a previous study (Sarré, Grosbois & Brudermann, 2019), we explored the effects of various corrective feedback (CF) strategies on interlanguage development for the online component of a blended English as a foreign language (EFL) course we had designed and implemented. Our results showed that unfocused indirect CF (feedback on all error types through the provision of metalinguistic comments on the nature of the errors made) combined with extra computer-mediated micro-tasks was the most efficient CF type to foster writing accuracy development in our context. Following up on this study, this paper further explores the effects of this specific CF type on learners’ written accuracy development in an online EFL course designed for freshmen STEM (science, technology, engineering, and mathematics) students. In the online course under study, this specific CF type was experimented with different cohorts of STEM learners (N = 1,150) over a five-year period (from 2014 to 2019) and was computer-assisted: CF provision online by a human tutor was combined with predetermined CF comments. The aim of this paper is to investigate the impact of this specific CF strategy on error types. In this respect, the data yield encouraging results in terms of writing accuracy development when learners benefit from this computer-assisted specific CF. This study thus helps to gain a better understanding of the role that CF plays in shaping students’ revision processes and could inform language (teacher) education regarding the use of digital tools for the development of foreign language accuracy and the issues related to online CF provision.

With the widespread development of leg exoskeletons to provide external force-based repetitive training for gait rehabilitation, the prospect of undesired movement adaptation due to applied forces and imposed constraints require adequate investigation. A cable-driven leg exoskeleton, CDLE, presents a lightweight, flexible, and redundantly actuated architecture that enables the possibility of system parameters modulation to alter human–robot interaction while applying the desired forces. In this work, multi-joint stiffness performance of CDLE is formulated to systematically analyze human–CDLE interaction. Further, potential alterations in CDLE architecture are presented to tune human–CDLE interaction that favors the desired human leg movement during a gait rehabilitation paradigm.