Forest diagrams for elements of Thompson's group F

We introduce forest diagrams to represent elements of Thompson's group F. These diagrams relate to a certain action of F on the real line in the same way that tree diagrams relate to the standard action of F on the unit interval. Using forest diagrams, we give a conceptually simple length formula for elements of F with respect to the {x_0,x_1} generating set, and we discuss the construction of minimum-length words for positive elements. Finally, we use forest diagrams and the length formula to examine the structure of the Cayley graph of F.Comment: 44 pages, 70 figure

Random Walks on Thompson\u27s Group F

In this paper we consider the statistical properties of random walks on Thompson’s group F . We use two-way forest diagrams to represent elements of F . First we describe the random walk of F by relating the steps of the walk to the possible interactions between two-way forest diagrams and the elements of {x0,x1}, the finite generating set of F, and their inverses. We then determine the long-term probabilistic and recurrence properties of the walk

Theoretical principles of landscape architecture: an exploration of the core landscape theories and their applications with special relevance to the contemporary landscape profession in Taiwan

This thesis presents research concerning the nature and underlying principles of landscape architecture. The whole research study is explorative; it is not about testing a presumed hypothesis, but it is a search for a better understanding of the theoretical groundings of landscape architecture. This thesis reflects the course of this exploration and addresses the outcome drawn from the study. The research was initiated by the concern arising from the widespread misunderstanding of landscape architecture in a particular country, Taiwan. While landscape architecture is recognised as a modern environmental profession with an Anglo-American history, the concept of this western -imported profession remains obscure to many Taiwanese people. A common question asked is: What is landscape architecture? This question is more profound than it appears, as it challenges the professional identity of landscape architecture. Knowing the shared theoretical stances of the field will help to strengthen the identity and cohesion of landscape architecture. Therefore, this research asks two key questions: What are the shared theoretical principles of landscape architecture? How are these core theoretical principles taken into account in practice, especially when applied in a specific cultural/local context? Through analysing a set of landscape projects in Taiwan, the universality and applications of the core landscape theories are explored and discussed. A further in-depth case study further explores the subcategories of landscape theories that were emphasised or emerged in the Taiwanese projects to learn more about the landscape practice in Taiwan. This research aims to achieve better understanding about the field of landscape architecture and the Taiwanese landscape practice

Pollen analysis and radiocarbon dating of lateglacial and early Flandrian deposits in southern Perthshire

