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

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

Continuum Nonsimple Loops and 2D Critical Percolation

Substantial progress has been made in recent years on the 2D critical percolation scaling limit and its conformal invariance properties. In particular, chordal SLE6 (the Stochastic Loewner Evolution with parameter k=6) was, in the work of Schramm and of Smirnov, identified as the scaling limit of the critical percolation ``exploration process.'' In this paper we use that and other results to construct what we argue is the full scaling limit of the collection of all closed contours surrounding the critical percolation clusters on the 2D triangular lattice. This random process or gas of continuum nonsimple loops in the plane is constructed inductively by repeated use of chordal SLE6. These loops do not cross but do touch each other -- indeed, any two loops are connected by a finite ``path'' of touching loops.Comment: 16 pages, 3 figure

The Ochodaeidae of Argentina (Coleoptera, Scarabaeoidea)

The Ochodaeidae (Coleoptera: Scarabaeoidea) of Argentina are revised. Previously, two species of Ochodaeinae were known from the country, both in the genus Parochodaeus Nikolajev: P. campsognathus (Arrow) and P. cornutus (Ohaus). An additional 7 species of Parochodaeus from Argentina are described here as new. In addition, Gauchodaeus patagonicus, new genus and new species in the subfamily Chaetocanthinae, is described. "is is the #rst record of the subfamily Chaetocanthinae in South America. Redescriptions, diagnoses, and maps are provided for each species. We also provide a key to genera and a key to species of Parochodaeus of Argentina. With this work, the number of ochodaeid species known from Argentina is increased from 2 to 10.Fil: Paulsen, M. J.. University of Nebraska; Estados UnidosFil: Ocampo, Federico Carlos. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mendoza. Instituto Argentino de Investigaciones de las Zonas Áridas. Provincia de Mendoza. Instituto Argentino de Investigaciones de las Zonas Áridas. Universidad Nacional de Cuyo. Instituto Argentino de Investigaciones de las Zonas Áridas; Argentin