Computing the Cassels–Tate pairing on the 3-Selmer group of an elliptic curve

We extend the method of Cassels for computing the Cassels-Tate pairing on the 2-Selmer group of an elliptic curve, to the case of 3-Selmer groups. This requires significant modifications to both the local and global parts of the calculation. Our method is practical in sufficiently small examples, and can be used to improve the upper bound for the rank of an elliptic curve obtained by 3-descent.

Evidence from neurolinguistic methodologies: can it actually inform linguistic/ language acquisition theories and translate to evidence-based applications?

This special issue is a testament to the recent burgeoning interest by theoretical linguists, language acquisitionists and teaching practitioners in the neuroscience of language. It offers a highly valuable, state-of-the-art overview of the neurophysiological methods that are currently being applied to questions in the field of second language (L2) acquisition, teaching and processing. Research in the area of neurolinguistics has developed dramatically in the past twenty years, providing a wealth of exciting findings, many of which are discussed in the papers in this volume. The goal of this commentary is twofold. The first is to critically assess the current state of neurolinguistic data from the point of view of language acquisition and processing—informed by the papers that comprise this special issue and the literature as a whole—pondering how the neuroscience of language/processing might inform us with respect to linguistic and language acquisition theories. The second goal is to offer some links from implications of exploring the first goal towards informing language teachers and the creation of linguistically and neurolinguistically-informed evidence-based pedagogies for non-native language teaching.