Celtic languages in European Higher Education: CRAMLAP - Celtic, Regional and Minority Languages Abroad Project

The Celtic, Regional and Minority Languages Abroad
Project (CRAMLAP) is funded by the European Commission
to research the provision and pedagogy of regional
and minority languages outside their national borders in
Europe. The teaching of Celtic languages across Europe
was the focus in year one (2003-2004). This article summarizes
the qualitative data received in response to
questionnaires sent to institutions across Europe offering
Celtic Studies. Responses indicated that Celtic Studies
are quite widely available across Europe. The languages
are taught in comparative linguistics, linguistics and English
departments, with few dedicated Celtic departments
or sections outside the Celtic countries. Irish is supported
abroad by Irish government grant aid which will
become more widely available in the immediate future.
Many of the teachers have considerable experience, but
limited pedagogic training. The lack of suitable teaching
resources is the most commonly expressed concern.

Spectrally bounded operators from von Neumann algebras

We prove that every unital spectrally bounded operator from a properly infinite von Neumann algebra onto a semisimple Banach algebra is a Jordan homomorphism.

Bounded Rationality and Repeated Network Formation

We define a finite-horizon repeated network formation game with consent and study the differences induced by two levels of individual rationality. Perfectly rational players will remain unconnected at the equilibrium, while nonempty equilibrium networks may form when players are assumed to behave as finite automata of limited complexity. We provide structural properties of the sequences of networks which are likely to form in Nash and subgame perfect Nash equilibria of the repeated game. For instance, players can form totally different connected networks at each period or the sequence of networks can exhibit a total order relationship.

Zipf and Type-Token rules for the English, Spanish, Irish and Latin languages

The Zipf curves of log of frequency against log of rank for a large English corpus of 500 million word tokens, 689,000 word types and for a large Spanish corpus of 16 million word tokens, 139,000 word types are shown to have the usual slope close to –1 for rank less than 5,000, but then for a higher rank they turn to give a slope close to –2. This is apparently mainly due to foreign words and place names. Other Zipf curves for highlyinflected Indo-European languages, Irish and ancient Latin, are also given. Because of the larger number of word types per lemma, they remain flatter than the English curve maintaining a slope of –1 until turning points of about ranks 30,000 for Irish and 10,000 for Latin. A formula which calculates the number of tokens given the number of types is derived in terms of the rank at the turning point, 5,000 for both English and Spanish, 30,000 for Irish and 10,000 for Latin.