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.

Saint Mathew Law and Bonini Paradox in Textual Theory of Complex Models

The mathematical models of the complex reality are texts belonging to a certain literature that is written in a semi-formal language, denominated L(MT) by the authors whose laws linguistic mathematics have been previously defined. This text possesses linguistic entropy that is the reflection of the physical entropy of the processes of real world that said text describes. Through the temperature of information defined by Mandelbrot, the authors begin a text-reality thermodynamic theory that drives to the existence of information attractors, or highly structured point, settling down a heterogeneity of the space text, the same one that of ontologic space, completing the well-known law of Saint Mathew, of the General Theory of Systems and formulated by Margalef saying: “To the one that has more he will be given, and to the one that doesn't have he will even be removed it little that it possesses.

The Size Distribution of US Banks and Credit Unions

This study examines the firm size distribution of US banks and credit unions. A truncated lognormal distribution describes the size distribution, measured using assets data, of a large population of small, community-based commercial banks. The size distribution of a smaller but increasingly dominant cohort of large banks, which operate a high-volume low-cost retail banking model, exhibits power-law behaviour. There is a progressive increase in skewness over time, and Zipf’s Law is rejected as a descriptor of the size distribution in the upper tail. By contrast, the asset size distribution of the population of credit unions conforms closely to the lognormal distribution.

The size distribution of all Cambodian establishments

This paper presents empirical evidence on the size distribution of all Cambodian establishments in the nonfarm sector for 2009. Small- and large-scale establishments account for the largest share of employment, pointing to a “missing middle” that is commonly observed in developing countries. The analysis provides little evidence for Zipf’s law because Cambodian industry is characterized by a more dense mass of small establishments than the Zipf distribution would predict.

A evolução da distribuição do tamanho das cidades: caso do nordeste brasileiro

A proposta deste artigo foi estudar a evolução do tamanho das cidades dos estados do nordeste do Brasil para os anos de 1990, 2000 e 2010 através da regularidade empírica conhecida como lei de Zipf, a qual pode ser representada por meio da distribuição de Pareto. Por meio da análise na dinâmica da distribuição das populações através do tempo, o crescimento urbano revelou uma persistência hierárquica das cidades de Salvador, Fortaleza e Recife, enquanto que São Luís experimentou o quarto lugar no rankinging das maiores cidades, que persistiu nas duas últimas décadas. A lei de Zipf não se verificou quando se considerou as cidades do Nordeste em conjunto, que pode ser devido ao menor grau de desenvolvimento urbano das cidades dessa região. Na análise dos estados em separado, também não se observou a lei de Zipf, embora tenha se verificado a lei de Gibrat, a qual postula que o crescimento das cidades é independente de seu tamanho. Por fim, acredita-se que a instalação do complexo minerometalúrgico do Maranhão tenha contribuído para o desenvolvimento e para a redução da desigualdade urbana intracidade nesta área.

Engaging Students in the Implementation of Criterion Referenced Assessment in First Year Law

The Queensland University of Technology (QUT) University Academic Board approved a new QUT Assessment Policy in September 2003, which requires a criterion-referenced approach as opposed to a norm-referenced approach to assessment across the university(QUT,MOPP,2003). In 2004, the QUT Law School embarked upon a process of awareness raising about criterion-referenced assessment amongst staff and from 2004 – 2005 staggered the implementation of criterion-referenced assessment in all first year core undergraduate law units. This paper will briefly discuss the benefits and potential pitfalls of criterion referenced assessment and the context for implementing it in the first year law program, report on student’s feedback on the introduction of criterion referenced assessment and the strategies adopted in 2005 to engage students more fully in criterion referenced assessment processes to enhance their learning outcomes.

Increasing relevance and interest : teaching environmental and planning law to built environment students

A new approach was taken to delivering a challenging "stewarship of land" unit to over 350 predominantly first year built environment students stewardship. The new approach involved incorporating environmental and planning law into the syllabus, exposing students to a wide range of statutes, selecting legal cases according to a et of criteria and revisiting the material using different modes of delivery and teaching resources. To evaluate the effectiveness of the new approach, the students were surveyed to elicit their learning experience and preferences. The survey found that most students perceived learning about environmental and planning law, including legal cases, worthwhile.----- Areas identified by the surcey for improvement included the perception by some students that: environmenatl and planning law is irrelevant to their discipline and future caree; studying law is dull and sometimes daunting; and the prescribed reading could be omitted.----- To address student perceptions, it is proposed to reorder the topics commencing with local, charismatic topics, while explanding international content and cases, to enlarge and enhance the repertoire of video clips to include sites of legal cawses and development projects, and to reformat the online weekly quizzes to promote reading of primary material.----- Overall, the approach to teaching environmental and planning law to built environment students, including the criteria for selecting legal cases, described in this paper, was found to be effective.

Contemporary issues in Australian family law: Do we need a more unified and interventionist judicial model

Recent decisions of the Family Court of Australian reflect concerns over the adversarial nature of the legal process. The processes and procedures of the judicial system militate against a detailed examination of the issues and rights of the parties in dispute. The limitations of the family law framework are particularly demonstrated in disputes over the custody of children where the Court has tended to neglect the rights and interests of the primary carer. An alternative "unified family court" framework will be examined in which the Court pursues a more active and interventionist approach in the determination of family law disputes.