Privileged Words and Sturmian Words

This dissertation has two almost unrelated themes: privileged words and Sturmian words. Privileged words are a new class of words introduced recently. A word is privileged if it is a complete first return to a shorter privileged word, the shortest privileged words being letters and the empty word. Here we give and prove almost all results on privileged words known to date. On the other hand, the study of Sturmian words is a well-established topic in combinatorics on words. In this dissertation, we focus on questions concerning repetitions in Sturmian words, reproving old results and giving new ones, and on establishing completely new research directions. The study of privileged words presented in this dissertation aims to derive their basic properties and to answer basic questions regarding them. We explore a connection between privileged words and palindromes and seek out answers to questions on context-freeness, computability, and enumeration. It turns out that the language of privileged words is not context-free, but privileged words are recognizable by a linear-time algorithm. A lower bound on the number of binary privileged words of given length is proven. The main interest, however, lies in the privileged complexity functions of the Thue-Morse word and Sturmian words. We derive recurrences for computing the privileged complexity function of the Thue-Morse word, and we prove that Sturmian words are characterized by their privileged complexity function. As a slightly separate topic, we give an overview of a certain method of automated theorem-proving and show how it can be applied to study privileged factors of automatic words. The second part of this dissertation is devoted to Sturmian words. We extensively exploit the interpretation of Sturmian words as irrational rotation words. The essential tools are continued fractions and elementary, but powerful, results of Diophantine approximation theory. With these tools at our disposal, we reprove old results on powers occurring in Sturmian words with emphasis on the fractional index of a Sturmian word. Further, we consider abelian powers and abelian repetitions and characterize the maximum exponents of abelian powers with given period occurring in a Sturmian word in terms of the continued fraction expansion of its slope. We define the notion of abelian critical exponent for Sturmian words and explore its connection to the Lagrange spectrum of irrational numbers. The results obtained are often specialized for the Fibonacci word; for instance, we show that the minimum abelian period of a factor of the Fibonacci word is a Fibonacci number. In addition, we propose a completely new research topic: the square root map. We prove that the square root map preserves the language of any Sturmian word. Moreover, we construct a family of non-Sturmian optimal squareful words whose language the square root map also preserves.This construction yields examples of aperiodic infinite words whose square roots are periodic.

High body mass index is not a barrier to physical activity: Analysis of international rugby players' anthropometric data

Recent data indicate that levels of overweight and obesity are increasing at an alarming rate throughout the world. At a population level (and commonly to assess individual health risk), the prevalence of overweight and obesity is calculated using cut-offs of the Body Mass Index (BMI) derived from height and weight. Similarly, the BMI is also used to classify individuals and to provide a notional indication of potential health risk. It is likely that epidemiologic surveys that are reliant on BMI as a measure of adiposity will overestimate the number of individuals in the overweight (and slightly obese) categories. This tendency to misclassify individuals may be more pronounced in athletic populations or groups in which the proportion of more active individuals is higher. This differential is most pronounced in sports where it is advantageous to have a high BMI (but not necessarily high fatness). To illustrate this point we calculated the BMIs of international professional rugby players from the four teams involved in the semi-finals of the 2003 Rugby Union World Cup. According to the World Health Organisation (WHO) cut-offs for BMI, approximately 65% of the players were classified as overweight and approximately 25% as obese. These findings demonstrate that a high BMI is commonplace (and a potentially desirable attribute for sport performance) in professional rugby players. An unanswered question is what proportion of the wider population, classified as overweight (or obese) according to the BMI, is misclassified according to both fatness and health risk? It is evident that being overweight should not be an obstacle to a physically active lifestyle. Similarly, a reliance on BMI alone may misclassify a number of individuals who might otherwise have been automatically considered fat and/or unfit.

Constructing an Internationalisation Readiness Index

In this study we incorporate a pre-internationalisation phase into the traditional Uppsala model of firm internationalisation to address the question: Where does the process begin? We identify through the literature four concepts fundamental to the ability of a firm to begin internationalisation of its operations: stimuli, attitudinal/psychological commitment, resources and lateral rigidity. Through a survey of 274 Australian exporting and non-exporting firms we collect data relating to the four pre-internationalisation concepts. An internationalisation readiness index is constructed and applied to some representative cases to establish its validity as a diagnostic tool.

Developing a rural land investment performance index for New Zealand

Agricultural production is one of the major industries in New Zealand and accounts for over 60% of all export trade. The farming industry comprises 70,000 entities ranging in size from small individual run farms to large corporate operations. The reliance of the New Zealand economy to the international rural sector has seen considerable volatility in the rural land markets over the past four decades, with significant shifts in rural land prices based on location, land use and underlying international rural commodity prices. With the increasing attention being paid to the rural sector, especially in relation to food production and bio-fuels, there has been an increasing corporate interest in rural land ownership in relatively low subsidised agricultural producing countries such as New Zealand and Australia. A factor that has limited this participation of institutional investors previously has been a lack of reliable and up-to-date investment performance data for this asset class. This paper is the initial starting phase in the development of a New Zealand South Island rural land investment performance index and covers the period 1990-2007. The research in this paper analyses all rural sales transactions in the South Island and develops a capital return index for rural property based on major rural property land use. Additional work on this index will cover both total return performance and geographic location.

Increase in Body Mass Index decreases body satisfaction of their abdominal, arm and thigh regions in young Japanese women [in Japanese]

The aim of the present study was to examine body concern and satisfactions in 191 female university students and their relationships with measured body composition and circumferences of selected body parts. Body composition and circumference measurements of participants were conducted after obtaining their consent. Body concern and satisfaction were determined using the Body Shape Questionnaire (BSQ) and the Body parts and General subscales from the Body Satisfaction Scales (BSS). Increase in body composition and circumferences were associated with decrease in body concern and satisfaction. Increase in body size, including circumferences did not decrease whole body satisfaction but increased dissatisfaction at the abdominal, arm and thigh regions.