We developed a version of the Joanisse and Seidenberg (1999) past-tense model to address two issues: whether the model’s performance depended on the use of localist semantic representations, and the challenges to this account presented by a patient who was impaired in generating irregular past tenses despite apparently intact semantics. The model also demonstrates the frequency by regularity in...

The construction of joins and secant varieties is studied in the combinatorial context of monomial ideals. For ideals generated by quadratic monomials, the generators of the secant ideals are obstructions to graph colorings, and this leads to a commutative algebra version of the Strong Perfect Graph Theorem. Given any projective variety and any term order, we explore whether the initial ideal o...

Perfect graphs were defined by Claude Berge in the 1960s. They are important objects for graph theory, linear programming and combinatorial optimization. Claude Berge made a conjecture about them, that was proved by Chudnovsky, Robertson, Seymour and Thomas in 2002, and is now called the strong perfect graph theorem. This is a survey about perfect graphs, mostly focused on the strong perfect gr...

In recent years there has been renewed discussion in the linguistic literature of periphrases, that is syntactic constructions that express information similar to that realised by inflection and thus seem to straddle the syntax–morphology divide. Structures like the English perfect or progressive are without doubt composed of more than one syntactic element, but at the same time the information...