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Linguistic borrowing is the phenomenon of transferring linguistic constructions (lexical, phonological, morphological, and syntactic) from a donor language to a recipient language as a result of contacts between communities speaking different languages. Borrowed words are found in all languages, andin contrast to cognate relationshipsborrowing relationships may exist across unrelated languages (for example, about 40% of Swahilis vocabulary is borrowed from the unrelated language Arabic). In this work, we develop a model of morpho-phonological transformations across languages. Its features are based on universal constraints from Optimality Theory (OT), and we show that compared to several standardbut linguistically more naïvebaselines, our OT-inspired model obtains good performance at predicting donor forms from borrowed forms with only a few dozen training examples, making this a cost-effective strategy for sharing lexical information across languages. We demonstrate applications of the lexical borrowing model in machine translation, using resource-rich donor language to obtain translations of out-of-vocabulary loanwords in a lower resource language. Our framework obtains substantial improvements (up to 1.6 BLEU) over standard baselines.