'n Analitiese ondersoek van sewe van Sergei Rachmaninof se Preludes, opp. 23 en 32

Bibliography: leaves 68-70.Ten spyte van toenemende belangstelling in die solo-klavierwerke van Sergei Rachmaninof, is daar nog steeds beperkte studies vir die bestudering daarvan beskikbaar. Die doel van hierdie studie is die ontleding van 'n aantal aspekte wat 'n invloed op die bestudering en uitvoering van sewe van Rachmaninof se Preludes,.Opp. 23 en 32, het. In die studie word die historiese gebeure rondom sy lewe bespreek, wat dien as agtergrond tot die komposissie van Rachmaninof se Preludes. Die bespreking oor die klawerbordprelude verwys na die onstaan van klawerbordpreludes, die preludes uit Das Wohltemperierte Clavier van J. S. Bach, en volg dan die ontwikkeling van diengenre met die Preludes van Chopin en Rachmaninof. Sodoende word Rachmaninof se Preludes binne perspektief tot die ontwikkeling van die genre geplaas. In die laaste hoofstuk word 'n styl-tegniese ontleding van die sewe preludes van Rachmaninof gedoen, met verwysing na musikale inhoud en uitvoeringsprobleme. Ten slotte word gevolgtrekkings ten opsigte van die bespreekte werk gemaak

Sparse image reconstruction on the sphere: implications of a new sampling theorem

We study the impact of sampling theorems on the fidelity of sparse image reconstruction on the sphere. We discuss how a reduction in the number of samples required to represent all information content of a band-limited signal acts to improve the fidelity of sparse image reconstruction, through both the dimensionality and sparsity of signals. To demonstrate this result we consider a simple inpainting problem on the sphere and consider images sparse in the magnitude of their gradient. We develop a framework for total variation (TV) inpainting on the sphere, including fast methods to render the inpainting problem computationally feasible at high-resolution. Recently a new sampling theorem on the sphere was developed, reducing the required number of samples by a factor of two for equiangular sampling schemes. Through numerical simulations we verify the enhanced fidelity of sparse image reconstruction due to the more efficient sampling of the sphere provided by the new sampling theorem.Comment: 11 pages, 5 figure

Implications for compressed sensing of a new sampling theorem on the sphere

A sampling theorem on the sphere has been developed recently, requiring half as many samples as alternative equiangular sampling theorems on the sphere. A reduction by a factor of two in the number of samples required to represent a band-limited signal on the sphere exactly has important implications for compressed sensing, both in terms of the dimensionality and sparsity of signals. We illustrate the impact of this property with an inpainting problem on the sphere, where we show the superior reconstruction performance when adopting the new sampling theorem compared to the alternative.Comment: 1 page, 2 figures, Signal Processing with Adaptive Sparse Structured Representations (SPARS) 201

Deference and Diffèrance: Judicial Review and the Perfect Gift

The highest courts in both Canada and South Africa have expressed themselves in favour of an approach of deference as respect in the review of administrative action. The notion of deference as respect derives from the thinking of David Dyzenhaus, who has developed a theory of democracy in support of this approach to judicial review. Dyzenhaus’ model of review attempts to steer clear from the problems he associates particularly with positivism and liberalism. Dyzenhaus’ model of review furthermore attempts to allow space for the administration to play a significant role in giving effect to democratic values, on the understanding that all such decisions need to be reasonably justifiable. In this article the views of Dyzenhaus are contrasted with those of Jacques Derrida, especially insofar as the latter has reflected on the relation between law and justice, as well as concepts such as the gift and democracy. The argument developed in this article is that Dyzenhaus’ model of review, despite its many positive features, needs to be rethought with reference to the perfect gift, unconditional justice and democracy to come. Such a rethinking is required because of the limited conception of justice – as simply ‘our’ justice – in Dyzenhaus’ model.  &nbsp

