There are various notions of positivity for matrices and linear matrix-valued maps that play important roles in quantum information theory. The cones of positive semidefinite matrices and completely positive linear maps, which represent quantum states and quantum channels respectively, are the most ubiquitous positive cones. There are also many natural cones that can been regarded as "more" or "less" positive than these standard examples. In particular, entanglement theory deals with the cones of separable operators and entanglement witnesses, which satisfy very strong and weak positivity properties respectively. Rather complementary to the various cones that arise in entanglement theory are norms. The trace norm (or operator norm, depending on context) for operators and the diamond norm (or completely bounded norm) for superoperators are the typical norms that are seen throughout quantum information theory. In this work our main goal is to develop a family of norms that play a role analogous to the cone of entanglement witnesses. We investigate the basic mathematical properties of these norms, including their relationships with other well-known norms, their isometry groups, and their dual norms. We also make the place of these norms in entanglement theory rigorous by showing that entanglement witnesses arise from minimal operator systems, and analogously our norms arise from minimal operator spaces. Finally, we connect the various cones and norms considered here to several seemingly unrelated problems from other areas. We characterize the problem of whether or not non-positive partial transpose bound entangled states exist in terms of one of our norms, and provide evidence in favour of their existence. We also characterize the minimum gate fidelity of a quantum channel, the maximum output purity and its completely bounded counterpart, and the geometric measure of entanglement in terms of these norms. / Natural Sciences and Engineering Research Council (Canada Graduate Scholarship), Brock Scholarship

The value of hierarchy as an essential trait of concept maps and a way to enhance recall is explored in this thesis. Undergraduate students (N = 40) were randomly assigned to one of two groups and completed an 18-question multiple-choice pre-test about the concept of animal physiology. Then each group studied one of two visual organizers that varied in the level of hierarchy used and finally both groups completed the same multiple-choice test. This research was guided by the following two research questions: Do undergraduate science students using expert-created concept maps differ in their ability to enhance their recall of information about animal physiology when compared to students using visual organizers with limited hierarchy? How does prior knowledge affect the recall of students using concept maps and other visual organizers with limited hierarchy? The data collected from the two groups was analyzed using regression analyses, ANOVA, and repeated-measures ANOVA. It was found that the hierarchical concept-mapping group grew more in their recall of information about animal physiology than the visual-organizer group [F(1,38) = 7.70, p = .009]. The results of these analyses were interpreted using the conceptual framework of cognitive load theory. This theory deals with the encumbrance on working memory that subsequently affects how one recalls information. The findings support the contention that hierarchical concept maps confer an advantage in the recall of science concepts when compared to visual organizers with limited hierarchy. This study lays the ground work for a doctoral study with 200 participants separated into four experimental groups (n = 50), with participants separated by high and low prior knowledge and the aforementioned visual organizers. / Thesis (Master, Education) -- Queen's University, 2012-06-02 18:28:40.415

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Agriculture and the use of arable land have long been assumed to be one of the key drivers behind eutrophication of lakes. However, little is known about how early agriculture has affected lakes in the past. The aims of this study were: i) quantify the within-region variability in historical land use and its linkage to soil cover and ii) test if the sediment geochemistry could be used to reconstruct inputs of phosphorus from early agricultural activities. The within-region variability was determined by digitalizing historical maps covering four centuries from the 18th to the 21st century for six selected regions across Sweden. To assess historical changes in lake-water phosphorus, a 6 m long 14C-dated sediment core from Ekoln was analyzed. The core was analyzed for 24 elements by X-ray fluorescence spectroscopy (XRF) together with the total concentration of nitrogen and carbon and their isotopes (δ13C, δ15N). Results show that there was a statistically significant difference (P<0.05) in agricultural activities between regions with soils rich in fine texture classes compared to soils with a more coarse texture. Agriculture also became less dependent on fine-grained soils due to new technological implements following the industrialization. The reconstructed long term-trend in Ekoln indicate limited inputs of phosphorus from early farming and that the lake had higher concentrations of phosphorus throughout the last millennia. Therefore, early farming was unlikely to be the prime driver of high phosphorus loadings, and that other factors should be considered, e.g. extensive urbanization and inputs of wastewater effluent.

