Binomial Skew Polynomial Rings, Artin-Schelter Regularity, and Binomial Solutions of the Yang-Baxter Equation

2000 Mathematics Subject Classification: Primary 81R50, 16W50, 16S36, 16S37.

Algebro-Geometric Aspects of the Classical Yang-Baxter Equation

In this thesis we consider algebro-geometric aspects of the Classical Yang-Baxter Equation and the Generalised Classical Yang-Baxter Equation. In chapter one we present a method to construct solutions of the Generalised Classical Yang-Baxter Equation starting with certain sheaves of Lie algebras on algebraic curves. Furthermore we discuss a criterion to check unitarity of such solutions. In chapter two we consider the special class of solutions coming from sheaves of traceless endomorphisms of simple vector bundles on the nodal cubic curve. These solutions are quasi-trigonometric and we describe how they fit into the classification scheme of such solutions. Moreover, we describe a concrete formula for these solutions. In the third and final chapter we show that any unitary, rational solution of the Classical Yang-Baxter Equation can be obtained via the method of chapter one applied to a sheaf of Lie algebras on the cuspidal cubic curve.

EL FILTRO BAXTER - KING, METODOLOGÍA Y APLICACIONES

La presente nota tiene como objetivo exponer de manera breve la metodología del filtro Baxter-King como herramienta útil para el análisis de ciclos económicos y de extracción de tendencia. También se repasan las propiedades matemáticas del filtro Hodrick-Prescott, para comprender en qué aspectos difiere del Baxter-King. Como aplicación del filtro, se analizan series con periodicidad mensual (IMAE, IPPI, Base Monetaria) trimestral (PIB) y anual (PIB e Importaciones) y se concluye que a pesar de que no difieren mucho sus resultados, el segundo es superior al Hodrick-Prescott por cuanto permite que el investigador determine el tipo de información que desea aislar de las series.

Membrane associated transporter protein gene (SLC45A2) and the genetic basis of normal human pigmentation variation

This work is concerned with the genetic basis of normal human pigmentation variation. Specifically, the role of polymorphisms within the solute carrier family 45 member 2 (SLC45A2 or membrane associated transporter protein; MATP) gene were investigated with respect to variation in hair, skin and eye colour ― both between and within populations. SLC45A2 is an important regulator of melanin production and mutations in the gene underly the most recently identified form of oculocutaneous albinism. There is evidence to suggest that non-synonymous polymorphisms in SLC45A2 are associated with normal pigmentation variation between populations. Therefore, the underlying hypothesis of this thesis is that polymorphisms in SLC45A2 will alter the function or regulation of the protein, thereby altering the important role it plays in melanogenesis and providing a mechanism for normal pigmentation variation. In order to investigate the role that SLC45A2 polymorphisms play in human pigmentation variation, a DNA database was established which collected pigmentation phenotypic information and blood samples of more than 700 individuals. This database was used as the foundation for two association studies outlined in this thesis, the first of which involved genotyping two previously-described non-synonymous polymorphisms, p.Glu272Lys and p.Phe374Leu, in four different population groups. For both polymorphisms, allele frequencies were significantly different between population groups and the 272Lys and 374Leu alleles were strongly associated with black hair, brown eyes and olive skin colour in Caucasians. This was the first report to show that SLC45A2 polymorphisms were associated with normal human intra-population pigmentation variation. The second association study involved genotyping several SLC45A2 promoter polymorphisms to determine if they also played a role in pigmentation variation. Firstly, the transcription start site (TSS), and hence putative proximal promoter region, was identified using 5' RNA ligase mediated rapid amplification of cDNA ends (RLM-RACE). Two alternate TSSs were identified and the putative promoter region was screened for novel polymorphisms using denaturing high performance liquid chromatography (dHPLC). A novel duplication (c.–1176_–1174dupAAT) was identified along with other previously described single nucleotide polymorphisms (c.–1721C>G and c.–1169G>A). Strong linkage disequilibrium ensured that all three polymorphisms were associated with skin colour such that the –1721G, +dup and –1169A alleles were associated with olive skin in Caucasians. No linkage disequilibrium was observed between the promoter and coding region polymorphisms, suggesting independent effects. The association analyses were complemented with functional data, showing that the –1721G, +dup and –1169A alleles significantly decreased SLC45A2 transcriptional activity. Based on in silico bioinformatic analysis that showed these alleles remove a microphthalmia-associated transcription factor (MITF) binding site, and that MITF is a known regulator of SLC45A2 (Baxter and Pavan, 2002; Du and Fisher, 2002), it was postulated that SLC45A2 promoter polymorphisms could contribute to the regulation of pigmentation by altering MITF binding affinity. Further characterisation of the SLC45A2 promoter was carried out using luciferase reporter assays to determine the transcriptional activity of different regions of the promoter. Five constructs were designed of increasing length and their promoter activity evaluated. Constitutive promoter activity was observed within the first ~200 bp and promoter activity increased as the construct size increased. The functional impact of the –1721G, +dup and –1169A alleles, which removed a MITF consensus binding site, were assessed using electrophoretic mobility shift assays (EMSA) and expression analysis of genotyped melanoblast and melanocyte cell lines. EMSA results confirmed that the promoter polymorphisms affected DNA-protein binding. Interestingly, however, the protein/s involved were not MITF, or at least MITF was not the protein directly binding to the DNA. In an effort to more thoroughly characterise the functional consequences of SLC45A2 promoter polymorphisms, the mRNA expression levels of SLC45A2 and MITF were determined in melanocyte/melanoblast cell lines. Based on SLC45A2’s role in processing and trafficking TYRP1 from the trans-Golgi network to stage 2 melanosmes, the mRNA expression of TYRP1 was also investigated. Expression results suggested a coordinated expression of pigmentation genes. This thesis has substantially contributed to the field of pigmentation by showing that SLC45A2 polymorphisms not only show allele frequency differences between population groups, but also contribute to normal pigmentation variation within a Caucasian population. In addition, promoter polymorphisms have been shown to have functional consequences for SLC45A2 transcription and the expression of other pigmentation genes. Combined, the data presented in this work supports the notion that SLC45A2 is an important contributor to normal pigmentation variation and should be the target of further research to elucidate its role in determining pigmentation phenotypes. Understanding SLC45A2’s function may lead to the development of therapeutic interventions for oculocutaneous albinism and other disorders of pigmentation. It may also help in our understanding of skin cancer susceptibility and evolutionary adaptation to different UV environments, and contribute to the forensic application of pigmentation phenotype prediction.

