Finiteness and children with specific language impairment: an exploratory study

Children with specific language impairment (SLI) are well known for their difficulties in mastering the inflectional paradigms; in the case of learning German they also have problems with the appropriate verb position, in particular with the verb in second position. This paper explores the possibilities of applying a broader concept of finiteness to data from children with SLI in order to put their deficits, or rather their skills, into a wider perspective. The concept, as developed by Klein (1998, 2000), suggests that finiteness is tied to the assertion that a certain state of affairs is valid with regard to some topic time; that is, finiteness relates the propositional content to the topic component. Its realization involves the interaction of various grammatical devices and, possibly, lexical means like temporal adverbs. Furthermore, in the acquisition of finiteness it has been found that scope particles play a major role in both first- and second-language learning. The purpose of this paper is to analyze to what extent three German-learning children with SLI have mastered these grammatical and lexical means and to pinpoint the phase in the development of finiteness they have reached. The data to be examined are mostly narrative and taken from conversations and experiments. It will be shown that each child chooses a different developmental path to come to grips with the interaction of these devices

Solving loop equations by Hitchin systems via holography in large-N QCD_4

For (planar) closed self-avoiding loops we construct a "holographic" map from the loop equations of large-N QCD_4 to an effective action defined over infinite rank Hitchin bundles. The effective action is constructed densely embedding Hitchin systems into the functional integral of a partially quenched or twisted Eguchi-Kawai model, by means of the resolution of identity into the gauge orbits of the microcanonical ensemble and by changing variables from the moduli fields of Hitchin systems to the moduli of the corresponding holomorphic de Rham local systems. The key point is that the contour integral that occurs in the loop equations for the de Rham local systems can be reduced to the computation of a residue in a certain regularization. The outcome is that, for self-avoiding loops, the original loop equations are implied by the critical equation of an effective action computed in terms of the localisation determinant and of the Jacobian of the change of variables to the de Rham local systems. We check, at lowest order in powers of the moduli fields, that the localisation determinant reproduces exactly the first coefficient of the beta function.Comment: 65 pages, late