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The starting point for this project was my MPhil thesis (University of Leeds, 1995) Aural Geographies. An Investigation of Sound In Everyday Space, which has as its subject matter the concept of sound in everyday space. The MPhil thesis argued that in considering everyday space more attention should be paid to the aural experience. The argument did not try to `bolt on' what is heard to what is seen. Rather it contemplated the intricate relationships between the visual and aural senses within everyday space. Following from the work which was undertaken for the MPhil it became clear that further and more substantial research into the area of sound and space was merited. This research has been carried out at the University of East London as a PhD programme, under the supervision of Professor Andrew Blake, who introduced me to numerous aspects of music analysis. The thesis acknowledges and expands upon the work on sound carried out by the limited number of social theorists who have addressed this issue such as Adorno, Attali and in particular Schafer and his work on soundscapes. There is discussion throughout of the inspirational ideas of John Cage. The aim of the thesis, which is explored through many inter-related pieces of analysis and empirical work, is to expand upon our knowledge of the role of sound in everyday life. The thesis contributes towards knowledge by providing many new insights about the soundworld and its place in human experience. As befits a thesis which centres on the aural, the research methods are also innovatory allowing the readers/listeners themselves to experience sound worlds. The thesis therefore relies 111 heavily on newly-developed new recording/mapping techniques, using high quality audio recordings which are then used to produce digital sound maps in the form of hypermedia made available on a CD-ROM. The thesis demonstrates how these maps enable us to comprehend some of the complex sensory processes associated with sound worlds. Sound worlds are the main focus here, and in particular the way in which sound worlds are constructed by individuals. Where the MPhil examined sound in public spaces, this thesis further reflects on that investigation before going on to investigate the sound worlds generated in the living room (a key everyday space). This enables us to hear/see how the sound worlds associated with the living room link up with other everyday spaces. The contention is that sound is crucial for the organisation and operation of everyday space Though the thesis is persuasive in indicating the importance of the aural in everyday life, the question arises as to how the relationship between the aural and the visual can be represented in academic work, and especially in the discipline of geography. This question is addressed in the thesis by the presentation of a number of specially developed aural terms, such as `sonic order' and `sound maps'. The thesis describes how people organise their activities around sonic order, and explains how conflicts arise over sonic order. The thesis concludes that sound maps are present in everyday space and that people use them to navigate everyday space. This sensitivity to sound spaces generates geographical (aur/imagin)ations, which are in turn subject to study from within the discipline of geography.

The value of measuring Vygotsky's 'zone of proximal development' (ZPD) is the main concern of this thesis. The theory and research described in the thesis examines the psychological and educational purpose of measuring the ZPD within the context of children's representational skills. The first chapter discusses the development of children's ability to understand and use spatial representations. Recent research in developmental psychology is criticised for measuring the ZPD and claiming that the ZPD corresponds to children's individual developmental level. The experiments in Chapter 2 show that previous research has overestimated the representational ability of young children and that a children's potential development is different from their actual development, as assessed by the ZPD. Chapter 3 examines the origins of Vygotsky's sociocultural theory and the ZPD within Soviet psychology and Hegelian philosophy. The next chapter presents contemporary interpretations of the ZPD which have to varying degrees attempted to extend this concept. The idea of dynamic assessment is introduced in this chapter and experiments using this notion are described in detail. Preliminary studies are described in Chapter 5, which examine the possible need for measurement of the ZPD and they also choose appropriate samples, methods and apparatus for future experiments which aim to measure the ZPD within a spatial task. The sixth chapter consists of three experimental studies, which all attempted to measure the ZPD using dynamic assessment techniques. These studies showed that measurement of the ZPD could provide important diagnostic information about children's spatial ability beyond that given by individual tests of intelligence. This was especially true in the case of children with learning difficulties. The results of all the experiments in the thesis are discussed in relation to measurement of the ZPD and its value within developmental psychology and educational psychology.

A method is presented for the determination of interface topography of multi-layered crustal models from gravity or magnetic data. The technique is developed within the framework of discrete linear inverse theory and exploits the quasi-linearity of the problem to derive a simple cost-effective algorithm suitable for use on large gridded data sets. / Variation of auxiliary parameters allows a suite of acceptable models to be produced rapidly and appraised in the light of available geological and geophysical evidence. When independent knowledge concerning the behaviour of specified interfaces is available, the incorporation of such data in the form of linear equality constraints is outlined. / The proposed method is applied to Curie isotherm and Moho mapping in the Abitibi greenstone belt.

The thesis consists of two main results. The first main result is a proof that C^1 rigidity holds for circle maps with a break point for almost all rotation numbers. The second main result is a proof that C^1 robust rigidity holds for circle maps in the fractional linear transformation (FLT) pair family. That is, for this family, C^1 rigidity holds for all irrational rotation numbers. The approach taken here of proving a more general theorem that C^1 rigidity holds for circle maps with a break point satisfying a `derivatives close condition', allows us to obtain both of our main results as corollaries of this more general theorem.