Unsupervised Terminological Ontology Learning based on Hierarchical Topic Modeling

In this paper, we present hierarchical relationbased latent Dirichlet allocation (hrLDA), a data-driven hierarchical topic model for extracting terminological ontologies from a large number of heterogeneous documents. In contrast to traditional topic models, hrLDA relies on noun phrases instead of unigrams, considers syntax and document structures, and enriches topic hierarchies with topic relations. Through a series of experiments, we demonstrate the superiority of hrLDA over existing topic models, especially for building hierarchies. Furthermore, we illustrate the robustness of hrLDA in the settings of noisy data sets, which are likely to occur in many practical scenarios. Our ontology evaluation results show that ontologies extracted from hrLDA are very competitive with the ontologies created by domain experts

Comparing hierarchies of total functionals

In this paper we consider two hierarchies of hereditarily total and continuous functionals over the reals based on one extensional and one intensional representation of real numbers, and we discuss under which asumptions these hierarchies coincide. This coincidense problem is equivalent to a statement about the topology of the Kleene-Kreisel continuous functionals. As a tool of independent interest, we show that the Kleene-Kreisel functionals may be embedded into both these hierarchies.Comment: 28 page

On Integrability and Exact Solvability in Deterministic and Stochastic Laplacian Growth

We review applications of theory of classical and quantum integrable systems to the free-boundary problems of fluid mechanics as well as to corresponding problems of statistical mechanics. We also review important exact results obtained in the theory of multi-fractal spectra of the stochastic models related to the Laplacian growth: Schramm-Loewner and Levy-Loewner evolutions

The augmented marking complex of a surface

We build an augmentation of the Masur-Minsky marking complex by Groves-Manning combinatorial horoballs to obtain a graph we call the augmented marking complex, $\mathcal{AM}(S)$. Adapting work of Masur-Minsky, we prove that $\mathcal{AM}(S)$ is quasiisometric to Teichm\"uller space with the Teichm\"uller metric. A similar construction was independently discovered by Eskin-Masur-Rafi. We also completely integrate the Masur-Minsky hierarchy machinery to $\mathcal{AM}(S)$ to build flexible families of uniform quasigeodesics in Teichm\"uller space. As an application, we give a new proof of Rafi's distance formula for the Teichm\"uller metric.Comment: 30 pages; significantly rewritten to strengthen main construction