The number of point-splitting circles

Let S be a set of 2n+1 points in the plane such that no three are collinear and no four are concyclic. A circle will be called point-splitting if it has 3 points of S on its circumference, n-1 points in its interior and n-1 in its exterior. We show the surprising property that S always has exactly n^2 point- splitting circles, and prove a more general result.Comment: 12 pages, 4 figure

Transfer of Company’s Registered Office and Forum-Shopping in International Insolvency Cases: an Important Decision from Italy

The Italian Supreme Court (Corte di Cassazione) has issued an important decision on companies’ freedom of establishment in the European Union (EU) and on jurisdiction over insolvency proceedings. It was a typical forum-shopping case in insolvency situations, in which a company decides to shift its registered office abroad before a court from its original country declares the insolvency. The Cassazione did not apply EC-Regulation 1346/2000 on cross-border insolvency, but declared the company as liquidated because of the transfer of the registered office. This solution leaves many questions unclear, both under EC-freedom of establishment and under jurisdiction rules for cross-border insolvenc

Systematic numerical investigation of the role of hierarchy in heterogeneous bio-inspired materials

It is well known that hierarchical structure is an important feature in biological materials to optimise various properties, including mechanical ones. It is however still unclear how these hierarchical architectures can improve material characteristics, for example strength. Also, the transposition of these structures from natural to artificial bioinspired materials remains to be perfected. In this paper, we introduce a numerical method to evaluate the strength of fibre-based heterogeneous biological materials and systematically investigate the role of hierarchy. Results show that hierarchy indeed plays an important role and that it is possible to “tune” the strength of bio-inspired materials in a wide range of values, in some cases improving the strength of non-hierarchical structures considerably

Language modeling and transcription of the TED corpus lectures

Transcribing lectures is a challenging task, both in acoustic and in language modeling. In this work, we present our first results on the automatic transcription of lectures from the TED corpus, recently released by ELRA and LDC. In particular, we concentrated our effort on language modeling. Baseline acoustic and language models were developed using respectively 8 hours of TED transcripts and various types of texts: conference proceedings, lecture transcripts, and conversational speech transcripts. Then, adaptation of the language model to single speakers was investigated by exploiting different kinds of information: automatic transcripts of the talk, the title of the talk, the abstract and, finally, the paper. In the last case, a 39.2% WER was achieved

Critical Percolation Exploration Path and SLE(6): a Proof of Convergence

It was argued by Schramm and Smirnov that the critical site percolation exploration path on the triangular lattice converges in distribution to the trace of chordal SLE(6). We provide here a detailed proof, which relies on Smirnov's theorem that crossing probabilities have a conformally invariant scaling limit (given by Cardy's formula). The version of convergence to SLE(6) that we prove suffices for the Smirnov-Werner derivation of certain critical percolation crossing exponents and for our analysis of the critical percolation full scaling limit as a process of continuum nonsimple loops.Comment: 45 pages, 14 figures; revised version following the comments of a refere