From surface dependencies towards deeper semantic representations [Semantic representations]

In the past, a divide could be seen between ’deep’ parsers on the one hand, which construct a semantic representation out of their input, but usually have significant coverage problems, and more robust parsers on the other hand, which are usually based on a (statistical) model derived from a treebank and have larger coverage, but leave the problem of semantic interpretation to the user. More recently, approaches have emerged that combine the robustness of datadriven (statistical) models with more detailed linguistic interpretation such that the output could be used for deeper semantic analysis. Cahill et al. (2002) use a PCFG-based parsing model in combination with a set of principles and heuristics to derive functional (f-)structures of Lexical-Functional Grammar (LFG). They show that the derived functional structures have a better quality than those generated by a parser based on a state-of-the-art hand-crafted LFG grammar. Advocates of Dependency Grammar usually point out that dependencies already are a semantically meaningful representation (cf. Menzel, 2003). However, parsers based on dependency grammar normally create underspecified representations with respect to certain phenomena such as coordination, apposition and control structures. In these areas they are too "shallow" to be directly used for semantic interpretation. In this paper, we adopt a similar approach to Cahill et al. (2002) using a dependency-based analysis to derive functional structure, and demonstrate the feasibility of this approach using German data. A major focus of our discussion is on the treatment of coordination and other potentially underspecified structures of the dependency data input. F-structure is one of the two core levels of syntactic representation in LFG (Bresnan, 2001). Independently of surface order, it encodes abstract syntactic functions that constitute predicate argument structure and other dependency relations such as subject, predicate, adjunct, but also further semantic information such as the semantic type of an adjunct (e.g. directional). Normally f-structure is captured as a recursive attribute value matrix, which is isomorphic to a directed graph representation. Figure 5 depicts an example target f-structure. As mentioned earlier, these deeper-level dependency relations can be used to construct logical forms as in the approaches of van Genabith and Crouch (1996), who construct underspecified discourse representations (UDRSs), and Spreyer and Frank (2005), who have robust minimal recursion semantics (RMRS) as their target representation. We therefore think that f-structures are a suitable target representation for automatic syntactic analysis in a larger pipeline of mapping text to interpretation. In this paper, we report on the conversion from dependency structures to fstructure. Firstly, we evaluate the f-structure conversion in isolation, starting from hand-corrected dependencies based on the TüBa-D/Z treebank and Versley (2005)´s conversion. Secondly, we start from tokenized text to evaluate the combined process of automatic parsing (using Foth and Menzel (2006)´s parser) and f-structure conversion. As a test set, we randomly selected 100 sentences from TüBa-D/Z which we annotated using a scheme very close to that of the TiGer Dependency Bank (Forst et al., 2004). In the next section, we sketch dependency analysis, the underlying theory of our input representations, and introduce four different representations of coordination. We also describe Weighted Constraint Dependency Grammar (WCDG), the dependency parsing formalism that we use in our experiments. Section 3 characterises the conversion of dependencies to f-structures. Our evaluation is presented in section 4, and finally, section 5 summarises our results and gives an overview of problems remaining to be solved

Carleson measures and chord-arc curves

Following Semmes and Zinsmeister, we continue the study of Carleson measures and their invariance under pull-back and push-forward operators. We also study the analogous statements for vanishing Carleson measures. As an application, we show that some quotient space of the space of chord-arc curves has a natural complex structure.Comment: 21 page

On the time schedule of Brownian Flights

We are interested on the statistics of the duration of Brownian diffusions started at distance \epsilon from a given boundary and stopped when they hit back the interface.Comment: 9 page

On the Hausdorff dimension of Julia sets of some real polynomials

We show that the supremum for $c$ real of the Hausdorff dimension of the Julia set of the polynomial $z\mapsto z^d+c$ ($d$ is an even natural number) is greater than $2d/(d+1)$.Comment: 10 page, 4 figure

Variations of Hausdorff Dimension in the Exponential Family

In this paper we deal with the following family of exponential maps $(f_\lambda:z\mapsto \lambda(e^z-1))_{\lambda\in [1,+\infty)}$. Denoting $d(\lambda)$ the hyperbolic dimension of $f_\lambda$. It is known that the function $\lambda\mapsto d(\lambda)$ is real analytic in $(1,+\infty)$, and that it is continuous in $[1,+\infty)$. In this paper we prove that this map is C$^1$ on $[1,+\infty)$, with $d'(1^+)=0$. Moreover, depending on the value of $d(1)$, we give estimates of the speed of convergence towards 0.Comment: 32 pages. A para\^itre dans Annales Academi{\ae} Scientiarum Fennic{\ae} Mathematic

On The Brownian Loop Measure

In 2003 Lawler and Werner introduced the Brownian loop measure and studied some of its properties. Cardy and Gamsa has predicted a formula for the total mass of the Brownian loop measure on the set of simple loops in the upper half plane and disconnect two given points from the boundary. In this paper we give a rigorous proof of the formula using a result by Beliaev and Viklund and heavy computations.Comment: 19 page

Integral means spectrum of whole-plane SLE

We complete the mathematical analysis of the fine structure of harmonic measure on SLE curves that was initiated by Beliaev and Smirnov, as described by the averaged integral means spectrum. For the unbounded version of whole-plane SLE as studied by Duplantier, Nguyen, Nguyen and Zinsmeister, and Loutsenko and Yermolayeva, a phase transition has been shown to occur for high enough moments from the bulk spectrum towards a novel spectrum related to the point at infinity. For the bounded version of whole-plane SLE studied here, a similar transition phenomenon, now associated with the SLE origin, is proved to exist for low enough moments, but we show that it is superseded by the earlier occurrence of the transition to the SLE tip spectrum.Comment: 14 pages, 1 figure; final versio