Dimension and projections in normed spaces and Riemannian manifolds

This thesis is concerned with the behavior of Hausdorff measure and Hausdorff dimension under projections. In 1954, Marstrand proved that given a Borel set A Ϲ R² of dimension strictly larger than 1, for almost every line L that passes through the origin, the orthogonal projection of A onto L is a set of positive Hausdorff 1-measure. This theorem marked the start of a long sequence of results in the same spirit that are nowadays known as Marstrand-type projection theorems. In the first part of this thesis, we establish Marstrand-type projection theorems for projections induced by linear foliations as well as for closest-point projections onto hyperplanes in finite dimensional normed spaces. By the same methods we obtain a Besicovitch-Federer-type characterization of purely unrectifiable sets in terms of these families of projections. Moreover, we give an example underlining the sharpness of our results. In the second part of the thesis, we establish Marstrand-type as well as Besicovitch-Federer-type projection theorems for orthogonal projections along geodesics in hyperbolic space as well as in the two-sphere. Several of these results are achievable by two different methods: potential theoretic methods and Fourier analytic methods. We discuss the scope of each of these methods in both settings

Capture

The piece consists of an interactive multimedia ‘game’ which requires the player to conceal themselves and remain still and silent to allow a landscape to grow and move. The work was curated for public display in the show The Image Looks Back, at RMIT Gallery, Melbourne, in Spring 2020, as part of the biennale PHOTO2020. The work was the product of a team comprising Adam Brown, Tabea Iseli and Alan Warburton, and won the 2018 Post-Photography Prototyping Prize, organised by Fotomuseum Winterthur, the Photographers’ Gallery, London and the Julius Baer Foundation. The piece was built in 24 hours, in a ‘hackathon’ involving competing teams selected by a panel of experts. It combined team members’ individual skills in games design, photography and CGI modelling

Projection theorems in hyperbolic space

We establish Marstrand-type projection theorems for orthogonal projections along geodesics onto m-dimensional subspaces of hyperbolic $n$-space by a geometric argument. Moreover, we obtain a Besicovitch-Federer type characterization of purely unrectifiable sets in terms of these hyperbolic orthogonal projections.Comment: 6 pages, 2 figure

The Aesthetics and Perception of Documentary Film: A mixed methods approach and Its implications for Artistic Research

The ongoing research project Gadgets, Phones and Drones at the Zurich University of the Arts investigates how innovations in camera technology have affected the visual aesthetics of documentary films since the 1990s. With specially produced variants of short films, historical paradigm shifts are being subjected to contemporary comparative analyses. Major aspects of the aesthetic change, as for instance the tendency towards a shallow depth of field, are linked to the concept of authenticity or perceived realism. The project’s use of interdisciplinary research is oriented towards artistic research, or more precisely, towards a practice-based approach and is combined with empirical audience experiments. The dialogue between qualitative and quantitative research, also known as mixed methods, has enabled surprising new insights. However, the comparability of quantitative methods risks narrowing down the aesthetic potential of the filmic products that are used to conduct the research. In order to maintain a discriminating discourse within the practice-based approach, it is therefore advantageous to extend the study’s framework beyond a quantitative and comparative research set-up and provide specific fields for artistic investigations

Sungrazing comets: Properties of nuclei and in-situ detectability of cometary ions at 1 AU

A one dimensional sublimation model for cometary nuclei is used to derive size limits for the nuclei of sungrazing comets, and to estimate oxygen ion fluxes at 1 AU from their evaporation. Given that none of the ~300 sungrazers detected by the SOlar and Heliospheric Observatory (SOHO) was observed after disappearing behind the sun, and that small nuclei with a radius of ~3.5m could be observed, it is assumed that all SOHO sungrazers were completely destroyed. For the case that sublimation alone is sufficient for destruction, the model yields an upper size limit as a function of nuclear density, albedo and perihelion distance. If the density of the nuclei is that typical of porous ice (600kg/m^3), the maximum size is 63m. These results confirm similar model calculations by Weissman (1983). An analytical expression is derived that approximates the model results well. We discuss possible modifications of our results by different disruption mechanisms. While disruption by thermal stress does not change the upper size limits significantly, they may be somewhat increased by tidal disruption (up to 100m for a density of 600kg/m^3) dependent on the isotropy of the sublimation process and the tensile strength of the comet. Implications for the Kreutz family of sungrazers are discussed. Oxygen ions from the sublimation of sungrazing comets form a tail. Fluxes from this tail are sufficiently high to be measured at 1 AU by particle detectors on spacecraft, but the duration of a tail crossing is only about half an hour. Therefore the probability of a spacecraft actually encountering a tail of an evaporating sungrazer is only of the order of two percent per year.Comment: 32 pages, 11 figures, accepted for publication in Icaru

Spyder:a reconfigurable processor development system

The Spyder project consists of the development of a reconfigurable processor as well as its application development environment. The name Spyder is an anagram of the first letters of "REconfigurable Processor Development SYstem", where the term reconfigurable means that the hardware of the processor can be specifically tailored for each application. Augmenting the performance of a processor implies either increasing its clock frequency or modifying its architecture. In the latter case, the solution usually adopted is to endow the processor with multiple execution units working in parallel (superscalar processors). The main problem with this kind of processors is to locate, in the sequential list of instructions of a program, batches of instructions susceptible of being executed in parallel by the different execution units of the processor. Thanks to the advent of field-programmable gate array (FPGA) circuits, new kind of superscalar processor architectures can be considered. In particular, the Spyder processor features multiple reconfigurable execution units, which can be redesigned to fit each application, a feature which greatly increases the opportunities to perform parallel computations, particularly when working with small data elements (e.g., 16 Boolean data can be packed into a single 16-bit data word and processed in parallel by a specifically designed operation in the execution unit). All the resources of the Spyder processor operate in parallel and are controlled by a very large instruction word (VLIW) 128 bits wide. The VLIW architecture allows the use of the full parallelism available to superscalar processors without requiring the complex dispatch unit needed by such processors to handle sequential scalar instructions. The goal of the Spyder project is to design and implement a superscalar processor with multiple reconfigurable execution units, as well as the software development tools (i.e., C++ compilers and a VLIW assembler) necessary to generate applications for this processor. A prototype of the Spyder processor has been implemented on a VME board, which has been installed in a VME rack along with a SPARC board acting as host computer. A C++ compiler generating netlist files for the ViewLogic CAD tools has been developed and has generated a lot of interest in the scientific community. It is now available by anonymous ftp on the Internet. Image processing applications and cellular automata simulations have been programmed on the Spyder processor. The Spyder prototype has demonstrated its ability to achieve a high level of performance with these applications