Deference and Diffèrance: Judicial Review and the Perfect Gift

The highest courts in both Canada and South Africa have expressed themselves in favour of an approach of deference as respect in the review of administrative action. The notion of deference as respect derives from the thinking of David Dyzenhaus, who has developed a theory of democracy in support of this approach to judicial review. Dyzenhaus’ model of review attempts to steer clear from the problems he associates particularly with positivism and liberalism. Dyzenhaus’ model of review furthermore attempts to allow space for the administration to play a significant role in giving effect to democratic values, on the understanding that all such decisions need to be reasonably justifiable. In this article the views of Dyzenhaus are contrasted with those of Jacques Derrida, especially insofar as the latter has reflected on the relation between law and justice, as well as concepts such as the gift and democracy. The argument developed in this article is that Dyzenhaus’ model of review, despite its many positive features, needs to be rethought with reference to the perfect gift, unconditional justice and democracy to come. Such a rethinking is required because of the limited conception of justice – as simply ‘our’ justice – in Dyzenhaus’ model

Harmonic analysis of spherical sampling in diffusion MRI

In the last decade diffusion MRI has become a powerful tool to non-invasively study white-matter integrity in the brain. Recently many research groups have focused their attention on multi-shell spherical acquisitions with the aim of effectively mapping the diffusion signal with a lower number of q-space samples, hence enabling a crucial reduction of acquisition time. One of the quantities commonly studied in this context is the so-called orientation distribution function (ODF). In this setting, the spherical harmonic (SH) transform has gained a great deal of popularity thanks to its ability to perform convolution operations efficiently and accurately, such as the Funk-Radon transform notably required for ODF computation from q-space data. However, if the q-space signal is described with an unsuitable angular resolution at any b-value probed, aliasing (or interpolation) artifacts are unavoidably created. So far this aspect has been tackled empirically and, to our knowledge, no study has addressed this problem in a quantitative approach. The aim of the present work is to study more theoretically the efficiency of multi-shell spherical sampling in diffusion MRI, in order to gain understanding in HYDI-like approaches, possibly paving the way to further optimization strategies.Comment: 1 page, 2 figures, 19th Annual Meeting of International Society for Magnetic Resonance in Medicin

Sunbiggin Tarn & Moors & Little Asby Common SSSI water quality monitoring survey

Report to Friends of the Lake District and Natural England. 1. Sunbiggin Tarn is a small marl lake on the Orton fells in North West England, where there is concern about nutrient levels and consequent algal growth that places the lake in an ecologically unfavourable state. This work was designed to investigate the causes of this nutrient enrichment based on monthly samples from seven inflow streams and the lake between April 2019 and February 2020 and a depth profile measured in mid-summer. 2. There are several lines of evidence for calcite precipitation in the tarn during summer. Alkalinity in summer is lower than in the winter; the tarn alkalinity in the winter is similar to the inflowing streams but lower than the streams in the summer; calculations show that the calcite was highly oversaturated in summer; finally, data from the Environment Agency from 2004 to 2006 show summer concentrations of dissolved calcium are about half that of winter concentrations. 3. There is some evidence for internal loading of total phosphorus during the summer since surface concentrations in May, June and July are higher than at other times of years. More frequent depth profiles would be needed to determine if this resulted from internal loading. The current data and calculations suggest that anoxia-triggered release of phosphorus from the sediment is likely to be more important than release of phosphorus from apatite dissolution at depth in producing the high concentrations of soluble reactive phosphorus measured at the bottom of the tarn. 4. The concentration of total phosphorus in the tarn seems to be consistent with the stream concentrations, although the effects of any groundwater inputs are unknown. In contrast, there is a large loss of total nitrogen within the tarn since the concentrations are much lower in the tarn than the inflowing streams. 5. The concentrations of total phosphorus in 2019-2020 was lower than in 2003 and 2004-2006 and the mean and median concentrations of phytoplankton chlorophyll a were lower in 2019-2020 than in 2004-2006 but slightly higher than in 2003. There is therefore some suggestion that the ecological conditions in the tarn are improving. 6. The concentrations of nitrate in the tarn are unlikely to inhibit charophyte growth directly but could have an indirect effect by stimulating phytoplankton and epiphytic algae growth that could shade the charophyte beds. The generally low concentrations of nitrogen in the tarn suggest that this is unlikely. Rather primary production could be limited by nitrogen rather than phosphorus, at least in some seasons. 7. More detailed, targeted future investigations are suggested to address some of the uncertainties noted in order to produce more evidence-based knowledge for the conservation and management of Sunbiggin Tarn