This is an introductory exposition to background material useful to appreciate various formulations of the Mordell–Lang conjecture (now established by recent spectacular work due to Vojta, Faltings, Hrushovski, Buium, Voloch, and others). It gives an exposition of some of the elementary and standard constructions of algebro-geometric models (rather than model-theoretic ones) with applications (...

Inference in Bayesian statistics involves the evaluation of marginal likelihood integrals. We present algebraic algorithms for computing such integrals exactly for discrete data of small sample size. Our methods apply to both uniform priors and Dirichlet priors. The underlying statistical models are mixtures of independent distributions, or, in geometric language, secant varieties of Segre-Vero...

We present here new hierarchies of literal varieties of languages. Each language under consideration is a disjoint union of a certain collection of “basic” languages described here. Our classes of languages correspond to certain literal varieties of homomorphisms from free monoids onto nilpotent groups of class ≤ 2.

Inference in Bayesian statistics involves the evaluation of marginal likelihood integrals. We present algebraic algorithms for computing such integrals exactly for discrete data of small sample size. The underlying statistical models are mixtures of independent distributions, or, in geometric language, secant varieties of Segre-Veronese varieties.

This paper reports the results of the WordNet.PTglobal project, an extension of WordNet.PT to all Portuguese varieties. Profiting from a theoretical model of high level explanatory adequacy and from a convenient and flexible development tool, WordNet.PTglobal achieves a rich and multipurpose lexical resource, suitable for contrastive studies and for a vast range of language-based applications c...

Code-switching (CS), an alternation between two or more languages or language varieties, has long been researched in language education. A great number of studies by applied linguists have explored the reasons for, and the potential usages of code-switching in foreign language education over the past years. This study explores the perceptions of English language learners across various proficie...

Developing resources which can be used for Natural Language Processing is an extremely difficult task for any language, but is even more so for less privileged (or less computerized) languages. One way to overcome this difficulty is to adapt the resources of a linguistically close resource rich language. In this paper we discuss how the cost of such adaption can be estimated using subjective an...