86 research outputs found
Brown's moduli spaces of curves and the gravity operad
This paper is built on the following observation: the purity of the mixed
Hodge structure on the cohomology of Brown's moduli spaces is essentially
equivalent to the freeness of the dihedral operad underlying the gravity
operad. We prove these two facts by relying on both the geometric and the
algebraic aspects of the problem: the complete geometric description of the
cohomology of Brown's moduli spaces and the coradical filtration of cofree
cooperads. This gives a conceptual proof of an identity of Bergstr\"om-Brown
which expresses the Betti numbers of Brown's moduli spaces via the inversion of
a generating series. This also generalizes the Salvatore-Tauraso theorem on the
nonsymmetric Lie operad.Comment: 26 pages; corrected Figure
Dependency structures and lexicalized grammars
In this dissertation, we show that that both the generative capacity and the parsing complexity of lexicalized grammar formalisms are systematically related to structural properties of the dependency structures that these formalisms can induce. Dependency structures model the syntactic dependencies among the words of a sentence. We identify three empirically relevant classes of dependency structures, and show how they can be characterized both in terms of restrictions on the relation between dependency and word-order and within an algebraic framework. In the second part of the dissertation, we develop natural notions of automata and grammars for dependency structures, show how these yield infinite hierarchies of ever more powerful dependency languages, and classify several grammar formalisms with respect to the languages in these hierarchies that they are able to characterize. Our results provide fundamental insights into the relation between dependency structures and lexicalized grammars.In dieser Arbeit zeigen wir, dass sowohl die Ausdrucksmächtigkeit als auch die Verarbeitungskomplexität von lexikalisierten Grammatikformalismen auf systematische Art und Weise von strukturellen Eigenschaften der Dependenzstrukturen abhängen, die diese Formalismen induzieren. Dependenzstrukturen modellieren die syntaktischen Abhängigkeiten zwischen den Wörtern eines Satzes. Wir identifizieren drei empirisch relevante Klassen von Dependenzstrukturen und zeigen, wie sich diese sowohl durch Einschränkungen der Interaktion zwischen Dependenz und Wortstellung, als auch in einem algebraischen Rahmen charakterisieren lassen. Im zweiten Teil der Arbeit entwickeln wir natürliche Begriffe von Automaten und Grammatiken für Dependenzstrukturen, zeigen, wie diese zu unendlichen Hierarchien immer ausdrucksmächtigerer Dependenzsprachen führen, und klassifizieren mehrere Grammatikformalismen in Bezug auf die Sprachen in diesen Hierarchien, die von ihnen charakterisiert werden können. Unsere Resultate liefern grundlegende Einsichten in das Verhältnis zwischen Dependenzstrukturen und lexikalisierten Grammatiken
Projective toric varieties as fine moduli spaces of quiver representations
This paper proves that every projective toric variety is the fine moduli
space for stable representations of an appropriate bound quiver. To accomplish
this, we study the quiver with relations corresponding to the
finite-dimensional algebra where
is a list of line bundles on a
projective toric variety . The quiver defines a smooth projective toric
variety, called the multilinear series , and a map . We provide necessary and sufficient conditions for the induced
map to be a closed embedding. As a consequence, we obtain a new geometric
quotient construction of projective toric varieties. Under slightly stronger
hypotheses on , the closed embedding identifies with the fine
moduli space of stable representations for the bound quiver .Comment: revised version: improved exposition, corrected typos and other minor
change
Strong generative capacity of RST, SDRT and discourse dependency DAGSs
The aim of this paper is to compare the discourse structures proposed in RST, SDRT and dependency DAGs which extend the semantic level of MTT for discourses. The key question is the following: do these formalisms allow the representation of all the discourse structures which correspond to felicitous discourses and exclude those which correspond to infelicitous discourses? Hence the term of “strong generative capacity” taken from formal grammars
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