The Queensland study of melanoma : Environmental and genetic associations (Q-MEGA); Study design, baseline characteristics, and repeatability of phenotype and sun exposure measures

Cutaneous malignant melanoma (CMM) is a major health issue in Queensland, Australia, which has the world’s highest incidence. Recent molecular and epidemiologic studies suggest that CMM arises through multiple etiological pathways involving gene-environment interactions. Understanding the potential mechanisms leading to CMM requires larger studies than those previously conducted. This article describes the design and baseline characteristics of Q-MEGA, the Queensland Study of Melanoma: Environmental and Genetic Associations, which followed up 4 population-based samples of CMM patients in Queensland, including children, adolescents, men aged over 50, and a large sample of adult cases and their families, including twins. Q-MEGA aims to investigate the roles of genetic and environmental factors, and their interaction, in the etiology of melanoma. Three thousand, four hundred and seventy-one participants took part in the follow-up study and were administered a computer-assisted telephone interview in 2002-2005. Updated data on environmental and phenotypic risk factors, and 2777 blood samples were collected from interviewed participants as well as a subset of relatives. This study provides a large and well-described population-based sample of CMM cases with follow-up data. Characteristics of the cases and repeatability of sun exposure and phenotype measures between the baseline and the follow-up surveys, from 6 to 17 years later, are also described.

Seasonal activity and abundance of Orosius orientalis (Hemiptera : Cicadellidae) at agricultural sites in Southeastern Australia

Orosius orientalis is a leafhopper vector of several viruses and phytoplasmas affecting a broad range of agricultural crops. Sweep net, yellow pan trap and yellow sticky trap collection techniques were evaluated. Seasonal distribution of O. orientalis was surveyed over two successive growing seasons around the borders of commercially grown tobacco crops. Orosius orientalis seasonal activity as assessed using pan and sticky traps was characterised by a trimodal peak and relative abundance as assessed using sweep nets differed between field sites with peak activity occurring in spring and summer months. Yellow pan traps consistently trapped a higher number of O. orientalis than yellow sticky traps.

The Eat Smart Study : a randomised controlled trial of a reduced carbohydrate versus a low fat diet for weight loss in obese adolescents

Background Despite the recognition of obesity in young people as a key health issue, there is limited evidence to inform health professionals regarding the most appropriate treatment options. The Eat Smart study aims to contribute to the knowledge base of effective dietary strategies for the clinical management of the obese adolescent and examine the cardiometablic effects of a reduced carbohydrate diet versus a low fat diet. Methods and design Eat Smart is a randomised controlled trial and aims to recruit 100 adolescents over a 2½ year period. Families will be invited to participate following referral by their health professional who has recommended weight management. Participants will be overweight as defined by a body mass index (BMI) greater than the 90th percentile, using CDC 2000 growth charts. An accredited 6-week psychological life skills program ‘FRIENDS for Life’, which is designed to provide behaviour change and coping skills will be undertaken prior to volunteers being randomised to group. The intervention arms include a structured reduced carbohydrate or a structured low fat dietary program based on an individualised energy prescription. The intervention will involve a series of dietetic appointments over 24 weeks. The control group will commence the dietary program of their choice after a 12 week period. Outcome measures will be assessed at baseline, week 12 and week 24. The primary outcome measure will be change in BMI z-score. A range of secondary outcome measures including body composition, lipid fractions, inflammatory markers, social and psychological measures will be measured. Discussion The chronic and difficult nature of treating the obese adolescent is increasingly recognised by clinicians and has highlighted the need for research aimed at providing effective intervention strategies, particularly for use in the tertiary setting. A structured reduced carbohydrate approach may provide a dietary pattern that some families will find more sustainable and effective than the conventional low fat dietary approach currently advocated. This study aims to investigate the acceptability and effectiveness of a structured reduced dietary carbohydrate intervention and will compare the outcomes of this approach with a structured low fat eating plan. Trial Registration: The protocol for this study is registered with the International Clinical Trials Registry (ISRCTN49438757).

Diversity of Cicadellidae in agricultural production areas in the Ovens Valley, Northeast Victoria, Australia

There is a paucity of data on the distribution of Cicadellidae (leafhoppers) in Australia. This study quantifies the relative abundance, seasonal activity and diversity of leafhoppers in the Ovens Valley region of north-east Victoria, Australia. Species diversity and abundance was assessed at four field sites in and around the field borders of commercially grown tobacco crops using three sampling techniques (pan trap, sticky trap and sweep net). Over 51 000 leafhopper samples were collected, with 57 species from 11 subfamilies and 19 tribes identified. Greater numbers and diversity of leafhoppers were collected in yellow pan traps. The predominant leafhopper collected was Orosius orientalis (Matsumura). Twenty-three leafhopper species were recorded for the first time in Victoria and eight economically important pest species were recorded. Seasonal activity of selected leafhopper species, covering two sampling seasons, is presented.