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Alexander Clark

Publications and source records attributed to Alexander Clark.

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Classification and nonexistence for $t$-structures on derived categories of schemes

Given a suitable Noetherian scheme, we classify tensor $t$-structures on the bounded derived category of coherent sheaves and its variants with prescribed support. Furthermore, we show that the existence of such $t$-structures restricting to perfect complexes detects regularity, recovering a theorem of Neeman in the affine case by different methods. Our tools establish local-to-global principles for tensor $t$-structures.

math.AG

Unsupervised Language Acquisition: Theory and Practice

In this thesis I present various algorithms for the unsupervised machine learning of aspects of natural languages using a variety of statistical models. The scientific object of the work is to examine the validity of the so-called Argument from the Poverty of the Stimulus advanced in favour of the proposition that humans have language-specific innate knowledge. I start by examining an a priori argument based on Gold's theorem, that purports to prove that natural languages cannot be learned, and some formal issues related to the choice of statistical grammars rather than symbolic grammars. I present three novel algorithms for learning various parts of natural languages: first, an algorithm for the induction of syntactic categories from unlabelled text using distributional information, that can deal with ambiguous and rare words; secondly, a set of algorithms for learning morphological processes in a variety of languages, including languages such as Arabic with non-concatenative morphology; thirdly an algorithm for the unsupervised induction of a context-free grammar from tagged text. I carefully examine the interaction between the various components, and show how these algorithms can form the basis for a empiricist model of language acquisition. I therefore conclude that the Argument from the Poverty of the Stimulus is unsupported by the evidence.

cs.CL