Daily Papers

Languages can encode temporal subordination lexically, via subordinating conjunctions, and morphologically, by marking the relation on the predicate. Systematic cross-linguistic variation among the former can be studied using well-established token-based typological approaches to token-aligned parallel corpora. Variation among different morphological means is instead much harder to tackle and therefore more poorly understood, despite being predominant in several language groups. This paper explores variation in the expression of generic temporal subordination ('when'-clauses) among the languages of Latin America and the Caribbean, where morphological marking is particularly common. It presents probabilistic semantic maps computed on the basis of the languages of the region, thus avoiding bias towards the many world's languages that exclusively use lexified connectors, incorporating associations between character n-grams and English when. The approach allows capturing morphological clause-linkage devices in addition to lexified connectors, paving the way for larger-scale, strategy-agnostic analyses of typological variation in temporal subordination.

We define a new class of set functions that in addition to being monotone and subadditive, also admit a very limited form of submodularity defined over a permutation of the ground set. We refer to this permutation as a submodular order. This class of functions includes monotone submodular functions as a sub-family. To understand the importance of this structure in optimization problems we consider the problem of maximizing function value under various types of constraints. To demonstrate the modeling power of submodular order functions we show applications in two different settings. First, we apply our results to the extensively studied problem of assortment optimization. While the objectives in assortment optimization are known to be non-submodular (and non-monotone) even for simple choice models, we show that they are compatible with the notion of submodular order. Consequently, we obtain new and in some cases the first constant factor guarantee for constrained assortment optimization in fundamental choice models. As a second application of submodular order functions, we show an intriguing connection to the maximization of monotone submodular functions in the streaming model. We recover some best known guarantees for this problem as a corollary of our results.