The interaction of gradient and categorical processes of long-distance vowel-to-vowel assimilation in Kazan Tatar

Vowel harmony and vowel-to-vowel coarticulation are long-distance assimilatory processes wherein certain vowels trigger systematic changes in adjacent vowels; harmony effects phonological change, resulting in phonemic alternation, while coarticulation effects phonetic change. This thesis offers a novel acoustic analysis of the coarticulatory processes present in disharmonic words in Kazan Tatar, a language with left-to-right palatal harmony. While right-to-left palatal coarticulation is found to be widespread, left-to-right palatal coarticulation is virtually nonexistent in Tatar. It is hypothesized that gradient and categorical processes sharing the same triggers, targets, target feature, and direction cannot coexist; the diachronic implication for Tatar is that, once coarticulation was phonologized into harmony, the original coarticulatory process that gave rise to harmony was eradicated. This two-way interaction between gradient and categorical processes argues in favor of the distinctly phonological nature of vowel harmony and against a phonetic account of harmony. ^ In the second part, an acoustic analysis of rounding assimilation in Kazan Tatar is undertaken. The acoustic data suggests that neither rounding harmony nor labial coarticulation are present in Kazan Tatar

On a generalization of iterated and randomized rounding

We give a general method for rounding linear programs that combines the commonly used iterated rounding and randomized rounding techniques. In particular, we show that whenever iterated rounding can be applied to a problem with some slack, there is a randomized procedure that returns an integral solution that satisfies the guarantees of iterated rounding and also has concentration properties. We use this to give new results for several classic problems where iterated rounding has been useful