Extending Zipf’s law to n-grams for large corpora

Experiments show that for a large corpus, Zipf’s law does not hold for all rank of words: the frequencies fall below those predicted by Zipf’s law for ranks greater than about 5,000 word types in the English language and about 30,000 word types in the inflected languages Irish and Latin. It also does not hold for syllables or words in the syllable-based languages, Chinese or Vietnamese. However, when single words are combined together with word n-grams in one list and put in rank order, the frequency of tokens in the combined list extends Zipf’s law with a slope close to -1 on a log-log plot in all five languages. Further experiments have demonstrated the validity of this extension of Zipf’s law to n-grams of letters, phonemes or binary bits in English. It is shown theoretically that probability theory
alone can predict this behavior in randomly created n-grams of binary bits.

The Great War in Irish Poetry

Second edition, 2003.

Troubled Geographies: A Spatial History of Religion and Society in Ireland

Ireland’s landscape is marked by fault lines of religious, ethnic, and political identity that have shaped its troubled history. Troubled Geographies maps this history by detailing the patterns of change in Ireland from 16th century attempts to “plant” areas of Ireland with loyal English Protestants to defend against threats posed by indigenous Catholics, through the violence of the latter part of the 20th century and the rise of the “Celtic Tiger.” The book is concerned with how a geography laid down in the 16th and 17th centuries led to an amalgam based on religious belief, ethnic/national identity, and political conviction that continues to shape the geographies of modern Ireland. Troubled Geographies shows how changes in religious affiliation, identity, and territoriality have impacted Irish society during this period. It explores the response of society in general and religion in particular to major cultural shocks such as the Famine and to long term processes such as urbanization.