This thesis describes the results of pollen analysis and radiocarbon dating of mainly basal sediments from enclosed presently peat-filled hollows in southern Perthshire, and the environmental implications of the results are discussed with special emphasis on the glacial sequence and the development of vegetation and soils during the Lateglacial and early Flandrian in southern Perthshire. The pollen diagrams presented are all based on relative pollen percentages, and in interpreting such diagrams two approaches are considered to be fundamental. Firstly, a number of major problems that affect the interpretation of pollen assemblages in general but Lateglacial assemblages in particular are discussed in detail prior to the correlation and interpretation of the local pollen zones. Secondly, since for a variety of reasons the regional importance of particular taxa may be strongly misrepresented in any individual pollen diagram, interpretations of the local pollen zones are to a large extent influenced by the results of similar investigations for other parts of the country. Thus reviews of and comparisons with data from other parts of Scotland (and selectively from the British Isles as a whole) form an important part of this thesis. In addition, useful indications of palaeoenvironmental changes have resulted from the analysis of deteriorated pollen grains. This aspect of pollen analysis is usually ignored in routine pollen counting. The causes of the different kinds of deterioration as well as interpretations of their varying frequency are discussed in some detail.Evidence from the Lateglacial deposits in southern Perthshire suggests that plant colonisation commenced shortly after 13,000 B.P. and that deglaciation was widespread by that time. Plant successions followed an uninterrupted sequence between about 13,000 and 11,000 B.P. (the Lateglacial Interstadial) from the predominantly open-habitat taxa of the colonisation period, to the closed grasslands with juniper, willow and copses of tree birch that characterised the lower-lying areas towards the end of the Interstadial. Moss heaths and poor grassland communities characterised the higher slopes. After 11,000 B.P. climatic conditions became much harsher, resulting in the Loch Lomond Readvance of glaciers, the break-up of existing soils, and revertence to openhabitat plant communities throughout southern Perthshire during the Loch Lomond Stadial (11 ,000 - 10,000 B.P.). A number of valley glaciers existed in southern Perthshire at this time, with the lowest and most southerly glacier terminus in this region near Callander. Rapid climatic amelioration shortly before 10,000 B.P. resulted in the cessation of solifluction processes, and a plant succession was then initiated that led to the immigration of birch woodland into parts of this area by about 9,500 B.P.During the Flandrian a basically similar vegetational history is recorded at each site, with the following main phases: the expansion of juniper, the immigration and expansion of birch woodland, the development of a dominant birch-hazel woodland, and the decline of hazel following the immigration of elm and oak. At three sites the main Alnus rise is recognised, and the Elm Decline is positively identified at only one site. The climax forest of lowland Perthshire was a mixed oak-elmbirch association probably associated with brown forest soils. On upland sites woodlands were much lighter with birch the most important tree, the climax forest varying between birch-alder-hazel and birchalder- pine, with oak invading some of the higher valleys. At about 6,500 B.P. marked changes in mire stratigraphy, pollen assemblages and amounts and type of deteriorated pollen are recorded, probably related to a major transition from a relatively dry climate to a climate with markedly oceanic characteristics.The Lateglacial and early Flandrian radiocarbon dates from sites in southern Perthshire are compared with other available dates from Scotland and the chronology and terminology of the Lateglacial are discussed. It is concluded that chronostratigraphic boundaries are at present poorly defined and that boundaries proposed in recent schemes may bear little relationship to times of major climatic change in Scotland. The thesis concludes by stressing the need for more detailed analyses for sites in southern Perthshire, employing absolute pollen counts, the analysis of deteriorated pollen and spores, and analysis of coleopteran remains in Lateglacial and early Flandrian sediments

Wiigwaas: An Indigenous Traditional Knowledge Informed Study of Sustainable Roofing Materials

The inadequacy of contemporary Indigenous housing has been recognized worldwide from historical problems related to colonization, dispossession, and resettlement. Indigenous housing on reservations is often substandard which meets the minimum regulations for low-income housing, with little regard to the health or cultural values of the people that live there. This study focuses on reincorporating traditional values into tribal housing with the use of wiigwaas, the Anishinaabe Ojibwe word for Paper Birch (Betula papyrifera) and a cultural keystone species of the Anishinaabe. The traditional ecological knowledge (TEK) surrounding wiigwaas is utilized to compare it to sustainable roofing materials. The researcher used methodologies which combined autoethnography, Indigenous Research Methodology, and quantitative data collection to analyze the potential of wiigwaas for covering structures. This study concluded that the durability of wiigwaas in terms of flexibility, strength, and energy allow this to be a valid sustainable roofing material for future use on Anishinaabe lands

Text-organizing metadiscourse: Tracking changes in rhetorical persuasion

Published academic writing often seems to be an unchanging form of discourse with its frozen informality remaining stable over time. Recent work has shown, however, that these texts are highly interactive and dialogic as writers anticipate and take into account readers' likely objections, background knowledge, rhetorical expectations and processing needs. In this paper, we explore one aspect of these interactions and how it has changed over the past fifty years. Focusing on what has been called interactive metadiscourse (Hyland 2005; Hyland and Tse 2004), or the ways authors organise their material for particular readers, we analyze a corpus of 2.2 million words compiled from articles in the top journals in four disciplines to discover whether, and to what extent, interactive metadiscourse has changed in different disciplines since 1965. The results show a considerable increase in an orientation to the reader over this period, reflecting changes in both research and publication practices